floatformat.c revision 169696
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 5This file is part of GDB. 6 7This program is free software; you can redistribute it and/or modify 8it under the terms of the GNU General Public License as published by 9the Free Software Foundation; either version 2 of the License, or 10(at your option) any later version. 11 12This program is distributed in the hope that it will be useful, 13but WITHOUT ANY WARRANTY; without even the implied warranty of 14MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 15GNU General Public License for more details. 16 17You should have received a copy of the GNU General Public License 18along with this program; if not, write to the Free Software 19Foundation, 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 59static unsigned long get_field (const unsigned char *, 60 enum floatformat_byteorders, 61 unsigned int, 62 unsigned int, 63 unsigned int); 64static int floatformat_always_valid (const struct floatformat *fmt, 65 const void *from); 66 67static int 68floatformat_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. */ 80const 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}; 87const 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}; 94const 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}; 101const 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 112const 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 122const 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}; 129const 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}; 136const 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 144static int floatformat_i387_ext_is_valid (const struct floatformat *fmt, 145 const void *from); 146 147static int 148floatformat_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 168const 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}; 175const 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}; 183const 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}; 191const 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}; 198const 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}; 207const 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}; 215const 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}; 223const 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}; 230const 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}; 237const 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}; 244const 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}; 251 252/* 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. */ 254static unsigned long 255get_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 303void 304floatformat_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 417static 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. */ 425static void 426put_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 474void 475floatformat_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 570int 571floatformat_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 583void 584ieee_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 621int 622main (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 643