libiberty/floatformat.c

   1 /* IEEE floating point support routines, for GDB, the GNU Debugger.
   2    Copyright 1991, 1994, 1999, 2000, 2003, 2005, 2006
   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 /* On some platforms, <float.h> provides DBL_QNAN.  */
  35 #ifdef STDC_HEADERS
  36 #include <float.h>
  37 #endif
  38
  39 #include "ansidecl.h"
  40 #include "libiberty.h"
  41 #include "floatformat.h"
  42
  43 #ifndef INFINITY
  44 #ifdef HUGE_VAL
  45 #define INFINITY HUGE_VAL
  46 #else
  47 #define INFINITY (1.0 / 0.0)
  48 #endif
  49 #endif
  50
  51 #ifndef NAN
  52 #ifdef DBL_QNAN
  53 #define NAN DBL_QNAN
  54 #else
  55 #define NAN (0.0 / 0.0)
  56 #endif
  57 #endif
  58
  59 static unsigned long get_field (const unsigned char *,
  60                                 enum floatformat_byteorders,
  61                                 unsigned int,
  62                                 unsigned int,
  63                                 unsigned int);
  64 static int floatformat_always_valid (const struct floatformat *fmt,
  65                                      const void *from);
  66
  67 static int
  68 floatformat_always_valid (const struct floatformat *fmt ATTRIBUTE_UNUSED,
  69                           const void *from ATTRIBUTE_UNUSED)
  70 {
  71   return 1;
  72 }
  73
  74 /* The odds that CHAR_BIT will be anything but 8 are low enough that I'm not
  75    going to bother with trying to muck around with whether it is defined in
  76    a system header, what we do if not, etc.  */
  77 #define FLOATFORMAT_CHAR_BIT 8
  78
  79 /* floatformats for IEEE single and double, big and little endian.  */
  80 const struct floatformat floatformat_ieee_single_big =
  81 {
  82   floatformat_big, 32, 0, 1, 8, 127, 255, 9, 23,
  83   floatformat_intbit_no,
  84   "floatformat_ieee_single_big",
  85   floatformat_always_valid
  86 };
  87 const struct floatformat floatformat_ieee_single_little =
  88 {
  89   floatformat_little, 32, 0, 1, 8, 127, 255, 9, 23,
  90   floatformat_intbit_no,
  91   "floatformat_ieee_single_little",
  92   floatformat_always_valid
  93 };
  94 const struct floatformat floatformat_ieee_double_big =
  95 {
  96   floatformat_big, 64, 0, 1, 11, 1023, 2047, 12, 52,
  97   floatformat_intbit_no,
  98   "floatformat_ieee_double_big",
  99   floatformat_always_valid
 100 };
 101 const struct floatformat floatformat_ieee_double_little =
 102 {
 103   floatformat_little, 64, 0, 1, 11, 1023, 2047, 12, 52,
 104   floatformat_intbit_no,
 105   "floatformat_ieee_double_little",
 106   floatformat_always_valid
 107 };
 108
 109 /* floatformat for IEEE double, little endian byte order, with big endian word
 110    ordering, as on the ARM.  */
 111
 112 const struct floatformat floatformat_ieee_double_littlebyte_bigword =
 113 {
 114   floatformat_littlebyte_bigword, 64, 0, 1, 11, 1023, 2047, 12, 52,
 115   floatformat_intbit_no,
 116   "floatformat_ieee_double_littlebyte_bigword",
 117   floatformat_always_valid
 118 };
 119
 120 /* floatformat for VAX.  Not quite IEEE, but close enough.  */
 121
 122 const struct floatformat floatformat_vax_f =
 123 {
 124   floatformat_vax, 32, 0, 1, 8, 129, 0, 9, 23,
 125   floatformat_intbit_no,
 126   "floatformat_vax_f",
 127   floatformat_always_valid
 128 };
 129 const struct floatformat floatformat_vax_d =
 130 {
 131   floatformat_vax, 64, 0, 1, 8, 129, 0, 9, 55,
 132   floatformat_intbit_no,
 133   "floatformat_vax_d",
 134   floatformat_always_valid
 135 };
 136 const struct floatformat floatformat_vax_g =
 137 {
 138   floatformat_vax, 64, 0, 1, 11, 1025, 0, 12, 52,
 139   floatformat_intbit_no,
 140   "floatformat_vax_g",
 141   floatformat_always_valid
 142 };
 143
 144 static int floatformat_i387_ext_is_valid (const struct floatformat *fmt,
 145                                           const void *from);
 146
 147 static int
 148 floatformat_i387_ext_is_valid (const struct floatformat *fmt, const void *from)
 149 {
 150   /* In the i387 double-extended format, if the exponent is all ones,
 151      then the integer bit must be set.  If the exponent is neither 0
 152      nor ~0, the intbit must also be set.  Only if the exponent is
 153      zero can it be zero, and then it must be zero.  */
 154   unsigned long exponent, int_bit;
 155   const unsigned char *ufrom = (const unsigned char *) from;
 156
 157   exponent = get_field (ufrom, fmt->byteorder, fmt->totalsize,
 158                         fmt->exp_start, fmt->exp_len);
 159   int_bit = get_field (ufrom, fmt->byteorder, fmt->totalsize,
 160                        fmt->man_start, 1);
 161
 162   if ((exponent == 0) != (int_bit == 0))
 163     return 0;
 164   else
 165     return 1;
 166 }
 167
 168 const struct floatformat floatformat_i387_ext =
 169 {
 170   floatformat_little, 80, 0, 1, 15, 0x3fff, 0x7fff, 16, 64,
 171   floatformat_intbit_yes,
 172   "floatformat_i387_ext",
 173   floatformat_i387_ext_is_valid
 174 };
 175 const struct floatformat floatformat_m68881_ext =
 176 {
 177   /* Note that the bits from 16 to 31 are unused.  */
 178   floatformat_big, 96, 0, 1, 15, 0x3fff, 0x7fff, 32, 64,
 179   floatformat_intbit_yes,
 180   "floatformat_m68881_ext",
 181   floatformat_always_valid
 182 };
 183 const struct floatformat floatformat_i960_ext =
 184 {
 185   /* Note that the bits from 0 to 15 are unused.  */
 186   floatformat_little, 96, 16, 17, 15, 0x3fff, 0x7fff, 32, 64,
 187   floatformat_intbit_yes,
 188   "floatformat_i960_ext",
 189   floatformat_always_valid
 190 };
 191 const struct floatformat floatformat_m88110_ext =
 192 {
 193   floatformat_big, 80, 0, 1, 15, 0x3fff, 0x7fff, 16, 64,
 194   floatformat_intbit_yes,
 195   "floatformat_m88110_ext",
 196   floatformat_always_valid
 197 };
 198 const struct floatformat floatformat_m88110_harris_ext =
 199 {
 200   /* Harris uses raw format 128 bytes long, but the number is just an ieee
 201      double, and the last 64 bits are wasted. */
 202   floatformat_big,128, 0, 1, 11,  0x3ff,  0x7ff, 12, 52,
 203   floatformat_intbit_no,
 204   "floatformat_m88110_ext_harris",
 205   floatformat_always_valid
 206 };
 207 const struct floatformat floatformat_arm_ext_big =
 208 {
 209   /* Bits 1 to 16 are unused.  */
 210   floatformat_big, 96, 0, 17, 15, 0x3fff, 0x7fff, 32, 64,
 211   floatformat_intbit_yes,
 212   "floatformat_arm_ext_big",
 213   floatformat_always_valid
 214 };
 215 const struct floatformat floatformat_arm_ext_littlebyte_bigword =
 216 {
 217   /* Bits 1 to 16 are unused.  */
 218   floatformat_littlebyte_bigword, 96, 0, 17, 15, 0x3fff, 0x7fff, 32, 64,
 219   floatformat_intbit_yes,
 220   "floatformat_arm_ext_littlebyte_bigword",
 221   floatformat_always_valid
 222 };
 223 const struct floatformat floatformat_ia64_spill_big =
 224 {
 225   floatformat_big, 128, 0, 1, 17, 65535, 0x1ffff, 18, 64,
 226   floatformat_intbit_yes,
 227   "floatformat_ia64_spill_big",
 228   floatformat_always_valid
 229 };
 230 const struct floatformat floatformat_ia64_spill_little =
 231 {
 232   floatformat_little, 128, 0, 1, 17, 65535, 0x1ffff, 18, 64,
 233   floatformat_intbit_yes,
 234   "floatformat_ia64_spill_little",
 235   floatformat_always_valid
 236 };
 237 const struct floatformat floatformat_ia64_quad_big =
 238 {
 239   floatformat_big, 128, 0, 1, 15, 16383, 0x7fff, 16, 112,
 240   floatformat_intbit_no,
 241   "floatformat_ia64_quad_big",
 242   floatformat_always_valid
 243 };
 244 const struct floatformat floatformat_ia64_quad_little =
 245 {
 246   floatformat_little, 128, 0, 1, 15, 16383, 0x7fff, 16, 112,
 247   floatformat_intbit_no,
 248   "floatformat_ia64_quad_little",
 249   floatformat_always_valid
 250 };
 251 \f
 252 /* Extract a field which starts at START and is LEN bits long.  DATA and
 253    TOTAL_LEN are the thing we are extracting it from, in byteorder ORDER.  */
 254 static unsigned long
 255 get_field (const unsigned char *data, enum floatformat_byteorders order,
 256            unsigned int total_len, unsigned int start, unsigned int len)
 257 {
 258   unsigned long result;
 259   unsigned int cur_byte;
 260   int cur_bitshift;
 261
 262   /* Start at the least significant part of the field.  */
 263   cur_byte = (start + len) / FLOATFORMAT_CHAR_BIT;
 264   if (order == floatformat_little)
 265     cur_byte = (total_len / FLOATFORMAT_CHAR_BIT) - cur_byte - 1;
 266   cur_bitshift =
 267     ((start + len) % FLOATFORMAT_CHAR_BIT) - FLOATFORMAT_CHAR_BIT;
 268   result = *(data + cur_byte) >> (-cur_bitshift);
 269   cur_bitshift += FLOATFORMAT_CHAR_BIT;
 270   if (order == floatformat_little)
 271     ++cur_byte;
 272   else
 273     --cur_byte;
 274
 275   /* Move towards the most significant part of the field.  */
 276   while ((unsigned int) cur_bitshift < len)
 277     {
 278       if (len - cur_bitshift < FLOATFORMAT_CHAR_BIT)
 279         /* This is the last byte; zero out the bits which are not part of
 280            this field.  */
 281         result |=
 282           (*(data + cur_byte) & ((1 << (len - cur_bitshift)) - 1))
 283             << cur_bitshift;
 284       else
 285         result |= *(data + cur_byte) << cur_bitshift;
 286       cur_bitshift += FLOATFORMAT_CHAR_BIT;
 287       if (order == floatformat_little)
 288         ++cur_byte;
 289       else
 290         --cur_byte;
 291     }
 292   return result;
 293 }
 294
 295 #ifndef min
 296 #define min(a, b) ((a) < (b) ? (a) : (b))
 297 #endif
 298
 299 /* Convert from FMT to a double.
 300    FROM is the address of the extended float.
 301    Store the double in *TO.  */
 302
 303 void
 304 floatformat_to_double (const struct floatformat *fmt,
 305                        const void *from, double *to)
 306 {
 307   const unsigned char *ufrom = (const unsigned char *) from;
 308   double dto;
 309   long exponent;
 310   unsigned long mant;
 311   unsigned int mant_bits, mant_off;
 312   int mant_bits_left;
 313   int special_exponent;         /* It's a NaN, denorm or zero */
 314
 315   exponent = get_field (ufrom, fmt->byteorder, fmt->totalsize,
 316                         fmt->exp_start, fmt->exp_len);
 317
 318   /* If the exponent indicates a NaN, we don't have information to
 319      decide what to do.  So we handle it like IEEE, except that we
 320      don't try to preserve the type of NaN.  FIXME.  */
 321   if ((unsigned long) exponent == fmt->exp_nan)
 322     {
 323       int nan;
 324
 325       mant_off = fmt->man_start;
 326       mant_bits_left = fmt->man_len;
 327       nan = 0;
 328       while (mant_bits_left > 0)
 329         {
 330           mant_bits = min (mant_bits_left, 32);
 331
 332           if (get_field (ufrom, fmt->byteorder, fmt->totalsize,
 333                          mant_off, mant_bits) != 0)
 334             {
 335               /* This is a NaN.  */
 336               nan = 1;
 337               break;
 338             }
 339
 340           mant_off += mant_bits;
 341           mant_bits_left -= mant_bits;
 342         }
 343
 344       /* On certain systems (such as GNU/Linux), the use of the
 345          INFINITY macro below may generate a warning that can not be
 346          silenced due to a bug in GCC (PR preprocessor/11931).  The
 347          preprocessor fails to recognise the __extension__ keyword in
 348          conjunction with the GNU/C99 extension for hexadecimal
 349          floating point constants and will issue a warning when
 350          compiling with -pedantic.  */
 351       if (nan)
 352         dto = NAN;
 353       else
 354         dto = INFINITY;
 355
 356       if (get_field (ufrom, fmt->byteorder, fmt->totalsize, fmt->sign_start, 1))
 357         dto = -dto;
 358
 359       *to = dto;
 360
 361       return;
 362     }
 363
 364   mant_bits_left = fmt->man_len;
 365   mant_off = fmt->man_start;
 366   dto = 0.0;
 367
 368   special_exponent = exponent == 0 || (unsigned long) exponent == fmt->exp_nan;
 369
 370   /* Don't bias zero's, denorms or NaNs.  */
 371   if (!special_exponent)
 372     exponent -= fmt->exp_bias;
 373
 374   /* Build the result algebraically.  Might go infinite, underflow, etc;
 375      who cares. */
 376
 377   /* If this format uses a hidden bit, explicitly add it in now.  Otherwise,
 378      increment the exponent by one to account for the integer bit.  */
 379
 380   if (!special_exponent)
 381     {
 382       if (fmt->intbit == floatformat_intbit_no)
 383         dto = ldexp (1.0, exponent);
 384       else
 385         exponent++;
 386     }
 387
 388   while (mant_bits_left > 0)
 389     {
 390       mant_bits = min (mant_bits_left, 32);
 391
 392       mant = get_field (ufrom, fmt->byteorder, fmt->totalsize,
 393                          mant_off, mant_bits);
 394
 395       /* Handle denormalized numbers.  FIXME: What should we do for
 396          non-IEEE formats?  */
 397       if (special_exponent && exponent == 0 && mant != 0)
 398         dto += ldexp ((double)mant,
 399                       (- fmt->exp_bias
 400                        - mant_bits
 401                        - (mant_off - fmt->man_start)
 402                        + 1));
 403       else
 404         dto += ldexp ((double)mant, exponent - mant_bits);
 405       if (exponent != 0)
 406         exponent -= mant_bits;
 407       mant_off += mant_bits;
 408       mant_bits_left -= mant_bits;
 409     }
 410
 411   /* Negate it if negative.  */
 412   if (get_field (ufrom, fmt->byteorder, fmt->totalsize, fmt->sign_start, 1))
 413     dto = -dto;
 414   *to = dto;
 415 }
 416 \f
 417 static void put_field (unsigned char *, enum floatformat_byteorders,
 418                        unsigned int,
 419                        unsigned int,
 420                        unsigned int,
 421                        unsigned long);
 422
 423 /* Set a field which starts at START and is LEN bits long.  DATA and
 424    TOTAL_LEN are the thing we are extracting it from, in byteorder ORDER.  */
 425 static void
 426 put_field (unsigned char *data, enum floatformat_byteorders order,
 427            unsigned int total_len, unsigned int start, unsigned int len,
 428            unsigned long stuff_to_put)
 429 {
 430   unsigned int cur_byte;
 431   int cur_bitshift;
 432
 433   /* Start at the least significant part of the field.  */
 434   cur_byte = (start + len) / FLOATFORMAT_CHAR_BIT;
 435   if (order == floatformat_little)
 436     cur_byte = (total_len / FLOATFORMAT_CHAR_BIT) - cur_byte - 1;
 437   cur_bitshift =
 438     ((start + len) % FLOATFORMAT_CHAR_BIT) - FLOATFORMAT_CHAR_BIT;
 439   *(data + cur_byte) &=
 440     ~(((1 << ((start + len) % FLOATFORMAT_CHAR_BIT)) - 1) << (-cur_bitshift));
 441   *(data + cur_byte) |=
 442     (stuff_to_put & ((1 << FLOATFORMAT_CHAR_BIT) - 1)) << (-cur_bitshift);
 443   cur_bitshift += FLOATFORMAT_CHAR_BIT;
 444   if (order == floatformat_little)
 445     ++cur_byte;
 446   else
 447     --cur_byte;
 448
 449   /* Move towards the most significant part of the field.  */
 450   while ((unsigned int) cur_bitshift < len)
 451     {
 452       if (len - cur_bitshift < FLOATFORMAT_CHAR_BIT)
 453         {
 454           /* This is the last byte.  */
 455           *(data + cur_byte) &=
 456             ~((1 << (len - cur_bitshift)) - 1);
 457           *(data + cur_byte) |= (stuff_to_put >> cur_bitshift);
 458         }
 459       else
 460         *(data + cur_byte) = ((stuff_to_put >> cur_bitshift)
 461                               & ((1 << FLOATFORMAT_CHAR_BIT) - 1));
 462       cur_bitshift += FLOATFORMAT_CHAR_BIT;
 463       if (order == floatformat_little)
 464         ++cur_byte;
 465       else
 466         --cur_byte;
 467     }
 468 }
 469
 470 /* The converse: convert the double *FROM to an extended float
 471    and store where TO points.  Neither FROM nor TO have any alignment
 472    restrictions.  */
 473
 474 void
 475 floatformat_from_double (const struct floatformat *fmt,
 476                          const double *from, void *to)
 477 {
 478   double dfrom;
 479   int exponent;
 480   double mant;
 481   unsigned int mant_bits, mant_off;
 482   int mant_bits_left;
 483   unsigned char *uto = (unsigned char *) to;
 484
 485   dfrom = *from;
 486   memset (uto, 0, fmt->totalsize / FLOATFORMAT_CHAR_BIT);
 487
 488   /* If negative, set the sign bit.  */
 489   if (dfrom < 0)
 490     {
 491       put_field (uto, fmt->byteorder, fmt->totalsize, fmt->sign_start, 1, 1);
 492       dfrom = -dfrom;
 493     }
 494
 495   if (dfrom == 0)
 496     {
 497       /* 0.0.  */
 498       return;
 499     }
 500
 501   if (dfrom != dfrom)
 502     {
 503       /* NaN.  */
 504       put_field (uto, fmt->byteorder, fmt->totalsize, fmt->exp_start,
 505                  fmt->exp_len, fmt->exp_nan);
 506       /* Be sure it's not infinity, but NaN value is irrelevant.  */
 507       put_field (uto, fmt->byteorder, fmt->totalsize, fmt->man_start,
 508                  32, 1);
 509       return;
 510     }
 511
 512   if (dfrom + dfrom == dfrom)
 513     {
 514       /* This can only happen for an infinite value (or zero, which we
 515          already handled above).  */
 516       put_field (uto, fmt->byteorder, fmt->totalsize, fmt->exp_start,
 517                  fmt->exp_len, fmt->exp_nan);
 518       return;
 519     }
 520
 521   mant = frexp (dfrom, &exponent);
 522   if (exponent + fmt->exp_bias - 1 > 0)
 523     put_field (uto, fmt->byteorder, fmt->totalsize, fmt->exp_start,
 524                fmt->exp_len, exponent + fmt->exp_bias - 1);
 525   else
 526     {
 527       /* Handle a denormalized number.  FIXME: What should we do for
 528          non-IEEE formats?  */
 529       put_field (uto, fmt->byteorder, fmt->totalsize, fmt->exp_start,
 530                  fmt->exp_len, 0);
 531       mant = ldexp (mant, exponent + fmt->exp_bias - 1);
 532     }
 533
 534   mant_bits_left = fmt->man_len;
 535   mant_off = fmt->man_start;
 536   while (mant_bits_left > 0)
 537     {
 538       unsigned long mant_long;
 539       mant_bits = mant_bits_left < 32 ? mant_bits_left : 32;
 540
 541       mant *= 4294967296.0;
 542       mant_long = (unsigned long)mant;
 543       mant -= mant_long;
 544
 545       /* If the integer bit is implicit, and we are not creating a
 546          denormalized number, then we need to discard it.  */
 547       if ((unsigned int) mant_bits_left == fmt->man_len
 548           && fmt->intbit == floatformat_intbit_no
 549           && exponent + fmt->exp_bias - 1 > 0)
 550         {
 551           mant_long &= 0x7fffffff;
 552           mant_bits -= 1;
 553         }
 554       else if (mant_bits < 32)
 555         {
 556           /* The bits we want are in the most significant MANT_BITS bits of
 557              mant_long.  Move them to the least significant.  */
 558           mant_long >>= 32 - mant_bits;
 559         }
 560
 561       put_field (uto, fmt->byteorder, fmt->totalsize,
 562                  mant_off, mant_bits, mant_long);
 563       mant_off += mant_bits;
 564       mant_bits_left -= mant_bits;
 565     }
 566 }
 567
 568 /* Return non-zero iff the data at FROM is a valid number in format FMT.  */
 569
 570 int
 571 floatformat_is_valid (const struct floatformat *fmt, const void *from)
 572 {
 573   return fmt->is_valid (fmt, from);
 574 }
 575
 576
 577 #ifdef IEEE_DEBUG
 578
 579 #include <stdio.h>
 580
 581 /* This is to be run on a host which uses IEEE floating point.  */
 582
 583 void
 584 ieee_test (double n)
 585 {
 586   double result;
 587
 588   floatformat_to_double (&floatformat_ieee_double_little, &n, &result);
 589   if ((n != result && (! isnan (n) || ! isnan (result)))
 590       || (n < 0 && result >= 0)
 591       || (n >= 0 && result < 0))
 592     printf ("Differ(to): %.20g -> %.20g\n", n, result);
 593
 594   floatformat_from_double (&floatformat_ieee_double_little, &n, &result);
 595   if ((n != result && (! isnan (n) || ! isnan (result)))
 596       || (n < 0 && result >= 0)
 597       || (n >= 0 && result < 0))
 598     printf ("Differ(from): %.20g -> %.20g\n", n, result);
 599
 600 #if 0
 601   {
 602     char exten[16];
 603
 604     floatformat_from_double (&floatformat_m68881_ext, &n, exten);
 605     floatformat_to_double (&floatformat_m68881_ext, exten, &result);
 606     if (n != result)
 607       printf ("Differ(to+from): %.20g -> %.20g\n", n, result);
 608   }
 609 #endif
 610
 611 #if IEEE_DEBUG > 1
 612   /* This is to be run on a host which uses 68881 format.  */
 613   {
 614     long double ex = *(long double *)exten;
 615     if (ex != n)
 616       printf ("Differ(from vs. extended): %.20g\n", n);
 617   }
 618 #endif
 619 }
 620
 621 int
 622 main (void)
 623 {
 624   ieee_test (0.0);
 625   ieee_test (0.5);
 626   ieee_test (256.0);
 627   ieee_test (0.12345);
 628   ieee_test (234235.78907234);
 629   ieee_test (-512.0);
 630   ieee_test (-0.004321);
 631   ieee_test (1.2E-70);
 632   ieee_test (1.2E-316);
 633   ieee_test (4.9406564584124654E-324);
 634   ieee_test (- 4.9406564584124654E-324);
 635   ieee_test (- 0.0);
 636   ieee_test (- INFINITY);
 637   ieee_test (- NAN);
 638   ieee_test (INFINITY);
 639   ieee_test (NAN);
 640   return 0;
 641 }
 642 #endif