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 and gdtoa. This will cause modes 4 and 5 to be
93 * treated the same as modes 2 and 3 for some inputs.
94 * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3.
95 * #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines
96 * that use extended-precision instructions to compute rounded
97 * products and quotients) with IBM.
98 * #define ROUND_BIASED for IEEE-format with biased rounding and arithmetic
99 * that rounds toward +Infinity.
100 * #define ROUND_BIASED_without_Round_Up for IEEE-format with biased
101 * rounding when the underlying floating-point arithmetic uses
102 * unbiased rounding. This prevent using ordinary floating-point
103 * arithmetic when the result could be computed with one rounding error.
104 * #define Inaccurate_Divide for IEEE-format with correctly rounded
105 * products but inaccurate quotients, e.g., for Intel i860.
106 * #define NO_LONG_LONG on machines that do not have a "long long"
107 * integer type (of >= 64 bits). On such machines, you can
108 * #define Just_16 to store 16 bits per 32-bit Long when doing
109 * high-precision integer arithmetic. Whether this speeds things
110 * up or slows things down depends on the machine and the number
111 * being converted. If long long is available and the name is
112 * something other than "long long", #define Llong to be the name,
113 * and if "unsigned Llong" does not work as an unsigned version of
114 * Llong, #define #ULLong to be the corresponding unsigned type.
115 * #define KR_headers for old-style C function headers.
116 * #define Bad_float_h if your system lacks a float.h or if it does not
117 * define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP,
118 * FLT_RADIX, FLT_ROUNDS, and DBL_MAX.
119 * #define MALLOC your_malloc, where your_malloc(n) acts like malloc(n)
120 * if memory is available and otherwise does something you deem
121 * appropriate. If MALLOC is undefined, malloc will be invoked
122 * directly -- and assumed always to succeed. Similarly, if you
123 * want something other than the system's free() to be called to
124 * recycle memory acquired from MALLOC, #define FREE to be the
125 * name of the alternate routine. (FREE or free is only called in
126 * pathological cases, e.g., in a gdtoa call after a gdtoa return in
127 * mode 3 with thousands of digits requested.)
128 * #define Omit_Private_Memory to omit logic (added Jan. 1998) for making
129 * memory allocations from a private pool of memory when possible.
130 * When used, the private pool is PRIVATE_MEM bytes long: 2304 bytes,
131 * unless #defined to be a different length. This default length
132 * suffices to get rid of MALLOC calls except for unusual cases,
133 * such as decimal-to-binary conversion of a very long string of
134 * digits. When converting IEEE double precision values, the
135 * longest string gdtoa can return is about 751 bytes long. For
136 * conversions by strtod of strings of 800 digits and all gdtoa
137 * conversions of IEEE doubles in single-threaded executions with
138 * 8-byte pointers, PRIVATE_MEM >= 7400 appears to suffice; with
139 * 4-byte pointers, PRIVATE_MEM >= 7112 appears adequate.
140 * #define NO_INFNAN_CHECK if you do not wish to have INFNAN_CHECK
141 * #defined automatically on IEEE systems. On such systems,
142 * when INFNAN_CHECK is #defined, strtod checks
143 * for Infinity and NaN (case insensitively).
144 * When INFNAN_CHECK is #defined and No_Hex_NaN is not #defined,
145 * strtodg also accepts (case insensitively) strings of the form
146 * NaN(x), where x is a string of hexadecimal digits (optionally
147 * preceded by 0x or 0X) and spaces; if there is only one string
148 * of hexadecimal digits, it is taken for the fraction bits of the
149 * resulting NaN; if there are two or more strings of hexadecimal
150 * digits, each string is assigned to the next available sequence
151 * of 32-bit words of fractions bits (starting with the most
152 * significant), right-aligned in each sequence.
153 * Unless GDTOA_NON_PEDANTIC_NANCHECK is #defined, input "NaN(...)"
154 * is consumed even when ... has the wrong form (in which case the
155 * "(...)" is consumed but ignored).
156 * #define MULTIPLE_THREADS if the system offers preemptively scheduled
157 * multiple threads. In this case, you must provide (or suitably
158 * #define) two locks, acquired by ACQUIRE_DTOA_LOCK(n) and freed
159 * by FREE_DTOA_LOCK(n) for n = 0 or 1. (The second lock, accessed
160 * in pow5mult, ensures lazy evaluation of only one copy of high
161 * powers of 5; omitting this lock would introduce a small
162 * probability of wasting memory, but would otherwise be harmless.)
163 * You must also invoke freedtoa(s) to free the value s returned by
164 * dtoa. You may do so whether or not MULTIPLE_THREADS is #defined.
165 * #define IMPRECISE_INEXACT if you do not care about the setting of
166 * the STRTOG_Inexact bits in the special case of doing IEEE double
167 * precision conversions (which could also be done by the strtod in
169 * #define NO_HEX_FP to disable recognition of C9x's hexadecimal
170 * floating-point constants.
171 * #define -DNO_ERRNO to suppress setting errno (in strtod.c and
173 * #define NO_STRING_H to use private versions of memcpy.
174 * On some K&R systems, it may also be necessary to
175 * #define DECLARE_SIZE_T in this case.
176 * #define USE_LOCALE to use the current locale's decimal_point value.
179 #ifndef GDTOAIMP_H_INCLUDED
180 #define GDTOAIMP_H_INCLUDED
183 #define Honor_FLT_ROUNDS
187 #ifdef Honor_FLT_ROUNDS
193 #define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}
199 #include "libc_private.h"
201 #include "namespace.h"
203 #include "un-namespace.h"
212 extern Char *MALLOC ANSI((size_t));
214 #define MALLOC malloc
218 #undef Avoid_Underflow
231 #define DBL_MAX_10_EXP 308
232 #define DBL_MAX_EXP 1024
234 #define DBL_MAX 1.7976931348623157e+308
239 #define DBL_MAX_10_EXP 75
240 #define DBL_MAX_EXP 63
242 #define DBL_MAX 7.2370055773322621e+75
247 #define DBL_MAX_10_EXP 38
248 #define DBL_MAX_EXP 127
250 #define DBL_MAX 1.7014118346046923e+38
255 #define LONG_MAX 2147483647
258 #else /* ifndef Bad_float_h */
260 #endif /* Bad_float_h */
263 #define Scale_Bit 0x10
283 #if defined(IEEE_8087) + defined(IEEE_MC68k) + defined(VAX) + defined(IBM) != 1
284 Exactly one of IEEE_8087, IEEE_MC68k, VAX, or IBM should be defined.
287 typedef union { double d; ULong L[2]; } U;
290 #define word0(x) (x)->L[1]
291 #define word1(x) (x)->L[0]
293 #define word0(x) (x)->L[0]
294 #define word1(x) (x)->L[1]
296 #define dval(x) (x)->d
298 /* The following definition of Storeinc is appropriate for MIPS processors.
299 * An alternative that might be better on some machines is
300 * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
302 #if defined(IEEE_8087) + defined(VAX)
303 #define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \
304 ((unsigned short *)a)[0] = (unsigned short)c, a++)
306 #define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \
307 ((unsigned short *)a)[1] = (unsigned short)c, a++)
310 /* #define P DBL_MANT_DIG */
311 /* Ten_pmax = floor(P*log(2)/log(5)) */
312 /* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
313 /* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
314 /* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
318 #define Exp_shift1 20
319 #define Exp_msk1 0x100000
320 #define Exp_msk11 0x100000
321 #define Exp_mask 0x7ff00000
325 #define Exp_1 0x3ff00000
326 #define Exp_11 0x3ff00000
328 #define Frac_mask 0xfffff
329 #define Frac_mask1 0xfffff
332 #define Bndry_mask 0xfffff
333 #define Bndry_mask1 0xfffff
335 #define Sign_bit 0x80000000
344 #define Flt_Rounds FLT_ROUNDS
348 #endif /*Flt_Rounds*/
350 #else /* ifndef IEEE_Arith */
351 #undef Sudden_Underflow
352 #define Sudden_Underflow
357 #define Exp_shift1 24
358 #define Exp_msk1 0x1000000
359 #define Exp_msk11 0x1000000
360 #define Exp_mask 0x7f000000
363 #define Exp_1 0x41000000
364 #define Exp_11 0x41000000
365 #define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */
366 #define Frac_mask 0xffffff
367 #define Frac_mask1 0xffffff
370 #define Bndry_mask 0xefffff
371 #define Bndry_mask1 0xffffff
373 #define Sign_bit 0x80000000
375 #define Tiny0 0x100000
384 #define Exp_msk1 0x80
385 #define Exp_msk11 0x800000
386 #define Exp_mask 0x7f80
389 #define Exp_1 0x40800000
390 #define Exp_11 0x4080
392 #define Frac_mask 0x7fffff
393 #define Frac_mask1 0xffff007f
396 #define Bndry_mask 0xffff007f
397 #define Bndry_mask1 0xffff007f
399 #define Sign_bit 0x8000
405 #endif /* IBM, VAX */
406 #endif /* IEEE_Arith */
411 #ifdef ROUND_BIASED_without_Round_Up
418 #define rounded_product(a,b) a = rnd_prod(a, b)
419 #define rounded_quotient(a,b) a = rnd_quot(a, b)
421 extern double rnd_prod(), rnd_quot();
423 extern double rnd_prod(double, double), rnd_quot(double, double);
426 #define rounded_product(a,b) a *= b
427 #define rounded_quotient(a,b) a /= b
430 #define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
431 #define Big1 0xffffffff
443 /* When Pack_32 is not defined, we store 16 bits per 32-bit Long.
444 * This makes some inner loops simpler and sometimes saves work
445 * during multiplications, but it often seems to make things slightly
446 * slower. Hence the default is now to store 32 bits per Long.
449 #else /* long long available */
451 #define Llong long long
454 #define ULLong unsigned Llong
456 #endif /* NO_LONG_LONG */
462 #define ALL_ON 0xffffffff
467 #define ALL_ON 0xffff
470 #define MULTIPLE_THREADS
471 extern pthread_mutex_t __gdtoa_locks[2];
472 #define ACQUIRE_DTOA_LOCK(n) do { \
474 _pthread_mutex_lock(&__gdtoa_locks[n]); \
476 #define FREE_DTOA_LOCK(n) do { \
478 _pthread_mutex_unlock(&__gdtoa_locks[n]); \
486 int k, maxwds, sign, wds;
490 typedef struct Bigint Bigint;
493 #ifdef DECLARE_SIZE_T
494 typedef unsigned int size_t;
496 extern void memcpy_D2A ANSI((void*, const void*, size_t));
497 #define Bcopy(x,y) memcpy_D2A(&x->sign,&y->sign,y->wds*sizeof(ULong) + 2*sizeof(int))
498 #else /* !NO_STRING_H */
499 #define Bcopy(x,y) memcpy(&x->sign,&y->sign,y->wds*sizeof(ULong) + 2*sizeof(int))
500 #endif /* NO_STRING_H */
503 * Paranoia: Protect exported symbols, including ones in files we don't
504 * compile right now. The standard strtof and strtod survive.
507 #define gdtoa __gdtoa
508 #define freedtoa __freedtoa
509 #define strtodg __strtodg
510 #define g_ddfmt __g_ddfmt
511 #define g_dfmt __g_dfmt
512 #define g_ffmt __g_ffmt
513 #define g_Qfmt __g_Qfmt
514 #define g_xfmt __g_xfmt
515 #define g_xLfmt __g_xLfmt
516 #define strtoId __strtoId
517 #define strtoIdd __strtoIdd
518 #define strtoIf __strtoIf
519 #define strtoIQ __strtoIQ
520 #define strtoIx __strtoIx
521 #define strtoIxL __strtoIxL
522 #define strtord __strtord
523 #define strtordd __strtordd
524 #define strtorf __strtorf
525 #define strtorQ __strtorQ
526 #define strtorx __strtorx
527 #define strtorxL __strtorxL
528 #define strtodI __strtodI
529 #define strtopd __strtopd
530 #define strtopdd __strtopdd
531 #define strtopf __strtopf
532 #define strtopQ __strtopQ
533 #define strtopx __strtopx
534 #define strtopxL __strtopxL
536 /* Protect gdtoa-internal symbols */
537 #define Balloc __Balloc_D2A
538 #define Bfree __Bfree_D2A
539 #define ULtoQ __ULtoQ_D2A
540 #define ULtof __ULtof_D2A
541 #define ULtod __ULtod_D2A
542 #define ULtodd __ULtodd_D2A
543 #define ULtox __ULtox_D2A
544 #define ULtoxL __ULtoxL_D2A
545 #define any_on __any_on_D2A
546 #define b2d __b2d_D2A
547 #define bigtens __bigtens_D2A
548 #define cmp __cmp_D2A
549 #define copybits __copybits_D2A
550 #define d2b __d2b_D2A
551 #define decrement __decrement_D2A
552 #define diff __diff_D2A
553 #define dtoa_result __dtoa_result_D2A
554 #define g__fmt __g__fmt_D2A
555 #define gethex __gethex_D2A
556 #define hexdig __hexdig_D2A
557 #define hexdig_init_D2A __hexdig_init_D2A
558 #define hexnan __hexnan_D2A
559 #define hi0bits(x) __hi0bits_D2A((ULong)(x))
560 #define hi0bits_D2A __hi0bits_D2A
561 #define i2b __i2b_D2A
562 #define increment __increment_D2A
563 #define lo0bits __lo0bits_D2A
564 #define lshift __lshift_D2A
565 #define match __match_D2A
566 #define mult __mult_D2A
567 #define multadd __multadd_D2A
568 #define nrv_alloc __nrv_alloc_D2A
569 #define pow5mult __pow5mult_D2A
570 #define quorem __quorem_D2A
571 #define ratio __ratio_D2A
572 #define rshift __rshift_D2A
573 #define rv_alloc __rv_alloc_D2A
574 #define s2b __s2b_D2A
575 #define set_ones __set_ones_D2A
576 #define strcp __strcp_D2A
577 #define strcp_D2A __strcp_D2A
578 #define strtoIg __strtoIg_D2A
579 #define sum __sum_D2A
580 #define tens __tens_D2A
581 #define tinytens __tinytens_D2A
582 #define tinytens __tinytens_D2A
583 #define trailz __trailz_D2A
584 #define ulp __ulp_D2A
586 extern char *dtoa_result;
587 extern CONST double bigtens[], tens[], tinytens[];
588 extern unsigned char hexdig[];
590 extern Bigint *Balloc ANSI((int));
591 extern void Bfree ANSI((Bigint*));
592 extern void ULtof ANSI((ULong*, ULong*, Long, int));
593 extern void ULtod ANSI((ULong*, ULong*, Long, int));
594 extern void ULtodd ANSI((ULong*, ULong*, Long, int));
595 extern void ULtoQ ANSI((ULong*, ULong*, Long, int));
596 extern void ULtox ANSI((UShort*, ULong*, Long, int));
597 extern void ULtoxL ANSI((ULong*, ULong*, Long, int));
598 extern ULong any_on ANSI((Bigint*, int));
599 extern double b2d ANSI((Bigint*, int*));
600 extern int cmp ANSI((Bigint*, Bigint*));
601 extern void copybits ANSI((ULong*, int, Bigint*));
602 extern Bigint *d2b ANSI((double, int*, int*));
603 extern void decrement ANSI((Bigint*));
604 extern Bigint *diff ANSI((Bigint*, Bigint*));
605 extern char *dtoa ANSI((double d, int mode, int ndigits,
606 int *decpt, int *sign, char **rve));
607 extern void freedtoa ANSI((char*));
608 extern char *g__fmt ANSI((char*, char*, char*, int, ULong, size_t));
609 extern char *gdtoa ANSI((FPI *fpi, int be, ULong *bits, int *kindp,
610 int mode, int ndigits, int *decpt, char **rve));
611 extern int gethex ANSI((CONST char**, FPI*, Long*, Bigint**, int));
612 extern void hexdig_init_D2A(Void);
613 extern int hexnan ANSI((CONST char**, FPI*, ULong*));
614 extern int hi0bits_D2A ANSI((ULong));
615 extern Bigint *i2b ANSI((int));
616 extern Bigint *increment ANSI((Bigint*));
617 extern int lo0bits ANSI((ULong*));
618 extern Bigint *lshift ANSI((Bigint*, int));
619 extern int match ANSI((CONST char**, char*));
620 extern Bigint *mult ANSI((Bigint*, Bigint*));
621 extern Bigint *multadd ANSI((Bigint*, int, int));
622 extern char *nrv_alloc ANSI((char*, char **, int));
623 extern Bigint *pow5mult ANSI((Bigint*, int));
624 extern int quorem ANSI((Bigint*, Bigint*));
625 extern double ratio ANSI((Bigint*, Bigint*));
626 extern void rshift ANSI((Bigint*, int));
627 extern char *rv_alloc ANSI((int));
628 extern Bigint *s2b ANSI((CONST char*, int, int, ULong, int));
629 extern Bigint *set_ones ANSI((Bigint*, int));
630 extern char *strcp ANSI((char*, const char*));
631 extern int strtodg ANSI((CONST char*, char**, FPI*, Long*, ULong*));
633 extern int strtoId ANSI((CONST char *, char **, double *, double *));
634 extern int strtoIdd ANSI((CONST char *, char **, double *, double *));
635 extern int strtoIf ANSI((CONST char *, char **, float *, float *));
636 extern int strtoIg ANSI((CONST char*, char**, FPI*, Long*, Bigint**, int*));
637 extern int strtoIQ ANSI((CONST char *, char **, void *, void *));
638 extern int strtoIx ANSI((CONST char *, char **, void *, void *));
639 extern int strtoIxL ANSI((CONST char *, char **, void *, void *));
640 extern double strtod ANSI((const char *s00, char **se));
641 extern int strtopQ ANSI((CONST char *, char **, Void *));
642 extern int strtopf ANSI((CONST char *, char **, float *));
643 extern int strtopd ANSI((CONST char *, char **, double *));
644 extern int strtopdd ANSI((CONST char *, char **, double *));
645 extern int strtopx ANSI((CONST char *, char **, Void *));
646 extern int strtopxL ANSI((CONST char *, char **, Void *));
647 extern int strtord ANSI((CONST char *, char **, int, double *));
648 extern int strtordd ANSI((CONST char *, char **, int, double *));
649 extern int strtorf ANSI((CONST char *, char **, int, float *));
650 extern int strtorQ ANSI((CONST char *, char **, int, void *));
651 extern int strtorx ANSI((CONST char *, char **, int, void *));
652 extern int strtorxL ANSI((CONST char *, char **, int, void *));
653 extern Bigint *sum ANSI((Bigint*, Bigint*));
654 extern int trailz ANSI((Bigint*));
655 extern double ulp ANSI((U*));
661 * NAN_WORD0 and NAN_WORD1 are only referenced in strtod.c. Prior to
662 * 20050115, they used to be hard-wired here (to 0x7ff80000 and 0,
663 * respectively), but now are determined by compiling and running
664 * qnan.c to generate gd_qnan.h, which specifies d_QNAN0 and d_QNAN1.
665 * Formerly gdtoaimp.h recommended supplying suitable -DNAN_WORD0=...
666 * and -DNAN_WORD1=... values if necessary. This should still work.
667 * (On HP Series 700/800 machines, -DNAN_WORD0=0x7ff40000 works.)
670 #ifndef NO_INFNAN_CHECK
678 #define NAN_WORD0 d_QNAN0
681 #define NAN_WORD1 d_QNAN1
687 #define NAN_WORD0 d_QNAN1
690 #define NAN_WORD1 d_QNAN0
698 #ifdef Sudden_Underflow
704 #endif /* GDTOAIMP_H_INCLUDED */