aboutsummaryrefslogtreecommitdiff
path: root/newlib/libc/stdlib/mprec.h
blob: 001f0c28430dafecf60d5f2dabb8298b579922ea (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
/****************************************************************
 *
 * The author of this software is David M. Gay.
 *
 * Copyright (c) 1991 by AT&T.
 *
 * Permission to use, copy, modify, and distribute this software for any
 * purpose without fee is hereby granted, provided that this entire notice
 * is included in all copies of any software which is or includes a copy
 * or modification of this software and in all copies of the supporting
 * documentation for such software.
 *
 * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
 * WARRANTY.  IN PARTICULAR, NEITHER THE AUTHOR NOR AT&T MAKES ANY
 * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
 * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
 *
 ***************************************************************/

/* Please send bug reports to
	David M. Gay
	AT&T Bell Laboratories, Room 2C-463
	600 Mountain Avenue
	Murray Hill, NJ 07974-2070
	U.S.A.
	dmg@research.att.com or research!dmg
 */

#include <ieeefp.h>
#include <math.h>
#include <float.h>
#include <errno.h>
#include <sys/config.h>

#ifdef __IEEE_LITTLE_ENDIAN
#define IEEE_8087
#endif

#ifdef __IEEE_BIG_ENDIAN
#define IEEE_MC68k
#endif

#ifdef __Z8000__
#define Just_16
#endif

#ifdef DEBUG
#include "stdio.h"
#define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}
#endif

#ifdef Unsigned_Shifts
#define Sign_Extend(a,b) if (b < 0) a |= (__uint32_t)0xffff0000;
#else
#define Sign_Extend(a,b) /*no-op*/
#endif

#if defined(IEEE_8087) + defined(IEEE_MC68k) + defined(VAX) + defined(IBM) != 1
Exactly one of IEEE_8087, IEEE_MC68k, VAX, or IBM should be defined.
#endif

/* If we are going to examine or modify specific bits in a double using
   the word0 and/or word1 macros, then we must wrap the double inside
   a union.  This is necessary to avoid undefined behavior according to
   the ANSI C spec.  */
union double_union
{
  double d;
  __uint32_t i[2];
};

#ifdef IEEE_8087
#define word0(x) (x.i[1])
#define word1(x) (x.i[0])
#else
#define word0(x) (x.i[0])
#define word1(x) (x.i[1])
#endif

/* The following definition of Storeinc is appropriate for MIPS processors.
 * An alternative that might be better on some machines is
 * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
 */
#if defined(IEEE_8087) + defined(VAX)
#define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \
((unsigned short *)a)[0] = (unsigned short)c, a++)
#else
#define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \
((unsigned short *)a)[1] = (unsigned short)c, a++)
#endif

/* #define P DBL_MANT_DIG */
/* Ten_pmax = floor(P*log(2)/log(5)) */
/* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
/* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
/* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */

#if defined(IEEE_8087) + defined(IEEE_MC68k)
#if defined (_DOUBLE_IS_32BITS) 
#define Exp_shift   23
#define Exp_shift1  23
#define Exp_msk1    ((__uint32_t)0x00800000L)
#define Exp_msk11   ((__uint32_t)0x00800000L)
#define Exp_mask    ((__uint32_t)0x7f800000L)
#define P    	    24
#define Bias 	    127
#if 0
#define IEEE_Arith  /* it is, but the code doesn't handle IEEE singles yet */
#endif
#define Emin        (-126)
#define Exp_1       ((__uint32_t)0x3f800000L)
#define Exp_11      ((__uint32_t)0x3f800000L)
#define Ebits 	    8
#define Frac_mask   ((__uint32_t)0x007fffffL)
#define Frac_mask1  ((__uint32_t)0x007fffffL)
#define Ten_pmax    10
#define Sign_bit    ((__uint32_t)0x80000000L)
#define Ten_pmax    10
#define Bletch	    2
#define Bndry_mask  ((__uint32_t)0x007fffffL)
#define Bndry_mask1 ((__uint32_t)0x007fffffL)
#define LSB 1
#define Sign_bit    ((__uint32_t)0x80000000L)
#define Log2P 	    1
#define Tiny0 	    0
#define Tiny1 	    1
#define Quick_max   5
#define Int_max     6
#define Infinite(x) (word0(x) == ((__uint32_t)0x7f800000L))
#undef word0
#undef word1

#define word0(x) (x.i[0])
#define word1(x) 0
#else

#define Exp_shift  20
#define Exp_shift1 20
#define Exp_msk1    ((__uint32_t)0x100000L)
#define Exp_msk11   ((__uint32_t)0x100000L)
#define Exp_mask  ((__uint32_t)0x7ff00000L)
#define P 53
#define Bias 1023
#define IEEE_Arith
#define Emin (-1022)
#define Exp_1  ((__uint32_t)0x3ff00000L)
#define Exp_11 ((__uint32_t)0x3ff00000L)
#define Ebits 11
#define Frac_mask  ((__uint32_t)0xfffffL)
#define Frac_mask1 ((__uint32_t)0xfffffL)
#define Ten_pmax 22
#define Bletch 0x10
#define Bndry_mask  ((__uint32_t)0xfffffL)
#define Bndry_mask1 ((__uint32_t)0xfffffL)
#define LSB 1
#define Sign_bit ((__uint32_t)0x80000000L)
#define Log2P 1
#define Tiny0 0
#define Tiny1 1
#define Quick_max 14
#define Int_max 14
#define Infinite(x) (word0(x) == ((__uint32_t)0x7ff00000L)) /* sufficient test for here */
#endif

#else
#undef  Sudden_Underflow
#define Sudden_Underflow
#ifdef IBM
#define Exp_shift  24
#define Exp_shift1 24
#define Exp_msk1   ((__uint32_t)0x1000000L)
#define Exp_msk11  ((__uint32_t)0x1000000L)
#define Exp_mask  ((__uint32_t)0x7f000000L)
#define P 14
#define Bias 65
#define Exp_1  ((__uint32_t)0x41000000L)
#define Exp_11 ((__uint32_t)0x41000000L)
#define Ebits 8	/* exponent has 7 bits, but 8 is the right value in b2d */
#define Frac_mask  ((__uint32_t)0xffffffL)
#define Frac_mask1 ((__uint32_t)0xffffffL)
#define Bletch 4
#define Ten_pmax 22
#define Bndry_mask  ((__uint32_t)0xefffffL)
#define Bndry_mask1 ((__uint32_t)0xffffffL)
#define LSB 1
#define Sign_bit ((__uint32_t)0x80000000L)
#define Log2P 4
#define Tiny0 ((__uint32_t)0x100000L)
#define Tiny1 0
#define Quick_max 14
#define Int_max 15
#else /* VAX */
#define Exp_shift  23
#define Exp_shift1 7
#define Exp_msk1    0x80
#define Exp_msk11   ((__uint32_t)0x800000L)
#define Exp_mask  ((__uint32_t)0x7f80L)
#define P 56
#define Bias 129
#define Exp_1  ((__uint32_t)0x40800000L)
#define Exp_11 ((__uint32_t)0x4080L)
#define Ebits 8
#define Frac_mask  ((__uint32_t)0x7fffffL)
#define Frac_mask1 ((__uint32_t)0xffff007fL)
#define Ten_pmax 24
#define Bletch 2
#define Bndry_mask  ((__uint32_t)0xffff007fL)
#define Bndry_mask1 ((__uint32_t)0xffff007fL)
#define LSB ((__uint32_t)0x10000L)
#define Sign_bit ((__uint32_t)0x8000L)
#define Log2P 1
#define Tiny0 0x80
#define Tiny1 0
#define Quick_max 15
#define Int_max 15
#endif
#endif

#ifndef IEEE_Arith
#define ROUND_BIASED
#endif

#ifdef RND_PRODQUOT
#define rounded_product(a,b) a = rnd_prod(a, b)
#define rounded_quotient(a,b) a = rnd_quot(a, b)
#ifdef KR_headers
extern double rnd_prod(), rnd_quot();
#else
extern double rnd_prod(double, double), rnd_quot(double, double);
#endif
#else
#define rounded_product(a,b) a *= b
#define rounded_quotient(a,b) a /= b
#endif

#define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
#define Big1 ((__uint32_t)0xffffffffL)

#ifndef Just_16
/* When Pack_32 is not defined, we store 16 bits per 32-bit long.
 * This makes some inner loops simpler and sometimes saves work
 * during multiplications, but it often seems to make things slightly
 * slower.  Hence the default is now to store 32 bits per long.
 */

#ifndef Pack_32
#define Pack_32
#endif
#endif


#ifdef __cplusplus
extern "C" double strtod(const char *s00, char **se);
extern "C" char *dtoa(double d, int mode, int ndigits,
			int *decpt, int *sign, char **rve);
#endif


typedef struct _Bigint _Bigint;

#define Balloc	_Balloc
#define Bfree	_Bfree
#define multadd _multadd
#define s2b	_s2b
#define lo0bits _lo0bits
#define hi0bits _hi0bits
#define i2b	_i2b
#define mult	_multiply
#define pow5mult	_pow5mult
#define lshift	_lshift
#define cmp	__mcmp
#define diff	__mdiff
#define ulp 	_ulp
#define b2d	_b2d
#define d2b	_d2b
#define ratio	_ratio

#define tens __mprec_tens
#define bigtens __mprec_bigtens
#define tinytens __mprec_tinytens

struct _reent ;
double 		_EXFUN(ulp,(double x));
double		_EXFUN(b2d,(_Bigint *a , int *e));
_Bigint *	_EXFUN(Balloc,(struct _reent *p, int k));
void 		_EXFUN(Bfree,(struct _reent *p, _Bigint *v));
_Bigint *	_EXFUN(multadd,(struct _reent *p, _Bigint *, int, int));
_Bigint *	_EXFUN(s2b,(struct _reent *, const char*, int, int, __ULong));
_Bigint	*	_EXFUN(i2b,(struct _reent *,int));
_Bigint *	_EXFUN(mult, (struct _reent *, _Bigint *, _Bigint *));
_Bigint *	_EXFUN(pow5mult, (struct _reent *, _Bigint *, int k));
int 		_EXFUN(hi0bits,(__ULong));
int 		_EXFUN(lo0bits,(__ULong *));
_Bigint *        _EXFUN(d2b,(struct _reent *p, double d, int *e, int *bits));
_Bigint *        _EXFUN(lshift,(struct _reent *p, _Bigint *b, int k));
_Bigint *        _EXFUN(diff,(struct _reent *p, _Bigint *a, _Bigint *b));
int             _EXFUN(cmp,(_Bigint *a, _Bigint *b));

double		_EXFUN(ratio,(_Bigint *a, _Bigint *b));
#define Bcopy(x,y) memcpy((char *)&x->_sign, (char *)&y->_sign, y->_wds*sizeof(__Long) + 2*sizeof(int))

#if defined(_DOUBLE_IS_32BITS) && defined(__v800)
#define n_bigtens 2
#else
#define n_bigtens 5
#endif

extern _CONST double tinytens[];
extern _CONST double bigtens[];
extern _CONST double tens[];


double _EXFUN(_mprec_log10,(int));