text: /* crypto/bn/bn_recp.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 "cryptlib.h"
  #include "bn_lcl.h"
  #ifdef OPENSSL_SYS_WINDOWS
  #include <stdio.h>
  #endif
  
  void BN_RECP_CTX_init(BN_RECP_CTX *recp)
  	{
  	BN_init(&(recp->N));
  	BN_init(&(recp->Nr));
  	recp->num_bits=0;
  	recp->flags=0;
  	}
  
  BN_RECP_CTX *BN_RECP_CTX_new(void)
  	{
  	BN_RECP_CTX *ret;
  
  	if ((ret=(BN_RECP_CTX *)OPENSSL_malloc(sizeof(BN_RECP_CTX))) == NULL)
  		return(NULL);
  
  	BN_RECP_CTX_init(ret);
  	ret->flags=BN_FLG_MALLOCED;
  	return(ret);
  	}
  
  void BN_RECP_CTX_free(BN_RECP_CTX *recp)
  	{
  	if(recp == NULL)
  	    return;
  
  	BN_free(&(recp->N));
  	BN_free(&(recp->Nr));
  	if (recp->flags & BN_FLG_MALLOCED)
  		OPENSSL_free(recp);
  	}
  
  int BN_RECP_CTX_set(BN_RECP_CTX *recp, const BIGNUM *d, BN_CTX *ctx)
  	{
  	if (!BN_copy(&(recp->N),d)) return 0;
  	BN_zero(&(recp->Nr));
  	recp->num_bits=BN_num_bits(d);
  	recp->shift=0;
  	return(1);
  	}
  
  int BN_mod_mul_reciprocal(BIGNUM *r, const BIGNUM *x, const BIGNUM *y,
  	BN_RECP_CTX *recp, BN_CTX *ctx)
  	{
  	int ret=0;
  	BIGNUM *a;
  	const BIGNUM *ca;
  
  	BN_CTX_start(ctx);
  	if ((a = BN_CTX_get(ctx)) == NULL) goto err;
  	if (y != NULL)
  		{
  		if (x == y)
  			{ if (!BN_sqr(a,x,ctx)) goto err; }
  		else
  			{ if (!BN_mul(a,x,y,ctx)) goto err; }
  		ca = a;
  		}
  	else
  		ca=x; /* Just do the mod */
  
  	ret = BN_div_recp(NULL,r,ca,recp,ctx);
  err:
  	BN_CTX_end(ctx);
  	bn_check_top(r);
  	return(ret);
  	}
  
  int BN_div_recp(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m,
  	BN_RECP_CTX *recp, BN_CTX *ctx)
  	{
  	int i,j,ret=0;
  	BIGNUM *a,*b,*d,*r;
  
  	BN_CTX_start(ctx);
  	a=BN_CTX_get(ctx);
  	b=BN_CTX_get(ctx);
  	if (dv != NULL)
  		d=dv;
  	else
  		d=BN_CTX_get(ctx);
  	if (rem != NULL)
  		r=rem;
  	else
  		r=BN_CTX_get(ctx);
  	if (a == NULL || b == NULL || d == NULL || r == NULL) goto err;
  
  	if (BN_ucmp(m,&(recp->N)) < 0)
  		{
  		BN_zero(d);
  		if (!BN_copy(r,m)) return 0;
  		BN_CTX_end(ctx);
  		return(1);
  		}
  
  	/* We want the remainder
  	 * Given input of ABCDEF / ab
  	 * we need multiply ABCDEF by 3 digests of the reciprocal of ab
  	 *
  	 */
  
  	/* i := max(BN_num_bits(m), 2*BN_num_bits(N)) */
  	i=BN_num_bits(m);
  	j=recp->num_bits<<1;
  	if (j>i) i=j;
  
  	/* Nr := round(2^i / N) */
  	if (i != recp->shift)
  		recp->shift=BN_reciprocal(&(recp->Nr),&(recp->N),
  			i,ctx); /* BN_reciprocal returns i, or -1 for an error */
  	if (recp->shift == -1) goto err;
  
  	/* d := |round(round(m / 2^BN_num_bits(N)) * recp->Nr / 2^(i - BN_num_bits(N)))|
  	 *    = |round(round(m / 2^BN_num_bits(N)) * round(2^i / N) / 2^(i - BN_num_bits(N)))|
  	 *   <= |(m / 2^BN_num_bits(N)) * (2^i / N) * (2^BN_num_bits(N) / 2^i)|
  	 *    = |m/N|
  	 */
  	if (!BN_rshift(a,m,recp->num_bits)) goto err;
  	if (!BN_mul(b,a,&(recp->Nr),ctx)) goto err;
  	if (!BN_rshift(d,b,i-recp->num_bits)) goto err;
  	d->neg=0;
  
  	if (!BN_mul(b,&(recp->N),d,ctx)) goto err;
  	if (!BN_usub(r,m,b)) goto err;
  	r->neg=0;
  
  #if 1
  	j=0;
  	while (BN_ucmp(r,&(recp->N)) >= 0)
  		{
  		if (j++ > 2)
  			{
  			BNerr(BN_F_BN_DIV_RECP,BN_R_BAD_RECIPROCAL);
  			goto err;
  			}
  		if (!BN_usub(r,r,&(recp->N))) goto err;
  		if (!BN_add_word(d,1)) goto err;
  		}
  #endif
  
  	r->neg=BN_is_zero(r)?0:m->neg;
  	d->neg=m->neg^recp->N.neg;
  	ret=1;
  err:
  	BN_CTX_end(ctx);
  	bn_check_top(dv);
  	bn_check_top(rem);
  	return(ret);
  	} 
  
  /* len is the expected size of the result
   * We actually calculate with an extra word of precision, so
   * we can do faster division if the remainder is not required.
   */
  /* r := 2^len / m */
  int BN_reciprocal(BIGNUM *r, const BIGNUM *m, int len, BN_CTX *ctx)
  	{
  	int ret= -1;
  	BIGNUM *t;
  
  	BN_CTX_start(ctx);
  	if((t = BN_CTX_get(ctx)) == NULL) goto err;
  
  	if (!BN_set_bit(t,len)) goto err;
  
  	if (!BN_div(r,NULL,t,m,ctx)) goto err;
  
  	ret=len;
  err:
  	bn_check_top(r);
  	BN_CTX_end(ctx);
  	return(ret);
  	}
  