1 /****************************************************************
3 The author of this software is David M. Gay.
5 Copyright (C) 1998-2000 by Lucent Technologies
8 Permission to use, copy, modify, and distribute this software and
9 its documentation for any purpose and without fee is hereby
10 granted, provided that the above copyright notice appear in all
11 copies and that both that the copyright notice and this
12 permission notice and warranty disclaimer appear in supporting
13 documentation, and that the name of Lucent or any of its entities
14 not be used in advertising or publicity pertaining to
15 distribution of the software without specific, written prior
18 LUCENT DISCLAIMS ALL WARRANTIES WITH REGARD TO THIS SOFTWARE,
19 INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS.
20 IN NO EVENT SHALL LUCENT OR ANY OF ITS ENTITIES BE LIABLE FOR ANY
21 SPECIAL, INDIRECT OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
22 WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER
23 IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION,
24 ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF
27 ****************************************************************/
29 /* This is a variation on dtoa.c that converts arbitary binary
30 floating-point formats to and from decimal notation. It uses
31 double-precision arithmetic internally, so there are still
32 various #ifdefs that adapt the calculations to the native
33 double-precision arithmetic (any of IEEE, VAX D_floating,
34 or IBM mainframe arithmetic).
36 Please send bug reports to David M. Gay (dmg at acm dot org,
37 with " at " changed at "@" and " dot " changed to ".").
40 /* On a machine with IEEE extended-precision registers, it is
41 * necessary to specify double-precision (53-bit) rounding precision
42 * before invoking strtod or dtoa. If the machine uses (the equivalent
43 * of) Intel 80x87 arithmetic, the call
44 * _control87(PC_53, MCW_PC);
45 * does this with many compilers. Whether this or another call is
46 * appropriate depends on the compiler; for this to work, it may be
47 * necessary to #include "float.h" or another system-dependent header
51 /* strtod for IEEE-, VAX-, and IBM-arithmetic machines.
53 * This strtod returns a nearest machine number to the input decimal
54 * string (or sets errno to ERANGE). With IEEE arithmetic, ties are
55 * broken by the IEEE round-even rule. Otherwise ties are broken by
56 * biased rounding (add half and chop).
58 * Inspired loosely by William D. Clinger's paper "How to Read Floating
59 * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 112-126].
63 * 1. We only require IEEE, IBM, or VAX double-precision
64 * arithmetic (not IEEE double-extended).
65 * 2. We get by with floating-point arithmetic in a case that
66 * Clinger missed -- when we're computing d * 10^n
67 * for a small integer d and the integer n is not too
68 * much larger than 22 (the maximum integer k for which
69 * we can represent 10^k exactly), we may be able to
70 * compute (d*10^k) * 10^(e-k) with just one roundoff.
71 * 3. Rather than a bit-at-a-time adjustment of the binary
72 * result in the hard case, we use floating-point
73 * arithmetic to determine the adjustment to within
74 * one bit; only in really hard cases do we need to
75 * compute a second residual.
76 * 4. Because of 3., we don't need a large table of powers of 10
77 * for ten-to-e (just some small tables, e.g. of 10^k
82 * #define IEEE_8087 for IEEE-arithmetic machines where the least
83 * significant byte has the lowest address.
84 * #define IEEE_MC68k for IEEE-arithmetic machines where the most
85 * significant byte has the lowest address.
86 * #define Long int on machines with 32-bit ints and 64-bit longs.
87 * #define Sudden_Underflow for IEEE-format machines without gradual
88 * underflow (i.e., that flush to zero on underflow).
89 * #define IBM for IBM mainframe-style floating-point arithmetic.
90 * #define VAX for VAX-style floating-point arithmetic (D_floating).
91 * #define No_leftright to omit left-right logic in fast floating-point
92 * computation of dtoa.
93 * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3.
94 * #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines
95 * that use extended-precision instructions to compute rounded
96 * products and quotients) with IBM.
97 * #define ROUND_BIASED for IEEE-format with biased rounding.
98 * #define Inaccurate_Divide for IEEE-format with correctly rounded
99 * products but inaccurate quotients, e.g., for Intel i860.
100 * #define NO_LONG_LONG on machines that do not have a "long long"
101 * integer type (of >= 64 bits). On such machines, you can
102 * #define Just_16 to store 16 bits per 32-bit Long when doing
103 * high-precision integer arithmetic. Whether this speeds things
104 * up or slows things down depends on the machine and the number
105 * being converted. If long long is available and the name is
106 * something other than "long long", #define Llong to be the name,
107 * and if "unsigned Llong" does not work as an unsigned version of
108 * Llong, #define #ULLong to be the corresponding unsigned type.
109 * #define KR_headers for old-style C function headers.
110 * #define Bad_float_h if your system lacks a float.h or if it does not
111 * define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP,
112 * FLT_RADIX, FLT_ROUNDS, and DBL_MAX.
113 * #define MALLOC your_malloc, where your_malloc(n) acts like malloc(n)
114 * if memory is available and otherwise does something you deem
115 * appropriate. If MALLOC is undefined, malloc will be invoked
116 * directly -- and assumed always to succeed. Similarly, if you
117 * want something other than the system's free() to be called to
118 * recycle memory acquired from MALLOC, #define FREE to be the
119 * name of the alternate routine. (FREE or free is only called in
120 * pathological cases, e.g., in a gdtoa call after a gdtoa return in
121 * mode 3 with thousands of digits requested.)
122 * #define Omit_Private_Memory to omit logic (added Jan. 1998) for making
123 * memory allocations from a private pool of memory when possible.
124 * When used, the private pool is PRIVATE_MEM bytes long: 2304 bytes,
125 * unless #defined to be a different length. This default length
126 * suffices to get rid of MALLOC calls except for unusual cases,
127 * such as decimal-to-binary conversion of a very long string of
128 * digits. When converting IEEE double precision values, the
129 * longest string gdtoa can return is about 751 bytes long. For
130 * conversions by strtod of strings of 800 digits and all gdtoa
131 * conversions of IEEE doubles in single-threaded executions with
132 * 8-byte pointers, PRIVATE_MEM >= 7400 appears to suffice; with
133 * 4-byte pointers, PRIVATE_MEM >= 7112 appears adequate.
134 * #define NO_INFNAN_CHECK if you do not wish to have INFNAN_CHECK
135 * #defined automatically on IEEE systems. On such systems,
136 * when INFNAN_CHECK is #defined, strtod checks
137 * for Infinity and NaN (case insensitively).
138 * When INFNAN_CHECK is #defined and No_Hex_NaN is not #defined,
139 * strtodg also accepts (case insensitively) strings of the form
140 * NaN(x), where x is a string of hexadecimal digits (optionally
141 * preceded by 0x or 0X) and spaces; if there is only one string
142 * of hexadecimal digits, it is taken for the fraction bits of the
143 * resulting NaN; if there are two or more strings of hexadecimal
144 * digits, each string is assigned to the next available sequence
145 * of 32-bit words of fractions bits (starting with the most
146 * significant), right-aligned in each sequence.
147 * Unless GDTOA_NON_PEDANTIC_NANCHECK is #defined, input "NaN(...)"
148 * is consumed even when ... has the wrong form (in which case the
149 * "(...)" is consumed but ignored).
150 * #define MULTIPLE_THREADS if the system offers preemptively scheduled
151 * multiple threads. In this case, you must provide (or suitably
152 * #define) two locks, acquired by ACQUIRE_DTOA_LOCK(n) and freed
153 * by FREE_DTOA_LOCK(n) for n = 0 or 1. (The second lock, accessed
154 * in pow5mult, ensures lazy evaluation of only one copy of high
155 * powers of 5; omitting this lock would introduce a small
156 * probability of wasting memory, but would otherwise be harmless.)
157 * You must also invoke freedtoa(s) to free the value s returned by
158 * dtoa. You may do so whether or not MULTIPLE_THREADS is #defined.
159 * #define IMPRECISE_INEXACT if you do not care about the setting of
160 * the STRTOG_Inexact bits in the special case of doing IEEE double
161 * precision conversions (which could also be done by the strtod in
163 * #define NO_HEX_FP to disable recognition of C9x's hexadecimal
164 * floating-point constants.
165 * #define -DNO_ERRNO to suppress setting errno (in strtod.c and
167 * #define NO_STRING_H to use private versions of memcpy.
168 * On some K&R systems, it may also be necessary to
169 * #define DECLARE_SIZE_T in this case.
170 * #define USE_LOCALE to use the current locale's decimal_point value.
173 #ifndef GDTOAIMP_H_INCLUDED
174 #define GDTOAIMP_H_INCLUDED
179 #define Honor_FLT_ROUNDS
183 #ifdef Honor_FLT_ROUNDS
189 #define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}
195 #include "libc_private.h"
197 #include "namespace.h"
199 #include "un-namespace.h"
208 extern Char *MALLOC ANSI((size_t));
210 #define MALLOC malloc
214 #undef Avoid_Underflow
227 #define DBL_MAX_10_EXP 308
228 #define DBL_MAX_EXP 1024
230 #define DBL_MAX 1.7976931348623157e+308
235 #define DBL_MAX_10_EXP 75
236 #define DBL_MAX_EXP 63
238 #define DBL_MAX 7.2370055773322621e+75
243 #define DBL_MAX_10_EXP 38
244 #define DBL_MAX_EXP 127
246 #define DBL_MAX 1.7014118346046923e+38
251 #define LONG_MAX 2147483647
254 #else /* ifndef Bad_float_h */
256 #endif /* Bad_float_h */
259 #define Scale_Bit 0x10
279 #if defined(IEEE_8087) + defined(IEEE_MC68k) + defined(VAX) + defined(IBM) != 1
280 Exactly one of IEEE_8087, IEEE_MC68k, VAX, or IBM should be defined.
283 typedef union { double d; ULong L[2]; } U;
286 #define word0(x) (x)->L[1]
287 #define word1(x) (x)->L[0]
289 #define word0(x) (x)->L[0]
290 #define word1(x) (x)->L[1]
292 #define dval(x) (x)->d
294 /* The following definition of Storeinc is appropriate for MIPS processors.
295 * An alternative that might be better on some machines is
296 * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
298 #if defined(IEEE_8087) + defined(VAX)
299 #define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \
300 ((unsigned short *)a)[0] = (unsigned short)c, a++)
302 #define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \
303 ((unsigned short *)a)[1] = (unsigned short)c, a++)
306 /* #define P DBL_MANT_DIG */
307 /* Ten_pmax = floor(P*log(2)/log(5)) */
308 /* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
309 /* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
310 /* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
314 #define Exp_shift1 20
315 #define Exp_msk1 0x100000
316 #define Exp_msk11 0x100000
317 #define Exp_mask 0x7ff00000
321 #define Exp_1 0x3ff00000
322 #define Exp_11 0x3ff00000
324 #define Frac_mask 0xfffff
325 #define Frac_mask1 0xfffff
328 #define Bndry_mask 0xfffff
329 #define Bndry_mask1 0xfffff
331 #define Sign_bit 0x80000000
340 #define Flt_Rounds FLT_ROUNDS
344 #endif /*Flt_Rounds*/
346 #else /* ifndef IEEE_Arith */
347 #undef Sudden_Underflow
348 #define Sudden_Underflow
353 #define Exp_shift1 24
354 #define Exp_msk1 0x1000000
355 #define Exp_msk11 0x1000000
356 #define Exp_mask 0x7f000000
359 #define Exp_1 0x41000000
360 #define Exp_11 0x41000000
361 #define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */
362 #define Frac_mask 0xffffff
363 #define Frac_mask1 0xffffff
366 #define Bndry_mask 0xefffff
367 #define Bndry_mask1 0xffffff
369 #define Sign_bit 0x80000000
371 #define Tiny0 0x100000
380 #define Exp_msk1 0x80
381 #define Exp_msk11 0x800000
382 #define Exp_mask 0x7f80
385 #define Exp_1 0x40800000
386 #define Exp_11 0x4080
388 #define Frac_mask 0x7fffff
389 #define Frac_mask1 0xffff007f
392 #define Bndry_mask 0xffff007f
393 #define Bndry_mask1 0xffff007f
395 #define Sign_bit 0x8000
401 #endif /* IBM, VAX */
402 #endif /* IEEE_Arith */
409 #define rounded_product(a,b) a = rnd_prod(a, b)
410 #define rounded_quotient(a,b) a = rnd_quot(a, b)
412 extern double rnd_prod(), rnd_quot();
414 extern double rnd_prod(double, double), rnd_quot(double, double);
417 #define rounded_product(a,b) a *= b
418 #define rounded_quotient(a,b) a /= b
421 #define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
422 #define Big1 0xffffffff
434 /* When Pack_32 is not defined, we store 16 bits per 32-bit Long.
435 * This makes some inner loops simpler and sometimes saves work
436 * during multiplications, but it often seems to make things slightly
437 * slower. Hence the default is now to store 32 bits per Long.
440 #else /* long long available */
442 #define Llong long long
445 #define ULLong unsigned Llong
447 #endif /* NO_LONG_LONG */
453 #define ALL_ON 0xffffffff
458 #define ALL_ON 0xffff
461 #define MULTIPLE_THREADS
462 extern pthread_mutex_t __gdtoa_locks[2];
463 #define ACQUIRE_DTOA_LOCK(n) do { \
465 _pthread_mutex_lock(&__gdtoa_locks[n]); \
467 #define FREE_DTOA_LOCK(n) do { \
469 _pthread_mutex_unlock(&__gdtoa_locks[n]); \
477 int k, maxwds, sign, wds;
481 typedef struct Bigint Bigint;
484 #ifdef DECLARE_SIZE_T
485 typedef unsigned int size_t;
487 extern void memcpy_D2A ANSI((void*, const void*, size_t));
488 #define Bcopy(x,y) memcpy_D2A(&x->sign,&y->sign,y->wds*sizeof(ULong) + 2*sizeof(int))
489 #else /* !NO_STRING_H */
490 #define Bcopy(x,y) memcpy(&x->sign,&y->sign,y->wds*sizeof(ULong) + 2*sizeof(int))
491 #endif /* NO_STRING_H */
494 * Paranoia: Protect exported symbols, including ones in files we don't
495 * compile right now. The standard strtof and strtod survive.
498 #define gdtoa __gdtoa
499 #define freedtoa __freedtoa
500 #define strtodg __strtodg
501 #define g_ddfmt __g_ddfmt
502 #define g_dfmt __g_dfmt
503 #define g_ffmt __g_ffmt
504 #define g_Qfmt __g_Qfmt
505 #define g_xfmt __g_xfmt
506 #define g_xLfmt __g_xLfmt
507 #define strtoId __strtoId
508 #define strtoIdd __strtoIdd
509 #define strtoIf __strtoIf
510 #define strtoIQ __strtoIQ
511 #define strtoIx __strtoIx
512 #define strtoIxL __strtoIxL
513 #define strtord __strtord
514 #define strtordd __strtordd
515 #define strtorf __strtorf
516 #define strtorQ __strtorQ
517 #define strtorx __strtorx
518 #define strtorxL __strtorxL
519 #define strtodI __strtodI
520 #define strtopd __strtopd
521 #define strtopdd __strtopdd
522 #define strtopf __strtopf
523 #define strtopQ __strtopQ
524 #define strtopx __strtopx
525 #define strtopxL __strtopxL
527 /* Protect gdtoa-internal symbols */
528 #define Balloc __Balloc_D2A
529 #define Bfree __Bfree_D2A
530 #define ULtoQ __ULtoQ_D2A
531 #define ULtof __ULtof_D2A
532 #define ULtod __ULtod_D2A
533 #define ULtodd __ULtodd_D2A
534 #define ULtox __ULtox_D2A
535 #define ULtoxL __ULtoxL_D2A
536 #define any_on __any_on_D2A
537 #define b2d __b2d_D2A
538 #define bigtens __bigtens_D2A
539 #define cmp __cmp_D2A
540 #define copybits __copybits_D2A
541 #define d2b __d2b_D2A
542 #define decrement __decrement_D2A
543 #define diff __diff_D2A
544 #define dtoa_result __dtoa_result_D2A
545 #define g__fmt __g__fmt_D2A
546 #define gethex __gethex_D2A
547 #define hexdig __hexdig_D2A
548 #define hexdig_init_D2A __hexdig_init_D2A
549 #define hexnan __hexnan_D2A
550 #define hi0bits(x) __hi0bits_D2A((ULong)(x))
551 #define hi0bits_D2A __hi0bits_D2A
552 #define i2b __i2b_D2A
553 #define increment __increment_D2A
554 #define lo0bits __lo0bits_D2A
555 #define lshift __lshift_D2A
556 #define match __match_D2A
557 #define mult __mult_D2A
558 #define multadd __multadd_D2A
559 #define nrv_alloc __nrv_alloc_D2A
560 #define pow5mult __pow5mult_D2A
561 #define quorem __quorem_D2A
562 #define ratio __ratio_D2A
563 #define rshift __rshift_D2A
564 #define rv_alloc __rv_alloc_D2A
565 #define s2b __s2b_D2A
566 #define set_ones __set_ones_D2A
567 #define strcp __strcp_D2A
568 #define strcp_D2A __strcp_D2A
569 #define strtoIg __strtoIg_D2A
570 #define sum __sum_D2A
571 #define tens __tens_D2A
572 #define tinytens __tinytens_D2A
573 #define tinytens __tinytens_D2A
574 #define trailz __trailz_D2A
575 #define ulp __ulp_D2A
577 extern char *dtoa_result;
578 extern CONST double bigtens[], tens[], tinytens[];
579 extern unsigned char hexdig[];
581 extern Bigint *Balloc ANSI((int));
582 extern void Bfree ANSI((Bigint*));
583 extern void ULtof ANSI((ULong*, ULong*, Long, int));
584 extern void ULtod ANSI((ULong*, ULong*, Long, int));
585 extern void ULtodd ANSI((ULong*, ULong*, Long, int));
586 extern void ULtoQ ANSI((ULong*, ULong*, Long, int));
587 extern void ULtox ANSI((UShort*, ULong*, Long, int));
588 extern void ULtoxL ANSI((ULong*, ULong*, Long, int));
589 extern ULong any_on ANSI((Bigint*, int));
590 extern double b2d ANSI((Bigint*, int*));
591 extern int cmp ANSI((Bigint*, Bigint*));
592 extern void copybits ANSI((ULong*, int, Bigint*));
593 extern Bigint *d2b ANSI((double, int*, int*));
594 extern void decrement ANSI((Bigint*));
595 extern Bigint *diff ANSI((Bigint*, Bigint*));
596 extern char *dtoa ANSI((double d, int mode, int ndigits,
597 int *decpt, int *sign, char **rve));
598 extern void freedtoa ANSI((char*));
599 extern char *g__fmt ANSI((char*, char*, char*, int, ULong, size_t));
600 extern char *gdtoa ANSI((FPI *fpi, int be, ULong *bits, int *kindp,
601 int mode, int ndigits, int *decpt, char **rve));
602 extern int gethex ANSI((CONST char**, FPI*, Long*, Bigint**, int));
603 extern void hexdig_init_D2A(Void);
604 extern int hexnan ANSI((CONST char**, FPI*, ULong*));
605 extern int hi0bits_D2A ANSI((ULong));
606 extern Bigint *i2b ANSI((int));
607 extern Bigint *increment ANSI((Bigint*));
608 extern int lo0bits ANSI((ULong*));
609 extern Bigint *lshift ANSI((Bigint*, int));
610 extern int match ANSI((CONST char**, char*));
611 extern Bigint *mult ANSI((Bigint*, Bigint*));
612 extern Bigint *multadd ANSI((Bigint*, int, int));
613 extern char *nrv_alloc ANSI((char*, char **, int));
614 extern Bigint *pow5mult ANSI((Bigint*, int));
615 extern int quorem ANSI((Bigint*, Bigint*));
616 extern double ratio ANSI((Bigint*, Bigint*));
617 extern void rshift ANSI((Bigint*, int));
618 extern char *rv_alloc ANSI((int));
619 extern Bigint *s2b ANSI((CONST char*, int, int, ULong, int));
620 extern Bigint *set_ones ANSI((Bigint*, int));
621 extern char *strcp ANSI((char*, const char*));
622 extern int strtodg ANSI((CONST char*, char**, FPI*, Long*, ULong*));
624 extern int strtoId ANSI((CONST char *, char **, double *, double *));
625 extern int strtoIdd ANSI((CONST char *, char **, double *, double *));
626 extern int strtoIf ANSI((CONST char *, char **, float *, float *));
627 extern int strtoIg ANSI((CONST char*, char**, FPI*, Long*, Bigint**, int*));
628 extern int strtoIQ ANSI((CONST char *, char **, void *, void *));
629 extern int strtoIx ANSI((CONST char *, char **, void *, void *));
630 extern int strtoIxL ANSI((CONST char *, char **, void *, void *));
631 extern double strtod ANSI((const char *s00, char **se));
632 extern int strtopQ ANSI((CONST char *, char **, Void *));
633 extern int strtopf ANSI((CONST char *, char **, float *));
634 extern int strtopd ANSI((CONST char *, char **, double *));
635 extern int strtopdd ANSI((CONST char *, char **, double *));
636 extern int strtopx ANSI((CONST char *, char **, Void *));
637 extern int strtopxL ANSI((CONST char *, char **, Void *));
638 extern int strtord ANSI((CONST char *, char **, int, double *));
639 extern int strtordd ANSI((CONST char *, char **, int, double *));
640 extern int strtorf ANSI((CONST char *, char **, int, float *));
641 extern int strtorQ ANSI((CONST char *, char **, int, void *));
642 extern int strtorx ANSI((CONST char *, char **, int, void *));
643 extern int strtorxL ANSI((CONST char *, char **, int, void *));
644 extern Bigint *sum ANSI((Bigint*, Bigint*));
645 extern int trailz ANSI((Bigint*));
646 extern double ulp ANSI((U*));
652 * NAN_WORD0 and NAN_WORD1 are only referenced in strtod.c. Prior to
653 * 20050115, they used to be hard-wired here (to 0x7ff80000 and 0,
654 * respectively), but now are determined by compiling and running
655 * qnan.c to generate gd_qnan.h, which specifies d_QNAN0 and d_QNAN1.
656 * Formerly gdtoaimp.h recommended supplying suitable -DNAN_WORD0=...
657 * and -DNAN_WORD1=... values if necessary. This should still work.
658 * (On HP Series 700/800 machines, -DNAN_WORD0=0x7ff40000 works.)
661 #ifndef NO_INFNAN_CHECK
669 #define NAN_WORD0 d_QNAN0
672 #define NAN_WORD1 d_QNAN1
678 #define NAN_WORD0 d_QNAN1
681 #define NAN_WORD1 d_QNAN0
689 #ifdef Sudden_Underflow
695 #endif /* GDTOAIMP_H_INCLUDED */