1 /* real.c - software floating point emulation. 2 Copyright (C) 1993-2013 Free Software Foundation, Inc. 3 Contributed by Stephen L. Moshier (moshier@world.std.com). 4 Re-written by Richard Henderson <rth@redhat.com> 5 6 This file is part of GCC. 7 8 GCC is free software; you can redistribute it and/or modify it under 9 the terms of the GNU General Public License as published by the Free 10 Software Foundation; either version 3, or (at your option) any later 11 version. 12 13 GCC is distributed in the hope that it will be useful, but WITHOUT ANY 14 WARRANTY; without even the implied warranty of MERCHANTABILITY or 15 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License 16 for more details. 17 18 You should have received a copy of the GNU General Public License 19 along with GCC; see the file COPYING3. If not see 20 <http://www.gnu.org/licenses/>. */ 21 22 #include "config.h" 23 #include "system.h" 24 #include "coretypes.h" 25 #include "tm.h" 26 #include "tree.h" 27 #include "diagnostic-core.h" 28 #include "real.h" 29 #include "realmpfr.h" 30 #include "tm_p.h" 31 #include "dfp.h" 32 33 /* The floating point model used internally is not exactly IEEE 754 34 compliant, and close to the description in the ISO C99 standard, 35 section 5.2.4.2.2 Characteristics of floating types. 36 37 Specifically 38 39 x = s * b^e * \sum_{k=1}^p f_k * b^{-k} 40 41 where 42 s = sign (+- 1) 43 b = base or radix, here always 2 44 e = exponent 45 p = precision (the number of base-b digits in the significand) 46 f_k = the digits of the significand. 47 48 We differ from typical IEEE 754 encodings in that the entire 49 significand is fractional. Normalized significands are in the 50 range [0.5, 1.0). 51 52 A requirement of the model is that P be larger than the largest 53 supported target floating-point type by at least 2 bits. This gives 54 us proper rounding when we truncate to the target type. In addition, 55 E must be large enough to hold the smallest supported denormal number 56 in a normalized form. 57 58 Both of these requirements are easily satisfied. The largest target 59 significand is 113 bits; we store at least 160. The smallest 60 denormal number fits in 17 exponent bits; we store 26. 61 62 Note that the decimal string conversion routines are sensitive to 63 rounding errors. Since the raw arithmetic routines do not themselves 64 have guard digits or rounding, the computation of 10**exp can 65 accumulate more than a few digits of error. The previous incarnation 66 of real.c successfully used a 144-bit fraction; given the current 67 layout of REAL_VALUE_TYPE we're forced to expand to at least 160 bits. */ 68 69 70 /* Used to classify two numbers simultaneously. */ 71 #define CLASS2(A, B) ((A) << 2 | (B)) 72 73 #if HOST_BITS_PER_LONG != 64 && HOST_BITS_PER_LONG != 32 74 #error "Some constant folding done by hand to avoid shift count warnings" 75 #endif 76 77 static void get_zero (REAL_VALUE_TYPE *, int); 78 static void get_canonical_qnan (REAL_VALUE_TYPE *, int); 79 static void get_canonical_snan (REAL_VALUE_TYPE *, int); 80 static void get_inf (REAL_VALUE_TYPE *, int); 81 static bool sticky_rshift_significand (REAL_VALUE_TYPE *, 82 const REAL_VALUE_TYPE *, unsigned int); 83 static void rshift_significand (REAL_VALUE_TYPE *, const REAL_VALUE_TYPE *, 84 unsigned int); 85 static void lshift_significand (REAL_VALUE_TYPE *, const REAL_VALUE_TYPE *, 86 unsigned int); 87 static void lshift_significand_1 (REAL_VALUE_TYPE *, const REAL_VALUE_TYPE *); 88 static bool add_significands (REAL_VALUE_TYPE *r, const REAL_VALUE_TYPE *, 89 const REAL_VALUE_TYPE *); 90 static bool sub_significands (REAL_VALUE_TYPE *, const REAL_VALUE_TYPE *, 91 const REAL_VALUE_TYPE *, int); 92 static void neg_significand (REAL_VALUE_TYPE *, const REAL_VALUE_TYPE *); 93 static int cmp_significands (const REAL_VALUE_TYPE *, const REAL_VALUE_TYPE *); 94 static int cmp_significand_0 (const REAL_VALUE_TYPE *); 95 static void set_significand_bit (REAL_VALUE_TYPE *, unsigned int); 96 static void clear_significand_bit (REAL_VALUE_TYPE *, unsigned int); 97 static bool test_significand_bit (REAL_VALUE_TYPE *, unsigned int); 98 static void clear_significand_below (REAL_VALUE_TYPE *, unsigned int); 99 static bool div_significands (REAL_VALUE_TYPE *, const REAL_VALUE_TYPE *, 100 const REAL_VALUE_TYPE *); 101 static void normalize (REAL_VALUE_TYPE *); 102 103 static bool do_add (REAL_VALUE_TYPE *, const REAL_VALUE_TYPE *, 104 const REAL_VALUE_TYPE *, int); 105 static bool do_multiply (REAL_VALUE_TYPE *, const REAL_VALUE_TYPE *, 106 const REAL_VALUE_TYPE *); 107 static bool do_divide (REAL_VALUE_TYPE *, const REAL_VALUE_TYPE *, 108 const REAL_VALUE_TYPE *); 109 static int do_compare (const REAL_VALUE_TYPE *, const REAL_VALUE_TYPE *, int); 110 static void do_fix_trunc (REAL_VALUE_TYPE *, const REAL_VALUE_TYPE *); 111 112 static unsigned long rtd_divmod (REAL_VALUE_TYPE *, REAL_VALUE_TYPE *); 113 static void decimal_from_integer (REAL_VALUE_TYPE *); 114 static void decimal_integer_string (char *, const REAL_VALUE_TYPE *, 115 size_t); 116 117 static const REAL_VALUE_TYPE * ten_to_ptwo (int); 118 static const REAL_VALUE_TYPE * ten_to_mptwo (int); 119 static const REAL_VALUE_TYPE * real_digit (int); 120 static void times_pten (REAL_VALUE_TYPE *, int); 121 122 static void round_for_format (const struct real_format *, REAL_VALUE_TYPE *); 123 124 /* Initialize R with a positive zero. */ 125 126 static inline void 127 get_zero (REAL_VALUE_TYPE *r, int sign) 128 { 129 memset (r, 0, sizeof (*r)); 130 r->sign = sign; 131 } 132 133 /* Initialize R with the canonical quiet NaN. */ 134 135 static inline void 136 get_canonical_qnan (REAL_VALUE_TYPE *r, int sign) 137 { 138 memset (r, 0, sizeof (*r)); 139 r->cl = rvc_nan; 140 r->sign = sign; 141 r->canonical = 1; 142 } 143 144 static inline void 145 get_canonical_snan (REAL_VALUE_TYPE *r, int sign) 146 { 147 memset (r, 0, sizeof (*r)); 148 r->cl = rvc_nan; 149 r->sign = sign; 150 r->signalling = 1; 151 r->canonical = 1; 152 } 153 154 static inline void 155 get_inf (REAL_VALUE_TYPE *r, int sign) 156 { 157 memset (r, 0, sizeof (*r)); 158 r->cl = rvc_inf; 159 r->sign = sign; 160 } 161 162 163 /* Right-shift the significand of A by N bits; put the result in the 164 significand of R. If any one bits are shifted out, return true. */ 165 166 static bool 167 sticky_rshift_significand (REAL_VALUE_TYPE *r, const REAL_VALUE_TYPE *a, 168 unsigned int n) 169 { 170 unsigned long sticky = 0; 171 unsigned int i, ofs = 0; 172 173 if (n >= HOST_BITS_PER_LONG) 174 { 175 for (i = 0, ofs = n / HOST_BITS_PER_LONG; i < ofs; ++i) 176 sticky |= a->sig[i]; 177 n &= HOST_BITS_PER_LONG - 1; 178 } 179 180 if (n != 0) 181 { 182 sticky |= a->sig[ofs] & (((unsigned long)1 << n) - 1); 183 for (i = 0; i < SIGSZ; ++i) 184 { 185 r->sig[i] 186 = (((ofs + i >= SIGSZ ? 0 : a->sig[ofs + i]) >> n) 187 | ((ofs + i + 1 >= SIGSZ ? 0 : a->sig[ofs + i + 1]) 188 << (HOST_BITS_PER_LONG - n))); 189 } 190 } 191 else 192 { 193 for (i = 0; ofs + i < SIGSZ; ++i) 194 r->sig[i] = a->sig[ofs + i]; 195 for (; i < SIGSZ; ++i) 196 r->sig[i] = 0; 197 } 198 199 return sticky != 0; 200 } 201 202 /* Right-shift the significand of A by N bits; put the result in the 203 significand of R. */ 204 205 static void 206 rshift_significand (REAL_VALUE_TYPE *r, const REAL_VALUE_TYPE *a, 207 unsigned int n) 208 { 209 unsigned int i, ofs = n / HOST_BITS_PER_LONG; 210 211 n &= HOST_BITS_PER_LONG - 1; 212 if (n != 0) 213 { 214 for (i = 0; i < SIGSZ; ++i) 215 { 216 r->sig[i] 217 = (((ofs + i >= SIGSZ ? 0 : a->sig[ofs + i]) >> n) 218 | ((ofs + i + 1 >= SIGSZ ? 0 : a->sig[ofs + i + 1]) 219 << (HOST_BITS_PER_LONG - n))); 220 } 221 } 222 else 223 { 224 for (i = 0; ofs + i < SIGSZ; ++i) 225 r->sig[i] = a->sig[ofs + i]; 226 for (; i < SIGSZ; ++i) 227 r->sig[i] = 0; 228 } 229 } 230 231 /* Left-shift the significand of A by N bits; put the result in the 232 significand of R. */ 233 234 static void 235 lshift_significand (REAL_VALUE_TYPE *r, const REAL_VALUE_TYPE *a, 236 unsigned int n) 237 { 238 unsigned int i, ofs = n / HOST_BITS_PER_LONG; 239 240 n &= HOST_BITS_PER_LONG - 1; 241 if (n == 0) 242 { 243 for (i = 0; ofs + i < SIGSZ; ++i) 244 r->sig[SIGSZ-1-i] = a->sig[SIGSZ-1-i-ofs]; 245 for (; i < SIGSZ; ++i) 246 r->sig[SIGSZ-1-i] = 0; 247 } 248 else 249 for (i = 0; i < SIGSZ; ++i) 250 { 251 r->sig[SIGSZ-1-i] 252 = (((ofs + i >= SIGSZ ? 0 : a->sig[SIGSZ-1-i-ofs]) << n) 253 | ((ofs + i + 1 >= SIGSZ ? 0 : a->sig[SIGSZ-1-i-ofs-1]) 254 >> (HOST_BITS_PER_LONG - n))); 255 } 256 } 257 258 /* Likewise, but N is specialized to 1. */ 259 260 static inline void 261 lshift_significand_1 (REAL_VALUE_TYPE *r, const REAL_VALUE_TYPE *a) 262 { 263 unsigned int i; 264 265 for (i = SIGSZ - 1; i > 0; --i) 266 r->sig[i] = (a->sig[i] << 1) | (a->sig[i-1] >> (HOST_BITS_PER_LONG - 1)); 267 r->sig[0] = a->sig[0] << 1; 268 } 269 270 /* Add the significands of A and B, placing the result in R. Return 271 true if there was carry out of the most significant word. */ 272 273 static inline bool 274 add_significands (REAL_VALUE_TYPE *r, const REAL_VALUE_TYPE *a, 275 const REAL_VALUE_TYPE *b) 276 { 277 bool carry = false; 278 int i; 279 280 for (i = 0; i < SIGSZ; ++i) 281 { 282 unsigned long ai = a->sig[i]; 283 unsigned long ri = ai + b->sig[i]; 284 285 if (carry) 286 { 287 carry = ri < ai; 288 carry |= ++ri == 0; 289 } 290 else 291 carry = ri < ai; 292 293 r->sig[i] = ri; 294 } 295 296 return carry; 297 } 298 299 /* Subtract the significands of A and B, placing the result in R. CARRY is 300 true if there's a borrow incoming to the least significant word. 301 Return true if there was borrow out of the most significant word. */ 302 303 static inline bool 304 sub_significands (REAL_VALUE_TYPE *r, const REAL_VALUE_TYPE *a, 305 const REAL_VALUE_TYPE *b, int carry) 306 { 307 int i; 308 309 for (i = 0; i < SIGSZ; ++i) 310 { 311 unsigned long ai = a->sig[i]; 312 unsigned long ri = ai - b->sig[i]; 313 314 if (carry) 315 { 316 carry = ri > ai; 317 carry |= ~--ri == 0; 318 } 319 else 320 carry = ri > ai; 321 322 r->sig[i] = ri; 323 } 324 325 return carry; 326 } 327 328 /* Negate the significand A, placing the result in R. */ 329 330 static inline void 331 neg_significand (REAL_VALUE_TYPE *r, const REAL_VALUE_TYPE *a) 332 { 333 bool carry = true; 334 int i; 335 336 for (i = 0; i < SIGSZ; ++i) 337 { 338 unsigned long ri, ai = a->sig[i]; 339 340 if (carry) 341 { 342 if (ai) 343 { 344 ri = -ai; 345 carry = false; 346 } 347 else 348 ri = ai; 349 } 350 else 351 ri = ~ai; 352 353 r->sig[i] = ri; 354 } 355 } 356 357 /* Compare significands. Return tri-state vs zero. */ 358 359 static inline int 360 cmp_significands (const REAL_VALUE_TYPE *a, const REAL_VALUE_TYPE *b) 361 { 362 int i; 363 364 for (i = SIGSZ - 1; i >= 0; --i) 365 { 366 unsigned long ai = a->sig[i]; 367 unsigned long bi = b->sig[i]; 368 369 if (ai > bi) 370 return 1; 371 if (ai < bi) 372 return -1; 373 } 374 375 return 0; 376 } 377 378 /* Return true if A is nonzero. */ 379 380 static inline int 381 cmp_significand_0 (const REAL_VALUE_TYPE *a) 382 { 383 int i; 384 385 for (i = SIGSZ - 1; i >= 0; --i) 386 if (a->sig[i]) 387 return 1; 388 389 return 0; 390 } 391 392 /* Set bit N of the significand of R. */ 393 394 static inline void 395 set_significand_bit (REAL_VALUE_TYPE *r, unsigned int n) 396 { 397 r->sig[n / HOST_BITS_PER_LONG] 398 |= (unsigned long)1 << (n % HOST_BITS_PER_LONG); 399 } 400 401 /* Clear bit N of the significand of R. */ 402 403 static inline void 404 clear_significand_bit (REAL_VALUE_TYPE *r, unsigned int n) 405 { 406 r->sig[n / HOST_BITS_PER_LONG] 407 &= ~((unsigned long)1 << (n % HOST_BITS_PER_LONG)); 408 } 409 410 /* Test bit N of the significand of R. */ 411 412 static inline bool 413 test_significand_bit (REAL_VALUE_TYPE *r, unsigned int n) 414 { 415 /* ??? Compiler bug here if we return this expression directly. 416 The conversion to bool strips the "&1" and we wind up testing 417 e.g. 2 != 0 -> true. Seen in gcc version 3.2 20020520. */ 418 int t = (r->sig[n / HOST_BITS_PER_LONG] >> (n % HOST_BITS_PER_LONG)) & 1; 419 return t; 420 } 421 422 /* Clear bits 0..N-1 of the significand of R. */ 423 424 static void 425 clear_significand_below (REAL_VALUE_TYPE *r, unsigned int n) 426 { 427 int i, w = n / HOST_BITS_PER_LONG; 428 429 for (i = 0; i < w; ++i) 430 r->sig[i] = 0; 431 432 r->sig[w] &= ~(((unsigned long)1 << (n % HOST_BITS_PER_LONG)) - 1); 433 } 434 435 /* Divide the significands of A and B, placing the result in R. Return 436 true if the division was inexact. */ 437 438 static inline bool 439 div_significands (REAL_VALUE_TYPE *r, const REAL_VALUE_TYPE *a, 440 const REAL_VALUE_TYPE *b) 441 { 442 REAL_VALUE_TYPE u; 443 int i, bit = SIGNIFICAND_BITS - 1; 444 unsigned long msb, inexact; 445 446 u = *a; 447 memset (r->sig, 0, sizeof (r->sig)); 448 449 msb = 0; 450 goto start; 451 do 452 { 453 msb = u.sig[SIGSZ-1] & SIG_MSB; 454 lshift_significand_1 (&u, &u); 455 start: 456 if (msb || cmp_significands (&u, b) >= 0) 457 { 458 sub_significands (&u, &u, b, 0); 459 set_significand_bit (r, bit); 460 } 461 } 462 while (--bit >= 0); 463 464 for (i = 0, inexact = 0; i < SIGSZ; i++) 465 inexact |= u.sig[i]; 466 467 return inexact != 0; 468 } 469 470 /* Adjust the exponent and significand of R such that the most 471 significant bit is set. We underflow to zero and overflow to 472 infinity here, without denormals. (The intermediate representation 473 exponent is large enough to handle target denormals normalized.) */ 474 475 static void 476 normalize (REAL_VALUE_TYPE *r) 477 { 478 int shift = 0, exp; 479 int i, j; 480 481 if (r->decimal) 482 return; 483 484 /* Find the first word that is nonzero. */ 485 for (i = SIGSZ - 1; i >= 0; i--) 486 if (r->sig[i] == 0) 487 shift += HOST_BITS_PER_LONG; 488 else 489 break; 490 491 /* Zero significand flushes to zero. */ 492 if (i < 0) 493 { 494 r->cl = rvc_zero; 495 SET_REAL_EXP (r, 0); 496 return; 497 } 498 499 /* Find the first bit that is nonzero. */ 500 for (j = 0; ; j++) 501 if (r->sig[i] & ((unsigned long)1 << (HOST_BITS_PER_LONG - 1 - j))) 502 break; 503 shift += j; 504 505 if (shift > 0) 506 { 507 exp = REAL_EXP (r) - shift; 508 if (exp > MAX_EXP) 509 get_inf (r, r->sign); 510 else if (exp < -MAX_EXP) 511 get_zero (r, r->sign); 512 else 513 { 514 SET_REAL_EXP (r, exp); 515 lshift_significand (r, r, shift); 516 } 517 } 518 } 519 520 /* Calculate R = A + (SUBTRACT_P ? -B : B). Return true if the 521 result may be inexact due to a loss of precision. */ 522 523 static bool 524 do_add (REAL_VALUE_TYPE *r, const REAL_VALUE_TYPE *a, 525 const REAL_VALUE_TYPE *b, int subtract_p) 526 { 527 int dexp, sign, exp; 528 REAL_VALUE_TYPE t; 529 bool inexact = false; 530 531 /* Determine if we need to add or subtract. */ 532 sign = a->sign; 533 subtract_p = (sign ^ b->sign) ^ subtract_p; 534 535 switch (CLASS2 (a->cl, b->cl)) 536 { 537 case CLASS2 (rvc_zero, rvc_zero): 538 /* -0 + -0 = -0, -0 - +0 = -0; all other cases yield +0. */ 539 get_zero (r, sign & !subtract_p); 540 return false; 541 542 case CLASS2 (rvc_zero, rvc_normal): 543 case CLASS2 (rvc_zero, rvc_inf): 544 case CLASS2 (rvc_zero, rvc_nan): 545 /* 0 + ANY = ANY. */ 546 case CLASS2 (rvc_normal, rvc_nan): 547 case CLASS2 (rvc_inf, rvc_nan): 548 case CLASS2 (rvc_nan, rvc_nan): 549 /* ANY + NaN = NaN. */ 550 case CLASS2 (rvc_normal, rvc_inf): 551 /* R + Inf = Inf. */ 552 *r = *b; 553 r->sign = sign ^ subtract_p; 554 return false; 555 556 case CLASS2 (rvc_normal, rvc_zero): 557 case CLASS2 (rvc_inf, rvc_zero): 558 case CLASS2 (rvc_nan, rvc_zero): 559 /* ANY + 0 = ANY. */ 560 case CLASS2 (rvc_nan, rvc_normal): 561 case CLASS2 (rvc_nan, rvc_inf): 562 /* NaN + ANY = NaN. */ 563 case CLASS2 (rvc_inf, rvc_normal): 564 /* Inf + R = Inf. */ 565 *r = *a; 566 return false; 567 568 case CLASS2 (rvc_inf, rvc_inf): 569 if (subtract_p) 570 /* Inf - Inf = NaN. */ 571 get_canonical_qnan (r, 0); 572 else 573 /* Inf + Inf = Inf. */ 574 *r = *a; 575 return false; 576 577 case CLASS2 (rvc_normal, rvc_normal): 578 break; 579 580 default: 581 gcc_unreachable (); 582 } 583 584 /* Swap the arguments such that A has the larger exponent. */ 585 dexp = REAL_EXP (a) - REAL_EXP (b); 586 if (dexp < 0) 587 { 588 const REAL_VALUE_TYPE *t; 589 t = a, a = b, b = t; 590 dexp = -dexp; 591 sign ^= subtract_p; 592 } 593 exp = REAL_EXP (a); 594 595 /* If the exponents are not identical, we need to shift the 596 significand of B down. */ 597 if (dexp > 0) 598 { 599 /* If the exponents are too far apart, the significands 600 do not overlap, which makes the subtraction a noop. */ 601 if (dexp >= SIGNIFICAND_BITS) 602 { 603 *r = *a; 604 r->sign = sign; 605 return true; 606 } 607 608 inexact |= sticky_rshift_significand (&t, b, dexp); 609 b = &t; 610 } 611 612 if (subtract_p) 613 { 614 if (sub_significands (r, a, b, inexact)) 615 { 616 /* We got a borrow out of the subtraction. That means that 617 A and B had the same exponent, and B had the larger 618 significand. We need to swap the sign and negate the 619 significand. */ 620 sign ^= 1; 621 neg_significand (r, r); 622 } 623 } 624 else 625 { 626 if (add_significands (r, a, b)) 627 { 628 /* We got carry out of the addition. This means we need to 629 shift the significand back down one bit and increase the 630 exponent. */ 631 inexact |= sticky_rshift_significand (r, r, 1); 632 r->sig[SIGSZ-1] |= SIG_MSB; 633 if (++exp > MAX_EXP) 634 { 635 get_inf (r, sign); 636 return true; 637 } 638 } 639 } 640 641 r->cl = rvc_normal; 642 r->sign = sign; 643 SET_REAL_EXP (r, exp); 644 /* Zero out the remaining fields. */ 645 r->signalling = 0; 646 r->canonical = 0; 647 r->decimal = 0; 648 649 /* Re-normalize the result. */ 650 normalize (r); 651 652 /* Special case: if the subtraction results in zero, the result 653 is positive. */ 654 if (r->cl == rvc_zero) 655 r->sign = 0; 656 else 657 r->sig[0] |= inexact; 658 659 return inexact; 660 } 661 662 /* Calculate R = A * B. Return true if the result may be inexact. */ 663 664 static bool 665 do_multiply (REAL_VALUE_TYPE *r, const REAL_VALUE_TYPE *a, 666 const REAL_VALUE_TYPE *b) 667 { 668 REAL_VALUE_TYPE u, t, *rr; 669 unsigned int i, j, k; 670 int sign = a->sign ^ b->sign; 671 bool inexact = false; 672 673 switch (CLASS2 (a->cl, b->cl)) 674 { 675 case CLASS2 (rvc_zero, rvc_zero): 676 case CLASS2 (rvc_zero, rvc_normal): 677 case CLASS2 (rvc_normal, rvc_zero): 678 /* +-0 * ANY = 0 with appropriate sign. */ 679 get_zero (r, sign); 680 return false; 681 682 case CLASS2 (rvc_zero, rvc_nan): 683 case CLASS2 (rvc_normal, rvc_nan): 684 case CLASS2 (rvc_inf, rvc_nan): 685 case CLASS2 (rvc_nan, rvc_nan): 686 /* ANY * NaN = NaN. */ 687 *r = *b; 688 r->sign = sign; 689 return false; 690 691 case CLASS2 (rvc_nan, rvc_zero): 692 case CLASS2 (rvc_nan, rvc_normal): 693 case CLASS2 (rvc_nan, rvc_inf): 694 /* NaN * ANY = NaN. */ 695 *r = *a; 696 r->sign = sign; 697 return false; 698 699 case CLASS2 (rvc_zero, rvc_inf): 700 case CLASS2 (rvc_inf, rvc_zero): 701 /* 0 * Inf = NaN */ 702 get_canonical_qnan (r, sign); 703 return false; 704 705 case CLASS2 (rvc_inf, rvc_inf): 706 case CLASS2 (rvc_normal, rvc_inf): 707 case CLASS2 (rvc_inf, rvc_normal): 708 /* Inf * Inf = Inf, R * Inf = Inf */ 709 get_inf (r, sign); 710 return false; 711 712 case CLASS2 (rvc_normal, rvc_normal): 713 break; 714 715 default: 716 gcc_unreachable (); 717 } 718 719 if (r == a || r == b) 720 rr = &t; 721 else 722 rr = r; 723 get_zero (rr, 0); 724 725 /* Collect all the partial products. Since we don't have sure access 726 to a widening multiply, we split each long into two half-words. 727 728 Consider the long-hand form of a four half-word multiplication: 729 730 A B C D 731 * E F G H 732 -------------- 733 DE DF DG DH 734 CE CF CG CH 735 BE BF BG BH 736 AE AF AG AH 737 738 We construct partial products of the widened half-word products 739 that are known to not overlap, e.g. DF+DH. Each such partial 740 product is given its proper exponent, which allows us to sum them 741 and obtain the finished product. */ 742 743 for (i = 0; i < SIGSZ * 2; ++i) 744 { 745 unsigned long ai = a->sig[i / 2]; 746 if (i & 1) 747 ai >>= HOST_BITS_PER_LONG / 2; 748 else 749 ai &= ((unsigned long)1 << (HOST_BITS_PER_LONG / 2)) - 1; 750 751 if (ai == 0) 752 continue; 753 754 for (j = 0; j < 2; ++j) 755 { 756 int exp = (REAL_EXP (a) - (2*SIGSZ-1-i)*(HOST_BITS_PER_LONG/2) 757 + (REAL_EXP (b) - (1-j)*(HOST_BITS_PER_LONG/2))); 758 759 if (exp > MAX_EXP) 760 { 761 get_inf (r, sign); 762 return true; 763 } 764 if (exp < -MAX_EXP) 765 { 766 /* Would underflow to zero, which we shouldn't bother adding. */ 767 inexact = true; 768 continue; 769 } 770 771 memset (&u, 0, sizeof (u)); 772 u.cl = rvc_normal; 773 SET_REAL_EXP (&u, exp); 774 775 for (k = j; k < SIGSZ * 2; k += 2) 776 { 777 unsigned long bi = b->sig[k / 2]; 778 if (k & 1) 779 bi >>= HOST_BITS_PER_LONG / 2; 780 else 781 bi &= ((unsigned long)1 << (HOST_BITS_PER_LONG / 2)) - 1; 782 783 u.sig[k / 2] = ai * bi; 784 } 785 786 normalize (&u); 787 inexact |= do_add (rr, rr, &u, 0); 788 } 789 } 790 791 rr->sign = sign; 792 if (rr != r) 793 *r = t; 794 795 return inexact; 796 } 797 798 /* Calculate R = A / B. Return true if the result may be inexact. */ 799 800 static bool 801 do_divide (REAL_VALUE_TYPE *r, const REAL_VALUE_TYPE *a, 802 const REAL_VALUE_TYPE *b) 803 { 804 int exp, sign = a->sign ^ b->sign; 805 REAL_VALUE_TYPE t, *rr; 806 bool inexact; 807 808 switch (CLASS2 (a->cl, b->cl)) 809 { 810 case CLASS2 (rvc_zero, rvc_zero): 811 /* 0 / 0 = NaN. */ 812 case CLASS2 (rvc_inf, rvc_inf): 813 /* Inf / Inf = NaN. */ 814 get_canonical_qnan (r, sign); 815 return false; 816 817 case CLASS2 (rvc_zero, rvc_normal): 818 case CLASS2 (rvc_zero, rvc_inf): 819 /* 0 / ANY = 0. */ 820 case CLASS2 (rvc_normal, rvc_inf): 821 /* R / Inf = 0. */ 822 get_zero (r, sign); 823 return false; 824 825 case CLASS2 (rvc_normal, rvc_zero): 826 /* R / 0 = Inf. */ 827 case CLASS2 (rvc_inf, rvc_zero): 828 /* Inf / 0 = Inf. */ 829 get_inf (r, sign); 830 return false; 831 832 case CLASS2 (rvc_zero, rvc_nan): 833 case CLASS2 (rvc_normal, rvc_nan): 834 case CLASS2 (rvc_inf, rvc_nan): 835 case CLASS2 (rvc_nan, rvc_nan): 836 /* ANY / NaN = NaN. */ 837 *r = *b; 838 r->sign = sign; 839 return false; 840 841 case CLASS2 (rvc_nan, rvc_zero): 842 case CLASS2 (rvc_nan, rvc_normal): 843 case CLASS2 (rvc_nan, rvc_inf): 844 /* NaN / ANY = NaN. */ 845 *r = *a; 846 r->sign = sign; 847 return false; 848 849 case CLASS2 (rvc_inf, rvc_normal): 850 /* Inf / R = Inf. */ 851 get_inf (r, sign); 852 return false; 853 854 case CLASS2 (rvc_normal, rvc_normal): 855 break; 856 857 default: 858 gcc_unreachable (); 859 } 860 861 if (r == a || r == b) 862 rr = &t; 863 else 864 rr = r; 865 866 /* Make sure all fields in the result are initialized. */ 867 get_zero (rr, 0); 868 rr->cl = rvc_normal; 869 rr->sign = sign; 870 871 exp = REAL_EXP (a) - REAL_EXP (b) + 1; 872 if (exp > MAX_EXP) 873 { 874 get_inf (r, sign); 875 return true; 876 } 877 if (exp < -MAX_EXP) 878 { 879 get_zero (r, sign); 880 return true; 881 } 882 SET_REAL_EXP (rr, exp); 883 884 inexact = div_significands (rr, a, b); 885 886 /* Re-normalize the result. */ 887 normalize (rr); 888 rr->sig[0] |= inexact; 889 890 if (rr != r) 891 *r = t; 892 893 return inexact; 894 } 895 896 /* Return a tri-state comparison of A vs B. Return NAN_RESULT if 897 one of the two operands is a NaN. */ 898 899 static int 900 do_compare (const REAL_VALUE_TYPE *a, const REAL_VALUE_TYPE *b, 901 int nan_result) 902 { 903 int ret; 904 905 switch (CLASS2 (a->cl, b->cl)) 906 { 907 case CLASS2 (rvc_zero, rvc_zero): 908 /* Sign of zero doesn't matter for compares. */ 909 return 0; 910 911 case CLASS2 (rvc_normal, rvc_zero): 912 /* Decimal float zero is special and uses rvc_normal, not rvc_zero. */ 913 if (a->decimal) 914 return decimal_do_compare (a, b, nan_result); 915 /* Fall through. */ 916 case CLASS2 (rvc_inf, rvc_zero): 917 case CLASS2 (rvc_inf, rvc_normal): 918 return (a->sign ? -1 : 1); 919 920 case CLASS2 (rvc_inf, rvc_inf): 921 return -a->sign - -b->sign; 922 923 case CLASS2 (rvc_zero, rvc_normal): 924 /* Decimal float zero is special and uses rvc_normal, not rvc_zero. */ 925 if (b->decimal) 926 return decimal_do_compare (a, b, nan_result); 927 /* Fall through. */ 928 case CLASS2 (rvc_zero, rvc_inf): 929 case CLASS2 (rvc_normal, rvc_inf): 930 return (b->sign ? 1 : -1); 931 932 case CLASS2 (rvc_zero, rvc_nan): 933 case CLASS2 (rvc_normal, rvc_nan): 934 case CLASS2 (rvc_inf, rvc_nan): 935 case CLASS2 (rvc_nan, rvc_nan): 936 case CLASS2 (rvc_nan, rvc_zero): 937 case CLASS2 (rvc_nan, rvc_normal): 938 case CLASS2 (rvc_nan, rvc_inf): 939 return nan_result; 940 941 case CLASS2 (rvc_normal, rvc_normal): 942 break; 943 944 default: 945 gcc_unreachable (); 946 } 947 948 if (a->sign != b->sign) 949 return -a->sign - -b->sign; 950 951 if (a->decimal || b->decimal) 952 return decimal_do_compare (a, b, nan_result); 953 954 if (REAL_EXP (a) > REAL_EXP (b)) 955 ret = 1; 956 else if (REAL_EXP (a) < REAL_EXP (b)) 957 ret = -1; 958 else 959 ret = cmp_significands (a, b); 960 961 return (a->sign ? -ret : ret); 962 } 963 964 /* Return A truncated to an integral value toward zero. */ 965 966 static void 967 do_fix_trunc (REAL_VALUE_TYPE *r, const REAL_VALUE_TYPE *a) 968 { 969 *r = *a; 970 971 switch (r->cl) 972 { 973 case rvc_zero: 974 case rvc_inf: 975 case rvc_nan: 976 break; 977 978 case rvc_normal: 979 if (r->decimal) 980 { 981 decimal_do_fix_trunc (r, a); 982 return; 983 } 984 if (REAL_EXP (r) <= 0) 985 get_zero (r, r->sign); 986 else if (REAL_EXP (r) < SIGNIFICAND_BITS) 987 clear_significand_below (r, SIGNIFICAND_BITS - REAL_EXP (r)); 988 break; 989 990 default: 991 gcc_unreachable (); 992 } 993 } 994 995 /* Perform the binary or unary operation described by CODE. 996 For a unary operation, leave OP1 NULL. This function returns 997 true if the result may be inexact due to loss of precision. */ 998 999 bool 1000 real_arithmetic (REAL_VALUE_TYPE *r, int icode, const REAL_VALUE_TYPE *op0, 1001 const REAL_VALUE_TYPE *op1) 1002 { 1003 enum tree_code code = (enum tree_code) icode; 1004 1005 if (op0->decimal || (op1 && op1->decimal)) 1006 return decimal_real_arithmetic (r, code, op0, op1); 1007 1008 switch (code) 1009 { 1010 case PLUS_EXPR: 1011 /* Clear any padding areas in *r if it isn't equal to one of the 1012 operands so that we can later do bitwise comparisons later on. */ 1013 if (r != op0 && r != op1) 1014 memset (r, '\0', sizeof (*r)); 1015 return do_add (r, op0, op1, 0); 1016 1017 case MINUS_EXPR: 1018 if (r != op0 && r != op1) 1019 memset (r, '\0', sizeof (*r)); 1020 return do_add (r, op0, op1, 1); 1021 1022 case MULT_EXPR: 1023 if (r != op0 && r != op1) 1024 memset (r, '\0', sizeof (*r)); 1025 return do_multiply (r, op0, op1); 1026 1027 case RDIV_EXPR: 1028 if (r != op0 && r != op1) 1029 memset (r, '\0', sizeof (*r)); 1030 return do_divide (r, op0, op1); 1031 1032 case MIN_EXPR: 1033 if (op1->cl == rvc_nan) 1034 *r = *op1; 1035 else if (do_compare (op0, op1, -1) < 0) 1036 *r = *op0; 1037 else 1038 *r = *op1; 1039 break; 1040 1041 case MAX_EXPR: 1042 if (op1->cl == rvc_nan) 1043 *r = *op1; 1044 else if (do_compare (op0, op1, 1) < 0) 1045 *r = *op1; 1046 else 1047 *r = *op0; 1048 break; 1049 1050 case NEGATE_EXPR: 1051 *r = *op0; 1052 r->sign ^= 1; 1053 break; 1054 1055 case ABS_EXPR: 1056 *r = *op0; 1057 r->sign = 0; 1058 break; 1059 1060 case FIX_TRUNC_EXPR: 1061 do_fix_trunc (r, op0); 1062 break; 1063 1064 default: 1065 gcc_unreachable (); 1066 } 1067 return false; 1068 } 1069 1070 REAL_VALUE_TYPE 1071 real_value_negate (const REAL_VALUE_TYPE *op0) 1072 { 1073 REAL_VALUE_TYPE r; 1074 real_arithmetic (&r, NEGATE_EXPR, op0, NULL); 1075 return r; 1076 } 1077 1078 REAL_VALUE_TYPE 1079 real_value_abs (const REAL_VALUE_TYPE *op0) 1080 { 1081 REAL_VALUE_TYPE r; 1082 real_arithmetic (&r, ABS_EXPR, op0, NULL); 1083 return r; 1084 } 1085 1086 bool 1087 real_compare (int icode, const REAL_VALUE_TYPE *op0, 1088 const REAL_VALUE_TYPE *op1) 1089 { 1090 enum tree_code code = (enum tree_code) icode; 1091 1092 switch (code) 1093 { 1094 case LT_EXPR: 1095 return do_compare (op0, op1, 1) < 0; 1096 case LE_EXPR: 1097 return do_compare (op0, op1, 1) <= 0; 1098 case GT_EXPR: 1099 return do_compare (op0, op1, -1) > 0; 1100 case GE_EXPR: 1101 return do_compare (op0, op1, -1) >= 0; 1102 case EQ_EXPR: 1103 return do_compare (op0, op1, -1) == 0; 1104 case NE_EXPR: 1105 return do_compare (op0, op1, -1) != 0; 1106 case UNORDERED_EXPR: 1107 return op0->cl == rvc_nan || op1->cl == rvc_nan; 1108 case ORDERED_EXPR: 1109 return op0->cl != rvc_nan && op1->cl != rvc_nan; 1110 case UNLT_EXPR: 1111 return do_compare (op0, op1, -1) < 0; 1112 case UNLE_EXPR: 1113 return do_compare (op0, op1, -1) <= 0; 1114 case UNGT_EXPR: 1115 return do_compare (op0, op1, 1) > 0; 1116 case UNGE_EXPR: 1117 return do_compare (op0, op1, 1) >= 0; 1118 case UNEQ_EXPR: 1119 return do_compare (op0, op1, 0) == 0; 1120 case LTGT_EXPR: 1121 return do_compare (op0, op1, 0) != 0; 1122 1123 default: 1124 gcc_unreachable (); 1125 } 1126 } 1127 1128 /* Return floor log2(R). */ 1129 1130 int 1131 real_exponent (const REAL_VALUE_TYPE *r) 1132 { 1133 switch (r->cl) 1134 { 1135 case rvc_zero: 1136 return 0; 1137 case rvc_inf: 1138 case rvc_nan: 1139 return (unsigned int)-1 >> 1; 1140 case rvc_normal: 1141 return REAL_EXP (r); 1142 default: 1143 gcc_unreachable (); 1144 } 1145 } 1146 1147 /* R = OP0 * 2**EXP. */ 1148 1149 void 1150 real_ldexp (REAL_VALUE_TYPE *r, const REAL_VALUE_TYPE *op0, int exp) 1151 { 1152 *r = *op0; 1153 switch (r->cl) 1154 { 1155 case rvc_zero: 1156 case rvc_inf: 1157 case rvc_nan: 1158 break; 1159 1160 case rvc_normal: 1161 exp += REAL_EXP (op0); 1162 if (exp > MAX_EXP) 1163 get_inf (r, r->sign); 1164 else if (exp < -MAX_EXP) 1165 get_zero (r, r->sign); 1166 else 1167 SET_REAL_EXP (r, exp); 1168 break; 1169 1170 default: 1171 gcc_unreachable (); 1172 } 1173 } 1174 1175 /* Determine whether a floating-point value X is infinite. */ 1176 1177 bool 1178 real_isinf (const REAL_VALUE_TYPE *r) 1179 { 1180 return (r->cl == rvc_inf); 1181 } 1182 1183 /* Determine whether a floating-point value X is a NaN. */ 1184 1185 bool 1186 real_isnan (const REAL_VALUE_TYPE *r) 1187 { 1188 return (r->cl == rvc_nan); 1189 } 1190 1191 /* Determine whether a floating-point value X is finite. */ 1192 1193 bool 1194 real_isfinite (const REAL_VALUE_TYPE *r) 1195 { 1196 return (r->cl != rvc_nan) && (r->cl != rvc_inf); 1197 } 1198 1199 /* Determine whether a floating-point value X is negative. */ 1200 1201 bool 1202 real_isneg (const REAL_VALUE_TYPE *r) 1203 { 1204 return r->sign; 1205 } 1206 1207 /* Determine whether a floating-point value X is minus zero. */ 1208 1209 bool 1210 real_isnegzero (const REAL_VALUE_TYPE *r) 1211 { 1212 return r->sign && r->cl == rvc_zero; 1213 } 1214 1215 /* Compare two floating-point objects for bitwise identity. */ 1216 1217 bool 1218 real_identical (const REAL_VALUE_TYPE *a, const REAL_VALUE_TYPE *b) 1219 { 1220 int i; 1221 1222 if (a->cl != b->cl) 1223 return false; 1224 if (a->sign != b->sign) 1225 return false; 1226 1227 switch (a->cl) 1228 { 1229 case rvc_zero: 1230 case rvc_inf: 1231 return true; 1232 1233 case rvc_normal: 1234 if (a->decimal != b->decimal) 1235 return false; 1236 if (REAL_EXP (a) != REAL_EXP (b)) 1237 return false; 1238 break; 1239 1240 case rvc_nan: 1241 if (a->signalling != b->signalling) 1242 return false; 1243 /* The significand is ignored for canonical NaNs. */ 1244 if (a->canonical || b->canonical) 1245 return a->canonical == b->canonical; 1246 break; 1247 1248 default: 1249 gcc_unreachable (); 1250 } 1251 1252 for (i = 0; i < SIGSZ; ++i) 1253 if (a->sig[i] != b->sig[i]) 1254 return false; 1255 1256 return true; 1257 } 1258 1259 /* Try to change R into its exact multiplicative inverse in machine 1260 mode MODE. Return true if successful. */ 1261 1262 bool 1263 exact_real_inverse (enum machine_mode mode, REAL_VALUE_TYPE *r) 1264 { 1265 const REAL_VALUE_TYPE *one = real_digit (1); 1266 REAL_VALUE_TYPE u; 1267 int i; 1268 1269 if (r->cl != rvc_normal) 1270 return false; 1271 1272 /* Check for a power of two: all significand bits zero except the MSB. */ 1273 for (i = 0; i < SIGSZ-1; ++i) 1274 if (r->sig[i] != 0) 1275 return false; 1276 if (r->sig[SIGSZ-1] != SIG_MSB) 1277 return false; 1278 1279 /* Find the inverse and truncate to the required mode. */ 1280 do_divide (&u, one, r); 1281 real_convert (&u, mode, &u); 1282 1283 /* The rounding may have overflowed. */ 1284 if (u.cl != rvc_normal) 1285 return false; 1286 for (i = 0; i < SIGSZ-1; ++i) 1287 if (u.sig[i] != 0) 1288 return false; 1289 if (u.sig[SIGSZ-1] != SIG_MSB) 1290 return false; 1291 1292 *r = u; 1293 return true; 1294 } 1295 1296 /* Return true if arithmetic on values in IMODE that were promoted 1297 from values in TMODE is equivalent to direct arithmetic on values 1298 in TMODE. */ 1299 1300 bool 1301 real_can_shorten_arithmetic (enum machine_mode imode, enum machine_mode tmode) 1302 { 1303 const struct real_format *tfmt, *ifmt; 1304 tfmt = REAL_MODE_FORMAT (tmode); 1305 ifmt = REAL_MODE_FORMAT (imode); 1306 /* These conditions are conservative rather than trying to catch the 1307 exact boundary conditions; the main case to allow is IEEE float 1308 and double. */ 1309 return (ifmt->b == tfmt->b 1310 && ifmt->p > 2 * tfmt->p 1311 && ifmt->emin < 2 * tfmt->emin - tfmt->p - 2 1312 && ifmt->emin < tfmt->emin - tfmt->emax - tfmt->p - 2 1313 && ifmt->emax > 2 * tfmt->emax + 2 1314 && ifmt->emax > tfmt->emax - tfmt->emin + tfmt->p + 2 1315 && ifmt->round_towards_zero == tfmt->round_towards_zero 1316 && (ifmt->has_sign_dependent_rounding 1317 == tfmt->has_sign_dependent_rounding) 1318 && ifmt->has_nans >= tfmt->has_nans 1319 && ifmt->has_inf >= tfmt->has_inf 1320 && ifmt->has_signed_zero >= tfmt->has_signed_zero 1321 && !MODE_COMPOSITE_P (tmode) 1322 && !MODE_COMPOSITE_P (imode)); 1323 } 1324 1325 /* Render R as an integer. */ 1326 1327 HOST_WIDE_INT 1328 real_to_integer (const REAL_VALUE_TYPE *r) 1329 { 1330 unsigned HOST_WIDE_INT i; 1331 1332 switch (r->cl) 1333 { 1334 case rvc_zero: 1335 underflow: 1336 return 0; 1337 1338 case rvc_inf: 1339 case rvc_nan: 1340 overflow: 1341 i = (unsigned HOST_WIDE_INT) 1 << (HOST_BITS_PER_WIDE_INT - 1); 1342 if (!r->sign) 1343 i--; 1344 return i; 1345 1346 case rvc_normal: 1347 if (r->decimal) 1348 return decimal_real_to_integer (r); 1349 1350 if (REAL_EXP (r) <= 0) 1351 goto underflow; 1352 /* Only force overflow for unsigned overflow. Signed overflow is 1353 undefined, so it doesn't matter what we return, and some callers 1354 expect to be able to use this routine for both signed and 1355 unsigned conversions. */ 1356 if (REAL_EXP (r) > HOST_BITS_PER_WIDE_INT) 1357 goto overflow; 1358 1359 if (HOST_BITS_PER_WIDE_INT == HOST_BITS_PER_LONG) 1360 i = r->sig[SIGSZ-1]; 1361 else 1362 { 1363 gcc_assert (HOST_BITS_PER_WIDE_INT == 2 * HOST_BITS_PER_LONG); 1364 i = r->sig[SIGSZ-1]; 1365 i = i << (HOST_BITS_PER_LONG - 1) << 1; 1366 i |= r->sig[SIGSZ-2]; 1367 } 1368 1369 i >>= HOST_BITS_PER_WIDE_INT - REAL_EXP (r); 1370 1371 if (r->sign) 1372 i = -i; 1373 return i; 1374 1375 default: 1376 gcc_unreachable (); 1377 } 1378 } 1379 1380 /* Likewise, but to an integer pair, HI+LOW. */ 1381 1382 void 1383 real_to_integer2 (HOST_WIDE_INT *plow, HOST_WIDE_INT *phigh, 1384 const REAL_VALUE_TYPE *r) 1385 { 1386 REAL_VALUE_TYPE t; 1387 HOST_WIDE_INT low, high; 1388 int exp; 1389 1390 switch (r->cl) 1391 { 1392 case rvc_zero: 1393 underflow: 1394 low = high = 0; 1395 break; 1396 1397 case rvc_inf: 1398 case rvc_nan: 1399 overflow: 1400 high = (unsigned HOST_WIDE_INT) 1 << (HOST_BITS_PER_WIDE_INT - 1); 1401 if (r->sign) 1402 low = 0; 1403 else 1404 { 1405 high--; 1406 low = -1; 1407 } 1408 break; 1409 1410 case rvc_normal: 1411 if (r->decimal) 1412 { 1413 decimal_real_to_integer2 (plow, phigh, r); 1414 return; 1415 } 1416 1417 exp = REAL_EXP (r); 1418 if (exp <= 0) 1419 goto underflow; 1420 /* Only force overflow for unsigned overflow. Signed overflow is 1421 undefined, so it doesn't matter what we return, and some callers 1422 expect to be able to use this routine for both signed and 1423 unsigned conversions. */ 1424 if (exp > HOST_BITS_PER_DOUBLE_INT) 1425 goto overflow; 1426 1427 rshift_significand (&t, r, HOST_BITS_PER_DOUBLE_INT - exp); 1428 if (HOST_BITS_PER_WIDE_INT == HOST_BITS_PER_LONG) 1429 { 1430 high = t.sig[SIGSZ-1]; 1431 low = t.sig[SIGSZ-2]; 1432 } 1433 else 1434 { 1435 gcc_assert (HOST_BITS_PER_WIDE_INT == 2*HOST_BITS_PER_LONG); 1436 high = t.sig[SIGSZ-1]; 1437 high = high << (HOST_BITS_PER_LONG - 1) << 1; 1438 high |= t.sig[SIGSZ-2]; 1439 1440 low = t.sig[SIGSZ-3]; 1441 low = low << (HOST_BITS_PER_LONG - 1) << 1; 1442 low |= t.sig[SIGSZ-4]; 1443 } 1444 1445 if (r->sign) 1446 { 1447 if (low == 0) 1448 high = -high; 1449 else 1450 low = -low, high = ~high; 1451 } 1452 break; 1453 1454 default: 1455 gcc_unreachable (); 1456 } 1457 1458 *plow = low; 1459 *phigh = high; 1460 } 1461 1462 /* A subroutine of real_to_decimal. Compute the quotient and remainder 1463 of NUM / DEN. Return the quotient and place the remainder in NUM. 1464 It is expected that NUM / DEN are close enough that the quotient is 1465 small. */ 1466 1467 static unsigned long 1468 rtd_divmod (REAL_VALUE_TYPE *num, REAL_VALUE_TYPE *den) 1469 { 1470 unsigned long q, msb; 1471 int expn = REAL_EXP (num), expd = REAL_EXP (den); 1472 1473 if (expn < expd) 1474 return 0; 1475 1476 q = msb = 0; 1477 goto start; 1478 do 1479 { 1480 msb = num->sig[SIGSZ-1] & SIG_MSB; 1481 q <<= 1; 1482 lshift_significand_1 (num, num); 1483 start: 1484 if (msb || cmp_significands (num, den) >= 0) 1485 { 1486 sub_significands (num, num, den, 0); 1487 q |= 1; 1488 } 1489 } 1490 while (--expn >= expd); 1491 1492 SET_REAL_EXP (num, expd); 1493 normalize (num); 1494 1495 return q; 1496 } 1497 1498 /* Render R as a decimal floating point constant. Emit DIGITS significant 1499 digits in the result, bounded by BUF_SIZE. If DIGITS is 0, choose the 1500 maximum for the representation. If CROP_TRAILING_ZEROS, strip trailing 1501 zeros. If MODE is VOIDmode, round to nearest value. Otherwise, round 1502 to a string that, when parsed back in mode MODE, yields the same value. */ 1503 1504 #define M_LOG10_2 0.30102999566398119521 1505 1506 void 1507 real_to_decimal_for_mode (char *str, const REAL_VALUE_TYPE *r_orig, 1508 size_t buf_size, size_t digits, 1509 int crop_trailing_zeros, enum machine_mode mode) 1510 { 1511 const struct real_format *fmt = NULL; 1512 const REAL_VALUE_TYPE *one, *ten; 1513 REAL_VALUE_TYPE r, pten, u, v; 1514 int dec_exp, cmp_one, digit; 1515 size_t max_digits; 1516 char *p, *first, *last; 1517 bool sign; 1518 bool round_up; 1519 1520 if (mode != VOIDmode) 1521 { 1522 fmt = REAL_MODE_FORMAT (mode); 1523 gcc_assert (fmt); 1524 } 1525 1526 r = *r_orig; 1527 switch (r.cl) 1528 { 1529 case rvc_zero: 1530 strcpy (str, (r.sign ? "-0.0" : "0.0")); 1531 return; 1532 case rvc_normal: 1533 break; 1534 case rvc_inf: 1535 strcpy (str, (r.sign ? "-Inf" : "+Inf")); 1536 return; 1537 case rvc_nan: 1538 /* ??? Print the significand as well, if not canonical? */ 1539 sprintf (str, "%c%cNaN", (r_orig->sign ? '-' : '+'), 1540 (r_orig->signalling ? 'S' : 'Q')); 1541 return; 1542 default: 1543 gcc_unreachable (); 1544 } 1545 1546 if (r.decimal) 1547 { 1548 decimal_real_to_decimal (str, &r, buf_size, digits, crop_trailing_zeros); 1549 return; 1550 } 1551 1552 /* Bound the number of digits printed by the size of the representation. */ 1553 max_digits = SIGNIFICAND_BITS * M_LOG10_2; 1554 if (digits == 0 || digits > max_digits) 1555 digits = max_digits; 1556 1557 /* Estimate the decimal exponent, and compute the length of the string it 1558 will print as. Be conservative and add one to account for possible 1559 overflow or rounding error. */ 1560 dec_exp = REAL_EXP (&r) * M_LOG10_2; 1561 for (max_digits = 1; dec_exp ; max_digits++) 1562 dec_exp /= 10; 1563 1564 /* Bound the number of digits printed by the size of the output buffer. */ 1565 max_digits = buf_size - 1 - 1 - 2 - max_digits - 1; 1566 gcc_assert (max_digits <= buf_size); 1567 if (digits > max_digits) 1568 digits = max_digits; 1569 1570 one = real_digit (1); 1571 ten = ten_to_ptwo (0); 1572 1573 sign = r.sign; 1574 r.sign = 0; 1575 1576 dec_exp = 0; 1577 pten = *one; 1578 1579 cmp_one = do_compare (&r, one, 0); 1580 if (cmp_one > 0) 1581 { 1582 int m; 1583 1584 /* Number is greater than one. Convert significand to an integer 1585 and strip trailing decimal zeros. */ 1586 1587 u = r; 1588 SET_REAL_EXP (&u, SIGNIFICAND_BITS - 1); 1589 1590 /* Largest M, such that 10**2**M fits within SIGNIFICAND_BITS. */ 1591 m = floor_log2 (max_digits); 1592 1593 /* Iterate over the bits of the possible powers of 10 that might 1594 be present in U and eliminate them. That is, if we find that 1595 10**2**M divides U evenly, keep the division and increase 1596 DEC_EXP by 2**M. */ 1597 do 1598 { 1599 REAL_VALUE_TYPE t; 1600 1601 do_divide (&t, &u, ten_to_ptwo (m)); 1602 do_fix_trunc (&v, &t); 1603 if (cmp_significands (&v, &t) == 0) 1604 { 1605 u = t; 1606 dec_exp += 1 << m; 1607 } 1608 } 1609 while (--m >= 0); 1610 1611 /* Revert the scaling to integer that we performed earlier. */ 1612 SET_REAL_EXP (&u, REAL_EXP (&u) + REAL_EXP (&r) 1613 - (SIGNIFICAND_BITS - 1)); 1614 r = u; 1615 1616 /* Find power of 10. Do this by dividing out 10**2**M when 1617 this is larger than the current remainder. Fill PTEN with 1618 the power of 10 that we compute. */ 1619 if (REAL_EXP (&r) > 0) 1620 { 1621 m = floor_log2 ((int)(REAL_EXP (&r) * M_LOG10_2)) + 1; 1622 do 1623 { 1624 const REAL_VALUE_TYPE *ptentwo = ten_to_ptwo (m); 1625 if (do_compare (&u, ptentwo, 0) >= 0) 1626 { 1627 do_divide (&u, &u, ptentwo); 1628 do_multiply (&pten, &pten, ptentwo); 1629 dec_exp += 1 << m; 1630 } 1631 } 1632 while (--m >= 0); 1633 } 1634 else 1635 /* We managed to divide off enough tens in the above reduction 1636 loop that we've now got a negative exponent. Fall into the 1637 less-than-one code to compute the proper value for PTEN. */ 1638 cmp_one = -1; 1639 } 1640 if (cmp_one < 0) 1641 { 1642 int m; 1643 1644 /* Number is less than one. Pad significand with leading 1645 decimal zeros. */ 1646 1647 v = r; 1648 while (1) 1649 { 1650 /* Stop if we'd shift bits off the bottom. */ 1651 if (v.sig[0] & 7) 1652 break; 1653 1654 do_multiply (&u, &v, ten); 1655 1656 /* Stop if we're now >= 1. */ 1657 if (REAL_EXP (&u) > 0) 1658 break; 1659 1660 v = u; 1661 dec_exp -= 1; 1662 } 1663 r = v; 1664 1665 /* Find power of 10. Do this by multiplying in P=10**2**M when 1666 the current remainder is smaller than 1/P. Fill PTEN with the 1667 power of 10 that we compute. */ 1668 m = floor_log2 ((int)(-REAL_EXP (&r) * M_LOG10_2)) + 1; 1669 do 1670 { 1671 const REAL_VALUE_TYPE *ptentwo = ten_to_ptwo (m); 1672 const REAL_VALUE_TYPE *ptenmtwo = ten_to_mptwo (m); 1673 1674 if (do_compare (&v, ptenmtwo, 0) <= 0) 1675 { 1676 do_multiply (&v, &v, ptentwo); 1677 do_multiply (&pten, &pten, ptentwo); 1678 dec_exp -= 1 << m; 1679 } 1680 } 1681 while (--m >= 0); 1682 1683 /* Invert the positive power of 10 that we've collected so far. */ 1684 do_divide (&pten, one, &pten); 1685 } 1686 1687 p = str; 1688 if (sign) 1689 *p++ = '-'; 1690 first = p++; 1691 1692 /* At this point, PTEN should contain the nearest power of 10 smaller 1693 than R, such that this division produces the first digit. 1694 1695 Using a divide-step primitive that returns the complete integral 1696 remainder avoids the rounding error that would be produced if 1697 we were to use do_divide here and then simply multiply by 10 for 1698 each subsequent digit. */ 1699 1700 digit = rtd_divmod (&r, &pten); 1701 1702 /* Be prepared for error in that division via underflow ... */ 1703 if (digit == 0 && cmp_significand_0 (&r)) 1704 { 1705 /* Multiply by 10 and try again. */ 1706 do_multiply (&r, &r, ten); 1707 digit = rtd_divmod (&r, &pten); 1708 dec_exp -= 1; 1709 gcc_assert (digit != 0); 1710 } 1711 1712 /* ... or overflow. */ 1713 if (digit == 10) 1714 { 1715 *p++ = '1'; 1716 if (--digits > 0) 1717 *p++ = '0'; 1718 dec_exp += 1; 1719 } 1720 else 1721 { 1722 gcc_assert (digit <= 10); 1723 *p++ = digit + '0'; 1724 } 1725 1726 /* Generate subsequent digits. */ 1727 while (--digits > 0) 1728 { 1729 do_multiply (&r, &r, ten); 1730 digit = rtd_divmod (&r, &pten); 1731 *p++ = digit + '0'; 1732 } 1733 last = p; 1734 1735 /* Generate one more digit with which to do rounding. */ 1736 do_multiply (&r, &r, ten); 1737 digit = rtd_divmod (&r, &pten); 1738 1739 /* Round the result. */ 1740 if (fmt && fmt->round_towards_zero) 1741 { 1742 /* If the format uses round towards zero when parsing the string 1743 back in, we need to always round away from zero here. */ 1744 if (cmp_significand_0 (&r)) 1745 digit++; 1746 round_up = digit > 0; 1747 } 1748 else 1749 { 1750 if (digit == 5) 1751 { 1752 /* Round to nearest. If R is nonzero there are additional 1753 nonzero digits to be extracted. */ 1754 if (cmp_significand_0 (&r)) 1755 digit++; 1756 /* Round to even. */ 1757 else if ((p[-1] - '0') & 1) 1758 digit++; 1759 } 1760 1761 round_up = digit > 5; 1762 } 1763 1764 if (round_up) 1765 { 1766 while (p > first) 1767 { 1768 digit = *--p; 1769 if (digit == '9') 1770 *p = '0'; 1771 else 1772 { 1773 *p = digit + 1; 1774 break; 1775 } 1776 } 1777 1778 /* Carry out of the first digit. This means we had all 9's and 1779 now have all 0's. "Prepend" a 1 by overwriting the first 0. */ 1780 if (p == first) 1781 { 1782 first[1] = '1'; 1783 dec_exp++; 1784 } 1785 } 1786 1787 /* Insert the decimal point. */ 1788 first[0] = first[1]; 1789 first[1] = '.'; 1790 1791 /* If requested, drop trailing zeros. Never crop past "1.0". */ 1792 if (crop_trailing_zeros) 1793 while (last > first + 3 && last[-1] == '0') 1794 last--; 1795 1796 /* Append the exponent. */ 1797 sprintf (last, "e%+d", dec_exp); 1798 1799 #ifdef ENABLE_CHECKING 1800 /* Verify that we can read the original value back in. */ 1801 if (mode != VOIDmode) 1802 { 1803 real_from_string (&r, str); 1804 real_convert (&r, mode, &r); 1805 gcc_assert (real_identical (&r, r_orig)); 1806 } 1807 #endif 1808 } 1809 1810 /* Likewise, except always uses round-to-nearest. */ 1811 1812 void 1813 real_to_decimal (char *str, const REAL_VALUE_TYPE *r_orig, size_t buf_size, 1814 size_t digits, int crop_trailing_zeros) 1815 { 1816 real_to_decimal_for_mode (str, r_orig, buf_size, 1817 digits, crop_trailing_zeros, VOIDmode); 1818 } 1819 1820 /* Render R as a hexadecimal floating point constant. Emit DIGITS 1821 significant digits in the result, bounded by BUF_SIZE. If DIGITS is 0, 1822 choose the maximum for the representation. If CROP_TRAILING_ZEROS, 1823 strip trailing zeros. */ 1824 1825 void 1826 real_to_hexadecimal (char *str, const REAL_VALUE_TYPE *r, size_t buf_size, 1827 size_t digits, int crop_trailing_zeros) 1828 { 1829 int i, j, exp = REAL_EXP (r); 1830 char *p, *first; 1831 char exp_buf[16]; 1832 size_t max_digits; 1833 1834 switch (r->cl) 1835 { 1836 case rvc_zero: 1837 exp = 0; 1838 break; 1839 case rvc_normal: 1840 break; 1841 case rvc_inf: 1842 strcpy (str, (r->sign ? "-Inf" : "+Inf")); 1843 return; 1844 case rvc_nan: 1845 /* ??? Print the significand as well, if not canonical? */ 1846 sprintf (str, "%c%cNaN", (r->sign ? '-' : '+'), 1847 (r->signalling ? 'S' : 'Q')); 1848 return; 1849 default: 1850 gcc_unreachable (); 1851 } 1852 1853 if (r->decimal) 1854 { 1855 /* Hexadecimal format for decimal floats is not interesting. */ 1856 strcpy (str, "N/A"); 1857 return; 1858 } 1859 1860 if (digits == 0) 1861 digits = SIGNIFICAND_BITS / 4; 1862 1863 /* Bound the number of digits printed by the size of the output buffer. */ 1864 1865 sprintf (exp_buf, "p%+d", exp); 1866 max_digits = buf_size - strlen (exp_buf) - r->sign - 4 - 1; 1867 gcc_assert (max_digits <= buf_size); 1868 if (digits > max_digits) 1869 digits = max_digits; 1870 1871 p = str; 1872 if (r->sign) 1873 *p++ = '-'; 1874 *p++ = '0'; 1875 *p++ = 'x'; 1876 *p++ = '0'; 1877 *p++ = '.'; 1878 first = p; 1879 1880 for (i = SIGSZ - 1; i >= 0; --i) 1881 for (j = HOST_BITS_PER_LONG - 4; j >= 0; j -= 4) 1882 { 1883 *p++ = "0123456789abcdef"[(r->sig[i] >> j) & 15]; 1884 if (--digits == 0) 1885 goto out; 1886 } 1887 1888 out: 1889 if (crop_trailing_zeros) 1890 while (p > first + 1 && p[-1] == '0') 1891 p--; 1892 1893 sprintf (p, "p%+d", exp); 1894 } 1895 1896 /* Initialize R from a decimal or hexadecimal string. The string is 1897 assumed to have been syntax checked already. Return -1 if the 1898 value underflows, +1 if overflows, and 0 otherwise. */ 1899 1900 int 1901 real_from_string (REAL_VALUE_TYPE *r, const char *str) 1902 { 1903 int exp = 0; 1904 bool sign = false; 1905 1906 get_zero (r, 0); 1907 1908 if (*str == '-') 1909 { 1910 sign = true; 1911 str++; 1912 } 1913 else if (*str == '+') 1914 str++; 1915 1916 if (!strncmp (str, "QNaN", 4)) 1917 { 1918 get_canonical_qnan (r, sign); 1919 return 0; 1920 } 1921 else if (!strncmp (str, "SNaN", 4)) 1922 { 1923 get_canonical_snan (r, sign); 1924 return 0; 1925 } 1926 else if (!strncmp (str, "Inf", 3)) 1927 { 1928 get_inf (r, sign); 1929 return 0; 1930 } 1931 1932 if (str[0] == '0' && (str[1] == 'x' || str[1] == 'X')) 1933 { 1934 /* Hexadecimal floating point. */ 1935 int pos = SIGNIFICAND_BITS - 4, d; 1936 1937 str += 2; 1938 1939 while (*str == '0') 1940 str++; 1941 while (1) 1942 { 1943 d = hex_value (*str); 1944 if (d == _hex_bad) 1945 break; 1946 if (pos >= 0) 1947 { 1948 r->sig[pos / HOST_BITS_PER_LONG] 1949 |= (unsigned long) d << (pos % HOST_BITS_PER_LONG); 1950 pos -= 4; 1951 } 1952 else if (d) 1953 /* Ensure correct rounding by setting last bit if there is 1954 a subsequent nonzero digit. */ 1955 r->sig[0] |= 1; 1956 exp += 4; 1957 str++; 1958 } 1959 if (*str == '.') 1960 { 1961 str++; 1962 if (pos == SIGNIFICAND_BITS - 4) 1963 { 1964 while (*str == '0') 1965 str++, exp -= 4; 1966 } 1967 while (1) 1968 { 1969 d = hex_value (*str); 1970 if (d == _hex_bad) 1971 break; 1972 if (pos >= 0) 1973 { 1974 r->sig[pos / HOST_BITS_PER_LONG] 1975 |= (unsigned long) d << (pos % HOST_BITS_PER_LONG); 1976 pos -= 4; 1977 } 1978 else if (d) 1979 /* Ensure correct rounding by setting last bit if there is 1980 a subsequent nonzero digit. */ 1981 r->sig[0] |= 1; 1982 str++; 1983 } 1984 } 1985 1986 /* If the mantissa is zero, ignore the exponent. */ 1987 if (!cmp_significand_0 (r)) 1988 goto is_a_zero; 1989 1990 if (*str == 'p' || *str == 'P') 1991 { 1992 bool exp_neg = false; 1993 1994 str++; 1995 if (*str == '-') 1996 { 1997 exp_neg = true; 1998 str++; 1999 } 2000 else if (*str == '+') 2001 str++; 2002 2003 d = 0; 2004 while (ISDIGIT (*str)) 2005 { 2006 d *= 10; 2007 d += *str - '0'; 2008 if (d > MAX_EXP) 2009 { 2010 /* Overflowed the exponent. */ 2011 if (exp_neg) 2012 goto underflow; 2013 else 2014 goto overflow; 2015 } 2016 str++; 2017 } 2018 if (exp_neg) 2019 d = -d; 2020 2021 exp += d; 2022 } 2023 2024 r->cl = rvc_normal; 2025 SET_REAL_EXP (r, exp); 2026 2027 normalize (r); 2028 } 2029 else 2030 { 2031 /* Decimal floating point. */ 2032 const REAL_VALUE_TYPE *ten = ten_to_ptwo (0); 2033 int d; 2034 2035 while (*str == '0') 2036 str++; 2037 while (ISDIGIT (*str)) 2038 { 2039 d = *str++ - '0'; 2040 do_multiply (r, r, ten); 2041 if (d) 2042 do_add (r, r, real_digit (d), 0); 2043 } 2044 if (*str == '.') 2045 { 2046 str++; 2047 if (r->cl == rvc_zero) 2048 { 2049 while (*str == '0') 2050 str++, exp--; 2051 } 2052 while (ISDIGIT (*str)) 2053 { 2054 d = *str++ - '0'; 2055 do_multiply (r, r, ten); 2056 if (d) 2057 do_add (r, r, real_digit (d), 0); 2058 exp--; 2059 } 2060 } 2061 2062 /* If the mantissa is zero, ignore the exponent. */ 2063 if (r->cl == rvc_zero) 2064 goto is_a_zero; 2065 2066 if (*str == 'e' || *str == 'E') 2067 { 2068 bool exp_neg = false; 2069 2070 str++; 2071 if (*str == '-') 2072 { 2073 exp_neg = true; 2074 str++; 2075 } 2076 else if (*str == '+') 2077 str++; 2078 2079 d = 0; 2080 while (ISDIGIT (*str)) 2081 { 2082 d *= 10; 2083 d += *str - '0'; 2084 if (d > MAX_EXP) 2085 { 2086 /* Overflowed the exponent. */ 2087 if (exp_neg) 2088 goto underflow; 2089 else 2090 goto overflow; 2091 } 2092 str++; 2093 } 2094 if (exp_neg) 2095 d = -d; 2096 exp += d; 2097 } 2098 2099 if (exp) 2100 times_pten (r, exp); 2101 } 2102 2103 r->sign = sign; 2104 return 0; 2105 2106 is_a_zero: 2107 get_zero (r, sign); 2108 return 0; 2109 2110 underflow: 2111 get_zero (r, sign); 2112 return -1; 2113 2114 overflow: 2115 get_inf (r, sign); 2116 return 1; 2117 } 2118 2119 /* Legacy. Similar, but return the result directly. */ 2120 2121 REAL_VALUE_TYPE 2122 real_from_string2 (const char *s, enum machine_mode mode) 2123 { 2124 REAL_VALUE_TYPE r; 2125 2126 real_from_string (&r, s); 2127 if (mode != VOIDmode) 2128 real_convert (&r, mode, &r); 2129 2130 return r; 2131 } 2132 2133 /* Initialize R from string S and desired MODE. */ 2134 2135 void 2136 real_from_string3 (REAL_VALUE_TYPE *r, const char *s, enum machine_mode mode) 2137 { 2138 if (DECIMAL_FLOAT_MODE_P (mode)) 2139 decimal_real_from_string (r, s); 2140 else 2141 real_from_string (r, s); 2142 2143 if (mode != VOIDmode) 2144 real_convert (r, mode, r); 2145 } 2146 2147 /* Initialize R from the integer pair HIGH+LOW. */ 2148 2149 void 2150 real_from_integer (REAL_VALUE_TYPE *r, enum machine_mode mode, 2151 unsigned HOST_WIDE_INT low, HOST_WIDE_INT high, 2152 int unsigned_p) 2153 { 2154 if (low == 0 && high == 0) 2155 get_zero (r, 0); 2156 else 2157 { 2158 memset (r, 0, sizeof (*r)); 2159 r->cl = rvc_normal; 2160 r->sign = high < 0 && !unsigned_p; 2161 SET_REAL_EXP (r, HOST_BITS_PER_DOUBLE_INT); 2162 2163 if (r->sign) 2164 { 2165 high = ~high; 2166 if (low == 0) 2167 high += 1; 2168 else 2169 low = -low; 2170 } 2171 2172 if (HOST_BITS_PER_LONG == HOST_BITS_PER_WIDE_INT) 2173 { 2174 r->sig[SIGSZ-1] = high; 2175 r->sig[SIGSZ-2] = low; 2176 } 2177 else 2178 { 2179 gcc_assert (HOST_BITS_PER_LONG*2 == HOST_BITS_PER_WIDE_INT); 2180 r->sig[SIGSZ-1] = high >> (HOST_BITS_PER_LONG - 1) >> 1; 2181 r->sig[SIGSZ-2] = high; 2182 r->sig[SIGSZ-3] = low >> (HOST_BITS_PER_LONG - 1) >> 1; 2183 r->sig[SIGSZ-4] = low; 2184 } 2185 2186 normalize (r); 2187 } 2188 2189 if (DECIMAL_FLOAT_MODE_P (mode)) 2190 decimal_from_integer (r); 2191 else if (mode != VOIDmode) 2192 real_convert (r, mode, r); 2193 } 2194 2195 /* Render R, an integral value, as a floating point constant with no 2196 specified exponent. */ 2197 2198 static void 2199 decimal_integer_string (char *str, const REAL_VALUE_TYPE *r_orig, 2200 size_t buf_size) 2201 { 2202 int dec_exp, digit, digits; 2203 REAL_VALUE_TYPE r, pten; 2204 char *p; 2205 bool sign; 2206 2207 r = *r_orig; 2208 2209 if (r.cl == rvc_zero) 2210 { 2211 strcpy (str, "0."); 2212 return; 2213 } 2214 2215 sign = r.sign; 2216 r.sign = 0; 2217 2218 dec_exp = REAL_EXP (&r) * M_LOG10_2; 2219 digits = dec_exp + 1; 2220 gcc_assert ((digits + 2) < (int)buf_size); 2221 2222 pten = *real_digit (1); 2223 times_pten (&pten, dec_exp); 2224 2225 p = str; 2226 if (sign) 2227 *p++ = '-'; 2228 2229 digit = rtd_divmod (&r, &pten); 2230 gcc_assert (digit >= 0 && digit <= 9); 2231 *p++ = digit + '0'; 2232 while (--digits > 0) 2233 { 2234 times_pten (&r, 1); 2235 digit = rtd_divmod (&r, &pten); 2236 *p++ = digit + '0'; 2237 } 2238 *p++ = '.'; 2239 *p++ = '\0'; 2240 } 2241 2242 /* Convert a real with an integral value to decimal float. */ 2243 2244 static void 2245 decimal_from_integer (REAL_VALUE_TYPE *r) 2246 { 2247 char str[256]; 2248 2249 decimal_integer_string (str, r, sizeof (str) - 1); 2250 decimal_real_from_string (r, str); 2251 } 2252 2253 /* Returns 10**2**N. */ 2254 2255 static const REAL_VALUE_TYPE * 2256 ten_to_ptwo (int n) 2257 { 2258 static REAL_VALUE_TYPE tens[EXP_BITS]; 2259 2260 gcc_assert (n >= 0); 2261 gcc_assert (n < EXP_BITS); 2262 2263 if (tens[n].cl == rvc_zero) 2264 { 2265 if (n < (HOST_BITS_PER_WIDE_INT == 64 ? 5 : 4)) 2266 { 2267 HOST_WIDE_INT t = 10; 2268 int i; 2269 2270 for (i = 0; i < n; ++i) 2271 t *= t; 2272 2273 real_from_integer (&tens[n], VOIDmode, t, 0, 1); 2274 } 2275 else 2276 { 2277 const REAL_VALUE_TYPE *t = ten_to_ptwo (n - 1); 2278 do_multiply (&tens[n], t, t); 2279 } 2280 } 2281 2282 return &tens[n]; 2283 } 2284 2285 /* Returns 10**(-2**N). */ 2286 2287 static const REAL_VALUE_TYPE * 2288 ten_to_mptwo (int n) 2289 { 2290 static REAL_VALUE_TYPE tens[EXP_BITS]; 2291 2292 gcc_assert (n >= 0); 2293 gcc_assert (n < EXP_BITS); 2294 2295 if (tens[n].cl == rvc_zero) 2296 do_divide (&tens[n], real_digit (1), ten_to_ptwo (n)); 2297 2298 return &tens[n]; 2299 } 2300 2301 /* Returns N. */ 2302 2303 static const REAL_VALUE_TYPE * 2304 real_digit (int n) 2305 { 2306 static REAL_VALUE_TYPE num[10]; 2307 2308 gcc_assert (n >= 0); 2309 gcc_assert (n <= 9); 2310 2311 if (n > 0 && num[n].cl == rvc_zero) 2312 real_from_integer (&num[n], VOIDmode, n, 0, 1); 2313 2314 return &num[n]; 2315 } 2316 2317 /* Multiply R by 10**EXP. */ 2318 2319 static void 2320 times_pten (REAL_VALUE_TYPE *r, int exp) 2321 { 2322 REAL_VALUE_TYPE pten, *rr; 2323 bool negative = (exp < 0); 2324 int i; 2325 2326 if (negative) 2327 { 2328 exp = -exp; 2329 pten = *real_digit (1); 2330 rr = &pten; 2331 } 2332 else 2333 rr = r; 2334 2335 for (i = 0; exp > 0; ++i, exp >>= 1) 2336 if (exp & 1) 2337 do_multiply (rr, rr, ten_to_ptwo (i)); 2338 2339 if (negative) 2340 do_divide (r, r, &pten); 2341 } 2342 2343 /* Returns the special REAL_VALUE_TYPE corresponding to 'e'. */ 2344 2345 const REAL_VALUE_TYPE * 2346 dconst_e_ptr (void) 2347 { 2348 static REAL_VALUE_TYPE value; 2349 2350 /* Initialize mathematical constants for constant folding builtins. 2351 These constants need to be given to at least 160 bits precision. */ 2352 if (value.cl == rvc_zero) 2353 { 2354 mpfr_t m; 2355 mpfr_init2 (m, SIGNIFICAND_BITS); 2356 mpfr_set_ui (m, 1, GMP_RNDN); 2357 mpfr_exp (m, m, GMP_RNDN); 2358 real_from_mpfr (&value, m, NULL_TREE, GMP_RNDN); 2359 mpfr_clear (m); 2360 2361 } 2362 return &value; 2363 } 2364 2365 /* Returns the special REAL_VALUE_TYPE corresponding to 1/3. */ 2366 2367 const REAL_VALUE_TYPE * 2368 dconst_third_ptr (void) 2369 { 2370 static REAL_VALUE_TYPE value; 2371 2372 /* Initialize mathematical constants for constant folding builtins. 2373 These constants need to be given to at least 160 bits precision. */ 2374 if (value.cl == rvc_zero) 2375 { 2376 real_arithmetic (&value, RDIV_EXPR, &dconst1, real_digit (3)); 2377 } 2378 return &value; 2379 } 2380 2381 /* Returns the special REAL_VALUE_TYPE corresponding to sqrt(2). */ 2382 2383 const REAL_VALUE_TYPE * 2384 dconst_sqrt2_ptr (void) 2385 { 2386 static REAL_VALUE_TYPE value; 2387 2388 /* Initialize mathematical constants for constant folding builtins. 2389 These constants need to be given to at least 160 bits precision. */ 2390 if (value.cl == rvc_zero) 2391 { 2392 mpfr_t m; 2393 mpfr_init2 (m, SIGNIFICAND_BITS); 2394 mpfr_sqrt_ui (m, 2, GMP_RNDN); 2395 real_from_mpfr (&value, m, NULL_TREE, GMP_RNDN); 2396 mpfr_clear (m); 2397 } 2398 return &value; 2399 } 2400 2401 /* Fills R with +Inf. */ 2402 2403 void 2404 real_inf (REAL_VALUE_TYPE *r) 2405 { 2406 get_inf (r, 0); 2407 } 2408 2409 /* Fills R with a NaN whose significand is described by STR. If QUIET, 2410 we force a QNaN, else we force an SNaN. The string, if not empty, 2411 is parsed as a number and placed in the significand. Return true 2412 if the string was successfully parsed. */ 2413 2414 bool 2415 real_nan (REAL_VALUE_TYPE *r, const char *str, int quiet, 2416 enum machine_mode mode) 2417 { 2418 const struct real_format *fmt; 2419 2420 fmt = REAL_MODE_FORMAT (mode); 2421 gcc_assert (fmt); 2422 2423 if (*str == 0) 2424 { 2425 if (quiet) 2426 get_canonical_qnan (r, 0); 2427 else 2428 get_canonical_snan (r, 0); 2429 } 2430 else 2431 { 2432 int base = 10, d; 2433 2434 memset (r, 0, sizeof (*r)); 2435 r->cl = rvc_nan; 2436 2437 /* Parse akin to strtol into the significand of R. */ 2438 2439 while (ISSPACE (*str)) 2440 str++; 2441 if (*str == '-') 2442 str++; 2443 else if (*str == '+') 2444 str++; 2445 if (*str == '0') 2446 { 2447 str++; 2448 if (*str == 'x' || *str == 'X') 2449 { 2450 base = 16; 2451 str++; 2452 } 2453 else 2454 base = 8; 2455 } 2456 2457 while ((d = hex_value (*str)) < base) 2458 { 2459 REAL_VALUE_TYPE u; 2460 2461 switch (base) 2462 { 2463 case 8: 2464 lshift_significand (r, r, 3); 2465 break; 2466 case 16: 2467 lshift_significand (r, r, 4); 2468 break; 2469 case 10: 2470 lshift_significand_1 (&u, r); 2471 lshift_significand (r, r, 3); 2472 add_significands (r, r, &u); 2473 break; 2474 default: 2475 gcc_unreachable (); 2476 } 2477 2478 get_zero (&u, 0); 2479 u.sig[0] = d; 2480 add_significands (r, r, &u); 2481 2482 str++; 2483 } 2484 2485 /* Must have consumed the entire string for success. */ 2486 if (*str != 0) 2487 return false; 2488 2489 /* Shift the significand into place such that the bits 2490 are in the most significant bits for the format. */ 2491 lshift_significand (r, r, SIGNIFICAND_BITS - fmt->pnan); 2492 2493 /* Our MSB is always unset for NaNs. */ 2494 r->sig[SIGSZ-1] &= ~SIG_MSB; 2495 2496 /* Force quiet or signalling NaN. */ 2497 r->signalling = !quiet; 2498 } 2499 2500 return true; 2501 } 2502 2503 /* Fills R with the largest finite value representable in mode MODE. 2504 If SIGN is nonzero, R is set to the most negative finite value. */ 2505 2506 void 2507 real_maxval (REAL_VALUE_TYPE *r, int sign, enum machine_mode mode) 2508 { 2509 const struct real_format *fmt; 2510 int np2; 2511 2512 fmt = REAL_MODE_FORMAT (mode); 2513 gcc_assert (fmt); 2514 memset (r, 0, sizeof (*r)); 2515 2516 if (fmt->b == 10) 2517 decimal_real_maxval (r, sign, mode); 2518 else 2519 { 2520 r->cl = rvc_normal; 2521 r->sign = sign; 2522 SET_REAL_EXP (r, fmt->emax); 2523 2524 np2 = SIGNIFICAND_BITS - fmt->p; 2525 memset (r->sig, -1, SIGSZ * sizeof (unsigned long)); 2526 clear_significand_below (r, np2); 2527 2528 if (fmt->pnan < fmt->p) 2529 /* This is an IBM extended double format made up of two IEEE 2530 doubles. The value of the long double is the sum of the 2531 values of the two parts. The most significant part is 2532 required to be the value of the long double rounded to the 2533 nearest double. Rounding means we need a slightly smaller 2534 value for LDBL_MAX. */ 2535 clear_significand_bit (r, SIGNIFICAND_BITS - fmt->pnan - 1); 2536 } 2537 } 2538 2539 /* Fills R with 2**N. */ 2540 2541 void 2542 real_2expN (REAL_VALUE_TYPE *r, int n, enum machine_mode fmode) 2543 { 2544 memset (r, 0, sizeof (*r)); 2545 2546 n++; 2547 if (n > MAX_EXP) 2548 r->cl = rvc_inf; 2549 else if (n < -MAX_EXP) 2550 ; 2551 else 2552 { 2553 r->cl = rvc_normal; 2554 SET_REAL_EXP (r, n); 2555 r->sig[SIGSZ-1] = SIG_MSB; 2556 } 2557 if (DECIMAL_FLOAT_MODE_P (fmode)) 2558 decimal_real_convert (r, fmode, r); 2559 } 2560 2561 2562 static void 2563 round_for_format (const struct real_format *fmt, REAL_VALUE_TYPE *r) 2564 { 2565 int p2, np2, i, w; 2566 int emin2m1, emax2; 2567 bool round_up = false; 2568 2569 if (r->decimal) 2570 { 2571 if (fmt->b == 10) 2572 { 2573 decimal_round_for_format (fmt, r); 2574 return; 2575 } 2576 /* FIXME. We can come here via fp_easy_constant 2577 (e.g. -O0 on '_Decimal32 x = 1.0 + 2.0dd'), but have not 2578 investigated whether this convert needs to be here, or 2579 something else is missing. */ 2580 decimal_real_convert (r, DFmode, r); 2581 } 2582 2583 p2 = fmt->p; 2584 emin2m1 = fmt->emin - 1; 2585 emax2 = fmt->emax; 2586 2587 np2 = SIGNIFICAND_BITS - p2; 2588 switch (r->cl) 2589 { 2590 underflow: 2591 get_zero (r, r->sign); 2592 case rvc_zero: 2593 if (!fmt->has_signed_zero) 2594 r->sign = 0; 2595 return; 2596 2597 overflow: 2598 get_inf (r, r->sign); 2599 case rvc_inf: 2600 return; 2601 2602 case rvc_nan: 2603 clear_significand_below (r, np2); 2604 return; 2605 2606 case rvc_normal: 2607 break; 2608 2609 default: 2610 gcc_unreachable (); 2611 } 2612 2613 /* Check the range of the exponent. If we're out of range, 2614 either underflow or overflow. */ 2615 if (REAL_EXP (r) > emax2) 2616 goto overflow; 2617 else if (REAL_EXP (r) <= emin2m1) 2618 { 2619 int diff; 2620 2621 if (!fmt->has_denorm) 2622 { 2623 /* Don't underflow completely until we've had a chance to round. */ 2624 if (REAL_EXP (r) < emin2m1) 2625 goto underflow; 2626 } 2627 else 2628 { 2629 diff = emin2m1 - REAL_EXP (r) + 1; 2630 if (diff > p2) 2631 goto underflow; 2632 2633 /* De-normalize the significand. */ 2634 r->sig[0] |= sticky_rshift_significand (r, r, diff); 2635 SET_REAL_EXP (r, REAL_EXP (r) + diff); 2636 } 2637 } 2638 2639 if (!fmt->round_towards_zero) 2640 { 2641 /* There are P2 true significand bits, followed by one guard bit, 2642 followed by one sticky bit, followed by stuff. Fold nonzero 2643 stuff into the sticky bit. */ 2644 unsigned long sticky; 2645 bool guard, lsb; 2646 2647 sticky = 0; 2648 for (i = 0, w = (np2 - 1) / HOST_BITS_PER_LONG; i < w; ++i) 2649 sticky |= r->sig[i]; 2650 sticky |= r->sig[w] 2651 & (((unsigned long)1 << ((np2 - 1) % HOST_BITS_PER_LONG)) - 1); 2652 2653 guard = test_significand_bit (r, np2 - 1); 2654 lsb = test_significand_bit (r, np2); 2655 2656 /* Round to even. */ 2657 round_up = guard && (sticky || lsb); 2658 } 2659 2660 if (round_up) 2661 { 2662 REAL_VALUE_TYPE u; 2663 get_zero (&u, 0); 2664 set_significand_bit (&u, np2); 2665 2666 if (add_significands (r, r, &u)) 2667 { 2668 /* Overflow. Means the significand had been all ones, and 2669 is now all zeros. Need to increase the exponent, and 2670 possibly re-normalize it. */ 2671 SET_REAL_EXP (r, REAL_EXP (r) + 1); 2672 if (REAL_EXP (r) > emax2) 2673 goto overflow; 2674 r->sig[SIGSZ-1] = SIG_MSB; 2675 } 2676 } 2677 2678 /* Catch underflow that we deferred until after rounding. */ 2679 if (REAL_EXP (r) <= emin2m1) 2680 goto underflow; 2681 2682 /* Clear out trailing garbage. */ 2683 clear_significand_below (r, np2); 2684 } 2685 2686 /* Extend or truncate to a new mode. */ 2687 2688 void 2689 real_convert (REAL_VALUE_TYPE *r, enum machine_mode mode, 2690 const REAL_VALUE_TYPE *a) 2691 { 2692 const struct real_format *fmt; 2693 2694 fmt = REAL_MODE_FORMAT (mode); 2695 gcc_assert (fmt); 2696 2697 *r = *a; 2698 2699 if (a->decimal || fmt->b == 10) 2700 decimal_real_convert (r, mode, a); 2701 2702 round_for_format (fmt, r); 2703 2704 /* round_for_format de-normalizes denormals. Undo just that part. */ 2705 if (r->cl == rvc_normal) 2706 normalize (r); 2707 } 2708 2709 /* Legacy. Likewise, except return the struct directly. */ 2710 2711 REAL_VALUE_TYPE 2712 real_value_truncate (enum machine_mode mode, REAL_VALUE_TYPE a) 2713 { 2714 REAL_VALUE_TYPE r; 2715 real_convert (&r, mode, &a); 2716 return r; 2717 } 2718 2719 /* Return true if truncating to MODE is exact. */ 2720 2721 bool 2722 exact_real_truncate (enum machine_mode mode, const REAL_VALUE_TYPE *a) 2723 { 2724 const struct real_format *fmt; 2725 REAL_VALUE_TYPE t; 2726 int emin2m1; 2727 2728 fmt = REAL_MODE_FORMAT (mode); 2729 gcc_assert (fmt); 2730 2731 /* Don't allow conversion to denormals. */ 2732 emin2m1 = fmt->emin - 1; 2733 if (REAL_EXP (a) <= emin2m1) 2734 return false; 2735 2736 /* After conversion to the new mode, the value must be identical. */ 2737 real_convert (&t, mode, a); 2738 return real_identical (&t, a); 2739 } 2740 2741 /* Write R to the given target format. Place the words of the result 2742 in target word order in BUF. There are always 32 bits in each 2743 long, no matter the size of the host long. 2744 2745 Legacy: return word 0 for implementing REAL_VALUE_TO_TARGET_SINGLE. */ 2746 2747 long 2748 real_to_target_fmt (long *buf, const REAL_VALUE_TYPE *r_orig, 2749 const struct real_format *fmt) 2750 { 2751 REAL_VALUE_TYPE r; 2752 long buf1; 2753 2754 r = *r_orig; 2755 round_for_format (fmt, &r); 2756 2757 if (!buf) 2758 buf = &buf1; 2759 (*fmt->encode) (fmt, buf, &r); 2760 2761 return *buf; 2762 } 2763 2764 /* Similar, but look up the format from MODE. */ 2765 2766 long 2767 real_to_target (long *buf, const REAL_VALUE_TYPE *r, enum machine_mode mode) 2768 { 2769 const struct real_format *fmt; 2770 2771 fmt = REAL_MODE_FORMAT (mode); 2772 gcc_assert (fmt); 2773 2774 return real_to_target_fmt (buf, r, fmt); 2775 } 2776 2777 /* Read R from the given target format. Read the words of the result 2778 in target word order in BUF. There are always 32 bits in each 2779 long, no matter the size of the host long. */ 2780 2781 void 2782 real_from_target_fmt (REAL_VALUE_TYPE *r, const long *buf, 2783 const struct real_format *fmt) 2784 { 2785 (*fmt->decode) (fmt, r, buf); 2786 } 2787 2788 /* Similar, but look up the format from MODE. */ 2789 2790 void 2791 real_from_target (REAL_VALUE_TYPE *r, const long *buf, enum machine_mode mode) 2792 { 2793 const struct real_format *fmt; 2794 2795 fmt = REAL_MODE_FORMAT (mode); 2796 gcc_assert (fmt); 2797 2798 (*fmt->decode) (fmt, r, buf); 2799 } 2800 2801 /* Return the number of bits of the largest binary value that the 2802 significand of MODE will hold. */ 2803 /* ??? Legacy. Should get access to real_format directly. */ 2804 2805 int 2806 significand_size (enum machine_mode mode) 2807 { 2808 const struct real_format *fmt; 2809 2810 fmt = REAL_MODE_FORMAT (mode); 2811 if (fmt == NULL) 2812 return 0; 2813 2814 if (fmt->b == 10) 2815 { 2816 /* Return the size in bits of the largest binary value that can be 2817 held by the decimal coefficient for this mode. This is one more 2818 than the number of bits required to hold the largest coefficient 2819 of this mode. */ 2820 double log2_10 = 3.3219281; 2821 return fmt->p * log2_10; 2822 } 2823 return fmt->p; 2824 } 2825 2826 /* Return a hash value for the given real value. */ 2827 /* ??? The "unsigned int" return value is intended to be hashval_t, 2828 but I didn't want to pull hashtab.h into real.h. */ 2829 2830 unsigned int 2831 real_hash (const REAL_VALUE_TYPE *r) 2832 { 2833 unsigned int h; 2834 size_t i; 2835 2836 h = r->cl | (r->sign << 2); 2837 switch (r->cl) 2838 { 2839 case rvc_zero: 2840 case rvc_inf: 2841 return h; 2842 2843 case rvc_normal: 2844 h |= REAL_EXP (r) << 3; 2845 break; 2846 2847 case rvc_nan: 2848 if (r->signalling) 2849 h ^= (unsigned int)-1; 2850 if (r->canonical) 2851 return h; 2852 break; 2853 2854 default: 2855 gcc_unreachable (); 2856 } 2857 2858 if (sizeof(unsigned long) > sizeof(unsigned int)) 2859 for (i = 0; i < SIGSZ; ++i) 2860 { 2861 unsigned long s = r->sig[i]; 2862 h ^= s ^ (s >> (HOST_BITS_PER_LONG / 2)); 2863 } 2864 else 2865 for (i = 0; i < SIGSZ; ++i) 2866 h ^= r->sig[i]; 2867 2868 return h; 2869 } 2870 2871 /* IEEE single-precision format. */ 2872 2873 static void encode_ieee_single (const struct real_format *fmt, 2874 long *, const REAL_VALUE_TYPE *); 2875 static void decode_ieee_single (const struct real_format *, 2876 REAL_VALUE_TYPE *, const long *); 2877 2878 static void 2879 encode_ieee_single (const struct real_format *fmt, long *buf, 2880 const REAL_VALUE_TYPE *r) 2881 { 2882 unsigned long image, sig, exp; 2883 unsigned long sign = r->sign; 2884 bool denormal = (r->sig[SIGSZ-1] & SIG_MSB) == 0; 2885 2886 image = sign << 31; 2887 sig = (r->sig[SIGSZ-1] >> (HOST_BITS_PER_LONG - 24)) & 0x7fffff; 2888 2889 switch (r->cl) 2890 { 2891 case rvc_zero: 2892 break; 2893 2894 case rvc_inf: 2895 if (fmt->has_inf) 2896 image |= 255 << 23; 2897 else 2898 image |= 0x7fffffff; 2899 break; 2900 2901 case rvc_nan: 2902 if (fmt->has_nans) 2903 { 2904 if (r->canonical) 2905 sig = (fmt->canonical_nan_lsbs_set ? (1 << 22) - 1 : 0); 2906 if (r->signalling == fmt->qnan_msb_set) 2907 sig &= ~(1 << 22); 2908 else 2909 sig |= 1 << 22; 2910 if (sig == 0) 2911 sig = 1 << 21; 2912 2913 image |= 255 << 23; 2914 image |= sig; 2915 } 2916 else 2917 image |= 0x7fffffff; 2918 break; 2919 2920 case rvc_normal: 2921 /* Recall that IEEE numbers are interpreted as 1.F x 2**exp, 2922 whereas the intermediate representation is 0.F x 2**exp. 2923 Which means we're off by one. */ 2924 if (denormal) 2925 exp = 0; 2926 else 2927 exp = REAL_EXP (r) + 127 - 1; 2928 image |= exp << 23; 2929 image |= sig; 2930 break; 2931 2932 default: 2933 gcc_unreachable (); 2934 } 2935 2936 buf[0] = image; 2937 } 2938 2939 static void 2940 decode_ieee_single (const struct real_format *fmt, REAL_VALUE_TYPE *r, 2941 const long *buf) 2942 { 2943 unsigned long image = buf[0] & 0xffffffff; 2944 bool sign = (image >> 31) & 1; 2945 int exp = (image >> 23) & 0xff; 2946 2947 memset (r, 0, sizeof (*r)); 2948 image <<= HOST_BITS_PER_LONG - 24; 2949 image &= ~SIG_MSB; 2950 2951 if (exp == 0) 2952 { 2953 if (image && fmt->has_denorm) 2954 { 2955 r->cl = rvc_normal; 2956 r->sign = sign; 2957 SET_REAL_EXP (r, -126); 2958 r->sig[SIGSZ-1] = image << 1; 2959 normalize (r); 2960 } 2961 else if (fmt->has_signed_zero) 2962 r->sign = sign; 2963 } 2964 else if (exp == 255 && (fmt->has_nans || fmt->has_inf)) 2965 { 2966 if (image) 2967 { 2968 r->cl = rvc_nan; 2969 r->sign = sign; 2970 r->signalling = (((image >> (HOST_BITS_PER_LONG - 2)) & 1) 2971 ^ fmt->qnan_msb_set); 2972 r->sig[SIGSZ-1] = image; 2973 } 2974 else 2975 { 2976 r->cl = rvc_inf; 2977 r->sign = sign; 2978 } 2979 } 2980 else 2981 { 2982 r->cl = rvc_normal; 2983 r->sign = sign; 2984 SET_REAL_EXP (r, exp - 127 + 1); 2985 r->sig[SIGSZ-1] = image | SIG_MSB; 2986 } 2987 } 2988 2989 const struct real_format ieee_single_format = 2990 { 2991 encode_ieee_single, 2992 decode_ieee_single, 2993 2, 2994 24, 2995 24, 2996 -125, 2997 128, 2998 31, 2999 31, 3000 false, 3001 true, 3002 true, 3003 true, 3004 true, 3005 true, 3006 true, 3007 false 3008 }; 3009 3010 const struct real_format mips_single_format = 3011 { 3012 encode_ieee_single, 3013 decode_ieee_single, 3014 2, 3015 24, 3016 24, 3017 -125, 3018 128, 3019 31, 3020 31, 3021 false, 3022 true, 3023 true, 3024 true, 3025 true, 3026 true, 3027 false, 3028 true 3029 }; 3030 3031 const struct real_format motorola_single_format = 3032 { 3033 encode_ieee_single, 3034 decode_ieee_single, 3035 2, 3036 24, 3037 24, 3038 -125, 3039 128, 3040 31, 3041 31, 3042 false, 3043 true, 3044 true, 3045 true, 3046 true, 3047 true, 3048 true, 3049 true 3050 }; 3051 3052 /* SPU Single Precision (Extended-Range Mode) format is the same as IEEE 3053 single precision with the following differences: 3054 - Infinities are not supported. Instead MAX_FLOAT or MIN_FLOAT 3055 are generated. 3056 - NaNs are not supported. 3057 - The range of non-zero numbers in binary is 3058 (001)[1.]000...000 to (255)[1.]111...111. 3059 - Denormals can be represented, but are treated as +0.0 when 3060 used as an operand and are never generated as a result. 3061 - -0.0 can be represented, but a zero result is always +0.0. 3062 - the only supported rounding mode is trunction (towards zero). */ 3063 const struct real_format spu_single_format = 3064 { 3065 encode_ieee_single, 3066 decode_ieee_single, 3067 2, 3068 24, 3069 24, 3070 -125, 3071 129, 3072 31, 3073 31, 3074 true, 3075 false, 3076 false, 3077 false, 3078 true, 3079 true, 3080 false, 3081 false 3082 }; 3083 3084 /* IEEE double-precision format. */ 3085 3086 static void encode_ieee_double (const struct real_format *fmt, 3087 long *, const REAL_VALUE_TYPE *); 3088 static void decode_ieee_double (const struct real_format *, 3089 REAL_VALUE_TYPE *, const long *); 3090 3091 static void 3092 encode_ieee_double (const struct real_format *fmt, long *buf, 3093 const REAL_VALUE_TYPE *r) 3094 { 3095 unsigned long image_lo, image_hi, sig_lo, sig_hi, exp; 3096 bool denormal = (r->sig[SIGSZ-1] & SIG_MSB) == 0; 3097 3098 image_hi = r->sign << 31; 3099 image_lo = 0; 3100 3101 if (HOST_BITS_PER_LONG == 64) 3102 { 3103 sig_hi = r->sig[SIGSZ-1]; 3104 sig_lo = (sig_hi >> (64 - 53)) & 0xffffffff; 3105 sig_hi = (sig_hi >> (64 - 53 + 1) >> 31) & 0xfffff; 3106 } 3107 else 3108 { 3109 sig_hi = r->sig[SIGSZ-1]; 3110 sig_lo = r->sig[SIGSZ-2]; 3111 sig_lo = (sig_hi << 21) | (sig_lo >> 11); 3112 sig_hi = (sig_hi >> 11) & 0xfffff; 3113 } 3114 3115 switch (r->cl) 3116 { 3117 case rvc_zero: 3118 break; 3119 3120 case rvc_inf: 3121 if (fmt->has_inf) 3122 image_hi |= 2047 << 20; 3123 else 3124 { 3125 image_hi |= 0x7fffffff; 3126 image_lo = 0xffffffff; 3127 } 3128 break; 3129 3130 case rvc_nan: 3131 if (fmt->has_nans) 3132 { 3133 if (r->canonical) 3134 { 3135 if (fmt->canonical_nan_lsbs_set) 3136 { 3137 sig_hi = (1 << 19) - 1; 3138 sig_lo = 0xffffffff; 3139 } 3140 else 3141 { 3142 sig_hi = 0; 3143 sig_lo = 0; 3144 } 3145 } 3146 if (r->signalling == fmt->qnan_msb_set) 3147 sig_hi &= ~(1 << 19); 3148 else 3149 sig_hi |= 1 << 19; 3150 if (sig_hi == 0 && sig_lo == 0) 3151 sig_hi = 1 << 18; 3152 3153 image_hi |= 2047 << 20; 3154 image_hi |= sig_hi; 3155 image_lo = sig_lo; 3156 } 3157 else 3158 { 3159 image_hi |= 0x7fffffff; 3160 image_lo = 0xffffffff; 3161 } 3162 break; 3163 3164 case rvc_normal: 3165 /* Recall that IEEE numbers are interpreted as 1.F x 2**exp, 3166 whereas the intermediate representation is 0.F x 2**exp. 3167 Which means we're off by one. */ 3168 if (denormal) 3169 exp = 0; 3170 else 3171 exp = REAL_EXP (r) + 1023 - 1; 3172 image_hi |= exp << 20; 3173 image_hi |= sig_hi; 3174 image_lo = sig_lo; 3175 break; 3176 3177 default: 3178 gcc_unreachable (); 3179 } 3180 3181 if (FLOAT_WORDS_BIG_ENDIAN) 3182 buf[0] = image_hi, buf[1] = image_lo; 3183 else 3184 buf[0] = image_lo, buf[1] = image_hi; 3185 } 3186 3187 static void 3188 decode_ieee_double (const struct real_format *fmt, REAL_VALUE_TYPE *r, 3189 const long *buf) 3190 { 3191 unsigned long image_hi, image_lo; 3192 bool sign; 3193 int exp; 3194 3195 if (FLOAT_WORDS_BIG_ENDIAN) 3196 image_hi = buf[0], image_lo = buf[1]; 3197 else 3198 image_lo = buf[0], image_hi = buf[1]; 3199 image_lo &= 0xffffffff; 3200 image_hi &= 0xffffffff; 3201 3202 sign = (image_hi >> 31) & 1; 3203 exp = (image_hi >> 20) & 0x7ff; 3204 3205 memset (r, 0, sizeof (*r)); 3206 3207 image_hi <<= 32 - 21; 3208 image_hi |= image_lo >> 21; 3209 image_hi &= 0x7fffffff; 3210 image_lo <<= 32 - 21; 3211 3212 if (exp == 0) 3213 { 3214 if ((image_hi || image_lo) && fmt->has_denorm) 3215 { 3216 r->cl = rvc_normal; 3217 r->sign = sign; 3218 SET_REAL_EXP (r, -1022); 3219 if (HOST_BITS_PER_LONG == 32) 3220 { 3221 image_hi = (image_hi << 1) | (image_lo >> 31); 3222 image_lo <<= 1; 3223 r->sig[SIGSZ-1] = image_hi; 3224 r->sig[SIGSZ-2] = image_lo; 3225 } 3226 else 3227 { 3228 image_hi = (image_hi << 31 << 2) | (image_lo << 1); 3229 r->sig[SIGSZ-1] = image_hi; 3230 } 3231 normalize (r); 3232 } 3233 else if (fmt->has_signed_zero) 3234 r->sign = sign; 3235 } 3236 else if (exp == 2047 && (fmt->has_nans || fmt->has_inf)) 3237 { 3238 if (image_hi || image_lo) 3239 { 3240 r->cl = rvc_nan; 3241 r->sign = sign; 3242 r->signalling = ((image_hi >> 30) & 1) ^ fmt->qnan_msb_set; 3243 if (HOST_BITS_PER_LONG == 32) 3244 { 3245 r->sig[SIGSZ-1] = image_hi; 3246 r->sig[SIGSZ-2] = image_lo; 3247 } 3248 else 3249 r->sig[SIGSZ-1] = (image_hi << 31 << 1) | image_lo; 3250 } 3251 else 3252 { 3253 r->cl = rvc_inf; 3254 r->sign = sign; 3255 } 3256 } 3257 else 3258 { 3259 r->cl = rvc_normal; 3260 r->sign = sign; 3261 SET_REAL_EXP (r, exp - 1023 + 1); 3262 if (HOST_BITS_PER_LONG == 32) 3263 { 3264 r->sig[SIGSZ-1] = image_hi | SIG_MSB; 3265 r->sig[SIGSZ-2] = image_lo; 3266 } 3267 else 3268 r->sig[SIGSZ-1] = (image_hi << 31 << 1) | image_lo | SIG_MSB; 3269 } 3270 } 3271 3272 const struct real_format ieee_double_format = 3273 { 3274 encode_ieee_double, 3275 decode_ieee_double, 3276 2, 3277 53, 3278 53, 3279 -1021, 3280 1024, 3281 63, 3282 63, 3283 false, 3284 true, 3285 true, 3286 true, 3287 true, 3288 true, 3289 true, 3290 false 3291 }; 3292 3293 const struct real_format mips_double_format = 3294 { 3295 encode_ieee_double, 3296 decode_ieee_double, 3297 2, 3298 53, 3299 53, 3300 -1021, 3301 1024, 3302 63, 3303 63, 3304 false, 3305 true, 3306 true, 3307 true, 3308 true, 3309 true, 3310 false, 3311 true 3312 }; 3313 3314 const struct real_format motorola_double_format = 3315 { 3316 encode_ieee_double, 3317 decode_ieee_double, 3318 2, 3319 53, 3320 53, 3321 -1021, 3322 1024, 3323 63, 3324 63, 3325 false, 3326 true, 3327 true, 3328 true, 3329 true, 3330 true, 3331 true, 3332 true 3333 }; 3334 3335 /* IEEE extended real format. This comes in three flavors: Intel's as 3336 a 12 byte image, Intel's as a 16 byte image, and Motorola's. Intel 3337 12- and 16-byte images may be big- or little endian; Motorola's is 3338 always big endian. */ 3339 3340 /* Helper subroutine which converts from the internal format to the 3341 12-byte little-endian Intel format. Functions below adjust this 3342 for the other possible formats. */ 3343 static void 3344 encode_ieee_extended (const struct real_format *fmt, long *buf, 3345 const REAL_VALUE_TYPE *r) 3346 { 3347 unsigned long image_hi, sig_hi, sig_lo; 3348 bool denormal = (r->sig[SIGSZ-1] & SIG_MSB) == 0; 3349 3350 image_hi = r->sign << 15; 3351 sig_hi = sig_lo = 0; 3352 3353 switch (r->cl) 3354 { 3355 case rvc_zero: 3356 break; 3357 3358 case rvc_inf: 3359 if (fmt->has_inf) 3360 { 3361 image_hi |= 32767; 3362 3363 /* Intel requires the explicit integer bit to be set, otherwise 3364 it considers the value a "pseudo-infinity". Motorola docs 3365 say it doesn't care. */ 3366 sig_hi = 0x80000000; 3367 } 3368 else 3369 { 3370 image_hi |= 32767; 3371 sig_lo = sig_hi = 0xffffffff; 3372 } 3373 break; 3374 3375 case rvc_nan: 3376 if (fmt->has_nans) 3377 { 3378 image_hi |= 32767; 3379 if (r->canonical) 3380 { 3381 if (fmt->canonical_nan_lsbs_set) 3382 { 3383 sig_hi = (1 << 30) - 1; 3384 sig_lo = 0xffffffff; 3385 } 3386 } 3387 else if (HOST_BITS_PER_LONG == 32) 3388 { 3389 sig_hi = r->sig[SIGSZ-1]; 3390 sig_lo = r->sig[SIGSZ-2]; 3391 } 3392 else 3393 { 3394 sig_lo = r->sig[SIGSZ-1]; 3395 sig_hi = sig_lo >> 31 >> 1; 3396 sig_lo &= 0xffffffff; 3397 } 3398 if (r->signalling == fmt->qnan_msb_set) 3399 sig_hi &= ~(1 << 30); 3400 else 3401 sig_hi |= 1 << 30; 3402 if ((sig_hi & 0x7fffffff) == 0 && sig_lo == 0) 3403 sig_hi = 1 << 29; 3404 3405 /* Intel requires the explicit integer bit to be set, otherwise 3406 it considers the value a "pseudo-nan". Motorola docs say it 3407 doesn't care. */ 3408 sig_hi |= 0x80000000; 3409 } 3410 else 3411 { 3412 image_hi |= 32767; 3413 sig_lo = sig_hi = 0xffffffff; 3414 } 3415 break; 3416 3417 case rvc_normal: 3418 { 3419 int exp = REAL_EXP (r); 3420 3421 /* Recall that IEEE numbers are interpreted as 1.F x 2**exp, 3422 whereas the intermediate representation is 0.F x 2**exp. 3423 Which means we're off by one. 3424 3425 Except for Motorola, which consider exp=0 and explicit 3426 integer bit set to continue to be normalized. In theory 3427 this discrepancy has been taken care of by the difference 3428 in fmt->emin in round_for_format. */ 3429 3430 if (denormal) 3431 exp = 0; 3432 else 3433 { 3434 exp += 16383 - 1; 3435 gcc_assert (exp >= 0); 3436 } 3437 image_hi |= exp; 3438 3439 if (HOST_BITS_PER_LONG == 32) 3440 { 3441 sig_hi = r->sig[SIGSZ-1]; 3442 sig_lo = r->sig[SIGSZ-2]; 3443 } 3444 else 3445 { 3446 sig_lo = r->sig[SIGSZ-1]; 3447 sig_hi = sig_lo >> 31 >> 1; 3448 sig_lo &= 0xffffffff; 3449 } 3450 } 3451 break; 3452 3453 default: 3454 gcc_unreachable (); 3455 } 3456 3457 buf[0] = sig_lo, buf[1] = sig_hi, buf[2] = image_hi; 3458 } 3459 3460 /* Convert from the internal format to the 12-byte Motorola format 3461 for an IEEE extended real. */ 3462 static void 3463 encode_ieee_extended_motorola (const struct real_format *fmt, long *buf, 3464 const REAL_VALUE_TYPE *r) 3465 { 3466 long intermed[3]; 3467 encode_ieee_extended (fmt, intermed, r); 3468 3469 /* Motorola chips are assumed always to be big-endian. Also, the 3470 padding in a Motorola extended real goes between the exponent and 3471 the mantissa. At this point the mantissa is entirely within 3472 elements 0 and 1 of intermed, and the exponent entirely within 3473 element 2, so all we have to do is swap the order around, and 3474 shift element 2 left 16 bits. */ 3475 buf[0] = intermed[2] << 16; 3476 buf[1] = intermed[1]; 3477 buf[2] = intermed[0]; 3478 } 3479 3480 /* Convert from the internal format to the 12-byte Intel format for 3481 an IEEE extended real. */ 3482 static void 3483 encode_ieee_extended_intel_96 (const struct real_format *fmt, long *buf, 3484 const REAL_VALUE_TYPE *r) 3485 { 3486 if (FLOAT_WORDS_BIG_ENDIAN) 3487 { 3488 /* All the padding in an Intel-format extended real goes at the high 3489 end, which in this case is after the mantissa, not the exponent. 3490 Therefore we must shift everything down 16 bits. */ 3491 long intermed[3]; 3492 encode_ieee_extended (fmt, intermed, r); 3493 buf[0] = ((intermed[2] << 16) | ((unsigned long)(intermed[1] & 0xFFFF0000) >> 16)); 3494 buf[1] = ((intermed[1] << 16) | ((unsigned long)(intermed[0] & 0xFFFF0000) >> 16)); 3495 buf[2] = (intermed[0] << 16); 3496 } 3497 else 3498 /* encode_ieee_extended produces what we want directly. */ 3499 encode_ieee_extended (fmt, buf, r); 3500 } 3501 3502 /* Convert from the internal format to the 16-byte Intel format for 3503 an IEEE extended real. */ 3504 static void 3505 encode_ieee_extended_intel_128 (const struct real_format *fmt, long *buf, 3506 const REAL_VALUE_TYPE *r) 3507 { 3508 /* All the padding in an Intel-format extended real goes at the high end. */ 3509 encode_ieee_extended_intel_96 (fmt, buf, r); 3510 buf[3] = 0; 3511 } 3512 3513 /* As above, we have a helper function which converts from 12-byte 3514 little-endian Intel format to internal format. Functions below 3515 adjust for the other possible formats. */ 3516 static void 3517 decode_ieee_extended (const struct real_format *fmt, REAL_VALUE_TYPE *r, 3518 const long *buf) 3519 { 3520 unsigned long image_hi, sig_hi, sig_lo; 3521 bool sign; 3522 int exp; 3523 3524 sig_lo = buf[0], sig_hi = buf[1], image_hi = buf[2]; 3525 sig_lo &= 0xffffffff; 3526 sig_hi &= 0xffffffff; 3527 image_hi &= 0xffffffff; 3528 3529 sign = (image_hi >> 15) & 1; 3530 exp = image_hi & 0x7fff; 3531 3532 memset (r, 0, sizeof (*r)); 3533 3534 if (exp == 0) 3535 { 3536 if ((sig_hi || sig_lo) && fmt->has_denorm) 3537 { 3538 r->cl = rvc_normal; 3539 r->sign = sign; 3540 3541 /* When the IEEE format contains a hidden bit, we know that 3542 it's zero at this point, and so shift up the significand 3543 and decrease the exponent to match. In this case, Motorola 3544 defines the explicit integer bit to be valid, so we don't 3545 know whether the msb is set or not. */ 3546 SET_REAL_EXP (r, fmt->emin); 3547 if (HOST_BITS_PER_LONG == 32) 3548 { 3549 r->sig[SIGSZ-1] = sig_hi; 3550 r->sig[SIGSZ-2] = sig_lo; 3551 } 3552 else 3553 r->sig[SIGSZ-1] = (sig_hi << 31 << 1) | sig_lo; 3554 3555 normalize (r); 3556 } 3557 else if (fmt->has_signed_zero) 3558 r->sign = sign; 3559 } 3560 else if (exp == 32767 && (fmt->has_nans || fmt->has_inf)) 3561 { 3562 /* See above re "pseudo-infinities" and "pseudo-nans". 3563 Short summary is that the MSB will likely always be 3564 set, and that we don't care about it. */ 3565 sig_hi &= 0x7fffffff; 3566 3567 if (sig_hi || sig_lo) 3568 { 3569 r->cl = rvc_nan; 3570 r->sign = sign; 3571 r->signalling = ((sig_hi >> 30) & 1) ^ fmt->qnan_msb_set; 3572 if (HOST_BITS_PER_LONG == 32) 3573 { 3574 r->sig[SIGSZ-1] = sig_hi; 3575 r->sig[SIGSZ-2] = sig_lo; 3576 } 3577 else 3578 r->sig[SIGSZ-1] = (sig_hi << 31 << 1) | sig_lo; 3579 } 3580 else 3581 { 3582 r->cl = rvc_inf; 3583 r->sign = sign; 3584 } 3585 } 3586 else 3587 { 3588 r->cl = rvc_normal; 3589 r->sign = sign; 3590 SET_REAL_EXP (r, exp - 16383 + 1); 3591 if (HOST_BITS_PER_LONG == 32) 3592 { 3593 r->sig[SIGSZ-1] = sig_hi; 3594 r->sig[SIGSZ-2] = sig_lo; 3595 } 3596 else 3597 r->sig[SIGSZ-1] = (sig_hi << 31 << 1) | sig_lo; 3598 } 3599 } 3600 3601 /* Convert from the internal format to the 12-byte Motorola format 3602 for an IEEE extended real. */ 3603 static void 3604 decode_ieee_extended_motorola (const struct real_format *fmt, REAL_VALUE_TYPE *r, 3605 const long *buf) 3606 { 3607 long intermed[3]; 3608 3609 /* Motorola chips are assumed always to be big-endian. Also, the 3610 padding in a Motorola extended real goes between the exponent and 3611 the mantissa; remove it. */ 3612 intermed[0] = buf[2]; 3613 intermed[1] = buf[1]; 3614 intermed[2] = (unsigned long)buf[0] >> 16; 3615 3616 decode_ieee_extended (fmt, r, intermed); 3617 } 3618 3619 /* Convert from the internal format to the 12-byte Intel format for 3620 an IEEE extended real. */ 3621 static void 3622 decode_ieee_extended_intel_96 (const struct real_format *fmt, REAL_VALUE_TYPE *r, 3623 const long *buf) 3624 { 3625 if (FLOAT_WORDS_BIG_ENDIAN) 3626 { 3627 /* All the padding in an Intel-format extended real goes at the high 3628 end, which in this case is after the mantissa, not the exponent. 3629 Therefore we must shift everything up 16 bits. */ 3630 long intermed[3]; 3631 3632 intermed[0] = (((unsigned long)buf[2] >> 16) | (buf[1] << 16)); 3633 intermed[1] = (((unsigned long)buf[1] >> 16) | (buf[0] << 16)); 3634 intermed[2] = ((unsigned long)buf[0] >> 16); 3635 3636 decode_ieee_extended (fmt, r, intermed); 3637 } 3638 else 3639 /* decode_ieee_extended produces what we want directly. */ 3640 decode_ieee_extended (fmt, r, buf); 3641 } 3642 3643 /* Convert from the internal format to the 16-byte Intel format for 3644 an IEEE extended real. */ 3645 static void 3646 decode_ieee_extended_intel_128 (const struct real_format *fmt, REAL_VALUE_TYPE *r, 3647 const long *buf) 3648 { 3649 /* All the padding in an Intel-format extended real goes at the high end. */ 3650 decode_ieee_extended_intel_96 (fmt, r, buf); 3651 } 3652 3653 const struct real_format ieee_extended_motorola_format = 3654 { 3655 encode_ieee_extended_motorola, 3656 decode_ieee_extended_motorola, 3657 2, 3658 64, 3659 64, 3660 -16382, 3661 16384, 3662 95, 3663 95, 3664 false, 3665 true, 3666 true, 3667 true, 3668 true, 3669 true, 3670 true, 3671 true 3672 }; 3673 3674 const struct real_format ieee_extended_intel_96_format = 3675 { 3676 encode_ieee_extended_intel_96, 3677 decode_ieee_extended_intel_96, 3678 2, 3679 64, 3680 64, 3681 -16381, 3682 16384, 3683 79, 3684 79, 3685 false, 3686 true, 3687 true, 3688 true, 3689 true, 3690 true, 3691 true, 3692 false 3693 }; 3694 3695 const struct real_format ieee_extended_intel_128_format = 3696 { 3697 encode_ieee_extended_intel_128, 3698 decode_ieee_extended_intel_128, 3699 2, 3700 64, 3701 64, 3702 -16381, 3703 16384, 3704 79, 3705 79, 3706 false, 3707 true, 3708 true, 3709 true, 3710 true, 3711 true, 3712 true, 3713 false 3714 }; 3715 3716 /* The following caters to i386 systems that set the rounding precision 3717 to 53 bits instead of 64, e.g. FreeBSD. */ 3718 const struct real_format ieee_extended_intel_96_round_53_format = 3719 { 3720 encode_ieee_extended_intel_96, 3721 decode_ieee_extended_intel_96, 3722 2, 3723 53, 3724 53, 3725 -16381, 3726 16384, 3727 79, 3728 79, 3729 false, 3730 true, 3731 true, 3732 true, 3733 true, 3734 true, 3735 true, 3736 false 3737 }; 3738 3739 /* IBM 128-bit extended precision format: a pair of IEEE double precision 3740 numbers whose sum is equal to the extended precision value. The number 3741 with greater magnitude is first. This format has the same magnitude 3742 range as an IEEE double precision value, but effectively 106 bits of 3743 significand precision. Infinity and NaN are represented by their IEEE 3744 double precision value stored in the first number, the second number is 3745 +0.0 or -0.0 for Infinity and don't-care for NaN. */ 3746 3747 static void encode_ibm_extended (const struct real_format *fmt, 3748 long *, const REAL_VALUE_TYPE *); 3749 static void decode_ibm_extended (const struct real_format *, 3750 REAL_VALUE_TYPE *, const long *); 3751 3752 static void 3753 encode_ibm_extended (const struct real_format *fmt, long *buf, 3754 const REAL_VALUE_TYPE *r) 3755 { 3756 REAL_VALUE_TYPE u, normr, v; 3757 const struct real_format *base_fmt; 3758 3759 base_fmt = fmt->qnan_msb_set ? &ieee_double_format : &mips_double_format; 3760 3761 /* Renormalize R before doing any arithmetic on it. */ 3762 normr = *r; 3763 if (normr.cl == rvc_normal) 3764 normalize (&normr); 3765 3766 /* u = IEEE double precision portion of significand. */ 3767 u = normr; 3768 round_for_format (base_fmt, &u); 3769 encode_ieee_double (base_fmt, &buf[0], &u); 3770 3771 if (u.cl == rvc_normal) 3772 { 3773 do_add (&v, &normr, &u, 1); 3774 /* Call round_for_format since we might need to denormalize. */ 3775 round_for_format (base_fmt, &v); 3776 encode_ieee_double (base_fmt, &buf[2], &v); 3777 } 3778 else 3779 { 3780 /* Inf, NaN, 0 are all representable as doubles, so the 3781 least-significant part can be 0.0. */ 3782 buf[2] = 0; 3783 buf[3] = 0; 3784 } 3785 } 3786 3787 static void 3788 decode_ibm_extended (const struct real_format *fmt ATTRIBUTE_UNUSED, REAL_VALUE_TYPE *r, 3789 const long *buf) 3790 { 3791 REAL_VALUE_TYPE u, v; 3792 const struct real_format *base_fmt; 3793 3794 base_fmt = fmt->qnan_msb_set ? &ieee_double_format : &mips_double_format; 3795 decode_ieee_double (base_fmt, &u, &buf[0]); 3796 3797 if (u.cl != rvc_zero && u.cl != rvc_inf && u.cl != rvc_nan) 3798 { 3799 decode_ieee_double (base_fmt, &v, &buf[2]); 3800 do_add (r, &u, &v, 0); 3801 } 3802 else 3803 *r = u; 3804 } 3805 3806 const struct real_format ibm_extended_format = 3807 { 3808 encode_ibm_extended, 3809 decode_ibm_extended, 3810 2, 3811 53 + 53, 3812 53, 3813 -1021 + 53, 3814 1024, 3815 127, 3816 -1, 3817 false, 3818 true, 3819 true, 3820 true, 3821 true, 3822 true, 3823 true, 3824 false 3825 }; 3826 3827 const struct real_format mips_extended_format = 3828 { 3829 encode_ibm_extended, 3830 decode_ibm_extended, 3831 2, 3832 53 + 53, 3833 53, 3834 -1021 + 53, 3835 1024, 3836 127, 3837 -1, 3838 false, 3839 true, 3840 true, 3841 true, 3842 true, 3843 true, 3844 false, 3845 true 3846 }; 3847 3848 3849 /* IEEE quad precision format. */ 3850 3851 static void encode_ieee_quad (const struct real_format *fmt, 3852 long *, const REAL_VALUE_TYPE *); 3853 static void decode_ieee_quad (const struct real_format *, 3854 REAL_VALUE_TYPE *, const long *); 3855 3856 static void 3857 encode_ieee_quad (const struct real_format *fmt, long *buf, 3858 const REAL_VALUE_TYPE *r) 3859 { 3860 unsigned long image3, image2, image1, image0, exp; 3861 bool denormal = (r->sig[SIGSZ-1] & SIG_MSB) == 0; 3862 REAL_VALUE_TYPE u; 3863 3864 image3 = r->sign << 31; 3865 image2 = 0; 3866 image1 = 0; 3867 image0 = 0; 3868 3869 rshift_significand (&u, r, SIGNIFICAND_BITS - 113); 3870 3871 switch (r->cl) 3872 { 3873 case rvc_zero: 3874 break; 3875 3876 case rvc_inf: 3877 if (fmt->has_inf) 3878 image3 |= 32767 << 16; 3879 else 3880 { 3881 image3 |= 0x7fffffff; 3882 image2 = 0xffffffff; 3883 image1 = 0xffffffff; 3884 image0 = 0xffffffff; 3885 } 3886 break; 3887 3888 case rvc_nan: 3889 if (fmt->has_nans) 3890 { 3891 image3 |= 32767 << 16; 3892 3893 if (r->canonical) 3894 { 3895 if (fmt->canonical_nan_lsbs_set) 3896 { 3897 image3 |= 0x7fff; 3898 image2 = image1 = image0 = 0xffffffff; 3899 } 3900 } 3901 else if (HOST_BITS_PER_LONG == 32) 3902 { 3903 image0 = u.sig[0]; 3904 image1 = u.sig[1]; 3905 image2 = u.sig[2]; 3906 image3 |= u.sig[3] & 0xffff; 3907 } 3908 else 3909 { 3910 image0 = u.sig[0]; 3911 image1 = image0 >> 31 >> 1; 3912 image2 = u.sig[1]; 3913 image3 |= (image2 >> 31 >> 1) & 0xffff; 3914 image0 &= 0xffffffff; 3915 image2 &= 0xffffffff; 3916 } 3917 if (r->signalling == fmt->qnan_msb_set) 3918 image3 &= ~0x8000; 3919 else 3920 image3 |= 0x8000; 3921 if (((image3 & 0xffff) | image2 | image1 | image0) == 0) 3922 image3 |= 0x4000; 3923 } 3924 else 3925 { 3926 image3 |= 0x7fffffff; 3927 image2 = 0xffffffff; 3928 image1 = 0xffffffff; 3929 image0 = 0xffffffff; 3930 } 3931 break; 3932 3933 case rvc_normal: 3934 /* Recall that IEEE numbers are interpreted as 1.F x 2**exp, 3935 whereas the intermediate representation is 0.F x 2**exp. 3936 Which means we're off by one. */ 3937 if (denormal) 3938 exp = 0; 3939 else 3940 exp = REAL_EXP (r) + 16383 - 1; 3941 image3 |= exp << 16; 3942 3943 if (HOST_BITS_PER_LONG == 32) 3944 { 3945 image0 = u.sig[0]; 3946 image1 = u.sig[1]; 3947 image2 = u.sig[2]; 3948 image3 |= u.sig[3] & 0xffff; 3949 } 3950 else 3951 { 3952 image0 = u.sig[0]; 3953 image1 = image0 >> 31 >> 1; 3954 image2 = u.sig[1]; 3955 image3 |= (image2 >> 31 >> 1) & 0xffff; 3956 image0 &= 0xffffffff; 3957 image2 &= 0xffffffff; 3958 } 3959 break; 3960 3961 default: 3962 gcc_unreachable (); 3963 } 3964 3965 if (FLOAT_WORDS_BIG_ENDIAN) 3966 { 3967 buf[0] = image3; 3968 buf[1] = image2; 3969 buf[2] = image1; 3970 buf[3] = image0; 3971 } 3972 else 3973 { 3974 buf[0] = image0; 3975 buf[1] = image1; 3976 buf[2] = image2; 3977 buf[3] = image3; 3978 } 3979 } 3980 3981 static void 3982 decode_ieee_quad (const struct real_format *fmt, REAL_VALUE_TYPE *r, 3983 const long *buf) 3984 { 3985 unsigned long image3, image2, image1, image0; 3986 bool sign; 3987 int exp; 3988 3989 if (FLOAT_WORDS_BIG_ENDIAN) 3990 { 3991 image3 = buf[0]; 3992 image2 = buf[1]; 3993 image1 = buf[2]; 3994 image0 = buf[3]; 3995 } 3996 else 3997 { 3998 image0 = buf[0]; 3999 image1 = buf[1]; 4000 image2 = buf[2]; 4001 image3 = buf[3]; 4002 } 4003 image0 &= 0xffffffff; 4004 image1 &= 0xffffffff; 4005 image2 &= 0xffffffff; 4006 4007 sign = (image3 >> 31) & 1; 4008 exp = (image3 >> 16) & 0x7fff; 4009 image3 &= 0xffff; 4010 4011 memset (r, 0, sizeof (*r)); 4012 4013 if (exp == 0) 4014 { 4015 if ((image3 | image2 | image1 | image0) && fmt->has_denorm) 4016 { 4017 r->cl = rvc_normal; 4018 r->sign = sign; 4019 4020 SET_REAL_EXP (r, -16382 + (SIGNIFICAND_BITS - 112)); 4021 if (HOST_BITS_PER_LONG == 32) 4022 { 4023 r->sig[0] = image0; 4024 r->sig[1] = image1; 4025 r->sig[2] = image2; 4026 r->sig[3] = image3; 4027 } 4028 else 4029 { 4030 r->sig[0] = (image1 << 31 << 1) | image0; 4031 r->sig[1] = (image3 << 31 << 1) | image2; 4032 } 4033 4034 normalize (r); 4035 } 4036 else if (fmt->has_signed_zero) 4037 r->sign = sign; 4038 } 4039 else if (exp == 32767 && (fmt->has_nans || fmt->has_inf)) 4040 { 4041 if (image3 | image2 | image1 | image0) 4042 { 4043 r->cl = rvc_nan; 4044 r->sign = sign; 4045 r->signalling = ((image3 >> 15) & 1) ^ fmt->qnan_msb_set; 4046 4047 if (HOST_BITS_PER_LONG == 32) 4048 { 4049 r->sig[0] = image0; 4050 r->sig[1] = image1; 4051 r->sig[2] = image2; 4052 r->sig[3] = image3; 4053 } 4054 else 4055 { 4056 r->sig[0] = (image1 << 31 << 1) | image0; 4057 r->sig[1] = (image3 << 31 << 1) | image2; 4058 } 4059 lshift_significand (r, r, SIGNIFICAND_BITS - 113); 4060 } 4061 else 4062 { 4063 r->cl = rvc_inf; 4064 r->sign = sign; 4065 } 4066 } 4067 else 4068 { 4069 r->cl = rvc_normal; 4070 r->sign = sign; 4071 SET_REAL_EXP (r, exp - 16383 + 1); 4072 4073 if (HOST_BITS_PER_LONG == 32) 4074 { 4075 r->sig[0] = image0; 4076 r->sig[1] = image1; 4077 r->sig[2] = image2; 4078 r->sig[3] = image3; 4079 } 4080 else 4081 { 4082 r->sig[0] = (image1 << 31 << 1) | image0; 4083 r->sig[1] = (image3 << 31 << 1) | image2; 4084 } 4085 lshift_significand (r, r, SIGNIFICAND_BITS - 113); 4086 r->sig[SIGSZ-1] |= SIG_MSB; 4087 } 4088 } 4089 4090 const struct real_format ieee_quad_format = 4091 { 4092 encode_ieee_quad, 4093 decode_ieee_quad, 4094 2, 4095 113, 4096 113, 4097 -16381, 4098 16384, 4099 127, 4100 127, 4101 false, 4102 true, 4103 true, 4104 true, 4105 true, 4106 true, 4107 true, 4108 false 4109 }; 4110 4111 const struct real_format mips_quad_format = 4112 { 4113 encode_ieee_quad, 4114 decode_ieee_quad, 4115 2, 4116 113, 4117 113, 4118 -16381, 4119 16384, 4120 127, 4121 127, 4122 false, 4123 true, 4124 true, 4125 true, 4126 true, 4127 true, 4128 false, 4129 true 4130 }; 4131 4132 /* Descriptions of VAX floating point formats can be found beginning at 4133 4134 http://h71000.www7.hp.com/doc/73FINAL/4515/4515pro_013.html#f_floating_point_format 4135 4136 The thing to remember is that they're almost IEEE, except for word 4137 order, exponent bias, and the lack of infinities, nans, and denormals. 4138 4139 We don't implement the H_floating format here, simply because neither 4140 the VAX or Alpha ports use it. */ 4141 4142 static void encode_vax_f (const struct real_format *fmt, 4143 long *, const REAL_VALUE_TYPE *); 4144 static void decode_vax_f (const struct real_format *, 4145 REAL_VALUE_TYPE *, const long *); 4146 static void encode_vax_d (const struct real_format *fmt, 4147 long *, const REAL_VALUE_TYPE *); 4148 static void decode_vax_d (const struct real_format *, 4149 REAL_VALUE_TYPE *, const long *); 4150 static void encode_vax_g (const struct real_format *fmt, 4151 long *, const REAL_VALUE_TYPE *); 4152 static void decode_vax_g (const struct real_format *, 4153 REAL_VALUE_TYPE *, const long *); 4154 4155 static void 4156 encode_vax_f (const struct real_format *fmt ATTRIBUTE_UNUSED, long *buf, 4157 const REAL_VALUE_TYPE *r) 4158 { 4159 unsigned long sign, exp, sig, image; 4160 4161 sign = r->sign << 15; 4162 4163 switch (r->cl) 4164 { 4165 case rvc_zero: 4166 image = 0; 4167 break; 4168 4169 case rvc_inf: 4170 case rvc_nan: 4171 image = 0xffff7fff | sign; 4172 break; 4173 4174 case rvc_normal: 4175 sig = (r->sig[SIGSZ-1] >> (HOST_BITS_PER_LONG - 24)) & 0x7fffff; 4176 exp = REAL_EXP (r) + 128; 4177 4178 image = (sig << 16) & 0xffff0000; 4179 image |= sign; 4180 image |= exp << 7; 4181 image |= sig >> 16; 4182 break; 4183 4184 default: 4185 gcc_unreachable (); 4186 } 4187 4188 buf[0] = image; 4189 } 4190 4191 static void 4192 decode_vax_f (const struct real_format *fmt ATTRIBUTE_UNUSED, 4193 REAL_VALUE_TYPE *r, const long *buf) 4194 { 4195 unsigned long image = buf[0] & 0xffffffff; 4196 int exp = (image >> 7) & 0xff; 4197 4198 memset (r, 0, sizeof (*r)); 4199 4200 if (exp != 0) 4201 { 4202 r->cl = rvc_normal; 4203 r->sign = (image >> 15) & 1; 4204 SET_REAL_EXP (r, exp - 128); 4205 4206 image = ((image & 0x7f) << 16) | ((image >> 16) & 0xffff); 4207 r->sig[SIGSZ-1] = (image << (HOST_BITS_PER_LONG - 24)) | SIG_MSB; 4208 } 4209 } 4210 4211 static void 4212 encode_vax_d (const struct real_format *fmt ATTRIBUTE_UNUSED, long *buf, 4213 const REAL_VALUE_TYPE *r) 4214 { 4215 unsigned long image0, image1, sign = r->sign << 15; 4216 4217 switch (r->cl) 4218 { 4219 case rvc_zero: 4220 image0 = image1 = 0; 4221 break; 4222 4223 case rvc_inf: 4224 case rvc_nan: 4225 image0 = 0xffff7fff | sign; 4226 image1 = 0xffffffff; 4227 break; 4228 4229 case rvc_normal: 4230 /* Extract the significand into straight hi:lo. */ 4231 if (HOST_BITS_PER_LONG == 64) 4232 { 4233 image0 = r->sig[SIGSZ-1]; 4234 image1 = (image0 >> (64 - 56)) & 0xffffffff; 4235 image0 = (image0 >> (64 - 56 + 1) >> 31) & 0x7fffff; 4236 } 4237 else 4238 { 4239 image0 = r->sig[SIGSZ-1]; 4240 image1 = r->sig[SIGSZ-2]; 4241 image1 = (image0 << 24) | (image1 >> 8); 4242 image0 = (image0 >> 8) & 0xffffff; 4243 } 4244 4245 /* Rearrange the half-words of the significand to match the 4246 external format. */ 4247 image0 = ((image0 << 16) | (image0 >> 16)) & 0xffff007f; 4248 image1 = ((image1 << 16) | (image1 >> 16)) & 0xffffffff; 4249 4250 /* Add the sign and exponent. */ 4251 image0 |= sign; 4252 image0 |= (REAL_EXP (r) + 128) << 7; 4253 break; 4254 4255 default: 4256 gcc_unreachable (); 4257 } 4258 4259 if (FLOAT_WORDS_BIG_ENDIAN) 4260 buf[0] = image1, buf[1] = image0; 4261 else 4262 buf[0] = image0, buf[1] = image1; 4263 } 4264 4265 static void 4266 decode_vax_d (const struct real_format *fmt ATTRIBUTE_UNUSED, 4267 REAL_VALUE_TYPE *r, const long *buf) 4268 { 4269 unsigned long image0, image1; 4270 int exp; 4271 4272 if (FLOAT_WORDS_BIG_ENDIAN) 4273 image1 = buf[0], image0 = buf[1]; 4274 else 4275 image0 = buf[0], image1 = buf[1]; 4276 image0 &= 0xffffffff; 4277 image1 &= 0xffffffff; 4278 4279 exp = (image0 >> 7) & 0xff; 4280 4281 memset (r, 0, sizeof (*r)); 4282 4283 if (exp != 0) 4284 { 4285 r->cl = rvc_normal; 4286 r->sign = (image0 >> 15) & 1; 4287 SET_REAL_EXP (r, exp - 128); 4288 4289 /* Rearrange the half-words of the external format into 4290 proper ascending order. */ 4291 image0 = ((image0 & 0x7f) << 16) | ((image0 >> 16) & 0xffff); 4292 image1 = ((image1 & 0xffff) << 16) | ((image1 >> 16) & 0xffff); 4293 4294 if (HOST_BITS_PER_LONG == 64) 4295 { 4296 image0 = (image0 << 31 << 1) | image1; 4297 image0 <<= 64 - 56; 4298 image0 |= SIG_MSB; 4299 r->sig[SIGSZ-1] = image0; 4300 } 4301 else 4302 { 4303 r->sig[SIGSZ-1] = image0; 4304 r->sig[SIGSZ-2] = image1; 4305 lshift_significand (r, r, 2*HOST_BITS_PER_LONG - 56); 4306 r->sig[SIGSZ-1] |= SIG_MSB; 4307 } 4308 } 4309 } 4310 4311 static void 4312 encode_vax_g (const struct real_format *fmt ATTRIBUTE_UNUSED, long *buf, 4313 const REAL_VALUE_TYPE *r) 4314 { 4315 unsigned long image0, image1, sign = r->sign << 15; 4316 4317 switch (r->cl) 4318 { 4319 case rvc_zero: 4320 image0 = image1 = 0; 4321 break; 4322 4323 case rvc_inf: 4324 case rvc_nan: 4325 image0 = 0xffff7fff | sign; 4326 image1 = 0xffffffff; 4327 break; 4328 4329 case rvc_normal: 4330 /* Extract the significand into straight hi:lo. */ 4331 if (HOST_BITS_PER_LONG == 64) 4332 { 4333 image0 = r->sig[SIGSZ-1]; 4334 image1 = (image0 >> (64 - 53)) & 0xffffffff; 4335 image0 = (image0 >> (64 - 53 + 1) >> 31) & 0xfffff; 4336 } 4337 else 4338 { 4339 image0 = r->sig[SIGSZ-1]; 4340 image1 = r->sig[SIGSZ-2]; 4341 image1 = (image0 << 21) | (image1 >> 11); 4342 image0 = (image0 >> 11) & 0xfffff; 4343 } 4344 4345 /* Rearrange the half-words of the significand to match the 4346 external format. */ 4347 image0 = ((image0 << 16) | (image0 >> 16)) & 0xffff000f; 4348 image1 = ((image1 << 16) | (image1 >> 16)) & 0xffffffff; 4349 4350 /* Add the sign and exponent. */ 4351 image0 |= sign; 4352 image0 |= (REAL_EXP (r) + 1024) << 4; 4353 break; 4354 4355 default: 4356 gcc_unreachable (); 4357 } 4358 4359 if (FLOAT_WORDS_BIG_ENDIAN) 4360 buf[0] = image1, buf[1] = image0; 4361 else 4362 buf[0] = image0, buf[1] = image1; 4363 } 4364 4365 static void 4366 decode_vax_g (const struct real_format *fmt ATTRIBUTE_UNUSED, 4367 REAL_VALUE_TYPE *r, const long *buf) 4368 { 4369 unsigned long image0, image1; 4370 int exp; 4371 4372 if (FLOAT_WORDS_BIG_ENDIAN) 4373 image1 = buf[0], image0 = buf[1]; 4374 else 4375 image0 = buf[0], image1 = buf[1]; 4376 image0 &= 0xffffffff; 4377 image1 &= 0xffffffff; 4378 4379 exp = (image0 >> 4) & 0x7ff; 4380 4381 memset (r, 0, sizeof (*r)); 4382 4383 if (exp != 0) 4384 { 4385 r->cl = rvc_normal; 4386 r->sign = (image0 >> 15) & 1; 4387 SET_REAL_EXP (r, exp - 1024); 4388 4389 /* Rearrange the half-words of the external format into 4390 proper ascending order. */ 4391 image0 = ((image0 & 0xf) << 16) | ((image0 >> 16) & 0xffff); 4392 image1 = ((image1 & 0xffff) << 16) | ((image1 >> 16) & 0xffff); 4393 4394 if (HOST_BITS_PER_LONG == 64) 4395 { 4396 image0 = (image0 << 31 << 1) | image1; 4397 image0 <<= 64 - 53; 4398 image0 |= SIG_MSB; 4399 r->sig[SIGSZ-1] = image0; 4400 } 4401 else 4402 { 4403 r->sig[SIGSZ-1] = image0; 4404 r->sig[SIGSZ-2] = image1; 4405 lshift_significand (r, r, 64 - 53); 4406 r->sig[SIGSZ-1] |= SIG_MSB; 4407 } 4408 } 4409 } 4410 4411 const struct real_format vax_f_format = 4412 { 4413 encode_vax_f, 4414 decode_vax_f, 4415 2, 4416 24, 4417 24, 4418 -127, 4419 127, 4420 15, 4421 15, 4422 false, 4423 false, 4424 false, 4425 false, 4426 false, 4427 false, 4428 false, 4429 false 4430 }; 4431 4432 const struct real_format vax_d_format = 4433 { 4434 encode_vax_d, 4435 decode_vax_d, 4436 2, 4437 56, 4438 56, 4439 -127, 4440 127, 4441 15, 4442 15, 4443 false, 4444 false, 4445 false, 4446 false, 4447 false, 4448 false, 4449 false, 4450 false 4451 }; 4452 4453 const struct real_format vax_g_format = 4454 { 4455 encode_vax_g, 4456 decode_vax_g, 4457 2, 4458 53, 4459 53, 4460 -1023, 4461 1023, 4462 15, 4463 15, 4464 false, 4465 false, 4466 false, 4467 false, 4468 false, 4469 false, 4470 false, 4471 false 4472 }; 4473 4474 /* Encode real R into a single precision DFP value in BUF. */ 4475 static void 4476 encode_decimal_single (const struct real_format *fmt ATTRIBUTE_UNUSED, 4477 long *buf ATTRIBUTE_UNUSED, 4478 const REAL_VALUE_TYPE *r ATTRIBUTE_UNUSED) 4479 { 4480 encode_decimal32 (fmt, buf, r); 4481 } 4482 4483 /* Decode a single precision DFP value in BUF into a real R. */ 4484 static void 4485 decode_decimal_single (const struct real_format *fmt ATTRIBUTE_UNUSED, 4486 REAL_VALUE_TYPE *r ATTRIBUTE_UNUSED, 4487 const long *buf ATTRIBUTE_UNUSED) 4488 { 4489 decode_decimal32 (fmt, r, buf); 4490 } 4491 4492 /* Encode real R into a double precision DFP value in BUF. */ 4493 static void 4494 encode_decimal_double (const struct real_format *fmt ATTRIBUTE_UNUSED, 4495 long *buf ATTRIBUTE_UNUSED, 4496 const REAL_VALUE_TYPE *r ATTRIBUTE_UNUSED) 4497 { 4498 encode_decimal64 (fmt, buf, r); 4499 } 4500 4501 /* Decode a double precision DFP value in BUF into a real R. */ 4502 static void 4503 decode_decimal_double (const struct real_format *fmt ATTRIBUTE_UNUSED, 4504 REAL_VALUE_TYPE *r ATTRIBUTE_UNUSED, 4505 const long *buf ATTRIBUTE_UNUSED) 4506 { 4507 decode_decimal64 (fmt, r, buf); 4508 } 4509 4510 /* Encode real R into a quad precision DFP value in BUF. */ 4511 static void 4512 encode_decimal_quad (const struct real_format *fmt ATTRIBUTE_UNUSED, 4513 long *buf ATTRIBUTE_UNUSED, 4514 const REAL_VALUE_TYPE *r ATTRIBUTE_UNUSED) 4515 { 4516 encode_decimal128 (fmt, buf, r); 4517 } 4518 4519 /* Decode a quad precision DFP value in BUF into a real R. */ 4520 static void 4521 decode_decimal_quad (const struct real_format *fmt ATTRIBUTE_UNUSED, 4522 REAL_VALUE_TYPE *r ATTRIBUTE_UNUSED, 4523 const long *buf ATTRIBUTE_UNUSED) 4524 { 4525 decode_decimal128 (fmt, r, buf); 4526 } 4527 4528 /* Single precision decimal floating point (IEEE 754). */ 4529 const struct real_format decimal_single_format = 4530 { 4531 encode_decimal_single, 4532 decode_decimal_single, 4533 10, 4534 7, 4535 7, 4536 -94, 4537 97, 4538 31, 4539 31, 4540 false, 4541 true, 4542 true, 4543 true, 4544 true, 4545 true, 4546 true, 4547 false 4548 }; 4549 4550 /* Double precision decimal floating point (IEEE 754). */ 4551 const struct real_format decimal_double_format = 4552 { 4553 encode_decimal_double, 4554 decode_decimal_double, 4555 10, 4556 16, 4557 16, 4558 -382, 4559 385, 4560 63, 4561 63, 4562 false, 4563 true, 4564 true, 4565 true, 4566 true, 4567 true, 4568 true, 4569 false 4570 }; 4571 4572 /* Quad precision decimal floating point (IEEE 754). */ 4573 const struct real_format decimal_quad_format = 4574 { 4575 encode_decimal_quad, 4576 decode_decimal_quad, 4577 10, 4578 34, 4579 34, 4580 -6142, 4581 6145, 4582 127, 4583 127, 4584 false, 4585 true, 4586 true, 4587 true, 4588 true, 4589 true, 4590 true, 4591 false 4592 }; 4593 4594 /* Encode half-precision floats. This routine is used both for the IEEE 4595 ARM alternative encodings. */ 4596 static void 4597 encode_ieee_half (const struct real_format *fmt, long *buf, 4598 const REAL_VALUE_TYPE *r) 4599 { 4600 unsigned long image, sig, exp; 4601 unsigned long sign = r->sign; 4602 bool denormal = (r->sig[SIGSZ-1] & SIG_MSB) == 0; 4603 4604 image = sign << 15; 4605 sig = (r->sig[SIGSZ-1] >> (HOST_BITS_PER_LONG - 11)) & 0x3ff; 4606 4607 switch (r->cl) 4608 { 4609 case rvc_zero: 4610 break; 4611 4612 case rvc_inf: 4613 if (fmt->has_inf) 4614 image |= 31 << 10; 4615 else 4616 image |= 0x7fff; 4617 break; 4618 4619 case rvc_nan: 4620 if (fmt->has_nans) 4621 { 4622 if (r->canonical) 4623 sig = (fmt->canonical_nan_lsbs_set ? (1 << 9) - 1 : 0); 4624 if (r->signalling == fmt->qnan_msb_set) 4625 sig &= ~(1 << 9); 4626 else 4627 sig |= 1 << 9; 4628 if (sig == 0) 4629 sig = 1 << 8; 4630 4631 image |= 31 << 10; 4632 image |= sig; 4633 } 4634 else 4635 image |= 0x3ff; 4636 break; 4637 4638 case rvc_normal: 4639 /* Recall that IEEE numbers are interpreted as 1.F x 2**exp, 4640 whereas the intermediate representation is 0.F x 2**exp. 4641 Which means we're off by one. */ 4642 if (denormal) 4643 exp = 0; 4644 else 4645 exp = REAL_EXP (r) + 15 - 1; 4646 image |= exp << 10; 4647 image |= sig; 4648 break; 4649 4650 default: 4651 gcc_unreachable (); 4652 } 4653 4654 buf[0] = image; 4655 } 4656 4657 /* Decode half-precision floats. This routine is used both for the IEEE 4658 ARM alternative encodings. */ 4659 static void 4660 decode_ieee_half (const struct real_format *fmt, REAL_VALUE_TYPE *r, 4661 const long *buf) 4662 { 4663 unsigned long image = buf[0] & 0xffff; 4664 bool sign = (image >> 15) & 1; 4665 int exp = (image >> 10) & 0x1f; 4666 4667 memset (r, 0, sizeof (*r)); 4668 image <<= HOST_BITS_PER_LONG - 11; 4669 image &= ~SIG_MSB; 4670 4671 if (exp == 0) 4672 { 4673 if (image && fmt->has_denorm) 4674 { 4675 r->cl = rvc_normal; 4676 r->sign = sign; 4677 SET_REAL_EXP (r, -14); 4678 r->sig[SIGSZ-1] = image << 1; 4679 normalize (r); 4680 } 4681 else if (fmt->has_signed_zero) 4682 r->sign = sign; 4683 } 4684 else if (exp == 31 && (fmt->has_nans || fmt->has_inf)) 4685 { 4686 if (image) 4687 { 4688 r->cl = rvc_nan; 4689 r->sign = sign; 4690 r->signalling = (((image >> (HOST_BITS_PER_LONG - 2)) & 1) 4691 ^ fmt->qnan_msb_set); 4692 r->sig[SIGSZ-1] = image; 4693 } 4694 else 4695 { 4696 r->cl = rvc_inf; 4697 r->sign = sign; 4698 } 4699 } 4700 else 4701 { 4702 r->cl = rvc_normal; 4703 r->sign = sign; 4704 SET_REAL_EXP (r, exp - 15 + 1); 4705 r->sig[SIGSZ-1] = image | SIG_MSB; 4706 } 4707 } 4708 4709 /* Half-precision format, as specified in IEEE 754R. */ 4710 const struct real_format ieee_half_format = 4711 { 4712 encode_ieee_half, 4713 decode_ieee_half, 4714 2, 4715 11, 4716 11, 4717 -13, 4718 16, 4719 15, 4720 15, 4721 false, 4722 true, 4723 true, 4724 true, 4725 true, 4726 true, 4727 true, 4728 false 4729 }; 4730 4731 /* ARM's alternative half-precision format, similar to IEEE but with 4732 no reserved exponent value for NaNs and infinities; rather, it just 4733 extends the range of exponents by one. */ 4734 const struct real_format arm_half_format = 4735 { 4736 encode_ieee_half, 4737 decode_ieee_half, 4738 2, 4739 11, 4740 11, 4741 -13, 4742 17, 4743 15, 4744 15, 4745 false, 4746 true, 4747 false, 4748 false, 4749 true, 4750 true, 4751 false, 4752 false 4753 }; 4754 4755 /* A synthetic "format" for internal arithmetic. It's the size of the 4756 internal significand minus the two bits needed for proper rounding. 4757 The encode and decode routines exist only to satisfy our paranoia 4758 harness. */ 4759 4760 static void encode_internal (const struct real_format *fmt, 4761 long *, const REAL_VALUE_TYPE *); 4762 static void decode_internal (const struct real_format *, 4763 REAL_VALUE_TYPE *, const long *); 4764 4765 static void 4766 encode_internal (const struct real_format *fmt ATTRIBUTE_UNUSED, long *buf, 4767 const REAL_VALUE_TYPE *r) 4768 { 4769 memcpy (buf, r, sizeof (*r)); 4770 } 4771 4772 static void 4773 decode_internal (const struct real_format *fmt ATTRIBUTE_UNUSED, 4774 REAL_VALUE_TYPE *r, const long *buf) 4775 { 4776 memcpy (r, buf, sizeof (*r)); 4777 } 4778 4779 const struct real_format real_internal_format = 4780 { 4781 encode_internal, 4782 decode_internal, 4783 2, 4784 SIGNIFICAND_BITS - 2, 4785 SIGNIFICAND_BITS - 2, 4786 -MAX_EXP, 4787 MAX_EXP, 4788 -1, 4789 -1, 4790 false, 4791 false, 4792 true, 4793 true, 4794 false, 4795 true, 4796 true, 4797 false 4798 }; 4799 4800 /* Calculate the square root of X in mode MODE, and store the result 4801 in R. Return TRUE if the operation does not raise an exception. 4802 For details see "High Precision Division and Square Root", 4803 Alan H. Karp and Peter Markstein, HP Lab Report 93-93-42, June 4804 1993. http://www.hpl.hp.com/techreports/93/HPL-93-42.pdf. */ 4805 4806 bool 4807 real_sqrt (REAL_VALUE_TYPE *r, enum machine_mode mode, 4808 const REAL_VALUE_TYPE *x) 4809 { 4810 static REAL_VALUE_TYPE halfthree; 4811 static bool init = false; 4812 REAL_VALUE_TYPE h, t, i; 4813 int iter, exp; 4814 4815 /* sqrt(-0.0) is -0.0. */ 4816 if (real_isnegzero (x)) 4817 { 4818 *r = *x; 4819 return false; 4820 } 4821 4822 /* Negative arguments return NaN. */ 4823 if (real_isneg (x)) 4824 { 4825 get_canonical_qnan (r, 0); 4826 return false; 4827 } 4828 4829 /* Infinity and NaN return themselves. */ 4830 if (!real_isfinite (x)) 4831 { 4832 *r = *x; 4833 return false; 4834 } 4835 4836 if (!init) 4837 { 4838 do_add (&halfthree, &dconst1, &dconsthalf, 0); 4839 init = true; 4840 } 4841 4842 /* Initial guess for reciprocal sqrt, i. */ 4843 exp = real_exponent (x); 4844 real_ldexp (&i, &dconst1, -exp/2); 4845 4846 /* Newton's iteration for reciprocal sqrt, i. */ 4847 for (iter = 0; iter < 16; iter++) 4848 { 4849 /* i(n+1) = i(n) * (1.5 - 0.5*i(n)*i(n)*x). */ 4850 do_multiply (&t, x, &i); 4851 do_multiply (&h, &t, &i); 4852 do_multiply (&t, &h, &dconsthalf); 4853 do_add (&h, &halfthree, &t, 1); 4854 do_multiply (&t, &i, &h); 4855 4856 /* Check for early convergence. */ 4857 if (iter >= 6 && real_identical (&i, &t)) 4858 break; 4859 4860 /* ??? Unroll loop to avoid copying. */ 4861 i = t; 4862 } 4863 4864 /* Final iteration: r = i*x + 0.5*i*x*(1.0 - i*(i*x)). */ 4865 do_multiply (&t, x, &i); 4866 do_multiply (&h, &t, &i); 4867 do_add (&i, &dconst1, &h, 1); 4868 do_multiply (&h, &t, &i); 4869 do_multiply (&i, &dconsthalf, &h); 4870 do_add (&h, &t, &i, 0); 4871 4872 /* ??? We need a Tuckerman test to get the last bit. */ 4873 4874 real_convert (r, mode, &h); 4875 return true; 4876 } 4877 4878 /* Calculate X raised to the integer exponent N in mode MODE and store 4879 the result in R. Return true if the result may be inexact due to 4880 loss of precision. The algorithm is the classic "left-to-right binary 4881 method" described in section 4.6.3 of Donald Knuth's "Seminumerical 4882 Algorithms", "The Art of Computer Programming", Volume 2. */ 4883 4884 bool 4885 real_powi (REAL_VALUE_TYPE *r, enum machine_mode mode, 4886 const REAL_VALUE_TYPE *x, HOST_WIDE_INT n) 4887 { 4888 unsigned HOST_WIDE_INT bit; 4889 REAL_VALUE_TYPE t; 4890 bool inexact = false; 4891 bool init = false; 4892 bool neg; 4893 int i; 4894 4895 if (n == 0) 4896 { 4897 *r = dconst1; 4898 return false; 4899 } 4900 else if (n < 0) 4901 { 4902 /* Don't worry about overflow, from now on n is unsigned. */ 4903 neg = true; 4904 n = -n; 4905 } 4906 else 4907 neg = false; 4908 4909 t = *x; 4910 bit = (unsigned HOST_WIDE_INT) 1 << (HOST_BITS_PER_WIDE_INT - 1); 4911 for (i = 0; i < HOST_BITS_PER_WIDE_INT; i++) 4912 { 4913 if (init) 4914 { 4915 inexact |= do_multiply (&t, &t, &t); 4916 if (n & bit) 4917 inexact |= do_multiply (&t, &t, x); 4918 } 4919 else if (n & bit) 4920 init = true; 4921 bit >>= 1; 4922 } 4923 4924 if (neg) 4925 inexact |= do_divide (&t, &dconst1, &t); 4926 4927 real_convert (r, mode, &t); 4928 return inexact; 4929 } 4930 4931 /* Round X to the nearest integer not larger in absolute value, i.e. 4932 towards zero, placing the result in R in mode MODE. */ 4933 4934 void 4935 real_trunc (REAL_VALUE_TYPE *r, enum machine_mode mode, 4936 const REAL_VALUE_TYPE *x) 4937 { 4938 do_fix_trunc (r, x); 4939 if (mode != VOIDmode) 4940 real_convert (r, mode, r); 4941 } 4942 4943 /* Round X to the largest integer not greater in value, i.e. round 4944 down, placing the result in R in mode MODE. */ 4945 4946 void 4947 real_floor (REAL_VALUE_TYPE *r, enum machine_mode mode, 4948 const REAL_VALUE_TYPE *x) 4949 { 4950 REAL_VALUE_TYPE t; 4951 4952 do_fix_trunc (&t, x); 4953 if (! real_identical (&t, x) && x->sign) 4954 do_add (&t, &t, &dconstm1, 0); 4955 if (mode != VOIDmode) 4956 real_convert (r, mode, &t); 4957 else 4958 *r = t; 4959 } 4960 4961 /* Round X to the smallest integer not less then argument, i.e. round 4962 up, placing the result in R in mode MODE. */ 4963 4964 void 4965 real_ceil (REAL_VALUE_TYPE *r, enum machine_mode mode, 4966 const REAL_VALUE_TYPE *x) 4967 { 4968 REAL_VALUE_TYPE t; 4969 4970 do_fix_trunc (&t, x); 4971 if (! real_identical (&t, x) && ! x->sign) 4972 do_add (&t, &t, &dconst1, 0); 4973 if (mode != VOIDmode) 4974 real_convert (r, mode, &t); 4975 else 4976 *r = t; 4977 } 4978 4979 /* Round X to the nearest integer, but round halfway cases away from 4980 zero. */ 4981 4982 void 4983 real_round (REAL_VALUE_TYPE *r, enum machine_mode mode, 4984 const REAL_VALUE_TYPE *x) 4985 { 4986 do_add (r, x, &dconsthalf, x->sign); 4987 do_fix_trunc (r, r); 4988 if (mode != VOIDmode) 4989 real_convert (r, mode, r); 4990 } 4991 4992 /* Set the sign of R to the sign of X. */ 4993 4994 void 4995 real_copysign (REAL_VALUE_TYPE *r, const REAL_VALUE_TYPE *x) 4996 { 4997 r->sign = x->sign; 4998 } 4999 5000 /* Check whether the real constant value given is an integer. */ 5001 5002 bool 5003 real_isinteger (const REAL_VALUE_TYPE *c, enum machine_mode mode) 5004 { 5005 REAL_VALUE_TYPE cint; 5006 5007 real_trunc (&cint, mode, c); 5008 return real_identical (c, &cint); 5009 } 5010 5011 /* Write into BUF the maximum representable finite floating-point 5012 number, (1 - b**-p) * b**emax for a given FP format FMT as a hex 5013 float string. LEN is the size of BUF, and the buffer must be large 5014 enough to contain the resulting string. */ 5015 5016 void 5017 get_max_float (const struct real_format *fmt, char *buf, size_t len) 5018 { 5019 int i, n; 5020 char *p; 5021 5022 strcpy (buf, "0x0."); 5023 n = fmt->p; 5024 for (i = 0, p = buf + 4; i + 3 < n; i += 4) 5025 *p++ = 'f'; 5026 if (i < n) 5027 *p++ = "08ce"[n - i]; 5028 sprintf (p, "p%d", fmt->emax); 5029 if (fmt->pnan < fmt->p) 5030 { 5031 /* This is an IBM extended double format made up of two IEEE 5032 doubles. The value of the long double is the sum of the 5033 values of the two parts. The most significant part is 5034 required to be the value of the long double rounded to the 5035 nearest double. Rounding means we need a slightly smaller 5036 value for LDBL_MAX. */ 5037 buf[4 + fmt->pnan / 4] = "7bde"[fmt->pnan % 4]; 5038 } 5039 5040 gcc_assert (strlen (buf) < len); 5041 } 5042