libdecnumber/dpd/decimal128.c

   1 /* Decimal 128-bit format 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 128-bit format module                                      */
  33 /* ------------------------------------------------------------------ */
  34 /* This module comprises the routines for decimal128 format numbers.  */
  35 /* Conversions are supplied to and from decNumber and String.         */
  36 /*                                                                    */
  37 /* This is used when decNumber provides operations, either for all    */
  38 /* operations or as a proxy between decNumber and decSingle.          */
  39 /*                                                                    */
  40 /* Error handling is the same as decNumber (qv.).                     */
  41 /* ------------------------------------------------------------------ */
  42 #include <string.h>           /* [for memset/memcpy] */
  43 #include <stdio.h>            /* [for printf] */
  44
  45 #include "dconfig.h"          /* GCC definitions */
  46 #define  DECNUMDIGITS 34      /* make decNumbers with space for 34 */
  47 #include "decNumber.h"        /* base number library */
  48 #include "decNumberLocal.h"   /* decNumber local types, etc. */
  49 #include "decimal128.h"       /* our primary include */
  50
  51 /* Utility routines and tables [in decimal64.c] */
  52 extern const uInt   COMBEXP[32], COMBMSD[32];
  53 extern const uShort DPD2BIN[1024];
  54 extern const uShort BIN2DPD[1000];      /* [not used] */
  55 extern const uByte  BIN2CHAR[4001];
  56
  57 extern void decDigitsFromDPD(decNumber *, const uInt *, Int);
  58 extern void decDigitsToDPD(const decNumber *, uInt *, Int);
  59
  60 #if DECTRACE || DECCHECK
  61 void decimal128Show(const decimal128 *);          /* for debug */
  62 extern void decNumberShow(const decNumber *);     /* .. */
  63 #endif
  64
  65 /* Useful macro */
  66 /* Clear a structure (e.g., a decNumber) */
  67 #define DEC_clear(d) memset(d, 0, sizeof(*d))
  68
  69 /* ------------------------------------------------------------------ */
  70 /* decimal128FromNumber -- convert decNumber to decimal128            */
  71 /*                                                                    */
  72 /*   ds is the target decimal128                                      */
  73 /*   dn is the source number (assumed valid)                          */
  74 /*   set is the context, used only for reporting errors               */
  75 /*                                                                    */
  76 /* The set argument is used only for status reporting and for the     */
  77 /* rounding mode (used if the coefficient is more than DECIMAL128_Pmax*/
  78 /* digits or an overflow is detected).  If the exponent is out of the */
  79 /* valid range then Overflow or Underflow will be raised.             */
  80 /* After Underflow a subnormal result is possible.                    */
  81 /*                                                                    */
  82 /* DEC_Clamped is set if the number has to be 'folded down' to fit,   */
  83 /* by reducing its exponent and multiplying the coefficient by a      */
  84 /* power of ten, or if the exponent on a zero had to be clamped.      */
  85 /* ------------------------------------------------------------------ */
  86 decimal128 * decimal128FromNumber(decimal128 *d128, const decNumber *dn,
  87                                   decContext *set) {
  88   uInt status=0;                   /* status accumulator */
  89   Int ae;                          /* adjusted exponent */
  90   decNumber  dw;                   /* work */
  91   decContext dc;                   /* .. */
  92   uInt comb, exp;                  /* .. */
  93   uInt uiwork;                     /* for macros */
  94   uInt targar[4]={0,0,0,0};        /* target 128-bit */
  95   #define targhi targar[3]         /* name the word with the sign */
  96   #define targmh targar[2]         /* name the words */
  97   #define targml targar[1]         /* .. */
  98   #define targlo targar[0]         /* .. */
  99
 100   /* If the number has too many digits, or the exponent could be */
 101   /* out of range then reduce the number under the appropriate */
 102   /* constraints.  This could push the number to Infinity or zero, */
 103   /* so this check and rounding must be done before generating the */
 104   /* decimal128] */
 105   ae=dn->exponent+dn->digits-1;              /* [0 if special] */
 106   if (dn->digits>DECIMAL128_Pmax             /* too many digits */
 107    || ae>DECIMAL128_Emax                     /* likely overflow */
 108    || ae<DECIMAL128_Emin) {                  /* likely underflow */
 109     decContextDefault(&dc, DEC_INIT_DECIMAL128); /* [no traps] */
 110     dc.round=set->round;                     /* use supplied rounding */
 111     decNumberPlus(&dw, dn, &dc);             /* (round and check) */
 112     /* [this changes -0 to 0, so enforce the sign...] */
 113     dw.bits|=dn->bits&DECNEG;
 114     status=dc.status;                        /* save status */
 115     dn=&dw;                                  /* use the work number */
 116     } /* maybe out of range */
 117
 118   if (dn->bits&DECSPECIAL) {                      /* a special value */
 119     if (dn->bits&DECINF) targhi=DECIMAL_Inf<<24;
 120      else {                                       /* sNaN or qNaN */
 121       if ((*dn->lsu!=0 || dn->digits>1)           /* non-zero coefficient */
 122        && (dn->digits<DECIMAL128_Pmax)) {         /* coefficient fits */
 123         decDigitsToDPD(dn, targar, 0);
 124         }
 125       if (dn->bits&DECNAN) targhi|=DECIMAL_NaN<<24;
 126        else targhi|=DECIMAL_sNaN<<24;
 127       } /* a NaN */
 128     } /* special */
 129
 130    else { /* is finite */
 131     if (decNumberIsZero(dn)) {               /* is a zero */
 132       /* set and clamp exponent */
 133       if (dn->exponent<-DECIMAL128_Bias) {
 134         exp=0;                               /* low clamp */
 135         status|=DEC_Clamped;
 136         }
 137        else {
 138         exp=dn->exponent+DECIMAL128_Bias;    /* bias exponent */
 139         if (exp>DECIMAL128_Ehigh) {          /* top clamp */
 140           exp=DECIMAL128_Ehigh;
 141           status|=DEC_Clamped;
 142           }
 143         }
 144       comb=(exp>>9) & 0x18;             /* msd=0, exp top 2 bits .. */
 145       }
 146      else {                             /* non-zero finite number */
 147       uInt msd;                         /* work */
 148       Int pad=0;                        /* coefficient pad digits */
 149
 150       /* the dn is known to fit, but it may need to be padded */
 151       exp=(uInt)(dn->exponent+DECIMAL128_Bias);    /* bias exponent */
 152       if (exp>DECIMAL128_Ehigh) {                  /* fold-down case */
 153         pad=exp-DECIMAL128_Ehigh;
 154         exp=DECIMAL128_Ehigh;                      /* [to maximum] */
 155         status|=DEC_Clamped;
 156         }
 157
 158       /* [fastpath for common case is not a win, here] */
 159       decDigitsToDPD(dn, targar, pad);
 160       /* save and clear the top digit */
 161       msd=targhi>>14;
 162       targhi&=0x00003fff;
 163
 164       /* create the combination field */
 165       if (msd>=8) comb=0x18 | ((exp>>11) & 0x06) | (msd & 0x01);
 166              else comb=((exp>>9) & 0x18) | msd;
 167       }
 168     targhi|=comb<<26;              /* add combination field .. */
 169     targhi|=(exp&0xfff)<<14;       /* .. and exponent continuation */
 170     } /* finite */
 171
 172   if (dn->bits&DECNEG) targhi|=0x80000000; /* add sign bit */
 173
 174   /* now write to storage; this is endian */
 175   if (DECLITEND) {
 176     /* lo -> hi */
 177     UBFROMUI(d128->bytes,    targlo);
 178     UBFROMUI(d128->bytes+4,  targml);
 179     UBFROMUI(d128->bytes+8,  targmh);
 180     UBFROMUI(d128->bytes+12, targhi);
 181     }
 182    else {
 183     /* hi -> lo */
 184     UBFROMUI(d128->bytes,    targhi);
 185     UBFROMUI(d128->bytes+4,  targmh);
 186     UBFROMUI(d128->bytes+8,  targml);
 187     UBFROMUI(d128->bytes+12, targlo);
 188     }
 189
 190   if (status!=0) decContextSetStatus(set, status); /* pass on status */
 191   /* decimal128Show(d128); */
 192   return d128;
 193   } /* decimal128FromNumber */
 194
 195 /* ------------------------------------------------------------------ */
 196 /* decimal128ToNumber -- convert decimal128 to decNumber              */
 197 /*   d128 is the source decimal128                                    */
 198 /*   dn is the target number, with appropriate space                  */
 199 /* No error is possible.                                              */
 200 /* ------------------------------------------------------------------ */
 201 decNumber * decimal128ToNumber(const decimal128 *d128, decNumber *dn) {
 202   uInt msd;                        /* coefficient MSD */
 203   uInt exp;                        /* exponent top two bits */
 204   uInt comb;                       /* combination field */
 205   Int  need;                       /* work */
 206   uInt uiwork;                     /* for macros */
 207   uInt sourar[4];                  /* source 128-bit */
 208   #define sourhi sourar[3]         /* name the word with the sign */
 209   #define sourmh sourar[2]         /* and the mid-high word */
 210   #define sourml sourar[1]         /* and the mod-low word */
 211   #define sourlo sourar[0]         /* and the lowest word */
 212
 213   /* load source from storage; this is endian */
 214   if (DECLITEND) {
 215     sourlo=UBTOUI(d128->bytes   ); /* directly load the low int */
 216     sourml=UBTOUI(d128->bytes+4 ); /* then the mid-low */
 217     sourmh=UBTOUI(d128->bytes+8 ); /* then the mid-high */
 218     sourhi=UBTOUI(d128->bytes+12); /* then the high int */
 219     }
 220    else {
 221     sourhi=UBTOUI(d128->bytes   ); /* directly load the high int */
 222     sourmh=UBTOUI(d128->bytes+4 ); /* then the mid-high */
 223     sourml=UBTOUI(d128->bytes+8 ); /* then the mid-low */
 224     sourlo=UBTOUI(d128->bytes+12); /* then the low int */
 225     }
 226
 227   comb=(sourhi>>26)&0x1f;          /* combination field */
 228
 229   decNumberZero(dn);               /* clean number */
 230   if (sourhi&0x80000000) dn->bits=DECNEG; /* set sign if negative */
 231
 232   msd=COMBMSD[comb];               /* decode the combination field */
 233   exp=COMBEXP[comb];               /* .. */
 234
 235   if (exp==3) {                    /* is a special */
 236     if (msd==0) {
 237       dn->bits|=DECINF;
 238       return dn;                   /* no coefficient needed */
 239       }
 240     else if (sourhi&0x02000000) dn->bits|=DECSNAN;
 241     else dn->bits|=DECNAN;
 242     msd=0;                         /* no top digit */
 243     }
 244    else {                          /* is a finite number */
 245     dn->exponent=(exp<<12)+((sourhi>>14)&0xfff)-DECIMAL128_Bias; /* unbiased */
 246     }
 247
 248   /* get the coefficient */
 249   sourhi&=0x00003fff;              /* clean coefficient continuation */
 250   if (msd) {                       /* non-zero msd */
 251     sourhi|=msd<<14;               /* prefix to coefficient */
 252     need=12;                       /* process 12 declets */
 253     }
 254    else { /* msd=0 */
 255     if (sourhi) need=11;           /* declets to process */
 256      else if (sourmh) need=10;
 257      else if (sourml) need=7;
 258      else if (sourlo) need=4;
 259      else return dn;               /* easy: coefficient is 0 */
 260     } /*msd=0 */
 261
 262   decDigitsFromDPD(dn, sourar, need);   /* process declets */
 263   /* decNumberShow(dn); */
 264   return dn;
 265   } /* decimal128ToNumber */
 266
 267 /* ------------------------------------------------------------------ */
 268 /* to-scientific-string -- conversion to numeric string               */
 269 /* to-engineering-string -- conversion to numeric string              */
 270 /*                                                                    */
 271 /*   decimal128ToString(d128, string);                                */
 272 /*   decimal128ToEngString(d128, string);                             */
 273 /*                                                                    */
 274 /*  d128 is the decimal128 format number to convert                   */
 275 /*  string is the string where the result will be laid out            */
 276 /*                                                                    */
 277 /*  string must be at least 24 characters                             */
 278 /*                                                                    */
 279 /*  No error is possible, and no status can be set.                   */
 280 /* ------------------------------------------------------------------ */
 281 char * decimal128ToEngString(const decimal128 *d128, char *string){
 282   decNumber dn;                         /* work */
 283   decimal128ToNumber(d128, &dn);
 284   decNumberToEngString(&dn, string);
 285   return string;
 286   } /* decimal128ToEngString */
 287
 288 char * decimal128ToString(const decimal128 *d128, char *string){
 289   uInt msd;                        /* coefficient MSD */
 290   Int  exp;                        /* exponent top two bits or full */
 291   uInt comb;                       /* combination field */
 292   char *cstart;                    /* coefficient start */
 293   char *c;                         /* output pointer in string */
 294   const uByte *u;                  /* work */
 295   char *s, *t;                     /* .. (source, target) */
 296   Int  dpd;                        /* .. */
 297   Int  pre, e;                     /* .. */
 298   uInt uiwork;                     /* for macros */
 299
 300   uInt sourar[4];                  /* source 128-bit */
 301   #define sourhi sourar[3]         /* name the word with the sign */
 302   #define sourmh sourar[2]         /* and the mid-high word */
 303   #define sourml sourar[1]         /* and the mod-low word */
 304   #define sourlo sourar[0]         /* and the lowest word */
 305
 306   /* load source from storage; this is endian */
 307   if (DECLITEND) {
 308     sourlo=UBTOUI(d128->bytes   ); /* directly load the low int */
 309     sourml=UBTOUI(d128->bytes+4 ); /* then the mid-low */
 310     sourmh=UBTOUI(d128->bytes+8 ); /* then the mid-high */
 311     sourhi=UBTOUI(d128->bytes+12); /* then the high int */
 312     }
 313    else {
 314     sourhi=UBTOUI(d128->bytes   ); /* directly load the high int */
 315     sourmh=UBTOUI(d128->bytes+4 ); /* then the mid-high */
 316     sourml=UBTOUI(d128->bytes+8 ); /* then the mid-low */
 317     sourlo=UBTOUI(d128->bytes+12); /* then the low int */
 318     }
 319
 320   c=string;                        /* where result will go */
 321   if (((Int)sourhi)<0) *c++='-';   /* handle sign */
 322
 323   comb=(sourhi>>26)&0x1f;          /* combination field */
 324   msd=COMBMSD[comb];               /* decode the combination field */
 325   exp=COMBEXP[comb];               /* .. */
 326
 327   if (exp==3) {
 328     if (msd==0) {                  /* infinity */
 329       strcpy(c,   "Inf");
 330       strcpy(c+3, "inity");
 331       return string;               /* easy */
 332       }
 333     if (sourhi&0x02000000) *c++='s'; /* sNaN */
 334     strcpy(c, "NaN");              /* complete word */
 335     c+=3;                          /* step past */
 336     if (sourlo==0 && sourml==0 && sourmh==0
 337      && (sourhi&0x0003ffff)==0) return string; /* zero payload */
 338     /* otherwise drop through to add integer; set correct exp */
 339     exp=0; msd=0;                  /* setup for following code */
 340     }
 341    else exp=(exp<<12)+((sourhi>>14)&0xfff)-DECIMAL128_Bias; /* unbiased */
 342
 343   /* convert 34 digits of significand to characters */
 344   cstart=c;                        /* save start of coefficient */
 345   if (msd) *c++='0'+(char)msd;     /* non-zero most significant digit */
 346
 347   /* Now decode the declets.  After extracting each one, it is */
 348   /* decoded to binary and then to a 4-char sequence by table lookup; */
 349   /* the 4-chars are a 1-char length (significant digits, except 000 */
 350   /* has length 0).  This allows us to left-align the first declet */
 351   /* with non-zero content, then remaining ones are full 3-char */
 352   /* length.  We use fixed-length memcpys because variable-length */
 353   /* causes a subroutine call in GCC.  (These are length 4 for speed */
 354   /* and are safe because the array has an extra terminator byte.) */
 355   #define dpd2char u=&BIN2CHAR[DPD2BIN[dpd]*4];                   \
 356                    if (c!=cstart) {memcpy(c, u+1, 4); c+=3;}      \
 357                     else if (*u)  {memcpy(c, u+4-*u, 4); c+=*u;}
 358   dpd=(sourhi>>4)&0x3ff;                     /* declet 1 */
 359   dpd2char;
 360   dpd=((sourhi&0xf)<<6) | (sourmh>>26);      /* declet 2 */
 361   dpd2char;
 362   dpd=(sourmh>>16)&0x3ff;                    /* declet 3 */
 363   dpd2char;
 364   dpd=(sourmh>>6)&0x3ff;                     /* declet 4 */
 365   dpd2char;
 366   dpd=((sourmh&0x3f)<<4) | (sourml>>28);     /* declet 5 */
 367   dpd2char;
 368   dpd=(sourml>>18)&0x3ff;                    /* declet 6 */
 369   dpd2char;
 370   dpd=(sourml>>8)&0x3ff;                     /* declet 7 */
 371   dpd2char;
 372   dpd=((sourml&0xff)<<2) | (sourlo>>30);     /* declet 8 */
 373   dpd2char;
 374   dpd=(sourlo>>20)&0x3ff;                    /* declet 9 */
 375   dpd2char;
 376   dpd=(sourlo>>10)&0x3ff;                    /* declet 10 */
 377   dpd2char;
 378   dpd=(sourlo)&0x3ff;                        /* declet 11 */
 379   dpd2char;
 380
 381   if (c==cstart) *c++='0';         /* all zeros -- make 0 */
 382
 383   if (exp==0) {                    /* integer or NaN case -- easy */
 384     *c='\0';                       /* terminate */
 385     return string;
 386     }
 387
 388   /* non-0 exponent */
 389   e=0;                             /* assume no E */
 390   pre=c-cstart+exp;
 391   /* [here, pre-exp is the digits count (==1 for zero)] */
 392   if (exp>0 || pre<-5) {           /* need exponential form */
 393     e=pre-1;                       /* calculate E value */
 394     pre=1;                         /* assume one digit before '.' */
 395     } /* exponential form */
 396
 397   /* modify the coefficient, adding 0s, '.', and E+nn as needed */
 398   s=c-1;                           /* source (LSD) */
 399   if (pre>0) {                     /* ddd.ddd (plain), perhaps with E */
 400     char *dotat=cstart+pre;
 401     if (dotat<c) {                 /* if embedded dot needed... */
 402       t=c;                              /* target */
 403       for (; s>=dotat; s--, t--) *t=*s; /* open the gap; leave t at gap */
 404       *t='.';                           /* insert the dot */
 405       c++;                              /* length increased by one */
 406       }
 407
 408     /* finally add the E-part, if needed; it will never be 0, and has */
 409     /* a maximum length of 4 digits */
 410     if (e!=0) {
 411       *c++='E';                    /* starts with E */
 412       *c++='+';                    /* assume positive */
 413       if (e<0) {
 414         *(c-1)='-';                /* oops, need '-' */
 415         e=-e;                      /* uInt, please */
 416         }
 417       if (e<1000) {                /* 3 (or fewer) digits case */
 418         u=&BIN2CHAR[e*4];          /* -> length byte */
 419         memcpy(c, u+4-*u, 4);      /* copy fixed 4 characters [is safe] */
 420         c+=*u;                     /* bump pointer appropriately */
 421         }
 422        else {                      /* 4-digits */
 423         Int thou=((e>>3)*1049)>>17; /* e/1000 */
 424         Int rem=e-(1000*thou);      /* e%1000 */
 425         *c++='0'+(char)thou;
 426         u=&BIN2CHAR[rem*4];        /* -> length byte */
 427         memcpy(c, u+1, 4);         /* copy fixed 3+1 characters [is safe] */
 428         c+=3;                      /* bump pointer, always 3 digits */
 429         }
 430       }
 431     *c='\0';                       /* add terminator */
 432     /*printf("res %s\n", string); */
 433     return string;
 434     } /* pre>0 */
 435
 436   /* -5<=pre<=0: here for plain 0.ddd or 0.000ddd forms (can never have E) */
 437   t=c+1-pre;
 438   *(t+1)='\0';                          /* can add terminator now */
 439   for (; s>=cstart; s--, t--) *t=*s;    /* shift whole coefficient right */
 440   c=cstart;
 441   *c++='0';                             /* always starts with 0. */
 442   *c++='.';
 443   for (; pre<0; pre++) *c++='0';        /* add any 0's after '.' */
 444   /*printf("res %s\n", string); */
 445   return string;
 446   } /* decimal128ToString */
 447
 448 /* ------------------------------------------------------------------ */
 449 /* to-number -- conversion from numeric string                        */
 450 /*                                                                    */
 451 /*   decimal128FromString(result, string, set);                       */
 452 /*                                                                    */
 453 /*  result  is the decimal128 format number which gets the result of  */
 454 /*          the conversion                                            */
 455 /*  *string is the character string which should contain a valid      */
 456 /*          number (which may be a special value)                     */
 457 /*  set     is the context                                            */
 458 /*                                                                    */
 459 /* The context is supplied to this routine is used for error handling */
 460 /* (setting of status and traps) and for the rounding mode, only.     */
 461 /* If an error occurs, the result will be a valid decimal128 NaN.     */
 462 /* ------------------------------------------------------------------ */
 463 decimal128 * decimal128FromString(decimal128 *result, const char *string,
 464                                   decContext *set) {
 465   decContext dc;                             /* work */
 466   decNumber dn;                              /* .. */
 467
 468   decContextDefault(&dc, DEC_INIT_DECIMAL128); /* no traps, please */
 469   dc.round=set->round;                         /* use supplied rounding */
 470
 471   decNumberFromString(&dn, string, &dc);     /* will round if needed */
 472   decimal128FromNumber(result, &dn, &dc);
 473   if (dc.status!=0) {                        /* something happened */
 474     decContextSetStatus(set, dc.status);     /* .. pass it on */
 475     }
 476   return result;
 477   } /* decimal128FromString */
 478
 479 /* ------------------------------------------------------------------ */
 480 /* decimal128IsCanonical -- test whether encoding is canonical        */
 481 /*   d128 is the source decimal128                                    */
 482 /*   returns 1 if the encoding of d128 is canonical, 0 otherwise      */
 483 /* No error is possible.                                              */
 484 /* ------------------------------------------------------------------ */
 485 uInt decimal128IsCanonical(const decimal128 *d128) {
 486   decNumber dn;                         /* work */
 487   decimal128 canon;                      /* .. */
 488   decContext dc;                        /* .. */
 489   decContextDefault(&dc, DEC_INIT_DECIMAL128);
 490   decimal128ToNumber(d128, &dn);
 491   decimal128FromNumber(&canon, &dn, &dc);/* canon will now be canonical */
 492   return memcmp(d128, &canon, DECIMAL128_Bytes)==0;
 493   } /* decimal128IsCanonical */
 494
 495 /* ------------------------------------------------------------------ */
 496 /* decimal128Canonical -- copy an encoding, ensuring it is canonical  */
 497 /*   d128 is the source decimal128                                    */
 498 /*   result is the target (may be the same decimal128)                */
 499 /*   returns result                                                   */
 500 /* No error is possible.                                              */
 501 /* ------------------------------------------------------------------ */
 502 decimal128 * decimal128Canonical(decimal128 *result, const decimal128 *d128) {
 503   decNumber dn;                         /* work */
 504   decContext dc;                        /* .. */
 505   decContextDefault(&dc, DEC_INIT_DECIMAL128);
 506   decimal128ToNumber(d128, &dn);
 507   decimal128FromNumber(result, &dn, &dc);/* result will now be canonical */
 508   return result;
 509   } /* decimal128Canonical */
 510
 511 #if DECTRACE || DECCHECK
 512 /* Macros for accessing decimal128 fields.  These assume the argument
 513    is a reference (pointer) to the decimal128 structure, and the
 514    decimal128 is in network byte order (big-endian) */
 515 /* Get sign */
 516 #define decimal128Sign(d)       ((unsigned)(d)->bytes[0]>>7)
 517
 518 /* Get combination field */
 519 #define decimal128Comb(d)       (((d)->bytes[0] & 0x7c)>>2)
 520
 521 /* Get exponent continuation [does not remove bias] */
 522 #define decimal128ExpCon(d)     ((((d)->bytes[0] & 0x03)<<10)         \
 523                               | ((unsigned)(d)->bytes[1]<<2)          \
 524                               | ((unsigned)(d)->bytes[2]>>6))
 525
 526 /* Set sign [this assumes sign previously 0] */
 527 #define decimal128SetSign(d, b) {                                     \
 528   (d)->bytes[0]|=((unsigned)(b)<<7);}
 529
 530 /* Set exponent continuation [does not apply bias] */
 531 /* This assumes range has been checked and exponent previously 0; */
 532 /* type of exponent must be unsigned */
 533 #define decimal128SetExpCon(d, e) {                                   \
 534   (d)->bytes[0]|=(uByte)((e)>>10);                                    \
 535   (d)->bytes[1] =(uByte)(((e)&0x3fc)>>2);                             \
 536   (d)->bytes[2]|=(uByte)(((e)&0x03)<<6);}
 537
 538 /* ------------------------------------------------------------------ */
 539 /* decimal128Show -- display a decimal128 in hexadecimal [debug aid]  */
 540 /*   d128 -- the number to show                                       */
 541 /* ------------------------------------------------------------------ */
 542 /* Also shows sign/cob/expconfields extracted */
 543 void decimal128Show(const decimal128 *d128) {
 544   char buf[DECIMAL128_Bytes*2+1];
 545   Int i, j=0;
 546
 547   if (DECLITEND) {
 548     for (i=0; i<DECIMAL128_Bytes; i++, j+=2) {
 549       sprintf(&buf[j], "%02x", d128->bytes[15-i]);
 550       }
 551     printf(" D128> %s [S:%d Cb:%02x Ec:%02x] LittleEndian\n", buf,
 552            d128->bytes[15]>>7, (d128->bytes[15]>>2)&0x1f,
 553            ((d128->bytes[15]&0x3)<<10)|(d128->bytes[14]<<2)|
 554            (d128->bytes[13]>>6));
 555     }
 556    else {
 557     for (i=0; i<DECIMAL128_Bytes; i++, j+=2) {
 558       sprintf(&buf[j], "%02x", d128->bytes[i]);
 559       }
 560     printf(" D128> %s [S:%d Cb:%02x Ec:%02x] BigEndian\n", buf,
 561            decimal128Sign(d128), decimal128Comb(d128),
 562            decimal128ExpCon(d128));
 563     }
 564   } /* decimal128Show */
 565 #endif