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4349 Serge 1
/****************************************************************
2
 *
3
 * The author of this software is David M. Gay.
4
 *
5
 * Copyright (c) 1991 by AT&T.
6
 *
7
 * Permission to use, copy, modify, and distribute this software for any
8
 * purpose without fee is hereby granted, provided that this entire notice
9
 * is included in all copies of any software which is or includes a copy
10
 * or modification of this software and in all copies of the supporting
11
 * documentation for such software.
12
 *
13
 * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
14
 * WARRANTY.  IN PARTICULAR, NEITHER THE AUTHOR NOR AT&T MAKES ANY
15
 * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
16
 * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
17
 *
18
 ***************************************************************/
19
 
20
/* Please send bug reports to
21
	David M. Gay
22
	AT&T Bell Laboratories, Room 2C-463
23
	600 Mountain Avenue
24
	Murray Hill, NJ 07974-2070
25
	U.S.A.
26
	dmg@research.att.com or research!dmg
27
 */
28
 
29
#include 
30
#include 
31
#include 
32
#include 
33
#include 
34
#include 
35
 
36
#ifdef __IEEE_LITTLE_ENDIAN
37
#define IEEE_8087
38
#endif
39
 
40
#ifdef __IEEE_BIG_ENDIAN
41
#define IEEE_MC68k
42
#endif
43
 
44
#ifdef __Z8000__
45
#define Just_16
46
#endif
47
 
48
#ifdef DEBUG
49
#include "stdio.h"
50
#define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}
51
#endif
52
 
53
#ifdef Unsigned_Shifts
54
#define Sign_Extend(a,b) if (b < 0) a |= (__uint32_t)0xffff0000;
55
#else
56
#define Sign_Extend(a,b) /*no-op*/
57
#endif
58
 
59
#if defined(IEEE_8087) + defined(IEEE_MC68k) + defined(VAX) + defined(IBM) != 1
60
Exactly one of IEEE_8087, IEEE_MC68k, VAX, or IBM should be defined.
61
#endif
62
 
63
/* If we are going to examine or modify specific bits in a double using
64
   the word0 and/or word1 macros, then we must wrap the double inside
65
   a union.  This is necessary to avoid undefined behavior according to
66
   the ANSI C spec.  */
67
union double_union
68
{
69
  double d;
70
  __uint32_t i[2];
71
};
72
 
73
#ifdef IEEE_8087
74
#define word0(x) (x.i[1])
75
#define word1(x) (x.i[0])
76
#else
77
#define word0(x) (x.i[0])
78
#define word1(x) (x.i[1])
79
#endif
80
 
81
/* The following is taken from gdtoaimp.h for use with new strtod, but
82
   adjusted to avoid invalid type-punning.  */
83
typedef __int32_t Long;
84
 
85
/* Unfortunately, because __ULong might be a different type than
86
   __uint32_t, we can't re-use union double_union as-is without
87
   further edits in strtod.c.  */
88
typedef union { double d; __ULong i[2]; } U;
89
 
90
#define dword0(x) word0(x)
91
#define dword1(x) word1(x)
92
#define dval(x) (x.d)
93
 
94
#undef SI
95
#ifdef Sudden_Underflow
96
#define SI 1
97
#else
98
#define SI 0
99
#endif
100
 
4921 Serge 101
#define Storeinc(a,b,c) (*(a)++ = ((b) << 16) | ((c) & 0xffff))
4349 Serge 102
 
103
/* #define P DBL_MANT_DIG */
104
/* Ten_pmax = floor(P*log(2)/log(5)) */
105
/* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
106
/* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
107
/* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
108
 
109
#if defined(IEEE_8087) + defined(IEEE_MC68k)
110
#if defined (_DOUBLE_IS_32BITS)
111
#define Exp_shift   23
112
#define Exp_shift1  23
113
#define Exp_msk1    ((__uint32_t)0x00800000L)
114
#define Exp_msk11   ((__uint32_t)0x00800000L)
115
#define Exp_mask    ((__uint32_t)0x7f800000L)
116
#define P    	    24
117
#define Bias 	    127
118
#define NO_HEX_FP   /* not supported in this case */
119
#define IEEE_Arith
120
#define Emin        (-126)
121
#define Exp_1       ((__uint32_t)0x3f800000L)
122
#define Exp_11      ((__uint32_t)0x3f800000L)
123
#define Ebits 	    8
124
#define Frac_mask   ((__uint32_t)0x007fffffL)
125
#define Frac_mask1  ((__uint32_t)0x007fffffL)
126
#define Ten_pmax    10
127
#define Sign_bit    ((__uint32_t)0x80000000L)
128
#define Ten_pmax    10
129
#define Bletch	    2
130
#define Bndry_mask  ((__uint32_t)0x007fffffL)
131
#define Bndry_mask1 ((__uint32_t)0x007fffffL)
132
#define LSB 1
133
#define Sign_bit    ((__uint32_t)0x80000000L)
134
#define Log2P 	    1
135
#define Tiny0 	    0
136
#define Tiny1 	    1
137
#define Quick_max   5
138
#define Int_max     6
139
#define Infinite(x) (word0(x) == ((__uint32_t)0x7f800000L))
140
#undef word0
141
#undef word1
142
#undef dword0
143
#undef dword1
144
 
145
#define word0(x) (x.i[0])
146
#define word1(x) 0
147
#define dword0(x) word0(x)
148
#define dword1(x) 0
149
#else
150
 
151
#define Exp_shift  20
152
#define Exp_shift1 20
153
#define Exp_msk1    ((__uint32_t)0x100000L)
154
#define Exp_msk11   ((__uint32_t)0x100000L)
155
#define Exp_mask  ((__uint32_t)0x7ff00000L)
156
#define P 53
157
#define Bias 1023
158
#define IEEE_Arith
159
#define Emin (-1022)
160
#define Exp_1  ((__uint32_t)0x3ff00000L)
161
#define Exp_11 ((__uint32_t)0x3ff00000L)
162
#define Ebits 11
163
#define Frac_mask  ((__uint32_t)0xfffffL)
164
#define Frac_mask1 ((__uint32_t)0xfffffL)
165
#define Ten_pmax 22
166
#define Bletch 0x10
167
#define Bndry_mask  ((__uint32_t)0xfffffL)
168
#define Bndry_mask1 ((__uint32_t)0xfffffL)
169
#define LSB 1
170
#define Sign_bit ((__uint32_t)0x80000000L)
171
#define Log2P 1
172
#define Tiny0 0
173
#define Tiny1 1
174
#define Quick_max 14
175
#define Int_max 14
176
#define Infinite(x) (word0(x) == ((__uint32_t)0x7ff00000L)) /* sufficient test for here */
177
 
178
#endif /* !_DOUBLE_IS_32BITS */
179
 
180
#ifndef Flt_Rounds
181
#ifdef FLT_ROUNDS
182
#define Flt_Rounds FLT_ROUNDS
183
#else
184
#define Flt_Rounds 1
185
#endif
186
#endif /*Flt_Rounds*/
187
 
188
#else /* !IEEE_8087 && !IEEE_MC68k */
189
#undef  Sudden_Underflow
190
#define Sudden_Underflow
191
#ifdef IBM
192
#define Flt_Rounds 0
193
#define Exp_shift  24
194
#define Exp_shift1 24
195
#define Exp_msk1   ((__uint32_t)0x1000000L)
196
#define Exp_msk11  ((__uint32_t)0x1000000L)
197
#define Exp_mask  ((__uint32_t)0x7f000000L)
198
#define P 14
199
#define Bias 65
200
#define Exp_1  ((__uint32_t)0x41000000L)
201
#define Exp_11 ((__uint32_t)0x41000000L)
202
#define Ebits 8	/* exponent has 7 bits, but 8 is the right value in b2d */
203
#define Frac_mask  ((__uint32_t)0xffffffL)
204
#define Frac_mask1 ((__uint32_t)0xffffffL)
205
#define Bletch 4
206
#define Ten_pmax 22
207
#define Bndry_mask  ((__uint32_t)0xefffffL)
208
#define Bndry_mask1 ((__uint32_t)0xffffffL)
209
#define LSB 1
210
#define Sign_bit ((__uint32_t)0x80000000L)
211
#define Log2P 4
212
#define Tiny0 ((__uint32_t)0x100000L)
213
#define Tiny1 0
214
#define Quick_max 14
215
#define Int_max 15
216
#else /* VAX */
217
#define Flt_Rounds 1
218
#define Exp_shift  23
219
#define Exp_shift1 7
220
#define Exp_msk1    0x80
221
#define Exp_msk11   ((__uint32_t)0x800000L)
222
#define Exp_mask  ((__uint32_t)0x7f80L)
223
#define P 56
224
#define Bias 129
225
#define Exp_1  ((__uint32_t)0x40800000L)
226
#define Exp_11 ((__uint32_t)0x4080L)
227
#define Ebits 8
228
#define Frac_mask  ((__uint32_t)0x7fffffL)
229
#define Frac_mask1 ((__uint32_t)0xffff007fL)
230
#define Ten_pmax 24
231
#define Bletch 2
232
#define Bndry_mask  ((__uint32_t)0xffff007fL)
233
#define Bndry_mask1 ((__uint32_t)0xffff007fL)
234
#define LSB ((__uint32_t)0x10000L)
235
#define Sign_bit ((__uint32_t)0x8000L)
236
#define Log2P 1
237
#define Tiny0 0x80
238
#define Tiny1 0
239
#define Quick_max 15
240
#define Int_max 15
241
#endif
242
#endif
243
 
244
#ifndef IEEE_Arith
245
#define ROUND_BIASED
246
#else
247
#define Scale_Bit 0x10
248
#if defined(_DOUBLE_IS_32BITS) && defined(__v800)
249
#define n_bigtens 2
250
#else
251
#define n_bigtens 5
252
#endif
253
#endif
254
 
255
#ifdef IBM
256
#define n_bigtens 3
257
#endif
258
 
259
#ifdef VAX
260
#define n_bigtens 2
261
#endif
262
 
263
#ifndef __NO_INFNAN_CHECK
264
#define INFNAN_CHECK
265
#endif
266
 
267
/*
268
 * NAN_WORD0 and NAN_WORD1 are only referenced in strtod.c.  Prior to
269
 * 20050115, they used to be hard-wired here (to 0x7ff80000 and 0,
270
 * respectively), but now are determined by compiling and running
271
 * qnan.c to generate gd_qnan.h, which specifies d_QNAN0 and d_QNAN1.
272
 * Formerly gdtoaimp.h recommended supplying suitable -DNAN_WORD0=...
273
 * and -DNAN_WORD1=...  values if necessary.  This should still work.
274
 * (On HP Series 700/800 machines, -DNAN_WORD0=0x7ff40000 works.)
275
 */
276
#ifdef IEEE_Arith
277
#ifdef IEEE_MC68k
278
#define _0 0
279
#define _1 1
280
#ifndef NAN_WORD0
281
#define NAN_WORD0 d_QNAN0
282
#endif
283
#ifndef NAN_WORD1
284
#define NAN_WORD1 d_QNAN1
285
#endif
286
#else
287
#define _0 1
288
#define _1 0
289
#ifndef NAN_WORD0
290
#define NAN_WORD0 d_QNAN1
291
#endif
292
#ifndef NAN_WORD1
293
#define NAN_WORD1 d_QNAN0
294
#endif
295
#endif
296
#else
297
#undef INFNAN_CHECK
298
#endif
299
 
300
#ifdef RND_PRODQUOT
301
#define rounded_product(a,b) a = rnd_prod(a, b)
302
#define rounded_quotient(a,b) a = rnd_quot(a, b)
303
#ifdef KR_headers
304
extern double rnd_prod(), rnd_quot();
305
#else
306
extern double rnd_prod(double, double), rnd_quot(double, double);
307
#endif
308
#else
309
#define rounded_product(a,b) a *= b
310
#define rounded_quotient(a,b) a /= b
311
#endif
312
 
313
#define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
314
#define Big1 ((__uint32_t)0xffffffffL)
315
 
316
#ifndef Just_16
317
/* When Pack_32 is not defined, we store 16 bits per 32-bit long.
318
 * This makes some inner loops simpler and sometimes saves work
319
 * during multiplications, but it often seems to make things slightly
320
 * slower.  Hence the default is now to store 32 bits per long.
321
 */
322
 
323
 #ifndef Pack_32
324
  #define Pack_32
325
 #endif
326
#else  /* Just_16 */
327
 #ifndef Pack_16
328
  #define Pack_16
329
 #endif
330
#endif /* Just_16 */
331
 
332
#ifdef Pack_32
333
#define ULbits 32
334
#define kshift 5
335
#define kmask 31
336
#define ALL_ON 0xffffffff
337
#else
338
#define ULbits 16
339
#define kshift 4
340
#define kmask 15
341
#define ALL_ON 0xffff
342
#endif
343
 
344
#ifdef __cplusplus
345
extern "C" double strtod(const char *s00, char **se);
346
extern "C" char *dtoa(double d, int mode, int ndigits,
347
			int *decpt, int *sign, char **rve);
348
#endif
349
 
350
 
351
typedef struct _Bigint _Bigint;
352
 
353
#define Balloc	_Balloc
354
#define Bfree	_Bfree
355
#define multadd __multadd
356
#define s2b	__s2b
357
#define lo0bits __lo0bits
358
#define hi0bits __hi0bits
359
#define i2b	__i2b
360
#define mult	__multiply
361
#define pow5mult	__pow5mult
362
#define lshift	__lshift
6099 serge 363
#define match   __match
4349 Serge 364
#define cmp	__mcmp
365
#define diff	__mdiff
366
#define ulp 	__ulp
367
#define b2d	__b2d
368
#define d2b	__d2b
369
#define ratio	__ratio
370
#define any_on	__any_on
371
#define gethex  __gethex
372
#define copybits 	__copybits
373
#define hexnan	__hexnan
374
 
4921 Serge 375
#if !defined(PREFER_SIZE_OVER_SPEED) && !defined(__OPTIMIZE_SIZE__) && !defined(_SMALL_HEXDIG)
376
#define __get_hexdig(x) __hexdig[x] /* NOTE: must evaluate arg only once */
377
#else /* !defined(PREFER_SIZE_OVER_SPEED) && !defined(__OPTIMIZE_SIZE__) && !defined(_SMALL_HEXDIG) */
378
#define __get_hexdig(x) __hexdig_fun(x)
379
#endif /* !defined(PREFER_SIZE_OVER_SPEED) && !defined(__OPTIMIZE_SIZE__) && !defined(_SMALL_HEXDIG) */
4349 Serge 380
 
381
#define tens __mprec_tens
382
#define bigtens __mprec_bigtens
383
#define tinytens __mprec_tinytens
384
 
385
struct _reent ;
386
struct FPI;
387
double 		_EXFUN(ulp,(double x));
388
double		_EXFUN(b2d,(_Bigint *a , int *e));
389
_Bigint *	_EXFUN(Balloc,(struct _reent *p, int k));
390
void 		_EXFUN(Bfree,(struct _reent *p, _Bigint *v));
391
_Bigint *	_EXFUN(multadd,(struct _reent *p, _Bigint *, int, int));
392
_Bigint *	_EXFUN(s2b,(struct _reent *, const char*, int, int, __ULong));
393
_Bigint	*	_EXFUN(i2b,(struct _reent *,int));
394
_Bigint *	_EXFUN(mult, (struct _reent *, _Bigint *, _Bigint *));
395
_Bigint *	_EXFUN(pow5mult, (struct _reent *, _Bigint *, int k));
396
int 		_EXFUN(hi0bits,(__ULong));
397
int 		_EXFUN(lo0bits,(__ULong *));
398
_Bigint *	_EXFUN(d2b,(struct _reent *p, double d, int *e, int *bits));
399
_Bigint *	_EXFUN(lshift,(struct _reent *p, _Bigint *b, int k));
6099 serge 400
int		_EXFUN(match,(const char**, char*));
4349 Serge 401
_Bigint *	_EXFUN(diff,(struct _reent *p, _Bigint *a, _Bigint *b));
402
int		_EXFUN(cmp,(_Bigint *a, _Bigint *b));
4921 Serge 403
int		_EXFUN(gethex,(struct _reent *p, _CONST char **sp, _CONST struct FPI *fpi, Long *exp, _Bigint **bp, int sign));
4349 Serge 404
double		_EXFUN(ratio,(_Bigint *a, _Bigint *b));
405
__ULong		_EXFUN(any_on,(_Bigint *b, int k));
406
void		_EXFUN(copybits,(__ULong *c, int n, _Bigint *b));
6099 serge 407
#if defined (_HAVE_LONG_DOUBLE) && !defined (_LDBL_EQ_DBL)
408
int		_EXFUN(_strtorx_r,(struct _reent *, _CONST char *, char **, int, void *));
409
int		_EXFUN(_strtodg_r,(struct _reent *p, _CONST char *s00, char **se, struct FPI *fpi, Long *exp, __ULong *bits));
410
#endif /* _HAVE_LONG_DOUBLE && !_LDBL_EQ_DBL */
411
 
4921 Serge 412
#if defined(PREFER_SIZE_OVER_SPEED) || defined(__OPTIMIZE_SIZE__) || defined(_SMALL_HEXDIG)
413
unsigned char _EXFUN(__hexdig_fun,(unsigned char));
414
#endif /* !defined(PREFER_SIZE_OVER_SPEED) && !defined(__OPTIMIZE_SIZE__) && !defined(_SMALL_HEXDIG) */
4349 Serge 415
#ifdef INFNAN_CHECK
4921 Serge 416
int		_EXFUN(hexnan,(_CONST char **sp, _CONST struct FPI *fpi, __ULong *x0));
4349 Serge 417
#endif
418
 
419
#define Bcopy(x,y) memcpy((char *)&x->_sign, (char *)&y->_sign, y->_wds*sizeof(__Long) + 2*sizeof(int))
420
 
421
extern _CONST double tinytens[];
422
extern _CONST double bigtens[];
423
extern _CONST double tens[];
4921 Serge 424
#if !defined(PREFER_SIZE_OVER_SPEED) && !defined(__OPTIMIZE_SIZE__) && !defined(_SMALL_HEXDIG)
425
extern _CONST unsigned char __hexdig[];
426
#endif /* !defined(PREFER_SIZE_OVER_SPEED) && !defined(__OPTIMIZE_SIZE__) && !defined(_SMALL_HEXDIG) */
4349 Serge 427
 
428
 
429
double _EXFUN(_mprec_log10,(int));