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
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
|
dnl AMD K6 mpn_divexact_1 -- mpn by limb exact division.
dnl Copyright 2000, 2001, 2002 Free Software Foundation, Inc.
dnl
dnl This file is part of the GNU MP Library.
dnl
dnl The GNU MP Library is free software; you can redistribute it and/or
dnl modify it under the terms of the GNU Lesser General Public License as
dnl published by the Free Software Foundation; either version 3 of the
dnl License, or (at your option) any later version.
dnl
dnl The GNU MP Library is distributed in the hope that it will be useful,
dnl but WITHOUT ANY WARRANTY; without even the implied warranty of
dnl MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
dnl Lesser General Public License for more details.
dnl
dnl You should have received a copy of the GNU Lesser General Public License
dnl along with the GNU MP Library. If not, see http://www.gnu.org/licenses/.
include(`../config.m4')
C divisor
C odd even
C K6: 10.0 12.0 cycles/limb
C K6-2: 10.0 11.5
C void mpn_divexact_1 (mp_ptr dst, mp_srcptr src, mp_size_t size,
C mp_limb_t divisor);
C
C A simple divl is used for size==1. This is about 10 cycles faster for an
C odd divisor or 20 cycles for an even divisor.
C
C The loops are quite sensitive to code alignment, speeds should be
C rechecked (odd and even divisor, pic and non-pic) if contemplating
C changing anything.
defframe(PARAM_DIVISOR,16)
defframe(PARAM_SIZE, 12)
defframe(PARAM_SRC, 8)
defframe(PARAM_DST, 4)
dnl re-use parameter space
define(VAR_INVERSE,`PARAM_DST')
TEXT
ALIGN(32)
PROLOGUE(mpn_divexact_1)
deflit(`FRAME',0)
movl PARAM_SIZE, %ecx
movl PARAM_SRC, %eax
xorl %edx, %edx
cmpl $1, %ecx
jnz L(two_or_more)
movl (%eax), %eax
divl PARAM_DIVISOR
movl PARAM_DST, %ecx
movl %eax, (%ecx)
ret
L(two_or_more):
movl PARAM_DIVISOR, %eax
pushl %ebx FRAME_pushl()
movl PARAM_SRC, %ebx
pushl %ebp FRAME_pushl()
L(strip_twos):
shrl %eax
incl %edx C will get shift+1
jnc L(strip_twos)
pushl %esi FRAME_pushl()
leal 1(%eax,%eax), %esi C d without twos
andl $127, %eax C d/2, 7 bits
ifdef(`PIC',`
call L(movl_eip_ebp)
addl $_GLOBAL_OFFSET_TABLE_, %ebp
C
movl modlimb_invert_table@GOT(%ebp), %ebp
C
Zdisp( movzbl, 0,(%eax,%ebp), %eax)
',`
dnl non-PIC
movzbl modlimb_invert_table(%eax), %eax C inv 8 bits
')
pushl %edi FRAME_pushl()
leal (%eax,%eax), %ebp C 2*inv
imull %eax, %eax C inv*inv
movl PARAM_DST, %edi
imull %esi, %eax C inv*inv*d
subl %eax, %ebp C inv = 2*inv - inv*inv*d
leal (%ebp,%ebp), %eax C 2*inv
imull %ebp, %ebp C inv*inv
movl %esi, PARAM_DIVISOR C d without twos
leal (%ebx,%ecx,4), %ebx C src end
imull %esi, %ebp C inv*inv*d
leal (%edi,%ecx,4), %edi C dst end
negl %ecx C -size
subl %ebp, %eax C inv = 2*inv - inv*inv*d
subl $1, %edx C shift amount, and clear carry
ASSERT(e,` C expect d*inv == 1 mod 2^BITS_PER_MP_LIMB
pushl %eax FRAME_pushl()
imull PARAM_DIVISOR, %eax
cmpl $1, %eax
popl %eax FRAME_popl()')
movl %eax, VAR_INVERSE
jnz L(even)
movl (%ebx,%ecx,4), %esi C src low limb
jmp L(odd_entry)
ALIGN(16)
nop C code alignment
L(odd_top):
C eax scratch
C ebx src end
C ecx counter, limbs, negative
C edx inverse
C esi next limb, adjusted for carry
C edi dst end
C ebp carry bit, 0 or -1
imull %edx, %esi
movl PARAM_DIVISOR, %eax
movl %esi, -4(%edi,%ecx,4)
mull %esi C carry limb in edx
subl %ebp, %edx C apply carry bit
movl (%ebx,%ecx,4), %esi
L(odd_entry):
subl %edx, %esi C apply carry limb
movl VAR_INVERSE, %edx
sbbl %ebp, %ebp C 0 or -1
incl %ecx
jnz L(odd_top)
imull %edx, %esi
movl %esi, -4(%edi,%ecx,4)
popl %edi
popl %esi
popl %ebp
popl %ebx
ret
ifdef(`PIC',`
L(movl_eip_ebp):
movl (%esp), %ebp
ret_internal
ALIGN(8)
nop C code alignment, necessary for claimed speed
nop
',`
C non-PIC code alignment already ok at 0x9a
')
L(even):
C eax
C ebx src end
C ecx -size
C edx twos
C esi
C edi dst end
C ebp
xorl %ebp, %ebp
Zdisp( movq, 0,(%ebx,%ecx,4), %mm0) C src[0,1]
movd %edx, %mm7
movl VAR_INVERSE, %edx
addl $2, %ecx
psrlq %mm7, %mm0
movd %mm0, %esi
jz L(even_two) C if only two limbs
C Out-of-order execution is good enough to hide the load/rshift/movd
C latency. Having imul at the top of the loop gives 11.5 c/l instead of 12,
C on K6-2. In fact there's only 11 of decode, but nothing running at 11 has
C been found. Maybe the fact every second movq is unaligned costs the extra
C 0.5.
L(even_top):
C eax scratch
C ebx src end
C ecx counter, limbs, negative
C edx inverse
C esi next limb, adjusted for carry
C edi dst end
C ebp carry bit, 0 or -1
C
C mm0 scratch, source limbs
C mm7 twos
imull %edx, %esi
movl %esi, -8(%edi,%ecx,4)
movl PARAM_DIVISOR, %eax
mull %esi C carry limb in edx
movq -4(%ebx,%ecx,4), %mm0
psrlq %mm7, %mm0
movd %mm0, %esi
subl %ebp, %edx C apply carry bit
subl %edx, %esi C apply carry limb
movl VAR_INVERSE, %edx
sbbl %ebp, %ebp C 0 or -1
incl %ecx
jnz L(even_top)
L(even_two):
movd -4(%ebx), %mm0 C src high limb
psrlq %mm7, %mm0
imull %edx, %esi
movl %esi, -8(%edi)
movl PARAM_DIVISOR, %eax
mull %esi C carry limb in edx
movd %mm0, %esi
subl %ebp, %edx C apply carry bit
movl VAR_INVERSE, %eax
subl %edx, %esi C apply carry limb
imull %eax, %esi
movl %esi, -4(%edi)
popl %edi
popl %esi
popl %ebp
popl %ebx
emms_or_femms
ret
EPILOGUE()
|
