aboutsummaryrefslogtreecommitdiff
path: root/crypto/bn/bn_mul.c
blob: a0e9ec3b4694cb896a565f2953c56f53eef1da1c (plain) (blame)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
1126
1127
1128
1129
1130
1131
1132
1133
1134
1135
1136
1137
1138
1139
1140
1141
1142
1143
1144
1145
1146
1147
1148
1149
1150
1151
1152
1153
1154
1155
1156
1157
1158
1159
1160
1161
1162
1163
1164
1165
1166
1167
1168
1169
1170
1171
/* crypto/bn/bn_mul.c */
/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
 * All rights reserved.
 *
 * This package is an SSL implementation written
 * by Eric Young (eay@cryptsoft.com).
 * The implementation was written so as to conform with Netscapes SSL.
 * 
 * This library is free for commercial and non-commercial use as long as
 * the following conditions are aheared to.  The following conditions
 * apply to all code found in this distribution, be it the RC4, RSA,
 * lhash, DES, etc., code; not just the SSL code.  The SSL documentation
 * included with this distribution is covered by the same copyright terms
 * except that the holder is Tim Hudson (tjh@cryptsoft.com).
 * 
 * Copyright remains Eric Young's, and as such any Copyright notices in
 * the code are not to be removed.
 * If this package is used in a product, Eric Young should be given attribution
 * as the author of the parts of the library used.
 * This can be in the form of a textual message at program startup or
 * in documentation (online or textual) provided with the package.
 * 
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 * 3. All advertising materials mentioning features or use of this software
 *    must display the following acknowledgement:
 *    "This product includes cryptographic software written by
 *     Eric Young (eay@cryptsoft.com)"
 *    The word 'cryptographic' can be left out if the rouines from the library
 *    being used are not cryptographic related :-).
 * 4. If you include any Windows specific code (or a derivative thereof) from 
 *    the apps directory (application code) you must include an acknowledgement:
 *    "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
 * 
 * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
 * SUCH DAMAGE.
 * 
 * The licence and distribution terms for any publically available version or
 * derivative of this code cannot be changed.  i.e. this code cannot simply be
 * copied and put under another distribution licence
 * [including the GNU Public Licence.]
 */

#ifndef BN_DEBUG
# undef NDEBUG /* avoid conflicting definitions */
# define NDEBUG
#endif

#include <stdio.h>
#include <assert.h>
#include "cryptlib.h"
#include "bn_lcl.h"

#if defined(OPENSSL_NO_ASM) || !defined(OPENSSL_BN_ASM_PART_WORDS)
/* Here follows specialised variants of bn_add_words() and
   bn_sub_words().  They have the property performing operations on
   arrays of different sizes.  The sizes of those arrays is expressed through
   cl, which is the common length ( basicall, min(len(a),len(b)) ), and dl,
   which is the delta between the two lengths, calculated as len(a)-len(b).
   All lengths are the number of BN_ULONGs...  For the operations that require
   a result array as parameter, it must have the length cl+abs(dl).
   These functions should probably end up in bn_asm.c as soon as there are
   assembler counterparts for the systems that use assembler files.  */

BN_ULONG bn_sub_part_words(BN_ULONG *r,
	const BN_ULONG *a, const BN_ULONG *b,
	int cl, int dl)
	{
	BN_ULONG c, t;

	assert(cl >= 0);
	c = bn_sub_words(r, a, b, cl);

	if (dl == 0)
		return c;

	r += cl;
	a += cl;
	b += cl;

	if (dl < 0)
		{
#ifdef BN_COUNT
		fprintf(stderr, "  bn_sub_part_words %d + %d (dl < 0, c = %d)\n", cl, dl, c);
#endif
		for (;;)
			{
			t = b[0];
			r[0] = (0-t-c)&BN_MASK2;
			if (t != 0) c=1;
			if (++dl >= 0) break;

			t = b[1];
			r[1] = (0-t-c)&BN_MASK2;
			if (t != 0) c=1;
			if (++dl >= 0) break;

			t = b[2];
			r[2] = (0-t-c)&BN_MASK2;
			if (t != 0) c=1;
			if (++dl >= 0) break;

			t = b[3];
			r[3] = (0-t-c)&BN_MASK2;
			if (t != 0) c=1;
			if (++dl >= 0) break;

			b += 4;
			r += 4;
			}
		}
	else
		{
		int save_dl = dl;
#ifdef BN_COUNT
		fprintf(stderr, "  bn_sub_part_words %d + %d (dl > 0, c = %d)\n", cl, dl, c);
#endif
		while(c)
			{
			t = a[0];
			r[0] = (t-c)&BN_MASK2;
			if (t != 0) c=0;
			if (--dl <= 0) break;

			t = a[1];
			r[1] = (t-c)&BN_MASK2;
			if (t != 0) c=0;
			if (--dl <= 0) break;

			t = a[2];
			r[2] = (t-c)&BN_MASK2;
			if (t != 0) c=0;
			if (--dl <= 0) break;

			t = a[3];
			r[3] = (t-c)&BN_MASK2;
			if (t != 0) c=0;
			if (--dl <= 0) break;

			save_dl = dl;
			a += 4;
			r += 4;
			}
		if (dl > 0)
			{
#ifdef BN_COUNT
			fprintf(stderr, "  bn_sub_part_words %d + %d (dl > 0, c == 0)\n", cl, dl);
#endif
			if (save_dl > dl)
				{
				switch (save_dl - dl)
					{
				case 1:
					r[1] = a[1];
					if (--dl <= 0) break;
				case 2:
					r[2] = a[2];
					if (--dl <= 0) break;
				case 3:
					r[3] = a[3];
					if (--dl <= 0) break;
					}
				a += 4;
				r += 4;
				}
			}
		if (dl > 0)
			{
#ifdef BN_COUNT
			fprintf(stderr, "  bn_sub_part_words %d + %d (dl > 0, copy)\n", cl, dl);
#endif
			for(;;)
				{
				r[0] = a[0];
				if (--dl <= 0) break;
				r[1] = a[1];
				if (--dl <= 0) break;
				r[2] = a[2];
				if (--dl <= 0) break;
				r[3] = a[3];
				if (--dl <= 0) break;

				a += 4;
				r += 4;
				}
			}
		}
	return c;
	}
#endif

BN_ULONG bn_add_part_words(BN_ULONG *r,
	const BN_ULONG *a, const BN_ULONG *b,
	int cl, int dl)
	{
	BN_ULONG c, l, t;

	assert(cl >= 0);
	c = bn_add_words(r, a, b, cl);

	if (dl == 0)
		return c;

	r += cl;
	a += cl;
	b += cl;

	if (dl < 0)
		{
		int save_dl = dl;
#ifdef BN_COUNT
		fprintf(stderr, "  bn_add_part_words %d + %d (dl < 0, c = %d)\n", cl, dl, c);
#endif
		while (c)
			{
			l=(c+b[0])&BN_MASK2;
			c=(l < c);
			r[0]=l;
			if (++dl >= 0) break;

			l=(c+b[1])&BN_MASK2;
			c=(l < c);
			r[1]=l;
			if (++dl >= 0) break;

			l=(c+b[2])&BN_MASK2;
			c=(l < c);
			r[2]=l;
			if (++dl >= 0) break;

			l=(c+b[3])&BN_MASK2;
			c=(l < c);
			r[3]=l;
			if (++dl >= 0) break;

			save_dl = dl;
			b+=4;
			r+=4;
			}
		if (dl < 0)
			{
#ifdef BN_COUNT
			fprintf(stderr, "  bn_add_part_words %d + %d (dl < 0, c == 0)\n", cl, dl);
#endif
			if (save_dl < dl)
				{
				switch (dl - save_dl)
					{
				case 1:
					r[1] = b[1];
					if (++dl >= 0) break;
				case 2:
					r[2] = b[2];
					if (++dl >= 0) break;
				case 3:
					r[3] = b[3];
					if (++dl >= 0) break;
					}
				b += 4;
				r += 4;
				}
			}
		if (dl < 0)
			{
#ifdef BN_COUNT
			fprintf(stderr, "  bn_add_part_words %d + %d (dl < 0, copy)\n", cl, dl);
#endif
			for(;;)
				{
				r[0] = b[0];
				if (++dl >= 0) break;
				r[1] = b[1];
				if (++dl >= 0) break;
				r[2] = b[2];
				if (++dl >= 0) break;
				r[3] = b[3];
				if (++dl >= 0) break;

				b += 4;
				r += 4;
				}
			}
		}
	else
		{
		int save_dl = dl;
#ifdef BN_COUNT
		fprintf(stderr, "  bn_add_part_words %d + %d (dl > 0)\n", cl, dl);
#endif
		while (c)
			{
			t=(a[0]+c)&BN_MASK2;
			c=(t < c);
			r[0]=t;
			if (--dl <= 0) break;

			t=(a[1]+c)&BN_MASK2;
			c=(t < c);
			r[1]=t;
			if (--dl <= 0) break;

			t=(a[2]+c)&BN_MASK2;
			c=(t < c);
			r[2]=t;
			if (--dl <= 0) break;

			t=(a[3]+c)&BN_MASK2;
			c=(t < c);
			r[3]=t;
			if (--dl <= 0) break;

			save_dl = dl;
			a+=4;
			r+=4;
			}
#ifdef BN_COUNT
		fprintf(stderr, "  bn_add_part_words %d + %d (dl > 0, c == 0)\n", cl, dl);
#endif
		if (dl > 0)
			{
			if (save_dl > dl)
				{
				switch (save_dl - dl)
					{
				case 1:
					r[1] = a[1];
					if (--dl <= 0) break;
				case 2:
					r[2] = a[2];
					if (--dl <= 0) break;
				case 3:
					r[3] = a[3];
					if (--dl <= 0) break;
					}
				a += 4;
				r += 4;
				}
			}
		if (dl > 0)
			{
#ifdef BN_COUNT
			fprintf(stderr, "  bn_add_part_words %d + %d (dl > 0, copy)\n", cl, dl);
#endif
			for(;;)
				{
				r[0] = a[0];
				if (--dl <= 0) break;
				r[1] = a[1];
				if (--dl <= 0) break;
				r[2] = a[2];
				if (--dl <= 0) break;
				r[3] = a[3];
				if (--dl <= 0) break;

				a += 4;
				r += 4;
				}
			}
		}
	return c;
	}

#ifdef BN_RECURSION
/* Karatsuba recursive multiplication algorithm
 * (cf. Knuth, The Art of Computer Programming, Vol. 2) */

/* r is 2*n2 words in size,
 * a and b are both n2 words in size.
 * n2 must be a power of 2.
 * We multiply and return the result.
 * t must be 2*n2 words in size
 * We calculate
 * a[0]*b[0]
 * a[0]*b[0]+a[1]*b[1]+(a[0]-a[1])*(b[1]-b[0])
 * a[1]*b[1]
 */
/* dnX may not be positive, but n2/2+dnX has to be */
void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
	int dna, int dnb, BN_ULONG *t)
	{
	int n=n2/2,c1,c2;
	int tna=n+dna, tnb=n+dnb;
	unsigned int neg,zero;
	BN_ULONG ln,lo,*p;

# ifdef BN_COUNT
	fprintf(stderr," bn_mul_recursive %d%+d * %d%+d\n",n2,dna,n2,dnb);
# endif
# ifdef BN_MUL_COMBA
#  if 0
	if (n2 == 4)
		{
		bn_mul_comba4(r,a,b);
		return;
		}
#  endif
	/* Only call bn_mul_comba 8 if n2 == 8 and the
	 * two arrays are complete [steve]
	 */
	if (n2 == 8 && dna == 0 && dnb == 0)
		{
		bn_mul_comba8(r,a,b);
		return; 
		}
# endif /* BN_MUL_COMBA */
	/* Else do normal multiply */
	if (n2 < BN_MUL_RECURSIVE_SIZE_NORMAL)
		{
		bn_mul_normal(r,a,n2+dna,b,n2+dnb);
		if ((dna + dnb) < 0)
			memset(&r[2*n2 + dna + dnb], 0,
				sizeof(BN_ULONG) * -(dna + dnb));
		return;
		}
	/* r=(a[0]-a[1])*(b[1]-b[0]) */
	c1=bn_cmp_part_words(a,&(a[n]),tna,n-tna);
	c2=bn_cmp_part_words(&(b[n]),b,tnb,tnb-n);
	zero=neg=0;
	switch (c1*3+c2)
		{
	case -4:
		bn_sub_part_words(t,      &(a[n]),a,      tna,tna-n); /* - */
		bn_sub_part_words(&(t[n]),b,      &(b[n]),tnb,n-tnb); /* - */
		break;
	case -3:
		zero=1;
		break;
	case -2:
		bn_sub_part_words(t,      &(a[n]),a,      tna,tna-n); /* - */
		bn_sub_part_words(&(t[n]),&(b[n]),b,      tnb,tnb-n); /* + */
		neg=1;
		break;
	case -1:
	case 0:
	case 1:
		zero=1;
		break;
	case 2:
		bn_sub_part_words(t,      a,      &(a[n]),tna,n-tna); /* + */
		bn_sub_part_words(&(t[n]),b,      &(b[n]),tnb,n-tnb); /* - */
		neg=1;
		break;
	case 3:
		zero=1;
		break;
	case 4:
		bn_sub_part_words(t,      a,      &(a[n]),tna,n-tna);
		bn_sub_part_words(&(t[n]),&(b[n]),b,      tnb,tnb-n);
		break;
		}

# ifdef BN_MUL_COMBA
	if (n == 4 && dna == 0 && dnb == 0) /* XXX: bn_mul_comba4 could take
					       extra args to do this well */
		{
		if (!zero)
			bn_mul_comba4(&(t[n2]),t,&(t[n]));
		else
			memset(&(t[n2]),0,8*sizeof(BN_ULONG));
		
		bn_mul_comba4(r,a,b);
		bn_mul_comba4(&(r[n2]),&(a[n]),&(b[n]));
		}
	else if (n == 8 && dna == 0 && dnb == 0) /* XXX: bn_mul_comba8 could
						    take extra args to do this
						    well */
		{
		if (!zero)
			bn_mul_comba8(&(t[n2]),t,&(t[n]));
		else
			memset(&(t[n2]),0,16*sizeof(BN_ULONG));
		
		bn_mul_comba8(r,a,b);
		bn_mul_comba8(&(r[n2]),&(a[n]),&(b[n]));
		}
	else
# endif /* BN_MUL_COMBA */
		{
		p= &(t[n2*2]);
		if (!zero)
			bn_mul_recursive(&(t[n2]),t,&(t[n]),n,0,0,p);
		else
			memset(&(t[n2]),0,n2*sizeof(BN_ULONG));
		bn_mul_recursive(r,a,b,n,0,0,p);
		bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),n,dna,dnb,p);
		}

	/* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
	 * r[10] holds (a[0]*b[0])
	 * r[32] holds (b[1]*b[1])
	 */

	c1=(int)(bn_add_words(t,r,&(r[n2]),n2));

	if (neg) /* if t[32] is negative */
		{
		c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2));
		}
	else
		{
		/* Might have a carry */
		c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),t,n2));
		}

	/* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
	 * r[10] holds (a[0]*b[0])
	 * r[32] holds (b[1]*b[1])
	 * c1 holds the carry bits
	 */
	c1+=(int)(bn_add_words(&(r[n]),&(r[n]),&(t[n2]),n2));
	if (c1)
		{
		p= &(r[n+n2]);
		lo= *p;
		ln=(lo+c1)&BN_MASK2;
		*p=ln;

		/* The overflow will stop before we over write
		 * words we should not overwrite */
		if (ln < (BN_ULONG)c1)
			{
			do	{
				p++;
				lo= *p;
				ln=(lo+1)&BN_MASK2;
				*p=ln;
				} while (ln == 0);
			}
		}
	}

/* n+tn is the word length
 * t needs to be n*4 is size, as does r */
/* tnX may not be negative but less than n */
void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n,
	     int tna, int tnb, BN_ULONG *t)
	{
	int i,j,n2=n*2;
	int c1,c2,neg,zero;
	BN_ULONG ln,lo,*p;

# ifdef BN_COUNT
	fprintf(stderr," bn_mul_part_recursive (%d%+d) * (%d%+d)\n",
		n, tna, n, tnb);
# endif
	if (n < 8)
		{
		bn_mul_normal(r,a,n+tna,b,n+tnb);
		return;
		}

	/* r=(a[0]-a[1])*(b[1]-b[0]) */
	c1=bn_cmp_part_words(a,&(a[n]),tna,n-tna);
	c2=bn_cmp_part_words(&(b[n]),b,tnb,tnb-n);
	zero=neg=0;
	switch (c1*3+c2)
		{
	case -4:
		bn_sub_part_words(t,      &(a[n]),a,      tna,tna-n); /* - */
		bn_sub_part_words(&(t[n]),b,      &(b[n]),tnb,n-tnb); /* - */
		break;
	case -3:
		zero=1;
		/* break; */
	case -2:
		bn_sub_part_words(t,      &(a[n]),a,      tna,tna-n); /* - */
		bn_sub_part_words(&(t[n]),&(b[n]),b,      tnb,tnb-n); /* + */
		neg=1;
		break;
	case -1:
	case 0:
	case 1:
		zero=1;
		/* break; */
	case 2:
		bn_sub_part_words(t,      a,      &(a[n]),tna,n-tna); /* + */
		bn_sub_part_words(&(t[n]),b,      &(b[n]),tnb,n-tnb); /* - */
		neg=1;
		break;
	case 3:
		zero=1;
		/* break; */
	case 4:
		bn_sub_part_words(t,      a,      &(a[n]),tna,n-tna);
		bn_sub_part_words(&(t[n]),&(b[n]),b,      tnb,tnb-n);
		break;
		}
		/* The zero case isn't yet implemented here. The speedup
		   would probably be negligible. */
# if 0
	if (n == 4)
		{
		bn_mul_comba4(&(t[n2]),t,&(t[n]));
		bn_mul_comba4(r,a,b);
		bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn);
		memset(&(r[n2+tn*2]),0,sizeof(BN_ULONG)*(n2-tn*2));
		}
	else
# endif
	if (n == 8)
		{
		bn_mul_comba8(&(t[n2]),t,&(t[n]));
		bn_mul_comba8(r,a,b);
		bn_mul_normal(&(r[n2]),&(a[n]),tna,&(b[n]),tnb);
		memset(&(r[n2+tna+tnb]),0,sizeof(BN_ULONG)*(n2-tna-tnb));
		}
	else
		{
		p= &(t[n2*2]);
		bn_mul_recursive(&(t[n2]),t,&(t[n]),n,0,0,p);
		bn_mul_recursive(r,a,b,n,0,0,p);
		i=n/2;
		/* If there is only a bottom half to the number,
		 * just do it */
		if (tna > tnb)
			j = tna - i;
		else
			j = tnb - i;
		if (j == 0)
			{
			bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),
				i,tna-i,tnb-i,p);
			memset(&(r[n2+i*2]),0,sizeof(BN_ULONG)*(n2-i*2));
			}
		else if (j > 0) /* eg, n == 16, i == 8 and tn == 11 */
				{
				bn_mul_part_recursive(&(r[n2]),&(a[n]),&(b[n]),
					i,tna-i,tnb-i,p);
				memset(&(r[n2+tna+tnb]),0,
					sizeof(BN_ULONG)*(n2-tna-tnb));
				}
		else /* (j < 0) eg, n == 16, i == 8 and tn == 5 */
			{
			memset(&(r[n2]),0,sizeof(BN_ULONG)*n2);
			if (tna < BN_MUL_RECURSIVE_SIZE_NORMAL
				&& tnb < BN_MUL_RECURSIVE_SIZE_NORMAL)
				{
				bn_mul_normal(&(r[n2]),&(a[n]),tna,&(b[n]),tnb);
				}
			else
				{
				for (;;)
					{
					i/=2;
					/* these simplified conditions work
					 * exclusively because difference
					 * between tna and tnb is 1 or 0 */
					if (i < tna || i < tnb)
						{
						bn_mul_part_recursive(&(r[n2]),
							&(a[n]),&(b[n]),
							i,tna-i,tnb-i,p);
						break;
						}
					else if (i == tna || i == tnb)
						{
						bn_mul_recursive(&(r[n2]),
							&(a[n]),&(b[n]),
							i,tna-i,tnb-i,p);
						break;
						}
					}
				}
			}
		}

	/* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
	 * r[10] holds (a[0]*b[0])
	 * r[32] holds (b[1]*b[1])
	 */

	c1=(int)(bn_add_words(t,r,&(r[n2]),n2));

	if (neg) /* if t[32] is negative */
		{
		c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2));
		}
	else
		{
		/* Might have a carry */
		c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),t,n2));
		}

	/* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
	 * r[10] holds (a[0]*b[0])
	 * r[32] holds (b[1]*b[1])
	 * c1 holds the carry bits
	 */
	c1+=(int)(bn_add_words(&(r[n]),&(r[n]),&(t[n2]),n2));
	if (c1)
		{
		p= &(r[n+n2]);
		lo= *p;
		ln=(lo+c1)&BN_MASK2;
		*p=ln;

		/* The overflow will stop before we over write
		 * words we should not overwrite */
		if (ln < (BN_ULONG)c1)
			{
			do	{
				p++;
				lo= *p;
				ln=(lo+1)&BN_MASK2;
				*p=ln;
				} while (ln == 0);
			}
		}
	}

/* a and b must be the same size, which is n2.
 * r needs to be n2 words and t needs to be n2*2
 */
void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
	     BN_ULONG *t)
	{
	int n=n2/2;

# ifdef BN_COUNT
	fprintf(stderr," bn_mul_low_recursive %d * %d\n",n2,n2);
# endif

	bn_mul_recursive(r,a,b,n,0,0,&(t[0]));
	if (n >= BN_MUL_LOW_RECURSIVE_SIZE_NORMAL)
		{
		bn_mul_low_recursive(&(t[0]),&(a[0]),&(b[n]),n,&(t[n2]));
		bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
		bn_mul_low_recursive(&(t[0]),&(a[n]),&(b[0]),n,&(t[n2]));
		bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
		}
	else
		{
		bn_mul_low_normal(&(t[0]),&(a[0]),&(b[n]),n);
		bn_mul_low_normal(&(t[n]),&(a[n]),&(b[0]),n);
		bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
		bn_add_words(&(r[n]),&(r[n]),&(t[n]),n);
		}
	}

/* a and b must be the same size, which is n2.
 * r needs to be n2 words and t needs to be n2*2
 * l is the low words of the output.
 * t needs to be n2*3
 */
void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l, int n2,
	     BN_ULONG *t)
	{
	int i,n;
	int c1,c2;
	int neg,oneg,zero;
	BN_ULONG ll,lc,*lp,*mp;

# ifdef BN_COUNT
	fprintf(stderr," bn_mul_high %d * %d\n",n2,n2);
# endif
	n=n2/2;

	/* Calculate (al-ah)*(bh-bl) */
	neg=zero=0;
	c1=bn_cmp_words(&(a[0]),&(a[n]),n);
	c2=bn_cmp_words(&(b[n]),&(b[0]),n);
	switch (c1*3+c2)
		{
	case -4:
		bn_sub_words(&(r[0]),&(a[n]),&(a[0]),n);
		bn_sub_words(&(r[n]),&(b[0]),&(b[n]),n);
		break;
	case -3:
		zero=1;
		break;
	case -2:
		bn_sub_words(&(r[0]),&(a[n]),&(a[0]),n);
		bn_sub_words(&(r[n]),&(b[n]),&(b[0]),n);
		neg=1;
		break;
	case -1:
	case 0:
	case 1:
		zero=1;
		break;
	case 2:
		bn_sub_words(&(r[0]),&(a[0]),&(a[n]),n);
		bn_sub_words(&(r[n]),&(b[0]),&(b[n]),n);
		neg=1;
		break;
	case 3:
		zero=1;
		break;
	case 4:
		bn_sub_words(&(r[0]),&(a[0]),&(a[n]),n);
		bn_sub_words(&(r[n]),&(b[n]),&(b[0]),n);
		break;
		}
		
	oneg=neg;
	/* t[10] = (a[0]-a[1])*(b[1]-b[0]) */
	/* r[10] = (a[1]*b[1]) */
# ifdef BN_MUL_COMBA
	if (n == 8)
		{
		bn_mul_comba8(&(t[0]),&(r[0]),&(r[n]));
		bn_mul_comba8(r,&(a[n]),&(b[n]));
		}
	else
# endif
		{
		bn_mul_recursive(&(t[0]),&(r[0]),&(r[n]),n,0,0,&(t[n2]));
		bn_mul_recursive(r,&(a[n]),&(b[n]),n,0,0,&(t[n2]));
		}

	/* s0 == low(al*bl)
	 * s1 == low(ah*bh)+low((al-ah)*(bh-bl))+low(al*bl)+high(al*bl)
	 * We know s0 and s1 so the only unknown is high(al*bl)
	 * high(al*bl) == s1 - low(ah*bh+s0+(al-ah)*(bh-bl))
	 * high(al*bl) == s1 - (r[0]+l[0]+t[0])
	 */
	if (l != NULL)
		{
		lp= &(t[n2+n]);
		c1=(int)(bn_add_words(lp,&(r[0]),&(l[0]),n));
		}
	else
		{
		c1=0;
		lp= &(r[0]);
		}

	if (neg)
		neg=(int)(bn_sub_words(&(t[n2]),lp,&(t[0]),n));
	else
		{
		bn_add_words(&(t[n2]),lp,&(t[0]),n);
		neg=0;
		}

	if (l != NULL)
		{
		bn_sub_words(&(t[n2+n]),&(l[n]),&(t[n2]),n);
		}
	else
		{
		lp= &(t[n2+n]);
		mp= &(t[n2]);
		for (i=0; i<n; i++)
			lp[i]=((~mp[i])+1)&BN_MASK2;
		}

	/* s[0] = low(al*bl)
	 * t[3] = high(al*bl)
	 * t[10] = (a[0]-a[1])*(b[1]-b[0]) neg is the sign
	 * r[10] = (a[1]*b[1])
	 */
	/* R[10] = al*bl
	 * R[21] = al*bl + ah*bh + (a[0]-a[1])*(b[1]-b[0])
	 * R[32] = ah*bh
	 */
	/* R[1]=t[3]+l[0]+r[0](+-)t[0] (have carry/borrow)
	 * R[2]=r[0]+t[3]+r[1](+-)t[1] (have carry/borrow)
	 * R[3]=r[1]+(carry/borrow)
	 */
	if (l != NULL)
		{
		lp= &(t[n2]);
		c1= (int)(bn_add_words(lp,&(t[n2+n]),&(l[0]),n));
		}
	else
		{
		lp= &(t[n2+n]);
		c1=0;
		}
	c1+=(int)(bn_add_words(&(t[n2]),lp,  &(r[0]),n));
	if (oneg)
		c1-=(int)(bn_sub_words(&(t[n2]),&(t[n2]),&(t[0]),n));
	else
		c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),&(t[0]),n));

	c2 =(int)(bn_add_words(&(r[0]),&(r[0]),&(t[n2+n]),n));
	c2+=(int)(bn_add_words(&(r[0]),&(r[0]),&(r[n]),n));
	if (oneg)
		c2-=(int)(bn_sub_words(&(r[0]),&(r[0]),&(t[n]),n));
	else
		c2+=(int)(bn_add_words(&(r[0]),&(r[0]),&(t[n]),n));
	
	if (c1 != 0) /* Add starting at r[0], could be +ve or -ve */
		{
		i=0;
		if (c1 > 0)
			{
			lc=c1;
			do	{
				ll=(r[i]+lc)&BN_MASK2;
				r[i++]=ll;
				lc=(lc > ll);
				} while (lc);
			}
		else
			{
			lc= -c1;
			do	{
				ll=r[i];
				r[i++]=(ll-lc)&BN_MASK2;
				lc=(lc > ll);
				} while (lc);
			}
		}
	if (c2 != 0) /* Add starting at r[1] */
		{
		i=n;
		if (c2 > 0)
			{
			lc=c2;
			do	{
				ll=(r[i]+lc)&BN_MASK2;
				r[i++]=ll;
				lc=(lc > ll);
				} while (lc);
			}
		else
			{
			lc= -c2;
			do	{
				ll=r[i];
				r[i++]=(ll-lc)&BN_MASK2;
				lc=(lc > ll);
				} while (lc);
			}
		}
	}
#endif /* BN_RECURSION */

int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
	{
	int ret=0;
	int top,al,bl;
	BIGNUM *rr;
#if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
	int i;
#endif
#ifdef BN_RECURSION
	BIGNUM *t=NULL;
	int j=0,k;
#endif

#ifdef BN_COUNT
	fprintf(stderr,"BN_mul %d * %d\n",a->top,b->top);
#endif

	bn_check_top(a);
	bn_check_top(b);
	bn_check_top(r);

	al=a->top;
	bl=b->top;

	if ((al == 0) || (bl == 0))
		{
		BN_zero(r);
		return(1);
		}
	top=al+bl;

	BN_CTX_start(ctx);
	if ((r == a) || (r == b))
		{
		if ((rr = BN_CTX_get(ctx)) == NULL) goto err;
		}
	else
		rr = r;
	rr->neg=a->neg^b->neg;

#if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
	i = al-bl;
#endif
#ifdef BN_MUL_COMBA
	if (i == 0)
		{
# if 0
		if (al == 4)
			{
			if (bn_wexpand(rr,8) == NULL) goto err;
			rr->top=8;
			bn_mul_comba4(rr->d,a->d,b->d);
			goto end;
			}
# endif
		if (al == 8)
			{
			if (bn_wexpand(rr,16) == NULL) goto err;
			rr->top=16;
			bn_mul_comba8(rr->d,a->d,b->d);
			goto end;
			}
		}
#endif /* BN_MUL_COMBA */
#ifdef BN_RECURSION
	if ((al >= BN_MULL_SIZE_NORMAL) && (bl >= BN_MULL_SIZE_NORMAL))
		{
		if (i >= -1 && i <= 1)
			{
			int sav_j =0;
			/* Find out the power of two lower or equal
			   to the longest of the two numbers */
			if (i >= 0)
				{
				j = BN_num_bits_word((BN_ULONG)al);
				}
			if (i == -1)
				{
				j = BN_num_bits_word((BN_ULONG)bl);
				}
			sav_j = j;
			j = 1<<(j-1);
			assert(j <= al || j <= bl);
			k = j+j;
			t = BN_CTX_get(ctx);
			if (t == NULL)
				goto err;
			if (al > j || bl > j)
				{
				if (bn_wexpand(t,k*4) == NULL) goto err;
				if (bn_wexpand(rr,k*4) == NULL) goto err;
				bn_mul_part_recursive(rr->d,a->d,b->d,
					j,al-j,bl-j,t->d);
				}
			else	/* al <= j || bl <= j */
				{
				if (bn_wexpand(t,k*2) == NULL) goto err;
				if (bn_wexpand(rr,k*2) == NULL) goto err;
				bn_mul_recursive(rr->d,a->d,b->d,
					j,al-j,bl-j,t->d);
				}
			rr->top=top;
			goto end;
			}
#if 0
		if (i == 1 && !BN_get_flags(b,BN_FLG_STATIC_DATA))
			{
			BIGNUM *tmp_bn = (BIGNUM *)b;
			if (bn_wexpand(tmp_bn,al) == NULL) goto err;
			tmp_bn->d[bl]=0;
			bl++;
			i--;
			}
		else if (i == -1 && !BN_get_flags(a,BN_FLG_STATIC_DATA))
			{
			BIGNUM *tmp_bn = (BIGNUM *)a;
			if (bn_wexpand(tmp_bn,bl) == NULL) goto err;
			tmp_bn->d[al]=0;
			al++;
			i++;
			}
		if (i == 0)
			{
			/* symmetric and > 4 */
			/* 16 or larger */
			j=BN_num_bits_word((BN_ULONG)al);
			j=1<<(j-1);
			k=j+j;
			t = BN_CTX_get(ctx);
			if (al == j) /* exact multiple */
				{
				if (bn_wexpand(t,k*2) == NULL) goto err;
				if (bn_wexpand(rr,k*2) == NULL) goto err;
				bn_mul_recursive(rr->d,a->d,b->d,al,t->d);
				}
			else
				{
				if (bn_wexpand(t,k*4) == NULL) goto err;
				if (bn_wexpand(rr,k*4) == NULL) goto err;
				bn_mul_part_recursive(rr->d,a->d,b->d,al-j,j,t->d);
				}
			rr->top=top;
			goto end;
			}
#endif
		}
#endif /* BN_RECURSION */
	if (bn_wexpand(rr,top) == NULL) goto err;
	rr->top=top;
	bn_mul_normal(rr->d,a->d,al,b->d,bl);

#if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
end:
#endif
	bn_correct_top(rr);
	if (r != rr) BN_copy(r,rr);
	ret=1;
err:
	bn_check_top(r);
	BN_CTX_end(ctx);
	return(ret);
	}

void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb)
	{
	BN_ULONG *rr;

#ifdef BN_COUNT
	fprintf(stderr," bn_mul_normal %d * %d\n",na,nb);
#endif

	if (na < nb)
		{
		int itmp;
		BN_ULONG *ltmp;

		itmp=na; na=nb; nb=itmp;
		ltmp=a;   a=b;   b=ltmp;

		}
	rr= &(r[na]);
	if (nb <= 0)
		{
		(void)bn_mul_words(r,a,na,0);
		return;
		}
	else
		rr[0]=bn_mul_words(r,a,na,b[0]);

	for (;;)
		{
		if (--nb <= 0) return;
		rr[1]=bn_mul_add_words(&(r[1]),a,na,b[1]);
		if (--nb <= 0) return;
		rr[2]=bn_mul_add_words(&(r[2]),a,na,b[2]);
		if (--nb <= 0) return;
		rr[3]=bn_mul_add_words(&(r[3]),a,na,b[3]);
		if (--nb <= 0) return;
		rr[4]=bn_mul_add_words(&(r[4]),a,na,b[4]);
		rr+=4;
		r+=4;
		b+=4;
		}
	}

void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n)
	{
#ifdef BN_COUNT
	fprintf(stderr," bn_mul_low_normal %d * %d\n",n,n);
#endif
	bn_mul_words(r,a,n,b[0]);

	for (;;)
		{
		if (--n <= 0) return;
		bn_mul_add_words(&(r[1]),a,n,b[1]);
		if (--n <= 0) return;
		bn_mul_add_words(&(r[2]),a,n,b[2]);
		if (--n <= 0) return;
		bn_mul_add_words(&(r[3]),a,n,b[3]);
		if (--n <= 0) return;
		bn_mul_add_words(&(r[4]),a,n,b[4]);
		r+=4;
		b+=4;
		}
	}