libdecnumber/decNumber.c

   1 /* Decimal number arithmetic module for the decNumber C Library.
   2    Copyright (C) 2005, 2007 Free Software Foundation, Inc.
   3    Contributed by IBM Corporation.  Author Mike Cowlishaw.
   4
   5    This file is part of GCC.
   6
   7    GCC is free software; you can redistribute it and/or modify it under
   8    the terms of the GNU General Public License as published by the Free
   9    Software Foundation; either version 2, or (at your option) any later
  10    version.
  11
  12    In addition to the permissions in the GNU General Public License,
  13    the Free Software Foundation gives you unlimited permission to link
  14    the compiled version of this file into combinations with other
  15    programs, and to distribute those combinations without any
  16    restriction coming from the use of this file.  (The General Public
  17    License restrictions do apply in other respects; for example, they
  18    cover modification of the file, and distribution when not linked
  19    into a combine executable.)
  20
  21    GCC is distributed in the hope that it will be useful, but WITHOUT ANY
  22    WARRANTY; without even the implied warranty of MERCHANTABILITY or
  23    FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
  24    for more details.
  25
  26    You should have received a copy of the GNU General Public License
  27    along with GCC; see the file COPYING.  If not, write to the Free
  28    Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA
  29    02110-1301, USA.  */
  30
  31 /* ------------------------------------------------------------------ */
  32 /* Decimal Number arithmetic module                                   */
  33 /* ------------------------------------------------------------------ */
  34 /* This module comprises the routines for General Decimal Arithmetic  */
  35 /* as defined in the specification which may be found on the          */
  36 /* http://www2.hursley.ibm.com/decimal web pages.  It implements both */
  37 /* the full ('extended') arithmetic and the simpler ('subset')        */
  38 /* arithmetic.                                                        */
  39 /*                                                                    */
  40 /* Usage notes:                                                       */
  41 /*                                                                    */
  42 /* 1. This code is ANSI C89 except:                                   */
  43 /*                                                                    */
  44 /*       If DECDPUN>4 or DECUSE64=1, the C99 64-bit int64_t and       */
  45 /*       uint64_t types may be used.  To avoid these, set DECUSE64=0  */
  46 /*       and DECDPUN<=4 (see documentation).                          */
  47 /*                                                                    */
  48 /* 2. The decNumber format which this library uses is optimized for   */
  49 /*    efficient processing of relatively short numbers; in particular */
  50 /*    it allows the use of fixed sized structures and minimizes copy  */
  51 /*    and move operations.  It does, however, support arbitrary       */
  52 /*    precision (up to 999,999,999 digits) and arbitrary exponent     */
  53 /*    range (Emax in the range 0 through 999,999,999 and Emin in the  */
  54 /*    range -999,999,999 through 0).  Mathematical functions (for     */
  55 /*    example decNumberExp) as identified below are restricted more   */
  56 /*    tightly: digits, emax, and -emin in the context must be <=      */
  57 /*    DEC_MAX_MATH (999999), and their operand(s) must be within      */
  58 /*    these bounds.                                                   */
  59 /*                                                                    */
  60 /* 3. Logical functions are further restricted; their operands must   */
  61 /*    be finite, positive, have an exponent of zero, and all digits   */
  62 /*    must be either 0 or 1.  The result will only contain digits     */
  63 /*    which are 0 or 1 (and will have exponent=0 and a sign of 0).    */
  64 /*                                                                    */
  65 /* 4. Operands to operator functions are never modified unless they   */
  66 /*    are also specified to be the result number (which is always     */
  67 /*    permitted).  Other than that case, operands must not overlap.   */
  68 /*                                                                    */
  69 /* 5. Error handling: the type of the error is ORed into the status   */
  70 /*    flags in the current context (decContext structure).  The       */
  71 /*    SIGFPE signal is then raised if the corresponding trap-enabler  */
  72 /*    flag in the decContext is set (is 1).                           */
  73 /*                                                                    */
  74 /*    It is the responsibility of the caller to clear the status      */
  75 /*    flags as required.                                              */
  76 /*                                                                    */
  77 /*    The result of any routine which returns a number will always    */
  78 /*    be a valid number (which may be a special value, such as an     */
  79 /*    Infinity or NaN).                                               */
  80 /*                                                                    */
  81 /* 6. The decNumber format is not an exchangeable concrete            */
  82 /*    representation as it comprises fields which may be machine-     */
  83 /*    dependent (packed or unpacked, or special length, for example). */
  84 /*    Canonical conversions to and from strings are provided; other   */
  85 /*    conversions are available in separate modules.                  */
  86 /*                                                                    */
  87 /* 7. Normally, input operands are assumed to be valid.  Set DECCHECK */
  88 /*    to 1 for extended operand checking (including NULL operands).   */
  89 /*    Results are undefined if a badly-formed structure (or a NULL    */
  90 /*    pointer to a structure) is provided, though with DECCHECK       */
  91 /*    enabled the operator routines are protected against exceptions. */
  92 /*    (Except if the result pointer is NULL, which is unrecoverable.) */
  93 /*                                                                    */
  94 /*    However, the routines will never cause exceptions if they are   */
  95 /*    given well-formed operands, even if the value of the operands   */
  96 /*    is inappropriate for the operation and DECCHECK is not set.     */
  97 /*    (Except for SIGFPE, as and where documented.)                   */
  98 /*                                                                    */
  99 /* 8. Subset arithmetic is available only if DECSUBSET is set to 1.   */
 100 /* ------------------------------------------------------------------ */
 101 /* Implementation notes for maintenance of this module:               */
 102 /*                                                                    */
 103 /* 1. Storage leak protection:  Routines which use malloc are not     */
 104 /*    permitted to use return for fastpath or error exits (i.e.,      */
 105 /*    they follow strict structured programming conventions).         */
 106 /*    Instead they have a do{}while(0); construct surrounding the     */
 107 /*    code which is protected -- break may be used to exit this.      */
 108 /*    Other routines can safely use the return statement inline.      */
 109 /*                                                                    */
 110 /*    Storage leak accounting can be enabled using DECALLOC.          */
 111 /*                                                                    */
 112 /* 2. All loops use the for(;;) construct.  Any do construct does     */
 113 /*    not loop; it is for allocation protection as just described.    */
 114 /*                                                                    */
 115 /* 3. Setting status in the context must always be the very last      */
 116 /*    action in a routine, as non-0 status may raise a trap and hence */
 117 /*    the call to set status may not return (if the handler uses long */
 118 /*    jump).  Therefore all cleanup must be done first.  In general,  */
 119 /*    to achieve this status is accumulated and is only applied just  */
 120 /*    before return by calling decContextSetStatus (via decStatus).   */
 121 /*                                                                    */
 122 /*    Routines which allocate storage cannot, in general, use the     */
 123 /*    'top level' routines which could cause a non-returning          */
 124 /*    transfer of control.  The decXxxxOp routines are safe (do not   */
 125 /*    call decStatus even if traps are set in the context) and should */
 126 /*    be used instead (they are also a little faster).                */
 127 /*                                                                    */
 128 /* 4. Exponent checking is minimized by allowing the exponent to      */
 129 /*    grow outside its limits during calculations, provided that      */
 130 /*    the decFinalize function is called later.  Multiplication and   */
 131 /*    division, and intermediate calculations in exponentiation,      */
 132 /*    require more careful checks because of the risk of 31-bit       */
 133 /*    overflow (the most negative valid exponent is -1999999997, for  */
 134 /*    a 999999999-digit number with adjusted exponent of -999999999). */
 135 /*                                                                    */
 136 /* 5. Rounding is deferred until finalization of results, with any    */
 137 /*    'off to the right' data being represented as a single digit     */
 138 /*    residue (in the range -1 through 9).  This avoids any double-   */
 139 /*    rounding when more than one shortening takes place (for         */
 140 /*    example, when a result is subnormal).                           */
 141 /*                                                                    */
 142 /* 6. The digits count is allowed to rise to a multiple of DECDPUN    */
 143 /*    during many operations, so whole Units are handled and exact    */
 144 /*    accounting of digits is not needed.  The correct digits value   */
 145 /*    is found by decGetDigits, which accounts for leading zeros.     */
 146 /*    This must be called before any rounding if the number of digits */
 147 /*    is not known exactly.                                           */
 148 /*                                                                    */
 149 /* 7. The multiply-by-reciprocal 'trick' is used for partitioning     */
 150 /*    numbers up to four digits, using appropriate constants.  This   */
 151 /*    is not useful for longer numbers because overflow of 32 bits    */
 152 /*    would lead to 4 multiplies, which is almost as expensive as     */
 153 /*    a divide (unless a floating-point or 64-bit multiply is         */
 154 /*    assumed to be available).                                       */
 155 /*                                                                    */
 156 /* 8. Unusual abbreviations that may be used in the commentary:       */
 157 /*      lhs -- left hand side (operand, of an operation)              */
 158 /*      lsd -- least significant digit (of coefficient)               */
 159 /*      lsu -- least significant Unit (of coefficient)                */
 160 /*      msd -- most significant digit (of coefficient)                */
 161 /*      msi -- most significant item (in an array)                    */
 162 /*      msu -- most significant Unit (of coefficient)                 */
 163 /*      rhs -- right hand side (operand, of an operation)             */
 164 /*      +ve -- positive                                               */
 165 /*      -ve -- negative                                               */
 166 /*      **  -- raise to the power                                     */
 167 /* ------------------------------------------------------------------ */
 168
 169 #include "qemu/osdep.h"
 170 #include "libdecnumber/dconfig.h"
 171 #include "libdecnumber/decNumber.h"
 172 #include "libdecnumber/decNumberLocal.h"
 173
 174 /* Constants */
 175 /* Public lookup table used by the D2U macro */
 176 const uByte d2utable[DECMAXD2U+1]=D2UTABLE;
 177
 178 #define DECVERB     1              /* set to 1 for verbose DECCHECK */
 179 #define powers      DECPOWERS      /* old internal name */
 180
 181 /* Local constants */
 182 #define DIVIDE      0x80           /* Divide operators */
 183 #define REMAINDER   0x40           /* .. */
 184 #define DIVIDEINT   0x20           /* .. */
 185 #define REMNEAR     0x10           /* .. */
 186 #define COMPARE     0x01           /* Compare operators */
 187 #define COMPMAX     0x02           /* .. */
 188 #define COMPMIN     0x03           /* .. */
 189 #define COMPTOTAL   0x04           /* .. */
 190 #define COMPNAN     0x05           /* .. [NaN processing] */
 191 #define COMPSIG     0x06           /* .. [signaling COMPARE] */
 192 #define COMPMAXMAG  0x07           /* .. */
 193 #define COMPMINMAG  0x08           /* .. */
 194
 195 #define DEC_sNaN     0x40000000    /* local status: sNaN signal */
 196 #define BADINT  (Int)0x80000000    /* most-negative Int; error indicator */
 197 /* Next two indicate an integer >= 10**6, and its parity (bottom bit) */
 198 #define BIGEVEN (Int)0x80000002
 199 #define BIGODD  (Int)0x80000003
 200
 201 static Unit uarrone[1]={1};   /* Unit array of 1, used for incrementing */
 202
 203 /* Granularity-dependent code */
 204 #if DECDPUN<=4
 205   #define eInt  Int           /* extended integer */
 206   #define ueInt uInt          /* unsigned extended integer */
 207   /* Constant multipliers for divide-by-power-of five using reciprocal */
 208   /* multiply, after removing powers of 2 by shifting, and final shift */
 209   /* of 17 [we only need up to **4] */
 210   static const uInt multies[]={131073, 26215, 5243, 1049, 210};
 211   /* QUOT10 -- macro to return the quotient of unit u divided by 10**n */
 212   #define QUOT10(u, n) ((((uInt)(u)>>(n))*multies[n])>>17)
 213 #else
 214   /* For DECDPUN>4 non-ANSI-89 64-bit types are needed. */
 215   #if !DECUSE64
 216     #error decNumber.c: DECUSE64 must be 1 when DECDPUN>4
 217   #endif
 218   #define eInt  Long          /* extended integer */
 219   #define ueInt uLong         /* unsigned extended integer */
 220 #endif
 221
 222 /* Local routines */
 223 static decNumber * decAddOp(decNumber *, const decNumber *, const decNumber *,
 224                               decContext *, uByte, uInt *);
 225 static Flag        decBiStr(const char *, const char *, const char *);
 226 static uInt        decCheckMath(const decNumber *, decContext *, uInt *);
 227 static void        decApplyRound(decNumber *, decContext *, Int, uInt *);
 228 static Int         decCompare(const decNumber *lhs, const decNumber *rhs, Flag);
 229 static decNumber * decCompareOp(decNumber *, const decNumber *,
 230                               const decNumber *, decContext *,
 231                               Flag, uInt *);
 232 static void        decCopyFit(decNumber *, const decNumber *, decContext *,
 233                               Int *, uInt *);
 234 static decNumber * decDecap(decNumber *, Int);
 235 static decNumber * decDivideOp(decNumber *, const decNumber *,
 236                               const decNumber *, decContext *, Flag, uInt *);
 237 static decNumber * decExpOp(decNumber *, const decNumber *,
 238                               decContext *, uInt *);
 239 static void        decFinalize(decNumber *, decContext *, Int *, uInt *);
 240 static Int         decGetDigits(Unit *, Int);
 241 static Int         decGetInt(const decNumber *);
 242 static decNumber * decLnOp(decNumber *, const decNumber *,
 243                               decContext *, uInt *);
 244 static decNumber * decMultiplyOp(decNumber *, const decNumber *,
 245                               const decNumber *, decContext *,
 246                               uInt *);
 247 static decNumber * decNaNs(decNumber *, const decNumber *,
 248                               const decNumber *, decContext *, uInt *);
 249 static decNumber * decQuantizeOp(decNumber *, const decNumber *,
 250                               const decNumber *, decContext *, Flag,
 251                               uInt *);
 252 static void        decReverse(Unit *, Unit *);
 253 static void        decSetCoeff(decNumber *, decContext *, const Unit *,
 254                               Int, Int *, uInt *);
 255 static void        decSetMaxValue(decNumber *, decContext *);
 256 static void        decSetOverflow(decNumber *, decContext *, uInt *);
 257 static void        decSetSubnormal(decNumber *, decContext *, Int *, uInt *);
 258 static Int         decShiftToLeast(Unit *, Int, Int);
 259 static Int         decShiftToMost(Unit *, Int, Int);
 260 static void        decStatus(decNumber *, uInt, decContext *);
 261 static void        decToString(const decNumber *, char[], Flag);
 262 static decNumber * decTrim(decNumber *, decContext *, Flag, Int *);
 263 static Int         decUnitAddSub(const Unit *, Int, const Unit *, Int, Int,
 264                               Unit *, Int);
 265 static Int         decUnitCompare(const Unit *, Int, const Unit *, Int, Int);
 266
 267 #if !DECSUBSET
 268 /* decFinish == decFinalize when no subset arithmetic needed */
 269 #define decFinish(a,b,c,d) decFinalize(a,b,c,d)
 270 #else
 271 static void        decFinish(decNumber *, decContext *, Int *, uInt *);
 272 static decNumber * decRoundOperand(const decNumber *, decContext *, uInt *);
 273 #endif
 274
 275 /* Local macros */
 276 /* masked special-values bits */
 277 #define SPECIALARG  (rhs->bits & DECSPECIAL)
 278 #define SPECIALARGS ((lhs->bits | rhs->bits) & DECSPECIAL)
 279
 280 /* Diagnostic macros, etc. */
 281 #if DECALLOC
 282 /* Handle malloc/free accounting.  If enabled, our accountable routines */
 283 /* are used; otherwise the code just goes straight to the system malloc */
 284 /* and free routines. */
 285 #define malloc(a) decMalloc(a)
 286 #define free(a) decFree(a)
 287 #define DECFENCE 0x5a              /* corruption detector */
 288 /* 'Our' malloc and free: */
 289 static void *decMalloc(size_t);
 290 static void  decFree(void *);
 291 uInt decAllocBytes=0;              /* count of bytes allocated */
 292 /* Note that DECALLOC code only checks for storage buffer overflow. */
 293 /* To check for memory leaks, the decAllocBytes variable must be */
 294 /* checked to be 0 at appropriate times (e.g., after the test */
 295 /* harness completes a set of tests).  This checking may be unreliable */
 296 /* if the testing is done in a multi-thread environment. */
 297 #endif
 298
 299 #if DECCHECK
 300 /* Optional checking routines.  Enabling these means that decNumber */
 301 /* and decContext operands to operator routines are checked for */
 302 /* correctness.  This roughly doubles the execution time of the */
 303 /* fastest routines (and adds 600+ bytes), so should not normally be */
 304 /* used in 'production'. */
 305 /* decCheckInexact is used to check that inexact results have a full */
 306 /* complement of digits (where appropriate -- this is not the case */
 307 /* for Quantize, for example) */
 308 #define DECUNRESU ((decNumber *)(void *)0xffffffff)
 309 #define DECUNUSED ((const decNumber *)(void *)0xffffffff)
 310 #define DECUNCONT ((decContext *)(void *)(0xffffffff))
 311 static Flag decCheckOperands(decNumber *, const decNumber *,
 312                              const decNumber *, decContext *);
 313 static Flag decCheckNumber(const decNumber *);
 314 static void decCheckInexact(const decNumber *, decContext *);
 315 #endif
 316
 317 #if DECTRACE || DECCHECK
 318 /* Optional trace/debugging routines (may or may not be used) */
 319 void decNumberShow(const decNumber *);  /* displays the components of a number */
 320 static void decDumpAr(char, const Unit *, Int);
 321 #endif
 322
 323 /* ================================================================== */
 324 /* Conversions                                                        */
 325 /* ================================================================== */
 326
 327 /* ------------------------------------------------------------------ */
 328 /* from-int32 -- conversion from Int or uInt                          */
 329 /*                                                                    */
 330 /*  dn is the decNumber to receive the integer                        */
 331 /*  in or uin is the integer to be converted                          */
 332 /*  returns dn                                                        */
 333 /*                                                                    */
 334 /* No error is possible.                                              */
 335 /* ------------------------------------------------------------------ */
 336 decNumber * decNumberFromInt32(decNumber *dn, Int in) {
 337   uInt unsig;
 338   if (in>=0) unsig=in;
 339    else {                               /* negative (possibly BADINT) */
 340     if (in==BADINT) unsig=(uInt)1073741824*2; /* special case */
 341      else unsig=-in;                    /* invert */
 342     }
 343   /* in is now positive */
 344   decNumberFromUInt32(dn, unsig);
 345   if (in<0) dn->bits=DECNEG;            /* sign needed */
 346   return dn;
 347   } /* decNumberFromInt32 */
 348
 349 decNumber * decNumberFromUInt32(decNumber *dn, uInt uin) {
 350   Unit *up;                             /* work pointer */
 351   decNumberZero(dn);                    /* clean */
 352   if (uin==0) return dn;                /* [or decGetDigits bad call] */
 353   for (up=dn->lsu; uin>0; up++) {
 354     *up=(Unit)(uin%(DECDPUNMAX+1));
 355     uin=uin/(DECDPUNMAX+1);
 356     }
 357   dn->digits=decGetDigits(dn->lsu, up-dn->lsu);
 358   return dn;
 359   } /* decNumberFromUInt32 */
 360
 361 /* ------------------------------------------------------------------ */
 362 /* to-int32 -- conversion to Int or uInt                              */
 363 /*                                                                    */
 364 /*  dn is the decNumber to convert                                    */
 365 /*  set is the context for reporting errors                           */
 366 /*  returns the converted decNumber, or 0 if Invalid is set           */
 367 /*                                                                    */
 368 /* Invalid is set if the decNumber does not have exponent==0 or if    */
 369 /* it is a NaN, Infinite, or out-of-range.                            */
 370 /* ------------------------------------------------------------------ */
 371 Int decNumberToInt32(const decNumber *dn, decContext *set) {
 372   #if DECCHECK
 373   if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0;
 374   #endif
 375
 376   /* special or too many digits, or bad exponent */
 377   if (dn->bits&DECSPECIAL || dn->digits>10 || dn->exponent!=0) ; /* bad */
 378    else { /* is a finite integer with 10 or fewer digits */
 379     Int d;                         /* work */
 380     const Unit *up;                /* .. */
 381     uInt hi=0, lo;                 /* .. */
 382     up=dn->lsu;                    /* -> lsu */
 383     lo=*up;                        /* get 1 to 9 digits */
 384     #if DECDPUN>1                  /* split to higher */
 385       hi=lo/10;
 386       lo=lo%10;
 387     #endif
 388     up++;
 389     /* collect remaining Units, if any, into hi */
 390     for (d=DECDPUN; d<dn->digits; up++, d+=DECDPUN) hi+=*up*powers[d-1];
 391     /* now low has the lsd, hi the remainder */
 392     if (hi>214748364 || (hi==214748364 && lo>7)) { /* out of range? */
 393       /* most-negative is a reprieve */
 394       if (dn->bits&DECNEG && hi==214748364 && lo==8) return 0x80000000;
 395       /* bad -- drop through */
 396       }
 397      else { /* in-range always */
 398       Int i=X10(hi)+lo;
 399       if (dn->bits&DECNEG) return -i;
 400       return i;
 401       }
 402     } /* integer */
 403   decContextSetStatus(set, DEC_Invalid_operation); /* [may not return] */
 404   return 0;
 405   } /* decNumberToInt32 */
 406
 407 uInt decNumberToUInt32(const decNumber *dn, decContext *set) {
 408   #if DECCHECK
 409   if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0;
 410   #endif
 411   /* special or too many digits, or bad exponent, or negative (<0) */
 412   if (dn->bits&DECSPECIAL || dn->digits>10 || dn->exponent!=0
 413     || (dn->bits&DECNEG && !ISZERO(dn)));                   /* bad */
 414    else { /* is a finite integer with 10 or fewer digits */
 415     Int d;                         /* work */
 416     const Unit *up;                /* .. */
 417     uInt hi=0, lo;                 /* .. */
 418     up=dn->lsu;                    /* -> lsu */
 419     lo=*up;                        /* get 1 to 9 digits */
 420     #if DECDPUN>1                  /* split to higher */
 421       hi=lo/10;
 422       lo=lo%10;
 423     #endif
 424     up++;
 425     /* collect remaining Units, if any, into hi */
 426     for (d=DECDPUN; d<dn->digits; up++, d+=DECDPUN) hi+=*up*powers[d-1];
 427
 428     /* now low has the lsd, hi the remainder */
 429     if (hi>429496729 || (hi==429496729 && lo>5)) ; /* no reprieve possible */
 430      else return X10(hi)+lo;
 431     } /* integer */
 432   decContextSetStatus(set, DEC_Invalid_operation); /* [may not return] */
 433   return 0;
 434   } /* decNumberToUInt32 */
 435
 436 decNumber *decNumberFromInt64(decNumber *dn, int64_t in)
 437 {
 438     uint64_t unsig = in;
 439     if (in < 0) {
 440         unsig = -unsig;
 441     }
 442
 443     decNumberFromUInt64(dn, unsig);
 444     if (in < 0) {
 445         dn->bits = DECNEG;        /* sign needed */
 446     }
 447     return dn;
 448 } /* decNumberFromInt64 */
 449
 450 decNumber *decNumberFromUInt64(decNumber *dn, uint64_t uin)
 451 {
 452     Unit *up;                             /* work pointer */
 453     decNumberZero(dn);                    /* clean */
 454     if (uin == 0) {
 455         return dn;                /* [or decGetDigits bad call] */
 456     }
 457     for (up = dn->lsu; uin > 0; up++) {
 458         *up = (Unit)(uin % (DECDPUNMAX + 1));
 459         uin = uin / (DECDPUNMAX + 1);
 460     }
 461     dn->digits = decGetDigits(dn->lsu, up-dn->lsu);
 462     return dn;
 463 } /* decNumberFromUInt64 */
 464
 465 /* ------------------------------------------------------------------ */
 466 /* to-int64 -- conversion to int64                                    */
 467 /*                                                                    */
 468 /*  dn is the decNumber to convert.  dn is assumed to have been       */
 469 /*    rounded to a floating point integer value.                      */
 470 /*  set is the context for reporting errors                           */
 471 /*  returns the converted decNumber, or 0 if Invalid is set           */
 472 /*                                                                    */
 473 /* Invalid is set if the decNumber is a NaN, Infinite or is out of    */
 474 /* range for a signed 64 bit integer.                                 */
 475 /* ------------------------------------------------------------------ */
 476
 477 int64_t decNumberIntegralToInt64(const decNumber *dn, decContext *set)
 478 {
 479     if (decNumberIsSpecial(dn) || (dn->exponent < 0) ||
 480        (dn->digits + dn->exponent > 19)) {
 481         goto Invalid;
 482     } else {
 483         int64_t d;        /* work */
 484         const Unit *up;   /* .. */
 485         uint64_t hi = 0;
 486         up = dn->lsu;     /* -> lsu */
 487
 488         for (d = 1; d <= dn->digits; up++, d += DECDPUN) {
 489             uint64_t prev = hi;
 490             hi += *up * powers[d-1];
 491             if ((hi < prev) || (hi > INT64_MAX)) {
 492                 goto Invalid;
 493             }
 494         }
 495
 496         uint64_t prev = hi;
 497         hi *= (uint64_t)powers[dn->exponent];
 498         if ((hi < prev) || (hi > INT64_MAX)) {
 499             goto Invalid;
 500         }
 501         return (decNumberIsNegative(dn)) ? -((int64_t)hi) : (int64_t)hi;
 502     }
 503
 504 Invalid:
 505     decContextSetStatus(set, DEC_Invalid_operation);
 506     return 0;
 507 } /* decNumberIntegralToInt64 */
 508
 509
 510 /* ------------------------------------------------------------------ */
 511 /* to-scientific-string -- conversion to numeric string               */
 512 /* to-engineering-string -- conversion to numeric string              */
 513 /*                                                                    */
 514 /*   decNumberToString(dn, string);                                   */
 515 /*   decNumberToEngString(dn, string);                                */
 516 /*                                                                    */
 517 /*  dn is the decNumber to convert                                    */
 518 /*  string is the string where the result will be laid out            */
 519 /*                                                                    */
 520 /*  string must be at least dn->digits+14 characters long             */
 521 /*                                                                    */
 522 /*  No error is possible, and no status can be set.                   */
 523 /* ------------------------------------------------------------------ */
 524 char * decNumberToString(const decNumber *dn, char *string){
 525   decToString(dn, string, 0);
 526   return string;
 527   } /* DecNumberToString */
 528
 529 char * decNumberToEngString(const decNumber *dn, char *string){
 530   decToString(dn, string, 1);
 531   return string;
 532   } /* DecNumberToEngString */
 533
 534 /* ------------------------------------------------------------------ */
 535 /* to-number -- conversion from numeric string                        */
 536 /*                                                                    */
 537 /* decNumberFromString -- convert string to decNumber                 */
 538 /*   dn        -- the number structure to fill                        */
 539 /*   chars[]   -- the string to convert ('\0' terminated)             */
 540 /*   set       -- the context used for processing any error,          */
 541 /*                determining the maximum precision available         */
 542 /*                (set.digits), determining the maximum and minimum   */
 543 /*                exponent (set.emax and set.emin), determining if    */
 544 /*                extended values are allowed, and checking the       */
 545 /*                rounding mode if overflow occurs or rounding is     */
 546 /*                needed.                                             */
 547 /*                                                                    */
 548 /* The length of the coefficient and the size of the exponent are     */
 549 /* checked by this routine, so the correct error (Underflow or        */
 550 /* Overflow) can be reported or rounding applied, as necessary.       */
 551 /*                                                                    */
 552 /* If bad syntax is detected, the result will be a quiet NaN.         */
 553 /* ------------------------------------------------------------------ */
 554 decNumber * decNumberFromString(decNumber *dn, const char chars[],
 555                                 decContext *set) {
 556   Int   exponent=0;                /* working exponent [assume 0] */
 557   uByte bits=0;                    /* working flags [assume +ve] */
 558   Unit  *res;                      /* where result will be built */
 559   Unit  resbuff[SD2U(DECBUFFER+9)];/* local buffer in case need temporary */
 560                                    /* [+9 allows for ln() constants] */
 561   Unit  *allocres=NULL;            /* -> allocated result, iff allocated */
 562   Int   d=0;                       /* count of digits found in decimal part */
 563   const char *dotchar=NULL;        /* where dot was found */
 564   const char *cfirst=chars;        /* -> first character of decimal part */
 565   const char *last=NULL;           /* -> last digit of decimal part */
 566   const char *c;                   /* work */
 567   Unit  *up;                       /* .. */
 568   #if DECDPUN>1
 569   Int   cut, out;                  /* .. */
 570   #endif
 571   Int   residue;                   /* rounding residue */
 572   uInt  status=0;                  /* error code */
 573
 574   #if DECCHECK
 575   if (decCheckOperands(DECUNRESU, DECUNUSED, DECUNUSED, set))
 576     return decNumberZero(dn);
 577   #endif
 578
 579   do {                             /* status & malloc protection */
 580     for (c=chars;; c++) {          /* -> input character */
 581       if (*c>='0' && *c<='9') {    /* test for Arabic digit */
 582         last=c;
 583         d++;                       /* count of real digits */
 584         continue;                  /* still in decimal part */
 585         }
 586       if (*c=='.' && dotchar==NULL) { /* first '.' */
 587         dotchar=c;                 /* record offset into decimal part */
 588         if (c==cfirst) cfirst++;   /* first digit must follow */
 589         continue;}
 590       if (c==chars) {              /* first in string... */
 591         if (*c=='-') {             /* valid - sign */
 592           cfirst++;
 593           bits=DECNEG;
 594           continue;}
 595         if (*c=='+') {             /* valid + sign */
 596           cfirst++;
 597           continue;}
 598         }
 599       /* *c is not a digit, or a valid +, -, or '.' */
 600       break;
 601       } /* c */
 602
 603     if (last==NULL) {              /* no digits yet */
 604       status=DEC_Conversion_syntax;/* assume the worst */
 605       if (*c=='\0') break;         /* and no more to come... */
 606       #if DECSUBSET
 607       /* if subset then infinities and NaNs are not allowed */
 608       if (!set->extended) break;   /* hopeless */
 609       #endif
 610       /* Infinities and NaNs are possible, here */
 611       if (dotchar!=NULL) break;    /* .. unless had a dot */
 612       decNumberZero(dn);           /* be optimistic */
 613       if (decBiStr(c, "infinity", "INFINITY")
 614        || decBiStr(c, "inf", "INF")) {
 615         dn->bits=bits | DECINF;
 616         status=0;                  /* is OK */
 617         break; /* all done */
 618         }
 619       /* a NaN expected */
 620       /* 2003.09.10 NaNs are now permitted to have a sign */
 621       dn->bits=bits | DECNAN;      /* assume simple NaN */
 622       if (*c=='s' || *c=='S') {    /* looks like an sNaN */
 623         c++;
 624         dn->bits=bits | DECSNAN;
 625         }
 626       if (*c!='n' && *c!='N') break;    /* check caseless "NaN" */
 627       c++;
 628       if (*c!='a' && *c!='A') break;    /* .. */
 629       c++;
 630       if (*c!='n' && *c!='N') break;    /* .. */
 631       c++;
 632       /* now either nothing, or nnnn payload, expected */
 633       /* -> start of integer and skip leading 0s [including plain 0] */
 634       for (cfirst=c; *cfirst=='0';) cfirst++;
 635       if (*cfirst=='\0') {         /* "NaN" or "sNaN", maybe with all 0s */
 636         status=0;                  /* it's good */
 637         break;                     /* .. */
 638         }
 639       /* something other than 0s; setup last and d as usual [no dots] */
 640       for (c=cfirst;; c++, d++) {
 641         if (*c<'0' || *c>'9') break; /* test for Arabic digit */
 642         last=c;
 643         }
 644       if (*c!='\0') break;         /* not all digits */
 645       if (d>set->digits-1) {
 646         /* [NB: payload in a decNumber can be full length unless */
 647         /* clamped, in which case can only be digits-1] */
 648         if (set->clamp) break;
 649         if (d>set->digits) break;
 650         } /* too many digits? */
 651       /* good; drop through to convert the integer to coefficient */
 652       status=0;                    /* syntax is OK */
 653       bits=dn->bits;               /* for copy-back */
 654       } /* last==NULL */
 655
 656      else if (*c!='\0') {          /* more to process... */
 657       /* had some digits; exponent is only valid sequence now */
 658       Flag nege;                   /* 1=negative exponent */
 659       const char *firstexp;        /* -> first significant exponent digit */
 660       status=DEC_Conversion_syntax;/* assume the worst */
 661       if (*c!='e' && *c!='E') break;
 662       /* Found 'e' or 'E' -- now process explicit exponent */
 663       /* 1998.07.11: sign no longer required */
 664       nege=0;
 665       c++;                         /* to (possible) sign */
 666       if (*c=='-') {nege=1; c++;}
 667        else if (*c=='+') c++;
 668       if (*c=='\0') break;
 669
 670       for (; *c=='0' && *(c+1)!='\0';) c++;  /* strip insignificant zeros */
 671       firstexp=c;                            /* save exponent digit place */
 672       for (; ;c++) {
 673         if (*c<'0' || *c>'9') break;         /* not a digit */
 674         exponent=X10(exponent)+(Int)*c-(Int)'0';
 675         } /* c */
 676       /* if not now on a '\0', *c must not be a digit */
 677       if (*c!='\0') break;
 678
 679       /* (this next test must be after the syntax checks) */
 680       /* if it was too long the exponent may have wrapped, so check */
 681       /* carefully and set it to a certain overflow if wrap possible */
 682       if (c>=firstexp+9+1) {
 683         if (c>firstexp+9+1 || *firstexp>'1') exponent=DECNUMMAXE*2;
 684         /* [up to 1999999999 is OK, for example 1E-1000000998] */
 685         }
 686       if (nege) exponent=-exponent;     /* was negative */
 687       status=0;                         /* is OK */
 688       } /* stuff after digits */
 689
 690     /* Here when whole string has been inspected; syntax is good */
 691     /* cfirst->first digit (never dot), last->last digit (ditto) */
 692
 693     /* strip leading zeros/dot [leave final 0 if all 0's] */
 694     if (*cfirst=='0') {                 /* [cfirst has stepped over .] */
 695       for (c=cfirst; c<last; c++, cfirst++) {
 696         if (*c=='.') continue;          /* ignore dots */
 697         if (*c!='0') break;             /* non-zero found */
 698         d--;                            /* 0 stripped */
 699         } /* c */
 700       #if DECSUBSET
 701       /* make a rapid exit for easy zeros if !extended */
 702       if (*cfirst=='0' && !set->extended) {
 703         decNumberZero(dn);              /* clean result */
 704         break;                          /* [could be return] */
 705         }
 706       #endif
 707       } /* at least one leading 0 */
 708
 709     /* Handle decimal point... */
 710     if (dotchar!=NULL && dotchar<last)  /* non-trailing '.' found? */
 711       exponent-=(last-dotchar);         /* adjust exponent */
 712     /* [we can now ignore the .] */
 713
 714     /* OK, the digits string is good.  Assemble in the decNumber, or in */
 715     /* a temporary units array if rounding is needed */
 716     if (d<=set->digits) res=dn->lsu;    /* fits into supplied decNumber */
 717      else {                             /* rounding needed */
 718       Int needbytes=D2U(d)*sizeof(Unit);/* bytes needed */
 719       res=resbuff;                      /* assume use local buffer */
 720       if (needbytes>(Int)sizeof(resbuff)) { /* too big for local */
 721         allocres=(Unit *)malloc(needbytes);
 722         if (allocres==NULL) {status|=DEC_Insufficient_storage; break;}
 723         res=allocres;
 724         }
 725       }
 726     /* res now -> number lsu, buffer, or allocated storage for Unit array */
 727
 728     /* Place the coefficient into the selected Unit array */
 729     /* [this is often 70% of the cost of this function when DECDPUN>1] */
 730     #if DECDPUN>1
 731     out=0;                         /* accumulator */
 732     up=res+D2U(d)-1;               /* -> msu */
 733     cut=d-(up-res)*DECDPUN;        /* digits in top unit */
 734     for (c=cfirst;; c++) {         /* along the digits */
 735       if (*c=='.') continue;       /* ignore '.' [don't decrement cut] */
 736       out=X10(out)+(Int)*c-(Int)'0';
 737       if (c==last) break;          /* done [never get to trailing '.'] */
 738       cut--;
 739       if (cut>0) continue;         /* more for this unit */
 740       *up=(Unit)out;               /* write unit */
 741       up--;                        /* prepare for unit below.. */
 742       cut=DECDPUN;                 /* .. */
 743       out=0;                       /* .. */
 744       } /* c */
 745     *up=(Unit)out;                 /* write lsu */
 746
 747     #else
 748     /* DECDPUN==1 */
 749     up=res;                        /* -> lsu */
 750     for (c=last; c>=cfirst; c--) { /* over each character, from least */
 751       if (*c=='.') continue;       /* ignore . [don't step up] */
 752       *up=(Unit)((Int)*c-(Int)'0');
 753       up++;
 754       } /* c */
 755     #endif
 756
 757     dn->bits=bits;
 758     dn->exponent=exponent;
 759     dn->digits=d;
 760
 761     /* if not in number (too long) shorten into the number */
 762     if (d>set->digits) {
 763       residue=0;
 764       decSetCoeff(dn, set, res, d, &residue, &status);
 765       /* always check for overflow or subnormal and round as needed */
 766       decFinalize(dn, set, &residue, &status);
 767       }
 768      else { /* no rounding, but may still have overflow or subnormal */
 769       /* [these tests are just for performance; finalize repeats them] */
 770       if ((dn->exponent-1<set->emin-dn->digits)
 771        || (dn->exponent-1>set->emax-set->digits)) {
 772         residue=0;
 773         decFinalize(dn, set, &residue, &status);
 774         }
 775       }
 776     /* decNumberShow(dn); */
 777     } while(0);                         /* [for break] */
 778
 779   if (allocres!=NULL) free(allocres);   /* drop any storage used */
 780   if (status!=0) decStatus(dn, status, set);
 781   return dn;
 782   } /* decNumberFromString */
 783
 784 /* ================================================================== */
 785 /* Operators                                                          */
 786 /* ================================================================== */
 787
 788 /* ------------------------------------------------------------------ */
 789 /* decNumberAbs -- absolute value operator                            */
 790 /*                                                                    */
 791 /*   This computes C = abs(A)                                         */
 792 /*                                                                    */
 793 /*   res is C, the result.  C may be A                                */
 794 /*   rhs is A                                                         */
 795 /*   set is the context                                               */
 796 /*                                                                    */
 797 /* See also decNumberCopyAbs for a quiet bitwise version of this.     */
 798 /* C must have space for set->digits digits.                          */
 799 /* ------------------------------------------------------------------ */
 800 /* This has the same effect as decNumberPlus unless A is negative,    */
 801 /* in which case it has the same effect as decNumberMinus.            */
 802 /* ------------------------------------------------------------------ */
 803 decNumber * decNumberAbs(decNumber *res, const decNumber *rhs,
 804                          decContext *set) {
 805   decNumber dzero;                      /* for 0 */
 806   uInt status=0;                        /* accumulator */
 807
 808   #if DECCHECK
 809   if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
 810   #endif
 811
 812   decNumberZero(&dzero);                /* set 0 */
 813   dzero.exponent=rhs->exponent;         /* [no coefficient expansion] */
 814   decAddOp(res, &dzero, rhs, set, (uByte)(rhs->bits & DECNEG), &status);
 815   if (status!=0) decStatus(res, status, set);
 816   #if DECCHECK
 817   decCheckInexact(res, set);
 818   #endif
 819   return res;
 820   } /* decNumberAbs */
 821
 822 /* ------------------------------------------------------------------ */
 823 /* decNumberAdd -- add two Numbers                                    */
 824 /*                                                                    */
 825 /*   This computes C = A + B                                          */
 826 /*                                                                    */
 827 /*   res is C, the result.  C may be A and/or B (e.g., X=X+X)         */
 828 /*   lhs is A                                                         */
 829 /*   rhs is B                                                         */
 830 /*   set is the context                                               */
 831 /*                                                                    */
 832 /* C must have space for set->digits digits.                          */
 833 /* ------------------------------------------------------------------ */
 834 /* This just calls the routine shared with Subtract                   */
 835 decNumber * decNumberAdd(decNumber *res, const decNumber *lhs,
 836                          const decNumber *rhs, decContext *set) {
 837   uInt status=0;                        /* accumulator */
 838   decAddOp(res, lhs, rhs, set, 0, &status);
 839   if (status!=0) decStatus(res, status, set);
 840   #if DECCHECK
 841   decCheckInexact(res, set);
 842   #endif
 843   return res;
 844   } /* decNumberAdd */
 845
 846 /* ------------------------------------------------------------------ */
 847 /* decNumberAnd -- AND two Numbers, digitwise                         */
 848 /*                                                                    */
 849 /*   This computes C = A & B                                          */
 850 /*                                                                    */
 851 /*   res is C, the result.  C may be A and/or B (e.g., X=X&X)         */
 852 /*   lhs is A                                                         */
 853 /*   rhs is B                                                         */
 854 /*   set is the context (used for result length and error report)     */
 855 /*                                                                    */
 856 /* C must have space for set->digits digits.                          */
 857 /*                                                                    */
 858 /* Logical function restrictions apply (see above); a NaN is          */
 859 /* returned with Invalid_operation if a restriction is violated.      */
 860 /* ------------------------------------------------------------------ */
 861 decNumber * decNumberAnd(decNumber *res, const decNumber *lhs,
 862                          const decNumber *rhs, decContext *set) {
 863   const Unit *ua, *ub;                  /* -> operands */
 864   const Unit *msua, *msub;              /* -> operand msus */
 865   Unit *uc,  *msuc;                     /* -> result and its msu */
 866   Int   msudigs;                        /* digits in res msu */
 867   #if DECCHECK
 868   if (decCheckOperands(res, lhs, rhs, set)) return res;
 869   #endif
 870
 871   if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs)
 872    || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) {
 873     decStatus(res, DEC_Invalid_operation, set);
 874     return res;
 875     }
 876
 877   /* operands are valid */
 878   ua=lhs->lsu;                          /* bottom-up */
 879   ub=rhs->lsu;                          /* .. */
 880   uc=res->lsu;                          /* .. */
 881   msua=ua+D2U(lhs->digits)-1;           /* -> msu of lhs */
 882   msub=ub+D2U(rhs->digits)-1;           /* -> msu of rhs */
 883   msuc=uc+D2U(set->digits)-1;           /* -> msu of result */
 884   msudigs=MSUDIGITS(set->digits);       /* [faster than remainder] */
 885   for (; uc<=msuc; ua++, ub++, uc++) {  /* Unit loop */
 886     Unit a, b;                          /* extract units */
 887     if (ua>msua) a=0;
 888      else a=*ua;
 889     if (ub>msub) b=0;
 890      else b=*ub;
 891     *uc=0;                              /* can now write back */
 892     if (a|b) {                          /* maybe 1 bits to examine */
 893       Int i, j;
 894       *uc=0;                            /* can now write back */
 895       /* This loop could be unrolled and/or use BIN2BCD tables */
 896       for (i=0; i<DECDPUN; i++) {
 897         if (a&b&1) *uc=*uc+(Unit)powers[i];  /* effect AND */
 898         j=a%10;
 899         a=a/10;
 900         j|=b%10;
 901         b=b/10;
 902         if (j>1) {
 903           decStatus(res, DEC_Invalid_operation, set);
 904           return res;
 905           }
 906         if (uc==msuc && i==msudigs-1) break; /* just did final digit */
 907         } /* each digit */
 908       } /* both OK */
 909     } /* each unit */
 910   /* [here uc-1 is the msu of the result] */
 911   res->digits=decGetDigits(res->lsu, uc-res->lsu);
 912   res->exponent=0;                      /* integer */
 913   res->bits=0;                          /* sign=0 */
 914   return res;  /* [no status to set] */
 915   } /* decNumberAnd */
 916
 917 /* ------------------------------------------------------------------ */
 918 /* decNumberCompare -- compare two Numbers                            */
 919 /*                                                                    */
 920 /*   This computes C = A ? B                                          */
 921 /*                                                                    */
 922 /*   res is C, the result.  C may be A and/or B (e.g., X=X?X)         */
 923 /*   lhs is A                                                         */
 924 /*   rhs is B                                                         */
 925 /*   set is the context                                               */
 926 /*                                                                    */
 927 /* C must have space for one digit (or NaN).                          */
 928 /* ------------------------------------------------------------------ */
 929 decNumber * decNumberCompare(decNumber *res, const decNumber *lhs,
 930                              const decNumber *rhs, decContext *set) {
 931   uInt status=0;                        /* accumulator */
 932   decCompareOp(res, lhs, rhs, set, COMPARE, &status);
 933   if (status!=0) decStatus(res, status, set);
 934   return res;
 935   } /* decNumberCompare */
 936
 937 /* ------------------------------------------------------------------ */
 938 /* decNumberCompareSignal -- compare, signalling on all NaNs          */
 939 /*                                                                    */
 940 /*   This computes C = A ? B                                          */
 941 /*                                                                    */
 942 /*   res is C, the result.  C may be A and/or B (e.g., X=X?X)         */
 943 /*   lhs is A                                                         */
 944 /*   rhs is B                                                         */
 945 /*   set is the context                                               */
 946 /*                                                                    */
 947 /* C must have space for one digit (or NaN).                          */
 948 /* ------------------------------------------------------------------ */
 949 decNumber * decNumberCompareSignal(decNumber *res, const decNumber *lhs,
 950                                    const decNumber *rhs, decContext *set) {
 951   uInt status=0;                        /* accumulator */
 952   decCompareOp(res, lhs, rhs, set, COMPSIG, &status);
 953   if (status!=0) decStatus(res, status, set);
 954   return res;
 955   } /* decNumberCompareSignal */
 956
 957 /* ------------------------------------------------------------------ */
 958 /* decNumberCompareTotal -- compare two Numbers, using total ordering */
 959 /*                                                                    */
 960 /*   This computes C = A ? B, under total ordering                    */
 961 /*                                                                    */
 962 /*   res is C, the result.  C may be A and/or B (e.g., X=X?X)         */
 963 /*   lhs is A                                                         */
 964 /*   rhs is B                                                         */
 965 /*   set is the context                                               */
 966 /*                                                                    */
 967 /* C must have space for one digit; the result will always be one of  */
 968 /* -1, 0, or 1.                                                       */
 969 /* ------------------------------------------------------------------ */
 970 decNumber * decNumberCompareTotal(decNumber *res, const decNumber *lhs,
 971                                   const decNumber *rhs, decContext *set) {
 972   uInt status=0;                        /* accumulator */
 973   decCompareOp(res, lhs, rhs, set, COMPTOTAL, &status);
 974   if (status!=0) decStatus(res, status, set);
 975   return res;
 976   } /* decNumberCompareTotal */
 977
 978 /* ------------------------------------------------------------------ */
 979 /* decNumberCompareTotalMag -- compare, total ordering of magnitudes  */
 980 /*                                                                    */
 981 /*   This computes C = |A| ? |B|, under total ordering                */
 982 /*                                                                    */
 983 /*   res is C, the result.  C may be A and/or B (e.g., X=X?X)         */
 984 /*   lhs is A                                                         */
 985 /*   rhs is B                                                         */
 986 /*   set is the context                                               */
 987 /*                                                                    */
 988 /* C must have space for one digit; the result will always be one of  */
 989 /* -1, 0, or 1.                                                       */
 990 /* ------------------------------------------------------------------ */
 991 decNumber * decNumberCompareTotalMag(decNumber *res, const decNumber *lhs,
 992                                      const decNumber *rhs, decContext *set) {
 993   uInt status=0;                   /* accumulator */
 994   uInt needbytes;                  /* for space calculations */
 995   decNumber bufa[D2N(DECBUFFER+1)];/* +1 in case DECBUFFER=0 */
 996   decNumber *allocbufa=NULL;       /* -> allocated bufa, iff allocated */
 997   decNumber bufb[D2N(DECBUFFER+1)];
 998   decNumber *allocbufb=NULL;       /* -> allocated bufb, iff allocated */
 999   decNumber *a, *b;                /* temporary pointers */
1000
1001   #if DECCHECK
1002   if (decCheckOperands(res, lhs, rhs, set)) return res;
1003   #endif
1004
1005   do {                                  /* protect allocated storage */
1006     /* if either is negative, take a copy and absolute */
1007     if (decNumberIsNegative(lhs)) {     /* lhs<0 */
1008       a=bufa;
1009       needbytes=sizeof(decNumber)+(D2U(lhs->digits)-1)*sizeof(Unit);
1010       if (needbytes>sizeof(bufa)) {     /* need malloc space */
1011         allocbufa=(decNumber *)malloc(needbytes);
1012         if (allocbufa==NULL) {          /* hopeless -- abandon */
1013           status|=DEC_Insufficient_storage;
1014           break;}
1015         a=allocbufa;                    /* use the allocated space */
1016         }
1017       decNumberCopy(a, lhs);            /* copy content */
1018       a->bits&=~DECNEG;                 /* .. and clear the sign */
1019       lhs=a;                            /* use copy from here on */
1020       }
1021     if (decNumberIsNegative(rhs)) {     /* rhs<0 */
1022       b=bufb;
1023       needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit);
1024       if (needbytes>sizeof(bufb)) {     /* need malloc space */
1025         allocbufb=(decNumber *)malloc(needbytes);
1026         if (allocbufb==NULL) {          /* hopeless -- abandon */
1027           status|=DEC_Insufficient_storage;
1028           break;}
1029         b=allocbufb;                    /* use the allocated space */
1030         }
1031       decNumberCopy(b, rhs);            /* copy content */
1032       b->bits&=~DECNEG;                 /* .. and clear the sign */
1033       rhs=b;                            /* use copy from here on */
1034       }
1035     decCompareOp(res, lhs, rhs, set, COMPTOTAL, &status);
1036     } while(0);                         /* end protected */
1037
1038   if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */
1039   if (allocbufb!=NULL) free(allocbufb); /* .. */
1040   if (status!=0) decStatus(res, status, set);
1041   return res;
1042   } /* decNumberCompareTotalMag */
1043
1044 /* ------------------------------------------------------------------ */
1045 /* decNumberDivide -- divide one number by another                    */
1046 /*                                                                    */
1047 /*   This computes C = A / B                                          */
1048 /*                                                                    */
1049 /*   res is C, the result.  C may be A and/or B (e.g., X=X/X)         */
1050 /*   lhs is A                                                         */
1051 /*   rhs is B                                                         */
1052 /*   set is the context                                               */
1053 /*                                                                    */
1054 /* C must have space for set->digits digits.                          */
1055 /* ------------------------------------------------------------------ */
1056 decNumber * decNumberDivide(decNumber *res, const decNumber *lhs,
1057                             const decNumber *rhs, decContext *set) {
1058   uInt status=0;                        /* accumulator */
1059   decDivideOp(res, lhs, rhs, set, DIVIDE, &status);
1060   if (status!=0) decStatus(res, status, set);
1061   #if DECCHECK
1062   decCheckInexact(res, set);
1063   #endif
1064   return res;
1065   } /* decNumberDivide */
1066
1067 /* ------------------------------------------------------------------ */
1068 /* decNumberDivideInteger -- divide and return integer quotient       */
1069 /*                                                                    */
1070 /*   This computes C = A # B, where # is the integer divide operator  */
1071 /*                                                                    */
1072 /*   res is C, the result.  C may be A and/or B (e.g., X=X#X)         */
1073 /*   lhs is A                                                         */
1074 /*   rhs is B                                                         */
1075 /*   set is the context                                               */
1076 /*                                                                    */
1077 /* C must have space for set->digits digits.                          */
1078 /* ------------------------------------------------------------------ */
1079 decNumber * decNumberDivideInteger(decNumber *res, const decNumber *lhs,
1080                                    const decNumber *rhs, decContext *set) {
1081   uInt status=0;                        /* accumulator */
1082   decDivideOp(res, lhs, rhs, set, DIVIDEINT, &status);
1083   if (status!=0) decStatus(res, status, set);
1084   return res;
1085   } /* decNumberDivideInteger */
1086
1087 /* ------------------------------------------------------------------ */
1088 /* decNumberExp -- exponentiation                                     */
1089 /*                                                                    */
1090 /*   This computes C = exp(A)                                         */
1091 /*                                                                    */
1092 /*   res is C, the result.  C may be A                                */
1093 /*   rhs is A                                                         */
1094 /*   set is the context; note that rounding mode has no effect        */
1095 /*                                                                    */
1096 /* C must have space for set->digits digits.                          */
1097 /*                                                                    */
1098 /* Mathematical function restrictions apply (see above); a NaN is     */
1099 /* returned with Invalid_operation if a restriction is violated.      */
1100 /*                                                                    */
1101 /* Finite results will always be full precision and Inexact, except   */
1102 /* when A is a zero or -Infinity (giving 1 or 0 respectively).        */
1103 /*                                                                    */
1104 /* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will    */
1105 /* almost always be correctly rounded, but may be up to 1 ulp in      */
1106 /* error in rare cases.                                               */
1107 /* ------------------------------------------------------------------ */
1108 /* This is a wrapper for decExpOp which can handle the slightly wider */
1109 /* (double) range needed by Ln (which has to be able to calculate     */
1110 /* exp(-a) where a can be the tiniest number (Ntiny).                 */
1111 /* ------------------------------------------------------------------ */
1112 decNumber * decNumberExp(decNumber *res, const decNumber *rhs,
1113                          decContext *set) {
1114   uInt status=0;                        /* accumulator */
1115   #if DECSUBSET
1116   decNumber *allocrhs=NULL;        /* non-NULL if rounded rhs allocated */
1117   #endif
1118
1119   #if DECCHECK
1120   if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
1121   #endif
1122
1123   /* Check restrictions; these restrictions ensure that if h=8 (see */
1124   /* decExpOp) then the result will either overflow or underflow to 0. */
1125   /* Other math functions restrict the input range, too, for inverses. */
1126   /* If not violated then carry out the operation. */
1127   if (!decCheckMath(rhs, set, &status)) do { /* protect allocation */
1128     #if DECSUBSET
1129     if (!set->extended) {
1130       /* reduce operand and set lostDigits status, as needed */
1131       if (rhs->digits>set->digits) {
1132         allocrhs=decRoundOperand(rhs, set, &status);
1133         if (allocrhs==NULL) break;
1134         rhs=allocrhs;
1135         }
1136       }
1137     #endif
1138     decExpOp(res, rhs, set, &status);
1139     } while(0);                         /* end protected */
1140
1141   #if DECSUBSET
1142   if (allocrhs !=NULL) free(allocrhs);  /* drop any storage used */
1143   #endif
1144   /* apply significant status */
1145   if (status!=0) decStatus(res, status, set);
1146   #if DECCHECK
1147   decCheckInexact(res, set);
1148   #endif
1149   return res;
1150   } /* decNumberExp */
1151
1152 /* ------------------------------------------------------------------ */
1153 /* decNumberFMA -- fused multiply add                                 */
1154 /*                                                                    */
1155 /*   This computes D = (A * B) + C with only one rounding             */
1156 /*                                                                    */
1157 /*   res is D, the result.  D may be A or B or C (e.g., X=FMA(X,X,X)) */
1158 /*   lhs is A                                                         */
1159 /*   rhs is B                                                         */
1160 /*   fhs is C [far hand side]                                         */
1161 /*   set is the context                                               */
1162 /*                                                                    */
1163 /* Mathematical function restrictions apply (see above); a NaN is     */
1164 /* returned with Invalid_operation if a restriction is violated.      */
1165 /*                                                                    */
1166 /* C must have space for set->digits digits.                          */
1167 /* ------------------------------------------------------------------ */
1168 decNumber * decNumberFMA(decNumber *res, const decNumber *lhs,
1169                          const decNumber *rhs, const decNumber *fhs,
1170                          decContext *set) {
1171   uInt status=0;                   /* accumulator */
1172   decContext dcmul;                /* context for the multiplication */
1173   uInt needbytes;                  /* for space calculations */
1174   decNumber bufa[D2N(DECBUFFER*2+1)];
1175   decNumber *allocbufa=NULL;       /* -> allocated bufa, iff allocated */
1176   decNumber *acc;                  /* accumulator pointer */
1177   decNumber dzero;                 /* work */
1178
1179   #if DECCHECK
1180   if (decCheckOperands(res, lhs, rhs, set)) return res;
1181   if (decCheckOperands(res, fhs, DECUNUSED, set)) return res;
1182   #endif
1183
1184   do {                                  /* protect allocated storage */
1185     #if DECSUBSET
1186     if (!set->extended) {               /* [undefined if subset] */
1187       status|=DEC_Invalid_operation;
1188       break;}
1189     #endif
1190     /* Check math restrictions [these ensure no overflow or underflow] */
1191     if ((!decNumberIsSpecial(lhs) && decCheckMath(lhs, set, &status))
1192      || (!decNumberIsSpecial(rhs) && decCheckMath(rhs, set, &status))
1193      || (!decNumberIsSpecial(fhs) && decCheckMath(fhs, set, &status))) break;
1194     /* set up context for multiply */
1195     dcmul=*set;
1196     dcmul.digits=lhs->digits+rhs->digits; /* just enough */
1197     /* [The above may be an over-estimate for subset arithmetic, but that's OK] */
1198     dcmul.emax=DEC_MAX_EMAX;            /* effectively unbounded .. */
1199     dcmul.emin=DEC_MIN_EMIN;            /* [thanks to Math restrictions] */
1200     /* set up decNumber space to receive the result of the multiply */
1201     acc=bufa;                           /* may fit */
1202     needbytes=sizeof(decNumber)+(D2U(dcmul.digits)-1)*sizeof(Unit);
1203     if (needbytes>sizeof(bufa)) {       /* need malloc space */
1204       allocbufa=(decNumber *)malloc(needbytes);
1205       if (allocbufa==NULL) {            /* hopeless -- abandon */
1206         status|=DEC_Insufficient_storage;
1207         break;}
1208       acc=allocbufa;                    /* use the allocated space */
1209       }
1210     /* multiply with extended range and necessary precision */
1211     /*printf("emin=%ld\n", dcmul.emin); */
1212     decMultiplyOp(acc, lhs, rhs, &dcmul, &status);
1213     /* Only Invalid operation (from sNaN or Inf * 0) is possible in */
1214     /* status; if either is seen than ignore fhs (in case it is */
1215     /* another sNaN) and set acc to NaN unless we had an sNaN */
1216     /* [decMultiplyOp leaves that to caller] */
1217     /* Note sNaN has to go through addOp to shorten payload if */
1218     /* necessary */
1219     if ((status&DEC_Invalid_operation)!=0) {
1220       if (!(status&DEC_sNaN)) {         /* but be true invalid */
1221         decNumberZero(res);             /* acc not yet set */
1222         res->bits=DECNAN;
1223         break;
1224         }
1225       decNumberZero(&dzero);            /* make 0 (any non-NaN would do) */
1226       fhs=&dzero;                       /* use that */
1227       }
1228     #if DECCHECK
1229      else { /* multiply was OK */
1230       if (status!=0) printf("Status=%08lx after FMA multiply\n", status);
1231       }
1232     #endif
1233     /* add the third operand and result -> res, and all is done */
1234     decAddOp(res, acc, fhs, set, 0, &status);
1235     } while(0);                         /* end protected */
1236
1237   if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */
1238   if (status!=0) decStatus(res, status, set);
1239   #if DECCHECK
1240   decCheckInexact(res, set);
1241   #endif
1242   return res;
1243   } /* decNumberFMA */
1244
1245 /* ------------------------------------------------------------------ */
1246 /* decNumberInvert -- invert a Number, digitwise                      */
1247 /*                                                                    */
1248 /*   This computes C = ~A                                             */
1249 /*                                                                    */
1250 /*   res is C, the result.  C may be A (e.g., X=~X)                   */
1251 /*   rhs is A                                                         */
1252 /*   set is the context (used for result length and error report)     */
1253 /*                                                                    */
1254 /* C must have space for set->digits digits.                          */
1255 /*                                                                    */
1256 /* Logical function restrictions apply (see above); a NaN is          */
1257 /* returned with Invalid_operation if a restriction is violated.      */
1258 /* ------------------------------------------------------------------ */
1259 decNumber * decNumberInvert(decNumber *res, const decNumber *rhs,
1260                             decContext *set) {
1261   const Unit *ua, *msua;                /* -> operand and its msu */
1262   Unit  *uc, *msuc;                     /* -> result and its msu */
1263   Int   msudigs;                        /* digits in res msu */
1264   #if DECCHECK
1265   if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
1266   #endif
1267
1268   if (rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) {
1269     decStatus(res, DEC_Invalid_operation, set);
1270     return res;
1271     }
1272   /* operand is valid */
1273   ua=rhs->lsu;                          /* bottom-up */
1274   uc=res->lsu;                          /* .. */
1275   msua=ua+D2U(rhs->digits)-1;           /* -> msu of rhs */
1276   msuc=uc+D2U(set->digits)-1;           /* -> msu of result */
1277   msudigs=MSUDIGITS(set->digits);       /* [faster than remainder] */
1278   for (; uc<=msuc; ua++, uc++) {        /* Unit loop */
1279     Unit a;                             /* extract unit */
1280     Int  i, j;                          /* work */
1281     if (ua>msua) a=0;
1282      else a=*ua;
1283     *uc=0;                              /* can now write back */
1284     /* always need to examine all bits in rhs */
1285     /* This loop could be unrolled and/or use BIN2BCD tables */
1286     for (i=0; i<DECDPUN; i++) {
1287       if ((~a)&1) *uc=*uc+(Unit)powers[i];   /* effect INVERT */
1288       j=a%10;
1289       a=a/10;
1290       if (j>1) {
1291         decStatus(res, DEC_Invalid_operation, set);
1292         return res;
1293         }
1294       if (uc==msuc && i==msudigs-1) break;   /* just did final digit */
1295       } /* each digit */
1296     } /* each unit */
1297   /* [here uc-1 is the msu of the result] */
1298   res->digits=decGetDigits(res->lsu, uc-res->lsu);
1299   res->exponent=0;                      /* integer */
1300   res->bits=0;                          /* sign=0 */
1301   return res;  /* [no status to set] */
1302   } /* decNumberInvert */
1303
1304 /* ------------------------------------------------------------------ */
1305 /* decNumberLn -- natural logarithm                                   */
1306 /*                                                                    */
1307 /*   This computes C = ln(A)                                          */
1308 /*                                                                    */
1309 /*   res is C, the result.  C may be A                                */
1310 /*   rhs is A                                                         */
1311 /*   set is the context; note that rounding mode has no effect        */
1312 /*                                                                    */
1313 /* C must have space for set->digits digits.                          */
1314 /*                                                                    */
1315 /* Notable cases:                                                     */
1316 /*   A<0 -> Invalid                                                   */
1317 /*   A=0 -> -Infinity (Exact)                                         */
1318 /*   A=+Infinity -> +Infinity (Exact)                                 */
1319 /*   A=1 exactly -> 0 (Exact)                                         */
1320 /*                                                                    */
1321 /* Mathematical function restrictions apply (see above); a NaN is     */
1322 /* returned with Invalid_operation if a restriction is violated.      */
1323 /*                                                                    */
1324 /* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will    */
1325 /* almost always be correctly rounded, but may be up to 1 ulp in      */
1326 /* error in rare cases.                                               */
1327 /* ------------------------------------------------------------------ */
1328 /* This is a wrapper for decLnOp which can handle the slightly wider  */
1329 /* (+11) range needed by Ln, Log10, etc. (which may have to be able   */
1330 /* to calculate at p+e+2).                                            */
1331 /* ------------------------------------------------------------------ */
1332 decNumber * decNumberLn(decNumber *res, const decNumber *rhs,
1333                         decContext *set) {
1334   uInt status=0;                   /* accumulator */
1335   #if DECSUBSET
1336   decNumber *allocrhs=NULL;        /* non-NULL if rounded rhs allocated */
1337   #endif
1338
1339   #if DECCHECK
1340   if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
1341   #endif
1342
1343   /* Check restrictions; this is a math function; if not violated */
1344   /* then carry out the operation. */
1345   if (!decCheckMath(rhs, set, &status)) do { /* protect allocation */
1346     #if DECSUBSET
1347     if (!set->extended) {
1348       /* reduce operand and set lostDigits status, as needed */
1349       if (rhs->digits>set->digits) {
1350         allocrhs=decRoundOperand(rhs, set, &status);
1351         if (allocrhs==NULL) break;
1352         rhs=allocrhs;
1353         }
1354       /* special check in subset for rhs=0 */
1355       if (ISZERO(rhs)) {                /* +/- zeros -> error */
1356         status|=DEC_Invalid_operation;
1357         break;}
1358       } /* extended=0 */
1359     #endif
1360     decLnOp(res, rhs, set, &status);
1361     } while(0);                         /* end protected */
1362
1363   #if DECSUBSET
1364   if (allocrhs !=NULL) free(allocrhs);  /* drop any storage used */
1365   #endif
1366   /* apply significant status */
1367   if (status!=0) decStatus(res, status, set);
1368   #if DECCHECK
1369   decCheckInexact(res, set);
1370   #endif
1371   return res;
1372   } /* decNumberLn */
1373
1374 /* ------------------------------------------------------------------ */
1375 /* decNumberLogB - get adjusted exponent, by 754r rules               */
1376 /*                                                                    */
1377 /*   This computes C = adjustedexponent(A)                            */
1378 /*                                                                    */
1379 /*   res is C, the result.  C may be A                                */
1380 /*   rhs is A                                                         */
1381 /*   set is the context, used only for digits and status              */
1382 /*                                                                    */
1383 /* C must have space for 10 digits (A might have 10**9 digits and     */
1384 /* an exponent of +999999999, or one digit and an exponent of         */
1385 /* -1999999999).                                                      */
1386 /*                                                                    */
1387 /* This returns the adjusted exponent of A after (in theory) padding  */
1388 /* with zeros on the right to set->digits digits while keeping the    */
1389 /* same value.  The exponent is not limited by emin/emax.             */
1390 /*                                                                    */
1391 /* Notable cases:                                                     */
1392 /*   A<0 -> Use |A|                                                   */
1393 /*   A=0 -> -Infinity (Division by zero)                              */
1394 /*   A=Infinite -> +Infinity (Exact)                                  */
1395 /*   A=1 exactly -> 0 (Exact)                                         */
1396 /*   NaNs are propagated as usual                                     */
1397 /* ------------------------------------------------------------------ */
1398 decNumber * decNumberLogB(decNumber *res, const decNumber *rhs,
1399                           decContext *set) {
1400   uInt status=0;                   /* accumulator */
1401
1402   #if DECCHECK
1403   if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
1404   #endif
1405
1406   /* NaNs as usual; Infinities return +Infinity; 0->oops */
1407   if (decNumberIsNaN(rhs)) decNaNs(res, rhs, NULL, set, &status);
1408    else if (decNumberIsInfinite(rhs)) decNumberCopyAbs(res, rhs);
1409    else if (decNumberIsZero(rhs)) {
1410     decNumberZero(res);                 /* prepare for Infinity */
1411     res->bits=DECNEG|DECINF;            /* -Infinity */
1412     status|=DEC_Division_by_zero;       /* as per 754r */
1413     }
1414    else { /* finite non-zero */
1415     Int ae=rhs->exponent+rhs->digits-1; /* adjusted exponent */
1416     decNumberFromInt32(res, ae);        /* lay it out */
1417     }
1418
1419   if (status!=0) decStatus(res, status, set);
1420   return res;
1421   } /* decNumberLogB */
1422
1423 /* ------------------------------------------------------------------ */
1424 /* decNumberLog10 -- logarithm in base 10                             */
1425 /*                                                                    */
1426 /*   This computes C = log10(A)                                       */
1427 /*                                                                    */
1428 /*   res is C, the result.  C may be A                                */
1429 /*   rhs is A                                                         */
1430 /*   set is the context; note that rounding mode has no effect        */
1431 /*                                                                    */
1432 /* C must have space for set->digits digits.                          */
1433 /*                                                                    */
1434 /* Notable cases:                                                     */
1435 /*   A<0 -> Invalid                                                   */
1436 /*   A=0 -> -Infinity (Exact)                                         */
1437 /*   A=+Infinity -> +Infinity (Exact)                                 */
1438 /*   A=10**n (if n is an integer) -> n (Exact)                        */
1439 /*                                                                    */
1440 /* Mathematical function restrictions apply (see above); a NaN is     */
1441 /* returned with Invalid_operation if a restriction is violated.      */
1442 /*                                                                    */
1443 /* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will    */
1444 /* almost always be correctly rounded, but may be up to 1 ulp in      */
1445 /* error in rare cases.                                               */
1446 /* ------------------------------------------------------------------ */
1447 /* This calculates ln(A)/ln(10) using appropriate precision.  For     */
1448 /* ln(A) this is the max(p, rhs->digits + t) + 3, where p is the      */
1449 /* requested digits and t is the number of digits in the exponent     */
1450 /* (maximum 6).  For ln(10) it is p + 3; this is often handled by the */
1451 /* fastpath in decLnOp.  The final division is done to the requested  */
1452 /* precision.                                                         */
1453 /* ------------------------------------------------------------------ */
1454 decNumber * decNumberLog10(decNumber *res, const decNumber *rhs,
1455                           decContext *set) {
1456   uInt status=0, ignore=0;         /* status accumulators */
1457   uInt needbytes;                  /* for space calculations */
1458   Int p;                           /* working precision */
1459   Int t;                           /* digits in exponent of A */
1460
1461   /* buffers for a and b working decimals */
1462   /* (adjustment calculator, same size) */
1463   decNumber bufa[D2N(DECBUFFER+2)];
1464   decNumber *allocbufa=NULL;       /* -> allocated bufa, iff allocated */
1465   decNumber *a=bufa;               /* temporary a */
1466   decNumber bufb[D2N(DECBUFFER+2)];
1467   decNumber *allocbufb=NULL;       /* -> allocated bufb, iff allocated */
1468   decNumber *b=bufb;               /* temporary b */
1469   decNumber bufw[D2N(10)];         /* working 2-10 digit number */
1470   decNumber *w=bufw;               /* .. */
1471   #if DECSUBSET
1472   decNumber *allocrhs=NULL;        /* non-NULL if rounded rhs allocated */
1473   #endif
1474
1475   decContext aset;                 /* working context */
1476
1477   #if DECCHECK
1478   if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
1479   #endif
1480
1481   /* Check restrictions; this is a math function; if not violated */
1482   /* then carry out the operation. */
1483   if (!decCheckMath(rhs, set, &status)) do { /* protect malloc */
1484     #if DECSUBSET
1485     if (!set->extended) {
1486       /* reduce operand and set lostDigits status, as needed */
1487       if (rhs->digits>set->digits) {
1488         allocrhs=decRoundOperand(rhs, set, &status);
1489         if (allocrhs==NULL) break;
1490         rhs=allocrhs;
1491         }
1492       /* special check in subset for rhs=0 */
1493       if (ISZERO(rhs)) {                /* +/- zeros -> error */
1494         status|=DEC_Invalid_operation;
1495         break;}
1496       } /* extended=0 */
1497     #endif
1498
1499     decContextDefault(&aset, DEC_INIT_DECIMAL64); /* clean context */
1500
1501     /* handle exact powers of 10; only check if +ve finite */
1502     if (!(rhs->bits&(DECNEG|DECSPECIAL)) && !ISZERO(rhs)) {
1503       Int residue=0;               /* (no residue) */
1504       uInt copystat=0;             /* clean status */
1505
1506       /* round to a single digit... */
1507       aset.digits=1;
1508       decCopyFit(w, rhs, &aset, &residue, &copystat); /* copy & shorten */
1509       /* if exact and the digit is 1, rhs is a power of 10 */
1510       if (!(copystat&DEC_Inexact) && w->lsu[0]==1) {
1511         /* the exponent, conveniently, is the power of 10; making */
1512         /* this the result needs a little care as it might not fit, */
1513         /* so first convert it into the working number, and then move */
1514         /* to res */
1515         decNumberFromInt32(w, w->exponent);
1516         residue=0;
1517         decCopyFit(res, w, set, &residue, &status); /* copy & round */
1518         decFinish(res, set, &residue, &status);     /* cleanup/set flags */
1519         break;
1520         } /* not a power of 10 */
1521       } /* not a candidate for exact */
1522
1523     /* simplify the information-content calculation to use 'total */
1524     /* number of digits in a, including exponent' as compared to the */
1525     /* requested digits, as increasing this will only rarely cost an */
1526     /* iteration in ln(a) anyway */
1527     t=6;                                /* it can never be >6 */
1528
1529     /* allocate space when needed... */
1530     p=(rhs->digits+t>set->digits?rhs->digits+t:set->digits)+3;
1531     needbytes=sizeof(decNumber)+(D2U(p)-1)*sizeof(Unit);
1532     if (needbytes>sizeof(bufa)) {       /* need malloc space */
1533       allocbufa=(decNumber *)malloc(needbytes);
1534       if (allocbufa==NULL) {            /* hopeless -- abandon */
1535         status|=DEC_Insufficient_storage;
1536         break;}
1537       a=allocbufa;                      /* use the allocated space */
1538       }
1539     aset.digits=p;                      /* as calculated */
1540     aset.emax=DEC_MAX_MATH;             /* usual bounds */
1541     aset.emin=-DEC_MAX_MATH;            /* .. */
1542     aset.clamp=0;                       /* and no concrete format */
1543     decLnOp(a, rhs, &aset, &status);    /* a=ln(rhs) */
1544
1545     /* skip the division if the result so far is infinite, NaN, or */
1546     /* zero, or there was an error; note NaN from sNaN needs copy */
1547     if (status&DEC_NaNs && !(status&DEC_sNaN)) break;
1548     if (a->bits&DECSPECIAL || ISZERO(a)) {
1549       decNumberCopy(res, a);            /* [will fit] */
1550       break;}
1551
1552     /* for ln(10) an extra 3 digits of precision are needed */
1553     p=set->digits+3;
1554     needbytes=sizeof(decNumber)+(D2U(p)-1)*sizeof(Unit);
1555     if (needbytes>sizeof(bufb)) {       /* need malloc space */
1556       allocbufb=(decNumber *)malloc(needbytes);
1557       if (allocbufb==NULL) {            /* hopeless -- abandon */
1558         status|=DEC_Insufficient_storage;
1559         break;}
1560       b=allocbufb;                      /* use the allocated space */
1561       }
1562     decNumberZero(w);                   /* set up 10... */
1563     #if DECDPUN==1
1564     w->lsu[1]=1; w->lsu[0]=0;           /* .. */
1565     #else
1566     w->lsu[0]=10;                       /* .. */
1567     #endif
1568     w->digits=2;                        /* .. */
1569
1570     aset.digits=p;
1571     decLnOp(b, w, &aset, &ignore);      /* b=ln(10) */
1572
1573     aset.digits=set->digits;            /* for final divide */
1574     decDivideOp(res, a, b, &aset, DIVIDE, &status); /* into result */
1575     } while(0);                         /* [for break] */
1576
1577   if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */
1578   if (allocbufb!=NULL) free(allocbufb); /* .. */
1579   #if DECSUBSET
1580   if (allocrhs !=NULL) free(allocrhs);  /* .. */
1581   #endif
1582   /* apply significant status */
1583   if (status!=0) decStatus(res, status, set);
1584   #if DECCHECK
1585   decCheckInexact(res, set);
1586   #endif
1587   return res;
1588   } /* decNumberLog10 */
1589
1590 /* ------------------------------------------------------------------ */
1591 /* decNumberMax -- compare two Numbers and return the maximum         */
1592 /*                                                                    */
1593 /*   This computes C = A ? B, returning the maximum by 754R rules     */
1594 /*                                                                    */
1595 /*   res is C, the result.  C may be A and/or B (e.g., X=X?X)         */
1596 /*   lhs is A                                                         */
1597 /*   rhs is B                                                         */
1598 /*   set is the context                                               */
1599 /*                                                                    */
1600 /* C must have space for set->digits digits.                          */
1601 /* ------------------------------------------------------------------ */
1602 decNumber * decNumberMax(decNumber *res, const decNumber *lhs,
1603                          const decNumber *rhs, decContext *set) {
1604   uInt status=0;                        /* accumulator */
1605   decCompareOp(res, lhs, rhs, set, COMPMAX, &status);
1606   if (status!=0) decStatus(res, status, set);
1607   #if DECCHECK
1608   decCheckInexact(res, set);
1609   #endif
1610   return res;
1611   } /* decNumberMax */
1612
1613 /* ------------------------------------------------------------------ */
1614 /* decNumberMaxMag -- compare and return the maximum by magnitude     */
1615 /*                                                                    */
1616 /*   This computes C = A ? B, returning the maximum by 754R rules     */
1617 /*                                                                    */
1618 /*   res is C, the result.  C may be A and/or B (e.g., X=X?X)         */
1619 /*   lhs is A                                                         */
1620 /*   rhs is B                                                         */
1621 /*   set is the context                                               */
1622 /*                                                                    */
1623 /* C must have space for set->digits digits.                          */
1624 /* ------------------------------------------------------------------ */
1625 decNumber * decNumberMaxMag(decNumber *res, const decNumber *lhs,
1626                          const decNumber *rhs, decContext *set) {
1627   uInt status=0;                        /* accumulator */
1628   decCompareOp(res, lhs, rhs, set, COMPMAXMAG, &status);
1629   if (status!=0) decStatus(res, status, set);
1630   #if DECCHECK
1631   decCheckInexact(res, set);
1632   #endif
1633   return res;
1634   } /* decNumberMaxMag */
1635
1636 /* ------------------------------------------------------------------ */
1637 /* decNumberMin -- compare two Numbers and return the minimum         */
1638 /*                                                                    */
1639 /*   This computes C = A ? B, returning the minimum by 754R rules     */
1640 /*                                                                    */
1641 /*   res is C, the result.  C may be A and/or B (e.g., X=X?X)         */
1642 /*   lhs is A                                                         */
1643 /*   rhs is B                                                         */
1644 /*   set is the context                                               */
1645 /*                                                                    */
1646 /* C must have space for set->digits digits.                          */
1647 /* ------------------------------------------------------------------ */
1648 decNumber * decNumberMin(decNumber *res, const decNumber *lhs,
1649                          const decNumber *rhs, decContext *set) {
1650   uInt status=0;                        /* accumulator */
1651   decCompareOp(res, lhs, rhs, set, COMPMIN, &status);
1652   if (status!=0) decStatus(res, status, set);
1653   #if DECCHECK
1654   decCheckInexact(res, set);
1655   #endif
1656   return res;
1657   } /* decNumberMin */
1658
1659 /* ------------------------------------------------------------------ */
1660 /* decNumberMinMag -- compare and return the minimum by magnitude     */
1661 /*                                                                    */
1662 /*   This computes C = A ? B, returning the minimum by 754R rules     */
1663 /*                                                                    */
1664 /*   res is C, the result.  C may be A and/or B (e.g., X=X?X)         */
1665 /*   lhs is A                                                         */
1666 /*   rhs is B                                                         */
1667 /*   set is the context                                               */
1668 /*                                                                    */
1669 /* C must have space for set->digits digits.                          */
1670 /* ------------------------------------------------------------------ */
1671 decNumber * decNumberMinMag(decNumber *res, const decNumber *lhs,
1672                          const decNumber *rhs, decContext *set) {
1673   uInt status=0;                        /* accumulator */
1674   decCompareOp(res, lhs, rhs, set, COMPMINMAG, &status);
1675   if (status!=0) decStatus(res, status, set);
1676   #if DECCHECK
1677   decCheckInexact(res, set);
1678   #endif
1679   return res;
1680   } /* decNumberMinMag */
1681
1682 /* ------------------------------------------------------------------ */
1683 /* decNumberMinus -- prefix minus operator                            */
1684 /*                                                                    */
1685 /*   This computes C = 0 - A                                          */
1686 /*                                                                    */
1687 /*   res is C, the result.  C may be A                                */
1688 /*   rhs is A                                                         */
1689 /*   set is the context                                               */
1690 /*                                                                    */
1691 /* See also decNumberCopyNegate for a quiet bitwise version of this.  */
1692 /* C must have space for set->digits digits.                          */
1693 /* ------------------------------------------------------------------ */
1694 /* Simply use AddOp for the subtract, which will do the necessary.    */
1695 /* ------------------------------------------------------------------ */
1696 decNumber * decNumberMinus(decNumber *res, const decNumber *rhs,
1697                            decContext *set) {
1698   decNumber dzero;
1699   uInt status=0;                        /* accumulator */
1700
1701   #if DECCHECK
1702   if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
1703   #endif
1704
1705   decNumberZero(&dzero);                /* make 0 */
1706   dzero.exponent=rhs->exponent;         /* [no coefficient expansion] */
1707   decAddOp(res, &dzero, rhs, set, DECNEG, &status);
1708   if (status!=0) decStatus(res, status, set);
1709   #if DECCHECK
1710   decCheckInexact(res, set);
1711   #endif
1712   return res;
1713   } /* decNumberMinus */
1714
1715 /* ------------------------------------------------------------------ */
1716 /* decNumberNextMinus -- next towards -Infinity                       */
1717 /*                                                                    */
1718 /*   This computes C = A - infinitesimal, rounded towards -Infinity   */
1719 /*                                                                    */
1720 /*   res is C, the result.  C may be A                                */
1721 /*   rhs is A                                                         */
1722 /*   set is the context                                               */
1723 /*                                                                    */
1724 /* This is a generalization of 754r NextDown.                         */
1725 /* ------------------------------------------------------------------ */
1726 decNumber * decNumberNextMinus(decNumber *res, const decNumber *rhs,
1727                                decContext *set) {
1728   decNumber dtiny;                           /* constant */
1729   decContext workset=*set;                   /* work */
1730   uInt status=0;                             /* accumulator */
1731   #if DECCHECK
1732   if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
1733   #endif
1734
1735   /* +Infinity is the special case */
1736   if ((rhs->bits&(DECINF|DECNEG))==DECINF) {
1737     decSetMaxValue(res, set);                /* is +ve */
1738     /* there is no status to set */
1739     return res;
1740     }
1741   decNumberZero(&dtiny);                     /* start with 0 */
1742   dtiny.lsu[0]=1;                            /* make number that is .. */
1743   dtiny.exponent=DEC_MIN_EMIN-1;             /* .. smaller than tiniest */
1744   workset.round=DEC_ROUND_FLOOR;
1745   decAddOp(res, rhs, &dtiny, &workset, DECNEG, &status);
1746   status&=DEC_Invalid_operation|DEC_sNaN;    /* only sNaN Invalid please */
1747   if (status!=0) decStatus(res, status, set);
1748   return res;
1749   } /* decNumberNextMinus */
1750
1751 /* ------------------------------------------------------------------ */
1752 /* decNumberNextPlus -- next towards +Infinity                        */
1753 /*                                                                    */
1754 /*   This computes C = A + infinitesimal, rounded towards +Infinity   */
1755 /*                                                                    */
1756 /*   res is C, the result.  C may be A                                */
1757 /*   rhs is A                                                         */
1758 /*   set is the context                                               */
1759 /*                                                                    */
1760 /* This is a generalization of 754r NextUp.                           */
1761 /* ------------------------------------------------------------------ */
1762 decNumber * decNumberNextPlus(decNumber *res, const decNumber *rhs,
1763                               decContext *set) {
1764   decNumber dtiny;                           /* constant */
1765   decContext workset=*set;                   /* work */
1766   uInt status=0;                             /* accumulator */
1767   #if DECCHECK
1768   if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
1769   #endif
1770
1771   /* -Infinity is the special case */
1772   if ((rhs->bits&(DECINF|DECNEG))==(DECINF|DECNEG)) {
1773     decSetMaxValue(res, set);
1774     res->bits=DECNEG;                        /* negative */
1775     /* there is no status to set */
1776     return res;
1777     }
1778   decNumberZero(&dtiny);                     /* start with 0 */
1779   dtiny.lsu[0]=1;                            /* make number that is .. */
1780   dtiny.exponent=DEC_MIN_EMIN-1;             /* .. smaller than tiniest */
1781   workset.round=DEC_ROUND_CEILING;
1782   decAddOp(res, rhs, &dtiny, &workset, 0, &status);
1783   status&=DEC_Invalid_operation|DEC_sNaN;    /* only sNaN Invalid please */
1784   if (status!=0) decStatus(res, status, set);
1785   return res;
1786   } /* decNumberNextPlus */
1787
1788 /* ------------------------------------------------------------------ */
1789 /* decNumberNextToward -- next towards rhs                            */
1790 /*                                                                    */
1791 /*   This computes C = A +/- infinitesimal, rounded towards           */
1792 /*   +/-Infinity in the direction of B, as per 754r nextafter rules   */
1793 /*                                                                    */
1794 /*   res is C, the result.  C may be A or B.                          */
1795 /*   lhs is A                                                         */
1796 /*   rhs is B                                                         */
1797 /*   set is the context                                               */
1798 /*                                                                    */
1799 /* This is a generalization of 754r NextAfter.                        */
1800 /* ------------------------------------------------------------------ */
1801 decNumber * decNumberNextToward(decNumber *res, const decNumber *lhs,
1802                                 const decNumber *rhs, decContext *set) {
1803   decNumber dtiny;                           /* constant */
1804   decContext workset=*set;                   /* work */
1805   Int result;                                /* .. */
1806   uInt status=0;                             /* accumulator */
1807   #if DECCHECK
1808   if (decCheckOperands(res, lhs, rhs, set)) return res;
1809   #endif
1810
1811   if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) {
1812     decNaNs(res, lhs, rhs, set, &status);
1813     }
1814    else { /* Is numeric, so no chance of sNaN Invalid, etc. */
1815     result=decCompare(lhs, rhs, 0);     /* sign matters */
1816     if (result==BADINT) status|=DEC_Insufficient_storage; /* rare */
1817      else { /* valid compare */
1818       if (result==0) decNumberCopySign(res, lhs, rhs); /* easy */
1819        else { /* differ: need NextPlus or NextMinus */
1820         uByte sub;                      /* add or subtract */
1821         if (result<0) {                 /* lhs<rhs, do nextplus */
1822           /* -Infinity is the special case */
1823           if ((lhs->bits&(DECINF|DECNEG))==(DECINF|DECNEG)) {
1824             decSetMaxValue(res, set);
1825             res->bits=DECNEG;           /* negative */
1826             return res;                 /* there is no status to set */
1827             }
1828           workset.round=DEC_ROUND_CEILING;
1829           sub=0;                        /* add, please */
1830           } /* plus */
1831          else {                         /* lhs>rhs, do nextminus */
1832           /* +Infinity is the special case */
1833           if ((lhs->bits&(DECINF|DECNEG))==DECINF) {
1834             decSetMaxValue(res, set);
1835             return res;                 /* there is no status to set */
1836             }
1837           workset.round=DEC_ROUND_FLOOR;
1838           sub=DECNEG;                   /* subtract, please */
1839           } /* minus */
1840         decNumberZero(&dtiny);          /* start with 0 */
1841         dtiny.lsu[0]=1;                 /* make number that is .. */
1842         dtiny.exponent=DEC_MIN_EMIN-1;  /* .. smaller than tiniest */
1843         decAddOp(res, lhs, &dtiny, &workset, sub, &status); /* + or - */
1844         /* turn off exceptions if the result is a normal number */
1845         /* (including Nmin), otherwise let all status through */
1846         if (decNumberIsNormal(res, set)) status=0;
1847         } /* unequal */
1848       } /* compare OK */
1849     } /* numeric */
1850   if (status!=0) decStatus(res, status, set);
1851   return res;
1852   } /* decNumberNextToward */
1853
1854 /* ------------------------------------------------------------------ */
1855 /* decNumberOr -- OR two Numbers, digitwise                           */
1856 /*                                                                    */
1857 /*   This computes C = A | B                                          */
1858 /*                                                                    */
1859 /*   res is C, the result.  C may be A and/or B (e.g., X=X|X)         */
1860 /*   lhs is A                                                         */
1861 /*   rhs is B                                                         */
1862 /*   set is the context (used for result length and error report)     */
1863 /*                                                                    */
1864 /* C must have space for set->digits digits.                          */
1865 /*                                                                    */
1866 /* Logical function restrictions apply (see above); a NaN is          */
1867 /* returned with Invalid_operation if a restriction is violated.      */
1868 /* ------------------------------------------------------------------ */
1869 decNumber * decNumberOr(decNumber *res, const decNumber *lhs,
1870                         const decNumber *rhs, decContext *set) {
1871   const Unit *ua, *ub;                  /* -> operands */
1872   const Unit *msua, *msub;              /* -> operand msus */
1873   Unit  *uc, *msuc;                     /* -> result and its msu */
1874   Int   msudigs;                        /* digits in res msu */
1875   #if DECCHECK
1876   if (decCheckOperands(res, lhs, rhs, set)) return res;
1877   #endif
1878
1879   if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs)
1880    || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) {
1881     decStatus(res, DEC_Invalid_operation, set);
1882     return res;
1883     }
1884   /* operands are valid */
1885   ua=lhs->lsu;                          /* bottom-up */
1886   ub=rhs->lsu;                          /* .. */
1887   uc=res->lsu;                          /* .. */
1888   msua=ua+D2U(lhs->digits)-1;           /* -> msu of lhs */
1889   msub=ub+D2U(rhs->digits)-1;           /* -> msu of rhs */
1890   msuc=uc+D2U(set->digits)-1;           /* -> msu of result */
1891   msudigs=MSUDIGITS(set->digits);       /* [faster than remainder] */
1892   for (; uc<=msuc; ua++, ub++, uc++) {  /* Unit loop */
1893     Unit a, b;                          /* extract units */
1894     if (ua>msua) a=0;
1895      else a=*ua;
1896     if (ub>msub) b=0;
1897      else b=*ub;
1898     *uc=0;                              /* can now write back */
1899     if (a|b) {                          /* maybe 1 bits to examine */
1900       Int i, j;
1901       /* This loop could be unrolled and/or use BIN2BCD tables */
1902       for (i=0; i<DECDPUN; i++) {
1903         if ((a|b)&1) *uc=*uc+(Unit)powers[i];     /* effect OR */
1904         j=a%10;
1905         a=a/10;
1906         j|=b%10;
1907         b=b/10;
1908         if (j>1) {
1909           decStatus(res, DEC_Invalid_operation, set);
1910           return res;
1911           }
1912         if (uc==msuc && i==msudigs-1) break;      /* just did final digit */
1913         } /* each digit */
1914       } /* non-zero */
1915     } /* each unit */
1916   /* [here uc-1 is the msu of the result] */
1917   res->digits=decGetDigits(res->lsu, uc-res->lsu);
1918   res->exponent=0;                      /* integer */
1919   res->bits=0;                          /* sign=0 */
1920   return res;  /* [no status to set] */
1921   } /* decNumberOr */
1922
1923 /* ------------------------------------------------------------------ */
1924 /* decNumberPlus -- prefix plus operator                              */
1925 /*                                                                    */
1926 /*   This computes C = 0 + A                                          */
1927 /*                                                                    */
1928 /*   res is C, the result.  C may be A                                */
1929 /*   rhs is A                                                         */
1930 /*   set is the context                                               */
1931 /*                                                                    */
1932 /* See also decNumberCopy for a quiet bitwise version of this.        */
1933 /* C must have space for set->digits digits.                          */
1934 /* ------------------------------------------------------------------ */
1935 /* This simply uses AddOp; Add will take fast path after preparing A. */
1936 /* Performance is a concern here, as this routine is often used to    */
1937 /* check operands and apply rounding and overflow/underflow testing.  */
1938 /* ------------------------------------------------------------------ */
1939 decNumber * decNumberPlus(decNumber *res, const decNumber *rhs,
1940                           decContext *set) {
1941   decNumber dzero;
1942   uInt status=0;                        /* accumulator */
1943   #if DECCHECK
1944   if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
1945   #endif
1946
1947   decNumberZero(&dzero);                /* make 0 */
1948   dzero.exponent=rhs->exponent;         /* [no coefficient expansion] */
1949   decAddOp(res, &dzero, rhs, set, 0, &status);
1950   if (status!=0) decStatus(res, status, set);
1951   #if DECCHECK
1952   decCheckInexact(res, set);
1953   #endif
1954   return res;
1955   } /* decNumberPlus */
1956
1957 /* ------------------------------------------------------------------ */
1958 /* decNumberMultiply -- multiply two Numbers                          */
1959 /*                                                                    */
1960 /*   This computes C = A x B                                          */
1961 /*                                                                    */
1962 /*   res is C, the result.  C may be A and/or B (e.g., X=X+X)         */
1963 /*   lhs is A                                                         */
1964 /*   rhs is B                                                         */
1965 /*   set is the context                                               */
1966 /*                                                                    */
1967 /* C must have space for set->digits digits.                          */
1968 /* ------------------------------------------------------------------ */
1969 decNumber * decNumberMultiply(decNumber *res, const decNumber *lhs,
1970                               const decNumber *rhs, decContext *set) {
1971   uInt status=0;                   /* accumulator */
1972   decMultiplyOp(res, lhs, rhs, set, &status);
1973   if (status!=0) decStatus(res, status, set);
1974   #if DECCHECK
1975   decCheckInexact(res, set);
1976   #endif
1977   return res;
1978   } /* decNumberMultiply */
1979
1980 /* ------------------------------------------------------------------ */
1981 /* decNumberPower -- raise a number to a power                        */
1982 /*                                                                    */
1983 /*   This computes C = A ** B                                         */
1984 /*                                                                    */
1985 /*   res is C, the result.  C may be A and/or B (e.g., X=X**X)        */
1986 /*   lhs is A                                                         */
1987 /*   rhs is B                                                         */
1988 /*   set is the context                                               */
1989 /*                                                                    */
1990 /* C must have space for set->digits digits.                          */
1991 /*                                                                    */
1992 /* Mathematical function restrictions apply (see above); a NaN is     */
1993 /* returned with Invalid_operation if a restriction is violated.      */
1994 /*                                                                    */
1995 /* However, if 1999999997<=B<=999999999 and B is an integer then the  */
1996 /* restrictions on A and the context are relaxed to the usual bounds, */
1997 /* for compatibility with the earlier (integer power only) version    */
1998 /* of this function.                                                  */
1999 /*                                                                    */
2000 /* When B is an integer, the result may be exact, even if rounded.    */
2001 /*                                                                    */
2002 /* The final result is rounded according to the context; it will      */
2003 /* almost always be correctly rounded, but may be up to 1 ulp in      */
2004 /* error in rare cases.                                               */
2005 /* ------------------------------------------------------------------ */
2006 decNumber * decNumberPower(decNumber *res, const decNumber *lhs,
2007                            const decNumber *rhs, decContext *set) {
2008   #if DECSUBSET
2009   decNumber *alloclhs=NULL;        /* non-NULL if rounded lhs allocated */
2010   decNumber *allocrhs=NULL;        /* .., rhs */
2011   #endif
2012   decNumber *allocdac=NULL;        /* -> allocated acc buffer, iff used */
2013   decNumber *allocinv=NULL;        /* -> allocated 1/x buffer, iff used */
2014   Int   reqdigits=set->digits;     /* requested DIGITS */
2015   Int   n;                         /* rhs in binary */
2016   Flag  rhsint=0;                  /* 1 if rhs is an integer */
2017   Flag  useint=0;                  /* 1 if can use integer calculation */
2018   Flag  isoddint=0;                /* 1 if rhs is an integer and odd */
2019   Int   i;                         /* work */
2020   #if DECSUBSET
2021   Int   dropped;                   /* .. */
2022   #endif
2023   uInt  needbytes;                 /* buffer size needed */
2024   Flag  seenbit;                   /* seen a bit while powering */
2025   Int   residue=0;                 /* rounding residue */
2026   uInt  status=0;                  /* accumulators */
2027   uByte bits=0;                    /* result sign if errors */
2028   decContext aset;                 /* working context */
2029   decNumber dnOne;                 /* work value 1... */
2030   /* local accumulator buffer [a decNumber, with digits+elength+1 digits] */
2031   decNumber dacbuff[D2N(DECBUFFER+9)];
2032   decNumber *dac=dacbuff;          /* -> result accumulator */
2033   /* same again for possible 1/lhs calculation */
2034   decNumber invbuff[D2N(DECBUFFER+9)];
2035
2036   #if DECCHECK
2037   if (decCheckOperands(res, lhs, rhs, set)) return res;
2038   #endif
2039
2040   do {                             /* protect allocated storage */
2041     #if DECSUBSET
2042     if (!set->extended) { /* reduce operands and set status, as needed */
2043       if (lhs->digits>reqdigits) {
2044         alloclhs=decRoundOperand(lhs, set, &status);
2045         if (alloclhs==NULL) break;
2046         lhs=alloclhs;
2047         }
2048       if (rhs->digits>reqdigits) {
2049         allocrhs=decRoundOperand(rhs, set, &status);
2050         if (allocrhs==NULL) break;
2051         rhs=allocrhs;
2052         }
2053       }
2054     #endif
2055     /* [following code does not require input rounding] */
2056
2057     /* handle NaNs and rhs Infinity (lhs infinity is harder) */
2058     if (SPECIALARGS) {
2059       if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) { /* NaNs */
2060         decNaNs(res, lhs, rhs, set, &status);
2061         break;}
2062       if (decNumberIsInfinite(rhs)) {   /* rhs Infinity */
2063         Flag rhsneg=rhs->bits&DECNEG;   /* save rhs sign */
2064         if (decNumberIsNegative(lhs)    /* lhs<0 */
2065          && !decNumberIsZero(lhs))      /* .. */
2066           status|=DEC_Invalid_operation;
2067          else {                         /* lhs >=0 */
2068           decNumberZero(&dnOne);        /* set up 1 */
2069           dnOne.lsu[0]=1;
2070           decNumberCompare(dac, lhs, &dnOne, set); /* lhs ? 1 */
2071           decNumberZero(res);           /* prepare for 0/1/Infinity */
2072           if (decNumberIsNegative(dac)) {    /* lhs<1 */
2073             if (rhsneg) res->bits|=DECINF;   /* +Infinity [else is +0] */
2074             }
2075            else if (dac->lsu[0]==0) {        /* lhs=1 */
2076             /* 1**Infinity is inexact, so return fully-padded 1.0000 */
2077             Int shift=set->digits-1;
2078             *res->lsu=1;                     /* was 0, make int 1 */
2079             res->digits=decShiftToMost(res->lsu, 1, shift);
2080             res->exponent=-shift;            /* make 1.0000... */
2081             status|=DEC_Inexact|DEC_Rounded; /* deemed inexact */
2082             }
2083            else {                            /* lhs>1 */
2084             if (!rhsneg) res->bits|=DECINF;  /* +Infinity [else is +0] */
2085             }
2086           } /* lhs>=0 */
2087         break;}
2088       /* [lhs infinity drops through] */
2089       } /* specials */
2090
2091     /* Original rhs may be an integer that fits and is in range */
2092     n=decGetInt(rhs);
2093     if (n!=BADINT) {                    /* it is an integer */
2094       rhsint=1;                         /* record the fact for 1**n */
2095       isoddint=(Flag)n&1;               /* [works even if big] */
2096       if (n!=BIGEVEN && n!=BIGODD)      /* can use integer path? */
2097         useint=1;                       /* looks good */
2098       }
2099
2100     if (decNumberIsNegative(lhs)        /* -x .. */
2101       && isoddint) bits=DECNEG;         /* .. to an odd power */
2102
2103     /* handle LHS infinity */
2104     if (decNumberIsInfinite(lhs)) {     /* [NaNs already handled] */
2105       uByte rbits=rhs->bits;            /* save */
2106       decNumberZero(res);               /* prepare */
2107       if (n==0) *res->lsu=1;            /* [-]Inf**0 => 1 */
2108        else {
2109         /* -Inf**nonint -> error */
2110         if (!rhsint && decNumberIsNegative(lhs)) {
2111           status|=DEC_Invalid_operation;     /* -Inf**nonint is error */
2112           break;}
2113         if (!(rbits & DECNEG)) bits|=DECINF; /* was not a **-n */
2114         /* [otherwise will be 0 or -0] */
2115         res->bits=bits;
2116         }
2117       break;}
2118
2119     /* similarly handle LHS zero */
2120     if (decNumberIsZero(lhs)) {
2121       if (n==0) {                            /* 0**0 => Error */
2122         #if DECSUBSET
2123         if (!set->extended) {                /* [unless subset] */
2124           decNumberZero(res);
2125           *res->lsu=1;                       /* return 1 */
2126           break;}
2127         #endif
2128         status|=DEC_Invalid_operation;
2129         }
2130        else {                                /* 0**x */
2131         uByte rbits=rhs->bits;               /* save */
2132         if (rbits & DECNEG) {                /* was a 0**(-n) */
2133           #if DECSUBSET
2134           if (!set->extended) {              /* [bad if subset] */
2135             status|=DEC_Invalid_operation;
2136             break;}
2137           #endif
2138           bits|=DECINF;
2139           }
2140         decNumberZero(res);                  /* prepare */
2141         /* [otherwise will be 0 or -0] */
2142         res->bits=bits;
2143         }
2144       break;}
2145
2146     /* here both lhs and rhs are finite; rhs==0 is handled in the */
2147     /* integer path.  Next handle the non-integer cases */
2148     if (!useint) {                      /* non-integral rhs */
2149       /* any -ve lhs is bad, as is either operand or context out of */
2150       /* bounds */
2151       if (decNumberIsNegative(lhs)) {
2152         status|=DEC_Invalid_operation;
2153         break;}
2154       if (decCheckMath(lhs, set, &status)
2155        || decCheckMath(rhs, set, &status)) break; /* variable status */
2156
2157       decContextDefault(&aset, DEC_INIT_DECIMAL64); /* clean context */
2158       aset.emax=DEC_MAX_MATH;           /* usual bounds */
2159       aset.emin=-DEC_MAX_MATH;          /* .. */
2160       aset.clamp=0;                     /* and no concrete format */
2161
2162       /* calculate the result using exp(ln(lhs)*rhs), which can */
2163       /* all be done into the accumulator, dac.  The precision needed */
2164       /* is enough to contain the full information in the lhs (which */
2165       /* is the total digits, including exponent), or the requested */
2166       /* precision, if larger, + 4; 6 is used for the exponent */
2167       /* maximum length, and this is also used when it is shorter */
2168       /* than the requested digits as it greatly reduces the >0.5 ulp */
2169       /* cases at little cost (because Ln doubles digits each */
2170       /* iteration so a few extra digits rarely causes an extra */
2171       /* iteration) */
2172       aset.digits=MAXI(lhs->digits, set->digits)+6+4;
2173       } /* non-integer rhs */
2174
2175      else { /* rhs is in-range integer */
2176       if (n==0) {                       /* x**0 = 1 */
2177         /* (0**0 was handled above) */
2178         decNumberZero(res);             /* result=1 */
2179         *res->lsu=1;                    /* .. */
2180         break;}
2181       /* rhs is a non-zero integer */
2182       if (n<0) n=-n;                    /* use abs(n) */
2183
2184       aset=*set;                        /* clone the context */
2185       aset.round=DEC_ROUND_HALF_EVEN;   /* internally use balanced */
2186       /* calculate the working DIGITS */
2187       aset.digits=reqdigits+(rhs->digits+rhs->exponent)+2;
2188       #if DECSUBSET
2189       if (!set->extended) aset.digits--;     /* use classic precision */
2190       #endif
2191       /* it's an error if this is more than can be handled */
2192       if (aset.digits>DECNUMMAXP) {status|=DEC_Invalid_operation; break;}
2193       } /* integer path */
2194
2195     /* aset.digits is the count of digits for the accumulator needed */
2196     /* if accumulator is too long for local storage, then allocate */
2197     needbytes=sizeof(decNumber)+(D2U(aset.digits)-1)*sizeof(Unit);
2198     /* [needbytes also used below if 1/lhs needed] */
2199     if (needbytes>sizeof(dacbuff)) {
2200       allocdac=(decNumber *)malloc(needbytes);
2201       if (allocdac==NULL) {   /* hopeless -- abandon */
2202         status|=DEC_Insufficient_storage;
2203         break;}
2204       dac=allocdac;           /* use the allocated space */
2205       }
2206     /* here, aset is set up and accumulator is ready for use */
2207
2208     if (!useint) {                           /* non-integral rhs */
2209       /* x ** y; special-case x=1 here as it will otherwise always */
2210       /* reduce to integer 1; decLnOp has a fastpath which detects */
2211       /* the case of x=1 */
2212       decLnOp(dac, lhs, &aset, &status);     /* dac=ln(lhs) */
2213       /* [no error possible, as lhs 0 already handled] */
2214       if (ISZERO(dac)) {                     /* x==1, 1.0, etc. */
2215         /* need to return fully-padded 1.0000 etc., but rhsint->1 */
2216         *dac->lsu=1;                         /* was 0, make int 1 */
2217         if (!rhsint) {                       /* add padding */
2218           Int shift=set->digits-1;
2219           dac->digits=decShiftToMost(dac->lsu, 1, shift);
2220           dac->exponent=-shift;              /* make 1.0000... */
2221           status|=DEC_Inexact|DEC_Rounded;   /* deemed inexact */
2222           }
2223         }
2224        else {
2225         decMultiplyOp(dac, dac, rhs, &aset, &status);  /* dac=dac*rhs */
2226         decExpOp(dac, dac, &aset, &status);            /* dac=exp(dac) */
2227         }
2228       /* and drop through for final rounding */
2229       } /* non-integer rhs */
2230
2231      else {                             /* carry on with integer */
2232       decNumberZero(dac);               /* acc=1 */
2233       *dac->lsu=1;                      /* .. */
2234
2235       /* if a negative power the constant 1 is needed, and if not subset */
2236       /* invert the lhs now rather than inverting the result later */
2237       if (decNumberIsNegative(rhs)) {   /* was a **-n [hence digits>0] */
2238         decNumber *inv=invbuff;         /* assume use fixed buffer */
2239         decNumberCopy(&dnOne, dac);     /* dnOne=1;  [needed now or later] */
2240         #if DECSUBSET
2241         if (set->extended) {            /* need to calculate 1/lhs */
2242         #endif
2243           /* divide lhs into 1, putting result in dac [dac=1/dac] */
2244           decDivideOp(dac, &dnOne, lhs, &aset, DIVIDE, &status);
2245           /* now locate or allocate space for the inverted lhs */
2246           if (needbytes>sizeof(invbuff)) {
2247             allocinv=(decNumber *)malloc(needbytes);
2248             if (allocinv==NULL) {       /* hopeless -- abandon */
2249               status|=DEC_Insufficient_storage;
2250               break;}
2251             inv=allocinv;               /* use the allocated space */
2252             }
2253           /* [inv now points to big-enough buffer or allocated storage] */
2254           decNumberCopy(inv, dac);      /* copy the 1/lhs */
2255           decNumberCopy(dac, &dnOne);   /* restore acc=1 */
2256           lhs=inv;                      /* .. and go forward with new lhs */
2257         #if DECSUBSET
2258           }
2259         #endif
2260         }
2261
2262       /* Raise-to-the-power loop... */
2263       seenbit=0;                   /* set once a 1-bit is encountered */
2264       for (i=1;;i++){              /* for each bit [top bit ignored] */
2265         /* abandon if had overflow or terminal underflow */
2266         if (status & (DEC_Overflow|DEC_Underflow)) { /* interesting? */
2267           if (status&DEC_Overflow || ISZERO(dac)) break;
2268           }
2269         /* [the following two lines revealed an optimizer bug in a C++ */
2270         /* compiler, with symptom: 5**3 -> 25, when n=n+n was used] */
2271         n=n<<1;                    /* move next bit to testable position */
2272         if (n<0) {                 /* top bit is set */
2273           seenbit=1;               /* OK, significant bit seen */
2274           decMultiplyOp(dac, dac, lhs, &aset, &status); /* dac=dac*x */
2275           }
2276         if (i==31) break;          /* that was the last bit */
2277         if (!seenbit) continue;    /* no need to square 1 */
2278         decMultiplyOp(dac, dac, dac, &aset, &status); /* dac=dac*dac [square] */
2279         } /*i*/ /* 32 bits */
2280
2281       /* complete internal overflow or underflow processing */
2282       if (status & (DEC_Overflow|DEC_Underflow)) {
2283         #if DECSUBSET
2284         /* If subset, and power was negative, reverse the kind of -erflow */
2285         /* [1/x not yet done] */
2286         if (!set->extended && decNumberIsNegative(rhs)) {
2287           if (status & DEC_Overflow)
2288             status^=DEC_Overflow | DEC_Underflow | DEC_Subnormal;
2289            else { /* trickier -- Underflow may or may not be set */
2290             status&=~(DEC_Underflow | DEC_Subnormal); /* [one or both] */
2291             status|=DEC_Overflow;
2292             }
2293           }
2294         #endif
2295         dac->bits=(dac->bits & ~DECNEG) | bits; /* force correct sign */
2296         /* round subnormals [to set.digits rather than aset.digits] */
2297         /* or set overflow result similarly as required */
2298         decFinalize(dac, set, &residue, &status);
2299         decNumberCopy(res, dac);   /* copy to result (is now OK length) */
2300         break;
2301         }
2302
2303       #if DECSUBSET
2304       if (!set->extended &&                  /* subset math */
2305           decNumberIsNegative(rhs)) {        /* was a **-n [hence digits>0] */
2306         /* so divide result into 1 [dac=1/dac] */
2307         decDivideOp(dac, &dnOne, dac, &aset, DIVIDE, &status);
2308         }
2309       #endif
2310       } /* rhs integer path */
2311
2312     /* reduce result to the requested length and copy to result */
2313     decCopyFit(res, dac, set, &residue, &status);
2314     decFinish(res, set, &residue, &status);  /* final cleanup */
2315     #if DECSUBSET
2316     if (!set->extended) decTrim(res, set, 0, &dropped); /* trailing zeros */
2317     #endif
2318     } while(0);                         /* end protected */
2319
2320   if (allocdac!=NULL) free(allocdac);   /* drop any storage used */
2321   if (allocinv!=NULL) free(allocinv);   /* .. */
2322   #if DECSUBSET
2323   if (alloclhs!=NULL) free(alloclhs);   /* .. */
2324   if (allocrhs!=NULL) free(allocrhs);   /* .. */
2325   #endif
2326   if (status!=0) decStatus(res, status, set);
2327   #if DECCHECK
2328   decCheckInexact(res, set);
2329   #endif
2330   return res;
2331   } /* decNumberPower */
2332
2333 /* ------------------------------------------------------------------ */
2334 /* decNumberQuantize -- force exponent to requested value             */
2335 /*                                                                    */
2336 /*   This computes C = op(A, B), where op adjusts the coefficient     */
2337 /*   of C (by rounding or shifting) such that the exponent (-scale)   */
2338 /*   of C has exponent of B.  The numerical value of C will equal A,  */
2339 /*   except for the effects of any rounding that occurred.            */
2340 /*                                                                    */
2341 /*   res is C, the result.  C may be A or B                           */
2342 /*   lhs is A, the number to adjust                                   */
2343 /*   rhs is B, the number with exponent to match                      */
2344 /*   set is the context                                               */
2345 /*                                                                    */
2346 /* C must have space for set->digits digits.                          */
2347 /*                                                                    */
2348 /* Unless there is an error or the result is infinite, the exponent   */
2349 /* after the operation is guaranteed to be equal to that of B.        */
2350 /* ------------------------------------------------------------------ */
2351 decNumber * decNumberQuantize(decNumber *res, const decNumber *lhs,
2352                               const decNumber *rhs, decContext *set) {
2353   uInt status=0;                        /* accumulator */
2354   decQuantizeOp(res, lhs, rhs, set, 1, &status);
2355   if (status!=0) decStatus(res, status, set);
2356   return res;
2357   } /* decNumberQuantize */
2358
2359 /* ------------------------------------------------------------------ */
2360 /* decNumberReduce -- remove trailing zeros                           */
2361 /*                                                                    */
2362 /*   This computes C = 0 + A, and normalizes the result               */
2363 /*                                                                    */
2364 /*   res is C, the result.  C may be A                                */
2365 /*   rhs is A                                                         */
2366 /*   set is the context                                               */
2367 /*                                                                    */
2368 /* C must have space for set->digits digits.                          */
2369 /* ------------------------------------------------------------------ */
2370 /* Previously known as Normalize */
2371 decNumber * decNumberNormalize(decNumber *res, const decNumber *rhs,
2372                                decContext *set) {
2373   return decNumberReduce(res, rhs, set);
2374   } /* decNumberNormalize */
2375
2376 decNumber * decNumberReduce(decNumber *res, const decNumber *rhs,
2377                             decContext *set) {
2378   #if DECSUBSET
2379   decNumber *allocrhs=NULL;        /* non-NULL if rounded rhs allocated */
2380   #endif
2381   uInt status=0;                   /* as usual */
2382   Int  residue=0;                  /* as usual */
2383   Int  dropped;                    /* work */
2384
2385   #if DECCHECK
2386   if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
2387   #endif
2388
2389   do {                             /* protect allocated storage */
2390     #if DECSUBSET
2391     if (!set->extended) {
2392       /* reduce operand and set lostDigits status, as needed */
2393       if (rhs->digits>set->digits) {
2394         allocrhs=decRoundOperand(rhs, set, &status);
2395         if (allocrhs==NULL) break;
2396         rhs=allocrhs;
2397         }
2398       }
2399     #endif
2400     /* [following code does not require input rounding] */
2401
2402     /* Infinities copy through; NaNs need usual treatment */
2403     if (decNumberIsNaN(rhs)) {
2404       decNaNs(res, rhs, NULL, set, &status);
2405       break;
2406       }
2407
2408     /* reduce result to the requested length and copy to result */
2409     decCopyFit(res, rhs, set, &residue, &status); /* copy & round */
2410     decFinish(res, set, &residue, &status);       /* cleanup/set flags */
2411     decTrim(res, set, 1, &dropped);               /* normalize in place */
2412     } while(0);                              /* end protected */
2413
2414   #if DECSUBSET
2415   if (allocrhs !=NULL) free(allocrhs);       /* .. */
2416   #endif
2417   if (status!=0) decStatus(res, status, set);/* then report status */
2418   return res;
2419   } /* decNumberReduce */
2420
2421 /* ------------------------------------------------------------------ */
2422 /* decNumberRescale -- force exponent to requested value              */
2423 /*                                                                    */
2424 /*   This computes C = op(A, B), where op adjusts the coefficient     */
2425 /*   of C (by rounding or shifting) such that the exponent (-scale)   */
2426 /*   of C has the value B.  The numerical value of C will equal A,    */
2427 /*   except for the effects of any rounding that occurred.            */
2428 /*                                                                    */
2429 /*   res is C, the result.  C may be A or B                           */
2430 /*   lhs is A, the number to adjust                                   */
2431 /*   rhs is B, the requested exponent                                 */
2432 /*   set is the context                                               */
2433 /*                                                                    */
2434 /* C must have space for set->digits digits.                          */
2435 /*                                                                    */
2436 /* Unless there is an error or the result is infinite, the exponent   */
2437 /* after the operation is guaranteed to be equal to B.                */
2438 /* ------------------------------------------------------------------ */
2439 decNumber * decNumberRescale(decNumber *res, const decNumber *lhs,
2440                              const decNumber *rhs, decContext *set) {
2441   uInt status=0;                        /* accumulator */
2442   decQuantizeOp(res, lhs, rhs, set, 0, &status);
2443   if (status!=0) decStatus(res, status, set);
2444   return res;
2445   } /* decNumberRescale */
2446
2447 /* ------------------------------------------------------------------ */
2448 /* decNumberRemainder -- divide and return remainder                  */
2449 /*                                                                    */
2450 /*   This computes C = A % B                                          */
2451 /*                                                                    */
2452 /*   res is C, the result.  C may be A and/or B (e.g., X=X%X)         */
2453 /*   lhs is A                                                         */
2454 /*   rhs is B                                                         */
2455 /*   set is the context                                               */
2456 /*                                                                    */
2457 /* C must have space for set->digits digits.                          */
2458 /* ------------------------------------------------------------------ */
2459 decNumber * decNumberRemainder(decNumber *res, const decNumber *lhs,
2460                                const decNumber *rhs, decContext *set) {
2461   uInt status=0;                        /* accumulator */
2462   decDivideOp(res, lhs, rhs, set, REMAINDER, &status);
2463   if (status!=0) decStatus(res, status, set);
2464   #if DECCHECK
2465   decCheckInexact(res, set);
2466   #endif
2467   return res;
2468   } /* decNumberRemainder */
2469
2470 /* ------------------------------------------------------------------ */
2471 /* decNumberRemainderNear -- divide and return remainder from nearest */
2472 /*                                                                    */
2473 /*   This computes C = A % B, where % is the IEEE remainder operator  */
2474 /*                                                                    */
2475 /*   res is C, the result.  C may be A and/or B (e.g., X=X%X)         */
2476 /*   lhs is A                                                         */
2477 /*   rhs is B                                                         */
2478 /*   set is the context                                               */
2479 /*                                                                    */
2480 /* C must have space for set->digits digits.                          */
2481 /* ------------------------------------------------------------------ */
2482 decNumber * decNumberRemainderNear(decNumber *res, const decNumber *lhs,
2483                                    const decNumber *rhs, decContext *set) {
2484   uInt status=0;                        /* accumulator */
2485   decDivideOp(res, lhs, rhs, set, REMNEAR, &status);
2486   if (status!=0) decStatus(res, status, set);
2487   #if DECCHECK
2488   decCheckInexact(res, set);
2489   #endif
2490   return res;
2491   } /* decNumberRemainderNear */
2492
2493 /* ------------------------------------------------------------------ */
2494 /* decNumberRotate -- rotate the coefficient of a Number left/right   */
2495 /*                                                                    */
2496 /*   This computes C = A rot B  (in base ten and rotating set->digits */
2497 /*   digits).                                                         */
2498 /*                                                                    */
2499 /*   res is C, the result.  C may be A and/or B (e.g., X=XrotX)       */
2500 /*   lhs is A                                                         */
2501 /*   rhs is B, the number of digits to rotate (-ve to right)          */
2502 /*   set is the context                                               */
2503 /*                                                                    */
2504 /* The digits of the coefficient of A are rotated to the left (if B   */
2505 /* is positive) or to the right (if B is negative) without adjusting  */
2506 /* the exponent or the sign of A.  If lhs->digits is less than        */
2507 /* set->digits the coefficient is padded with zeros on the left       */
2508 /* before the rotate.  Any leading zeros in the result are removed    */
2509 /* as usual.                                                          */
2510 /*                                                                    */
2511 /* B must be an integer (q=0) and in the range -set->digits through   */
2512 /* +set->digits.                                                      */
2513 /* C must have space for set->digits digits.                          */
2514 /* NaNs are propagated as usual.  Infinities are unaffected (but      */
2515 /* B must be valid).  No status is set unless B is invalid or an      */
2516 /* operand is an sNaN.                                                */
2517 /* ------------------------------------------------------------------ */
2518 decNumber * decNumberRotate(decNumber *res, const decNumber *lhs,
2519                            const decNumber *rhs, decContext *set) {
2520   uInt status=0;              /* accumulator */
2521   Int  rotate;                /* rhs as an Int */
2522
2523   #if DECCHECK
2524   if (decCheckOperands(res, lhs, rhs, set)) return res;
2525   #endif
2526
2527   /* NaNs propagate as normal */
2528   if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs))
2529     decNaNs(res, lhs, rhs, set, &status);
2530    /* rhs must be an integer */
2531    else if (decNumberIsInfinite(rhs) || rhs->exponent!=0)
2532     status=DEC_Invalid_operation;
2533    else { /* both numeric, rhs is an integer */
2534     rotate=decGetInt(rhs);                   /* [cannot fail] */
2535     if (rotate==BADINT                       /* something bad .. */
2536      || rotate==BIGODD || rotate==BIGEVEN    /* .. very big .. */
2537      || abs(rotate)>set->digits)             /* .. or out of range */
2538       status=DEC_Invalid_operation;
2539      else {                                  /* rhs is OK */
2540       decNumberCopy(res, lhs);
2541       /* convert -ve rotate to equivalent positive rotation */
2542       if (rotate<0) rotate=set->digits+rotate;
2543       if (rotate!=0 && rotate!=set->digits   /* zero or full rotation */
2544        && !decNumberIsInfinite(res)) {       /* lhs was infinite */
2545         /* left-rotate to do; 0 < rotate < set->digits */
2546         uInt units, shift;                   /* work */
2547         uInt msudigits;                      /* digits in result msu */
2548         Unit *msu=res->lsu+D2U(res->digits)-1;    /* current msu */
2549         Unit *msumax=res->lsu+D2U(set->digits)-1; /* rotation msu */
2550         for (msu++; msu<=msumax; msu++) *msu=0;   /* ensure high units=0 */
2551         res->digits=set->digits;                  /* now full-length */
2552         msudigits=MSUDIGITS(res->digits);         /* actual digits in msu */
2553
2554         /* rotation here is done in-place, in three steps */
2555         /* 1. shift all to least up to one unit to unit-align final */
2556         /*    lsd [any digits shifted out are rotated to the left, */
2557         /*    abutted to the original msd (which may require split)] */
2558         /* */
2559         /*    [if there are no whole units left to rotate, the */
2560         /*    rotation is now complete] */
2561         /* */
2562         /* 2. shift to least, from below the split point only, so that */
2563         /*    the final msd is in the right place in its Unit [any */
2564         /*    digits shifted out will fit exactly in the current msu, */
2565         /*    left aligned, no split required] */
2566         /* */
2567         /* 3. rotate all the units by reversing left part, right */
2568         /*    part, and then whole */
2569         /* */
2570         /* example: rotate right 8 digits (2 units + 2), DECDPUN=3. */
2571         /* */
2572         /*   start: 00a bcd efg hij klm npq */
2573         /* */
2574         /*      1a  000 0ab cde fgh|ijk lmn [pq saved] */
2575         /*      1b  00p qab cde fgh|ijk lmn */
2576         /* */
2577         /*      2a  00p qab cde fgh|00i jkl [mn saved] */
2578         /*      2b  mnp qab cde fgh|00i jkl */
2579         /* */
2580         /*      3a  fgh cde qab mnp|00i jkl */
2581         /*      3b  fgh cde qab mnp|jkl 00i */
2582         /*      3c  00i jkl mnp qab cde fgh */
2583
2584         /* Step 1: amount to shift is the partial right-rotate count */
2585         rotate=set->digits-rotate;      /* make it right-rotate */
2586         units=rotate/DECDPUN;           /* whole units to rotate */
2587         shift=rotate%DECDPUN;           /* left-over digits count */
2588         if (shift>0) {                  /* not an exact number of units */
2589           uInt save=res->lsu[0]%powers[shift];    /* save low digit(s) */
2590           decShiftToLeast(res->lsu, D2U(res->digits), shift);
2591           if (shift>msudigits) {        /* msumax-1 needs >0 digits */
2592             uInt rem=save%powers[shift-msudigits];/* split save */
2593             *msumax=(Unit)(save/powers[shift-msudigits]); /* and insert */
2594             *(msumax-1)=*(msumax-1)
2595                        +(Unit)(rem*powers[DECDPUN-(shift-msudigits)]); /* .. */
2596             }
2597            else { /* all fits in msumax */
2598             *msumax=*msumax+(Unit)(save*powers[msudigits-shift]); /* [maybe *1] */
2599             }
2600           } /* digits shift needed */
2601
2602         /* If whole units to rotate... */
2603         if (units>0) {                  /* some to do */
2604           /* Step 2: the units to touch are the whole ones in rotate, */
2605           /*   if any, and the shift is DECDPUN-msudigits (which may be */
2606           /*   0, again) */
2607           shift=DECDPUN-msudigits;
2608           if (shift>0) {                /* not an exact number of units */
2609             uInt save=res->lsu[0]%powers[shift];  /* save low digit(s) */
2610             decShiftToLeast(res->lsu, units, shift);
2611             *msumax=*msumax+(Unit)(save*powers[msudigits]);
2612             } /* partial shift needed */
2613
2614           /* Step 3: rotate the units array using triple reverse */
2615           /* (reversing is easy and fast) */
2616           decReverse(res->lsu+units, msumax);     /* left part */
2617           decReverse(res->lsu, res->lsu+units-1); /* right part */
2618           decReverse(res->lsu, msumax);           /* whole */
2619           } /* whole units to rotate */
2620         /* the rotation may have left an undetermined number of zeros */
2621         /* on the left, so true length needs to be calculated */
2622         res->digits=decGetDigits(res->lsu, msumax-res->lsu+1);
2623         } /* rotate needed */
2624       } /* rhs OK */
2625     } /* numerics */
2626   if (status!=0) decStatus(res, status, set);
2627   return res;
2628   } /* decNumberRotate */
2629
2630 /* ------------------------------------------------------------------ */
2631 /* decNumberSameQuantum -- test for equal exponents                   */
2632 /*                                                                    */
2633 /*   res is the result number, which will contain either 0 or 1       */
2634 /*   lhs is a number to test                                          */
2635 /*   rhs is the second (usually a pattern)                            */
2636 /*                                                                    */
2637 /* No errors are possible and no context is needed.                   */
2638 /* ------------------------------------------------------------------ */
2639 decNumber * decNumberSameQuantum(decNumber *res, const decNumber *lhs,
2640                                  const decNumber *rhs) {
2641   Unit ret=0;                      /* return value */
2642
2643   #if DECCHECK
2644   if (decCheckOperands(res, lhs, rhs, DECUNCONT)) return res;
2645   #endif
2646
2647   if (SPECIALARGS) {
2648     if (decNumberIsNaN(lhs) && decNumberIsNaN(rhs)) ret=1;
2649      else if (decNumberIsInfinite(lhs) && decNumberIsInfinite(rhs)) ret=1;
2650      /* [anything else with a special gives 0] */
2651     }
2652    else if (lhs->exponent==rhs->exponent) ret=1;
2653
2654   decNumberZero(res);              /* OK to overwrite an operand now */
2655   *res->lsu=ret;
2656   return res;
2657   } /* decNumberSameQuantum */
2658
2659 /* ------------------------------------------------------------------ */
2660 /* decNumberScaleB -- multiply by a power of 10                       */
2661 /*                                                                    */
2662 /* This computes C = A x 10**B where B is an integer (q=0) with       */
2663 /* maximum magnitude 2*(emax+digits)                                  */
2664 /*                                                                    */
2665 /*   res is C, the result.  C may be A or B                           */
2666 /*   lhs is A, the number to adjust                                   */
2667 /*   rhs is B, the requested power of ten to use                      */
2668 /*   set is the context                                               */
2669 /*                                                                    */
2670 /* C must have space for set->digits digits.                          */
2671 /*                                                                    */
2672 /* The result may underflow or overflow.                              */
2673 /* ------------------------------------------------------------------ */
2674 decNumber * decNumberScaleB(decNumber *res, const decNumber *lhs,
2675                             const decNumber *rhs, decContext *set) {
2676   Int  reqexp;                /* requested exponent change [B] */
2677   uInt status=0;              /* accumulator */
2678   Int  residue;               /* work */
2679
2680   #if DECCHECK
2681   if (decCheckOperands(res, lhs, rhs, set)) return res;
2682   #endif
2683
2684   /* Handle special values except lhs infinite */
2685   if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs))
2686     decNaNs(res, lhs, rhs, set, &status);
2687     /* rhs must be an integer */
2688    else if (decNumberIsInfinite(rhs) || rhs->exponent!=0)
2689     status=DEC_Invalid_operation;
2690    else {
2691     /* lhs is a number; rhs is a finite with q==0 */
2692     reqexp=decGetInt(rhs);                   /* [cannot fail] */
2693     if (reqexp==BADINT                       /* something bad .. */
2694      || reqexp==BIGODD || reqexp==BIGEVEN    /* .. very big .. */
2695      || abs(reqexp)>(2*(set->digits+set->emax))) /* .. or out of range */
2696       status=DEC_Invalid_operation;
2697      else {                                  /* rhs is OK */
2698       decNumberCopy(res, lhs);               /* all done if infinite lhs */
2699       if (!decNumberIsInfinite(res)) {       /* prepare to scale */
2700         res->exponent+=reqexp;               /* adjust the exponent */
2701         residue=0;
2702         decFinalize(res, set, &residue, &status); /* .. and check */
2703         } /* finite LHS */
2704       } /* rhs OK */
2705     } /* rhs finite */
2706   if (status!=0) decStatus(res, status, set);
2707   return res;
2708   } /* decNumberScaleB */
2709
2710 /* ------------------------------------------------------------------ */
2711 /* decNumberShift -- shift the coefficient of a Number left or right  */
2712 /*                                                                    */
2713 /*   This computes C = A << B or C = A >> -B  (in base ten).          */
2714 /*                                                                    */
2715 /*   res is C, the result.  C may be A and/or B (e.g., X=X<<X)        */
2716 /*   lhs is A                                                         */
2717 /*   rhs is B, the number of digits to shift (-ve to right)           */
2718 /*   set is the context                                               */
2719 /*                                                                    */
2720 /* The digits of the coefficient of A are shifted to the left (if B   */
2721 /* is positive) or to the right (if B is negative) without adjusting  */
2722 /* the exponent or the sign of A.                                     */
2723 /*                                                                    */
2724 /* B must be an integer (q=0) and in the range -set->digits through   */
2725 /* +set->digits.                                                      */
2726 /* C must have space for set->digits digits.                          */
2727 /* NaNs are propagated as usual.  Infinities are unaffected (but      */
2728 /* B must be valid).  No status is set unless B is invalid or an      */
2729 /* operand is an sNaN.                                                */
2730 /* ------------------------------------------------------------------ */
2731 decNumber * decNumberShift(decNumber *res, const decNumber *lhs,
2732                            const decNumber *rhs, decContext *set) {
2733   uInt status=0;              /* accumulator */
2734   Int  shift;                 /* rhs as an Int */
2735
2736   #if DECCHECK
2737   if (decCheckOperands(res, lhs, rhs, set)) return res;
2738   #endif
2739
2740   /* NaNs propagate as normal */
2741   if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs))
2742     decNaNs(res, lhs, rhs, set, &status);
2743    /* rhs must be an integer */
2744    else if (decNumberIsInfinite(rhs) || rhs->exponent!=0)
2745     status=DEC_Invalid_operation;
2746    else { /* both numeric, rhs is an integer */
2747     shift=decGetInt(rhs);                    /* [cannot fail] */
2748     if (shift==BADINT                        /* something bad .. */
2749      || shift==BIGODD || shift==BIGEVEN      /* .. very big .. */
2750      || abs(shift)>set->digits)              /* .. or out of range */
2751       status=DEC_Invalid_operation;
2752      else {                                  /* rhs is OK */
2753       decNumberCopy(res, lhs);
2754       if (shift!=0 && !decNumberIsInfinite(res)) { /* something to do */
2755         if (shift>0) {                       /* to left */
2756           if (shift==set->digits) {          /* removing all */
2757             *res->lsu=0;                     /* so place 0 */
2758             res->digits=1;                   /* .. */
2759             }
2760            else {                            /* */
2761             /* first remove leading digits if necessary */
2762             if (res->digits+shift>set->digits) {
2763               decDecap(res, res->digits+shift-set->digits);
2764               /* that updated res->digits; may have gone to 1 (for a */
2765               /* single digit or for zero */
2766               }
2767             if (res->digits>1 || *res->lsu)  /* if non-zero.. */
2768               res->digits=decShiftToMost(res->lsu, res->digits, shift);
2769             } /* partial left */
2770           } /* left */
2771          else { /* to right */
2772           if (-shift>=res->digits) {         /* discarding all */
2773             *res->lsu=0;                     /* so place 0 */
2774             res->digits=1;                   /* .. */
2775             }
2776            else {
2777             decShiftToLeast(res->lsu, D2U(res->digits), -shift);
2778             res->digits-=(-shift);
2779             }
2780           } /* to right */
2781         } /* non-0 non-Inf shift */
2782       } /* rhs OK */
2783     } /* numerics */
2784   if (status!=0) decStatus(res, status, set);
2785   return res;
2786   } /* decNumberShift */
2787
2788 /* ------------------------------------------------------------------ */
2789 /* decNumberSquareRoot -- square root operator                        */
2790 /*                                                                    */
2791 /*   This computes C = squareroot(A)                                  */
2792 /*                                                                    */
2793 /*   res is C, the result.  C may be A                                */
2794 /*   rhs is A                                                         */
2795 /*   set is the context; note that rounding mode has no effect        */
2796 /*                                                                    */
2797 /* C must have space for set->digits digits.                          */
2798 /* ------------------------------------------------------------------ */
2799 /* This uses the following varying-precision algorithm in:            */
2800 /*                                                                    */
2801 /*   Properly Rounded Variable Precision Square Root, T. E. Hull and  */
2802 /*   A. Abrham, ACM Transactions on Mathematical Software, Vol 11 #3, */
2803 /*   pp229-237, ACM, September 1985.                                  */
2804 /*                                                                    */
2805 /* The square-root is calculated using Newton's method, after which   */
2806 /* a check is made to ensure the result is correctly rounded.         */
2807 /*                                                                    */
2808 /* % [Reformatted original Numerical Turing source code follows.]     */
2809 /* function sqrt(x : real) : real                                     */
2810 /* % sqrt(x) returns the properly rounded approximation to the square */
2811 /* % root of x, in the precision of the calling environment, or it    */
2812 /* % fails if x < 0.                                                  */
2813 /* % t e hull and a abrham, august, 1984                              */
2814 /* if x <= 0 then                                                     */
2815 /*   if x < 0 then                                                    */
2816 /*     assert false                                                   */
2817 /*   else                                                             */
2818 /*     result 0                                                       */
2819 /*   end if                                                           */
2820 /* end if                                                             */
2821 /* var f := setexp(x, 0)  % fraction part of x   [0.1 <= x < 1]       */
2822 /* var e := getexp(x)     % exponent part of x                        */
2823 /* var approx : real                                                  */
2824 /* if e mod 2 = 0  then                                               */
2825 /*   approx := .259 + .819 * f   % approx to root of f                */
2826 /* else                                                               */
2827 /*   f := f/l0                   % adjustments                        */
2828 /*   e := e + 1                  %   for odd                          */
2829 /*   approx := .0819 + 2.59 * f  %   exponent                         */
2830 /* end if                                                             */
2831 /*                                                                    */
2832 /* var p:= 3                                                          */
2833 /* const maxp := currentprecision + 2                                 */
2834 /* loop                                                               */
2835 /*   p := min(2*p - 2, maxp)     % p = 4,6,10, . . . , maxp           */
2836 /*   precision p                                                      */
2837 /*   approx := .5 * (approx + f/approx)                               */
2838 /*   exit when p = maxp                                               */
2839 /* end loop                                                           */
2840 /*                                                                    */
2841 /* % approx is now within 1 ulp of the properly rounded square root   */
2842 /* % of f; to ensure proper rounding, compare squares of (approx -    */
2843 /* % l/2 ulp) and (approx + l/2 ulp) with f.                          */
2844 /* p := currentprecision                                              */
2845 /* begin                                                              */
2846 /*   precision p + 2                                                  */
2847 /*   const approxsubhalf := approx - setexp(.5, -p)                   */
2848 /*   if mulru(approxsubhalf, approxsubhalf) > f then                  */
2849 /*     approx := approx - setexp(.l, -p + 1)                          */
2850 /*   else                                                             */
2851 /*     const approxaddhalf := approx + setexp(.5, -p)                 */
2852 /*     if mulrd(approxaddhalf, approxaddhalf) < f then                */
2853 /*       approx := approx + setexp(.l, -p + 1)                        */
2854 /*     end if                                                         */
2855 /*   end if                                                           */
2856 /* end                                                                */
2857 /* result setexp(approx, e div 2)  % fix exponent                     */
2858 /* end sqrt                                                           */
2859 /* ------------------------------------------------------------------ */
2860 decNumber * decNumberSquareRoot(decNumber *res, const decNumber *rhs,
2861                                 decContext *set) {
2862   decContext workset, approxset;   /* work contexts */
2863   decNumber dzero;                 /* used for constant zero */
2864   Int  maxp;                       /* largest working precision */
2865   Int  workp;                      /* working precision */
2866   Int  residue=0;                  /* rounding residue */
2867   uInt status=0, ignore=0;         /* status accumulators */
2868   uInt rstatus;                    /* .. */
2869   Int  exp;                        /* working exponent */
2870   Int  ideal;                      /* ideal (preferred) exponent */
2871   Int  needbytes;                  /* work */
2872   Int  dropped;                    /* .. */
2873
2874   #if DECSUBSET
2875   decNumber *allocrhs=NULL;        /* non-NULL if rounded rhs allocated */
2876   #endif
2877   /* buffer for f [needs +1 in case DECBUFFER 0] */
2878   decNumber buff[D2N(DECBUFFER+1)];
2879   /* buffer for a [needs +2 to match likely maxp] */
2880   decNumber bufa[D2N(DECBUFFER+2)];
2881   /* buffer for temporary, b [must be same size as a] */
2882   decNumber bufb[D2N(DECBUFFER+2)];
2883   decNumber *allocbuff=NULL;       /* -> allocated buff, iff allocated */
2884   decNumber *allocbufa=NULL;       /* -> allocated bufa, iff allocated */
2885   decNumber *allocbufb=NULL;       /* -> allocated bufb, iff allocated */
2886   decNumber *f=buff;               /* reduced fraction */
2887   decNumber *a=bufa;               /* approximation to result */
2888   decNumber *b=bufb;               /* intermediate result */
2889   /* buffer for temporary variable, up to 3 digits */
2890   decNumber buft[D2N(3)];
2891   decNumber *t=buft;               /* up-to-3-digit constant or work */
2892
2893   #if DECCHECK
2894   if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
2895   #endif
2896
2897   do {                             /* protect allocated storage */
2898     #if DECSUBSET
2899     if (!set->extended) {
2900       /* reduce operand and set lostDigits status, as needed */
2901       if (rhs->digits>set->digits) {
2902         allocrhs=decRoundOperand(rhs, set, &status);
2903         if (allocrhs==NULL) break;
2904         /* [Note: 'f' allocation below could reuse this buffer if */
2905         /* used, but as this is rare they are kept separate for clarity.] */
2906         rhs=allocrhs;
2907         }
2908       }
2909     #endif
2910     /* [following code does not require input rounding] */
2911
2912     /* handle infinities and NaNs */
2913     if (SPECIALARG) {
2914       if (decNumberIsInfinite(rhs)) {         /* an infinity */
2915         if (decNumberIsNegative(rhs)) status|=DEC_Invalid_operation;
2916          else decNumberCopy(res, rhs);        /* +Infinity */
2917         }
2918        else decNaNs(res, rhs, NULL, set, &status); /* a NaN */
2919       break;
2920       }
2921
2922     /* calculate the ideal (preferred) exponent [floor(exp/2)] */
2923     /* [We would like to write: ideal=rhs->exponent>>1, but this */
2924     /* generates a compiler warning.  Generated code is the same.] */
2925     ideal=(rhs->exponent&~1)/2;         /* target */
2926
2927     /* handle zeros */
2928     if (ISZERO(rhs)) {
2929       decNumberCopy(res, rhs);          /* could be 0 or -0 */
2930       res->exponent=ideal;              /* use the ideal [safe] */
2931       /* use decFinish to clamp any out-of-range exponent, etc. */
2932       decFinish(res, set, &residue, &status);
2933       break;
2934       }
2935
2936     /* any other -x is an oops */
2937     if (decNumberIsNegative(rhs)) {
2938       status|=DEC_Invalid_operation;
2939       break;
2940       }
2941
2942     /* space is needed for three working variables */
2943     /*   f -- the same precision as the RHS, reduced to 0.01->0.99... */
2944     /*   a -- Hull's approximation -- precision, when assigned, is */
2945     /*        currentprecision+1 or the input argument precision, */
2946     /*        whichever is larger (+2 for use as temporary) */
2947     /*   b -- intermediate temporary result (same size as a) */
2948     /* if any is too long for local storage, then allocate */
2949     workp=MAXI(set->digits+1, rhs->digits);  /* actual rounding precision */
2950     maxp=workp+2;                            /* largest working precision */
2951
2952     needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit);
2953     if (needbytes>(Int)sizeof(buff)) {
2954       allocbuff=(decNumber *)malloc(needbytes);
2955       if (allocbuff==NULL) {  /* hopeless -- abandon */
2956         status|=DEC_Insufficient_storage;
2957         break;}
2958       f=allocbuff;            /* use the allocated space */
2959       }
2960     /* a and b both need to be able to hold a maxp-length number */
2961     needbytes=sizeof(decNumber)+(D2U(maxp)-1)*sizeof(Unit);
2962     if (needbytes>(Int)sizeof(bufa)) {            /* [same applies to b] */
2963       allocbufa=(decNumber *)malloc(needbytes);
2964       allocbufb=(decNumber *)malloc(needbytes);
2965       if (allocbufa==NULL || allocbufb==NULL) {   /* hopeless */
2966         status|=DEC_Insufficient_storage;
2967         break;}
2968       a=allocbufa;            /* use the allocated spaces */
2969       b=allocbufb;            /* .. */
2970       }
2971
2972     /* copy rhs -> f, save exponent, and reduce so 0.1 <= f < 1 */
2973     decNumberCopy(f, rhs);
2974     exp=f->exponent+f->digits;               /* adjusted to Hull rules */
2975     f->exponent=-(f->digits);                /* to range */
2976
2977     /* set up working context */
2978     decContextDefault(&workset, DEC_INIT_DECIMAL64);
2979
2980     /* [Until further notice, no error is possible and status bits */
2981     /* (Rounded, etc.) should be ignored, not accumulated.] */
2982
2983     /* Calculate initial approximation, and allow for odd exponent */
2984     workset.digits=workp;                    /* p for initial calculation */
2985     t->bits=0; t->digits=3;
2986     a->bits=0; a->digits=3;
2987     if ((exp & 1)==0) {                      /* even exponent */
2988       /* Set t=0.259, a=0.819 */
2989       t->exponent=-3;
2990       a->exponent=-3;
2991       #if DECDPUN>=3
2992         t->lsu[0]=259;
2993         a->lsu[0]=819;
2994       #elif DECDPUN==2
2995         t->lsu[0]=59; t->lsu[1]=2;
2996         a->lsu[0]=19; a->lsu[1]=8;
2997       #else
2998         t->lsu[0]=9; t->lsu[1]=5; t->lsu[2]=2;
2999         a->lsu[0]=9; a->lsu[1]=1; a->lsu[2]=8;
3000       #endif
3001       }
3002      else {                                  /* odd exponent */
3003       /* Set t=0.0819, a=2.59 */
3004       f->exponent--;                         /* f=f/10 */
3005       exp++;                                 /* e=e+1 */
3006       t->exponent=-4;
3007       a->exponent=-2;
3008       #if DECDPUN>=3
3009         t->lsu[0]=819;
3010         a->lsu[0]=259;
3011       #elif DECDPUN==2
3012         t->lsu[0]=19; t->lsu[1]=8;
3013         a->lsu[0]=59; a->lsu[1]=2;
3014       #else
3015         t->lsu[0]=9; t->lsu[1]=1; t->lsu[2]=8;
3016         a->lsu[0]=9; a->lsu[1]=5; a->lsu[2]=2;
3017       #endif
3018       }
3019     decMultiplyOp(a, a, f, &workset, &ignore);    /* a=a*f */
3020     decAddOp(a, a, t, &workset, 0, &ignore);      /* ..+t */
3021     /* [a is now the initial approximation for sqrt(f), calculated with */
3022     /* currentprecision, which is also a's precision.] */
3023
3024     /* the main calculation loop */
3025     decNumberZero(&dzero);                   /* make 0 */
3026     decNumberZero(t);                        /* set t = 0.5 */
3027     t->lsu[0]=5;                             /* .. */
3028     t->exponent=-1;                          /* .. */
3029     workset.digits=3;                        /* initial p */
3030     for (;;) {
3031       /* set p to min(2*p - 2, maxp)  [hence 3; or: 4, 6, 10, ... , maxp] */
3032       workset.digits=workset.digits*2-2;
3033       if (workset.digits>maxp) workset.digits=maxp;
3034       /* a = 0.5 * (a + f/a) */
3035       /* [calculated at p then rounded to currentprecision] */
3036       decDivideOp(b, f, a, &workset, DIVIDE, &ignore); /* b=f/a */
3037       decAddOp(b, b, a, &workset, 0, &ignore);    /* b=b+a */
3038       decMultiplyOp(a, b, t, &workset, &ignore);  /* a=b*0.5 */
3039       if (a->digits==maxp) break;            /* have required digits */
3040       } /* loop */
3041
3042     /* Here, 0.1 <= a < 1 [Hull], and a has maxp digits */
3043     /* now reduce to length, etc.; this needs to be done with a */
3044     /* having the correct exponent so as to handle subnormals */
3045     /* correctly */
3046     approxset=*set;                          /* get emin, emax, etc. */
3047     approxset.round=DEC_ROUND_HALF_EVEN;
3048     a->exponent+=exp/2;                      /* set correct exponent */
3049
3050     rstatus=0;                               /* clear status */
3051     residue=0;                               /* .. and accumulator */
3052     decCopyFit(a, a, &approxset, &residue, &rstatus);  /* reduce (if needed) */
3053     decFinish(a, &approxset, &residue, &rstatus);      /* clean and finalize */
3054
3055     /* Overflow was possible if the input exponent was out-of-range, */
3056     /* in which case quit */
3057     if (rstatus&DEC_Overflow) {
3058       status=rstatus;                        /* use the status as-is */
3059       decNumberCopy(res, a);                 /* copy to result */
3060       break;
3061       }
3062
3063     /* Preserve status except Inexact/Rounded */
3064     status|=(rstatus & ~(DEC_Rounded|DEC_Inexact));
3065
3066     /* Carry out the Hull correction */
3067     a->exponent-=exp/2;                      /* back to 0.1->1 */
3068
3069     /* a is now at final precision and within 1 ulp of the properly */
3070     /* rounded square root of f; to ensure proper rounding, compare */
3071     /* squares of (a - l/2 ulp) and (a + l/2 ulp) with f. */
3072     /* Here workset.digits=maxp and t=0.5, and a->digits determines */
3073     /* the ulp */
3074     workset.digits--;                             /* maxp-1 is OK now */
3075     t->exponent=-a->digits-1;                     /* make 0.5 ulp */
3076     decAddOp(b, a, t, &workset, DECNEG, &ignore); /* b = a - 0.5 ulp */
3077     workset.round=DEC_ROUND_UP;
3078     decMultiplyOp(b, b, b, &workset, &ignore);    /* b = mulru(b, b) */
3079     decCompareOp(b, f, b, &workset, COMPARE, &ignore); /* b ? f, reversed */
3080     if (decNumberIsNegative(b)) {                 /* f < b [i.e., b > f] */
3081       /* this is the more common adjustment, though both are rare */
3082       t->exponent++;                              /* make 1.0 ulp */
3083       t->lsu[0]=1;                                /* .. */
3084       decAddOp(a, a, t, &workset, DECNEG, &ignore); /* a = a - 1 ulp */
3085       /* assign to approx [round to length] */
3086       approxset.emin-=exp/2;                      /* adjust to match a */
3087       approxset.emax-=exp/2;
3088       decAddOp(a, &dzero, a, &approxset, 0, &ignore);
3089       }
3090      else {
3091       decAddOp(b, a, t, &workset, 0, &ignore);    /* b = a + 0.5 ulp */
3092       workset.round=DEC_ROUND_DOWN;
3093       decMultiplyOp(b, b, b, &workset, &ignore);  /* b = mulrd(b, b) */
3094       decCompareOp(b, b, f, &workset, COMPARE, &ignore);   /* b ? f */
3095       if (decNumberIsNegative(b)) {               /* b < f */
3096         t->exponent++;                            /* make 1.0 ulp */
3097         t->lsu[0]=1;                              /* .. */
3098         decAddOp(a, a, t, &workset, 0, &ignore);  /* a = a + 1 ulp */
3099         /* assign to approx [round to length] */
3100         approxset.emin-=exp/2;                    /* adjust to match a */
3101         approxset.emax-=exp/2;
3102         decAddOp(a, &dzero, a, &approxset, 0, &ignore);
3103         }
3104       }
3105     /* [no errors are possible in the above, and rounding/inexact during */
3106     /* estimation are irrelevant, so status was not accumulated] */
3107
3108     /* Here, 0.1 <= a < 1  (still), so adjust back */
3109     a->exponent+=exp/2;                      /* set correct exponent */
3110
3111     /* count droppable zeros [after any subnormal rounding] by */
3112     /* trimming a copy */
3113     decNumberCopy(b, a);
3114     decTrim(b, set, 1, &dropped);            /* [drops trailing zeros] */
3115
3116     /* Set Inexact and Rounded.  The answer can only be exact if */
3117     /* it is short enough so that squaring it could fit in workp digits, */
3118     /* and it cannot have trailing zeros due to clamping, so these are */
3119     /* the only (relatively rare) conditions a careful check is needed */
3120     if (b->digits*2-1 > workp && !set->clamp) { /* cannot fit */
3121       status|=DEC_Inexact|DEC_Rounded;
3122       }
3123      else {                                  /* could be exact/unrounded */
3124       uInt mstatus=0;                        /* local status */
3125       decMultiplyOp(b, b, b, &workset, &mstatus); /* try the multiply */
3126       if (mstatus&DEC_Overflow) {            /* result just won't fit */
3127         status|=DEC_Inexact|DEC_Rounded;
3128         }
3129        else {                                /* plausible */
3130         decCompareOp(t, b, rhs, &workset, COMPARE, &mstatus); /* b ? rhs */
3131         if (!ISZERO(t)) status|=DEC_Inexact|DEC_Rounded; /* not equal */
3132          else {                              /* is Exact */
3133           /* here, dropped is the count of trailing zeros in 'a' */
3134           /* use closest exponent to ideal... */
3135           Int todrop=ideal-a->exponent;      /* most that can be dropped */
3136           if (todrop<0) status|=DEC_Rounded; /* ideally would add 0s */
3137            else {                            /* unrounded */
3138             if (dropped<todrop) {            /* clamp to those available */
3139               todrop=dropped;
3140               status|=DEC_Clamped;
3141               }
3142             if (todrop>0) {                  /* have some to drop */
3143               decShiftToLeast(a->lsu, D2U(a->digits), todrop);
3144               a->exponent+=todrop;           /* maintain numerical value */
3145               a->digits-=todrop;             /* new length */
3146               }
3147             }
3148           }
3149         }
3150       }
3151
3152     /* double-check Underflow, as perhaps the result could not have */
3153     /* been subnormal (initial argument too big), or it is now Exact */
3154     if (status&DEC_Underflow) {
3155       Int ae=rhs->exponent+rhs->digits-1;    /* adjusted exponent */
3156       /* check if truly subnormal */
3157       #if DECEXTFLAG                         /* DEC_Subnormal too */
3158         if (ae>=set->emin*2) status&=~(DEC_Subnormal|DEC_Underflow);
3159       #else
3160         if (ae>=set->emin*2) status&=~DEC_Underflow;
3161       #endif
3162       /* check if truly inexact */
3163       if (!(status&DEC_Inexact)) status&=~DEC_Underflow;
3164       }
3165
3166     decNumberCopy(res, a);                   /* a is now the result */
3167     } while(0);                              /* end protected */
3168
3169   if (allocbuff!=NULL) free(allocbuff);      /* drop any storage used */
3170   if (allocbufa!=NULL) free(allocbufa);      /* .. */
3171   if (allocbufb!=NULL) free(allocbufb);      /* .. */
3172   #if DECSUBSET
3173   if (allocrhs !=NULL) free(allocrhs);       /* .. */
3174   #endif
3175   if (status!=0) decStatus(res, status, set);/* then report status */
3176   #if DECCHECK
3177   decCheckInexact(res, set);
3178   #endif
3179   return res;
3180   } /* decNumberSquareRoot */
3181
3182 /* ------------------------------------------------------------------ */
3183 /* decNumberSubtract -- subtract two Numbers                          */
3184 /*                                                                    */
3185 /*   This computes C = A - B                                          */
3186 /*                                                                    */
3187 /*   res is C, the result.  C may be A and/or B (e.g., X=X-X)         */
3188 /*   lhs is A                                                         */
3189 /*   rhs is B                                                         */
3190 /*   set is the context                                               */
3191 /*                                                                    */
3192 /* C must have space for set->digits digits.                          */
3193 /* ------------------------------------------------------------------ */
3194 decNumber * decNumberSubtract(decNumber *res, const decNumber *lhs,
3195                               const decNumber *rhs, decContext *set) {
3196   uInt status=0;                        /* accumulator */
3197
3198   decAddOp(res, lhs, rhs, set, DECNEG, &status);
3199   if (status!=0) decStatus(res, status, set);
3200   #if DECCHECK
3201   decCheckInexact(res, set);
3202   #endif
3203   return res;
3204   } /* decNumberSubtract */
3205
3206 /* ------------------------------------------------------------------ */
3207 /* decNumberToIntegralExact -- round-to-integral-value with InExact   */
3208 /* decNumberToIntegralValue -- round-to-integral-value                */
3209 /*                                                                    */
3210 /*   res is the result                                                */
3211 /*   rhs is input number                                              */
3212 /*   set is the context                                               */
3213 /*                                                                    */
3214 /* res must have space for any value of rhs.                          */
3215 /*                                                                    */
3216 /* This implements the IEEE special operators and therefore treats    */
3217 /* special values as valid.  For finite numbers it returns            */
3218 /* rescale(rhs, 0) if rhs->exponent is <0.                            */
3219 /* Otherwise the result is rhs (so no error is possible, except for   */
3220 /* sNaN).                                                             */
3221 /*                                                                    */
3222 /* The context is used for rounding mode and status after sNaN, but   */
3223 /* the digits setting is ignored.  The Exact version will signal      */
3224 /* Inexact if the result differs numerically from rhs; the other      */
3225 /* never signals Inexact.                                             */
3226 /* ------------------------------------------------------------------ */
3227 decNumber * decNumberToIntegralExact(decNumber *res, const decNumber *rhs,
3228                                      decContext *set) {
3229   decNumber dn;
3230   decContext workset;              /* working context */
3231   uInt status=0;                   /* accumulator */
3232
3233   #if DECCHECK
3234   if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
3235   #endif
3236
3237   /* handle infinities and NaNs */
3238   if (SPECIALARG) {
3239     if (decNumberIsInfinite(rhs)) decNumberCopy(res, rhs); /* an Infinity */
3240      else decNaNs(res, rhs, NULL, set, &status); /* a NaN */
3241     }
3242    else { /* finite */
3243     /* have a finite number; no error possible (res must be big enough) */
3244     if (rhs->exponent>=0) return decNumberCopy(res, rhs);
3245     /* that was easy, but if negative exponent there is work to do... */
3246     workset=*set;                  /* clone rounding, etc. */
3247     workset.digits=rhs->digits;    /* no length rounding */
3248     workset.traps=0;               /* no traps */
3249     decNumberZero(&dn);            /* make a number with exponent 0 */
3250     decNumberQuantize(res, rhs, &dn, &workset);
3251     status|=workset.status;
3252     }
3253   if (status!=0) decStatus(res, status, set);
3254   return res;
3255   } /* decNumberToIntegralExact */
3256
3257 decNumber * decNumberToIntegralValue(decNumber *res, const decNumber *rhs,
3258                                      decContext *set) {
3259   decContext workset=*set;         /* working context */
3260   workset.traps=0;                 /* no traps */
3261   decNumberToIntegralExact(res, rhs, &workset);
3262   /* this never affects set, except for sNaNs; NaN will have been set */
3263   /* or propagated already, so no need to call decStatus */
3264   set->status|=workset.status&DEC_Invalid_operation;
3265   return res;
3266   } /* decNumberToIntegralValue */
3267
3268 /* ------------------------------------------------------------------ */
3269 /* decNumberXor -- XOR two Numbers, digitwise                         */
3270 /*                                                                    */
3271 /*   This computes C = A ^ B                                          */
3272 /*                                                                    */
3273 /*   res is C, the result.  C may be A and/or B (e.g., X=X^X)         */
3274 /*   lhs is A                                                         */
3275 /*   rhs is B                                                         */
3276 /*   set is the context (used for result length and error report)     */
3277 /*                                                                    */
3278 /* C must have space for set->digits digits.                          */
3279 /*                                                                    */
3280 /* Logical function restrictions apply (see above); a NaN is          */
3281 /* returned with Invalid_operation if a restriction is violated.      */
3282 /* ------------------------------------------------------------------ */
3283 decNumber * decNumberXor(decNumber *res, const decNumber *lhs,
3284                          const decNumber *rhs, decContext *set) {
3285   const Unit *ua, *ub;                  /* -> operands */
3286   const Unit *msua, *msub;              /* -> operand msus */
3287   Unit  *uc, *msuc;                     /* -> result and its msu */
3288   Int   msudigs;                        /* digits in res msu */
3289   #if DECCHECK
3290   if (decCheckOperands(res, lhs, rhs, set)) return res;
3291   #endif
3292
3293   if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs)
3294    || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) {
3295     decStatus(res, DEC_Invalid_operation, set);
3296     return res;
3297     }
3298   /* operands are valid */
3299   ua=lhs->lsu;                          /* bottom-up */
3300   ub=rhs->lsu;                          /* .. */
3301   uc=res->lsu;                          /* .. */
3302   msua=ua+D2U(lhs->digits)-1;           /* -> msu of lhs */
3303   msub=ub+D2U(rhs->digits)-1;           /* -> msu of rhs */
3304   msuc=uc+D2U(set->digits)-1;           /* -> msu of result */
3305   msudigs=MSUDIGITS(set->digits);       /* [faster than remainder] */
3306   for (; uc<=msuc; ua++, ub++, uc++) {  /* Unit loop */
3307     Unit a, b;                          /* extract units */
3308     if (ua>msua) a=0;
3309      else a=*ua;
3310     if (ub>msub) b=0;
3311      else b=*ub;
3312     *uc=0;                              /* can now write back */
3313     if (a|b) {                          /* maybe 1 bits to examine */
3314       Int i, j;
3315       /* This loop could be unrolled and/or use BIN2BCD tables */
3316       for (i=0; i<DECDPUN; i++) {
3317         if ((a^b)&1) *uc=*uc+(Unit)powers[i];     /* effect XOR */
3318         j=a%10;
3319         a=a/10;
3320         j|=b%10;
3321         b=b/10;
3322         if (j>1) {
3323           decStatus(res, DEC_Invalid_operation, set);
3324           return res;
3325           }
3326         if (uc==msuc && i==msudigs-1) break;      /* just did final digit */
3327         } /* each digit */
3328       } /* non-zero */
3329     } /* each unit */
3330   /* [here uc-1 is the msu of the result] */
3331   res->digits=decGetDigits(res->lsu, uc-res->lsu);
3332   res->exponent=0;                      /* integer */
3333   res->bits=0;                          /* sign=0 */
3334   return res;  /* [no status to set] */
3335   } /* decNumberXor */
3336
3337
3338 /* ================================================================== */
3339 /* Utility routines                                                   */
3340 /* ================================================================== */
3341
3342 /* ------------------------------------------------------------------ */
3343 /* decNumberClass -- return the decClass of a decNumber               */
3344 /*   dn -- the decNumber to test                                      */
3345 /*   set -- the context to use for Emin                               */
3346 /*   returns the decClass enum                                        */
3347 /* ------------------------------------------------------------------ */
3348 enum decClass decNumberClass(const decNumber *dn, decContext *set) {
3349   if (decNumberIsSpecial(dn)) {
3350     if (decNumberIsQNaN(dn)) return DEC_CLASS_QNAN;
3351     if (decNumberIsSNaN(dn)) return DEC_CLASS_SNAN;
3352     /* must be an infinity */
3353     if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_INF;
3354     return DEC_CLASS_POS_INF;
3355     }
3356   /* is finite */
3357   if (decNumberIsNormal(dn, set)) { /* most common */
3358     if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_NORMAL;
3359     return DEC_CLASS_POS_NORMAL;
3360     }
3361   /* is subnormal or zero */
3362   if (decNumberIsZero(dn)) {    /* most common */
3363     if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_ZERO;
3364     return DEC_CLASS_POS_ZERO;
3365     }
3366   if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_SUBNORMAL;
3367   return DEC_CLASS_POS_SUBNORMAL;
3368   } /* decNumberClass */
3369
3370 /* ------------------------------------------------------------------ */
3371 /* decNumberClassToString -- convert decClass to a string             */
3372 /*                                                                    */
3373 /*  eclass is a valid decClass                                        */
3374 /*  returns a constant string describing the class (max 13+1 chars)   */
3375 /* ------------------------------------------------------------------ */
3376 const char *decNumberClassToString(enum decClass eclass) {
3377   if (eclass==DEC_CLASS_POS_NORMAL)    return DEC_ClassString_PN;
3378   if (eclass==DEC_CLASS_NEG_NORMAL)    return DEC_ClassString_NN;
3379   if (eclass==DEC_CLASS_POS_ZERO)      return DEC_ClassString_PZ;
3380   if (eclass==DEC_CLASS_NEG_ZERO)      return DEC_ClassString_NZ;
3381   if (eclass==DEC_CLASS_POS_SUBNORMAL) return DEC_ClassString_PS;
3382   if (eclass==DEC_CLASS_NEG_SUBNORMAL) return DEC_ClassString_NS;
3383   if (eclass==DEC_CLASS_POS_INF)       return DEC_ClassString_PI;
3384   if (eclass==DEC_CLASS_NEG_INF)       return DEC_ClassString_NI;
3385   if (eclass==DEC_CLASS_QNAN)          return DEC_ClassString_QN;
3386   if (eclass==DEC_CLASS_SNAN)          return DEC_ClassString_SN;
3387   return DEC_ClassString_UN;           /* Unknown */
3388   } /* decNumberClassToString */
3389
3390 /* ------------------------------------------------------------------ */
3391 /* decNumberCopy -- copy a number                                     */
3392 /*                                                                    */
3393 /*   dest is the target decNumber                                     */
3394 /*   src  is the source decNumber                                     */
3395 /*   returns dest                                                     */
3396 /*                                                                    */
3397 /* (dest==src is allowed and is a no-op)                              */
3398 /* All fields are updated as required.  This is a utility operation,  */
3399 /* so special values are unchanged and no error is possible.          */
3400 /* ------------------------------------------------------------------ */
3401 decNumber * decNumberCopy(decNumber *dest, const decNumber *src) {
3402
3403   #if DECCHECK
3404   if (src==NULL) return decNumberZero(dest);
3405   #endif
3406
3407   if (dest==src) return dest;                /* no copy required */
3408
3409   /* Use explicit assignments here as structure assignment could copy */
3410   /* more than just the lsu (for small DECDPUN).  This would not affect */
3411   /* the value of the results, but could disturb test harness spill */
3412   /* checking. */
3413   dest->bits=src->bits;
3414   dest->exponent=src->exponent;
3415   dest->digits=src->digits;
3416   dest->lsu[0]=src->lsu[0];
3417   if (src->digits>DECDPUN) {                 /* more Units to come */
3418     const Unit *smsup, *s;                   /* work */
3419     Unit  *d;                                /* .. */
3420     /* memcpy for the remaining Units would be safe as they cannot */
3421     /* overlap.  However, this explicit loop is faster in short cases. */
3422     d=dest->lsu+1;                           /* -> first destination */
3423     smsup=src->lsu+D2U(src->digits);         /* -> source msu+1 */
3424     for (s=src->lsu+1; s<smsup; s++, d++) *d=*s;
3425     }
3426   return dest;
3427   } /* decNumberCopy */
3428
3429 /* ------------------------------------------------------------------ */
3430 /* decNumberCopyAbs -- quiet absolute value operator                  */
3431 /*                                                                    */
3432 /*   This sets C = abs(A)                                             */
3433 /*                                                                    */
3434 /*   res is C, the result.  C may be A                                */
3435 /*   rhs is A                                                         */
3436 /*                                                                    */
3437 /* C must have space for set->digits digits.                          */
3438 /* No exception or error can occur; this is a quiet bitwise operation.*/
3439 /* See also decNumberAbs for a checking version of this.              */
3440 /* ------------------------------------------------------------------ */
3441 decNumber * decNumberCopyAbs(decNumber *res, const decNumber *rhs) {
3442   #if DECCHECK
3443   if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res;
3444   #endif
3445   decNumberCopy(res, rhs);
3446   res->bits&=~DECNEG;                   /* turn off sign */
3447   return res;
3448   } /* decNumberCopyAbs */
3449
3450 /* ------------------------------------------------------------------ */
3451 /* decNumberCopyNegate -- quiet negate value operator                 */
3452 /*                                                                    */
3453 /*   This sets C = negate(A)                                          */
3454 /*                                                                    */
3455 /*   res is C, the result.  C may be A                                */
3456 /*   rhs is A                                                         */
3457 /*                                                                    */
3458 /* C must have space for set->digits digits.                          */
3459 /* No exception or error can occur; this is a quiet bitwise operation.*/
3460 /* See also decNumberMinus for a checking version of this.            */
3461 /* ------------------------------------------------------------------ */
3462 decNumber * decNumberCopyNegate(decNumber *res, const decNumber *rhs) {
3463   #if DECCHECK
3464   if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res;
3465   #endif
3466   decNumberCopy(res, rhs);
3467   res->bits^=DECNEG;                    /* invert the sign */
3468   return res;
3469   } /* decNumberCopyNegate */
3470
3471 /* ------------------------------------------------------------------ */
3472 /* decNumberCopySign -- quiet copy and set sign operator              */
3473 /*                                                                    */
3474 /*   This sets C = A with the sign of B                               */
3475 /*                                                                    */
3476 /*   res is C, the result.  C may be A                                */
3477 /*   lhs is A                                                         */
3478 /*   rhs is B                                                         */
3479 /*                                                                    */
3480 /* C must have space for set->digits digits.                          */
3481 /* No exception or error can occur; this is a quiet bitwise operation.*/
3482 /* ------------------------------------------------------------------ */
3483 decNumber * decNumberCopySign(decNumber *res, const decNumber *lhs,
3484                               const decNumber *rhs) {
3485   uByte sign;                           /* rhs sign */
3486   #if DECCHECK
3487   if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res;
3488   #endif
3489   sign=rhs->bits & DECNEG;              /* save sign bit */
3490   decNumberCopy(res, lhs);
3491   res->bits&=~DECNEG;                   /* clear the sign */
3492   res->bits|=sign;                      /* set from rhs */
3493   return res;
3494   } /* decNumberCopySign */
3495
3496 /* ------------------------------------------------------------------ */
3497 /* decNumberGetBCD -- get the coefficient in BCD8                     */
3498 /*   dn is the source decNumber                                       */
3499 /*   bcd is the uInt array that will receive dn->digits BCD bytes,    */
3500 /*     most-significant at offset 0                                   */
3501 /*   returns bcd                                                      */
3502 /*                                                                    */
3503 /* bcd must have at least dn->digits bytes.  No error is possible; if */
3504 /* dn is a NaN or Infinite, digits must be 1 and the coefficient 0.   */
3505 /* ------------------------------------------------------------------ */
3506 uByte * decNumberGetBCD(const decNumber *dn, uint8_t *bcd) {
3507   uByte *ub=bcd+dn->digits-1;      /* -> lsd */
3508   const Unit *up=dn->lsu;          /* Unit pointer, -> lsu */
3509
3510   #if DECDPUN==1                   /* trivial simple copy */
3511     for (; ub>=bcd; ub--, up++) *ub=*up;
3512   #else                            /* chopping needed */
3513     uInt u=*up;                    /* work */
3514     uInt cut=DECDPUN;              /* downcounter through unit */
3515     for (; ub>=bcd; ub--) {
3516       *ub=(uByte)(u%10);           /* [*6554 trick inhibits, here] */
3517       u=u/10;
3518       cut--;
3519       if (cut>0) continue;         /* more in this unit */
3520       up++;
3521       u=*up;
3522       cut=DECDPUN;
3523       }
3524   #endif
3525   return bcd;
3526   } /* decNumberGetBCD */
3527
3528 /* ------------------------------------------------------------------ */
3529 /* decNumberSetBCD -- set (replace) the coefficient from BCD8         */
3530 /*   dn is the target decNumber                                       */
3531 /*   bcd is the uInt array that will source n BCD bytes, most-        */
3532 /*     significant at offset 0                                        */
3533 /*   n is the number of digits in the source BCD array (bcd)          */
3534 /*   returns dn                                                       */
3535 /*                                                                    */
3536 /* dn must have space for at least n digits.  No error is possible;   */
3537 /* if dn is a NaN, or Infinite, or is to become a zero, n must be 1   */
3538 /* and bcd[0] zero.                                                   */
3539 /* ------------------------------------------------------------------ */
3540 decNumber * decNumberSetBCD(decNumber *dn, const uByte *bcd, uInt n) {
3541   Unit *up = dn->lsu + D2U(n) - 1;      /* -> msu [target pointer] */
3542   const uByte *ub=bcd;                  /* -> source msd */
3543
3544   #if DECDPUN==1                        /* trivial simple copy */
3545     for (; ub<bcd+n; ub++, up--) *up=*ub;
3546   #else                                 /* some assembly needed */
3547     /* calculate how many digits in msu, and hence first cut */
3548     Int cut=MSUDIGITS(n);               /* [faster than remainder] */
3549     for (;up>=dn->lsu; up--) {          /* each Unit from msu */
3550       *up=0;                            /* will take <=DECDPUN digits */
3551       for (; cut>0; ub++, cut--) *up=X10(*up)+*ub;
3552       cut=DECDPUN;                      /* next Unit has all digits */
3553       }
3554   #endif
3555   dn->digits=n;                         /* set digit count */
3556   return dn;
3557   } /* decNumberSetBCD */
3558
3559 /* ------------------------------------------------------------------ */
3560 /* decNumberIsNormal -- test normality of a decNumber                 */
3561 /*   dn is the decNumber to test                                      */
3562 /*   set is the context to use for Emin                               */
3563 /*   returns 1 if |dn| is finite and >=Nmin, 0 otherwise              */
3564 /* ------------------------------------------------------------------ */
3565 Int decNumberIsNormal(const decNumber *dn, decContext *set) {
3566   Int ae;                               /* adjusted exponent */
3567   #if DECCHECK
3568   if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0;
3569   #endif
3570
3571   if (decNumberIsSpecial(dn)) return 0; /* not finite */
3572   if (decNumberIsZero(dn)) return 0;    /* not non-zero */
3573
3574   ae=dn->exponent+dn->digits-1;         /* adjusted exponent */
3575   if (ae<set->emin) return 0;           /* is subnormal */
3576   return 1;
3577   } /* decNumberIsNormal */
3578
3579 /* ------------------------------------------------------------------ */
3580 /* decNumberIsSubnormal -- test subnormality of a decNumber           */
3581 /*   dn is the decNumber to test                                      */
3582 /*   set is the context to use for Emin                               */
3583 /*   returns 1 if |dn| is finite, non-zero, and <Nmin, 0 otherwise    */
3584 /* ------------------------------------------------------------------ */
3585 Int decNumberIsSubnormal(const decNumber *dn, decContext *set) {
3586   Int ae;                               /* adjusted exponent */
3587   #if DECCHECK
3588   if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0;
3589   #endif
3590
3591   if (decNumberIsSpecial(dn)) return 0; /* not finite */
3592   if (decNumberIsZero(dn)) return 0;    /* not non-zero */
3593
3594   ae=dn->exponent+dn->digits-1;         /* adjusted exponent */
3595   if (ae<set->emin) return 1;           /* is subnormal */
3596   return 0;
3597   } /* decNumberIsSubnormal */
3598
3599 /* ------------------------------------------------------------------ */
3600 /* decNumberTrim -- remove insignificant zeros                        */
3601 /*                                                                    */
3602 /*   dn is the number to trim                                         */
3603 /*   returns dn                                                       */
3604 /*                                                                    */
3605 /* All fields are updated as required.  This is a utility operation,  */
3606 /* so special values are unchanged and no error is possible.          */
3607 /* ------------------------------------------------------------------ */
3608 decNumber * decNumberTrim(decNumber *dn) {
3609   Int  dropped;                    /* work */
3610   decContext set;                  /* .. */
3611   #if DECCHECK
3612   if (decCheckOperands(DECUNRESU, DECUNUSED, dn, DECUNCONT)) return dn;
3613   #endif
3614   decContextDefault(&set, DEC_INIT_BASE);    /* clamp=0 */
3615   return decTrim(dn, &set, 0, &dropped);
3616   } /* decNumberTrim */
3617
3618 /* ------------------------------------------------------------------ */
3619 /* decNumberVersion -- return the name and version of this module     */
3620 /*                                                                    */
3621 /* No error is possible.                                              */
3622 /* ------------------------------------------------------------------ */
3623 const char * decNumberVersion(void) {
3624   return DECVERSION;
3625   } /* decNumberVersion */
3626
3627 /* ------------------------------------------------------------------ */
3628 /* decNumberZero -- set a number to 0                                 */
3629 /*                                                                    */
3630 /*   dn is the number to set, with space for one digit                */
3631 /*   returns dn                                                       */
3632 /*                                                                    */
3633 /* No error is possible.                                              */
3634 /* ------------------------------------------------------------------ */
3635 /* Memset is not used as it is much slower in some environments. */
3636 decNumber * decNumberZero(decNumber *dn) {
3637
3638   #if DECCHECK
3639   if (decCheckOperands(dn, DECUNUSED, DECUNUSED, DECUNCONT)) return dn;
3640   #endif
3641
3642   dn->bits=0;
3643   dn->exponent=0;
3644   dn->digits=1;
3645   dn->lsu[0]=0;
3646   return dn;
3647   } /* decNumberZero */
3648
3649 /* ================================================================== */
3650 /* Local routines                                                     */
3651 /* ================================================================== */
3652
3653 /* ------------------------------------------------------------------ */
3654 /* decToString -- lay out a number into a string                      */
3655 /*                                                                    */
3656 /*   dn     is the number to lay out                                  */
3657 /*   string is where to lay out the number                            */
3658 /*   eng    is 1 if Engineering, 0 if Scientific                      */
3659 /*                                                                    */
3660 /* string must be at least dn->digits+14 characters long              */
3661 /* No error is possible.                                              */
3662 /*                                                                    */
3663 /* Note that this routine can generate a -0 or 0.000.  These are      */
3664 /* never generated in subset to-number or arithmetic, but can occur   */
3665 /* in non-subset arithmetic (e.g., -1*0 or 1.234-1.234).              */
3666 /* ------------------------------------------------------------------ */
3667 /* If DECCHECK is enabled the string "?" is returned if a number is */
3668 /* invalid. */
3669 static void decToString(const decNumber *dn, char *string, Flag eng) {
3670   Int exp=dn->exponent;       /* local copy */
3671   Int e;                      /* E-part value */
3672   Int pre;                    /* digits before the '.' */
3673   Int cut;                    /* for counting digits in a Unit */
3674   char *c=string;             /* work [output pointer] */
3675   const Unit *up=dn->lsu+D2U(dn->digits)-1; /* -> msu [input pointer] */
3676   uInt u, pow;                /* work */
3677
3678   #if DECCHECK
3679   if (decCheckOperands(DECUNRESU, dn, DECUNUSED, DECUNCONT)) {
3680     strcpy(string, "?");
3681     return;}
3682   #endif
3683
3684   if (decNumberIsNegative(dn)) {   /* Negatives get a minus */
3685     *c='-';
3686     c++;
3687     }
3688   if (dn->bits&DECSPECIAL) {       /* Is a special value */
3689     if (decNumberIsInfinite(dn)) {
3690       strcpy(c,   "Inf");
3691       strcpy(c+3, "inity");
3692       return;}
3693     /* a NaN */
3694     if (dn->bits&DECSNAN) {        /* signalling NaN */
3695       *c='s';
3696       c++;
3697       }
3698     strcpy(c, "NaN");
3699     c+=3;                          /* step past */
3700     /* if not a clean non-zero coefficient, that's all there is in a */
3701     /* NaN string */
3702     if (exp!=0 || (*dn->lsu==0 && dn->digits==1)) return;
3703     /* [drop through to add integer] */
3704     }
3705
3706   /* calculate how many digits in msu, and hence first cut */
3707   cut=MSUDIGITS(dn->digits);       /* [faster than remainder] */
3708   cut--;                           /* power of ten for digit */
3709
3710   if (exp==0) {                    /* simple integer [common fastpath] */
3711     for (;up>=dn->lsu; up--) {     /* each Unit from msu */
3712       u=*up;                       /* contains DECDPUN digits to lay out */
3713       for (; cut>=0; c++, cut--) TODIGIT(u, cut, c, pow);
3714       cut=DECDPUN-1;               /* next Unit has all digits */
3715       }
3716     *c='\0';                       /* terminate the string */
3717     return;}
3718
3719   /* non-0 exponent -- assume plain form */
3720   pre=dn->digits+exp;              /* digits before '.' */
3721   e=0;                             /* no E */
3722   if ((exp>0) || (pre<-5)) {       /* need exponential form */
3723     e=exp+dn->digits-1;            /* calculate E value */
3724     pre=1;                         /* assume one digit before '.' */
3725     if (eng && (e!=0)) {           /* engineering: may need to adjust */
3726       Int adj;                     /* adjustment */
3727       /* The C remainder operator is undefined for negative numbers, so */
3728       /* a positive remainder calculation must be used here */
3729       if (e<0) {
3730         adj=(-e)%3;
3731         if (adj!=0) adj=3-adj;
3732         }
3733        else { /* e>0 */
3734         adj=e%3;
3735         }
3736       e=e-adj;
3737       /* if dealing with zero still produce an exponent which is a */
3738       /* multiple of three, as expected, but there will only be the */
3739       /* one zero before the E, still.  Otherwise note the padding. */
3740       if (!ISZERO(dn)) pre+=adj;
3741        else {  /* is zero */
3742         if (adj!=0) {              /* 0.00Esnn needed */
3743           e=e+3;
3744           pre=-(2-adj);
3745           }
3746         } /* zero */
3747       } /* eng */
3748     } /* need exponent */
3749
3750   /* lay out the digits of the coefficient, adding 0s and . as needed */
3751   u=*up;
3752   if (pre>0) {                     /* xxx.xxx or xx00 (engineering) form */
3753     Int n=pre;
3754     for (; pre>0; pre--, c++, cut--) {
3755       if (cut<0) {                 /* need new Unit */
3756         if (up==dn->lsu) break;    /* out of input digits (pre>digits) */
3757         up--;
3758         cut=DECDPUN-1;
3759         u=*up;
3760         }
3761       TODIGIT(u, cut, c, pow);
3762       }
3763     if (n<dn->digits) {            /* more to come, after '.' */
3764       *c='.'; c++;
3765       for (;; c++, cut--) {
3766         if (cut<0) {               /* need new Unit */
3767           if (up==dn->lsu) break;  /* out of input digits */
3768           up--;
3769           cut=DECDPUN-1;
3770           u=*up;
3771           }
3772         TODIGIT(u, cut, c, pow);
3773         }
3774       }
3775      else for (; pre>0; pre--, c++) *c='0'; /* 0 padding (for engineering) needed */
3776     }
3777    else {                          /* 0.xxx or 0.000xxx form */
3778     *c='0'; c++;
3779     *c='.'; c++;
3780     for (; pre<0; pre++, c++) *c='0';   /* add any 0's after '.' */
3781     for (; ; c++, cut--) {
3782       if (cut<0) {                 /* need new Unit */
3783         if (up==dn->lsu) break;    /* out of input digits */
3784         up--;
3785         cut=DECDPUN-1;
3786         u=*up;
3787         }
3788       TODIGIT(u, cut, c, pow);
3789       }
3790     }
3791
3792   /* Finally add the E-part, if needed.  It will never be 0, has a
3793      base maximum and minimum of +999999999 through -999999999, but
3794      could range down to -1999999998 for anormal numbers */
3795   if (e!=0) {
3796     Flag had=0;               /* 1=had non-zero */
3797     *c='E'; c++;
3798     *c='+'; c++;              /* assume positive */
3799     u=e;                      /* .. */
3800     if (e<0) {
3801       *(c-1)='-';             /* oops, need - */
3802       u=-e;                   /* uInt, please */
3803       }
3804     /* lay out the exponent [_itoa or equivalent is not ANSI C] */
3805     for (cut=9; cut>=0; cut--) {
3806       TODIGIT(u, cut, c, pow);
3807       if (*c=='0' && !had) continue;    /* skip leading zeros */
3808       had=1;                            /* had non-0 */
3809       c++;                              /* step for next */
3810       } /* cut */
3811     }
3812   *c='\0';          /* terminate the string (all paths) */
3813   return;
3814   } /* decToString */
3815
3816 /* ------------------------------------------------------------------ */
3817 /* decAddOp -- add/subtract operation                                 */
3818 /*                                                                    */
3819 /*   This computes C = A + B                                          */
3820 /*                                                                    */
3821 /*   res is C, the result.  C may be A and/or B (e.g., X=X+X)         */
3822 /*   lhs is A                                                         */
3823 /*   rhs is B                                                         */
3824 /*   set is the context                                               */
3825 /*   negate is DECNEG if rhs should be negated, or 0 otherwise        */
3826 /*   status accumulates status for the caller                         */
3827 /*                                                                    */
3828 /* C must have space for set->digits digits.                          */
3829 /* Inexact in status must be 0 for correct Exact zero sign in result  */
3830 /* ------------------------------------------------------------------ */
3831 /* If possible, the coefficient is calculated directly into C.        */
3832 /* However, if:                                                       */
3833 /*   -- a digits+1 calculation is needed because the numbers are      */
3834 /*      unaligned and span more than set->digits digits               */
3835 /*   -- a carry to digits+1 digits looks possible                     */
3836 /*   -- C is the same as A or B, and the result would destructively   */
3837 /*      overlap the A or B coefficient                                */
3838 /* then the result must be calculated into a temporary buffer.  In    */
3839 /* this case a local (stack) buffer is used if possible, and only if  */
3840 /* too long for that does malloc become the final resort.             */
3841 /*                                                                    */
3842 /* Misalignment is handled as follows:                                */
3843 /*   Apad: (AExp>BExp) Swap operands and proceed as for BExp>AExp.    */
3844 /*   BPad: Apply the padding by a combination of shifting (whole      */
3845 /*         units) and multiplication (part units).                    */
3846 /*                                                                    */
3847 /* Addition, especially x=x+1, is speed-critical.                     */
3848 /* The static buffer is larger than might be expected to allow for    */
3849 /* calls from higher-level functions (notably exp).                   */
3850 /* ------------------------------------------------------------------ */
3851 static decNumber * decAddOp(decNumber *res, const decNumber *lhs,
3852                             const decNumber *rhs, decContext *set,
3853                             uByte negate, uInt *status) {
3854   #if DECSUBSET
3855   decNumber *alloclhs=NULL;        /* non-NULL if rounded lhs allocated */
3856   decNumber *allocrhs=NULL;        /* .., rhs */
3857   #endif
3858   Int   rhsshift;                  /* working shift (in Units) */
3859   Int   maxdigits;                 /* longest logical length */
3860   Int   mult;                      /* multiplier */
3861   Int   residue;                   /* rounding accumulator */
3862   uByte bits;                      /* result bits */
3863   Flag  diffsign;                  /* non-0 if arguments have different sign */
3864   Unit  *acc;                      /* accumulator for result */
3865   Unit  accbuff[SD2U(DECBUFFER*2+20)]; /* local buffer [*2+20 reduces many */
3866                                    /* allocations when called from */
3867                                    /* other operations, notable exp] */
3868   Unit  *allocacc=NULL;            /* -> allocated acc buffer, iff allocated */
3869   Int   reqdigits=set->digits;     /* local copy; requested DIGITS */
3870   Int   padding;                   /* work */
3871
3872   #if DECCHECK
3873   if (decCheckOperands(res, lhs, rhs, set)) return res;
3874   #endif
3875
3876   do {                             /* protect allocated storage */
3877     #if DECSUBSET
3878     if (!set->extended) {
3879       /* reduce operands and set lostDigits status, as needed */
3880       if (lhs->digits>reqdigits) {
3881         alloclhs=decRoundOperand(lhs, set, status);
3882         if (alloclhs==NULL) break;
3883         lhs=alloclhs;
3884         }
3885       if (rhs->digits>reqdigits) {
3886         allocrhs=decRoundOperand(rhs, set, status);
3887         if (allocrhs==NULL) break;
3888         rhs=allocrhs;
3889         }
3890       }
3891     #endif
3892     /* [following code does not require input rounding] */
3893
3894     /* note whether signs differ [used all paths] */
3895     diffsign=(Flag)((lhs->bits^rhs->bits^negate)&DECNEG);
3896
3897     /* handle infinities and NaNs */
3898     if (SPECIALARGS) {                  /* a special bit set */
3899       if (SPECIALARGS & (DECSNAN | DECNAN))  /* a NaN */
3900         decNaNs(res, lhs, rhs, set, status);
3901        else { /* one or two infinities */
3902         if (decNumberIsInfinite(lhs)) { /* LHS is infinity */
3903           /* two infinities with different signs is invalid */
3904           if (decNumberIsInfinite(rhs) && diffsign) {
3905             *status|=DEC_Invalid_operation;
3906             break;
3907             }
3908           bits=lhs->bits & DECNEG;      /* get sign from LHS */
3909           }
3910          else bits=(rhs->bits^negate) & DECNEG;/* RHS must be Infinity */
3911         bits|=DECINF;
3912         decNumberZero(res);
3913         res->bits=bits;                 /* set +/- infinity */
3914         } /* an infinity */
3915       break;
3916       }
3917
3918     /* Quick exit for add 0s; return the non-0, modified as need be */
3919     if (ISZERO(lhs)) {
3920       Int adjust;                       /* work */
3921       Int lexp=lhs->exponent;           /* save in case LHS==RES */
3922       bits=lhs->bits;                   /* .. */
3923       residue=0;                        /* clear accumulator */
3924       decCopyFit(res, rhs, set, &residue, status); /* copy (as needed) */
3925       res->bits^=negate;                /* flip if rhs was negated */
3926       #if DECSUBSET
3927       if (set->extended) {              /* exponents on zeros count */
3928       #endif
3929         /* exponent will be the lower of the two */
3930         adjust=lexp-res->exponent;      /* adjustment needed [if -ve] */
3931         if (ISZERO(res)) {              /* both 0: special IEEE 854 rules */
3932           if (adjust<0) res->exponent=lexp;  /* set exponent */
3933           /* 0-0 gives +0 unless rounding to -infinity, and -0-0 gives -0 */
3934           if (diffsign) {
3935             if (set->round!=DEC_ROUND_FLOOR) res->bits=0;
3936              else res->bits=DECNEG;     /* preserve 0 sign */
3937             }
3938           }
3939          else { /* non-0 res */
3940           if (adjust<0) {     /* 0-padding needed */
3941             if ((res->digits-adjust)>set->digits) {
3942               adjust=res->digits-set->digits;     /* to fit exactly */
3943               *status|=DEC_Rounded;               /* [but exact] */
3944               }
3945             res->digits=decShiftToMost(res->lsu, res->digits, -adjust);
3946             res->exponent+=adjust;                /* set the exponent. */
3947             }
3948           } /* non-0 res */
3949       #if DECSUBSET
3950         } /* extended */
3951       #endif
3952       decFinish(res, set, &residue, status);      /* clean and finalize */
3953       break;}
3954
3955     if (ISZERO(rhs)) {                  /* [lhs is non-zero] */
3956       Int adjust;                       /* work */
3957       Int rexp=rhs->exponent;           /* save in case RHS==RES */
3958       bits=rhs->bits;                   /* be clean */
3959       residue=0;                        /* clear accumulator */
3960       decCopyFit(res, lhs, set, &residue, status); /* copy (as needed) */
3961       #if DECSUBSET
3962       if (set->extended) {              /* exponents on zeros count */
3963       #endif
3964         /* exponent will be the lower of the two */
3965         /* [0-0 case handled above] */
3966         adjust=rexp-res->exponent;      /* adjustment needed [if -ve] */
3967         if (adjust<0) {     /* 0-padding needed */
3968           if ((res->digits-adjust)>set->digits) {
3969             adjust=res->digits-set->digits;     /* to fit exactly */
3970             *status|=DEC_Rounded;               /* [but exact] */
3971             }
3972           res->digits=decShiftToMost(res->lsu, res->digits, -adjust);
3973           res->exponent+=adjust;                /* set the exponent. */
3974           }
3975       #if DECSUBSET
3976         } /* extended */
3977       #endif
3978       decFinish(res, set, &residue, status);      /* clean and finalize */
3979       break;}
3980
3981     /* [NB: both fastpath and mainpath code below assume these cases */
3982     /* (notably 0-0) have already been handled] */
3983
3984     /* calculate the padding needed to align the operands */
3985     padding=rhs->exponent-lhs->exponent;
3986
3987     /* Fastpath cases where the numbers are aligned and normal, the RHS */
3988     /* is all in one unit, no operand rounding is needed, and no carry, */
3989     /* lengthening, or borrow is needed */
3990     if (padding==0
3991         && rhs->digits<=DECDPUN
3992         && rhs->exponent>=set->emin     /* [some normals drop through] */
3993         && rhs->exponent<=set->emax-set->digits+1 /* [could clamp] */
3994         && rhs->digits<=reqdigits
3995         && lhs->digits<=reqdigits) {
3996       Int partial=*lhs->lsu;
3997       if (!diffsign) {                  /* adding */
3998         partial+=*rhs->lsu;
3999         if ((partial<=DECDPUNMAX)       /* result fits in unit */
4000          && (lhs->digits>=DECDPUN ||    /* .. and no digits-count change */
4001              partial<(Int)powers[lhs->digits])) { /* .. */
4002           if (res!=lhs) decNumberCopy(res, lhs);  /* not in place */
4003           *res->lsu=(Unit)partial;      /* [copy could have overwritten RHS] */
4004           break;
4005           }
4006         /* else drop out for careful add */
4007         }
4008        else {                           /* signs differ */
4009         partial-=*rhs->lsu;
4010         if (partial>0) { /* no borrow needed, and non-0 result */
4011           if (res!=lhs) decNumberCopy(res, lhs);  /* not in place */
4012           *res->lsu=(Unit)partial;
4013           /* this could have reduced digits [but result>0] */
4014           res->digits=decGetDigits(res->lsu, D2U(res->digits));
4015           break;
4016           }
4017         /* else drop out for careful subtract */
4018         }
4019       }
4020
4021     /* Now align (pad) the lhs or rhs so they can be added or */
4022     /* subtracted, as necessary.  If one number is much larger than */
4023     /* the other (that is, if in plain form there is a least one */
4024     /* digit between the lowest digit of one and the highest of the */
4025     /* other) padding with up to DIGITS-1 trailing zeros may be */
4026     /* needed; then apply rounding (as exotic rounding modes may be */
4027     /* affected by the residue). */
4028     rhsshift=0;               /* rhs shift to left (padding) in Units */
4029     bits=lhs->bits;           /* assume sign is that of LHS */
4030     mult=1;                   /* likely multiplier */
4031
4032     /* [if padding==0 the operands are aligned; no padding is needed] */
4033     if (padding!=0) {
4034       /* some padding needed; always pad the RHS, as any required */
4035       /* padding can then be effected by a simple combination of */
4036       /* shifts and a multiply */
4037       Flag swapped=0;
4038       if (padding<0) {                  /* LHS needs the padding */
4039         const decNumber *t;
4040         padding=-padding;               /* will be +ve */
4041         bits=(uByte)(rhs->bits^negate); /* assumed sign is now that of RHS */
4042         t=lhs; lhs=rhs; rhs=t;
4043         swapped=1;
4044         }
4045
4046       /* If, after pad, rhs would be longer than lhs by digits+1 or */
4047       /* more then lhs cannot affect the answer, except as a residue, */
4048       /* so only need to pad up to a length of DIGITS+1. */
4049       if (rhs->digits+padding > lhs->digits+reqdigits+1) {
4050         /* The RHS is sufficient */
4051         /* for residue use the relative sign indication... */
4052         Int shift=reqdigits-rhs->digits;     /* left shift needed */
4053         residue=1;                           /* residue for rounding */
4054         if (diffsign) residue=-residue;      /* signs differ */
4055         /* copy, shortening if necessary */
4056         decCopyFit(res, rhs, set, &residue, status);
4057         /* if it was already shorter, then need to pad with zeros */
4058         if (shift>0) {
4059           res->digits=decShiftToMost(res->lsu, res->digits, shift);
4060           res->exponent-=shift;              /* adjust the exponent. */
4061           }
4062         /* flip the result sign if unswapped and rhs was negated */
4063         if (!swapped) res->bits^=negate;
4064         decFinish(res, set, &residue, status);    /* done */
4065         break;}
4066
4067       /* LHS digits may affect result */
4068       rhsshift=D2U(padding+1)-1;        /* this much by Unit shift .. */
4069       mult=powers[padding-(rhsshift*DECDPUN)]; /* .. this by multiplication */
4070       } /* padding needed */
4071
4072     if (diffsign) mult=-mult;           /* signs differ */
4073
4074     /* determine the longer operand */
4075     maxdigits=rhs->digits+padding;      /* virtual length of RHS */
4076     if (lhs->digits>maxdigits) maxdigits=lhs->digits;
4077
4078     /* Decide on the result buffer to use; if possible place directly */
4079     /* into result. */
4080     acc=res->lsu;                       /* assume add direct to result */
4081     /* If destructive overlap, or the number is too long, or a carry or */
4082     /* borrow to DIGITS+1 might be possible, a buffer must be used. */
4083     /* [Might be worth more sophisticated tests when maxdigits==reqdigits] */
4084     if ((maxdigits>=reqdigits)          /* is, or could be, too large */
4085      || (res==rhs && rhsshift>0)) {     /* destructive overlap */
4086       /* buffer needed, choose it; units for maxdigits digits will be */
4087       /* needed, +1 Unit for carry or borrow */
4088       Int need=D2U(maxdigits)+1;
4089       acc=accbuff;                      /* assume use local buffer */
4090       if (need*sizeof(Unit)>sizeof(accbuff)) {
4091         /* printf("malloc add %ld %ld\n", need, sizeof(accbuff)); */
4092         allocacc=(Unit *)malloc(need*sizeof(Unit));
4093         if (allocacc==NULL) {           /* hopeless -- abandon */
4094           *status|=DEC_Insufficient_storage;
4095           break;}
4096         acc=allocacc;
4097         }
4098       }
4099
4100     res->bits=(uByte)(bits&DECNEG);     /* it's now safe to overwrite.. */
4101     res->exponent=lhs->exponent;        /* .. operands (even if aliased) */
4102
4103     #if DECTRACE
4104       decDumpAr('A', lhs->lsu, D2U(lhs->digits));
4105       decDumpAr('B', rhs->lsu, D2U(rhs->digits));
4106       printf("  :h: %ld %ld\n", rhsshift, mult);
4107     #endif
4108
4109     /* add [A+B*m] or subtract [A+B*(-m)] */
4110     res->digits=decUnitAddSub(lhs->lsu, D2U(lhs->digits),
4111                               rhs->lsu, D2U(rhs->digits),
4112                               rhsshift, acc, mult)
4113                *DECDPUN;           /* [units -> digits] */
4114     if (res->digits<0) {           /* borrowed... */
4115       res->digits=-res->digits;
4116       res->bits^=DECNEG;           /* flip the sign */
4117       }
4118     #if DECTRACE
4119       decDumpAr('+', acc, D2U(res->digits));
4120     #endif
4121
4122     /* If a buffer was used the result must be copied back, possibly */
4123     /* shortening.  (If no buffer was used then the result must have */
4124     /* fit, so can't need rounding and residue must be 0.) */
4125     residue=0;                     /* clear accumulator */
4126     if (acc!=res->lsu) {
4127       #if DECSUBSET
4128       if (set->extended) {         /* round from first significant digit */
4129       #endif
4130         /* remove leading zeros that were added due to rounding up to */
4131         /* integral Units -- before the test for rounding. */
4132         if (res->digits>reqdigits)
4133           res->digits=decGetDigits(acc, D2U(res->digits));
4134         decSetCoeff(res, set, acc, res->digits, &residue, status);
4135       #if DECSUBSET
4136         }
4137        else { /* subset arithmetic rounds from original significant digit */
4138         /* May have an underestimate.  This only occurs when both */
4139         /* numbers fit in DECDPUN digits and are padding with a */
4140         /* negative multiple (-10, -100...) and the top digit(s) become */
4141         /* 0.  (This only matters when using X3.274 rules where the */
4142         /* leading zero could be included in the rounding.) */
4143         if (res->digits<maxdigits) {
4144           *(acc+D2U(res->digits))=0; /* ensure leading 0 is there */
4145           res->digits=maxdigits;
4146           }
4147          else {
4148           /* remove leading zeros that added due to rounding up to */
4149           /* integral Units (but only those in excess of the original */
4150           /* maxdigits length, unless extended) before test for rounding. */
4151           if (res->digits>reqdigits) {
4152             res->digits=decGetDigits(acc, D2U(res->digits));
4153             if (res->digits<maxdigits) res->digits=maxdigits;
4154             }
4155           }
4156         decSetCoeff(res, set, acc, res->digits, &residue, status);
4157         /* Now apply rounding if needed before removing leading zeros. */
4158         /* This is safe because subnormals are not a possibility */
4159         if (residue!=0) {
4160           decApplyRound(res, set, residue, status);
4161           residue=0;                 /* did what needed to be done */
4162           }
4163         } /* subset */
4164       #endif
4165       } /* used buffer */
4166
4167     /* strip leading zeros [these were left on in case of subset subtract] */
4168     res->digits=decGetDigits(res->lsu, D2U(res->digits));
4169
4170     /* apply checks and rounding */
4171     decFinish(res, set, &residue, status);
4172
4173     /* "When the sum of two operands with opposite signs is exactly */
4174     /* zero, the sign of that sum shall be '+' in all rounding modes */
4175     /* except round toward -Infinity, in which mode that sign shall be */
4176     /* '-'."  [Subset zeros also never have '-', set by decFinish.] */
4177     if (ISZERO(res) && diffsign
4178      #if DECSUBSET
4179      && set->extended
4180      #endif
4181      && (*status&DEC_Inexact)==0) {
4182       if (set->round==DEC_ROUND_FLOOR) res->bits|=DECNEG;   /* sign - */
4183                                   else res->bits&=~DECNEG;  /* sign + */
4184       }
4185     } while(0);                              /* end protected */
4186
4187   if (allocacc!=NULL) free(allocacc);        /* drop any storage used */
4188   #if DECSUBSET
4189   if (allocrhs!=NULL) free(allocrhs);        /* .. */
4190   if (alloclhs!=NULL) free(alloclhs);        /* .. */
4191   #endif
4192   return res;
4193   } /* decAddOp */
4194
4195 /* ------------------------------------------------------------------ */
4196 /* decDivideOp -- division operation                                  */
4197 /*                                                                    */
4198 /*  This routine performs the calculations for all four division      */
4199 /*  operators (divide, divideInteger, remainder, remainderNear).      */
4200 /*                                                                    */
4201 /*  C=A op B                                                          */
4202 /*                                                                    */
4203 /*   res is C, the result.  C may be A and/or B (e.g., X=X/X)         */
4204 /*   lhs is A                                                         */
4205 /*   rhs is B                                                         */
4206 /*   set is the context                                               */
4207 /*   op  is DIVIDE, DIVIDEINT, REMAINDER, or REMNEAR respectively.    */
4208 /*   status is the usual accumulator                                  */
4209 /*                                                                    */
4210 /* C must have space for set->digits digits.                          */
4211 /*                                                                    */
4212 /* ------------------------------------------------------------------ */
4213 /*   The underlying algorithm of this routine is the same as in the   */
4214 /*   1981 S/370 implementation, that is, non-restoring long division  */
4215 /*   with bi-unit (rather than bi-digit) estimation for each unit     */
4216 /*   multiplier.  In this pseudocode overview, complications for the  */
4217 /*   Remainder operators and division residues for exact rounding are */
4218 /*   omitted for clarity.                                             */
4219 /*                                                                    */
4220 /*     Prepare operands and handle special values                     */
4221 /*     Test for x/0 and then 0/x                                      */
4222 /*     Exp =Exp1 - Exp2                                               */
4223 /*     Exp =Exp +len(var1) -len(var2)                                 */
4224 /*     Sign=Sign1 * Sign2                                             */
4225 /*     Pad accumulator (Var1) to double-length with 0's (pad1)        */
4226 /*     Pad Var2 to same length as Var1                                */
4227 /*     msu2pair/plus=1st 2 or 1 units of var2, +1 to allow for round  */
4228 /*     have=0                                                         */
4229 /*     Do until (have=digits+1 OR residue=0)                          */
4230 /*       if exp<0 then if integer divide/residue then leave           */
4231 /*       this_unit=0                                                  */
4232 /*       Do forever                                                   */
4233 /*          compare numbers                                           */
4234 /*          if <0 then leave inner_loop                               */
4235 /*          if =0 then (* quick exit without subtract *) do           */
4236 /*             this_unit=this_unit+1; output this_unit                */
4237 /*             leave outer_loop; end                                  */
4238 /*          Compare lengths of numbers (mantissae):                   */
4239 /*          If same then tops2=msu2pair -- {units 1&2 of var2}        */
4240 /*                  else tops2=msu2plus -- {0, unit 1 of var2}        */
4241 /*          tops1=first_unit_of_Var1*10**DECDPUN +second_unit_of_var1 */
4242 /*          mult=tops1/tops2  -- Good and safe guess at divisor       */
4243 /*          if mult=0 then mult=1                                     */
4244 /*          this_unit=this_unit+mult                                  */
4245 /*          subtract                                                  */
4246 /*          end inner_loop                                            */
4247 /*        if have\=0 | this_unit\=0 then do                           */
4248 /*          output this_unit                                          */
4249 /*          have=have+1; end                                          */
4250 /*        var2=var2/10                                                */
4251 /*        exp=exp-1                                                   */
4252 /*        end outer_loop                                              */
4253 /*     exp=exp+1   -- set the proper exponent                         */
4254 /*     if have=0 then generate answer=0                               */
4255 /*     Return (Result is defined by Var1)                             */
4256 /*                                                                    */
4257 /* ------------------------------------------------------------------ */
4258 /* Two working buffers are needed during the division; one (digits+   */
4259 /* 1) to accumulate the result, and the other (up to 2*digits+1) for  */
4260 /* long subtractions.  These are acc and var1 respectively.           */
4261 /* var1 is a copy of the lhs coefficient, var2 is the rhs coefficient.*/
4262 /* The static buffers may be larger than might be expected to allow   */
4263 /* for calls from higher-level functions (notably exp).               */
4264 /* ------------------------------------------------------------------ */
4265 static decNumber * decDivideOp(decNumber *res,
4266                                const decNumber *lhs, const decNumber *rhs,
4267                                decContext *set, Flag op, uInt *status) {
4268   #if DECSUBSET
4269   decNumber *alloclhs=NULL;        /* non-NULL if rounded lhs allocated */
4270   decNumber *allocrhs=NULL;        /* .., rhs */
4271   #endif
4272   Unit  accbuff[SD2U(DECBUFFER+DECDPUN+10)]; /* local buffer */
4273   Unit  *acc=accbuff;              /* -> accumulator array for result */
4274   Unit  *allocacc=NULL;            /* -> allocated buffer, iff allocated */
4275   Unit  *accnext;                  /* -> where next digit will go */
4276   Int   acclength;                 /* length of acc needed [Units] */
4277   Int   accunits;                  /* count of units accumulated */
4278   Int   accdigits;                 /* count of digits accumulated */
4279
4280   Unit  varbuff[SD2U(DECBUFFER*2+DECDPUN)*sizeof(Unit)]; /* buffer for var1 */
4281   Unit  *var1=varbuff;             /* -> var1 array for long subtraction */
4282   Unit  *varalloc=NULL;            /* -> allocated buffer, iff used */
4283   Unit  *msu1;                     /* -> msu of var1 */
4284
4285   const Unit *var2;                /* -> var2 array */
4286   const Unit *msu2;                /* -> msu of var2 */
4287   Int   msu2plus;                  /* msu2 plus one [does not vary] */
4288   eInt  msu2pair;                  /* msu2 pair plus one [does not vary] */
4289
4290   Int   var1units, var2units;      /* actual lengths */
4291   Int   var2ulen;                  /* logical length (units) */
4292   Int   var1initpad=0;             /* var1 initial padding (digits) */
4293   Int   maxdigits;                 /* longest LHS or required acc length */
4294   Int   mult;                      /* multiplier for subtraction */
4295   Unit  thisunit;                  /* current unit being accumulated */
4296   Int   residue;                   /* for rounding */
4297   Int   reqdigits=set->digits;     /* requested DIGITS */
4298   Int   exponent;                  /* working exponent */
4299   Int   maxexponent=0;             /* DIVIDE maximum exponent if unrounded */
4300   uByte bits;                      /* working sign */
4301   Unit  *target;                   /* work */
4302   const Unit *source;              /* .. */
4303   uLong const *pow;                /* .. */
4304   Int   shift, cut;                /* .. */
4305   #if DECSUBSET
4306   Int   dropped;                   /* work */
4307   #endif
4308
4309   #if DECCHECK
4310   if (decCheckOperands(res, lhs, rhs, set)) return res;
4311   #endif
4312
4313   do {                             /* protect allocated storage */
4314     #if DECSUBSET
4315     if (!set->extended) {
4316       /* reduce operands and set lostDigits status, as needed */
4317       if (lhs->digits>reqdigits) {
4318         alloclhs=decRoundOperand(lhs, set, status);
4319         if (alloclhs==NULL) break;
4320         lhs=alloclhs;
4321         }
4322       if (rhs->digits>reqdigits) {
4323         allocrhs=decRoundOperand(rhs, set, status);
4324         if (allocrhs==NULL) break;
4325         rhs=allocrhs;
4326         }
4327       }
4328     #endif
4329     /* [following code does not require input rounding] */
4330
4331     bits=(lhs->bits^rhs->bits)&DECNEG;  /* assumed sign for divisions */
4332
4333     /* handle infinities and NaNs */
4334     if (SPECIALARGS) {                  /* a special bit set */
4335       if (SPECIALARGS & (DECSNAN | DECNAN)) { /* one or two NaNs */
4336         decNaNs(res, lhs, rhs, set, status);
4337         break;
4338         }
4339       /* one or two infinities */
4340       if (decNumberIsInfinite(lhs)) {   /* LHS (dividend) is infinite */
4341         if (decNumberIsInfinite(rhs) || /* two infinities are invalid .. */
4342             op & (REMAINDER | REMNEAR)) { /* as is remainder of infinity */
4343           *status|=DEC_Invalid_operation;
4344           break;
4345           }
4346         /* [Note that infinity/0 raises no exceptions] */
4347         decNumberZero(res);
4348         res->bits=bits|DECINF;          /* set +/- infinity */
4349         break;
4350         }
4351        else {                           /* RHS (divisor) is infinite */
4352         residue=0;
4353         if (op&(REMAINDER|REMNEAR)) {
4354           /* result is [finished clone of] lhs */
4355           decCopyFit(res, lhs, set, &residue, status);
4356           }
4357          else {  /* a division */
4358           decNumberZero(res);
4359           res->bits=bits;               /* set +/- zero */
4360           /* for DIVIDEINT the exponent is always 0.  For DIVIDE, result */
4361           /* is a 0 with infinitely negative exponent, clamped to minimum */
4362           if (op&DIVIDE) {
4363             res->exponent=set->emin-set->digits+1;
4364             *status|=DEC_Clamped;
4365             }
4366           }
4367         decFinish(res, set, &residue, status);
4368         break;
4369         }
4370       }
4371
4372     /* handle 0 rhs (x/0) */
4373     if (ISZERO(rhs)) {                  /* x/0 is always exceptional */
4374       if (ISZERO(lhs)) {
4375         decNumberZero(res);             /* [after lhs test] */
4376         *status|=DEC_Division_undefined;/* 0/0 will become NaN */
4377         }
4378        else {
4379         decNumberZero(res);
4380         if (op&(REMAINDER|REMNEAR)) *status|=DEC_Invalid_operation;
4381          else {
4382           *status|=DEC_Division_by_zero; /* x/0 */
4383           res->bits=bits|DECINF;         /* .. is +/- Infinity */
4384           }
4385         }
4386       break;}
4387
4388     /* handle 0 lhs (0/x) */
4389     if (ISZERO(lhs)) {                  /* 0/x [x!=0] */
4390       #if DECSUBSET
4391       if (!set->extended) decNumberZero(res);
4392        else {
4393       #endif
4394         if (op&DIVIDE) {
4395           residue=0;
4396           exponent=lhs->exponent-rhs->exponent; /* ideal exponent */
4397           decNumberCopy(res, lhs);      /* [zeros always fit] */
4398           res->bits=bits;               /* sign as computed */
4399           res->exponent=exponent;       /* exponent, too */
4400           decFinalize(res, set, &residue, status);   /* check exponent */
4401           }
4402          else if (op&DIVIDEINT) {
4403           decNumberZero(res);           /* integer 0 */
4404           res->bits=bits;               /* sign as computed */
4405           }
4406          else {                         /* a remainder */
4407           exponent=rhs->exponent;       /* [save in case overwrite] */
4408           decNumberCopy(res, lhs);      /* [zeros always fit] */
4409           if (exponent<res->exponent) res->exponent=exponent; /* use lower */
4410           }
4411       #if DECSUBSET
4412         }
4413       #endif
4414       break;}
4415
4416     /* Precalculate exponent.  This starts off adjusted (and hence fits */
4417     /* in 31 bits) and becomes the usual unadjusted exponent as the */
4418     /* division proceeds.  The order of evaluation is important, here, */
4419     /* to avoid wrap. */
4420     exponent=(lhs->exponent+lhs->digits)-(rhs->exponent+rhs->digits);
4421
4422     /* If the working exponent is -ve, then some quick exits are */
4423     /* possible because the quotient is known to be <1 */
4424     /* [for REMNEAR, it needs to be < -1, as -0.5 could need work] */
4425     if (exponent<0 && !(op==DIVIDE)) {
4426       if (op&DIVIDEINT) {
4427         decNumberZero(res);                  /* integer part is 0 */
4428         #if DECSUBSET
4429         if (set->extended)
4430         #endif
4431           res->bits=bits;                    /* set +/- zero */
4432         break;}
4433       /* fastpath remainders so long as the lhs has the smaller */
4434       /* (or equal) exponent */
4435       if (lhs->exponent<=rhs->exponent) {
4436         if (op&REMAINDER || exponent<-1) {
4437           /* It is REMAINDER or safe REMNEAR; result is [finished */
4438           /* clone of] lhs  (r = x - 0*y) */
4439           residue=0;
4440           decCopyFit(res, lhs, set, &residue, status);
4441           decFinish(res, set, &residue, status);
4442           break;
4443           }
4444         /* [unsafe REMNEAR drops through] */
4445         }
4446       } /* fastpaths */
4447
4448     /* Long (slow) division is needed; roll up the sleeves... */
4449
4450     /* The accumulator will hold the quotient of the division. */
4451     /* If it needs to be too long for stack storage, then allocate. */
4452     acclength=D2U(reqdigits+DECDPUN);   /* in Units */
4453     if (acclength*sizeof(Unit)>sizeof(accbuff)) {
4454       /* printf("malloc dvacc %ld units\n", acclength); */
4455       allocacc=(Unit *)malloc(acclength*sizeof(Unit));
4456       if (allocacc==NULL) {             /* hopeless -- abandon */
4457         *status|=DEC_Insufficient_storage;
4458         break;}
4459       acc=allocacc;                     /* use the allocated space */
4460       }
4461
4462     /* var1 is the padded LHS ready for subtractions. */
4463     /* If it needs to be too long for stack storage, then allocate. */
4464     /* The maximum units needed for var1 (long subtraction) is: */
4465     /* Enough for */
4466     /*     (rhs->digits+reqdigits-1) -- to allow full slide to right */
4467     /* or  (lhs->digits)             -- to allow for long lhs */
4468     /* whichever is larger */
4469     /*   +1                -- for rounding of slide to right */
4470     /*   +1                -- for leading 0s */
4471     /*   +1                -- for pre-adjust if a remainder or DIVIDEINT */
4472     /* [Note: unused units do not participate in decUnitAddSub data] */
4473     maxdigits=rhs->digits+reqdigits-1;
4474     if (lhs->digits>maxdigits) maxdigits=lhs->digits;
4475     var1units=D2U(maxdigits)+2;
4476     /* allocate a guard unit above msu1 for REMAINDERNEAR */
4477     if (!(op&DIVIDE)) var1units++;
4478     if ((var1units+1)*sizeof(Unit)>sizeof(varbuff)) {
4479       /* printf("malloc dvvar %ld units\n", var1units+1); */
4480       varalloc=(Unit *)malloc((var1units+1)*sizeof(Unit));
4481       if (varalloc==NULL) {             /* hopeless -- abandon */
4482         *status|=DEC_Insufficient_storage;
4483         break;}
4484       var1=varalloc;                    /* use the allocated space */
4485       }
4486
4487     /* Extend the lhs and rhs to full long subtraction length.  The lhs */
4488     /* is truly extended into the var1 buffer, with 0 padding, so a */
4489     /* subtract in place is always possible.  The rhs (var2) has */
4490     /* virtual padding (implemented by decUnitAddSub). */
4491     /* One guard unit was allocated above msu1 for rem=rem+rem in */
4492     /* REMAINDERNEAR. */
4493     msu1=var1+var1units-1;              /* msu of var1 */
4494     source=lhs->lsu+D2U(lhs->digits)-1; /* msu of input array */
4495     for (target=msu1; source>=lhs->lsu; source--, target--) *target=*source;
4496     for (; target>=var1; target--) *target=0;
4497
4498     /* rhs (var2) is left-aligned with var1 at the start */
4499     var2ulen=var1units;                 /* rhs logical length (units) */
4500     var2units=D2U(rhs->digits);         /* rhs actual length (units) */
4501     var2=rhs->lsu;                      /* -> rhs array */
4502     msu2=var2+var2units-1;              /* -> msu of var2 [never changes] */
4503     /* now set up the variables which will be used for estimating the */
4504     /* multiplication factor.  If these variables are not exact, add */
4505     /* 1 to make sure that the multiplier is never overestimated. */
4506     msu2plus=*msu2;                     /* it's value .. */
4507     if (var2units>1) msu2plus++;        /* .. +1 if any more */
4508     msu2pair=(eInt)*msu2*(DECDPUNMAX+1);/* top two pair .. */
4509     if (var2units>1) {                  /* .. [else treat 2nd as 0] */
4510       msu2pair+=*(msu2-1);              /* .. */
4511       if (var2units>2) msu2pair++;      /* .. +1 if any more */
4512       }
4513
4514     /* The calculation is working in units, which may have leading zeros, */
4515     /* but the exponent was calculated on the assumption that they are */
4516     /* both left-aligned.  Adjust the exponent to compensate: add the */
4517     /* number of leading zeros in var1 msu and subtract those in var2 msu. */
4518     /* [This is actually done by counting the digits and negating, as */
4519     /* lead1=DECDPUN-digits1, and similarly for lead2.] */
4520     for (pow=&powers[1]; *msu1>=*pow; pow++) exponent--;
4521     for (pow=&powers[1]; *msu2>=*pow; pow++) exponent++;
4522
4523     /* Now, if doing an integer divide or remainder, ensure that */
4524     /* the result will be Unit-aligned.  To do this, shift the var1 */
4525     /* accumulator towards least if need be.  (It's much easier to */
4526     /* do this now than to reassemble the residue afterwards, if */
4527     /* doing a remainder.)  Also ensure the exponent is not negative. */
4528     if (!(op&DIVIDE)) {
4529       Unit *u;                          /* work */
4530       /* save the initial 'false' padding of var1, in digits */
4531       var1initpad=(var1units-D2U(lhs->digits))*DECDPUN;
4532       /* Determine the shift to do. */
4533       if (exponent<0) cut=-exponent;
4534        else cut=DECDPUN-exponent%DECDPUN;
4535       decShiftToLeast(var1, var1units, cut);
4536       exponent+=cut;                    /* maintain numerical value */
4537       var1initpad-=cut;                 /* .. and reduce padding */
4538       /* clean any most-significant units which were just emptied */
4539       for (u=msu1; cut>=DECDPUN; cut-=DECDPUN, u--) *u=0;
4540       } /* align */
4541      else { /* is DIVIDE */
4542       maxexponent=lhs->exponent-rhs->exponent;    /* save */
4543       /* optimization: if the first iteration will just produce 0, */
4544       /* preadjust to skip it [valid for DIVIDE only] */
4545       if (*msu1<*msu2) {
4546         var2ulen--;                     /* shift down */
4547         exponent-=DECDPUN;              /* update the exponent */
4548         }
4549       }
4550
4551     /* ---- start the long-division loops ------------------------------ */
4552     accunits=0;                         /* no units accumulated yet */
4553     accdigits=0;                        /* .. or digits */
4554     accnext=acc+acclength-1;            /* -> msu of acc [NB: allows digits+1] */
4555     for (;;) {                          /* outer forever loop */
4556       thisunit=0;                       /* current unit assumed 0 */
4557       /* find the next unit */
4558       for (;;) {                        /* inner forever loop */
4559         /* strip leading zero units [from either pre-adjust or from */
4560         /* subtract last time around].  Leave at least one unit. */
4561         for (; *msu1==0 && msu1>var1; msu1--) var1units--;
4562
4563         if (var1units<var2ulen) break;       /* var1 too low for subtract */
4564         if (var1units==var2ulen) {           /* unit-by-unit compare needed */
4565           /* compare the two numbers, from msu */
4566           const Unit *pv1, *pv2;
4567           Unit v2;                           /* units to compare */
4568           pv2=msu2;                          /* -> msu */
4569           for (pv1=msu1; ; pv1--, pv2--) {
4570             /* v1=*pv1 -- always OK */
4571             v2=0;                            /* assume in padding */
4572             if (pv2>=var2) v2=*pv2;          /* in range */
4573             if (*pv1!=v2) break;             /* no longer the same */
4574             if (pv1==var1) break;            /* done; leave pv1 as is */
4575             }
4576           /* here when all inspected or a difference seen */
4577           if (*pv1<v2) break;                /* var1 too low to subtract */
4578           if (*pv1==v2) {                    /* var1 == var2 */
4579             /* reach here if var1 and var2 are identical; subtraction */
4580             /* would increase digit by one, and the residue will be 0 so */
4581             /* the calculation is done; leave the loop with residue=0. */
4582             thisunit++;                      /* as though subtracted */
4583             *var1=0;                         /* set var1 to 0 */
4584             var1units=1;                     /* .. */
4585             break;  /* from inner */
4586             } /* var1 == var2 */
4587           /* *pv1>v2.  Prepare for real subtraction; the lengths are equal */
4588           /* Estimate the multiplier (there's always a msu1-1)... */
4589           /* Bring in two units of var2 to provide a good estimate. */
4590           mult=(Int)(((eInt)*msu1*(DECDPUNMAX+1)+*(msu1-1))/msu2pair);
4591           } /* lengths the same */
4592          else { /* var1units > var2ulen, so subtraction is safe */
4593           /* The var2 msu is one unit towards the lsu of the var1 msu, */
4594           /* so only one unit for var2 can be used. */
4595           mult=(Int)(((eInt)*msu1*(DECDPUNMAX+1)+*(msu1-1))/msu2plus);
4596           }
4597         if (mult==0) mult=1;                 /* must always be at least 1 */
4598         /* subtraction needed; var1 is > var2 */
4599         thisunit=(Unit)(thisunit+mult);      /* accumulate */
4600         /* subtract var1-var2, into var1; only the overlap needs */
4601         /* processing, as this is an in-place calculation */
4602         shift=var2ulen-var2units;
4603         #if DECTRACE
4604           decDumpAr('1', &var1[shift], var1units-shift);
4605           decDumpAr('2', var2, var2units);
4606           printf("m=%ld\n", -mult);
4607         #endif
4608         decUnitAddSub(&var1[shift], var1units-shift,
4609                       var2, var2units, 0,
4610                       &var1[shift], -mult);
4611         #if DECTRACE
4612           decDumpAr('#', &var1[shift], var1units-shift);
4613         #endif
4614         /* var1 now probably has leading zeros; these are removed at the */
4615         /* top of the inner loop. */
4616         } /* inner loop */
4617
4618       /* The next unit has been calculated in full; unless it's a */
4619       /* leading zero, add to acc */
4620       if (accunits!=0 || thisunit!=0) {      /* is first or non-zero */
4621         *accnext=thisunit;                   /* store in accumulator */
4622         /* account exactly for the new digits */
4623         if (accunits==0) {
4624           accdigits++;                       /* at least one */
4625           for (pow=&powers[1]; thisunit>=*pow; pow++) accdigits++;
4626           }
4627          else accdigits+=DECDPUN;
4628         accunits++;                          /* update count */
4629         accnext--;                           /* ready for next */
4630         if (accdigits>reqdigits) break;      /* have enough digits */
4631         }
4632
4633       /* if the residue is zero, the operation is done (unless divide */
4634       /* or divideInteger and still not enough digits yet) */
4635       if (*var1==0 && var1units==1) {        /* residue is 0 */
4636         if (op&(REMAINDER|REMNEAR)) break;
4637         if ((op&DIVIDE) && (exponent<=maxexponent)) break;
4638         /* [drop through if divideInteger] */
4639         }
4640       /* also done enough if calculating remainder or integer */
4641       /* divide and just did the last ('units') unit */
4642       if (exponent==0 && !(op&DIVIDE)) break;
4643
4644       /* to get here, var1 is less than var2, so divide var2 by the per- */
4645       /* Unit power of ten and go for the next digit */
4646       var2ulen--;                            /* shift down */
4647       exponent-=DECDPUN;                     /* update the exponent */
4648       } /* outer loop */
4649
4650     /* ---- division is complete --------------------------------------- */
4651     /* here: acc      has at least reqdigits+1 of good results (or fewer */
4652     /*                if early stop), starting at accnext+1 (its lsu) */
4653     /*       var1     has any residue at the stopping point */
4654     /*       accunits is the number of digits collected in acc */
4655     if (accunits==0) {             /* acc is 0 */
4656       accunits=1;                  /* show have a unit .. */
4657       accdigits=1;                 /* .. */
4658       *accnext=0;                  /* .. whose value is 0 */
4659       }
4660      else accnext++;               /* back to last placed */
4661     /* accnext now -> lowest unit of result */
4662
4663     residue=0;                     /* assume no residue */
4664     if (op&DIVIDE) {
4665       /* record the presence of any residue, for rounding */
4666       if (*var1!=0 || var1units>1) residue=1;
4667        else { /* no residue */
4668         /* Had an exact division; clean up spurious trailing 0s. */
4669         /* There will be at most DECDPUN-1, from the final multiply, */
4670         /* and then only if the result is non-0 (and even) and the */
4671         /* exponent is 'loose'. */
4672         #if DECDPUN>1
4673         Unit lsu=*accnext;
4674         if (!(lsu&0x01) && (lsu!=0)) {
4675           /* count the trailing zeros */
4676           Int drop=0;
4677           for (;; drop++) {    /* [will terminate because lsu!=0] */
4678             if (exponent>=maxexponent) break;     /* don't chop real 0s */
4679             #if DECDPUN<=4
4680               if ((lsu-QUOT10(lsu, drop+1)
4681                   *powers[drop+1])!=0) break;     /* found non-0 digit */
4682             #else
4683               if (lsu%powers[drop+1]!=0) break;   /* found non-0 digit */
4684             #endif
4685             exponent++;
4686             }
4687           if (drop>0) {
4688             accunits=decShiftToLeast(accnext, accunits, drop);
4689             accdigits=decGetDigits(accnext, accunits);
4690             accunits=D2U(accdigits);
4691             /* [exponent was adjusted in the loop] */
4692             }
4693           } /* neither odd nor 0 */
4694         #endif
4695         } /* exact divide */
4696       } /* divide */
4697      else /* op!=DIVIDE */ {
4698       /* check for coefficient overflow */
4699       if (accdigits+exponent>reqdigits) {
4700         *status|=DEC_Division_impossible;
4701         break;
4702         }
4703       if (op & (REMAINDER|REMNEAR)) {
4704         /* [Here, the exponent will be 0, because var1 was adjusted */
4705         /* appropriately.] */
4706         Int postshift;                       /* work */
4707         Flag wasodd=0;                       /* integer was odd */
4708         Unit *quotlsu;                       /* for save */
4709         Int  quotdigits;                     /* .. */
4710
4711         bits=lhs->bits;                      /* remainder sign is always as lhs */
4712
4713         /* Fastpath when residue is truly 0 is worthwhile [and */
4714         /* simplifies the code below] */
4715         if (*var1==0 && var1units==1) {      /* residue is 0 */
4716           Int exp=lhs->exponent;             /* save min(exponents) */
4717           if (rhs->exponent<exp) exp=rhs->exponent;
4718           decNumberZero(res);                /* 0 coefficient */
4719           #if DECSUBSET
4720           if (set->extended)
4721           #endif
4722           res->exponent=exp;                 /* .. with proper exponent */
4723           res->bits=(uByte)(bits&DECNEG);          /* [cleaned] */
4724           decFinish(res, set, &residue, status);   /* might clamp */
4725           break;
4726           }
4727         /* note if the quotient was odd */
4728         if (*accnext & 0x01) wasodd=1;       /* acc is odd */
4729         quotlsu=accnext;                     /* save in case need to reinspect */
4730         quotdigits=accdigits;                /* .. */
4731
4732         /* treat the residue, in var1, as the value to return, via acc */
4733         /* calculate the unused zero digits.  This is the smaller of: */
4734         /*   var1 initial padding (saved above) */
4735         /*   var2 residual padding, which happens to be given by: */
4736         postshift=var1initpad+exponent-lhs->exponent+rhs->exponent;
4737         /* [the 'exponent' term accounts for the shifts during divide] */
4738         if (var1initpad<postshift) postshift=var1initpad;
4739
4740         /* shift var1 the requested amount, and adjust its digits */
4741         var1units=decShiftToLeast(var1, var1units, postshift);
4742         accnext=var1;
4743         accdigits=decGetDigits(var1, var1units);
4744         accunits=D2U(accdigits);
4745
4746         exponent=lhs->exponent;         /* exponent is smaller of lhs & rhs */
4747         if (rhs->exponent<exponent) exponent=rhs->exponent;
4748
4749         /* Now correct the result if doing remainderNear; if it */
4750         /* (looking just at coefficients) is > rhs/2, or == rhs/2 and */
4751         /* the integer was odd then the result should be rem-rhs. */
4752         if (op&REMNEAR) {
4753           Int compare, tarunits;        /* work */
4754           Unit *up;                     /* .. */
4755           /* calculate remainder*2 into the var1 buffer (which has */
4756           /* 'headroom' of an extra unit and hence enough space) */
4757           /* [a dedicated 'double' loop would be faster, here] */
4758           tarunits=decUnitAddSub(accnext, accunits, accnext, accunits,
4759                                  0, accnext, 1);
4760           /* decDumpAr('r', accnext, tarunits); */
4761
4762           /* Here, accnext (var1) holds tarunits Units with twice the */
4763           /* remainder's coefficient, which must now be compared to the */
4764           /* RHS.  The remainder's exponent may be smaller than the RHS's. */
4765           compare=decUnitCompare(accnext, tarunits, rhs->lsu, D2U(rhs->digits),
4766                                  rhs->exponent-exponent);
4767           if (compare==BADINT) {             /* deep trouble */
4768             *status|=DEC_Insufficient_storage;
4769             break;}
4770
4771           /* now restore the remainder by dividing by two; the lsu */
4772           /* is known to be even. */
4773           for (up=accnext; up<accnext+tarunits; up++) {
4774             Int half;              /* half to add to lower unit */
4775             half=*up & 0x01;
4776             *up/=2;                /* [shift] */
4777             if (!half) continue;
4778             *(up-1)+=(DECDPUNMAX+1)/2;
4779             }
4780           /* [accunits still describes the original remainder length] */
4781
4782           if (compare>0 || (compare==0 && wasodd)) { /* adjustment needed */
4783             Int exp, expunits, exprem;       /* work */
4784             /* This is effectively causing round-up of the quotient, */
4785             /* so if it was the rare case where it was full and all */
4786             /* nines, it would overflow and hence division-impossible */
4787             /* should be raised */
4788             Flag allnines=0;                 /* 1 if quotient all nines */
4789             if (quotdigits==reqdigits) {     /* could be borderline */
4790               for (up=quotlsu; ; up++) {
4791                 if (quotdigits>DECDPUN) {
4792                   if (*up!=DECDPUNMAX) break;/* non-nines */
4793                   }
4794                  else {                      /* this is the last Unit */
4795                   if (*up==powers[quotdigits]-1) allnines=1;
4796                   break;
4797                   }
4798                 quotdigits-=DECDPUN;         /* checked those digits */
4799                 } /* up */
4800               } /* borderline check */
4801             if (allnines) {
4802               *status|=DEC_Division_impossible;
4803               break;}
4804
4805             /* rem-rhs is needed; the sign will invert.  Again, var1 */
4806             /* can safely be used for the working Units array. */
4807             exp=rhs->exponent-exponent;      /* RHS padding needed */
4808             /* Calculate units and remainder from exponent. */
4809             expunits=exp/DECDPUN;
4810             exprem=exp%DECDPUN;
4811             /* subtract [A+B*(-m)]; the result will always be negative */
4812             accunits=-decUnitAddSub(accnext, accunits,
4813                                     rhs->lsu, D2U(rhs->digits),
4814                                     expunits, accnext, -(Int)powers[exprem]);
4815             accdigits=decGetDigits(accnext, accunits); /* count digits exactly */
4816             accunits=D2U(accdigits);    /* and recalculate the units for copy */
4817             /* [exponent is as for original remainder] */
4818             bits^=DECNEG;               /* flip the sign */
4819             }
4820           } /* REMNEAR */
4821         } /* REMAINDER or REMNEAR */
4822       } /* not DIVIDE */
4823
4824     /* Set exponent and bits */
4825     res->exponent=exponent;
4826     res->bits=(uByte)(bits&DECNEG);          /* [cleaned] */
4827
4828     /* Now the coefficient. */
4829     decSetCoeff(res, set, accnext, accdigits, &residue, status);
4830
4831     decFinish(res, set, &residue, status);   /* final cleanup */
4832
4833     #if DECSUBSET
4834     /* If a divide then strip trailing zeros if subset [after round] */
4835     if (!set->extended && (op==DIVIDE)) decTrim(res, set, 0, &dropped);
4836     #endif
4837     } while(0);                              /* end protected */
4838
4839   if (varalloc!=NULL) free(varalloc);   /* drop any storage used */
4840   if (allocacc!=NULL) free(allocacc);   /* .. */
4841   #if DECSUBSET
4842   if (allocrhs!=NULL) free(allocrhs);   /* .. */
4843   if (alloclhs!=NULL) free(alloclhs);   /* .. */
4844   #endif
4845   return res;
4846   } /* decDivideOp */
4847
4848 /* ------------------------------------------------------------------ */
4849 /* decMultiplyOp -- multiplication operation                          */
4850 /*                                                                    */
4851 /*  This routine performs the multiplication C=A x B.                 */
4852 /*                                                                    */
4853 /*   res is C, the result.  C may be A and/or B (e.g., X=X*X)         */
4854 /*   lhs is A                                                         */
4855 /*   rhs is B                                                         */
4856 /*   set is the context                                               */
4857 /*   status is the usual accumulator                                  */
4858 /*                                                                    */
4859 /* C must have space for set->digits digits.                          */
4860 /*                                                                    */
4861 /* ------------------------------------------------------------------ */
4862 /* 'Classic' multiplication is used rather than Karatsuba, as the     */
4863 /* latter would give only a minor improvement for the short numbers   */
4864 /* expected to be handled most (and uses much more memory).           */
4865 /*                                                                    */
4866 /* There are two major paths here: the general-purpose ('old code')   */
4867 /* path which handles all DECDPUN values, and a fastpath version      */
4868 /* which is used if 64-bit ints are available, DECDPUN<=4, and more   */
4869 /* than two calls to decUnitAddSub would be made.                     */
4870 /*                                                                    */
4871 /* The fastpath version lumps units together into 8-digit or 9-digit  */
4872 /* chunks, and also uses a lazy carry strategy to minimise expensive  */
4873 /* 64-bit divisions.  The chunks are then broken apart again into     */
4874 /* units for continuing processing.  Despite this overhead, the       */
4875 /* fastpath can speed up some 16-digit operations by 10x (and much    */
4876 /* more for higher-precision calculations).                           */
4877 /*                                                                    */
4878 /* A buffer always has to be used for the accumulator; in the         */
4879 /* fastpath, buffers are also always needed for the chunked copies of */
4880 /* of the operand coefficients.                                       */
4881 /* Static buffers are larger than needed just for multiply, to allow  */
4882 /* for calls from other operations (notably exp).                     */
4883 /* ------------------------------------------------------------------ */
4884 #define FASTMUL (DECUSE64 && DECDPUN<5)
4885 static decNumber * decMultiplyOp(decNumber *res, const decNumber *lhs,
4886                                  const decNumber *rhs, decContext *set,
4887                                  uInt *status) {
4888   Int    accunits;                 /* Units of accumulator in use */
4889   Int    exponent;                 /* work */
4890   Int    residue=0;                /* rounding residue */
4891   uByte  bits;                     /* result sign */
4892   Unit  *acc;                      /* -> accumulator Unit array */
4893   Int    needbytes;                /* size calculator */
4894   void  *allocacc=NULL;            /* -> allocated accumulator, iff allocated */
4895   Unit  accbuff[SD2U(DECBUFFER*4+1)]; /* buffer (+1 for DECBUFFER==0, */
4896                                    /* *4 for calls from other operations) */
4897   const Unit *mer, *mermsup;       /* work */
4898   Int   madlength;                 /* Units in multiplicand */
4899   Int   shift;                     /* Units to shift multiplicand by */
4900
4901   #if FASTMUL
4902     /* if DECDPUN is 1 or 3 work in base 10**9, otherwise */
4903     /* (DECDPUN is 2 or 4) then work in base 10**8 */
4904     #if DECDPUN & 1                /* odd */
4905       #define FASTBASE 1000000000  /* base */
4906       #define FASTDIGS          9  /* digits in base */
4907       #define FASTLAZY         18  /* carry resolution point [1->18] */
4908     #else
4909       #define FASTBASE  100000000
4910       #define FASTDIGS          8
4911       #define FASTLAZY       1844  /* carry resolution point [1->1844] */
4912     #endif
4913     /* three buffers are used, two for chunked copies of the operands */
4914     /* (base 10**8 or base 10**9) and one base 2**64 accumulator with */
4915     /* lazy carry evaluation */
4916     uInt   zlhibuff[(DECBUFFER*2+1)/8+1]; /* buffer (+1 for DECBUFFER==0) */
4917     uInt  *zlhi=zlhibuff;                 /* -> lhs array */
4918     uInt  *alloclhi=NULL;                 /* -> allocated buffer, iff allocated */
4919     uInt   zrhibuff[(DECBUFFER*2+1)/8+1]; /* buffer (+1 for DECBUFFER==0) */
4920     uInt  *zrhi=zrhibuff;                 /* -> rhs array */
4921     uInt  *allocrhi=NULL;                 /* -> allocated buffer, iff allocated */
4922     uLong  zaccbuff[(DECBUFFER*2+1)/4+2]; /* buffer (+1 for DECBUFFER==0) */
4923     /* [allocacc is shared for both paths, as only one will run] */
4924     uLong *zacc=zaccbuff;          /* -> accumulator array for exact result */
4925     #if DECDPUN==1
4926     Int    zoff;                   /* accumulator offset */
4927     #endif
4928     uInt  *lip, *rip;              /* item pointers */
4929     uInt  *lmsi, *rmsi;            /* most significant items */
4930     Int    ilhs, irhs, iacc;       /* item counts in the arrays */
4931     Int    lazy;                   /* lazy carry counter */
4932     uLong  lcarry;                 /* uLong carry */
4933     uInt   carry;                  /* carry (NB not uLong) */
4934     Int    count;                  /* work */
4935     const  Unit *cup;              /* .. */
4936     Unit  *up;                     /* .. */
4937     uLong *lp;                     /* .. */
4938     Int    p;                      /* .. */
4939   #endif
4940
4941   #if DECSUBSET
4942     decNumber *alloclhs=NULL;      /* -> allocated buffer, iff allocated */
4943     decNumber *allocrhs=NULL;      /* -> allocated buffer, iff allocated */
4944   #endif
4945
4946   #if DECCHECK
4947   if (decCheckOperands(res, lhs, rhs, set)) return res;
4948   #endif
4949
4950   /* precalculate result sign */
4951   bits=(uByte)((lhs->bits^rhs->bits)&DECNEG);
4952
4953   /* handle infinities and NaNs */
4954   if (SPECIALARGS) {               /* a special bit set */
4955     if (SPECIALARGS & (DECSNAN | DECNAN)) { /* one or two NaNs */
4956       decNaNs(res, lhs, rhs, set, status);
4957       return res;}
4958     /* one or two infinities; Infinity * 0 is invalid */
4959     if (((lhs->bits & DECINF)==0 && ISZERO(lhs))
4960       ||((rhs->bits & DECINF)==0 && ISZERO(rhs))) {
4961       *status|=DEC_Invalid_operation;
4962       return res;}
4963     decNumberZero(res);
4964     res->bits=bits|DECINF;         /* infinity */
4965     return res;}
4966
4967   /* For best speed, as in DMSRCN [the original Rexx numerics */
4968   /* module], use the shorter number as the multiplier (rhs) and */
4969   /* the longer as the multiplicand (lhs) to minimise the number of */
4970   /* adds (partial products) */
4971   if (lhs->digits<rhs->digits) {   /* swap... */
4972     const decNumber *hold=lhs;
4973     lhs=rhs;
4974     rhs=hold;
4975     }
4976
4977   do {                             /* protect allocated storage */
4978     #if DECSUBSET
4979     if (!set->extended) {
4980       /* reduce operands and set lostDigits status, as needed */
4981       if (lhs->digits>set->digits) {
4982         alloclhs=decRoundOperand(lhs, set, status);
4983         if (alloclhs==NULL) break;
4984         lhs=alloclhs;
4985         }
4986       if (rhs->digits>set->digits) {
4987         allocrhs=decRoundOperand(rhs, set, status);
4988         if (allocrhs==NULL) break;
4989         rhs=allocrhs;
4990         }
4991       }
4992     #endif
4993     /* [following code does not require input rounding] */
4994
4995     #if FASTMUL                    /* fastpath can be used */
4996     /* use the fast path if there are enough digits in the shorter */
4997     /* operand to make the setup and takedown worthwhile */
4998     #define NEEDTWO (DECDPUN*2)    /* within two decUnitAddSub calls */
4999     if (rhs->digits>NEEDTWO) {     /* use fastpath... */
5000       /* calculate the number of elements in each array */
5001       ilhs=(lhs->digits+FASTDIGS-1)/FASTDIGS; /* [ceiling] */
5002       irhs=(rhs->digits+FASTDIGS-1)/FASTDIGS; /* .. */
5003       iacc=ilhs+irhs;
5004
5005       /* allocate buffers if required, as usual */
5006       needbytes=ilhs*sizeof(uInt);
5007       if (needbytes>(Int)sizeof(zlhibuff)) {
5008         alloclhi=(uInt *)malloc(needbytes);
5009         zlhi=alloclhi;}
5010       needbytes=irhs*sizeof(uInt);
5011       if (needbytes>(Int)sizeof(zrhibuff)) {
5012         allocrhi=(uInt *)malloc(needbytes);
5013         zrhi=allocrhi;}
5014
5015       /* Allocating the accumulator space needs a special case when */
5016       /* DECDPUN=1 because when converting the accumulator to Units */
5017       /* after the multiplication each 8-byte item becomes 9 1-byte */
5018       /* units.  Therefore iacc extra bytes are needed at the front */
5019       /* (rounded up to a multiple of 8 bytes), and the uLong */
5020       /* accumulator starts offset the appropriate number of units */
5021       /* to the right to avoid overwrite during the unchunking. */
5022       needbytes=iacc*sizeof(uLong);
5023       #if DECDPUN==1
5024       zoff=(iacc+7)/8;        /* items to offset by */
5025       needbytes+=zoff*8;
5026       #endif
5027       if (needbytes>(Int)sizeof(zaccbuff)) {
5028         allocacc=(uLong *)malloc(needbytes);
5029         zacc=(uLong *)allocacc;}
5030       if (zlhi==NULL||zrhi==NULL||zacc==NULL) {
5031         *status|=DEC_Insufficient_storage;
5032         break;}
5033
5034       acc=(Unit *)zacc;       /* -> target Unit array */
5035       #if DECDPUN==1
5036       zacc+=zoff;             /* start uLong accumulator to right */
5037       #endif
5038
5039       /* assemble the chunked copies of the left and right sides */
5040       for (count=lhs->digits, cup=lhs->lsu, lip=zlhi; count>0; lip++)
5041         for (p=0, *lip=0; p<FASTDIGS && count>0;
5042              p+=DECDPUN, cup++, count-=DECDPUN)
5043           *lip+=*cup*powers[p];
5044       lmsi=lip-1;     /* save -> msi */
5045       for (count=rhs->digits, cup=rhs->lsu, rip=zrhi; count>0; rip++)
5046         for (p=0, *rip=0; p<FASTDIGS && count>0;
5047              p+=DECDPUN, cup++, count-=DECDPUN)
5048           *rip+=*cup*powers[p];
5049       rmsi=rip-1;     /* save -> msi */
5050
5051       /* zero the accumulator */
5052       for (lp=zacc; lp<zacc+iacc; lp++) *lp=0;
5053
5054       /* Start the multiplication */
5055       /* Resolving carries can dominate the cost of accumulating the */
5056       /* partial products, so this is only done when necessary. */
5057       /* Each uLong item in the accumulator can hold values up to */
5058       /* 2**64-1, and each partial product can be as large as */
5059       /* (10**FASTDIGS-1)**2.  When FASTDIGS=9, this can be added to */
5060       /* itself 18.4 times in a uLong without overflowing, so during */
5061       /* the main calculation resolution is carried out every 18th */
5062       /* add -- every 162 digits.  Similarly, when FASTDIGS=8, the */
5063       /* partial products can be added to themselves 1844.6 times in */
5064       /* a uLong without overflowing, so intermediate carry */
5065       /* resolution occurs only every 14752 digits.  Hence for common */
5066       /* short numbers usually only the one final carry resolution */
5067       /* occurs. */
5068       /* (The count is set via FASTLAZY to simplify experiments to */
5069       /* measure the value of this approach: a 35% improvement on a */
5070       /* [34x34] multiply.) */
5071       lazy=FASTLAZY;                         /* carry delay count */
5072       for (rip=zrhi; rip<=rmsi; rip++) {     /* over each item in rhs */
5073         lp=zacc+(rip-zrhi);                  /* where to add the lhs */
5074         for (lip=zlhi; lip<=lmsi; lip++, lp++) { /* over each item in lhs */
5075           *lp+=(uLong)(*lip)*(*rip);         /* [this should in-line] */
5076           } /* lip loop */
5077         lazy--;
5078         if (lazy>0 && rip!=rmsi) continue;
5079         lazy=FASTLAZY;                       /* reset delay count */
5080         /* spin up the accumulator resolving overflows */
5081         for (lp=zacc; lp<zacc+iacc; lp++) {
5082           if (*lp<FASTBASE) continue;        /* it fits */
5083           lcarry=*lp/FASTBASE;               /* top part [slow divide] */
5084           /* lcarry can exceed 2**32-1, so check again; this check */
5085           /* and occasional extra divide (slow) is well worth it, as */
5086           /* it allows FASTLAZY to be increased to 18 rather than 4 */
5087           /* in the FASTDIGS=9 case */
5088           if (lcarry<FASTBASE) carry=(uInt)lcarry;  /* [usual] */
5089            else { /* two-place carry [fairly rare] */
5090             uInt carry2=(uInt)(lcarry/FASTBASE);    /* top top part */
5091             *(lp+2)+=carry2;                        /* add to item+2 */
5092             *lp-=((uLong)FASTBASE*FASTBASE*carry2); /* [slow] */
5093             carry=(uInt)(lcarry-((uLong)FASTBASE*carry2)); /* [inline] */
5094             }
5095           *(lp+1)+=carry;                    /* add to item above [inline] */
5096           *lp-=((uLong)FASTBASE*carry);      /* [inline] */
5097           } /* carry resolution */
5098         } /* rip loop */
5099
5100       /* The multiplication is complete; time to convert back into */
5101       /* units.  This can be done in-place in the accumulator and in */
5102       /* 32-bit operations, because carries were resolved after the */
5103       /* final add.  This needs N-1 divides and multiplies for */
5104       /* each item in the accumulator (which will become up to N */
5105       /* units, where 2<=N<=9). */
5106       for (lp=zacc, up=acc; lp<zacc+iacc; lp++) {
5107         uInt item=(uInt)*lp;                 /* decapitate to uInt */
5108         for (p=0; p<FASTDIGS-DECDPUN; p+=DECDPUN, up++) {
5109           uInt part=item/(DECDPUNMAX+1);
5110           *up=(Unit)(item-(part*(DECDPUNMAX+1)));
5111           item=part;
5112           } /* p */
5113         *up=(Unit)item; up++;                /* [final needs no division] */
5114         } /* lp */
5115       accunits=up-acc;                       /* count of units */
5116       }
5117      else { /* here to use units directly, without chunking ['old code'] */
5118     #endif
5119
5120       /* if accumulator will be too long for local storage, then allocate */
5121       acc=accbuff;                 /* -> assume buffer for accumulator */
5122       needbytes=(D2U(lhs->digits)+D2U(rhs->digits))*sizeof(Unit);
5123       if (needbytes>(Int)sizeof(accbuff)) {
5124         allocacc=(Unit *)malloc(needbytes);
5125         if (allocacc==NULL) {*status|=DEC_Insufficient_storage; break;}
5126         acc=(Unit *)allocacc;                /* use the allocated space */
5127         }
5128
5129       /* Now the main long multiplication loop */
5130       /* Unlike the equivalent in the IBM Java implementation, there */
5131       /* is no advantage in calculating from msu to lsu.  So, do it */
5132       /* by the book, as it were. */
5133       /* Each iteration calculates ACC=ACC+MULTAND*MULT */
5134       accunits=1;                  /* accumulator starts at '0' */
5135       *acc=0;                      /* .. (lsu=0) */
5136       shift=0;                     /* no multiplicand shift at first */
5137       madlength=D2U(lhs->digits);  /* this won't change */
5138       mermsup=rhs->lsu+D2U(rhs->digits); /* -> msu+1 of multiplier */
5139
5140       for (mer=rhs->lsu; mer<mermsup; mer++) {
5141         /* Here, *mer is the next Unit in the multiplier to use */
5142         /* If non-zero [optimization] add it... */
5143         if (*mer!=0) accunits=decUnitAddSub(&acc[shift], accunits-shift,
5144                                             lhs->lsu, madlength, 0,
5145                                             &acc[shift], *mer)
5146                                             + shift;
5147          else { /* extend acc with a 0; it will be used shortly */
5148           *(acc+accunits)=0;       /* [this avoids length of <=0 later] */
5149           accunits++;
5150           }
5151         /* multiply multiplicand by 10**DECDPUN for next Unit to left */
5152         shift++;                   /* add this for 'logical length' */
5153         } /* n */
5154     #if FASTMUL
5155       } /* unchunked units */
5156     #endif
5157     /* common end-path */
5158     #if DECTRACE
5159       decDumpAr('*', acc, accunits);         /* Show exact result */
5160     #endif
5161
5162     /* acc now contains the exact result of the multiplication, */
5163     /* possibly with a leading zero unit; build the decNumber from */
5164     /* it, noting if any residue */
5165     res->bits=bits;                          /* set sign */
5166     res->digits=decGetDigits(acc, accunits); /* count digits exactly */
5167
5168     /* There can be a 31-bit wrap in calculating the exponent. */
5169     /* This can only happen if both input exponents are negative and */
5170     /* both their magnitudes are large.  If there was a wrap, set a */
5171     /* safe very negative exponent, from which decFinalize() will */
5172     /* raise a hard underflow shortly. */
5173     exponent=lhs->exponent+rhs->exponent;    /* calculate exponent */
5174     if (lhs->exponent<0 && rhs->exponent<0 && exponent>0)
5175       exponent=-2*DECNUMMAXE;                /* force underflow */
5176     res->exponent=exponent;                  /* OK to overwrite now */
5177
5178
5179     /* Set the coefficient.  If any rounding, residue records */
5180     decSetCoeff(res, set, acc, res->digits, &residue, status);
5181     decFinish(res, set, &residue, status);   /* final cleanup */
5182     } while(0);                         /* end protected */
5183
5184   if (allocacc!=NULL) free(allocacc);   /* drop any storage used */
5185   #if DECSUBSET
5186   if (allocrhs!=NULL) free(allocrhs);   /* .. */
5187   if (alloclhs!=NULL) free(alloclhs);   /* .. */
5188   #endif
5189   #if FASTMUL
5190   if (allocrhi!=NULL) free(allocrhi);   /* .. */
5191   if (alloclhi!=NULL) free(alloclhi);   /* .. */
5192   #endif
5193   return res;
5194   } /* decMultiplyOp */
5195
5196 /* ------------------------------------------------------------------ */
5197 /* decExpOp -- effect exponentiation                                  */
5198 /*                                                                    */
5199 /*   This computes C = exp(A)                                         */
5200 /*                                                                    */
5201 /*   res is C, the result.  C may be A                                */
5202 /*   rhs is A                                                         */
5203 /*   set is the context; note that rounding mode has no effect        */
5204 /*                                                                    */
5205 /* C must have space for set->digits digits. status is updated but    */
5206 /* not set.                                                           */
5207 /*                                                                    */
5208 /* Restrictions:                                                      */
5209 /*                                                                    */
5210 /*   digits, emax, and -emin in the context must be less than         */
5211 /*   2*DEC_MAX_MATH (1999998), and the rhs must be within these       */
5212 /*   bounds or a zero.  This is an internal routine, so these         */
5213 /*   restrictions are contractual and not enforced.                   */
5214 /*                                                                    */
5215 /* A finite result is rounded using DEC_ROUND_HALF_EVEN; it will      */
5216 /* almost always be correctly rounded, but may be up to 1 ulp in      */
5217 /* error in rare cases.                                               */
5218 /*                                                                    */
5219 /* Finite results will always be full precision and Inexact, except   */
5220 /* when A is a zero or -Infinity (giving 1 or 0 respectively).        */
5221 /* ------------------------------------------------------------------ */
5222 /* This approach used here is similar to the algorithm described in   */
5223 /*                                                                    */
5224 /*   Variable Precision Exponential Function, T. E. Hull and          */
5225 /*   A. Abrham, ACM Transactions on Mathematical Software, Vol 12 #2, */
5226 /*   pp79-91, ACM, June 1986.                                         */
5227 /*                                                                    */
5228 /* with the main difference being that the iterations in the series   */
5229 /* evaluation are terminated dynamically (which does not require the  */
5230 /* extra variable-precision variables which are expensive in this     */
5231 /* context).                                                          */
5232 /*                                                                    */
5233 /* The error analysis in Hull & Abrham's paper applies except for the */
5234 /* round-off error accumulation during the series evaluation.  This   */
5235 /* code does not precalculate the number of iterations and so cannot  */
5236 /* use Horner's scheme.  Instead, the accumulation is done at double- */
5237 /* precision, which ensures that the additions of the terms are exact */
5238 /* and do not accumulate round-off (and any round-off errors in the   */
5239 /* terms themselves move 'to the right' faster than they can          */
5240 /* accumulate).  This code also extends the calculation by allowing,  */
5241 /* in the spirit of other decNumber operators, the input to be more   */
5242 /* precise than the result (the precision used is based on the more   */
5243 /* precise of the input or requested result).                         */
5244 /*                                                                    */
5245 /* Implementation notes:                                              */
5246 /*                                                                    */
5247 /* 1. This is separated out as decExpOp so it can be called from      */
5248 /*    other Mathematical functions (notably Ln) with a wider range    */
5249 /*    than normal.  In particular, it can handle the slightly wider   */
5250 /*    (double) range needed by Ln (which has to be able to calculate  */
5251 /*    exp(-x) where x can be the tiniest number (Ntiny).              */
5252 /*                                                                    */
5253 /* 2. Normalizing x to be <=0.1 (instead of <=1) reduces loop         */
5254 /*    iterations by approximately a third with additional (although    */
5255 /*    diminishing) returns as the range is reduced to even smaller    */
5256 /*    fractions.  However, h (the power of 10 used to correct the     */
5257 /*    result at the end, see below) must be kept <=8 as otherwise     */
5258 /*    the final result cannot be computed.  Hence the leverage is a   */
5259 /*    sliding value (8-h), where potentially the range is reduced     */
5260 /*    more for smaller values.                                        */
5261 /*                                                                    */
5262 /*    The leverage that can be applied in this way is severely        */
5263 /*    limited by the cost of the raise-to-the power at the end,       */
5264 /*    which dominates when the number of iterations is small (less    */
5265 /*    than ten) or when rhs is short.  As an example, the adjustment  */
5266 /*    x**10,000,000 needs 31 multiplications, all but one full-width. */
5267 /*                                                                    */
5268 /* 3. The restrictions (especially precision) could be raised with    */
5269 /*    care, but the full decNumber range seems very hard within the   */
5270 /*    32-bit limits.                                                  */
5271 /*                                                                    */
5272 /* 4. The working precisions for the static buffers are twice the     */
5273 /*    obvious size to allow for calls from decNumberPower.            */
5274 /* ------------------------------------------------------------------ */
5275 static decNumber *decExpOp(decNumber *res, const decNumber *rhs,
5276                            decContext *set, uInt *status) {
5277   uInt ignore=0;                   /* working status */
5278   Int h;                           /* adjusted exponent for 0.xxxx */
5279   Int p;                           /* working precision */
5280   Int residue;                     /* rounding residue */
5281   uInt needbytes;                  /* for space calculations */
5282   const decNumber *x=rhs;          /* (may point to safe copy later) */
5283   decContext aset, tset, dset;     /* working contexts */
5284   Int comp;                        /* work */
5285
5286   /* the argument is often copied to normalize it, so (unusually) it */
5287   /* is treated like other buffers, using DECBUFFER, +1 in case */
5288   /* DECBUFFER is 0 */
5289   decNumber bufr[D2N(DECBUFFER*2+1)];
5290   decNumber *allocrhs=NULL;        /* non-NULL if rhs buffer allocated */
5291
5292   /* the working precision will be no more than set->digits+8+1 */
5293   /* so for on-stack buffers DECBUFFER+9 is used, +1 in case DECBUFFER */
5294   /* is 0 (and twice that for the accumulator) */
5295
5296   /* buffer for t, term (working precision plus) */
5297   decNumber buft[D2N(DECBUFFER*2+9+1)];
5298   decNumber *allocbuft=NULL;       /* -> allocated buft, iff allocated */
5299   decNumber *t=buft;               /* term */
5300   /* buffer for a, accumulator (working precision * 2), at least 9 */
5301   decNumber bufa[D2N(DECBUFFER*4+18+1)];
5302   decNumber *allocbufa=NULL;       /* -> allocated bufa, iff allocated */
5303   decNumber *a=bufa;               /* accumulator */
5304   /* decNumber for the divisor term; this needs at most 9 digits */
5305   /* and so can be fixed size [16 so can use standard context] */
5306   decNumber bufd[D2N(16)];
5307   decNumber *d=bufd;               /* divisor */
5308   decNumber numone;                /* constant 1 */
5309
5310   #if DECCHECK
5311   Int iterations=0;                /* for later sanity check */
5312   if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
5313   #endif
5314
5315   do {                                  /* protect allocated storage */
5316     if (SPECIALARG) {                   /* handle infinities and NaNs */
5317       if (decNumberIsInfinite(rhs)) {   /* an infinity */
5318         if (decNumberIsNegative(rhs))   /* -Infinity -> +0 */
5319           decNumberZero(res);
5320          else decNumberCopy(res, rhs);  /* +Infinity -> self */
5321         }
5322        else decNaNs(res, rhs, NULL, set, status); /* a NaN */
5323       break;}
5324
5325     if (ISZERO(rhs)) {                  /* zeros -> exact 1 */
5326       decNumberZero(res);               /* make clean 1 */
5327       *res->lsu=1;                      /* .. */
5328       break;}                           /* [no status to set] */
5329
5330     /* e**x when 0 < x < 0.66 is < 1+3x/2, hence can fast-path */
5331     /* positive and negative tiny cases which will result in inexact */
5332     /* 1.  This also allows the later add-accumulate to always be */
5333     /* exact (because its length will never be more than twice the */
5334     /* working precision). */
5335     /* The comparator (tiny) needs just one digit, so use the */
5336     /* decNumber d for it (reused as the divisor, etc., below); its */
5337     /* exponent is such that if x is positive it will have */
5338     /* set->digits-1 zeros between the decimal point and the digit, */
5339     /* which is 4, and if x is negative one more zero there as the */
5340     /* more precise result will be of the form 0.9999999 rather than */
5341     /* 1.0000001.  Hence, tiny will be 0.0000004  if digits=7 and x>0 */
5342     /* or 0.00000004 if digits=7 and x<0.  If RHS not larger than */
5343     /* this then the result will be 1.000000 */
5344     decNumberZero(d);                   /* clean */
5345     *d->lsu=4;                          /* set 4 .. */
5346     d->exponent=-set->digits;           /* * 10**(-d) */
5347     if (decNumberIsNegative(rhs)) d->exponent--;  /* negative case */
5348     comp=decCompare(d, rhs, 1);         /* signless compare */
5349     if (comp==BADINT) {
5350       *status|=DEC_Insufficient_storage;
5351       break;}
5352     if (comp>=0) {                      /* rhs < d */
5353       Int shift=set->digits-1;
5354       decNumberZero(res);               /* set 1 */
5355       *res->lsu=1;                      /* .. */
5356       res->digits=decShiftToMost(res->lsu, 1, shift);
5357       res->exponent=-shift;                  /* make 1.0000... */
5358       *status|=DEC_Inexact | DEC_Rounded;    /* .. inexactly */
5359       break;} /* tiny */
5360
5361     /* set up the context to be used for calculating a, as this is */
5362     /* used on both paths below */
5363     decContextDefault(&aset, DEC_INIT_DECIMAL64);
5364     /* accumulator bounds are as requested (could underflow) */
5365     aset.emax=set->emax;                /* usual bounds */
5366     aset.emin=set->emin;                /* .. */
5367     aset.clamp=0;                       /* and no concrete format */
5368
5369     /* calculate the adjusted (Hull & Abrham) exponent (where the */
5370     /* decimal point is just to the left of the coefficient msd) */
5371     h=rhs->exponent+rhs->digits;
5372     /* if h>8 then 10**h cannot be calculated safely; however, when */
5373     /* h=8 then exp(|rhs|) will be at least exp(1E+7) which is at */
5374     /* least 6.59E+4342944, so (due to the restriction on Emax/Emin) */
5375     /* overflow (or underflow to 0) is guaranteed -- so this case can */
5376     /* be handled by simply forcing the appropriate excess */
5377     if (h>8) {                          /* overflow/underflow */
5378       /* set up here so Power call below will over or underflow to */
5379       /* zero; set accumulator to either 2 or 0.02 */
5380       /* [stack buffer for a is always big enough for this] */
5381       decNumberZero(a);
5382       *a->lsu=2;                        /* not 1 but < exp(1) */
5383       if (decNumberIsNegative(rhs)) a->exponent=-2; /* make 0.02 */
5384       h=8;                              /* clamp so 10**h computable */
5385       p=9;                              /* set a working precision */
5386       }
5387      else {                             /* h<=8 */
5388       Int maxlever=(rhs->digits>8?1:0);
5389       /* [could/should increase this for precisions >40 or so, too] */
5390
5391       /* if h is 8, cannot normalize to a lower upper limit because */
5392       /* the final result will not be computable (see notes above), */
5393       /* but leverage can be applied whenever h is less than 8. */
5394       /* Apply as much as possible, up to a MAXLEVER digits, which */
5395       /* sets the tradeoff against the cost of the later a**(10**h). */
5396       /* As h is increased, the working precision below also */
5397       /* increases to compensate for the "constant digits at the */
5398       /* front" effect. */
5399       Int lever=MINI(8-h, maxlever);    /* leverage attainable */
5400       Int use=-rhs->digits-lever;       /* exponent to use for RHS */
5401       h+=lever;                         /* apply leverage selected */
5402       if (h<0) {                        /* clamp */
5403         use+=h;                         /* [may end up subnormal] */
5404         h=0;
5405         }
5406       /* Take a copy of RHS if it needs normalization (true whenever x>=1) */
5407       if (rhs->exponent!=use) {
5408         decNumber *newrhs=bufr;         /* assume will fit on stack */
5409         needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit);
5410         if (needbytes>sizeof(bufr)) {   /* need malloc space */
5411           allocrhs=(decNumber *)malloc(needbytes);
5412           if (allocrhs==NULL) {         /* hopeless -- abandon */
5413             *status|=DEC_Insufficient_storage;
5414             break;}
5415           newrhs=allocrhs;              /* use the allocated space */
5416           }
5417         decNumberCopy(newrhs, rhs);     /* copy to safe space */
5418         newrhs->exponent=use;           /* normalize; now <1 */
5419         x=newrhs;                       /* ready for use */
5420         /* decNumberShow(x); */
5421         }
5422
5423       /* Now use the usual power series to evaluate exp(x).  The */
5424       /* series starts as 1 + x + x^2/2 ... so prime ready for the */
5425       /* third term by setting the term variable t=x, the accumulator */
5426       /* a=1, and the divisor d=2. */
5427
5428       /* First determine the working precision.  From Hull & Abrham */
5429       /* this is set->digits+h+2.  However, if x is 'over-precise' we */
5430       /* need to allow for all its digits to potentially participate */
5431       /* (consider an x where all the excess digits are 9s) so in */
5432       /* this case use x->digits+h+2 */
5433       p=MAXI(x->digits, set->digits)+h+2;    /* [h<=8] */
5434
5435       /* a and t are variable precision, and depend on p, so space */
5436       /* must be allocated for them if necessary */
5437
5438       /* the accumulator needs to be able to hold 2p digits so that */
5439       /* the additions on the second and subsequent iterations are */
5440       /* sufficiently exact. */
5441       needbytes=sizeof(decNumber)+(D2U(p*2)-1)*sizeof(Unit);
5442       if (needbytes>sizeof(bufa)) {     /* need malloc space */
5443         allocbufa=(decNumber *)malloc(needbytes);
5444         if (allocbufa==NULL) {          /* hopeless -- abandon */
5445           *status|=DEC_Insufficient_storage;
5446           break;}
5447         a=allocbufa;                    /* use the allocated space */
5448         }
5449       /* the term needs to be able to hold p digits (which is */
5450       /* guaranteed to be larger than x->digits, so the initial copy */
5451       /* is safe); it may also be used for the raise-to-power */
5452       /* calculation below, which needs an extra two digits */
5453       needbytes=sizeof(decNumber)+(D2U(p+2)-1)*sizeof(Unit);
5454       if (needbytes>sizeof(buft)) {     /* need malloc space */
5455         allocbuft=(decNumber *)malloc(needbytes);
5456         if (allocbuft==NULL) {          /* hopeless -- abandon */
5457           *status|=DEC_Insufficient_storage;
5458           break;}
5459         t=allocbuft;                    /* use the allocated space */
5460         }
5461
5462       decNumberCopy(t, x);              /* term=x */
5463       decNumberZero(a); *a->lsu=1;      /* accumulator=1 */
5464       decNumberZero(d); *d->lsu=2;      /* divisor=2 */
5465       decNumberZero(&numone); *numone.lsu=1; /* constant 1 for increment */
5466
5467       /* set up the contexts for calculating a, t, and d */
5468       decContextDefault(&tset, DEC_INIT_DECIMAL64);
5469       dset=tset;
5470       /* accumulator bounds are set above, set precision now */
5471       aset.digits=p*2;                  /* double */
5472       /* term bounds avoid any underflow or overflow */
5473       tset.digits=p;
5474       tset.emin=DEC_MIN_EMIN;           /* [emax is plenty] */
5475       /* [dset.digits=16, etc., are sufficient] */
5476
5477       /* finally ready to roll */
5478       for (;;) {
5479         #if DECCHECK
5480         iterations++;
5481         #endif
5482         /* only the status from the accumulation is interesting */
5483         /* [but it should remain unchanged after first add] */
5484         decAddOp(a, a, t, &aset, 0, status);           /* a=a+t */
5485         decMultiplyOp(t, t, x, &tset, &ignore);        /* t=t*x */
5486         decDivideOp(t, t, d, &tset, DIVIDE, &ignore);  /* t=t/d */
5487         /* the iteration ends when the term cannot affect the result, */
5488         /* if rounded to p digits, which is when its value is smaller */
5489         /* than the accumulator by p+1 digits.  There must also be */
5490         /* full precision in a. */
5491         if (((a->digits+a->exponent)>=(t->digits+t->exponent+p+1))
5492             && (a->digits>=p)) break;
5493         decAddOp(d, d, &numone, &dset, 0, &ignore);    /* d=d+1 */
5494         } /* iterate */
5495
5496       #if DECCHECK
5497       /* just a sanity check; comment out test to show always */
5498       if (iterations>p+3)
5499         printf("Exp iterations=%ld, status=%08lx, p=%ld, d=%ld\n",
5500                iterations, *status, p, x->digits);
5501       #endif
5502       } /* h<=8 */
5503
5504     /* apply postconditioning: a=a**(10**h) -- this is calculated */
5505     /* at a slightly higher precision than Hull & Abrham suggest */
5506     if (h>0) {
5507       Int seenbit=0;               /* set once a 1-bit is seen */
5508       Int i;                       /* counter */
5509       Int n=powers[h];             /* always positive */
5510       aset.digits=p+2;             /* sufficient precision */
5511       /* avoid the overhead and many extra digits of decNumberPower */
5512       /* as all that is needed is the short 'multipliers' loop; here */
5513       /* accumulate the answer into t */
5514       decNumberZero(t); *t->lsu=1; /* acc=1 */
5515       for (i=1;;i++){              /* for each bit [top bit ignored] */
5516         /* abandon if have had overflow or terminal underflow */
5517         if (*status & (DEC_Overflow|DEC_Underflow)) { /* interesting? */
5518           if (*status&DEC_Overflow || ISZERO(t)) break;}
5519         n=n<<1;                    /* move next bit to testable position */
5520         if (n<0) {                 /* top bit is set */
5521           seenbit=1;               /* OK, have a significant bit */
5522           decMultiplyOp(t, t, a, &aset, status); /* acc=acc*x */
5523           }
5524         if (i==31) break;          /* that was the last bit */
5525         if (!seenbit) continue;    /* no need to square 1 */
5526         decMultiplyOp(t, t, t, &aset, status); /* acc=acc*acc [square] */
5527         } /*i*/ /* 32 bits */
5528       /* decNumberShow(t); */
5529       a=t;                         /* and carry on using t instead of a */
5530       }
5531
5532     /* Copy and round the result to res */
5533     residue=1;                          /* indicate dirt to right .. */
5534     if (ISZERO(a)) residue=0;           /* .. unless underflowed to 0 */
5535     aset.digits=set->digits;            /* [use default rounding] */
5536     decCopyFit(res, a, &aset, &residue, status); /* copy & shorten */
5537     decFinish(res, set, &residue, status);       /* cleanup/set flags */
5538     } while(0);                         /* end protected */
5539
5540   if (allocrhs !=NULL) free(allocrhs);  /* drop any storage used */
5541   if (allocbufa!=NULL) free(allocbufa); /* .. */
5542   if (allocbuft!=NULL) free(allocbuft); /* .. */
5543   /* [status is handled by caller] */
5544   return res;
5545   } /* decExpOp */
5546
5547 /* ------------------------------------------------------------------ */
5548 /* Initial-estimate natural logarithm table                           */
5549 /*                                                                    */
5550 /*   LNnn -- 90-entry 16-bit table for values from .10 through .99.   */
5551 /*           The result is a 4-digit encode of the coefficient (c=the */
5552 /*           top 14 bits encoding 0-9999) and a 2-digit encode of the */
5553 /*           exponent (e=the bottom 2 bits encoding 0-3)              */
5554 /*                                                                    */
5555 /*           The resulting value is given by:                         */
5556 /*                                                                    */
5557 /*             v = -c * 10**(-e-3)                                    */
5558 /*                                                                    */
5559 /*           where e and c are extracted from entry k = LNnn[x-10]    */
5560 /*           where x is truncated (NB) into the range 10 through 99,  */
5561 /*           and then c = k>>2 and e = k&3.                           */
5562 /* ------------------------------------------------------------------ */
5563 static const uShort LNnn[90] = {
5564   9016,  8652,  8316,  8008,  7724,  7456,  7208,
5565   6972,  6748,  6540,  6340,  6148,  5968,  5792,  5628,  5464,  5312,
5566   5164,  5020,  4884,  4748,  4620,  4496,  4376,  4256,  4144,  4032,
5567  39233, 38181, 37157, 36157, 35181, 34229, 33297, 32389, 31501, 30629,
5568  29777, 28945, 28129, 27329, 26545, 25777, 25021, 24281, 23553, 22837,
5569  22137, 21445, 20769, 20101, 19445, 18801, 18165, 17541, 16925, 16321,
5570  15721, 15133, 14553, 13985, 13421, 12865, 12317, 11777, 11241, 10717,
5571  10197,  9685,  9177,  8677,  8185,  7697,  7213,  6737,  6269,  5801,
5572   5341,  4889,  4437, 39930, 35534, 31186, 26886, 22630, 18418, 14254,
5573  10130,  6046, 20055};
5574
5575 /* ------------------------------------------------------------------ */
5576 /* decLnOp -- effect natural logarithm                                */
5577 /*                                                                    */
5578 /*   This computes C = ln(A)                                          */
5579 /*                                                                    */
5580 /*   res is C, the result.  C may be A                                */
5581 /*   rhs is A                                                         */
5582 /*   set is the context; note that rounding mode has no effect        */
5583 /*                                                                    */
5584 /* C must have space for set->digits digits.                          */
5585 /*                                                                    */
5586 /* Notable cases:                                                     */
5587 /*   A<0 -> Invalid                                                   */
5588 /*   A=0 -> -Infinity (Exact)                                         */
5589 /*   A=+Infinity -> +Infinity (Exact)                                 */
5590 /*   A=1 exactly -> 0 (Exact)                                         */
5591 /*                                                                    */
5592 /* Restrictions (as for Exp):                                         */
5593 /*                                                                    */
5594 /*   digits, emax, and -emin in the context must be less than         */
5595 /*   DEC_MAX_MATH+11 (1000010), and the rhs must be within these      */
5596 /*   bounds or a zero.  This is an internal routine, so these         */
5597 /*   restrictions are contractual and not enforced.                   */
5598 /*                                                                    */
5599 /* A finite result is rounded using DEC_ROUND_HALF_EVEN; it will      */
5600 /* almost always be correctly rounded, but may be up to 1 ulp in      */
5601 /* error in rare cases.                                               */
5602 /* ------------------------------------------------------------------ */
5603 /* The result is calculated using Newton's method, with each          */
5604 /* iteration calculating a' = a + x * exp(-a) - 1.  See, for example, */
5605 /* Epperson 1989.                                                     */
5606 /*                                                                    */
5607 /* The iteration ends when the adjustment x*exp(-a)-1 is tiny enough. */
5608 /* This has to be calculated at the sum of the precision of x and the */
5609 /* working precision.                                                 */
5610 /*                                                                    */
5611 /* Implementation notes:                                              */
5612 /*                                                                    */
5613 /* 1. This is separated out as decLnOp so it can be called from       */
5614 /*    other Mathematical functions (e.g., Log 10) with a wider range  */
5615 /*    than normal.  In particular, it can handle the slightly wider   */
5616 /*    (+9+2) range needed by a power function.                        */
5617 /*                                                                    */
5618 /* 2. The speed of this function is about 10x slower than exp, as     */
5619 /*    it typically needs 4-6 iterations for short numbers, and the    */
5620 /*    extra precision needed adds a squaring effect, twice.           */
5621 /*                                                                    */
5622 /* 3. Fastpaths are included for ln(10) and ln(2), up to length 40,   */
5623 /*    as these are common requests.  ln(10) is used by log10(x).      */
5624 /*                                                                    */
5625 /* 4. An iteration might be saved by widening the LNnn table, and     */
5626 /*    would certainly save at least one if it were made ten times     */
5627 /*    bigger, too (for truncated fractions 0.100 through 0.999).      */
5628 /*    However, for most practical evaluations, at least four or five  */
5629 /*    iterations will be neede -- so this would only speed up by      */
5630 /*    20-25% and that probably does not justify increasing the table  */
5631 /*    size.                                                           */
5632 /*                                                                    */
5633 /* 5. The static buffers are larger than might be expected to allow   */
5634 /*    for calls from decNumberPower.                                  */
5635 /* ------------------------------------------------------------------ */
5636 static decNumber *decLnOp(decNumber *res, const decNumber *rhs,
5637                           decContext *set, uInt *status) {
5638   uInt ignore=0;                   /* working status accumulator */
5639   uInt needbytes;                  /* for space calculations */
5640   Int residue;                     /* rounding residue */
5641   Int r;                           /* rhs=f*10**r [see below] */
5642   Int p;                           /* working precision */
5643   Int pp;                          /* precision for iteration */
5644   Int t;                           /* work */
5645
5646   /* buffers for a (accumulator, typically precision+2) and b */
5647   /* (adjustment calculator, same size) */
5648   decNumber bufa[D2N(DECBUFFER+12)];
5649   decNumber *allocbufa=NULL;       /* -> allocated bufa, iff allocated */
5650   decNumber *a=bufa;               /* accumulator/work */
5651   decNumber bufb[D2N(DECBUFFER*2+2)];
5652   decNumber *allocbufb=NULL;       /* -> allocated bufa, iff allocated */
5653   decNumber *b=bufb;               /* adjustment/work */
5654
5655   decNumber  numone;               /* constant 1 */
5656   decNumber  cmp;                  /* work */
5657   decContext aset, bset;           /* working contexts */
5658
5659   #if DECCHECK
5660   Int iterations=0;                /* for later sanity check */
5661   if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
5662   #endif
5663
5664   do {                                  /* protect allocated storage */
5665     if (SPECIALARG) {                   /* handle infinities and NaNs */
5666       if (decNumberIsInfinite(rhs)) {   /* an infinity */
5667         if (decNumberIsNegative(rhs))   /* -Infinity -> error */
5668           *status|=DEC_Invalid_operation;
5669          else decNumberCopy(res, rhs);  /* +Infinity -> self */
5670         }
5671        else decNaNs(res, rhs, NULL, set, status); /* a NaN */
5672       break;}
5673
5674     if (ISZERO(rhs)) {                  /* +/- zeros -> -Infinity */
5675       decNumberZero(res);               /* make clean */
5676       res->bits=DECINF|DECNEG;          /* set - infinity */
5677       break;}                           /* [no status to set] */
5678
5679     /* Non-zero negatives are bad... */
5680     if (decNumberIsNegative(rhs)) {     /* -x -> error */
5681       *status|=DEC_Invalid_operation;
5682       break;}
5683
5684     /* Here, rhs is positive, finite, and in range */
5685
5686     /* lookaside fastpath code for ln(2) and ln(10) at common lengths */
5687     if (rhs->exponent==0 && set->digits<=40) {
5688       #if DECDPUN==1
5689       if (rhs->lsu[0]==0 && rhs->lsu[1]==1 && rhs->digits==2) { /* ln(10) */
5690       #else
5691       if (rhs->lsu[0]==10 && rhs->digits==2) {                  /* ln(10) */
5692       #endif
5693         aset=*set; aset.round=DEC_ROUND_HALF_EVEN;
5694         #define LN10 "2.302585092994045684017991454684364207601"
5695         decNumberFromString(res, LN10, &aset);
5696         *status|=(DEC_Inexact | DEC_Rounded); /* is inexact */
5697         break;}
5698       if (rhs->lsu[0]==2 && rhs->digits==1) { /* ln(2) */
5699         aset=*set; aset.round=DEC_ROUND_HALF_EVEN;
5700         #define LN2 "0.6931471805599453094172321214581765680755"
5701         decNumberFromString(res, LN2, &aset);
5702         *status|=(DEC_Inexact | DEC_Rounded);
5703         break;}
5704       } /* integer and short */
5705
5706     /* Determine the working precision.  This is normally the */
5707     /* requested precision + 2, with a minimum of 9.  However, if */
5708     /* the rhs is 'over-precise' then allow for all its digits to */
5709     /* potentially participate (consider an rhs where all the excess */
5710     /* digits are 9s) so in this case use rhs->digits+2. */
5711     p=MAXI(rhs->digits, MAXI(set->digits, 7))+2;
5712
5713     /* Allocate space for the accumulator and the high-precision */
5714     /* adjustment calculator, if necessary.  The accumulator must */
5715     /* be able to hold p digits, and the adjustment up to */
5716     /* rhs->digits+p digits.  They are also made big enough for 16 */
5717     /* digits so that they can be used for calculating the initial */
5718     /* estimate. */
5719     needbytes=sizeof(decNumber)+(D2U(MAXI(p,16))-1)*sizeof(Unit);
5720     if (needbytes>sizeof(bufa)) {     /* need malloc space */
5721       allocbufa=(decNumber *)malloc(needbytes);
5722       if (allocbufa==NULL) {          /* hopeless -- abandon */
5723         *status|=DEC_Insufficient_storage;
5724         break;}
5725       a=allocbufa;                    /* use the allocated space */
5726       }
5727     pp=p+rhs->digits;
5728     needbytes=sizeof(decNumber)+(D2U(MAXI(pp,16))-1)*sizeof(Unit);
5729     if (needbytes>sizeof(bufb)) {     /* need malloc space */
5730       allocbufb=(decNumber *)malloc(needbytes);
5731       if (allocbufb==NULL) {          /* hopeless -- abandon */
5732         *status|=DEC_Insufficient_storage;
5733         break;}
5734       b=allocbufb;                    /* use the allocated space */
5735       }
5736
5737     /* Prepare an initial estimate in acc. Calculate this by */
5738     /* considering the coefficient of x to be a normalized fraction, */
5739     /* f, with the decimal point at far left and multiplied by */
5740     /* 10**r.  Then, rhs=f*10**r and 0.1<=f<1, and */
5741     /*   ln(x) = ln(f) + ln(10)*r */
5742     /* Get the initial estimate for ln(f) from a small lookup */
5743     /* table (see above) indexed by the first two digits of f, */
5744     /* truncated. */
5745
5746     decContextDefault(&aset, DEC_INIT_DECIMAL64); /* 16-digit extended */
5747     r=rhs->exponent+rhs->digits;        /* 'normalised' exponent */
5748     decNumberFromInt32(a, r);           /* a=r */
5749     decNumberFromInt32(b, 2302585);     /* b=ln(10) (2.302585) */
5750     b->exponent=-6;                     /*  .. */
5751     decMultiplyOp(a, a, b, &aset, &ignore);  /* a=a*b */
5752     /* now get top two digits of rhs into b by simple truncate and */
5753     /* force to integer */
5754     residue=0;                          /* (no residue) */
5755     aset.digits=2; aset.round=DEC_ROUND_DOWN;
5756     decCopyFit(b, rhs, &aset, &residue, &ignore); /* copy & shorten */
5757     b->exponent=0;                      /* make integer */
5758     t=decGetInt(b);                     /* [cannot fail] */
5759     if (t<10) t=X10(t);                 /* adjust single-digit b */
5760     t=LNnn[t-10];                       /* look up ln(b) */
5761     decNumberFromInt32(b, t>>2);        /* b=ln(b) coefficient */
5762     b->exponent=-(t&3)-3;               /* set exponent */
5763     b->bits=DECNEG;                     /* ln(0.10)->ln(0.99) always -ve */
5764     aset.digits=16; aset.round=DEC_ROUND_HALF_EVEN; /* restore */
5765     decAddOp(a, a, b, &aset, 0, &ignore); /* acc=a+b */
5766     /* the initial estimate is now in a, with up to 4 digits correct. */
5767     /* When rhs is at or near Nmax the estimate will be low, so we */
5768     /* will approach it from below, avoiding overflow when calling exp. */
5769
5770     decNumberZero(&numone); *numone.lsu=1;   /* constant 1 for adjustment */
5771
5772     /* accumulator bounds are as requested (could underflow, but */
5773     /* cannot overflow) */
5774     aset.emax=set->emax;
5775     aset.emin=set->emin;
5776     aset.clamp=0;                       /* no concrete format */
5777     /* set up a context to be used for the multiply and subtract */
5778     bset=aset;
5779     bset.emax=DEC_MAX_MATH*2;           /* use double bounds for the */
5780     bset.emin=-DEC_MAX_MATH*2;          /* adjustment calculation */
5781                                         /* [see decExpOp call below] */
5782     /* for each iteration double the number of digits to calculate, */
5783     /* up to a maximum of p */
5784     pp=9;                               /* initial precision */
5785     /* [initially 9 as then the sequence starts 7+2, 16+2, and */
5786     /* 34+2, which is ideal for standard-sized numbers] */
5787     aset.digits=pp;                     /* working context */
5788     bset.digits=pp+rhs->digits;         /* wider context */
5789     for (;;) {                          /* iterate */
5790       #if DECCHECK
5791       iterations++;
5792       if (iterations>24) break;         /* consider 9 * 2**24 */
5793       #endif
5794       /* calculate the adjustment (exp(-a)*x-1) into b.  This is a */
5795       /* catastrophic subtraction but it really is the difference */
5796       /* from 1 that is of interest. */
5797       /* Use the internal entry point to Exp as it allows the double */
5798       /* range for calculating exp(-a) when a is the tiniest subnormal. */
5799       a->bits^=DECNEG;                  /* make -a */
5800       decExpOp(b, a, &bset, &ignore);   /* b=exp(-a) */
5801       a->bits^=DECNEG;                  /* restore sign of a */
5802       /* now multiply by rhs and subtract 1, at the wider precision */
5803       decMultiplyOp(b, b, rhs, &bset, &ignore);        /* b=b*rhs */
5804       decAddOp(b, b, &numone, &bset, DECNEG, &ignore); /* b=b-1 */
5805
5806       /* the iteration ends when the adjustment cannot affect the */
5807       /* result by >=0.5 ulp (at the requested digits), which */
5808       /* is when its value is smaller than the accumulator by */
5809       /* set->digits+1 digits (or it is zero) -- this is a looser */
5810       /* requirement than for Exp because all that happens to the */
5811       /* accumulator after this is the final rounding (but note that */
5812       /* there must also be full precision in a, or a=0). */
5813
5814       if (decNumberIsZero(b) ||
5815           (a->digits+a->exponent)>=(b->digits+b->exponent+set->digits+1)) {
5816         if (a->digits==p) break;
5817         if (decNumberIsZero(a)) {
5818           decCompareOp(&cmp, rhs, &numone, &aset, COMPARE, &ignore); /* rhs=1 ? */
5819           if (cmp.lsu[0]==0) a->exponent=0;            /* yes, exact 0 */
5820            else *status|=(DEC_Inexact | DEC_Rounded);  /* no, inexact */
5821           break;
5822           }
5823         /* force padding if adjustment has gone to 0 before full length */
5824         if (decNumberIsZero(b)) b->exponent=a->exponent-p;
5825         }
5826
5827       /* not done yet ... */
5828       decAddOp(a, a, b, &aset, 0, &ignore);  /* a=a+b for next estimate */
5829       if (pp==p) continue;                   /* precision is at maximum */
5830       /* lengthen the next calculation */
5831       pp=pp*2;                               /* double precision */
5832       if (pp>p) pp=p;                        /* clamp to maximum */
5833       aset.digits=pp;                        /* working context */
5834       bset.digits=pp+rhs->digits;            /* wider context */
5835       } /* Newton's iteration */
5836
5837     #if DECCHECK
5838     /* just a sanity check; remove the test to show always */
5839     if (iterations>24)
5840       printf("Ln iterations=%ld, status=%08lx, p=%ld, d=%ld\n",
5841             iterations, *status, p, rhs->digits);
5842     #endif
5843
5844     /* Copy and round the result to res */
5845     residue=1;                          /* indicate dirt to right */
5846     if (ISZERO(a)) residue=0;           /* .. unless underflowed to 0 */
5847     aset.digits=set->digits;            /* [use default rounding] */
5848     decCopyFit(res, a, &aset, &residue, status); /* copy & shorten */
5849     decFinish(res, set, &residue, status);       /* cleanup/set flags */
5850     } while(0);                         /* end protected */
5851
5852   if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */
5853   if (allocbufb!=NULL) free(allocbufb); /* .. */
5854   /* [status is handled by caller] */
5855   return res;
5856   } /* decLnOp */
5857
5858 /* ------------------------------------------------------------------ */
5859 /* decQuantizeOp  -- force exponent to requested value                */
5860 /*                                                                    */
5861 /*   This computes C = op(A, B), where op adjusts the coefficient     */
5862 /*   of C (by rounding or shifting) such that the exponent (-scale)   */
5863 /*   of C has the value B or matches the exponent of B.               */
5864 /*   The numerical value of C will equal A, except for the effects of */
5865 /*   any rounding that occurred.                                      */
5866 /*                                                                    */
5867 /*   res is C, the result.  C may be A or B                           */
5868 /*   lhs is A, the number to adjust                                   */
5869 /*   rhs is B, the requested exponent                                 */
5870 /*   set is the context                                               */
5871 /*   quant is 1 for quantize or 0 for rescale                         */
5872 /*   status is the status accumulator (this can be called without     */
5873 /*          risk of control loss)                                     */
5874 /*                                                                    */
5875 /* C must have space for set->digits digits.                          */
5876 /*                                                                    */
5877 /* Unless there is an error or the result is infinite, the exponent   */
5878 /* after the operation is guaranteed to be that requested.            */
5879 /* ------------------------------------------------------------------ */
5880 static decNumber * decQuantizeOp(decNumber *res, const decNumber *lhs,
5881                                  const decNumber *rhs, decContext *set,
5882                                  Flag quant, uInt *status) {
5883   #if DECSUBSET
5884   decNumber *alloclhs=NULL;        /* non-NULL if rounded lhs allocated */
5885   decNumber *allocrhs=NULL;        /* .., rhs */
5886   #endif
5887   const decNumber *inrhs=rhs;      /* save original rhs */
5888   Int   reqdigits=set->digits;     /* requested DIGITS */
5889   Int   reqexp;                    /* requested exponent [-scale] */
5890   Int   residue=0;                 /* rounding residue */
5891   Int   etiny=set->emin-(reqdigits-1);
5892
5893   #if DECCHECK
5894   if (decCheckOperands(res, lhs, rhs, set)) return res;
5895   #endif
5896
5897   do {                             /* protect allocated storage */
5898     #if DECSUBSET
5899     if (!set->extended) {
5900       /* reduce operands and set lostDigits status, as needed */
5901       if (lhs->digits>reqdigits) {
5902         alloclhs=decRoundOperand(lhs, set, status);
5903         if (alloclhs==NULL) break;
5904         lhs=alloclhs;
5905         }
5906       if (rhs->digits>reqdigits) { /* [this only checks lostDigits] */
5907         allocrhs=decRoundOperand(rhs, set, status);
5908         if (allocrhs==NULL) break;
5909         rhs=allocrhs;
5910         }
5911       }
5912     #endif
5913     /* [following code does not require input rounding] */
5914
5915     /* Handle special values */
5916     if (SPECIALARGS) {
5917       /* NaNs get usual processing */
5918       if (SPECIALARGS & (DECSNAN | DECNAN))
5919         decNaNs(res, lhs, rhs, set, status);
5920       /* one infinity but not both is bad */
5921       else if ((lhs->bits ^ rhs->bits) & DECINF)
5922         *status|=DEC_Invalid_operation;
5923       /* both infinity: return lhs */
5924       else decNumberCopy(res, lhs);          /* [nop if in place] */
5925       break;
5926       }
5927
5928     /* set requested exponent */
5929     if (quant) reqexp=inrhs->exponent;  /* quantize -- match exponents */
5930      else {                             /* rescale -- use value of rhs */
5931       /* Original rhs must be an integer that fits and is in range, */
5932       /* which could be from -1999999997 to +999999999, thanks to */
5933       /* subnormals */
5934       reqexp=decGetInt(inrhs);               /* [cannot fail] */
5935       }
5936
5937     #if DECSUBSET
5938     if (!set->extended) etiny=set->emin;     /* no subnormals */
5939     #endif
5940
5941     if (reqexp==BADINT                       /* bad (rescale only) or .. */
5942      || reqexp==BIGODD || reqexp==BIGEVEN    /* very big (ditto) or .. */
5943      || (reqexp<etiny)                       /* < lowest */
5944      || (reqexp>set->emax)) {                /* > emax */
5945       *status|=DEC_Invalid_operation;
5946       break;}
5947
5948     /* the RHS has been processed, so it can be overwritten now if necessary */
5949     if (ISZERO(lhs)) {                       /* zero coefficient unchanged */
5950       decNumberCopy(res, lhs);               /* [nop if in place] */
5951       res->exponent=reqexp;                  /* .. just set exponent */
5952       #if DECSUBSET
5953       if (!set->extended) res->bits=0;       /* subset specification; no -0 */
5954       #endif
5955       }
5956      else {                                  /* non-zero lhs */
5957       Int adjust=reqexp-lhs->exponent;       /* digit adjustment needed */
5958       /* if adjusted coefficient will definitely not fit, give up now */
5959       if ((lhs->digits-adjust)>reqdigits) {
5960         *status|=DEC_Invalid_operation;
5961         break;
5962         }
5963
5964       if (adjust>0) {                        /* increasing exponent */
5965         /* this will decrease the length of the coefficient by adjust */
5966         /* digits, and must round as it does so */
5967         decContext workset;                  /* work */
5968         workset=*set;                        /* clone rounding, etc. */
5969         workset.digits=lhs->digits-adjust;   /* set requested length */
5970         /* [note that the latter can be <1, here] */
5971         decCopyFit(res, lhs, &workset, &residue, status); /* fit to result */
5972         decApplyRound(res, &workset, residue, status);    /* .. and round */
5973         residue=0;                                        /* [used] */
5974         /* If just rounded a 999s case, exponent will be off by one; */
5975         /* adjust back (after checking space), if so. */
5976         if (res->exponent>reqexp) {
5977           /* re-check needed, e.g., for quantize(0.9999, 0.001) under */
5978           /* set->digits==3 */
5979           if (res->digits==reqdigits) {      /* cannot shift by 1 */
5980             *status&=~(DEC_Inexact | DEC_Rounded); /* [clean these] */
5981             *status|=DEC_Invalid_operation;
5982             break;
5983             }
5984           res->digits=decShiftToMost(res->lsu, res->digits, 1); /* shift */
5985           res->exponent--;                   /* (re)adjust the exponent. */
5986           }
5987         #if DECSUBSET
5988         if (ISZERO(res) && !set->extended) res->bits=0; /* subset; no -0 */
5989         #endif
5990         } /* increase */
5991        else /* adjust<=0 */ {                /* decreasing or = exponent */
5992         /* this will increase the length of the coefficient by -adjust */
5993         /* digits, by adding zero or more trailing zeros; this is */
5994         /* already checked for fit, above */
5995         decNumberCopy(res, lhs);             /* [it will fit] */
5996         /* if padding needed (adjust<0), add it now... */
5997         if (adjust<0) {
5998           res->digits=decShiftToMost(res->lsu, res->digits, -adjust);
5999           res->exponent+=adjust;             /* adjust the exponent */
6000           }
6001         } /* decrease */
6002       } /* non-zero */
6003
6004     /* Check for overflow [do not use Finalize in this case, as an */
6005     /* overflow here is a "don't fit" situation] */
6006     if (res->exponent>set->emax-res->digits+1) {  /* too big */
6007       *status|=DEC_Invalid_operation;
6008       break;
6009       }
6010      else {
6011       decFinalize(res, set, &residue, status);    /* set subnormal flags */
6012       *status&=~DEC_Underflow;          /* suppress Underflow [754r] */
6013       }
6014     } while(0);                         /* end protected */
6015
6016   #if DECSUBSET
6017   if (allocrhs!=NULL) free(allocrhs);   /* drop any storage used */
6018   if (alloclhs!=NULL) free(alloclhs);   /* .. */
6019   #endif
6020   return res;
6021   } /* decQuantizeOp */
6022
6023 /* ------------------------------------------------------------------ */
6024 /* decCompareOp -- compare, min, or max two Numbers                   */
6025 /*                                                                    */
6026 /*   This computes C = A ? B and carries out one of four operations:  */
6027 /*     COMPARE    -- returns the signum (as a number) giving the      */
6028 /*                   result of a comparison unless one or both        */
6029 /*                   operands is a NaN (in which case a NaN results)  */
6030 /*     COMPSIG    -- as COMPARE except that a quiet NaN raises        */
6031 /*                   Invalid operation.                               */
6032 /*     COMPMAX    -- returns the larger of the operands, using the    */
6033 /*                   754r maxnum operation                            */
6034 /*     COMPMAXMAG -- ditto, comparing absolute values                 */
6035 /*     COMPMIN    -- the 754r minnum operation                        */
6036 /*     COMPMINMAG -- ditto, comparing absolute values                 */
6037 /*     COMTOTAL   -- returns the signum (as a number) giving the      */
6038 /*                   result of a comparison using 754r total ordering */
6039 /*                                                                    */
6040 /*   res is C, the result.  C may be A and/or B (e.g., X=X?X)         */
6041 /*   lhs is A                                                         */
6042 /*   rhs is B                                                         */
6043 /*   set is the context                                               */
6044 /*   op  is the operation flag                                        */
6045 /*   status is the usual accumulator                                  */
6046 /*                                                                    */
6047 /* C must have space for one digit for COMPARE or set->digits for     */
6048 /* COMPMAX, COMPMIN, COMPMAXMAG, or COMPMINMAG.                       */
6049 /* ------------------------------------------------------------------ */
6050 /* The emphasis here is on speed for common cases, and avoiding       */
6051 /* coefficient comparison if possible.                                */
6052 /* ------------------------------------------------------------------ */
6053 static decNumber *decCompareOp(decNumber *res, const decNumber *lhs,
6054                                const decNumber *rhs, decContext *set,
6055                                Flag op, uInt *status) {
6056   #if DECSUBSET
6057   decNumber *alloclhs=NULL;        /* non-NULL if rounded lhs allocated */
6058   decNumber *allocrhs=NULL;        /* .., rhs */
6059   #endif
6060   Int   result=0;                  /* default result value */
6061   uByte merged;                    /* work */
6062
6063   #if DECCHECK
6064   if (decCheckOperands(res, lhs, rhs, set)) return res;
6065   #endif
6066
6067   do {                             /* protect allocated storage */
6068     #if DECSUBSET
6069     if (!set->extended) {
6070       /* reduce operands and set lostDigits status, as needed */
6071       if (lhs->digits>set->digits) {
6072         alloclhs=decRoundOperand(lhs, set, status);
6073         if (alloclhs==NULL) {result=BADINT; break;}
6074         lhs=alloclhs;
6075         }
6076       if (rhs->digits>set->digits) {
6077         allocrhs=decRoundOperand(rhs, set, status);
6078         if (allocrhs==NULL) {result=BADINT; break;}
6079         rhs=allocrhs;
6080         }
6081       }
6082     #endif
6083     /* [following code does not require input rounding] */
6084
6085     /* If total ordering then handle differing signs 'up front' */
6086     if (op==COMPTOTAL) {                /* total ordering */
6087       if (decNumberIsNegative(lhs) && !decNumberIsNegative(rhs)) {
6088         result=-1;
6089         break;
6090         }
6091       if (!decNumberIsNegative(lhs) && decNumberIsNegative(rhs)) {
6092         result=+1;
6093         break;
6094         }
6095       }
6096
6097     /* handle NaNs specially; let infinities drop through */
6098     /* This assumes sNaN (even just one) leads to NaN. */
6099     merged=(lhs->bits | rhs->bits) & (DECSNAN | DECNAN);
6100     if (merged) {                       /* a NaN bit set */
6101       if (op==COMPARE);                 /* result will be NaN */
6102        else if (op==COMPSIG)            /* treat qNaN as sNaN */
6103         *status|=DEC_Invalid_operation | DEC_sNaN;
6104        else if (op==COMPTOTAL) {        /* total ordering, always finite */
6105         /* signs are known to be the same; compute the ordering here */
6106         /* as if the signs are both positive, then invert for negatives */
6107         if (!decNumberIsNaN(lhs)) result=-1;
6108          else if (!decNumberIsNaN(rhs)) result=+1;
6109          /* here if both NaNs */
6110          else if (decNumberIsSNaN(lhs) && decNumberIsQNaN(rhs)) result=-1;
6111          else if (decNumberIsQNaN(lhs) && decNumberIsSNaN(rhs)) result=+1;
6112          else { /* both NaN or both sNaN */
6113           /* now it just depends on the payload */
6114           result=decUnitCompare(lhs->lsu, D2U(lhs->digits),
6115                                 rhs->lsu, D2U(rhs->digits), 0);
6116           /* [Error not possible, as these are 'aligned'] */
6117           } /* both same NaNs */
6118         if (decNumberIsNegative(lhs)) result=-result;
6119         break;
6120         } /* total order */
6121
6122        else if (merged & DECSNAN);           /* sNaN -> qNaN */
6123        else { /* here if MIN or MAX and one or two quiet NaNs */
6124         /* min or max -- 754r rules ignore single NaN */
6125         if (!decNumberIsNaN(lhs) || !decNumberIsNaN(rhs)) {
6126           /* just one NaN; force choice to be the non-NaN operand */
6127           op=COMPMAX;
6128           if (lhs->bits & DECNAN) result=-1; /* pick rhs */
6129                              else result=+1; /* pick lhs */
6130           break;
6131           }
6132         } /* max or min */
6133       op=COMPNAN;                            /* use special path */
6134       decNaNs(res, lhs, rhs, set, status);   /* propagate NaN */
6135       break;
6136       }
6137     /* have numbers */
6138     if (op==COMPMAXMAG || op==COMPMINMAG) result=decCompare(lhs, rhs, 1);
6139      else result=decCompare(lhs, rhs, 0);    /* sign matters */
6140     } while(0);                              /* end protected */
6141
6142   if (result==BADINT) *status|=DEC_Insufficient_storage; /* rare */
6143    else {
6144     if (op==COMPARE || op==COMPSIG ||op==COMPTOTAL) { /* returning signum */
6145       if (op==COMPTOTAL && result==0) {
6146         /* operands are numerically equal or same NaN (and same sign, */
6147         /* tested first); if identical, leave result 0 */
6148         if (lhs->exponent!=rhs->exponent) {
6149           if (lhs->exponent<rhs->exponent) result=-1;
6150            else result=+1;
6151           if (decNumberIsNegative(lhs)) result=-result;
6152           } /* lexp!=rexp */
6153         } /* total-order by exponent */
6154       decNumberZero(res);               /* [always a valid result] */
6155       if (result!=0) {                  /* must be -1 or +1 */
6156         *res->lsu=1;
6157         if (result<0) res->bits=DECNEG;
6158         }
6159       }
6160      else if (op==COMPNAN);             /* special, drop through */
6161      else {                             /* MAX or MIN, non-NaN result */
6162       Int residue=0;                    /* rounding accumulator */
6163       /* choose the operand for the result */
6164       const decNumber *choice;
6165       if (result==0) { /* operands are numerically equal */
6166         /* choose according to sign then exponent (see 754r) */
6167         uByte slhs=(lhs->bits & DECNEG);
6168         uByte srhs=(rhs->bits & DECNEG);
6169         #if DECSUBSET
6170         if (!set->extended) {           /* subset: force left-hand */
6171           op=COMPMAX;
6172           result=+1;
6173           }
6174         else
6175         #endif
6176         if (slhs!=srhs) {          /* signs differ */
6177           if (slhs) result=-1;     /* rhs is max */
6178                else result=+1;     /* lhs is max */
6179           }
6180          else if (slhs && srhs) {  /* both negative */
6181           if (lhs->exponent<rhs->exponent) result=+1;
6182                                       else result=-1;
6183           /* [if equal, use lhs, technically identical] */
6184           }
6185          else {                    /* both positive */
6186           if (lhs->exponent>rhs->exponent) result=+1;
6187                                       else result=-1;
6188           /* [ditto] */
6189           }
6190         } /* numerically equal */
6191       /* here result will be non-0; reverse if looking for MIN */
6192       if (op==COMPMIN || op==COMPMINMAG) result=-result;
6193       choice=(result>0 ? lhs : rhs);    /* choose */
6194       /* copy chosen to result, rounding if need be */
6195       decCopyFit(res, choice, set, &residue, status);
6196       decFinish(res, set, &residue, status);
6197       }
6198     }
6199   #if DECSUBSET
6200   if (allocrhs!=NULL) free(allocrhs);   /* free any storage used */
6201   if (alloclhs!=NULL) free(alloclhs);   /* .. */
6202   #endif
6203   return res;
6204   } /* decCompareOp */
6205
6206 /* ------------------------------------------------------------------ */
6207 /* decCompare -- compare two decNumbers by numerical value            */
6208 /*                                                                    */
6209 /*  This routine compares A ? B without altering them.                */
6210 /*                                                                    */
6211 /*  Arg1 is A, a decNumber which is not a NaN                         */
6212 /*  Arg2 is B, a decNumber which is not a NaN                         */
6213 /*  Arg3 is 1 for a sign-independent compare, 0 otherwise             */
6214 /*                                                                    */
6215 /*  returns -1, 0, or 1 for A<B, A==B, or A>B, or BADINT if failure   */
6216 /*  (the only possible failure is an allocation error)                */
6217 /* ------------------------------------------------------------------ */
6218 static Int decCompare(const decNumber *lhs, const decNumber *rhs,
6219                       Flag abs) {
6220   Int   result;                    /* result value */
6221   Int   sigr;                      /* rhs signum */
6222   Int   compare;                   /* work */
6223
6224   result=1;                                  /* assume signum(lhs) */
6225   if (ISZERO(lhs)) result=0;
6226   if (abs) {
6227     if (ISZERO(rhs)) return result;          /* LHS wins or both 0 */
6228     /* RHS is non-zero */
6229     if (result==0) return -1;                /* LHS is 0; RHS wins */
6230     /* [here, both non-zero, result=1] */
6231     }
6232    else {                                    /* signs matter */
6233     if (result && decNumberIsNegative(lhs)) result=-1;
6234     sigr=1;                                  /* compute signum(rhs) */
6235     if (ISZERO(rhs)) sigr=0;
6236      else if (decNumberIsNegative(rhs)) sigr=-1;
6237     if (result > sigr) return +1;            /* L > R, return 1 */
6238     if (result < sigr) return -1;            /* L < R, return -1 */
6239     if (result==0) return 0;                   /* both 0 */
6240     }
6241
6242   /* signums are the same; both are non-zero */
6243   if ((lhs->bits | rhs->bits) & DECINF) {    /* one or more infinities */
6244     if (decNumberIsInfinite(rhs)) {
6245       if (decNumberIsInfinite(lhs)) result=0;/* both infinite */
6246        else result=-result;                  /* only rhs infinite */
6247       }
6248     return result;
6249     }
6250   /* must compare the coefficients, allowing for exponents */
6251   if (lhs->exponent>rhs->exponent) {         /* LHS exponent larger */
6252     /* swap sides, and sign */
6253     const decNumber *temp=lhs;
6254     lhs=rhs;
6255     rhs=temp;
6256     result=-result;
6257     }
6258   compare=decUnitCompare(lhs->lsu, D2U(lhs->digits),
6259                          rhs->lsu, D2U(rhs->digits),
6260                          rhs->exponent-lhs->exponent);
6261   if (compare!=BADINT) compare*=result;      /* comparison succeeded */
6262   return compare;
6263   } /* decCompare */
6264
6265 /* ------------------------------------------------------------------ */
6266 /* decUnitCompare -- compare two >=0 integers in Unit arrays          */
6267 /*                                                                    */
6268 /*  This routine compares A ? B*10**E where A and B are unit arrays   */
6269 /*  A is a plain integer                                              */
6270 /*  B has an exponent of E (which must be non-negative)               */
6271 /*                                                                    */
6272 /*  Arg1 is A first Unit (lsu)                                        */
6273 /*  Arg2 is A length in Units                                         */
6274 /*  Arg3 is B first Unit (lsu)                                        */
6275 /*  Arg4 is B length in Units                                         */
6276 /*  Arg5 is E (0 if the units are aligned)                            */
6277 /*                                                                    */
6278 /*  returns -1, 0, or 1 for A<B, A==B, or A>B, or BADINT if failure   */
6279 /*  (the only possible failure is an allocation error, which can      */
6280 /*  only occur if E!=0)                                               */
6281 /* ------------------------------------------------------------------ */
6282 static Int decUnitCompare(const Unit *a, Int alength,
6283                           const Unit *b, Int blength, Int exp) {
6284   Unit  *acc;                      /* accumulator for result */
6285   Unit  accbuff[SD2U(DECBUFFER*2+1)]; /* local buffer */
6286   Unit  *allocacc=NULL;            /* -> allocated acc buffer, iff allocated */
6287   Int   accunits, need;            /* units in use or needed for acc */
6288   const Unit *l, *r, *u;           /* work */
6289   Int   expunits, exprem, result;  /* .. */
6290
6291   if (exp==0) {                    /* aligned; fastpath */
6292     if (alength>blength) return 1;
6293     if (alength<blength) return -1;
6294     /* same number of units in both -- need unit-by-unit compare */
6295     l=a+alength-1;
6296     r=b+alength-1;
6297     for (;l>=a; l--, r--) {
6298       if (*l>*r) return 1;
6299       if (*l<*r) return -1;
6300       }
6301     return 0;                      /* all units match */
6302     } /* aligned */
6303
6304   /* Unaligned.  If one is >1 unit longer than the other, padded */
6305   /* approximately, then can return easily */
6306   if (alength>blength+(Int)D2U(exp)) return 1;
6307   if (alength+1<blength+(Int)D2U(exp)) return -1;
6308
6309   /* Need to do a real subtract.  For this, a result buffer is needed */
6310   /* even though only the sign is of interest.  Its length needs */
6311   /* to be the larger of alength and padded blength, +2 */
6312   need=blength+D2U(exp);                /* maximum real length of B */
6313   if (need<alength) need=alength;
6314   need+=2;
6315   acc=accbuff;                          /* assume use local buffer */
6316   if (need*sizeof(Unit)>sizeof(accbuff)) {
6317     allocacc=(Unit *)malloc(need*sizeof(Unit));
6318     if (allocacc==NULL) return BADINT;  /* hopeless -- abandon */
6319     acc=allocacc;
6320     }
6321   /* Calculate units and remainder from exponent. */
6322   expunits=exp/DECDPUN;
6323   exprem=exp%DECDPUN;
6324   /* subtract [A+B*(-m)] */
6325   accunits=decUnitAddSub(a, alength, b, blength, expunits, acc,
6326                          -(Int)powers[exprem]);
6327   /* [UnitAddSub result may have leading zeros, even on zero] */
6328   if (accunits<0) result=-1;            /* negative result */
6329    else {                               /* non-negative result */
6330     /* check units of the result before freeing any storage */
6331     for (u=acc; u<acc+accunits-1 && *u==0;) u++;
6332     result=(*u==0 ? 0 : +1);
6333     }
6334   /* clean up and return the result */
6335   if (allocacc!=NULL) free(allocacc);   /* drop any storage used */
6336   return result;
6337   } /* decUnitCompare */
6338
6339 /* ------------------------------------------------------------------ */
6340 /* decUnitAddSub -- add or subtract two >=0 integers in Unit arrays   */
6341 /*                                                                    */
6342 /*  This routine performs the calculation:                            */
6343 /*                                                                    */
6344 /*  C=A+(B*M)                                                         */
6345 /*                                                                    */
6346 /*  Where M is in the range -DECDPUNMAX through +DECDPUNMAX.          */
6347 /*                                                                    */
6348 /*  A may be shorter or longer than B.                                */
6349 /*                                                                    */
6350 /*  Leading zeros are not removed after a calculation.  The result is */
6351 /*  either the same length as the longer of A and B (adding any       */
6352 /*  shift), or one Unit longer than that (if a Unit carry occurred).  */
6353 /*                                                                    */
6354 /*  A and B content are not altered unless C is also A or B.          */
6355 /*  C may be the same array as A or B, but only if no zero padding is */
6356 /*  requested (that is, C may be B only if bshift==0).                */
6357 /*  C is filled from the lsu; only those units necessary to complete  */
6358 /*  the calculation are referenced.                                   */
6359 /*                                                                    */
6360 /*  Arg1 is A first Unit (lsu)                                        */
6361 /*  Arg2 is A length in Units                                         */
6362 /*  Arg3 is B first Unit (lsu)                                        */
6363 /*  Arg4 is B length in Units                                         */
6364 /*  Arg5 is B shift in Units  (>=0; pads with 0 units if positive)    */
6365 /*  Arg6 is C first Unit (lsu)                                        */
6366 /*  Arg7 is M, the multiplier                                         */
6367 /*                                                                    */
6368 /*  returns the count of Units written to C, which will be non-zero   */
6369 /*  and negated if the result is negative.  That is, the sign of the  */
6370 /*  returned Int is the sign of the result (positive for zero) and    */
6371 /*  the absolute value of the Int is the count of Units.              */
6372 /*                                                                    */
6373 /*  It is the caller's responsibility to make sure that C size is     */
6374 /*  safe, allowing space if necessary for a one-Unit carry.           */
6375 /*                                                                    */
6376 /*  This routine is severely performance-critical; *any* change here  */
6377 /*  must be measured (timed) to assure no performance degradation.    */
6378 /*  In particular, trickery here tends to be counter-productive, as   */
6379 /*  increased complexity of code hurts register optimizations on      */
6380 /*  register-poor architectures.  Avoiding divisions is nearly        */
6381 /*  always a Good Idea, however.                                      */
6382 /*                                                                    */
6383 /* Special thanks to Rick McGuire (IBM Cambridge, MA) and Dave Clark  */
6384 /* (IBM Warwick, UK) for some of the ideas used in this routine.      */
6385 /* ------------------------------------------------------------------ */
6386 static Int decUnitAddSub(const Unit *a, Int alength,
6387                          const Unit *b, Int blength, Int bshift,
6388                          Unit *c, Int m) {
6389   const Unit *alsu=a;              /* A lsu [need to remember it] */
6390   Unit *clsu=c;                    /* C ditto */
6391   Unit *minC;                      /* low water mark for C */
6392   Unit *maxC;                      /* high water mark for C */
6393   eInt carry=0;                    /* carry integer (could be Long) */
6394   Int  add;                        /* work */
6395   #if DECDPUN<=4                   /* myriadal, millenary, etc. */
6396   Int  est;                        /* estimated quotient */
6397   #endif
6398
6399   #if DECTRACE
6400   if (alength<1 || blength<1)
6401     printf("decUnitAddSub: alen blen m %ld %ld [%ld]\n", alength, blength, m);
6402   #endif
6403
6404   maxC=c+alength;                  /* A is usually the longer */
6405   minC=c+blength;                  /* .. and B the shorter */
6406   if (bshift!=0) {                 /* B is shifted; low As copy across */
6407     minC+=bshift;
6408     /* if in place [common], skip copy unless there's a gap [rare] */
6409     if (a==c && bshift<=alength) {
6410       c+=bshift;
6411       a+=bshift;
6412       }
6413      else for (; c<clsu+bshift; a++, c++) {  /* copy needed */
6414       if (a<alsu+alength) *c=*a;
6415        else *c=0;
6416       }
6417     }
6418   if (minC>maxC) { /* swap */
6419     Unit *hold=minC;
6420     minC=maxC;
6421     maxC=hold;
6422     }
6423
6424   /* For speed, do the addition as two loops; the first where both A */
6425   /* and B contribute, and the second (if necessary) where only one or */
6426   /* other of the numbers contribute. */
6427   /* Carry handling is the same (i.e., duplicated) in each case. */
6428   for (; c<minC; c++) {
6429     carry+=*a;
6430     a++;
6431     carry+=((eInt)*b)*m;                /* [special-casing m=1/-1 */
6432     b++;                                /* here is not a win] */
6433     /* here carry is new Unit of digits; it could be +ve or -ve */
6434     if ((ueInt)carry<=DECDPUNMAX) {     /* fastpath 0-DECDPUNMAX */
6435       *c=(Unit)carry;
6436       carry=0;
6437       continue;
6438       }
6439     #if DECDPUN==4                           /* use divide-by-multiply */
6440       if (carry>=0) {
6441         est=(((ueInt)carry>>11)*53687)>>18;
6442         *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */
6443         carry=est;                           /* likely quotient [89%] */
6444         if (*c<DECDPUNMAX+1) continue;       /* estimate was correct */
6445         carry++;
6446         *c-=DECDPUNMAX+1;
6447         continue;
6448         }
6449       /* negative case */
6450       carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */
6451       est=(((ueInt)carry>>11)*53687)>>18;
6452       *c=(Unit)(carry-est*(DECDPUNMAX+1));
6453       carry=est-(DECDPUNMAX+1);              /* correctly negative */
6454       if (*c<DECDPUNMAX+1) continue;         /* was OK */
6455       carry++;
6456       *c-=DECDPUNMAX+1;
6457     #elif DECDPUN==3
6458       if (carry>=0) {
6459         est=(((ueInt)carry>>3)*16777)>>21;
6460         *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */
6461         carry=est;                           /* likely quotient [99%] */
6462         if (*c<DECDPUNMAX+1) continue;       /* estimate was correct */
6463         carry++;
6464         *c-=DECDPUNMAX+1;
6465         continue;
6466         }
6467       /* negative case */
6468       carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */
6469       est=(((ueInt)carry>>3)*16777)>>21;
6470       *c=(Unit)(carry-est*(DECDPUNMAX+1));
6471       carry=est-(DECDPUNMAX+1);              /* correctly negative */
6472       if (*c<DECDPUNMAX+1) continue;         /* was OK */
6473       carry++;
6474       *c-=DECDPUNMAX+1;
6475     #elif DECDPUN<=2
6476       /* Can use QUOT10 as carry <= 4 digits */
6477       if (carry>=0) {
6478         est=QUOT10(carry, DECDPUN);
6479         *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */
6480         carry=est;                           /* quotient */
6481         continue;
6482         }
6483       /* negative case */
6484       carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */
6485       est=QUOT10(carry, DECDPUN);
6486       *c=(Unit)(carry-est*(DECDPUNMAX+1));
6487       carry=est-(DECDPUNMAX+1);              /* correctly negative */
6488     #else
6489       /* remainder operator is undefined if negative, so must test */
6490       if ((ueInt)carry<(DECDPUNMAX+1)*2) {   /* fastpath carry +1 */
6491         *c=(Unit)(carry-(DECDPUNMAX+1));     /* [helps additions] */
6492         carry=1;
6493         continue;
6494         }
6495       if (carry>=0) {
6496         *c=(Unit)(carry%(DECDPUNMAX+1));
6497         carry=carry/(DECDPUNMAX+1);
6498         continue;
6499         }
6500       /* negative case */
6501       carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */
6502       *c=(Unit)(carry%(DECDPUNMAX+1));
6503       carry=carry/(DECDPUNMAX+1)-(DECDPUNMAX+1);
6504     #endif
6505     } /* c */
6506
6507   /* now may have one or other to complete */
6508   /* [pretest to avoid loop setup/shutdown] */
6509   if (c<maxC) for (; c<maxC; c++) {
6510     if (a<alsu+alength) {               /* still in A */
6511       carry+=*a;
6512       a++;
6513       }
6514      else {                             /* inside B */
6515       carry+=((eInt)*b)*m;
6516       b++;
6517       }
6518     /* here carry is new Unit of digits; it could be +ve or -ve and */
6519     /* magnitude up to DECDPUNMAX squared */
6520     if ((ueInt)carry<=DECDPUNMAX) {     /* fastpath 0-DECDPUNMAX */
6521       *c=(Unit)carry;
6522       carry=0;
6523       continue;
6524       }
6525     /* result for this unit is negative or >DECDPUNMAX */
6526     #if DECDPUN==4                           /* use divide-by-multiply */
6527       if (carry>=0) {
6528         est=(((ueInt)carry>>11)*53687)>>18;
6529         *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */
6530         carry=est;                           /* likely quotient [79.7%] */
6531         if (*c<DECDPUNMAX+1) continue;       /* estimate was correct */
6532         carry++;
6533         *c-=DECDPUNMAX+1;
6534         continue;
6535         }
6536       /* negative case */
6537       carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */
6538       est=(((ueInt)carry>>11)*53687)>>18;
6539       *c=(Unit)(carry-est*(DECDPUNMAX+1));
6540       carry=est-(DECDPUNMAX+1);              /* correctly negative */
6541       if (*c<DECDPUNMAX+1) continue;         /* was OK */
6542       carry++;
6543       *c-=DECDPUNMAX+1;
6544     #elif DECDPUN==3
6545       if (carry>=0) {
6546         est=(((ueInt)carry>>3)*16777)>>21;
6547         *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */
6548         carry=est;                           /* likely quotient [99%] */
6549         if (*c<DECDPUNMAX+1) continue;       /* estimate was correct */
6550         carry++;
6551         *c-=DECDPUNMAX+1;
6552         continue;
6553         }
6554       /* negative case */
6555       carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */
6556       est=(((ueInt)carry>>3)*16777)>>21;
6557       *c=(Unit)(carry-est*(DECDPUNMAX+1));
6558       carry=est-(DECDPUNMAX+1);              /* correctly negative */
6559       if (*c<DECDPUNMAX+1) continue;         /* was OK */
6560       carry++;
6561       *c-=DECDPUNMAX+1;
6562     #elif DECDPUN<=2
6563       if (carry>=0) {
6564         est=QUOT10(carry, DECDPUN);
6565         *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */
6566         carry=est;                           /* quotient */
6567         continue;
6568         }
6569       /* negative case */
6570       carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */
6571       est=QUOT10(carry, DECDPUN);
6572       *c=(Unit)(carry-est*(DECDPUNMAX+1));
6573       carry=est-(DECDPUNMAX+1);              /* correctly negative */
6574     #else
6575       if ((ueInt)carry<(DECDPUNMAX+1)*2){    /* fastpath carry 1 */
6576         *c=(Unit)(carry-(DECDPUNMAX+1));
6577         carry=1;
6578         continue;
6579         }
6580       /* remainder operator is undefined if negative, so must test */
6581       if (carry>=0) {
6582         *c=(Unit)(carry%(DECDPUNMAX+1));
6583         carry=carry/(DECDPUNMAX+1);
6584         continue;
6585         }
6586       /* negative case */
6587       carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */
6588       *c=(Unit)(carry%(DECDPUNMAX+1));
6589       carry=carry/(DECDPUNMAX+1)-(DECDPUNMAX+1);
6590     #endif
6591     } /* c */
6592
6593   /* OK, all A and B processed; might still have carry or borrow */
6594   /* return number of Units in the result, negated if a borrow */
6595   if (carry==0) return c-clsu;     /* no carry, so no more to do */
6596   if (carry>0) {                   /* positive carry */
6597     *c=(Unit)carry;                /* place as new unit */
6598     c++;                           /* .. */
6599     return c-clsu;
6600     }
6601   /* -ve carry: it's a borrow; complement needed */
6602   add=1;                           /* temporary carry... */
6603   for (c=clsu; c<maxC; c++) {
6604     add=DECDPUNMAX+add-*c;
6605     if (add<=DECDPUNMAX) {
6606       *c=(Unit)add;
6607       add=0;
6608       }
6609      else {
6610       *c=0;
6611       add=1;
6612       }
6613     }
6614   /* add an extra unit iff it would be non-zero */
6615   #if DECTRACE
6616     printf("UAS borrow: add %ld, carry %ld\n", add, carry);
6617   #endif
6618   if ((add-carry-1)!=0) {
6619     *c=(Unit)(add-carry-1);
6620     c++;                      /* interesting, include it */
6621     }
6622   return clsu-c;              /* -ve result indicates borrowed */
6623   } /* decUnitAddSub */
6624
6625 /* ------------------------------------------------------------------ */
6626 /* decTrim -- trim trailing zeros or normalize                        */
6627 /*                                                                    */
6628 /*   dn is the number to trim or normalize                            */
6629 /*   set is the context to use to check for clamp                     */
6630 /*   all is 1 to remove all trailing zeros, 0 for just fraction ones  */
6631 /*   dropped returns the number of discarded trailing zeros           */
6632 /*   returns dn                                                       */
6633 /*                                                                    */
6634 /* If clamp is set in the context then the number of zeros trimmed    */
6635 /* may be limited if the exponent is high.                            */
6636 /* All fields are updated as required.  This is a utility operation,  */
6637 /* so special values are unchanged and no error is possible.          */
6638 /* ------------------------------------------------------------------ */
6639 static decNumber * decTrim(decNumber *dn, decContext *set, Flag all,
6640                            Int *dropped) {
6641   Int   d, exp;                    /* work */
6642   uInt  cut;                       /* .. */
6643   Unit  *up;                       /* -> current Unit */
6644
6645   #if DECCHECK
6646   if (decCheckOperands(dn, DECUNUSED, DECUNUSED, DECUNCONT)) return dn;
6647   #endif
6648
6649   *dropped=0;                           /* assume no zeros dropped */
6650   if ((dn->bits & DECSPECIAL)           /* fast exit if special .. */
6651     || (*dn->lsu & 0x01)) return dn;    /* .. or odd */
6652   if (ISZERO(dn)) {                     /* .. or 0 */
6653     dn->exponent=0;                     /* (sign is preserved) */
6654     return dn;
6655     }
6656
6657   /* have a finite number which is even */
6658   exp=dn->exponent;
6659   cut=1;                           /* digit (1-DECDPUN) in Unit */
6660   up=dn->lsu;                      /* -> current Unit */
6661   for (d=0; d<dn->digits-1; d++) { /* [don't strip the final digit] */
6662     /* slice by powers */
6663     #if DECDPUN<=4
6664       uInt quot=QUOT10(*up, cut);
6665       if ((*up-quot*powers[cut])!=0) break;  /* found non-0 digit */
6666     #else
6667       if (*up%powers[cut]!=0) break;         /* found non-0 digit */
6668     #endif
6669     /* have a trailing 0 */
6670     if (!all) {                    /* trimming */
6671       /* [if exp>0 then all trailing 0s are significant for trim] */
6672       if (exp<=0) {                /* if digit might be significant */
6673         if (exp==0) break;         /* then quit */
6674         exp++;                     /* next digit might be significant */
6675         }
6676       }
6677     cut++;                         /* next power */
6678     if (cut>DECDPUN) {             /* need new Unit */
6679       up++;
6680       cut=1;
6681       }
6682     } /* d */
6683   if (d==0) return dn;             /* none to drop */
6684
6685   /* may need to limit drop if clamping */
6686   if (set->clamp) {
6687     Int maxd=set->emax-set->digits+1-dn->exponent;
6688     if (maxd<=0) return dn;        /* nothing possible */
6689     if (d>maxd) d=maxd;
6690     }
6691
6692   /* effect the drop */
6693   decShiftToLeast(dn->lsu, D2U(dn->digits), d);
6694   dn->exponent+=d;                 /* maintain numerical value */
6695   dn->digits-=d;                   /* new length */
6696   *dropped=d;                      /* report the count */
6697   return dn;
6698   } /* decTrim */
6699
6700 /* ------------------------------------------------------------------ */
6701 /* decReverse -- reverse a Unit array in place                        */
6702 /*                                                                    */
6703 /*   ulo    is the start of the array                                 */
6704 /*   uhi    is the end of the array (highest Unit to include)         */
6705 /*                                                                    */
6706 /* The units ulo through uhi are reversed in place (if the number     */
6707 /* of units is odd, the middle one is untouched).  Note that the      */
6708 /* digit(s) in each unit are unaffected.                              */
6709 /* ------------------------------------------------------------------ */
6710 static void decReverse(Unit *ulo, Unit *uhi) {
6711   Unit temp;
6712   for (; ulo<uhi; ulo++, uhi--) {
6713     temp=*ulo;
6714     *ulo=*uhi;
6715     *uhi=temp;
6716     }
6717   return;
6718   } /* decReverse */
6719
6720 /* ------------------------------------------------------------------ */
6721 /* decShiftToMost -- shift digits in array towards most significant   */
6722 /*                                                                    */
6723 /*   uar    is the array                                              */
6724 /*   digits is the count of digits in use in the array                */
6725 /*   shift  is the number of zeros to pad with (least significant);   */
6726 /*     it must be zero or positive                                    */
6727 /*                                                                    */
6728 /*   returns the new length of the integer in the array, in digits    */
6729 /*                                                                    */
6730 /* No overflow is permitted (that is, the uar array must be known to  */
6731 /* be large enough to hold the result, after shifting).               */
6732 /* ------------------------------------------------------------------ */
6733 static Int decShiftToMost(Unit *uar, Int digits, Int shift) {
6734   Unit  *target, *source, *first;  /* work */
6735   Int   cut;                       /* odd 0's to add */
6736   uInt  next;                      /* work */
6737
6738   if (shift==0) return digits;     /* [fastpath] nothing to do */
6739   if ((digits+shift)<=DECDPUN) {   /* [fastpath] single-unit case */
6740     *uar=(Unit)(*uar*powers[shift]);
6741     return digits+shift;
6742     }
6743
6744   next=0;                          /* all paths */
6745   source=uar+D2U(digits)-1;        /* where msu comes from */
6746   target=source+D2U(shift);        /* where upper part of first cut goes */
6747   cut=DECDPUN-MSUDIGITS(shift);    /* where to slice */
6748   if (cut==0) {                    /* unit-boundary case */
6749     for (; source>=uar; source--, target--) *target=*source;
6750     }
6751    else {
6752     first=uar+D2U(digits+shift)-1; /* where msu of source will end up */
6753     for (; source>=uar; source--, target--) {
6754       /* split the source Unit and accumulate remainder for next */
6755       #if DECDPUN<=4
6756         uInt quot=QUOT10(*source, cut);
6757         uInt rem=*source-quot*powers[cut];
6758         next+=quot;
6759       #else
6760         uInt rem=*source%powers[cut];
6761         next+=*source/powers[cut];
6762       #endif
6763       if (target<=first) *target=(Unit)next;   /* write to target iff valid */
6764       next=rem*powers[DECDPUN-cut];            /* save remainder for next Unit */
6765       }
6766     } /* shift-move */
6767
6768   /* propagate any partial unit to one below and clear the rest */
6769   for (; target>=uar; target--) {
6770     *target=(Unit)next;
6771     next=0;
6772     }
6773   return digits+shift;
6774   } /* decShiftToMost */
6775
6776 /* ------------------------------------------------------------------ */
6777 /* decShiftToLeast -- shift digits in array towards least significant */
6778 /*                                                                    */
6779 /*   uar   is the array                                               */
6780 /*   units is length of the array, in units                           */
6781 /*   shift is the number of digits to remove from the lsu end; it     */
6782 /*     must be zero or positive and <= than units*DECDPUN.            */
6783 /*                                                                    */
6784 /*   returns the new length of the integer in the array, in units     */
6785 /*                                                                    */
6786 /* Removed digits are discarded (lost).  Units not required to hold   */
6787 /* the final result are unchanged.                                    */
6788 /* ------------------------------------------------------------------ */
6789 static Int decShiftToLeast(Unit *uar, Int units, Int shift) {
6790   Unit  *target, *up;              /* work */
6791   Int   cut, count;                /* work */
6792   Int   quot, rem;                 /* for division */
6793
6794   if (shift==0) return units;      /* [fastpath] nothing to do */
6795   if (shift==units*DECDPUN) {      /* [fastpath] little to do */
6796     *uar=0;                        /* all digits cleared gives zero */
6797     return 1;                      /* leaves just the one */
6798     }
6799
6800   target=uar;                      /* both paths */
6801   cut=MSUDIGITS(shift);
6802   if (cut==DECDPUN) {              /* unit-boundary case; easy */
6803     up=uar+D2U(shift);
6804     for (; up<uar+units; target++, up++) *target=*up;
6805     return target-uar;
6806     }
6807
6808   /* messier */
6809   up=uar+D2U(shift-cut);           /* source; correct to whole Units */
6810   count=units*DECDPUN-shift;       /* the maximum new length */
6811   #if DECDPUN<=4
6812     quot=QUOT10(*up, cut);
6813   #else
6814     quot=*up/powers[cut];
6815   #endif
6816   for (; ; target++) {
6817     *target=(Unit)quot;
6818     count-=(DECDPUN-cut);
6819     if (count<=0) break;
6820     up++;
6821     quot=*up;
6822     #if DECDPUN<=4
6823       quot=QUOT10(quot, cut);
6824       rem=*up-quot*powers[cut];
6825     #else
6826       rem=quot%powers[cut];
6827       quot=quot/powers[cut];
6828     #endif
6829     *target=(Unit)(*target+rem*powers[DECDPUN-cut]);
6830     count-=cut;
6831     if (count<=0) break;
6832     }
6833   return target-uar+1;
6834   } /* decShiftToLeast */
6835
6836 #if DECSUBSET
6837 /* ------------------------------------------------------------------ */
6838 /* decRoundOperand -- round an operand  [used for subset only]        */
6839 /*                                                                    */
6840 /*   dn is the number to round (dn->digits is > set->digits)          */
6841 /*   set is the relevant context                                      */
6842 /*   status is the status accumulator                                 */
6843 /*                                                                    */
6844 /*   returns an allocated decNumber with the rounded result.          */
6845 /*                                                                    */
6846 /* lostDigits and other status may be set by this.                    */
6847 /*                                                                    */
6848 /* Since the input is an operand, it must not be modified.            */
6849 /* Instead, return an allocated decNumber, rounded as required.       */
6850 /* It is the caller's responsibility to free the allocated storage.   */
6851 /*                                                                    */
6852 /* If no storage is available then the result cannot be used, so NULL */
6853 /* is returned.                                                       */
6854 /* ------------------------------------------------------------------ */
6855 static decNumber *decRoundOperand(const decNumber *dn, decContext *set,
6856                                   uInt *status) {
6857   decNumber *res;                       /* result structure */
6858   uInt newstatus=0;                     /* status from round */
6859   Int  residue=0;                       /* rounding accumulator */
6860
6861   /* Allocate storage for the returned decNumber, big enough for the */
6862   /* length specified by the context */
6863   res=(decNumber *)malloc(sizeof(decNumber)
6864                           +(D2U(set->digits)-1)*sizeof(Unit));
6865   if (res==NULL) {
6866     *status|=DEC_Insufficient_storage;
6867     return NULL;
6868     }
6869   decCopyFit(res, dn, set, &residue, &newstatus);
6870   decApplyRound(res, set, residue, &newstatus);
6871
6872   /* If that set Inexact then "lost digits" is raised... */
6873   if (newstatus & DEC_Inexact) newstatus|=DEC_Lost_digits;
6874   *status|=newstatus;
6875   return res;
6876   } /* decRoundOperand */
6877 #endif
6878
6879 /* ------------------------------------------------------------------ */
6880 /* decCopyFit -- copy a number, truncating the coefficient if needed  */
6881 /*                                                                    */
6882 /*   dest is the target decNumber                                     */
6883 /*   src  is the source decNumber                                     */
6884 /*   set is the context [used for length (digits) and rounding mode]  */
6885 /*   residue is the residue accumulator                               */
6886 /*   status contains the current status to be updated                 */
6887 /*                                                                    */
6888 /* (dest==src is allowed and will be a no-op if fits)                 */
6889 /* All fields are updated as required.                                */
6890 /* ------------------------------------------------------------------ */
6891 static void decCopyFit(decNumber *dest, const decNumber *src,
6892                        decContext *set, Int *residue, uInt *status) {
6893   dest->bits=src->bits;
6894   dest->exponent=src->exponent;
6895   decSetCoeff(dest, set, src->lsu, src->digits, residue, status);
6896   } /* decCopyFit */
6897
6898 /* ------------------------------------------------------------------ */
6899 /* decSetCoeff -- set the coefficient of a number                     */
6900 /*                                                                    */
6901 /*   dn    is the number whose coefficient array is to be set.        */
6902 /*         It must have space for set->digits digits                  */
6903 /*   set   is the context [for size]                                  */
6904 /*   lsu   -> lsu of the source coefficient [may be dn->lsu]          */
6905 /*   len   is digits in the source coefficient [may be dn->digits]    */
6906 /*   residue is the residue accumulator.  This has values as in       */
6907 /*         decApplyRound, and will be unchanged unless the            */
6908 /*         target size is less than len.  In this case, the           */
6909 /*         coefficient is truncated and the residue is updated to     */
6910 /*         reflect the previous residue and the dropped digits.       */
6911 /*   status is the status accumulator, as usual                       */
6912 /*                                                                    */
6913 /* The coefficient may already be in the number, or it can be an      */
6914 /* external intermediate array.  If it is in the number, lsu must ==  */
6915 /* dn->lsu and len must == dn->digits.                                */
6916 /*                                                                    */
6917 /* Note that the coefficient length (len) may be < set->digits, and   */
6918 /* in this case this merely copies the coefficient (or is a no-op     */
6919 /* if dn->lsu==lsu).                                                  */
6920 /*                                                                    */
6921 /* Note also that (only internally, from decQuantizeOp and            */
6922 /* decSetSubnormal) the value of set->digits may be less than one,    */
6923 /* indicating a round to left.  This routine handles that case        */
6924 /* correctly; caller ensures space.                                   */
6925 /*                                                                    */
6926 /* dn->digits, dn->lsu (and as required), and dn->exponent are        */
6927 /* updated as necessary.   dn->bits (sign) is unchanged.              */
6928 /*                                                                    */
6929 /* DEC_Rounded status is set if any digits are discarded.             */
6930 /* DEC_Inexact status is set if any non-zero digits are discarded, or */
6931 /*                       incoming residue was non-0 (implies rounded) */
6932 /* ------------------------------------------------------------------ */
6933 /* mapping array: maps 0-9 to canonical residues, so that a residue */
6934 /* can be adjusted in the range [-1, +1] and achieve correct rounding */
6935 /*                             0  1  2  3  4  5  6  7  8  9 */
6936 static const uByte resmap[10]={0, 3, 3, 3, 3, 5, 7, 7, 7, 7};
6937 static void decSetCoeff(decNumber *dn, decContext *set, const Unit *lsu,
6938                         Int len, Int *residue, uInt *status) {
6939   Int   discard;              /* number of digits to discard */
6940   uInt  cut;                  /* cut point in Unit */
6941   const Unit *up;             /* work */
6942   Unit  *target;              /* .. */
6943   Int   count;                /* .. */
6944   #if DECDPUN<=4
6945   uInt  temp;                 /* .. */
6946   #endif
6947
6948   discard=len-set->digits;    /* digits to discard */
6949   if (discard<=0) {           /* no digits are being discarded */
6950     if (dn->lsu!=lsu) {       /* copy needed */
6951       /* copy the coefficient array to the result number; no shift needed */
6952       count=len;              /* avoids D2U */
6953       up=lsu;
6954       for (target=dn->lsu; count>0; target++, up++, count-=DECDPUN)
6955         *target=*up;
6956       dn->digits=len;         /* set the new length */
6957       }
6958     /* dn->exponent and residue are unchanged, record any inexactitude */
6959     if (*residue!=0) *status|=(DEC_Inexact | DEC_Rounded);
6960     return;
6961     }
6962
6963   /* some digits must be discarded ... */
6964   dn->exponent+=discard;      /* maintain numerical value */
6965   *status|=DEC_Rounded;       /* accumulate Rounded status */
6966   if (*residue>1) *residue=1; /* previous residue now to right, so reduce */
6967
6968   if (discard>len) {          /* everything, +1, is being discarded */
6969     /* guard digit is 0 */
6970     /* residue is all the number [NB could be all 0s] */
6971     if (*residue<=0) {        /* not already positive */
6972       count=len;              /* avoids D2U */
6973       for (up=lsu; count>0; up++, count-=DECDPUN) if (*up!=0) { /* found non-0 */
6974         *residue=1;
6975         break;                /* no need to check any others */
6976         }
6977       }
6978     if (*residue!=0) *status|=DEC_Inexact; /* record inexactitude */
6979     *dn->lsu=0;               /* coefficient will now be 0 */
6980     dn->digits=1;             /* .. */
6981     return;
6982     } /* total discard */
6983
6984   /* partial discard [most common case] */
6985   /* here, at least the first (most significant) discarded digit exists */
6986
6987   /* spin up the number, noting residue during the spin, until get to */
6988   /* the Unit with the first discarded digit.  When reach it, extract */
6989   /* it and remember its position */
6990   count=0;
6991   for (up=lsu;; up++) {
6992     count+=DECDPUN;
6993     if (count>=discard) break; /* full ones all checked */
6994     if (*up!=0) *residue=1;
6995     } /* up */
6996
6997   /* here up -> Unit with first discarded digit */
6998   cut=discard-(count-DECDPUN)-1;
6999   if (cut==DECDPUN-1) {       /* unit-boundary case (fast) */
7000     Unit half=(Unit)powers[DECDPUN]>>1;
7001     /* set residue directly */
7002     if (*up>=half) {
7003       if (*up>half) *residue=7;
7004       else *residue+=5;       /* add sticky bit */
7005       }
7006      else { /* <half */
7007       if (*up!=0) *residue=3; /* [else is 0, leave as sticky bit] */
7008       }
7009     if (set->digits<=0) {     /* special for Quantize/Subnormal :-( */
7010       *dn->lsu=0;             /* .. result is 0 */
7011       dn->digits=1;           /* .. */
7012       }
7013      else {                   /* shift to least */
7014       count=set->digits;      /* now digits to end up with */
7015       dn->digits=count;       /* set the new length */
7016       up++;                   /* move to next */
7017       /* on unit boundary, so shift-down copy loop is simple */
7018       for (target=dn->lsu; count>0; target++, up++, count-=DECDPUN)
7019         *target=*up;
7020       }
7021     } /* unit-boundary case */
7022
7023    else { /* discard digit is in low digit(s), and not top digit */
7024     uInt  discard1;                /* first discarded digit */
7025     uInt  quot, rem;               /* for divisions */
7026     if (cut==0) quot=*up;          /* is at bottom of unit */
7027      else /* cut>0 */ {            /* it's not at bottom of unit */
7028       #if DECDPUN<=4
7029         quot=QUOT10(*up, cut);
7030         rem=*up-quot*powers[cut];
7031       #else
7032         rem=*up%powers[cut];
7033         quot=*up/powers[cut];
7034       #endif
7035       if (rem!=0) *residue=1;
7036       }
7037     /* discard digit is now at bottom of quot */
7038     #if DECDPUN<=4
7039       temp=(quot*6554)>>16;        /* fast /10 */
7040       /* Vowels algorithm here not a win (9 instructions) */
7041       discard1=quot-X10(temp);
7042       quot=temp;
7043     #else
7044       discard1=quot%10;
7045       quot=quot/10;
7046     #endif
7047     /* here, discard1 is the guard digit, and residue is everything */
7048     /* else [use mapping array to accumulate residue safely] */
7049     *residue+=resmap[discard1];
7050     cut++;                         /* update cut */
7051     /* here: up -> Unit of the array with bottom digit */
7052     /*       cut is the division point for each Unit */
7053     /*       quot holds the uncut high-order digits for the current unit */
7054     if (set->digits<=0) {          /* special for Quantize/Subnormal :-( */
7055       *dn->lsu=0;                  /* .. result is 0 */
7056       dn->digits=1;                /* .. */
7057       }
7058      else {                        /* shift to least needed */
7059       count=set->digits;           /* now digits to end up with */
7060       dn->digits=count;            /* set the new length */
7061       /* shift-copy the coefficient array to the result number */
7062       for (target=dn->lsu; ; target++) {
7063         *target=(Unit)quot;
7064         count-=(DECDPUN-cut);
7065         if (count<=0) break;
7066         up++;
7067         quot=*up;
7068         #if DECDPUN<=4
7069           quot=QUOT10(quot, cut);
7070           rem=*up-quot*powers[cut];
7071         #else
7072           rem=quot%powers[cut];
7073           quot=quot/powers[cut];
7074         #endif
7075         *target=(Unit)(*target+rem*powers[DECDPUN-cut]);
7076         count-=cut;
7077         if (count<=0) break;
7078         } /* shift-copy loop */
7079       } /* shift to least */
7080     } /* not unit boundary */
7081
7082   if (*residue!=0) *status|=DEC_Inexact; /* record inexactitude */
7083   return;
7084   } /* decSetCoeff */
7085
7086 /* ------------------------------------------------------------------ */
7087 /* decApplyRound -- apply pending rounding to a number                */
7088 /*                                                                    */
7089 /*   dn    is the number, with space for set->digits digits           */
7090 /*   set   is the context [for size and rounding mode]                */
7091 /*   residue indicates pending rounding, being any accumulated        */
7092 /*         guard and sticky information.  It may be:                  */
7093 /*         6-9: rounding digit is >5                                  */
7094 /*         5:   rounding digit is exactly half-way                    */
7095 /*         1-4: rounding digit is <5 and >0                           */
7096 /*         0:   the coefficient is exact                              */
7097 /*        -1:   as 1, but the hidden digits are subtractive, that     */
7098 /*              is, of the opposite sign to dn.  In this case the     */
7099 /*              coefficient must be non-0.  This case occurs when     */
7100 /*              subtracting a small number (which can be reduced to   */
7101 /*              a sticky bit); see decAddOp.                          */
7102 /*   status is the status accumulator, as usual                       */
7103 /*                                                                    */
7104 /* This routine applies rounding while keeping the length of the      */
7105 /* coefficient constant.  The exponent and status are unchanged       */
7106 /* except if:                                                         */
7107 /*                                                                    */
7108 /*   -- the coefficient was increased and is all nines (in which      */
7109 /*      case Overflow could occur, and is handled directly here so    */
7110 /*      the caller does not need to re-test for overflow)             */
7111 /*                                                                    */
7112 /*   -- the coefficient was decreased and becomes all nines (in which */
7113 /*      case Underflow could occur, and is also handled directly).    */
7114 /*                                                                    */
7115 /* All fields in dn are updated as required.                          */
7116 /*                                                                    */
7117 /* ------------------------------------------------------------------ */
7118 static void decApplyRound(decNumber *dn, decContext *set, Int residue,
7119                           uInt *status) {
7120   Int  bump;                  /* 1 if coefficient needs to be incremented */
7121                               /* -1 if coefficient needs to be decremented */
7122
7123   if (residue==0) return;     /* nothing to apply */
7124
7125   bump=0;                     /* assume a smooth ride */
7126
7127   /* now decide whether, and how, to round, depending on mode */
7128   switch (set->round) {
7129     case DEC_ROUND_05UP: {    /* round zero or five up (for reround) */
7130       /* This is the same as DEC_ROUND_DOWN unless there is a */
7131       /* positive residue and the lsd of dn is 0 or 5, in which case */
7132       /* it is bumped; when residue is <0, the number is therefore */
7133       /* bumped down unless the final digit was 1 or 6 (in which */
7134       /* case it is bumped down and then up -- a no-op) */
7135       Int lsd5=*dn->lsu%5;     /* get lsd and quintate */
7136       if (residue<0 && lsd5!=1) bump=-1;
7137        else if (residue>0 && lsd5==0) bump=1;
7138       /* [bump==1 could be applied directly; use common path for clarity] */
7139       break;} /* r-05 */
7140
7141     case DEC_ROUND_DOWN: {
7142       /* no change, except if negative residue */
7143       if (residue<0) bump=-1;
7144       break;} /* r-d */
7145
7146     case DEC_ROUND_HALF_DOWN: {
7147       if (residue>5) bump=1;
7148       break;} /* r-h-d */
7149
7150     case DEC_ROUND_HALF_EVEN: {
7151       if (residue>5) bump=1;            /* >0.5 goes up */
7152        else if (residue==5) {           /* exactly 0.5000... */
7153         /* 0.5 goes up iff [new] lsd is odd */
7154         if (*dn->lsu & 0x01) bump=1;
7155         }
7156       break;} /* r-h-e */
7157
7158     case DEC_ROUND_HALF_UP: {
7159       if (residue>=5) bump=1;
7160       break;} /* r-h-u */
7161
7162     case DEC_ROUND_UP: {
7163       if (residue>0) bump=1;
7164       break;} /* r-u */
7165
7166     case DEC_ROUND_CEILING: {
7167       /* same as _UP for positive numbers, and as _DOWN for negatives */
7168       /* [negative residue cannot occur on 0] */
7169       if (decNumberIsNegative(dn)) {
7170         if (residue<0) bump=-1;
7171         }
7172        else {
7173         if (residue>0) bump=1;
7174         }
7175       break;} /* r-c */
7176
7177     case DEC_ROUND_FLOOR: {
7178       /* same as _UP for negative numbers, and as _DOWN for positive */
7179       /* [negative residue cannot occur on 0] */
7180       if (!decNumberIsNegative(dn)) {
7181         if (residue<0) bump=-1;
7182         }
7183        else {
7184         if (residue>0) bump=1;
7185         }
7186       break;} /* r-f */
7187
7188     default: {      /* e.g., DEC_ROUND_MAX */
7189       *status|=DEC_Invalid_context;
7190       #if DECTRACE || (DECCHECK && DECVERB)
7191       printf("Unknown rounding mode: %d\n", set->round);
7192       #endif
7193       break;}
7194     } /* switch */
7195
7196   /* now bump the number, up or down, if need be */
7197   if (bump==0) return;                       /* no action required */
7198
7199   /* Simply use decUnitAddSub unless bumping up and the number is */
7200   /* all nines.  In this special case set to 100... explicitly */
7201   /* and adjust the exponent by one (as otherwise could overflow */
7202   /* the array) */
7203   /* Similarly handle all-nines result if bumping down. */
7204   if (bump>0) {
7205     Unit *up;                                /* work */
7206     uInt count=dn->digits;                   /* digits to be checked */
7207     for (up=dn->lsu; ; up++) {
7208       if (count<=DECDPUN) {
7209         /* this is the last Unit (the msu) */
7210         if (*up!=powers[count]-1) break;     /* not still 9s */
7211         /* here if it, too, is all nines */
7212         *up=(Unit)powers[count-1];           /* here 999 -> 100 etc. */
7213         for (up=up-1; up>=dn->lsu; up--) *up=0; /* others all to 0 */
7214         dn->exponent++;                      /* and bump exponent */
7215         /* [which, very rarely, could cause Overflow...] */
7216         if ((dn->exponent+dn->digits)>set->emax+1) {
7217           decSetOverflow(dn, set, status);
7218           }
7219         return;                              /* done */
7220         }
7221       /* a full unit to check, with more to come */
7222       if (*up!=DECDPUNMAX) break;            /* not still 9s */
7223       count-=DECDPUN;
7224       } /* up */
7225     } /* bump>0 */
7226    else {                                    /* -1 */
7227     /* here checking for a pre-bump of 1000... (leading 1, all */
7228     /* other digits zero) */
7229     Unit *up, *sup;                          /* work */
7230     uInt count=dn->digits;                   /* digits to be checked */
7231     for (up=dn->lsu; ; up++) {
7232       if (count<=DECDPUN) {
7233         /* this is the last Unit (the msu) */
7234         if (*up!=powers[count-1]) break;     /* not 100.. */
7235         /* here if have the 1000... case */
7236         sup=up;                              /* save msu pointer */
7237         *up=(Unit)powers[count]-1;           /* here 100 in msu -> 999 */
7238         /* others all to all-nines, too */
7239         for (up=up-1; up>=dn->lsu; up--) *up=(Unit)powers[DECDPUN]-1;
7240         dn->exponent--;                      /* and bump exponent */
7241
7242         /* iff the number was at the subnormal boundary (exponent=etiny) */
7243         /* then the exponent is now out of range, so it will in fact get */
7244         /* clamped to etiny and the final 9 dropped. */
7245         /* printf(">> emin=%d exp=%d sdig=%d\n", set->emin, */
7246         /*        dn->exponent, set->digits); */
7247         if (dn->exponent+1==set->emin-set->digits+1) {
7248           if (count==1 && dn->digits==1) *sup=0;  /* here 9 -> 0[.9] */
7249            else {
7250             *sup=(Unit)powers[count-1]-1;    /* here 999.. in msu -> 99.. */
7251             dn->digits--;
7252             }
7253           dn->exponent++;
7254           *status|=DEC_Underflow | DEC_Subnormal | DEC_Inexact | DEC_Rounded;
7255           }
7256         return;                              /* done */
7257         }
7258
7259       /* a full unit to check, with more to come */
7260       if (*up!=0) break;                     /* not still 0s */
7261       count-=DECDPUN;
7262       } /* up */
7263
7264     } /* bump<0 */
7265
7266   /* Actual bump needed.  Do it. */
7267   decUnitAddSub(dn->lsu, D2U(dn->digits), uarrone, 1, 0, dn->lsu, bump);
7268   } /* decApplyRound */
7269
7270 #if DECSUBSET
7271 /* ------------------------------------------------------------------ */
7272 /* decFinish -- finish processing a number                            */
7273 /*                                                                    */
7274 /*   dn is the number                                                 */
7275 /*   set is the context                                               */
7276 /*   residue is the rounding accumulator (as in decApplyRound)        */
7277 /*   status is the accumulator                                        */
7278 /*                                                                    */
7279 /* This finishes off the current number by:                           */
7280 /*    1. If not extended:                                             */
7281 /*       a. Converting a zero result to clean '0'                     */
7282 /*       b. Reducing positive exponents to 0, if would fit in digits  */
7283 /*    2. Checking for overflow and subnormals (always)                */
7284 /* Note this is just Finalize when no subset arithmetic.              */
7285 /* All fields are updated as required.                                */
7286 /* ------------------------------------------------------------------ */
7287 static void decFinish(decNumber *dn, decContext *set, Int *residue,
7288                       uInt *status) {
7289   if (!set->extended) {
7290     if ISZERO(dn) {                /* value is zero */
7291       dn->exponent=0;              /* clean exponent .. */
7292       dn->bits=0;                  /* .. and sign */
7293       return;                      /* no error possible */
7294       }
7295     if (dn->exponent>=0) {         /* non-negative exponent */
7296       /* >0; reduce to integer if possible */
7297       if (set->digits >= (dn->exponent+dn->digits)) {
7298         dn->digits=decShiftToMost(dn->lsu, dn->digits, dn->exponent);
7299         dn->exponent=0;
7300         }
7301       }
7302     } /* !extended */
7303
7304   decFinalize(dn, set, residue, status);
7305   } /* decFinish */
7306 #endif
7307
7308 /* ------------------------------------------------------------------ */
7309 /* decFinalize -- final check, clamp, and round of a number           */
7310 /*                                                                    */
7311 /*   dn is the number                                                 */
7312 /*   set is the context                                               */
7313 /*   residue is the rounding accumulator (as in decApplyRound)        */
7314 /*   status is the status accumulator                                 */
7315 /*                                                                    */
7316 /* This finishes off the current number by checking for subnormal     */
7317 /* results, applying any pending rounding, checking for overflow,     */
7318 /* and applying any clamping.                                         */
7319 /* Underflow and overflow conditions are raised as appropriate.       */
7320 /* All fields are updated as required.                                */
7321 /* ------------------------------------------------------------------ */
7322 static void decFinalize(decNumber *dn, decContext *set, Int *residue,
7323                         uInt *status) {
7324   Int shift;                            /* shift needed if clamping */
7325   Int tinyexp=set->emin-dn->digits+1;   /* precalculate subnormal boundary */
7326
7327   /* Must be careful, here, when checking the exponent as the */
7328   /* adjusted exponent could overflow 31 bits [because it may already */
7329   /* be up to twice the expected]. */
7330
7331   /* First test for subnormal.  This must be done before any final */
7332   /* round as the result could be rounded to Nmin or 0. */
7333   if (dn->exponent<=tinyexp) {          /* prefilter */
7334     Int comp;
7335     decNumber nmin;
7336     /* A very nasty case here is dn == Nmin and residue<0 */
7337     if (dn->exponent<tinyexp) {
7338       /* Go handle subnormals; this will apply round if needed. */
7339       decSetSubnormal(dn, set, residue, status);
7340       return;
7341       }
7342     /* Equals case: only subnormal if dn=Nmin and negative residue */
7343     decNumberZero(&nmin);
7344     nmin.lsu[0]=1;
7345     nmin.exponent=set->emin;
7346     comp=decCompare(dn, &nmin, 1);                /* (signless compare) */
7347     if (comp==BADINT) {                           /* oops */
7348       *status|=DEC_Insufficient_storage;          /* abandon... */
7349       return;
7350       }
7351     if (*residue<0 && comp==0) {                  /* neg residue and dn==Nmin */
7352       decApplyRound(dn, set, *residue, status);   /* might force down */
7353       decSetSubnormal(dn, set, residue, status);
7354       return;
7355       }
7356     }
7357
7358   /* now apply any pending round (this could raise overflow). */
7359   if (*residue!=0) decApplyRound(dn, set, *residue, status);
7360
7361   /* Check for overflow [redundant in the 'rare' case] or clamp */
7362   if (dn->exponent<=set->emax-set->digits+1) return;   /* neither needed */
7363
7364
7365   /* here when might have an overflow or clamp to do */
7366   if (dn->exponent>set->emax-dn->digits+1) {           /* too big */
7367     decSetOverflow(dn, set, status);
7368     return;
7369     }
7370   /* here when the result is normal but in clamp range */
7371   if (!set->clamp) return;
7372
7373   /* here when need to apply the IEEE exponent clamp (fold-down) */
7374   shift=dn->exponent-(set->emax-set->digits+1);
7375
7376   /* shift coefficient (if non-zero) */
7377   if (!ISZERO(dn)) {
7378     dn->digits=decShiftToMost(dn->lsu, dn->digits, shift);
7379     }
7380   dn->exponent-=shift;   /* adjust the exponent to match */
7381   *status|=DEC_Clamped;  /* and record the dirty deed */
7382   return;
7383   } /* decFinalize */
7384
7385 /* ------------------------------------------------------------------ */
7386 /* decSetOverflow -- set number to proper overflow value              */
7387 /*                                                                    */
7388 /*   dn is the number (used for sign [only] and result)               */
7389 /*   set is the context [used for the rounding mode, etc.]            */
7390 /*   status contains the current status to be updated                 */
7391 /*                                                                    */
7392 /* This sets the sign of a number and sets its value to either        */
7393 /* Infinity or the maximum finite value, depending on the sign of     */
7394 /* dn and the rounding mode, following IEEE 854 rules.                */
7395 /* ------------------------------------------------------------------ */
7396 static void decSetOverflow(decNumber *dn, decContext *set, uInt *status) {
7397   Flag needmax=0;                  /* result is maximum finite value */
7398   uByte sign=dn->bits&DECNEG;      /* clean and save sign bit */
7399
7400   if (ISZERO(dn)) {                /* zero does not overflow magnitude */
7401     Int emax=set->emax;                      /* limit value */
7402     if (set->clamp) emax-=set->digits-1;     /* lower if clamping */
7403     if (dn->exponent>emax) {                 /* clamp required */
7404       dn->exponent=emax;
7405       *status|=DEC_Clamped;
7406       }
7407     return;
7408     }
7409
7410   decNumberZero(dn);
7411   switch (set->round) {
7412     case DEC_ROUND_DOWN: {
7413       needmax=1;                   /* never Infinity */
7414       break;} /* r-d */
7415     case DEC_ROUND_05UP: {
7416       needmax=1;                   /* never Infinity */
7417       break;} /* r-05 */
7418     case DEC_ROUND_CEILING: {
7419       if (sign) needmax=1;         /* Infinity if non-negative */
7420       break;} /* r-c */
7421     case DEC_ROUND_FLOOR: {
7422       if (!sign) needmax=1;        /* Infinity if negative */
7423       break;} /* r-f */
7424     default: break;                /* Infinity in all other cases */
7425     }
7426   if (needmax) {
7427     decSetMaxValue(dn, set);
7428     dn->bits=sign;                 /* set sign */
7429     }
7430    else dn->bits=sign|DECINF;      /* Value is +/-Infinity */
7431   *status|=DEC_Overflow | DEC_Inexact | DEC_Rounded;
7432   } /* decSetOverflow */
7433
7434 /* ------------------------------------------------------------------ */
7435 /* decSetMaxValue -- set number to +Nmax (maximum normal value)       */
7436 /*                                                                    */
7437 /*   dn is the number to set                                          */
7438 /*   set is the context [used for digits and emax]                    */
7439 /*                                                                    */
7440 /* This sets the number to the maximum positive value.                */
7441 /* ------------------------------------------------------------------ */
7442 static void decSetMaxValue(decNumber *dn, decContext *set) {
7443   Unit *up;                        /* work */
7444   Int count=set->digits;           /* nines to add */
7445   dn->digits=count;
7446   /* fill in all nines to set maximum value */
7447   for (up=dn->lsu; ; up++) {
7448     if (count>DECDPUN) *up=DECDPUNMAX;  /* unit full o'nines */
7449      else {                             /* this is the msu */
7450       *up=(Unit)(powers[count]-1);
7451       break;
7452       }
7453     count-=DECDPUN;                /* filled those digits */
7454     } /* up */
7455   dn->bits=0;                      /* + sign */
7456   dn->exponent=set->emax-set->digits+1;
7457   } /* decSetMaxValue */
7458
7459 /* ------------------------------------------------------------------ */
7460 /* decSetSubnormal -- process value whose exponent is <Emin           */
7461 /*                                                                    */
7462 /*   dn is the number (used as input as well as output; it may have   */
7463 /*         an allowed subnormal value, which may need to be rounded)  */
7464 /*   set is the context [used for the rounding mode]                  */
7465 /*   residue is any pending residue                                   */
7466 /*   status contains the current status to be updated                 */
7467 /*                                                                    */
7468 /* If subset mode, set result to zero and set Underflow flags.        */
7469 /*                                                                    */
7470 /* Value may be zero with a low exponent; this does not set Subnormal */
7471 /* but the exponent will be clamped to Etiny.                         */
7472 /*                                                                    */
7473 /* Otherwise ensure exponent is not out of range, and round as        */
7474 /* necessary.  Underflow is set if the result is Inexact.             */
7475 /* ------------------------------------------------------------------ */
7476 static void decSetSubnormal(decNumber *dn, decContext *set, Int *residue,
7477                             uInt *status) {
7478   decContext workset;         /* work */
7479   Int        etiny, adjust;   /* .. */
7480
7481   #if DECSUBSET
7482   /* simple set to zero and 'hard underflow' for subset */
7483   if (!set->extended) {
7484     decNumberZero(dn);
7485     /* always full overflow */
7486     *status|=DEC_Underflow | DEC_Subnormal | DEC_Inexact | DEC_Rounded;
7487     return;
7488     }
7489   #endif
7490
7491   /* Full arithmetic -- allow subnormals, rounded to minimum exponent */
7492   /* (Etiny) if needed */
7493   etiny=set->emin-(set->digits-1);      /* smallest allowed exponent */
7494
7495   if ISZERO(dn) {                       /* value is zero */
7496     /* residue can never be non-zero here */
7497     #if DECCHECK
7498       if (*residue!=0) {
7499         printf("++ Subnormal 0 residue %ld\n", (LI)*residue);
7500         *status|=DEC_Invalid_operation;
7501         }
7502     #endif
7503     if (dn->exponent<etiny) {           /* clamp required */
7504       dn->exponent=etiny;
7505       *status|=DEC_Clamped;
7506       }
7507     return;
7508     }
7509
7510   *status|=DEC_Subnormal;               /* have a non-zero subnormal */
7511   adjust=etiny-dn->exponent;            /* calculate digits to remove */
7512   if (adjust<=0) {                      /* not out of range; unrounded */
7513     /* residue can never be non-zero here, except in the Nmin-residue */
7514     /* case (which is a subnormal result), so can take fast-path here */
7515     /* it may already be inexact (from setting the coefficient) */
7516     if (*status&DEC_Inexact) *status|=DEC_Underflow;
7517     return;
7518     }
7519
7520   /* adjust>0, so need to rescale the result so exponent becomes Etiny */
7521   /* [this code is similar to that in rescale] */
7522   workset=*set;                         /* clone rounding, etc. */
7523   workset.digits=dn->digits-adjust;     /* set requested length */
7524   workset.emin-=adjust;                 /* and adjust emin to match */
7525   /* [note that the latter can be <1, here, similar to Rescale case] */
7526   decSetCoeff(dn, &workset, dn->lsu, dn->digits, residue, status);
7527   decApplyRound(dn, &workset, *residue, status);
7528
7529   /* Use 754R/854 default rule: Underflow is set iff Inexact */
7530   /* [independent of whether trapped] */
7531   if (*status&DEC_Inexact) *status|=DEC_Underflow;
7532
7533   /* if rounded up a 999s case, exponent will be off by one; adjust */
7534   /* back if so [it will fit, because it was shortened earlier] */
7535   if (dn->exponent>etiny) {
7536     dn->digits=decShiftToMost(dn->lsu, dn->digits, 1);
7537     dn->exponent--;                     /* (re)adjust the exponent. */
7538     }
7539
7540   /* if rounded to zero, it is by definition clamped... */
7541   if (ISZERO(dn)) *status|=DEC_Clamped;
7542   } /* decSetSubnormal */
7543
7544 /* ------------------------------------------------------------------ */
7545 /* decCheckMath - check entry conditions for a math function          */
7546 /*                                                                    */
7547 /*   This checks the context and the operand                          */
7548 /*                                                                    */
7549 /*   rhs is the operand to check                                      */
7550 /*   set is the context to check                                      */
7551 /*   status is unchanged if both are good                             */
7552 /*                                                                    */
7553 /* returns non-zero if status is changed, 0 otherwise                 */
7554 /*                                                                    */
7555 /* Restrictions enforced:                                             */
7556 /*                                                                    */
7557 /*   digits, emax, and -emin in the context must be less than         */
7558 /*   DEC_MAX_MATH (999999), and A must be within these bounds if      */
7559 /*   non-zero.  Invalid_operation is set in the status if a           */
7560 /*   restriction is violated.                                         */
7561 /* ------------------------------------------------------------------ */
7562 static uInt decCheckMath(const decNumber *rhs, decContext *set,
7563                          uInt *status) {
7564   uInt save=*status;                         /* record */
7565   if (set->digits>DEC_MAX_MATH
7566    || set->emax>DEC_MAX_MATH
7567    || -set->emin>DEC_MAX_MATH) *status|=DEC_Invalid_context;
7568    else if ((rhs->digits>DEC_MAX_MATH
7569      || rhs->exponent+rhs->digits>DEC_MAX_MATH+1
7570      || rhs->exponent+rhs->digits<2*(1-DEC_MAX_MATH))
7571      && !ISZERO(rhs)) *status|=DEC_Invalid_operation;
7572   return (*status!=save);
7573   } /* decCheckMath */
7574
7575 /* ------------------------------------------------------------------ */
7576 /* decGetInt -- get integer from a number                             */
7577 /*                                                                    */
7578 /*   dn is the number [which will not be altered]                     */
7579 /*                                                                    */
7580 /*   returns one of:                                                  */
7581 /*     BADINT if there is a non-zero fraction                         */
7582 /*     the converted integer                                          */
7583 /*     BIGEVEN if the integer is even and magnitude > 2*10**9         */
7584 /*     BIGODD  if the integer is odd  and magnitude > 2*10**9         */
7585 /*                                                                    */
7586 /* This checks and gets a whole number from the input decNumber.      */
7587 /* The sign can be determined from dn by the caller when BIGEVEN or   */
7588 /* BIGODD is returned.                                                */
7589 /* ------------------------------------------------------------------ */
7590 static Int decGetInt(const decNumber *dn) {
7591   Int  theInt;                          /* result accumulator */
7592   const Unit *up;                       /* work */
7593   Int  got;                             /* digits (real or not) processed */
7594   Int  ilength=dn->digits+dn->exponent; /* integral length */
7595   Flag neg=decNumberIsNegative(dn);     /* 1 if -ve */
7596
7597   /* The number must be an integer that fits in 10 digits */
7598   /* Assert, here, that 10 is enough for any rescale Etiny */
7599   #if DEC_MAX_EMAX > 999999999
7600     #error GetInt may need updating [for Emax]
7601   #endif
7602   #if DEC_MIN_EMIN < -999999999
7603     #error GetInt may need updating [for Emin]
7604   #endif
7605   if (ISZERO(dn)) return 0;             /* zeros are OK, with any exponent */
7606
7607   up=dn->lsu;                           /* ready for lsu */
7608   theInt=0;                             /* ready to accumulate */
7609   if (dn->exponent>=0) {                /* relatively easy */
7610     /* no fractional part [usual]; allow for positive exponent */
7611     got=dn->exponent;
7612     }
7613    else { /* -ve exponent; some fractional part to check and discard */
7614     Int count=-dn->exponent;            /* digits to discard */
7615     /* spin up whole units until reach the Unit with the unit digit */
7616     for (; count>=DECDPUN; up++) {
7617       if (*up!=0) return BADINT;        /* non-zero Unit to discard */
7618       count-=DECDPUN;
7619       }
7620     if (count==0) got=0;                /* [a multiple of DECDPUN] */
7621      else {                             /* [not multiple of DECDPUN] */
7622       Int rem;                          /* work */
7623       /* slice off fraction digits and check for non-zero */
7624       #if DECDPUN<=4
7625         theInt=QUOT10(*up, count);
7626         rem=*up-theInt*powers[count];
7627       #else
7628         rem=*up%powers[count];          /* slice off discards */
7629         theInt=*up/powers[count];
7630       #endif
7631       if (rem!=0) return BADINT;        /* non-zero fraction */
7632       /* it looks good */
7633       got=DECDPUN-count;                /* number of digits so far */
7634       up++;                             /* ready for next */
7635       }
7636     }
7637   /* now it's known there's no fractional part */
7638
7639   /* tricky code now, to accumulate up to 9.3 digits */
7640   if (got==0) {theInt=*up; got+=DECDPUN; up++;} /* ensure lsu is there */
7641
7642   if (ilength<11) {
7643     Int save=theInt;
7644     /* collect any remaining unit(s) */
7645     for (; got<ilength; up++) {
7646       theInt+=*up*powers[got];
7647       got+=DECDPUN;
7648       }
7649     if (ilength==10) {                  /* need to check for wrap */
7650       if (theInt/(Int)powers[got-DECDPUN]!=(Int)*(up-1)) ilength=11;
7651          /* [that test also disallows the BADINT result case] */
7652        else if (neg && theInt>1999999997) ilength=11;
7653        else if (!neg && theInt>999999999) ilength=11;
7654       if (ilength==11) theInt=save;     /* restore correct low bit */
7655       }
7656     }
7657
7658   if (ilength>10) {                     /* too big */
7659     if (theInt&1) return BIGODD;        /* bottom bit 1 */
7660     return BIGEVEN;                     /* bottom bit 0 */
7661     }
7662
7663   if (neg) theInt=-theInt;              /* apply sign */
7664   return theInt;
7665   } /* decGetInt */
7666
7667 /* ------------------------------------------------------------------ */
7668 /* decDecap -- decapitate the coefficient of a number                 */
7669 /*                                                                    */
7670 /*   dn   is the number to be decapitated                             */
7671 /*   drop is the number of digits to be removed from the left of dn;  */
7672 /*     this must be <= dn->digits (if equal, the coefficient is       */
7673 /*     set to 0)                                                      */
7674 /*                                                                    */
7675 /* Returns dn; dn->digits will be <= the initial digits less drop     */
7676 /* (after removing drop digits there may be leading zero digits       */
7677 /* which will also be removed).  Only dn->lsu and dn->digits change.  */
7678 /* ------------------------------------------------------------------ */
7679 static decNumber *decDecap(decNumber *dn, Int drop) {
7680   Unit *msu;                            /* -> target cut point */
7681   Int cut;                              /* work */
7682   if (drop>=dn->digits) {               /* losing the whole thing */
7683     #if DECCHECK
7684     if (drop>dn->digits)
7685       printf("decDecap called with drop>digits [%ld>%ld]\n",
7686              (LI)drop, (LI)dn->digits);
7687     #endif
7688     dn->lsu[0]=0;
7689     dn->digits=1;
7690     return dn;
7691     }
7692   msu=dn->lsu+D2U(dn->digits-drop)-1;   /* -> likely msu */
7693   cut=MSUDIGITS(dn->digits-drop);       /* digits to be in use in msu */
7694   if (cut!=DECDPUN) *msu%=powers[cut];  /* clear left digits */
7695   /* that may have left leading zero digits, so do a proper count... */
7696   dn->digits=decGetDigits(dn->lsu, msu-dn->lsu+1);
7697   return dn;
7698   } /* decDecap */
7699
7700 /* ------------------------------------------------------------------ */
7701 /* decBiStr -- compare string with pairwise options                   */
7702 /*                                                                    */
7703 /*   targ is the string to compare                                    */
7704 /*   str1 is one of the strings to compare against (length may be 0)  */
7705 /*   str2 is the other; it must be the same length as str1            */
7706 /*                                                                    */
7707 /*   returns 1 if strings compare equal, (that is, it is the same     */
7708 /*   length as str1 and str2, and each character of targ is in either */
7709 /*   str1 or str2 in the corresponding position), or 0 otherwise      */
7710 /*                                                                    */
7711 /* This is used for generic caseless compare, including the awkward   */
7712 /* case of the Turkish dotted and dotless Is.  Use as (for example):  */
7713 /*   if (decBiStr(test, "mike", "MIKE")) ...                          */
7714 /* ------------------------------------------------------------------ */
7715 static Flag decBiStr(const char *targ, const char *str1, const char *str2) {
7716   for (;;targ++, str1++, str2++) {
7717     if (*targ!=*str1 && *targ!=*str2) return 0;
7718     /* *targ has a match in one (or both, if terminator) */
7719     if (*targ=='\0') break;
7720     } /* forever */
7721   return 1;
7722   } /* decBiStr */
7723
7724 /* ------------------------------------------------------------------ */
7725 /* decNaNs -- handle NaN operand or operands                          */
7726 /*                                                                    */
7727 /*   res     is the result number                                     */
7728 /*   lhs     is the first operand                                     */
7729 /*   rhs     is the second operand, or NULL if none                   */
7730 /*   context is used to limit payload length                          */
7731 /*   status  contains the current status                              */
7732 /*   returns res in case convenient                                   */
7733 /*                                                                    */
7734 /* Called when one or both operands is a NaN, and propagates the      */
7735 /* appropriate result to res.  When an sNaN is found, it is changed   */
7736 /* to a qNaN and Invalid operation is set.                            */
7737 /* ------------------------------------------------------------------ */
7738 static decNumber * decNaNs(decNumber *res, const decNumber *lhs,
7739                            const decNumber *rhs, decContext *set,
7740                            uInt *status) {
7741   /* This decision tree ends up with LHS being the source pointer, */
7742   /* and status updated if need be */
7743   if (lhs->bits & DECSNAN)
7744     *status|=DEC_Invalid_operation | DEC_sNaN;
7745    else if (rhs==NULL);
7746    else if (rhs->bits & DECSNAN) {
7747     lhs=rhs;
7748     *status|=DEC_Invalid_operation | DEC_sNaN;
7749     }
7750    else if (lhs->bits & DECNAN);
7751    else lhs=rhs;
7752
7753   /* propagate the payload */
7754   if (lhs->digits<=set->digits) decNumberCopy(res, lhs); /* easy */
7755    else { /* too long */
7756     const Unit *ul;
7757     Unit *ur, *uresp1;
7758     /* copy safe number of units, then decapitate */
7759     res->bits=lhs->bits;                /* need sign etc. */
7760     uresp1=res->lsu+D2U(set->digits);
7761     for (ur=res->lsu, ul=lhs->lsu; ur<uresp1; ur++, ul++) *ur=*ul;
7762     res->digits=D2U(set->digits)*DECDPUN;
7763     /* maybe still too long */
7764     if (res->digits>set->digits) decDecap(res, res->digits-set->digits);
7765     }
7766
7767   res->bits&=~DECSNAN;        /* convert any sNaN to NaN, while */
7768   res->bits|=DECNAN;          /* .. preserving sign */
7769   res->exponent=0;            /* clean exponent */
7770                               /* [coefficient was copied/decapitated] */
7771   return res;
7772   } /* decNaNs */
7773
7774 /* ------------------------------------------------------------------ */
7775 /* decStatus -- apply non-zero status                                 */
7776 /*                                                                    */
7777 /*   dn     is the number to set if error                             */
7778 /*   status contains the current status (not yet in context)          */
7779 /*   set    is the context                                            */
7780 /*                                                                    */
7781 /* If the status is an error status, the number is set to a NaN,      */
7782 /* unless the error was an overflow, divide-by-zero, or underflow,    */
7783 /* in which case the number will have already been set.               */
7784 /*                                                                    */
7785 /* The context status is then updated with the new status.  Note that */
7786 /* this may raise a signal, so control may never return from this     */
7787 /* routine (hence resources must be recovered before it is called).   */
7788 /* ------------------------------------------------------------------ */
7789 static void decStatus(decNumber *dn, uInt status, decContext *set) {
7790   if (status & DEC_NaNs) {              /* error status -> NaN */
7791     /* if cause was an sNaN, clear and propagate [NaN is already set up] */
7792     if (status & DEC_sNaN) status&=~DEC_sNaN;
7793      else {
7794       decNumberZero(dn);                /* other error: clean throughout */
7795       dn->bits=DECNAN;                  /* and make a quiet NaN */
7796       }
7797     }
7798   decContextSetStatus(set, status);     /* [may not return] */
7799   return;
7800   } /* decStatus */
7801
7802 /* ------------------------------------------------------------------ */
7803 /* decGetDigits -- count digits in a Units array                      */
7804 /*                                                                    */
7805 /*   uar is the Unit array holding the number (this is often an       */
7806 /*          accumulator of some sort)                                 */
7807 /*   len is the length of the array in units [>=1]                    */
7808 /*                                                                    */
7809 /*   returns the number of (significant) digits in the array          */
7810 /*                                                                    */
7811 /* All leading zeros are excluded, except the last if the array has   */
7812 /* only zero Units.                                                   */
7813 /* ------------------------------------------------------------------ */
7814 /* This may be called twice during some operations. */
7815 static Int decGetDigits(Unit *uar, Int len) {
7816   Unit *up=uar+(len-1);            /* -> msu */
7817   Int  digits=(len-1)*DECDPUN+1;   /* possible digits excluding msu */
7818   #if DECDPUN>4
7819   uInt const *pow;                 /* work */
7820   #endif
7821                                    /* (at least 1 in final msu) */
7822   #if DECCHECK
7823   if (len<1) printf("decGetDigits called with len<1 [%ld]\n", (LI)len);
7824   #endif
7825
7826   for (; up>=uar; up--) {
7827     if (*up==0) {                  /* unit is all 0s */
7828       if (digits==1) break;        /* a zero has one digit */
7829       digits-=DECDPUN;             /* adjust for 0 unit */
7830       continue;}
7831     /* found the first (most significant) non-zero Unit */
7832     #if DECDPUN>1                  /* not done yet */
7833     if (*up<10) break;             /* is 1-9 */
7834     digits++;
7835     #if DECDPUN>2                  /* not done yet */
7836     if (*up<100) break;            /* is 10-99 */
7837     digits++;
7838     #if DECDPUN>3                  /* not done yet */
7839     if (*up<1000) break;           /* is 100-999 */
7840     digits++;
7841     #if DECDPUN>4                  /* count the rest ... */
7842     for (pow=&powers[4]; *up>=*pow; pow++) digits++;
7843     #endif
7844     #endif
7845     #endif
7846     #endif
7847     break;
7848     } /* up */
7849   return digits;
7850   } /* decGetDigits */
7851
7852 #if DECTRACE | DECCHECK
7853 /* ------------------------------------------------------------------ */
7854 /* decNumberShow -- display a number [debug aid]                      */
7855 /*   dn is the number to show                                         */
7856 /*                                                                    */
7857 /* Shows: sign, exponent, coefficient (msu first), digits             */
7858 /*    or: sign, special-value                                         */
7859 /* ------------------------------------------------------------------ */
7860 /* this is public so other modules can use it */
7861 void decNumberShow(const decNumber *dn) {
7862   const Unit *up;                  /* work */
7863   uInt u, d;                       /* .. */
7864   Int cut;                         /* .. */
7865   char isign='+';                  /* main sign */
7866   if (dn==NULL) {
7867     printf("NULL\n");
7868     return;}
7869   if (decNumberIsNegative(dn)) isign='-';
7870   printf(" >> %c ", isign);
7871   if (dn->bits&DECSPECIAL) {       /* Is a special value */
7872     if (decNumberIsInfinite(dn)) printf("Infinity");
7873      else {                                  /* a NaN */
7874       if (dn->bits&DECSNAN) printf("sNaN");  /* signalling NaN */
7875        else printf("NaN");
7876       }
7877     /* if coefficient and exponent are 0, no more to do */
7878     if (dn->exponent==0 && dn->digits==1 && *dn->lsu==0) {
7879       printf("\n");
7880       return;}
7881     /* drop through to report other information */
7882     printf(" ");
7883     }
7884
7885   /* now carefully display the coefficient */
7886   up=dn->lsu+D2U(dn->digits)-1;         /* msu */
7887   printf("%ld", (LI)*up);
7888   for (up=up-1; up>=dn->lsu; up--) {
7889     u=*up;
7890     printf(":");
7891     for (cut=DECDPUN-1; cut>=0; cut--) {
7892       d=u/powers[cut];
7893       u-=d*powers[cut];
7894       printf("%ld", (LI)d);
7895       } /* cut */
7896     } /* up */
7897   if (dn->exponent!=0) {
7898     char esign='+';
7899     if (dn->exponent<0) esign='-';
7900     printf(" E%c%ld", esign, (LI)abs(dn->exponent));
7901     }
7902   printf(" [%ld]\n", (LI)dn->digits);
7903   } /* decNumberShow */
7904 #endif
7905
7906 #if DECTRACE || DECCHECK
7907 /* ------------------------------------------------------------------ */
7908 /* decDumpAr -- display a unit array [debug/check aid]                */
7909 /*   name is a single-character tag name                              */
7910 /*   ar   is the array to display                                     */
7911 /*   len  is the length of the array in Units                         */
7912 /* ------------------------------------------------------------------ */
7913 static void decDumpAr(char name, const Unit *ar, Int len) {
7914   Int i;
7915   const char *spec;
7916   #if DECDPUN==9
7917     spec="%09d ";
7918   #elif DECDPUN==8
7919     spec="%08d ";
7920   #elif DECDPUN==7
7921     spec="%07d ";
7922   #elif DECDPUN==6
7923     spec="%06d ";
7924   #elif DECDPUN==5
7925     spec="%05d ";
7926   #elif DECDPUN==4
7927     spec="%04d ";
7928   #elif DECDPUN==3
7929     spec="%03d ";
7930   #elif DECDPUN==2
7931     spec="%02d ";
7932   #else
7933     spec="%d ";
7934   #endif
7935   printf("  :%c: ", name);
7936   for (i=len-1; i>=0; i--) {
7937     if (i==len-1) printf("%ld ", (LI)ar[i]);
7938      else printf(spec, ar[i]);
7939     }
7940   printf("\n");
7941   return;}
7942 #endif
7943
7944 #if DECCHECK
7945 /* ------------------------------------------------------------------ */
7946 /* decCheckOperands -- check operand(s) to a routine                  */
7947 /*   res is the result structure (not checked; it will be set to      */
7948 /*          quiet NaN if error found (and it is not NULL))            */
7949 /*   lhs is the first operand (may be DECUNRESU)                      */
7950 /*   rhs is the second (may be DECUNUSED)                             */
7951 /*   set is the context (may be DECUNCONT)                            */
7952 /*   returns 0 if both operands, and the context are clean, or 1      */
7953 /*     otherwise (in which case the context will show an error,       */
7954 /*     unless NULL).  Note that res is not cleaned; caller should     */
7955 /*     handle this so res=NULL case is safe.                          */
7956 /* The caller is expected to abandon immediately if 1 is returned.    */
7957 /* ------------------------------------------------------------------ */
7958 static Flag decCheckOperands(decNumber *res, const decNumber *lhs,
7959                              const decNumber *rhs, decContext *set) {
7960   Flag bad=0;
7961   if (set==NULL) {                 /* oops; hopeless */
7962     #if DECTRACE || DECVERB
7963     printf("Reference to context is NULL.\n");
7964     #endif
7965     bad=1;
7966     return 1;}
7967    else if (set!=DECUNCONT
7968      && (set->digits<1 || set->round>=DEC_ROUND_MAX)) {
7969     bad=1;
7970     #if DECTRACE || DECVERB
7971     printf("Bad context [digits=%ld round=%ld].\n",
7972            (LI)set->digits, (LI)set->round);
7973     #endif
7974     }
7975    else {
7976     if (res==NULL) {
7977       bad=1;
7978       #if DECTRACE
7979       /* this one not DECVERB as standard tests include NULL */
7980       printf("Reference to result is NULL.\n");
7981       #endif
7982       }
7983     if (!bad && lhs!=DECUNUSED) bad=(decCheckNumber(lhs));
7984     if (!bad && rhs!=DECUNUSED) bad=(decCheckNumber(rhs));
7985     }
7986   if (bad) {
7987     if (set!=DECUNCONT) decContextSetStatus(set, DEC_Invalid_operation);
7988     if (res!=DECUNRESU && res!=NULL) {
7989       decNumberZero(res);
7990       res->bits=DECNAN;       /* qNaN */
7991       }
7992     }
7993   return bad;
7994   } /* decCheckOperands */
7995
7996 /* ------------------------------------------------------------------ */
7997 /* decCheckNumber -- check a number                                   */
7998 /*   dn is the number to check                                        */
7999 /*   returns 0 if the number is clean, or 1 otherwise                 */
8000 /*                                                                    */
8001 /* The number is considered valid if it could be a result from some   */
8002 /* operation in some valid context.                                   */
8003 /* ------------------------------------------------------------------ */
8004 static Flag decCheckNumber(const decNumber *dn) {
8005   const Unit *up;             /* work */
8006   uInt maxuint;               /* .. */
8007   Int ae, d, digits;          /* .. */
8008   Int emin, emax;             /* .. */
8009
8010   if (dn==NULL) {             /* hopeless */
8011     #if DECTRACE
8012     /* this one not DECVERB as standard tests include NULL */
8013     printf("Reference to decNumber is NULL.\n");
8014     #endif
8015     return 1;}
8016
8017   /* check special values */
8018   if (dn->bits & DECSPECIAL) {
8019     if (dn->exponent!=0) {
8020       #if DECTRACE || DECVERB
8021       printf("Exponent %ld (not 0) for a special value [%02x].\n",
8022              (LI)dn->exponent, dn->bits);
8023       #endif
8024       return 1;}
8025
8026     /* 2003.09.08: NaNs may now have coefficients, so next tests Inf only */
8027     if (decNumberIsInfinite(dn)) {
8028       if (dn->digits!=1) {
8029         #if DECTRACE || DECVERB
8030         printf("Digits %ld (not 1) for an infinity.\n", (LI)dn->digits);
8031         #endif
8032         return 1;}
8033       if (*dn->lsu!=0) {
8034         #if DECTRACE || DECVERB
8035         printf("LSU %ld (not 0) for an infinity.\n", (LI)*dn->lsu);
8036         #endif
8037         decDumpAr('I', dn->lsu, D2U(dn->digits));
8038         return 1;}
8039       } /* Inf */
8040     /* 2002.12.26: negative NaNs can now appear through proposed IEEE */
8041     /*             concrete formats (decimal64, etc.). */
8042     return 0;
8043     }
8044
8045   /* check the coefficient */
8046   if (dn->digits<1 || dn->digits>DECNUMMAXP) {
8047     #if DECTRACE || DECVERB
8048     printf("Digits %ld in number.\n", (LI)dn->digits);
8049     #endif
8050     return 1;}
8051
8052   d=dn->digits;
8053
8054   for (up=dn->lsu; d>0; up++) {
8055     if (d>DECDPUN) maxuint=DECDPUNMAX;
8056      else {                   /* reached the msu */
8057       maxuint=powers[d]-1;
8058       if (dn->digits>1 && *up<powers[d-1]) {
8059         #if DECTRACE || DECVERB
8060         printf("Leading 0 in number.\n");
8061         decNumberShow(dn);
8062         #endif
8063         return 1;}
8064       }
8065     if (*up>maxuint) {
8066       #if DECTRACE || DECVERB
8067       printf("Bad Unit [%08lx] in %ld-digit number at offset %ld [maxuint %ld].\n",
8068               (LI)*up, (LI)dn->digits, (LI)(up-dn->lsu), (LI)maxuint);
8069       #endif
8070       return 1;}
8071     d-=DECDPUN;
8072     }
8073
8074   /* check the exponent.  Note that input operands can have exponents */
8075   /* which are out of the set->emin/set->emax and set->digits range */
8076   /* (just as they can have more digits than set->digits). */
8077   ae=dn->exponent+dn->digits-1;    /* adjusted exponent */
8078   emax=DECNUMMAXE;
8079   emin=DECNUMMINE;
8080   digits=DECNUMMAXP;
8081   if (ae<emin-(digits-1)) {
8082     #if DECTRACE || DECVERB
8083     printf("Adjusted exponent underflow [%ld].\n", (LI)ae);
8084     decNumberShow(dn);
8085     #endif
8086     return 1;}
8087   if (ae>+emax) {
8088     #if DECTRACE || DECVERB
8089     printf("Adjusted exponent overflow [%ld].\n", (LI)ae);
8090     decNumberShow(dn);
8091     #endif
8092     return 1;}
8093
8094   return 0;              /* it's OK */
8095   } /* decCheckNumber */
8096
8097 /* ------------------------------------------------------------------ */
8098 /* decCheckInexact -- check a normal finite inexact result has digits */
8099 /*   dn is the number to check                                        */
8100 /*   set is the context (for status and precision)                    */
8101 /*   sets Invalid operation, etc., if some digits are missing         */
8102 /* [this check is not made for DECSUBSET compilation or when          */
8103 /* subnormal is not set]                                              */
8104 /* ------------------------------------------------------------------ */
8105 static void decCheckInexact(const decNumber *dn, decContext *set) {
8106   #if !DECSUBSET && DECEXTFLAG
8107     if ((set->status & (DEC_Inexact|DEC_Subnormal))==DEC_Inexact
8108      && (set->digits!=dn->digits) && !(dn->bits & DECSPECIAL)) {
8109       #if DECTRACE || DECVERB
8110       printf("Insufficient digits [%ld] on normal Inexact result.\n",
8111              (LI)dn->digits);
8112       decNumberShow(dn);
8113       #endif
8114       decContextSetStatus(set, DEC_Invalid_operation);
8115       }
8116   #else
8117     /* next is a noop for quiet compiler */
8118     if (dn!=NULL && dn->digits==0) set->status|=DEC_Invalid_operation;
8119   #endif
8120   return;
8121   } /* decCheckInexact */
8122 #endif
8123
8124 #if DECALLOC
8125 #undef malloc
8126 #undef free
8127 /* ------------------------------------------------------------------ */
8128 /* decMalloc -- accountable allocation routine                        */
8129 /*   n is the number of bytes to allocate                             */
8130 /*                                                                    */
8131 /* Semantics is the same as the stdlib malloc routine, but bytes      */
8132 /* allocated are accounted for globally, and corruption fences are    */
8133 /* added before and after the 'actual' storage.                       */
8134 /* ------------------------------------------------------------------ */
8135 /* This routine allocates storage with an extra twelve bytes; 8 are   */
8136 /* at the start and hold:                                             */
8137 /*   0-3 the original length requested                                */
8138 /*   4-7 buffer corruption detection fence (DECFENCE, x4)             */
8139 /* The 4 bytes at the end also hold a corruption fence (DECFENCE, x4) */
8140 /* ------------------------------------------------------------------ */
8141 static void *decMalloc(size_t n) {
8142   uInt  size=n+12;                 /* true size */
8143   void  *alloc;                    /* -> allocated storage */
8144   uInt  *j;                        /* work */
8145   uByte *b, *b0;                   /* .. */
8146
8147   alloc=malloc(size);              /* -> allocated storage */
8148   if (alloc==NULL) return NULL;    /* out of strorage */
8149   b0=(uByte *)alloc;               /* as bytes */
8150   decAllocBytes+=n;                /* account for storage */
8151   j=(uInt *)alloc;                 /* -> first four bytes */
8152   *j=n;                            /* save n */
8153   /* printf(" alloc ++ dAB: %ld (%d)\n", decAllocBytes, n); */
8154   for (b=b0+4; b<b0+8; b++) *b=DECFENCE;
8155   for (b=b0+n+8; b<b0+n+12; b++) *b=DECFENCE;
8156   return b0+8;                     /* -> play area */
8157   } /* decMalloc */
8158
8159 /* ------------------------------------------------------------------ */
8160 /* decFree -- accountable free routine                                */
8161 /*   alloc is the storage to free                                     */
8162 /*                                                                    */
8163 /* Semantics is the same as the stdlib malloc routine, except that    */
8164 /* the global storage accounting is updated and the fences are        */
8165 /* checked to ensure that no routine has written 'out of bounds'.     */
8166 /* ------------------------------------------------------------------ */
8167 /* This routine first checks that the fences have not been corrupted. */
8168 /* It then frees the storage using the 'truw' storage address (that   */
8169 /* is, offset by 8).                                                  */
8170 /* ------------------------------------------------------------------ */
8171 static void decFree(void *alloc) {
8172   uInt  *j, n;                     /* pointer, original length */
8173   uByte *b, *b0;                   /* work */
8174
8175   if (alloc==NULL) return;         /* allowed; it's a nop */
8176   b0=(uByte *)alloc;               /* as bytes */
8177   b0-=8;                           /* -> true start of storage */
8178   j=(uInt *)b0;                    /* -> first four bytes */
8179   n=*j;                            /* lift */
8180   for (b=b0+4; b<b0+8; b++) if (*b!=DECFENCE)
8181     printf("=== Corrupt byte [%02x] at offset %d from %ld ===\n", *b,
8182            b-b0-8, (Int)b0);
8183   for (b=b0+n+8; b<b0+n+12; b++) if (*b!=DECFENCE)
8184     printf("=== Corrupt byte [%02x] at offset +%d from %ld, n=%ld ===\n", *b,
8185            b-b0-8, (Int)b0, n);
8186   free(b0);                        /* drop the storage */
8187   decAllocBytes-=n;                /* account for storage */
8188   /* printf(" free -- dAB: %d (%d)\n", decAllocBytes, -n); */
8189   } /* decFree */
8190 #define malloc(a) decMalloc(a)
8191 #define free(a) decFree(a)
8192 #endif