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
|
/* $NetBSD: ldexp.S,v 1.8 2003/08/07 16:42:15 agc Exp $ */
/*-
* Copyright (c) 1991, 1993
* The Regents of the University of California. All rights reserved.
*
* This code is derived from software contributed to Berkeley by
* Ralph Campbell.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
* 3. Neither the name of the University nor the names of its contributors
* may be used to endorse or promote products derived from this software
* without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
*/
#include <machine/asm.h>
__FBSDID("$FreeBSD$");
#if defined(LIBC_SCCS) && !defined(lint)
ASMSTR("from: @(#)ldexp.s 8.1 (Berkeley) 6/4/93")
ASMSTR("$NetBSD: ldexp.S,v 1.8 2003/08/07 16:42:15 agc Exp $")
#endif /* LIBC_SCCS and not lint */
#ifdef __ABICALLS__
.abicalls
#endif
#define DEXP_INF 0x7ff
#define DEXP_BIAS 1023
#define DEXP_MIN -1022
#define DEXP_MAX 1023
#define DFRAC_BITS 52
#define DIMPL_ONE 0x00100000
#define DLEAD_ZEROS 31 - 20
#define STICKYBIT 1
#define GUARDBIT 0x80000000
#define DSIGNAL_NAN 0x00040000
#define DQUIET_NAN0 0x0007ffff
#define DQUIET_NAN1 0xffffffff
/*
* double ldexp(x, N)
* double x; int N;
*
* Return x * (2**N), for integer values N.
*/
LEAF(ldexp)
mfc1 v1, $f13 # get MSW of x
mfc1 t3, $f12 # get LSW of x
sll t1, v1, 1 # get x exponent
srl t1, t1, 32 - 11
beq t1, DEXP_INF, 9f # is it a NAN or infinity?
beq t1, zero, 1f # zero or denormalized number?
addu t1, t1, a2 # scale exponent
sll v0, a2, 20 # position N for addition
bge t1, DEXP_INF, 8f # overflow?
addu v0, v0, v1 # multiply by (2**N)
ble t1, zero, 4f # underflow?
mtc1 v0, $f1 # save MSW of result
mtc1 t3, $f0 # save LSW of result
j ra
1:
sll t2, v1, 32 - 20 # get x fraction
srl t2, t2, 32 - 20
srl t0, v1, 31 # get x sign
bne t2, zero, 1f
beq t3, zero, 9f # result is zero
1:
/*
* Find out how many leading zero bits are in t2,t3 and put in t9.
*/
move v0, t2
move t9, zero
bne t2, zero, 1f
move v0, t3
addu t9, 32
1:
srl ta0, v0, 16
bne ta0, zero, 1f
addu t9, 16
sll v0, 16
1:
srl ta0, v0, 24
bne ta0, zero, 1f
addu t9, 8
sll v0, 8
1:
srl ta0, v0, 28
bne ta0, zero, 1f
addu t9, 4
sll v0, 4
1:
srl ta0, v0, 30
bne ta0, zero, 1f
addu t9, 2
sll v0, 2
1:
srl ta0, v0, 31
bne ta0, zero, 1f
addu t9, 1
/*
* Now shift t2,t3 the correct number of bits.
*/
1:
subu t9, t9, DLEAD_ZEROS # dont count normal leading zeros
li t1, DEXP_MIN + DEXP_BIAS
subu t1, t1, t9 # adjust exponent
addu t1, t1, a2 # scale exponent
li v0, 32
blt t9, v0, 1f
subu t9, t9, v0 # shift fraction left >= 32 bits
sll t2, t3, t9
move t3, zero
b 2f
1:
subu v0, v0, t9 # shift fraction left < 32 bits
sll t2, t2, t9
srl ta0, t3, v0
or t2, t2, ta0
sll t3, t3, t9
2:
bge t1, DEXP_INF, 8f # overflow?
ble t1, zero, 4f # underflow?
sll t2, t2, 32 - 20 # clear implied one bit
srl t2, t2, 32 - 20
3:
sll t1, t1, 31 - 11 # reposition exponent
sll t0, t0, 31 # reposition sign
or t0, t0, t1 # put result back together
or t0, t0, t2
mtc1 t0, $f1 # save MSW of result
mtc1 t3, $f0 # save LSW of result
j ra
4:
li v0, 0x80000000
ble t1, -52, 7f # is result too small for denorm?
sll t2, v1, 31 - 20 # clear exponent, extract fraction
or t2, t2, v0 # set implied one bit
blt t1, -30, 2f # will all bits in t3 be shifted out?
srl t2, t2, 31 - 20 # shift fraction back to normal position
subu t1, t1, 1
sll ta0, t2, t1 # shift right t2,t3 based on exponent
srl t8, t3, t1 # save bits shifted out
negu t1
srl t3, t3, t1
or t3, t3, ta0
srl t2, t2, t1
bge t8, zero, 1f # does result need to be rounded?
addu t3, t3, 1 # round result
sltu ta0, t3, 1
sll t8, t8, 1
addu t2, t2, ta0
bne t8, zero, 1f # round result to nearest
and t3, t3, ~1
1:
mtc1 t3, $f0 # save denormalized result (LSW)
mtc1 t2, $f1 # save denormalized result (MSW)
bge v1, zero, 1f # should result be negative?
neg.d $f0, $f0 # negate result
1:
j ra
2:
mtc1 zero, $f1 # exponent and upper fraction
addu t1, t1, 20 # compute amount to shift right by
sll t8, t2, t1 # save bits shifted out
negu t1
srl t3, t2, t1
bge t8, zero, 1f # does result need to be rounded?
addu t3, t3, 1 # round result
sltu ta0, t3, 1
sll t8, t8, 1
mtc1 ta0, $f1 # exponent and upper fraction
bne t8, zero, 1f # round result to nearest
and t3, t3, ~1
1:
mtc1 t3, $f0
bge v1, zero, 1f # is result negative?
neg.d $f0, $f0 # negate result
1:
j ra
7:
mtc1 zero, $f0 # result is zero
mtc1 zero, $f1
beq t0, zero, 1f # is result positive?
neg.d $f0, $f0 # negate result
1:
j ra
8:
li t1, 0x7ff00000 # result is infinity (MSW)
mtc1 t1, $f1
mtc1 zero, $f0 # result is infinity (LSW)
bge v1, zero, 1f # should result be negative infinity?
neg.d $f0, $f0 # result is negative infinity
1:
add.d $f0, $f0 # cause overflow faults if enabled
j ra
9:
mov.d $f0, $f12 # yes, result is just x
j ra
END(ldexp)
|
