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
|
/*
* IBM Accurate Mathematical Library
* Written by International Business Machines Corp.
* Copyright (C) 2001-2014 Free Software Foundation, Inc.
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation; either version 2.1 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this program; if not, see <http://www.gnu.org/licenses/>.
*/
/************************************************************************/
/* MODULE_NAME: mpa.h */
/* */
/* FUNCTIONS: */
/* mcr */
/* acr */
/* cpy */
/* mp_dbl */
/* dbl_mp */
/* add */
/* sub */
/* mul */
/* dvd */
/* */
/* Arithmetic functions for multiple precision numbers. */
/* Common types and definition */
/************************************************************************/
#include <mpa-arch.h>
/* The mp_no structure holds the details of a multi-precision floating point
number.
- The radix of the number (R) is 2 ^ 24.
- E: The exponent of the number.
- D[0]: The sign (-1, 1) or 0 if the value is 0. In the latter case, the
values of the remaining members of the structure are ignored.
- D[1] - D[p]: The mantissa of the number where:
0 <= D[i] < R and
P is the precision of the number and 1 <= p <= 32
D[p+1] ... D[39] have no significance.
- The value of the number is:
D[1] * R ^ (E - 1) + D[2] * R ^ (E - 2) ... D[p] * R ^ (E - p)
*/
typedef struct
{
int e;
mantissa_t d[40];
} mp_no;
typedef union
{
int i[2];
double d;
} number;
extern const mp_no mpone;
extern const mp_no mptwo;
#define X x->d
#define Y y->d
#define Z z->d
#define EX x->e
#define EY y->e
#define EZ z->e
#define ABS(x) ((x) < 0 ? -(x) : (x))
#ifndef RADIXI
# define RADIXI 0x1.0p-24 /* 2^-24 */
#endif
#ifndef TWO52
# define TWO52 0x1.0p52 /* 2^52 */
#endif
#define TWO5 TWOPOW (5) /* 2^5 */
#define TWO8 TWOPOW (8) /* 2^52 */
#define TWO10 TWOPOW (10) /* 2^10 */
#define TWO18 TWOPOW (18) /* 2^18 */
#define TWO19 TWOPOW (19) /* 2^19 */
#define TWO23 TWOPOW (23) /* 2^23 */
#define HALFRAD TWO23
#define TWO57 0x1.0p57 /* 2^57 */
#define TWO71 0x1.0p71 /* 2^71 */
#define TWOM1032 0x1.0p-1032 /* 2^-1032 */
#define TWOM1022 0x1.0p-1022 /* 2^-1022 */
#define HALF 0x1.0p-1 /* 1/2 */
#define MHALF -0x1.0p-1 /* -1/2 */
int __acr (const mp_no *, const mp_no *, int);
void __cpy (const mp_no *, mp_no *, int);
void __mp_dbl (const mp_no *, double *, int);
void __dbl_mp (double, mp_no *, int);
void __add (const mp_no *, const mp_no *, mp_no *, int);
void __sub (const mp_no *, const mp_no *, mp_no *, int);
void __mul (const mp_no *, const mp_no *, mp_no *, int);
void __sqr (const mp_no *, mp_no *, int);
void __dvd (const mp_no *, const mp_no *, mp_no *, int);
extern void __mpatan (mp_no *, mp_no *, int);
extern void __mpatan2 (mp_no *, mp_no *, mp_no *, int);
extern void __mpsqrt (mp_no *, mp_no *, int);
extern void __mpexp (mp_no *, mp_no *, int);
extern void __c32 (mp_no *, mp_no *, mp_no *, int);
extern int __mpranred (double, mp_no *, int);
/* Given a power POW, build a multiprecision number 2^POW. */
static inline void
__pow_mp (int pow, mp_no *y, int p)
{
int i, rem;
/* The exponent is E such that E is a factor of 2^24. The remainder (of the
form 2^x) goes entirely into the first digit of the mantissa as it is
always less than 2^24. */
EY = pow / 24;
rem = pow - EY * 24;
EY++;
/* If the remainder is negative, it means that POW was negative since
|EY * 24| <= |pow|. Adjust so that REM is positive and still less than
24 because of which, the mantissa digit is less than 2^24. */
if (rem < 0)
{
EY--;
rem += 24;
}
/* The sign of any 2^x is always positive. */
Y[0] = 1;
Y[1] = 1 << rem;
/* Everything else is 0. */
for (i = 2; i <= p; i++)
Y[i] = 0;
}
|
