1 /* crypto/bn/bn_mul.c */
2 /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
5 * This package is an SSL implementation written
6 * by Eric Young (eay@cryptsoft.com).
7 * The implementation was written so as to conform with Netscapes SSL.
9 * This library is free for commercial and non-commercial use as long as
10 * the following conditions are aheared to. The following conditions
11 * apply to all code found in this distribution, be it the RC4, RSA,
12 * lhash, DES, etc., code; not just the SSL code. The SSL documentation
13 * included with this distribution is covered by the same copyright terms
14 * except that the holder is Tim Hudson (tjh@cryptsoft.com).
16 * Copyright remains Eric Young's, and as such any Copyright notices in
17 * the code are not to be removed.
18 * If this package is used in a product, Eric Young should be given attribution
19 * as the author of the parts of the library used.
20 * This can be in the form of a textual message at program startup or
21 * in documentation (online or textual) provided with the package.
23 * Redistribution and use in source and binary forms, with or without
24 * modification, are permitted provided that the following conditions
26 * 1. Redistributions of source code must retain the copyright
27 * notice, this list of conditions and the following disclaimer.
28 * 2. Redistributions in binary form must reproduce the above copyright
29 * notice, this list of conditions and the following disclaimer in the
30 * documentation and/or other materials provided with the distribution.
31 * 3. All advertising materials mentioning features or use of this software
32 * must display the following acknowledgement:
33 * "This product includes cryptographic software written by
34 * Eric Young (eay@cryptsoft.com)"
35 * The word 'cryptographic' can be left out if the rouines from the library
36 * being used are not cryptographic related :-).
37 * 4. If you include any Windows specific code (or a derivative thereof) from
38 * the apps directory (application code) you must include an acknowledgement:
39 * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
41 * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
42 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
43 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
44 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
45 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
46 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
47 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
48 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
49 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
50 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
53 * The licence and distribution terms for any publically available version or
54 * derivative of this code cannot be changed. i.e. this code cannot simply be
55 * copied and put under another distribution licence
56 * [including the GNU Public Licence.]
64 /* Karatsuba recursive multiplication algorithm
65 * (cf. Knuth, The Art of Computer Programming, Vol. 2) */
67 /* r is 2*n2 words in size,
68 * a and b are both n2 words in size.
69 * n2 must be a power of 2.
70 * We multiply and return the result.
71 * t must be 2*n2 words in size
74 * a[0]*b[0]+a[1]*b[1]+(a[0]-a[1])*(b[1]-b[0])
77 void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
81 unsigned int neg,zero;
85 printf(" bn_mul_recursive %d * %d\n",n2,n2);
100 # endif /* BN_MUL_COMBA */
101 if (n2 < BN_MUL_RECURSIVE_SIZE_NORMAL)
103 /* This should not happen */
104 bn_mul_normal(r,a,n2,b,n2);
107 /* r=(a[0]-a[1])*(b[1]-b[0]) */
108 c1=bn_cmp_words(a,&(a[n]),n);
109 c2=bn_cmp_words(&(b[n]),b,n);
114 bn_sub_words(t, &(a[n]),a, n); /* - */
115 bn_sub_words(&(t[n]),b, &(b[n]),n); /* - */
121 bn_sub_words(t, &(a[n]),a, n); /* - */
122 bn_sub_words(&(t[n]),&(b[n]),b, n); /* + */
131 bn_sub_words(t, a, &(a[n]),n); /* + */
132 bn_sub_words(&(t[n]),b, &(b[n]),n); /* - */
139 bn_sub_words(t, a, &(a[n]),n);
140 bn_sub_words(&(t[n]),&(b[n]),b, n);
148 bn_mul_comba4(&(t[n2]),t,&(t[n]));
150 memset(&(t[n2]),0,8*sizeof(BN_ULONG));
152 bn_mul_comba4(r,a,b);
153 bn_mul_comba4(&(r[n2]),&(a[n]),&(b[n]));
158 bn_mul_comba8(&(t[n2]),t,&(t[n]));
160 memset(&(t[n2]),0,16*sizeof(BN_ULONG));
162 bn_mul_comba8(r,a,b);
163 bn_mul_comba8(&(r[n2]),&(a[n]),&(b[n]));
166 # endif /* BN_MUL_COMBA */
170 bn_mul_recursive(&(t[n2]),t,&(t[n]),n,p);
172 memset(&(t[n2]),0,n2*sizeof(BN_ULONG));
173 bn_mul_recursive(r,a,b,n,p);
174 bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),n,p);
177 /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
178 * r[10] holds (a[0]*b[0])
179 * r[32] holds (b[1]*b[1])
182 c1=(int)(bn_add_words(t,r,&(r[n2]),n2));
184 if (neg) /* if t[32] is negative */
186 c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2));
190 /* Might have a carry */
191 c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),t,n2));
194 /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
195 * r[10] holds (a[0]*b[0])
196 * r[32] holds (b[1]*b[1])
197 * c1 holds the carry bits
199 c1+=(int)(bn_add_words(&(r[n]),&(r[n]),&(t[n2]),n2));
207 /* The overflow will stop before we over write
208 * words we should not overwrite */
209 if (ln < (BN_ULONG)c1)
221 /* n+tn is the word length
222 * t needs to be n*4 is size, as does r */
223 void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int tn,
227 unsigned int c1,c2,neg,zero;
231 printf(" bn_mul_part_recursive %d * %d\n",tn+n,tn+n);
236 bn_mul_normal(r,a,i,b,i);
240 /* r=(a[0]-a[1])*(b[1]-b[0]) */
241 c1=bn_cmp_words(a,&(a[n]),n);
242 c2=bn_cmp_words(&(b[n]),b,n);
247 bn_sub_words(t, &(a[n]),a, n); /* - */
248 bn_sub_words(&(t[n]),b, &(b[n]),n); /* - */
254 bn_sub_words(t, &(a[n]),a, n); /* - */
255 bn_sub_words(&(t[n]),&(b[n]),b, n); /* + */
264 bn_sub_words(t, a, &(a[n]),n); /* + */
265 bn_sub_words(&(t[n]),b, &(b[n]),n); /* - */
272 bn_sub_words(t, a, &(a[n]),n);
273 bn_sub_words(&(t[n]),&(b[n]),b, n);
276 /* The zero case isn't yet implemented here. The speedup
277 would probably be negligible. */
281 bn_mul_comba4(&(t[n2]),t,&(t[n]));
282 bn_mul_comba4(r,a,b);
283 bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn);
284 memset(&(r[n2+tn*2]),0,sizeof(BN_ULONG)*(n2-tn*2));
290 bn_mul_comba8(&(t[n2]),t,&(t[n]));
291 bn_mul_comba8(r,a,b);
292 bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn);
293 memset(&(r[n2+tn*2]),0,sizeof(BN_ULONG)*(n2-tn*2));
298 bn_mul_recursive(&(t[n2]),t,&(t[n]),n,p);
299 bn_mul_recursive(r,a,b,n,p);
301 /* If there is only a bottom half to the number,
306 bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),i,p);
307 memset(&(r[n2+i*2]),0,sizeof(BN_ULONG)*(n2-i*2));
309 else if (j > 0) /* eg, n == 16, i == 8 and tn == 11 */
311 bn_mul_part_recursive(&(r[n2]),&(a[n]),&(b[n]),
313 memset(&(r[n2+tn*2]),0,
314 sizeof(BN_ULONG)*(n2-tn*2));
316 else /* (j < 0) eg, n == 16, i == 8 and tn == 5 */
318 memset(&(r[n2]),0,sizeof(BN_ULONG)*n2);
319 if (tn < BN_MUL_RECURSIVE_SIZE_NORMAL)
321 bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn);
330 bn_mul_part_recursive(&(r[n2]),
337 bn_mul_recursive(&(r[n2]),
347 /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
348 * r[10] holds (a[0]*b[0])
349 * r[32] holds (b[1]*b[1])
352 c1=(int)(bn_add_words(t,r,&(r[n2]),n2));
354 if (neg) /* if t[32] is negative */
356 c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2));
360 /* Might have a carry */
361 c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),t,n2));
364 /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
365 * r[10] holds (a[0]*b[0])
366 * r[32] holds (b[1]*b[1])
367 * c1 holds the carry bits
369 c1+=(int)(bn_add_words(&(r[n]),&(r[n]),&(t[n2]),n2));
377 /* The overflow will stop before we over write
378 * words we should not overwrite */
391 /* a and b must be the same size, which is n2.
392 * r needs to be n2 words and t needs to be n2*2
394 void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
400 printf(" bn_mul_low_recursive %d * %d\n",n2,n2);
403 bn_mul_recursive(r,a,b,n,&(t[0]));
404 if (n >= BN_MUL_LOW_RECURSIVE_SIZE_NORMAL)
406 bn_mul_low_recursive(&(t[0]),&(a[0]),&(b[n]),n,&(t[n2]));
407 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
408 bn_mul_low_recursive(&(t[0]),&(a[n]),&(b[0]),n,&(t[n2]));
409 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
413 bn_mul_low_normal(&(t[0]),&(a[0]),&(b[n]),n);
414 bn_mul_low_normal(&(t[n]),&(a[n]),&(b[0]),n);
415 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
416 bn_add_words(&(r[n]),&(r[n]),&(t[n]),n);
420 /* a and b must be the same size, which is n2.
421 * r needs to be n2 words and t needs to be n2*2
422 * l is the low words of the output.
425 void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l, int n2,
431 BN_ULONG ll,lc,*lp,*mp;
434 printf(" bn_mul_high %d * %d\n",n2,n2);
438 /* Calculate (al-ah)*(bh-bl) */
440 c1=bn_cmp_words(&(a[0]),&(a[n]),n);
441 c2=bn_cmp_words(&(b[n]),&(b[0]),n);
445 bn_sub_words(&(r[0]),&(a[n]),&(a[0]),n);
446 bn_sub_words(&(r[n]),&(b[0]),&(b[n]),n);
452 bn_sub_words(&(r[0]),&(a[n]),&(a[0]),n);
453 bn_sub_words(&(r[n]),&(b[n]),&(b[0]),n);
462 bn_sub_words(&(r[0]),&(a[0]),&(a[n]),n);
463 bn_sub_words(&(r[n]),&(b[0]),&(b[n]),n);
470 bn_sub_words(&(r[0]),&(a[0]),&(a[n]),n);
471 bn_sub_words(&(r[n]),&(b[n]),&(b[0]),n);
476 /* t[10] = (a[0]-a[1])*(b[1]-b[0]) */
477 /* r[10] = (a[1]*b[1]) */
481 bn_mul_comba8(&(t[0]),&(r[0]),&(r[n]));
482 bn_mul_comba8(r,&(a[n]),&(b[n]));
487 bn_mul_recursive(&(t[0]),&(r[0]),&(r[n]),n,&(t[n2]));
488 bn_mul_recursive(r,&(a[n]),&(b[n]),n,&(t[n2]));
492 * s1 == low(ah*bh)+low((al-ah)*(bh-bl))+low(al*bl)+high(al*bl)
493 * We know s0 and s1 so the only unknown is high(al*bl)
494 * high(al*bl) == s1 - low(ah*bh+s0+(al-ah)*(bh-bl))
495 * high(al*bl) == s1 - (r[0]+l[0]+t[0])
500 c1=(int)(bn_add_words(lp,&(r[0]),&(l[0]),n));
509 neg=(int)(bn_sub_words(&(t[n2]),lp,&(t[0]),n));
512 bn_add_words(&(t[n2]),lp,&(t[0]),n);
518 bn_sub_words(&(t[n2+n]),&(l[n]),&(t[n2]),n);
525 lp[i]=((~mp[i])+1)&BN_MASK2;
530 * t[10] = (a[0]-a[1])*(b[1]-b[0]) neg is the sign
531 * r[10] = (a[1]*b[1])
534 * R[21] = al*bl + ah*bh + (a[0]-a[1])*(b[1]-b[0])
537 /* R[1]=t[3]+l[0]+r[0](+-)t[0] (have carry/borrow)
538 * R[2]=r[0]+t[3]+r[1](+-)t[1] (have carry/borrow)
539 * R[3]=r[1]+(carry/borrow)
544 c1= (int)(bn_add_words(lp,&(t[n2+n]),&(l[0]),n));
551 c1+=(int)(bn_add_words(&(t[n2]),lp, &(r[0]),n));
553 c1-=(int)(bn_sub_words(&(t[n2]),&(t[n2]),&(t[0]),n));
555 c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),&(t[0]),n));
557 c2 =(int)(bn_add_words(&(r[0]),&(r[0]),&(t[n2+n]),n));
558 c2+=(int)(bn_add_words(&(r[0]),&(r[0]),&(r[n]),n));
560 c2-=(int)(bn_sub_words(&(r[0]),&(r[0]),&(t[n]),n));
562 c2+=(int)(bn_add_words(&(r[0]),&(r[0]),&(t[n]),n));
564 if (c1 != 0) /* Add starting at r[0], could be +ve or -ve */
571 ll=(r[i]+lc)&BN_MASK2;
581 r[i++]=(ll-lc)&BN_MASK2;
586 if (c2 != 0) /* Add starting at r[1] */
593 ll=(r[i]+lc)&BN_MASK2;
603 r[i++]=(ll-lc)&BN_MASK2;
609 #endif /* BN_RECURSION */
611 int BN_mul(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx)
616 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
625 printf("BN_mul %d * %d\n",a->top,b->top);
635 if ((al == 0) || (bl == 0))
643 if ((r == a) || (r == b))
645 if ((rr = BN_CTX_get(ctx)) == NULL) goto err;
649 rr->neg=a->neg^b->neg;
651 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
660 if (bn_wexpand(rr,8) == NULL) goto err;
662 bn_mul_comba4(rr->d,a->d,b->d);
668 if (bn_wexpand(rr,16) == NULL) goto err;
670 bn_mul_comba8(rr->d,a->d,b->d);
674 #endif /* BN_MUL_COMBA */
676 if ((al >= BN_MULL_SIZE_NORMAL) && (bl >= BN_MULL_SIZE_NORMAL))
678 if (i == 1 && !BN_get_flags(b,BN_FLG_STATIC_DATA))
685 else if (i == -1 && !BN_get_flags(a,BN_FLG_STATIC_DATA))
694 /* symmetric and > 4 */
696 j=BN_num_bits_word((BN_ULONG)al);
700 if (al == j) /* exact multiple */
704 bn_mul_recursive(rr->d,a->d,b->d,al,t->d);
712 for (i=a->top; i<k; i++)
714 for (i=b->top; i<k; i++)
716 bn_mul_part_recursive(rr->d,a->d,b->d,al-j,j,t->d);
722 #endif /* BN_RECURSION */
723 if (bn_wexpand(rr,top) == NULL) goto err;
725 bn_mul_normal(rr->d,a->d,al,b->d,bl);
727 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
731 if (r != rr) BN_copy(r,rr);
738 void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb)
743 printf(" bn_mul_normal %d * %d\n",na,nb);
751 itmp=na; na=nb; nb=itmp;
756 rr[0]=bn_mul_words(r,a,na,b[0]);
760 if (--nb <= 0) return;
761 rr[1]=bn_mul_add_words(&(r[1]),a,na,b[1]);
762 if (--nb <= 0) return;
763 rr[2]=bn_mul_add_words(&(r[2]),a,na,b[2]);
764 if (--nb <= 0) return;
765 rr[3]=bn_mul_add_words(&(r[3]),a,na,b[3]);
766 if (--nb <= 0) return;
767 rr[4]=bn_mul_add_words(&(r[4]),a,na,b[4]);
774 void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n)
777 printf(" bn_mul_low_normal %d * %d\n",n,n);
779 bn_mul_words(r,a,n,b[0]);
783 if (--n <= 0) return;
784 bn_mul_add_words(&(r[1]),a,n,b[1]);
785 if (--n <= 0) return;
786 bn_mul_add_words(&(r[2]),a,n,b[2]);
787 if (--n <= 0) return;
788 bn_mul_add_words(&(r[3]),a,n,b[3]);
789 if (--n <= 0) return;
790 bn_mul_add_words(&(r[4]),a,n,b[4]);