1 /* -*- Mode: C; tab-width: 8; indent-tabs-mode: t; c-basic-offset: 8 -*- */
2 /****************************************************************
4 * The author of this software is David M. Gay.
6 * Copyright (c) 1991, 2000, 2001 by Lucent Technologies.
8 * Permission to use, copy, modify, and distribute this software for any
9 * purpose without fee is hereby granted, provided that this entire notice
10 * is included in all copies of any software which is or includes a copy
11 * or modification of this software and in all copies of the supporting
12 * documentation for such software.
14 * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
15 * WARRANTY. IN PARTICULAR, NEITHER THE AUTHOR NOR LUCENT MAKES ANY
16 * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
17 * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
19 ***************************************************************/
21 /* Please send bug reports to David M. Gay (dmg at acm dot org,
22 * with " at " changed at "@" and " dot " changed to "."). */
24 /* On a machine with IEEE extended-precision registers, it is
25 * necessary to specify double-precision (53-bit) rounding precision
26 * before invoking strtod or dtoa. If the machine uses (the equivalent
27 * of) Intel 80x87 arithmetic, the call
28 * _control87(PC_53, MCW_PC);
29 * does this with many compilers. Whether this or another call is
30 * appropriate depends on the compiler; for this to work, it may be
31 * necessary to #include "float.h" or another system-dependent header
35 /* strtod for IEEE-, VAX-, and IBM-arithmetic machines.
37 * This strtod returns a nearest machine number to the input decimal
38 * string (or sets errno to ERANGE). With IEEE arithmetic, ties are
39 * broken by the IEEE round-even rule. Otherwise ties are broken by
40 * biased rounding (add half and chop).
42 * Inspired loosely by William D. Clinger's paper "How to Read Floating
43 * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101].
47 * 1. We only require IEEE, IBM, or VAX double-precision
48 * arithmetic (not IEEE double-extended).
49 * 2. We get by with floating-point arithmetic in a case that
50 * Clinger missed -- when we're computing d * 10^n
51 * for a small integer d and the integer n is not too
52 * much larger than 22 (the maximum integer k for which
53 * we can represent 10^k exactly), we may be able to
54 * compute (d*10^k) * 10^(e-k) with just one roundoff.
55 * 3. Rather than a bit-at-a-time adjustment of the binary
56 * result in the hard case, we use floating-point
57 * arithmetic to determine the adjustment to within
58 * one bit; only in really hard cases do we need to
59 * compute a second residual.
60 * 4. Because of 3., we don't need a large table of powers of 10
61 * for ten-to-e (just some small tables, e.g. of 10^k
66 * #define IEEE_8087 for IEEE-arithmetic machines where the least
67 * significant byte has the lowest address.
68 * #define IEEE_MC68k for IEEE-arithmetic machines where the most
69 * significant byte has the lowest address.
70 * #define Long int on machines with 32-bit ints and 64-bit longs.
71 * #define IBM for IBM mainframe-style floating-point arithmetic.
72 * #define VAX for VAX-style floating-point arithmetic (D_floating).
73 * #define No_leftright to omit left-right logic in fast floating-point
74 * computation of dtoa.
75 * #define Honor_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
76 * and strtod and dtoa should round accordingly.
77 * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
78 * and Honor_FLT_ROUNDS is not #defined.
79 * #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines
80 * that use extended-precision instructions to compute rounded
81 * products and quotients) with IBM.
82 * #define ROUND_BIASED for IEEE-format with biased rounding.
83 * #define Inaccurate_Divide for IEEE-format with correctly rounded
84 * products but inaccurate quotients, e.g., for Intel i860.
85 * #define NO_LONG_LONG on machines that do not have a "long long"
86 * integer type (of >= 64 bits). On such machines, you can
87 * #define Just_16 to store 16 bits per 32-bit Long when doing
88 * high-precision integer arithmetic. Whether this speeds things
89 * up or slows things down depends on the machine and the number
90 * being converted. If long long is available and the name is
91 * something other than "long long", #define Llong to be the name,
92 * and if "unsigned Llong" does not work as an unsigned version of
93 * Llong, #define #ULLong to be the corresponding unsigned type.
94 * #define KR_headers for old-style C function headers.
95 * #define Bad_float_h if your system lacks a float.h or if it does not
96 * define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP,
97 * FLT_RADIX, FLT_ROUNDS, and DBL_MAX.
98 * #define MALLOC your_malloc, where your_malloc(n) acts like malloc(n)
99 * if memory is available and otherwise does something you deem
100 * appropriate. If MALLOC is undefined, malloc will be invoked
101 * directly -- and assumed always to succeed.
102 * #define Omit_Private_Memory to omit logic (added Jan. 1998) for making
103 * memory allocations from a private pool of memory when possible.
104 * When used, the private pool is PRIVATE_MEM bytes long: 2304 bytes,
105 * unless #defined to be a different length. This default length
106 * suffices to get rid of MALLOC calls except for unusual cases,
107 * such as decimal-to-binary conversion of a very long string of
108 * digits. The longest string dtoa can return is about 751 bytes
109 * long. For conversions by strtod of strings of 800 digits and
110 * all dtoa conversions in single-threaded executions with 8-byte
111 * pointers, PRIVATE_MEM >= 7400 appears to suffice; with 4-byte
112 * pointers, PRIVATE_MEM >= 7112 appears adequate.
113 * #define NO_INFNAN_CHECK if you do not wish to have INFNAN_CHECK
114 * #defined automatically on IEEE systems. On such systems,
115 * when INFNAN_CHECK is #defined, strtod checks
116 * for Infinity and NaN (case insensitively). On some systems
117 * (e.g., some HP systems), it may be necessary to #define NAN_WORD0
118 * appropriately -- to the most significant word of a quiet NaN.
119 * (On HP Series 700/800 machines, -DNAN_WORD0=0x7ff40000 works.)
120 * When INFNAN_CHECK is #defined and No_Hex_NaN is not #defined,
121 * strtod also accepts (case insensitively) strings of the form
122 * NaN(x), where x is a string of hexadecimal digits and spaces;
123 * if there is only one string of hexadecimal digits, it is taken
124 * for the 52 fraction bits of the resulting NaN; if there are two
125 * or more strings of hex digits, the first is for the high 20 bits,
126 * the second and subsequent for the low 32 bits, with intervening
127 * white space ignored; but if this results in none of the 52
128 * fraction bits being on (an IEEE Infinity symbol), then NAN_WORD0
129 * and NAN_WORD1 are used instead.
130 * #define MULTIPLE_THREADS if the system offers preemptively scheduled
131 * multiple threads. In this case, you must provide (or suitably
132 * #define) two locks, acquired by ACQUIRE_DTOA_LOCK(n) and freed
133 * by FREE_DTOA_LOCK(n) for n = 0 or 1. (The second lock, accessed
134 * in pow5mult, ensures lazy evaluation of only one copy of high
135 * powers of 5; omitting this lock would introduce a small
136 * probability of wasting memory, but would otherwise be harmless.)
137 * You must also invoke freedtoa(s) to free the value s returned by
138 * dtoa. You may do so whether or not MULTIPLE_THREADS is #defined.
139 * #define NO_IEEE_Scale to disable new (Feb. 1997) logic in strtod that
140 * avoids underflows on inputs whose result does not underflow.
141 * If you #define NO_IEEE_Scale on a machine that uses IEEE-format
142 * floating-point numbers and flushes underflows to zero rather
143 * than implementing gradual underflow, then you must also #define
145 * #define USE_LOCALE to use the current locale's decimal_point value.
146 * #define SET_INEXACT if IEEE arithmetic is being used and extra
147 * computation should be done to set the inexact flag when the
148 * result is inexact and avoid setting inexact when the result
149 * is exact. In this case, dtoa.c must be compiled in
150 * an environment, perhaps provided by #include "dtoa.c" in a
151 * suitable wrapper, that defines two functions,
152 * int get_inexact(void);
153 * void clear_inexact(void);
154 * such that get_inexact() returns a nonzero value if the
155 * inexact bit is already set, and clear_inexact() sets the
156 * inexact bit to 0. When SET_INEXACT is #defined, strtod
157 * also does extra computations to set the underflow and overflow
158 * flags when appropriate (i.e., when the result is tiny and
159 * inexact or when it is a numeric value rounded to +-infinity).
160 * #define NO_ERRNO if strtod should not assign errno = ERANGE when
161 * the result overflows to +-Infinity or underflows to 0.
168 typedef unsigned Long ULong
;
173 #define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}
185 extern char *MALLOC();
187 extern void *MALLOC(size_t);
190 #define MALLOC malloc
193 #ifndef Omit_Private_Memory
195 #define PRIVATE_MEM 2304
197 #define PRIVATE_mem ((PRIVATE_MEM+sizeof(double)-1)/sizeof(double))
198 static double private_mem
[PRIVATE_mem
], *pmem_next
= private_mem
;
202 #undef Avoid_Underflow
211 #ifndef NO_INFNAN_CHECK
225 #define DBL_MAX_10_EXP 308
226 #define DBL_MAX_EXP 1024
228 #endif /*IEEE_Arith*/
232 #define DBL_MAX_10_EXP 75
233 #define DBL_MAX_EXP 63
235 #define DBL_MAX 7.2370055773322621e+75
240 #define DBL_MAX_10_EXP 38
241 #define DBL_MAX_EXP 127
243 #define DBL_MAX 1.7014118346046923e+38
247 #define LONG_MAX 2147483647
250 #else /* ifndef Bad_float_h */
252 #endif /* Bad_float_h */
264 #define CONST /* blank */
270 #if defined(IEEE_8087) + defined(IEEE_MC68k) + defined(VAX) + defined(IBM) != 1
271 Exactly one of IEEE_8087
, IEEE_MC68k
, VAX
, or IBM should be defined
.
274 typedef union { double d
; ULong L
[2]; } U
;
276 #define dval(x) ((x).d)
278 #define word0(x) ((x).L[1])
279 #define word1(x) ((x).L[0])
281 #define word0(x) ((x).L[0])
282 #define word1(x) ((x).L[1])
285 /* The following definition of Storeinc is appropriate for MIPS processors.
286 * An alternative that might be better on some machines is
287 * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
289 #if defined(IEEE_8087) + defined(VAX)
290 #define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \
291 ((unsigned short *)a)[0] = (unsigned short)c, a++)
293 #define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \
294 ((unsigned short *)a)[1] = (unsigned short)c, a++)
297 /* #define P DBL_MANT_DIG */
298 /* Ten_pmax = floor(P*log(2)/log(5)) */
299 /* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
300 /* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
301 /* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
305 #define Exp_shift1 20
306 #define Exp_msk1 0x100000
307 #define Exp_msk11 0x100000
308 #define Exp_mask 0x7ff00000
312 #define Exp_1 0x3ff00000
313 #define Exp_11 0x3ff00000
315 #define Frac_mask 0xfffff
316 #define Frac_mask1 0xfffff
319 #define Bndry_mask 0xfffff
320 #define Bndry_mask1 0xfffff
322 #define Sign_bit 0x80000000
328 #ifndef NO_IEEE_Scale
329 #define Avoid_Underflow
330 #ifdef Flush_Denorm /* debugging option */
331 #undef Sudden_Underflow
337 #define Flt_Rounds FLT_ROUNDS
341 #endif /*Flt_Rounds*/
343 #ifdef Honor_FLT_ROUNDS
344 #define Rounding rounding
345 #undef Check_FLT_ROUNDS
346 #define Check_FLT_ROUNDS
348 #define Rounding Flt_Rounds
351 #else /* ifndef IEEE_Arith */
352 #undef Check_FLT_ROUNDS
353 #undef Honor_FLT_ROUNDS
355 #undef Sudden_Underflow
356 #define Sudden_Underflow
361 #define Exp_shift1 24
362 #define Exp_msk1 0x1000000
363 #define Exp_msk11 0x1000000
364 #define Exp_mask 0x7f000000
367 #define Exp_1 0x41000000
368 #define Exp_11 0x41000000
369 #define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */
370 #define Frac_mask 0xffffff
371 #define Frac_mask1 0xffffff
374 #define Bndry_mask 0xefffff
375 #define Bndry_mask1 0xffffff
377 #define Sign_bit 0x80000000
379 #define Tiny0 0x100000
388 #define Exp_msk1 0x80
389 #define Exp_msk11 0x800000
390 #define Exp_mask 0x7f80
393 #define Exp_1 0x40800000
394 #define Exp_11 0x4080
396 #define Frac_mask 0x7fffff
397 #define Frac_mask1 0xffff007f
400 #define Bndry_mask 0xffff007f
401 #define Bndry_mask1 0xffff007f
403 #define Sign_bit 0x8000
409 #endif /* IBM, VAX */
410 #endif /* IEEE_Arith */
417 #define rounded_product(a,b) a = rnd_prod(a, b)
418 #define rounded_quotient(a,b) a = rnd_quot(a, b)
420 extern double rnd_prod(), rnd_quot();
422 extern double rnd_prod(double, double), rnd_quot(double, double);
425 #define rounded_product(a,b) a *= b
426 #define rounded_quotient(a,b) a /= b
429 #define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
430 #define Big1 0xffffffff
437 #define FFFFFFFF ((((unsigned long)0xffff)<<16)|(unsigned long)0xffff)
439 #define FFFFFFFF 0xffffffffUL
446 /* When Pack_32 is not defined, we store 16 bits per 32-bit Long.
447 * This makes some inner loops simpler and sometimes saves work
448 * during multiplications, but it often seems to make things slightly
449 * slower. Hence the default is now to store 32 bits per Long.
452 #else /* long long available */
454 #define Llong long long
457 #define ULLong unsigned Llong
459 #endif /* NO_LONG_LONG */
461 #ifndef MULTIPLE_THREADS
462 #define ACQUIRE_DTOA_LOCK(n) /*nothing*/
463 #define FREE_DTOA_LOCK(n) /*nothing*/
471 int k
, maxwds
, sign
, wds
;
475 typedef struct Bigint Bigint
;
477 static Bigint
*freelist
[Kmax
+1];
489 #ifndef Omit_Private_Memory
493 ACQUIRE_DTOA_LOCK(0);
494 if ((rv
= freelist
[k
])) {
495 freelist
[k
] = rv
->next
;
499 #ifdef Omit_Private_Memory
500 rv
= (Bigint
*)MALLOC(sizeof(Bigint
) + (x
-1)*sizeof(ULong
));
502 len
= (sizeof(Bigint
) + (x
-1)*sizeof(ULong
) + sizeof(double) - 1)
504 if (pmem_next
- private_mem
+ len
<= PRIVATE_mem
) {
505 rv
= (Bigint
*)pmem_next
;
509 rv
= (Bigint
*)MALLOC(len
*sizeof(double));
515 rv
->sign
= rv
->wds
= 0;
528 ACQUIRE_DTOA_LOCK(0);
529 v
->next
= freelist
[v
->k
];
535 #define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \
536 y->wds*sizeof(Long) + 2*sizeof(int))
541 (b
, m
, a
) Bigint
*b
; int m
, a
;
543 (Bigint
*b
, int m
, int a
) /* multiply by m and add a */
564 y
= *x
* (ULLong
)m
+ carry
;
566 *x
++ = (ULong
) y
& FFFFFFFF
;
570 y
= (xi
& 0xffff) * m
+ carry
;
571 z
= (xi
>> 16) * m
+ (y
>> 16);
573 *x
++ = (z
<< 16) + (y
& 0xffff);
583 if (wds
>= b
->maxwds
) {
589 b
->x
[wds
++] = (ULong
) carry
;
598 (s
, nd0
, nd
, y9
) CONST
char *s
; int nd0
, nd
; ULong y9
;
600 (CONST
char *s
, int nd0
, int nd
, ULong y9
)
608 for(k
= 0, y
= 1; x
> y
; y
<<= 1, k
++) ;
615 b
->x
[0] = y9
& 0xffff;
616 b
->wds
= (b
->x
[1] = y9
>> 16) ? 2 : 1;
622 do b
= multadd(b
, 10, *s
++ - '0');
629 b
= multadd(b
, 10, *s
++ - '0');
636 (x
) register ULong x
;
643 if (!(x
& 0xffff0000)) {
647 if (!(x
& 0xff000000)) {
651 if (!(x
& 0xf0000000)) {
655 if (!(x
& 0xc0000000)) {
659 if (!(x
& 0x80000000)) {
661 if (!(x
& 0x40000000))
676 register ULong x
= *y
;
734 (a
, b
) Bigint
*a
, *b
;
736 (Bigint
*a
, Bigint
*b
)
741 ULong
*x
, *xa
, *xae
, *xb
, *xbe
, *xc
, *xc0
;
752 if (a
->wds
< b
->wds
) {
764 for(x
= c
->x
, xa
= x
+ wc
; x
< xa
; x
++)
772 for(; xb
< xbe
; xc0
++) {
778 z
= *x
++ * (ULLong
)y
+ *xc
+ carry
;
780 *xc
++ = (ULong
) z
& FFFFFFFF
;
788 for(; xb
< xbe
; xb
++, xc0
++) {
789 if (y
= *xb
& 0xffff) {
794 z
= (*x
& 0xffff) * y
+ (*xc
& 0xffff) + carry
;
796 z2
= (*x
++ >> 16) * y
+ (*xc
>> 16) + carry
;
809 z
= (*x
& 0xffff) * y
+ (*xc
>> 16) + carry
;
812 z2
= (*x
++ >> 16) * y
+ (*xc
& 0xffff) + carry
;
820 for(; xb
< xbe
; xc0
++) {
826 z
= *x
++ * y
+ *xc
+ carry
;
836 for(xc0
= c
->x
, xc
= xc0
+ wc
; wc
> 0 && !*--xc
; --wc
) ;
846 (b
, k
) Bigint
*b
; int k
;
851 Bigint
*b1
, *p5
, *p51
;
853 static int p05
[3] = { 5, 25, 125 };
856 b
= multadd(b
, p05
[i
-1], 0);
862 #ifdef MULTIPLE_THREADS
863 ACQUIRE_DTOA_LOCK(1);
882 if (!(p51
= p5
->next
)) {
883 #ifdef MULTIPLE_THREADS
884 ACQUIRE_DTOA_LOCK(1);
885 if (!(p51
= p5
->next
)) {
886 p51
= p5
->next
= mult(p5
,p5
);
891 p51
= p5
->next
= mult(p5
,p5
);
903 (b
, k
) Bigint
*b
; int k
;
910 ULong
*x
, *x1
, *xe
, z
;
919 for(i
= b
->maxwds
; n1
> i
; i
<<= 1)
923 for(i
= 0; i
< n
; i
++)
944 *x1
++ = *x
<< k
& 0xffff | z
;
963 (a
, b
) Bigint
*a
, *b
;
965 (Bigint
*a
, Bigint
*b
)
968 ULong
*xa
, *xa0
, *xb
, *xb0
;
974 if (i
> 1 && !a
->x
[i
-1])
975 Bug("cmp called with a->x[a->wds-1] == 0");
976 if (j
> 1 && !b
->x
[j
-1])
977 Bug("cmp called with b->x[b->wds-1] == 0");
987 return *xa
< *xb
? -1 : 1;
997 (a
, b
) Bigint
*a
, *b
;
999 (Bigint
*a
, Bigint
*b
)
1004 ULong
*xa
, *xae
, *xb
, *xbe
, *xc
;
1041 y
= (ULLong
)*xa
++ - *xb
++ - borrow
;
1042 borrow
= y
>> 32 & (ULong
)1;
1043 *xc
++ = (ULong
) y
& FFFFFFFF
;
1048 borrow
= y
>> 32 & (ULong
)1;
1049 *xc
++ = (ULong
) y
& FFFFFFFF
;
1054 y
= (*xa
& 0xffff) - (*xb
& 0xffff) - borrow
;
1055 borrow
= (y
& 0x10000) >> 16;
1056 z
= (*xa
++ >> 16) - (*xb
++ >> 16) - borrow
;
1057 borrow
= (z
& 0x10000) >> 16;
1062 y
= (*xa
& 0xffff) - borrow
;
1063 borrow
= (y
& 0x10000) >> 16;
1064 z
= (*xa
++ >> 16) - borrow
;
1065 borrow
= (z
& 0x10000) >> 16;
1070 y
= *xa
++ - *xb
++ - borrow
;
1071 borrow
= (y
& 0x10000) >> 16;
1077 borrow
= (y
& 0x10000) >> 16;
1099 L
= (word0(x
) & Exp_mask
) - (P
-1)*Exp_msk1
;
1100 #ifndef Avoid_Underflow
1101 #ifndef Sudden_Underflow
1110 #ifndef Avoid_Underflow
1111 #ifndef Sudden_Underflow
1114 L
= -L
>> Exp_shift
;
1115 if (L
< Exp_shift
) {
1116 word0(a
) = 0x80000 >> L
;
1122 word1(a
) = L
>= 31 ? 1 : 1 << 31 - L
;
1133 (a
, e
) Bigint
*a
; int *e
;
1138 ULong
*xa
, *xa0
, w
, y
, z
;
1152 if (!y
) Bug("zero y in b2d");
1158 d0
= Exp_1
| y
>> (Ebits
- k
);
1159 w
= xa
> xa0
? *--xa
: 0;
1160 d1
= y
<< ((32-Ebits
) + k
) | w
>> (Ebits
- k
);
1163 z
= xa
> xa0
? *--xa
: 0;
1165 d0
= Exp_1
| y
<< k
| z
>> (32 - k
);
1166 y
= xa
> xa0
? *--xa
: 0;
1167 d1
= z
<< k
| y
>> (32 - k
);
1174 if (k
< Ebits
+ 16) {
1175 z
= xa
> xa0
? *--xa
: 0;
1176 d0
= Exp_1
| y
<< k
- Ebits
| z
>> Ebits
+ 16 - k
;
1177 w
= xa
> xa0
? *--xa
: 0;
1178 y
= xa
> xa0
? *--xa
: 0;
1179 d1
= z
<< k
+ 16 - Ebits
| w
<< k
- Ebits
| y
>> 16 + Ebits
- k
;
1182 z
= xa
> xa0
? *--xa
: 0;
1183 w
= xa
> xa0
? *--xa
: 0;
1185 d0
= Exp_1
| y
<< k
+ 16 | z
<< k
| w
>> 16 - k
;
1186 y
= xa
> xa0
? *--xa
: 0;
1187 d1
= w
<< k
+ 16 | y
<< k
;
1191 word0(d
) = d0
>> 16 | d0
<< 16;
1192 word1(d
) = d1
>> 16 | d1
<< 16;
1203 (d
, e
, bits
) U d
; int *e
, *bits
;
1205 (U d
, int *e
, int *bits
)
1211 #ifndef Sudden_Underflow
1216 d0
= word0(d
) >> 16 | word0(d
) << 16;
1217 d1
= word1(d
) >> 16 | word1(d
) << 16;
1231 d0
&= 0x7fffffff; /* clear sign bit, which we ignore */
1232 #ifdef Sudden_Underflow
1233 de
= (int)(d0
>> Exp_shift
);
1238 if ((de
= (int)(d0
>> Exp_shift
)))
1243 if ((k
= lo0bits(&y
))) {
1244 x
[0] = y
| z
<< (32 - k
);
1249 #ifndef Sudden_Underflow
1252 b
->wds
= (x
[1] = z
) ? 2 : 1;
1257 Bug("Zero passed to d2b");
1261 #ifndef Sudden_Underflow
1269 if (k
= lo0bits(&y
))
1271 x
[0] = y
| z
<< 32 - k
& 0xffff;
1272 x
[1] = z
>> k
- 16 & 0xffff;
1278 x
[1] = y
>> 16 | z
<< 16 - k
& 0xffff;
1279 x
[2] = z
>> k
& 0xffff;
1294 Bug("Zero passed to d2b");
1312 #ifndef Sudden_Underflow
1316 *e
= (de
- Bias
- (P
-1) << 2) + k
;
1317 *bits
= 4*P
+ 8 - k
- hi0bits(word0(d
) & Frac_mask
);
1319 *e
= de
- Bias
- (P
-1) + k
;
1322 #ifndef Sudden_Underflow
1325 *e
= de
- Bias
- (P
-1) + 1 + k
;
1327 *bits
= 32*i
- hi0bits(x
[i
-1]);
1329 *bits
= (i
+2)*16 - hi0bits(x
[i
]);
1341 (a
, b
) Bigint
*a
, *b
;
1343 (Bigint
*a
, Bigint
*b
)
1349 dval(da
) = b2d(a
, &ka
);
1350 dval(db
) = b2d(b
, &kb
);
1352 k
= ka
- kb
+ 32*(a
->wds
- b
->wds
);
1354 k
= ka
- kb
+ 16*(a
->wds
- b
->wds
);
1358 word0(da
) += (k
>> 2)*Exp_msk1
;
1364 word0(db
) += (k
>> 2)*Exp_msk1
;
1370 word0(da
) += k
*Exp_msk1
;
1373 word0(db
) += k
*Exp_msk1
;
1376 return dval(da
) / dval(db
);
1381 1e0
, 1e1
, 1e2
, 1e3
, 1e4
, 1e5
, 1e6
, 1e7
, 1e8
, 1e9
,
1382 1e10
, 1e11
, 1e12
, 1e13
, 1e14
, 1e15
, 1e16
, 1e17
, 1e18
, 1e19
,
1391 bigtens
[] = { 1e16
, 1e32
, 1e64
, 1e128
, 1e256
};
1392 static CONST
double tinytens
[] = { 1e-16, 1e-32, 1e-64, 1e-128,
1393 #ifdef Avoid_Underflow
1394 9007199254740992.*9007199254740992.e
-256
1395 /* = 2^106 * 1e-53 */
1400 /* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */
1401 /* flag unnecessarily. It leads to a song and dance at the end of strtod. */
1402 #define Scale_Bit 0x10
1406 bigtens
[] = { 1e16
, 1e32
, 1e64
};
1407 static CONST
double tinytens
[] = { 1e-16, 1e-32, 1e-64 };
1410 bigtens
[] = { 1e16
, 1e32
};
1411 static CONST
double tinytens
[] = { 1e-16, 1e-32 };
1419 #define NAN_WORD0 0x7ff80000
1429 (sp
, t
) char **sp
, *t
;
1431 (CONST
char **sp
, CONST
char *t
)
1435 CONST
char *s
= *sp
;
1438 if ((c
= *++s
) >= 'A' && c
<= 'Z')
1451 (rvp
, sp
) U
*rvp
; CONST
char **sp
;
1453 (U
*rvp
, CONST
char **sp
)
1458 int havedig
, udx0
, xshift
;
1461 havedig
= xshift
= 0;
1464 /* allow optional initial 0x or 0X */
1465 while((c
= *(CONST
unsigned char*)(s
+1)) && c
<= ' ')
1467 if (s
[1] == '0' && (s
[2] == 'x' || s
[2] == 'X'))
1469 while((c
= *(CONST
unsigned char*)++s
)) {
1470 if (c
>= '0' && c
<= '9')
1472 else if (c
>= 'a' && c
<= 'f')
1474 else if (c
>= 'A' && c
<= 'F')
1476 else if (c
<= ' ') {
1477 if (udx0
&& havedig
) {
1483 #ifdef GDTOA_NON_PEDANTIC_NANCHECK
1484 else if (/*(*/ c
== ')' && havedig
) {
1489 return; /* invalid form: don't change *sp */
1493 if (/*(*/ c
== ')') {
1497 } while((c
= *++s
));
1508 x
[0] = (x
[0] << 4) | (x
[1] >> 28);
1509 x
[1] = (x
[1] << 4) | c
;
1511 if ((x
[0] &= 0xfffff) || x
[1]) {
1512 word0(*rvp
) = Exp_mask
| x
[0];
1516 #endif /*No_Hex_NaN*/
1517 #endif /* INFNAN_CHECK */
1522 (s00
, se
) CONST
char *s00
; char **se
;
1524 (CONST
char *s00
, char **se
)
1527 #ifdef Avoid_Underflow
1530 int bb2
, bb5
, bbe
, bd2
, bd5
, bbbits
, bs2
, c
, dsign
,
1531 e
, e1
, esign
, i
, j
, k
, nd
, nd0
, nf
, nz
, nz0
, sign
;
1532 CONST
char *s
, *s0
, *s1
;
1537 Bigint
*bb
, *bb1
, *bd
, *bd0
, *bs
, *delta
;
1539 int inexact
, oldinexact
;
1541 #ifdef Honor_FLT_ROUNDS
1549 delta
= bb
= bd
= bs
= 0;
1552 sign
= nz0
= nz
= 0;
1554 for(s
= s00
;;s
++) switch(*s
) {
1577 while(*++s
== '0') ;
1583 for(nd
= nf
= 0; (c
= *s
) >= '0' && c
<= '9'; nd
++, s
++)
1590 s1
= localeconv()->decimal_point
;
1611 for(; c
== '0'; c
= *++s
)
1613 if (c
> '0' && c
<= '9') {
1621 for(; c
>= '0' && c
<= '9'; c
= *++s
) {
1626 for(i
= 1; i
< nz
; i
++)
1629 else if (nd
<= DBL_DIG
+ 1)
1633 else if (nd
<= DBL_DIG
+ 1)
1641 if (c
== 'e' || c
== 'E') {
1642 if (!nd
&& !nz
&& !nz0
) {
1653 if (c
>= '0' && c
<= '9') {
1656 if (c
> '0' && c
<= '9') {
1659 while((c
= *++s
) >= '0' && c
<= '9')
1661 if (s
- s1
> 8 || L
> 19999)
1662 /* Avoid confusion from exponents
1663 * so large that e might overflow.
1665 e
= 19999; /* safe for 16 bit ints */
1680 /* Check for Nan and Infinity */
1684 if (match(&s
,"nf")) {
1686 if (!match(&s
,"inity"))
1688 word0(rv
) = 0x7ff00000;
1695 if (match(&s
, "an")) {
1696 word0(rv
) = NAN_WORD0
;
1697 word1(rv
) = NAN_WORD1
;
1699 if (*s
== '(') /*)*/
1705 #endif /* INFNAN_CHECK */
1714 /* Now we have nd0 digits, starting at s0, followed by a
1715 * decimal point, followed by nd-nd0 digits. The number we're
1716 * after is the integer represented by those digits times
1721 k
= nd
< DBL_DIG
+ 1 ? nd
: DBL_DIG
+ 1;
1726 oldinexact
= get_inexact();
1728 dval(rv
) = tens
[k
- 9] * dval(rv
) + z
;
1732 #ifndef RND_PRODQUOT
1733 #ifndef Honor_FLT_ROUNDS
1741 if (e
<= Ten_pmax
) {
1743 goto vax_ovfl_check
;
1745 #ifdef Honor_FLT_ROUNDS
1746 /* round correctly FLT_ROUNDS = 2 or 3 */
1752 /* rv = */ rounded_product(dval(rv
), tens
[e
]);
1757 if (e
<= Ten_pmax
+ i
) {
1758 /* A fancier test would sometimes let us do
1759 * this for larger i values.
1761 #ifdef Honor_FLT_ROUNDS
1762 /* round correctly FLT_ROUNDS = 2 or 3 */
1769 dval(rv
) *= tens
[i
];
1771 /* VAX exponent range is so narrow we must
1772 * worry about overflow here...
1775 word0(rv
) -= P
*Exp_msk1
;
1776 /* rv = */ rounded_product(dval(rv
), tens
[e
]);
1777 if ((word0(rv
) & Exp_mask
)
1778 > Exp_msk1
*(DBL_MAX_EXP
+Bias
-1-P
))
1780 word0(rv
) += P
*Exp_msk1
;
1782 /* rv = */ rounded_product(dval(rv
), tens
[e
]);
1787 #ifndef Inaccurate_Divide
1788 else if (e
>= -Ten_pmax
) {
1789 #ifdef Honor_FLT_ROUNDS
1790 /* round correctly FLT_ROUNDS = 2 or 3 */
1796 /* rv = */ rounded_quotient(dval(rv
), tens
[-e
]);
1807 oldinexact
= get_inexact();
1809 #ifdef Avoid_Underflow
1812 #ifdef Honor_FLT_ROUNDS
1813 if ((rounding
= Flt_Rounds
) >= 2) {
1815 rounding
= rounding
== 2 ? 0 : 2;
1821 #endif /*IEEE_Arith*/
1823 /* Get starting approximation = rv * 10**e1 */
1827 dval(rv
) *= tens
[i
];
1829 if (e1
> DBL_MAX_10_EXP
) {
1834 /* Can't trust HUGE_VAL */
1836 #ifdef Honor_FLT_ROUNDS
1838 case 0: /* toward 0 */
1839 case 3: /* toward -infinity */
1844 word0(rv
) = Exp_mask
;
1847 #else /*Honor_FLT_ROUNDS*/
1848 word0(rv
) = Exp_mask
;
1850 #endif /*Honor_FLT_ROUNDS*/
1852 /* set overflow bit */
1854 dval(rv0
) *= dval(rv0
);
1856 #else /*IEEE_Arith*/
1859 #endif /*IEEE_Arith*/
1865 for(j
= 0; e1
> 1; j
++, e1
>>= 1)
1867 dval(rv
) *= bigtens
[j
];
1868 /* The last multiplication could overflow. */
1869 word0(rv
) -= P
*Exp_msk1
;
1870 dval(rv
) *= bigtens
[j
];
1871 if ((z
= word0(rv
) & Exp_mask
)
1872 > Exp_msk1
*(DBL_MAX_EXP
+Bias
-P
))
1874 if (z
> Exp_msk1
*(DBL_MAX_EXP
+Bias
-1-P
)) {
1875 /* set to largest number */
1876 /* (Can't trust DBL_MAX) */
1881 word0(rv
) += P
*Exp_msk1
;
1887 dval(rv
) /= tens
[i
];
1889 if (e1
>= 1 << n_bigtens
)
1891 #ifdef Avoid_Underflow
1894 for(j
= 0; e1
> 0; j
++, e1
>>= 1)
1896 dval(rv
) *= tinytens
[j
];
1897 if (scale
&& (j
= 2*P
+ 1 - ((word0(rv
) & Exp_mask
)
1898 >> Exp_shift
)) > 0) {
1899 /* scaled rv is denormal; zap j low bits */
1903 word0(rv
) = (P
+2)*Exp_msk1
;
1905 word0(rv
) &= 0xffffffff << (j
-32);
1908 word1(rv
) &= 0xffffffff << j
;
1911 for(j
= 0; e1
> 1; j
++, e1
>>= 1)
1913 dval(rv
) *= tinytens
[j
];
1914 /* The last multiplication could underflow. */
1915 dval(rv0
) = dval(rv
);
1916 dval(rv
) *= tinytens
[j
];
1918 dval(rv
) = 2.*dval(rv0
);
1919 dval(rv
) *= tinytens
[j
];
1931 #ifndef Avoid_Underflow
1934 /* The refinement below will clean
1935 * this approximation up.
1942 /* Now the hard part -- adjusting rv to the correct value.*/
1944 /* Put digits into bd: true value = bd * 10^e */
1946 bd0
= s2b(s0
, nd0
, nd
, y
);
1949 bd
= Balloc(bd0
->k
);
1951 bb
= d2b(rv
, &bbe
, &bbbits
); /* rv = bb * 2^bbe */
1967 #ifdef Honor_FLT_ROUNDS
1971 #ifdef Avoid_Underflow
1973 i
= j
+ bbbits
- 1; /* logb(rv) */
1974 if (i
< Emin
) /* denormal */
1978 #else /*Avoid_Underflow*/
1979 #ifdef Sudden_Underflow
1981 j
= 1 + 4*P
- 3 - bbbits
+ ((bbe
+ bbbits
- 1) & 3);
1985 #else /*Sudden_Underflow*/
1987 i
= j
+ bbbits
- 1; /* logb(rv) */
1988 if (i
< Emin
) /* denormal */
1992 #endif /*Sudden_Underflow*/
1993 #endif /*Avoid_Underflow*/
1996 #ifdef Avoid_Underflow
1999 i
= bb2
< bd2
? bb2
: bd2
;
2008 bs
= pow5mult(bs
, bb5
);
2014 bb
= lshift(bb
, bb2
);
2016 bd
= pow5mult(bd
, bd5
);
2018 bd
= lshift(bd
, bd2
);
2020 bs
= lshift(bs
, bs2
);
2021 delta
= diff(bb
, bd
);
2022 dsign
= delta
->sign
;
2025 #ifdef Honor_FLT_ROUNDS
2026 if (rounding
!= 1) {
2028 /* Error is less than an ulp */
2029 if (!delta
->x
[0] && delta
->wds
<= 1) {
2045 && !(word0(rv
) & Frac_mask
)) {
2046 y
= word0(rv
) & Exp_mask
;
2047 #ifdef Avoid_Underflow
2048 if (!scale
|| y
> 2*P
*Exp_msk1
)
2053 delta
= lshift(delta
,Log2P
);
2054 if (cmp(delta
, bs
) <= 0)
2059 #ifdef Avoid_Underflow
2060 if (scale
&& (y
= word0(rv
) & Exp_mask
)
2062 word0(adj
) += (2*P
+1)*Exp_msk1
- y
;
2064 #ifdef Sudden_Underflow
2065 if ((word0(rv
) & Exp_mask
) <=
2067 word0(rv
) += P
*Exp_msk1
;
2068 dval(rv
) += adj
*ulp(rv
);
2069 word0(rv
) -= P
*Exp_msk1
;
2072 #endif /*Sudden_Underflow*/
2073 #endif /*Avoid_Underflow*/
2074 dval(rv
) += adj
*ulp(rv
);
2078 adj
= ratio(delta
, bs
);
2081 if (adj
<= 0x7ffffffe) {
2082 /* adj = rounding ? ceil(adj) : floor(adj); */
2085 if (!((rounding
>>1) ^ dsign
))
2090 #ifdef Avoid_Underflow
2091 if (scale
&& (y
= word0(rv
) & Exp_mask
) <= 2*P
*Exp_msk1
)
2092 word0(adj
) += (2*P
+1)*Exp_msk1
- y
;
2094 #ifdef Sudden_Underflow
2095 if ((word0(rv
) & Exp_mask
) <= P
*Exp_msk1
) {
2096 word0(rv
) += P
*Exp_msk1
;
2102 word0(rv
) -= P
*Exp_msk1
;
2105 #endif /*Sudden_Underflow*/
2106 #endif /*Avoid_Underflow*/
2114 #endif /*Honor_FLT_ROUNDS*/
2117 /* Error is less than half an ulp -- check for
2118 * special case of mantissa a power of two.
2120 if (dsign
|| word1(rv
) || word0(rv
) & Bndry_mask
2122 #ifdef Avoid_Underflow
2123 || (word0(rv
) & Exp_mask
) <= (2*P
+1)*Exp_msk1
2125 || (word0(rv
) & Exp_mask
) <= Exp_msk1
2130 if (!delta
->x
[0] && delta
->wds
<= 1)
2135 if (!delta
->x
[0] && delta
->wds
<= 1) {
2142 delta
= lshift(delta
,Log2P
);
2143 if (cmp(delta
, bs
) > 0)
2148 /* exactly half-way between */
2150 if ((word0(rv
) & Bndry_mask1
) == Bndry_mask1
2152 #ifdef Avoid_Underflow
2153 (scale
&& (y
= word0(rv
) & Exp_mask
) <= 2*P
*Exp_msk1
)
2154 ? (0xffffffff & (0xffffffff << (2*P
+1-(y
>>Exp_shift
)))) :
2157 /*boundary case -- increment exponent*/
2158 word0(rv
) = (word0(rv
) & Exp_mask
)
2165 #ifdef Avoid_Underflow
2171 else if (!(word0(rv
) & Bndry_mask
) && !word1(rv
)) {
2173 /* boundary case -- decrement exponent */
2174 #ifdef Sudden_Underflow /*{{*/
2175 L
= word0(rv
) & Exp_mask
;
2179 #ifdef Avoid_Underflow
2180 if (L
<= (scale
? (2*P
+1)*Exp_msk1
: Exp_msk1
))
2183 #endif /*Avoid_Underflow*/
2187 #else /*Sudden_Underflow}{*/
2188 #ifdef Avoid_Underflow
2190 L
= word0(rv
) & Exp_mask
;
2191 if (L
<= (2*P
+1)*Exp_msk1
) {
2192 if (L
> (P
+2)*Exp_msk1
)
2193 /* round even ==> */
2196 /* rv = smallest denormal */
2200 #endif /*Avoid_Underflow*/
2201 L
= (word0(rv
) & Exp_mask
) - Exp_msk1
;
2202 #endif /*Sudden_Underflow}}*/
2203 word0(rv
) = L
| Bndry_mask1
;
2204 word1(rv
) = 0xffffffff;
2211 #ifndef ROUND_BIASED
2212 if (!(word1(rv
) & LSB
))
2216 dval(rv
) += ulp(rv
);
2217 #ifndef ROUND_BIASED
2219 dval(rv
) -= ulp(rv
);
2220 #ifndef Sudden_Underflow
2225 #ifdef Avoid_Underflow
2231 if ((aadj
= ratio(delta
, bs
)) <= 2.) {
2233 aadj
= dval(aadj1
) = 1.;
2234 else if (word1(rv
) || word0(rv
) & Bndry_mask
) {
2235 #ifndef Sudden_Underflow
2236 if (word1(rv
) == Tiny1
&& !word0(rv
))
2243 /* special case -- power of FLT_RADIX to be */
2244 /* rounded down... */
2246 if (aadj
< 2./FLT_RADIX
)
2247 aadj
= 1./FLT_RADIX
;
2250 dval(aadj1
) = -aadj
;
2255 dval(aadj1
) = dsign
? aadj
: -aadj
;
2256 #ifdef Check_FLT_ROUNDS
2258 case 2: /* towards +infinity */
2261 case 0: /* towards 0 */
2262 case 3: /* towards -infinity */
2266 if (Flt_Rounds
== 0)
2268 #endif /*Check_FLT_ROUNDS*/
2270 y
= word0(rv
) & Exp_mask
;
2272 /* Check for overflow */
2274 if (y
== Exp_msk1
*(DBL_MAX_EXP
+Bias
-1)) {
2275 dval(rv0
) = dval(rv
);
2276 word0(rv
) -= P
*Exp_msk1
;
2277 adj
= dval(aadj1
) * ulp(rv
);
2279 if ((word0(rv
) & Exp_mask
) >=
2280 Exp_msk1
*(DBL_MAX_EXP
+Bias
-P
)) {
2281 if (word0(rv0
) == Big0
&& word1(rv0
) == Big1
)
2288 word0(rv
) += P
*Exp_msk1
;
2291 #ifdef Avoid_Underflow
2292 if (scale
&& y
<= 2*P
*Exp_msk1
) {
2293 if (aadj
<= 0x7fffffff) {
2294 if ((z
= (ULong
) aadj
) <= 0)
2297 dval(aadj1
) = dsign
? aadj
: -aadj
;
2299 word0(aadj1
) += (2*P
+1)*Exp_msk1
- y
;
2301 adj
= dval(aadj1
) * ulp(rv
);
2304 #ifdef Sudden_Underflow
2305 if ((word0(rv
) & Exp_mask
) <= P
*Exp_msk1
) {
2306 dval(rv0
) = dval(rv
);
2307 word0(rv
) += P
*Exp_msk1
;
2308 adj
= dval(aadj1
) * ulp(rv
);
2311 if ((word0(rv
) & Exp_mask
) < P
*Exp_msk1
)
2313 if ((word0(rv
) & Exp_mask
) <= P
*Exp_msk1
)
2316 if (word0(rv0
) == Tiny0
2317 && word1(rv0
) == Tiny1
)
2324 word0(rv
) -= P
*Exp_msk1
;
2327 adj
= dval(aadj1
) * ulp(rv
);
2330 #else /*Sudden_Underflow*/
2331 /* Compute adj so that the IEEE rounding rules will
2332 * correctly round rv + adj in some half-way cases.
2333 * If rv * ulp(rv) is denormalized (i.e.,
2334 * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid
2335 * trouble from bits lost to denormalization;
2336 * example: 1.2e-307 .
2338 if (y
<= (P
-1)*Exp_msk1
&& aadj
> 1.) {
2339 dval(aadj1
) = (double)(int)(aadj
+ 0.5);
2341 dval(aadj1
) = -dval(aadj1
);
2343 adj
= dval(aadj1
) * ulp(rv
);
2345 #endif /*Sudden_Underflow*/
2346 #endif /*Avoid_Underflow*/
2348 z
= word0(rv
) & Exp_mask
;
2350 #ifdef Avoid_Underflow
2354 /* Can we stop now? */
2357 /* The tolerances below are conservative. */
2358 if (dsign
|| word1(rv
) || word0(rv
) & Bndry_mask
) {
2359 if (aadj
< .4999999 || aadj
> .5000001)
2362 else if (aadj
< .4999999/FLT_RADIX
)
2375 word0(rv0
) = Exp_1
+ (70 << Exp_shift
);
2380 else if (!oldinexact
)
2383 #ifdef Avoid_Underflow
2385 word0(rv0
) = Exp_1
- 2*P
*Exp_msk1
;
2387 dval(rv
) *= dval(rv0
);
2389 /* try to avoid the bug of testing an 8087 register value */
2390 if (word0(rv
) == 0 && word1(rv
) == 0)
2394 #endif /* Avoid_Underflow */
2396 if (inexact
&& !(word0(rv
) & Exp_mask
)) {
2397 /* set underflow bit */
2399 dval(rv0
) *= dval(rv0
);
2411 return sign
? -dval(rv
) : dval(rv
);
2417 (b
, S
) Bigint
*b
, *S
;
2419 (Bigint
*b
, Bigint
*S
)
2423 ULong
*bx
, *bxe
, q
, *sx
, *sxe
;
2425 ULLong borrow
, carry
, y
, ys
;
2427 ULong borrow
, carry
, y
, ys
;
2435 /*debug*/ if (b
->wds
> n
)
2436 /*debug*/ Bug("oversize b in quorem");
2444 q
= *bxe
/ (*sxe
+ 1); /* ensure q <= true quotient */
2446 /*debug*/ if (q
> 9)
2447 /*debug*/ Bug("oversized quotient in quorem");
2454 ys
= *sx
++ * (ULLong
)q
+ carry
;
2456 y
= *bx
- (ys
& FFFFFFFF
) - borrow
;
2457 borrow
= y
>> 32 & (ULong
)1;
2458 *bx
++ = (ULong
) y
& FFFFFFFF
;
2462 ys
= (si
& 0xffff) * q
+ carry
;
2463 zs
= (si
>> 16) * q
+ (ys
>> 16);
2465 y
= (*bx
& 0xffff) - (ys
& 0xffff) - borrow
;
2466 borrow
= (y
& 0x10000) >> 16;
2467 z
= (*bx
>> 16) - (zs
& 0xffff) - borrow
;
2468 borrow
= (z
& 0x10000) >> 16;
2471 ys
= *sx
++ * q
+ carry
;
2473 y
= *bx
- (ys
& 0xffff) - borrow
;
2474 borrow
= (y
& 0x10000) >> 16;
2482 while(--bxe
> bx
&& !*bxe
)
2487 if (cmp(b
, S
) >= 0) {
2497 y
= *bx
- (ys
& FFFFFFFF
) - borrow
;
2498 borrow
= y
>> 32 & (ULong
)1;
2499 *bx
++ = (ULong
) y
& FFFFFFFF
;
2503 ys
= (si
& 0xffff) + carry
;
2504 zs
= (si
>> 16) + (ys
>> 16);
2506 y
= (*bx
& 0xffff) - (ys
& 0xffff) - borrow
;
2507 borrow
= (y
& 0x10000) >> 16;
2508 z
= (*bx
>> 16) - (zs
& 0xffff) - borrow
;
2509 borrow
= (z
& 0x10000) >> 16;
2514 y
= *bx
- (ys
& 0xffff) - borrow
;
2515 borrow
= (y
& 0x10000) >> 16;
2524 while(--bxe
> bx
&& !*bxe
)
2532 #ifndef MULTIPLE_THREADS
2533 static char *dtoa_result
;
2547 sizeof(Bigint
) - sizeof(ULong
) - sizeof(int) + j
<= (unsigned) i
;
2550 r
= (int*)Balloc(k
);
2553 #ifndef MULTIPLE_THREADS
2561 nrv_alloc(s
, rve
, n
) char *s
, **rve
; int n
;
2563 nrv_alloc(CONST
char *s
, char **rve
, int n
)
2568 t
= rv
= rv_alloc(n
);
2569 while((*t
= *s
++)) t
++;
2575 /* freedtoa(s) must be used to free values s returned by dtoa
2576 * when MULTIPLE_THREADS is #defined. It should be used in all cases,
2577 * but for consistency with earlier versions of dtoa, it is optional
2578 * when MULTIPLE_THREADS is not defined.
2583 freedtoa(s
) char *s
;
2588 Bigint
*b
= (Bigint
*)((int *)s
- 1);
2589 b
->maxwds
= 1 << (b
->k
= *(int*)b
);
2591 #ifndef MULTIPLE_THREADS
2592 if (s
== dtoa_result
)
2597 /* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
2599 * Inspired by "How to Print Floating-Point Numbers Accurately" by
2600 * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 112-126].
2603 * 1. Rather than iterating, we use a simple numeric overestimate
2604 * to determine k = floor(log10(d)). We scale relevant
2605 * quantities using O(log2(k)) rather than O(k) multiplications.
2606 * 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
2607 * try to generate digits strictly left to right. Instead, we
2608 * compute with fewer bits and propagate the carry if necessary
2609 * when rounding the final digit up. This is often faster.
2610 * 3. Under the assumption that input will be rounded nearest,
2611 * mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
2612 * That is, we allow equality in stopping tests when the
2613 * round-nearest rule will give the same floating-point value
2614 * as would satisfaction of the stopping test with strict
2616 * 4. We remove common factors of powers of 2 from relevant
2618 * 5. When converting floating-point integers less than 1e16,
2619 * we use floating-point arithmetic rather than resorting
2620 * to multiple-precision integers.
2621 * 6. When asked to produce fewer than 15 digits, we first try
2622 * to get by with floating-point arithmetic; we resort to
2623 * multiple-precision integer arithmetic only if we cannot
2624 * guarantee that the floating-point calculation has given
2625 * the correctly rounded result. For k requested digits and
2626 * "uniformly" distributed input, the probability is
2627 * something like 10^(k-15) that we must resort to the Long
2634 (d
, mode
, ndigits
, decpt
, sign
, rve
)
2635 U d
; int mode
, ndigits
, *decpt
, *sign
; char **rve
;
2637 (U d
, int mode
, int ndigits
, int *decpt
, int *sign
, char **rve
)
2640 /* Arguments ndigits, decpt, sign are similar to those
2641 of ecvt and fcvt; trailing zeros are suppressed from
2642 the returned string. If not null, *rve is set to point
2643 to the end of the return value. If d is +-Infinity or NaN,
2644 then *decpt is set to 9999.
2647 0 ==> shortest string that yields d when read in
2648 and rounded to nearest.
2649 1 ==> like 0, but with Steele & White stopping rule;
2650 e.g. with IEEE P754 arithmetic , mode 0 gives
2651 1e23 whereas mode 1 gives 9.999999999999999e22.
2652 2 ==> max(1,ndigits) significant digits. This gives a
2653 return value similar to that of ecvt, except
2654 that trailing zeros are suppressed.
2655 3 ==> through ndigits past the decimal point. This
2656 gives a return value similar to that from fcvt,
2657 except that trailing zeros are suppressed, and
2658 ndigits can be negative.
2659 4,5 ==> similar to 2 and 3, respectively, but (in
2660 round-nearest mode) with the tests of mode 0 to
2661 possibly return a shorter string that rounds to d.
2662 With IEEE arithmetic and compilation with
2663 -DHonor_FLT_ROUNDS, modes 4 and 5 behave the same
2664 as modes 2 and 3 when FLT_ROUNDS != 1.
2665 6-9 ==> Debugging modes similar to mode - 4: don't try
2666 fast floating-point estimate (if applicable).
2668 Values of mode other than 0-9 are treated as mode 0.
2670 Sufficient space is allocated to the return value
2671 to hold the suppressed trailing zeros.
2674 int bbits
, b2
, b5
, be
, dig
, i
, ieps
, ilim
, ilim0
, ilim1
,
2675 j
, j1
, k
, k0
, k_check
, leftright
, m2
, m5
, s2
, s5
,
2676 spec_case
, try_quick
;
2678 #ifndef Sudden_Underflow
2682 Bigint
*b
, *b1
, *delta
, *mlo
, *mhi
, *S
;
2686 #ifdef Honor_FLT_ROUNDS
2690 int inexact
, oldinexact
;
2698 #ifndef MULTIPLE_THREADS
2700 freedtoa(dtoa_result
);
2705 if (word0(d
) & Sign_bit
) {
2706 /* set sign for everything, including 0's and NaNs */
2708 word0(d
) &= ~Sign_bit
; /* clear sign bit */
2713 #if defined(IEEE_Arith) + defined(VAX)
2715 if ((word0(d
) & Exp_mask
) == Exp_mask
)
2717 if (word0(d
) == 0x8000)
2720 /* Infinity or NaN */
2723 if (!word1(d
) && !(word0(d
) & 0xfffff))
2724 return nrv_alloc("Infinity", rve
, 8);
2726 return nrv_alloc("NaN", rve
, 3);
2730 dval(d
) += 0; /* normalize */
2734 return nrv_alloc("0", rve
, 1);
2738 try_quick
= oldinexact
= get_inexact();
2741 #ifdef Honor_FLT_ROUNDS
2742 if ((rounding
= Flt_Rounds
) >= 2) {
2744 rounding
= rounding
== 2 ? 0 : 2;
2751 b
= d2b(d
, &be
, &bbits
);
2752 #ifdef Sudden_Underflow
2753 i
= (int)(word0(d
) >> Exp_shift1
& (Exp_mask
>>Exp_shift1
));
2755 if ((i
= (int)(word0(d
) >> Exp_shift1
& (Exp_mask
>>Exp_shift1
)))) {
2758 word0(d2
) &= Frac_mask1
;
2759 word0(d2
) |= Exp_11
;
2761 if (j
= 11 - hi0bits(word0(d2
) & Frac_mask
))
2765 /* log(x) ~=~ log(1.5) + (x-1.5)/1.5
2766 * log10(x) = log(x) / log(10)
2767 * ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
2768 * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
2770 * This suggests computing an approximation k to log10(d) by
2772 * k = (i - Bias)*0.301029995663981
2773 * + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
2775 * We want k to be too large rather than too small.
2776 * The error in the first-order Taylor series approximation
2777 * is in our favor, so we just round up the constant enough
2778 * to compensate for any error in the multiplication of
2779 * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
2780 * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
2781 * adding 1e-13 to the constant term more than suffices.
2782 * Hence we adjust the constant term to 0.1760912590558.
2783 * (We could get a more accurate k by invoking log10,
2784 * but this is probably not worthwhile.)
2792 #ifndef Sudden_Underflow
2796 /* d is denormalized */
2798 i
= bbits
+ be
+ (Bias
+ (P
-1) - 1);
2799 x
= i
> 32 ? word0(d
) << (64 - i
) | word1(d
) >> (i
- 32)
2800 : word1(d
) << (32 - i
);
2802 word0(d2
) -= 31*Exp_msk1
; /* adjust exponent */
2803 i
-= (Bias
+ (P
-1) - 1) + 1;
2807 ds
= (dval(d2
)-1.5)*0.289529654602168 + 0.1760912590558 + i
*0.301029995663981;
2809 if (ds
< 0. && ds
!= k
)
2810 k
--; /* want k = floor(ds) */
2812 if (k
>= 0 && k
<= Ten_pmax
) {
2813 if (dval(d
) < tens
[k
])
2836 if (mode
< 0 || mode
> 9)
2840 #ifdef Check_FLT_ROUNDS
2841 try_quick
= Rounding
== 1;
2845 #endif /*SET_INEXACT*/
2865 ilim
= ilim1
= i
= ndigits
;
2871 i
= ndigits
+ k
+ 1;
2877 s
= s0
= rv_alloc(i
);
2879 #ifdef Honor_FLT_ROUNDS
2880 if (mode
> 1 && rounding
!= 1)
2884 if (ilim
>= 0 && ilim
<= Quick_max
&& try_quick
) {
2886 /* Try to get by with floating-point arithmetic. */
2892 ieps
= 2; /* conservative */
2897 /* prevent overflows */
2899 dval(d
) /= bigtens
[n_bigtens
-1];
2902 for(; j
; j
>>= 1, i
++)
2909 else if ((j1
= -k
)) {
2910 dval(d
) *= tens
[j1
& 0xf];
2911 for(j
= j1
>> 4; j
; j
>>= 1, i
++)
2914 dval(d
) *= bigtens
[i
];
2917 if (k_check
&& dval(d
) < 1. && ilim
> 0) {
2925 dval(eps
) = ieps
*dval(d
) + 7.;
2926 word0(eps
) -= (P
-1)*Exp_msk1
;
2930 if (dval(d
) > dval(eps
))
2932 if (dval(d
) < -dval(eps
))
2936 #ifndef No_leftright
2938 /* Use Steele & White method of only
2939 * generating digits needed.
2941 dval(eps
) = 0.5/tens
[ilim
-1] - dval(eps
);
2943 L
= (ULong
) dval(d
);
2945 *s
++ = '0' + (int)L
;
2946 if (dval(d
) < dval(eps
))
2948 if (1. - dval(d
) < dval(eps
))
2958 /* Generate ilim digits, then fix them up. */
2959 dval(eps
) *= tens
[ilim
-1];
2960 for(i
= 1;; i
++, dval(d
) *= 10.) {
2961 L
= (Long
)(dval(d
));
2962 if (!(dval(d
) -= L
))
2964 *s
++ = '0' + (int)L
;
2966 if (dval(d
) > 0.5 + dval(eps
))
2968 else if (dval(d
) < 0.5 - dval(eps
)) {
2976 #ifndef No_leftright
2986 /* Do we have a "small" integer? */
2988 if (be
>= 0 && k
<= Int_max
) {
2991 if (ndigits
< 0 && ilim
<= 0) {
2993 if (ilim
< 0 || dval(d
) < 5*ds
)
2997 for(i
= 1;; i
++, dval(d
) *= 10.) {
2998 L
= (Long
)(dval(d
) / ds
);
3000 #ifdef Check_FLT_ROUNDS
3001 /* If FLT_ROUNDS == 2, L will usually be high by 1 */
3007 *s
++ = '0' + (int)L
;
3015 #ifdef Honor_FLT_ROUNDS
3019 case 2: goto bump_up
;
3023 if (dval(d
) > ds
|| (dval(d
) == ds
&& L
& 1)) {
3044 #ifndef Sudden_Underflow
3045 denorm
? be
+ (Bias
+ (P
-1) - 1 + 1) :
3048 1 + 4*P
- 3 - bbits
+ ((bbits
+ be
- 1) & 3);
3056 if (m2
> 0 && s2
> 0) {
3057 i
= m2
< s2
? m2
: s2
;
3065 mhi
= pow5mult(mhi
, m5
);
3074 b
= pow5mult(b
, b5
);
3078 S
= pow5mult(S
, s5
);
3080 /* Check for special case that d is a normalized power of 2. */
3083 if ((mode
< 2 || leftright
)
3084 #ifdef Honor_FLT_ROUNDS
3088 if (!word1(d
) && !(word0(d
) & Bndry_mask
)
3089 #ifndef Sudden_Underflow
3090 && word0(d
) & (Exp_mask
& ~Exp_msk1
)
3093 /* The special case */
3100 /* Arrange for convenient computation of quotients:
3101 * shift left if necessary so divisor has 4 leading 0 bits.
3103 * Perhaps we should just compute leading 28 bits of S once
3104 * and for all and pass them and a shift to quorem, so it
3105 * can do shifts and ors to compute the numerator for q.
3108 if ((i
= ((s5
? 32 - hi0bits(S
->x
[S
->wds
-1]) : 1) + s2
) & 0x1f))
3111 if (i
= ((s5
? 32 - hi0bits(S
->x
[S
->wds
-1]) : 1) + s2
) & 0xf)
3133 b
= multadd(b
, 10, 0); /* we botched the k estimate */
3135 mhi
= multadd(mhi
, 10, 0);
3139 if (ilim
<= 0 && (mode
== 3 || mode
== 5)) {
3140 if (ilim
< 0 || cmp(b
,S
= multadd(S
,5,0)) < 0) {
3141 /* no digits, fcvt style */
3143 /* MOZILLA CHANGE: Always return a non-empty string. */
3155 mhi
= lshift(mhi
, m2
);
3157 /* Compute mlo -- check for special case
3158 * that d is a normalized power of 2.
3163 mhi
= Balloc(mhi
->k
);
3165 mhi
= lshift(mhi
, Log2P
);
3169 dig
= quorem(b
,S
) + '0';
3170 /* Do we yet have the shortest decimal string
3171 * that will round to d?
3174 delta
= diff(S
, mhi
);
3175 j1
= delta
->sign
? 1 : cmp(b
, delta
);
3177 #ifndef ROUND_BIASED
3178 if (j1
== 0 && mode
!= 1 && !(word1(d
) & 1)
3179 #ifdef Honor_FLT_ROUNDS
3188 else if (!b
->x
[0] && b
->wds
<= 1)
3195 if (j
< 0 || (j
== 0 && mode
!= 1
3196 #ifndef ROUND_BIASED
3200 if (!b
->x
[0] && b
->wds
<= 1) {
3206 #ifdef Honor_FLT_ROUNDS
3209 case 0: goto accept_dig
;
3210 case 2: goto keep_dig
;
3212 #endif /*Honor_FLT_ROUNDS*/
3216 if ((j1
> 0 || (j1
== 0 && dig
& 1))
3225 #ifdef Honor_FLT_ROUNDS
3229 if (dig
== '9') { /* possible if i == 1 */
3237 #ifdef Honor_FLT_ROUNDS
3243 b
= multadd(b
, 10, 0);
3245 mlo
= mhi
= multadd(mhi
, 10, 0);
3247 mlo
= multadd(mlo
, 10, 0);
3248 mhi
= multadd(mhi
, 10, 0);
3254 *s
++ = dig
= quorem(b
,S
) + '0';
3255 if (!b
->x
[0] && b
->wds
<= 1) {
3263 b
= multadd(b
, 10, 0);
3266 /* Round off last digit */
3268 #ifdef Honor_FLT_ROUNDS
3270 case 0: goto trimzeros
;
3271 case 2: goto roundoff
;
3276 if (j
>= 0) { /* ECMA compatible rounding needed by Spidermonkey */
3287 #ifdef Honor_FLT_ROUNDS
3296 if (mlo
&& mlo
!= mhi
)
3304 word0(d
) = Exp_1
+ (70 << Exp_shift
);
3309 else if (!oldinexact
)