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, 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 * Keep in mind that carrying into high part of multiplication result
278 * can not overflow, because it cannot be all-ones.
281 /* original macros are kept for reference purposes */
282 #define mul_add_c(a,b,c0,c1,c2) { \
283 BN_ULONG ta=(a),tb=(b); \
285 t2 = BN_UMULT_HIGH(ta,tb); \
286 c0 += t1; t2 += (c0<t1)?1:0; \
287 c1 += t2; c2 += (c1<t2)?1:0; \
290 #define mul_add_c2(a,b,c0,c1,c2) { \
291 BN_ULONG ta=(a),tb=(b),t0; \
292 t1 = BN_UMULT_HIGH(ta,tb); \
294 c0 += t0; t2 = t1+((c0<t0)?1:0);\
295 c1 += t2; c2 += (c1<t2)?1:0; \
296 c0 += t0; t1 += (c0<t0)?1:0; \
297 c1 += t1; c2 += (c1<t1)?1:0; \
300 #define mul_add_c(a,b,c0,c1,c2) do { \
302 : "=a"(t1),"=d"(t2) \
305 asm ("addq %2,%0; adcq %3,%1" \
306 : "+r"(c0),"+d"(t2) \
309 asm ("addq %2,%0; adcq %3,%1" \
310 : "+r"(c1),"+r"(c2) \
315 #define sqr_add_c(a,i,c0,c1,c2) do { \
317 : "=a"(t1),"=d"(t2) \
320 asm ("addq %2,%0; adcq %3,%1" \
321 : "+r"(c0),"+d"(t2) \
324 asm ("addq %2,%0; adcq %3,%1" \
325 : "+r"(c1),"+r"(c2) \
330 #define mul_add_c2(a,b,c0,c1,c2) do { \
332 : "=a"(t1),"=d"(t2) \
335 asm ("addq %3,%0; adcq %4,%1; adcq %5,%2" \
336 : "+r"(c0),"+r"(c1),"+r"(c2) \
337 : "r"(t1),"r"(t2),"g"(0) \
339 asm ("addq %3,%0; adcq %4,%1; adcq %5,%2" \
340 : "+r"(c0),"+r"(c1),"+r"(c2) \
341 : "r"(t1),"r"(t2),"g"(0) \
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);