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
|
/*---------------------------------------------------------------------------+
| poly_l2.c |
| |
| Compute the base 2 log of a FPU_REG, using a polynomial approximation. |
| |
| Copyright (C) 1992,1993,1994 |
| W. Metzenthen, 22 Parker St, Ormond, Vic 3163, |
| Australia. E-mail billm@vaxc.cc.monash.edu.au |
| |
| |
+---------------------------------------------------------------------------*/
#include "exception.h"
#include "reg_constant.h"
#include "fpu_emu.h"
#include "control_w.h"
#include "poly.h"
static void log2_kernel(FPU_REG const *arg,
Xsig *accum_result, long int *expon);
/*--- poly_l2() -------------------------------------------------------------+
| Base 2 logarithm by a polynomial approximation. |
+---------------------------------------------------------------------------*/
void poly_l2(FPU_REG const *arg, FPU_REG const *y, FPU_REG *result)
{
long int exponent, expon, expon_expon;
Xsig accumulator, expon_accum, yaccum;
char sign;
FPU_REG x;
exponent = arg->exp - EXP_BIAS;
/* From arg, make a number > sqrt(2)/2 and < sqrt(2) */
if ( arg->sigh > (unsigned)0xb504f334 )
{
/* Treat as sqrt(2)/2 < arg < 1 */
significand(&x) = - significand(arg);
x.sign = SIGN_NEG;
x.tag = TW_Valid;
x.exp = EXP_BIAS-1;
exponent++;
normalize(&x);
}
else
{
/* Treat as 1 <= arg < sqrt(2) */
x.sigh = arg->sigh - 0x80000000;
x.sigl = arg->sigl;
x.sign = SIGN_POS;
x.tag = TW_Valid;
x.exp = EXP_BIAS;
normalize(&x);
}
if ( x.tag == TW_Zero )
{
expon = 0;
accumulator.msw = accumulator.midw = accumulator.lsw = 0;
}
else
{
log2_kernel(&x, &accumulator, &expon);
}
sign = exponent < 0;
if ( sign ) exponent = -exponent;
expon_accum.msw = exponent; expon_accum.midw = expon_accum.lsw = 0;
if ( exponent )
{
expon_expon = 31 + norm_Xsig(&expon_accum);
shr_Xsig(&accumulator, expon_expon - expon);
if ( sign ^ (x.sign == SIGN_NEG) )
negate_Xsig(&accumulator);
add_Xsig_Xsig(&accumulator, &expon_accum);
}
else
{
expon_expon = expon;
sign = x.sign;
}
yaccum.lsw = 0; XSIG_LL(yaccum) = significand(y);
mul_Xsig_Xsig(&accumulator, &yaccum);
expon_expon += round_Xsig(&accumulator);
if ( accumulator.msw == 0 )
{
reg_move(&CONST_Z, y);
}
else
{
result->exp = expon_expon + y->exp + 1;
significand(result) = XSIG_LL(accumulator);
result->tag = TW_Valid; /* set the tags to Valid */
result->sign = sign ^ y->sign;
}
return;
}
/*--- poly_l2p1() -----------------------------------------------------------+
| Base 2 logarithm by a polynomial approximation. |
| log2(x+1) |
+---------------------------------------------------------------------------*/
int poly_l2p1(FPU_REG const *arg, FPU_REG const *y, FPU_REG *result)
{
char sign;
long int exponent;
Xsig accumulator, yaccum;
sign = arg->sign;
if ( arg->exp < EXP_BIAS )
{
log2_kernel(arg, &accumulator, &exponent);
yaccum.lsw = 0;
XSIG_LL(yaccum) = significand(y);
mul_Xsig_Xsig(&accumulator, &yaccum);
exponent += round_Xsig(&accumulator);
result->exp = exponent + y->exp + 1;
significand(result) = XSIG_LL(accumulator);
result->tag = TW_Valid; /* set the tags to Valid */
result->sign = sign ^ y->sign;
return 0;
}
else
{
/* The magnitude of arg is far too large. */
reg_move(y, result);
if ( sign != SIGN_POS )
{
/* Trying to get the log of a negative number. */
return 1;
}
else
{
return 0;
}
}
}
#undef HIPOWER
#define HIPOWER 10
static const unsigned long long logterms[HIPOWER] =
{
0x2a8eca5705fc2ef0LL,
0xf6384ee1d01febceLL,
0x093bb62877cdf642LL,
0x006985d8a9ec439bLL,
0x0005212c4f55a9c8LL,
0x00004326a16927f0LL,
0x0000038d1d80a0e7LL,
0x0000003141cc80c6LL,
0x00000002b1668c9fLL,
0x000000002c7a46aaLL
};
static const unsigned long leadterm = 0xb8000000;
/*--- log2_kernel() ---------------------------------------------------------+
| Base 2 logarithm by a polynomial approximation. |
| log2(x+1) |
+---------------------------------------------------------------------------*/
static void log2_kernel(FPU_REG const *arg, Xsig *accum_result,
long int *expon)
{
char sign;
long int exponent, adj;
unsigned long long Xsq;
Xsig accumulator, Numer, Denom, argSignif, arg_signif;
sign = arg->sign;
exponent = arg->exp - EXP_BIAS;
Numer.lsw = Denom.lsw = 0;
XSIG_LL(Numer) = XSIG_LL(Denom) = significand(arg);
if ( sign == SIGN_POS )
{
shr_Xsig(&Denom, 2 - (1 + exponent));
Denom.msw |= 0x80000000;
div_Xsig(&Numer, &Denom, &argSignif);
}
else
{
shr_Xsig(&Denom, 1 - (1 + exponent));
negate_Xsig(&Denom);
if ( Denom.msw & 0x80000000 )
{
div_Xsig(&Numer, &Denom, &argSignif);
exponent ++;
}
else
{
/* Denom must be 1.0 */
argSignif.lsw = Numer.lsw; argSignif.midw = Numer.midw;
argSignif.msw = Numer.msw;
}
}
#ifndef PECULIAR_486
/* Should check here that |local_arg| is within the valid range */
if ( exponent >= -2 )
{
if ( (exponent > -2) ||
(argSignif.msw > (unsigned)0xafb0ccc0) )
{
/* The argument is too large */
}
}
#endif PECULIAR_486
arg_signif.lsw = argSignif.lsw; XSIG_LL(arg_signif) = XSIG_LL(argSignif);
adj = norm_Xsig(&argSignif);
accumulator.lsw = argSignif.lsw; XSIG_LL(accumulator) = XSIG_LL(argSignif);
mul_Xsig_Xsig(&accumulator, &accumulator);
shr_Xsig(&accumulator, 2*(-1 - (1 + exponent + adj)));
Xsq = XSIG_LL(accumulator);
if ( accumulator.lsw & 0x80000000 )
Xsq++;
accumulator.msw = accumulator.midw = accumulator.lsw = 0;
/* Do the basic fixed point polynomial evaluation */
polynomial_Xsig(&accumulator, &Xsq, logterms, HIPOWER-1);
mul_Xsig_Xsig(&accumulator, &argSignif);
shr_Xsig(&accumulator, 6 - adj);
mul32_Xsig(&arg_signif, leadterm);
add_two_Xsig(&accumulator, &arg_signif, &exponent);
*expon = exponent + 1;
accum_result->lsw = accumulator.lsw;
accum_result->midw = accumulator.midw;
accum_result->msw = accumulator.msw;
}
|
