1 /* real.c - software floating point emulation.
2 Copyright (C) 1993, 1994, 1995, 1996, 1997, 1998, 1999,
3 2000, 2002, 2003, 2004 Free Software Foundation, Inc.
4 Contributed by Stephen L. Moshier (moshier@world.std.com).
5 Re-written by Richard Henderson <rth@redhat.com>
7 This file is part of GCC.
9 GCC is free software; you can redistribute it and/or modify it under
10 the terms of the GNU General Public License as published by the Free
11 Software Foundation; either version 2, or (at your option) any later
14 GCC is distributed in the hope that it will be useful, but WITHOUT ANY
15 WARRANTY; without even the implied warranty of MERCHANTABILITY or
16 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
19 You should have received a copy of the GNU General Public License
20 along with GCC; see the file COPYING. If not, write to the Free
21 Software Foundation, 59 Temple Place - Suite 330, Boston, MA
26 #include "coretypes.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.
39 x = s * b^e * \sum_{k=1}^p f_k * b^{-k}
43 b = base or radix, here always 2
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
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
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 27.
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.
69 Target floating point models that use base 16 instead of base 2
70 (i.e. IBM 370), are handled during round_for_format, in which we
71 canonicalize the exponent to be a multiple of 4 (log2(16)), and
72 adjust the significand to match. */
75 /* Used to classify two numbers simultaneously. */
76 #define CLASS2(A, B) ((A) << 2 | (B))
78 #if HOST_BITS_PER_LONG != 64 && HOST_BITS_PER_LONG != 32
79 #error "Some constant folding done by hand to avoid shift count warnings"
82 static void get_zero (REAL_VALUE_TYPE *, int);
83 static void get_canonical_qnan (REAL_VALUE_TYPE *, int);
84 static void get_canonical_snan (REAL_VALUE_TYPE *, int);
85 static void get_inf (REAL_VALUE_TYPE *, int);
86 static bool sticky_rshift_significand (REAL_VALUE_TYPE *,
87 const REAL_VALUE_TYPE *, unsigned int);
88 static void rshift_significand (REAL_VALUE_TYPE *, const REAL_VALUE_TYPE *,
90 static void lshift_significand (REAL_VALUE_TYPE *, const REAL_VALUE_TYPE *,
92 static void lshift_significand_1 (REAL_VALUE_TYPE *, const REAL_VALUE_TYPE *);
93 static bool add_significands (REAL_VALUE_TYPE *r, const REAL_VALUE_TYPE *,
94 const REAL_VALUE_TYPE *);
95 static bool sub_significands (REAL_VALUE_TYPE *, const REAL_VALUE_TYPE *,
96 const REAL_VALUE_TYPE *, int);
97 static void neg_significand (REAL_VALUE_TYPE *, const REAL_VALUE_TYPE *);
98 static int cmp_significands (const REAL_VALUE_TYPE *, const REAL_VALUE_TYPE *);
99 static int cmp_significand_0 (const REAL_VALUE_TYPE *);
100 static void set_significand_bit (REAL_VALUE_TYPE *, unsigned int);
101 static void clear_significand_bit (REAL_VALUE_TYPE *, unsigned int);
102 static bool test_significand_bit (REAL_VALUE_TYPE *, unsigned int);
103 static void clear_significand_below (REAL_VALUE_TYPE *, unsigned int);
104 static bool div_significands (REAL_VALUE_TYPE *, const REAL_VALUE_TYPE *,
105 const REAL_VALUE_TYPE *);
106 static void normalize (REAL_VALUE_TYPE *);
108 static bool do_add (REAL_VALUE_TYPE *, const REAL_VALUE_TYPE *,
109 const REAL_VALUE_TYPE *, int);
110 static bool do_multiply (REAL_VALUE_TYPE *, const REAL_VALUE_TYPE *,
111 const REAL_VALUE_TYPE *);
112 static bool do_divide (REAL_VALUE_TYPE *, const REAL_VALUE_TYPE *,
113 const REAL_VALUE_TYPE *);
114 static int do_compare (const REAL_VALUE_TYPE *, const REAL_VALUE_TYPE *, int);
115 static void do_fix_trunc (REAL_VALUE_TYPE *, const REAL_VALUE_TYPE *);
117 static unsigned long rtd_divmod (REAL_VALUE_TYPE *, REAL_VALUE_TYPE *);
119 static const REAL_VALUE_TYPE * ten_to_ptwo (int);
120 static const REAL_VALUE_TYPE * ten_to_mptwo (int);
121 static const REAL_VALUE_TYPE * real_digit (int);
122 static void times_pten (REAL_VALUE_TYPE *, int);
124 static void round_for_format (const struct real_format *, REAL_VALUE_TYPE *);
126 /* Initialize R with a positive zero. */
129 get_zero (REAL_VALUE_TYPE *r, int sign)
131 memset (r, 0, sizeof (*r));
135 /* Initialize R with the canonical quiet NaN. */
138 get_canonical_qnan (REAL_VALUE_TYPE *r, int sign)
140 memset (r, 0, sizeof (*r));
147 get_canonical_snan (REAL_VALUE_TYPE *r, int sign)
149 memset (r, 0, sizeof (*r));
157 get_inf (REAL_VALUE_TYPE *r, int sign)
159 memset (r, 0, sizeof (*r));
165 /* Right-shift the significand of A by N bits; put the result in the
166 significand of R. If any one bits are shifted out, return true. */
169 sticky_rshift_significand (REAL_VALUE_TYPE *r, const REAL_VALUE_TYPE *a,
172 unsigned long sticky = 0;
173 unsigned int i, ofs = 0;
175 if (n >= HOST_BITS_PER_LONG)
177 for (i = 0, ofs = n / HOST_BITS_PER_LONG; i < ofs; ++i)
179 n &= HOST_BITS_PER_LONG - 1;
184 sticky |= a->sig[ofs] & (((unsigned long)1 << n) - 1);
185 for (i = 0; i < SIGSZ; ++i)
188 = (((ofs + i >= SIGSZ ? 0 : a->sig[ofs + i]) >> n)
189 | ((ofs + i + 1 >= SIGSZ ? 0 : a->sig[ofs + i + 1])
190 << (HOST_BITS_PER_LONG - n)));
195 for (i = 0; ofs + i < SIGSZ; ++i)
196 r->sig[i] = a->sig[ofs + i];
197 for (; i < SIGSZ; ++i)
204 /* Right-shift the significand of A by N bits; put the result in the
208 rshift_significand (REAL_VALUE_TYPE *r, const REAL_VALUE_TYPE *a,
211 unsigned int i, ofs = n / HOST_BITS_PER_LONG;
213 n &= HOST_BITS_PER_LONG - 1;
216 for (i = 0; i < SIGSZ; ++i)
219 = (((ofs + i >= SIGSZ ? 0 : a->sig[ofs + i]) >> n)
220 | ((ofs + i + 1 >= SIGSZ ? 0 : a->sig[ofs + i + 1])
221 << (HOST_BITS_PER_LONG - n)));
226 for (i = 0; ofs + i < SIGSZ; ++i)
227 r->sig[i] = a->sig[ofs + i];
228 for (; i < SIGSZ; ++i)
233 /* Left-shift the significand of A by N bits; put the result in the
237 lshift_significand (REAL_VALUE_TYPE *r, const REAL_VALUE_TYPE *a,
240 unsigned int i, ofs = n / HOST_BITS_PER_LONG;
242 n &= HOST_BITS_PER_LONG - 1;
245 for (i = 0; ofs + i < SIGSZ; ++i)
246 r->sig[SIGSZ-1-i] = a->sig[SIGSZ-1-i-ofs];
247 for (; i < SIGSZ; ++i)
248 r->sig[SIGSZ-1-i] = 0;
251 for (i = 0; i < SIGSZ; ++i)
254 = (((ofs + i >= SIGSZ ? 0 : a->sig[SIGSZ-1-i-ofs]) << n)
255 | ((ofs + i + 1 >= SIGSZ ? 0 : a->sig[SIGSZ-1-i-ofs-1])
256 >> (HOST_BITS_PER_LONG - n)));
260 /* Likewise, but N is specialized to 1. */
263 lshift_significand_1 (REAL_VALUE_TYPE *r, const REAL_VALUE_TYPE *a)
267 for (i = SIGSZ - 1; i > 0; --i)
268 r->sig[i] = (a->sig[i] << 1) | (a->sig[i-1] >> (HOST_BITS_PER_LONG - 1));
269 r->sig[0] = a->sig[0] << 1;
272 /* Add the significands of A and B, placing the result in R. Return
273 true if there was carry out of the most significant word. */
276 add_significands (REAL_VALUE_TYPE *r, const REAL_VALUE_TYPE *a,
277 const REAL_VALUE_TYPE *b)
282 for (i = 0; i < SIGSZ; ++i)
284 unsigned long ai = a->sig[i];
285 unsigned long ri = ai + b->sig[i];
301 /* Subtract the significands of A and B, placing the result in R. CARRY is
302 true if there's a borrow incoming to the least significant word.
303 Return true if there was borrow out of the most significant word. */
306 sub_significands (REAL_VALUE_TYPE *r, const REAL_VALUE_TYPE *a,
307 const REAL_VALUE_TYPE *b, int carry)
311 for (i = 0; i < SIGSZ; ++i)
313 unsigned long ai = a->sig[i];
314 unsigned long ri = ai - b->sig[i];
330 /* Negate the significand A, placing the result in R. */
333 neg_significand (REAL_VALUE_TYPE *r, const REAL_VALUE_TYPE *a)
338 for (i = 0; i < SIGSZ; ++i)
340 unsigned long ri, ai = a->sig[i];
359 /* Compare significands. Return tri-state vs zero. */
362 cmp_significands (const REAL_VALUE_TYPE *a, const REAL_VALUE_TYPE *b)
366 for (i = SIGSZ - 1; i >= 0; --i)
368 unsigned long ai = a->sig[i];
369 unsigned long bi = b->sig[i];
380 /* Return true if A is nonzero. */
383 cmp_significand_0 (const REAL_VALUE_TYPE *a)
387 for (i = SIGSZ - 1; i >= 0; --i)
394 /* Set bit N of the significand of R. */
397 set_significand_bit (REAL_VALUE_TYPE *r, unsigned int n)
399 r->sig[n / HOST_BITS_PER_LONG]
400 |= (unsigned long)1 << (n % HOST_BITS_PER_LONG);
403 /* Clear bit N of the significand of R. */
406 clear_significand_bit (REAL_VALUE_TYPE *r, unsigned int n)
408 r->sig[n / HOST_BITS_PER_LONG]
409 &= ~((unsigned long)1 << (n % HOST_BITS_PER_LONG));
412 /* Test bit N of the significand of R. */
415 test_significand_bit (REAL_VALUE_TYPE *r, unsigned int n)
417 /* ??? Compiler bug here if we return this expression directly.
418 The conversion to bool strips the "&1" and we wind up testing
419 e.g. 2 != 0 -> true. Seen in gcc version 3.2 20020520. */
420 int t = (r->sig[n / HOST_BITS_PER_LONG] >> (n % HOST_BITS_PER_LONG)) & 1;
424 /* Clear bits 0..N-1 of the significand of R. */
427 clear_significand_below (REAL_VALUE_TYPE *r, unsigned int n)
429 int i, w = n / HOST_BITS_PER_LONG;
431 for (i = 0; i < w; ++i)
434 r->sig[w] &= ~(((unsigned long)1 << (n % HOST_BITS_PER_LONG)) - 1);
437 /* Divide the significands of A and B, placing the result in R. Return
438 true if the division was inexact. */
441 div_significands (REAL_VALUE_TYPE *r, const REAL_VALUE_TYPE *a,
442 const REAL_VALUE_TYPE *b)
445 int i, bit = SIGNIFICAND_BITS - 1;
446 unsigned long msb, inexact;
449 memset (r->sig, 0, sizeof (r->sig));
455 msb = u.sig[SIGSZ-1] & SIG_MSB;
456 lshift_significand_1 (&u, &u);
458 if (msb || cmp_significands (&u, b) >= 0)
460 sub_significands (&u, &u, b, 0);
461 set_significand_bit (r, bit);
466 for (i = 0, inexact = 0; i < SIGSZ; i++)
472 /* Adjust the exponent and significand of R such that the most
473 significant bit is set. We underflow to zero and overflow to
474 infinity here, without denormals. (The intermediate representation
475 exponent is large enough to handle target denormals normalized.) */
478 normalize (REAL_VALUE_TYPE *r)
483 /* Find the first word that is nonzero. */
484 for (i = SIGSZ - 1; i >= 0; i--)
486 shift += HOST_BITS_PER_LONG;
490 /* Zero significand flushes to zero. */
498 /* Find the first bit that is nonzero. */
500 if (r->sig[i] & ((unsigned long)1 << (HOST_BITS_PER_LONG - 1 - j)))
506 exp = r->exp - shift;
508 get_inf (r, r->sign);
509 else if (exp < -MAX_EXP)
510 get_zero (r, r->sign);
514 lshift_significand (r, r, shift);
519 /* Calculate R = A + (SUBTRACT_P ? -B : B). Return true if the
520 result may be inexact due to a loss of precision. */
523 do_add (REAL_VALUE_TYPE *r, const REAL_VALUE_TYPE *a,
524 const REAL_VALUE_TYPE *b, int subtract_p)
528 bool inexact = false;
530 /* Determine if we need to add or subtract. */
532 subtract_p = (sign ^ b->sign) ^ subtract_p;
534 switch (CLASS2 (a->class, b->class))
536 case CLASS2 (rvc_zero, rvc_zero):
537 /* -0 + -0 = -0, -0 - +0 = -0; all other cases yield +0. */
538 get_zero (r, sign & !subtract_p);
541 case CLASS2 (rvc_zero, rvc_normal):
542 case CLASS2 (rvc_zero, rvc_inf):
543 case CLASS2 (rvc_zero, rvc_nan):
545 case CLASS2 (rvc_normal, rvc_nan):
546 case CLASS2 (rvc_inf, rvc_nan):
547 case CLASS2 (rvc_nan, rvc_nan):
548 /* ANY + NaN = NaN. */
549 case CLASS2 (rvc_normal, rvc_inf):
552 r->sign = sign ^ subtract_p;
555 case CLASS2 (rvc_normal, rvc_zero):
556 case CLASS2 (rvc_inf, rvc_zero):
557 case CLASS2 (rvc_nan, rvc_zero):
559 case CLASS2 (rvc_nan, rvc_normal):
560 case CLASS2 (rvc_nan, rvc_inf):
561 /* NaN + ANY = NaN. */
562 case CLASS2 (rvc_inf, rvc_normal):
567 case CLASS2 (rvc_inf, rvc_inf):
569 /* Inf - Inf = NaN. */
570 get_canonical_qnan (r, 0);
572 /* Inf + Inf = Inf. */
576 case CLASS2 (rvc_normal, rvc_normal):
583 /* Swap the arguments such that A has the larger exponent. */
584 dexp = a->exp - b->exp;
587 const REAL_VALUE_TYPE *t;
594 /* If the exponents are not identical, we need to shift the
595 significand of B down. */
598 /* If the exponents are too far apart, the significands
599 do not overlap, which makes the subtraction a noop. */
600 if (dexp >= SIGNIFICAND_BITS)
607 inexact |= sticky_rshift_significand (&t, b, dexp);
613 if (sub_significands (r, a, b, inexact))
615 /* We got a borrow out of the subtraction. That means that
616 A and B had the same exponent, and B had the larger
617 significand. We need to swap the sign and negate the
620 neg_significand (r, r);
625 if (add_significands (r, a, b))
627 /* We got carry out of the addition. This means we need to
628 shift the significand back down one bit and increase the
630 inexact |= sticky_rshift_significand (r, r, 1);
631 r->sig[SIGSZ-1] |= SIG_MSB;
640 r->class = rvc_normal;
644 /* Re-normalize the result. */
647 /* Special case: if the subtraction results in zero, the result
649 if (r->class == rvc_zero)
652 r->sig[0] |= inexact;
657 /* Calculate R = A * B. Return true if the result may be inexact. */
660 do_multiply (REAL_VALUE_TYPE *r, const REAL_VALUE_TYPE *a,
661 const REAL_VALUE_TYPE *b)
663 REAL_VALUE_TYPE u, t, *rr;
664 unsigned int i, j, k;
665 int sign = a->sign ^ b->sign;
666 bool inexact = false;
668 switch (CLASS2 (a->class, b->class))
670 case CLASS2 (rvc_zero, rvc_zero):
671 case CLASS2 (rvc_zero, rvc_normal):
672 case CLASS2 (rvc_normal, rvc_zero):
673 /* +-0 * ANY = 0 with appropriate sign. */
677 case CLASS2 (rvc_zero, rvc_nan):
678 case CLASS2 (rvc_normal, rvc_nan):
679 case CLASS2 (rvc_inf, rvc_nan):
680 case CLASS2 (rvc_nan, rvc_nan):
681 /* ANY * NaN = NaN. */
686 case CLASS2 (rvc_nan, rvc_zero):
687 case CLASS2 (rvc_nan, rvc_normal):
688 case CLASS2 (rvc_nan, rvc_inf):
689 /* NaN * ANY = NaN. */
694 case CLASS2 (rvc_zero, rvc_inf):
695 case CLASS2 (rvc_inf, rvc_zero):
697 get_canonical_qnan (r, sign);
700 case CLASS2 (rvc_inf, rvc_inf):
701 case CLASS2 (rvc_normal, rvc_inf):
702 case CLASS2 (rvc_inf, rvc_normal):
703 /* Inf * Inf = Inf, R * Inf = Inf */
707 case CLASS2 (rvc_normal, rvc_normal):
714 if (r == a || r == b)
720 /* Collect all the partial products. Since we don't have sure access
721 to a widening multiply, we split each long into two half-words.
723 Consider the long-hand form of a four half-word multiplication:
733 We construct partial products of the widened half-word products
734 that are known to not overlap, e.g. DF+DH. Each such partial
735 product is given its proper exponent, which allows us to sum them
736 and obtain the finished product. */
738 for (i = 0; i < SIGSZ * 2; ++i)
740 unsigned long ai = a->sig[i / 2];
742 ai >>= HOST_BITS_PER_LONG / 2;
744 ai &= ((unsigned long)1 << (HOST_BITS_PER_LONG / 2)) - 1;
749 for (j = 0; j < 2; ++j)
751 int exp = (a->exp - (2*SIGSZ-1-i)*(HOST_BITS_PER_LONG/2)
752 + (b->exp - (1-j)*(HOST_BITS_PER_LONG/2)));
761 /* Would underflow to zero, which we shouldn't bother adding. */
766 memset (&u, 0, sizeof (u));
767 u.class = rvc_normal;
770 for (k = j; k < SIGSZ * 2; k += 2)
772 unsigned long bi = b->sig[k / 2];
774 bi >>= HOST_BITS_PER_LONG / 2;
776 bi &= ((unsigned long)1 << (HOST_BITS_PER_LONG / 2)) - 1;
778 u.sig[k / 2] = ai * bi;
782 inexact |= do_add (rr, rr, &u, 0);
793 /* Calculate R = A / B. Return true if the result may be inexact. */
796 do_divide (REAL_VALUE_TYPE *r, const REAL_VALUE_TYPE *a,
797 const REAL_VALUE_TYPE *b)
799 int exp, sign = a->sign ^ b->sign;
800 REAL_VALUE_TYPE t, *rr;
803 switch (CLASS2 (a->class, b->class))
805 case CLASS2 (rvc_zero, rvc_zero):
807 case CLASS2 (rvc_inf, rvc_inf):
808 /* Inf / Inf = NaN. */
809 get_canonical_qnan (r, sign);
812 case CLASS2 (rvc_zero, rvc_normal):
813 case CLASS2 (rvc_zero, rvc_inf):
815 case CLASS2 (rvc_normal, rvc_inf):
820 case CLASS2 (rvc_normal, rvc_zero):
822 case CLASS2 (rvc_inf, rvc_zero):
827 case CLASS2 (rvc_zero, rvc_nan):
828 case CLASS2 (rvc_normal, rvc_nan):
829 case CLASS2 (rvc_inf, rvc_nan):
830 case CLASS2 (rvc_nan, rvc_nan):
831 /* ANY / NaN = NaN. */
836 case CLASS2 (rvc_nan, rvc_zero):
837 case CLASS2 (rvc_nan, rvc_normal):
838 case CLASS2 (rvc_nan, rvc_inf):
839 /* NaN / ANY = NaN. */
844 case CLASS2 (rvc_inf, rvc_normal):
849 case CLASS2 (rvc_normal, rvc_normal):
856 if (r == a || r == b)
861 /* Make sure all fields in the result are initialized. */
863 rr->class = rvc_normal;
866 exp = a->exp - b->exp + 1;
879 inexact = div_significands (rr, a, b);
881 /* Re-normalize the result. */
883 rr->sig[0] |= inexact;
891 /* Return a tri-state comparison of A vs B. Return NAN_RESULT if
892 one of the two operands is a NaN. */
895 do_compare (const REAL_VALUE_TYPE *a, const REAL_VALUE_TYPE *b,
900 switch (CLASS2 (a->class, b->class))
902 case CLASS2 (rvc_zero, rvc_zero):
903 /* Sign of zero doesn't matter for compares. */
906 case CLASS2 (rvc_inf, rvc_zero):
907 case CLASS2 (rvc_inf, rvc_normal):
908 case CLASS2 (rvc_normal, rvc_zero):
909 return (a->sign ? -1 : 1);
911 case CLASS2 (rvc_inf, rvc_inf):
912 return -a->sign - -b->sign;
914 case CLASS2 (rvc_zero, rvc_normal):
915 case CLASS2 (rvc_zero, rvc_inf):
916 case CLASS2 (rvc_normal, rvc_inf):
917 return (b->sign ? 1 : -1);
919 case CLASS2 (rvc_zero, rvc_nan):
920 case CLASS2 (rvc_normal, rvc_nan):
921 case CLASS2 (rvc_inf, rvc_nan):
922 case CLASS2 (rvc_nan, rvc_nan):
923 case CLASS2 (rvc_nan, rvc_zero):
924 case CLASS2 (rvc_nan, rvc_normal):
925 case CLASS2 (rvc_nan, rvc_inf):
928 case CLASS2 (rvc_normal, rvc_normal):
935 if (a->sign != b->sign)
936 return -a->sign - -b->sign;
940 else if (a->exp < b->exp)
943 ret = cmp_significands (a, b);
945 return (a->sign ? -ret : ret);
948 /* Return A truncated to an integral value toward zero. */
951 do_fix_trunc (REAL_VALUE_TYPE *r, const REAL_VALUE_TYPE *a)
964 get_zero (r, r->sign);
965 else if (r->exp < SIGNIFICAND_BITS)
966 clear_significand_below (r, SIGNIFICAND_BITS - r->exp);
974 /* Perform the binary or unary operation described by CODE.
975 For a unary operation, leave OP1 NULL. */
978 real_arithmetic (REAL_VALUE_TYPE *r, int icode, const REAL_VALUE_TYPE *op0,
979 const REAL_VALUE_TYPE *op1)
981 enum tree_code code = icode;
986 do_add (r, op0, op1, 0);
990 do_add (r, op0, op1, 1);
994 do_multiply (r, op0, op1);
998 do_divide (r, op0, op1);
1002 if (op1->class == rvc_nan)
1004 else if (do_compare (op0, op1, -1) < 0)
1011 if (op1->class == rvc_nan)
1013 else if (do_compare (op0, op1, 1) < 0)
1029 case FIX_TRUNC_EXPR:
1030 do_fix_trunc (r, op0);
1038 /* Legacy. Similar, but return the result directly. */
1041 real_arithmetic2 (int icode, const REAL_VALUE_TYPE *op0,
1042 const REAL_VALUE_TYPE *op1)
1045 real_arithmetic (&r, icode, op0, op1);
1050 real_compare (int icode, const REAL_VALUE_TYPE *op0,
1051 const REAL_VALUE_TYPE *op1)
1053 enum tree_code code = icode;
1058 return do_compare (op0, op1, 1) < 0;
1060 return do_compare (op0, op1, 1) <= 0;
1062 return do_compare (op0, op1, -1) > 0;
1064 return do_compare (op0, op1, -1) >= 0;
1066 return do_compare (op0, op1, -1) == 0;
1068 return do_compare (op0, op1, -1) != 0;
1069 case UNORDERED_EXPR:
1070 return op0->class == rvc_nan || op1->class == rvc_nan;
1072 return op0->class != rvc_nan && op1->class != rvc_nan;
1074 return do_compare (op0, op1, -1) < 0;
1076 return do_compare (op0, op1, -1) <= 0;
1078 return do_compare (op0, op1, 1) > 0;
1080 return do_compare (op0, op1, 1) >= 0;
1082 return do_compare (op0, op1, 0) == 0;
1089 /* Return floor log2(R). */
1092 real_exponent (const REAL_VALUE_TYPE *r)
1100 return (unsigned int)-1 >> 1;
1108 /* R = OP0 * 2**EXP. */
1111 real_ldexp (REAL_VALUE_TYPE *r, const REAL_VALUE_TYPE *op0, int exp)
1124 get_inf (r, r->sign);
1125 else if (exp < -MAX_EXP)
1126 get_zero (r, r->sign);
1136 /* Determine whether a floating-point value X is infinite. */
1139 real_isinf (const REAL_VALUE_TYPE *r)
1141 return (r->class == rvc_inf);
1144 /* Determine whether a floating-point value X is a NaN. */
1147 real_isnan (const REAL_VALUE_TYPE *r)
1149 return (r->class == rvc_nan);
1152 /* Determine whether a floating-point value X is negative. */
1155 real_isneg (const REAL_VALUE_TYPE *r)
1160 /* Determine whether a floating-point value X is minus zero. */
1163 real_isnegzero (const REAL_VALUE_TYPE *r)
1165 return r->sign && r->class == rvc_zero;
1168 /* Compare two floating-point objects for bitwise identity. */
1171 real_identical (const REAL_VALUE_TYPE *a, const REAL_VALUE_TYPE *b)
1175 if (a->class != b->class)
1177 if (a->sign != b->sign)
1187 if (a->exp != b->exp)
1192 if (a->signalling != b->signalling)
1194 /* The significand is ignored for canonical NaNs. */
1195 if (a->canonical || b->canonical)
1196 return a->canonical == b->canonical;
1203 for (i = 0; i < SIGSZ; ++i)
1204 if (a->sig[i] != b->sig[i])
1210 /* Try to change R into its exact multiplicative inverse in machine
1211 mode MODE. Return true if successful. */
1214 exact_real_inverse (enum machine_mode mode, REAL_VALUE_TYPE *r)
1216 const REAL_VALUE_TYPE *one = real_digit (1);
1220 if (r->class != rvc_normal)
1223 /* Check for a power of two: all significand bits zero except the MSB. */
1224 for (i = 0; i < SIGSZ-1; ++i)
1227 if (r->sig[SIGSZ-1] != SIG_MSB)
1230 /* Find the inverse and truncate to the required mode. */
1231 do_divide (&u, one, r);
1232 real_convert (&u, mode, &u);
1234 /* The rounding may have overflowed. */
1235 if (u.class != rvc_normal)
1237 for (i = 0; i < SIGSZ-1; ++i)
1240 if (u.sig[SIGSZ-1] != SIG_MSB)
1247 /* Render R as an integer. */
1250 real_to_integer (const REAL_VALUE_TYPE *r)
1252 unsigned HOST_WIDE_INT i;
1263 i = (unsigned HOST_WIDE_INT) 1 << (HOST_BITS_PER_WIDE_INT - 1);
1271 /* Only force overflow for unsigned overflow. Signed overflow is
1272 undefined, so it doesn't matter what we return, and some callers
1273 expect to be able to use this routine for both signed and
1274 unsigned conversions. */
1275 if (r->exp > HOST_BITS_PER_WIDE_INT)
1278 if (HOST_BITS_PER_WIDE_INT == HOST_BITS_PER_LONG)
1279 i = r->sig[SIGSZ-1];
1280 else if (HOST_BITS_PER_WIDE_INT == 2*HOST_BITS_PER_LONG)
1282 i = r->sig[SIGSZ-1];
1283 i = i << (HOST_BITS_PER_LONG - 1) << 1;
1284 i |= r->sig[SIGSZ-2];
1289 i >>= HOST_BITS_PER_WIDE_INT - r->exp;
1300 /* Likewise, but to an integer pair, HI+LOW. */
1303 real_to_integer2 (HOST_WIDE_INT *plow, HOST_WIDE_INT *phigh,
1304 const REAL_VALUE_TYPE *r)
1307 HOST_WIDE_INT low, high;
1320 high = (unsigned HOST_WIDE_INT) 1 << (HOST_BITS_PER_WIDE_INT - 1);
1334 /* Only force overflow for unsigned overflow. Signed overflow is
1335 undefined, so it doesn't matter what we return, and some callers
1336 expect to be able to use this routine for both signed and
1337 unsigned conversions. */
1338 if (exp > 2*HOST_BITS_PER_WIDE_INT)
1341 rshift_significand (&t, r, 2*HOST_BITS_PER_WIDE_INT - exp);
1342 if (HOST_BITS_PER_WIDE_INT == HOST_BITS_PER_LONG)
1344 high = t.sig[SIGSZ-1];
1345 low = t.sig[SIGSZ-2];
1347 else if (HOST_BITS_PER_WIDE_INT == 2*HOST_BITS_PER_LONG)
1349 high = t.sig[SIGSZ-1];
1350 high = high << (HOST_BITS_PER_LONG - 1) << 1;
1351 high |= t.sig[SIGSZ-2];
1353 low = t.sig[SIGSZ-3];
1354 low = low << (HOST_BITS_PER_LONG - 1) << 1;
1355 low |= t.sig[SIGSZ-4];
1365 low = -low, high = ~high;
1377 /* A subroutine of real_to_decimal. Compute the quotient and remainder
1378 of NUM / DEN. Return the quotient and place the remainder in NUM.
1379 It is expected that NUM / DEN are close enough that the quotient is
1382 static unsigned long
1383 rtd_divmod (REAL_VALUE_TYPE *num, REAL_VALUE_TYPE *den)
1385 unsigned long q, msb;
1386 int expn = num->exp, expd = den->exp;
1395 msb = num->sig[SIGSZ-1] & SIG_MSB;
1397 lshift_significand_1 (num, num);
1399 if (msb || cmp_significands (num, den) >= 0)
1401 sub_significands (num, num, den, 0);
1405 while (--expn >= expd);
1413 /* Render R as a decimal floating point constant. Emit DIGITS significant
1414 digits in the result, bounded by BUF_SIZE. If DIGITS is 0, choose the
1415 maximum for the representation. If CROP_TRAILING_ZEROS, strip trailing
1418 #define M_LOG10_2 0.30102999566398119521
1421 real_to_decimal (char *str, const REAL_VALUE_TYPE *r_orig, size_t buf_size,
1422 size_t digits, int crop_trailing_zeros)
1424 const REAL_VALUE_TYPE *one, *ten;
1425 REAL_VALUE_TYPE r, pten, u, v;
1426 int dec_exp, cmp_one, digit;
1428 char *p, *first, *last;
1435 strcpy (str, (r.sign ? "-0.0" : "0.0"));
1440 strcpy (str, (r.sign ? "-Inf" : "+Inf"));
1443 /* ??? Print the significand as well, if not canonical? */
1444 strcpy (str, (r.sign ? "-NaN" : "+NaN"));
1450 /* Bound the number of digits printed by the size of the representation. */
1451 max_digits = SIGNIFICAND_BITS * M_LOG10_2;
1452 if (digits == 0 || digits > max_digits)
1453 digits = max_digits;
1455 /* Estimate the decimal exponent, and compute the length of the string it
1456 will print as. Be conservative and add one to account for possible
1457 overflow or rounding error. */
1458 dec_exp = r.exp * M_LOG10_2;
1459 for (max_digits = 1; dec_exp ; max_digits++)
1462 /* Bound the number of digits printed by the size of the output buffer. */
1463 max_digits = buf_size - 1 - 1 - 2 - max_digits - 1;
1464 if (max_digits > buf_size)
1466 if (digits > max_digits)
1467 digits = max_digits;
1469 one = real_digit (1);
1470 ten = ten_to_ptwo (0);
1478 cmp_one = do_compare (&r, one, 0);
1483 /* Number is greater than one. Convert significand to an integer
1484 and strip trailing decimal zeros. */
1487 u.exp = SIGNIFICAND_BITS - 1;
1489 /* Largest M, such that 10**2**M fits within SIGNIFICAND_BITS. */
1490 m = floor_log2 (max_digits);
1492 /* Iterate over the bits of the possible powers of 10 that might
1493 be present in U and eliminate them. That is, if we find that
1494 10**2**M divides U evenly, keep the division and increase
1500 do_divide (&t, &u, ten_to_ptwo (m));
1501 do_fix_trunc (&v, &t);
1502 if (cmp_significands (&v, &t) == 0)
1510 /* Revert the scaling to integer that we performed earlier. */
1511 u.exp += r.exp - (SIGNIFICAND_BITS - 1);
1514 /* Find power of 10. Do this by dividing out 10**2**M when
1515 this is larger than the current remainder. Fill PTEN with
1516 the power of 10 that we compute. */
1519 m = floor_log2 ((int)(r.exp * M_LOG10_2)) + 1;
1522 const REAL_VALUE_TYPE *ptentwo = ten_to_ptwo (m);
1523 if (do_compare (&u, ptentwo, 0) >= 0)
1525 do_divide (&u, &u, ptentwo);
1526 do_multiply (&pten, &pten, ptentwo);
1533 /* We managed to divide off enough tens in the above reduction
1534 loop that we've now got a negative exponent. Fall into the
1535 less-than-one code to compute the proper value for PTEN. */
1542 /* Number is less than one. Pad significand with leading
1548 /* Stop if we'd shift bits off the bottom. */
1552 do_multiply (&u, &v, ten);
1554 /* Stop if we're now >= 1. */
1563 /* Find power of 10. Do this by multiplying in P=10**2**M when
1564 the current remainder is smaller than 1/P. Fill PTEN with the
1565 power of 10 that we compute. */
1566 m = floor_log2 ((int)(-r.exp * M_LOG10_2)) + 1;
1569 const REAL_VALUE_TYPE *ptentwo = ten_to_ptwo (m);
1570 const REAL_VALUE_TYPE *ptenmtwo = ten_to_mptwo (m);
1572 if (do_compare (&v, ptenmtwo, 0) <= 0)
1574 do_multiply (&v, &v, ptentwo);
1575 do_multiply (&pten, &pten, ptentwo);
1581 /* Invert the positive power of 10 that we've collected so far. */
1582 do_divide (&pten, one, &pten);
1590 /* At this point, PTEN should contain the nearest power of 10 smaller
1591 than R, such that this division produces the first digit.
1593 Using a divide-step primitive that returns the complete integral
1594 remainder avoids the rounding error that would be produced if
1595 we were to use do_divide here and then simply multiply by 10 for
1596 each subsequent digit. */
1598 digit = rtd_divmod (&r, &pten);
1600 /* Be prepared for error in that division via underflow ... */
1601 if (digit == 0 && cmp_significand_0 (&r))
1603 /* Multiply by 10 and try again. */
1604 do_multiply (&r, &r, ten);
1605 digit = rtd_divmod (&r, &pten);
1611 /* ... or overflow. */
1619 else if (digit > 10)
1624 /* Generate subsequent digits. */
1625 while (--digits > 0)
1627 do_multiply (&r, &r, ten);
1628 digit = rtd_divmod (&r, &pten);
1633 /* Generate one more digit with which to do rounding. */
1634 do_multiply (&r, &r, ten);
1635 digit = rtd_divmod (&r, &pten);
1637 /* Round the result. */
1640 /* Round to nearest. If R is nonzero there are additional
1641 nonzero digits to be extracted. */
1642 if (cmp_significand_0 (&r))
1644 /* Round to even. */
1645 else if ((p[-1] - '0') & 1)
1662 /* Carry out of the first digit. This means we had all 9's and
1663 now have all 0's. "Prepend" a 1 by overwriting the first 0. */
1671 /* Insert the decimal point. */
1672 first[0] = first[1];
1675 /* If requested, drop trailing zeros. Never crop past "1.0". */
1676 if (crop_trailing_zeros)
1677 while (last > first + 3 && last[-1] == '0')
1680 /* Append the exponent. */
1681 sprintf (last, "e%+d", dec_exp);
1684 /* Render R as a hexadecimal floating point constant. Emit DIGITS
1685 significant digits in the result, bounded by BUF_SIZE. If DIGITS is 0,
1686 choose the maximum for the representation. If CROP_TRAILING_ZEROS,
1687 strip trailing zeros. */
1690 real_to_hexadecimal (char *str, const REAL_VALUE_TYPE *r, size_t buf_size,
1691 size_t digits, int crop_trailing_zeros)
1693 int i, j, exp = r->exp;
1706 strcpy (str, (r->sign ? "-Inf" : "+Inf"));
1709 /* ??? Print the significand as well, if not canonical? */
1710 strcpy (str, (r->sign ? "-NaN" : "+NaN"));
1717 digits = SIGNIFICAND_BITS / 4;
1719 /* Bound the number of digits printed by the size of the output buffer. */
1721 sprintf (exp_buf, "p%+d", exp);
1722 max_digits = buf_size - strlen (exp_buf) - r->sign - 4 - 1;
1723 if (max_digits > buf_size)
1725 if (digits > max_digits)
1726 digits = max_digits;
1737 for (i = SIGSZ - 1; i >= 0; --i)
1738 for (j = HOST_BITS_PER_LONG - 4; j >= 0; j -= 4)
1740 *p++ = "0123456789abcdef"[(r->sig[i] >> j) & 15];
1746 if (crop_trailing_zeros)
1747 while (p > first + 1 && p[-1] == '0')
1750 sprintf (p, "p%+d", exp);
1753 /* Initialize R from a decimal or hexadecimal string. The string is
1754 assumed to have been syntax checked already. */
1757 real_from_string (REAL_VALUE_TYPE *r, const char *str)
1769 else if (*str == '+')
1772 if (str[0] == '0' && (str[1] == 'x' || str[1] == 'X'))
1774 /* Hexadecimal floating point. */
1775 int pos = SIGNIFICAND_BITS - 4, d;
1783 d = hex_value (*str);
1788 r->sig[pos / HOST_BITS_PER_LONG]
1789 |= (unsigned long) d << (pos % HOST_BITS_PER_LONG);
1798 if (pos == SIGNIFICAND_BITS - 4)
1805 d = hex_value (*str);
1810 r->sig[pos / HOST_BITS_PER_LONG]
1811 |= (unsigned long) d << (pos % HOST_BITS_PER_LONG);
1817 if (*str == 'p' || *str == 'P')
1819 bool exp_neg = false;
1827 else if (*str == '+')
1831 while (ISDIGIT (*str))
1837 /* Overflowed the exponent. */
1851 r->class = rvc_normal;
1858 /* Decimal floating point. */
1859 const REAL_VALUE_TYPE *ten = ten_to_ptwo (0);
1864 while (ISDIGIT (*str))
1867 do_multiply (r, r, ten);
1869 do_add (r, r, real_digit (d), 0);
1874 if (r->class == rvc_zero)
1879 while (ISDIGIT (*str))
1882 do_multiply (r, r, ten);
1884 do_add (r, r, real_digit (d), 0);
1889 if (*str == 'e' || *str == 'E')
1891 bool exp_neg = false;
1899 else if (*str == '+')
1903 while (ISDIGIT (*str))
1909 /* Overflowed the exponent. */
1923 times_pten (r, exp);
1938 /* Legacy. Similar, but return the result directly. */
1941 real_from_string2 (const char *s, enum machine_mode mode)
1945 real_from_string (&r, s);
1946 if (mode != VOIDmode)
1947 real_convert (&r, mode, &r);
1952 /* Initialize R from the integer pair HIGH+LOW. */
1955 real_from_integer (REAL_VALUE_TYPE *r, enum machine_mode mode,
1956 unsigned HOST_WIDE_INT low, HOST_WIDE_INT high,
1959 if (low == 0 && high == 0)
1963 r->class = rvc_normal;
1964 r->sign = high < 0 && !unsigned_p;
1965 r->exp = 2 * HOST_BITS_PER_WIDE_INT;
1976 if (HOST_BITS_PER_LONG == HOST_BITS_PER_WIDE_INT)
1978 r->sig[SIGSZ-1] = high;
1979 r->sig[SIGSZ-2] = low;
1980 memset (r->sig, 0, sizeof(long)*(SIGSZ-2));
1982 else if (HOST_BITS_PER_LONG*2 == HOST_BITS_PER_WIDE_INT)
1984 r->sig[SIGSZ-1] = high >> (HOST_BITS_PER_LONG - 1) >> 1;
1985 r->sig[SIGSZ-2] = high;
1986 r->sig[SIGSZ-3] = low >> (HOST_BITS_PER_LONG - 1) >> 1;
1987 r->sig[SIGSZ-4] = low;
1989 memset (r->sig, 0, sizeof(long)*(SIGSZ-4));
1997 if (mode != VOIDmode)
1998 real_convert (r, mode, r);
2001 /* Returns 10**2**N. */
2003 static const REAL_VALUE_TYPE *
2006 static REAL_VALUE_TYPE tens[EXP_BITS];
2008 if (n < 0 || n >= EXP_BITS)
2011 if (tens[n].class == rvc_zero)
2013 if (n < (HOST_BITS_PER_WIDE_INT == 64 ? 5 : 4))
2015 HOST_WIDE_INT t = 10;
2018 for (i = 0; i < n; ++i)
2021 real_from_integer (&tens[n], VOIDmode, t, 0, 1);
2025 const REAL_VALUE_TYPE *t = ten_to_ptwo (n - 1);
2026 do_multiply (&tens[n], t, t);
2033 /* Returns 10**(-2**N). */
2035 static const REAL_VALUE_TYPE *
2036 ten_to_mptwo (int n)
2038 static REAL_VALUE_TYPE tens[EXP_BITS];
2040 if (n < 0 || n >= EXP_BITS)
2043 if (tens[n].class == rvc_zero)
2044 do_divide (&tens[n], real_digit (1), ten_to_ptwo (n));
2051 static const REAL_VALUE_TYPE *
2054 static REAL_VALUE_TYPE num[10];
2059 if (n > 0 && num[n].class == rvc_zero)
2060 real_from_integer (&num[n], VOIDmode, n, 0, 1);
2065 /* Multiply R by 10**EXP. */
2068 times_pten (REAL_VALUE_TYPE *r, int exp)
2070 REAL_VALUE_TYPE pten, *rr;
2071 bool negative = (exp < 0);
2077 pten = *real_digit (1);
2083 for (i = 0; exp > 0; ++i, exp >>= 1)
2085 do_multiply (rr, rr, ten_to_ptwo (i));
2088 do_divide (r, r, &pten);
2091 /* Fills R with +Inf. */
2094 real_inf (REAL_VALUE_TYPE *r)
2099 /* Fills R with a NaN whose significand is described by STR. If QUIET,
2100 we force a QNaN, else we force an SNaN. The string, if not empty,
2101 is parsed as a number and placed in the significand. Return true
2102 if the string was successfully parsed. */
2105 real_nan (REAL_VALUE_TYPE *r, const char *str, int quiet,
2106 enum machine_mode mode)
2108 const struct real_format *fmt;
2110 fmt = REAL_MODE_FORMAT (mode);
2117 get_canonical_qnan (r, 0);
2119 get_canonical_snan (r, 0);
2126 memset (r, 0, sizeof (*r));
2129 /* Parse akin to strtol into the significand of R. */
2131 while (ISSPACE (*str))
2135 else if (*str == '+')
2145 while ((d = hex_value (*str)) < base)
2152 lshift_significand (r, r, 3);
2155 lshift_significand (r, r, 4);
2158 lshift_significand_1 (&u, r);
2159 lshift_significand (r, r, 3);
2160 add_significands (r, r, &u);
2168 add_significands (r, r, &u);
2173 /* Must have consumed the entire string for success. */
2177 /* Shift the significand into place such that the bits
2178 are in the most significant bits for the format. */
2179 lshift_significand (r, r, SIGNIFICAND_BITS - fmt->pnan);
2181 /* Our MSB is always unset for NaNs. */
2182 r->sig[SIGSZ-1] &= ~SIG_MSB;
2184 /* Force quiet or signalling NaN. */
2185 r->signalling = !quiet;
2191 /* Fills R with the largest finite value representable in mode MODE.
2192 If SIGN is nonzero, R is set to the most negative finite value. */
2195 real_maxval (REAL_VALUE_TYPE *r, int sign, enum machine_mode mode)
2197 const struct real_format *fmt;
2200 fmt = REAL_MODE_FORMAT (mode);
2204 r->class = rvc_normal;
2208 r->exp = fmt->emax * fmt->log2_b;
2210 np2 = SIGNIFICAND_BITS - fmt->p * fmt->log2_b;
2211 memset (r->sig, -1, SIGSZ * sizeof (unsigned long));
2212 clear_significand_below (r, np2);
2215 /* Fills R with 2**N. */
2218 real_2expN (REAL_VALUE_TYPE *r, int n)
2220 memset (r, 0, sizeof (*r));
2225 else if (n < -MAX_EXP)
2229 r->class = rvc_normal;
2231 r->sig[SIGSZ-1] = SIG_MSB;
2237 round_for_format (const struct real_format *fmt, REAL_VALUE_TYPE *r)
2240 unsigned long sticky;
2244 p2 = fmt->p * fmt->log2_b;
2245 emin2m1 = (fmt->emin - 1) * fmt->log2_b;
2246 emax2 = fmt->emax * fmt->log2_b;
2248 np2 = SIGNIFICAND_BITS - p2;
2252 get_zero (r, r->sign);
2254 if (!fmt->has_signed_zero)
2259 get_inf (r, r->sign);
2264 clear_significand_below (r, np2);
2274 /* If we're not base2, normalize the exponent to a multiple of
2276 if (fmt->log2_b != 1)
2278 int shift = r->exp & (fmt->log2_b - 1);
2281 shift = fmt->log2_b - shift;
2282 r->sig[0] |= sticky_rshift_significand (r, r, shift);
2287 /* Check the range of the exponent. If we're out of range,
2288 either underflow or overflow. */
2291 else if (r->exp <= emin2m1)
2295 if (!fmt->has_denorm)
2297 /* Don't underflow completely until we've had a chance to round. */
2298 if (r->exp < emin2m1)
2303 diff = emin2m1 - r->exp + 1;
2307 /* De-normalize the significand. */
2308 r->sig[0] |= sticky_rshift_significand (r, r, diff);
2313 /* There are P2 true significand bits, followed by one guard bit,
2314 followed by one sticky bit, followed by stuff. Fold nonzero
2315 stuff into the sticky bit. */
2318 for (i = 0, w = (np2 - 1) / HOST_BITS_PER_LONG; i < w; ++i)
2319 sticky |= r->sig[i];
2321 r->sig[w] & (((unsigned long)1 << ((np2 - 1) % HOST_BITS_PER_LONG)) - 1);
2323 guard = test_significand_bit (r, np2 - 1);
2324 lsb = test_significand_bit (r, np2);
2326 /* Round to even. */
2327 if (guard && (sticky || lsb))
2331 set_significand_bit (&u, np2);
2333 if (add_significands (r, r, &u))
2335 /* Overflow. Means the significand had been all ones, and
2336 is now all zeros. Need to increase the exponent, and
2337 possibly re-normalize it. */
2338 if (++r->exp > emax2)
2340 r->sig[SIGSZ-1] = SIG_MSB;
2342 if (fmt->log2_b != 1)
2344 int shift = r->exp & (fmt->log2_b - 1);
2347 shift = fmt->log2_b - shift;
2348 rshift_significand (r, r, shift);
2357 /* Catch underflow that we deferred until after rounding. */
2358 if (r->exp <= emin2m1)
2361 /* Clear out trailing garbage. */
2362 clear_significand_below (r, np2);
2365 /* Extend or truncate to a new mode. */
2368 real_convert (REAL_VALUE_TYPE *r, enum machine_mode mode,
2369 const REAL_VALUE_TYPE *a)
2371 const struct real_format *fmt;
2373 fmt = REAL_MODE_FORMAT (mode);
2378 round_for_format (fmt, r);
2380 /* round_for_format de-normalizes denormals. Undo just that part. */
2381 if (r->class == rvc_normal)
2385 /* Legacy. Likewise, except return the struct directly. */
2388 real_value_truncate (enum machine_mode mode, REAL_VALUE_TYPE a)
2391 real_convert (&r, mode, &a);
2395 /* Return true if truncating to MODE is exact. */
2398 exact_real_truncate (enum machine_mode mode, const REAL_VALUE_TYPE *a)
2401 real_convert (&t, mode, a);
2402 return real_identical (&t, a);
2405 /* Write R to the given target format. Place the words of the result
2406 in target word order in BUF. There are always 32 bits in each
2407 long, no matter the size of the host long.
2409 Legacy: return word 0 for implementing REAL_VALUE_TO_TARGET_SINGLE. */
2412 real_to_target_fmt (long *buf, const REAL_VALUE_TYPE *r_orig,
2413 const struct real_format *fmt)
2419 round_for_format (fmt, &r);
2423 (*fmt->encode) (fmt, buf, &r);
2428 /* Similar, but look up the format from MODE. */
2431 real_to_target (long *buf, const REAL_VALUE_TYPE *r, enum machine_mode mode)
2433 const struct real_format *fmt;
2435 fmt = REAL_MODE_FORMAT (mode);
2439 return real_to_target_fmt (buf, r, fmt);
2442 /* Read R from the given target format. Read the words of the result
2443 in target word order in BUF. There are always 32 bits in each
2444 long, no matter the size of the host long. */
2447 real_from_target_fmt (REAL_VALUE_TYPE *r, const long *buf,
2448 const struct real_format *fmt)
2450 (*fmt->decode) (fmt, r, buf);
2453 /* Similar, but look up the format from MODE. */
2456 real_from_target (REAL_VALUE_TYPE *r, const long *buf, enum machine_mode mode)
2458 const struct real_format *fmt;
2460 fmt = REAL_MODE_FORMAT (mode);
2464 (*fmt->decode) (fmt, r, buf);
2467 /* Return the number of bits in the significand for MODE. */
2468 /* ??? Legacy. Should get access to real_format directly. */
2471 significand_size (enum machine_mode mode)
2473 const struct real_format *fmt;
2475 fmt = REAL_MODE_FORMAT (mode);
2479 return fmt->p * fmt->log2_b;
2482 /* Return a hash value for the given real value. */
2483 /* ??? The "unsigned int" return value is intended to be hashval_t,
2484 but I didn't want to pull hashtab.h into real.h. */
2487 real_hash (const REAL_VALUE_TYPE *r)
2492 h = r->class | (r->sign << 2);
2505 h ^= (unsigned int)-1;
2514 if (sizeof(unsigned long) > sizeof(unsigned int))
2515 for (i = 0; i < SIGSZ; ++i)
2517 unsigned long s = r->sig[i];
2518 h ^= s ^ (s >> (HOST_BITS_PER_LONG / 2));
2521 for (i = 0; i < SIGSZ; ++i)
2527 /* IEEE single-precision format. */
2529 static void encode_ieee_single (const struct real_format *fmt,
2530 long *, const REAL_VALUE_TYPE *);
2531 static void decode_ieee_single (const struct real_format *,
2532 REAL_VALUE_TYPE *, const long *);
2535 encode_ieee_single (const struct real_format *fmt, long *buf,
2536 const REAL_VALUE_TYPE *r)
2538 unsigned long image, sig, exp;
2539 unsigned long sign = r->sign;
2540 bool denormal = (r->sig[SIGSZ-1] & SIG_MSB) == 0;
2543 sig = (r->sig[SIGSZ-1] >> (HOST_BITS_PER_LONG - 24)) & 0x7fffff;
2554 image |= 0x7fffffff;
2562 if (r->signalling == fmt->qnan_msb_set)
2566 /* We overload qnan_msb_set here: it's only clear for
2567 mips_ieee_single, which wants all mantissa bits but the
2568 quiet/signalling one set in canonical NaNs (at least
2570 if (r->canonical && !fmt->qnan_msb_set)
2571 sig |= (1 << 22) - 1;
2579 image |= 0x7fffffff;
2583 /* Recall that IEEE numbers are interpreted as 1.F x 2**exp,
2584 whereas the intermediate representation is 0.F x 2**exp.
2585 Which means we're off by one. */
2589 exp = r->exp + 127 - 1;
2602 decode_ieee_single (const struct real_format *fmt, REAL_VALUE_TYPE *r,
2605 unsigned long image = buf[0] & 0xffffffff;
2606 bool sign = (image >> 31) & 1;
2607 int exp = (image >> 23) & 0xff;
2609 memset (r, 0, sizeof (*r));
2610 image <<= HOST_BITS_PER_LONG - 24;
2615 if (image && fmt->has_denorm)
2617 r->class = rvc_normal;
2620 r->sig[SIGSZ-1] = image << 1;
2623 else if (fmt->has_signed_zero)
2626 else if (exp == 255 && (fmt->has_nans || fmt->has_inf))
2632 r->signalling = (((image >> (HOST_BITS_PER_LONG - 2)) & 1)
2633 ^ fmt->qnan_msb_set);
2634 r->sig[SIGSZ-1] = image;
2644 r->class = rvc_normal;
2646 r->exp = exp - 127 + 1;
2647 r->sig[SIGSZ-1] = image | SIG_MSB;
2651 const struct real_format ieee_single_format =
2669 const struct real_format mips_single_format =
2688 /* IEEE double-precision format. */
2690 static void encode_ieee_double (const struct real_format *fmt,
2691 long *, const REAL_VALUE_TYPE *);
2692 static void decode_ieee_double (const struct real_format *,
2693 REAL_VALUE_TYPE *, const long *);
2696 encode_ieee_double (const struct real_format *fmt, long *buf,
2697 const REAL_VALUE_TYPE *r)
2699 unsigned long image_lo, image_hi, sig_lo, sig_hi, exp;
2700 bool denormal = (r->sig[SIGSZ-1] & SIG_MSB) == 0;
2702 image_hi = r->sign << 31;
2705 if (HOST_BITS_PER_LONG == 64)
2707 sig_hi = r->sig[SIGSZ-1];
2708 sig_lo = (sig_hi >> (64 - 53)) & 0xffffffff;
2709 sig_hi = (sig_hi >> (64 - 53 + 1) >> 31) & 0xfffff;
2713 sig_hi = r->sig[SIGSZ-1];
2714 sig_lo = r->sig[SIGSZ-2];
2715 sig_lo = (sig_hi << 21) | (sig_lo >> 11);
2716 sig_hi = (sig_hi >> 11) & 0xfffff;
2726 image_hi |= 2047 << 20;
2729 image_hi |= 0x7fffffff;
2730 image_lo = 0xffffffff;
2738 sig_hi = sig_lo = 0;
2739 if (r->signalling == fmt->qnan_msb_set)
2740 sig_hi &= ~(1 << 19);
2743 /* We overload qnan_msb_set here: it's only clear for
2744 mips_ieee_single, which wants all mantissa bits but the
2745 quiet/signalling one set in canonical NaNs (at least
2747 if (r->canonical && !fmt->qnan_msb_set)
2749 sig_hi |= (1 << 19) - 1;
2750 sig_lo = 0xffffffff;
2752 else if (sig_hi == 0 && sig_lo == 0)
2755 image_hi |= 2047 << 20;
2761 image_hi |= 0x7fffffff;
2762 image_lo = 0xffffffff;
2767 /* Recall that IEEE numbers are interpreted as 1.F x 2**exp,
2768 whereas the intermediate representation is 0.F x 2**exp.
2769 Which means we're off by one. */
2773 exp = r->exp + 1023 - 1;
2774 image_hi |= exp << 20;
2783 if (FLOAT_WORDS_BIG_ENDIAN)
2784 buf[0] = image_hi, buf[1] = image_lo;
2786 buf[0] = image_lo, buf[1] = image_hi;
2790 decode_ieee_double (const struct real_format *fmt, REAL_VALUE_TYPE *r,
2793 unsigned long image_hi, image_lo;
2797 if (FLOAT_WORDS_BIG_ENDIAN)
2798 image_hi = buf[0], image_lo = buf[1];
2800 image_lo = buf[0], image_hi = buf[1];
2801 image_lo &= 0xffffffff;
2802 image_hi &= 0xffffffff;
2804 sign = (image_hi >> 31) & 1;
2805 exp = (image_hi >> 20) & 0x7ff;
2807 memset (r, 0, sizeof (*r));
2809 image_hi <<= 32 - 21;
2810 image_hi |= image_lo >> 21;
2811 image_hi &= 0x7fffffff;
2812 image_lo <<= 32 - 21;
2816 if ((image_hi || image_lo) && fmt->has_denorm)
2818 r->class = rvc_normal;
2821 if (HOST_BITS_PER_LONG == 32)
2823 image_hi = (image_hi << 1) | (image_lo >> 31);
2825 r->sig[SIGSZ-1] = image_hi;
2826 r->sig[SIGSZ-2] = image_lo;
2830 image_hi = (image_hi << 31 << 2) | (image_lo << 1);
2831 r->sig[SIGSZ-1] = image_hi;
2835 else if (fmt->has_signed_zero)
2838 else if (exp == 2047 && (fmt->has_nans || fmt->has_inf))
2840 if (image_hi || image_lo)
2844 r->signalling = ((image_hi >> 30) & 1) ^ fmt->qnan_msb_set;
2845 if (HOST_BITS_PER_LONG == 32)
2847 r->sig[SIGSZ-1] = image_hi;
2848 r->sig[SIGSZ-2] = image_lo;
2851 r->sig[SIGSZ-1] = (image_hi << 31 << 1) | image_lo;
2861 r->class = rvc_normal;
2863 r->exp = exp - 1023 + 1;
2864 if (HOST_BITS_PER_LONG == 32)
2866 r->sig[SIGSZ-1] = image_hi | SIG_MSB;
2867 r->sig[SIGSZ-2] = image_lo;
2870 r->sig[SIGSZ-1] = (image_hi << 31 << 1) | image_lo | SIG_MSB;
2874 const struct real_format ieee_double_format =
2892 const struct real_format mips_double_format =
2911 /* IEEE extended real format. This comes in three flavors: Intel's as
2912 a 12 byte image, Intel's as a 16 byte image, and Motorola's. Intel
2913 12- and 16-byte images may be big- or little endian; Motorola's is
2914 always big endian. */
2916 /* Helper subroutine which converts from the internal format to the
2917 12-byte little-endian Intel format. Functions below adjust this
2918 for the other possible formats. */
2920 encode_ieee_extended (const struct real_format *fmt, long *buf,
2921 const REAL_VALUE_TYPE *r)
2923 unsigned long image_hi, sig_hi, sig_lo;
2924 bool denormal = (r->sig[SIGSZ-1] & SIG_MSB) == 0;
2926 image_hi = r->sign << 15;
2927 sig_hi = sig_lo = 0;
2939 /* Intel requires the explicit integer bit to be set, otherwise
2940 it considers the value a "pseudo-infinity". Motorola docs
2941 say it doesn't care. */
2942 sig_hi = 0x80000000;
2947 sig_lo = sig_hi = 0xffffffff;
2955 if (HOST_BITS_PER_LONG == 32)
2957 sig_hi = r->sig[SIGSZ-1];
2958 sig_lo = r->sig[SIGSZ-2];
2962 sig_lo = r->sig[SIGSZ-1];
2963 sig_hi = sig_lo >> 31 >> 1;
2964 sig_lo &= 0xffffffff;
2966 if (r->signalling == fmt->qnan_msb_set)
2967 sig_hi &= ~(1 << 30);
2970 if ((sig_hi & 0x7fffffff) == 0 && sig_lo == 0)
2973 /* Intel requires the explicit integer bit to be set, otherwise
2974 it considers the value a "pseudo-nan". Motorola docs say it
2976 sig_hi |= 0x80000000;
2981 sig_lo = sig_hi = 0xffffffff;
2989 /* Recall that IEEE numbers are interpreted as 1.F x 2**exp,
2990 whereas the intermediate representation is 0.F x 2**exp.
2991 Which means we're off by one.
2993 Except for Motorola, which consider exp=0 and explicit
2994 integer bit set to continue to be normalized. In theory
2995 this discrepancy has been taken care of by the difference
2996 in fmt->emin in round_for_format. */
3008 if (HOST_BITS_PER_LONG == 32)
3010 sig_hi = r->sig[SIGSZ-1];
3011 sig_lo = r->sig[SIGSZ-2];
3015 sig_lo = r->sig[SIGSZ-1];
3016 sig_hi = sig_lo >> 31 >> 1;
3017 sig_lo &= 0xffffffff;
3026 buf[0] = sig_lo, buf[1] = sig_hi, buf[2] = image_hi;
3029 /* Convert from the internal format to the 12-byte Motorola format
3030 for an IEEE extended real. */
3032 encode_ieee_extended_motorola (const struct real_format *fmt, long *buf,
3033 const REAL_VALUE_TYPE *r)
3036 encode_ieee_extended (fmt, intermed, r);
3038 /* Motorola chips are assumed always to be big-endian. Also, the
3039 padding in a Motorola extended real goes between the exponent and
3040 the mantissa. At this point the mantissa is entirely within
3041 elements 0 and 1 of intermed, and the exponent entirely within
3042 element 2, so all we have to do is swap the order around, and
3043 shift element 2 left 16 bits. */
3044 buf[0] = intermed[2] << 16;
3045 buf[1] = intermed[1];
3046 buf[2] = intermed[0];
3049 /* Convert from the internal format to the 12-byte Intel format for
3050 an IEEE extended real. */
3052 encode_ieee_extended_intel_96 (const struct real_format *fmt, long *buf,
3053 const REAL_VALUE_TYPE *r)
3055 if (FLOAT_WORDS_BIG_ENDIAN)
3057 /* All the padding in an Intel-format extended real goes at the high
3058 end, which in this case is after the mantissa, not the exponent.
3059 Therefore we must shift everything down 16 bits. */
3061 encode_ieee_extended (fmt, intermed, r);
3062 buf[0] = ((intermed[2] << 16) | ((unsigned long)(intermed[1] & 0xFFFF0000) >> 16));
3063 buf[1] = ((intermed[1] << 16) | ((unsigned long)(intermed[0] & 0xFFFF0000) >> 16));
3064 buf[2] = (intermed[0] << 16);
3067 /* encode_ieee_extended produces what we want directly. */
3068 encode_ieee_extended (fmt, buf, r);
3071 /* Convert from the internal format to the 16-byte Intel format for
3072 an IEEE extended real. */
3074 encode_ieee_extended_intel_128 (const struct real_format *fmt, long *buf,
3075 const REAL_VALUE_TYPE *r)
3077 /* All the padding in an Intel-format extended real goes at the high end. */
3078 encode_ieee_extended_intel_96 (fmt, buf, r);
3082 /* As above, we have a helper function which converts from 12-byte
3083 little-endian Intel format to internal format. Functions below
3084 adjust for the other possible formats. */
3086 decode_ieee_extended (const struct real_format *fmt, REAL_VALUE_TYPE *r,
3089 unsigned long image_hi, sig_hi, sig_lo;
3093 sig_lo = buf[0], sig_hi = buf[1], image_hi = buf[2];
3094 sig_lo &= 0xffffffff;
3095 sig_hi &= 0xffffffff;
3096 image_hi &= 0xffffffff;
3098 sign = (image_hi >> 15) & 1;
3099 exp = image_hi & 0x7fff;
3101 memset (r, 0, sizeof (*r));
3105 if ((sig_hi || sig_lo) && fmt->has_denorm)
3107 r->class = rvc_normal;
3110 /* When the IEEE format contains a hidden bit, we know that
3111 it's zero at this point, and so shift up the significand
3112 and decrease the exponent to match. In this case, Motorola
3113 defines the explicit integer bit to be valid, so we don't
3114 know whether the msb is set or not. */
3116 if (HOST_BITS_PER_LONG == 32)
3118 r->sig[SIGSZ-1] = sig_hi;
3119 r->sig[SIGSZ-2] = sig_lo;
3122 r->sig[SIGSZ-1] = (sig_hi << 31 << 1) | sig_lo;
3126 else if (fmt->has_signed_zero)
3129 else if (exp == 32767 && (fmt->has_nans || fmt->has_inf))
3131 /* See above re "pseudo-infinities" and "pseudo-nans".
3132 Short summary is that the MSB will likely always be
3133 set, and that we don't care about it. */
3134 sig_hi &= 0x7fffffff;
3136 if (sig_hi || sig_lo)
3140 r->signalling = ((sig_hi >> 30) & 1) ^ fmt->qnan_msb_set;
3141 if (HOST_BITS_PER_LONG == 32)
3143 r->sig[SIGSZ-1] = sig_hi;
3144 r->sig[SIGSZ-2] = sig_lo;
3147 r->sig[SIGSZ-1] = (sig_hi << 31 << 1) | sig_lo;
3157 r->class = rvc_normal;
3159 r->exp = exp - 16383 + 1;
3160 if (HOST_BITS_PER_LONG == 32)
3162 r->sig[SIGSZ-1] = sig_hi;
3163 r->sig[SIGSZ-2] = sig_lo;
3166 r->sig[SIGSZ-1] = (sig_hi << 31 << 1) | sig_lo;
3170 /* Convert from the internal format to the 12-byte Motorola format
3171 for an IEEE extended real. */
3173 decode_ieee_extended_motorola (const struct real_format *fmt, REAL_VALUE_TYPE *r,
3178 /* Motorola chips are assumed always to be big-endian. Also, the
3179 padding in a Motorola extended real goes between the exponent and
3180 the mantissa; remove it. */
3181 intermed[0] = buf[2];
3182 intermed[1] = buf[1];
3183 intermed[2] = (unsigned long)buf[0] >> 16;
3185 decode_ieee_extended (fmt, r, intermed);
3188 /* Convert from the internal format to the 12-byte Intel format for
3189 an IEEE extended real. */
3191 decode_ieee_extended_intel_96 (const struct real_format *fmt, REAL_VALUE_TYPE *r,
3194 if (FLOAT_WORDS_BIG_ENDIAN)
3196 /* All the padding in an Intel-format extended real goes at the high
3197 end, which in this case is after the mantissa, not the exponent.
3198 Therefore we must shift everything up 16 bits. */
3201 intermed[0] = (((unsigned long)buf[2] >> 16) | (buf[1] << 16));
3202 intermed[1] = (((unsigned long)buf[1] >> 16) | (buf[0] << 16));
3203 intermed[2] = ((unsigned long)buf[0] >> 16);
3205 decode_ieee_extended (fmt, r, intermed);
3208 /* decode_ieee_extended produces what we want directly. */
3209 decode_ieee_extended (fmt, r, buf);
3212 /* Convert from the internal format to the 16-byte Intel format for
3213 an IEEE extended real. */
3215 decode_ieee_extended_intel_128 (const struct real_format *fmt, REAL_VALUE_TYPE *r,
3218 /* All the padding in an Intel-format extended real goes at the high end. */
3219 decode_ieee_extended_intel_96 (fmt, r, buf);
3222 const struct real_format ieee_extended_motorola_format =
3224 encode_ieee_extended_motorola,
3225 decode_ieee_extended_motorola,
3240 const struct real_format ieee_extended_intel_96_format =
3242 encode_ieee_extended_intel_96,
3243 decode_ieee_extended_intel_96,
3258 const struct real_format ieee_extended_intel_128_format =
3260 encode_ieee_extended_intel_128,
3261 decode_ieee_extended_intel_128,
3276 /* The following caters to i386 systems that set the rounding precision
3277 to 53 bits instead of 64, e.g. FreeBSD. */
3278 const struct real_format ieee_extended_intel_96_round_53_format =
3280 encode_ieee_extended_intel_96,
3281 decode_ieee_extended_intel_96,
3296 /* IBM 128-bit extended precision format: a pair of IEEE double precision
3297 numbers whose sum is equal to the extended precision value. The number
3298 with greater magnitude is first. This format has the same magnitude
3299 range as an IEEE double precision value, but effectively 106 bits of
3300 significand precision. Infinity and NaN are represented by their IEEE
3301 double precision value stored in the first number, the second number is
3302 ignored. Zeroes, Infinities, and NaNs are set in both doubles
3303 due to precedent. */
3305 static void encode_ibm_extended (const struct real_format *fmt,
3306 long *, const REAL_VALUE_TYPE *);
3307 static void decode_ibm_extended (const struct real_format *,
3308 REAL_VALUE_TYPE *, const long *);
3311 encode_ibm_extended (const struct real_format *fmt, long *buf,
3312 const REAL_VALUE_TYPE *r)
3314 REAL_VALUE_TYPE u, normr, v;
3315 const struct real_format *base_fmt;
3317 base_fmt = fmt->qnan_msb_set ? &ieee_double_format : &mips_double_format;
3319 /* Renormlize R before doing any arithmetic on it. */
3321 if (normr.class == rvc_normal)
3324 /* u = IEEE double precision portion of significand. */
3326 round_for_format (base_fmt, &u);
3327 encode_ieee_double (base_fmt, &buf[0], &u);
3329 if (u.class == rvc_normal)
3331 do_add (&v, &normr, &u, 1);
3332 /* Call round_for_format since we might need to denormalize. */
3333 round_for_format (base_fmt, &v);
3334 encode_ieee_double (base_fmt, &buf[2], &v);
3338 /* Inf, NaN, 0 are all representable as doubles, so the
3339 least-significant part can be 0.0. */
3346 decode_ibm_extended (const struct real_format *fmt ATTRIBUTE_UNUSED, REAL_VALUE_TYPE *r,
3349 REAL_VALUE_TYPE u, v;
3350 const struct real_format *base_fmt;
3352 base_fmt = fmt->qnan_msb_set ? &ieee_double_format : &mips_double_format;
3353 decode_ieee_double (base_fmt, &u, &buf[0]);
3355 if (u.class != rvc_zero && u.class != rvc_inf && u.class != rvc_nan)
3357 decode_ieee_double (base_fmt, &v, &buf[2]);
3358 do_add (r, &u, &v, 0);
3364 const struct real_format ibm_extended_format =
3366 encode_ibm_extended,
3367 decode_ibm_extended,
3382 const struct real_format mips_extended_format =
3384 encode_ibm_extended,
3385 decode_ibm_extended,
3401 /* IEEE quad precision format. */
3403 static void encode_ieee_quad (const struct real_format *fmt,
3404 long *, const REAL_VALUE_TYPE *);
3405 static void decode_ieee_quad (const struct real_format *,
3406 REAL_VALUE_TYPE *, const long *);
3409 encode_ieee_quad (const struct real_format *fmt, long *buf,
3410 const REAL_VALUE_TYPE *r)
3412 unsigned long image3, image2, image1, image0, exp;
3413 bool denormal = (r->sig[SIGSZ-1] & SIG_MSB) == 0;
3416 image3 = r->sign << 31;
3421 rshift_significand (&u, r, SIGNIFICAND_BITS - 113);
3430 image3 |= 32767 << 16;
3433 image3 |= 0x7fffffff;
3434 image2 = 0xffffffff;
3435 image1 = 0xffffffff;
3436 image0 = 0xffffffff;
3443 image3 |= 32767 << 16;
3447 /* Don't use bits from the significand. The
3448 initialization above is right. */
3450 else if (HOST_BITS_PER_LONG == 32)
3455 image3 |= u.sig[3] & 0xffff;
3460 image1 = image0 >> 31 >> 1;
3462 image3 |= (image2 >> 31 >> 1) & 0xffff;
3463 image0 &= 0xffffffff;
3464 image2 &= 0xffffffff;
3466 if (r->signalling == fmt->qnan_msb_set)
3470 /* We overload qnan_msb_set here: it's only clear for
3471 mips_ieee_single, which wants all mantissa bits but the
3472 quiet/signalling one set in canonical NaNs (at least
3474 if (r->canonical && !fmt->qnan_msb_set)
3477 image2 = image1 = image0 = 0xffffffff;
3479 else if (((image3 & 0xffff) | image2 | image1 | image0) == 0)
3484 image3 |= 0x7fffffff;
3485 image2 = 0xffffffff;
3486 image1 = 0xffffffff;
3487 image0 = 0xffffffff;
3492 /* Recall that IEEE numbers are interpreted as 1.F x 2**exp,
3493 whereas the intermediate representation is 0.F x 2**exp.
3494 Which means we're off by one. */
3498 exp = r->exp + 16383 - 1;
3499 image3 |= exp << 16;
3501 if (HOST_BITS_PER_LONG == 32)
3506 image3 |= u.sig[3] & 0xffff;
3511 image1 = image0 >> 31 >> 1;
3513 image3 |= (image2 >> 31 >> 1) & 0xffff;
3514 image0 &= 0xffffffff;
3515 image2 &= 0xffffffff;
3523 if (FLOAT_WORDS_BIG_ENDIAN)
3540 decode_ieee_quad (const struct real_format *fmt, REAL_VALUE_TYPE *r,
3543 unsigned long image3, image2, image1, image0;
3547 if (FLOAT_WORDS_BIG_ENDIAN)
3561 image0 &= 0xffffffff;
3562 image1 &= 0xffffffff;
3563 image2 &= 0xffffffff;
3565 sign = (image3 >> 31) & 1;
3566 exp = (image3 >> 16) & 0x7fff;
3569 memset (r, 0, sizeof (*r));
3573 if ((image3 | image2 | image1 | image0) && fmt->has_denorm)
3575 r->class = rvc_normal;
3578 r->exp = -16382 + (SIGNIFICAND_BITS - 112);
3579 if (HOST_BITS_PER_LONG == 32)
3588 r->sig[0] = (image1 << 31 << 1) | image0;
3589 r->sig[1] = (image3 << 31 << 1) | image2;
3594 else if (fmt->has_signed_zero)
3597 else if (exp == 32767 && (fmt->has_nans || fmt->has_inf))
3599 if (image3 | image2 | image1 | image0)
3603 r->signalling = ((image3 >> 15) & 1) ^ fmt->qnan_msb_set;
3605 if (HOST_BITS_PER_LONG == 32)
3614 r->sig[0] = (image1 << 31 << 1) | image0;
3615 r->sig[1] = (image3 << 31 << 1) | image2;
3617 lshift_significand (r, r, SIGNIFICAND_BITS - 113);
3627 r->class = rvc_normal;
3629 r->exp = exp - 16383 + 1;
3631 if (HOST_BITS_PER_LONG == 32)
3640 r->sig[0] = (image1 << 31 << 1) | image0;
3641 r->sig[1] = (image3 << 31 << 1) | image2;
3643 lshift_significand (r, r, SIGNIFICAND_BITS - 113);
3644 r->sig[SIGSZ-1] |= SIG_MSB;
3648 const struct real_format ieee_quad_format =
3666 const struct real_format mips_quad_format =
3684 /* Descriptions of VAX floating point formats can be found beginning at
3686 http://h71000.www7.hp.com/doc/73FINAL/4515/4515pro_013.html#f_floating_point_format
3688 The thing to remember is that they're almost IEEE, except for word
3689 order, exponent bias, and the lack of infinities, nans, and denormals.
3691 We don't implement the H_floating format here, simply because neither
3692 the VAX or Alpha ports use it. */
3694 static void encode_vax_f (const struct real_format *fmt,
3695 long *, const REAL_VALUE_TYPE *);
3696 static void decode_vax_f (const struct real_format *,
3697 REAL_VALUE_TYPE *, const long *);
3698 static void encode_vax_d (const struct real_format *fmt,
3699 long *, const REAL_VALUE_TYPE *);
3700 static void decode_vax_d (const struct real_format *,
3701 REAL_VALUE_TYPE *, const long *);
3702 static void encode_vax_g (const struct real_format *fmt,
3703 long *, const REAL_VALUE_TYPE *);
3704 static void decode_vax_g (const struct real_format *,
3705 REAL_VALUE_TYPE *, const long *);
3708 encode_vax_f (const struct real_format *fmt ATTRIBUTE_UNUSED, long *buf,
3709 const REAL_VALUE_TYPE *r)
3711 unsigned long sign, exp, sig, image;
3713 sign = r->sign << 15;
3723 image = 0xffff7fff | sign;
3727 sig = (r->sig[SIGSZ-1] >> (HOST_BITS_PER_LONG - 24)) & 0x7fffff;
3730 image = (sig << 16) & 0xffff0000;
3744 decode_vax_f (const struct real_format *fmt ATTRIBUTE_UNUSED,
3745 REAL_VALUE_TYPE *r, const long *buf)
3747 unsigned long image = buf[0] & 0xffffffff;
3748 int exp = (image >> 7) & 0xff;
3750 memset (r, 0, sizeof (*r));
3754 r->class = rvc_normal;
3755 r->sign = (image >> 15) & 1;
3758 image = ((image & 0x7f) << 16) | ((image >> 16) & 0xffff);
3759 r->sig[SIGSZ-1] = (image << (HOST_BITS_PER_LONG - 24)) | SIG_MSB;
3764 encode_vax_d (const struct real_format *fmt ATTRIBUTE_UNUSED, long *buf,
3765 const REAL_VALUE_TYPE *r)
3767 unsigned long image0, image1, sign = r->sign << 15;
3772 image0 = image1 = 0;
3777 image0 = 0xffff7fff | sign;
3778 image1 = 0xffffffff;
3782 /* Extract the significand into straight hi:lo. */
3783 if (HOST_BITS_PER_LONG == 64)
3785 image0 = r->sig[SIGSZ-1];
3786 image1 = (image0 >> (64 - 56)) & 0xffffffff;
3787 image0 = (image0 >> (64 - 56 + 1) >> 31) & 0x7fffff;
3791 image0 = r->sig[SIGSZ-1];
3792 image1 = r->sig[SIGSZ-2];
3793 image1 = (image0 << 24) | (image1 >> 8);
3794 image0 = (image0 >> 8) & 0xffffff;
3797 /* Rearrange the half-words of the significand to match the
3799 image0 = ((image0 << 16) | (image0 >> 16)) & 0xffff007f;
3800 image1 = ((image1 << 16) | (image1 >> 16)) & 0xffffffff;
3802 /* Add the sign and exponent. */
3804 image0 |= (r->exp + 128) << 7;
3811 if (FLOAT_WORDS_BIG_ENDIAN)
3812 buf[0] = image1, buf[1] = image0;
3814 buf[0] = image0, buf[1] = image1;
3818 decode_vax_d (const struct real_format *fmt ATTRIBUTE_UNUSED,
3819 REAL_VALUE_TYPE *r, const long *buf)
3821 unsigned long image0, image1;
3824 if (FLOAT_WORDS_BIG_ENDIAN)
3825 image1 = buf[0], image0 = buf[1];
3827 image0 = buf[0], image1 = buf[1];
3828 image0 &= 0xffffffff;
3829 image1 &= 0xffffffff;
3831 exp = (image0 >> 7) & 0xff;
3833 memset (r, 0, sizeof (*r));
3837 r->class = rvc_normal;
3838 r->sign = (image0 >> 15) & 1;
3841 /* Rearrange the half-words of the external format into
3842 proper ascending order. */
3843 image0 = ((image0 & 0x7f) << 16) | ((image0 >> 16) & 0xffff);
3844 image1 = ((image1 & 0xffff) << 16) | ((image1 >> 16) & 0xffff);
3846 if (HOST_BITS_PER_LONG == 64)
3848 image0 = (image0 << 31 << 1) | image1;
3851 r->sig[SIGSZ-1] = image0;
3855 r->sig[SIGSZ-1] = image0;
3856 r->sig[SIGSZ-2] = image1;
3857 lshift_significand (r, r, 2*HOST_BITS_PER_LONG - 56);
3858 r->sig[SIGSZ-1] |= SIG_MSB;
3864 encode_vax_g (const struct real_format *fmt ATTRIBUTE_UNUSED, long *buf,
3865 const REAL_VALUE_TYPE *r)
3867 unsigned long image0, image1, sign = r->sign << 15;
3872 image0 = image1 = 0;
3877 image0 = 0xffff7fff | sign;
3878 image1 = 0xffffffff;
3882 /* Extract the significand into straight hi:lo. */
3883 if (HOST_BITS_PER_LONG == 64)
3885 image0 = r->sig[SIGSZ-1];
3886 image1 = (image0 >> (64 - 53)) & 0xffffffff;
3887 image0 = (image0 >> (64 - 53 + 1) >> 31) & 0xfffff;
3891 image0 = r->sig[SIGSZ-1];
3892 image1 = r->sig[SIGSZ-2];
3893 image1 = (image0 << 21) | (image1 >> 11);
3894 image0 = (image0 >> 11) & 0xfffff;
3897 /* Rearrange the half-words of the significand to match the
3899 image0 = ((image0 << 16) | (image0 >> 16)) & 0xffff000f;
3900 image1 = ((image1 << 16) | (image1 >> 16)) & 0xffffffff;
3902 /* Add the sign and exponent. */
3904 image0 |= (r->exp + 1024) << 4;
3911 if (FLOAT_WORDS_BIG_ENDIAN)
3912 buf[0] = image1, buf[1] = image0;
3914 buf[0] = image0, buf[1] = image1;
3918 decode_vax_g (const struct real_format *fmt ATTRIBUTE_UNUSED,
3919 REAL_VALUE_TYPE *r, const long *buf)
3921 unsigned long image0, image1;
3924 if (FLOAT_WORDS_BIG_ENDIAN)
3925 image1 = buf[0], image0 = buf[1];
3927 image0 = buf[0], image1 = buf[1];
3928 image0 &= 0xffffffff;
3929 image1 &= 0xffffffff;
3931 exp = (image0 >> 4) & 0x7ff;
3933 memset (r, 0, sizeof (*r));
3937 r->class = rvc_normal;
3938 r->sign = (image0 >> 15) & 1;
3939 r->exp = exp - 1024;
3941 /* Rearrange the half-words of the external format into
3942 proper ascending order. */
3943 image0 = ((image0 & 0xf) << 16) | ((image0 >> 16) & 0xffff);
3944 image1 = ((image1 & 0xffff) << 16) | ((image1 >> 16) & 0xffff);
3946 if (HOST_BITS_PER_LONG == 64)
3948 image0 = (image0 << 31 << 1) | image1;
3951 r->sig[SIGSZ-1] = image0;
3955 r->sig[SIGSZ-1] = image0;
3956 r->sig[SIGSZ-2] = image1;
3957 lshift_significand (r, r, 64 - 53);
3958 r->sig[SIGSZ-1] |= SIG_MSB;
3963 const struct real_format vax_f_format =
3981 const struct real_format vax_d_format =
3999 const struct real_format vax_g_format =
4017 /* A good reference for these can be found in chapter 9 of
4018 "ESA/390 Principles of Operation", IBM document number SA22-7201-01.
4019 An on-line version can be found here:
4021 http://publibz.boulder.ibm.com/cgi-bin/bookmgr_OS390/BOOKS/DZ9AR001/9.1?DT=19930923083613
4024 static void encode_i370_single (const struct real_format *fmt,
4025 long *, const REAL_VALUE_TYPE *);
4026 static void decode_i370_single (const struct real_format *,
4027 REAL_VALUE_TYPE *, const long *);
4028 static void encode_i370_double (const struct real_format *fmt,
4029 long *, const REAL_VALUE_TYPE *);
4030 static void decode_i370_double (const struct real_format *,
4031 REAL_VALUE_TYPE *, const long *);
4034 encode_i370_single (const struct real_format *fmt ATTRIBUTE_UNUSED,
4035 long *buf, const REAL_VALUE_TYPE *r)
4037 unsigned long sign, exp, sig, image;
4039 sign = r->sign << 31;
4049 image = 0x7fffffff | sign;
4053 sig = (r->sig[SIGSZ-1] >> (HOST_BITS_PER_LONG - 24)) & 0xffffff;
4054 exp = ((r->exp / 4) + 64) << 24;
4055 image = sign | exp | sig;
4066 decode_i370_single (const struct real_format *fmt ATTRIBUTE_UNUSED,
4067 REAL_VALUE_TYPE *r, const long *buf)
4069 unsigned long sign, sig, image = buf[0];
4072 sign = (image >> 31) & 1;
4073 exp = (image >> 24) & 0x7f;
4074 sig = image & 0xffffff;
4076 memset (r, 0, sizeof (*r));
4080 r->class = rvc_normal;
4082 r->exp = (exp - 64) * 4;
4083 r->sig[SIGSZ-1] = sig << (HOST_BITS_PER_LONG - 24);
4089 encode_i370_double (const struct real_format *fmt ATTRIBUTE_UNUSED,
4090 long *buf, const REAL_VALUE_TYPE *r)
4092 unsigned long sign, exp, image_hi, image_lo;
4094 sign = r->sign << 31;
4099 image_hi = image_lo = 0;
4104 image_hi = 0x7fffffff | sign;
4105 image_lo = 0xffffffff;
4109 if (HOST_BITS_PER_LONG == 64)
4111 image_hi = r->sig[SIGSZ-1];
4112 image_lo = (image_hi >> (64 - 56)) & 0xffffffff;
4113 image_hi = (image_hi >> (64 - 56 + 1) >> 31) & 0xffffff;
4117 image_hi = r->sig[SIGSZ-1];
4118 image_lo = r->sig[SIGSZ-2];
4119 image_lo = (image_lo >> 8) | (image_hi << 24);
4123 exp = ((r->exp / 4) + 64) << 24;
4124 image_hi |= sign | exp;
4131 if (FLOAT_WORDS_BIG_ENDIAN)
4132 buf[0] = image_hi, buf[1] = image_lo;
4134 buf[0] = image_lo, buf[1] = image_hi;
4138 decode_i370_double (const struct real_format *fmt ATTRIBUTE_UNUSED,
4139 REAL_VALUE_TYPE *r, const long *buf)
4141 unsigned long sign, image_hi, image_lo;
4144 if (FLOAT_WORDS_BIG_ENDIAN)
4145 image_hi = buf[0], image_lo = buf[1];
4147 image_lo = buf[0], image_hi = buf[1];
4149 sign = (image_hi >> 31) & 1;
4150 exp = (image_hi >> 24) & 0x7f;
4151 image_hi &= 0xffffff;
4152 image_lo &= 0xffffffff;
4154 memset (r, 0, sizeof (*r));
4156 if (exp || image_hi || image_lo)
4158 r->class = rvc_normal;
4160 r->exp = (exp - 64) * 4 + (SIGNIFICAND_BITS - 56);
4162 if (HOST_BITS_PER_LONG == 32)
4164 r->sig[0] = image_lo;
4165 r->sig[1] = image_hi;
4168 r->sig[0] = image_lo | (image_hi << 31 << 1);
4174 const struct real_format i370_single_format =
4187 false, /* ??? The encoding does allow for "unnormals". */
4188 false, /* ??? The encoding does allow for "unnormals". */
4192 const struct real_format i370_double_format =
4205 false, /* ??? The encoding does allow for "unnormals". */
4206 false, /* ??? The encoding does allow for "unnormals". */
4210 /* The "twos-complement" c4x format is officially defined as
4214 This is rather misleading. One must remember that F is signed.
4215 A better description would be
4217 x = -1**s * ((s + 1 + .f) * 2**e
4219 So if we have a (4 bit) fraction of .1000 with a sign bit of 1,
4220 that's -1 * (1+1+(-.5)) == -1.5. I think.
4222 The constructions here are taken from Tables 5-1 and 5-2 of the
4223 TMS320C4x User's Guide wherein step-by-step instructions for
4224 conversion from IEEE are presented. That's close enough to our
4225 internal representation so as to make things easy.
4227 See http://www-s.ti.com/sc/psheets/spru063c/spru063c.pdf */
4229 static void encode_c4x_single (const struct real_format *fmt,
4230 long *, const REAL_VALUE_TYPE *);
4231 static void decode_c4x_single (const struct real_format *,
4232 REAL_VALUE_TYPE *, const long *);
4233 static void encode_c4x_extended (const struct real_format *fmt,
4234 long *, const REAL_VALUE_TYPE *);
4235 static void decode_c4x_extended (const struct real_format *,
4236 REAL_VALUE_TYPE *, const long *);
4239 encode_c4x_single (const struct real_format *fmt ATTRIBUTE_UNUSED,
4240 long *buf, const REAL_VALUE_TYPE *r)
4242 unsigned long image, exp, sig;
4254 sig = 0x800000 - r->sign;
4259 sig = (r->sig[SIGSZ-1] >> (HOST_BITS_PER_LONG - 24)) & 0x7fffff;
4274 image = ((exp & 0xff) << 24) | (sig & 0xffffff);
4279 decode_c4x_single (const struct real_format *fmt ATTRIBUTE_UNUSED,
4280 REAL_VALUE_TYPE *r, const long *buf)
4282 unsigned long image = buf[0];
4286 exp = (((image >> 24) & 0xff) ^ 0x80) - 0x80;
4287 sf = ((image & 0xffffff) ^ 0x800000) - 0x800000;
4289 memset (r, 0, sizeof (*r));
4293 r->class = rvc_normal;
4295 sig = sf & 0x7fffff;
4304 sig = (sig << (HOST_BITS_PER_LONG - 24)) | SIG_MSB;
4307 r->sig[SIGSZ-1] = sig;
4312 encode_c4x_extended (const struct real_format *fmt ATTRIBUTE_UNUSED,
4313 long *buf, const REAL_VALUE_TYPE *r)
4315 unsigned long exp, sig;
4327 sig = 0x80000000 - r->sign;
4333 sig = r->sig[SIGSZ-1];
4334 if (HOST_BITS_PER_LONG == 64)
4335 sig = sig >> 1 >> 31;
4352 exp = (exp & 0xff) << 24;
4355 if (FLOAT_WORDS_BIG_ENDIAN)
4356 buf[0] = exp, buf[1] = sig;
4358 buf[0] = sig, buf[0] = exp;
4362 decode_c4x_extended (const struct real_format *fmt ATTRIBUTE_UNUSED,
4363 REAL_VALUE_TYPE *r, const long *buf)
4368 if (FLOAT_WORDS_BIG_ENDIAN)
4369 exp = buf[0], sf = buf[1];
4371 sf = buf[0], exp = buf[1];
4373 exp = (((exp >> 24) & 0xff) & 0x80) - 0x80;
4374 sf = ((sf & 0xffffffff) ^ 0x80000000) - 0x80000000;
4376 memset (r, 0, sizeof (*r));
4380 r->class = rvc_normal;
4382 sig = sf & 0x7fffffff;
4391 if (HOST_BITS_PER_LONG == 64)
4392 sig = sig << 1 << 31;
4396 r->sig[SIGSZ-1] = sig;
4400 const struct real_format c4x_single_format =
4418 const struct real_format c4x_extended_format =
4420 encode_c4x_extended,
4421 decode_c4x_extended,
4437 /* A synthetic "format" for internal arithmetic. It's the size of the
4438 internal significand minus the two bits needed for proper rounding.
4439 The encode and decode routines exist only to satisfy our paranoia
4442 static void encode_internal (const struct real_format *fmt,
4443 long *, const REAL_VALUE_TYPE *);
4444 static void decode_internal (const struct real_format *,
4445 REAL_VALUE_TYPE *, const long *);
4448 encode_internal (const struct real_format *fmt ATTRIBUTE_UNUSED, long *buf,
4449 const REAL_VALUE_TYPE *r)
4451 memcpy (buf, r, sizeof (*r));
4455 decode_internal (const struct real_format *fmt ATTRIBUTE_UNUSED,
4456 REAL_VALUE_TYPE *r, const long *buf)
4458 memcpy (r, buf, sizeof (*r));
4461 const struct real_format real_internal_format =
4467 SIGNIFICAND_BITS - 2,
4468 SIGNIFICAND_BITS - 2,
4479 /* Calculate the square root of X in mode MODE, and store the result
4480 in R. Return TRUE if the operation does not raise an exception.
4481 For details see "High Precision Division and Square Root",
4482 Alan H. Karp and Peter Markstein, HP Lab Report 93-93-42, June
4483 1993. http://www.hpl.hp.com/techreports/93/HPL-93-42.pdf. */
4486 real_sqrt (REAL_VALUE_TYPE *r, enum machine_mode mode,
4487 const REAL_VALUE_TYPE *x)
4489 static REAL_VALUE_TYPE halfthree;
4490 static bool init = false;
4491 REAL_VALUE_TYPE h, t, i;
4494 /* sqrt(-0.0) is -0.0. */
4495 if (real_isnegzero (x))
4501 /* Negative arguments return NaN. */
4504 get_canonical_qnan (r, 0);
4508 /* Infinity and NaN return themselves. */
4509 if (real_isinf (x) || real_isnan (x))
4517 do_add (&halfthree, &dconst1, &dconsthalf, 0);
4521 /* Initial guess for reciprocal sqrt, i. */
4522 exp = real_exponent (x);
4523 real_ldexp (&i, &dconst1, -exp/2);
4525 /* Newton's iteration for reciprocal sqrt, i. */
4526 for (iter = 0; iter < 16; iter++)
4528 /* i(n+1) = i(n) * (1.5 - 0.5*i(n)*i(n)*x). */
4529 do_multiply (&t, x, &i);
4530 do_multiply (&h, &t, &i);
4531 do_multiply (&t, &h, &dconsthalf);
4532 do_add (&h, &halfthree, &t, 1);
4533 do_multiply (&t, &i, &h);
4535 /* Check for early convergence. */
4536 if (iter >= 6 && real_identical (&i, &t))
4539 /* ??? Unroll loop to avoid copying. */
4543 /* Final iteration: r = i*x + 0.5*i*x*(1.0 - i*(i*x)). */
4544 do_multiply (&t, x, &i);
4545 do_multiply (&h, &t, &i);
4546 do_add (&i, &dconst1, &h, 1);
4547 do_multiply (&h, &t, &i);
4548 do_multiply (&i, &dconsthalf, &h);
4549 do_add (&h, &t, &i, 0);
4551 /* ??? We need a Tuckerman test to get the last bit. */
4553 real_convert (r, mode, &h);
4557 /* Calculate X raised to the integer exponent N in mode MODE and store
4558 the result in R. Return true if the result may be inexact due to
4559 loss of precision. The algorithm is the classic "left-to-right binary
4560 method" described in section 4.6.3 of Donald Knuth's "Seminumerical
4561 Algorithms", "The Art of Computer Programming", Volume 2. */
4564 real_powi (REAL_VALUE_TYPE *r, enum machine_mode mode,
4565 const REAL_VALUE_TYPE *x, HOST_WIDE_INT n)
4567 unsigned HOST_WIDE_INT bit;
4569 bool inexact = false;
4581 /* Don't worry about overflow, from now on n is unsigned. */
4589 bit = (unsigned HOST_WIDE_INT) 1 << (HOST_BITS_PER_WIDE_INT - 1);
4590 for (i = 0; i < HOST_BITS_PER_WIDE_INT; i++)
4594 inexact |= do_multiply (&t, &t, &t);
4596 inexact |= do_multiply (&t, &t, x);
4604 inexact |= do_divide (&t, &dconst1, &t);
4606 real_convert (r, mode, &t);
4610 /* Round X to the nearest integer not larger in absolute value, i.e.
4611 towards zero, placing the result in R in mode MODE. */
4614 real_trunc (REAL_VALUE_TYPE *r, enum machine_mode mode,
4615 const REAL_VALUE_TYPE *x)
4617 do_fix_trunc (r, x);
4618 if (mode != VOIDmode)
4619 real_convert (r, mode, r);
4622 /* Round X to the largest integer not greater in value, i.e. round
4623 down, placing the result in R in mode MODE. */
4626 real_floor (REAL_VALUE_TYPE *r, enum machine_mode mode,
4627 const REAL_VALUE_TYPE *x)
4629 do_fix_trunc (r, x);
4630 if (! real_identical (r, x) && r->sign)
4631 do_add (r, r, &dconstm1, 0);
4632 if (mode != VOIDmode)
4633 real_convert (r, mode, r);
4636 /* Round X to the smallest integer not less then argument, i.e. round
4637 up, placing the result in R in mode MODE. */
4640 real_ceil (REAL_VALUE_TYPE *r, enum machine_mode mode,
4641 const REAL_VALUE_TYPE *x)
4643 do_fix_trunc (r, x);
4644 if (! real_identical (r, x) && ! r->sign)
4645 do_add (r, r, &dconst1, 0);
4646 if (mode != VOIDmode)
4647 real_convert (r, mode, r);