libdecnumber/decNumberLocal.h

   1 /* Local definitions for the decNumber C Library.
   2    Copyright (C) 2007-2022 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 3, or (at your option) any later
  10    version.
  11
  12    GCC is distributed in the hope that it will be useful, but WITHOUT ANY
  13    WARRANTY; without even the implied warranty of MERCHANTABILITY or
  14    FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
  15    for more details.
  16
  17 Under Section 7 of GPL version 3, you are granted additional
  18 permissions described in the GCC Runtime Library Exception, version
  19 3.1, as published by the Free Software Foundation.
  20
  21 You should have received a copy of the GNU General Public License and
  22 a copy of the GCC Runtime Library Exception along with this program;
  23 see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
  24 <http://www.gnu.org/licenses/>.  */
  25
  26 /* ------------------------------------------------------------------ */
  27 /* decNumber package local type, tuning, and macro definitions        */
  28 /* ------------------------------------------------------------------ */
  29 /* This header file is included by all modules in the decNumber       */
  30 /* library, and contains local type definitions, tuning parameters,   */
  31 /* etc.  It should not need to be used by application programs.       */
  32 /* decNumber.h or one of decDouble (etc.) must be included first.     */
  33 /* ------------------------------------------------------------------ */
  34
  35 #if !defined(DECNUMBERLOC)
  36   #define DECNUMBERLOC
  37   #define DECVERSION    "decNumber 3.61" /* Package Version [16 max.] */
  38   #define DECNLAUTHOR   "Mike Cowlishaw"              /* Who to blame */
  39
  40   #include <stdlib.h>         /* for abs                              */
  41   #include <string.h>         /* for memset, strcpy                   */
  42   #include "dconfig.h"        /* for WORDS_BIGENDIAN                  */
  43
  44   /* Conditional code flag -- set this to match hardware platform     */
  45   /* 1=little-endian, 0=big-endian                                   */
  46   #if WORDS_BIGENDIAN
  47   #define DECLITEND 0
  48   #else
  49   #define DECLITEND 1
  50   #endif
  51
  52   #if !defined(DECLITEND)
  53   #define DECLITEND 1         /* 1=little-endian, 0=big-endian        */
  54   #endif
  55
  56   /* Conditional code flag -- set this to 1 for best performance      */
  57   #if !defined(DECUSE64)
  58   #define DECUSE64  1         /* 1=use int64s, 0=int32 & smaller only */
  59   #endif
  60
  61   /* Conditional check flags -- set these to 0 for best performance   */
  62   #if !defined(DECCHECK)
  63   #define DECCHECK  0         /* 1 to enable robust checking          */
  64   #endif
  65   #if !defined(DECALLOC)
  66   #define DECALLOC  0         /* 1 to enable memory accounting        */
  67   #endif
  68   #if !defined(DECTRACE)
  69   #define DECTRACE  0         /* 1 to trace certain internals, etc.   */
  70   #endif
  71
  72   /* Tuning parameter for decNumber (arbitrary precision) module      */
  73   #if !defined(DECBUFFER)
  74   #define DECBUFFER 36        /* Size basis for local buffers.  This  */
  75                               /* should be a common maximum precision */
  76                               /* rounded up to a multiple of 4; must  */
  77                               /* be zero or positive.                 */
  78   #endif
  79
  80   /* ---------------------------------------------------------------- */
  81   /* Definitions for all modules (general-purpose)                    */
  82   /* ---------------------------------------------------------------- */
  83
  84   /* Local names for common types -- for safety, decNumber modules do */
  85   /* not use int or long directly.                                    */
  86   #define Flag   uint8_t
  87   #define Byte   int8_t
  88   #define uByte  uint8_t
  89   #define Short  int16_t
  90   #define uShort uint16_t
  91   #define Int    int32_t
  92   #define uInt   uint32_t
  93   #define Unit   decNumberUnit
  94   #if DECUSE64
  95   #define Long   int64_t
  96   #define uLong  uint64_t
  97   #endif
  98
  99   /* Development-use definitions                                      */
 100   typedef long int LI;        /* for printf arguments only            */
 101   #define DECNOINT  0         /* 1 to check no internal use of 'int'  */
 102                               /*   or stdint types                    */
 103   #if DECNOINT
 104     /* if these interfere with your C includes, do not set DECNOINT   */
 105     #define int     ?         /* enable to ensure that plain C 'int'  */
 106     #define long    ??        /* .. or 'long' types are not used      */
 107   #endif
 108
 109   /* Shared lookup tables                                             */
 110   extern const uByte  DECSTICKYTAB[10]; /* re-round digits if sticky  */
 111   extern const uInt   DECPOWERS[10];    /* powers of ten table        */
 112   /* The following are included from decDPD.h                         */
 113   #include "decDPDSymbols.h"
 114   extern const uShort DPD2BIN[1024];    /* DPD -> 0-999               */
 115   extern const uShort BIN2DPD[1000];    /* 0-999 -> DPD               */
 116   extern const uInt   DPD2BINK[1024];   /* DPD -> 0-999000            */
 117   extern const uInt   DPD2BINM[1024];   /* DPD -> 0-999000000         */
 118   extern const uByte  DPD2BCD8[4096];   /* DPD -> ddd + len           */
 119   extern const uByte  BIN2BCD8[4000];   /* 0-999 -> ddd + len         */
 120   extern const uShort BCD2DPD[2458];    /* 0-0x999 -> DPD (0x999=2457)*/
 121
 122   /* LONGMUL32HI -- set w=(u*v)>>32, where w, u, and v are uInts      */
 123   /* (that is, sets w to be the high-order word of the 64-bit result; */
 124   /* the low-order word is simply u*v.)                               */
 125   /* This version is derived from Knuth via Hacker's Delight;         */
 126   /* it seems to optimize better than some others tried               */
 127   #define LONGMUL32HI(w, u, v) {             \
 128     uInt u0, u1, v0, v1, w0, w1, w2, t;      \
 129     u0=u & 0xffff; u1=u>>16;                 \
 130     v0=v & 0xffff; v1=v>>16;                 \
 131     w0=u0*v0;                                \
 132     t=u1*v0 + (w0>>16);                      \
 133     w1=t & 0xffff; w2=t>>16;                 \
 134     w1=u0*v1 + w1;                           \
 135     (w)=u1*v1 + w2 + (w1>>16);}
 136
 137   /* ROUNDUP -- round an integer up to a multiple of n                */
 138   #define ROUNDUP(i, n) ((((i)+(n)-1)/n)*n)
 139   #define ROUNDUP4(i)   (((i)+3)&~3)    /* special for n=4            */
 140
 141   /* ROUNDDOWN -- round an integer down to a multiple of n            */
 142   #define ROUNDDOWN(i, n) (((i)/n)*n)
 143   #define ROUNDDOWN4(i)   ((i)&~3)      /* special for n=4            */
 144
 145   /* References to multi-byte sequences under different sizes; these  */
 146   /* require locally declared variables, but do not violate strict    */
 147   /* aliasing or alignment (as did the UINTAT simple cast to uInt).   */
 148   /* Variables needed are uswork, uiwork, etc. [so do not use at same */
 149   /* level in an expression, e.g., UBTOUI(x)==UBTOUI(y) may fail].    */
 150
 151   /* Return a uInt, etc., from bytes starting at a char* or uByte*    */
 152   #define UBTOUS(b)  (memcpy((void *)&uswork, b, 2), uswork)
 153   #define UBTOUI(b)  (memcpy((void *)&uiwork, b, 4), uiwork)
 154
 155   /* Store a uInt, etc., into bytes starting at a char* or uByte*.    */
 156   /* Has to use uiwork because i may be an expression.                */
 157   #define UBFROMUS(b, i)  (uswork=(i), memcpy(b, (void *)&uswork, 2))
 158   #define UBFROMUI(b, i)  (uiwork=(i), memcpy(b, (void *)&uiwork, 4))
 159
 160   /* X10 and X100 -- multiply integer i by 10 or 100                  */
 161   /* [shifts are usually faster than multiply; could be conditional]  */
 162   #define X10(i)  (((i)<<1)+((i)<<3))
 163   #define X100(i) (((i)<<2)+((i)<<5)+((i)<<6))
 164
 165   /* MAXI and MINI -- general max & min (not in ANSI) for integers    */
 166   #define MAXI(x,y) ((x)<(y)?(y):(x))
 167   #define MINI(x,y) ((x)>(y)?(y):(x))
 168
 169   /* Useful constants                                                 */
 170   #define BILLION      1000000000            /* 10**9                 */
 171   /* CHARMASK: 0x30303030 for ASCII/UTF8; 0xF0F0F0F0 for EBCDIC       */
 172   #define CHARMASK ((((((((uInt)'0')<<8)+'0')<<8)+'0')<<8)+'0')
 173
 174
 175   /* ---------------------------------------------------------------- */
 176   /* Definitions for arbitary-precision modules (only valid after     */
 177   /* decNumber.h has been included)                                   */
 178   /* ---------------------------------------------------------------- */
 179
 180   /* Limits and constants                                             */
 181   #define DECNUMMAXP 999999999  /* maximum precision code can handle  */
 182   #define DECNUMMAXE 999999999  /* maximum adjusted exponent ditto    */
 183   #define DECNUMMINE -999999999 /* minimum adjusted exponent ditto    */
 184   #if (DECNUMMAXP != DEC_MAX_DIGITS)
 185     #error Maximum digits mismatch
 186   #endif
 187   #if (DECNUMMAXE != DEC_MAX_EMAX)
 188     #error Maximum exponent mismatch
 189   #endif
 190   #if (DECNUMMINE != DEC_MIN_EMIN)
 191     #error Minimum exponent mismatch
 192   #endif
 193
 194   /* Set DECDPUNMAX -- the maximum integer that fits in DECDPUN       */
 195   /* digits, and D2UTABLE -- the initializer for the D2U table        */
 196   #if   DECDPUN==1
 197     #define DECDPUNMAX 9
 198     #define D2UTABLE {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,  \
 199                       18,19,20,21,22,23,24,25,26,27,28,29,30,31,32, \
 200                       33,34,35,36,37,38,39,40,41,42,43,44,45,46,47, \
 201                       48,49}
 202   #elif DECDPUN==2
 203     #define DECDPUNMAX 99
 204     #define D2UTABLE {0,1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,  \
 205                       11,11,12,12,13,13,14,14,15,15,16,16,17,17,18, \
 206                       18,19,19,20,20,21,21,22,22,23,23,24,24,25}
 207   #elif DECDPUN==3
 208     #define DECDPUNMAX 999
 209     #define D2UTABLE {0,1,1,1,2,2,2,3,3,3,4,4,4,5,5,5,6,6,6,7,7,7,  \
 210                       8,8,8,9,9,9,10,10,10,11,11,11,12,12,12,13,13, \
 211                       13,14,14,14,15,15,15,16,16,16,17}
 212   #elif DECDPUN==4
 213     #define DECDPUNMAX 9999
 214     #define D2UTABLE {0,1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,6,  \
 215                       6,6,6,7,7,7,7,8,8,8,8,9,9,9,9,10,10,10,10,11, \
 216                       11,11,11,12,12,12,12,13}
 217   #elif DECDPUN==5
 218     #define DECDPUNMAX 99999
 219     #define D2UTABLE {0,1,1,1,1,1,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,5,  \
 220                       5,5,5,5,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,9,9,9,  \
 221                       9,9,10,10,10,10}
 222   #elif DECDPUN==6
 223     #define DECDPUNMAX 999999
 224     #define D2UTABLE {0,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,  \
 225                       4,4,4,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,8,  \
 226                       8,8,8,8,8,9}
 227   #elif DECDPUN==7
 228     #define DECDPUNMAX 9999999
 229     #define D2UTABLE {0,1,1,1,1,1,1,1,2,2,2,2,2,2,2,3,3,3,3,3,3,3,  \
 230                       4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,6,7,  \
 231                       7,7,7,7,7,7}
 232   #elif DECDPUN==8
 233     #define DECDPUNMAX 99999999
 234     #define D2UTABLE {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,  \
 235                       3,3,3,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,  \
 236                       6,6,6,6,6,7}
 237   #elif DECDPUN==9
 238     #define DECDPUNMAX 999999999
 239     #define D2UTABLE {0,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,3,3,3,  \
 240                       3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,  \
 241                       5,5,6,6,6,6}
 242   #elif defined(DECDPUN)
 243     #error DECDPUN must be in the range 1-9
 244   #endif
 245
 246   /* ----- Shared data (in decNumber.c) ----- */
 247   /* Public lookup table used by the D2U macro (see below)            */
 248   #define DECMAXD2U 49
 249   extern const uByte d2utable[DECMAXD2U+1];
 250
 251   /* ----- Macros ----- */
 252   /* ISZERO -- return true if decNumber dn is a zero                  */
 253   /* [performance-critical in some situations]                        */
 254   #define ISZERO(dn) decNumberIsZero(dn)     /* now just a local name */
 255
 256   /* D2U -- return the number of Units needed to hold d digits        */
 257   /* (runtime version, with table lookaside for small d)              */
 258   #if DECDPUN==8
 259     #define D2U(d) ((unsigned)((d)<=DECMAXD2U?d2utable[d]:((d)+7)>>3))
 260   #elif DECDPUN==4
 261     #define D2U(d) ((unsigned)((d)<=DECMAXD2U?d2utable[d]:((d)+3)>>2))
 262   #else
 263     #define D2U(d) ((d)<=DECMAXD2U?d2utable[d]:((d)+DECDPUN-1)/DECDPUN)
 264   #endif
 265   /* SD2U -- static D2U macro (for compile-time calculation)          */
 266   #define SD2U(d) (((d)+DECDPUN-1)/DECDPUN)
 267
 268   /* MSUDIGITS -- returns digits in msu, from digits, calculated      */
 269   /* using D2U                                                        */
 270   #define MSUDIGITS(d) ((d)-(D2U(d)-1)*DECDPUN)
 271
 272   /* D2N -- return the number of decNumber structs that would be      */
 273   /* needed to contain that number of digits (and the initial         */
 274   /* decNumber struct) safely.  Note that one Unit is included in the */
 275   /* initial structure.  Used for allocating space that is aligned on */
 276   /* a decNumber struct boundary. */
 277   #define D2N(d) \
 278     ((((SD2U(d)-1)*sizeof(Unit))+sizeof(decNumber)*2-1)/sizeof(decNumber))
 279
 280   /* TODIGIT -- macro to remove the leading digit from the unsigned   */
 281   /* integer u at column cut (counting from the right, LSD=0) and     */
 282   /* place it as an ASCII character into the character pointed to by  */
 283   /* c.  Note that cut must be <= 9, and the maximum value for u is   */
 284   /* 2,000,000,000 (as is needed for negative exponents of            */
 285   /* subnormals).  The unsigned integer pow is used as a temporary    */
 286   /* variable. */
 287   #define TODIGIT(u, cut, c, pow) {       \
 288     *(c)='0';                             \
 289     pow=DECPOWERS[cut]*2;                 \
 290     if ((u)>pow) {                        \
 291       pow*=4;                             \
 292       if ((u)>=pow) {(u)-=pow; *(c)+=8;}  \
 293       pow/=2;                             \
 294       if ((u)>=pow) {(u)-=pow; *(c)+=4;}  \
 295       pow/=2;                             \
 296       }                                   \
 297     if ((u)>=pow) {(u)-=pow; *(c)+=2;}    \
 298     pow/=2;                               \
 299     if ((u)>=pow) {(u)-=pow; *(c)+=1;}    \
 300     }
 301
 302   /* ---------------------------------------------------------------- */
 303   /* Definitions for fixed-precision modules (only valid after        */
 304   /* decSingle.h, decDouble.h, or decQuad.h has been included)        */
 305   /* ---------------------------------------------------------------- */
 306
 307   /* bcdnum -- a structure describing a format-independent finite     */
 308   /* number, whose coefficient is a string of bcd8 uBytes             */
 309   typedef struct {
 310     uByte   *msd;             /* -> most significant digit            */
 311     uByte   *lsd;             /* -> least ditto                       */
 312     uInt     sign;            /* 0=positive, DECFLOAT_Sign=negative   */
 313     Int      exponent;        /* Unadjusted signed exponent (q), or   */
 314                               /* DECFLOAT_NaN etc. for a special      */
 315     } bcdnum;
 316
 317   /* Test if exponent or bcdnum exponent must be a special, etc.      */
 318   #define EXPISSPECIAL(exp) ((exp)>=DECFLOAT_MinSp)
 319   #define EXPISINF(exp) (exp==DECFLOAT_Inf)
 320   #define EXPISNAN(exp) (exp==DECFLOAT_qNaN || exp==DECFLOAT_sNaN)
 321   #define NUMISSPECIAL(num) (EXPISSPECIAL((num)->exponent))
 322
 323   /* Refer to a 32-bit word or byte in a decFloat (df) by big-endian  */
 324   /* (array) notation (the 0 word or byte contains the sign bit),     */
 325   /* automatically adjusting for endianness; similarly address a word */
 326   /* in the next-wider format (decFloatWider, or dfw)                 */
 327   #define DECWORDS  (DECBYTES/4)
 328   #define DECWWORDS (DECWBYTES/4)
 329   #if DECLITEND
 330     #define DFBYTE(df, off)   ((df)->bytes[DECBYTES-1-(off)])
 331     #define DFWORD(df, off)   ((df)->words[DECWORDS-1-(off)])
 332     #define DFWWORD(dfw, off) ((dfw)->words[DECWWORDS-1-(off)])
 333   #else
 334     #define DFBYTE(df, off)   ((df)->bytes[off])
 335     #define DFWORD(df, off)   ((df)->words[off])
 336     #define DFWWORD(dfw, off) ((dfw)->words[off])
 337   #endif
 338
 339   /* Tests for sign or specials, directly on DECFLOATs                */
 340   #define DFISSIGNED(df)   (DFWORD(df, 0)&0x80000000)
 341   #define DFISSPECIAL(df) ((DFWORD(df, 0)&0x78000000)==0x78000000)
 342   #define DFISINF(df)     ((DFWORD(df, 0)&0x7c000000)==0x78000000)
 343   #define DFISNAN(df)     ((DFWORD(df, 0)&0x7c000000)==0x7c000000)
 344   #define DFISQNAN(df)    ((DFWORD(df, 0)&0x7e000000)==0x7c000000)
 345   #define DFISSNAN(df)    ((DFWORD(df, 0)&0x7e000000)==0x7e000000)
 346
 347   /* Shared lookup tables                                             */
 348 #include "decCommonSymbols.h"
 349   extern const uInt   DECCOMBMSD[64];   /* Combination field -> MSD   */
 350   extern const uInt   DECCOMBFROM[48];  /* exp+msd -> Combination     */
 351
 352   /* Private generic (utility) routine                                */
 353   #if DECCHECK || DECTRACE
 354     extern void decShowNum(const bcdnum *, const char *);
 355   #endif
 356
 357   /* Format-dependent macros and constants                            */
 358   #if defined(DECPMAX)
 359
 360     /* Useful constants                                               */
 361     #define DECPMAX9  (ROUNDUP(DECPMAX, 9)/9)  /* 'Pmax' in 10**9s    */
 362     /* Top words for a zero                                           */
 363     #define SINGLEZERO   0x22500000
 364     #define DOUBLEZERO   0x22380000
 365     #define QUADZERO     0x22080000
 366     /* [ZEROWORD is defined to be one of these in the DFISZERO macro] */
 367
 368     /* Format-dependent common tests:                                 */
 369     /*   DFISZERO   -- test for (any) zero                            */
 370     /*   DFISCCZERO -- test for coefficient continuation being zero   */
 371     /*   DFISCC01   -- test for coefficient contains only 0s and 1s   */
 372     /*   DFISINT    -- test for finite and exponent q=0               */
 373     /*   DFISUINT01 -- test for sign=0, finite, exponent q=0, and     */
 374     /*                 MSD=0 or 1                                     */
 375     /*   ZEROWORD is also defined here.                               */
 376     /* In DFISZERO the first test checks the least-significant word   */
 377     /* (most likely to be non-zero); the penultimate tests MSD and    */
 378     /* DPDs in the signword, and the final test excludes specials and */
 379     /* MSD>7.  DFISINT similarly has to allow for the two forms of    */
 380     /* MSD codes.  DFISUINT01 only has to allow for one form of MSD   */
 381     /* code.                                                          */
 382     #if DECPMAX==7
 383       #define ZEROWORD SINGLEZERO
 384       /* [test macros not needed except for Zero]                     */
 385       #define DFISZERO(df)  ((DFWORD(df, 0)&0x1c0fffff)==0         \
 386                           && (DFWORD(df, 0)&0x60000000)!=0x60000000)
 387     #elif DECPMAX==16
 388       #define ZEROWORD DOUBLEZERO
 389       #define DFISZERO(df)  ((DFWORD(df, 1)==0                     \
 390                           && (DFWORD(df, 0)&0x1c03ffff)==0         \
 391                           && (DFWORD(df, 0)&0x60000000)!=0x60000000))
 392       #define DFISINT(df) ((DFWORD(df, 0)&0x63fc0000)==0x22380000  \
 393                          ||(DFWORD(df, 0)&0x7bfc0000)==0x6a380000)
 394       #define DFISUINT01(df) ((DFWORD(df, 0)&0xfbfc0000)==0x22380000)
 395       #define DFISCCZERO(df) (DFWORD(df, 1)==0                     \
 396                           && (DFWORD(df, 0)&0x0003ffff)==0)
 397       #define DFISCC01(df)  ((DFWORD(df, 0)&~0xfffc9124)==0        \
 398                           && (DFWORD(df, 1)&~0x49124491)==0)
 399     #elif DECPMAX==34
 400       #define ZEROWORD QUADZERO
 401       #define DFISZERO(df)  ((DFWORD(df, 3)==0                     \
 402                           &&  DFWORD(df, 2)==0                     \
 403                           &&  DFWORD(df, 1)==0                     \
 404                           && (DFWORD(df, 0)&0x1c003fff)==0         \
 405                           && (DFWORD(df, 0)&0x60000000)!=0x60000000))
 406       #define DFISINT(df) ((DFWORD(df, 0)&0x63ffc000)==0x22080000  \
 407                          ||(DFWORD(df, 0)&0x7bffc000)==0x6a080000)
 408       #define DFISUINT01(df) ((DFWORD(df, 0)&0xfbffc000)==0x22080000)
 409       #define DFISCCZERO(df) (DFWORD(df, 3)==0                     \
 410                           &&  DFWORD(df, 2)==0                     \
 411                           &&  DFWORD(df, 1)==0                     \
 412                           && (DFWORD(df, 0)&0x00003fff)==0)
 413
 414       #define DFISCC01(df)   ((DFWORD(df, 0)&~0xffffc912)==0       \
 415                           &&  (DFWORD(df, 1)&~0x44912449)==0       \
 416                           &&  (DFWORD(df, 2)&~0x12449124)==0       \
 417                           &&  (DFWORD(df, 3)&~0x49124491)==0)
 418     #endif
 419
 420     /* Macros to test if a certain 10 bits of a uInt or pair of uInts */
 421     /* are a canonical declet [higher or lower bits are ignored].     */
 422     /* declet is at offset 0 (from the right) in a uInt:              */
 423     #define CANONDPD(dpd) (((dpd)&0x300)==0 || ((dpd)&0x6e)!=0x6e)
 424     /* declet is at offset k (a multiple of 2) in a uInt:             */
 425     #define CANONDPDOFF(dpd, k) (((dpd)&(0x300<<(k)))==0            \
 426       || ((dpd)&(((uInt)0x6e)<<(k)))!=(((uInt)0x6e)<<(k)))
 427     /* declet is at offset k (a multiple of 2) in a pair of uInts:    */
 428     /* [the top 2 bits will always be in the more-significant uInt]   */
 429     #define CANONDPDTWO(hi, lo, k) (((hi)&(0x300>>(32-(k))))==0     \
 430       || ((hi)&(0x6e>>(32-(k))))!=(0x6e>>(32-(k)))                  \
 431       || ((lo)&(((uInt)0x6e)<<(k)))!=(((uInt)0x6e)<<(k)))
 432
 433     /* Macro to test whether a full-length (length DECPMAX) BCD8      */
 434     /* coefficient, starting at uByte u, is all zeros                 */
 435     /* Test just the LSWord first, then the remainder as a sequence   */
 436     /* of tests in order to avoid same-level use of UBTOUI            */
 437     #if DECPMAX==7
 438       #define ISCOEFFZERO(u) (                                      \
 439            UBTOUI((u)+DECPMAX-4)==0                                 \
 440         && UBTOUS((u)+DECPMAX-6)==0                                 \
 441         && *(u)==0)
 442     #elif DECPMAX==16
 443       #define ISCOEFFZERO(u) (                                      \
 444            UBTOUI((u)+DECPMAX-4)==0                                 \
 445         && UBTOUI((u)+DECPMAX-8)==0                                 \
 446         && UBTOUI((u)+DECPMAX-12)==0                                \
 447         && UBTOUI(u)==0)
 448     #elif DECPMAX==34
 449       #define ISCOEFFZERO(u) (                                      \
 450            UBTOUI((u)+DECPMAX-4)==0                                 \
 451         && UBTOUI((u)+DECPMAX-8)==0                                 \
 452         && UBTOUI((u)+DECPMAX-12)==0                                \
 453         && UBTOUI((u)+DECPMAX-16)==0                                \
 454         && UBTOUI((u)+DECPMAX-20)==0                                \
 455         && UBTOUI((u)+DECPMAX-24)==0                                \
 456         && UBTOUI((u)+DECPMAX-28)==0                                \
 457         && UBTOUI((u)+DECPMAX-32)==0                                \
 458         && UBTOUS(u)==0)
 459     #endif
 460
 461     /* Macros and masks for the exponent continuation field and MSD   */
 462     /* Get the exponent continuation from a decFloat *df as an Int    */
 463     #define GETECON(df) ((Int)((DFWORD((df), 0)&0x03ffffff)>>(32-6-DECECONL)))
 464     /* Ditto, from the next-wider format                              */
 465     #define GETWECON(df) ((Int)((DFWWORD((df), 0)&0x03ffffff)>>(32-6-DECWECONL)))
 466     /* Get the biased exponent similarly                              */
 467     #define GETEXP(df)  ((Int)(DECCOMBEXP[DFWORD((df), 0)>>26]+GETECON(df)))
 468     /* Get the unbiased exponent similarly                            */
 469     #define GETEXPUN(df) ((Int)GETEXP(df)-DECBIAS)
 470     /* Get the MSD similarly (as uInt)                                */
 471     #define GETMSD(df)   (DECCOMBMSD[DFWORD((df), 0)>>26])
 472
 473     /* Compile-time computes of the exponent continuation field masks */
 474     /* full exponent continuation field:                              */
 475     #define ECONMASK ((0x03ffffff>>(32-6-DECECONL))<<(32-6-DECECONL))
 476     /* same, not including its first digit (the qNaN/sNaN selector):  */
 477     #define ECONNANMASK ((0x01ffffff>>(32-6-DECECONL))<<(32-6-DECECONL))
 478
 479     /* Macros to decode the coefficient in a finite decFloat *df into */
 480     /* a BCD string (uByte *bcdin) of length DECPMAX uBytes.          */
 481
 482     /* In-line sequence to convert least significant 10 bits of uInt  */
 483     /* dpd to three BCD8 digits starting at uByte u.  Note that an    */
 484     /* extra byte is written to the right of the three digits because */
 485     /* four bytes are moved at a time for speed; the alternative      */
 486     /* macro moves exactly three bytes (usually slower).              */
 487     #define dpd2bcd8(u, dpd)  memcpy(u, &DPD2BCD8[((dpd)&0x3ff)*4], 4)
 488     #define dpd2bcd83(u, dpd) memcpy(u, &DPD2BCD8[((dpd)&0x3ff)*4], 3)
 489
 490     /* Decode the declets.  After extracting each one, it is decoded  */
 491     /* to BCD8 using a table lookup (also used for variable-length    */
 492     /* decode).  Each DPD decode is 3 bytes BCD8 plus a one-byte      */
 493     /* length which is not used, here).  Fixed-length 4-byte moves    */
 494     /* are fast, however, almost everywhere, and so are used except   */
 495     /* for the final three bytes (to avoid overrun).  The code below  */
 496     /* is 36 instructions for Doubles and about 70 for Quads, even    */
 497     /* on IA32.                                                       */
 498
 499     /* Two macros are defined for each format:                        */
 500     /*   GETCOEFF extracts the coefficient of the current format      */
 501     /*   GETWCOEFF extracts the coefficient of the next-wider format. */
 502     /* The latter is a copy of the next-wider GETCOEFF using DFWWORD. */
 503
 504     #if DECPMAX==7
 505     #define GETCOEFF(df, bcd) {                          \
 506       uInt sourhi=DFWORD(df, 0);                         \
 507       *(bcd)=(uByte)DECCOMBMSD[sourhi>>26];              \
 508       dpd2bcd8(bcd+1, sourhi>>10);                       \
 509       dpd2bcd83(bcd+4, sourhi);}
 510     #define GETWCOEFF(df, bcd) {                         \
 511       uInt sourhi=DFWWORD(df, 0);                        \
 512       uInt sourlo=DFWWORD(df, 1);                        \
 513       *(bcd)=(uByte)DECCOMBMSD[sourhi>>26];              \
 514       dpd2bcd8(bcd+1, sourhi>>8);                        \
 515       dpd2bcd8(bcd+4, (sourhi<<2) | (sourlo>>30));       \
 516       dpd2bcd8(bcd+7, sourlo>>20);                       \
 517       dpd2bcd8(bcd+10, sourlo>>10);                      \
 518       dpd2bcd83(bcd+13, sourlo);}
 519
 520     #elif DECPMAX==16
 521     #define GETCOEFF(df, bcd) {                          \
 522       uInt sourhi=DFWORD(df, 0);                         \
 523       uInt sourlo=DFWORD(df, 1);                         \
 524       *(bcd)=(uByte)DECCOMBMSD[sourhi>>26];              \
 525       dpd2bcd8(bcd+1, sourhi>>8);                        \
 526       dpd2bcd8(bcd+4, (sourhi<<2) | (sourlo>>30));       \
 527       dpd2bcd8(bcd+7, sourlo>>20);                       \
 528       dpd2bcd8(bcd+10, sourlo>>10);                      \
 529       dpd2bcd83(bcd+13, sourlo);}
 530     #define GETWCOEFF(df, bcd) {                         \
 531       uInt sourhi=DFWWORD(df, 0);                        \
 532       uInt sourmh=DFWWORD(df, 1);                        \
 533       uInt sourml=DFWWORD(df, 2);                        \
 534       uInt sourlo=DFWWORD(df, 3);                        \
 535       *(bcd)=(uByte)DECCOMBMSD[sourhi>>26];              \
 536       dpd2bcd8(bcd+1, sourhi>>4);                        \
 537       dpd2bcd8(bcd+4, ((sourhi)<<6) | (sourmh>>26));     \
 538       dpd2bcd8(bcd+7, sourmh>>16);                       \
 539       dpd2bcd8(bcd+10, sourmh>>6);                       \
 540       dpd2bcd8(bcd+13, ((sourmh)<<4) | (sourml>>28));    \
 541       dpd2bcd8(bcd+16, sourml>>18);                      \
 542       dpd2bcd8(bcd+19, sourml>>8);                       \
 543       dpd2bcd8(bcd+22, ((sourml)<<2) | (sourlo>>30));    \
 544       dpd2bcd8(bcd+25, sourlo>>20);                      \
 545       dpd2bcd8(bcd+28, sourlo>>10);                      \
 546       dpd2bcd83(bcd+31, sourlo);}
 547
 548     #elif DECPMAX==34
 549     #define GETCOEFF(df, bcd) {                          \
 550       uInt sourhi=DFWORD(df, 0);                         \
 551       uInt sourmh=DFWORD(df, 1);                         \
 552       uInt sourml=DFWORD(df, 2);                         \
 553       uInt sourlo=DFWORD(df, 3);                         \
 554       *(bcd)=(uByte)DECCOMBMSD[sourhi>>26];              \
 555       dpd2bcd8(bcd+1, sourhi>>4);                        \
 556       dpd2bcd8(bcd+4, ((sourhi)<<6) | (sourmh>>26));     \
 557       dpd2bcd8(bcd+7, sourmh>>16);                       \
 558       dpd2bcd8(bcd+10, sourmh>>6);                       \
 559       dpd2bcd8(bcd+13, ((sourmh)<<4) | (sourml>>28));    \
 560       dpd2bcd8(bcd+16, sourml>>18);                      \
 561       dpd2bcd8(bcd+19, sourml>>8);                       \
 562       dpd2bcd8(bcd+22, ((sourml)<<2) | (sourlo>>30));    \
 563       dpd2bcd8(bcd+25, sourlo>>20);                      \
 564       dpd2bcd8(bcd+28, sourlo>>10);                      \
 565       dpd2bcd83(bcd+31, sourlo);}
 566
 567       #define GETWCOEFF(df, bcd) {??} /* [should never be used]       */
 568     #endif
 569
 570     /* Macros to decode the coefficient in a finite decFloat *df into */
 571     /* a base-billion uInt array, with the least-significant          */
 572     /* 0-999999999 'digit' at offset 0.                               */
 573
 574     /* Decode the declets.  After extracting each one, it is decoded  */
 575     /* to binary using a table lookup.  Three tables are used; one    */
 576     /* the usual DPD to binary, the other two pre-multiplied by 1000  */
 577     /* and 1000000 to avoid multiplication during decode.  These      */
 578     /* tables can also be used for multiplying up the MSD as the DPD  */
 579     /* code for 0 through 9 is the identity.                          */
 580     #define DPD2BIN0 DPD2BIN         /* for prettier code             */
 581
 582     #if DECPMAX==7
 583     #define GETCOEFFBILL(df, buf) {                           \
 584       uInt sourhi=DFWORD(df, 0);                              \
 585       (buf)[0]=DPD2BIN0[sourhi&0x3ff]                         \
 586               +DPD2BINK[(sourhi>>10)&0x3ff]                   \
 587               +DPD2BINM[DECCOMBMSD[sourhi>>26]];}
 588
 589     #elif DECPMAX==16
 590     #define GETCOEFFBILL(df, buf) {                           \
 591       uInt sourhi, sourlo;                                    \
 592       sourlo=DFWORD(df, 1);                                   \
 593       (buf)[0]=DPD2BIN0[sourlo&0x3ff]                         \
 594               +DPD2BINK[(sourlo>>10)&0x3ff]                   \
 595               +DPD2BINM[(sourlo>>20)&0x3ff];                  \
 596       sourhi=DFWORD(df, 0);                                   \
 597       (buf)[1]=DPD2BIN0[((sourhi<<2) | (sourlo>>30))&0x3ff]   \
 598               +DPD2BINK[(sourhi>>8)&0x3ff]                    \
 599               +DPD2BINM[DECCOMBMSD[sourhi>>26]];}
 600
 601     #elif DECPMAX==34
 602     #define GETCOEFFBILL(df, buf) {                           \
 603       uInt sourhi, sourmh, sourml, sourlo;                    \
 604       sourlo=DFWORD(df, 3);                                   \
 605       (buf)[0]=DPD2BIN0[sourlo&0x3ff]                         \
 606               +DPD2BINK[(sourlo>>10)&0x3ff]                   \
 607               +DPD2BINM[(sourlo>>20)&0x3ff];                  \
 608       sourml=DFWORD(df, 2);                                   \
 609       (buf)[1]=DPD2BIN0[((sourml<<2) | (sourlo>>30))&0x3ff]   \
 610               +DPD2BINK[(sourml>>8)&0x3ff]                    \
 611               +DPD2BINM[(sourml>>18)&0x3ff];                  \
 612       sourmh=DFWORD(df, 1);                                   \
 613       (buf)[2]=DPD2BIN0[((sourmh<<4) | (sourml>>28))&0x3ff]   \
 614               +DPD2BINK[(sourmh>>6)&0x3ff]                    \
 615               +DPD2BINM[(sourmh>>16)&0x3ff];                  \
 616       sourhi=DFWORD(df, 0);                                   \
 617       (buf)[3]=DPD2BIN0[((sourhi<<6) | (sourmh>>26))&0x3ff]   \
 618               +DPD2BINK[(sourhi>>4)&0x3ff]                    \
 619               +DPD2BINM[DECCOMBMSD[sourhi>>26]];}
 620
 621     #endif
 622
 623     /* Macros to decode the coefficient in a finite decFloat *df into */
 624     /* a base-thousand uInt array (of size DECLETS+1, to allow for    */
 625     /* the MSD), with the least-significant 0-999 'digit' at offset 0.*/
 626
 627     /* Decode the declets.  After extracting each one, it is decoded  */
 628     /* to binary using a table lookup.                                */
 629     #if DECPMAX==7
 630     #define GETCOEFFTHOU(df, buf) {                           \
 631       uInt sourhi=DFWORD(df, 0);                              \
 632       (buf)[0]=DPD2BIN[sourhi&0x3ff];                         \
 633       (buf)[1]=DPD2BIN[(sourhi>>10)&0x3ff];                   \
 634       (buf)[2]=DECCOMBMSD[sourhi>>26];}
 635
 636     #elif DECPMAX==16
 637     #define GETCOEFFTHOU(df, buf) {                           \
 638       uInt sourhi, sourlo;                                    \
 639       sourlo=DFWORD(df, 1);                                   \
 640       (buf)[0]=DPD2BIN[sourlo&0x3ff];                         \
 641       (buf)[1]=DPD2BIN[(sourlo>>10)&0x3ff];                   \
 642       (buf)[2]=DPD2BIN[(sourlo>>20)&0x3ff];                   \
 643       sourhi=DFWORD(df, 0);                                   \
 644       (buf)[3]=DPD2BIN[((sourhi<<2) | (sourlo>>30))&0x3ff];   \
 645       (buf)[4]=DPD2BIN[(sourhi>>8)&0x3ff];                    \
 646       (buf)[5]=DECCOMBMSD[sourhi>>26];}
 647
 648     #elif DECPMAX==34
 649     #define GETCOEFFTHOU(df, buf) {                           \
 650       uInt sourhi, sourmh, sourml, sourlo;                    \
 651       sourlo=DFWORD(df, 3);                                   \
 652       (buf)[0]=DPD2BIN[sourlo&0x3ff];                         \
 653       (buf)[1]=DPD2BIN[(sourlo>>10)&0x3ff];                   \
 654       (buf)[2]=DPD2BIN[(sourlo>>20)&0x3ff];                   \
 655       sourml=DFWORD(df, 2);                                   \
 656       (buf)[3]=DPD2BIN[((sourml<<2) | (sourlo>>30))&0x3ff];   \
 657       (buf)[4]=DPD2BIN[(sourml>>8)&0x3ff];                    \
 658       (buf)[5]=DPD2BIN[(sourml>>18)&0x3ff];                   \
 659       sourmh=DFWORD(df, 1);                                   \
 660       (buf)[6]=DPD2BIN[((sourmh<<4) | (sourml>>28))&0x3ff];   \
 661       (buf)[7]=DPD2BIN[(sourmh>>6)&0x3ff];                    \
 662       (buf)[8]=DPD2BIN[(sourmh>>16)&0x3ff];                   \
 663       sourhi=DFWORD(df, 0);                                   \
 664       (buf)[9]=DPD2BIN[((sourhi<<6) | (sourmh>>26))&0x3ff];   \
 665       (buf)[10]=DPD2BIN[(sourhi>>4)&0x3ff];                   \
 666       (buf)[11]=DECCOMBMSD[sourhi>>26];}
 667     #endif
 668
 669
 670     /* Macros to decode the coefficient in a finite decFloat *df and  */
 671     /* add to a base-thousand uInt array (as for GETCOEFFTHOU).       */
 672     /* After the addition then most significant 'digit' in the array  */
 673     /* might have a value larger then 10 (with a maximum of 19).      */
 674     #if DECPMAX==7
 675     #define ADDCOEFFTHOU(df, buf) {                           \
 676       uInt sourhi=DFWORD(df, 0);                              \
 677       (buf)[0]+=DPD2BIN[sourhi&0x3ff];                        \
 678       if (buf[0]>999) {buf[0]-=1000; buf[1]++;}               \
 679       (buf)[1]+=DPD2BIN[(sourhi>>10)&0x3ff];                  \
 680       if (buf[1]>999) {buf[1]-=1000; buf[2]++;}               \
 681       (buf)[2]+=DECCOMBMSD[sourhi>>26];}
 682
 683     #elif DECPMAX==16
 684     #define ADDCOEFFTHOU(df, buf) {                           \
 685       uInt sourhi, sourlo;                                    \
 686       sourlo=DFWORD(df, 1);                                   \
 687       (buf)[0]+=DPD2BIN[sourlo&0x3ff];                        \
 688       if (buf[0]>999) {buf[0]-=1000; buf[1]++;}               \
 689       (buf)[1]+=DPD2BIN[(sourlo>>10)&0x3ff];                  \
 690       if (buf[1]>999) {buf[1]-=1000; buf[2]++;}               \
 691       (buf)[2]+=DPD2BIN[(sourlo>>20)&0x3ff];                  \
 692       if (buf[2]>999) {buf[2]-=1000; buf[3]++;}               \
 693       sourhi=DFWORD(df, 0);                                   \
 694       (buf)[3]+=DPD2BIN[((sourhi<<2) | (sourlo>>30))&0x3ff];  \
 695       if (buf[3]>999) {buf[3]-=1000; buf[4]++;}               \
 696       (buf)[4]+=DPD2BIN[(sourhi>>8)&0x3ff];                   \
 697       if (buf[4]>999) {buf[4]-=1000; buf[5]++;}               \
 698       (buf)[5]+=DECCOMBMSD[sourhi>>26];}
 699
 700     #elif DECPMAX==34
 701     #define ADDCOEFFTHOU(df, buf) {                           \
 702       uInt sourhi, sourmh, sourml, sourlo;                    \
 703       sourlo=DFWORD(df, 3);                                   \
 704       (buf)[0]+=DPD2BIN[sourlo&0x3ff];                        \
 705       if (buf[0]>999) {buf[0]-=1000; buf[1]++;}               \
 706       (buf)[1]+=DPD2BIN[(sourlo>>10)&0x3ff];                  \
 707       if (buf[1]>999) {buf[1]-=1000; buf[2]++;}               \
 708       (buf)[2]+=DPD2BIN[(sourlo>>20)&0x3ff];                  \
 709       if (buf[2]>999) {buf[2]-=1000; buf[3]++;}               \
 710       sourml=DFWORD(df, 2);                                   \
 711       (buf)[3]+=DPD2BIN[((sourml<<2) | (sourlo>>30))&0x3ff];  \
 712       if (buf[3]>999) {buf[3]-=1000; buf[4]++;}               \
 713       (buf)[4]+=DPD2BIN[(sourml>>8)&0x3ff];                   \
 714       if (buf[4]>999) {buf[4]-=1000; buf[5]++;}               \
 715       (buf)[5]+=DPD2BIN[(sourml>>18)&0x3ff];                  \
 716       if (buf[5]>999) {buf[5]-=1000; buf[6]++;}               \
 717       sourmh=DFWORD(df, 1);                                   \
 718       (buf)[6]+=DPD2BIN[((sourmh<<4) | (sourml>>28))&0x3ff];  \
 719       if (buf[6]>999) {buf[6]-=1000; buf[7]++;}               \
 720       (buf)[7]+=DPD2BIN[(sourmh>>6)&0x3ff];                   \
 721       if (buf[7]>999) {buf[7]-=1000; buf[8]++;}               \
 722       (buf)[8]+=DPD2BIN[(sourmh>>16)&0x3ff];                  \
 723       if (buf[8]>999) {buf[8]-=1000; buf[9]++;}               \
 724       sourhi=DFWORD(df, 0);                                   \
 725       (buf)[9]+=DPD2BIN[((sourhi<<6) | (sourmh>>26))&0x3ff];  \
 726       if (buf[9]>999) {buf[9]-=1000; buf[10]++;}              \
 727       (buf)[10]+=DPD2BIN[(sourhi>>4)&0x3ff];                  \
 728       if (buf[10]>999) {buf[10]-=1000; buf[11]++;}            \
 729       (buf)[11]+=DECCOMBMSD[sourhi>>26];}
 730     #endif
 731
 732
 733     /* Set a decFloat to the maximum positive finite number (Nmax)    */
 734     #if DECPMAX==7
 735     #define DFSETNMAX(df)            \
 736       {DFWORD(df, 0)=0x77f3fcff;}
 737     #elif DECPMAX==16
 738     #define DFSETNMAX(df)            \
 739       {DFWORD(df, 0)=0x77fcff3f;     \
 740        DFWORD(df, 1)=0xcff3fcff;}
 741     #elif DECPMAX==34
 742     #define DFSETNMAX(df)            \
 743       {DFWORD(df, 0)=0x77ffcff3;     \
 744        DFWORD(df, 1)=0xfcff3fcf;     \
 745        DFWORD(df, 2)=0xf3fcff3f;     \
 746        DFWORD(df, 3)=0xcff3fcff;}
 747     #endif
 748
 749   /* [end of format-dependent macros and constants]                   */
 750   #endif
 751
 752 #else
 753   #error decNumberLocal included more than once
 754 #endif