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
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
|
dnl AMD64 mpn_redc_1 optimised for Intel Haswell.
dnl Contributed to the GNU project by Torbjörn Granlund.
dnl Copyright 2013 Free Software Foundation, Inc.
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 modify
dnl it under the terms of either:
dnl
dnl * the GNU Lesser General Public License as published by the Free
dnl Software Foundation; either version 3 of the License, or (at your
dnl option) any later version.
dnl
dnl or
dnl
dnl * the GNU General Public License as published by the Free Software
dnl Foundation; either version 2 of the License, or (at your option) any
dnl later version.
dnl
dnl or both in parallel, as here.
dnl
dnl The GNU MP Library is distributed in the hope that it will be useful, but
dnl WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
dnl or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
dnl for more details.
dnl
dnl You should have received copies of the GNU General Public License and the
dnl GNU Lesser General Public License along with the GNU MP Library. If not,
dnl see https://www.gnu.org/licenses/.
include(`../config.m4')
C cycles/limb
C AMD K8,K9 n/a
C AMD K10 n/a
C AMD bull n/a
C AMD pile n/a
C AMD steam ?
C AMD bobcat n/a
C AMD jaguar ?
C Intel P4 n/a
C Intel core n/a
C Intel NHM n/a
C Intel SBR n/a
C Intel IBR n/a
C Intel HWL 2.32
C Intel BWL ?
C Intel atom n/a
C VIA nano n/a
C The inner loops of this code are the result of running a code generation and
C optimisation tool suite written by David Harvey and Torbjörn Granlund.
C TODO
C * Micro-optimise.
C * Consider inlining mpn_add_n. Tests indicate that this saves just 1-2
C cycles, though.
define(`rp', `%rdi') C rcx
define(`up', `%rsi') C rdx
define(`mp_param', `%rdx') C r8
define(`n', `%rcx') C r9
define(`u0inv_param', `%r8') C stack
define(`i', `%r14')
define(`j', `%r15')
define(`mp', `%rdi')
define(`u0inv', `(%rsp)') C stack
ABI_SUPPORT(DOS64) C FIXME: needs verification
ABI_SUPPORT(STD64)
ASM_START()
TEXT
ALIGN(16)
PROLOGUE(mpn_redc_1)
FUNC_ENTRY(4)
IFDOS(` mov 56(%rsp), %r8 ')
push %rbx
push %rbp
push %r12
push %r13
push %r14
push %r15
push rp
mov mp_param, mp C note that rp and mp shares register
mov (up), %rdx
neg n
push %r8 C put u0inv on stack
imul u0inv_param, %rdx C first iteration q0
mov n, j C outer loop induction var
test $1, R8(n)
jnz L(bx1)
L(bx0): test $2, R8(n)
jz L(o0b)
cmp $-2, R32(n)
jnz L(o2)
C Special code for n = 2 since general code cannot handle it
mov 8(%rsp), %rbx C rp
lea 16(%rsp), %rsp C deallocate two slots
mulx( (mp), %r9, %r12)
mulx( 8,(mp), %r11, %r10)
add %r12, %r11
adc $0, %r10
add (up), %r9 C = 0
adc 8(up), %r11 C r11 = up[1]
adc $0, %r10 C -> up[0]
mov %r11, %rdx
imul u0inv_param, %rdx
mulx( (mp), %r13, %r12)
mulx( 8,(mp), %r14, %r15)
xor R32(%rax), R32(%rax)
add %r12, %r14
adc $0, %r15
add %r11, %r13 C = 0
adc 16(up), %r14 C rp[2]
adc $0, %r15 C -> up[1]
add %r14, %r10
adc 24(up), %r15
mov %r10, (%rbx)
mov %r15, 8(%rbx)
setc R8(%rax)
jmp L(ret)
L(o2): lea 2(n), i C inner loop induction var
mulx( (mp), %r9, %r8)
mulx( 8,(mp), %r11, %r10)
sar $2, i
add %r8, %r11
jmp L(lo2)
ALIGN(16)
L(tp2): adc %rax, %r9
lea 32(up), up
adc %r8, %r11
L(lo2): mulx( 16,(mp), %r13, %r12)
mov (up), %r8
mulx( 24,(mp), %rbx, %rax)
lea 32(mp), mp
adc %r10, %r13
adc %r12, %rbx
adc $0, %rax
mov 8(up), %r10
mov 16(up), %r12
add %r9, %r8
mov 24(up), %rbp
mov %r8, (up)
adc %r11, %r10
mulx( (mp), %r9, %r8)
mov %r10, 8(up)
adc %r13, %r12
mov %r12, 16(up)
adc %rbx, %rbp
mulx( 8,(mp), %r11, %r10)
mov %rbp, 24(up)
inc i
jnz L(tp2)
L(ed2): mov 56(up,n,8), %rdx C next iteration up[0]
lea 16(mp,n,8), mp C mp = (last starting mp)
adc %rax, %r9
adc %r8, %r11
mov 32(up), %r8
adc $0, %r10
imul u0inv, %rdx C next iteration q0
mov 40(up), %rax
add %r9, %r8
mov %r8, 32(up)
adc %r11, %rax
mov %rax, 40(up)
lea 56(up,n,8), up C up = (last starting up) + 1
adc $0, %r10
mov %r10, -8(up)
inc j
jnz L(o2)
jmp L(cj)
L(bx1): test $2, R8(n)
jz L(o3a)
L(o1a): cmp $-1, R32(n)
jnz L(o1b)
C Special code for n = 1 since general code cannot handle it
mov 8(%rsp), %rbx C rp
lea 16(%rsp), %rsp C deallocate two slots
mulx( (mp), %r11, %r10)
add (up), %r11
adc 8(up), %r10
mov %r10, (%rbx)
mov $0, R32(%rax)
setc R8(%rax)
jmp L(ret)
L(o1b): lea 24(mp), mp
L(o1): lea 1(n), i C inner loop induction var
mulx( -24,(mp), %r11, %r10)
mulx( -16,(mp), %r13, %r12)
mulx( -8,(mp), %rbx, %rax)
sar $2, i
add %r10, %r13
adc %r12, %rbx
adc $0, %rax
mov (up), %r10
mov 8(up), %r12
mov 16(up), %rbp
add %r11, %r10
jmp L(lo1)
ALIGN(16)
L(tp1): adc %rax, %r9
lea 32(up), up
adc %r8, %r11
mulx( 16,(mp), %r13, %r12)
mov -8(up), %r8
mulx( 24,(mp), %rbx, %rax)
lea 32(mp), mp
adc %r10, %r13
adc %r12, %rbx
adc $0, %rax
mov (up), %r10
mov 8(up), %r12
add %r9, %r8
mov 16(up), %rbp
mov %r8, -8(up)
adc %r11, %r10
L(lo1): mulx( (mp), %r9, %r8)
mov %r10, (up)
adc %r13, %r12
mov %r12, 8(up)
adc %rbx, %rbp
mulx( 8,(mp), %r11, %r10)
mov %rbp, 16(up)
inc i
jnz L(tp1)
L(ed1): mov 48(up,n,8), %rdx C next iteration up[0]
lea 40(mp,n,8), mp C mp = (last starting mp)
adc %rax, %r9
adc %r8, %r11
mov 24(up), %r8
adc $0, %r10
imul u0inv, %rdx C next iteration q0
mov 32(up), %rax
add %r9, %r8
mov %r8, 24(up)
adc %r11, %rax
mov %rax, 32(up)
lea 48(up,n,8), up C up = (last starting up) + 1
adc $0, %r10
mov %r10, -8(up)
inc j
jnz L(o1)
jmp L(cj)
L(o3a): cmp $-3, R32(n)
jnz L(o3b)
C Special code for n = 3 since general code cannot handle it
L(n3): mulx( (mp), %rbx, %rax)
mulx( 8,(mp), %r9, %r14)
add (up), %rbx
mulx( 16,(mp), %r11, %r10)
adc %rax, %r9 C W 1
adc %r14, %r11 C W 2
mov 8(up), %r14
mov u0inv_param, %rdx
adc $0, %r10 C W 3
mov 16(up), %rax
add %r9, %r14 C W 1
mov %r14, 8(up)
mulx( %r14, %rdx, %r13) C next iteration q0
adc %r11, %rax C W 2
mov %rax, 16(up)
adc $0, %r10 C W 3
mov %r10, (up)
lea 8(up), up C up = (last starting up) + 1
inc j
jnz L(n3)
jmp L(cj)
L(o3b): lea 8(mp), mp
L(o3): lea 4(n), i C inner loop induction var
mulx( -8,(mp), %rbx, %rax)
mulx( (mp), %r9, %r8)
mov (up), %rbp
mulx( 8,(mp), %r11, %r10)
sar $2, i
add %rbx, %rbp
nop
adc %rax, %r9
jmp L(lo3)
ALIGN(16)
L(tp3): adc %rax, %r9
lea 32(up), up
L(lo3): adc %r8, %r11
mulx( 16,(mp), %r13, %r12)
mov 8(up), %r8
mulx( 24,(mp), %rbx, %rax)
lea 32(mp), mp
adc %r10, %r13
adc %r12, %rbx
adc $0, %rax
mov 16(up), %r10
mov 24(up), %r12
add %r9, %r8
mov 32(up), %rbp
mov %r8, 8(up)
adc %r11, %r10
mulx( (mp), %r9, %r8)
mov %r10, 16(up)
adc %r13, %r12
mov %r12, 24(up)
adc %rbx, %rbp
mulx( 8,(mp), %r11, %r10)
mov %rbp, 32(up)
inc i
jnz L(tp3)
L(ed3): mov 64(up,n,8), %rdx C next iteration up[0]
lea 24(mp,n,8), mp C mp = (last starting mp)
adc %rax, %r9
adc %r8, %r11
mov 40(up), %r8
adc $0, %r10
imul u0inv, %rdx C next iteration q0
mov 48(up), %rax
add %r9, %r8
mov %r8, 40(up)
adc %r11, %rax
mov %rax, 48(up)
lea 64(up,n,8), up C up = (last starting up) + 1
adc $0, %r10
mov %r10, -8(up)
inc j
jnz L(o3)
jmp L(cj)
L(o0b): lea 16(mp), mp
L(o0): mov n, i C inner loop induction var
mulx( -16,(mp), %r13, %r12)
mulx( -8,(mp), %rbx, %rax)
sar $2, i
add %r12, %rbx
adc $0, %rax
mov (up), %r12
mov 8(up), %rbp
mulx( (mp), %r9, %r8)
add %r13, %r12
jmp L(lo0)
ALIGN(16)
L(tp0): adc %rax, %r9
lea 32(up), up
adc %r8, %r11
mulx( 16,(mp), %r13, %r12)
mov -16(up), %r8
mulx( 24,(mp), %rbx, %rax)
lea 32(mp), mp
adc %r10, %r13
adc %r12, %rbx
adc $0, %rax
mov -8(up), %r10
mov (up), %r12
add %r9, %r8
mov 8(up), %rbp
mov %r8, -16(up)
adc %r11, %r10
mulx( (mp), %r9, %r8)
mov %r10, -8(up)
adc %r13, %r12
mov %r12, (up)
L(lo0): adc %rbx, %rbp
mulx( 8,(mp), %r11, %r10)
mov %rbp, 8(up)
inc i
jnz L(tp0)
L(ed0): mov 40(up,n,8), %rdx C next iteration up[0]
lea 32(mp,n,8), mp C mp = (last starting mp)
adc %rax, %r9
adc %r8, %r11
mov 16(up), %r8
adc $0, %r10
imul u0inv, %rdx C next iteration q0
mov 24(up), %rax
add %r9, %r8
mov %r8, 16(up)
adc %r11, %rax
mov %rax, 24(up)
lea 40(up,n,8), up C up = (last starting up) + 1
adc $0, %r10
mov %r10, -8(up)
inc j
jnz L(o0)
L(cj):
IFSTD(` mov 8(%rsp), %rdi C param 1: rp
lea 16-8(%rsp), %rsp C deallocate 2, add back for alignment
lea (up,n,8), %rdx C param 3: up - n
neg R32(n) ') C param 4: n
IFDOS(` mov up, %rdx C param 2: up
lea (up,n,8), %r8 C param 3: up - n
neg R32(n)
mov n, %r9 C param 4: n
mov 8(%rsp), %rcx C param 1: rp
lea 16-32-8(%rsp), %rsp') C deallocate 2, allocate shadow, align
ASSERT(nz, `test $15, %rsp')
CALL( mpn_add_n)
IFSTD(` lea 8(%rsp), %rsp ')
IFDOS(` lea 32+8(%rsp), %rsp')
L(ret): pop %r15
pop %r14
pop %r13
pop %r12
pop %rbp
pop %rbx
FUNC_EXIT()
ret
EPILOGUE()
|
