libdecnumber/decNumberLocal.h

   1 /* Local definitions for the decNumber C Library.
   2    Copyright (C) 2007-2013 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   /* Returns i, evaluated, for convenience; has to use uiwork because */
 157   /* i may be an expression.                                          */
 158   #define UBFROMUS(b, i)  (uswork=(i), memcpy(b, (void *)&uswork, 2), uswork)
 159   #define UBFROMUI(b, i)  (uiwork=(i), memcpy(b, (void *)&uiwork, 4), uiwork)
 160
 161   /* X10 and X100 -- multiply integer i by 10 or 100                  */
 162   /* [shifts are usually faster than multiply; could be conditional]  */
 163   #define X10(i)  (((i)<<1)+((i)<<3))
 164   #define X100(i) (((i)<<2)+((i)<<5)+((i)<<6))
 165
 166   /* MAXI and MINI -- general max & min (not in ANSI) for integers    */
 167   #define MAXI(x,y) ((x)<(y)?(y):(x))
 168   #define MINI(x,y) ((x)>(y)?(y):(x))
 169
 170   /* Useful constants                                                 */
 171   #define BILLION      1000000000            /* 10**9                 */
 172   /* CHARMASK: 0x30303030 for ASCII/UTF8; 0xF0F0F0F0 for EBCDIC       */
 173   #define CHARMASK ((((((((uInt)'0')<<8)+'0')<<8)+'0')<<8)+'0')
 174
 175
 176   /* ---------------------------------------------------------------- */
 177   /* Definitions for arbitary-precision modules (only valid after     */
 178   /* decNumber.h has been included)                                   */
 179   /* ---------------------------------------------------------------- */
 180
 181   /* Limits and constants                                             */
 182   #define DECNUMMAXP 999999999  /* maximum precision code can handle  */
 183   #define DECNUMMAXE 999999999  /* maximum adjusted exponent ditto    */
 184   #define DECNUMMINE -999999999 /* minimum adjusted exponent ditto    */
 185   #if (DECNUMMAXP != DEC_MAX_DIGITS)
 186     #error Maximum digits mismatch
 187   #endif
 188   #if (DECNUMMAXE != DEC_MAX_EMAX)
 189     #error Maximum exponent mismatch
 190   #endif
 191   #if (DECNUMMINE != DEC_MIN_EMIN)
 192     #error Minimum exponent mismatch
 193   #endif
 194
 195   /* Set DECDPUNMAX -- the maximum integer that fits in DECDPUN       */
 196   /* digits, and D2UTABLE -- the initializer for the D2U table        */
 197   #if   DECDPUN==1
 198     #define DECDPUNMAX 9
 199     #define D2UTABLE {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,  \
 200                       18,19,20,21,22,23,24,25,26,27,28,29,30,31,32, \
 201                       33,34,35,36,37,38,39,40,41,42,43,44,45,46,47, \
 202                       48,49}
 203   #elif DECDPUN==2
 204     #define DECDPUNMAX 99
 205     #define D2UTABLE {0,1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,  \
 206                       11,11,12,12,13,13,14,14,15,15,16,16,17,17,18, \
 207                       18,19,19,20,20,21,21,22,22,23,23,24,24,25}
 208   #elif DECDPUN==3
 209     #define DECDPUNMAX 999
 210     #define D2UTABLE {0,1,1,1,2,2,2,3,3,3,4,4,4,5,5,5,6,6,6,7,7,7,  \
 211                       8,8,8,9,9,9,10,10,10,11,11,11,12,12,12,13,13, \
 212                       13,14,14,14,15,15,15,16,16,16,17}
 213   #elif DECDPUN==4
 214     #define DECDPUNMAX 9999
 215     #define D2UTABLE {0,1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,6,  \
 216                       6,6,6,7,7,7,7,8,8,8,8,9,9,9,9,10,10,10,10,11, \
 217                       11,11,11,12,12,12,12,13}
 218   #elif DECDPUN==5
 219     #define DECDPUNMAX 99999
 220     #define D2UTABLE {0,1,1,1,1,1,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,5,  \
 221                       5,5,5,5,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,9,9,9,  \
 222                       9,9,10,10,10,10}
 223   #elif DECDPUN==6
 224     #define DECDPUNMAX 999999
 225     #define D2UTABLE {0,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,  \
 226                       4,4,4,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,8,  \
 227                       8,8,8,8,8,9}
 228   #elif DECDPUN==7
 229     #define DECDPUNMAX 9999999
 230     #define D2UTABLE {0,1,1,1,1,1,1,1,2,2,2,2,2,2,2,3,3,3,3,3,3,3,  \
 231                       4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,6,7,  \
 232                       7,7,7,7,7,7}
 233   #elif DECDPUN==8
 234     #define DECDPUNMAX 99999999
 235     #define D2UTABLE {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,  \
 236                       3,3,3,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,  \
 237                       6,6,6,6,6,7}
 238   #elif DECDPUN==9
 239     #define DECDPUNMAX 999999999
 240     #define D2UTABLE {0,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,3,3,3,  \
 241                       3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,  \
 242                       5,5,6,6,6,6}
 243   #elif defined(DECDPUN)
 244     #error DECDPUN must be in the range 1-9
 245   #endif
 246
 247   /* ----- Shared data (in decNumber.c) ----- */
 248   /* Public lookup table used by the D2U macro (see below)            */
 249   #define DECMAXD2U 49
 250   extern const uByte d2utable[DECMAXD2U+1];
 251
 252   /* ----- Macros ----- */
 253   /* ISZERO -- return true if decNumber dn is a zero                  */
 254   /* [performance-critical in some situations]                        */
 255   #define ISZERO(dn) decNumberIsZero(dn)     /* now just a local name */
 256
 257   /* D2U -- return the number of Units needed to hold d digits        */
 258   /* (runtime version, with table lookaside for small d)              */
 259   #if DECDPUN==8
 260     #define D2U(d) ((unsigned)((d)<=DECMAXD2U?d2utable[d]:((d)+7)>>3))
 261   #elif DECDPUN==4
 262     #define D2U(d) ((unsigned)((d)<=DECMAXD2U?d2utable[d]:((d)+3)>>2))
 263   #else
 264     #define D2U(d) ((d)<=DECMAXD2U?d2utable[d]:((d)+DECDPUN-1)/DECDPUN)
 265   #endif
 266   /* SD2U -- static D2U macro (for compile-time calculation)          */
 267   #define SD2U(d) (((d)+DECDPUN-1)/DECDPUN)
 268
 269   /* MSUDIGITS -- returns digits in msu, from digits, calculated      */
 270   /* using D2U                                                        */
 271   #define MSUDIGITS(d) ((d)-(D2U(d)-1)*DECDPUN)
 272
 273   /* D2N -- return the number of decNumber structs that would be      */
 274   /* needed to contain that number of digits (and the initial         */
 275   /* decNumber struct) safely.  Note that one Unit is included in the */
 276   /* initial structure.  Used for allocating space that is aligned on */
 277   /* a decNumber struct boundary. */
 278   #define D2N(d) \
 279     ((((SD2U(d)-1)*sizeof(Unit))+sizeof(decNumber)*2-1)/sizeof(decNumber))
 280
 281   /* TODIGIT -- macro to remove the leading digit from the unsigned   */
 282   /* integer u at column cut (counting from the right, LSD=0) and     */
 283   /* place it as an ASCII character into the character pointed to by  */
 284   /* c.  Note that cut must be <= 9, and the maximum value for u is   */
 285   /* 2,000,000,000 (as is needed for negative exponents of            */
 286   /* subnormals).  The unsigned integer pow is used as a temporary    */
 287   /* variable. */
 288   #define TODIGIT(u, cut, c, pow) {       \
 289     *(c)='0';                             \
 290     pow=DECPOWERS[cut]*2;                 \
 291     if ((u)>pow) {                        \
 292       pow*=4;                             \
 293       if ((u)>=pow) {(u)-=pow; *(c)+=8;}  \
 294       pow/=2;                             \
 295       if ((u)>=pow) {(u)-=pow; *(c)+=4;}  \
 296       pow/=2;                             \
 297       }                                   \
 298     if ((u)>=pow) {(u)-=pow; *(c)+=2;}    \
 299     pow/=2;                               \
 300     if ((u)>=pow) {(u)-=pow; *(c)+=1;}    \
 301     }
 302
 303   /* ---------------------------------------------------------------- */
 304   /* Definitions for fixed-precision modules (only valid after        */
 305   /* decSingle.h, decDouble.h, or decQuad.h has been included)        */
 306   /* ---------------------------------------------------------------- */
 307
 308   /* bcdnum -- a structure describing a format-independent finite     */
 309   /* number, whose coefficient is a string of bcd8 uBytes             */
 310   typedef struct {
 311     uByte   *msd;             /* -> most significant digit            */
 312     uByte   *lsd;             /* -> least ditto                       */
 313     uInt     sign;            /* 0=positive, DECFLOAT_Sign=negative   */
 314     Int      exponent;        /* Unadjusted signed exponent (q), or   */
 315                               /* DECFLOAT_NaN etc. for a special      */
 316     } bcdnum;
 317
 318   /* Test if exponent or bcdnum exponent must be a special, etc.      */
 319   #define EXPISSPECIAL(exp) ((exp)>=DECFLOAT_MinSp)
 320   #define EXPISINF(exp) (exp==DECFLOAT_Inf)
 321   #define EXPISNAN(exp) (exp==DECFLOAT_qNaN || exp==DECFLOAT_sNaN)
 322   #define NUMISSPECIAL(num) (EXPISSPECIAL((num)->exponent))
 323
 324   /* Refer to a 32-bit word or byte in a decFloat (df) by big-endian  */
 325   /* (array) notation (the 0 word or byte contains the sign bit),     */
 326   /* automatically adjusting for endianness; similarly address a word */
 327   /* in the next-wider format (decFloatWider, or dfw)                 */
 328   #define DECWORDS  (DECBYTES/4)
 329   #define DECWWORDS (DECWBYTES/4)
 330   #if DECLITEND
 331     #define DFBYTE(df, off)   ((df)->bytes[DECBYTES-1-(off)])
 332     #define DFWORD(df, off)   ((df)->words[DECWORDS-1-(off)])
 333     #define DFWWORD(dfw, off) ((dfw)->words[DECWWORDS-1-(off)])
 334   #else
 335     #define DFBYTE(df, off)   ((df)->bytes[off])
 336     #define DFWORD(df, off)   ((df)->words[off])
 337     #define DFWWORD(dfw, off) ((dfw)->words[off])
 338   #endif
 339
 340   /* Tests for sign or specials, directly on DECFLOATs                */
 341   #define DFISSIGNED(df)   (DFWORD(df, 0)&0x80000000)
 342   #define DFISSPECIAL(df) ((DFWORD(df, 0)&0x78000000)==0x78000000)
 343   #define DFISINF(df)     ((DFWORD(df, 0)&0x7c000000)==0x78000000)
 344   #define DFISNAN(df)     ((DFWORD(df, 0)&0x7c000000)==0x7c000000)
 345   #define DFISQNAN(df)    ((DFWORD(df, 0)&0x7e000000)==0x7c000000)
 346   #define DFISSNAN(df)    ((DFWORD(df, 0)&0x7e000000)==0x7e000000)
 347
 348   /* Shared lookup tables                                             */
 349 #include "decCommonSymbols.h"
 350   extern const uInt   DECCOMBMSD[64];   /* Combination field -> MSD   */
 351   extern const uInt   DECCOMBFROM[48];  /* exp+msd -> Combination     */
 352
 353   /* Private generic (utility) routine                                */
 354   #if DECCHECK || DECTRACE
 355     extern void decShowNum(const bcdnum *, const char *);
 356   #endif
 357
 358   /* Format-dependent macros and constants                            */
 359   #if defined(DECPMAX)
 360
 361     /* Useful constants                                               */
 362     #define DECPMAX9  (ROUNDUP(DECPMAX, 9)/9)  /* 'Pmax' in 10**9s    */
 363     /* Top words for a zero                                           */
 364     #define SINGLEZERO   0x22500000
 365     #define DOUBLEZERO   0x22380000
 366     #define QUADZERO     0x22080000
 367     /* [ZEROWORD is defined to be one of these in the DFISZERO macro] */
 368
 369     /* Format-dependent common tests:                                 */
 370     /*   DFISZERO   -- test for (any) zero                            */
 371     /*   DFISCCZERO -- test for coefficient continuation being zero   */
 372     /*   DFISCC01   -- test for coefficient contains only 0s and 1s   */
 373     /*   DFISINT    -- test for finite and exponent q=0               */
 374     /*   DFISUINT01 -- test for sign=0, finite, exponent q=0, and     */
 375     /*                 MSD=0 or 1                                     */
 376     /*   ZEROWORD is also defined here.                               */
 377     /* In DFISZERO the first test checks the least-significant word   */
 378     /* (most likely to be non-zero); the penultimate tests MSD and    */
 379     /* DPDs in the signword, and the final test excludes specials and */
 380     /* MSD>7.  DFISINT similarly has to allow for the two forms of    */
 381     /* MSD codes.  DFISUINT01 only has to allow for one form of MSD   */
 382     /* code.                                                          */
 383     #if DECPMAX==7
 384       #define ZEROWORD SINGLEZERO
 385       /* [test macros not needed except for Zero]                     */
 386       #define DFISZERO(df)  ((DFWORD(df, 0)&0x1c0fffff)==0         \
 387                           && (DFWORD(df, 0)&0x60000000)!=0x60000000)
 388     #elif DECPMAX==16
 389       #define ZEROWORD DOUBLEZERO
 390       #define DFISZERO(df)  ((DFWORD(df, 1)==0                     \
 391                           && (DFWORD(df, 0)&0x1c03ffff)==0         \
 392                           && (DFWORD(df, 0)&0x60000000)!=0x60000000))
 393       #define DFISINT(df) ((DFWORD(df, 0)&0x63fc0000)==0x22380000  \
 394                          ||(DFWORD(df, 0)&0x7bfc0000)==0x6a380000)
 395       #define DFISUINT01(df) ((DFWORD(df, 0)&0xfbfc0000)==0x22380000)
 396       #define DFISCCZERO(df) (DFWORD(df, 1)==0                     \
 397                           && (DFWORD(df, 0)&0x0003ffff)==0)
 398       #define DFISCC01(df)  ((DFWORD(df, 0)&~0xfffc9124)==0        \
 399                           && (DFWORD(df, 1)&~0x49124491)==0)
 400     #elif DECPMAX==34
 401       #define ZEROWORD QUADZERO
 402       #define DFISZERO(df)  ((DFWORD(df, 3)==0                     \
 403                           &&  DFWORD(df, 2)==0                     \
 404                           &&  DFWORD(df, 1)==0                     \
 405                           && (DFWORD(df, 0)&0x1c003fff)==0         \
 406                           && (DFWORD(df, 0)&0x60000000)!=0x60000000))
 407       #define DFISINT(df) ((DFWORD(df, 0)&0x63ffc000)==0x22080000  \
 408                          ||(DFWORD(df, 0)&0x7bffc000)==0x6a080000)
 409       #define DFISUINT01(df) ((DFWORD(df, 0)&0xfbffc000)==0x22080000)
 410       #define DFISCCZERO(df) (DFWORD(df, 3)==0                     \
 411                           &&  DFWORD(df, 2)==0                     \
 412                           &&  DFWORD(df, 1)==0                     \
 413                           && (DFWORD(df, 0)&0x00003fff)==0)
 414
 415       #define DFISCC01(df)   ((DFWORD(df, 0)&~0xffffc912)==0       \
 416                           &&  (DFWORD(df, 1)&~0x44912449)==0       \
 417                           &&  (DFWORD(df, 2)&~0x12449124)==0       \
 418                           &&  (DFWORD(df, 3)&~0x49124491)==0)
 419     #endif
 420
 421     /* Macros to test if a certain 10 bits of a uInt or pair of uInts */
 422     /* are a canonical declet [higher or lower bits are ignored].     */
 423     /* declet is at offset 0 (from the right) in a uInt:              */
 424     #define CANONDPD(dpd) (((dpd)&0x300)==0 || ((dpd)&0x6e)!=0x6e)
 425     /* declet is at offset k (a multiple of 2) in a uInt:             */
 426     #define CANONDPDOFF(dpd, k) (((dpd)&(0x300<<(k)))==0            \
 427       || ((dpd)&(((uInt)0x6e)<<(k)))!=(((uInt)0x6e)<<(k)))
 428     /* declet is at offset k (a multiple of 2) in a pair of uInts:    */
 429     /* [the top 2 bits will always be in the more-significant uInt]   */
 430     #define CANONDPDTWO(hi, lo, k) (((hi)&(0x300>>(32-(k))))==0     \
 431       || ((hi)&(0x6e>>(32-(k))))!=(0x6e>>(32-(k)))                  \
 432       || ((lo)&(((uInt)0x6e)<<(k)))!=(((uInt)0x6e)<<(k)))
 433
 434     /* Macro to test whether a full-length (length DECPMAX) BCD8      */
 435     /* coefficient, starting at uByte u, is all zeros                 */
 436     /* Test just the LSWord first, then the remainder as a sequence   */
 437     /* of tests in order to avoid same-level use of UBTOUI            */
 438     #if DECPMAX==7
 439       #define ISCOEFFZERO(u) (                                      \
 440            UBTOUI((u)+DECPMAX-4)==0                                 \
 441         && UBTOUS((u)+DECPMAX-6)==0                                 \
 442         && *(u)==0)
 443     #elif DECPMAX==16
 444       #define ISCOEFFZERO(u) (                                      \
 445            UBTOUI((u)+DECPMAX-4)==0                                 \
 446         && UBTOUI((u)+DECPMAX-8)==0                                 \
 447         && UBTOUI((u)+DECPMAX-12)==0                                \
 448         && UBTOUI(u)==0)
 449     #elif DECPMAX==34
 450       #define ISCOEFFZERO(u) (                                      \
 451            UBTOUI((u)+DECPMAX-4)==0                                 \
 452         && UBTOUI((u)+DECPMAX-8)==0                                 \
 453         && UBTOUI((u)+DECPMAX-12)==0                                \
 454         && UBTOUI((u)+DECPMAX-16)==0                                \
 455         && UBTOUI((u)+DECPMAX-20)==0                                \
 456         && UBTOUI((u)+DECPMAX-24)==0                                \
 457         && UBTOUI((u)+DECPMAX-28)==0                                \
 458         && UBTOUI((u)+DECPMAX-32)==0                                \
 459         && UBTOUS(u)==0)
 460     #endif
 461
 462     /* Macros and masks for the exponent continuation field and MSD   */
 463     /* Get the exponent continuation from a decFloat *df as an Int    */
 464     #define GETECON(df) ((Int)((DFWORD((df), 0)&0x03ffffff)>>(32-6-DECECONL)))
 465     /* Ditto, from the next-wider format                              */
 466     #define GETWECON(df) ((Int)((DFWWORD((df), 0)&0x03ffffff)>>(32-6-DECWECONL)))
 467     /* Get the biased exponent similarly                              */
 468     #define GETEXP(df)  ((Int)(DECCOMBEXP[DFWORD((df), 0)>>26]+GETECON(df)))
 469     /* Get the unbiased exponent similarly                            */
 470     #define GETEXPUN(df) ((Int)GETEXP(df)-DECBIAS)
 471     /* Get the MSD similarly (as uInt)                                */
 472     #define GETMSD(df)   (DECCOMBMSD[DFWORD((df), 0)>>26])
 473
 474     /* Compile-time computes of the exponent continuation field masks */
 475     /* full exponent continuation field:                              */
 476     #define ECONMASK ((0x03ffffff>>(32-6-DECECONL))<<(32-6-DECECONL))
 477     /* same, not including its first digit (the qNaN/sNaN selector):  */
 478     #define ECONNANMASK ((0x01ffffff>>(32-6-DECECONL))<<(32-6-DECECONL))
 479
 480     /* Macros to decode the coefficient in a finite decFloat *df into */
 481     /* a BCD string (uByte *bcdin) of length DECPMAX uBytes.          */
 482
 483     /* In-line sequence to convert least significant 10 bits of uInt  */
 484     /* dpd to three BCD8 digits starting at uByte u.  Note that an    */
 485     /* extra byte is written to the right of the three digits because */
 486     /* four bytes are moved at a time for speed; the alternative      */
 487     /* macro moves exactly three bytes (usually slower).              */
 488     #define dpd2bcd8(u, dpd)  memcpy(u, &DPD2BCD8[((dpd)&0x3ff)*4], 4)
 489     #define dpd2bcd83(u, dpd) memcpy(u, &DPD2BCD8[((dpd)&0x3ff)*4], 3)
 490
 491     /* Decode the declets.  After extracting each one, it is decoded  */
 492     /* to BCD8 using a table lookup (also used for variable-length    */
 493     /* decode).  Each DPD decode is 3 bytes BCD8 plus a one-byte      */
 494     /* length which is not used, here).  Fixed-length 4-byte moves    */
 495     /* are fast, however, almost everywhere, and so are used except   */
 496     /* for the final three bytes (to avoid overrun).  The code below  */
 497     /* is 36 instructions for Doubles and about 70 for Quads, even    */
 498     /* on IA32.                                                       */
 499
 500     /* Two macros are defined for each format:                        */
 501     /*   GETCOEFF extracts the coefficient of the current format      */
 502     /*   GETWCOEFF extracts the coefficient of the next-wider format. */
 503     /* The latter is a copy of the next-wider GETCOEFF using DFWWORD. */
 504
 505     #if DECPMAX==7
 506     #define GETCOEFF(df, bcd) {                          \
 507       uInt sourhi=DFWORD(df, 0);                         \
 508       *(bcd)=(uByte)DECCOMBMSD[sourhi>>26];              \
 509       dpd2bcd8(bcd+1, sourhi>>10);                       \
 510       dpd2bcd83(bcd+4, sourhi);}
 511     #define GETWCOEFF(df, bcd) {                         \
 512       uInt sourhi=DFWWORD(df, 0);                        \
 513       uInt sourlo=DFWWORD(df, 1);                        \
 514       *(bcd)=(uByte)DECCOMBMSD[sourhi>>26];              \
 515       dpd2bcd8(bcd+1, sourhi>>8);                        \
 516       dpd2bcd8(bcd+4, (sourhi<<2) | (sourlo>>30));       \
 517       dpd2bcd8(bcd+7, sourlo>>20);                       \
 518       dpd2bcd8(bcd+10, sourlo>>10);                      \
 519       dpd2bcd83(bcd+13, sourlo);}
 520
 521     #elif DECPMAX==16
 522     #define GETCOEFF(df, bcd) {                          \
 523       uInt sourhi=DFWORD(df, 0);                         \
 524       uInt sourlo=DFWORD(df, 1);                         \
 525       *(bcd)=(uByte)DECCOMBMSD[sourhi>>26];              \
 526       dpd2bcd8(bcd+1, sourhi>>8);                        \
 527       dpd2bcd8(bcd+4, (sourhi<<2) | (sourlo>>30));       \
 528       dpd2bcd8(bcd+7, sourlo>>20);                       \
 529       dpd2bcd8(bcd+10, sourlo>>10);                      \
 530       dpd2bcd83(bcd+13, sourlo);}
 531     #define GETWCOEFF(df, bcd) {                         \
 532       uInt sourhi=DFWWORD(df, 0);                        \
 533       uInt sourmh=DFWWORD(df, 1);                        \
 534       uInt sourml=DFWWORD(df, 2);                        \
 535       uInt sourlo=DFWWORD(df, 3);                        \
 536       *(bcd)=(uByte)DECCOMBMSD[sourhi>>26];              \
 537       dpd2bcd8(bcd+1, sourhi>>4);                        \
 538       dpd2bcd8(bcd+4, ((sourhi)<<6) | (sourmh>>26));     \
 539       dpd2bcd8(bcd+7, sourmh>>16);                       \
 540       dpd2bcd8(bcd+10, sourmh>>6);                       \
 541       dpd2bcd8(bcd+13, ((sourmh)<<4) | (sourml>>28));    \
 542       dpd2bcd8(bcd+16, sourml>>18);                      \
 543       dpd2bcd8(bcd+19, sourml>>8);                       \
 544       dpd2bcd8(bcd+22, ((sourml)<<2) | (sourlo>>30));    \
 545       dpd2bcd8(bcd+25, sourlo>>20);                      \
 546       dpd2bcd8(bcd+28, sourlo>>10);                      \
 547       dpd2bcd83(bcd+31, sourlo);}
 548
 549     #elif DECPMAX==34
 550     #define GETCOEFF(df, bcd) {                          \
 551       uInt sourhi=DFWORD(df, 0);                         \
 552       uInt sourmh=DFWORD(df, 1);                         \
 553       uInt sourml=DFWORD(df, 2);                         \
 554       uInt sourlo=DFWORD(df, 3);                         \
 555       *(bcd)=(uByte)DECCOMBMSD[sourhi>>26];              \
 556       dpd2bcd8(bcd+1, sourhi>>4);                        \
 557       dpd2bcd8(bcd+4, ((sourhi)<<6) | (sourmh>>26));     \
 558       dpd2bcd8(bcd+7, sourmh>>16);                       \
 559       dpd2bcd8(bcd+10, sourmh>>6);                       \
 560       dpd2bcd8(bcd+13, ((sourmh)<<4) | (sourml>>28));    \
 561       dpd2bcd8(bcd+16, sourml>>18);                      \
 562       dpd2bcd8(bcd+19, sourml>>8);                       \
 563       dpd2bcd8(bcd+22, ((sourml)<<2) | (sourlo>>30));    \
 564       dpd2bcd8(bcd+25, sourlo>>20);                      \
 565       dpd2bcd8(bcd+28, sourlo>>10);                      \
 566       dpd2bcd83(bcd+31, sourlo);}
 567
 568       #define GETWCOEFF(df, bcd) {??} /* [should never be used]       */
 569     #endif
 570
 571     /* Macros to decode the coefficient in a finite decFloat *df into */
 572     /* a base-billion uInt array, with the least-significant          */
 573     /* 0-999999999 'digit' at offset 0.                               */
 574
 575     /* Decode the declets.  After extracting each one, it is decoded  */
 576     /* to binary using a table lookup.  Three tables are used; one    */
 577     /* the usual DPD to binary, the other two pre-multiplied by 1000  */
 578     /* and 1000000 to avoid multiplication during decode.  These      */
 579     /* tables can also be used for multiplying up the MSD as the DPD  */
 580     /* code for 0 through 9 is the identity.                          */
 581     #define DPD2BIN0 DPD2BIN         /* for prettier code             */
 582
 583     #if DECPMAX==7
 584     #define GETCOEFFBILL(df, buf) {                           \
 585       uInt sourhi=DFWORD(df, 0);                              \
 586       (buf)[0]=DPD2BIN0[sourhi&0x3ff]                         \
 587               +DPD2BINK[(sourhi>>10)&0x3ff]                   \
 588               +DPD2BINM[DECCOMBMSD[sourhi>>26]];}
 589
 590     #elif DECPMAX==16
 591     #define GETCOEFFBILL(df, buf) {                           \
 592       uInt sourhi, sourlo;                                    \
 593       sourlo=DFWORD(df, 1);                                   \
 594       (buf)[0]=DPD2BIN0[sourlo&0x3ff]                         \
 595               +DPD2BINK[(sourlo>>10)&0x3ff]                   \
 596               +DPD2BINM[(sourlo>>20)&0x3ff];                  \
 597       sourhi=DFWORD(df, 0);                                   \
 598       (buf)[1]=DPD2BIN0[((sourhi<<2) | (sourlo>>30))&0x3ff]   \
 599               +DPD2BINK[(sourhi>>8)&0x3ff]                    \
 600               +DPD2BINM[DECCOMBMSD[sourhi>>26]];}
 601
 602     #elif DECPMAX==34
 603     #define GETCOEFFBILL(df, buf) {                           \
 604       uInt sourhi, sourmh, sourml, sourlo;                    \
 605       sourlo=DFWORD(df, 3);                                   \
 606       (buf)[0]=DPD2BIN0[sourlo&0x3ff]                         \
 607               +DPD2BINK[(sourlo>>10)&0x3ff]                   \
 608               +DPD2BINM[(sourlo>>20)&0x3ff];                  \
 609       sourml=DFWORD(df, 2);                                   \
 610       (buf)[1]=DPD2BIN0[((sourml<<2) | (sourlo>>30))&0x3ff]   \
 611               +DPD2BINK[(sourml>>8)&0x3ff]                    \
 612               +DPD2BINM[(sourml>>18)&0x3ff];                  \
 613       sourmh=DFWORD(df, 1);                                   \
 614       (buf)[2]=DPD2BIN0[((sourmh<<4) | (sourml>>28))&0x3ff]   \
 615               +DPD2BINK[(sourmh>>6)&0x3ff]                    \
 616               +DPD2BINM[(sourmh>>16)&0x3ff];                  \
 617       sourhi=DFWORD(df, 0);                                   \
 618       (buf)[3]=DPD2BIN0[((sourhi<<6) | (sourmh>>26))&0x3ff]   \
 619               +DPD2BINK[(sourhi>>4)&0x3ff]                    \
 620               +DPD2BINM[DECCOMBMSD[sourhi>>26]];}
 621
 622     #endif
 623
 624     /* Macros to decode the coefficient in a finite decFloat *df into */
 625     /* a base-thousand uInt array (of size DECLETS+1, to allow for    */
 626     /* the MSD), with the least-significant 0-999 'digit' at offset 0.*/
 627
 628     /* Decode the declets.  After extracting each one, it is decoded  */
 629     /* to binary using a table lookup.                                */
 630     #if DECPMAX==7
 631     #define GETCOEFFTHOU(df, buf) {                           \
 632       uInt sourhi=DFWORD(df, 0);                              \
 633       (buf)[0]=DPD2BIN[sourhi&0x3ff];                         \
 634       (buf)[1]=DPD2BIN[(sourhi>>10)&0x3ff];                   \
 635       (buf)[2]=DECCOMBMSD[sourhi>>26];}
 636
 637     #elif DECPMAX==16
 638     #define GETCOEFFTHOU(df, buf) {                           \
 639       uInt sourhi, sourlo;                                    \
 640       sourlo=DFWORD(df, 1);                                   \
 641       (buf)[0]=DPD2BIN[sourlo&0x3ff];                         \
 642       (buf)[1]=DPD2BIN[(sourlo>>10)&0x3ff];                   \
 643       (buf)[2]=DPD2BIN[(sourlo>>20)&0x3ff];                   \
 644       sourhi=DFWORD(df, 0);                                   \
 645       (buf)[3]=DPD2BIN[((sourhi<<2) | (sourlo>>30))&0x3ff];   \
 646       (buf)[4]=DPD2BIN[(sourhi>>8)&0x3ff];                    \
 647       (buf)[5]=DECCOMBMSD[sourhi>>26];}
 648
 649     #elif DECPMAX==34
 650     #define GETCOEFFTHOU(df, buf) {                           \
 651       uInt sourhi, sourmh, sourml, sourlo;                    \
 652       sourlo=DFWORD(df, 3);                                   \
 653       (buf)[0]=DPD2BIN[sourlo&0x3ff];                         \
 654       (buf)[1]=DPD2BIN[(sourlo>>10)&0x3ff];                   \
 655       (buf)[2]=DPD2BIN[(sourlo>>20)&0x3ff];                   \
 656       sourml=DFWORD(df, 2);                                   \
 657       (buf)[3]=DPD2BIN[((sourml<<2) | (sourlo>>30))&0x3ff];   \
 658       (buf)[4]=DPD2BIN[(sourml>>8)&0x3ff];                    \
 659       (buf)[5]=DPD2BIN[(sourml>>18)&0x3ff];                   \
 660       sourmh=DFWORD(df, 1);                                   \
 661       (buf)[6]=DPD2BIN[((sourmh<<4) | (sourml>>28))&0x3ff];   \
 662       (buf)[7]=DPD2BIN[(sourmh>>6)&0x3ff];                    \
 663       (buf)[8]=DPD2BIN[(sourmh>>16)&0x3ff];                   \
 664       sourhi=DFWORD(df, 0);                                   \
 665       (buf)[9]=DPD2BIN[((sourhi<<6) | (sourmh>>26))&0x3ff];   \
 666       (buf)[10]=DPD2BIN[(sourhi>>4)&0x3ff];                   \
 667       (buf)[11]=DECCOMBMSD[sourhi>>26];}
 668     #endif
 669
 670
 671     /* Macros to decode the coefficient in a finite decFloat *df and  */
 672     /* add to a base-thousand uInt array (as for GETCOEFFTHOU).       */
 673     /* After the addition then most significant 'digit' in the array  */
 674     /* might have a value larger then 10 (with a maximum of 19).      */
 675     #if DECPMAX==7
 676     #define ADDCOEFFTHOU(df, buf) {                           \
 677       uInt sourhi=DFWORD(df, 0);                              \
 678       (buf)[0]+=DPD2BIN[sourhi&0x3ff];                        \
 679       if (buf[0]>999) {buf[0]-=1000; buf[1]++;}               \
 680       (buf)[1]+=DPD2BIN[(sourhi>>10)&0x3ff];                  \
 681       if (buf[1]>999) {buf[1]-=1000; buf[2]++;}               \
 682       (buf)[2]+=DECCOMBMSD[sourhi>>26];}
 683
 684     #elif DECPMAX==16
 685     #define ADDCOEFFTHOU(df, buf) {                           \
 686       uInt sourhi, sourlo;                                    \
 687       sourlo=DFWORD(df, 1);                                   \
 688       (buf)[0]+=DPD2BIN[sourlo&0x3ff];                        \
 689       if (buf[0]>999) {buf[0]-=1000; buf[1]++;}               \
 690       (buf)[1]+=DPD2BIN[(sourlo>>10)&0x3ff];                  \
 691       if (buf[1]>999) {buf[1]-=1000; buf[2]++;}               \
 692       (buf)[2]+=DPD2BIN[(sourlo>>20)&0x3ff];                  \
 693       if (buf[2]>999) {buf[2]-=1000; buf[3]++;}               \
 694       sourhi=DFWORD(df, 0);                                   \
 695       (buf)[3]+=DPD2BIN[((sourhi<<2) | (sourlo>>30))&0x3ff];  \
 696       if (buf[3]>999) {buf[3]-=1000; buf[4]++;}               \
 697       (buf)[4]+=DPD2BIN[(sourhi>>8)&0x3ff];                   \
 698       if (buf[4]>999) {buf[4]-=1000; buf[5]++;}               \
 699       (buf)[5]+=DECCOMBMSD[sourhi>>26];}
 700
 701     #elif DECPMAX==34
 702     #define ADDCOEFFTHOU(df, buf) {                           \
 703       uInt sourhi, sourmh, sourml, sourlo;                    \
 704       sourlo=DFWORD(df, 3);                                   \
 705       (buf)[0]+=DPD2BIN[sourlo&0x3ff];                        \
 706       if (buf[0]>999) {buf[0]-=1000; buf[1]++;}               \
 707       (buf)[1]+=DPD2BIN[(sourlo>>10)&0x3ff];                  \
 708       if (buf[1]>999) {buf[1]-=1000; buf[2]++;}               \
 709       (buf)[2]+=DPD2BIN[(sourlo>>20)&0x3ff];                  \
 710       if (buf[2]>999) {buf[2]-=1000; buf[3]++;}               \
 711       sourml=DFWORD(df, 2);                                   \
 712       (buf)[3]+=DPD2BIN[((sourml<<2) | (sourlo>>30))&0x3ff];  \
 713       if (buf[3]>999) {buf[3]-=1000; buf[4]++;}               \
 714       (buf)[4]+=DPD2BIN[(sourml>>8)&0x3ff];                   \
 715       if (buf[4]>999) {buf[4]-=1000; buf[5]++;}               \
 716       (buf)[5]+=DPD2BIN[(sourml>>18)&0x3ff];                  \
 717       if (buf[5]>999) {buf[5]-=1000; buf[6]++;}               \
 718       sourmh=DFWORD(df, 1);                                   \
 719       (buf)[6]+=DPD2BIN[((sourmh<<4) | (sourml>>28))&0x3ff];  \
 720       if (buf[6]>999) {buf[6]-=1000; buf[7]++;}               \
 721       (buf)[7]+=DPD2BIN[(sourmh>>6)&0x3ff];                   \
 722       if (buf[7]>999) {buf[7]-=1000; buf[8]++;}               \
 723       (buf)[8]+=DPD2BIN[(sourmh>>16)&0x3ff];                  \
 724       if (buf[8]>999) {buf[8]-=1000; buf[9]++;}               \
 725       sourhi=DFWORD(df, 0);                                   \
 726       (buf)[9]+=DPD2BIN[((sourhi<<6) | (sourmh>>26))&0x3ff];  \
 727       if (buf[9]>999) {buf[9]-=1000; buf[10]++;}              \
 728       (buf)[10]+=DPD2BIN[(sourhi>>4)&0x3ff];                  \
 729       if (buf[10]>999) {buf[10]-=1000; buf[11]++;}            \
 730       (buf)[11]+=DECCOMBMSD[sourhi>>26];}
 731     #endif
 732
 733
 734     /* Set a decFloat to the maximum positive finite number (Nmax)    */
 735     #if DECPMAX==7
 736     #define DFSETNMAX(df)            \
 737       {DFWORD(df, 0)=0x77f3fcff;}
 738     #elif DECPMAX==16
 739     #define DFSETNMAX(df)            \
 740       {DFWORD(df, 0)=0x77fcff3f;     \
 741        DFWORD(df, 1)=0xcff3fcff;}
 742     #elif DECPMAX==34
 743     #define DFSETNMAX(df)            \
 744       {DFWORD(df, 0)=0x77ffcff3;     \
 745        DFWORD(df, 1)=0xfcff3fcf;     \
 746        DFWORD(df, 2)=0xf3fcff3f;     \
 747        DFWORD(df, 3)=0xcff3fcff;}
 748     #endif
 749
 750   /* [end of format-dependent macros and constants]                   */
 751   #endif
 752
 753 #else
 754   #error decNumberLocal included more than once
 755 #endif