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bn_mul.c
/* 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;
      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);
      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:
            /* 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:
            /* 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:
            /* 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)
                  {
                  /* 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);
                        }
                  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;
            }
      }

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