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 ****************************************************************/
31 /* This is a variation on dtoa.c that converts arbitary binary
32 floating-point formats to and from decimal notation. It uses
33 double-precision arithmetic internally, so there are still
34 various #ifdefs that adapt the calculations to the native
35 double-precision arithmetic (any of IEEE, VAX D_floating,
36 or IBM mainframe arithmetic).
38 Please send bug reports to
40 Bell Laboratories, Room 2C-463
42 Murray Hill, NJ 07974-0636
47 /* On a machine with IEEE extended-precision registers, it is
48 * necessary to specify double-precision (53-bit) rounding precision
49 * before invoking strtod or dtoa. If the machine uses (the equivalent
50 * of) Intel 80x87 arithmetic, the call
51 * _control87(PC_53, MCW_PC);
52 * does this with many compilers. Whether this or another call is
53 * appropriate depends on the compiler; for this to work, it may be
54 * necessary to #include "float.h" or another system-dependent header
58 /* strtod for IEEE-, VAX-, and IBM-arithmetic machines.
60 * This strtod returns a nearest machine number to the input decimal
61 * string (or sets errno to ERANGE). With IEEE arithmetic, ties are
62 * broken by the IEEE round-even rule. Otherwise ties are broken by
63 * biased rounding (add half and chop).
65 * Inspired loosely by William D. Clinger's paper "How to Read Floating
66 * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101].
70 * 1. We only require IEEE, IBM, or VAX double-precision
71 * arithmetic (not IEEE double-extended).
72 * 2. We get by with floating-point arithmetic in a case that
73 * Clinger missed -- when we're computing d * 10^n
74 * for a small integer d and the integer n is not too
75 * much larger than 22 (the maximum integer k for which
76 * we can represent 10^k exactly), we may be able to
77 * compute (d*10^k) * 10^(e-k) with just one roundoff.
78 * 3. Rather than a bit-at-a-time adjustment of the binary
79 * result in the hard case, we use floating-point
80 * arithmetic to determine the adjustment to within
81 * one bit; only in really hard cases do we need to
82 * compute a second residual.
83 * 4. Because of 3., we don't need a large table of powers of 10
84 * for ten-to-e (just some small tables, e.g. of 10^k
89 * #define IEEE_8087 for IEEE-arithmetic machines where the least
90 * significant byte has the lowest address.
91 * #define IEEE_MC68k for IEEE-arithmetic machines where the most
92 * significant byte has the lowest address.
93 * #define Long int on machines with 32-bit ints and 64-bit longs.
94 * #define Sudden_Underflow for IEEE-format machines without gradual
95 * underflow (i.e., that flush to zero on underflow).
96 * #define IBM for IBM mainframe-style floating-point arithmetic.
97 * #define VAX for VAX-style floating-point arithmetic (D_floating).
98 * #define No_leftright to omit left-right logic in fast floating-point
99 * computation of dtoa.
100 * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3.
101 * #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines
102 * that use extended-precision instructions to compute rounded
103 * products and quotients) with IBM.
104 * #define ROUND_BIASED for IEEE-format with biased rounding.
105 * #define Inaccurate_Divide for IEEE-format with correctly rounded
106 * products but inaccurate quotients, e.g., for Intel i860.
107 * #define NO_LONG_LONG on machines that do not have a "long long"
108 * integer type (of >= 64 bits). On such machines, you can
109 * #define Just_16 to store 16 bits per 32-bit Long when doing
110 * high-precision integer arithmetic. Whether this speeds things
111 * up or slows things down depends on the machine and the number
112 * being converted. If long long is available and the name is
113 * something other than "long long", #define Llong to be the name,
114 * and if "unsigned Llong" does not work as an unsigned version of
115 * Llong, #define #ULLong to be the corresponding unsigned type.
116 * #define KR_headers for old-style C function headers.
117 * #define Bad_float_h if your system lacks a float.h or if it does not
118 * define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP,
119 * FLT_RADIX, FLT_ROUNDS, and DBL_MAX.
120 * #define MALLOC your_malloc, where your_malloc(n) acts like malloc(n)
121 * if memory is available and otherwise does something you deem
122 * appropriate. If MALLOC is undefined, malloc will be invoked
123 * directly -- and assumed always to succeed.
124 * #define Omit_Private_Memory to omit logic (added Jan. 1998) for making
125 * memory allocations from a private pool of memory when possible.
126 * When used, the private pool is PRIVATE_MEM bytes long: 2304 bytes,
127 * unless #defined to be a different length. This default length
128 * suffices to get rid of MALLOC calls except for unusual cases,
129 * such as decimal-to-binary conversion of a very long string of
130 * digits. When converting IEEE double precision values, the
131 * longest string gdtoa can return is about 751 bytes long. For
132 * conversions by strtod of strings of 800 digits and all gdtoa
133 * conversions of IEEE doubles in single-threaded executions with
134 * 8-byte pointers, PRIVATE_MEM >= 7400 appears to suffice; with
135 * 4-byte pointers, PRIVATE_MEM >= 7112 appears adequate.
136 * #define INFNAN_CHECK on IEEE systems to cause strtod to check for
137 * Infinity and NaN (case insensitively). On some systems (e.g.,
138 * some HP systems), it may be necessary to #define NAN_WORD0
139 * appropriately -- to the most significant word of a quiet NaN.
140 * (On HP Series 700/800 machines, -DNAN_WORD0=0x7ff40000 works.)
141 * When INFNAN_CHECK is #defined and No_Hex_NaN is not #defined,
142 * strtodg also accepts (case insensitively) strings of the form
143 * NaN(x), where x is a string of hexadecimal digits and spaces;
144 * if there is only one string of hexadecimal digits, it is taken
145 * for the fraction bits of the resulting NaN; if there are two or
146 * more strings of hexadecimal digits, each string is assigned
147 * to the next available sequence of 32-bit words of fractions
148 * bits (starting with the most significant), right-aligned in
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 strtog 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 YES_ALIAS to permit aliasing certain double values with
171 * arrays of ULongs. This leads to slightly better code with
172 * some compilers and was always used prior to 19990916, but it
173 * is not strictly legal and can cause trouble with aggressively
174 * optimizing compilers (e.g., gcc 2.95.1 under -O2).
175 * #define USE_LOCALE to use the current locale's decimal_point value.
178 #ifndef GDTOAIMP_H_INCLUDED
179 #define GDTOAIMP_H_INCLUDED
184 #define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}
190 #include "libc_private.h"
192 #include "namespace.h"
194 #include "un-namespace.h"
203 extern Char *MALLOC ANSI((size_t));
205 #define MALLOC malloc
210 #define Honor_FLT_ROUNDS
213 #undef Avoid_Underflow
226 #define DBL_MAX_10_EXP 308
227 #define DBL_MAX_EXP 1024
229 #define DBL_MAX 1.7976931348623157e+308
234 #define DBL_MAX_10_EXP 75
235 #define DBL_MAX_EXP 63
237 #define DBL_MAX 7.2370055773322621e+75
242 #define DBL_MAX_10_EXP 38
243 #define DBL_MAX_EXP 127
245 #define DBL_MAX 1.7014118346046923e+38
250 #define LONG_MAX 2147483647
253 #else /* ifndef Bad_float_h */
255 #endif /* Bad_float_h */
258 #define Scale_Bit 0x10
278 #if defined(IEEE_8087) + defined(IEEE_MC68k) + defined(VAX) + defined(IBM) != 1
279 Exactly one of IEEE_8087, IEEE_MC68k, VAX, or IBM should be defined.
282 typedef union { double d; ULong L[2]; } U;
287 #define word0(x) ((ULong *)&x)[1]
288 #define word1(x) ((ULong *)&x)[0]
290 #define word0(x) ((ULong *)&x)[0]
291 #define word1(x) ((ULong *)&x)[1]
293 #else /* !YES_ALIAS */
295 #define word0(x) ((U*)&x)->L[1]
296 #define word1(x) ((U*)&x)->L[0]
298 #define word0(x) ((U*)&x)->L[0]
299 #define word1(x) ((U*)&x)->L[1]
301 #define dval(x) ((U*)&x)->d
302 #endif /* YES_ALIAS */
304 /* The following definition of Storeinc is appropriate for MIPS processors.
305 * An alternative that might be better on some machines is
306 * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
308 #if defined(IEEE_8087) + defined(VAX)
309 #define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \
310 ((unsigned short *)a)[0] = (unsigned short)c, a++)
312 #define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \
313 ((unsigned short *)a)[1] = (unsigned short)c, a++)
316 /* #define P DBL_MANT_DIG */
317 /* Ten_pmax = floor(P*log(2)/log(5)) */
318 /* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
319 /* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
320 /* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
324 #define Exp_shift1 20
325 #define Exp_msk1 0x100000
326 #define Exp_msk11 0x100000
327 #define Exp_mask 0x7ff00000
331 #define Exp_1 0x3ff00000
332 #define Exp_11 0x3ff00000
334 #define Frac_mask 0xfffff
335 #define Frac_mask1 0xfffff
338 #define Bndry_mask 0xfffff
339 #define Bndry_mask1 0xfffff
341 #define Sign_bit 0x80000000
350 #define Flt_Rounds FLT_ROUNDS
354 #endif /*Flt_Rounds*/
356 #else /* ifndef IEEE_Arith */
357 #undef Sudden_Underflow
358 #define Sudden_Underflow
363 #define Exp_shift1 24
364 #define Exp_msk1 0x1000000
365 #define Exp_msk11 0x1000000
366 #define Exp_mask 0x7f000000
369 #define Exp_1 0x41000000
370 #define Exp_11 0x41000000
371 #define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */
372 #define Frac_mask 0xffffff
373 #define Frac_mask1 0xffffff
376 #define Bndry_mask 0xefffff
377 #define Bndry_mask1 0xffffff
379 #define Sign_bit 0x80000000
381 #define Tiny0 0x100000
390 #define Exp_msk1 0x80
391 #define Exp_msk11 0x800000
392 #define Exp_mask 0x7f80
395 #define Exp_1 0x40800000
396 #define Exp_11 0x4080
398 #define Frac_mask 0x7fffff
399 #define Frac_mask1 0xffff007f
402 #define Bndry_mask 0xffff007f
403 #define Bndry_mask1 0xffff007f
405 #define Sign_bit 0x8000
411 #endif /* IBM, VAX */
412 #endif /* IEEE_Arith */
419 #define rounded_product(a,b) a = rnd_prod(a, b)
420 #define rounded_quotient(a,b) a = rnd_quot(a, b)
422 extern double rnd_prod(), rnd_quot();
424 extern double rnd_prod(double, double), rnd_quot(double, double);
427 #define rounded_product(a,b) a *= b
428 #define rounded_quotient(a,b) a /= b
431 #define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
432 #define Big1 0xffffffff
444 /* When Pack_32 is not defined, we store 16 bits per 32-bit Long.
445 * This makes some inner loops simpler and sometimes saves work
446 * during multiplications, but it often seems to make things slightly
447 * slower. Hence the default is now to store 32 bits per Long.
450 #else /* long long available */
452 #define Llong long long
455 #define ULLong unsigned Llong
457 #endif /* NO_LONG_LONG */
463 #define ALL_ON 0xffffffff
468 #define ALL_ON 0xffff
471 #define MULTIPLE_THREADS
472 extern pthread_mutex_t __gdtoa_locks[2];
473 #define ACQUIRE_DTOA_LOCK(n) do { \
475 _pthread_mutex_lock(&__gdtoa_locks[n]); \
477 #define FREE_DTOA_LOCK(n) do { \
479 _pthread_mutex_unlock(&__gdtoa_locks[n]); \
487 int k, maxwds, sign, wds;
491 typedef struct Bigint Bigint;
494 #ifdef DECLARE_SIZE_T
495 typedef unsigned int size_t;
497 extern void memcpy_D2A ANSI((void*, const void*, size_t));
498 #define Bcopy(x,y) memcpy_D2A(&x->sign,&y->sign,y->wds*sizeof(ULong) + 2*sizeof(int))
499 #else /* !NO_STRING_H */
500 #define Bcopy(x,y) memcpy(&x->sign,&y->sign,y->wds*sizeof(ULong) + 2*sizeof(int))
501 #endif /* NO_STRING_H */
504 * Paranoia: Protect exported symbols, including ones in files we don't
505 * compile right now. The standard strtof and strtod survive.
508 #define gdtoa __gdtoa
509 #define freedtoa __freedtoa
510 #define strtodg __strtodg
511 #define g_ddfmt __g_ddfmt
512 #define g_dfmt __g_dfmt
513 #define g_ffmt __g_ffmt
514 #define g_Qfmt __g_Qfmt
515 #define g_xfmt __g_xfmt
516 #define g_xLfmt __g_xLfmt
517 #define strtoId __strtoId
518 #define strtoIdd __strtoIdd
519 #define strtoIf __strtoIf
520 #define strtoIQ __strtoIQ
521 #define strtoIx __strtoIx
522 #define strtoIxL __strtoIxL
523 #define strtord __strtord
524 #define strtordd __strtordd
525 #define strtorf __strtorf
526 #define strtorQ __strtorQ
527 #define strtorx __strtorx
528 #define strtorxL __strtorxL
529 #define strtodI __strtodI
530 #define strtopd __strtopd
531 #define strtopdd __strtopdd
532 #define strtopf __strtopf
533 #define strtopQ __strtopQ
534 #define strtopx __strtopx
535 #define strtopxL __strtopxL
537 /* Protect gdtoa-internal symbols */
538 #define Balloc __Balloc_D2A
539 #define Bfree __Bfree_D2A
540 #define ULtoQ __ULtoQ_D2A
541 #define ULtof __ULtof_D2A
542 #define ULtod __ULtod_D2A
543 #define ULtodd __ULtodd_D2A
544 #define ULtox __ULtox_D2A
545 #define ULtoxL __ULtoxL_D2A
546 #define any_on __any_on_D2A
547 #define b2d __b2d_D2A
548 #define bigtens __bigtens_D2A
549 #define cmp __cmp_D2A
550 #define copybits __copybits_D2A
551 #define d2b __d2b_D2A
552 #define decrement __decrement_D2A
553 #define diff __diff_D2A
554 #define dtoa_result __dtoa_result_D2A
555 #define g__fmt __g__fmt_D2A
556 #define gethex __gethex_D2A
557 #define hexdig __hexdig_D2A
558 #define hexdig_init_D2A __hexdig_init_D2A
559 #define hexnan __hexnan_D2A
560 #define hi0bits __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 int 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 *gdtoa ANSI((FPI *fpi, int be, ULong *bits, int *kindp,
609 int mode, int ndigits, int *decpt, char **rve));
610 extern char *g__fmt ANSI((char*, char*, char*, int, ULong));
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 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));
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((double));
677 #define NAN_WORD0 0x7ff80000
683 #endif /* INFNAN_CHECK */
686 #ifdef Sudden_Underflow
692 #endif /* GDTOAIMP_H_INCLUDED */