Daily bump.
[official-gcc.git] / gcc / real.c
blobb80aeac843f26927c37ac7ae9750148f4340d637
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>
6 This file is part of GCC.
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.
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.
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/>. */
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"
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.
37 Specifically
39 x = s * b^e * \sum_{k=1}^p f_k * b^{-k}
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.
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).
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.
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.
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. */
70 /* Used to classify two numbers simultaneously. */
71 #define CLASS2(A, B) ((A) << 2 | (B))
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
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 *);
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 *);
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);
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);
122 static void round_for_format (const struct real_format *, REAL_VALUE_TYPE *);
124 /* Initialize R with a positive zero. */
126 static inline void
127 get_zero (REAL_VALUE_TYPE *r, int sign)
129 memset (r, 0, sizeof (*r));
130 r->sign = sign;
133 /* Initialize R with the canonical quiet NaN. */
135 static inline void
136 get_canonical_qnan (REAL_VALUE_TYPE *r, int sign)
138 memset (r, 0, sizeof (*r));
139 r->cl = rvc_nan;
140 r->sign = sign;
141 r->canonical = 1;
144 static inline void
145 get_canonical_snan (REAL_VALUE_TYPE *r, int sign)
147 memset (r, 0, sizeof (*r));
148 r->cl = rvc_nan;
149 r->sign = sign;
150 r->signalling = 1;
151 r->canonical = 1;
154 static inline void
155 get_inf (REAL_VALUE_TYPE *r, int sign)
157 memset (r, 0, sizeof (*r));
158 r->cl = rvc_inf;
159 r->sign = sign;
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. */
166 static bool
167 sticky_rshift_significand (REAL_VALUE_TYPE *r, const REAL_VALUE_TYPE *a,
168 unsigned int n)
170 unsigned long sticky = 0;
171 unsigned int i, ofs = 0;
173 if (n >= HOST_BITS_PER_LONG)
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;
180 if (n != 0)
182 sticky |= a->sig[ofs] & (((unsigned long)1 << n) - 1);
183 for (i = 0; i < SIGSZ; ++i)
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)));
191 else
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;
199 return sticky != 0;
202 /* Right-shift the significand of A by N bits; put the result in the
203 significand of R. */
205 static void
206 rshift_significand (REAL_VALUE_TYPE *r, const REAL_VALUE_TYPE *a,
207 unsigned int n)
209 unsigned int i, ofs = n / HOST_BITS_PER_LONG;
211 n &= HOST_BITS_PER_LONG - 1;
212 if (n != 0)
214 for (i = 0; i < SIGSZ; ++i)
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)));
222 else
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;
231 /* Left-shift the significand of A by N bits; put the result in the
232 significand of R. */
234 static void
235 lshift_significand (REAL_VALUE_TYPE *r, const REAL_VALUE_TYPE *a,
236 unsigned int n)
238 unsigned int i, ofs = n / HOST_BITS_PER_LONG;
240 n &= HOST_BITS_PER_LONG - 1;
241 if (n == 0)
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;
248 else
249 for (i = 0; i < SIGSZ; ++i)
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)));
258 /* Likewise, but N is specialized to 1. */
260 static inline void
261 lshift_significand_1 (REAL_VALUE_TYPE *r, const REAL_VALUE_TYPE *a)
263 unsigned int i;
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;
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. */
273 static inline bool
274 add_significands (REAL_VALUE_TYPE *r, const REAL_VALUE_TYPE *a,
275 const REAL_VALUE_TYPE *b)
277 bool carry = false;
278 int i;
280 for (i = 0; i < SIGSZ; ++i)
282 unsigned long ai = a->sig[i];
283 unsigned long ri = ai + b->sig[i];
285 if (carry)
287 carry = ri < ai;
288 carry |= ++ri == 0;
290 else
291 carry = ri < ai;
293 r->sig[i] = ri;
296 return carry;
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. */
303 static inline bool
304 sub_significands (REAL_VALUE_TYPE *r, const REAL_VALUE_TYPE *a,
305 const REAL_VALUE_TYPE *b, int carry)
307 int i;
309 for (i = 0; i < SIGSZ; ++i)
311 unsigned long ai = a->sig[i];
312 unsigned long ri = ai - b->sig[i];
314 if (carry)
316 carry = ri > ai;
317 carry |= ~--ri == 0;
319 else
320 carry = ri > ai;
322 r->sig[i] = ri;
325 return carry;
328 /* Negate the significand A, placing the result in R. */
330 static inline void
331 neg_significand (REAL_VALUE_TYPE *r, const REAL_VALUE_TYPE *a)
333 bool carry = true;
334 int i;
336 for (i = 0; i < SIGSZ; ++i)
338 unsigned long ri, ai = a->sig[i];
340 if (carry)
342 if (ai)
344 ri = -ai;
345 carry = false;
347 else
348 ri = ai;
350 else
351 ri = ~ai;
353 r->sig[i] = ri;
357 /* Compare significands. Return tri-state vs zero. */
359 static inline int
360 cmp_significands (const REAL_VALUE_TYPE *a, const REAL_VALUE_TYPE *b)
362 int i;
364 for (i = SIGSZ - 1; i >= 0; --i)
366 unsigned long ai = a->sig[i];
367 unsigned long bi = b->sig[i];
369 if (ai > bi)
370 return 1;
371 if (ai < bi)
372 return -1;
375 return 0;
378 /* Return true if A is nonzero. */
380 static inline int
381 cmp_significand_0 (const REAL_VALUE_TYPE *a)
383 int i;
385 for (i = SIGSZ - 1; i >= 0; --i)
386 if (a->sig[i])
387 return 1;
389 return 0;
392 /* Set bit N of the significand of R. */
394 static inline void
395 set_significand_bit (REAL_VALUE_TYPE *r, unsigned int n)
397 r->sig[n / HOST_BITS_PER_LONG]
398 |= (unsigned long)1 << (n % HOST_BITS_PER_LONG);
401 /* Clear bit N of the significand of R. */
403 static inline void
404 clear_significand_bit (REAL_VALUE_TYPE *r, unsigned int n)
406 r->sig[n / HOST_BITS_PER_LONG]
407 &= ~((unsigned long)1 << (n % HOST_BITS_PER_LONG));
410 /* Test bit N of the significand of R. */
412 static inline bool
413 test_significand_bit (REAL_VALUE_TYPE *r, unsigned int n)
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;
422 /* Clear bits 0..N-1 of the significand of R. */
424 static void
425 clear_significand_below (REAL_VALUE_TYPE *r, unsigned int n)
427 int i, w = n / HOST_BITS_PER_LONG;
429 for (i = 0; i < w; ++i)
430 r->sig[i] = 0;
432 r->sig[w] &= ~(((unsigned long)1 << (n % HOST_BITS_PER_LONG)) - 1);
435 /* Divide the significands of A and B, placing the result in R. Return
436 true if the division was inexact. */
438 static inline bool
439 div_significands (REAL_VALUE_TYPE *r, const REAL_VALUE_TYPE *a,
440 const REAL_VALUE_TYPE *b)
442 REAL_VALUE_TYPE u;
443 int i, bit = SIGNIFICAND_BITS - 1;
444 unsigned long msb, inexact;
446 u = *a;
447 memset (r->sig, 0, sizeof (r->sig));
449 msb = 0;
450 goto start;
453 msb = u.sig[SIGSZ-1] & SIG_MSB;
454 lshift_significand_1 (&u, &u);
455 start:
456 if (msb || cmp_significands (&u, b) >= 0)
458 sub_significands (&u, &u, b, 0);
459 set_significand_bit (r, bit);
462 while (--bit >= 0);
464 for (i = 0, inexact = 0; i < SIGSZ; i++)
465 inexact |= u.sig[i];
467 return inexact != 0;
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.) */
475 static void
476 normalize (REAL_VALUE_TYPE *r)
478 int shift = 0, exp;
479 int i, j;
481 if (r->decimal)
482 return;
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;
491 /* Zero significand flushes to zero. */
492 if (i < 0)
494 r->cl = rvc_zero;
495 SET_REAL_EXP (r, 0);
496 return;
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;
505 if (shift > 0)
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
514 SET_REAL_EXP (r, exp);
515 lshift_significand (r, r, shift);
520 /* Calculate R = A + (SUBTRACT_P ? -B : B). Return true if the
521 result may be inexact due to a loss of precision. */
523 static bool
524 do_add (REAL_VALUE_TYPE *r, const REAL_VALUE_TYPE *a,
525 const REAL_VALUE_TYPE *b, int subtract_p)
527 int dexp, sign, exp;
528 REAL_VALUE_TYPE t;
529 bool inexact = false;
531 /* Determine if we need to add or subtract. */
532 sign = a->sign;
533 subtract_p = (sign ^ b->sign) ^ subtract_p;
535 switch (CLASS2 (a->cl, b->cl))
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;
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;
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;
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;
577 case CLASS2 (rvc_normal, rvc_normal):
578 break;
580 default:
581 gcc_unreachable ();
584 /* Swap the arguments such that A has the larger exponent. */
585 dexp = REAL_EXP (a) - REAL_EXP (b);
586 if (dexp < 0)
588 const REAL_VALUE_TYPE *t;
589 t = a, a = b, b = t;
590 dexp = -dexp;
591 sign ^= subtract_p;
593 exp = REAL_EXP (a);
595 /* If the exponents are not identical, we need to shift the
596 significand of B down. */
597 if (dexp > 0)
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)
603 *r = *a;
604 r->sign = sign;
605 return true;
608 inexact |= sticky_rshift_significand (&t, b, dexp);
609 b = &t;
612 if (subtract_p)
614 if (sub_significands (r, a, b, inexact))
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);
624 else
626 if (add_significands (r, a, b))
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)
635 get_inf (r, sign);
636 return true;
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;
649 /* Re-normalize the result. */
650 normalize (r);
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;
659 return inexact;
662 /* Calculate R = A * B. Return true if the result may be inexact. */
664 static bool
665 do_multiply (REAL_VALUE_TYPE *r, const REAL_VALUE_TYPE *a,
666 const REAL_VALUE_TYPE *b)
668 REAL_VALUE_TYPE u, t, *rr;
669 unsigned int i, j, k;
670 int sign = a->sign ^ b->sign;
671 bool inexact = false;
673 switch (CLASS2 (a->cl, b->cl))
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;
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;
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;
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;
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;
712 case CLASS2 (rvc_normal, rvc_normal):
713 break;
715 default:
716 gcc_unreachable ();
719 if (r == a || r == b)
720 rr = &t;
721 else
722 rr = r;
723 get_zero (rr, 0);
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.
728 Consider the long-hand form of a four half-word multiplication:
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
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. */
743 for (i = 0; i < SIGSZ * 2; ++i)
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;
751 if (ai == 0)
752 continue;
754 for (j = 0; j < 2; ++j)
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)));
759 if (exp > MAX_EXP)
761 get_inf (r, sign);
762 return true;
764 if (exp < -MAX_EXP)
766 /* Would underflow to zero, which we shouldn't bother adding. */
767 inexact = true;
768 continue;
771 memset (&u, 0, sizeof (u));
772 u.cl = rvc_normal;
773 SET_REAL_EXP (&u, exp);
775 for (k = j; k < SIGSZ * 2; k += 2)
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;
783 u.sig[k / 2] = ai * bi;
786 normalize (&u);
787 inexact |= do_add (rr, rr, &u, 0);
791 rr->sign = sign;
792 if (rr != r)
793 *r = t;
795 return inexact;
798 /* Calculate R = A / B. Return true if the result may be inexact. */
800 static bool
801 do_divide (REAL_VALUE_TYPE *r, const REAL_VALUE_TYPE *a,
802 const REAL_VALUE_TYPE *b)
804 int exp, sign = a->sign ^ b->sign;
805 REAL_VALUE_TYPE t, *rr;
806 bool inexact;
808 switch (CLASS2 (a->cl, b->cl))
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;
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;
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;
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;
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;
849 case CLASS2 (rvc_inf, rvc_normal):
850 /* Inf / R = Inf. */
851 get_inf (r, sign);
852 return false;
854 case CLASS2 (rvc_normal, rvc_normal):
855 break;
857 default:
858 gcc_unreachable ();
861 if (r == a || r == b)
862 rr = &t;
863 else
864 rr = r;
866 /* Make sure all fields in the result are initialized. */
867 get_zero (rr, 0);
868 rr->cl = rvc_normal;
869 rr->sign = sign;
871 exp = REAL_EXP (a) - REAL_EXP (b) + 1;
872 if (exp > MAX_EXP)
874 get_inf (r, sign);
875 return true;
877 if (exp < -MAX_EXP)
879 get_zero (r, sign);
880 return true;
882 SET_REAL_EXP (rr, exp);
884 inexact = div_significands (rr, a, b);
886 /* Re-normalize the result. */
887 normalize (rr);
888 rr->sig[0] |= inexact;
890 if (rr != r)
891 *r = t;
893 return inexact;
896 /* Return a tri-state comparison of A vs B. Return NAN_RESULT if
897 one of the two operands is a NaN. */
899 static int
900 do_compare (const REAL_VALUE_TYPE *a, const REAL_VALUE_TYPE *b,
901 int nan_result)
903 int ret;
905 switch (CLASS2 (a->cl, b->cl))
907 case CLASS2 (rvc_zero, rvc_zero):
908 /* Sign of zero doesn't matter for compares. */
909 return 0;
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);
920 case CLASS2 (rvc_inf, rvc_inf):
921 return -a->sign - -b->sign;
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);
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;
941 case CLASS2 (rvc_normal, rvc_normal):
942 break;
944 default:
945 gcc_unreachable ();
948 if (a->sign != b->sign)
949 return -a->sign - -b->sign;
951 if (a->decimal || b->decimal)
952 return decimal_do_compare (a, b, nan_result);
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);
961 return (a->sign ? -ret : ret);
964 /* Return A truncated to an integral value toward zero. */
966 static void
967 do_fix_trunc (REAL_VALUE_TYPE *r, const REAL_VALUE_TYPE *a)
969 *r = *a;
971 switch (r->cl)
973 case rvc_zero:
974 case rvc_inf:
975 case rvc_nan:
976 break;
978 case rvc_normal:
979 if (r->decimal)
981 decimal_do_fix_trunc (r, a);
982 return;
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;
990 default:
991 gcc_unreachable ();
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. */
999 bool
1000 real_arithmetic (REAL_VALUE_TYPE *r, int icode, const REAL_VALUE_TYPE *op0,
1001 const REAL_VALUE_TYPE *op1)
1003 enum tree_code code = (enum tree_code) icode;
1005 if (op0->decimal || (op1 && op1->decimal))
1006 return decimal_real_arithmetic (r, code, op0, op1);
1008 switch (code)
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);
1017 case MINUS_EXPR:
1018 if (r != op0 && r != op1)
1019 memset (r, '\0', sizeof (*r));
1020 return do_add (r, op0, op1, 1);
1022 case MULT_EXPR:
1023 if (r != op0 && r != op1)
1024 memset (r, '\0', sizeof (*r));
1025 return do_multiply (r, op0, op1);
1027 case RDIV_EXPR:
1028 if (r != op0 && r != op1)
1029 memset (r, '\0', sizeof (*r));
1030 return do_divide (r, op0, op1);
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;
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;
1050 case NEGATE_EXPR:
1051 *r = *op0;
1052 r->sign ^= 1;
1053 break;
1055 case ABS_EXPR:
1056 *r = *op0;
1057 r->sign = 0;
1058 break;
1060 case FIX_TRUNC_EXPR:
1061 do_fix_trunc (r, op0);
1062 break;
1064 default:
1065 gcc_unreachable ();
1067 return false;
1070 REAL_VALUE_TYPE
1071 real_value_negate (const REAL_VALUE_TYPE *op0)
1073 REAL_VALUE_TYPE r;
1074 real_arithmetic (&r, NEGATE_EXPR, op0, NULL);
1075 return r;
1078 REAL_VALUE_TYPE
1079 real_value_abs (const REAL_VALUE_TYPE *op0)
1081 REAL_VALUE_TYPE r;
1082 real_arithmetic (&r, ABS_EXPR, op0, NULL);
1083 return r;
1086 bool
1087 real_compare (int icode, const REAL_VALUE_TYPE *op0,
1088 const REAL_VALUE_TYPE *op1)
1090 enum tree_code code = (enum tree_code) icode;
1092 switch (code)
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;
1123 default:
1124 gcc_unreachable ();
1128 /* Return floor log2(R). */
1131 real_exponent (const REAL_VALUE_TYPE *r)
1133 switch (r->cl)
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 ();
1147 /* R = OP0 * 2**EXP. */
1149 void
1150 real_ldexp (REAL_VALUE_TYPE *r, const REAL_VALUE_TYPE *op0, int exp)
1152 *r = *op0;
1153 switch (r->cl)
1155 case rvc_zero:
1156 case rvc_inf:
1157 case rvc_nan:
1158 break;
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;
1170 default:
1171 gcc_unreachable ();
1175 /* Determine whether a floating-point value X is infinite. */
1177 bool
1178 real_isinf (const REAL_VALUE_TYPE *r)
1180 return (r->cl == rvc_inf);
1183 /* Determine whether a floating-point value X is a NaN. */
1185 bool
1186 real_isnan (const REAL_VALUE_TYPE *r)
1188 return (r->cl == rvc_nan);
1191 /* Determine whether a floating-point value X is finite. */
1193 bool
1194 real_isfinite (const REAL_VALUE_TYPE *r)
1196 return (r->cl != rvc_nan) && (r->cl != rvc_inf);
1199 /* Determine whether a floating-point value X is negative. */
1201 bool
1202 real_isneg (const REAL_VALUE_TYPE *r)
1204 return r->sign;
1207 /* Determine whether a floating-point value X is minus zero. */
1209 bool
1210 real_isnegzero (const REAL_VALUE_TYPE *r)
1212 return r->sign && r->cl == rvc_zero;
1215 /* Compare two floating-point objects for bitwise identity. */
1217 bool
1218 real_identical (const REAL_VALUE_TYPE *a, const REAL_VALUE_TYPE *b)
1220 int i;
1222 if (a->cl != b->cl)
1223 return false;
1224 if (a->sign != b->sign)
1225 return false;
1227 switch (a->cl)
1229 case rvc_zero:
1230 case rvc_inf:
1231 return true;
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;
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;
1248 default:
1249 gcc_unreachable ();
1252 for (i = 0; i < SIGSZ; ++i)
1253 if (a->sig[i] != b->sig[i])
1254 return false;
1256 return true;
1259 /* Try to change R into its exact multiplicative inverse in machine
1260 mode MODE. Return true if successful. */
1262 bool
1263 exact_real_inverse (enum machine_mode mode, REAL_VALUE_TYPE *r)
1265 const REAL_VALUE_TYPE *one = real_digit (1);
1266 REAL_VALUE_TYPE u;
1267 int i;
1269 if (r->cl != rvc_normal)
1270 return false;
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;
1279 /* Find the inverse and truncate to the required mode. */
1280 do_divide (&u, one, r);
1281 real_convert (&u, mode, &u);
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;
1292 *r = u;
1293 return true;
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. */
1300 bool
1301 real_can_shorten_arithmetic (enum machine_mode imode, enum machine_mode tmode)
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));
1325 /* Render R as an integer. */
1327 HOST_WIDE_INT
1328 real_to_integer (const REAL_VALUE_TYPE *r)
1330 unsigned HOST_WIDE_INT i;
1332 switch (r->cl)
1334 case rvc_zero:
1335 underflow:
1336 return 0;
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;
1346 case rvc_normal:
1347 if (r->decimal)
1348 return decimal_real_to_integer (r);
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;
1359 if (HOST_BITS_PER_WIDE_INT == HOST_BITS_PER_LONG)
1360 i = r->sig[SIGSZ-1];
1361 else
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];
1369 i >>= HOST_BITS_PER_WIDE_INT - REAL_EXP (r);
1371 if (r->sign)
1372 i = -i;
1373 return i;
1375 default:
1376 gcc_unreachable ();
1380 /* Likewise, but to an integer pair, HI+LOW. */
1382 void
1383 real_to_integer2 (HOST_WIDE_INT *plow, HOST_WIDE_INT *phigh,
1384 const REAL_VALUE_TYPE *r)
1386 REAL_VALUE_TYPE t;
1387 HOST_WIDE_INT low, high;
1388 int exp;
1390 switch (r->cl)
1392 case rvc_zero:
1393 underflow:
1394 low = high = 0;
1395 break;
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
1405 high--;
1406 low = -1;
1408 break;
1410 case rvc_normal:
1411 if (r->decimal)
1413 decimal_real_to_integer2 (plow, phigh, r);
1414 return;
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;
1427 rshift_significand (&t, r, HOST_BITS_PER_DOUBLE_INT - exp);
1428 if (HOST_BITS_PER_WIDE_INT == HOST_BITS_PER_LONG)
1430 high = t.sig[SIGSZ-1];
1431 low = t.sig[SIGSZ-2];
1433 else
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];
1440 low = t.sig[SIGSZ-3];
1441 low = low << (HOST_BITS_PER_LONG - 1) << 1;
1442 low |= t.sig[SIGSZ-4];
1445 if (r->sign)
1447 if (low == 0)
1448 high = -high;
1449 else
1450 low = -low, high = ~high;
1452 break;
1454 default:
1455 gcc_unreachable ();
1458 *plow = low;
1459 *phigh = high;
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. */
1467 static unsigned long
1468 rtd_divmod (REAL_VALUE_TYPE *num, REAL_VALUE_TYPE *den)
1470 unsigned long q, msb;
1471 int expn = REAL_EXP (num), expd = REAL_EXP (den);
1473 if (expn < expd)
1474 return 0;
1476 q = msb = 0;
1477 goto start;
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)
1486 sub_significands (num, num, den, 0);
1487 q |= 1;
1490 while (--expn >= expd);
1492 SET_REAL_EXP (num, expd);
1493 normalize (num);
1495 return q;
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. */
1504 #define M_LOG10_2 0.30102999566398119521
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)
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;
1520 if (mode != VOIDmode)
1522 fmt = REAL_MODE_FORMAT (mode);
1523 gcc_assert (fmt);
1526 r = *r_orig;
1527 switch (r.cl)
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 ();
1546 if (r.decimal)
1548 decimal_real_to_decimal (str, &r, buf_size, digits, crop_trailing_zeros);
1549 return;
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;
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;
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;
1570 one = real_digit (1);
1571 ten = ten_to_ptwo (0);
1573 sign = r.sign;
1574 r.sign = 0;
1576 dec_exp = 0;
1577 pten = *one;
1579 cmp_one = do_compare (&r, one, 0);
1580 if (cmp_one > 0)
1582 int m;
1584 /* Number is greater than one. Convert significand to an integer
1585 and strip trailing decimal zeros. */
1587 u = r;
1588 SET_REAL_EXP (&u, SIGNIFICAND_BITS - 1);
1590 /* Largest M, such that 10**2**M fits within SIGNIFICAND_BITS. */
1591 m = floor_log2 (max_digits);
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. */
1599 REAL_VALUE_TYPE t;
1601 do_divide (&t, &u, ten_to_ptwo (m));
1602 do_fix_trunc (&v, &t);
1603 if (cmp_significands (&v, &t) == 0)
1605 u = t;
1606 dec_exp += 1 << m;
1609 while (--m >= 0);
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;
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)
1621 m = floor_log2 ((int)(REAL_EXP (&r) * M_LOG10_2)) + 1;
1624 const REAL_VALUE_TYPE *ptentwo = ten_to_ptwo (m);
1625 if (do_compare (&u, ptentwo, 0) >= 0)
1627 do_divide (&u, &u, ptentwo);
1628 do_multiply (&pten, &pten, ptentwo);
1629 dec_exp += 1 << m;
1632 while (--m >= 0);
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;
1640 if (cmp_one < 0)
1642 int m;
1644 /* Number is less than one. Pad significand with leading
1645 decimal zeros. */
1647 v = r;
1648 while (1)
1650 /* Stop if we'd shift bits off the bottom. */
1651 if (v.sig[0] & 7)
1652 break;
1654 do_multiply (&u, &v, ten);
1656 /* Stop if we're now >= 1. */
1657 if (REAL_EXP (&u) > 0)
1658 break;
1660 v = u;
1661 dec_exp -= 1;
1663 r = v;
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;
1671 const REAL_VALUE_TYPE *ptentwo = ten_to_ptwo (m);
1672 const REAL_VALUE_TYPE *ptenmtwo = ten_to_mptwo (m);
1674 if (do_compare (&v, ptenmtwo, 0) <= 0)
1676 do_multiply (&v, &v, ptentwo);
1677 do_multiply (&pten, &pten, ptentwo);
1678 dec_exp -= 1 << m;
1681 while (--m >= 0);
1683 /* Invert the positive power of 10 that we've collected so far. */
1684 do_divide (&pten, one, &pten);
1687 p = str;
1688 if (sign)
1689 *p++ = '-';
1690 first = p++;
1692 /* At this point, PTEN should contain the nearest power of 10 smaller
1693 than R, such that this division produces the first digit.
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. */
1700 digit = rtd_divmod (&r, &pten);
1702 /* Be prepared for error in that division via underflow ... */
1703 if (digit == 0 && cmp_significand_0 (&r))
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);
1712 /* ... or overflow. */
1713 if (digit == 10)
1715 *p++ = '1';
1716 if (--digits > 0)
1717 *p++ = '0';
1718 dec_exp += 1;
1720 else
1722 gcc_assert (digit <= 10);
1723 *p++ = digit + '0';
1726 /* Generate subsequent digits. */
1727 while (--digits > 0)
1729 do_multiply (&r, &r, ten);
1730 digit = rtd_divmod (&r, &pten);
1731 *p++ = digit + '0';
1733 last = p;
1735 /* Generate one more digit with which to do rounding. */
1736 do_multiply (&r, &r, ten);
1737 digit = rtd_divmod (&r, &pten);
1739 /* Round the result. */
1740 if (fmt && fmt->round_towards_zero)
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;
1748 else
1750 if (digit == 5)
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++;
1761 round_up = digit > 5;
1764 if (round_up)
1766 while (p > first)
1768 digit = *--p;
1769 if (digit == '9')
1770 *p = '0';
1771 else
1773 *p = digit + 1;
1774 break;
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)
1782 first[1] = '1';
1783 dec_exp++;
1787 /* Insert the decimal point. */
1788 first[0] = first[1];
1789 first[1] = '.';
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--;
1796 /* Append the exponent. */
1797 sprintf (last, "e%+d", dec_exp);
1799 #ifdef ENABLE_CHECKING
1800 /* Verify that we can read the original value back in. */
1801 if (mode != VOIDmode)
1803 real_from_string (&r, str);
1804 real_convert (&r, mode, &r);
1805 gcc_assert (real_identical (&r, r_orig));
1807 #endif
1810 /* Likewise, except always uses round-to-nearest. */
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)
1816 real_to_decimal_for_mode (str, r_orig, buf_size,
1817 digits, crop_trailing_zeros, VOIDmode);
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. */
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)
1829 int i, j, exp = REAL_EXP (r);
1830 char *p, *first;
1831 char exp_buf[16];
1832 size_t max_digits;
1834 switch (r->cl)
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 ();
1853 if (r->decimal)
1855 /* Hexadecimal format for decimal floats is not interesting. */
1856 strcpy (str, "N/A");
1857 return;
1860 if (digits == 0)
1861 digits = SIGNIFICAND_BITS / 4;
1863 /* Bound the number of digits printed by the size of the output buffer. */
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;
1871 p = str;
1872 if (r->sign)
1873 *p++ = '-';
1874 *p++ = '0';
1875 *p++ = 'x';
1876 *p++ = '0';
1877 *p++ = '.';
1878 first = p;
1880 for (i = SIGSZ - 1; i >= 0; --i)
1881 for (j = HOST_BITS_PER_LONG - 4; j >= 0; j -= 4)
1883 *p++ = "0123456789abcdef"[(r->sig[i] >> j) & 15];
1884 if (--digits == 0)
1885 goto out;
1888 out:
1889 if (crop_trailing_zeros)
1890 while (p > first + 1 && p[-1] == '0')
1891 p--;
1893 sprintf (p, "p%+d", exp);
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. */
1901 real_from_string (REAL_VALUE_TYPE *r, const char *str)
1903 int exp = 0;
1904 bool sign = false;
1906 get_zero (r, 0);
1908 if (*str == '-')
1910 sign = true;
1911 str++;
1913 else if (*str == '+')
1914 str++;
1916 if (!strncmp (str, "QNaN", 4))
1918 get_canonical_qnan (r, sign);
1919 return 0;
1921 else if (!strncmp (str, "SNaN", 4))
1923 get_canonical_snan (r, sign);
1924 return 0;
1926 else if (!strncmp (str, "Inf", 3))
1928 get_inf (r, sign);
1929 return 0;
1932 if (str[0] == '0' && (str[1] == 'x' || str[1] == 'X'))
1934 /* Hexadecimal floating point. */
1935 int pos = SIGNIFICAND_BITS - 4, d;
1937 str += 2;
1939 while (*str == '0')
1940 str++;
1941 while (1)
1943 d = hex_value (*str);
1944 if (d == _hex_bad)
1945 break;
1946 if (pos >= 0)
1948 r->sig[pos / HOST_BITS_PER_LONG]
1949 |= (unsigned long) d << (pos % HOST_BITS_PER_LONG);
1950 pos -= 4;
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++;
1959 if (*str == '.')
1961 str++;
1962 if (pos == SIGNIFICAND_BITS - 4)
1964 while (*str == '0')
1965 str++, exp -= 4;
1967 while (1)
1969 d = hex_value (*str);
1970 if (d == _hex_bad)
1971 break;
1972 if (pos >= 0)
1974 r->sig[pos / HOST_BITS_PER_LONG]
1975 |= (unsigned long) d << (pos % HOST_BITS_PER_LONG);
1976 pos -= 4;
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++;
1986 /* If the mantissa is zero, ignore the exponent. */
1987 if (!cmp_significand_0 (r))
1988 goto is_a_zero;
1990 if (*str == 'p' || *str == 'P')
1992 bool exp_neg = false;
1994 str++;
1995 if (*str == '-')
1997 exp_neg = true;
1998 str++;
2000 else if (*str == '+')
2001 str++;
2003 d = 0;
2004 while (ISDIGIT (*str))
2006 d *= 10;
2007 d += *str - '0';
2008 if (d > MAX_EXP)
2010 /* Overflowed the exponent. */
2011 if (exp_neg)
2012 goto underflow;
2013 else
2014 goto overflow;
2016 str++;
2018 if (exp_neg)
2019 d = -d;
2021 exp += d;
2024 r->cl = rvc_normal;
2025 SET_REAL_EXP (r, exp);
2027 normalize (r);
2029 else
2031 /* Decimal floating point. */
2032 const REAL_VALUE_TYPE *ten = ten_to_ptwo (0);
2033 int d;
2035 while (*str == '0')
2036 str++;
2037 while (ISDIGIT (*str))
2039 d = *str++ - '0';
2040 do_multiply (r, r, ten);
2041 if (d)
2042 do_add (r, r, real_digit (d), 0);
2044 if (*str == '.')
2046 str++;
2047 if (r->cl == rvc_zero)
2049 while (*str == '0')
2050 str++, exp--;
2052 while (ISDIGIT (*str))
2054 d = *str++ - '0';
2055 do_multiply (r, r, ten);
2056 if (d)
2057 do_add (r, r, real_digit (d), 0);
2058 exp--;
2062 /* If the mantissa is zero, ignore the exponent. */
2063 if (r->cl == rvc_zero)
2064 goto is_a_zero;
2066 if (*str == 'e' || *str == 'E')
2068 bool exp_neg = false;
2070 str++;
2071 if (*str == '-')
2073 exp_neg = true;
2074 str++;
2076 else if (*str == '+')
2077 str++;
2079 d = 0;
2080 while (ISDIGIT (*str))
2082 d *= 10;
2083 d += *str - '0';
2084 if (d > MAX_EXP)
2086 /* Overflowed the exponent. */
2087 if (exp_neg)
2088 goto underflow;
2089 else
2090 goto overflow;
2092 str++;
2094 if (exp_neg)
2095 d = -d;
2096 exp += d;
2099 if (exp)
2100 times_pten (r, exp);
2103 r->sign = sign;
2104 return 0;
2106 is_a_zero:
2107 get_zero (r, sign);
2108 return 0;
2110 underflow:
2111 get_zero (r, sign);
2112 return -1;
2114 overflow:
2115 get_inf (r, sign);
2116 return 1;
2119 /* Legacy. Similar, but return the result directly. */
2121 REAL_VALUE_TYPE
2122 real_from_string2 (const char *s, enum machine_mode mode)
2124 REAL_VALUE_TYPE r;
2126 real_from_string (&r, s);
2127 if (mode != VOIDmode)
2128 real_convert (&r, mode, &r);
2130 return r;
2133 /* Initialize R from string S and desired MODE. */
2135 void
2136 real_from_string3 (REAL_VALUE_TYPE *r, const char *s, enum machine_mode mode)
2138 if (DECIMAL_FLOAT_MODE_P (mode))
2139 decimal_real_from_string (r, s);
2140 else
2141 real_from_string (r, s);
2143 if (mode != VOIDmode)
2144 real_convert (r, mode, r);
2147 /* Initialize R from the integer pair HIGH+LOW. */
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)
2154 if (low == 0 && high == 0)
2155 get_zero (r, 0);
2156 else
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);
2163 if (r->sign)
2165 high = ~high;
2166 if (low == 0)
2167 high += 1;
2168 else
2169 low = -low;
2172 if (HOST_BITS_PER_LONG == HOST_BITS_PER_WIDE_INT)
2174 r->sig[SIGSZ-1] = high;
2175 r->sig[SIGSZ-2] = low;
2177 else
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;
2186 normalize (r);
2189 if (DECIMAL_FLOAT_MODE_P (mode))
2190 decimal_from_integer (r);
2191 else if (mode != VOIDmode)
2192 real_convert (r, mode, r);
2195 /* Render R, an integral value, as a floating point constant with no
2196 specified exponent. */
2198 static void
2199 decimal_integer_string (char *str, const REAL_VALUE_TYPE *r_orig,
2200 size_t buf_size)
2202 int dec_exp, digit, digits;
2203 REAL_VALUE_TYPE r, pten;
2204 char *p;
2205 bool sign;
2207 r = *r_orig;
2209 if (r.cl == rvc_zero)
2211 strcpy (str, "0.");
2212 return;
2215 sign = r.sign;
2216 r.sign = 0;
2218 dec_exp = REAL_EXP (&r) * M_LOG10_2;
2219 digits = dec_exp + 1;
2220 gcc_assert ((digits + 2) < (int)buf_size);
2222 pten = *real_digit (1);
2223 times_pten (&pten, dec_exp);
2225 p = str;
2226 if (sign)
2227 *p++ = '-';
2229 digit = rtd_divmod (&r, &pten);
2230 gcc_assert (digit >= 0 && digit <= 9);
2231 *p++ = digit + '0';
2232 while (--digits > 0)
2234 times_pten (&r, 1);
2235 digit = rtd_divmod (&r, &pten);
2236 *p++ = digit + '0';
2238 *p++ = '.';
2239 *p++ = '\0';
2242 /* Convert a real with an integral value to decimal float. */
2244 static void
2245 decimal_from_integer (REAL_VALUE_TYPE *r)
2247 char str[256];
2249 decimal_integer_string (str, r, sizeof (str) - 1);
2250 decimal_real_from_string (r, str);
2253 /* Returns 10**2**N. */
2255 static const REAL_VALUE_TYPE *
2256 ten_to_ptwo (int n)
2258 static REAL_VALUE_TYPE tens[EXP_BITS];
2260 gcc_assert (n >= 0);
2261 gcc_assert (n < EXP_BITS);
2263 if (tens[n].cl == rvc_zero)
2265 if (n < (HOST_BITS_PER_WIDE_INT == 64 ? 5 : 4))
2267 HOST_WIDE_INT t = 10;
2268 int i;
2270 for (i = 0; i < n; ++i)
2271 t *= t;
2273 real_from_integer (&tens[n], VOIDmode, t, 0, 1);
2275 else
2277 const REAL_VALUE_TYPE *t = ten_to_ptwo (n - 1);
2278 do_multiply (&tens[n], t, t);
2282 return &tens[n];
2285 /* Returns 10**(-2**N). */
2287 static const REAL_VALUE_TYPE *
2288 ten_to_mptwo (int n)
2290 static REAL_VALUE_TYPE tens[EXP_BITS];
2292 gcc_assert (n >= 0);
2293 gcc_assert (n < EXP_BITS);
2295 if (tens[n].cl == rvc_zero)
2296 do_divide (&tens[n], real_digit (1), ten_to_ptwo (n));
2298 return &tens[n];
2301 /* Returns N. */
2303 static const REAL_VALUE_TYPE *
2304 real_digit (int n)
2306 static REAL_VALUE_TYPE num[10];
2308 gcc_assert (n >= 0);
2309 gcc_assert (n <= 9);
2311 if (n > 0 && num[n].cl == rvc_zero)
2312 real_from_integer (&num[n], VOIDmode, n, 0, 1);
2314 return &num[n];
2317 /* Multiply R by 10**EXP. */
2319 static void
2320 times_pten (REAL_VALUE_TYPE *r, int exp)
2322 REAL_VALUE_TYPE pten, *rr;
2323 bool negative = (exp < 0);
2324 int i;
2326 if (negative)
2328 exp = -exp;
2329 pten = *real_digit (1);
2330 rr = &pten;
2332 else
2333 rr = r;
2335 for (i = 0; exp > 0; ++i, exp >>= 1)
2336 if (exp & 1)
2337 do_multiply (rr, rr, ten_to_ptwo (i));
2339 if (negative)
2340 do_divide (r, r, &pten);
2343 /* Returns the special REAL_VALUE_TYPE corresponding to 'e'. */
2345 const REAL_VALUE_TYPE *
2346 dconst_e_ptr (void)
2348 static REAL_VALUE_TYPE value;
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)
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);
2362 return &value;
2365 /* Returns the special REAL_VALUE_TYPE corresponding to 1/3. */
2367 const REAL_VALUE_TYPE *
2368 dconst_third_ptr (void)
2370 static REAL_VALUE_TYPE value;
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)
2376 real_arithmetic (&value, RDIV_EXPR, &dconst1, real_digit (3));
2378 return &value;
2381 /* Returns the special REAL_VALUE_TYPE corresponding to sqrt(2). */
2383 const REAL_VALUE_TYPE *
2384 dconst_sqrt2_ptr (void)
2386 static REAL_VALUE_TYPE value;
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)
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);
2398 return &value;
2401 /* Fills R with +Inf. */
2403 void
2404 real_inf (REAL_VALUE_TYPE *r)
2406 get_inf (r, 0);
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. */
2414 bool
2415 real_nan (REAL_VALUE_TYPE *r, const char *str, int quiet,
2416 enum machine_mode mode)
2418 const struct real_format *fmt;
2420 fmt = REAL_MODE_FORMAT (mode);
2421 gcc_assert (fmt);
2423 if (*str == 0)
2425 if (quiet)
2426 get_canonical_qnan (r, 0);
2427 else
2428 get_canonical_snan (r, 0);
2430 else
2432 int base = 10, d;
2434 memset (r, 0, sizeof (*r));
2435 r->cl = rvc_nan;
2437 /* Parse akin to strtol into the significand of R. */
2439 while (ISSPACE (*str))
2440 str++;
2441 if (*str == '-')
2442 str++;
2443 else if (*str == '+')
2444 str++;
2445 if (*str == '0')
2447 str++;
2448 if (*str == 'x' || *str == 'X')
2450 base = 16;
2451 str++;
2453 else
2454 base = 8;
2457 while ((d = hex_value (*str)) < base)
2459 REAL_VALUE_TYPE u;
2461 switch (base)
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 ();
2478 get_zero (&u, 0);
2479 u.sig[0] = d;
2480 add_significands (r, r, &u);
2482 str++;
2485 /* Must have consumed the entire string for success. */
2486 if (*str != 0)
2487 return false;
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);
2493 /* Our MSB is always unset for NaNs. */
2494 r->sig[SIGSZ-1] &= ~SIG_MSB;
2496 /* Force quiet or signalling NaN. */
2497 r->signalling = !quiet;
2500 return true;
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. */
2506 void
2507 real_maxval (REAL_VALUE_TYPE *r, int sign, enum machine_mode mode)
2509 const struct real_format *fmt;
2510 int np2;
2512 fmt = REAL_MODE_FORMAT (mode);
2513 gcc_assert (fmt);
2514 memset (r, 0, sizeof (*r));
2516 if (fmt->b == 10)
2517 decimal_real_maxval (r, sign, mode);
2518 else
2520 r->cl = rvc_normal;
2521 r->sign = sign;
2522 SET_REAL_EXP (r, fmt->emax);
2524 np2 = SIGNIFICAND_BITS - fmt->p;
2525 memset (r->sig, -1, SIGSZ * sizeof (unsigned long));
2526 clear_significand_below (r, np2);
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);
2539 /* Fills R with 2**N. */
2541 void
2542 real_2expN (REAL_VALUE_TYPE *r, int n, enum machine_mode fmode)
2544 memset (r, 0, sizeof (*r));
2546 n++;
2547 if (n > MAX_EXP)
2548 r->cl = rvc_inf;
2549 else if (n < -MAX_EXP)
2551 else
2553 r->cl = rvc_normal;
2554 SET_REAL_EXP (r, n);
2555 r->sig[SIGSZ-1] = SIG_MSB;
2557 if (DECIMAL_FLOAT_MODE_P (fmode))
2558 decimal_real_convert (r, fmode, r);
2562 static void
2563 round_for_format (const struct real_format *fmt, REAL_VALUE_TYPE *r)
2565 int p2, np2, i, w;
2566 int emin2m1, emax2;
2567 bool round_up = false;
2569 if (r->decimal)
2571 if (fmt->b == 10)
2573 decimal_round_for_format (fmt, r);
2574 return;
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);
2583 p2 = fmt->p;
2584 emin2m1 = fmt->emin - 1;
2585 emax2 = fmt->emax;
2587 np2 = SIGNIFICAND_BITS - p2;
2588 switch (r->cl)
2590 underflow:
2591 get_zero (r, r->sign);
2592 case rvc_zero:
2593 if (!fmt->has_signed_zero)
2594 r->sign = 0;
2595 return;
2597 overflow:
2598 get_inf (r, r->sign);
2599 case rvc_inf:
2600 return;
2602 case rvc_nan:
2603 clear_significand_below (r, np2);
2604 return;
2606 case rvc_normal:
2607 break;
2609 default:
2610 gcc_unreachable ();
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)
2619 int diff;
2621 if (!fmt->has_denorm)
2623 /* Don't underflow completely until we've had a chance to round. */
2624 if (REAL_EXP (r) < emin2m1)
2625 goto underflow;
2627 else
2629 diff = emin2m1 - REAL_EXP (r) + 1;
2630 if (diff > p2)
2631 goto underflow;
2633 /* De-normalize the significand. */
2634 r->sig[0] |= sticky_rshift_significand (r, r, diff);
2635 SET_REAL_EXP (r, REAL_EXP (r) + diff);
2639 if (!fmt->round_towards_zero)
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;
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);
2653 guard = test_significand_bit (r, np2 - 1);
2654 lsb = test_significand_bit (r, np2);
2656 /* Round to even. */
2657 round_up = guard && (sticky || lsb);
2660 if (round_up)
2662 REAL_VALUE_TYPE u;
2663 get_zero (&u, 0);
2664 set_significand_bit (&u, np2);
2666 if (add_significands (r, r, &u))
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;
2678 /* Catch underflow that we deferred until after rounding. */
2679 if (REAL_EXP (r) <= emin2m1)
2680 goto underflow;
2682 /* Clear out trailing garbage. */
2683 clear_significand_below (r, np2);
2686 /* Extend or truncate to a new mode. */
2688 void
2689 real_convert (REAL_VALUE_TYPE *r, enum machine_mode mode,
2690 const REAL_VALUE_TYPE *a)
2692 const struct real_format *fmt;
2694 fmt = REAL_MODE_FORMAT (mode);
2695 gcc_assert (fmt);
2697 *r = *a;
2699 if (a->decimal || fmt->b == 10)
2700 decimal_real_convert (r, mode, a);
2702 round_for_format (fmt, r);
2704 /* round_for_format de-normalizes denormals. Undo just that part. */
2705 if (r->cl == rvc_normal)
2706 normalize (r);
2709 /* Legacy. Likewise, except return the struct directly. */
2711 REAL_VALUE_TYPE
2712 real_value_truncate (enum machine_mode mode, REAL_VALUE_TYPE a)
2714 REAL_VALUE_TYPE r;
2715 real_convert (&r, mode, &a);
2716 return r;
2719 /* Return true if truncating to MODE is exact. */
2721 bool
2722 exact_real_truncate (enum machine_mode mode, const REAL_VALUE_TYPE *a)
2724 const struct real_format *fmt;
2725 REAL_VALUE_TYPE t;
2726 int emin2m1;
2728 fmt = REAL_MODE_FORMAT (mode);
2729 gcc_assert (fmt);
2731 /* Don't allow conversion to denormals. */
2732 emin2m1 = fmt->emin - 1;
2733 if (REAL_EXP (a) <= emin2m1)
2734 return false;
2736 /* After conversion to the new mode, the value must be identical. */
2737 real_convert (&t, mode, a);
2738 return real_identical (&t, a);
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.
2745 Legacy: return word 0 for implementing REAL_VALUE_TO_TARGET_SINGLE. */
2747 long
2748 real_to_target_fmt (long *buf, const REAL_VALUE_TYPE *r_orig,
2749 const struct real_format *fmt)
2751 REAL_VALUE_TYPE r;
2752 long buf1;
2754 r = *r_orig;
2755 round_for_format (fmt, &r);
2757 if (!buf)
2758 buf = &buf1;
2759 (*fmt->encode) (fmt, buf, &r);
2761 return *buf;
2764 /* Similar, but look up the format from MODE. */
2766 long
2767 real_to_target (long *buf, const REAL_VALUE_TYPE *r, enum machine_mode mode)
2769 const struct real_format *fmt;
2771 fmt = REAL_MODE_FORMAT (mode);
2772 gcc_assert (fmt);
2774 return real_to_target_fmt (buf, r, fmt);
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. */
2781 void
2782 real_from_target_fmt (REAL_VALUE_TYPE *r, const long *buf,
2783 const struct real_format *fmt)
2785 (*fmt->decode) (fmt, r, buf);
2788 /* Similar, but look up the format from MODE. */
2790 void
2791 real_from_target (REAL_VALUE_TYPE *r, const long *buf, enum machine_mode mode)
2793 const struct real_format *fmt;
2795 fmt = REAL_MODE_FORMAT (mode);
2796 gcc_assert (fmt);
2798 (*fmt->decode) (fmt, r, buf);
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. */
2806 significand_size (enum machine_mode mode)
2808 const struct real_format *fmt;
2810 fmt = REAL_MODE_FORMAT (mode);
2811 if (fmt == NULL)
2812 return 0;
2814 if (fmt->b == 10)
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;
2823 return fmt->p;
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. */
2830 unsigned int
2831 real_hash (const REAL_VALUE_TYPE *r)
2833 unsigned int h;
2834 size_t i;
2836 h = r->cl | (r->sign << 2);
2837 switch (r->cl)
2839 case rvc_zero:
2840 case rvc_inf:
2841 return h;
2843 case rvc_normal:
2844 h |= REAL_EXP (r) << 3;
2845 break;
2847 case rvc_nan:
2848 if (r->signalling)
2849 h ^= (unsigned int)-1;
2850 if (r->canonical)
2851 return h;
2852 break;
2854 default:
2855 gcc_unreachable ();
2858 if (sizeof(unsigned long) > sizeof(unsigned int))
2859 for (i = 0; i < SIGSZ; ++i)
2861 unsigned long s = r->sig[i];
2862 h ^= s ^ (s >> (HOST_BITS_PER_LONG / 2));
2864 else
2865 for (i = 0; i < SIGSZ; ++i)
2866 h ^= r->sig[i];
2868 return h;
2871 /* IEEE single-precision format. */
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 *);
2878 static void
2879 encode_ieee_single (const struct real_format *fmt, long *buf,
2880 const REAL_VALUE_TYPE *r)
2882 unsigned long image, sig, exp;
2883 unsigned long sign = r->sign;
2884 bool denormal = (r->sig[SIGSZ-1] & SIG_MSB) == 0;
2886 image = sign << 31;
2887 sig = (r->sig[SIGSZ-1] >> (HOST_BITS_PER_LONG - 24)) & 0x7fffff;
2889 switch (r->cl)
2891 case rvc_zero:
2892 break;
2894 case rvc_inf:
2895 if (fmt->has_inf)
2896 image |= 255 << 23;
2897 else
2898 image |= 0x7fffffff;
2899 break;
2901 case rvc_nan:
2902 if (fmt->has_nans)
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;
2913 image |= 255 << 23;
2914 image |= sig;
2916 else
2917 image |= 0x7fffffff;
2918 break;
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;
2932 default:
2933 gcc_unreachable ();
2936 buf[0] = image;
2939 static void
2940 decode_ieee_single (const struct real_format *fmt, REAL_VALUE_TYPE *r,
2941 const long *buf)
2943 unsigned long image = buf[0] & 0xffffffff;
2944 bool sign = (image >> 31) & 1;
2945 int exp = (image >> 23) & 0xff;
2947 memset (r, 0, sizeof (*r));
2948 image <<= HOST_BITS_PER_LONG - 24;
2949 image &= ~SIG_MSB;
2951 if (exp == 0)
2953 if (image && fmt->has_denorm)
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);
2961 else if (fmt->has_signed_zero)
2962 r->sign = sign;
2964 else if (exp == 255 && (fmt->has_nans || fmt->has_inf))
2966 if (image)
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;
2974 else
2976 r->cl = rvc_inf;
2977 r->sign = sign;
2980 else
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;
2989 const struct real_format ieee_single_format =
2991 encode_ieee_single,
2992 decode_ieee_single,
2996 -125,
2997 128,
3000 false,
3001 true,
3002 true,
3003 true,
3004 true,
3005 true,
3006 true,
3007 false
3010 const struct real_format mips_single_format =
3012 encode_ieee_single,
3013 decode_ieee_single,
3017 -125,
3018 128,
3021 false,
3022 true,
3023 true,
3024 true,
3025 true,
3026 true,
3027 false,
3028 true
3031 const struct real_format motorola_single_format =
3033 encode_ieee_single,
3034 decode_ieee_single,
3038 -125,
3039 128,
3042 false,
3043 true,
3044 true,
3045 true,
3046 true,
3047 true,
3048 true,
3049 true
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 =
3065 encode_ieee_single,
3066 decode_ieee_single,
3070 -125,
3071 129,
3074 true,
3075 false,
3076 false,
3077 false,
3078 true,
3079 true,
3080 false,
3081 false
3084 /* IEEE double-precision format. */
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 *);
3091 static void
3092 encode_ieee_double (const struct real_format *fmt, long *buf,
3093 const REAL_VALUE_TYPE *r)
3095 unsigned long image_lo, image_hi, sig_lo, sig_hi, exp;
3096 bool denormal = (r->sig[SIGSZ-1] & SIG_MSB) == 0;
3098 image_hi = r->sign << 31;
3099 image_lo = 0;
3101 if (HOST_BITS_PER_LONG == 64)
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;
3107 else
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;
3115 switch (r->cl)
3117 case rvc_zero:
3118 break;
3120 case rvc_inf:
3121 if (fmt->has_inf)
3122 image_hi |= 2047 << 20;
3123 else
3125 image_hi |= 0x7fffffff;
3126 image_lo = 0xffffffff;
3128 break;
3130 case rvc_nan:
3131 if (fmt->has_nans)
3133 if (r->canonical)
3135 if (fmt->canonical_nan_lsbs_set)
3137 sig_hi = (1 << 19) - 1;
3138 sig_lo = 0xffffffff;
3140 else
3142 sig_hi = 0;
3143 sig_lo = 0;
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;
3153 image_hi |= 2047 << 20;
3154 image_hi |= sig_hi;
3155 image_lo = sig_lo;
3157 else
3159 image_hi |= 0x7fffffff;
3160 image_lo = 0xffffffff;
3162 break;
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;
3177 default:
3178 gcc_unreachable ();
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;
3187 static void
3188 decode_ieee_double (const struct real_format *fmt, REAL_VALUE_TYPE *r,
3189 const long *buf)
3191 unsigned long image_hi, image_lo;
3192 bool sign;
3193 int exp;
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;
3202 sign = (image_hi >> 31) & 1;
3203 exp = (image_hi >> 20) & 0x7ff;
3205 memset (r, 0, sizeof (*r));
3207 image_hi <<= 32 - 21;
3208 image_hi |= image_lo >> 21;
3209 image_hi &= 0x7fffffff;
3210 image_lo <<= 32 - 21;
3212 if (exp == 0)
3214 if ((image_hi || image_lo) && fmt->has_denorm)
3216 r->cl = rvc_normal;
3217 r->sign = sign;
3218 SET_REAL_EXP (r, -1022);
3219 if (HOST_BITS_PER_LONG == 32)
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;
3226 else
3228 image_hi = (image_hi << 31 << 2) | (image_lo << 1);
3229 r->sig[SIGSZ-1] = image_hi;
3231 normalize (r);
3233 else if (fmt->has_signed_zero)
3234 r->sign = sign;
3236 else if (exp == 2047 && (fmt->has_nans || fmt->has_inf))
3238 if (image_hi || image_lo)
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)
3245 r->sig[SIGSZ-1] = image_hi;
3246 r->sig[SIGSZ-2] = image_lo;
3248 else
3249 r->sig[SIGSZ-1] = (image_hi << 31 << 1) | image_lo;
3251 else
3253 r->cl = rvc_inf;
3254 r->sign = sign;
3257 else
3259 r->cl = rvc_normal;
3260 r->sign = sign;
3261 SET_REAL_EXP (r, exp - 1023 + 1);
3262 if (HOST_BITS_PER_LONG == 32)
3264 r->sig[SIGSZ-1] = image_hi | SIG_MSB;
3265 r->sig[SIGSZ-2] = image_lo;
3267 else
3268 r->sig[SIGSZ-1] = (image_hi << 31 << 1) | image_lo | SIG_MSB;
3272 const struct real_format ieee_double_format =
3274 encode_ieee_double,
3275 decode_ieee_double,
3279 -1021,
3280 1024,
3283 false,
3284 true,
3285 true,
3286 true,
3287 true,
3288 true,
3289 true,
3290 false
3293 const struct real_format mips_double_format =
3295 encode_ieee_double,
3296 decode_ieee_double,
3300 -1021,
3301 1024,
3304 false,
3305 true,
3306 true,
3307 true,
3308 true,
3309 true,
3310 false,
3311 true
3314 const struct real_format motorola_double_format =
3316 encode_ieee_double,
3317 decode_ieee_double,
3321 -1021,
3322 1024,
3325 false,
3326 true,
3327 true,
3328 true,
3329 true,
3330 true,
3331 true,
3332 true
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. */
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)
3347 unsigned long image_hi, sig_hi, sig_lo;
3348 bool denormal = (r->sig[SIGSZ-1] & SIG_MSB) == 0;
3350 image_hi = r->sign << 15;
3351 sig_hi = sig_lo = 0;
3353 switch (r->cl)
3355 case rvc_zero:
3356 break;
3358 case rvc_inf:
3359 if (fmt->has_inf)
3361 image_hi |= 32767;
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;
3368 else
3370 image_hi |= 32767;
3371 sig_lo = sig_hi = 0xffffffff;
3373 break;
3375 case rvc_nan:
3376 if (fmt->has_nans)
3378 image_hi |= 32767;
3379 if (r->canonical)
3381 if (fmt->canonical_nan_lsbs_set)
3383 sig_hi = (1 << 30) - 1;
3384 sig_lo = 0xffffffff;
3387 else if (HOST_BITS_PER_LONG == 32)
3389 sig_hi = r->sig[SIGSZ-1];
3390 sig_lo = r->sig[SIGSZ-2];
3392 else
3394 sig_lo = r->sig[SIGSZ-1];
3395 sig_hi = sig_lo >> 31 >> 1;
3396 sig_lo &= 0xffffffff;
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;
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;
3410 else
3412 image_hi |= 32767;
3413 sig_lo = sig_hi = 0xffffffff;
3415 break;
3417 case rvc_normal:
3419 int exp = REAL_EXP (r);
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.
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. */
3430 if (denormal)
3431 exp = 0;
3432 else
3434 exp += 16383 - 1;
3435 gcc_assert (exp >= 0);
3437 image_hi |= exp;
3439 if (HOST_BITS_PER_LONG == 32)
3441 sig_hi = r->sig[SIGSZ-1];
3442 sig_lo = r->sig[SIGSZ-2];
3444 else
3446 sig_lo = r->sig[SIGSZ-1];
3447 sig_hi = sig_lo >> 31 >> 1;
3448 sig_lo &= 0xffffffff;
3451 break;
3453 default:
3454 gcc_unreachable ();
3457 buf[0] = sig_lo, buf[1] = sig_hi, buf[2] = image_hi;
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)
3466 long intermed[3];
3467 encode_ieee_extended (fmt, intermed, r);
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];
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)
3486 if (FLOAT_WORDS_BIG_ENDIAN)
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);
3497 else
3498 /* encode_ieee_extended produces what we want directly. */
3499 encode_ieee_extended (fmt, buf, r);
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)
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;
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)
3520 unsigned long image_hi, sig_hi, sig_lo;
3521 bool sign;
3522 int exp;
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;
3529 sign = (image_hi >> 15) & 1;
3530 exp = image_hi & 0x7fff;
3532 memset (r, 0, sizeof (*r));
3534 if (exp == 0)
3536 if ((sig_hi || sig_lo) && fmt->has_denorm)
3538 r->cl = rvc_normal;
3539 r->sign = sign;
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)
3549 r->sig[SIGSZ-1] = sig_hi;
3550 r->sig[SIGSZ-2] = sig_lo;
3552 else
3553 r->sig[SIGSZ-1] = (sig_hi << 31 << 1) | sig_lo;
3555 normalize (r);
3557 else if (fmt->has_signed_zero)
3558 r->sign = sign;
3560 else if (exp == 32767 && (fmt->has_nans || fmt->has_inf))
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;
3567 if (sig_hi || sig_lo)
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)
3574 r->sig[SIGSZ-1] = sig_hi;
3575 r->sig[SIGSZ-2] = sig_lo;
3577 else
3578 r->sig[SIGSZ-1] = (sig_hi << 31 << 1) | sig_lo;
3580 else
3582 r->cl = rvc_inf;
3583 r->sign = sign;
3586 else
3588 r->cl = rvc_normal;
3589 r->sign = sign;
3590 SET_REAL_EXP (r, exp - 16383 + 1);
3591 if (HOST_BITS_PER_LONG == 32)
3593 r->sig[SIGSZ-1] = sig_hi;
3594 r->sig[SIGSZ-2] = sig_lo;
3596 else
3597 r->sig[SIGSZ-1] = (sig_hi << 31 << 1) | sig_lo;
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)
3607 long intermed[3];
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;
3616 decode_ieee_extended (fmt, r, intermed);
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)
3625 if (FLOAT_WORDS_BIG_ENDIAN)
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];
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);
3636 decode_ieee_extended (fmt, r, intermed);
3638 else
3639 /* decode_ieee_extended produces what we want directly. */
3640 decode_ieee_extended (fmt, r, buf);
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)
3649 /* All the padding in an Intel-format extended real goes at the high end. */
3650 decode_ieee_extended_intel_96 (fmt, r, buf);
3653 const struct real_format ieee_extended_motorola_format =
3655 encode_ieee_extended_motorola,
3656 decode_ieee_extended_motorola,
3660 -16382,
3661 16384,
3664 false,
3665 true,
3666 true,
3667 true,
3668 true,
3669 true,
3670 true,
3671 true
3674 const struct real_format ieee_extended_intel_96_format =
3676 encode_ieee_extended_intel_96,
3677 decode_ieee_extended_intel_96,
3681 -16381,
3682 16384,
3685 false,
3686 true,
3687 true,
3688 true,
3689 true,
3690 true,
3691 true,
3692 false
3695 const struct real_format ieee_extended_intel_128_format =
3697 encode_ieee_extended_intel_128,
3698 decode_ieee_extended_intel_128,
3702 -16381,
3703 16384,
3706 false,
3707 true,
3708 true,
3709 true,
3710 true,
3711 true,
3712 true,
3713 false
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 =
3720 encode_ieee_extended_intel_96,
3721 decode_ieee_extended_intel_96,
3725 -16381,
3726 16384,
3729 false,
3730 true,
3731 true,
3732 true,
3733 true,
3734 true,
3735 true,
3736 false
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. */
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 *);
3752 static void
3753 encode_ibm_extended (const struct real_format *fmt, long *buf,
3754 const REAL_VALUE_TYPE *r)
3756 REAL_VALUE_TYPE u, normr, v;
3757 const struct real_format *base_fmt;
3759 base_fmt = fmt->qnan_msb_set ? &ieee_double_format : &mips_double_format;
3761 /* Renormalize R before doing any arithmetic on it. */
3762 normr = *r;
3763 if (normr.cl == rvc_normal)
3764 normalize (&normr);
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);
3771 if (u.cl == rvc_normal)
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);
3778 else
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;
3787 static void
3788 decode_ibm_extended (const struct real_format *fmt ATTRIBUTE_UNUSED, REAL_VALUE_TYPE *r,
3789 const long *buf)
3791 REAL_VALUE_TYPE u, v;
3792 const struct real_format *base_fmt;
3794 base_fmt = fmt->qnan_msb_set ? &ieee_double_format : &mips_double_format;
3795 decode_ieee_double (base_fmt, &u, &buf[0]);
3797 if (u.cl != rvc_zero && u.cl != rvc_inf && u.cl != rvc_nan)
3799 decode_ieee_double (base_fmt, &v, &buf[2]);
3800 do_add (r, &u, &v, 0);
3802 else
3803 *r = u;
3806 const struct real_format ibm_extended_format =
3808 encode_ibm_extended,
3809 decode_ibm_extended,
3811 53 + 53,
3813 -1021 + 53,
3814 1024,
3815 127,
3817 false,
3818 true,
3819 true,
3820 true,
3821 true,
3822 true,
3823 true,
3824 false
3827 const struct real_format mips_extended_format =
3829 encode_ibm_extended,
3830 decode_ibm_extended,
3832 53 + 53,
3834 -1021 + 53,
3835 1024,
3836 127,
3838 false,
3839 true,
3840 true,
3841 true,
3842 true,
3843 true,
3844 false,
3845 true
3849 /* IEEE quad precision format. */
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 *);
3856 static void
3857 encode_ieee_quad (const struct real_format *fmt, long *buf,
3858 const REAL_VALUE_TYPE *r)
3860 unsigned long image3, image2, image1, image0, exp;
3861 bool denormal = (r->sig[SIGSZ-1] & SIG_MSB) == 0;
3862 REAL_VALUE_TYPE u;
3864 image3 = r->sign << 31;
3865 image2 = 0;
3866 image1 = 0;
3867 image0 = 0;
3869 rshift_significand (&u, r, SIGNIFICAND_BITS - 113);
3871 switch (r->cl)
3873 case rvc_zero:
3874 break;
3876 case rvc_inf:
3877 if (fmt->has_inf)
3878 image3 |= 32767 << 16;
3879 else
3881 image3 |= 0x7fffffff;
3882 image2 = 0xffffffff;
3883 image1 = 0xffffffff;
3884 image0 = 0xffffffff;
3886 break;
3888 case rvc_nan:
3889 if (fmt->has_nans)
3891 image3 |= 32767 << 16;
3893 if (r->canonical)
3895 if (fmt->canonical_nan_lsbs_set)
3897 image3 |= 0x7fff;
3898 image2 = image1 = image0 = 0xffffffff;
3901 else if (HOST_BITS_PER_LONG == 32)
3903 image0 = u.sig[0];
3904 image1 = u.sig[1];
3905 image2 = u.sig[2];
3906 image3 |= u.sig[3] & 0xffff;
3908 else
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;
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;
3924 else
3926 image3 |= 0x7fffffff;
3927 image2 = 0xffffffff;
3928 image1 = 0xffffffff;
3929 image0 = 0xffffffff;
3931 break;
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;
3943 if (HOST_BITS_PER_LONG == 32)
3945 image0 = u.sig[0];
3946 image1 = u.sig[1];
3947 image2 = u.sig[2];
3948 image3 |= u.sig[3] & 0xffff;
3950 else
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;
3959 break;
3961 default:
3962 gcc_unreachable ();
3965 if (FLOAT_WORDS_BIG_ENDIAN)
3967 buf[0] = image3;
3968 buf[1] = image2;
3969 buf[2] = image1;
3970 buf[3] = image0;
3972 else
3974 buf[0] = image0;
3975 buf[1] = image1;
3976 buf[2] = image2;
3977 buf[3] = image3;
3981 static void
3982 decode_ieee_quad (const struct real_format *fmt, REAL_VALUE_TYPE *r,
3983 const long *buf)
3985 unsigned long image3, image2, image1, image0;
3986 bool sign;
3987 int exp;
3989 if (FLOAT_WORDS_BIG_ENDIAN)
3991 image3 = buf[0];
3992 image2 = buf[1];
3993 image1 = buf[2];
3994 image0 = buf[3];
3996 else
3998 image0 = buf[0];
3999 image1 = buf[1];
4000 image2 = buf[2];
4001 image3 = buf[3];
4003 image0 &= 0xffffffff;
4004 image1 &= 0xffffffff;
4005 image2 &= 0xffffffff;
4007 sign = (image3 >> 31) & 1;
4008 exp = (image3 >> 16) & 0x7fff;
4009 image3 &= 0xffff;
4011 memset (r, 0, sizeof (*r));
4013 if (exp == 0)
4015 if ((image3 | image2 | image1 | image0) && fmt->has_denorm)
4017 r->cl = rvc_normal;
4018 r->sign = sign;
4020 SET_REAL_EXP (r, -16382 + (SIGNIFICAND_BITS - 112));
4021 if (HOST_BITS_PER_LONG == 32)
4023 r->sig[0] = image0;
4024 r->sig[1] = image1;
4025 r->sig[2] = image2;
4026 r->sig[3] = image3;
4028 else
4030 r->sig[0] = (image1 << 31 << 1) | image0;
4031 r->sig[1] = (image3 << 31 << 1) | image2;
4034 normalize (r);
4036 else if (fmt->has_signed_zero)
4037 r->sign = sign;
4039 else if (exp == 32767 && (fmt->has_nans || fmt->has_inf))
4041 if (image3 | image2 | image1 | image0)
4043 r->cl = rvc_nan;
4044 r->sign = sign;
4045 r->signalling = ((image3 >> 15) & 1) ^ fmt->qnan_msb_set;
4047 if (HOST_BITS_PER_LONG == 32)
4049 r->sig[0] = image0;
4050 r->sig[1] = image1;
4051 r->sig[2] = image2;
4052 r->sig[3] = image3;
4054 else
4056 r->sig[0] = (image1 << 31 << 1) | image0;
4057 r->sig[1] = (image3 << 31 << 1) | image2;
4059 lshift_significand (r, r, SIGNIFICAND_BITS - 113);
4061 else
4063 r->cl = rvc_inf;
4064 r->sign = sign;
4067 else
4069 r->cl = rvc_normal;
4070 r->sign = sign;
4071 SET_REAL_EXP (r, exp - 16383 + 1);
4073 if (HOST_BITS_PER_LONG == 32)
4075 r->sig[0] = image0;
4076 r->sig[1] = image1;
4077 r->sig[2] = image2;
4078 r->sig[3] = image3;
4080 else
4082 r->sig[0] = (image1 << 31 << 1) | image0;
4083 r->sig[1] = (image3 << 31 << 1) | image2;
4085 lshift_significand (r, r, SIGNIFICAND_BITS - 113);
4086 r->sig[SIGSZ-1] |= SIG_MSB;
4090 const struct real_format ieee_quad_format =
4092 encode_ieee_quad,
4093 decode_ieee_quad,
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
4111 const struct real_format mips_quad_format =
4113 encode_ieee_quad,
4114 decode_ieee_quad,
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
4132 /* Descriptions of VAX floating point formats can be found beginning at
4134 http://h71000.www7.hp.com/doc/73FINAL/4515/4515pro_013.html#f_floating_point_format
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.
4139 We don't implement the H_floating format here, simply because neither
4140 the VAX or Alpha ports use it. */
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 *);
4155 static void
4156 encode_vax_f (const struct real_format *fmt ATTRIBUTE_UNUSED, long *buf,
4157 const REAL_VALUE_TYPE *r)
4159 unsigned long sign, exp, sig, image;
4161 sign = r->sign << 15;
4163 switch (r->cl)
4165 case rvc_zero:
4166 image = 0;
4167 break;
4169 case rvc_inf:
4170 case rvc_nan:
4171 image = 0xffff7fff | sign;
4172 break;
4174 case rvc_normal:
4175 sig = (r->sig[SIGSZ-1] >> (HOST_BITS_PER_LONG - 24)) & 0x7fffff;
4176 exp = REAL_EXP (r) + 128;
4178 image = (sig << 16) & 0xffff0000;
4179 image |= sign;
4180 image |= exp << 7;
4181 image |= sig >> 16;
4182 break;
4184 default:
4185 gcc_unreachable ();
4188 buf[0] = image;
4191 static void
4192 decode_vax_f (const struct real_format *fmt ATTRIBUTE_UNUSED,
4193 REAL_VALUE_TYPE *r, const long *buf)
4195 unsigned long image = buf[0] & 0xffffffff;
4196 int exp = (image >> 7) & 0xff;
4198 memset (r, 0, sizeof (*r));
4200 if (exp != 0)
4202 r->cl = rvc_normal;
4203 r->sign = (image >> 15) & 1;
4204 SET_REAL_EXP (r, exp - 128);
4206 image = ((image & 0x7f) << 16) | ((image >> 16) & 0xffff);
4207 r->sig[SIGSZ-1] = (image << (HOST_BITS_PER_LONG - 24)) | SIG_MSB;
4211 static void
4212 encode_vax_d (const struct real_format *fmt ATTRIBUTE_UNUSED, long *buf,
4213 const REAL_VALUE_TYPE *r)
4215 unsigned long image0, image1, sign = r->sign << 15;
4217 switch (r->cl)
4219 case rvc_zero:
4220 image0 = image1 = 0;
4221 break;
4223 case rvc_inf:
4224 case rvc_nan:
4225 image0 = 0xffff7fff | sign;
4226 image1 = 0xffffffff;
4227 break;
4229 case rvc_normal:
4230 /* Extract the significand into straight hi:lo. */
4231 if (HOST_BITS_PER_LONG == 64)
4233 image0 = r->sig[SIGSZ-1];
4234 image1 = (image0 >> (64 - 56)) & 0xffffffff;
4235 image0 = (image0 >> (64 - 56 + 1) >> 31) & 0x7fffff;
4237 else
4239 image0 = r->sig[SIGSZ-1];
4240 image1 = r->sig[SIGSZ-2];
4241 image1 = (image0 << 24) | (image1 >> 8);
4242 image0 = (image0 >> 8) & 0xffffff;
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;
4250 /* Add the sign and exponent. */
4251 image0 |= sign;
4252 image0 |= (REAL_EXP (r) + 128) << 7;
4253 break;
4255 default:
4256 gcc_unreachable ();
4259 if (FLOAT_WORDS_BIG_ENDIAN)
4260 buf[0] = image1, buf[1] = image0;
4261 else
4262 buf[0] = image0, buf[1] = image1;
4265 static void
4266 decode_vax_d (const struct real_format *fmt ATTRIBUTE_UNUSED,
4267 REAL_VALUE_TYPE *r, const long *buf)
4269 unsigned long image0, image1;
4270 int exp;
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;
4279 exp = (image0 >> 7) & 0xff;
4281 memset (r, 0, sizeof (*r));
4283 if (exp != 0)
4285 r->cl = rvc_normal;
4286 r->sign = (image0 >> 15) & 1;
4287 SET_REAL_EXP (r, exp - 128);
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);
4294 if (HOST_BITS_PER_LONG == 64)
4296 image0 = (image0 << 31 << 1) | image1;
4297 image0 <<= 64 - 56;
4298 image0 |= SIG_MSB;
4299 r->sig[SIGSZ-1] = image0;
4301 else
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;
4311 static void
4312 encode_vax_g (const struct real_format *fmt ATTRIBUTE_UNUSED, long *buf,
4313 const REAL_VALUE_TYPE *r)
4315 unsigned long image0, image1, sign = r->sign << 15;
4317 switch (r->cl)
4319 case rvc_zero:
4320 image0 = image1 = 0;
4321 break;
4323 case rvc_inf:
4324 case rvc_nan:
4325 image0 = 0xffff7fff | sign;
4326 image1 = 0xffffffff;
4327 break;
4329 case rvc_normal:
4330 /* Extract the significand into straight hi:lo. */
4331 if (HOST_BITS_PER_LONG == 64)
4333 image0 = r->sig[SIGSZ-1];
4334 image1 = (image0 >> (64 - 53)) & 0xffffffff;
4335 image0 = (image0 >> (64 - 53 + 1) >> 31) & 0xfffff;
4337 else
4339 image0 = r->sig[SIGSZ-1];
4340 image1 = r->sig[SIGSZ-2];
4341 image1 = (image0 << 21) | (image1 >> 11);
4342 image0 = (image0 >> 11) & 0xfffff;
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;
4350 /* Add the sign and exponent. */
4351 image0 |= sign;
4352 image0 |= (REAL_EXP (r) + 1024) << 4;
4353 break;
4355 default:
4356 gcc_unreachable ();
4359 if (FLOAT_WORDS_BIG_ENDIAN)
4360 buf[0] = image1, buf[1] = image0;
4361 else
4362 buf[0] = image0, buf[1] = image1;
4365 static void
4366 decode_vax_g (const struct real_format *fmt ATTRIBUTE_UNUSED,
4367 REAL_VALUE_TYPE *r, const long *buf)
4369 unsigned long image0, image1;
4370 int exp;
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;
4379 exp = (image0 >> 4) & 0x7ff;
4381 memset (r, 0, sizeof (*r));
4383 if (exp != 0)
4385 r->cl = rvc_normal;
4386 r->sign = (image0 >> 15) & 1;
4387 SET_REAL_EXP (r, exp - 1024);
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);
4394 if (HOST_BITS_PER_LONG == 64)
4396 image0 = (image0 << 31 << 1) | image1;
4397 image0 <<= 64 - 53;
4398 image0 |= SIG_MSB;
4399 r->sig[SIGSZ-1] = image0;
4401 else
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;
4411 const struct real_format vax_f_format =
4413 encode_vax_f,
4414 decode_vax_f,
4418 -127,
4419 127,
4422 false,
4423 false,
4424 false,
4425 false,
4426 false,
4427 false,
4428 false,
4429 false
4432 const struct real_format vax_d_format =
4434 encode_vax_d,
4435 decode_vax_d,
4439 -127,
4440 127,
4443 false,
4444 false,
4445 false,
4446 false,
4447 false,
4448 false,
4449 false,
4450 false
4453 const struct real_format vax_g_format =
4455 encode_vax_g,
4456 decode_vax_g,
4460 -1023,
4461 1023,
4464 false,
4465 false,
4466 false,
4467 false,
4468 false,
4469 false,
4470 false,
4471 false
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)
4480 encode_decimal32 (fmt, buf, r);
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)
4489 decode_decimal32 (fmt, r, buf);
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)
4498 encode_decimal64 (fmt, buf, r);
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)
4507 decode_decimal64 (fmt, r, buf);
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)
4516 encode_decimal128 (fmt, buf, r);
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)
4525 decode_decimal128 (fmt, r, buf);
4528 /* Single precision decimal floating point (IEEE 754). */
4529 const struct real_format decimal_single_format =
4531 encode_decimal_single,
4532 decode_decimal_single,
4536 -94,
4540 false,
4541 true,
4542 true,
4543 true,
4544 true,
4545 true,
4546 true,
4547 false
4550 /* Double precision decimal floating point (IEEE 754). */
4551 const struct real_format decimal_double_format =
4553 encode_decimal_double,
4554 decode_decimal_double,
4558 -382,
4559 385,
4562 false,
4563 true,
4564 true,
4565 true,
4566 true,
4567 true,
4568 true,
4569 false
4572 /* Quad precision decimal floating point (IEEE 754). */
4573 const struct real_format decimal_quad_format =
4575 encode_decimal_quad,
4576 decode_decimal_quad,
4580 -6142,
4581 6145,
4582 127,
4583 127,
4584 false,
4585 true,
4586 true,
4587 true,
4588 true,
4589 true,
4590 true,
4591 false
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)
4600 unsigned long image, sig, exp;
4601 unsigned long sign = r->sign;
4602 bool denormal = (r->sig[SIGSZ-1] & SIG_MSB) == 0;
4604 image = sign << 15;
4605 sig = (r->sig[SIGSZ-1] >> (HOST_BITS_PER_LONG - 11)) & 0x3ff;
4607 switch (r->cl)
4609 case rvc_zero:
4610 break;
4612 case rvc_inf:
4613 if (fmt->has_inf)
4614 image |= 31 << 10;
4615 else
4616 image |= 0x7fff;
4617 break;
4619 case rvc_nan:
4620 if (fmt->has_nans)
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;
4631 image |= 31 << 10;
4632 image |= sig;
4634 else
4635 image |= 0x3ff;
4636 break;
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;
4650 default:
4651 gcc_unreachable ();
4654 buf[0] = image;
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)
4663 unsigned long image = buf[0] & 0xffff;
4664 bool sign = (image >> 15) & 1;
4665 int exp = (image >> 10) & 0x1f;
4667 memset (r, 0, sizeof (*r));
4668 image <<= HOST_BITS_PER_LONG - 11;
4669 image &= ~SIG_MSB;
4671 if (exp == 0)
4673 if (image && fmt->has_denorm)
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);
4681 else if (fmt->has_signed_zero)
4682 r->sign = sign;
4684 else if (exp == 31 && (fmt->has_nans || fmt->has_inf))
4686 if (image)
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;
4694 else
4696 r->cl = rvc_inf;
4697 r->sign = sign;
4700 else
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;
4709 /* Half-precision format, as specified in IEEE 754R. */
4710 const struct real_format ieee_half_format =
4712 encode_ieee_half,
4713 decode_ieee_half,
4717 -13,
4721 false,
4722 true,
4723 true,
4724 true,
4725 true,
4726 true,
4727 true,
4728 false
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 =
4736 encode_ieee_half,
4737 decode_ieee_half,
4741 -13,
4745 false,
4746 true,
4747 false,
4748 false,
4749 true,
4750 true,
4751 false,
4752 false
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. */
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 *);
4765 static void
4766 encode_internal (const struct real_format *fmt ATTRIBUTE_UNUSED, long *buf,
4767 const REAL_VALUE_TYPE *r)
4769 memcpy (buf, r, sizeof (*r));
4772 static void
4773 decode_internal (const struct real_format *fmt ATTRIBUTE_UNUSED,
4774 REAL_VALUE_TYPE *r, const long *buf)
4776 memcpy (r, buf, sizeof (*r));
4779 const struct real_format real_internal_format =
4781 encode_internal,
4782 decode_internal,
4784 SIGNIFICAND_BITS - 2,
4785 SIGNIFICAND_BITS - 2,
4786 -MAX_EXP,
4787 MAX_EXP,
4790 false,
4791 false,
4792 true,
4793 true,
4794 false,
4795 true,
4796 true,
4797 false
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. */
4806 bool
4807 real_sqrt (REAL_VALUE_TYPE *r, enum machine_mode mode,
4808 const REAL_VALUE_TYPE *x)
4810 static REAL_VALUE_TYPE halfthree;
4811 static bool init = false;
4812 REAL_VALUE_TYPE h, t, i;
4813 int iter, exp;
4815 /* sqrt(-0.0) is -0.0. */
4816 if (real_isnegzero (x))
4818 *r = *x;
4819 return false;
4822 /* Negative arguments return NaN. */
4823 if (real_isneg (x))
4825 get_canonical_qnan (r, 0);
4826 return false;
4829 /* Infinity and NaN return themselves. */
4830 if (!real_isfinite (x))
4832 *r = *x;
4833 return false;
4836 if (!init)
4838 do_add (&halfthree, &dconst1, &dconsthalf, 0);
4839 init = true;
4842 /* Initial guess for reciprocal sqrt, i. */
4843 exp = real_exponent (x);
4844 real_ldexp (&i, &dconst1, -exp/2);
4846 /* Newton's iteration for reciprocal sqrt, i. */
4847 for (iter = 0; iter < 16; iter++)
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);
4856 /* Check for early convergence. */
4857 if (iter >= 6 && real_identical (&i, &t))
4858 break;
4860 /* ??? Unroll loop to avoid copying. */
4861 i = t;
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);
4872 /* ??? We need a Tuckerman test to get the last bit. */
4874 real_convert (r, mode, &h);
4875 return true;
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. */
4884 bool
4885 real_powi (REAL_VALUE_TYPE *r, enum machine_mode mode,
4886 const REAL_VALUE_TYPE *x, HOST_WIDE_INT n)
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;
4895 if (n == 0)
4897 *r = dconst1;
4898 return false;
4900 else if (n < 0)
4902 /* Don't worry about overflow, from now on n is unsigned. */
4903 neg = true;
4904 n = -n;
4906 else
4907 neg = false;
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++)
4913 if (init)
4915 inexact |= do_multiply (&t, &t, &t);
4916 if (n & bit)
4917 inexact |= do_multiply (&t, &t, x);
4919 else if (n & bit)
4920 init = true;
4921 bit >>= 1;
4924 if (neg)
4925 inexact |= do_divide (&t, &dconst1, &t);
4927 real_convert (r, mode, &t);
4928 return inexact;
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. */
4934 void
4935 real_trunc (REAL_VALUE_TYPE *r, enum machine_mode mode,
4936 const REAL_VALUE_TYPE *x)
4938 do_fix_trunc (r, x);
4939 if (mode != VOIDmode)
4940 real_convert (r, mode, r);
4943 /* Round X to the largest integer not greater in value, i.e. round
4944 down, placing the result in R in mode MODE. */
4946 void
4947 real_floor (REAL_VALUE_TYPE *r, enum machine_mode mode,
4948 const REAL_VALUE_TYPE *x)
4950 REAL_VALUE_TYPE t;
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;
4961 /* Round X to the smallest integer not less then argument, i.e. round
4962 up, placing the result in R in mode MODE. */
4964 void
4965 real_ceil (REAL_VALUE_TYPE *r, enum machine_mode mode,
4966 const REAL_VALUE_TYPE *x)
4968 REAL_VALUE_TYPE t;
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;
4979 /* Round X to the nearest integer, but round halfway cases away from
4980 zero. */
4982 void
4983 real_round (REAL_VALUE_TYPE *r, enum machine_mode mode,
4984 const REAL_VALUE_TYPE *x)
4986 do_add (r, x, &dconsthalf, x->sign);
4987 do_fix_trunc (r, r);
4988 if (mode != VOIDmode)
4989 real_convert (r, mode, r);
4992 /* Set the sign of R to the sign of X. */
4994 void
4995 real_copysign (REAL_VALUE_TYPE *r, const REAL_VALUE_TYPE *x)
4997 r->sign = x->sign;
5000 /* Check whether the real constant value given is an integer. */
5002 bool
5003 real_isinteger (const REAL_VALUE_TYPE *c, enum machine_mode mode)
5005 REAL_VALUE_TYPE cint;
5007 real_trunc (&cint, mode, c);
5008 return real_identical (c, &cint);
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. */
5016 void
5017 get_max_float (const struct real_format *fmt, char *buf, size_t len)
5019 int i, n;
5020 char *p;
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)
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];
5040 gcc_assert (strlen (buf) < len);