1 /* real.c - software floating point emulation.
2 Copyright (C) 1993, 1994, 1995, 1996, 1997, 1998, 1999,
3 2000, 2002, 2003 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 C 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 than the
53 largest supported target floating-point type by at least 2 bits.
54 This gives us proper rounding when we truncate to the target type.
55 In addition, E must be large enough to hold the smallest supported
56 denormal number 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 29.
62 Note that the decimal string conversion routines are sensitive to
63 rounding error. 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
PARAMS ((REAL_VALUE_TYPE
*, int));
83 static void get_canonical_qnan
PARAMS ((REAL_VALUE_TYPE
*, int));
84 static void get_canonical_snan
PARAMS ((REAL_VALUE_TYPE
*, int));
85 static void get_inf
PARAMS ((REAL_VALUE_TYPE
*, int));
86 static bool sticky_rshift_significand
PARAMS ((REAL_VALUE_TYPE
*,
87 const REAL_VALUE_TYPE
*,
89 static void rshift_significand
PARAMS ((REAL_VALUE_TYPE
*,
90 const REAL_VALUE_TYPE
*,
92 static void lshift_significand
PARAMS ((REAL_VALUE_TYPE
*,
93 const REAL_VALUE_TYPE
*,
95 static void lshift_significand_1
PARAMS ((REAL_VALUE_TYPE
*,
96 const REAL_VALUE_TYPE
*));
97 static bool add_significands
PARAMS ((REAL_VALUE_TYPE
*r
,
98 const REAL_VALUE_TYPE
*,
99 const REAL_VALUE_TYPE
*));
100 static bool sub_significands
PARAMS ((REAL_VALUE_TYPE
*,
101 const REAL_VALUE_TYPE
*,
102 const REAL_VALUE_TYPE
*, int));
103 static void neg_significand
PARAMS ((REAL_VALUE_TYPE
*,
104 const REAL_VALUE_TYPE
*));
105 static int cmp_significands
PARAMS ((const REAL_VALUE_TYPE
*,
106 const REAL_VALUE_TYPE
*));
107 static int cmp_significand_0
PARAMS ((const REAL_VALUE_TYPE
*));
108 static void set_significand_bit
PARAMS ((REAL_VALUE_TYPE
*, unsigned int));
109 static void clear_significand_bit
PARAMS ((REAL_VALUE_TYPE
*, unsigned int));
110 static bool test_significand_bit
PARAMS ((REAL_VALUE_TYPE
*, unsigned int));
111 static void clear_significand_below
PARAMS ((REAL_VALUE_TYPE
*,
113 static bool div_significands
PARAMS ((REAL_VALUE_TYPE
*,
114 const REAL_VALUE_TYPE
*,
115 const REAL_VALUE_TYPE
*));
116 static void normalize
PARAMS ((REAL_VALUE_TYPE
*));
118 static bool do_add
PARAMS ((REAL_VALUE_TYPE
*, const REAL_VALUE_TYPE
*,
119 const REAL_VALUE_TYPE
*, int));
120 static bool do_multiply
PARAMS ((REAL_VALUE_TYPE
*,
121 const REAL_VALUE_TYPE
*,
122 const REAL_VALUE_TYPE
*));
123 static bool do_divide
PARAMS ((REAL_VALUE_TYPE
*, const REAL_VALUE_TYPE
*,
124 const REAL_VALUE_TYPE
*));
125 static int do_compare
PARAMS ((const REAL_VALUE_TYPE
*,
126 const REAL_VALUE_TYPE
*, int));
127 static void do_fix_trunc
PARAMS ((REAL_VALUE_TYPE
*, const REAL_VALUE_TYPE
*));
129 static unsigned long rtd_divmod
PARAMS ((REAL_VALUE_TYPE
*,
132 static const REAL_VALUE_TYPE
* ten_to_ptwo
PARAMS ((int));
133 static const REAL_VALUE_TYPE
* ten_to_mptwo
PARAMS ((int));
134 static const REAL_VALUE_TYPE
* real_digit
PARAMS ((int));
135 static void times_pten
PARAMS ((REAL_VALUE_TYPE
*, int));
137 static void round_for_format
PARAMS ((const struct real_format
*,
140 /* Initialize R with a positive zero. */
147 memset (r
, 0, sizeof (*r
));
151 /* Initialize R with the canonical quiet NaN. */
154 get_canonical_qnan (r
, sign
)
158 memset (r
, 0, sizeof (*r
));
165 get_canonical_snan (r
, sign
)
169 memset (r
, 0, sizeof (*r
));
181 memset (r
, 0, sizeof (*r
));
187 /* Right-shift the significand of A by N bits; put the result in the
188 significand of R. If any one bits are shifted out, return true. */
191 sticky_rshift_significand (r
, a
, n
)
193 const REAL_VALUE_TYPE
*a
;
196 unsigned long sticky
= 0;
197 unsigned int i
, ofs
= 0;
199 if (n
>= HOST_BITS_PER_LONG
)
201 for (i
= 0, ofs
= n
/ HOST_BITS_PER_LONG
; i
< ofs
; ++i
)
203 n
&= HOST_BITS_PER_LONG
- 1;
208 sticky
|= a
->sig
[ofs
] & (((unsigned long)1 << n
) - 1);
209 for (i
= 0; i
< SIGSZ
; ++i
)
212 = (((ofs
+ i
>= SIGSZ
? 0 : a
->sig
[ofs
+ i
]) >> n
)
213 | ((ofs
+ i
+ 1 >= SIGSZ
? 0 : a
->sig
[ofs
+ i
+ 1])
214 << (HOST_BITS_PER_LONG
- n
)));
219 for (i
= 0; ofs
+ i
< SIGSZ
; ++i
)
220 r
->sig
[i
] = a
->sig
[ofs
+ i
];
221 for (; i
< SIGSZ
; ++i
)
228 /* Right-shift the significand of A by N bits; put the result in the
232 rshift_significand (r
, a
, n
)
234 const REAL_VALUE_TYPE
*a
;
237 unsigned int i
, ofs
= n
/ HOST_BITS_PER_LONG
;
239 n
&= HOST_BITS_PER_LONG
- 1;
242 for (i
= 0; i
< SIGSZ
; ++i
)
245 = (((ofs
+ i
>= SIGSZ
? 0 : a
->sig
[ofs
+ i
]) >> n
)
246 | ((ofs
+ i
+ 1 >= SIGSZ
? 0 : a
->sig
[ofs
+ i
+ 1])
247 << (HOST_BITS_PER_LONG
- n
)));
252 for (i
= 0; ofs
+ i
< SIGSZ
; ++i
)
253 r
->sig
[i
] = a
->sig
[ofs
+ i
];
254 for (; i
< SIGSZ
; ++i
)
259 /* Left-shift the significand of A by N bits; put the result in the
263 lshift_significand (r
, a
, n
)
265 const REAL_VALUE_TYPE
*a
;
268 unsigned int i
, ofs
= n
/ HOST_BITS_PER_LONG
;
270 n
&= HOST_BITS_PER_LONG
- 1;
273 for (i
= 0; ofs
+ i
< SIGSZ
; ++i
)
274 r
->sig
[SIGSZ
-1-i
] = a
->sig
[SIGSZ
-1-i
-ofs
];
275 for (; i
< SIGSZ
; ++i
)
276 r
->sig
[SIGSZ
-1-i
] = 0;
279 for (i
= 0; i
< SIGSZ
; ++i
)
282 = (((ofs
+ i
>= SIGSZ
? 0 : a
->sig
[SIGSZ
-1-i
-ofs
]) << n
)
283 | ((ofs
+ i
+ 1 >= SIGSZ
? 0 : a
->sig
[SIGSZ
-1-i
-ofs
-1])
284 >> (HOST_BITS_PER_LONG
- n
)));
288 /* Likewise, but N is specialized to 1. */
291 lshift_significand_1 (r
, a
)
293 const REAL_VALUE_TYPE
*a
;
297 for (i
= SIGSZ
- 1; i
> 0; --i
)
298 r
->sig
[i
] = (a
->sig
[i
] << 1) | (a
->sig
[i
-1] >> (HOST_BITS_PER_LONG
- 1));
299 r
->sig
[0] = a
->sig
[0] << 1;
302 /* Add the significands of A and B, placing the result in R. Return
303 true if there was carry out of the most significant word. */
306 add_significands (r
, a
, b
)
308 const REAL_VALUE_TYPE
*a
, *b
;
313 for (i
= 0; i
< SIGSZ
; ++i
)
315 unsigned long ai
= a
->sig
[i
];
316 unsigned long ri
= ai
+ b
->sig
[i
];
332 /* Subtract the significands of A and B, placing the result in R. CARRY is
333 true if there's a borrow incoming to the least significant word.
334 Return true if there was borrow out of the most significant word. */
337 sub_significands (r
, a
, b
, carry
)
339 const REAL_VALUE_TYPE
*a
, *b
;
344 for (i
= 0; i
< SIGSZ
; ++i
)
346 unsigned long ai
= a
->sig
[i
];
347 unsigned long ri
= ai
- b
->sig
[i
];
363 /* Negate the significand A, placing the result in R. */
366 neg_significand (r
, a
)
368 const REAL_VALUE_TYPE
*a
;
373 for (i
= 0; i
< SIGSZ
; ++i
)
375 unsigned long ri
, ai
= a
->sig
[i
];
394 /* Compare significands. Return tri-state vs zero. */
397 cmp_significands (a
, b
)
398 const REAL_VALUE_TYPE
*a
, *b
;
402 for (i
= SIGSZ
- 1; i
>= 0; --i
)
404 unsigned long ai
= a
->sig
[i
];
405 unsigned long bi
= b
->sig
[i
];
416 /* Return true if A is nonzero. */
419 cmp_significand_0 (a
)
420 const REAL_VALUE_TYPE
*a
;
424 for (i
= SIGSZ
- 1; i
>= 0; --i
)
431 /* Set bit N of the significand of R. */
434 set_significand_bit (r
, n
)
438 r
->sig
[n
/ HOST_BITS_PER_LONG
]
439 |= (unsigned long)1 << (n
% HOST_BITS_PER_LONG
);
442 /* Clear bit N of the significand of R. */
445 clear_significand_bit (r
, n
)
449 r
->sig
[n
/ HOST_BITS_PER_LONG
]
450 &= ~((unsigned long)1 << (n
% HOST_BITS_PER_LONG
));
453 /* Test bit N of the significand of R. */
456 test_significand_bit (r
, n
)
460 /* ??? Compiler bug here if we return this expression directly.
461 The conversion to bool strips the "&1" and we wind up testing
462 e.g. 2 != 0 -> true. Seen in gcc version 3.2 20020520. */
463 int t
= (r
->sig
[n
/ HOST_BITS_PER_LONG
] >> (n
% HOST_BITS_PER_LONG
)) & 1;
467 /* Clear bits 0..N-1 of the significand of R. */
470 clear_significand_below (r
, n
)
474 int i
, w
= n
/ HOST_BITS_PER_LONG
;
476 for (i
= 0; i
< w
; ++i
)
479 r
->sig
[w
] &= ~(((unsigned long)1 << (n
% HOST_BITS_PER_LONG
)) - 1);
482 /* Divide the significands of A and B, placing the result in R. Return
483 true if the division was inexact. */
486 div_significands (r
, a
, b
)
488 const REAL_VALUE_TYPE
*a
, *b
;
491 int i
, bit
= SIGNIFICAND_BITS
- 1;
492 unsigned long msb
, inexact
;
495 memset (r
->sig
, 0, sizeof (r
->sig
));
501 msb
= u
.sig
[SIGSZ
-1] & SIG_MSB
;
502 lshift_significand_1 (&u
, &u
);
504 if (msb
|| cmp_significands (&u
, b
) >= 0)
506 sub_significands (&u
, &u
, b
, 0);
507 set_significand_bit (r
, bit
);
512 for (i
= 0, inexact
= 0; i
< SIGSZ
; i
++)
518 /* Adjust the exponent and significand of R such that the most
519 significant bit is set. We underflow to zero and overflow to
520 infinity here, without denormals. (The intermediate representation
521 exponent is large enough to handle target denormals normalized.) */
530 /* Find the first word that is nonzero. */
531 for (i
= SIGSZ
- 1; i
>= 0; i
--)
533 shift
+= HOST_BITS_PER_LONG
;
537 /* Zero significand flushes to zero. */
545 /* Find the first bit that is nonzero. */
547 if (r
->sig
[i
] & ((unsigned long)1 << (HOST_BITS_PER_LONG
- 1 - j
)))
553 exp
= r
->exp
- shift
;
555 get_inf (r
, r
->sign
);
556 else if (exp
< -MAX_EXP
)
557 get_zero (r
, r
->sign
);
561 lshift_significand (r
, r
, shift
);
566 /* Calculate R = A + (SUBTRACT_P ? -B : B). Return true if the
567 result may be inexact due to a loss of precision. */
570 do_add (r
, a
, b
, subtract_p
)
572 const REAL_VALUE_TYPE
*a
, *b
;
577 bool inexact
= false;
579 /* Determine if we need to add or subtract. */
581 subtract_p
= (sign
^ b
->sign
) ^ subtract_p
;
583 switch (CLASS2 (a
->class, b
->class))
585 case CLASS2 (rvc_zero
, rvc_zero
):
586 /* -0 + -0 = -0, -0 - +0 = -0; all other cases yield +0. */
587 get_zero (r
, sign
& !subtract_p
);
590 case CLASS2 (rvc_zero
, rvc_normal
):
591 case CLASS2 (rvc_zero
, rvc_inf
):
592 case CLASS2 (rvc_zero
, rvc_nan
):
594 case CLASS2 (rvc_normal
, rvc_nan
):
595 case CLASS2 (rvc_inf
, rvc_nan
):
596 case CLASS2 (rvc_nan
, rvc_nan
):
597 /* ANY + NaN = NaN. */
598 case CLASS2 (rvc_normal
, rvc_inf
):
601 r
->sign
= sign
^ subtract_p
;
604 case CLASS2 (rvc_normal
, rvc_zero
):
605 case CLASS2 (rvc_inf
, rvc_zero
):
606 case CLASS2 (rvc_nan
, rvc_zero
):
608 case CLASS2 (rvc_nan
, rvc_normal
):
609 case CLASS2 (rvc_nan
, rvc_inf
):
610 /* NaN + ANY = NaN. */
611 case CLASS2 (rvc_inf
, rvc_normal
):
616 case CLASS2 (rvc_inf
, rvc_inf
):
618 /* Inf - Inf = NaN. */
619 get_canonical_qnan (r
, 0);
621 /* Inf + Inf = Inf. */
625 case CLASS2 (rvc_normal
, rvc_normal
):
632 /* Swap the arguments such that A has the larger exponent. */
633 dexp
= a
->exp
- b
->exp
;
636 const REAL_VALUE_TYPE
*t
;
643 /* If the exponents are not identical, we need to shift the
644 significand of B down. */
647 /* If the exponents are too far apart, the significands
648 do not overlap, which makes the subtraction a noop. */
649 if (dexp
>= SIGNIFICAND_BITS
)
656 inexact
|= sticky_rshift_significand (&t
, b
, dexp
);
662 if (sub_significands (r
, a
, b
, inexact
))
664 /* We got a borrow out of the subtraction. That means that
665 A and B had the same exponent, and B had the larger
666 significand. We need to swap the sign and negate the
669 neg_significand (r
, r
);
674 if (add_significands (r
, a
, b
))
676 /* We got carry out of the addition. This means we need to
677 shift the significand back down one bit and increase the
679 inexact
|= sticky_rshift_significand (r
, r
, 1);
680 r
->sig
[SIGSZ
-1] |= SIG_MSB
;
689 r
->class = rvc_normal
;
693 /* Re-normalize the result. */
696 /* Special case: if the subtraction results in zero, the result
698 if (r
->class == rvc_zero
)
701 r
->sig
[0] |= inexact
;
706 /* Calculate R = A * B. Return true if the result may be inexact. */
709 do_multiply (r
, a
, b
)
711 const REAL_VALUE_TYPE
*a
, *b
;
713 REAL_VALUE_TYPE u
, t
, *rr
;
714 unsigned int i
, j
, k
;
715 int sign
= a
->sign
^ b
->sign
;
716 bool inexact
= false;
718 switch (CLASS2 (a
->class, b
->class))
720 case CLASS2 (rvc_zero
, rvc_zero
):
721 case CLASS2 (rvc_zero
, rvc_normal
):
722 case CLASS2 (rvc_normal
, rvc_zero
):
723 /* +-0 * ANY = 0 with appropriate sign. */
727 case CLASS2 (rvc_zero
, rvc_nan
):
728 case CLASS2 (rvc_normal
, rvc_nan
):
729 case CLASS2 (rvc_inf
, rvc_nan
):
730 case CLASS2 (rvc_nan
, rvc_nan
):
731 /* ANY * NaN = NaN. */
736 case CLASS2 (rvc_nan
, rvc_zero
):
737 case CLASS2 (rvc_nan
, rvc_normal
):
738 case CLASS2 (rvc_nan
, rvc_inf
):
739 /* NaN * ANY = NaN. */
744 case CLASS2 (rvc_zero
, rvc_inf
):
745 case CLASS2 (rvc_inf
, rvc_zero
):
747 get_canonical_qnan (r
, sign
);
750 case CLASS2 (rvc_inf
, rvc_inf
):
751 case CLASS2 (rvc_normal
, rvc_inf
):
752 case CLASS2 (rvc_inf
, rvc_normal
):
753 /* Inf * Inf = Inf, R * Inf = Inf */
757 case CLASS2 (rvc_normal
, rvc_normal
):
764 if (r
== a
|| r
== b
)
770 /* Collect all the partial products. Since we don't have sure access
771 to a widening multiply, we split each long into two half-words.
773 Consider the long-hand form of a four half-word multiplication:
783 We construct partial products of the widened half-word products
784 that are known to not overlap, e.g. DF+DH. Each such partial
785 product is given its proper exponent, which allows us to sum them
786 and obtain the finished product. */
788 for (i
= 0; i
< SIGSZ
* 2; ++i
)
790 unsigned long ai
= a
->sig
[i
/ 2];
792 ai
>>= HOST_BITS_PER_LONG
/ 2;
794 ai
&= ((unsigned long)1 << (HOST_BITS_PER_LONG
/ 2)) - 1;
799 for (j
= 0; j
< 2; ++j
)
801 int exp
= (a
->exp
- (2*SIGSZ
-1-i
)*(HOST_BITS_PER_LONG
/2)
802 + (b
->exp
- (1-j
)*(HOST_BITS_PER_LONG
/2)));
811 /* Would underflow to zero, which we shouldn't bother adding. */
816 u
.class = rvc_normal
;
820 for (k
= j
; k
< SIGSZ
* 2; k
+= 2)
822 unsigned long bi
= b
->sig
[k
/ 2];
824 bi
>>= HOST_BITS_PER_LONG
/ 2;
826 bi
&= ((unsigned long)1 << (HOST_BITS_PER_LONG
/ 2)) - 1;
828 u
.sig
[k
/ 2] = ai
* bi
;
832 inexact
|= do_add (rr
, rr
, &u
, 0);
843 /* Calculate R = A / B. Return true if the result may be inexact. */
848 const REAL_VALUE_TYPE
*a
, *b
;
850 int exp
, sign
= a
->sign
^ b
->sign
;
851 REAL_VALUE_TYPE t
, *rr
;
854 switch (CLASS2 (a
->class, b
->class))
856 case CLASS2 (rvc_zero
, rvc_zero
):
858 case CLASS2 (rvc_inf
, rvc_inf
):
859 /* Inf / Inf = NaN. */
860 get_canonical_qnan (r
, sign
);
863 case CLASS2 (rvc_zero
, rvc_normal
):
864 case CLASS2 (rvc_zero
, rvc_inf
):
866 case CLASS2 (rvc_normal
, rvc_inf
):
871 case CLASS2 (rvc_normal
, rvc_zero
):
873 case CLASS2 (rvc_inf
, rvc_zero
):
878 case CLASS2 (rvc_zero
, rvc_nan
):
879 case CLASS2 (rvc_normal
, rvc_nan
):
880 case CLASS2 (rvc_inf
, rvc_nan
):
881 case CLASS2 (rvc_nan
, rvc_nan
):
882 /* ANY / NaN = NaN. */
887 case CLASS2 (rvc_nan
, rvc_zero
):
888 case CLASS2 (rvc_nan
, rvc_normal
):
889 case CLASS2 (rvc_nan
, rvc_inf
):
890 /* NaN / ANY = NaN. */
895 case CLASS2 (rvc_inf
, rvc_normal
):
900 case CLASS2 (rvc_normal
, rvc_normal
):
907 if (r
== a
|| r
== b
)
912 rr
->class = rvc_normal
;
915 exp
= a
->exp
- b
->exp
+ 1;
928 inexact
= div_significands (rr
, a
, b
);
930 /* Re-normalize the result. */
932 rr
->sig
[0] |= inexact
;
940 /* Return a tri-state comparison of A vs B. Return NAN_RESULT if
941 one of the two operands is a NaN. */
944 do_compare (a
, b
, nan_result
)
945 const REAL_VALUE_TYPE
*a
, *b
;
950 switch (CLASS2 (a
->class, b
->class))
952 case CLASS2 (rvc_zero
, rvc_zero
):
953 /* Sign of zero doesn't matter for compares. */
956 case CLASS2 (rvc_inf
, rvc_zero
):
957 case CLASS2 (rvc_inf
, rvc_normal
):
958 case CLASS2 (rvc_normal
, rvc_zero
):
959 return (a
->sign
? -1 : 1);
961 case CLASS2 (rvc_inf
, rvc_inf
):
962 return -a
->sign
- -b
->sign
;
964 case CLASS2 (rvc_zero
, rvc_normal
):
965 case CLASS2 (rvc_zero
, rvc_inf
):
966 case CLASS2 (rvc_normal
, rvc_inf
):
967 return (b
->sign
? 1 : -1);
969 case CLASS2 (rvc_zero
, rvc_nan
):
970 case CLASS2 (rvc_normal
, rvc_nan
):
971 case CLASS2 (rvc_inf
, rvc_nan
):
972 case CLASS2 (rvc_nan
, rvc_nan
):
973 case CLASS2 (rvc_nan
, rvc_zero
):
974 case CLASS2 (rvc_nan
, rvc_normal
):
975 case CLASS2 (rvc_nan
, rvc_inf
):
978 case CLASS2 (rvc_normal
, rvc_normal
):
985 if (a
->sign
!= b
->sign
)
986 return -a
->sign
- -b
->sign
;
990 else if (a
->exp
< b
->exp
)
993 ret
= cmp_significands (a
, b
);
995 return (a
->sign
? -ret
: ret
);
998 /* Return A truncated to an integral value toward zero. */
1003 const REAL_VALUE_TYPE
*a
;
1016 get_zero (r
, r
->sign
);
1017 else if (r
->exp
< SIGNIFICAND_BITS
)
1018 clear_significand_below (r
, SIGNIFICAND_BITS
- r
->exp
);
1026 /* Perform the binary or unary operation described by CODE.
1027 For a unary operation, leave OP1 NULL. */
1030 real_arithmetic (r
, icode
, op0
, op1
)
1033 const REAL_VALUE_TYPE
*op0
, *op1
;
1035 enum tree_code code
= icode
;
1040 do_add (r
, op0
, op1
, 0);
1044 do_add (r
, op0
, op1
, 1);
1048 do_multiply (r
, op0
, op1
);
1052 do_divide (r
, op0
, op1
);
1056 if (op1
->class == rvc_nan
)
1058 else if (do_compare (op0
, op1
, -1) < 0)
1065 if (op1
->class == rvc_nan
)
1067 else if (do_compare (op0
, op1
, 1) < 0)
1083 case FIX_TRUNC_EXPR
:
1084 do_fix_trunc (r
, op0
);
1092 /* Legacy. Similar, but return the result directly. */
1095 real_arithmetic2 (icode
, op0
, op1
)
1097 const REAL_VALUE_TYPE
*op0
, *op1
;
1100 real_arithmetic (&r
, icode
, op0
, op1
);
1105 real_compare (icode
, op0
, op1
)
1107 const REAL_VALUE_TYPE
*op0
, *op1
;
1109 enum tree_code code
= icode
;
1114 return do_compare (op0
, op1
, 1) < 0;
1116 return do_compare (op0
, op1
, 1) <= 0;
1118 return do_compare (op0
, op1
, -1) > 0;
1120 return do_compare (op0
, op1
, -1) >= 0;
1122 return do_compare (op0
, op1
, -1) == 0;
1124 return do_compare (op0
, op1
, -1) != 0;
1125 case UNORDERED_EXPR
:
1126 return op0
->class == rvc_nan
|| op1
->class == rvc_nan
;
1128 return op0
->class != rvc_nan
&& op1
->class != rvc_nan
;
1130 return do_compare (op0
, op1
, -1) < 0;
1132 return do_compare (op0
, op1
, -1) <= 0;
1134 return do_compare (op0
, op1
, 1) > 0;
1136 return do_compare (op0
, op1
, 1) >= 0;
1138 return do_compare (op0
, op1
, 0) == 0;
1145 /* Return floor log2(R). */
1149 const REAL_VALUE_TYPE
*r
;
1157 return (unsigned int)-1 >> 1;
1165 /* R = OP0 * 2**EXP. */
1168 real_ldexp (r
, op0
, exp
)
1170 const REAL_VALUE_TYPE
*op0
;
1184 get_inf (r
, r
->sign
);
1185 else if (exp
< -MAX_EXP
)
1186 get_zero (r
, r
->sign
);
1196 /* Determine whether a floating-point value X is infinite. */
1200 const REAL_VALUE_TYPE
*r
;
1202 return (r
->class == rvc_inf
);
1205 /* Determine whether a floating-point value X is a NaN. */
1209 const REAL_VALUE_TYPE
*r
;
1211 return (r
->class == rvc_nan
);
1214 /* Determine whether a floating-point value X is negative. */
1218 const REAL_VALUE_TYPE
*r
;
1223 /* Determine whether a floating-point value X is minus zero. */
1227 const REAL_VALUE_TYPE
*r
;
1229 return r
->sign
&& r
->class == rvc_zero
;
1232 /* Compare two floating-point objects for bitwise identity. */
1235 real_identical (a
, b
)
1236 const REAL_VALUE_TYPE
*a
, *b
;
1240 if (a
->class != b
->class)
1242 if (a
->sign
!= b
->sign
)
1252 if (a
->exp
!= b
->exp
)
1257 if (a
->signalling
!= b
->signalling
)
1259 /* The significand is ignored for canonical NaNs. */
1260 if (a
->canonical
|| b
->canonical
)
1261 return a
->canonical
== b
->canonical
;
1268 for (i
= 0; i
< SIGSZ
; ++i
)
1269 if (a
->sig
[i
] != b
->sig
[i
])
1275 /* Try to change R into its exact multiplicative inverse in machine
1276 mode MODE. Return true if successful. */
1279 exact_real_inverse (mode
, r
)
1280 enum machine_mode mode
;
1283 const REAL_VALUE_TYPE
*one
= real_digit (1);
1287 if (r
->class != rvc_normal
)
1290 /* Check for a power of two: all significand bits zero except the MSB. */
1291 for (i
= 0; i
< SIGSZ
-1; ++i
)
1294 if (r
->sig
[SIGSZ
-1] != SIG_MSB
)
1297 /* Find the inverse and truncate to the required mode. */
1298 do_divide (&u
, one
, r
);
1299 real_convert (&u
, mode
, &u
);
1301 /* The rounding may have overflowed. */
1302 if (u
.class != rvc_normal
)
1304 for (i
= 0; i
< SIGSZ
-1; ++i
)
1307 if (u
.sig
[SIGSZ
-1] != SIG_MSB
)
1314 /* Render R as an integer. */
1318 const REAL_VALUE_TYPE
*r
;
1320 unsigned HOST_WIDE_INT i
;
1331 i
= (unsigned HOST_WIDE_INT
) 1 << (HOST_BITS_PER_WIDE_INT
- 1);
1339 /* Only force overflow for unsigned overflow. Signed overflow is
1340 undefined, so it doesn't matter what we return, and some callers
1341 expect to be able to use this routine for both signed and
1342 unsigned conversions. */
1343 if (r
->exp
> HOST_BITS_PER_WIDE_INT
)
1346 if (HOST_BITS_PER_WIDE_INT
== HOST_BITS_PER_LONG
)
1347 i
= r
->sig
[SIGSZ
-1];
1348 else if (HOST_BITS_PER_WIDE_INT
== 2*HOST_BITS_PER_LONG
)
1350 i
= r
->sig
[SIGSZ
-1];
1351 i
= i
<< (HOST_BITS_PER_LONG
- 1) << 1;
1352 i
|= r
->sig
[SIGSZ
-2];
1357 i
>>= HOST_BITS_PER_WIDE_INT
- r
->exp
;
1368 /* Likewise, but to an integer pair, HI+LOW. */
1371 real_to_integer2 (plow
, phigh
, r
)
1372 HOST_WIDE_INT
*plow
, *phigh
;
1373 const REAL_VALUE_TYPE
*r
;
1376 HOST_WIDE_INT low
, high
;
1389 high
= (unsigned HOST_WIDE_INT
) 1 << (HOST_BITS_PER_WIDE_INT
- 1);
1403 /* Only force overflow for unsigned overflow. Signed overflow is
1404 undefined, so it doesn't matter what we return, and some callers
1405 expect to be able to use this routine for both signed and
1406 unsigned conversions. */
1407 if (exp
> 2*HOST_BITS_PER_WIDE_INT
)
1410 rshift_significand (&t
, r
, 2*HOST_BITS_PER_WIDE_INT
- exp
);
1411 if (HOST_BITS_PER_WIDE_INT
== HOST_BITS_PER_LONG
)
1413 high
= t
.sig
[SIGSZ
-1];
1414 low
= t
.sig
[SIGSZ
-2];
1416 else if (HOST_BITS_PER_WIDE_INT
== 2*HOST_BITS_PER_LONG
)
1418 high
= t
.sig
[SIGSZ
-1];
1419 high
= high
<< (HOST_BITS_PER_LONG
- 1) << 1;
1420 high
|= t
.sig
[SIGSZ
-2];
1422 low
= t
.sig
[SIGSZ
-3];
1423 low
= low
<< (HOST_BITS_PER_LONG
- 1) << 1;
1424 low
|= t
.sig
[SIGSZ
-4];
1434 low
= -low
, high
= ~high
;
1446 /* A subroutine of real_to_decimal. Compute the quotient and remainder
1447 of NUM / DEN. Return the quotient and place the remainder in NUM.
1448 It is expected that NUM / DEN are close enough that the quotient is
1451 static unsigned long
1452 rtd_divmod (num
, den
)
1453 REAL_VALUE_TYPE
*num
, *den
;
1455 unsigned long q
, msb
;
1456 int expn
= num
->exp
, expd
= den
->exp
;
1465 msb
= num
->sig
[SIGSZ
-1] & SIG_MSB
;
1467 lshift_significand_1 (num
, num
);
1469 if (msb
|| cmp_significands (num
, den
) >= 0)
1471 sub_significands (num
, num
, den
, 0);
1475 while (--expn
>= expd
);
1483 /* Render R as a decimal floating point constant. Emit DIGITS significant
1484 digits in the result, bounded by BUF_SIZE. If DIGITS is 0, choose the
1485 maximum for the representation. If CROP_TRAILING_ZEROS, strip trailing
1488 #define M_LOG10_2 0.30102999566398119521
1491 real_to_decimal (str
, r_orig
, buf_size
, digits
, crop_trailing_zeros
)
1493 const REAL_VALUE_TYPE
*r_orig
;
1494 size_t buf_size
, digits
;
1495 int crop_trailing_zeros
;
1497 const REAL_VALUE_TYPE
*one
, *ten
;
1498 REAL_VALUE_TYPE r
, pten
, u
, v
;
1499 int dec_exp
, cmp_one
, digit
;
1501 char *p
, *first
, *last
;
1508 strcpy (str
, (r
.sign
? "-0.0" : "0.0"));
1513 strcpy (str
, (r
.sign
? "-Inf" : "+Inf"));
1516 /* ??? Print the significand as well, if not canonical? */
1517 strcpy (str
, (r
.sign
? "-NaN" : "+NaN"));
1523 /* Bound the number of digits printed by the size of the representation. */
1524 max_digits
= SIGNIFICAND_BITS
* M_LOG10_2
;
1525 if (digits
== 0 || digits
> max_digits
)
1526 digits
= max_digits
;
1528 /* Estimate the decimal exponent, and compute the length of the string it
1529 will print as. Be conservative and add one to account for possible
1530 overflow or rounding error. */
1531 dec_exp
= r
.exp
* M_LOG10_2
;
1532 for (max_digits
= 1; dec_exp
; max_digits
++)
1535 /* Bound the number of digits printed by the size of the output buffer. */
1536 max_digits
= buf_size
- 1 - 1 - 2 - max_digits
- 1;
1537 if (max_digits
> buf_size
)
1539 if (digits
> max_digits
)
1540 digits
= max_digits
;
1542 one
= real_digit (1);
1543 ten
= ten_to_ptwo (0);
1551 cmp_one
= do_compare (&r
, one
, 0);
1556 /* Number is greater than one. Convert significand to an integer
1557 and strip trailing decimal zeros. */
1560 u
.exp
= SIGNIFICAND_BITS
- 1;
1562 /* Largest M, such that 10**2**M fits within SIGNIFICAND_BITS. */
1563 m
= floor_log2 (max_digits
);
1565 /* Iterate over the bits of the possible powers of 10 that might
1566 be present in U and eliminate them. That is, if we find that
1567 10**2**M divides U evenly, keep the division and increase
1573 do_divide (&t
, &u
, ten_to_ptwo (m
));
1574 do_fix_trunc (&v
, &t
);
1575 if (cmp_significands (&v
, &t
) == 0)
1583 /* Revert the scaling to integer that we performed earlier. */
1584 u
.exp
+= r
.exp
- (SIGNIFICAND_BITS
- 1);
1587 /* Find power of 10. Do this by dividing out 10**2**M when
1588 this is larger than the current remainder. Fill PTEN with
1589 the power of 10 that we compute. */
1592 m
= floor_log2 ((int)(r
.exp
* M_LOG10_2
)) + 1;
1595 const REAL_VALUE_TYPE
*ptentwo
= ten_to_ptwo (m
);
1596 if (do_compare (&u
, ptentwo
, 0) >= 0)
1598 do_divide (&u
, &u
, ptentwo
);
1599 do_multiply (&pten
, &pten
, ptentwo
);
1606 /* We managed to divide off enough tens in the above reduction
1607 loop that we've now got a negative exponent. Fall into the
1608 less-than-one code to compute the proper value for PTEN. */
1615 /* Number is less than one. Pad significand with leading
1621 /* Stop if we'd shift bits off the bottom. */
1625 do_multiply (&u
, &v
, ten
);
1627 /* Stop if we're now >= 1. */
1636 /* Find power of 10. Do this by multiplying in P=10**2**M when
1637 the current remainder is smaller than 1/P. Fill PTEN with the
1638 power of 10 that we compute. */
1639 m
= floor_log2 ((int)(-r
.exp
* M_LOG10_2
)) + 1;
1642 const REAL_VALUE_TYPE
*ptentwo
= ten_to_ptwo (m
);
1643 const REAL_VALUE_TYPE
*ptenmtwo
= ten_to_mptwo (m
);
1645 if (do_compare (&v
, ptenmtwo
, 0) <= 0)
1647 do_multiply (&v
, &v
, ptentwo
);
1648 do_multiply (&pten
, &pten
, ptentwo
);
1654 /* Invert the positive power of 10 that we've collected so far. */
1655 do_divide (&pten
, one
, &pten
);
1663 /* At this point, PTEN should contain the nearest power of 10 smaller
1664 than R, such that this division produces the first digit.
1666 Using a divide-step primitive that returns the complete integral
1667 remainder avoids the rounding error that would be produced if
1668 we were to use do_divide here and then simply multiply by 10 for
1669 each subsequent digit. */
1671 digit
= rtd_divmod (&r
, &pten
);
1673 /* Be prepared for error in that division via underflow ... */
1674 if (digit
== 0 && cmp_significand_0 (&r
))
1676 /* Multiply by 10 and try again. */
1677 do_multiply (&r
, &r
, ten
);
1678 digit
= rtd_divmod (&r
, &pten
);
1684 /* ... or overflow. */
1692 else if (digit
> 10)
1697 /* Generate subsequent digits. */
1698 while (--digits
> 0)
1700 do_multiply (&r
, &r
, ten
);
1701 digit
= rtd_divmod (&r
, &pten
);
1706 /* Generate one more digit with which to do rounding. */
1707 do_multiply (&r
, &r
, ten
);
1708 digit
= rtd_divmod (&r
, &pten
);
1710 /* Round the result. */
1713 /* Round to nearest. If R is nonzero there are additional
1714 nonzero digits to be extracted. */
1715 if (cmp_significand_0 (&r
))
1717 /* Round to even. */
1718 else if ((p
[-1] - '0') & 1)
1735 /* Carry out of the first digit. This means we had all 9's and
1736 now have all 0's. "Prepend" a 1 by overwriting the first 0. */
1744 /* Insert the decimal point. */
1745 first
[0] = first
[1];
1748 /* If requested, drop trailing zeros. Never crop past "1.0". */
1749 if (crop_trailing_zeros
)
1750 while (last
> first
+ 3 && last
[-1] == '0')
1753 /* Append the exponent. */
1754 sprintf (last
, "e%+d", dec_exp
);
1757 /* Render R as a hexadecimal floating point constant. Emit DIGITS
1758 significant digits in the result, bounded by BUF_SIZE. If DIGITS is 0,
1759 choose the maximum for the representation. If CROP_TRAILING_ZEROS,
1760 strip trailing zeros. */
1763 real_to_hexadecimal (str
, r
, buf_size
, digits
, crop_trailing_zeros
)
1765 const REAL_VALUE_TYPE
*r
;
1766 size_t buf_size
, digits
;
1767 int crop_trailing_zeros
;
1769 int i
, j
, exp
= r
->exp
;
1782 strcpy (str
, (r
->sign
? "-Inf" : "+Inf"));
1785 /* ??? Print the significand as well, if not canonical? */
1786 strcpy (str
, (r
->sign
? "-NaN" : "+NaN"));
1793 digits
= SIGNIFICAND_BITS
/ 4;
1795 /* Bound the number of digits printed by the size of the output buffer. */
1797 sprintf (exp_buf
, "p%+d", exp
);
1798 max_digits
= buf_size
- strlen (exp_buf
) - r
->sign
- 4 - 1;
1799 if (max_digits
> buf_size
)
1801 if (digits
> max_digits
)
1802 digits
= max_digits
;
1813 for (i
= SIGSZ
- 1; i
>= 0; --i
)
1814 for (j
= HOST_BITS_PER_LONG
- 4; j
>= 0; j
-= 4)
1816 *p
++ = "0123456789abcdef"[(r
->sig
[i
] >> j
) & 15];
1822 if (crop_trailing_zeros
)
1823 while (p
> first
+ 1 && p
[-1] == '0')
1826 sprintf (p
, "p%+d", exp
);
1829 /* Initialize R from a decimal or hexadecimal string. The string is
1830 assumed to have been syntax checked already. */
1833 real_from_string (r
, str
)
1847 else if (*str
== '+')
1850 if (str
[0] == '0' && str
[1] == 'x')
1852 /* Hexadecimal floating point. */
1853 int pos
= SIGNIFICAND_BITS
- 4, d
;
1861 d
= hex_value (*str
);
1866 r
->sig
[pos
/ HOST_BITS_PER_LONG
]
1867 |= (unsigned long) d
<< (pos
% HOST_BITS_PER_LONG
);
1876 if (pos
== SIGNIFICAND_BITS
- 4)
1883 d
= hex_value (*str
);
1888 r
->sig
[pos
/ HOST_BITS_PER_LONG
]
1889 |= (unsigned long) d
<< (pos
% HOST_BITS_PER_LONG
);
1895 if (*str
== 'p' || *str
== 'P')
1897 bool exp_neg
= false;
1905 else if (*str
== '+')
1909 while (ISDIGIT (*str
))
1915 /* Overflowed the exponent. */
1929 r
->class = rvc_normal
;
1936 /* Decimal floating point. */
1937 const REAL_VALUE_TYPE
*ten
= ten_to_ptwo (0);
1942 while (ISDIGIT (*str
))
1945 do_multiply (r
, r
, ten
);
1947 do_add (r
, r
, real_digit (d
), 0);
1952 if (r
->class == rvc_zero
)
1957 while (ISDIGIT (*str
))
1960 do_multiply (r
, r
, ten
);
1962 do_add (r
, r
, real_digit (d
), 0);
1967 if (*str
== 'e' || *str
== 'E')
1969 bool exp_neg
= false;
1977 else if (*str
== '+')
1981 while (ISDIGIT (*str
))
1987 /* Overflowed the exponent. */
2001 times_pten (r
, exp
);
2016 /* Legacy. Similar, but return the result directly. */
2019 real_from_string2 (s
, mode
)
2021 enum machine_mode mode
;
2025 real_from_string (&r
, s
);
2026 if (mode
!= VOIDmode
)
2027 real_convert (&r
, mode
, &r
);
2032 /* Initialize R from the integer pair HIGH+LOW. */
2035 real_from_integer (r
, mode
, low
, high
, unsigned_p
)
2037 enum machine_mode mode
;
2038 unsigned HOST_WIDE_INT low
;
2042 if (low
== 0 && high
== 0)
2046 r
->class = rvc_normal
;
2047 r
->sign
= high
< 0 && !unsigned_p
;
2048 r
->exp
= 2 * HOST_BITS_PER_WIDE_INT
;
2059 if (HOST_BITS_PER_LONG
== HOST_BITS_PER_WIDE_INT
)
2061 r
->sig
[SIGSZ
-1] = high
;
2062 r
->sig
[SIGSZ
-2] = low
;
2063 memset (r
->sig
, 0, sizeof(long)*(SIGSZ
-2));
2065 else if (HOST_BITS_PER_LONG
*2 == HOST_BITS_PER_WIDE_INT
)
2067 r
->sig
[SIGSZ
-1] = high
>> (HOST_BITS_PER_LONG
- 1) >> 1;
2068 r
->sig
[SIGSZ
-2] = high
;
2069 r
->sig
[SIGSZ
-3] = low
>> (HOST_BITS_PER_LONG
- 1) >> 1;
2070 r
->sig
[SIGSZ
-4] = low
;
2072 memset (r
->sig
, 0, sizeof(long)*(SIGSZ
-4));
2080 if (mode
!= VOIDmode
)
2081 real_convert (r
, mode
, r
);
2084 /* Returns 10**2**N. */
2086 static const REAL_VALUE_TYPE
*
2090 static REAL_VALUE_TYPE tens
[EXP_BITS
];
2092 if (n
< 0 || n
>= EXP_BITS
)
2095 if (tens
[n
].class == rvc_zero
)
2097 if (n
< (HOST_BITS_PER_WIDE_INT
== 64 ? 5 : 4))
2099 HOST_WIDE_INT t
= 10;
2102 for (i
= 0; i
< n
; ++i
)
2105 real_from_integer (&tens
[n
], VOIDmode
, t
, 0, 1);
2109 const REAL_VALUE_TYPE
*t
= ten_to_ptwo (n
- 1);
2110 do_multiply (&tens
[n
], t
, t
);
2117 /* Returns 10**(-2**N). */
2119 static const REAL_VALUE_TYPE
*
2123 static REAL_VALUE_TYPE tens
[EXP_BITS
];
2125 if (n
< 0 || n
>= EXP_BITS
)
2128 if (tens
[n
].class == rvc_zero
)
2129 do_divide (&tens
[n
], real_digit (1), ten_to_ptwo (n
));
2136 static const REAL_VALUE_TYPE
*
2140 static REAL_VALUE_TYPE num
[10];
2145 if (n
> 0 && num
[n
].class == rvc_zero
)
2146 real_from_integer (&num
[n
], VOIDmode
, n
, 0, 1);
2151 /* Multiply R by 10**EXP. */
2158 REAL_VALUE_TYPE pten
, *rr
;
2159 bool negative
= (exp
< 0);
2165 pten
= *real_digit (1);
2171 for (i
= 0; exp
> 0; ++i
, exp
>>= 1)
2173 do_multiply (rr
, rr
, ten_to_ptwo (i
));
2176 do_divide (r
, r
, &pten
);
2179 /* Fills R with +Inf. */
2188 /* Fills R with a NaN whose significand is described by STR. If QUIET,
2189 we force a QNaN, else we force an SNaN. The string, if not empty,
2190 is parsed as a number and placed in the significand. Return true
2191 if the string was successfully parsed. */
2194 real_nan (r
, str
, quiet
, mode
)
2198 enum machine_mode mode
;
2200 const struct real_format
*fmt
;
2202 fmt
= real_format_for_mode
[mode
- QFmode
];
2209 get_canonical_qnan (r
, 0);
2211 get_canonical_snan (r
, 0);
2218 memset (r
, 0, sizeof (*r
));
2221 /* Parse akin to strtol into the significand of R. */
2223 while (ISSPACE (*str
))
2227 else if (*str
== '+')
2237 while ((d
= hex_value (*str
)) < base
)
2244 lshift_significand (r
, r
, 3);
2247 lshift_significand (r
, r
, 4);
2250 lshift_significand_1 (&u
, r
);
2251 lshift_significand (r
, r
, 3);
2252 add_significands (r
, r
, &u
);
2260 add_significands (r
, r
, &u
);
2265 /* Must have consumed the entire string for success. */
2269 /* Shift the significand into place such that the bits
2270 are in the most significant bits for the format. */
2271 lshift_significand (r
, r
, SIGNIFICAND_BITS
- fmt
->pnan
);
2273 /* Our MSB is always unset for NaNs. */
2274 r
->sig
[SIGSZ
-1] &= ~SIG_MSB
;
2276 /* Force quiet or signalling NaN. */
2277 r
->signalling
= !quiet
;
2283 /* Fills R with 2**N. */
2290 memset (r
, 0, sizeof (*r
));
2295 else if (n
< -MAX_EXP
)
2299 r
->class = rvc_normal
;
2301 r
->sig
[SIGSZ
-1] = SIG_MSB
;
2307 round_for_format (fmt
, r
)
2308 const struct real_format
*fmt
;
2312 unsigned long sticky
;
2316 p2
= fmt
->p
* fmt
->log2_b
;
2317 emin2m1
= (fmt
->emin
- 1) * fmt
->log2_b
;
2318 emax2
= fmt
->emax
* fmt
->log2_b
;
2320 np2
= SIGNIFICAND_BITS
- p2
;
2324 get_zero (r
, r
->sign
);
2326 if (!fmt
->has_signed_zero
)
2331 get_inf (r
, r
->sign
);
2336 clear_significand_below (r
, np2
);
2346 /* If we're not base2, normalize the exponent to a multiple of
2348 if (fmt
->log2_b
!= 1)
2350 int shift
= r
->exp
& (fmt
->log2_b
- 1);
2353 shift
= fmt
->log2_b
- shift
;
2354 r
->sig
[0] |= sticky_rshift_significand (r
, r
, shift
);
2359 /* Check the range of the exponent. If we're out of range,
2360 either underflow or overflow. */
2363 else if (r
->exp
<= emin2m1
)
2367 if (!fmt
->has_denorm
)
2369 /* Don't underflow completely until we've had a chance to round. */
2370 if (r
->exp
< emin2m1
)
2375 diff
= emin2m1
- r
->exp
+ 1;
2379 /* De-normalize the significand. */
2380 r
->sig
[0] |= sticky_rshift_significand (r
, r
, diff
);
2385 /* There are P2 true significand bits, followed by one guard bit,
2386 followed by one sticky bit, followed by stuff. Fold nonzero
2387 stuff into the sticky bit. */
2390 for (i
= 0, w
= (np2
- 1) / HOST_BITS_PER_LONG
; i
< w
; ++i
)
2391 sticky
|= r
->sig
[i
];
2393 r
->sig
[w
] & (((unsigned long)1 << ((np2
- 1) % HOST_BITS_PER_LONG
)) - 1);
2395 guard
= test_significand_bit (r
, np2
- 1);
2396 lsb
= test_significand_bit (r
, np2
);
2398 /* Round to even. */
2399 if (guard
&& (sticky
|| lsb
))
2403 set_significand_bit (&u
, np2
);
2405 if (add_significands (r
, r
, &u
))
2407 /* Overflow. Means the significand had been all ones, and
2408 is now all zeros. Need to increase the exponent, and
2409 possibly re-normalize it. */
2410 if (++r
->exp
> emax2
)
2412 r
->sig
[SIGSZ
-1] = SIG_MSB
;
2414 if (fmt
->log2_b
!= 1)
2416 int shift
= r
->exp
& (fmt
->log2_b
- 1);
2419 shift
= fmt
->log2_b
- shift
;
2420 rshift_significand (r
, r
, shift
);
2429 /* Catch underflow that we deferred until after rounding. */
2430 if (r
->exp
<= emin2m1
)
2433 /* Clear out trailing garbage. */
2434 clear_significand_below (r
, np2
);
2437 /* Extend or truncate to a new mode. */
2440 real_convert (r
, mode
, a
)
2442 enum machine_mode mode
;
2443 const REAL_VALUE_TYPE
*a
;
2445 const struct real_format
*fmt
;
2447 fmt
= real_format_for_mode
[mode
- QFmode
];
2452 round_for_format (fmt
, r
);
2454 /* round_for_format de-normalizes denormals. Undo just that part. */
2455 if (r
->class == rvc_normal
)
2459 /* Legacy. Likewise, except return the struct directly. */
2462 real_value_truncate (mode
, a
)
2463 enum machine_mode mode
;
2467 real_convert (&r
, mode
, &a
);
2471 /* Return true if truncating to MODE is exact. */
2474 exact_real_truncate (mode
, a
)
2475 enum machine_mode mode
;
2476 const REAL_VALUE_TYPE
*a
;
2479 real_convert (&t
, mode
, a
);
2480 return real_identical (&t
, a
);
2483 /* Write R to the given target format. Place the words of the result
2484 in target word order in BUF. There are always 32 bits in each
2485 long, no matter the size of the host long.
2487 Legacy: return word 0 for implementing REAL_VALUE_TO_TARGET_SINGLE. */
2490 real_to_target_fmt (buf
, r_orig
, fmt
)
2492 const REAL_VALUE_TYPE
*r_orig
;
2493 const struct real_format
*fmt
;
2499 round_for_format (fmt
, &r
);
2503 (*fmt
->encode
) (fmt
, buf
, &r
);
2508 /* Similar, but look up the format from MODE. */
2511 real_to_target (buf
, r
, mode
)
2513 const REAL_VALUE_TYPE
*r
;
2514 enum machine_mode mode
;
2516 const struct real_format
*fmt
;
2518 fmt
= real_format_for_mode
[mode
- QFmode
];
2522 return real_to_target_fmt (buf
, r
, fmt
);
2525 /* Read R from the given target format. Read the words of the result
2526 in target word order in BUF. There are always 32 bits in each
2527 long, no matter the size of the host long. */
2530 real_from_target_fmt (r
, buf
, fmt
)
2533 const struct real_format
*fmt
;
2535 (*fmt
->decode
) (fmt
, r
, buf
);
2538 /* Similar, but look up the format from MODE. */
2541 real_from_target (r
, buf
, mode
)
2544 enum machine_mode mode
;
2546 const struct real_format
*fmt
;
2548 fmt
= real_format_for_mode
[mode
- QFmode
];
2552 (*fmt
->decode
) (fmt
, r
, buf
);
2555 /* Return the number of bits in the significand for MODE. */
2556 /* ??? Legacy. Should get access to real_format directly. */
2559 significand_size (mode
)
2560 enum machine_mode mode
;
2562 const struct real_format
*fmt
;
2564 fmt
= real_format_for_mode
[mode
- QFmode
];
2568 return fmt
->p
* fmt
->log2_b
;
2571 /* Return a hash value for the given real value. */
2572 /* ??? The "unsigned int" return value is intended to be hashval_t,
2573 but I didn't want to pull hashtab.h into real.h. */
2577 const REAL_VALUE_TYPE
*r
;
2582 h
= r
->class | (r
->sign
<< 2);
2595 h
^= (unsigned int)-1;
2604 if (sizeof(unsigned long) > sizeof(unsigned int))
2605 for (i
= 0; i
< SIGSZ
; ++i
)
2607 unsigned long s
= r
->sig
[i
];
2608 h
^= s
^ (s
>> (HOST_BITS_PER_LONG
/ 2));
2611 for (i
= 0; i
< SIGSZ
; ++i
)
2617 /* IEEE single-precision format. */
2619 static void encode_ieee_single
PARAMS ((const struct real_format
*fmt
,
2620 long *, const REAL_VALUE_TYPE
*));
2621 static void decode_ieee_single
PARAMS ((const struct real_format
*,
2622 REAL_VALUE_TYPE
*, const long *));
2625 encode_ieee_single (fmt
, buf
, r
)
2626 const struct real_format
*fmt
;
2628 const REAL_VALUE_TYPE
*r
;
2630 unsigned long image
, sig
, exp
;
2631 bool denormal
= (r
->sig
[SIGSZ
-1] & SIG_MSB
) == 0;
2633 image
= r
->sign
<< 31;
2634 sig
= (r
->sig
[SIGSZ
-1] >> (HOST_BITS_PER_LONG
- 24)) & 0x7fffff;
2645 image
|= 0x7fffffff;
2653 if (r
->signalling
== fmt
->qnan_msb_set
)
2657 /* We overload qnan_msb_set here: it's only clear for
2658 mips_ieee_single, which wants all mantissa bits but the
2659 quiet/signalling one set in canonical NaNs (at least
2661 if (r
->canonical
&& !fmt
->qnan_msb_set
)
2662 sig
|= (1 << 22) - 1;
2670 image
|= 0x7fffffff;
2674 /* Recall that IEEE numbers are interpreted as 1.F x 2**exp,
2675 whereas the intermediate representation is 0.F x 2**exp.
2676 Which means we're off by one. */
2680 exp
= r
->exp
+ 127 - 1;
2693 decode_ieee_single (fmt
, r
, buf
)
2694 const struct real_format
*fmt
;
2698 unsigned long image
= buf
[0] & 0xffffffff;
2699 bool sign
= (image
>> 31) & 1;
2700 int exp
= (image
>> 23) & 0xff;
2702 memset (r
, 0, sizeof (*r
));
2703 image
<<= HOST_BITS_PER_LONG
- 24;
2708 if (image
&& fmt
->has_denorm
)
2710 r
->class = rvc_normal
;
2713 r
->sig
[SIGSZ
-1] = image
<< 1;
2716 else if (fmt
->has_signed_zero
)
2719 else if (exp
== 255 && (fmt
->has_nans
|| fmt
->has_inf
))
2725 r
->signalling
= (((image
>> (HOST_BITS_PER_LONG
- 2)) & 1)
2726 ^ fmt
->qnan_msb_set
);
2727 r
->sig
[SIGSZ
-1] = image
;
2737 r
->class = rvc_normal
;
2739 r
->exp
= exp
- 127 + 1;
2740 r
->sig
[SIGSZ
-1] = image
| SIG_MSB
;
2744 const struct real_format ieee_single_format
=
2762 const struct real_format mips_single_format
=
2781 /* IEEE double-precision format. */
2783 static void encode_ieee_double
PARAMS ((const struct real_format
*fmt
,
2784 long *, const REAL_VALUE_TYPE
*));
2785 static void decode_ieee_double
PARAMS ((const struct real_format
*,
2786 REAL_VALUE_TYPE
*, const long *));
2789 encode_ieee_double (fmt
, buf
, r
)
2790 const struct real_format
*fmt
;
2792 const REAL_VALUE_TYPE
*r
;
2794 unsigned long image_lo
, image_hi
, sig_lo
, sig_hi
, exp
;
2795 bool denormal
= (r
->sig
[SIGSZ
-1] & SIG_MSB
) == 0;
2797 image_hi
= r
->sign
<< 31;
2800 if (HOST_BITS_PER_LONG
== 64)
2802 sig_hi
= r
->sig
[SIGSZ
-1];
2803 sig_lo
= (sig_hi
>> (64 - 53)) & 0xffffffff;
2804 sig_hi
= (sig_hi
>> (64 - 53 + 1) >> 31) & 0xfffff;
2808 sig_hi
= r
->sig
[SIGSZ
-1];
2809 sig_lo
= r
->sig
[SIGSZ
-2];
2810 sig_lo
= (sig_hi
<< 21) | (sig_lo
>> 11);
2811 sig_hi
= (sig_hi
>> 11) & 0xfffff;
2821 image_hi
|= 2047 << 20;
2824 image_hi
|= 0x7fffffff;
2825 image_lo
= 0xffffffff;
2833 sig_hi
= sig_lo
= 0;
2834 if (r
->signalling
== fmt
->qnan_msb_set
)
2835 sig_hi
&= ~(1 << 19);
2838 /* We overload qnan_msb_set here: it's only clear for
2839 mips_ieee_single, which wants all mantissa bits but the
2840 quiet/signalling one set in canonical NaNs (at least
2842 if (r
->canonical
&& !fmt
->qnan_msb_set
)
2844 sig_hi
|= (1 << 19) - 1;
2845 sig_lo
= 0xffffffff;
2847 else if (sig_hi
== 0 && sig_lo
== 0)
2850 image_hi
|= 2047 << 20;
2856 image_hi
|= 0x7fffffff;
2857 image_lo
= 0xffffffff;
2862 /* Recall that IEEE numbers are interpreted as 1.F x 2**exp,
2863 whereas the intermediate representation is 0.F x 2**exp.
2864 Which means we're off by one. */
2868 exp
= r
->exp
+ 1023 - 1;
2869 image_hi
|= exp
<< 20;
2878 if (FLOAT_WORDS_BIG_ENDIAN
)
2879 buf
[0] = image_hi
, buf
[1] = image_lo
;
2881 buf
[0] = image_lo
, buf
[1] = image_hi
;
2885 decode_ieee_double (fmt
, r
, buf
)
2886 const struct real_format
*fmt
;
2890 unsigned long image_hi
, image_lo
;
2894 if (FLOAT_WORDS_BIG_ENDIAN
)
2895 image_hi
= buf
[0], image_lo
= buf
[1];
2897 image_lo
= buf
[0], image_hi
= buf
[1];
2898 image_lo
&= 0xffffffff;
2899 image_hi
&= 0xffffffff;
2901 sign
= (image_hi
>> 31) & 1;
2902 exp
= (image_hi
>> 20) & 0x7ff;
2904 memset (r
, 0, sizeof (*r
));
2906 image_hi
<<= 32 - 21;
2907 image_hi
|= image_lo
>> 21;
2908 image_hi
&= 0x7fffffff;
2909 image_lo
<<= 32 - 21;
2913 if ((image_hi
|| image_lo
) && fmt
->has_denorm
)
2915 r
->class = rvc_normal
;
2918 if (HOST_BITS_PER_LONG
== 32)
2920 image_hi
= (image_hi
<< 1) | (image_lo
>> 31);
2922 r
->sig
[SIGSZ
-1] = image_hi
;
2923 r
->sig
[SIGSZ
-2] = image_lo
;
2927 image_hi
= (image_hi
<< 31 << 2) | (image_lo
<< 1);
2928 r
->sig
[SIGSZ
-1] = image_hi
;
2932 else if (fmt
->has_signed_zero
)
2935 else if (exp
== 2047 && (fmt
->has_nans
|| fmt
->has_inf
))
2937 if (image_hi
|| image_lo
)
2941 r
->signalling
= ((image_hi
>> 30) & 1) ^ fmt
->qnan_msb_set
;
2942 if (HOST_BITS_PER_LONG
== 32)
2944 r
->sig
[SIGSZ
-1] = image_hi
;
2945 r
->sig
[SIGSZ
-2] = image_lo
;
2948 r
->sig
[SIGSZ
-1] = (image_hi
<< 31 << 1) | image_lo
;
2958 r
->class = rvc_normal
;
2960 r
->exp
= exp
- 1023 + 1;
2961 if (HOST_BITS_PER_LONG
== 32)
2963 r
->sig
[SIGSZ
-1] = image_hi
| SIG_MSB
;
2964 r
->sig
[SIGSZ
-2] = image_lo
;
2967 r
->sig
[SIGSZ
-1] = (image_hi
<< 31 << 1) | image_lo
| SIG_MSB
;
2971 const struct real_format ieee_double_format
=
2989 const struct real_format mips_double_format
=
3008 /* IEEE extended double precision format. This comes in three
3009 flavours: Intel's as a 12 byte image, Intel's as a 16 byte image,
3012 static void encode_ieee_extended
PARAMS ((const struct real_format
*fmt
,
3013 long *, const REAL_VALUE_TYPE
*));
3014 static void decode_ieee_extended
PARAMS ((const struct real_format
*,
3015 REAL_VALUE_TYPE
*, const long *));
3017 static void encode_ieee_extended_128
PARAMS ((const struct real_format
*fmt
,
3019 const REAL_VALUE_TYPE
*));
3020 static void decode_ieee_extended_128
PARAMS ((const struct real_format
*,
3025 encode_ieee_extended (fmt
, buf
, r
)
3026 const struct real_format
*fmt
;
3028 const REAL_VALUE_TYPE
*r
;
3030 unsigned long image_hi
, sig_hi
, sig_lo
;
3031 bool denormal
= (r
->sig
[SIGSZ
-1] & SIG_MSB
) == 0;
3033 image_hi
= r
->sign
<< 15;
3034 sig_hi
= sig_lo
= 0;
3046 /* Intel requires the explicit integer bit to be set, otherwise
3047 it considers the value a "pseudo-infinity". Motorola docs
3048 say it doesn't care. */
3049 sig_hi
= 0x80000000;
3054 sig_lo
= sig_hi
= 0xffffffff;
3062 if (HOST_BITS_PER_LONG
== 32)
3064 sig_hi
= r
->sig
[SIGSZ
-1];
3065 sig_lo
= r
->sig
[SIGSZ
-2];
3069 sig_lo
= r
->sig
[SIGSZ
-1];
3070 sig_hi
= sig_lo
>> 31 >> 1;
3071 sig_lo
&= 0xffffffff;
3073 if (r
->signalling
== fmt
->qnan_msb_set
)
3074 sig_hi
&= ~(1 << 30);
3077 if ((sig_hi
& 0x7fffffff) == 0 && sig_lo
== 0)
3080 /* Intel requires the explicit integer bit to be set, otherwise
3081 it considers the value a "pseudo-nan". Motorola docs say it
3083 sig_hi
|= 0x80000000;
3088 sig_lo
= sig_hi
= 0xffffffff;
3096 /* Recall that IEEE numbers are interpreted as 1.F x 2**exp,
3097 whereas the intermediate representation is 0.F x 2**exp.
3098 Which means we're off by one.
3100 Except for Motorola, which consider exp=0 and explicit
3101 integer bit set to continue to be normalized. In theory
3102 this discrepancy has been taken care of by the difference
3103 in fmt->emin in round_for_format. */
3115 if (HOST_BITS_PER_LONG
== 32)
3117 sig_hi
= r
->sig
[SIGSZ
-1];
3118 sig_lo
= r
->sig
[SIGSZ
-2];
3122 sig_lo
= r
->sig
[SIGSZ
-1];
3123 sig_hi
= sig_lo
>> 31 >> 1;
3124 sig_lo
&= 0xffffffff;
3133 if (FLOAT_WORDS_BIG_ENDIAN
)
3134 buf
[0] = image_hi
<< 16, buf
[1] = sig_hi
, buf
[2] = sig_lo
;
3136 buf
[0] = sig_lo
, buf
[1] = sig_hi
, buf
[2] = image_hi
;
3140 encode_ieee_extended_128 (fmt
, buf
, r
)
3141 const struct real_format
*fmt
;
3143 const REAL_VALUE_TYPE
*r
;
3145 buf
[3 * !FLOAT_WORDS_BIG_ENDIAN
] = 0;
3146 encode_ieee_extended (fmt
, buf
+!!FLOAT_WORDS_BIG_ENDIAN
, r
);
3150 decode_ieee_extended (fmt
, r
, buf
)
3151 const struct real_format
*fmt
;
3155 unsigned long image_hi
, sig_hi
, sig_lo
;
3159 if (FLOAT_WORDS_BIG_ENDIAN
)
3160 image_hi
= buf
[0] >> 16, sig_hi
= buf
[1], sig_lo
= buf
[2];
3162 sig_lo
= buf
[0], sig_hi
= buf
[1], image_hi
= buf
[2];
3163 sig_lo
&= 0xffffffff;
3164 sig_hi
&= 0xffffffff;
3165 image_hi
&= 0xffffffff;
3167 sign
= (image_hi
>> 15) & 1;
3168 exp
= image_hi
& 0x7fff;
3170 memset (r
, 0, sizeof (*r
));
3174 if ((sig_hi
|| sig_lo
) && fmt
->has_denorm
)
3176 r
->class = rvc_normal
;
3179 /* When the IEEE format contains a hidden bit, we know that
3180 it's zero at this point, and so shift up the significand
3181 and decrease the exponent to match. In this case, Motorola
3182 defines the explicit integer bit to be valid, so we don't
3183 know whether the msb is set or not. */
3185 if (HOST_BITS_PER_LONG
== 32)
3187 r
->sig
[SIGSZ
-1] = sig_hi
;
3188 r
->sig
[SIGSZ
-2] = sig_lo
;
3191 r
->sig
[SIGSZ
-1] = (sig_hi
<< 31 << 1) | sig_lo
;
3195 else if (fmt
->has_signed_zero
)
3198 else if (exp
== 32767 && (fmt
->has_nans
|| fmt
->has_inf
))
3200 /* See above re "pseudo-infinities" and "pseudo-nans".
3201 Short summary is that the MSB will likely always be
3202 set, and that we don't care about it. */
3203 sig_hi
&= 0x7fffffff;
3205 if (sig_hi
|| sig_lo
)
3209 r
->signalling
= ((sig_hi
>> 30) & 1) ^ fmt
->qnan_msb_set
;
3210 if (HOST_BITS_PER_LONG
== 32)
3212 r
->sig
[SIGSZ
-1] = sig_hi
;
3213 r
->sig
[SIGSZ
-2] = sig_lo
;
3216 r
->sig
[SIGSZ
-1] = (sig_hi
<< 31 << 1) | sig_lo
;
3226 r
->class = rvc_normal
;
3228 r
->exp
= exp
- 16383 + 1;
3229 if (HOST_BITS_PER_LONG
== 32)
3231 r
->sig
[SIGSZ
-1] = sig_hi
;
3232 r
->sig
[SIGSZ
-2] = sig_lo
;
3235 r
->sig
[SIGSZ
-1] = (sig_hi
<< 31 << 1) | sig_lo
;
3240 decode_ieee_extended_128 (fmt
, r
, buf
)
3241 const struct real_format
*fmt
;
3245 decode_ieee_extended (fmt
, r
, buf
+!!FLOAT_WORDS_BIG_ENDIAN
);
3248 const struct real_format ieee_extended_motorola_format
=
3250 encode_ieee_extended
,
3251 decode_ieee_extended
,
3266 const struct real_format ieee_extended_intel_96_format
=
3268 encode_ieee_extended
,
3269 decode_ieee_extended
,
3284 const struct real_format ieee_extended_intel_128_format
=
3286 encode_ieee_extended_128
,
3287 decode_ieee_extended_128
,
3303 /* IBM 128-bit extended precision format: a pair of IEEE double precision
3304 numbers whose sum is equal to the extended precision value. The number
3305 with greater magnitude is first. This format has the same magnitude
3306 range as an IEEE double precision value, but effectively 106 bits of
3307 significand precision. Infinity and NaN are represented by their IEEE
3308 double precision value stored in the first number, the second number is
3309 ignored. Zeroes, Infinities, and NaNs are set in both doubles
3310 due to precedent. */
3312 static void encode_ibm_extended
PARAMS ((const struct real_format
*fmt
,
3313 long *, const REAL_VALUE_TYPE
*));
3314 static void decode_ibm_extended
PARAMS ((const struct real_format
*,
3315 REAL_VALUE_TYPE
*, const long *));
3318 encode_ibm_extended (fmt
, buf
, r
)
3319 const struct real_format
*fmt
;
3321 const REAL_VALUE_TYPE
*r
;
3323 REAL_VALUE_TYPE u
, v
;
3324 const struct real_format
*base_fmt
;
3326 base_fmt
= fmt
->qnan_msb_set
? &ieee_double_format
: &mips_double_format
;
3331 /* Both doubles have sign bit set. */
3332 buf
[0] = FLOAT_WORDS_BIG_ENDIAN
? r
->sign
<< 31 : 0;
3333 buf
[1] = FLOAT_WORDS_BIG_ENDIAN
? 0 : r
->sign
<< 31;
3340 /* Both doubles set to Inf / NaN. */
3341 encode_ieee_double (base_fmt
, &buf
[0], r
);
3347 /* u = IEEE double precision portion of significand. */
3349 clear_significand_below (&u
, SIGNIFICAND_BITS
- 53);
3352 /* If the upper double is zero, we have a denormal double, so
3353 move it to the first double and leave the second as zero. */
3354 if (u
.class == rvc_zero
)
3362 /* v = remainder containing additional 53 bits of significand. */
3363 do_add (&v
, r
, &u
, 1);
3364 round_for_format (base_fmt
, &v
);
3367 round_for_format (base_fmt
, &u
);
3369 encode_ieee_double (base_fmt
, &buf
[0], &u
);
3370 encode_ieee_double (base_fmt
, &buf
[2], &v
);
3379 decode_ibm_extended (fmt
, r
, buf
)
3380 const struct real_format
*fmt ATTRIBUTE_UNUSED
;
3384 REAL_VALUE_TYPE u
, v
;
3385 const struct real_format
*base_fmt
;
3387 base_fmt
= fmt
->qnan_msb_set
? &ieee_double_format
: &mips_double_format
;
3388 decode_ieee_double (base_fmt
, &u
, &buf
[0]);
3390 if (u
.class != rvc_zero
&& u
.class != rvc_inf
&& u
.class != rvc_nan
)
3392 decode_ieee_double (base_fmt
, &v
, &buf
[2]);
3393 do_add (r
, &u
, &v
, 0);
3399 const struct real_format ibm_extended_format
=
3401 encode_ibm_extended
,
3402 decode_ibm_extended
,
3417 const struct real_format mips_extended_format
=
3419 encode_ibm_extended
,
3420 decode_ibm_extended
,
3436 /* IEEE quad precision format. */
3438 static void encode_ieee_quad
PARAMS ((const struct real_format
*fmt
,
3439 long *, const REAL_VALUE_TYPE
*));
3440 static void decode_ieee_quad
PARAMS ((const struct real_format
*,
3441 REAL_VALUE_TYPE
*, const long *));
3444 encode_ieee_quad (fmt
, buf
, r
)
3445 const struct real_format
*fmt
;
3447 const REAL_VALUE_TYPE
*r
;
3449 unsigned long image3
, image2
, image1
, image0
, exp
;
3450 bool denormal
= (r
->sig
[SIGSZ
-1] & SIG_MSB
) == 0;
3453 image3
= r
->sign
<< 31;
3458 rshift_significand (&u
, r
, SIGNIFICAND_BITS
- 113);
3467 image3
|= 32767 << 16;
3470 image3
|= 0x7fffffff;
3471 image2
= 0xffffffff;
3472 image1
= 0xffffffff;
3473 image0
= 0xffffffff;
3480 image3
|= 32767 << 16;
3484 /* Don't use bits from the significand. The
3485 initialization above is right. */
3487 else if (HOST_BITS_PER_LONG
== 32)
3492 image3
|= u
.sig
[3] & 0xffff;
3497 image1
= image0
>> 31 >> 1;
3499 image3
|= (image2
>> 31 >> 1) & 0xffff;
3500 image0
&= 0xffffffff;
3501 image2
&= 0xffffffff;
3503 if (r
->signalling
== fmt
->qnan_msb_set
)
3507 /* We overload qnan_msb_set here: it's only clear for
3508 mips_ieee_single, which wants all mantissa bits but the
3509 quiet/signalling one set in canonical NaNs (at least
3511 if (r
->canonical
&& !fmt
->qnan_msb_set
)
3514 image2
= image1
= image0
= 0xffffffff;
3516 else if (((image3
& 0xffff) | image2
| image1
| image0
) == 0)
3521 image3
|= 0x7fffffff;
3522 image2
= 0xffffffff;
3523 image1
= 0xffffffff;
3524 image0
= 0xffffffff;
3529 /* Recall that IEEE numbers are interpreted as 1.F x 2**exp,
3530 whereas the intermediate representation is 0.F x 2**exp.
3531 Which means we're off by one. */
3535 exp
= r
->exp
+ 16383 - 1;
3536 image3
|= exp
<< 16;
3538 if (HOST_BITS_PER_LONG
== 32)
3543 image3
|= u
.sig
[3] & 0xffff;
3548 image1
= image0
>> 31 >> 1;
3550 image3
|= (image2
>> 31 >> 1) & 0xffff;
3551 image0
&= 0xffffffff;
3552 image2
&= 0xffffffff;
3560 if (FLOAT_WORDS_BIG_ENDIAN
)
3577 decode_ieee_quad (fmt
, r
, buf
)
3578 const struct real_format
*fmt
;
3582 unsigned long image3
, image2
, image1
, image0
;
3586 if (FLOAT_WORDS_BIG_ENDIAN
)
3600 image0
&= 0xffffffff;
3601 image1
&= 0xffffffff;
3602 image2
&= 0xffffffff;
3604 sign
= (image3
>> 31) & 1;
3605 exp
= (image3
>> 16) & 0x7fff;
3608 memset (r
, 0, sizeof (*r
));
3612 if ((image3
| image2
| image1
| image0
) && fmt
->has_denorm
)
3614 r
->class = rvc_normal
;
3617 r
->exp
= -16382 + (SIGNIFICAND_BITS
- 112);
3618 if (HOST_BITS_PER_LONG
== 32)
3627 r
->sig
[0] = (image1
<< 31 << 1) | image0
;
3628 r
->sig
[1] = (image3
<< 31 << 1) | image2
;
3633 else if (fmt
->has_signed_zero
)
3636 else if (exp
== 32767 && (fmt
->has_nans
|| fmt
->has_inf
))
3638 if (image3
| image2
| image1
| image0
)
3642 r
->signalling
= ((image3
>> 15) & 1) ^ fmt
->qnan_msb_set
;
3644 if (HOST_BITS_PER_LONG
== 32)
3653 r
->sig
[0] = (image1
<< 31 << 1) | image0
;
3654 r
->sig
[1] = (image3
<< 31 << 1) | image2
;
3656 lshift_significand (r
, r
, SIGNIFICAND_BITS
- 113);
3666 r
->class = rvc_normal
;
3668 r
->exp
= exp
- 16383 + 1;
3670 if (HOST_BITS_PER_LONG
== 32)
3679 r
->sig
[0] = (image1
<< 31 << 1) | image0
;
3680 r
->sig
[1] = (image3
<< 31 << 1) | image2
;
3682 lshift_significand (r
, r
, SIGNIFICAND_BITS
- 113);
3683 r
->sig
[SIGSZ
-1] |= SIG_MSB
;
3687 const struct real_format ieee_quad_format
=
3705 const struct real_format mips_quad_format
=
3723 /* Descriptions of VAX floating point formats can be found beginning at
3725 http://www.openvms.compaq.com:8000/73final/4515/4515pro_013.html#f_floating_point_format
3727 The thing to remember is that they're almost IEEE, except for word
3728 order, exponent bias, and the lack of infinities, nans, and denormals.
3730 We don't implement the H_floating format here, simply because neither
3731 the VAX or Alpha ports use it. */
3733 static void encode_vax_f
PARAMS ((const struct real_format
*fmt
,
3734 long *, const REAL_VALUE_TYPE
*));
3735 static void decode_vax_f
PARAMS ((const struct real_format
*,
3736 REAL_VALUE_TYPE
*, const long *));
3737 static void encode_vax_d
PARAMS ((const struct real_format
*fmt
,
3738 long *, const REAL_VALUE_TYPE
*));
3739 static void decode_vax_d
PARAMS ((const struct real_format
*,
3740 REAL_VALUE_TYPE
*, const long *));
3741 static void encode_vax_g
PARAMS ((const struct real_format
*fmt
,
3742 long *, const REAL_VALUE_TYPE
*));
3743 static void decode_vax_g
PARAMS ((const struct real_format
*,
3744 REAL_VALUE_TYPE
*, const long *));
3747 encode_vax_f (fmt
, buf
, r
)
3748 const struct real_format
*fmt ATTRIBUTE_UNUSED
;
3750 const REAL_VALUE_TYPE
*r
;
3752 unsigned long sign
, exp
, sig
, image
;
3754 sign
= r
->sign
<< 15;
3764 image
= 0xffff7fff | sign
;
3768 sig
= (r
->sig
[SIGSZ
-1] >> (HOST_BITS_PER_LONG
- 24)) & 0x7fffff;
3771 image
= (sig
<< 16) & 0xffff0000;
3785 decode_vax_f (fmt
, r
, buf
)
3786 const struct real_format
*fmt ATTRIBUTE_UNUSED
;
3790 unsigned long image
= buf
[0] & 0xffffffff;
3791 int exp
= (image
>> 7) & 0xff;
3793 memset (r
, 0, sizeof (*r
));
3797 r
->class = rvc_normal
;
3798 r
->sign
= (image
>> 15) & 1;
3801 image
= ((image
& 0x7f) << 16) | ((image
>> 16) & 0xffff);
3802 r
->sig
[SIGSZ
-1] = (image
<< (HOST_BITS_PER_LONG
- 24)) | SIG_MSB
;
3807 encode_vax_d (fmt
, buf
, r
)
3808 const struct real_format
*fmt ATTRIBUTE_UNUSED
;
3810 const REAL_VALUE_TYPE
*r
;
3812 unsigned long image0
, image1
, sign
= r
->sign
<< 15;
3817 image0
= image1
= 0;
3822 image0
= 0xffff7fff | sign
;
3823 image1
= 0xffffffff;
3827 /* Extract the significand into straight hi:lo. */
3828 if (HOST_BITS_PER_LONG
== 64)
3830 image0
= r
->sig
[SIGSZ
-1];
3831 image1
= (image0
>> (64 - 56)) & 0xffffffff;
3832 image0
= (image0
>> (64 - 56 + 1) >> 31) & 0x7fffff;
3836 image0
= r
->sig
[SIGSZ
-1];
3837 image1
= r
->sig
[SIGSZ
-2];
3838 image1
= (image0
<< 24) | (image1
>> 8);
3839 image0
= (image0
>> 8) & 0xffffff;
3842 /* Rearrange the half-words of the significand to match the
3844 image0
= ((image0
<< 16) | (image0
>> 16)) & 0xffff007f;
3845 image1
= ((image1
<< 16) | (image1
>> 16)) & 0xffffffff;
3847 /* Add the sign and exponent. */
3849 image0
|= (r
->exp
+ 128) << 7;
3856 if (FLOAT_WORDS_BIG_ENDIAN
)
3857 buf
[0] = image1
, buf
[1] = image0
;
3859 buf
[0] = image0
, buf
[1] = image1
;
3863 decode_vax_d (fmt
, r
, buf
)
3864 const struct real_format
*fmt ATTRIBUTE_UNUSED
;
3868 unsigned long image0
, image1
;
3871 if (FLOAT_WORDS_BIG_ENDIAN
)
3872 image1
= buf
[0], image0
= buf
[1];
3874 image0
= buf
[0], image1
= buf
[1];
3875 image0
&= 0xffffffff;
3876 image1
&= 0xffffffff;
3878 exp
= (image0
>> 7) & 0x7f;
3880 memset (r
, 0, sizeof (*r
));
3884 r
->class = rvc_normal
;
3885 r
->sign
= (image0
>> 15) & 1;
3888 /* Rearrange the half-words of the external format into
3889 proper ascending order. */
3890 image0
= ((image0
& 0x7f) << 16) | ((image0
>> 16) & 0xffff);
3891 image1
= ((image1
& 0xffff) << 16) | ((image1
>> 16) & 0xffff);
3893 if (HOST_BITS_PER_LONG
== 64)
3895 image0
= (image0
<< 31 << 1) | image1
;
3898 r
->sig
[SIGSZ
-1] = image0
;
3902 r
->sig
[SIGSZ
-1] = image0
;
3903 r
->sig
[SIGSZ
-2] = image1
;
3904 lshift_significand (r
, r
, 2*HOST_BITS_PER_LONG
- 56);
3905 r
->sig
[SIGSZ
-1] |= SIG_MSB
;
3911 encode_vax_g (fmt
, buf
, r
)
3912 const struct real_format
*fmt ATTRIBUTE_UNUSED
;
3914 const REAL_VALUE_TYPE
*r
;
3916 unsigned long image0
, image1
, sign
= r
->sign
<< 15;
3921 image0
= image1
= 0;
3926 image0
= 0xffff7fff | sign
;
3927 image1
= 0xffffffff;
3931 /* Extract the significand into straight hi:lo. */
3932 if (HOST_BITS_PER_LONG
== 64)
3934 image0
= r
->sig
[SIGSZ
-1];
3935 image1
= (image0
>> (64 - 53)) & 0xffffffff;
3936 image0
= (image0
>> (64 - 53 + 1) >> 31) & 0xfffff;
3940 image0
= r
->sig
[SIGSZ
-1];
3941 image1
= r
->sig
[SIGSZ
-2];
3942 image1
= (image0
<< 21) | (image1
>> 11);
3943 image0
= (image0
>> 11) & 0xfffff;
3946 /* Rearrange the half-words of the significand to match the
3948 image0
= ((image0
<< 16) | (image0
>> 16)) & 0xffff000f;
3949 image1
= ((image1
<< 16) | (image1
>> 16)) & 0xffffffff;
3951 /* Add the sign and exponent. */
3953 image0
|= (r
->exp
+ 1024) << 4;
3960 if (FLOAT_WORDS_BIG_ENDIAN
)
3961 buf
[0] = image1
, buf
[1] = image0
;
3963 buf
[0] = image0
, buf
[1] = image1
;
3967 decode_vax_g (fmt
, r
, buf
)
3968 const struct real_format
*fmt ATTRIBUTE_UNUSED
;
3972 unsigned long image0
, image1
;
3975 if (FLOAT_WORDS_BIG_ENDIAN
)
3976 image1
= buf
[0], image0
= buf
[1];
3978 image0
= buf
[0], image1
= buf
[1];
3979 image0
&= 0xffffffff;
3980 image1
&= 0xffffffff;
3982 exp
= (image0
>> 4) & 0x7ff;
3984 memset (r
, 0, sizeof (*r
));
3988 r
->class = rvc_normal
;
3989 r
->sign
= (image0
>> 15) & 1;
3990 r
->exp
= exp
- 1024;
3992 /* Rearrange the half-words of the external format into
3993 proper ascending order. */
3994 image0
= ((image0
& 0xf) << 16) | ((image0
>> 16) & 0xffff);
3995 image1
= ((image1
& 0xffff) << 16) | ((image1
>> 16) & 0xffff);
3997 if (HOST_BITS_PER_LONG
== 64)
3999 image0
= (image0
<< 31 << 1) | image1
;
4002 r
->sig
[SIGSZ
-1] = image0
;
4006 r
->sig
[SIGSZ
-1] = image0
;
4007 r
->sig
[SIGSZ
-2] = image1
;
4008 lshift_significand (r
, r
, 64 - 53);
4009 r
->sig
[SIGSZ
-1] |= SIG_MSB
;
4014 const struct real_format vax_f_format
=
4032 const struct real_format vax_d_format
=
4050 const struct real_format vax_g_format
=
4068 /* A good reference for these can be found in chapter 9 of
4069 "ESA/390 Principles of Operation", IBM document number SA22-7201-01.
4070 An on-line version can be found here:
4072 http://publibz.boulder.ibm.com/cgi-bin/bookmgr_OS390/BOOKS/DZ9AR001/9.1?DT=19930923083613
4075 static void encode_i370_single
PARAMS ((const struct real_format
*fmt
,
4076 long *, const REAL_VALUE_TYPE
*));
4077 static void decode_i370_single
PARAMS ((const struct real_format
*,
4078 REAL_VALUE_TYPE
*, const long *));
4079 static void encode_i370_double
PARAMS ((const struct real_format
*fmt
,
4080 long *, const REAL_VALUE_TYPE
*));
4081 static void decode_i370_double
PARAMS ((const struct real_format
*,
4082 REAL_VALUE_TYPE
*, const long *));
4085 encode_i370_single (fmt
, buf
, r
)
4086 const struct real_format
*fmt ATTRIBUTE_UNUSED
;
4088 const REAL_VALUE_TYPE
*r
;
4090 unsigned long sign
, exp
, sig
, image
;
4092 sign
= r
->sign
<< 31;
4102 image
= 0x7fffffff | sign
;
4106 sig
= (r
->sig
[SIGSZ
-1] >> (HOST_BITS_PER_LONG
- 24)) & 0xffffff;
4107 exp
= ((r
->exp
/ 4) + 64) << 24;
4108 image
= sign
| exp
| sig
;
4119 decode_i370_single (fmt
, r
, buf
)
4120 const struct real_format
*fmt ATTRIBUTE_UNUSED
;
4124 unsigned long sign
, sig
, image
= buf
[0];
4127 sign
= (image
>> 31) & 1;
4128 exp
= (image
>> 24) & 0x7f;
4129 sig
= image
& 0xffffff;
4131 memset (r
, 0, sizeof (*r
));
4135 r
->class = rvc_normal
;
4137 r
->exp
= (exp
- 64) * 4;
4138 r
->sig
[SIGSZ
-1] = sig
<< (HOST_BITS_PER_LONG
- 24);
4144 encode_i370_double (fmt
, buf
, r
)
4145 const struct real_format
*fmt ATTRIBUTE_UNUSED
;
4147 const REAL_VALUE_TYPE
*r
;
4149 unsigned long sign
, exp
, image_hi
, image_lo
;
4151 sign
= r
->sign
<< 31;
4156 image_hi
= image_lo
= 0;
4161 image_hi
= 0x7fffffff | sign
;
4162 image_lo
= 0xffffffff;
4166 if (HOST_BITS_PER_LONG
== 64)
4168 image_hi
= r
->sig
[SIGSZ
-1];
4169 image_lo
= (image_hi
>> (64 - 56)) & 0xffffffff;
4170 image_hi
= (image_hi
>> (64 - 56 + 1) >> 31) & 0xffffff;
4174 image_hi
= r
->sig
[SIGSZ
-1];
4175 image_lo
= r
->sig
[SIGSZ
-2];
4176 image_lo
= (image_lo
>> 8) | (image_hi
<< 24);
4180 exp
= ((r
->exp
/ 4) + 64) << 24;
4181 image_hi
|= sign
| exp
;
4188 if (FLOAT_WORDS_BIG_ENDIAN
)
4189 buf
[0] = image_hi
, buf
[1] = image_lo
;
4191 buf
[0] = image_lo
, buf
[1] = image_hi
;
4195 decode_i370_double (fmt
, r
, buf
)
4196 const struct real_format
*fmt ATTRIBUTE_UNUSED
;
4200 unsigned long sign
, image_hi
, image_lo
;
4203 if (FLOAT_WORDS_BIG_ENDIAN
)
4204 image_hi
= buf
[0], image_lo
= buf
[1];
4206 image_lo
= buf
[0], image_hi
= buf
[1];
4208 sign
= (image_hi
>> 31) & 1;
4209 exp
= (image_hi
>> 24) & 0x7f;
4210 image_hi
&= 0xffffff;
4211 image_lo
&= 0xffffffff;
4213 memset (r
, 0, sizeof (*r
));
4215 if (exp
|| image_hi
|| image_lo
)
4217 r
->class = rvc_normal
;
4219 r
->exp
= (exp
- 64) * 4 + (SIGNIFICAND_BITS
- 56);
4221 if (HOST_BITS_PER_LONG
== 32)
4223 r
->sig
[0] = image_lo
;
4224 r
->sig
[1] = image_hi
;
4227 r
->sig
[0] = image_lo
| (image_hi
<< 31 << 1);
4233 const struct real_format i370_single_format
=
4246 false, /* ??? The encoding does allow for "unnormals". */
4247 false, /* ??? The encoding does allow for "unnormals". */
4251 const struct real_format i370_double_format
=
4264 false, /* ??? The encoding does allow for "unnormals". */
4265 false, /* ??? The encoding does allow for "unnormals". */
4269 /* The "twos-complement" c4x format is officially defined as
4273 This is rather misleading. One must remember that F is signed.
4274 A better description would be
4276 x = -1**s * ((s + 1 + .f) * 2**e
4278 So if we have a (4 bit) fraction of .1000 with a sign bit of 1,
4279 that's -1 * (1+1+(-.5)) == -1.5. I think.
4281 The constructions here are taken from Tables 5-1 and 5-2 of the
4282 TMS320C4x User's Guide wherein step-by-step instructions for
4283 conversion from IEEE are presented. That's close enough to our
4284 internal representation so as to make things easy.
4286 See http://www-s.ti.com/sc/psheets/spru063c/spru063c.pdf */
4288 static void encode_c4x_single
PARAMS ((const struct real_format
*fmt
,
4289 long *, const REAL_VALUE_TYPE
*));
4290 static void decode_c4x_single
PARAMS ((const struct real_format
*,
4291 REAL_VALUE_TYPE
*, const long *));
4292 static void encode_c4x_extended
PARAMS ((const struct real_format
*fmt
,
4293 long *, const REAL_VALUE_TYPE
*));
4294 static void decode_c4x_extended
PARAMS ((const struct real_format
*,
4295 REAL_VALUE_TYPE
*, const long *));
4298 encode_c4x_single (fmt
, buf
, r
)
4299 const struct real_format
*fmt ATTRIBUTE_UNUSED
;
4301 const REAL_VALUE_TYPE
*r
;
4303 unsigned long image
, exp
, sig
;
4315 sig
= 0x800000 - r
->sign
;
4320 sig
= (r
->sig
[SIGSZ
-1] >> (HOST_BITS_PER_LONG
- 24)) & 0x7fffff;
4335 image
= ((exp
& 0xff) << 24) | (sig
& 0xffffff);
4340 decode_c4x_single (fmt
, r
, buf
)
4341 const struct real_format
*fmt ATTRIBUTE_UNUSED
;
4345 unsigned long image
= buf
[0];
4349 exp
= (((image
>> 24) & 0xff) ^ 0x80) - 0x80;
4350 sf
= ((image
& 0xffffff) ^ 0x800000) - 0x800000;
4352 memset (r
, 0, sizeof (*r
));
4356 r
->class = rvc_normal
;
4358 sig
= sf
& 0x7fffff;
4367 sig
= (sig
<< (HOST_BITS_PER_LONG
- 24)) | SIG_MSB
;
4370 r
->sig
[SIGSZ
-1] = sig
;
4375 encode_c4x_extended (fmt
, buf
, r
)
4376 const struct real_format
*fmt ATTRIBUTE_UNUSED
;
4378 const REAL_VALUE_TYPE
*r
;
4380 unsigned long exp
, sig
;
4392 sig
= 0x80000000 - r
->sign
;
4398 sig
= r
->sig
[SIGSZ
-1];
4399 if (HOST_BITS_PER_LONG
== 64)
4400 sig
= sig
>> 1 >> 31;
4417 exp
= (exp
& 0xff) << 24;
4420 if (FLOAT_WORDS_BIG_ENDIAN
)
4421 buf
[0] = exp
, buf
[1] = sig
;
4423 buf
[0] = sig
, buf
[0] = exp
;
4427 decode_c4x_extended (fmt
, r
, buf
)
4428 const struct real_format
*fmt ATTRIBUTE_UNUSED
;
4435 if (FLOAT_WORDS_BIG_ENDIAN
)
4436 exp
= buf
[0], sf
= buf
[1];
4438 sf
= buf
[0], exp
= buf
[1];
4440 exp
= (((exp
>> 24) & 0xff) & 0x80) - 0x80;
4441 sf
= ((sf
& 0xffffffff) ^ 0x80000000) - 0x80000000;
4443 memset (r
, 0, sizeof (*r
));
4447 r
->class = rvc_normal
;
4449 sig
= sf
& 0x7fffffff;
4458 if (HOST_BITS_PER_LONG
== 64)
4459 sig
= sig
<< 1 << 31;
4463 r
->sig
[SIGSZ
-1] = sig
;
4467 const struct real_format c4x_single_format
=
4485 const struct real_format c4x_extended_format
=
4487 encode_c4x_extended
,
4488 decode_c4x_extended
,
4504 /* A synthetic "format" for internal arithmetic. It's the size of the
4505 internal significand minus the two bits needed for proper rounding.
4506 The encode and decode routines exist only to satisfy our paranoia
4509 static void encode_internal
PARAMS ((const struct real_format
*fmt
,
4510 long *, const REAL_VALUE_TYPE
*));
4511 static void decode_internal
PARAMS ((const struct real_format
*,
4512 REAL_VALUE_TYPE
*, const long *));
4515 encode_internal (fmt
, buf
, r
)
4516 const struct real_format
*fmt ATTRIBUTE_UNUSED
;
4518 const REAL_VALUE_TYPE
*r
;
4520 memcpy (buf
, r
, sizeof (*r
));
4524 decode_internal (fmt
, r
, buf
)
4525 const struct real_format
*fmt ATTRIBUTE_UNUSED
;
4529 memcpy (r
, buf
, sizeof (*r
));
4532 const struct real_format real_internal_format
=
4538 SIGNIFICAND_BITS
- 2,
4539 SIGNIFICAND_BITS
- 2,
4550 /* Set up default mode to format mapping for IEEE. Everyone else has
4551 to set these values in OVERRIDE_OPTIONS. */
4553 const struct real_format
*real_format_for_mode
[TFmode
- QFmode
+ 1] =
4558 &ieee_single_format
, /* SFmode */
4559 &ieee_double_format
, /* DFmode */
4561 /* We explicitly don't handle XFmode. There are two formats,
4562 pretty much equally common. Choose one in OVERRIDE_OPTIONS. */
4564 &ieee_quad_format
/* TFmode */
4568 /* Calculate the square root of X in mode MODE, and store the result
4569 in R. Return TRUE if the operation does not raise an exception.
4570 For details see "High Precision Division and Square Root",
4571 Alan H. Karp and Peter Markstein, HP Lab Report 93-93-42, June
4572 1993. http://www.hpl.hp.com/techreports/93/HPL-93-42.pdf. */
4575 real_sqrt (r
, mode
, x
)
4577 enum machine_mode mode
;
4578 const REAL_VALUE_TYPE
*x
;
4580 static REAL_VALUE_TYPE halfthree
;
4581 static bool init
= false;
4582 REAL_VALUE_TYPE h
, t
, i
;
4585 /* sqrt(-0.0) is -0.0. */
4586 if (real_isnegzero (x
))
4592 /* Negative arguments return NaN. */
4595 /* Mode is ignored for canonical NaN. */
4596 real_nan (r
, "", 1, SFmode
);
4600 /* Infinity and NaN return themselves. */
4601 if (real_isinf (x
) || real_isnan (x
))
4609 do_add (&halfthree
, &dconst1
, &dconsthalf
, 0);
4613 /* Initial guess for reciprocal sqrt, i. */
4614 exp
= real_exponent (x
);
4615 real_ldexp (&i
, &dconst1
, -exp
/2);
4617 /* Newton's iteration for reciprocal sqrt, i. */
4618 for (iter
= 0; iter
< 16; iter
++)
4620 /* i(n+1) = i(n) * (1.5 - 0.5*i(n)*i(n)*x). */
4621 do_multiply (&t
, x
, &i
);
4622 do_multiply (&h
, &t
, &i
);
4623 do_multiply (&t
, &h
, &dconsthalf
);
4624 do_add (&h
, &halfthree
, &t
, 1);
4625 do_multiply (&t
, &i
, &h
);
4627 /* Check for early convergence. */
4628 if (iter
>= 6 && real_identical (&i
, &t
))
4631 /* ??? Unroll loop to avoid copying. */
4635 /* Final iteration: r = i*x + 0.5*i*x*(1.0 - i*(i*x)). */
4636 do_multiply (&t
, x
, &i
);
4637 do_multiply (&h
, &t
, &i
);
4638 do_add (&i
, &dconst1
, &h
, 1);
4639 do_multiply (&h
, &t
, &i
);
4640 do_multiply (&i
, &dconsthalf
, &h
);
4641 do_add (&h
, &t
, &i
, 0);
4643 /* ??? We need a Tuckerman test to get the last bit. */
4645 real_convert (r
, mode
, &h
);
4649 /* Calculate X raised to the integer exponent N in mode MODE and store
4650 the result in R. Return true if the result may be inexact due to
4651 loss of precision. The algorithm is the classic "left-to-right binary
4652 method" described in section 4.6.3 of Donald Knuth's "Seminumerical
4653 Algorithms", "The Art of Computer Programming", Volume 2. */
4656 real_powi (r
, mode
, x
, n
)
4658 enum machine_mode mode
;
4659 const REAL_VALUE_TYPE
*x
;
4662 unsigned HOST_WIDE_INT bit
;
4664 bool inexact
= false;
4676 /* Don't worry about overflow, from now on n is unsigned. */
4684 bit
= (unsigned HOST_WIDE_INT
) 1 << (HOST_BITS_PER_WIDE_INT
- 1);
4685 for (i
= 0; i
< HOST_BITS_PER_WIDE_INT
; i
++)
4689 inexact
|= do_multiply (&t
, &t
, &t
);
4691 inexact
|= do_multiply (&t
, &t
, x
);
4699 inexact
|= do_divide (&t
, &dconst1
, &t
);
4701 real_convert (r
, mode
, &t
);