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 /* $FreeBSD: src/contrib/gdtoa/gdtoaimp.h,v 1.8 2007/01/03 04:59:33 das Exp $ */
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 David M. Gay (dmg at acm dot org,
39 with " at " changed at "@" and " dot " changed to ".").
42 /* On a machine with IEEE extended-precision registers, it is
43 * necessary to specify double-precision (53-bit) rounding precision
44 * before invoking strtod or dtoa. If the machine uses (the equivalent
45 * of) Intel 80x87 arithmetic, the call
46 * _control87(PC_53, MCW_PC);
47 * does this with many compilers. Whether this or another call is
48 * appropriate depends on the compiler; for this to work, it may be
49 * necessary to #include "float.h" or another system-dependent header
53 /* strtod for IEEE-, VAX-, and IBM-arithmetic machines.
55 * This strtod returns a nearest machine number to the input decimal
56 * string (or sets errno to ERANGE). With IEEE arithmetic, ties are
57 * broken by the IEEE round-even rule. Otherwise ties are broken by
58 * biased rounding (add half and chop).
60 * Inspired loosely by William D. Clinger's paper "How to Read Floating
61 * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 112-126].
65 * 1. We only require IEEE, IBM, or VAX double-precision
66 * arithmetic (not IEEE double-extended).
67 * 2. We get by with floating-point arithmetic in a case that
68 * Clinger missed -- when we're computing d * 10^n
69 * for a small integer d and the integer n is not too
70 * much larger than 22 (the maximum integer k for which
71 * we can represent 10^k exactly), we may be able to
72 * compute (d*10^k) * 10^(e-k) with just one roundoff.
73 * 3. Rather than a bit-at-a-time adjustment of the binary
74 * result in the hard case, we use floating-point
75 * arithmetic to determine the adjustment to within
76 * one bit; only in really hard cases do we need to
77 * compute a second residual.
78 * 4. Because of 3., we don't need a large table of powers of 10
79 * for ten-to-e (just some small tables, e.g. of 10^k
84 * #define IEEE_8087 for IEEE-arithmetic machines where the least
85 * significant byte has the lowest address.
86 * #define IEEE_MC68k for IEEE-arithmetic machines where the most
87 * significant byte has the lowest address.
88 * #define Long int on machines with 32-bit ints and 64-bit longs.
89 * #define Sudden_Underflow for IEEE-format machines without gradual
90 * underflow (i.e., that flush to zero on underflow).
91 * #define IBM for IBM mainframe-style floating-point arithmetic.
92 * #define VAX for VAX-style floating-point arithmetic (D_floating).
93 * #define No_leftright to omit left-right logic in fast floating-point
94 * computation of dtoa.
95 * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3.
96 * #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines
97 * that use extended-precision instructions to compute rounded
98 * products and quotients) with IBM.
99 * #define ROUND_BIASED for IEEE-format with biased rounding.
100 * #define Inaccurate_Divide for IEEE-format with correctly rounded
101 * products but inaccurate quotients, e.g., for Intel i860.
102 * #define NO_LONG_LONG on machines that do not have a "long long"
103 * integer type (of >= 64 bits). On such machines, you can
104 * #define Just_16 to store 16 bits per 32-bit Long when doing
105 * high-precision integer arithmetic. Whether this speeds things
106 * up or slows things down depends on the machine and the number
107 * being converted. If long long is available and the name is
108 * something other than "long long", #define Llong to be the name,
109 * and if "unsigned Llong" does not work as an unsigned version of
110 * Llong, #define #ULLong to be the corresponding unsigned type.
111 * #define KR_headers for old-style C function headers.
112 * #define Bad_float_h if your system lacks a float.h or if it does not
113 * define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP,
114 * FLT_RADIX, FLT_ROUNDS, and DBL_MAX.
115 * #define MALLOC your_malloc, where your_malloc(n) acts like malloc(n)
116 * if memory is available and otherwise does something you deem
117 * appropriate. If MALLOC is undefined, malloc will be invoked
118 * directly -- and assumed always to succeed.
119 * #define Omit_Private_Memory to omit logic (added Jan. 1998) for making
120 * memory allocations from a private pool of memory when possible.
121 * When used, the private pool is PRIVATE_MEM bytes long: 2304 bytes,
122 * unless #defined to be a different length. This default length
123 * suffices to get rid of MALLOC calls except for unusual cases,
124 * such as decimal-to-binary conversion of a very long string of
125 * digits. When converting IEEE double precision values, the
126 * longest string gdtoa can return is about 751 bytes long. For
127 * conversions by strtod of strings of 800 digits and all gdtoa
128 * conversions of IEEE doubles in single-threaded executions with
129 * 8-byte pointers, PRIVATE_MEM >= 7400 appears to suffice; with
130 * 4-byte pointers, PRIVATE_MEM >= 7112 appears adequate.
131 * #define INFNAN_CHECK on IEEE systems to cause strtod to check for
132 * Infinity and NaN (case insensitively).
133 * When INFNAN_CHECK is #defined and No_Hex_NaN is not #defined,
134 * strtodg also accepts (case insensitively) strings of the form
135 * NaN(x), where x is a string of hexadecimal digits and spaces;
136 * if there is only one string of hexadecimal digits, it is taken
137 * for the fraction bits of the resulting NaN; if there are two or
138 * more strings of hexadecimal digits, each string is assigned
139 * to the next available sequence of 32-bit words of fractions
140 * bits (starting with the most significant), right-aligned in
142 * #define MULTIPLE_THREADS if the system offers preemptively scheduled
143 * multiple threads. In this case, you must provide (or suitably
144 * #define) two locks, acquired by ACQUIRE_DTOA_LOCK(n) and freed
145 * by FREE_DTOA_LOCK(n) for n = 0 or 1. (The second lock, accessed
146 * in pow5mult, ensures lazy evaluation of only one copy of high
147 * powers of 5; omitting this lock would introduce a small
148 * probability of wasting memory, but would otherwise be harmless.)
149 * You must also invoke freedtoa(s) to free the value s returned by
150 * dtoa. You may do so whether or not MULTIPLE_THREADS is #defined.
151 * #define IMPRECISE_INEXACT if you do not care about the setting of
152 * the STRTOG_Inexact bits in the special case of doing IEEE double
153 * precision conversions (which could also be done by the strtog in
155 * #define NO_HEX_FP to disable recognition of C9x's hexadecimal
156 * floating-point constants.
157 * #define -DNO_ERRNO to suppress setting errno (in strtod.c and
159 * #define NO_STRING_H to use private versions of memcpy.
160 * On some K&R systems, it may also be necessary to
161 * #define DECLARE_SIZE_T in this case.
162 * #define YES_ALIAS to permit aliasing certain double values with
163 * arrays of ULongs. This leads to slightly better code with
164 * some compilers and was always used prior to 19990916, but it
165 * is not strictly legal and can cause trouble with aggressively
166 * optimizing compilers (e.g., gcc 2.95.1 under -O2).
167 * #define USE_LOCALE to use the current locale's decimal_point value.
170 #ifndef GDTOAIMP_H_INCLUDED
171 #define GDTOAIMP_H_INCLUDED
177 #define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}
191 extern Char
*MALLOC
ANSI((size_t));
193 #define MALLOC malloc
198 #define Honor_FLT_ROUNDS
201 #undef Avoid_Underflow
214 #define DBL_MAX_10_EXP 308
215 #define DBL_MAX_EXP 1024
217 #define DBL_MAX 1.7976931348623157e+308
222 #define DBL_MAX_10_EXP 75
223 #define DBL_MAX_EXP 63
225 #define DBL_MAX 7.2370055773322621e+75
230 #define DBL_MAX_10_EXP 38
231 #define DBL_MAX_EXP 127
233 #define DBL_MAX 1.7014118346046923e+38
238 #define LONG_MAX 2147483647
241 #else /* ifndef Bad_float_h */
243 #endif /* Bad_float_h */
246 #define Scale_Bit 0x10
266 #if defined(IEEE_8087) + defined(IEEE_MC68k) + defined(VAX) + defined(IBM) != 1
267 Exactly one of IEEE_8087
, IEEE_MC68k
, VAX
, or IBM should be defined
.
270 typedef union { double d
; ULong L
[2]; } U
;
275 #define word0(x) ((ULong *)&x)[1]
276 #define word1(x) ((ULong *)&x)[0]
278 #define word0(x) ((ULong *)&x)[0]
279 #define word1(x) ((ULong *)&x)[1]
281 #else /* !YES_ALIAS */
283 #define word0(x) ((U*)&x)->L[1]
284 #define word1(x) ((U*)&x)->L[0]
286 #define word0(x) ((U*)&x)->L[0]
287 #define word1(x) ((U*)&x)->L[1]
289 #define dval(x) ((U*)&x)->d
290 #endif /* YES_ALIAS */
292 /* The following definition of Storeinc is appropriate for MIPS processors.
293 * An alternative that might be better on some machines is
294 * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
296 #if defined(IEEE_8087) + defined(VAX)
297 #define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \
298 ((unsigned short *)a)[0] = (unsigned short)c, a++)
300 #define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \
301 ((unsigned short *)a)[1] = (unsigned short)c, a++)
304 /* #define P DBL_MANT_DIG */
305 /* Ten_pmax = floor(P*log(2)/log(5)) */
306 /* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
307 /* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
308 /* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
312 #define Exp_shift1 20
313 #define Exp_msk1 0x100000
314 #define Exp_msk11 0x100000
315 #define Exp_mask 0x7ff00000
319 #define Exp_1 0x3ff00000
320 #define Exp_11 0x3ff00000
322 #define Frac_mask 0xfffff
323 #define Frac_mask1 0xfffff
326 #define Bndry_mask 0xfffff
327 #define Bndry_mask1 0xfffff
329 #define Sign_bit 0x80000000
338 #define Flt_Rounds FLT_ROUNDS
342 #endif /*Flt_Rounds*/
344 #else /* ifndef IEEE_Arith */
345 #undef Sudden_Underflow
346 #define Sudden_Underflow
351 #define Exp_shift1 24
352 #define Exp_msk1 0x1000000
353 #define Exp_msk11 0x1000000
354 #define Exp_mask 0x7f000000
357 #define Exp_1 0x41000000
358 #define Exp_11 0x41000000
359 #define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */
360 #define Frac_mask 0xffffff
361 #define Frac_mask1 0xffffff
364 #define Bndry_mask 0xefffff
365 #define Bndry_mask1 0xffffff
367 #define Sign_bit 0x80000000
369 #define Tiny0 0x100000
378 #define Exp_msk1 0x80
379 #define Exp_msk11 0x800000
380 #define Exp_mask 0x7f80
383 #define Exp_1 0x40800000
384 #define Exp_11 0x4080
386 #define Frac_mask 0x7fffff
387 #define Frac_mask1 0xffff007f
390 #define Bndry_mask 0xffff007f
391 #define Bndry_mask1 0xffff007f
393 #define Sign_bit 0x8000
399 #endif /* IBM, VAX */
400 #endif /* IEEE_Arith */
407 #define rounded_product(a,b) a = rnd_prod(a, b)
408 #define rounded_quotient(a,b) a = rnd_quot(a, b)
410 extern double rnd_prod(), rnd_quot();
412 extern double rnd_prod(double, double), rnd_quot(double, double);
415 #define rounded_product(a,b) a *= b
416 #define rounded_quotient(a,b) a /= b
419 #define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
420 #define Big1 0xffffffff
432 /* When Pack_32 is not defined, we store 16 bits per 32-bit Long.
433 * This makes some inner loops simpler and sometimes saves work
434 * during multiplications, but it often seems to make things slightly
435 * slower. Hence the default is now to store 32 bits per Long.
438 #else /* long long available */
440 #define Llong long long
443 #define ULLong unsigned Llong
445 #endif /* NO_LONG_LONG */
451 #define ALL_ON 0xffffffff
456 #define ALL_ON 0xffff
459 /* Copied from ruby1.9 util.c r15761
460 * http://svn.ruby-lang.org/repos/ruby/trunk
462 #ifndef MULTIPLE_THREADS
463 #define ACQUIRE_DTOA_LOCK(n) /*nothing*/
464 #define FREE_DTOA_LOCK(n) /*nothing*/
472 int k
, maxwds
, sign
, wds
;
476 typedef struct Bigint Bigint
;
479 #ifdef DECLARE_SIZE_T
480 typedef unsigned int size_t;
482 extern void memcpy_D2A
ANSI((void*, const void*, size_t));
483 #define Bcopy(x,y) memcpy_D2A(&x->sign,&y->sign,y->wds*sizeof(ULong) + 2*sizeof(int))
484 #else /* !NO_STRING_H */
485 #define Bcopy(x,y) memcpy(&x->sign,&y->sign,y->wds*sizeof(ULong) + 2*sizeof(int))
486 #endif /* NO_STRING_H */
488 #ifdef GDTOA_PARANOIA
490 * Paranoia: Protect exported symbols, including ones in files we don't
491 * compile right now. The standard strtof and strtod survive.
494 #define gdtoa __gdtoa
495 #define freedtoa __freedtoa
496 #define strtodg __strtodg
497 #define g_ddfmt __g_ddfmt
498 #define g_dfmt __g_dfmt
499 #define g_ffmt __g_ffmt
500 #define g_Qfmt __g_Qfmt
501 #define g_xfmt __g_xfmt
502 #define g_xLfmt __g_xLfmt
503 #define strtoId __strtoId
504 #define strtoIdd __strtoIdd
505 #define strtoIf __strtoIf
506 #define strtoIQ __strtoIQ
507 #define strtoIx __strtoIx
508 #define strtoIxL __strtoIxL
509 #define strtord __strtord
510 #define strtordd __strtordd
511 #define strtorf __strtorf
512 #define strtorQ __strtorQ
513 #define strtorx __strtorx
514 #define strtorxL __strtorxL
515 #define strtodI __strtodI
516 #define strtopd __strtopd
517 #define strtopdd __strtopdd
518 #define strtopf __strtopf
519 #define strtopQ __strtopQ
520 #define strtopx __strtopx
521 #define strtopxL __strtopxL
524 /* Protect gdtoa-internal symbols */
525 #define Balloc __Balloc_D2A
526 #define Bfree __Bfree_D2A
527 #define ULtoQ __ULtoQ_D2A
528 #define ULtof __ULtof_D2A
529 #define ULtod __ULtod_D2A
530 #define ULtodd __ULtodd_D2A
531 #define ULtox __ULtox_D2A
532 #define ULtoxL __ULtoxL_D2A
533 #define any_on __any_on_D2A
534 #define b2d __b2d_D2A
535 #define bigtens __bigtens_D2A
536 #define cmp __cmp_D2A
537 #define copybits __copybits_D2A
538 #define d2b __d2b_D2A
539 #define decrement __decrement_D2A
540 #define diff __diff_D2A
541 #define dtoa_result __dtoa_result_D2A
542 #define g__fmt __g__fmt_D2A
543 #define gethex __gethex_D2A
544 #define hexdig __hexdig_D2A
545 #define hexdig_init_D2A __hexdig_init_D2A
546 #define hexnan __hexnan_D2A
547 #define hi0bits __hi0bits_D2A
548 #define hi0bits_D2A __hi0bits_D2A
549 #define i2b __i2b_D2A
550 #define increment __increment_D2A
551 #define lo0bits __lo0bits_D2A
552 #define lshift __lshift_D2A
553 #define match __match_D2A
554 #define mult __mult_D2A
555 #define multadd __multadd_D2A
556 #define nrv_alloc __nrv_alloc_D2A
557 #define pow5mult __pow5mult_D2A
558 #define quorem __quorem_D2A
559 #define ratio __ratio_D2A
560 #define rshift __rshift_D2A
561 #define rv_alloc __rv_alloc_D2A
562 #define s2b __s2b_D2A
563 #define set_ones __set_ones_D2A
564 #define strcp __strcp_D2A
565 #define strcp_D2A __strcp_D2A
566 #define strtoIg __strtoIg_D2A
567 #define sum __sum_D2A
568 #define tens __tens_D2A
569 #define tinytens __tinytens_D2A
570 #define tinytens __tinytens_D2A
571 #define trailz __trailz_D2A
572 #define ulp __ulp_D2A
574 extern char *dtoa_result
;
575 extern CONST
double bigtens
[], tens
[], tinytens
[];
576 extern unsigned char hexdig
[];
578 extern Bigint
*Balloc
ANSI((int));
579 extern void Bfree
ANSI((Bigint
*));
580 extern void ULtof
ANSI((ULong
*, ULong
*, Long
, int));
581 extern void ULtod
ANSI((ULong
*, ULong
*, Long
, int));
582 extern void ULtodd
ANSI((ULong
*, ULong
*, Long
, int));
583 extern void ULtoQ
ANSI((ULong
*, ULong
*, Long
, int));
584 extern void ULtox
ANSI((UShort
*, ULong
*, Long
, int));
585 extern void ULtoxL
ANSI((ULong
*, ULong
*, Long
, int));
586 extern ULong any_on
ANSI((Bigint
*, int));
587 extern double b2d
ANSI((Bigint
*, int*));
588 extern int cmp
ANSI((Bigint
*, Bigint
*));
589 extern void copybits
ANSI((ULong
*, int, Bigint
*));
590 extern Bigint
*d2b
ANSI((double, int*, int*));
591 extern int decrement
ANSI((Bigint
*));
592 extern Bigint
*diff
ANSI((Bigint
*, Bigint
*));
593 extern char *dtoa
ANSI((double d
, int mode
, int ndigits
,
594 int *decpt
, int *sign
, char **rve
));
595 extern void freedtoa
ANSI((char*));
596 extern char *gdtoa
ANSI((FPI
*fpi
, int be
, ULong
*bits
, int *kindp
,
597 int mode
, int ndigits
, int *decpt
, char **rve
));
598 extern char *g__fmt
ANSI((char*, char*, char*, int, ULong
));
599 extern int gethex
ANSI((CONST
char**, FPI
*, Long
*, Bigint
**, int));
600 extern void hexdig_init_D2A(Void
);
601 extern int hexnan
ANSI((CONST
char**, FPI
*, ULong
*));
602 extern int hi0bits
ANSI((ULong
));
603 extern Bigint
*i2b
ANSI((int));
604 extern Bigint
*increment
ANSI((Bigint
*));
605 extern int lo0bits
ANSI((ULong
*));
606 extern Bigint
*lshift
ANSI((Bigint
*, int));
607 extern int match
ANSI((CONST
char**, char*));
608 extern Bigint
*mult
ANSI((Bigint
*, Bigint
*));
609 extern Bigint
*multadd
ANSI((Bigint
*, int, int));
610 extern char *nrv_alloc
ANSI((char*, char **, int));
611 extern Bigint
*pow5mult
ANSI((Bigint
*, int));
612 extern int quorem
ANSI((Bigint
*, Bigint
*));
613 extern double ratio
ANSI((Bigint
*, Bigint
*));
614 extern void rshift
ANSI((Bigint
*, int));
615 extern char *rv_alloc
ANSI((int));
616 extern Bigint
*s2b
ANSI((CONST
char*, int, int, ULong
));
617 extern Bigint
*set_ones
ANSI((Bigint
*, int));
618 extern char *strcp
ANSI((char*, const char*));
619 extern int strtodg
ANSI((CONST
char*, char**, FPI
*, Long
*, ULong
*));
621 extern int strtoId
ANSI((CONST
char *, char **, double *, double *));
622 extern int strtoIdd
ANSI((CONST
char *, char **, double *, double *));
623 extern int strtoIf
ANSI((CONST
char *, char **, float *, float *));
624 extern int strtoIg
ANSI((CONST
char*, char**, FPI
*, Long
*, Bigint
**, int*));
625 extern int strtoIQ
ANSI((CONST
char *, char **, void *, void *));
626 extern int strtoIx
ANSI((CONST
char *, char **, void *, void *));
627 extern int strtoIxL
ANSI((CONST
char *, char **, void *, void *));
628 extern double ruby_strtod
ANSI((const char *s00
, char **se
));
629 extern int strtopQ
ANSI((CONST
char *, char **, Void
*));
630 extern int strtopf
ANSI((CONST
char *, char **, float *));
631 extern int strtopd
ANSI((CONST
char *, char **, double *));
632 extern int strtopdd
ANSI((CONST
char *, char **, double *));
633 extern int strtopx
ANSI((CONST
char *, char **, Void
*));
634 extern int strtopxL
ANSI((CONST
char *, char **, Void
*));
635 extern int strtord
ANSI((CONST
char *, char **, int, double *));
636 extern int strtordd
ANSI((CONST
char *, char **, int, double *));
637 extern int strtorf
ANSI((CONST
char *, char **, int, float *));
638 extern int strtorQ
ANSI((CONST
char *, char **, int, void *));
639 extern int strtorx
ANSI((CONST
char *, char **, int, void *));
640 extern int strtorxL
ANSI((CONST
char *, char **, int, void *));
641 extern Bigint
*sum
ANSI((Bigint
*, Bigint
*));
642 extern int trailz
ANSI((Bigint
*));
643 extern double ulp
ANSI((double));
649 * NAN_WORD0 and NAN_WORD1 are only referenced in strtod.c. Prior to
650 * 20050115, they used to be hard-wired here (to 0x7ff80000 and 0,
651 * respectively), but now are determined by compiling and running
652 * qnan.c to generate gd_qnan.h, which specifies d_QNAN0 and d_QNAN1.
653 * Formerly gdtoaimp.h recommended supplying suitable -DNAN_WORD0=...
654 * and -DNAN_WORD1=... values if necessary. This should still work.
655 * (On HP Series 700/800 machines, -DNAN_WORD0=0x7ff40000 works.)
662 #define NAN_WORD0 d_QNAN0
665 #define NAN_WORD1 d_QNAN1
671 #define NAN_WORD0 d_QNAN1
674 #define NAN_WORD1 d_QNAN0
682 #ifdef Sudden_Underflow
688 #endif /* GDTOAIMP_H_INCLUDED */