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
|
/*---------------------------------------------------------------------------+
| poly_tan.c |
| |
| Compute the tan of a FPU_REG, using a polynomial approximation. |
| |
| Copyright (C) 1992,1993,1994,1997,1999 |
| W. Metzenthen, 22 Parker St, Ormond, Vic 3163, |
| Australia. E-mail billm@melbpc.org.au |
| |
| |
+---------------------------------------------------------------------------*/
#include "exception.h"
#include "reg_constant.h"
#include "fpu_emu.h"
#include "fpu_system.h"
#include "control_w.h"
#include "poly.h"
#define HiPOWERop 3 /* odd poly, positive terms */
static const unsigned long long oddplterm[HiPOWERop] =
{
0x0000000000000000LL,
0x0051a1cf08fca228LL,
0x0000000071284ff7LL
};
#define HiPOWERon 2 /* odd poly, negative terms */
static const unsigned long long oddnegterm[HiPOWERon] =
{
0x1291a9a184244e80LL,
0x0000583245819c21LL
};
#define HiPOWERep 2 /* even poly, positive terms */
static const unsigned long long evenplterm[HiPOWERep] =
{
0x0e848884b539e888LL,
0x00003c7f18b887daLL
};
#define HiPOWERen 2 /* even poly, negative terms */
static const unsigned long long evennegterm[HiPOWERen] =
{
0xf1f0200fd51569ccLL,
0x003afb46105c4432LL
};
static const unsigned long long twothirds = 0xaaaaaaaaaaaaaaabLL;
/*--- poly_tan() ------------------------------------------------------------+
| |
+---------------------------------------------------------------------------*/
void poly_tan(FPU_REG *st0_ptr)
{
long int exponent;
int invert;
Xsig argSq, argSqSq, accumulatoro, accumulatore, accum,
argSignif, fix_up;
unsigned long adj;
exponent = exponent(st0_ptr);
#ifdef PARANOID
if ( signnegative(st0_ptr) ) /* Can't hack a number < 0.0 */
{ arith_invalid(0); return; } /* Need a positive number */
#endif PARANOID
/* Split the problem into two domains, smaller and larger than pi/4 */
if ( (exponent == 0) || ((exponent == -1) && (st0_ptr->sigh > 0xc90fdaa2)) )
{
/* The argument is greater than (approx) pi/4 */
invert = 1;
accum.lsw = 0;
XSIG_LL(accum) = significand(st0_ptr);
if ( exponent == 0 )
{
/* The argument is >= 1.0 */
/* Put the binary point at the left. */
XSIG_LL(accum) <<= 1;
}
/* pi/2 in hex is: 1.921fb54442d18469 898CC51701B839A2 52049C1 */
XSIG_LL(accum) = 0x921fb54442d18469LL - XSIG_LL(accum);
/* This is a special case which arises due to rounding. */
if ( XSIG_LL(accum) == 0xffffffffffffffffLL )
{
FPU_settag0(TAG_Valid);
significand(st0_ptr) = 0x8a51e04daabda360LL;
setexponent16(st0_ptr, (0x41 + EXTENDED_Ebias) | SIGN_Negative);
return;
}
argSignif.lsw = accum.lsw;
XSIG_LL(argSignif) = XSIG_LL(accum);
exponent = -1 + norm_Xsig(&argSignif);
}
else
{
invert = 0;
argSignif.lsw = 0;
XSIG_LL(accum) = XSIG_LL(argSignif) = significand(st0_ptr);
if ( exponent < -1 )
{
/* shift the argument right by the required places */
if ( FPU_shrx(&XSIG_LL(accum), -1-exponent) >= 0x80000000U )
XSIG_LL(accum) ++; /* round up */
}
}
XSIG_LL(argSq) = XSIG_LL(accum); argSq.lsw = accum.lsw;
mul_Xsig_Xsig(&argSq, &argSq);
XSIG_LL(argSqSq) = XSIG_LL(argSq); argSqSq.lsw = argSq.lsw;
mul_Xsig_Xsig(&argSqSq, &argSqSq);
/* Compute the negative terms for the numerator polynomial */
accumulatoro.msw = accumulatoro.midw = accumulatoro.lsw = 0;
polynomial_Xsig(&accumulatoro, &XSIG_LL(argSqSq), oddnegterm, HiPOWERon-1);
mul_Xsig_Xsig(&accumulatoro, &argSq);
negate_Xsig(&accumulatoro);
/* Add the positive terms */
polynomial_Xsig(&accumulatoro, &XSIG_LL(argSqSq), oddplterm, HiPOWERop-1);
/* Compute the positive terms for the denominator polynomial */
accumulatore.msw = accumulatore.midw = accumulatore.lsw = 0;
polynomial_Xsig(&accumulatore, &XSIG_LL(argSqSq), evenplterm, HiPOWERep-1);
mul_Xsig_Xsig(&accumulatore, &argSq);
negate_Xsig(&accumulatore);
/* Add the negative terms */
polynomial_Xsig(&accumulatore, &XSIG_LL(argSqSq), evennegterm, HiPOWERen-1);
/* Multiply by arg^2 */
mul64_Xsig(&accumulatore, &XSIG_LL(argSignif));
mul64_Xsig(&accumulatore, &XSIG_LL(argSignif));
/* de-normalize and divide by 2 */
shr_Xsig(&accumulatore, -2*(1+exponent) + 1);
negate_Xsig(&accumulatore); /* This does 1 - accumulator */
/* Now find the ratio. */
if ( accumulatore.msw == 0 )
{
/* accumulatoro must contain 1.0 here, (actually, 0) but it
really doesn't matter what value we use because it will
have negligible effect in later calculations
*/
XSIG_LL(accum) = 0x8000000000000000LL;
accum.lsw = 0;
}
else
{
div_Xsig(&accumulatoro, &accumulatore, &accum);
}
/* Multiply by 1/3 * arg^3 */
mul64_Xsig(&accum, &XSIG_LL(argSignif));
mul64_Xsig(&accum, &XSIG_LL(argSignif));
mul64_Xsig(&accum, &XSIG_LL(argSignif));
mul64_Xsig(&accum, &twothirds);
shr_Xsig(&accum, -2*(exponent+1));
/* tan(arg) = arg + accum */
add_two_Xsig(&accum, &argSignif, &exponent);
if ( invert )
{
/* We now have the value of tan(pi_2 - arg) where pi_2 is an
approximation for pi/2
*/
/* The next step is to fix the answer to compensate for the
error due to the approximation used for pi/2
*/
/* This is (approx) delta, the error in our approx for pi/2
(see above). It has an exponent of -65
*/
XSIG_LL(fix_up) = 0x898cc51701b839a2LL;
fix_up.lsw = 0;
if ( exponent == 0 )
adj = 0xffffffff; /* We want approx 1.0 here, but
this is close enough. */
else if ( exponent > -30 )
{
adj = accum.msw >> -(exponent+1); /* tan */
adj = mul_32_32(adj, adj); /* tan^2 */
}
else
adj = 0;
adj = mul_32_32(0x898cc517, adj); /* delta * tan^2 */
fix_up.msw += adj;
if ( !(fix_up.msw & 0x80000000) ) /* did fix_up overflow ? */
{
/* Yes, we need to add an msb */
shr_Xsig(&fix_up, 1);
fix_up.msw |= 0x80000000;
shr_Xsig(&fix_up, 64 + exponent);
}
else
shr_Xsig(&fix_up, 65 + exponent);
add_two_Xsig(&accum, &fix_up, &exponent);
/* accum now contains tan(pi/2 - arg).
Use tan(arg) = 1.0 / tan(pi/2 - arg)
*/
accumulatoro.lsw = accumulatoro.midw = 0;
accumulatoro.msw = 0x80000000;
div_Xsig(&accumulatoro, &accum, &accum);
exponent = - exponent - 1;
}
/* Transfer the result */
round_Xsig(&accum);
FPU_settag0(TAG_Valid);
significand(st0_ptr) = XSIG_LL(accum);
setexponent16(st0_ptr, exponent + EXTENDED_Ebias); /* Result is positive. */
}
|
