2 # include "../bn_asm.c" /* kind of dirty hack for Sun Studio */
5 * x86_64 BIGNUM accelerator version 0.1, December 2002.
7 * Implemented by Andy Polyakov <appro@fy.chalmers.se> for the OpenSSL
10 * Rights for redistribution and usage in source and binary forms are
11 * granted according to the OpenSSL license. Warranty of any kind is
14 * Q. Version 0.1? It doesn't sound like Andy, he used to assign real
15 * versions, like 1.0...
16 * A. Well, that's because this code is basically a quick-n-dirty
17 * proof-of-concept hack. As you can see it's implemented with
18 * inline assembler, which means that you're bound to GCC and that
19 * there might be enough room for further improvement.
21 * Q. Why inline assembler?
22 * A. x86_64 features own ABI which I'm not familiar with. This is
23 * why I decided to let the compiler take care of subroutine
24 * prologue/epilogue as well as register allocation. For reference.
25 * Win64 implements different ABI for AMD64, different from Linux.
27 * Q. How much faster does it get?
28 * A. 'apps/openssl speed rsa dsa' output with no-asm:
30 * sign verify sign/s verify/s
31 * rsa 512 bits 0.0006s 0.0001s 1683.8 18456.2
32 * rsa 1024 bits 0.0028s 0.0002s 356.0 6407.0
33 * rsa 2048 bits 0.0172s 0.0005s 58.0 1957.8
34 * rsa 4096 bits 0.1155s 0.0018s 8.7 555.6
35 * sign verify sign/s verify/s
36 * dsa 512 bits 0.0005s 0.0006s 2100.8 1768.3
37 * dsa 1024 bits 0.0014s 0.0018s 692.3 559.2
38 * dsa 2048 bits 0.0049s 0.0061s 204.7 165.0
40 * 'apps/openssl speed rsa dsa' output with this module:
42 * sign verify sign/s verify/s
43 * rsa 512 bits 0.0004s 0.0000s 2767.1 33297.9
44 * rsa 1024 bits 0.0012s 0.0001s 867.4 14674.7
45 * rsa 2048 bits 0.0061s 0.0002s 164.0 5270.0
46 * rsa 4096 bits 0.0384s 0.0006s 26.1 1650.8
47 * sign verify sign/s verify/s
48 * dsa 512 bits 0.0002s 0.0003s 4442.2 3786.3
49 * dsa 1024 bits 0.0005s 0.0007s 1835.1 1497.4
50 * dsa 2048 bits 0.0016s 0.0020s 620.4 504.6
52 * For the reference. IA-32 assembler implementation performs
53 * very much like 64-bit code compiled with no-asm on the same
57 #define BN_ULONG unsigned long
60 * "m"(a), "+m"(r) is the way to favor DirectPath ยต-code;
61 * "g"(0) let the compiler to decide where does it
62 * want to keep the value of zero;
64 #define mul_add(r,a,word,carry) do { \
65 register BN_ULONG high,low; \
67 : "=a"(low),"=d"(high) \
70 asm ("addq %2,%0; adcq %3,%1" \
71 : "+r"(carry),"+d"(high)\
74 asm ("addq %2,%0; adcq %3,%1" \
75 : "+m"(r),"+d"(high) \
81 #define mul(r,a,word,carry) do { \
82 register BN_ULONG high,low; \
84 : "=a"(low),"=d"(high) \
87 asm ("addq %2,%0; adcq %3,%1" \
88 : "+r"(carry),"+d"(high)\
91 (r)=carry, carry=high; \
94 #define sqr(r0,r1,a) \
100 BN_ULONG bn_mul_add_words(BN_ULONG *rp, BN_ULONG *ap, int num, BN_ULONG w)
104 if (num <= 0) return(c1);
108 mul_add(rp[0],ap[0],w,c1);
109 mul_add(rp[1],ap[1],w,c1);
110 mul_add(rp[2],ap[2],w,c1);
111 mul_add(rp[3],ap[3],w,c1);
112 ap+=4; rp+=4; num-=4;
116 mul_add(rp[0],ap[0],w,c1); if (--num==0) return c1;
117 mul_add(rp[1],ap[1],w,c1); if (--num==0) return c1;
118 mul_add(rp[2],ap[2],w,c1); return c1;
124 BN_ULONG bn_mul_words(BN_ULONG *rp, BN_ULONG *ap, int num, BN_ULONG w)
128 if (num <= 0) return(c1);
132 mul(rp[0],ap[0],w,c1);
133 mul(rp[1],ap[1],w,c1);
134 mul(rp[2],ap[2],w,c1);
135 mul(rp[3],ap[3],w,c1);
136 ap+=4; rp+=4; num-=4;
140 mul(rp[0],ap[0],w,c1); if (--num == 0) return c1;
141 mul(rp[1],ap[1],w,c1); if (--num == 0) return c1;
142 mul(rp[2],ap[2],w,c1);
147 void bn_sqr_words(BN_ULONG *r, BN_ULONG *a, int n)
161 sqr(r[0],r[1],a[0]); if (--n == 0) return;
162 sqr(r[2],r[3],a[1]); if (--n == 0) return;
167 BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d)
168 { BN_ULONG ret,waste;
171 : "=a"(ret),"=d"(waste)
172 : "a"(l),"d"(h),"g"(d)
178 BN_ULONG bn_add_words (BN_ULONG *rp, BN_ULONG *ap, BN_ULONG *bp,int n)
179 { BN_ULONG ret=0,i=0;
181 if (n <= 0) return 0;
186 "1: movq (%4,%2,8),%0 \n"
187 " adcq (%5,%2,8),%0 \n"
188 " movq %0,(%3,%2,8) \n"
192 : "=&a"(ret),"+c"(n),"=&r"(i)
193 : "r"(rp),"r"(ap),"r"(bp)
201 BN_ULONG bn_sub_words (BN_ULONG *rp, BN_ULONG *ap, BN_ULONG *bp,int n)
202 { BN_ULONG ret=0,i=0;
204 if (n <= 0) return 0;
209 "1: movq (%4,%2,8),%0 \n"
210 " sbbq (%5,%2,8),%0 \n"
211 " movq %0,(%3,%2,8) \n"
215 : "=&a"(ret),"+c"(n),"=&r"(i)
216 : "r"(rp),"r"(ap),"r"(bp)
223 /* Simics 1.4<7 has buggy sbbq:-( */
224 #define BN_MASK2 0xffffffffffffffffL
225 BN_ULONG bn_sub_words(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n)
230 if (n <= 0) return((BN_ULONG)0);
235 r[0]=(t1-t2-c)&BN_MASK2;
236 if (t1 != t2) c=(t1 < t2);
240 r[1]=(t1-t2-c)&BN_MASK2;
241 if (t1 != t2) c=(t1 < t2);
245 r[2]=(t1-t2-c)&BN_MASK2;
246 if (t1 != t2) c=(t1 < t2);
250 r[3]=(t1-t2-c)&BN_MASK2;
251 if (t1 != t2) c=(t1 < t2);
262 /* mul_add_c(a,b,c0,c1,c2) -- c+=a*b for three word number c=(c2,c1,c0) */
263 /* mul_add_c2(a,b,c0,c1,c2) -- c+=2*a*b for three word number c=(c2,c1,c0) */
264 /* sqr_add_c(a,i,c0,c1,c2) -- c+=a[i]^2 for three word number c=(c2,c1,c0) */
265 /* sqr_add_c2(a,i,c0,c1,c2) -- c+=2*a[i]*a[j] for three word number c=(c2,c1,c0) */
268 /* original macros are kept for reference purposes */
269 #define mul_add_c(a,b,c0,c1,c2) { \
270 BN_ULONG ta=(a),tb=(b); \
272 t2 = BN_UMULT_HIGH(ta,tb); \
273 c0 += t1; t2 += (c0<t1)?1:0; \
274 c1 += t2; c2 += (c1<t2)?1:0; \
277 #define mul_add_c2(a,b,c0,c1,c2) { \
278 BN_ULONG ta=(a),tb=(b),t0; \
279 t1 = BN_UMULT_HIGH(ta,tb); \
281 t2 = t1+t1; c2 += (t2<t1)?1:0; \
282 t1 = t0+t0; t2 += (t1<t0)?1:0; \
283 c0 += t1; t2 += (c0<t1)?1:0; \
284 c1 += t2; c2 += (c1<t2)?1:0; \
287 #define mul_add_c(a,b,c0,c1,c2) do { \
289 : "=a"(t1),"=d"(t2) \
292 asm ("addq %2,%0; adcq %3,%1" \
293 : "+r"(c0),"+d"(t2) \
296 asm ("addq %2,%0; adcq %3,%1" \
297 : "+r"(c1),"+r"(c2) \
302 #define sqr_add_c(a,i,c0,c1,c2) do { \
304 : "=a"(t1),"=d"(t2) \
307 asm ("addq %2,%0; adcq %3,%1" \
308 : "+r"(c0),"+d"(t2) \
311 asm ("addq %2,%0; adcq %3,%1" \
312 : "+r"(c1),"+r"(c2) \
317 #define mul_add_c2(a,b,c0,c1,c2) do { \
319 : "=a"(t1),"=d"(t2) \
322 asm ("addq %0,%0; adcq %2,%1" \
323 : "+d"(t2),"+r"(c2) \
326 asm ("addq %0,%0; adcq %2,%1" \
327 : "+a"(t1),"+d"(t2) \
330 asm ("addq %2,%0; adcq %3,%1" \
331 : "+r"(c0),"+d"(t2) \
334 asm ("addq %2,%0; adcq %3,%1" \
335 : "+r"(c1),"+r"(c2) \
341 #define sqr_add_c2(a,i,j,c0,c1,c2) \
342 mul_add_c2((a)[i],(a)[j],c0,c1,c2)
344 void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b)
352 mul_add_c(a[0],b[0],c1,c2,c3);
355 mul_add_c(a[0],b[1],c2,c3,c1);
356 mul_add_c(a[1],b[0],c2,c3,c1);
359 mul_add_c(a[2],b[0],c3,c1,c2);
360 mul_add_c(a[1],b[1],c3,c1,c2);
361 mul_add_c(a[0],b[2],c3,c1,c2);
364 mul_add_c(a[0],b[3],c1,c2,c3);
365 mul_add_c(a[1],b[2],c1,c2,c3);
366 mul_add_c(a[2],b[1],c1,c2,c3);
367 mul_add_c(a[3],b[0],c1,c2,c3);
370 mul_add_c(a[4],b[0],c2,c3,c1);
371 mul_add_c(a[3],b[1],c2,c3,c1);
372 mul_add_c(a[2],b[2],c2,c3,c1);
373 mul_add_c(a[1],b[3],c2,c3,c1);
374 mul_add_c(a[0],b[4],c2,c3,c1);
377 mul_add_c(a[0],b[5],c3,c1,c2);
378 mul_add_c(a[1],b[4],c3,c1,c2);
379 mul_add_c(a[2],b[3],c3,c1,c2);
380 mul_add_c(a[3],b[2],c3,c1,c2);
381 mul_add_c(a[4],b[1],c3,c1,c2);
382 mul_add_c(a[5],b[0],c3,c1,c2);
385 mul_add_c(a[6],b[0],c1,c2,c3);
386 mul_add_c(a[5],b[1],c1,c2,c3);
387 mul_add_c(a[4],b[2],c1,c2,c3);
388 mul_add_c(a[3],b[3],c1,c2,c3);
389 mul_add_c(a[2],b[4],c1,c2,c3);
390 mul_add_c(a[1],b[5],c1,c2,c3);
391 mul_add_c(a[0],b[6],c1,c2,c3);
394 mul_add_c(a[0],b[7],c2,c3,c1);
395 mul_add_c(a[1],b[6],c2,c3,c1);
396 mul_add_c(a[2],b[5],c2,c3,c1);
397 mul_add_c(a[3],b[4],c2,c3,c1);
398 mul_add_c(a[4],b[3],c2,c3,c1);
399 mul_add_c(a[5],b[2],c2,c3,c1);
400 mul_add_c(a[6],b[1],c2,c3,c1);
401 mul_add_c(a[7],b[0],c2,c3,c1);
404 mul_add_c(a[7],b[1],c3,c1,c2);
405 mul_add_c(a[6],b[2],c3,c1,c2);
406 mul_add_c(a[5],b[3],c3,c1,c2);
407 mul_add_c(a[4],b[4],c3,c1,c2);
408 mul_add_c(a[3],b[5],c3,c1,c2);
409 mul_add_c(a[2],b[6],c3,c1,c2);
410 mul_add_c(a[1],b[7],c3,c1,c2);
413 mul_add_c(a[2],b[7],c1,c2,c3);
414 mul_add_c(a[3],b[6],c1,c2,c3);
415 mul_add_c(a[4],b[5],c1,c2,c3);
416 mul_add_c(a[5],b[4],c1,c2,c3);
417 mul_add_c(a[6],b[3],c1,c2,c3);
418 mul_add_c(a[7],b[2],c1,c2,c3);
421 mul_add_c(a[7],b[3],c2,c3,c1);
422 mul_add_c(a[6],b[4],c2,c3,c1);
423 mul_add_c(a[5],b[5],c2,c3,c1);
424 mul_add_c(a[4],b[6],c2,c3,c1);
425 mul_add_c(a[3],b[7],c2,c3,c1);
428 mul_add_c(a[4],b[7],c3,c1,c2);
429 mul_add_c(a[5],b[6],c3,c1,c2);
430 mul_add_c(a[6],b[5],c3,c1,c2);
431 mul_add_c(a[7],b[4],c3,c1,c2);
434 mul_add_c(a[7],b[5],c1,c2,c3);
435 mul_add_c(a[6],b[6],c1,c2,c3);
436 mul_add_c(a[5],b[7],c1,c2,c3);
439 mul_add_c(a[6],b[7],c2,c3,c1);
440 mul_add_c(a[7],b[6],c2,c3,c1);
443 mul_add_c(a[7],b[7],c3,c1,c2);
448 void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b)
456 mul_add_c(a[0],b[0],c1,c2,c3);
459 mul_add_c(a[0],b[1],c2,c3,c1);
460 mul_add_c(a[1],b[0],c2,c3,c1);
463 mul_add_c(a[2],b[0],c3,c1,c2);
464 mul_add_c(a[1],b[1],c3,c1,c2);
465 mul_add_c(a[0],b[2],c3,c1,c2);
468 mul_add_c(a[0],b[3],c1,c2,c3);
469 mul_add_c(a[1],b[2],c1,c2,c3);
470 mul_add_c(a[2],b[1],c1,c2,c3);
471 mul_add_c(a[3],b[0],c1,c2,c3);
474 mul_add_c(a[3],b[1],c2,c3,c1);
475 mul_add_c(a[2],b[2],c2,c3,c1);
476 mul_add_c(a[1],b[3],c2,c3,c1);
479 mul_add_c(a[2],b[3],c3,c1,c2);
480 mul_add_c(a[3],b[2],c3,c1,c2);
483 mul_add_c(a[3],b[3],c1,c2,c3);
488 void bn_sqr_comba8(BN_ULONG *r, BN_ULONG *a)
496 sqr_add_c(a,0,c1,c2,c3);
499 sqr_add_c2(a,1,0,c2,c3,c1);
502 sqr_add_c(a,1,c3,c1,c2);
503 sqr_add_c2(a,2,0,c3,c1,c2);
506 sqr_add_c2(a,3,0,c1,c2,c3);
507 sqr_add_c2(a,2,1,c1,c2,c3);
510 sqr_add_c(a,2,c2,c3,c1);
511 sqr_add_c2(a,3,1,c2,c3,c1);
512 sqr_add_c2(a,4,0,c2,c3,c1);
515 sqr_add_c2(a,5,0,c3,c1,c2);
516 sqr_add_c2(a,4,1,c3,c1,c2);
517 sqr_add_c2(a,3,2,c3,c1,c2);
520 sqr_add_c(a,3,c1,c2,c3);
521 sqr_add_c2(a,4,2,c1,c2,c3);
522 sqr_add_c2(a,5,1,c1,c2,c3);
523 sqr_add_c2(a,6,0,c1,c2,c3);
526 sqr_add_c2(a,7,0,c2,c3,c1);
527 sqr_add_c2(a,6,1,c2,c3,c1);
528 sqr_add_c2(a,5,2,c2,c3,c1);
529 sqr_add_c2(a,4,3,c2,c3,c1);
532 sqr_add_c(a,4,c3,c1,c2);
533 sqr_add_c2(a,5,3,c3,c1,c2);
534 sqr_add_c2(a,6,2,c3,c1,c2);
535 sqr_add_c2(a,7,1,c3,c1,c2);
538 sqr_add_c2(a,7,2,c1,c2,c3);
539 sqr_add_c2(a,6,3,c1,c2,c3);
540 sqr_add_c2(a,5,4,c1,c2,c3);
543 sqr_add_c(a,5,c2,c3,c1);
544 sqr_add_c2(a,6,4,c2,c3,c1);
545 sqr_add_c2(a,7,3,c2,c3,c1);
548 sqr_add_c2(a,7,4,c3,c1,c2);
549 sqr_add_c2(a,6,5,c3,c1,c2);
552 sqr_add_c(a,6,c1,c2,c3);
553 sqr_add_c2(a,7,5,c1,c2,c3);
556 sqr_add_c2(a,7,6,c2,c3,c1);
559 sqr_add_c(a,7,c3,c1,c2);
564 void bn_sqr_comba4(BN_ULONG *r, BN_ULONG *a)
572 sqr_add_c(a,0,c1,c2,c3);
575 sqr_add_c2(a,1,0,c2,c3,c1);
578 sqr_add_c(a,1,c3,c1,c2);
579 sqr_add_c2(a,2,0,c3,c1,c2);
582 sqr_add_c2(a,3,0,c1,c2,c3);
583 sqr_add_c2(a,2,1,c1,c2,c3);
586 sqr_add_c(a,2,c2,c3,c1);
587 sqr_add_c2(a,3,1,c2,c3,c1);
590 sqr_add_c2(a,3,2,c3,c1,c2);
593 sqr_add_c(a,3,c1,c2,c3);