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
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
|
dnl Power9 mpn_sqr_basecase.
dnl Copyright 1999-2001, 2003-2006, 2008, 2017-2018 Free Software Foundation,
dnl 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 POWER3/PPC630 -
C POWER4/PPC970 -
C POWER5 -
C POWER6 -
C POWER7 -
C POWER8 -
C POWER9 1.62
C TODO
C * Completely separate evn and odd code into two outer loops. Also consider
C unrolling these two outer loops and thereby eliminate all branches.
C * Avoid the reloading of u1 before every loop start.
C * Reduce register usage.
C * Consider getting rid of cy and instead load 3 u limbs, use addc+adde+adde.
C * Consider skewing conditional adjustments to allow mask creation with subfe
C like in the un=3 code. It might streamline the adjustments (or not).
C INPUT PARAMETERS
define(`rp', `r3')
define(`up', `r4')
define(`un', `r5')
define(`u0', `r0')
define(`u1', `r7')
define(`rp2', `r24')
define(`up2', `r25')
define(`cy', `r6')
define(`LSHU1U0',`
addc u0, u0, u0
adde u1, u1, u1
li cy, 0
addze cy, cy
')
define(`LSHU1U',`
addc u0, u0, u0
add u0, u0, cy
adde u1, u1, u1
li cy, 0
addze cy, cy
')
define(`LSHU1UF',`
addc u0, u0, u0
add u0, u0, cy
adde u1, u1, u1
')
define(`LSHU1UHF',`
add u0, u0, u0
add u0, u0, cy
')
C These are cleverer replacements, but they tend to leave CA set, disturbing
C the main accumulation code! Breaking that false dependency might have a
C positive performance impact. Note that the subfe here results in a mask for
C our adjustments.
define(`xLSHU1U0',`
addc u0, u0, u0
adde u1, u1, u1
subfe cy, cy, cy
')
define(`xLSHU1U',`
subfic cy, cy, 0
adde u0, u0, u0
adde u1, u1, u1
subfe cy, cy, cy
')
define(`xLSHU1U',`
subfic cy, cy, 0
adde u0, u0, u0
')
ASM_START()
PROLOGUE(mpn_sqr_basecase)
ld r0, 0(up) C n = 1
mulld r8, r0, r0 C weight 0
mulhdu r9, r0, r0 C weight 1
std r8, 0(rp)
cmpdi cr0, un, 2
bge cr0, L(ge2)
std r9, 8(rp)
blr
L(ge2): bgt cr0, L(gt2)
ld r6, 8(up)
mulld r10, r6, r6 C u1 * u1
mulhdu r11, r6, r6 C u1 * u1
mulld r4, r6, r0 C u1 * u0
mulhdu r5, r6, r0 C u1 * u0
addc r4, r4, r4
adde r5, r5, r5
addze r11, r11
addc r9, r9, r4
adde r10, r10, r5
addze r11, r11
std r9, 8(rp)
std r10, 16(rp)
std r11, 24(rp)
blr
L(gt2): cmpdi cr0, un, 3
bgt cr0, L(gt3)
std r30, -16(r1)
std r31, -8(r1)
subfo r12, r12, r12 C clear OV (and result register)
ld r8, 8(r4)
mulld r5, r8, r8 C W2
mulhdu r10, r8, r8 C W3
sradi r11, u0, 63 C CAUTION: clobbers CA
and r11, r11, r8 C W3
addc u0, u0, u0
adde u1, r8, r8
subfe r6, r6, r6 C mask
ld r4, 16(r4) C W2
mulld r12, r8, u0 C W1 u1 x u0
mulhdu r8, r8, u0 C W2 u1 x u0
maddld( r31, r4, u0, r11) C W2
maddhdu(r30, r4, u0, r11) C W3
andc r6, r4, r6 C W4
addc r9, r12, r9 C W1
std r9, 8(rp) C W1
mulld r9, r4, u1 C W3
mulhdu r11, r4, u1 C W4
addex( r5, r5, r8, 0) C W2
adde r5, r31, r5 C W2
std r5, 16(rp) C W2
maddld( r5, r4, r4, r6) C W4 u2^2
maddhdu(r6, r4, r4, r6) C W5 u2^2
addex( r9, r9, r30, 0) C W3
adde r9, r9, r10 C W3
std r9, 24(rp) C W3
adde r5, r5, r11 C W4
addze r6, r6 C W5
li r8, 0
addex( r5, r5, r8, 0) C W4
std r5, 32(rp) C W4
addex( r6, r6, r8, 0) C W5
std r6, 40(rp) C W5
ld r30, -16(r1)
ld r31, -8(r1)
blr
L(gt3): std r22, -80(r1)
std r23, -72(r1)
std r24, -64(r1)
std r25, -56(r1)
std r26, -48(r1)
std r27, -40(r1)
std r28, -32(r1)
std r29, -24(r1)
std r30, -16(r1)
std r31, -8(r1)
mr rp2, rp
mr up2, up
addi r22, un, -1 C count for loop FIXME: Adjust
subfo r0, r0, r0 C clear OV (and r0)
rldicl r0, un, 0, 63 C r0 = un & 1
cmpdi cr7, r0, 0
ld u0, 0(up2)
ld u1, 8(up2)
cmpdi cr5, r22, 4
srdi r31, r22, 2
addi r22, r22, -2
mtctr r31
beq cr7, L(m2_evn)
L(m2_odd):
rldicl. r31, r22, 63, 63 C r22 & 2
mulld r23, u0, u0
mulhdu r12, u0, u0
mulld r5, u1, u1
mulhdu r10, u1, u1
sradi r11, u0, 63
and r11, r11, u1
LSHU1U0
ld r8, 8(up2)
ld r9, 16(up2)
mulld r28, r8, u0 C W u1 x u0
mulhdu r31, r8, u0 C W u1 x u0
std r23, 0(rp2)
bne cr0, L(m2_11)
L(m2_01):
addi up, up2, 16
addi rp, rp2, 0
b L(m2_lo2)
L(m2_11):
addi up, up2, 0
addi rp, rp2, -16
b L(m2_lo0)
L(m2_evn):
rldicl. r31, r22, 63, 63 C r22 & 2
mulld r23, u0, u0
mulhdu r5, u0, u0
mulld r12, u1, u1
mulhdu r11, u1, u1
sradi r10, u0, 63
and r10, r10, u1
LSHU1U0
ld r9, 8(up2)
ld r8, 16(up2)
mulld r29, r9, u0 C W u1 x u0
mulhdu r30, r9, u0 C W u1 x u0
std r23, 0(rp2)
beq cr0, L(m2_10)
L(m2_00):
addi up, up2, 8
addi rp, rp2, -8
b L(m2_lo1)
L(m2_10):
addi up, up2, 24
addi rp, rp2, 8
ble cr5, L(m2_end)
L(m2_top):
ld r9, 0(up)
maddld( r28, r8, u0, r10)
maddhdu(r31, r8, u0, r10)
adde r5, r29, r5
std r5, 0(rp)
mulld r5, r8, u1
mulhdu r10, r8, u1
addex( r12, r12, r30, 0)
L(m2_lo2):
ld r8, 8(up)
maddld( r29, r9, u0, r11)
maddhdu(r30, r9, u0, r11)
adde r12, r28, r12
std r12, 8(rp)
mulld r12, r9, u1
mulhdu r11, r9, u1
addex( r5, r5, r31, 0)
L(m2_lo1):
ld r9, 16(up)
maddld( r28, r8, u0, r10)
maddhdu(r31, r8, u0, r10)
adde r5, r29, r5
std r5, 16(rp)
mulld r5, r8, u1
mulhdu r10, r8, u1
addex( r12, r12, r30, 0)
L(m2_lo0):
ld r8, 24(up)
maddld( r29, r9, u0, r11)
maddhdu(r30, r9, u0, r11)
adde r12, r28, r12
std r12, 24(rp)
mulld r12, r9, u1
mulhdu r11, r9, u1
addex( r5, r5, r31, 0)
addi up, up, 32
addi rp, rp, 32
bdnz L(m2_top)
L(m2_end):
ld r9, 0(up)
maddld( r28, r8, u0, r10)
maddhdu(r31, r8, u0, r10)
adde r5, r29, r5
std r5, 0(rp)
mulld r5, r8, u1
mulhdu r10, r8, u1
b L(cj) C jump to addmul_2 tail
L(outer):
addi up2, up2, 16
addi rp2, rp2, 32
ld u0, 0(up2)
ld u1, 8(up2)
cmpdi cr5, r22, 4
srdi r31, r22, 2
addi r22, r22, -2
mtctr r31
ld r26, 0(rp2)
ld r27, 16(rp2)
rldicl. r31, r22, 63, 63 C r22 & 2
beq cr7, L(evn)
L(odd): maddld( r23, u0, u0, r26) C W u2^2
maddhdu(r12, u0, u0, r26) C W u2^2
maddld( r5, u1, u1, r27) C W u3^2
maddhdu(r10, u1, u1, r27) C W u3^2
ld r26, 8(rp2)
ld r8, -8(up2)
sradi r8, r8, 63 C CAUTION: clobbers CA
and r8, r8, u0
sradi r11, u0, 63 C CAUTION: clobbers CA
and r11, r11, u1
LSHU1U
addc r23, r23, r8
ld r8, 8(up2)
ld r9, 16(up2)
maddld( r28, r8, u0, r26) C W u3 x u2
maddhdu(r31, r8, u0, r26) C W u3 x u2
ld r26, 24(rp2)
std r23, 0(rp2) C W0
bne cr0, L(11)
L(01):
addi up, up2, 16
addi rp, rp2, 0
b L(lo2)
L(11):
addi up, up2, 0
addi rp, rp2, -16
b L(lo0)
L(evn): maddld( r23, u0, u0, r26) C W u2^2
maddhdu(r5, u0, u0, r26) C W u2^2
maddld( r12, u1, u1, r27) C W u3^2
maddhdu(r11, u1, u1, r27) C W u3^2
ld r27, 8(rp2)
ld r9, -8(up2)
sradi r9, r9, 63 C CAUTION: clobbers CA
and r9, r9, u0
sradi r10, u0, 63 C CAUTION: clobbers CA
and r10, r10, u1
LSHU1U
addc r23, r23, r9
ld r9, 8(up2)
ld r8, 16(up2)
maddld( r29, r9, u0, r27) C W u3 x u2
maddhdu(r30, r9, u0, r27) C W u3 x u2
ld r27, 24(rp2)
std r23, 0(rp2) C W0
beq cr0, L(10)
L(00):
addi up, up2, 8
addi rp, rp2, -8
b L(lo1)
L(10):
addi up, up2, 24
addi rp, rp2, 8
ble cr5, L(end)
L(top): ld r9, 0(up)
maddld( r28, r8, u0, r10)
maddhdu(r31, r8, u0, r10)
adde r5, r29, r5
ld r26, 24(rp)
std r5, 0(rp)
maddld( r5, r8, u1, r27)
maddhdu(r10, r8, u1, r27)
addex( r12, r12, r30, 0)
L(lo2): ld r8, 8(up)
maddld( r29, r9, u0, r11)
maddhdu(r30, r9, u0, r11)
adde r12, r28, r12
ld r27, 32(rp)
std r12, 8(rp)
maddld( r12, r9, u1, r26)
maddhdu(r11, r9, u1, r26)
addex( r5, r5, r31, 0)
L(lo1): ld r9, 16(up)
maddld( r28, r8, u0, r10)
maddhdu(r31, r8, u0, r10)
adde r5, r29, r5
ld r26, 40(rp)
std r5, 16(rp)
maddld( r5, r8, u1, r27)
maddhdu(r10, r8, u1, r27)
addex( r12, r12, r30, 0)
L(lo0): ld r8, 24(up)
maddld( r29, r9, u0, r11)
maddhdu(r30, r9, u0, r11)
adde r12, r28, r12
ld r27, 48(rp)
std r12, 24(rp)
maddld( r12, r9, u1, r26)
maddhdu(r11, r9, u1, r26)
addex( r5, r5, r31, 0)
addi up, up, 32
addi rp, rp, 32
bdnz L(top)
L(end): ld r9, 0(up)
maddld( r28, r8, u0, r10)
maddhdu(r31, r8, u0, r10)
adde r5, r29, r5
std r5, 0(rp)
maddld( r5, r8, u1, r27)
maddhdu(r10, r8, u1, r27)
L(cj): addex( r12, r12, r30, 0)
maddld( r29, r9, u0, r11)
maddhdu(r30, r9, u0, r11)
adde r12, r28, r12
std r12, 8(rp)
mulld r12, r9, u1
mulhdu r11, r9, u1
addex( r5, r5, r31, 0)
adde r5, r29, r5
std r5, 16(rp)
addex( r12, r12, r30, 0)
adde r12, r12, r10
std r12, 24(rp)
li r4, 0
addze r5, r11
addex( r5, r5, r4, 0)
std r5, 32(rp)
bgt cr5, L(outer)
L(corner):
ld u0, 16(up2)
ld u1, 24(up2)
ld r26, 32(rp2)
bne cr7, L(corner_odd)
L(corner_evn):
ld r27, 40(rp2)
maddld( r23, u0, u0, r26) C W u2^2
maddhdu(r5, u0, u0, r26) C W u2^2
mulld r12, u1, u1 C W u3^2
mulhdu r11, u1, u1 C W u3^2
ld r9, 8(up2)
sradi r9, r9, 63 C CAUTION: clobbers CA
and r9, r9, u0
sradi r10, u0, 63 C CAUTION: clobbers CA
and r10, r10, u1
LSHU1UHF
addc r23, r23, r9
ld r9, 24(up2)
maddld( r29, r9, u0, r27) C W u3 x u2
maddhdu(r30, r9, u0, r27) C W u3 x u2
std r23, 32(rp2)
adde r5, r29, r5
std r5, 40(rp2)
addex( r12, r12, r30, 0)
adde r12, r12, r10 C W FIXME can this co?
std r12, 48(rp2)
li r4, 0
addex( r5, r11, r4, 0)
addze r5, r5
std r5, 56(rp2)
b L(ret)
L(corner_odd):
ld r27, 48(rp2)
maddld( r23, u0, u0, r26) C W u2^2
maddhdu(r12, u0, u0, r26) C W u2^2
maddld( r5, u1, u1, r27) C W u3^2
maddhdu(r10, u1, u1, r27) C W u3^2
ld r26, 40(rp2)
ld r8, 8(up2)
sradi r8, r8, 63 C CAUTION: clobbers CA
and r8, r8, u0
sradi r11, u0, 63 C CAUTION: clobbers CA
and r11, r11, u1
LSHU1UF
addc r23, r23, r8
ld r8, 24(up2)
ld r9, 32(up2)
maddld( r28, r8, u0, r26) C W u3 x u2
maddhdu(r31, r8, u0, r26) C W u3 x u2
std r23, 32(rp2)
maddld( r29, r9, u0, r11)
maddhdu(r30, r9, u0, r11)
adde r12, r28, r12
std r12, 40(rp2)
mulld r12, r9, u1
mulhdu r11, r9, u1
addex( r5, r5, r31, 0)
adde r5, r29, r5
std r5, 48(rp2)
addex( r12, r12, r30, 0)
adde r12, r12, r10
std r12, 56(rp2)
mulld r23, r9, r9 C W u2^2
mulhdu r12, r9, r9 C W u2^2
adde r23, r23, r11
addze r12, r12
sradi r4, r8, 63 C CAUTION: clobbers CA
and r4, r4, r9
addex( r23, r23, r4, 0)
std r23, 64(rp2)
li r4, 0
addex( r12, r12, r4, 0)
std r12, 72(rp2)
L(ret): ld r22, -80(r1)
ld r23, -72(r1)
ld r24, -64(r1)
ld r25, -56(r1)
ld r26, -48(r1)
ld r27, -40(r1)
ld r28, -32(r1)
ld r29, -24(r1)
ld r30, -16(r1)
ld r31, -8(r1)
blr
EPILOGUE()
ASM_END()
|
