source: trunk/cscrypt/bn_mul.c@ 1

/* 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.]
 */

#include <stdio.h>
#include <string.h>
#include "bn_lcl.h"
#include "openssl_mods.h"

#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,
         BN_ULONG *t)
    {
    int n=n2/2,c1,c2;
    unsigned int neg,zero;
    BN_ULONG ln,lo,*p;

# ifdef BN_COUNT
    printf(" 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_words(a,&(a[n]),n);
    c2=bn_cmp_words(&(b[n]),b,n);
    zero=neg=0;
    switch (c1*3+c2)
        {
    case -4:
        bn_sub_words(t,      &(a[n]),a,      n); /* - */
        bn_sub_words(&(t[n]),b,      &(b[n]),n); /* - */
        break;
    case -3:
        zero=1;
        break;
    case -2:
        bn_sub_words(t,      &(a[n]),a,      n); /* - */
        bn_sub_words(&(t[n]),&(b[n]),b,      n); /* + */
        neg=1;
        break;
    case -1:
    case 0:
    case 1:
        zero=1;
        break;
    case 2:
        bn_sub_words(t,      a,      &(a[n]),n); /* + */
        bn_sub_words(&(t[n]),b,      &(b[n]),n); /* - */
        neg=1;
        break;
    case 3:
        zero=1;
        break;
    case 4:
        bn_sub_words(t,      a,      &(a[n]),n);
        bn_sub_words(&(t[n]),&(b[n]),b,      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,p);
        else
            memset(&(t[n2]),0,n2*sizeof(BN_ULONG));
        bn_mul_recursive(r,a,b,n,p);
        bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),n,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 tn,
         int n, BN_ULONG *t)
    {
    int i,j,n2=n*2;
    unsigned int c1,c2,neg,zero;
    BN_ULONG ln,lo,*p;

# ifdef BN_COUNT
    printf(" bn_mul_part_recursive %d * %d\n",tn+n,tn+n);
# endif
    if (n < 8)
        {
        i=tn+n;
        bn_mul_normal(r,a,i,b,i);
        return;
        }

    /* r=(a[0]-a[1])*(b[1]-b[0]) */
    c1=bn_cmp_words(a,&(a[n]),n);
    c2=bn_cmp_words(&(b[n]),b,n);
    zero=neg=0;
    switch (c1*3+c2)
        {
    case -4:
        bn_sub_words(t,      &(a[n]),a,      n); /* - */
        bn_sub_words(&(t[n]),b,      &(b[n]),n); /* - */
        break;
    case -3:
        zero=1;
        /* break; */
    case -2:
        bn_sub_words(t,      &(a[n]),a,      n); /* - */
        bn_sub_words(&(t[n]),&(b[n]),b,      n); /* + */
        neg=1;
        break;
    case -1:
    case 0:
    case 1:
        zero=1;
        /* break; */
    case 2:
        bn_sub_words(t,      a,      &(a[n]),n); /* + */
        bn_sub_words(&(t[n]),b,      &(b[n]),n); /* - */
        neg=1;
        break;
    case 3:
        zero=1;
        /* break; */
    case 4:
        bn_sub_words(t,      a,      &(a[n]),n);
        bn_sub_words(&(t[n]),&(b[n]),b,      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]),tn,&(b[n]),tn);
        memset(&(r[n2+tn*2]),0,sizeof(BN_ULONG)*(n2-tn*2));
        }
    else
        {
        p= &(t[n2*2]);
        bn_mul_recursive(&(t[n2]),t,&(t[n]),n,p);
        bn_mul_recursive(r,a,b,n,p);
        i=n/2;
        /* If there is only a bottom half to the number,
         * just do it */
        j=tn-i;
        if (j == 0)
            {
            bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),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]),
                    j,i,p);
                memset(&(r[n2+tn*2]),0,
                    sizeof(BN_ULONG)*(n2-tn*2));
                }
        else /* (j < 0) eg, n == 16, i == 8 and tn == 5 */
            {
            memset(&(r[n2]),0,sizeof(BN_ULONG)*n2);
            if (tn < BN_MUL_RECURSIVE_SIZE_NORMAL)
                {
                bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn);
                }
            else
                {
                for (;;)
                    {
                    i/=2;
                    if (i < tn)
                        {
                        bn_mul_part_recursive(&(r[n2]),
                            &(a[n]),&(b[n]),
                            tn-i,i,p);
                        break;
                        }
                    else if (i == tn)
                        {
                        bn_mul_recursive(&(r[n2]),
                            &(a[n]),&(b[n]),
                            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
    printf(" bn_mul_low_recursive %d * %d\n",n2,n2);
# endif

    bn_mul_recursive(r,a,b,n,&(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
    printf(" 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,&(t[n2]));
        bn_mul_recursive(r,&(a[n]),&(b[n]),n,&(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, BIGNUM *a, BIGNUM *b, BN_CTX *ctx)
    {
    int top,al,bl;
    BIGNUM *rr;
    int ret = 0;
#if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
    int i;
#endif
#ifdef BN_RECURSION
    BIGNUM *t;
    int j,k;
#endif

#ifdef BN_COUNT
    printf("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 && !BN_get_flags(b,BN_FLG_STATIC_DATA))
            {
            bn_wexpand(b,al);
            b->d[bl]=0;
            bl++;
            i--;
            }
        else if (i == -1 && !BN_get_flags(a,BN_FLG_STATIC_DATA))
            {
            bn_wexpand(a,bl);
            a->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(a,k);
                bn_wexpand(b,k);
                bn_wexpand(t,k*4);
                bn_wexpand(rr,k*4);
                for (i=a->top; i<k; i++)
                    a->d[i]=0;
                for (i=b->top; i<k; i++)
                    b->d[i]=0;
                bn_mul_part_recursive(rr->d,a->d,b->d,al-j,j,t->d);
                }
            rr->top=top;
            goto end;
            }
        }
#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;

#ifdef BN_COUNT
    printf(" 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]);
    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
    printf(" 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;
        }
    }