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bn_sqr.c
/* crypto/bn/bn_sqr.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 "cryptlib.h"
#include "bn_lcl.h"

/* r must not be a */
/* I've just gone over this and it is now %20 faster on x86 - eay - 27 Jun 96 */
int BN_sqr(BIGNUM *r, const BIGNUM *a, BN_CTX *ctx)
      {
      int max,al;
      int ret = 0;
      BIGNUM *tmp,*rr;

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

      al=a->top;
      if (al <= 0)
            {
            r->top=0;
            return 1;
            }

      BN_CTX_start(ctx);
      rr=(a != r) ? r : BN_CTX_get(ctx);
      tmp=BN_CTX_get(ctx);
      if (!rr || !tmp) goto err;

      max = 2 * al; /* Non-zero (from above) */
      if (bn_wexpand(rr,max) == NULL) goto err;

      if (al == 4)
            {
#ifndef BN_SQR_COMBA
            BN_ULONG t[8];
            bn_sqr_normal(rr->d,a->d,4,t);
#else
            bn_sqr_comba4(rr->d,a->d);
#endif
            }
      else if (al == 8)
            {
#ifndef BN_SQR_COMBA
            BN_ULONG t[16];
            bn_sqr_normal(rr->d,a->d,8,t);
#else
            bn_sqr_comba8(rr->d,a->d);
#endif
            }
      else 
            {
#if defined(BN_RECURSION)
            if (al < BN_SQR_RECURSIVE_SIZE_NORMAL)
                  {
                  BN_ULONG t[BN_SQR_RECURSIVE_SIZE_NORMAL*2];
                  bn_sqr_normal(rr->d,a->d,al,t);
                  }
            else
                  {
                  int j,k;

                  j=BN_num_bits_word((BN_ULONG)al);
                  j=1<<(j-1);
                  k=j+j;
                  if (al == j)
                        {
                        if (bn_wexpand(tmp,k*2) == NULL) goto err;
                        bn_sqr_recursive(rr->d,a->d,al,tmp->d);
                        }
                  else
                        {
                        if (bn_wexpand(tmp,max) == NULL) goto err;
                        bn_sqr_normal(rr->d,a->d,al,tmp->d);
                        }
                  }
#else
            if (bn_wexpand(tmp,max) == NULL) goto err;
            bn_sqr_normal(rr->d,a->d,al,tmp->d);
#endif
            }

      rr->neg=0;
      /* If the most-significant half of the top word of 'a' is zero, then
       * the square of 'a' will max-1 words. */
      if(a->d[al - 1] == (a->d[al - 1] & BN_MASK2l))
            rr->top = max - 1;
      else
            rr->top = max;
      if (rr != r) BN_copy(r,rr);
      ret = 1;
 err:
      bn_check_top(rr);
      bn_check_top(tmp);
      BN_CTX_end(ctx);
      return(ret);
      }

/* tmp must have 2*n words */
void bn_sqr_normal(BN_ULONG *r, const BN_ULONG *a, int n, BN_ULONG *tmp)
      {
      int i,j,max;
      const BN_ULONG *ap;
      BN_ULONG *rp;

      max=n*2;
      ap=a;
      rp=r;
      rp[0]=rp[max-1]=0;
      rp++;
      j=n;

      if (--j > 0)
            {
            ap++;
            rp[j]=bn_mul_words(rp,ap,j,ap[-1]);
            rp+=2;
            }

      for (i=n-2; i>0; i--)
            {
            j--;
            ap++;
            rp[j]=bn_mul_add_words(rp,ap,j,ap[-1]);
            rp+=2;
            }

      bn_add_words(r,r,r,max);

      /* There will not be a carry */

      bn_sqr_words(tmp,a,n);

      bn_add_words(r,r,tmp,max);
      }

#ifdef BN_RECURSION
/* r is 2*n words in size,
 * a and b are both n words in size.    (There's not actually a 'b' here ...)
 * n must be a power of 2.
 * We multiply and return the result.
 * t must be 2*n 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_sqr_recursive(BN_ULONG *r, const BN_ULONG *a, int n2, BN_ULONG *t)
      {
      int n=n2/2;
      int zero,c1;
      BN_ULONG ln,lo,*p;

#ifdef BN_COUNT
      fprintf(stderr," bn_sqr_recursive %d * %d\n",n2,n2);
#endif
      if (n2 == 4)
            {
#ifndef BN_SQR_COMBA
            bn_sqr_normal(r,a,4,t);
#else
            bn_sqr_comba4(r,a);
#endif
            return;
            }
      else if (n2 == 8)
            {
#ifndef BN_SQR_COMBA
            bn_sqr_normal(r,a,8,t);
#else
            bn_sqr_comba8(r,a);
#endif
            return;
            }
      if (n2 < BN_SQR_RECURSIVE_SIZE_NORMAL)
            {
            bn_sqr_normal(r,a,n2,t);
            return;
            }
      /* r=(a[0]-a[1])*(a[1]-a[0]) */
      c1=bn_cmp_words(a,&(a[n]),n);
      zero=0;
      if (c1 > 0)
            bn_sub_words(t,a,&(a[n]),n);
      else if (c1 < 0)
            bn_sub_words(t,&(a[n]),a,n);
      else
            zero=1;

      /* The result will always be negative unless it is zero */
      p= &(t[n2*2]);

      if (!zero)
            bn_sqr_recursive(&(t[n2]),t,n,p);
      else
            memset(&(t[n2]),0,n2*sizeof(BN_ULONG));
      bn_sqr_recursive(r,a,n,p);
      bn_sqr_recursive(&(r[n2]),&(a[n]),n,p);

      /* t[32] holds (a[0]-a[1])*(a[1]-a[0]), it is negative or zero
       * r[10] holds (a[0]*b[0])
       * r[32] holds (b[1]*b[1])
       */

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

      /* t[32] is negative */
      c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2));

      /* t[32] holds (a[0]-a[1])*(a[1]-a[0])+(a[0]*a[0])+(a[1]*a[1])
       * r[10] holds (a[0]*a[0])
       * r[32] holds (a[1]*a[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);
                  }
            }
      }
#endif

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