bn_mul.c revision 1.3
1/* crypto/bn/bn_mul.c */
2/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
3 * All rights reserved.
4 *
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.
8 *
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).
15 *
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.
22 *
23 * Redistribution and use in source and binary forms, with or without
24 * modification, are permitted provided that the following conditions
25 * are met:
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)"
40 *
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
51 * SUCH DAMAGE.
52 *
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.]
57 */
58
59#include <stdio.h>
60#include "cryptlib.h"
61#include "bn_lcl.h"
62
63#ifdef BN_RECURSION
64/* r is 2*n2 words in size,
65 * a and b are both n2 words in size.
66 * n2 must be a power of 2.
67 * We multiply and return the result.
68 * t must be 2*n2 words in size
69 * We calculate
70 * a[0]*b[0]
71 * a[0]*b[0]+a[1]*b[1]+(a[0]-a[1])*(b[1]-b[0])
72 * a[1]*b[1]
73 */
74void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
75	     BN_ULONG *t)
76	{
77	int n=n2/2,c1,c2;
78	unsigned int neg,zero;
79	BN_ULONG ln,lo,*p;
80
81# ifdef BN_COUNT
82	printf(" bn_mul_recursive %d * %d\n",n2,n2);
83# endif
84# ifdef BN_MUL_COMBA
85#  if 0
86	if (n2 == 4)
87		{
88		bn_mul_comba4(r,a,b);
89		return;
90		}
91#  endif
92	if (n2 == 8)
93		{
94		bn_mul_comba8(r,a,b);
95		return;
96		}
97# endif /* BN_MUL_COMBA */
98	if (n2 < BN_MUL_RECURSIVE_SIZE_NORMAL)
99		{
100		/* This should not happen */
101		bn_mul_normal(r,a,n2,b,n2);
102		return;
103		}
104	/* r=(a[0]-a[1])*(b[1]-b[0]) */
105	c1=bn_cmp_words(a,&(a[n]),n);
106	c2=bn_cmp_words(&(b[n]),b,n);
107	zero=neg=0;
108	switch (c1*3+c2)
109		{
110	case -4:
111		bn_sub_words(t,      &(a[n]),a,      n); /* - */
112		bn_sub_words(&(t[n]),b,      &(b[n]),n); /* - */
113		break;
114	case -3:
115		zero=1;
116		break;
117	case -2:
118		bn_sub_words(t,      &(a[n]),a,      n); /* - */
119		bn_sub_words(&(t[n]),&(b[n]),b,      n); /* + */
120		neg=1;
121		break;
122	case -1:
123	case 0:
124	case 1:
125		zero=1;
126		break;
127	case 2:
128		bn_sub_words(t,      a,      &(a[n]),n); /* + */
129		bn_sub_words(&(t[n]),b,      &(b[n]),n); /* - */
130		neg=1;
131		break;
132	case 3:
133		zero=1;
134		break;
135	case 4:
136		bn_sub_words(t,      a,      &(a[n]),n);
137		bn_sub_words(&(t[n]),&(b[n]),b,      n);
138		break;
139		}
140
141# ifdef BN_MUL_COMBA
142	if (n == 4)
143		{
144		if (!zero)
145			bn_mul_comba4(&(t[n2]),t,&(t[n]));
146		else
147			memset(&(t[n2]),0,8*sizeof(BN_ULONG));
148
149		bn_mul_comba4(r,a,b);
150		bn_mul_comba4(&(r[n2]),&(a[n]),&(b[n]));
151		}
152	else if (n == 8)
153		{
154		if (!zero)
155			bn_mul_comba8(&(t[n2]),t,&(t[n]));
156		else
157			memset(&(t[n2]),0,16*sizeof(BN_ULONG));
158
159		bn_mul_comba8(r,a,b);
160		bn_mul_comba8(&(r[n2]),&(a[n]),&(b[n]));
161		}
162	else
163# endif /* BN_MUL_COMBA */
164		{
165		p= &(t[n2*2]);
166		if (!zero)
167			bn_mul_recursive(&(t[n2]),t,&(t[n]),n,p);
168		else
169			memset(&(t[n2]),0,n2*sizeof(BN_ULONG));
170		bn_mul_recursive(r,a,b,n,p);
171		bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),n,p);
172		}
173
174	/* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
175	 * r[10] holds (a[0]*b[0])
176	 * r[32] holds (b[1]*b[1])
177	 */
178
179	c1=(int)(bn_add_words(t,r,&(r[n2]),n2));
180
181	if (neg) /* if t[32] is negative */
182		{
183		c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2));
184		}
185	else
186		{
187		/* Might have a carry */
188		c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),t,n2));
189		}
190
191	/* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
192	 * r[10] holds (a[0]*b[0])
193	 * r[32] holds (b[1]*b[1])
194	 * c1 holds the carry bits
195	 */
196	c1+=(int)(bn_add_words(&(r[n]),&(r[n]),&(t[n2]),n2));
197	if (c1)
198		{
199		p= &(r[n+n2]);
200		lo= *p;
201		ln=(lo+c1)&BN_MASK2;
202		*p=ln;
203
204		/* The overflow will stop before we over write
205		 * words we should not overwrite */
206		if (ln < (BN_ULONG)c1)
207			{
208			do	{
209				p++;
210				lo= *p;
211				ln=(lo+1)&BN_MASK2;
212				*p=ln;
213				} while (ln == 0);
214			}
215		}
216	}
217
218/* n+tn is the word length
219 * t needs to be n*4 is size, as does r */
220void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int tn,
221	     int n, BN_ULONG *t)
222	{
223	int i,j,n2=n*2;
224	unsigned int c1,c2,neg,zero;
225	BN_ULONG ln,lo,*p;
226
227# ifdef BN_COUNT
228	printf(" bn_mul_part_recursive %d * %d\n",tn+n,tn+n);
229# endif
230	if (n < 8)
231		{
232		i=tn+n;
233		bn_mul_normal(r,a,i,b,i);
234		return;
235		}
236
237	/* r=(a[0]-a[1])*(b[1]-b[0]) */
238	c1=bn_cmp_words(a,&(a[n]),n);
239	c2=bn_cmp_words(&(b[n]),b,n);
240	zero=neg=0;
241	switch (c1*3+c2)
242		{
243	case -4:
244		bn_sub_words(t,      &(a[n]),a,      n); /* - */
245		bn_sub_words(&(t[n]),b,      &(b[n]),n); /* - */
246		break;
247	case -3:
248		zero=1;
249		/* break; */
250	case -2:
251		bn_sub_words(t,      &(a[n]),a,      n); /* - */
252		bn_sub_words(&(t[n]),&(b[n]),b,      n); /* + */
253		neg=1;
254		break;
255	case -1:
256	case 0:
257	case 1:
258		zero=1;
259		/* break; */
260	case 2:
261		bn_sub_words(t,      a,      &(a[n]),n); /* + */
262		bn_sub_words(&(t[n]),b,      &(b[n]),n); /* - */
263		neg=1;
264		break;
265	case 3:
266		zero=1;
267		/* break; */
268	case 4:
269		bn_sub_words(t,      a,      &(a[n]),n);
270		bn_sub_words(&(t[n]),&(b[n]),b,      n);
271		break;
272		}
273		/* The zero case isn't yet implemented here. The speedup
274		   would probably be negligible. */
275# if 0
276	if (n == 4)
277		{
278		bn_mul_comba4(&(t[n2]),t,&(t[n]));
279		bn_mul_comba4(r,a,b);
280		bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn);
281		memset(&(r[n2+tn*2]),0,sizeof(BN_ULONG)*(n2-tn*2));
282		}
283	else
284# endif
285	if (n == 8)
286		{
287		bn_mul_comba8(&(t[n2]),t,&(t[n]));
288		bn_mul_comba8(r,a,b);
289		bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn);
290		memset(&(r[n2+tn*2]),0,sizeof(BN_ULONG)*(n2-tn*2));
291		}
292	else
293		{
294		p= &(t[n2*2]);
295		bn_mul_recursive(&(t[n2]),t,&(t[n]),n,p);
296		bn_mul_recursive(r,a,b,n,p);
297		i=n/2;
298		/* If there is only a bottom half to the number,
299		 * just do it */
300		j=tn-i;
301		if (j == 0)
302			{
303			bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),i,p);
304			memset(&(r[n2+i*2]),0,sizeof(BN_ULONG)*(n2-i*2));
305			}
306		else if (j > 0) /* eg, n == 16, i == 8 and tn == 11 */
307				{
308				bn_mul_part_recursive(&(r[n2]),&(a[n]),&(b[n]),
309					j,i,p);
310				memset(&(r[n2+tn*2]),0,
311					sizeof(BN_ULONG)*(n2-tn*2));
312				}
313		else /* (j < 0) eg, n == 16, i == 8 and tn == 5 */
314			{
315			memset(&(r[n2]),0,sizeof(BN_ULONG)*n2);
316			if (tn < BN_MUL_RECURSIVE_SIZE_NORMAL)
317				{
318				bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn);
319				}
320			else
321				{
322				for (;;)
323					{
324					i/=2;
325					if (i < tn)
326						{
327						bn_mul_part_recursive(&(r[n2]),
328							&(a[n]),&(b[n]),
329							tn-i,i,p);
330						break;
331						}
332					else if (i == tn)
333						{
334						bn_mul_recursive(&(r[n2]),
335							&(a[n]),&(b[n]),
336							i,p);
337						break;
338						}
339					}
340				}
341			}
342		}
343
344	/* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
345	 * r[10] holds (a[0]*b[0])
346	 * r[32] holds (b[1]*b[1])
347	 */
348
349	c1=(int)(bn_add_words(t,r,&(r[n2]),n2));
350
351	if (neg) /* if t[32] is negative */
352		{
353		c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2));
354		}
355	else
356		{
357		/* Might have a carry */
358		c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),t,n2));
359		}
360
361	/* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
362	 * r[10] holds (a[0]*b[0])
363	 * r[32] holds (b[1]*b[1])
364	 * c1 holds the carry bits
365	 */
366	c1+=(int)(bn_add_words(&(r[n]),&(r[n]),&(t[n2]),n2));
367	if (c1)
368		{
369		p= &(r[n+n2]);
370		lo= *p;
371		ln=(lo+c1)&BN_MASK2;
372		*p=ln;
373
374		/* The overflow will stop before we over write
375		 * words we should not overwrite */
376		if (ln < c1)
377			{
378			do	{
379				p++;
380				lo= *p;
381				ln=(lo+1)&BN_MASK2;
382				*p=ln;
383				} while (ln == 0);
384			}
385		}
386	}
387
388/* a and b must be the same size, which is n2.
389 * r needs to be n2 words and t needs to be n2*2
390 */
391void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
392	     BN_ULONG *t)
393	{
394	int n=n2/2;
395
396# ifdef BN_COUNT
397	printf(" bn_mul_low_recursive %d * %d\n",n2,n2);
398# endif
399
400	bn_mul_recursive(r,a,b,n,&(t[0]));
401	if (n >= BN_MUL_LOW_RECURSIVE_SIZE_NORMAL)
402		{
403		bn_mul_low_recursive(&(t[0]),&(a[0]),&(b[n]),n,&(t[n2]));
404		bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
405		bn_mul_low_recursive(&(t[0]),&(a[n]),&(b[0]),n,&(t[n2]));
406		bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
407		}
408	else
409		{
410		bn_mul_low_normal(&(t[0]),&(a[0]),&(b[n]),n);
411		bn_mul_low_normal(&(t[n]),&(a[n]),&(b[0]),n);
412		bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
413		bn_add_words(&(r[n]),&(r[n]),&(t[n]),n);
414		}
415	}
416
417/* a and b must be the same size, which is n2.
418 * r needs to be n2 words and t needs to be n2*2
419 * l is the low words of the output.
420 * t needs to be n2*3
421 */
422void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l, int n2,
423	     BN_ULONG *t)
424	{
425	int i,n;
426	int c1,c2;
427	int neg,oneg,zero;
428	BN_ULONG ll,lc,*lp,*mp;
429
430# ifdef BN_COUNT
431	printf(" bn_mul_high %d * %d\n",n2,n2);
432# endif
433	n=n2/2;
434
435	/* Calculate (al-ah)*(bh-bl) */
436	neg=zero=0;
437	c1=bn_cmp_words(&(a[0]),&(a[n]),n);
438	c2=bn_cmp_words(&(b[n]),&(b[0]),n);
439	switch (c1*3+c2)
440		{
441	case -4:
442		bn_sub_words(&(r[0]),&(a[n]),&(a[0]),n);
443		bn_sub_words(&(r[n]),&(b[0]),&(b[n]),n);
444		break;
445	case -3:
446		zero=1;
447		break;
448	case -2:
449		bn_sub_words(&(r[0]),&(a[n]),&(a[0]),n);
450		bn_sub_words(&(r[n]),&(b[n]),&(b[0]),n);
451		neg=1;
452		break;
453	case -1:
454	case 0:
455	case 1:
456		zero=1;
457		break;
458	case 2:
459		bn_sub_words(&(r[0]),&(a[0]),&(a[n]),n);
460		bn_sub_words(&(r[n]),&(b[0]),&(b[n]),n);
461		neg=1;
462		break;
463	case 3:
464		zero=1;
465		break;
466	case 4:
467		bn_sub_words(&(r[0]),&(a[0]),&(a[n]),n);
468		bn_sub_words(&(r[n]),&(b[n]),&(b[0]),n);
469		break;
470		}
471
472	oneg=neg;
473	/* t[10] = (a[0]-a[1])*(b[1]-b[0]) */
474	/* r[10] = (a[1]*b[1]) */
475# ifdef BN_MUL_COMBA
476	if (n == 8)
477		{
478		bn_mul_comba8(&(t[0]),&(r[0]),&(r[n]));
479		bn_mul_comba8(r,&(a[n]),&(b[n]));
480		}
481	else
482# endif
483		{
484		bn_mul_recursive(&(t[0]),&(r[0]),&(r[n]),n,&(t[n2]));
485		bn_mul_recursive(r,&(a[n]),&(b[n]),n,&(t[n2]));
486		}
487
488	/* s0 == low(al*bl)
489	 * s1 == low(ah*bh)+low((al-ah)*(bh-bl))+low(al*bl)+high(al*bl)
490	 * We know s0 and s1 so the only unknown is high(al*bl)
491	 * high(al*bl) == s1 - low(ah*bh+s0+(al-ah)*(bh-bl))
492	 * high(al*bl) == s1 - (r[0]+l[0]+t[0])
493	 */
494	if (l != NULL)
495		{
496		lp= &(t[n2+n]);
497		c1=(int)(bn_add_words(lp,&(r[0]),&(l[0]),n));
498		}
499	else
500		{
501		c1=0;
502		lp= &(r[0]);
503		}
504
505	if (neg)
506		neg=(int)(bn_sub_words(&(t[n2]),lp,&(t[0]),n));
507	else
508		{
509		bn_add_words(&(t[n2]),lp,&(t[0]),n);
510		neg=0;
511		}
512
513	if (l != NULL)
514		{
515		bn_sub_words(&(t[n2+n]),&(l[n]),&(t[n2]),n);
516		}
517	else
518		{
519		lp= &(t[n2+n]);
520		mp= &(t[n2]);
521		for (i=0; i<n; i++)
522			lp[i]=((~mp[i])+1)&BN_MASK2;
523		}
524
525	/* s[0] = low(al*bl)
526	 * t[3] = high(al*bl)
527	 * t[10] = (a[0]-a[1])*(b[1]-b[0]) neg is the sign
528	 * r[10] = (a[1]*b[1])
529	 */
530	/* R[10] = al*bl
531	 * R[21] = al*bl + ah*bh + (a[0]-a[1])*(b[1]-b[0])
532	 * R[32] = ah*bh
533	 */
534	/* R[1]=t[3]+l[0]+r[0](+-)t[0] (have carry/borrow)
535	 * R[2]=r[0]+t[3]+r[1](+-)t[1] (have carry/borrow)
536	 * R[3]=r[1]+(carry/borrow)
537	 */
538	if (l != NULL)
539		{
540		lp= &(t[n2]);
541		c1= (int)(bn_add_words(lp,&(t[n2+n]),&(l[0]),n));
542		}
543	else
544		{
545		lp= &(t[n2+n]);
546		c1=0;
547		}
548	c1+=(int)(bn_add_words(&(t[n2]),lp,  &(r[0]),n));
549	if (oneg)
550		c1-=(int)(bn_sub_words(&(t[n2]),&(t[n2]),&(t[0]),n));
551	else
552		c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),&(t[0]),n));
553
554	c2 =(int)(bn_add_words(&(r[0]),&(r[0]),&(t[n2+n]),n));
555	c2+=(int)(bn_add_words(&(r[0]),&(r[0]),&(r[n]),n));
556	if (oneg)
557		c2-=(int)(bn_sub_words(&(r[0]),&(r[0]),&(t[n]),n));
558	else
559		c2+=(int)(bn_add_words(&(r[0]),&(r[0]),&(t[n]),n));
560
561	if (c1 != 0) /* Add starting at r[0], could be +ve or -ve */
562		{
563		i=0;
564		if (c1 > 0)
565			{
566			lc=c1;
567			do	{
568				ll=(r[i]+lc)&BN_MASK2;
569				r[i++]=ll;
570				lc=(lc > ll);
571				} while (lc);
572			}
573		else
574			{
575			lc= -c1;
576			do	{
577				ll=r[i];
578				r[i++]=(ll-lc)&BN_MASK2;
579				lc=(lc > ll);
580				} while (lc);
581			}
582		}
583	if (c2 != 0) /* Add starting at r[1] */
584		{
585		i=n;
586		if (c2 > 0)
587			{
588			lc=c2;
589			do	{
590				ll=(r[i]+lc)&BN_MASK2;
591				r[i++]=ll;
592				lc=(lc > ll);
593				} while (lc);
594			}
595		else
596			{
597			lc= -c2;
598			do	{
599				ll=r[i];
600				r[i++]=(ll-lc)&BN_MASK2;
601				lc=(lc > ll);
602				} while (lc);
603			}
604		}
605	}
606#endif /* BN_RECURSION */
607
608int BN_mul(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx)
609	{
610	int top,al,bl;
611	BIGNUM *rr;
612	int ret = 0;
613#if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
614	int i;
615#endif
616#ifdef BN_RECURSION
617	BIGNUM *t;
618	int j,k;
619#endif
620
621#ifdef BN_COUNT
622	printf("BN_mul %d * %d\n",a->top,b->top);
623#endif
624
625	bn_check_top(a);
626	bn_check_top(b);
627	bn_check_top(r);
628
629	al=a->top;
630	bl=b->top;
631	r->neg=a->neg^b->neg;
632
633	if ((al == 0) || (bl == 0))
634		{
635		BN_zero(r);
636		return(1);
637		}
638	top=al+bl;
639
640	BN_CTX_start(ctx);
641	if ((r == a) || (r == b))
642		{
643		if ((rr = BN_CTX_get(ctx)) == NULL) goto err;
644		}
645	else
646		rr = r;
647
648#if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
649	i = al-bl;
650#endif
651#ifdef BN_MUL_COMBA
652	if (i == 0)
653		{
654# if 0
655		if (al == 4)
656			{
657			if (bn_wexpand(rr,8) == NULL) goto err;
658			rr->top=8;
659			bn_mul_comba4(rr->d,a->d,b->d);
660			goto end;
661			}
662# endif
663		if (al == 8)
664			{
665			if (bn_wexpand(rr,16) == NULL) goto err;
666			rr->top=16;
667			bn_mul_comba8(rr->d,a->d,b->d);
668			goto end;
669			}
670		}
671#endif /* BN_MUL_COMBA */
672#ifdef BN_RECURSION
673	if ((al >= BN_MULL_SIZE_NORMAL) && (bl >= BN_MULL_SIZE_NORMAL))
674		{
675		if (i == 1 && !BN_get_flags(b,BN_FLG_STATIC_DATA))
676			{
677			bn_wexpand(b,al);
678			b->d[bl]=0;
679			bl++;
680			i--;
681			}
682		else if (i == -1 && !BN_get_flags(a,BN_FLG_STATIC_DATA))
683			{
684			bn_wexpand(a,bl);
685			a->d[al]=0;
686			al++;
687			i++;
688			}
689		if (i == 0)
690			{
691			/* symmetric and > 4 */
692			/* 16 or larger */
693			j=BN_num_bits_word((BN_ULONG)al);
694			j=1<<(j-1);
695			k=j+j;
696			t = BN_CTX_get(ctx);
697			if (al == j) /* exact multiple */
698				{
699				bn_wexpand(t,k*2);
700				bn_wexpand(rr,k*2);
701				bn_mul_recursive(rr->d,a->d,b->d,al,t->d);
702				}
703			else
704				{
705				bn_wexpand(a,k);
706				bn_wexpand(b,k);
707				bn_wexpand(t,k*4);
708				bn_wexpand(rr,k*4);
709				for (i=a->top; i<k; i++)
710					a->d[i]=0;
711				for (i=b->top; i<k; i++)
712					b->d[i]=0;
713				bn_mul_part_recursive(rr->d,a->d,b->d,al-j,j,t->d);
714				}
715			rr->top=top;
716			goto end;
717			}
718		}
719#endif /* BN_RECURSION */
720	if (bn_wexpand(rr,top) == NULL) goto err;
721	rr->top=top;
722	bn_mul_normal(rr->d,a->d,al,b->d,bl);
723
724#if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
725end:
726#endif
727	bn_fix_top(rr);
728	if (r != rr) BN_copy(r,rr);
729	ret=1;
730err:
731	BN_CTX_end(ctx);
732	return(ret);
733	}
734
735void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb)
736	{
737	BN_ULONG *rr;
738
739#ifdef BN_COUNT
740	printf(" bn_mul_normal %d * %d\n",na,nb);
741#endif
742
743	if (na < nb)
744		{
745		int itmp;
746		BN_ULONG *ltmp;
747
748		itmp=na; na=nb; nb=itmp;
749		ltmp=a;   a=b;   b=ltmp;
750
751		}
752	rr= &(r[na]);
753	rr[0]=bn_mul_words(r,a,na,b[0]);
754
755	for (;;)
756		{
757		if (--nb <= 0) return;
758		rr[1]=bn_mul_add_words(&(r[1]),a,na,b[1]);
759		if (--nb <= 0) return;
760		rr[2]=bn_mul_add_words(&(r[2]),a,na,b[2]);
761		if (--nb <= 0) return;
762		rr[3]=bn_mul_add_words(&(r[3]),a,na,b[3]);
763		if (--nb <= 0) return;
764		rr[4]=bn_mul_add_words(&(r[4]),a,na,b[4]);
765		rr+=4;
766		r+=4;
767		b+=4;
768		}
769	}
770
771void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n)
772	{
773#ifdef BN_COUNT
774	printf(" bn_mul_low_normal %d * %d\n",n,n);
775#endif
776	bn_mul_words(r,a,n,b[0]);
777
778	for (;;)
779		{
780		if (--n <= 0) return;
781		bn_mul_add_words(&(r[1]),a,n,b[1]);
782		if (--n <= 0) return;
783		bn_mul_add_words(&(r[2]),a,n,b[2]);
784		if (--n <= 0) return;
785		bn_mul_add_words(&(r[3]),a,n,b[3]);
786		if (--n <= 0) return;
787		bn_mul_add_words(&(r[4]),a,n,b[4]);
788		r+=4;
789		b+=4;
790		}
791	}
792