libiberty/floatformat.c

   1 /* IEEE floating point support routines, for GDB, the GNU Debugger.
   2    Copyright 1991, 1994, 1999, 2000, 2003, 2005
   3    Free Software Foundation, Inc.
   4
   5 This file is part of GDB.
   6
   7 This program is free software; you can redistribute it and/or modify
   8 it under the terms of the GNU General Public License as published by
   9 the Free Software Foundation; either version 2 of the License, or
  10 (at your option) any later version.
  11
  12 This program is distributed in the hope that it will be useful,
  13 but WITHOUT ANY WARRANTY; without even the implied warranty of
  14 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  15 GNU General Public License for more details.
  16
  17 You should have received a copy of the GNU General Public License
  18 along with this program; if not, write to the Free Software
  19 Foundation, Inc., 51 Franklin Street - Fifth Floor, Boston, MA 02110-1301, USA.  */
  20
  21 /* This is needed to pick up the NAN macro on some systems.  */
  22 #define _GNU_SOURCE
  23
  24 #ifdef HAVE_CONFIG_H
  25 #include "config.h"
  26 #endif
  27
  28 #include <math.h>
  29
  30 #ifdef HAVE_STRING_H
  31 #include <string.h>
  32 #endif
  33
  34 #include "ansidecl.h"
  35 #include "libiberty.h"
  36 #include "floatformat.h"
  37
  38 #ifndef INFINITY
  39 #ifdef HUGE_VAL
  40 #define INFINITY HUGE_VAL
  41 #else
  42 #define INFINITY (1.0 / 0.0)
  43 #endif
  44 #endif
  45
  46 #ifndef NAN
  47 #define NAN (0.0 / 0.0)
  48 #endif
  49
  50 static unsigned long get_field (const unsigned char *,
  51                                 enum floatformat_byteorders,
  52                                 unsigned int,
  53                                 unsigned int,
  54                                 unsigned int);
  55 static int floatformat_always_valid (const struct floatformat *fmt,
  56                                      const void *from);
  57
  58 static int
  59 floatformat_always_valid (const struct floatformat *fmt ATTRIBUTE_UNUSED,
  60                           const void *from ATTRIBUTE_UNUSED)
  61 {
  62   return 1;
  63 }
  64
  65 /* The odds that CHAR_BIT will be anything but 8 are low enough that I'm not
  66    going to bother with trying to muck around with whether it is defined in
  67    a system header, what we do if not, etc.  */
  68 #define FLOATFORMAT_CHAR_BIT 8
  69
  70 /* floatformats for IEEE single and double, big and little endian.  */
  71 const struct floatformat floatformat_ieee_single_big =
  72 {
  73   floatformat_big, 32, 0, 1, 8, 127, 255, 9, 23,
  74   floatformat_intbit_no,
  75   "floatformat_ieee_single_big",
  76   floatformat_always_valid
  77 };
  78 const struct floatformat floatformat_ieee_single_little =
  79 {
  80   floatformat_little, 32, 0, 1, 8, 127, 255, 9, 23,
  81   floatformat_intbit_no,
  82   "floatformat_ieee_single_little",
  83   floatformat_always_valid
  84 };
  85 const struct floatformat floatformat_ieee_double_big =
  86 {
  87   floatformat_big, 64, 0, 1, 11, 1023, 2047, 12, 52,
  88   floatformat_intbit_no,
  89   "floatformat_ieee_double_big",
  90   floatformat_always_valid
  91 };
  92 const struct floatformat floatformat_ieee_double_little =
  93 {
  94   floatformat_little, 64, 0, 1, 11, 1023, 2047, 12, 52,
  95   floatformat_intbit_no,
  96   "floatformat_ieee_double_little",
  97   floatformat_always_valid
  98 };
  99
 100 /* floatformat for IEEE double, little endian byte order, with big endian word
 101    ordering, as on the ARM.  */
 102
 103 const struct floatformat floatformat_ieee_double_littlebyte_bigword =
 104 {
 105   floatformat_littlebyte_bigword, 64, 0, 1, 11, 1023, 2047, 12, 52,
 106   floatformat_intbit_no,
 107   "floatformat_ieee_double_littlebyte_bigword",
 108   floatformat_always_valid
 109 };
 110
 111 /* floatformat for VAX.  Not quite IEEE, but close enough.  */
 112
 113 const struct floatformat floatformat_vax_f =
 114 {
 115   floatformat_vax, 32, 0, 1, 8, 129, 0, 9, 23,
 116   floatformat_intbit_no,
 117   "floatformat_vax_f",
 118   floatformat_always_valid
 119 };
 120 const struct floatformat floatformat_vax_d =
 121 {
 122   floatformat_vax, 64, 0, 1, 8, 129, 0, 9, 55,
 123   floatformat_intbit_no,
 124   "floatformat_vax_d",
 125   floatformat_always_valid
 126 };
 127 const struct floatformat floatformat_vax_g =
 128 {
 129   floatformat_vax, 64, 0, 1, 11, 1025, 0, 12, 52,
 130   floatformat_intbit_no,
 131   "floatformat_vax_g",
 132   floatformat_always_valid
 133 };
 134
 135 static int floatformat_i387_ext_is_valid (const struct floatformat *fmt,
 136                                           const void *from);
 137
 138 static int
 139 floatformat_i387_ext_is_valid (const struct floatformat *fmt, const void *from)
 140 {
 141   /* In the i387 double-extended format, if the exponent is all ones,
 142      then the integer bit must be set.  If the exponent is neither 0
 143      nor ~0, the intbit must also be set.  Only if the exponent is
 144      zero can it be zero, and then it must be zero.  */
 145   unsigned long exponent, int_bit;
 146   const unsigned char *ufrom = (const unsigned char *) from;
 147
 148   exponent = get_field (ufrom, fmt->byteorder, fmt->totalsize,
 149                         fmt->exp_start, fmt->exp_len);
 150   int_bit = get_field (ufrom, fmt->byteorder, fmt->totalsize,
 151                        fmt->man_start, 1);
 152
 153   if ((exponent == 0) != (int_bit == 0))
 154     return 0;
 155   else
 156     return 1;
 157 }
 158
 159 const struct floatformat floatformat_i387_ext =
 160 {
 161   floatformat_little, 80, 0, 1, 15, 0x3fff, 0x7fff, 16, 64,
 162   floatformat_intbit_yes,
 163   "floatformat_i387_ext",
 164   floatformat_i387_ext_is_valid
 165 };
 166 const struct floatformat floatformat_m68881_ext =
 167 {
 168   /* Note that the bits from 16 to 31 are unused.  */
 169   floatformat_big, 96, 0, 1, 15, 0x3fff, 0x7fff, 32, 64,
 170   floatformat_intbit_yes,
 171   "floatformat_m68881_ext",
 172   floatformat_always_valid
 173 };
 174 const struct floatformat floatformat_i960_ext =
 175 {
 176   /* Note that the bits from 0 to 15 are unused.  */
 177   floatformat_little, 96, 16, 17, 15, 0x3fff, 0x7fff, 32, 64,
 178   floatformat_intbit_yes,
 179   "floatformat_i960_ext",
 180   floatformat_always_valid
 181 };
 182 const struct floatformat floatformat_m88110_ext =
 183 {
 184   floatformat_big, 80, 0, 1, 15, 0x3fff, 0x7fff, 16, 64,
 185   floatformat_intbit_yes,
 186   "floatformat_m88110_ext",
 187   floatformat_always_valid
 188 };
 189 const struct floatformat floatformat_m88110_harris_ext =
 190 {
 191   /* Harris uses raw format 128 bytes long, but the number is just an ieee
 192      double, and the last 64 bits are wasted. */
 193   floatformat_big,128, 0, 1, 11,  0x3ff,  0x7ff, 12, 52,
 194   floatformat_intbit_no,
 195   "floatformat_m88110_ext_harris",
 196   floatformat_always_valid
 197 };
 198 const struct floatformat floatformat_arm_ext_big =
 199 {
 200   /* Bits 1 to 16 are unused.  */
 201   floatformat_big, 96, 0, 17, 15, 0x3fff, 0x7fff, 32, 64,
 202   floatformat_intbit_yes,
 203   "floatformat_arm_ext_big",
 204   floatformat_always_valid
 205 };
 206 const struct floatformat floatformat_arm_ext_littlebyte_bigword =
 207 {
 208   /* Bits 1 to 16 are unused.  */
 209   floatformat_littlebyte_bigword, 96, 0, 17, 15, 0x3fff, 0x7fff, 32, 64,
 210   floatformat_intbit_yes,
 211   "floatformat_arm_ext_littlebyte_bigword",
 212   floatformat_always_valid
 213 };
 214 const struct floatformat floatformat_ia64_spill_big =
 215 {
 216   floatformat_big, 128, 0, 1, 17, 65535, 0x1ffff, 18, 64,
 217   floatformat_intbit_yes,
 218   "floatformat_ia64_spill_big",
 219   floatformat_always_valid
 220 };
 221 const struct floatformat floatformat_ia64_spill_little =
 222 {
 223   floatformat_little, 128, 0, 1, 17, 65535, 0x1ffff, 18, 64,
 224   floatformat_intbit_yes,
 225   "floatformat_ia64_spill_little",
 226   floatformat_always_valid
 227 };
 228 const struct floatformat floatformat_ia64_quad_big =
 229 {
 230   floatformat_big, 128, 0, 1, 15, 16383, 0x7fff, 16, 112,
 231   floatformat_intbit_no,
 232   "floatformat_ia64_quad_big",
 233   floatformat_always_valid
 234 };
 235 const struct floatformat floatformat_ia64_quad_little =
 236 {
 237   floatformat_little, 128, 0, 1, 15, 16383, 0x7fff, 16, 112,
 238   floatformat_intbit_no,
 239   "floatformat_ia64_quad_little",
 240   floatformat_always_valid
 241 };
 242 \f
 243 /* Extract a field which starts at START and is LEN bits long.  DATA and
 244    TOTAL_LEN are the thing we are extracting it from, in byteorder ORDER.  */
 245 static unsigned long
 246 get_field (const unsigned char *data, enum floatformat_byteorders order,
 247            unsigned int total_len, unsigned int start, unsigned int len)
 248 {
 249   unsigned long result;
 250   unsigned int cur_byte;
 251   int cur_bitshift;
 252
 253   /* Start at the least significant part of the field.  */
 254   cur_byte = (start + len) / FLOATFORMAT_CHAR_BIT;
 255   if (order == floatformat_little)
 256     cur_byte = (total_len / FLOATFORMAT_CHAR_BIT) - cur_byte - 1;
 257   cur_bitshift =
 258     ((start + len) % FLOATFORMAT_CHAR_BIT) - FLOATFORMAT_CHAR_BIT;
 259   result = *(data + cur_byte) >> (-cur_bitshift);
 260   cur_bitshift += FLOATFORMAT_CHAR_BIT;
 261   if (order == floatformat_little)
 262     ++cur_byte;
 263   else
 264     --cur_byte;
 265
 266   /* Move towards the most significant part of the field.  */
 267   while ((unsigned int) cur_bitshift < len)
 268     {
 269       if (len - cur_bitshift < FLOATFORMAT_CHAR_BIT)
 270         /* This is the last byte; zero out the bits which are not part of
 271            this field.  */
 272         result |=
 273           (*(data + cur_byte) & ((1 << (len - cur_bitshift)) - 1))
 274             << cur_bitshift;
 275       else
 276         result |= *(data + cur_byte) << cur_bitshift;
 277       cur_bitshift += FLOATFORMAT_CHAR_BIT;
 278       if (order == floatformat_little)
 279         ++cur_byte;
 280       else
 281         --cur_byte;
 282     }
 283   return result;
 284 }
 285
 286 #ifndef min
 287 #define min(a, b) ((a) < (b) ? (a) : (b))
 288 #endif
 289
 290 /* Convert from FMT to a double.
 291    FROM is the address of the extended float.
 292    Store the double in *TO.  */
 293
 294 void
 295 floatformat_to_double (const struct floatformat *fmt,
 296                        const void *from, double *to)
 297 {
 298   const unsigned char *ufrom = (const unsigned char *) from;
 299   double dto;
 300   long exponent;
 301   unsigned long mant;
 302   unsigned int mant_bits, mant_off;
 303   int mant_bits_left;
 304   int special_exponent;         /* It's a NaN, denorm or zero */
 305
 306   exponent = get_field (ufrom, fmt->byteorder, fmt->totalsize,
 307                         fmt->exp_start, fmt->exp_len);
 308
 309   /* If the exponent indicates a NaN, we don't have information to
 310      decide what to do.  So we handle it like IEEE, except that we
 311      don't try to preserve the type of NaN.  FIXME.  */
 312   if ((unsigned long) exponent == fmt->exp_nan)
 313     {
 314       int nan;
 315
 316       mant_off = fmt->man_start;
 317       mant_bits_left = fmt->man_len;
 318       nan = 0;
 319       while (mant_bits_left > 0)
 320         {
 321           mant_bits = min (mant_bits_left, 32);
 322
 323           if (get_field (ufrom, fmt->byteorder, fmt->totalsize,
 324                          mant_off, mant_bits) != 0)
 325             {
 326               /* This is a NaN.  */
 327               nan = 1;
 328               break;
 329             }
 330
 331           mant_off += mant_bits;
 332           mant_bits_left -= mant_bits;
 333         }
 334
 335       /* On certain systems (such as GNU/Linux), the use of the
 336          INFINITY macro below may generate a warning that can not be
 337          silenced due to a bug in GCC (PR preprocessor/11931).  The
 338          preprocessor fails to recognise the __extension__ keyword in
 339          conjunction with the GNU/C99 extension for hexadecimal
 340          floating point constants and will issue a warning when
 341          compiling with -pedantic.  */
 342       if (nan)
 343         dto = NAN;
 344       else
 345         dto = INFINITY;
 346
 347       if (get_field (ufrom, fmt->byteorder, fmt->totalsize, fmt->sign_start, 1))
 348         dto = -dto;
 349
 350       *to = dto;
 351
 352       return;
 353     }
 354
 355   mant_bits_left = fmt->man_len;
 356   mant_off = fmt->man_start;
 357   dto = 0.0;
 358
 359   special_exponent = exponent == 0 || (unsigned long) exponent == fmt->exp_nan;
 360
 361   /* Don't bias zero's, denorms or NaNs.  */
 362   if (!special_exponent)
 363     exponent -= fmt->exp_bias;
 364
 365   /* Build the result algebraically.  Might go infinite, underflow, etc;
 366      who cares. */
 367
 368   /* If this format uses a hidden bit, explicitly add it in now.  Otherwise,
 369      increment the exponent by one to account for the integer bit.  */
 370
 371   if (!special_exponent)
 372     {
 373       if (fmt->intbit == floatformat_intbit_no)
 374         dto = ldexp (1.0, exponent);
 375       else
 376         exponent++;
 377     }
 378
 379   while (mant_bits_left > 0)
 380     {
 381       mant_bits = min (mant_bits_left, 32);
 382
 383       mant = get_field (ufrom, fmt->byteorder, fmt->totalsize,
 384                          mant_off, mant_bits);
 385
 386       /* Handle denormalized numbers.  FIXME: What should we do for
 387          non-IEEE formats?  */
 388       if (exponent == 0 && mant != 0)
 389         dto += ldexp ((double)mant,
 390                       (- fmt->exp_bias
 391                        - mant_bits
 392                        - (mant_off - fmt->man_start)
 393                        + 1));
 394       else
 395         dto += ldexp ((double)mant, exponent - mant_bits);
 396       if (exponent != 0)
 397         exponent -= mant_bits;
 398       mant_off += mant_bits;
 399       mant_bits_left -= mant_bits;
 400     }
 401
 402   /* Negate it if negative.  */
 403   if (get_field (ufrom, fmt->byteorder, fmt->totalsize, fmt->sign_start, 1))
 404     dto = -dto;
 405   *to = dto;
 406 }
 407 \f
 408 static void put_field (unsigned char *, enum floatformat_byteorders,
 409                        unsigned int,
 410                        unsigned int,
 411                        unsigned int,
 412                        unsigned long);
 413
 414 /* Set a field which starts at START and is LEN bits long.  DATA and
 415    TOTAL_LEN are the thing we are extracting it from, in byteorder ORDER.  */
 416 static void
 417 put_field (unsigned char *data, enum floatformat_byteorders order,
 418            unsigned int total_len, unsigned int start, unsigned int len,
 419            unsigned long stuff_to_put)
 420 {
 421   unsigned int cur_byte;
 422   int cur_bitshift;
 423
 424   /* Start at the least significant part of the field.  */
 425   cur_byte = (start + len) / FLOATFORMAT_CHAR_BIT;
 426   if (order == floatformat_little)
 427     cur_byte = (total_len / FLOATFORMAT_CHAR_BIT) - cur_byte - 1;
 428   cur_bitshift =
 429     ((start + len) % FLOATFORMAT_CHAR_BIT) - FLOATFORMAT_CHAR_BIT;
 430   *(data + cur_byte) &=
 431     ~(((1 << ((start + len) % FLOATFORMAT_CHAR_BIT)) - 1) << (-cur_bitshift));
 432   *(data + cur_byte) |=
 433     (stuff_to_put & ((1 << FLOATFORMAT_CHAR_BIT) - 1)) << (-cur_bitshift);
 434   cur_bitshift += FLOATFORMAT_CHAR_BIT;
 435   if (order == floatformat_little)
 436     ++cur_byte;
 437   else
 438     --cur_byte;
 439
 440   /* Move towards the most significant part of the field.  */
 441   while ((unsigned int) cur_bitshift < len)
 442     {
 443       if (len - cur_bitshift < FLOATFORMAT_CHAR_BIT)
 444         {
 445           /* This is the last byte.  */
 446           *(data + cur_byte) &=
 447             ~((1 << (len - cur_bitshift)) - 1);
 448           *(data + cur_byte) |= (stuff_to_put >> cur_bitshift);
 449         }
 450       else
 451         *(data + cur_byte) = ((stuff_to_put >> cur_bitshift)
 452                               & ((1 << FLOATFORMAT_CHAR_BIT) - 1));
 453       cur_bitshift += FLOATFORMAT_CHAR_BIT;
 454       if (order == floatformat_little)
 455         ++cur_byte;
 456       else
 457         --cur_byte;
 458     }
 459 }
 460
 461 /* The converse: convert the double *FROM to an extended float
 462    and store where TO points.  Neither FROM nor TO have any alignment
 463    restrictions.  */
 464
 465 void
 466 floatformat_from_double (const struct floatformat *fmt,
 467                          const double *from, void *to)
 468 {
 469   double dfrom;
 470   int exponent;
 471   double mant;
 472   unsigned int mant_bits, mant_off;
 473   int mant_bits_left;
 474   unsigned char *uto = (unsigned char *) to;
 475
 476   dfrom = *from;
 477   memset (uto, 0, fmt->totalsize / FLOATFORMAT_CHAR_BIT);
 478
 479   /* If negative, set the sign bit.  */
 480   if (dfrom < 0)
 481     {
 482       put_field (uto, fmt->byteorder, fmt->totalsize, fmt->sign_start, 1, 1);
 483       dfrom = -dfrom;
 484     }
 485
 486   if (dfrom == 0)
 487     {
 488       /* 0.0.  */
 489       return;
 490     }
 491
 492   if (dfrom != dfrom)
 493     {
 494       /* NaN.  */
 495       put_field (uto, fmt->byteorder, fmt->totalsize, fmt->exp_start,
 496                  fmt->exp_len, fmt->exp_nan);
 497       /* Be sure it's not infinity, but NaN value is irrelevant.  */
 498       put_field (uto, fmt->byteorder, fmt->totalsize, fmt->man_start,
 499                  32, 1);
 500       return;
 501     }
 502
 503   if (dfrom + dfrom == dfrom)
 504     {
 505       /* This can only happen for an infinite value (or zero, which we
 506          already handled above).  */
 507       put_field (uto, fmt->byteorder, fmt->totalsize, fmt->exp_start,
 508                  fmt->exp_len, fmt->exp_nan);
 509       return;
 510     }
 511
 512   mant = frexp (dfrom, &exponent);
 513   if (exponent + fmt->exp_bias - 1 > 0)
 514     put_field (uto, fmt->byteorder, fmt->totalsize, fmt->exp_start,
 515                fmt->exp_len, exponent + fmt->exp_bias - 1);
 516   else
 517     {
 518       /* Handle a denormalized number.  FIXME: What should we do for
 519          non-IEEE formats?  */
 520       put_field (uto, fmt->byteorder, fmt->totalsize, fmt->exp_start,
 521                  fmt->exp_len, 0);
 522       mant = ldexp (mant, exponent + fmt->exp_bias - 1);
 523     }
 524
 525   mant_bits_left = fmt->man_len;
 526   mant_off = fmt->man_start;
 527   while (mant_bits_left > 0)
 528     {
 529       unsigned long mant_long;
 530       mant_bits = mant_bits_left < 32 ? mant_bits_left : 32;
 531
 532       mant *= 4294967296.0;
 533       mant_long = (unsigned long)mant;
 534       mant -= mant_long;
 535
 536       /* If the integer bit is implicit, and we are not creating a
 537          denormalized number, then we need to discard it.  */
 538       if ((unsigned int) mant_bits_left == fmt->man_len
 539           && fmt->intbit == floatformat_intbit_no
 540           && exponent + fmt->exp_bias - 1 > 0)
 541         {
 542           mant_long &= 0x7fffffff;
 543           mant_bits -= 1;
 544         }
 545       else if (mant_bits < 32)
 546         {
 547           /* The bits we want are in the most significant MANT_BITS bits of
 548              mant_long.  Move them to the least significant.  */
 549           mant_long >>= 32 - mant_bits;
 550         }
 551
 552       put_field (uto, fmt->byteorder, fmt->totalsize,
 553                  mant_off, mant_bits, mant_long);
 554       mant_off += mant_bits;
 555       mant_bits_left -= mant_bits;
 556     }
 557 }
 558
 559 /* Return non-zero iff the data at FROM is a valid number in format FMT.  */
 560
 561 int
 562 floatformat_is_valid (const struct floatformat *fmt, const void *from)
 563 {
 564   return fmt->is_valid (fmt, from);
 565 }
 566
 567
 568 #ifdef IEEE_DEBUG
 569
 570 #include <stdio.h>
 571
 572 /* This is to be run on a host which uses IEEE floating point.  */
 573
 574 void
 575 ieee_test (double n)
 576 {
 577   double result;
 578
 579   floatformat_to_double (&floatformat_ieee_double_little, &n, &result);
 580   if ((n != result && (! isnan (n) || ! isnan (result)))
 581       || (n < 0 && result >= 0)
 582       || (n >= 0 && result < 0))
 583     printf ("Differ(to): %.20g -> %.20g\n", n, result);
 584
 585   floatformat_from_double (&floatformat_ieee_double_little, &n, &result);
 586   if ((n != result && (! isnan (n) || ! isnan (result)))
 587       || (n < 0 && result >= 0)
 588       || (n >= 0 && result < 0))
 589     printf ("Differ(from): %.20g -> %.20g\n", n, result);
 590
 591 #if 0
 592   {
 593     char exten[16];
 594
 595     floatformat_from_double (&floatformat_m68881_ext, &n, exten);
 596     floatformat_to_double (&floatformat_m68881_ext, exten, &result);
 597     if (n != result)
 598       printf ("Differ(to+from): %.20g -> %.20g\n", n, result);
 599   }
 600 #endif
 601
 602 #if IEEE_DEBUG > 1
 603   /* This is to be run on a host which uses 68881 format.  */
 604   {
 605     long double ex = *(long double *)exten;
 606     if (ex != n)
 607       printf ("Differ(from vs. extended): %.20g\n", n);
 608   }
 609 #endif
 610 }
 611
 612 int
 613 main (void)
 614 {
 615   ieee_test (0.0);
 616   ieee_test (0.5);
 617   ieee_test (256.0);
 618   ieee_test (0.12345);
 619   ieee_test (234235.78907234);
 620   ieee_test (-512.0);
 621   ieee_test (-0.004321);
 622   ieee_test (1.2E-70);
 623   ieee_test (1.2E-316);
 624   ieee_test (4.9406564584124654E-324);
 625   ieee_test (- 4.9406564584124654E-324);
 626   ieee_test (- 0.0);
 627   ieee_test (- INFINITY);
 628   ieee_test (- NAN);
 629   ieee_test (INFINITY);
 630   ieee_test (NAN);
 631   return 0;
 632 }
 633 #endif