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
58
#define BN_ULONG unsigned long
65
* "m"(a), "+m"(r) is the way to favor DirectPath ļæ½-code;
66
* "g"(0) let the compiler to decide where does it
67
* want to keep the value of zero;
69
#define mul_add(r,a,word,carry) do { \
70
register BN_ULONG high,low; \
72
: "=a"(low),"=d"(high) \
75
asm ("addq %2,%0; adcq %3,%1" \
76
: "+r"(carry),"+d"(high)\
79
asm ("addq %2,%0; adcq %3,%1" \
80
: "+m"(r),"+d"(high) \
86
#define mul(r,a,word,carry) do { \
87
register BN_ULONG high,low; \
89
: "=a"(low),"=d"(high) \
92
asm ("addq %2,%0; adcq %3,%1" \
93
: "+r"(carry),"+d"(high)\
96
(r)=carry, carry=high; \
99
#define sqr(r0,r1,a) \
101
: "=a"(r0),"=d"(r1) \
105
BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w)
109
if (num <= 0) return(c1);
113
mul_add(rp[0],ap[0],w,c1);
114
mul_add(rp[1],ap[1],w,c1);
115
mul_add(rp[2],ap[2],w,c1);
116
mul_add(rp[3],ap[3],w,c1);
117
ap+=4; rp+=4; num-=4;
121
mul_add(rp[0],ap[0],w,c1); if (--num==0) return c1;
122
mul_add(rp[1],ap[1],w,c1); if (--num==0) return c1;
123
mul_add(rp[2],ap[2],w,c1); return c1;
129
BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w)
133
if (num <= 0) return(c1);
137
mul(rp[0],ap[0],w,c1);
138
mul(rp[1],ap[1],w,c1);
139
mul(rp[2],ap[2],w,c1);
140
mul(rp[3],ap[3],w,c1);
141
ap+=4; rp+=4; num-=4;
145
mul(rp[0],ap[0],w,c1); if (--num == 0) return c1;
146
mul(rp[1],ap[1],w,c1); if (--num == 0) return c1;
147
mul(rp[2],ap[2],w,c1);
152
void bn_sqr_words(BN_ULONG *r, const BN_ULONG *a, int n)
166
sqr(r[0],r[1],a[0]); if (--n == 0) return;
167
sqr(r[2],r[3],a[1]); if (--n == 0) return;
172
BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d)
173
{ BN_ULONG ret,waste;
176
: "=a"(ret),"=d"(waste)
177
: "a"(l),"d"(h),"g"(d)
183
BN_ULONG bn_add_words (BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,int n)
184
{ BN_ULONG ret=0,i=0;
186
if (n <= 0) return 0;
191
"1: movq (%4,%2,8),%0 \n"
192
" adcq (%5,%2,8),%0 \n"
193
" movq %0,(%3,%2,8) \n"
197
: "=&a"(ret),"+c"(n),"=&r"(i)
198
: "r"(rp),"r"(ap),"r"(bp)
206
BN_ULONG bn_sub_words (BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,int n)
207
{ BN_ULONG ret=0,i=0;
209
if (n <= 0) return 0;
214
"1: movq (%4,%2,8),%0 \n"
215
" sbbq (%5,%2,8),%0 \n"
216
" movq %0,(%3,%2,8) \n"
220
: "=&a"(ret),"+c"(n),"=&r"(i)
221
: "r"(rp),"r"(ap),"r"(bp)
228
/* Simics 1.4<7 has buggy sbbq:-( */
229
#define BN_MASK2 0xffffffffffffffffL
230
BN_ULONG bn_sub_words(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n)
235
if (n <= 0) return((BN_ULONG)0);
240
r[0]=(t1-t2-c)&BN_MASK2;
241
if (t1 != t2) c=(t1 < t2);
245
r[1]=(t1-t2-c)&BN_MASK2;
246
if (t1 != t2) c=(t1 < t2);
250
r[2]=(t1-t2-c)&BN_MASK2;
251
if (t1 != t2) c=(t1 < t2);
255
r[3]=(t1-t2-c)&BN_MASK2;
256
if (t1 != t2) c=(t1 < t2);
267
/* mul_add_c(a,b,c0,c1,c2) -- c+=a*b for three word number c=(c2,c1,c0) */
268
/* mul_add_c2(a,b,c0,c1,c2) -- c+=2*a*b for three word number c=(c2,c1,c0) */
269
/* sqr_add_c(a,i,c0,c1,c2) -- c+=a[i]^2 for three word number c=(c2,c1,c0) */
270
/* sqr_add_c2(a,i,c0,c1,c2) -- c+=2*a[i]*a[j] for three word number c=(c2,c1,c0) */
273
/* original macros are kept for reference purposes */
274
#define mul_add_c(a,b,c0,c1,c2) { \
275
BN_ULONG ta=(a),tb=(b); \
277
t2 = BN_UMULT_HIGH(ta,tb); \
278
c0 += t1; t2 += (c0<t1)?1:0; \
279
c1 += t2; c2 += (c1<t2)?1:0; \
282
#define mul_add_c2(a,b,c0,c1,c2) { \
283
BN_ULONG ta=(a),tb=(b),t0; \
284
t1 = BN_UMULT_HIGH(ta,tb); \
286
t2 = t1+t1; c2 += (t2<t1)?1:0; \
287
t1 = t0+t0; t2 += (t1<t0)?1:0; \
288
c0 += t1; t2 += (c0<t1)?1:0; \
289
c1 += t2; c2 += (c1<t2)?1:0; \
292
#define mul_add_c(a,b,c0,c1,c2) do { \
294
: "=a"(t1),"=d"(t2) \
297
asm ("addq %2,%0; adcq %3,%1" \
298
: "+r"(c0),"+d"(t2) \
301
asm ("addq %2,%0; adcq %3,%1" \
302
: "+r"(c1),"+r"(c2) \
307
#define sqr_add_c(a,i,c0,c1,c2) do { \
309
: "=a"(t1),"=d"(t2) \
312
asm ("addq %2,%0; adcq %3,%1" \
313
: "+r"(c0),"+d"(t2) \
316
asm ("addq %2,%0; adcq %3,%1" \
317
: "+r"(c1),"+r"(c2) \
322
#define mul_add_c2(a,b,c0,c1,c2) do { \
324
: "=a"(t1),"=d"(t2) \
327
asm ("addq %0,%0; adcq %2,%1" \
328
: "+d"(t2),"+r"(c2) \
331
asm ("addq %0,%0; adcq %2,%1" \
332
: "+a"(t1),"+d"(t2) \
335
asm ("addq %2,%0; adcq %3,%1" \
336
: "+r"(c0),"+d"(t2) \
339
asm ("addq %2,%0; adcq %3,%1" \
340
: "+r"(c1),"+r"(c2) \
346
#define sqr_add_c2(a,i,j,c0,c1,c2) \
347
mul_add_c2((a)[i],(a)[j],c0,c1,c2)
349
void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b)
357
mul_add_c(a[0],b[0],c1,c2,c3);
360
mul_add_c(a[0],b[1],c2,c3,c1);
361
mul_add_c(a[1],b[0],c2,c3,c1);
364
mul_add_c(a[2],b[0],c3,c1,c2);
365
mul_add_c(a[1],b[1],c3,c1,c2);
366
mul_add_c(a[0],b[2],c3,c1,c2);
369
mul_add_c(a[0],b[3],c1,c2,c3);
370
mul_add_c(a[1],b[2],c1,c2,c3);
371
mul_add_c(a[2],b[1],c1,c2,c3);
372
mul_add_c(a[3],b[0],c1,c2,c3);
375
mul_add_c(a[4],b[0],c2,c3,c1);
376
mul_add_c(a[3],b[1],c2,c3,c1);
377
mul_add_c(a[2],b[2],c2,c3,c1);
378
mul_add_c(a[1],b[3],c2,c3,c1);
379
mul_add_c(a[0],b[4],c2,c3,c1);
382
mul_add_c(a[0],b[5],c3,c1,c2);
383
mul_add_c(a[1],b[4],c3,c1,c2);
384
mul_add_c(a[2],b[3],c3,c1,c2);
385
mul_add_c(a[3],b[2],c3,c1,c2);
386
mul_add_c(a[4],b[1],c3,c1,c2);
387
mul_add_c(a[5],b[0],c3,c1,c2);
390
mul_add_c(a[6],b[0],c1,c2,c3);
391
mul_add_c(a[5],b[1],c1,c2,c3);
392
mul_add_c(a[4],b[2],c1,c2,c3);
393
mul_add_c(a[3],b[3],c1,c2,c3);
394
mul_add_c(a[2],b[4],c1,c2,c3);
395
mul_add_c(a[1],b[5],c1,c2,c3);
396
mul_add_c(a[0],b[6],c1,c2,c3);
399
mul_add_c(a[0],b[7],c2,c3,c1);
400
mul_add_c(a[1],b[6],c2,c3,c1);
401
mul_add_c(a[2],b[5],c2,c3,c1);
402
mul_add_c(a[3],b[4],c2,c3,c1);
403
mul_add_c(a[4],b[3],c2,c3,c1);
404
mul_add_c(a[5],b[2],c2,c3,c1);
405
mul_add_c(a[6],b[1],c2,c3,c1);
406
mul_add_c(a[7],b[0],c2,c3,c1);
409
mul_add_c(a[7],b[1],c3,c1,c2);
410
mul_add_c(a[6],b[2],c3,c1,c2);
411
mul_add_c(a[5],b[3],c3,c1,c2);
412
mul_add_c(a[4],b[4],c3,c1,c2);
413
mul_add_c(a[3],b[5],c3,c1,c2);
414
mul_add_c(a[2],b[6],c3,c1,c2);
415
mul_add_c(a[1],b[7],c3,c1,c2);
418
mul_add_c(a[2],b[7],c1,c2,c3);
419
mul_add_c(a[3],b[6],c1,c2,c3);
420
mul_add_c(a[4],b[5],c1,c2,c3);
421
mul_add_c(a[5],b[4],c1,c2,c3);
422
mul_add_c(a[6],b[3],c1,c2,c3);
423
mul_add_c(a[7],b[2],c1,c2,c3);
426
mul_add_c(a[7],b[3],c2,c3,c1);
427
mul_add_c(a[6],b[4],c2,c3,c1);
428
mul_add_c(a[5],b[5],c2,c3,c1);
429
mul_add_c(a[4],b[6],c2,c3,c1);
430
mul_add_c(a[3],b[7],c2,c3,c1);
433
mul_add_c(a[4],b[7],c3,c1,c2);
434
mul_add_c(a[5],b[6],c3,c1,c2);
435
mul_add_c(a[6],b[5],c3,c1,c2);
436
mul_add_c(a[7],b[4],c3,c1,c2);
439
mul_add_c(a[7],b[5],c1,c2,c3);
440
mul_add_c(a[6],b[6],c1,c2,c3);
441
mul_add_c(a[5],b[7],c1,c2,c3);
444
mul_add_c(a[6],b[7],c2,c3,c1);
445
mul_add_c(a[7],b[6],c2,c3,c1);
448
mul_add_c(a[7],b[7],c3,c1,c2);
453
void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b)
461
mul_add_c(a[0],b[0],c1,c2,c3);
464
mul_add_c(a[0],b[1],c2,c3,c1);
465
mul_add_c(a[1],b[0],c2,c3,c1);
468
mul_add_c(a[2],b[0],c3,c1,c2);
469
mul_add_c(a[1],b[1],c3,c1,c2);
470
mul_add_c(a[0],b[2],c3,c1,c2);
473
mul_add_c(a[0],b[3],c1,c2,c3);
474
mul_add_c(a[1],b[2],c1,c2,c3);
475
mul_add_c(a[2],b[1],c1,c2,c3);
476
mul_add_c(a[3],b[0],c1,c2,c3);
479
mul_add_c(a[3],b[1],c2,c3,c1);
480
mul_add_c(a[2],b[2],c2,c3,c1);
481
mul_add_c(a[1],b[3],c2,c3,c1);
484
mul_add_c(a[2],b[3],c3,c1,c2);
485
mul_add_c(a[3],b[2],c3,c1,c2);
488
mul_add_c(a[3],b[3],c1,c2,c3);
493
void bn_sqr_comba8(BN_ULONG *r, const BN_ULONG *a)
501
sqr_add_c(a,0,c1,c2,c3);
504
sqr_add_c2(a,1,0,c2,c3,c1);
507
sqr_add_c(a,1,c3,c1,c2);
508
sqr_add_c2(a,2,0,c3,c1,c2);
511
sqr_add_c2(a,3,0,c1,c2,c3);
512
sqr_add_c2(a,2,1,c1,c2,c3);
515
sqr_add_c(a,2,c2,c3,c1);
516
sqr_add_c2(a,3,1,c2,c3,c1);
517
sqr_add_c2(a,4,0,c2,c3,c1);
520
sqr_add_c2(a,5,0,c3,c1,c2);
521
sqr_add_c2(a,4,1,c3,c1,c2);
522
sqr_add_c2(a,3,2,c3,c1,c2);
525
sqr_add_c(a,3,c1,c2,c3);
526
sqr_add_c2(a,4,2,c1,c2,c3);
527
sqr_add_c2(a,5,1,c1,c2,c3);
528
sqr_add_c2(a,6,0,c1,c2,c3);
531
sqr_add_c2(a,7,0,c2,c3,c1);
532
sqr_add_c2(a,6,1,c2,c3,c1);
533
sqr_add_c2(a,5,2,c2,c3,c1);
534
sqr_add_c2(a,4,3,c2,c3,c1);
537
sqr_add_c(a,4,c3,c1,c2);
538
sqr_add_c2(a,5,3,c3,c1,c2);
539
sqr_add_c2(a,6,2,c3,c1,c2);
540
sqr_add_c2(a,7,1,c3,c1,c2);
543
sqr_add_c2(a,7,2,c1,c2,c3);
544
sqr_add_c2(a,6,3,c1,c2,c3);
545
sqr_add_c2(a,5,4,c1,c2,c3);
548
sqr_add_c(a,5,c2,c3,c1);
549
sqr_add_c2(a,6,4,c2,c3,c1);
550
sqr_add_c2(a,7,3,c2,c3,c1);
553
sqr_add_c2(a,7,4,c3,c1,c2);
554
sqr_add_c2(a,6,5,c3,c1,c2);
557
sqr_add_c(a,6,c1,c2,c3);
558
sqr_add_c2(a,7,5,c1,c2,c3);
561
sqr_add_c2(a,7,6,c2,c3,c1);
564
sqr_add_c(a,7,c3,c1,c2);
569
void bn_sqr_comba4(BN_ULONG *r, const BN_ULONG *a)
577
sqr_add_c(a,0,c1,c2,c3);
580
sqr_add_c2(a,1,0,c2,c3,c1);
583
sqr_add_c(a,1,c3,c1,c2);
584
sqr_add_c2(a,2,0,c3,c1,c2);
587
sqr_add_c2(a,3,0,c1,c2,c3);
588
sqr_add_c2(a,2,1,c1,c2,c3);
591
sqr_add_c(a,2,c2,c3,c1);
592
sqr_add_c2(a,3,1,c2,c3,c1);
595
sqr_add_c2(a,3,2,c3,c1,c2);
598
sqr_add_c(a,3,c1,c2,c3);