1/* atof_ieee.c - turn a Flonum into an IEEE floating point number 2 Copyright 1987, 1992, 1994, 1996, 1997, 1998, 1999, 2000, 2001, 2005 3 Free Software Foundation, Inc. 4 5 This file is part of GAS, the GNU Assembler. 6 7 GAS 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, or (at your option) 10 any later version. 11 12 GAS 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 GAS; see the file COPYING. If not, write to the Free 19 Software Foundation, 51 Franklin Street - Fifth Floor, Boston, MA 20 02110-1301, USA. */ 21 22#include "as.h" 23 24/* Flonums returned here. */ 25extern FLONUM_TYPE generic_floating_point_number; 26 27extern const char EXP_CHARS[]; 28/* Precision in LittleNums. */ 29/* Don't count the gap in the m68k extended precision format. */ 30#define MAX_PRECISION 5 31#define F_PRECISION 2 32#define D_PRECISION 4 33#define X_PRECISION 5 34#define P_PRECISION 5 35 36/* Length in LittleNums of guard bits. */ 37#define GUARD 2 38 39#ifndef TC_LARGEST_EXPONENT_IS_NORMAL 40#define TC_LARGEST_EXPONENT_IS_NORMAL(PRECISION) 0 41#endif 42 43static const unsigned long mask[] = 44{ 45 0x00000000, 46 0x00000001, 47 0x00000003, 48 0x00000007, 49 0x0000000f, 50 0x0000001f, 51 0x0000003f, 52 0x0000007f, 53 0x000000ff, 54 0x000001ff, 55 0x000003ff, 56 0x000007ff, 57 0x00000fff, 58 0x00001fff, 59 0x00003fff, 60 0x00007fff, 61 0x0000ffff, 62 0x0001ffff, 63 0x0003ffff, 64 0x0007ffff, 65 0x000fffff, 66 0x001fffff, 67 0x003fffff, 68 0x007fffff, 69 0x00ffffff, 70 0x01ffffff, 71 0x03ffffff, 72 0x07ffffff, 73 0x0fffffff, 74 0x1fffffff, 75 0x3fffffff, 76 0x7fffffff, 77 0xffffffff, 78}; 79 80static int bits_left_in_littlenum; 81static int littlenums_left; 82static LITTLENUM_TYPE *littlenum_pointer; 83 84static int 85next_bits (int number_of_bits) 86{ 87 int return_value; 88 89 if (!littlenums_left) 90 return 0; 91 92 if (number_of_bits >= bits_left_in_littlenum) 93 { 94 return_value = mask[bits_left_in_littlenum] & *littlenum_pointer; 95 number_of_bits -= bits_left_in_littlenum; 96 return_value <<= number_of_bits; 97 98 if (--littlenums_left) 99 { 100 bits_left_in_littlenum = LITTLENUM_NUMBER_OF_BITS - number_of_bits; 101 --littlenum_pointer; 102 return_value |= 103 (*littlenum_pointer >> bits_left_in_littlenum) 104 & mask[number_of_bits]; 105 } 106 } 107 else 108 { 109 bits_left_in_littlenum -= number_of_bits; 110 return_value = 111 mask[number_of_bits] & (*littlenum_pointer >> bits_left_in_littlenum); 112 } 113 return return_value; 114} 115 116/* Num had better be less than LITTLENUM_NUMBER_OF_BITS. */ 117 118static void 119unget_bits (int num) 120{ 121 if (!littlenums_left) 122 { 123 ++littlenum_pointer; 124 ++littlenums_left; 125 bits_left_in_littlenum = num; 126 } 127 else if (bits_left_in_littlenum + num > LITTLENUM_NUMBER_OF_BITS) 128 { 129 bits_left_in_littlenum = 130 num - (LITTLENUM_NUMBER_OF_BITS - bits_left_in_littlenum); 131 ++littlenum_pointer; 132 ++littlenums_left; 133 } 134 else 135 bits_left_in_littlenum += num; 136} 137 138static void 139make_invalid_floating_point_number (LITTLENUM_TYPE *words) 140{ 141 as_bad (_("cannot create floating-point number")); 142 /* Zero the leftmost bit. */ 143 words[0] = (LITTLENUM_TYPE) ((unsigned) -1) >> 1; 144 words[1] = (LITTLENUM_TYPE) -1; 145 words[2] = (LITTLENUM_TYPE) -1; 146 words[3] = (LITTLENUM_TYPE) -1; 147 words[4] = (LITTLENUM_TYPE) -1; 148 words[5] = (LITTLENUM_TYPE) -1; 149} 150 151/* Warning: This returns 16-bit LITTLENUMs. It is up to the caller to 152 figure out any alignment problems and to conspire for the 153 bytes/word to be emitted in the right order. Bigendians beware! */ 154 155/* Note that atof-ieee always has X and P precisions enabled. it is up 156 to md_atof to filter them out if the target machine does not support 157 them. */ 158 159/* Returns pointer past text consumed. */ 160 161char * 162atof_ieee (char *str, /* Text to convert to binary. */ 163 int what_kind, /* 'd', 'f', 'g', 'h'. */ 164 LITTLENUM_TYPE *words) /* Build the binary here. */ 165{ 166 /* Extra bits for zeroed low-order bits. 167 The 1st MAX_PRECISION are zeroed, the last contain flonum bits. */ 168 static LITTLENUM_TYPE bits[MAX_PRECISION + MAX_PRECISION + GUARD]; 169 char *return_value; 170 /* Number of 16-bit words in the format. */ 171 int precision; 172 long exponent_bits; 173 FLONUM_TYPE save_gen_flonum; 174 175 /* We have to save the generic_floating_point_number because it 176 contains storage allocation about the array of LITTLENUMs where 177 the value is actually stored. We will allocate our own array of 178 littlenums below, but have to restore the global one on exit. */ 179 save_gen_flonum = generic_floating_point_number; 180 181 return_value = str; 182 generic_floating_point_number.low = bits + MAX_PRECISION; 183 generic_floating_point_number.high = NULL; 184 generic_floating_point_number.leader = NULL; 185 generic_floating_point_number.exponent = 0; 186 generic_floating_point_number.sign = '\0'; 187 188 /* Use more LittleNums than seems necessary: the highest flonum may 189 have 15 leading 0 bits, so could be useless. */ 190 191 memset (bits, '\0', sizeof (LITTLENUM_TYPE) * MAX_PRECISION); 192 193 switch (what_kind) 194 { 195 case 'f': 196 case 'F': 197 case 's': 198 case 'S': 199 precision = F_PRECISION; 200 exponent_bits = 8; 201 break; 202 203 case 'd': 204 case 'D': 205 case 'r': 206 case 'R': 207 precision = D_PRECISION; 208 exponent_bits = 11; 209 break; 210 211 case 'x': 212 case 'X': 213 case 'e': 214 case 'E': 215 precision = X_PRECISION; 216 exponent_bits = 15; 217 break; 218 219 case 'p': 220 case 'P': 221 222 precision = P_PRECISION; 223 exponent_bits = -1; 224 break; 225 226 default: 227 make_invalid_floating_point_number (words); 228 return (NULL); 229 } 230 231 generic_floating_point_number.high 232 = generic_floating_point_number.low + precision - 1 + GUARD; 233 234 if (atof_generic (&return_value, ".", EXP_CHARS, 235 &generic_floating_point_number)) 236 { 237 make_invalid_floating_point_number (words); 238 return NULL; 239 } 240 gen_to_words (words, precision, exponent_bits); 241 242 /* Restore the generic_floating_point_number's storage alloc (and 243 everything else). */ 244 generic_floating_point_number = save_gen_flonum; 245 246 return return_value; 247} 248 249/* Turn generic_floating_point_number into a real float/double/extended. */ 250 251int 252gen_to_words (LITTLENUM_TYPE *words, int precision, long exponent_bits) 253{ 254 int return_value = 0; 255 256 long exponent_1; 257 long exponent_2; 258 long exponent_3; 259 long exponent_4; 260 int exponent_skippage; 261 LITTLENUM_TYPE word1; 262 LITTLENUM_TYPE *lp; 263 LITTLENUM_TYPE *words_end; 264 265 words_end = words + precision; 266#ifdef TC_M68K 267 if (precision == X_PRECISION) 268 /* On the m68k the extended precision format has a gap of 16 bits 269 between the exponent and the mantissa. */ 270 words_end++; 271#endif 272 273 if (generic_floating_point_number.low > generic_floating_point_number.leader) 274 { 275 /* 0.0e0 seen. */ 276 if (generic_floating_point_number.sign == '+') 277 words[0] = 0x0000; 278 else 279 words[0] = 0x8000; 280 memset (&words[1], '\0', 281 (words_end - words - 1) * sizeof (LITTLENUM_TYPE)); 282 return return_value; 283 } 284 285 /* NaN: Do the right thing. */ 286 if (generic_floating_point_number.sign == 0) 287 { 288 if (TC_LARGEST_EXPONENT_IS_NORMAL (precision)) 289 as_warn ("NaNs are not supported by this target\n"); 290 if (precision == F_PRECISION) 291 { 292 words[0] = 0x7fff; 293 words[1] = 0xffff; 294 } 295 else if (precision == X_PRECISION) 296 { 297#ifdef TC_M68K 298 words[0] = 0x7fff; 299 words[1] = 0; 300 words[2] = 0xffff; 301 words[3] = 0xffff; 302 words[4] = 0xffff; 303 words[5] = 0xffff; 304#else /* ! TC_M68K */ 305#ifdef TC_I386 306 words[0] = 0xffff; 307 words[1] = 0xc000; 308 words[2] = 0; 309 words[3] = 0; 310 words[4] = 0; 311#else /* ! TC_I386 */ 312 abort (); 313#endif /* ! TC_I386 */ 314#endif /* ! TC_M68K */ 315 } 316 else 317 { 318 words[0] = 0x7fff; 319 words[1] = 0xffff; 320 words[2] = 0xffff; 321 words[3] = 0xffff; 322 } 323 return return_value; 324 } 325 else if (generic_floating_point_number.sign == 'P') 326 { 327 if (TC_LARGEST_EXPONENT_IS_NORMAL (precision)) 328 as_warn ("Infinities are not supported by this target\n"); 329 330 /* +INF: Do the right thing. */ 331 if (precision == F_PRECISION) 332 { 333 words[0] = 0x7f80; 334 words[1] = 0; 335 } 336 else if (precision == X_PRECISION) 337 { 338#ifdef TC_M68K 339 words[0] = 0x7fff; 340 words[1] = 0; 341 words[2] = 0; 342 words[3] = 0; 343 words[4] = 0; 344 words[5] = 0; 345#else /* ! TC_M68K */ 346#ifdef TC_I386 347 words[0] = 0x7fff; 348 words[1] = 0x8000; 349 words[2] = 0; 350 words[3] = 0; 351 words[4] = 0; 352#else /* ! TC_I386 */ 353 abort (); 354#endif /* ! TC_I386 */ 355#endif /* ! TC_M68K */ 356 } 357 else 358 { 359 words[0] = 0x7ff0; 360 words[1] = 0; 361 words[2] = 0; 362 words[3] = 0; 363 } 364 return return_value; 365 } 366 else if (generic_floating_point_number.sign == 'N') 367 { 368 if (TC_LARGEST_EXPONENT_IS_NORMAL (precision)) 369 as_warn ("Infinities are not supported by this target\n"); 370 371 /* Negative INF. */ 372 if (precision == F_PRECISION) 373 { 374 words[0] = 0xff80; 375 words[1] = 0x0; 376 } 377 else if (precision == X_PRECISION) 378 { 379#ifdef TC_M68K 380 words[0] = 0xffff; 381 words[1] = 0; 382 words[2] = 0; 383 words[3] = 0; 384 words[4] = 0; 385 words[5] = 0; 386#else /* ! TC_M68K */ 387#ifdef TC_I386 388 words[0] = 0xffff; 389 words[1] = 0x8000; 390 words[2] = 0; 391 words[3] = 0; 392 words[4] = 0; 393#else /* ! TC_I386 */ 394 abort (); 395#endif /* ! TC_I386 */ 396#endif /* ! TC_M68K */ 397 } 398 else 399 { 400 words[0] = 0xfff0; 401 words[1] = 0x0; 402 words[2] = 0x0; 403 words[3] = 0x0; 404 } 405 return return_value; 406 } 407 408 /* The floating point formats we support have: 409 Bit 15 is sign bit. 410 Bits 14:n are excess-whatever exponent. 411 Bits n-1:0 (if any) are most significant bits of fraction. 412 Bits 15:0 of the next word(s) are the next most significant bits. 413 414 So we need: number of bits of exponent, number of bits of 415 mantissa. */ 416 bits_left_in_littlenum = LITTLENUM_NUMBER_OF_BITS; 417 littlenum_pointer = generic_floating_point_number.leader; 418 littlenums_left = (1 419 + generic_floating_point_number.leader 420 - generic_floating_point_number.low); 421 422 /* Seek (and forget) 1st significant bit. */ 423 for (exponent_skippage = 0; !next_bits (1); ++exponent_skippage);; 424 exponent_1 = (generic_floating_point_number.exponent 425 + generic_floating_point_number.leader 426 + 1 427 - generic_floating_point_number.low); 428 429 /* Radix LITTLENUM_RADIX, point just higher than 430 generic_floating_point_number.leader. */ 431 exponent_2 = exponent_1 * LITTLENUM_NUMBER_OF_BITS; 432 433 /* Radix 2. */ 434 exponent_3 = exponent_2 - exponent_skippage; 435 436 /* Forget leading zeros, forget 1st bit. */ 437 exponent_4 = exponent_3 + ((1 << (exponent_bits - 1)) - 2); 438 439 /* Offset exponent. */ 440 lp = words; 441 442 /* Word 1. Sign, exponent and perhaps high bits. */ 443 word1 = ((generic_floating_point_number.sign == '+') 444 ? 0 445 : (1 << (LITTLENUM_NUMBER_OF_BITS - 1))); 446 447 /* Assume 2's complement integers. */ 448 if (exponent_4 <= 0) 449 { 450 int prec_bits; 451 int num_bits; 452 453 unget_bits (1); 454 num_bits = -exponent_4; 455 prec_bits = 456 LITTLENUM_NUMBER_OF_BITS * precision - (exponent_bits + 1 + num_bits); 457#ifdef TC_I386 458 if (precision == X_PRECISION && exponent_bits == 15) 459 { 460 /* On the i386 a denormalized extended precision float is 461 shifted down by one, effectively decreasing the exponent 462 bias by one. */ 463 prec_bits -= 1; 464 num_bits += 1; 465 } 466#endif 467 468 if (num_bits >= LITTLENUM_NUMBER_OF_BITS - exponent_bits) 469 { 470 /* Bigger than one littlenum. */ 471 num_bits -= (LITTLENUM_NUMBER_OF_BITS - 1) - exponent_bits; 472 *lp++ = word1; 473 if (num_bits + exponent_bits + 1 474 > precision * LITTLENUM_NUMBER_OF_BITS) 475 { 476 /* Exponent overflow. */ 477 make_invalid_floating_point_number (words); 478 return return_value; 479 } 480#ifdef TC_M68K 481 if (precision == X_PRECISION && exponent_bits == 15) 482 *lp++ = 0; 483#endif 484 while (num_bits >= LITTLENUM_NUMBER_OF_BITS) 485 { 486 num_bits -= LITTLENUM_NUMBER_OF_BITS; 487 *lp++ = 0; 488 } 489 if (num_bits) 490 *lp++ = next_bits (LITTLENUM_NUMBER_OF_BITS - (num_bits)); 491 } 492 else 493 { 494 if (precision == X_PRECISION && exponent_bits == 15) 495 { 496 *lp++ = word1; 497#ifdef TC_M68K 498 *lp++ = 0; 499#endif 500 *lp++ = next_bits (LITTLENUM_NUMBER_OF_BITS - num_bits); 501 } 502 else 503 { 504 word1 |= next_bits ((LITTLENUM_NUMBER_OF_BITS - 1) 505 - (exponent_bits + num_bits)); 506 *lp++ = word1; 507 } 508 } 509 while (lp < words_end) 510 *lp++ = next_bits (LITTLENUM_NUMBER_OF_BITS); 511 512 /* Round the mantissa up, but don't change the number. */ 513 if (next_bits (1)) 514 { 515 --lp; 516 if (prec_bits >= LITTLENUM_NUMBER_OF_BITS) 517 { 518 int n = 0; 519 int tmp_bits; 520 521 n = 0; 522 tmp_bits = prec_bits; 523 while (tmp_bits > LITTLENUM_NUMBER_OF_BITS) 524 { 525 if (lp[n] != (LITTLENUM_TYPE) - 1) 526 break; 527 --n; 528 tmp_bits -= LITTLENUM_NUMBER_OF_BITS; 529 } 530 if (tmp_bits > LITTLENUM_NUMBER_OF_BITS 531 || (lp[n] & mask[tmp_bits]) != mask[tmp_bits] 532 || (prec_bits != (precision * LITTLENUM_NUMBER_OF_BITS 533 - exponent_bits - 1) 534#ifdef TC_I386 535 /* An extended precision float with only the integer 536 bit set would be invalid. That must be converted 537 to the smallest normalized number. */ 538 && !(precision == X_PRECISION 539 && prec_bits == (precision * LITTLENUM_NUMBER_OF_BITS 540 - exponent_bits - 2)) 541#endif 542 )) 543 { 544 unsigned long carry; 545 546 for (carry = 1; carry && (lp >= words); lp--) 547 { 548 carry = *lp + carry; 549 *lp = carry; 550 carry >>= LITTLENUM_NUMBER_OF_BITS; 551 } 552 } 553 else 554 { 555 /* This is an overflow of the denormal numbers. We 556 need to forget what we have produced, and instead 557 generate the smallest normalized number. */ 558 lp = words; 559 word1 = ((generic_floating_point_number.sign == '+') 560 ? 0 561 : (1 << (LITTLENUM_NUMBER_OF_BITS - 1))); 562 word1 |= (1 563 << ((LITTLENUM_NUMBER_OF_BITS - 1) 564 - exponent_bits)); 565 *lp++ = word1; 566#ifdef TC_I386 567 /* Set the integer bit in the extended precision format. 568 This cannot happen on the m68k where the mantissa 569 just overflows into the integer bit above. */ 570 if (precision == X_PRECISION) 571 *lp++ = 1 << (LITTLENUM_NUMBER_OF_BITS - 1); 572#endif 573 while (lp < words_end) 574 *lp++ = 0; 575 } 576 } 577 else 578 *lp += 1; 579 } 580 581 return return_value; 582 } 583 else if ((unsigned long) exponent_4 > mask[exponent_bits] 584 || (! TC_LARGEST_EXPONENT_IS_NORMAL (precision) 585 && (unsigned long) exponent_4 == mask[exponent_bits])) 586 { 587 /* Exponent overflow. Lose immediately. */ 588 589 /* We leave return_value alone: admit we read the 590 number, but return a floating exception 591 because we can't encode the number. */ 592 make_invalid_floating_point_number (words); 593 return return_value; 594 } 595 else 596 { 597 word1 |= (exponent_4 << ((LITTLENUM_NUMBER_OF_BITS - 1) - exponent_bits)) 598 | next_bits ((LITTLENUM_NUMBER_OF_BITS - 1) - exponent_bits); 599 } 600 601 *lp++ = word1; 602 603 /* X_PRECISION is special: on the 68k, it has 16 bits of zero in the 604 middle. Either way, it is then followed by a 1 bit. */ 605 if (exponent_bits == 15 && precision == X_PRECISION) 606 { 607#ifdef TC_M68K 608 *lp++ = 0; 609#endif 610 *lp++ = (1 << (LITTLENUM_NUMBER_OF_BITS - 1) 611 | next_bits (LITTLENUM_NUMBER_OF_BITS - 1)); 612 } 613 614 /* The rest of the words are just mantissa bits. */ 615 while (lp < words_end) 616 *lp++ = next_bits (LITTLENUM_NUMBER_OF_BITS); 617 618 if (next_bits (1)) 619 { 620 unsigned long carry; 621 /* Since the NEXT bit is a 1, round UP the mantissa. 622 The cunning design of these hidden-1 floats permits 623 us to let the mantissa overflow into the exponent, and 624 it 'does the right thing'. However, we lose if the 625 highest-order bit of the lowest-order word flips. 626 Is that clear? */ 627 628 /* #if (sizeof(carry)) < ((sizeof(bits[0]) * BITS_PER_CHAR) + 2) 629 Please allow at least 1 more bit in carry than is in a LITTLENUM. 630 We need that extra bit to hold a carry during a LITTLENUM carry 631 propagation. Another extra bit (kept 0) will assure us that we 632 don't get a sticky sign bit after shifting right, and that 633 permits us to propagate the carry without any masking of bits. 634 #endif */ 635 for (carry = 1, lp--; carry; lp--) 636 { 637 carry = *lp + carry; 638 *lp = carry; 639 carry >>= LITTLENUM_NUMBER_OF_BITS; 640 if (lp == words) 641 break; 642 } 643 if (precision == X_PRECISION && exponent_bits == 15) 644 { 645 /* Extended precision numbers have an explicit integer bit 646 that we may have to restore. */ 647 if (lp == words) 648 { 649#ifdef TC_M68K 650 /* On the m68k there is a gap of 16 bits. We must 651 explicitly propagate the carry into the exponent. */ 652 words[0] += words[1]; 653 words[1] = 0; 654 lp++; 655#endif 656 /* Put back the integer bit. */ 657 lp[1] |= 1 << (LITTLENUM_NUMBER_OF_BITS - 1); 658 } 659 } 660 if ((word1 ^ *words) & (1 << (LITTLENUM_NUMBER_OF_BITS - 1))) 661 { 662 /* We leave return_value alone: admit we read the number, 663 but return a floating exception because we can't encode 664 the number. */ 665 *words &= ~(1 << (LITTLENUM_NUMBER_OF_BITS - 1)); 666 } 667 } 668 return return_value; 669} 670 671#ifdef TEST 672char * 673print_gen (gen) 674 FLONUM_TYPE *gen; 675{ 676 FLONUM_TYPE f; 677 LITTLENUM_TYPE arr[10]; 678 double dv; 679 float fv; 680 static char sbuf[40]; 681 682 if (gen) 683 { 684 f = generic_floating_point_number; 685 generic_floating_point_number = *gen; 686 } 687 gen_to_words (&arr[0], 4, 11); 688 memcpy (&dv, &arr[0], sizeof (double)); 689 sprintf (sbuf, "%x %x %x %x %.14G ", arr[0], arr[1], arr[2], arr[3], dv); 690 gen_to_words (&arr[0], 2, 8); 691 memcpy (&fv, &arr[0], sizeof (float)); 692 sprintf (sbuf + strlen (sbuf), "%x %x %.12g\n", arr[0], arr[1], fv); 693 694 if (gen) 695 generic_floating_point_number = f; 696 697 return (sbuf); 698} 699 700#endif 701