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}; 251 252 253#ifndef min 254#define min(a, b) ((a) < (b) ? (a) : (b)) 255#endif 256 257/* Extract a field which starts at START and is LEN bits long. DATA and 258 TOTAL_LEN are the thing we are extracting it from, in byteorder ORDER. */ 259static unsigned long 260get_field (const unsigned char *data, enum floatformat_byteorders order, 261 unsigned int total_len, unsigned int start, unsigned int len) 262{ 263 unsigned long result = 0; 264 unsigned int cur_byte; 265 int lo_bit, hi_bit, cur_bitshift = 0; 266 int nextbyte = (order == floatformat_little) ? 1 : -1; 267 268 /* Start is in big-endian bit order! Fix that first. */ 269 start = total_len - (start + len); 270 271 /* Start at the least significant part of the field. */ 272 if (order == floatformat_little) 273 cur_byte = start / FLOATFORMAT_CHAR_BIT; 274 else 275 cur_byte = (total_len - start - 1) / FLOATFORMAT_CHAR_BIT; 276 277 lo_bit = start % FLOATFORMAT_CHAR_BIT; 278 hi_bit = min (lo_bit + len, FLOATFORMAT_CHAR_BIT); 279 280 do 281 { 282 unsigned int shifted = *(data + cur_byte) >> lo_bit; 283 unsigned int bits = hi_bit - lo_bit; 284 unsigned int mask = (1 << bits) - 1; 285 result |= (shifted & mask) << cur_bitshift; 286 len -= bits; 287 cur_bitshift += bits; 288 cur_byte += nextbyte; 289 lo_bit = 0; 290 hi_bit = min (len, FLOATFORMAT_CHAR_BIT); 291 } 292 while (len != 0); 293 294 return result; 295} 296 297/* Convert from FMT to a double. 298 FROM is the address of the extended float. 299 Store the double in *TO. */ 300 301void 302floatformat_to_double (const struct floatformat *fmt, 303 const void *from, double *to) 304{ 305 const unsigned char *ufrom = (const unsigned char *) from; 306 double dto; 307 long exponent; 308 unsigned long mant; 309 unsigned int mant_bits, mant_off; 310 int mant_bits_left; 311 int special_exponent; /* It's a NaN, denorm or zero */ 312 313 exponent = get_field (ufrom, fmt->byteorder, fmt->totalsize, 314 fmt->exp_start, fmt->exp_len); 315 316 /* If the exponent indicates a NaN, we don't have information to 317 decide what to do. So we handle it like IEEE, except that we 318 don't try to preserve the type of NaN. FIXME. */ 319 if ((unsigned long) exponent == fmt->exp_nan) 320 { 321 int nan; 322 323 mant_off = fmt->man_start; 324 mant_bits_left = fmt->man_len; 325 nan = 0; 326 while (mant_bits_left > 0) 327 { 328 mant_bits = min (mant_bits_left, 32); 329 330 if (get_field (ufrom, fmt->byteorder, fmt->totalsize, 331 mant_off, mant_bits) != 0) 332 { 333 /* This is a NaN. */ 334 nan = 1; 335 break; 336 } 337 338 mant_off += mant_bits; 339 mant_bits_left -= mant_bits; 340 } 341 342 /* On certain systems (such as GNU/Linux), the use of the 343 INFINITY macro below may generate a warning that can not be 344 silenced due to a bug in GCC (PR preprocessor/11931). The 345 preprocessor fails to recognise the __extension__ keyword in 346 conjunction with the GNU/C99 extension for hexadecimal 347 floating point constants and will issue a warning when 348 compiling with -pedantic. */ 349 if (nan) 350 dto = NAN; 351 else 352 dto = INFINITY; 353 354 if (get_field (ufrom, fmt->byteorder, fmt->totalsize, fmt->sign_start, 1)) 355 dto = -dto; 356 357 *to = dto; 358 359 return; 360 } 361 362 mant_bits_left = fmt->man_len; 363 mant_off = fmt->man_start; 364 dto = 0.0; 365 366 special_exponent = exponent == 0 || (unsigned long) exponent == fmt->exp_nan; 367 368 /* Don't bias zero's, denorms or NaNs. */ 369 if (!special_exponent) 370 exponent -= fmt->exp_bias; 371 372 /* Build the result algebraically. Might go infinite, underflow, etc; 373 who cares. */ 374 375 /* If this format uses a hidden bit, explicitly add it in now. Otherwise, 376 increment the exponent by one to account for the integer bit. */ 377 378 if (!special_exponent) 379 { 380 if (fmt->intbit == floatformat_intbit_no) 381 dto = ldexp (1.0, exponent); 382 else 383 exponent++; 384 } 385 386 while (mant_bits_left > 0) 387 { 388 mant_bits = min (mant_bits_left, 32); 389 390 mant = get_field (ufrom, fmt->byteorder, fmt->totalsize, 391 mant_off, mant_bits); 392 393 /* Handle denormalized numbers. FIXME: What should we do for 394 non-IEEE formats? */ 395 if (special_exponent && exponent == 0 && mant != 0) 396 dto += ldexp ((double)mant, 397 (- fmt->exp_bias 398 - mant_bits 399 - (mant_off - fmt->man_start) 400 + 1)); 401 else 402 dto += ldexp ((double)mant, exponent - mant_bits); 403 if (exponent != 0) 404 exponent -= mant_bits; 405 mant_off += mant_bits; 406 mant_bits_left -= mant_bits; 407 } 408 409 /* Negate it if negative. */ 410 if (get_field (ufrom, fmt->byteorder, fmt->totalsize, fmt->sign_start, 1)) 411 dto = -dto; 412 *to = dto; 413} 414 415static void put_field (unsigned char *, enum floatformat_byteorders, 416 unsigned int, 417 unsigned int, 418 unsigned int, 419 unsigned long); 420 421/* Set a field which starts at START and is LEN bits long. DATA and 422 TOTAL_LEN are the thing we are extracting it from, in byteorder ORDER. */ 423static void 424put_field (unsigned char *data, enum floatformat_byteorders order, 425 unsigned int total_len, unsigned int start, unsigned int len, 426 unsigned long stuff_to_put) 427{ 428 unsigned int cur_byte; 429 int lo_bit, hi_bit; 430 int nextbyte = (order == floatformat_little) ? 1 : -1; 431 432 /* Start is in big-endian bit order! Fix that first. */ 433 start = total_len - (start + len); 434 435 /* Start at the least significant part of the field. */ 436 if (order == floatformat_little) 437 cur_byte = start / FLOATFORMAT_CHAR_BIT; 438 else 439 cur_byte = (total_len - start - 1) / FLOATFORMAT_CHAR_BIT; 440 441 lo_bit = start % FLOATFORMAT_CHAR_BIT; 442 hi_bit = min (lo_bit + len, FLOATFORMAT_CHAR_BIT); 443 444 do 445 { 446 unsigned char *byte_ptr = data + cur_byte; 447 unsigned int bits = hi_bit - lo_bit; 448 unsigned int mask = ((1 << bits) - 1) << lo_bit; 449 *byte_ptr = (*byte_ptr & ~mask) | ((stuff_to_put << lo_bit) & mask); 450 stuff_to_put >>= bits; 451 len -= bits; 452 cur_byte += nextbyte; 453 lo_bit = 0; 454 hi_bit = min (len, FLOATFORMAT_CHAR_BIT); 455 } 456 while (len != 0); 457} 458 459/* The converse: convert the double *FROM to an extended float 460 and store where TO points. Neither FROM nor TO have any alignment 461 restrictions. */ 462 463void 464floatformat_from_double (const struct floatformat *fmt, 465 const double *from, void *to) 466{ 467 double dfrom; 468 int exponent; 469 double mant; 470 unsigned int mant_bits, mant_off; 471 int mant_bits_left; 472 unsigned char *uto = (unsigned char *) to; 473 474 dfrom = *from; 475 memset (uto, 0, fmt->totalsize / FLOATFORMAT_CHAR_BIT); 476 477 /* If negative, set the sign bit. */ 478 if (dfrom < 0) 479 { 480 put_field (uto, fmt->byteorder, fmt->totalsize, fmt->sign_start, 1, 1); 481 dfrom = -dfrom; 482 } 483 484 if (dfrom == 0) 485 { 486 /* 0.0. */ 487 return; 488 } 489 490 if (dfrom != dfrom) 491 { 492 /* NaN. */ 493 put_field (uto, fmt->byteorder, fmt->totalsize, fmt->exp_start, 494 fmt->exp_len, fmt->exp_nan); 495 /* Be sure it's not infinity, but NaN value is irrelevant. */ 496 put_field (uto, fmt->byteorder, fmt->totalsize, fmt->man_start, 497 32, 1); 498 return; 499 } 500 501 if (dfrom + dfrom == dfrom) 502 { 503 /* This can only happen for an infinite value (or zero, which we 504 already handled above). */ 505 put_field (uto, fmt->byteorder, fmt->totalsize, fmt->exp_start, 506 fmt->exp_len, fmt->exp_nan); 507 return; 508 } 509 510 mant = frexp (dfrom, &exponent); 511 if (exponent + fmt->exp_bias - 1 > 0) 512 put_field (uto, fmt->byteorder, fmt->totalsize, fmt->exp_start, 513 fmt->exp_len, exponent + fmt->exp_bias - 1); 514 else 515 { 516 /* Handle a denormalized number. FIXME: What should we do for 517 non-IEEE formats? */ 518 put_field (uto, fmt->byteorder, fmt->totalsize, fmt->exp_start, 519 fmt->exp_len, 0); 520 mant = ldexp (mant, exponent + fmt->exp_bias - 1); 521 } 522 523 mant_bits_left = fmt->man_len; 524 mant_off = fmt->man_start; 525 while (mant_bits_left > 0) 526 { 527 unsigned long mant_long; 528 mant_bits = mant_bits_left < 32 ? mant_bits_left : 32; 529 530 mant *= 4294967296.0; 531 mant_long = (unsigned long)mant; 532 mant -= mant_long; 533 534 /* If the integer bit is implicit, and we are not creating a 535 denormalized number, then we need to discard it. */ 536 if ((unsigned int) mant_bits_left == fmt->man_len 537 && fmt->intbit == floatformat_intbit_no 538 && exponent + fmt->exp_bias - 1 > 0) 539 { 540 mant_long &= 0x7fffffff; 541 mant_bits -= 1; 542 } 543 else if (mant_bits < 32) 544 { 545 /* The bits we want are in the most significant MANT_BITS bits of 546 mant_long. Move them to the least significant. */ 547 mant_long >>= 32 - mant_bits; 548 } 549 550 put_field (uto, fmt->byteorder, fmt->totalsize, 551 mant_off, mant_bits, mant_long); 552 mant_off += mant_bits; 553 mant_bits_left -= mant_bits; 554 } 555} 556 557/* Return non-zero iff the data at FROM is a valid number in format FMT. */ 558 559int 560floatformat_is_valid (const struct floatformat *fmt, const void *from) 561{ 562 return fmt->is_valid (fmt, from); 563} 564 565 566#ifdef IEEE_DEBUG 567 568#include <stdio.h> 569 570/* This is to be run on a host which uses IEEE floating point. */ 571 572void 573ieee_test (double n) 574{ 575 double result; 576 577 floatformat_to_double (&floatformat_ieee_double_little, &n, &result); 578 if ((n != result && (! isnan (n) || ! isnan (result))) 579 || (n < 0 && result >= 0) 580 || (n >= 0 && result < 0)) 581 printf ("Differ(to): %.20g -> %.20g\n", n, result); 582 583 floatformat_from_double (&floatformat_ieee_double_little, &n, &result); 584 if ((n != result && (! isnan (n) || ! isnan (result))) 585 || (n < 0 && result >= 0) 586 || (n >= 0 && result < 0)) 587 printf ("Differ(from): %.20g -> %.20g\n", n, result); 588 589#if 0 590 { 591 char exten[16]; 592 593 floatformat_from_double (&floatformat_m68881_ext, &n, exten); 594 floatformat_to_double (&floatformat_m68881_ext, exten, &result); 595 if (n != result) 596 printf ("Differ(to+from): %.20g -> %.20g\n", n, result); 597 } 598#endif 599 600#if IEEE_DEBUG > 1 601 /* This is to be run on a host which uses 68881 format. */ 602 { 603 long double ex = *(long double *)exten; 604 if (ex != n) 605 printf ("Differ(from vs. extended): %.20g\n", n); 606 } 607#endif 608} 609 610int 611main (void) 612{ 613 ieee_test (0.0); 614 ieee_test (0.5); 615 ieee_test (256.0); 616 ieee_test (0.12345); 617 ieee_test (234235.78907234); 618 ieee_test (-512.0); 619 ieee_test (-0.004321); 620 ieee_test (1.2E-70); 621 ieee_test (1.2E-316); 622 ieee_test (4.9406564584124654E-324); 623 ieee_test (- 4.9406564584124654E-324); 624 ieee_test (- 0.0); 625 ieee_test (- INFINITY); 626 ieee_test (- NAN); 627 ieee_test (INFINITY); 628 ieee_test (NAN); 629 return 0; 630} 631#endif 632