2
#if !(defined(__GNUC__) && __GNUC__>=2)
3
# include "../bn_asm.c" /* kind of dirty hack for Sun Studio */
6
* x86_64 BIGNUM accelerator version 0.1, December 2002.
8
* Implemented by Andy Polyakov <appro@fy.chalmers.se> for the OpenSSL
11
* Rights for redistribution and usage in source and binary forms are
12
* granted according to the OpenSSL license. Warranty of any kind is
15
* Q. Version 0.1? It doesn't sound like Andy, he used to assign real
16
* versions, like 1.0...
17
* A. Well, that's because this code is basically a quick-n-dirty
18
* proof-of-concept hack. As you can see it's implemented with
19
* inline assembler, which means that you're bound to GCC and that
20
* there might be enough room for further improvement.
22
* Q. Why inline assembler?
23
* A. x86_64 features own ABI which I'm not familiar with. This is
24
* why I decided to let the compiler take care of subroutine
25
* prologue/epilogue as well as register allocation. For reference.
26
* Win64 implements different ABI for AMD64, different from Linux.
28
* Q. How much faster does it get?
29
* A. 'apps/openssl speed rsa dsa' output with no-asm:
31
* sign verify sign/s verify/s
32
* rsa 512 bits 0.0006s 0.0001s 1683.8 18456.2
33
* rsa 1024 bits 0.0028s 0.0002s 356.0 6407.0
34
* rsa 2048 bits 0.0172s 0.0005s 58.0 1957.8
35
* rsa 4096 bits 0.1155s 0.0018s 8.7 555.6
36
* sign verify sign/s verify/s
37
* dsa 512 bits 0.0005s 0.0006s 2100.8 1768.3
38
* dsa 1024 bits 0.0014s 0.0018s 692.3 559.2
39
* dsa 2048 bits 0.0049s 0.0061s 204.7 165.0
41
* 'apps/openssl speed rsa dsa' output with this module:
43
* sign verify sign/s verify/s
44
* rsa 512 bits 0.0004s 0.0000s 2767.1 33297.9
45
* rsa 1024 bits 0.0012s 0.0001s 867.4 14674.7
46
* rsa 2048 bits 0.0061s 0.0002s 164.0 5270.0
47
* rsa 4096 bits 0.0384s 0.0006s 26.1 1650.8
48
* sign verify sign/s verify/s
49
* dsa 512 bits 0.0002s 0.0003s 4442.2 3786.3
50
* dsa 1024 bits 0.0005s 0.0007s 1835.1 1497.4
51
* dsa 2048 bits 0.0016s 0.0020s 620.4 504.6
53
* For the reference. IA-32 assembler implementation performs
54
* very much like 64-bit code compiled with no-asm on the same
59
#define BN_ULONG unsigned long long
61
#define BN_ULONG unsigned long
69
* "m"(a), "+m"(r) is the way to favor DirectPath �-code;
70
* "g"(0) let the compiler to decide where does it
71
* want to keep the value of zero;
73
#define mul_add(r,a,word,carry) do { \
74
register BN_ULONG high,low; \
76
: "=a"(low),"=d"(high) \
79
asm ("addq %2,%0; adcq %3,%1" \
80
: "+r"(carry),"+d"(high)\
83
asm ("addq %2,%0; adcq %3,%1" \
84
: "+m"(r),"+d"(high) \
90
#define mul(r,a,word,carry) do { \
91
register BN_ULONG high,low; \
93
: "=a"(low),"=d"(high) \
96
asm ("addq %2,%0; adcq %3,%1" \
97
: "+r"(carry),"+d"(high)\
100
(r)=carry, carry=high; \
103
#define sqr(r0,r1,a) \
105
: "=a"(r0),"=d"(r1) \
109
BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w)
113
if (num <= 0) return(c1);
117
mul_add(rp[0],ap[0],w,c1);
118
mul_add(rp[1],ap[1],w,c1);
119
mul_add(rp[2],ap[2],w,c1);
120
mul_add(rp[3],ap[3],w,c1);
121
ap+=4; rp+=4; num-=4;
125
mul_add(rp[0],ap[0],w,c1); if (--num==0) return c1;
126
mul_add(rp[1],ap[1],w,c1); if (--num==0) return c1;
127
mul_add(rp[2],ap[2],w,c1); return c1;
133
BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w)
137
if (num <= 0) return(c1);
141
mul(rp[0],ap[0],w,c1);
142
mul(rp[1],ap[1],w,c1);
143
mul(rp[2],ap[2],w,c1);
144
mul(rp[3],ap[3],w,c1);
145
ap+=4; rp+=4; num-=4;
149
mul(rp[0],ap[0],w,c1); if (--num == 0) return c1;
150
mul(rp[1],ap[1],w,c1); if (--num == 0) return c1;
151
mul(rp[2],ap[2],w,c1);
156
void bn_sqr_words(BN_ULONG *r, const BN_ULONG *a, int n)
170
sqr(r[0],r[1],a[0]); if (--n == 0) return;
171
sqr(r[2],r[3],a[1]); if (--n == 0) return;
176
BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d)
177
{ BN_ULONG ret,waste;
180
: "=a"(ret),"=d"(waste)
181
: "a"(l),"d"(h),"g"(d)
187
BN_ULONG bn_add_words (BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,int n)
188
{ BN_ULONG ret=0,i=0;
190
if (n <= 0) return 0;
195
"1: movq (%4,%2,8),%0 \n"
196
" adcq (%5,%2,8),%0 \n"
197
" movq %0,(%3,%2,8) \n"
201
: "=&a"(ret),"+c"(n),"=&r"(i)
202
: "r"(rp),"r"(ap),"r"(bp)
210
BN_ULONG bn_sub_words (BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,int n)
211
{ BN_ULONG ret=0,i=0;
213
if (n <= 0) return 0;
218
"1: movq (%4,%2,8),%0 \n"
219
" sbbq (%5,%2,8),%0 \n"
220
" movq %0,(%3,%2,8) \n"
224
: "=&a"(ret),"+c"(n),"=&r"(i)
225
: "r"(rp),"r"(ap),"r"(bp)
232
/* Simics 1.4<7 has buggy sbbq:-( */
233
#define BN_MASK2 0xffffffffffffffffL
234
BN_ULONG bn_sub_words(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n)
239
if (n <= 0) return((BN_ULONG)0);
244
r[0]=(t1-t2-c)&BN_MASK2;
245
if (t1 != t2) c=(t1 < t2);
249
r[1]=(t1-t2-c)&BN_MASK2;
250
if (t1 != t2) c=(t1 < t2);
254
r[2]=(t1-t2-c)&BN_MASK2;
255
if (t1 != t2) c=(t1 < t2);
259
r[3]=(t1-t2-c)&BN_MASK2;
260
if (t1 != t2) c=(t1 < t2);
271
/* mul_add_c(a,b,c0,c1,c2) -- c+=a*b for three word number c=(c2,c1,c0) */
272
/* mul_add_c2(a,b,c0,c1,c2) -- c+=2*a*b for three word number c=(c2,c1,c0) */
273
/* sqr_add_c(a,i,c0,c1,c2) -- c+=a[i]^2 for three word number c=(c2,c1,c0) */
274
/* sqr_add_c2(a,i,c0,c1,c2) -- c+=2*a[i]*a[j] for three word number c=(c2,c1,c0) */
277
/* original macros are kept for reference purposes */
278
#define mul_add_c(a,b,c0,c1,c2) { \
279
BN_ULONG ta=(a),tb=(b); \
281
t2 = BN_UMULT_HIGH(ta,tb); \
282
c0 += t1; t2 += (c0<t1)?1:0; \
283
c1 += t2; c2 += (c1<t2)?1:0; \
286
#define mul_add_c2(a,b,c0,c1,c2) { \
287
BN_ULONG ta=(a),tb=(b),t0; \
288
t1 = BN_UMULT_HIGH(ta,tb); \
290
t2 = t1+t1; c2 += (t2<t1)?1:0; \
291
t1 = t0+t0; t2 += (t1<t0)?1:0; \
292
c0 += t1; t2 += (c0<t1)?1:0; \
293
c1 += t2; c2 += (c1<t2)?1:0; \
296
#define mul_add_c(a,b,c0,c1,c2) do { \
298
: "=a"(t1),"=d"(t2) \
301
asm ("addq %2,%0; adcq %3,%1" \
302
: "+r"(c0),"+d"(t2) \
305
asm ("addq %2,%0; adcq %3,%1" \
306
: "+r"(c1),"+r"(c2) \
311
#define sqr_add_c(a,i,c0,c1,c2) do { \
313
: "=a"(t1),"=d"(t2) \
316
asm ("addq %2,%0; adcq %3,%1" \
317
: "+r"(c0),"+d"(t2) \
320
asm ("addq %2,%0; adcq %3,%1" \
321
: "+r"(c1),"+r"(c2) \
326
#define mul_add_c2(a,b,c0,c1,c2) do { \
328
: "=a"(t1),"=d"(t2) \
331
asm ("addq %0,%0; adcq %2,%1" \
332
: "+d"(t2),"+r"(c2) \
335
asm ("addq %0,%0; adcq %2,%1" \
336
: "+a"(t1),"+d"(t2) \
339
asm ("addq %2,%0; adcq %3,%1" \
340
: "+r"(c0),"+d"(t2) \
343
asm ("addq %2,%0; adcq %3,%1" \
344
: "+r"(c1),"+r"(c2) \
350
#define sqr_add_c2(a,i,j,c0,c1,c2) \
351
mul_add_c2((a)[i],(a)[j],c0,c1,c2)
353
void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b)
361
mul_add_c(a[0],b[0],c1,c2,c3);
364
mul_add_c(a[0],b[1],c2,c3,c1);
365
mul_add_c(a[1],b[0],c2,c3,c1);
368
mul_add_c(a[2],b[0],c3,c1,c2);
369
mul_add_c(a[1],b[1],c3,c1,c2);
370
mul_add_c(a[0],b[2],c3,c1,c2);
373
mul_add_c(a[0],b[3],c1,c2,c3);
374
mul_add_c(a[1],b[2],c1,c2,c3);
375
mul_add_c(a[2],b[1],c1,c2,c3);
376
mul_add_c(a[3],b[0],c1,c2,c3);
379
mul_add_c(a[4],b[0],c2,c3,c1);
380
mul_add_c(a[3],b[1],c2,c3,c1);
381
mul_add_c(a[2],b[2],c2,c3,c1);
382
mul_add_c(a[1],b[3],c2,c3,c1);
383
mul_add_c(a[0],b[4],c2,c3,c1);
386
mul_add_c(a[0],b[5],c3,c1,c2);
387
mul_add_c(a[1],b[4],c3,c1,c2);
388
mul_add_c(a[2],b[3],c3,c1,c2);
389
mul_add_c(a[3],b[2],c3,c1,c2);
390
mul_add_c(a[4],b[1],c3,c1,c2);
391
mul_add_c(a[5],b[0],c3,c1,c2);
394
mul_add_c(a[6],b[0],c1,c2,c3);
395
mul_add_c(a[5],b[1],c1,c2,c3);
396
mul_add_c(a[4],b[2],c1,c2,c3);
397
mul_add_c(a[3],b[3],c1,c2,c3);
398
mul_add_c(a[2],b[4],c1,c2,c3);
399
mul_add_c(a[1],b[5],c1,c2,c3);
400
mul_add_c(a[0],b[6],c1,c2,c3);
403
mul_add_c(a[0],b[7],c2,c3,c1);
404
mul_add_c(a[1],b[6],c2,c3,c1);
405
mul_add_c(a[2],b[5],c2,c3,c1);
406
mul_add_c(a[3],b[4],c2,c3,c1);
407
mul_add_c(a[4],b[3],c2,c3,c1);
408
mul_add_c(a[5],b[2],c2,c3,c1);
409
mul_add_c(a[6],b[1],c2,c3,c1);
410
mul_add_c(a[7],b[0],c2,c3,c1);
413
mul_add_c(a[7],b[1],c3,c1,c2);
414
mul_add_c(a[6],b[2],c3,c1,c2);
415
mul_add_c(a[5],b[3],c3,c1,c2);
416
mul_add_c(a[4],b[4],c3,c1,c2);
417
mul_add_c(a[3],b[5],c3,c1,c2);
418
mul_add_c(a[2],b[6],c3,c1,c2);
419
mul_add_c(a[1],b[7],c3,c1,c2);
422
mul_add_c(a[2],b[7],c1,c2,c3);
423
mul_add_c(a[3],b[6],c1,c2,c3);
424
mul_add_c(a[4],b[5],c1,c2,c3);
425
mul_add_c(a[5],b[4],c1,c2,c3);
426
mul_add_c(a[6],b[3],c1,c2,c3);
427
mul_add_c(a[7],b[2],c1,c2,c3);
430
mul_add_c(a[7],b[3],c2,c3,c1);
431
mul_add_c(a[6],b[4],c2,c3,c1);
432
mul_add_c(a[5],b[5],c2,c3,c1);
433
mul_add_c(a[4],b[6],c2,c3,c1);
434
mul_add_c(a[3],b[7],c2,c3,c1);
437
mul_add_c(a[4],b[7],c3,c1,c2);
438
mul_add_c(a[5],b[6],c3,c1,c2);
439
mul_add_c(a[6],b[5],c3,c1,c2);
440
mul_add_c(a[7],b[4],c3,c1,c2);
443
mul_add_c(a[7],b[5],c1,c2,c3);
444
mul_add_c(a[6],b[6],c1,c2,c3);
445
mul_add_c(a[5],b[7],c1,c2,c3);
448
mul_add_c(a[6],b[7],c2,c3,c1);
449
mul_add_c(a[7],b[6],c2,c3,c1);
452
mul_add_c(a[7],b[7],c3,c1,c2);
457
void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b)
465
mul_add_c(a[0],b[0],c1,c2,c3);
468
mul_add_c(a[0],b[1],c2,c3,c1);
469
mul_add_c(a[1],b[0],c2,c3,c1);
472
mul_add_c(a[2],b[0],c3,c1,c2);
473
mul_add_c(a[1],b[1],c3,c1,c2);
474
mul_add_c(a[0],b[2],c3,c1,c2);
477
mul_add_c(a[0],b[3],c1,c2,c3);
478
mul_add_c(a[1],b[2],c1,c2,c3);
479
mul_add_c(a[2],b[1],c1,c2,c3);
480
mul_add_c(a[3],b[0],c1,c2,c3);
483
mul_add_c(a[3],b[1],c2,c3,c1);
484
mul_add_c(a[2],b[2],c2,c3,c1);
485
mul_add_c(a[1],b[3],c2,c3,c1);
488
mul_add_c(a[2],b[3],c3,c1,c2);
489
mul_add_c(a[3],b[2],c3,c1,c2);
492
mul_add_c(a[3],b[3],c1,c2,c3);
497
void bn_sqr_comba8(BN_ULONG *r, const BN_ULONG *a)
505
sqr_add_c(a,0,c1,c2,c3);
508
sqr_add_c2(a,1,0,c2,c3,c1);
511
sqr_add_c(a,1,c3,c1,c2);
512
sqr_add_c2(a,2,0,c3,c1,c2);
515
sqr_add_c2(a,3,0,c1,c2,c3);
516
sqr_add_c2(a,2,1,c1,c2,c3);
519
sqr_add_c(a,2,c2,c3,c1);
520
sqr_add_c2(a,3,1,c2,c3,c1);
521
sqr_add_c2(a,4,0,c2,c3,c1);
524
sqr_add_c2(a,5,0,c3,c1,c2);
525
sqr_add_c2(a,4,1,c3,c1,c2);
526
sqr_add_c2(a,3,2,c3,c1,c2);
529
sqr_add_c(a,3,c1,c2,c3);
530
sqr_add_c2(a,4,2,c1,c2,c3);
531
sqr_add_c2(a,5,1,c1,c2,c3);
532
sqr_add_c2(a,6,0,c1,c2,c3);
535
sqr_add_c2(a,7,0,c2,c3,c1);
536
sqr_add_c2(a,6,1,c2,c3,c1);
537
sqr_add_c2(a,5,2,c2,c3,c1);
538
sqr_add_c2(a,4,3,c2,c3,c1);
541
sqr_add_c(a,4,c3,c1,c2);
542
sqr_add_c2(a,5,3,c3,c1,c2);
543
sqr_add_c2(a,6,2,c3,c1,c2);
544
sqr_add_c2(a,7,1,c3,c1,c2);
547
sqr_add_c2(a,7,2,c1,c2,c3);
548
sqr_add_c2(a,6,3,c1,c2,c3);
549
sqr_add_c2(a,5,4,c1,c2,c3);
552
sqr_add_c(a,5,c2,c3,c1);
553
sqr_add_c2(a,6,4,c2,c3,c1);
554
sqr_add_c2(a,7,3,c2,c3,c1);
557
sqr_add_c2(a,7,4,c3,c1,c2);
558
sqr_add_c2(a,6,5,c3,c1,c2);
561
sqr_add_c(a,6,c1,c2,c3);
562
sqr_add_c2(a,7,5,c1,c2,c3);
565
sqr_add_c2(a,7,6,c2,c3,c1);
568
sqr_add_c(a,7,c3,c1,c2);
573
void bn_sqr_comba4(BN_ULONG *r, const BN_ULONG *a)
581
sqr_add_c(a,0,c1,c2,c3);
584
sqr_add_c2(a,1,0,c2,c3,c1);
587
sqr_add_c(a,1,c3,c1,c2);
588
sqr_add_c2(a,2,0,c3,c1,c2);
591
sqr_add_c2(a,3,0,c1,c2,c3);
592
sqr_add_c2(a,2,1,c1,c2,c3);
595
sqr_add_c(a,2,c2,c3,c1);
596
sqr_add_c2(a,3,1,c2,c3,c1);
599
sqr_add_c2(a,3,2,c3,c1,c2);
602
sqr_add_c(a,3,c1,c2,c3);