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 ยต-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,
118 mul_add(rp[0], ap[0], w, c1);
119 mul_add(rp[1], ap[1], w, c1);
120 mul_add(rp[2], ap[2], w, c1);
121 mul_add(rp[3], ap[3], w, c1);
127 mul_add(rp[0], ap[0], w, c1);
130 mul_add(rp[1], ap[1], w, c1);
133 mul_add(rp[2], ap[2], w, c1);
140 BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w)
148 mul(rp[0], ap[0], w, c1);
149 mul(rp[1], ap[1], w, c1);
150 mul(rp[2], ap[2], w, c1);
151 mul(rp[3], ap[3], w, c1);
157 mul(rp[0], ap[0], w, c1);
160 mul(rp[1], ap[1], w, c1);
163 mul(rp[2], ap[2], w, c1);
168 void bn_sqr_words(BN_ULONG *r, const BN_ULONG *a, int n)
174 sqr(r[0], r[1], a[0]);
175 sqr(r[2], r[3], a[1]);
176 sqr(r[4], r[5], a[2]);
177 sqr(r[6], r[7], a[3]);
183 sqr(r[0], r[1], a[0]);
186 sqr(r[2], r[3], a[1]);
189 sqr(r[4], r[5], a[2]);
193 BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d)
197 asm("divq %4":"=a"(ret), "=d"(waste)
198 : "a"(l), "d"(h), "g"(d)
204 BN_ULONG bn_add_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
207 BN_ULONG ret = 0, i = 0;
212 asm volatile (" subq %2,%2 \n"
214 "1: movq (%4,%2,8),%0 \n"
215 " adcq (%5,%2,8),%0 \n"
216 " movq %0,(%3,%2,8) \n"
219 " sbbq %0,%0 \n":"=&a" (ret), "+c"(n),
221 :"r"(rp), "r"(ap), "r"(bp)
228 BN_ULONG bn_sub_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
231 BN_ULONG ret = 0, i = 0;
236 asm volatile (" subq %2,%2 \n"
238 "1: movq (%4,%2,8),%0 \n"
239 " sbbq (%5,%2,8),%0 \n"
240 " movq %0,(%3,%2,8) \n"
243 " sbbq %0,%0 \n":"=&a" (ret), "+c"(n),
245 :"r"(rp), "r"(ap), "r"(bp)
251 /* Simics 1.4<7 has buggy sbbq:-( */
252 # define BN_MASK2 0xffffffffffffffffL
253 BN_ULONG bn_sub_words(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n)
259 return ((BN_ULONG)0);
264 r[0] = (t1 - t2 - c) & BN_MASK2;
272 r[1] = (t1 - t2 - c) & BN_MASK2;
280 r[2] = (t1 - t2 - c) & BN_MASK2;
288 r[3] = (t1 - t2 - c) & BN_MASK2;
302 /* mul_add_c(a,b,c0,c1,c2) -- c+=a*b for three word number c=(c2,c1,c0) */
303 /* mul_add_c2(a,b,c0,c1,c2) -- c+=2*a*b for three word number c=(c2,c1,c0) */
304 /* sqr_add_c(a,i,c0,c1,c2) -- c+=a[i]^2 for three word number c=(c2,c1,c0) */
306 * sqr_add_c2(a,i,c0,c1,c2) -- c+=2*a[i]*a[j] for three word number
311 * Keep in mind that carrying into high part of multiplication result
312 * can not overflow, because it cannot be all-ones.
315 /* original macros are kept for reference purposes */
316 # define mul_add_c(a,b,c0,c1,c2) { \
317 BN_ULONG ta=(a),tb=(b); \
319 t2 = BN_UMULT_HIGH(ta,tb); \
320 c0 += t1; t2 += (c0<t1)?1:0; \
321 c1 += t2; c2 += (c1<t2)?1:0; \
324 # define mul_add_c2(a,b,c0,c1,c2) { \
325 BN_ULONG ta=(a),tb=(b),t0; \
326 t1 = BN_UMULT_HIGH(ta,tb); \
328 c0 += t0; t2 = t1+((c0<t0)?1:0);\
329 c1 += t2; c2 += (c1<t2)?1:0; \
330 c0 += t0; t1 += (c0<t0)?1:0; \
331 c1 += t1; c2 += (c1<t1)?1:0; \
334 # define mul_add_c(a,b,c0,c1,c2) do { \
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) \
349 # define sqr_add_c(a,i,c0,c1,c2) do { \
351 : "=a"(t1),"=d"(t2) \
354 asm ("addq %2,%0; adcq %3,%1" \
355 : "+r"(c0),"+d"(t2) \
358 asm ("addq %2,%0; adcq %3,%1" \
359 : "+r"(c1),"+r"(c2) \
364 # define mul_add_c2(a,b,c0,c1,c2) do { \
366 : "=a"(t1),"=d"(t2) \
369 asm ("addq %3,%0; adcq %4,%1; adcq %5,%2" \
370 : "+r"(c0),"+r"(c1),"+r"(c2) \
371 : "r"(t1),"r"(t2),"g"(0) \
373 asm ("addq %3,%0; adcq %4,%1; adcq %5,%2" \
374 : "+r"(c0),"+r"(c1),"+r"(c2) \
375 : "r"(t1),"r"(t2),"g"(0) \
380 # define sqr_add_c2(a,i,j,c0,c1,c2) \
381 mul_add_c2((a)[i],(a)[j],c0,c1,c2)
383 void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b)
391 mul_add_c(a[0], b[0], c1, c2, c3);
394 mul_add_c(a[0], b[1], c2, c3, c1);
395 mul_add_c(a[1], b[0], c2, c3, c1);
398 mul_add_c(a[2], b[0], c3, c1, c2);
399 mul_add_c(a[1], b[1], c3, c1, c2);
400 mul_add_c(a[0], b[2], c3, c1, c2);
403 mul_add_c(a[0], b[3], c1, c2, c3);
404 mul_add_c(a[1], b[2], c1, c2, c3);
405 mul_add_c(a[2], b[1], c1, c2, c3);
406 mul_add_c(a[3], b[0], c1, c2, c3);
409 mul_add_c(a[4], b[0], c2, c3, c1);
410 mul_add_c(a[3], b[1], c2, c3, c1);
411 mul_add_c(a[2], b[2], c2, c3, c1);
412 mul_add_c(a[1], b[3], c2, c3, c1);
413 mul_add_c(a[0], b[4], c2, c3, c1);
416 mul_add_c(a[0], b[5], c3, c1, c2);
417 mul_add_c(a[1], b[4], c3, c1, c2);
418 mul_add_c(a[2], b[3], c3, c1, c2);
419 mul_add_c(a[3], b[2], c3, c1, c2);
420 mul_add_c(a[4], b[1], c3, c1, c2);
421 mul_add_c(a[5], b[0], c3, c1, c2);
424 mul_add_c(a[6], b[0], c1, c2, c3);
425 mul_add_c(a[5], b[1], c1, c2, c3);
426 mul_add_c(a[4], b[2], c1, c2, c3);
427 mul_add_c(a[3], b[3], c1, c2, c3);
428 mul_add_c(a[2], b[4], c1, c2, c3);
429 mul_add_c(a[1], b[5], c1, c2, c3);
430 mul_add_c(a[0], b[6], c1, c2, c3);
433 mul_add_c(a[0], b[7], c2, c3, c1);
434 mul_add_c(a[1], b[6], c2, c3, c1);
435 mul_add_c(a[2], b[5], c2, c3, c1);
436 mul_add_c(a[3], b[4], c2, c3, c1);
437 mul_add_c(a[4], b[3], c2, c3, c1);
438 mul_add_c(a[5], b[2], c2, c3, c1);
439 mul_add_c(a[6], b[1], c2, c3, c1);
440 mul_add_c(a[7], b[0], c2, c3, c1);
443 mul_add_c(a[7], b[1], c3, c1, c2);
444 mul_add_c(a[6], b[2], c3, c1, c2);
445 mul_add_c(a[5], b[3], c3, c1, c2);
446 mul_add_c(a[4], b[4], c3, c1, c2);
447 mul_add_c(a[3], b[5], c3, c1, c2);
448 mul_add_c(a[2], b[6], c3, c1, c2);
449 mul_add_c(a[1], b[7], c3, c1, c2);
452 mul_add_c(a[2], b[7], c1, c2, c3);
453 mul_add_c(a[3], b[6], c1, c2, c3);
454 mul_add_c(a[4], b[5], c1, c2, c3);
455 mul_add_c(a[5], b[4], c1, c2, c3);
456 mul_add_c(a[6], b[3], c1, c2, c3);
457 mul_add_c(a[7], b[2], c1, c2, c3);
460 mul_add_c(a[7], b[3], c2, c3, c1);
461 mul_add_c(a[6], b[4], c2, c3, c1);
462 mul_add_c(a[5], b[5], c2, c3, c1);
463 mul_add_c(a[4], b[6], c2, c3, c1);
464 mul_add_c(a[3], b[7], c2, c3, c1);
467 mul_add_c(a[4], b[7], c3, c1, c2);
468 mul_add_c(a[5], b[6], c3, c1, c2);
469 mul_add_c(a[6], b[5], c3, c1, c2);
470 mul_add_c(a[7], b[4], c3, c1, c2);
473 mul_add_c(a[7], b[5], c1, c2, c3);
474 mul_add_c(a[6], b[6], c1, c2, c3);
475 mul_add_c(a[5], b[7], c1, c2, c3);
478 mul_add_c(a[6], b[7], c2, c3, c1);
479 mul_add_c(a[7], b[6], c2, c3, c1);
482 mul_add_c(a[7], b[7], c3, c1, c2);
487 void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b)
495 mul_add_c(a[0], b[0], c1, c2, c3);
498 mul_add_c(a[0], b[1], c2, c3, c1);
499 mul_add_c(a[1], b[0], c2, c3, c1);
502 mul_add_c(a[2], b[0], c3, c1, c2);
503 mul_add_c(a[1], b[1], c3, c1, c2);
504 mul_add_c(a[0], b[2], c3, c1, c2);
507 mul_add_c(a[0], b[3], c1, c2, c3);
508 mul_add_c(a[1], b[2], c1, c2, c3);
509 mul_add_c(a[2], b[1], c1, c2, c3);
510 mul_add_c(a[3], b[0], c1, c2, c3);
513 mul_add_c(a[3], b[1], c2, c3, c1);
514 mul_add_c(a[2], b[2], c2, c3, c1);
515 mul_add_c(a[1], b[3], c2, c3, c1);
518 mul_add_c(a[2], b[3], c3, c1, c2);
519 mul_add_c(a[3], b[2], c3, c1, c2);
522 mul_add_c(a[3], b[3], c1, c2, c3);
527 void bn_sqr_comba8(BN_ULONG *r, const BN_ULONG *a)
535 sqr_add_c(a, 0, c1, c2, c3);
538 sqr_add_c2(a, 1, 0, c2, c3, c1);
541 sqr_add_c(a, 1, c3, c1, c2);
542 sqr_add_c2(a, 2, 0, c3, c1, c2);
545 sqr_add_c2(a, 3, 0, c1, c2, c3);
546 sqr_add_c2(a, 2, 1, c1, c2, c3);
549 sqr_add_c(a, 2, c2, c3, c1);
550 sqr_add_c2(a, 3, 1, c2, c3, c1);
551 sqr_add_c2(a, 4, 0, c2, c3, c1);
554 sqr_add_c2(a, 5, 0, c3, c1, c2);
555 sqr_add_c2(a, 4, 1, c3, c1, c2);
556 sqr_add_c2(a, 3, 2, c3, c1, c2);
559 sqr_add_c(a, 3, c1, c2, c3);
560 sqr_add_c2(a, 4, 2, c1, c2, c3);
561 sqr_add_c2(a, 5, 1, c1, c2, c3);
562 sqr_add_c2(a, 6, 0, c1, c2, c3);
565 sqr_add_c2(a, 7, 0, c2, c3, c1);
566 sqr_add_c2(a, 6, 1, c2, c3, c1);
567 sqr_add_c2(a, 5, 2, c2, c3, c1);
568 sqr_add_c2(a, 4, 3, c2, c3, c1);
571 sqr_add_c(a, 4, c3, c1, c2);
572 sqr_add_c2(a, 5, 3, c3, c1, c2);
573 sqr_add_c2(a, 6, 2, c3, c1, c2);
574 sqr_add_c2(a, 7, 1, c3, c1, c2);
577 sqr_add_c2(a, 7, 2, c1, c2, c3);
578 sqr_add_c2(a, 6, 3, c1, c2, c3);
579 sqr_add_c2(a, 5, 4, c1, c2, c3);
582 sqr_add_c(a, 5, c2, c3, c1);
583 sqr_add_c2(a, 6, 4, c2, c3, c1);
584 sqr_add_c2(a, 7, 3, c2, c3, c1);
587 sqr_add_c2(a, 7, 4, c3, c1, c2);
588 sqr_add_c2(a, 6, 5, c3, c1, c2);
591 sqr_add_c(a, 6, c1, c2, c3);
592 sqr_add_c2(a, 7, 5, c1, c2, c3);
595 sqr_add_c2(a, 7, 6, c2, c3, c1);
598 sqr_add_c(a, 7, c3, c1, c2);
603 void bn_sqr_comba4(BN_ULONG *r, const BN_ULONG *a)
611 sqr_add_c(a, 0, c1, c2, c3);
614 sqr_add_c2(a, 1, 0, c2, c3, c1);
617 sqr_add_c(a, 1, c3, c1, c2);
618 sqr_add_c2(a, 2, 0, c3, c1, c2);
621 sqr_add_c2(a, 3, 0, c1, c2, c3);
622 sqr_add_c2(a, 2, 1, c1, c2, c3);
625 sqr_add_c(a, 2, c2, c3, c1);
626 sqr_add_c2(a, 3, 1, c2, c3, c1);
629 sqr_add_c2(a, 3, 2, c3, c1, c2);
632 sqr_add_c(a, 3, c1, c2, c3);