/* crypto/bn/bn_mul.c */
-/* Copyright (C) 1995-1997 Eric Young (eay@cryptsoft.com)
+/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
* All rights reserved.
*
* This package is an SSL implementation written
* [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"
-/* r must be different to a and b */
-int BN_mul(r, a, b)
-BIGNUM *r;
-BIGNUM *a;
-BIGNUM *b;
+#if defined(NO_ASM) || !defined(i386)
+/* 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]
+ */
+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\n",n2,n2);
+# endif
+# ifdef BN_MUL_COMBA
+# if 0
+ if (n2 == 4)
+ {
+ bn_mul_comba4(r,a,b);
+ return;
+ }
+# endif
+ if (n2 == 8)
+ {
+ bn_mul_comba8(r,a,b);
+ return;
+ }
+# endif /* BN_MUL_COMBA */
+ if (n2 < BN_MUL_RECURSIVE_SIZE_NORMAL)
+ {
+ /* This should not happen */
+ bn_mul_normal(r,a,n2,b,n2);
+ 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)
+ {
+ 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)
+ {
+ 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 */
+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;
+ unsigned int c1,c2,neg,zero;
+ BN_ULONG ln,lo,*p;
+
+# ifdef BN_COUNT
+ fprintf(stderr," bn_mul_part_recursive (%d+%d) * (%d+%d)\n",
+ tna, n, tnb, n);
+# 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;
+ 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 < 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;
- int max,al,bl;
- BN_ULONG *ap,*bp,*rp;
+#endif
+#ifdef BN_RECURSION
+ BIGNUM *t;
+ int j,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))
{
- r->top=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 (al > j || bl > j)
+ {
+ bn_wexpand(t,k*4);
+ bn_wexpand(rr,k*4);
+ bn_mul_part_recursive(rr->d,a->d,b->d,
+ j,al-j,bl-j,t->d);
+ }
+ else /* al <= j || bl <= j */
+ {
+ bn_wexpand(t,k*2);
+ bn_wexpand(rr,k*2);
+ 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;
+ bn_wexpand(tmp_bn,al);
+ tmp_bn->d[bl]=0;
+ bl++;
+ i--;
+ }
+ else if (i == -1 && !BN_get_flags(a,BN_FLG_STATIC_DATA))
+ {
+ BIGNUM *tmp_bn = (BIGNUM *)a;
+ bn_wexpand(tmp_bn,bl);
+ 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 */
+ {
+ bn_wexpand(t,k*2);
+ bn_wexpand(rr,k*2);
+ bn_mul_recursive(rr->d,a->d,b->d,al,t->d);
+ }
+ else
+ {
+ bn_wexpand(t,k*4);
+ bn_wexpand(rr,k*4);
+ 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_fix_top(rr);
+ if (r != rr) BN_copy(r,rr);
+ ret=1;
+err:
+ 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;
- max=(al+bl);
- if (bn_expand(r,(max)*BN_BITS2) == NULL) return(0);
- r->top=max;
- r->neg=a->neg^b->neg;
- ap=a->d;
- bp=b->d;
- rp=r->d;
+#ifdef BN_COUNT
+ fprintf(stderr," bn_mul_normal %d * %d\n",na,nb);
+#endif
- rp[al]=bn_mul_word(rp,ap,al,*(bp++));
- rp++;
- for (i=1; i<bl; i++)
+ if (na < nb)
{
- rp[al]=bn_mul_add_word(rp,ap,al,*(bp++));
- rp++;
+ int itmp;
+ BN_ULONG *ltmp;
+
+ itmp=na; na=nb; nb=itmp;
+ ltmp=a; a=b; b=ltmp;
+
+ }
+ rr= &(r[na]);
+ 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;
}
- if (r->d[max-1] == 0) r->top--;
- return(1);
}
+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;
+ }
+ }
projects / openssl.git / blobdiff