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
|
/*---------------------------------------------------------------------------+
| poly_2xm1.c |
| |
| Function to compute 2^x-1 by a polynomial approximation. |
| |
| Copyright (C) 1992,1993,1994,1997 |
| W. Metzenthen, 22 Parker St, Ormond, Vic 3163, Australia |
| E-mail billm@suburbia.net |
| |
| |
+---------------------------------------------------------------------------*/
#include "exception.h"
#include "reg_constant.h"
#include "fpu_emu.h"
#include "fpu_system.h"
#include "control_w.h"
#include "poly.h"
#define HIPOWER 11
static const unsigned long long lterms[HIPOWER] = {
0x0000000000000000LL, /* This term done separately as 12 bytes */
0xf5fdeffc162c7543LL,
0x1c6b08d704a0bfa6LL,
0x0276556df749cc21LL,
0x002bb0ffcf14f6b8LL,
0x0002861225ef751cLL,
0x00001ffcbfcd5422LL,
0x00000162c005d5f1LL,
0x0000000da96ccb1bLL,
0x0000000078d1b897LL,
0x000000000422b029LL
};
static const Xsig hiterm = MK_XSIG(0xb17217f7, 0xd1cf79ab, 0xc8a39194);
/* Four slices: 0.0 : 0.25 : 0.50 : 0.75 : 1.0,
These numbers are 2^(1/4), 2^(1/2), and 2^(3/4)
*/
static const Xsig shiftterm0 = MK_XSIG(0, 0, 0);
static const Xsig shiftterm1 = MK_XSIG(0x9837f051, 0x8db8a96f, 0x46ad2318);
static const Xsig shiftterm2 = MK_XSIG(0xb504f333, 0xf9de6484, 0x597d89b3);
static const Xsig shiftterm3 = MK_XSIG(0xd744fcca, 0xd69d6af4, 0x39a68bb9);
static const Xsig *shiftterm[] = { &shiftterm0, &shiftterm1,
&shiftterm2, &shiftterm3
};
/*--- poly_2xm1() -----------------------------------------------------------+
| Requires st(0) which is TAG_Valid and < 1. |
+---------------------------------------------------------------------------*/
int poly_2xm1(u_char sign, FPU_REG *arg, FPU_REG *result)
{
long int exponent, shift;
unsigned long long Xll;
Xsig accumulator, Denom, argSignif;
u_char tag;
exponent = exponent16(arg);
#ifdef PARANOID
if (exponent >= 0) { /* Don't want a |number| >= 1.0 */
/* Number negative, too large, or not Valid. */
EXCEPTION(EX_INTERNAL | 0x127);
return 1;
}
#endif /* PARANOID */
argSignif.lsw = 0;
XSIG_LL(argSignif) = Xll = significand(arg);
if (exponent == -1) {
shift = (argSignif.msw & 0x40000000) ? 3 : 2;
/* subtract 0.5 or 0.75 */
exponent -= 2;
XSIG_LL(argSignif) <<= 2;
Xll <<= 2;
} else if (exponent == -2) {
shift = 1;
/* subtract 0.25 */
exponent--;
XSIG_LL(argSignif) <<= 1;
Xll <<= 1;
} else
shift = 0;
if (exponent < -2) {
/* Shift the argument right by the required places. */
if (FPU_shrx(&Xll, -2 - exponent) >= 0x80000000U)
Xll++; /* round up */
}
accumulator.lsw = accumulator.midw = accumulator.msw = 0;
polynomial_Xsig(&accumulator, &Xll, lterms, HIPOWER - 1);
mul_Xsig_Xsig(&accumulator, &argSignif);
shr_Xsig(&accumulator, 3);
mul_Xsig_Xsig(&argSignif, &hiterm); /* The leading term */
add_two_Xsig(&accumulator, &argSignif, &exponent);
if (shift) {
/* The argument is large, use the identity:
f(x+a) = f(a) * (f(x) + 1) - 1;
*/
shr_Xsig(&accumulator, -exponent);
accumulator.msw |= 0x80000000; /* add 1.0 */
mul_Xsig_Xsig(&accumulator, shiftterm[shift]);
accumulator.msw &= 0x3fffffff; /* subtract 1.0 */
exponent = 1;
}
if (sign != SIGN_POS) {
/* The argument is negative, use the identity:
f(-x) = -f(x) / (1 + f(x))
*/
Denom.lsw = accumulator.lsw;
XSIG_LL(Denom) = XSIG_LL(accumulator);
if (exponent < 0)
shr_Xsig(&Denom, -exponent);
else if (exponent > 0) {
/* exponent must be 1 here */
XSIG_LL(Denom) <<= 1;
if (Denom.lsw & 0x80000000)
XSIG_LL(Denom) |= 1;
(Denom.lsw) <<= 1;
}
Denom.msw |= 0x80000000; /* add 1.0 */
div_Xsig(&accumulator, &Denom, &accumulator);
}
/* Convert to 64 bit signed-compatible */
exponent += round_Xsig(&accumulator);
result = &st(0);
significand(result) = XSIG_LL(accumulator);
setexponent16(result, exponent);
tag = FPU_round(result, 1, 0, FULL_PRECISION, sign);
setsign(result, sign);
FPU_settag0(tag);
return 0;
}
|
