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
|
// SPDX-License-Identifier: GPL-2.0
/*---------------------------------------------------------------------------+
| poly_atan.c |
| |
| Compute the arctan of a FPU_REG, using 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 "status_w.h"
#include "control_w.h"
#include "poly.h"
#define HIPOWERon 6 /* odd poly, negative terms */
static const unsigned long long oddnegterms[HIPOWERon] = {
0x0000000000000000LL, /* Dummy (not for - 1.0) */
0x015328437f756467LL,
0x0005dda27b73dec6LL,
0x0000226bf2bfb91aLL,
0x000000ccc439c5f7LL,
0x0000000355438407LL
};
#define HIPOWERop 6 /* odd poly, positive terms */
static const unsigned long long oddplterms[HIPOWERop] = {
/* 0xaaaaaaaaaaaaaaabLL, transferred to fixedpterm[] */
0x0db55a71875c9ac2LL,
0x0029fce2d67880b0LL,
0x0000dfd3908b4596LL,
0x00000550fd61dab4LL,
0x0000001c9422b3f9LL,
0x000000003e3301e1LL
};
static const unsigned long long denomterm = 0xebd9b842c5c53a0eLL;
static const Xsig fixedpterm = MK_XSIG(0xaaaaaaaa, 0xaaaaaaaa, 0xaaaaaaaa);
static const Xsig pi_signif = MK_XSIG(0xc90fdaa2, 0x2168c234, 0xc4c6628b);
/*--- poly_atan() -----------------------------------------------------------+
| |
+---------------------------------------------------------------------------*/
void poly_atan(FPU_REG *st0_ptr, u_char st0_tag,
FPU_REG *st1_ptr, u_char st1_tag)
{
u_char transformed, inverted, sign1, sign2;
int exponent;
long int dummy_exp;
Xsig accumulator, Numer, Denom, accumulatore, argSignif, argSq, argSqSq;
u_char tag;
sign1 = getsign(st0_ptr);
sign2 = getsign(st1_ptr);
if (st0_tag == TAG_Valid) {
exponent = exponent(st0_ptr);
} else {
/* This gives non-compatible stack contents... */
FPU_to_exp16(st0_ptr, st0_ptr);
exponent = exponent16(st0_ptr);
}
if (st1_tag == TAG_Valid) {
exponent -= exponent(st1_ptr);
} else {
/* This gives non-compatible stack contents... */
FPU_to_exp16(st1_ptr, st1_ptr);
exponent -= exponent16(st1_ptr);
}
if ((exponent < 0) || ((exponent == 0) &&
((st0_ptr->sigh < st1_ptr->sigh) ||
((st0_ptr->sigh == st1_ptr->sigh) &&
(st0_ptr->sigl < st1_ptr->sigl))))) {
inverted = 1;
Numer.lsw = Denom.lsw = 0;
XSIG_LL(Numer) = significand(st0_ptr);
XSIG_LL(Denom) = significand(st1_ptr);
} else {
inverted = 0;
exponent = -exponent;
Numer.lsw = Denom.lsw = 0;
XSIG_LL(Numer) = significand(st1_ptr);
XSIG_LL(Denom) = significand(st0_ptr);
}
div_Xsig(&Numer, &Denom, &argSignif);
exponent += norm_Xsig(&argSignif);
if ((exponent >= -1)
|| ((exponent == -2) && (argSignif.msw > 0xd413ccd0))) {
/* The argument is greater than sqrt(2)-1 (=0.414213562...) */
/* Convert the argument by an identity for atan */
transformed = 1;
if (exponent >= 0) {
#ifdef PARANOID
if (!((exponent == 0) &&
(argSignif.lsw == 0) && (argSignif.midw == 0) &&
(argSignif.msw == 0x80000000))) {
EXCEPTION(EX_INTERNAL | 0x104); /* There must be a logic error */
return;
}
#endif /* PARANOID */
argSignif.msw = 0; /* Make the transformed arg -> 0.0 */
} else {
Numer.lsw = Denom.lsw = argSignif.lsw;
XSIG_LL(Numer) = XSIG_LL(Denom) = XSIG_LL(argSignif);
if (exponent < -1)
shr_Xsig(&Numer, -1 - exponent);
negate_Xsig(&Numer);
shr_Xsig(&Denom, -exponent);
Denom.msw |= 0x80000000;
div_Xsig(&Numer, &Denom, &argSignif);
exponent = -1 + norm_Xsig(&argSignif);
}
} else {
transformed = 0;
}
argSq.lsw = argSignif.lsw;
argSq.midw = argSignif.midw;
argSq.msw = argSignif.msw;
mul_Xsig_Xsig(&argSq, &argSq);
argSqSq.lsw = argSq.lsw;
argSqSq.midw = argSq.midw;
argSqSq.msw = argSq.msw;
mul_Xsig_Xsig(&argSqSq, &argSqSq);
accumulatore.lsw = argSq.lsw;
XSIG_LL(accumulatore) = XSIG_LL(argSq);
shr_Xsig(&argSq, 2 * (-1 - exponent - 1));
shr_Xsig(&argSqSq, 4 * (-1 - exponent - 1));
/* Now have argSq etc with binary point at the left
.1xxxxxxxx */
/* Do the basic fixed point polynomial evaluation */
accumulator.msw = accumulator.midw = accumulator.lsw = 0;
polynomial_Xsig(&accumulator, &XSIG_LL(argSqSq),
oddplterms, HIPOWERop - 1);
mul64_Xsig(&accumulator, &XSIG_LL(argSq));
negate_Xsig(&accumulator);
polynomial_Xsig(&accumulator, &XSIG_LL(argSqSq), oddnegterms,
HIPOWERon - 1);
negate_Xsig(&accumulator);
add_two_Xsig(&accumulator, &fixedpterm, &dummy_exp);
mul64_Xsig(&accumulatore, &denomterm);
shr_Xsig(&accumulatore, 1 + 2 * (-1 - exponent));
accumulatore.msw |= 0x80000000;
div_Xsig(&accumulator, &accumulatore, &accumulator);
mul_Xsig_Xsig(&accumulator, &argSignif);
mul_Xsig_Xsig(&accumulator, &argSq);
shr_Xsig(&accumulator, 3);
negate_Xsig(&accumulator);
add_Xsig_Xsig(&accumulator, &argSignif);
if (transformed) {
/* compute pi/4 - accumulator */
shr_Xsig(&accumulator, -1 - exponent);
negate_Xsig(&accumulator);
add_Xsig_Xsig(&accumulator, &pi_signif);
exponent = -1;
}
if (inverted) {
/* compute pi/2 - accumulator */
shr_Xsig(&accumulator, -exponent);
negate_Xsig(&accumulator);
add_Xsig_Xsig(&accumulator, &pi_signif);
exponent = 0;
}
if (sign1) {
/* compute pi - accumulator */
shr_Xsig(&accumulator, 1 - exponent);
negate_Xsig(&accumulator);
add_Xsig_Xsig(&accumulator, &pi_signif);
exponent = 1;
}
exponent += round_Xsig(&accumulator);
significand(st1_ptr) = XSIG_LL(accumulator);
setexponent16(st1_ptr, exponent);
tag = FPU_round(st1_ptr, 1, 0, FULL_PRECISION, sign2);
FPU_settagi(1, tag);
set_precision_flag_up(); /* We do not really know if up or down,
use this as the default. */
}
|
