sl@0: /* crypto/bn/bn_div.c */
sl@0: /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
sl@0:  * All rights reserved.
sl@0:  *
sl@0:  * This package is an SSL implementation written
sl@0:  * by Eric Young (eay@cryptsoft.com).
sl@0:  * The implementation was written so as to conform with Netscapes SSL.
sl@0:  * 
sl@0:  * This library is free for commercial and non-commercial use as long as
sl@0:  * the following conditions are aheared to.  The following conditions
sl@0:  * apply to all code found in this distribution, be it the RC4, RSA,
sl@0:  * lhash, DES, etc., code; not just the SSL code.  The SSL documentation
sl@0:  * included with this distribution is covered by the same copyright terms
sl@0:  * except that the holder is Tim Hudson (tjh@cryptsoft.com).
sl@0:  * 
sl@0:  * Copyright remains Eric Young's, and as such any Copyright notices in
sl@0:  * the code are not to be removed.
sl@0:  * If this package is used in a product, Eric Young should be given attribution
sl@0:  * as the author of the parts of the library used.
sl@0:  * This can be in the form of a textual message at program startup or
sl@0:  * in documentation (online or textual) provided with the package.
sl@0:  * 
sl@0:  * Redistribution and use in source and binary forms, with or without
sl@0:  * modification, are permitted provided that the following conditions
sl@0:  * are met:
sl@0:  * 1. Redistributions of source code must retain the copyright
sl@0:  *    notice, this list of conditions and the following disclaimer.
sl@0:  * 2. Redistributions in binary form must reproduce the above copyright
sl@0:  *    notice, this list of conditions and the following disclaimer in the
sl@0:  *    documentation and/or other materials provided with the distribution.
sl@0:  * 3. All advertising materials mentioning features or use of this software
sl@0:  *    must display the following acknowledgement:
sl@0:  *    "This product includes cryptographic software written by
sl@0:  *     Eric Young (eay@cryptsoft.com)"
sl@0:  *    The word 'cryptographic' can be left out if the rouines from the library
sl@0:  *    being used are not cryptographic related :-).
sl@0:  * 4. If you include any Windows specific code (or a derivative thereof) from 
sl@0:  *    the apps directory (application code) you must include an acknowledgement:
sl@0:  *    "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
sl@0:  * 
sl@0:  * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
sl@0:  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
sl@0:  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
sl@0:  * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
sl@0:  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
sl@0:  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
sl@0:  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
sl@0:  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
sl@0:  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
sl@0:  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
sl@0:  * SUCH DAMAGE.
sl@0:  * 
sl@0:  * The licence and distribution terms for any publically available version or
sl@0:  * derivative of this code cannot be changed.  i.e. this code cannot simply be
sl@0:  * copied and put under another distribution licence
sl@0:  * [including the GNU Public Licence.]
sl@0:  */
sl@0: 
sl@0: #include <stdio.h>
sl@0: #include <openssl/bn.h>
sl@0: #include "cryptlib.h"
sl@0: #include "bn_lcl.h"
sl@0: 
sl@0: 
sl@0: /* The old slow way */
sl@0: #if 0
sl@0: EXPORT_C int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, const BIGNUM *d,
sl@0: 	   BN_CTX *ctx)
sl@0: 	{
sl@0: 	int i,nm,nd;
sl@0: 	int ret = 0;
sl@0: 	BIGNUM *D;
sl@0: 
sl@0: 	bn_check_top(m);
sl@0: 	bn_check_top(d);
sl@0: 	if (BN_is_zero(d))
sl@0: 		{
sl@0: 		BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO);
sl@0: 		return(0);
sl@0: 		}
sl@0: 
sl@0: 	if (BN_ucmp(m,d) < 0)
sl@0: 		{
sl@0: 		if (rem != NULL)
sl@0: 			{ if (BN_copy(rem,m) == NULL) return(0); }
sl@0: 		if (dv != NULL) BN_zero(dv);
sl@0: 		return(1);
sl@0: 		}
sl@0: 
sl@0: 	BN_CTX_start(ctx);
sl@0: 	D = BN_CTX_get(ctx);
sl@0: 	if (dv == NULL) dv = BN_CTX_get(ctx);
sl@0: 	if (rem == NULL) rem = BN_CTX_get(ctx);
sl@0: 	if (D == NULL || dv == NULL || rem == NULL)
sl@0: 		goto end;
sl@0: 
sl@0: 	nd=BN_num_bits(d);
sl@0: 	nm=BN_num_bits(m);
sl@0: 	if (BN_copy(D,d) == NULL) goto end;
sl@0: 	if (BN_copy(rem,m) == NULL) goto end;
sl@0: 
sl@0: 	/* The next 2 are needed so we can do a dv->d[0]|=1 later
sl@0: 	 * since BN_lshift1 will only work once there is a value :-) */
sl@0: 	BN_zero(dv);
sl@0: 	bn_wexpand(dv,1);
sl@0: 	dv->top=1;
sl@0: 
sl@0: 	if (!BN_lshift(D,D,nm-nd)) goto end;
sl@0: 	for (i=nm-nd; i>=0; i--)
sl@0: 		{
sl@0: 		if (!BN_lshift1(dv,dv)) goto end;
sl@0: 		if (BN_ucmp(rem,D) >= 0)
sl@0: 			{
sl@0: 			dv->d[0]|=1;
sl@0: 			if (!BN_usub(rem,rem,D)) goto end;
sl@0: 			}
sl@0: /* CAN IMPROVE (and have now :=) */
sl@0: 		if (!BN_rshift1(D,D)) goto end;
sl@0: 		}
sl@0: 	rem->neg=BN_is_zero(rem)?0:m->neg;
sl@0: 	dv->neg=m->neg^d->neg;
sl@0: 	ret = 1;
sl@0:  end:
sl@0: 	BN_CTX_end(ctx);
sl@0: 	return(ret);
sl@0: 	}
sl@0: 
sl@0: #else
sl@0: 
sl@0: #if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM) \
sl@0:     && !defined(PEDANTIC) && !defined(BN_DIV3W)
sl@0: # if defined(__GNUC__) && __GNUC__>=2
sl@0: #  if defined(__i386) || defined (__i386__)
sl@0:    /*
sl@0:     * There were two reasons for implementing this template:
sl@0:     * - GNU C generates a call to a function (__udivdi3 to be exact)
sl@0:     *   in reply to ((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0 (I fail to
sl@0:     *   understand why...);
sl@0:     * - divl doesn't only calculate quotient, but also leaves
sl@0:     *   remainder in %edx which we can definitely use here:-)
sl@0:     *
sl@0:     *					<appro@fy.chalmers.se>
sl@0:     */
sl@0: #  define bn_div_words(n0,n1,d0)		\
sl@0: 	({  asm volatile (			\
sl@0: 		"divl	%4"			\
sl@0: 		: "=a"(q), "=d"(rem)		\
sl@0: 		: "a"(n1), "d"(n0), "g"(d0)	\
sl@0: 		: "cc");			\
sl@0: 	    q;					\
sl@0: 	})
sl@0: #  define REMAINDER_IS_ALREADY_CALCULATED
sl@0: #  elif defined(__x86_64) && defined(SIXTY_FOUR_BIT_LONG)
sl@0:    /*
sl@0:     * Same story here, but it's 128-bit by 64-bit division. Wow!
sl@0:     *					<appro@fy.chalmers.se>
sl@0:     */
sl@0: #  define bn_div_words(n0,n1,d0)		\
sl@0: 	({  asm volatile (			\
sl@0: 		"divq	%4"			\
sl@0: 		: "=a"(q), "=d"(rem)		\
sl@0: 		: "a"(n1), "d"(n0), "g"(d0)	\
sl@0: 		: "cc");			\
sl@0: 	    q;					\
sl@0: 	})
sl@0: #  define REMAINDER_IS_ALREADY_CALCULATED
sl@0: #  endif /* __<cpu> */
sl@0: # endif /* __GNUC__ */
sl@0: #endif /* OPENSSL_NO_ASM */
sl@0: 
sl@0: 
sl@0: /* BN_div[_no_branch] computes  dv := num / divisor,  rounding towards
sl@0:  * zero, and sets up rm  such that  dv*divisor + rm = num  holds.
sl@0:  * Thus:
sl@0:  *     dv->neg == num->neg ^ divisor->neg  (unless the result is zero)
sl@0:  *     rm->neg == num->neg                 (unless the remainder is zero)
sl@0:  * If 'dv' or 'rm' is NULL, the respective value is not returned.
sl@0:  */
sl@0: static int BN_div_no_branch(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num,
sl@0:         const BIGNUM *divisor, BN_CTX *ctx);
sl@0: EXPORT_C int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor,
sl@0: 	   BN_CTX *ctx)
sl@0: 	{
sl@0: 	int norm_shift,i,loop;
sl@0: 	BIGNUM *tmp,wnum,*snum,*sdiv,*res;
sl@0: 	BN_ULONG *resp,*wnump;
sl@0: 	BN_ULONG d0,d1;
sl@0: 	int num_n,div_n;
sl@0: 	if ((BN_get_flags(num, BN_FLG_CONSTTIME) != 0) || (BN_get_flags(divisor, BN_FLG_CONSTTIME) != 0))
sl@0: 		{
sl@0: 		return BN_div_no_branch(dv, rm, num, divisor, ctx);
sl@0: 		}
sl@0: 
sl@0: 	bn_check_top(dv);
sl@0: 	bn_check_top(rm);
sl@0: 	bn_check_top(num);
sl@0: 	bn_check_top(divisor);
sl@0: 
sl@0: 	if (BN_is_zero(divisor))
sl@0: 		{
sl@0: 		BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO);
sl@0: 		return(0);
sl@0: 		}
sl@0: 
sl@0: 	if (BN_ucmp(num,divisor) < 0)
sl@0: 		{
sl@0: 		if (rm != NULL)
sl@0: 			{ if (BN_copy(rm,num) == NULL) return(0); }
sl@0: 		if (dv != NULL) BN_zero(dv);
sl@0: 		return(1);
sl@0: 		}
sl@0: 
sl@0: 	BN_CTX_start(ctx);
sl@0: 	tmp=BN_CTX_get(ctx);
sl@0: 	snum=BN_CTX_get(ctx);
sl@0: 	sdiv=BN_CTX_get(ctx);
sl@0: 	if (dv == NULL)
sl@0: 		res=BN_CTX_get(ctx);
sl@0: 	else	res=dv;
sl@0: 	if (sdiv == NULL || res == NULL) goto err;
sl@0: 
sl@0: 	/* First we normalise the numbers */
sl@0: 	norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2);
sl@0: 	if (!(BN_lshift(sdiv,divisor,norm_shift))) goto err;
sl@0: 	sdiv->neg=0;
sl@0: 	norm_shift+=BN_BITS2;
sl@0: 	if (!(BN_lshift(snum,num,norm_shift))) goto err;
sl@0: 	snum->neg=0;
sl@0: 	div_n=sdiv->top;
sl@0: 	num_n=snum->top;
sl@0: 	loop=num_n-div_n;
sl@0: 	/* Lets setup a 'window' into snum
sl@0: 	 * This is the part that corresponds to the current
sl@0: 	 * 'area' being divided */
sl@0: 	wnum.neg   = 0;
sl@0: 	wnum.d     = &(snum->d[loop]);
sl@0: 	wnum.top   = div_n;
sl@0: 	/* only needed when BN_ucmp messes up the values between top and max */
sl@0: 	wnum.dmax  = snum->dmax - loop; /* so we don't step out of bounds */
sl@0: 
sl@0: 	/* Get the top 2 words of sdiv */
sl@0: 	/* div_n=sdiv->top; */
sl@0: 	d0=sdiv->d[div_n-1];
sl@0: 	d1=(div_n == 1)?0:sdiv->d[div_n-2];
sl@0: 
sl@0: 	/* pointer to the 'top' of snum */
sl@0: 	wnump= &(snum->d[num_n-1]);
sl@0: 
sl@0: 	/* Setup to 'res' */
sl@0: 	res->neg= (num->neg^divisor->neg);
sl@0: 	if (!bn_wexpand(res,(loop+1))) goto err;
sl@0: 	res->top=loop;
sl@0: 	resp= &(res->d[loop-1]);
sl@0: 
sl@0: 	/* space for temp */
sl@0: 	if (!bn_wexpand(tmp,(div_n+1))) goto err;
sl@0: 
sl@0: 	if (BN_ucmp(&wnum,sdiv) >= 0)
sl@0: 		{
sl@0: 		/* If BN_DEBUG_RAND is defined BN_ucmp changes (via
sl@0: 		 * bn_pollute) the const bignum arguments =>
sl@0: 		 * clean the values between top and max again */
sl@0: 		bn_clear_top2max(&wnum);
sl@0: 		bn_sub_words(wnum.d, wnum.d, sdiv->d, div_n);
sl@0: 		*resp=1;
sl@0: 		}
sl@0: 	else
sl@0: 		res->top--;
sl@0: 	/* if res->top == 0 then clear the neg value otherwise decrease
sl@0: 	 * the resp pointer */
sl@0: 	if (res->top == 0)
sl@0: 		res->neg = 0;
sl@0: 	else
sl@0: 		resp--;
sl@0: 
sl@0: 	for (i=0; i<loop-1; i++, wnump--, resp--)
sl@0: 		{
sl@0: 		BN_ULONG q,l0;
sl@0: 		/* the first part of the loop uses the top two words of
sl@0: 		 * snum and sdiv to calculate a BN_ULONG q such that
sl@0: 		 * | wnum - sdiv * q | < sdiv */
sl@0: #if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM)
sl@0: 		BN_ULONG bn_div_3_words(BN_ULONG*,BN_ULONG,BN_ULONG);
sl@0: 		q=bn_div_3_words(wnump,d1,d0);
sl@0: #else
sl@0: 		BN_ULONG n0,n1,rem=0;
sl@0: 
sl@0: 		n0=wnump[0];
sl@0: 		n1=wnump[-1];
sl@0: 		if (n0 == d0)
sl@0: 			q=BN_MASK2;
sl@0: 		else 			/* n0 < d0 */
sl@0: 			{
sl@0: #ifdef BN_LLONG
sl@0: 			BN_ULLONG t2;
sl@0: 
sl@0: #if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
sl@0: 			q=(BN_ULONG)(((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0);
sl@0: #else
sl@0: 			q=bn_div_words(n0,n1,d0);
sl@0: #ifdef BN_DEBUG_LEVITTE
sl@0: 			fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
sl@0: X) -> 0x%08X\n",
sl@0: 				n0, n1, d0, q);
sl@0: #endif
sl@0: #endif
sl@0: 
sl@0: #ifndef REMAINDER_IS_ALREADY_CALCULATED
sl@0: 			/*
sl@0: 			 * rem doesn't have to be BN_ULLONG. The least we
sl@0: 			 * know it's less that d0, isn't it?
sl@0: 			 */
sl@0: 			rem=(n1-q*d0)&BN_MASK2;
sl@0: #endif
sl@0: 			t2=(BN_ULLONG)d1*q;
sl@0: 
sl@0: 			for (;;)
sl@0: 				{
sl@0: 				if (t2 <= ((((BN_ULLONG)rem)<<BN_BITS2)|wnump[-2]))
sl@0: 					break;
sl@0: 				q--;
sl@0: 				rem += d0;
sl@0: 				if (rem < d0) break; /* don't let rem overflow */
sl@0: 				t2 -= d1;
sl@0: 				}
sl@0: #else /* !BN_LLONG */
sl@0: 			BN_ULONG t2l,t2h,ql,qh;
sl@0: 
sl@0: 			q=bn_div_words(n0,n1,d0);
sl@0: #ifdef BN_DEBUG_LEVITTE
sl@0: 			fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
sl@0: X) -> 0x%08X\n",
sl@0: 				n0, n1, d0, q);
sl@0: #endif
sl@0: #ifndef REMAINDER_IS_ALREADY_CALCULATED
sl@0: 			rem=(n1-q*d0)&BN_MASK2;
sl@0: #endif
sl@0: 
sl@0: #if defined(BN_UMULT_LOHI)
sl@0: 			BN_UMULT_LOHI(t2l,t2h,d1,q);
sl@0: #elif defined(BN_UMULT_HIGH)
sl@0: 			t2l = d1 * q;
sl@0: 			t2h = BN_UMULT_HIGH(d1,q);
sl@0: #else
sl@0: 			t2l=LBITS(d1); t2h=HBITS(d1);
sl@0: 			ql =LBITS(q);  qh =HBITS(q);
sl@0: 			mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */
sl@0: #endif
sl@0: 
sl@0: 			for (;;)
sl@0: 				{
sl@0: 				if ((t2h < rem) ||
sl@0: 					((t2h == rem) && (t2l <= wnump[-2])))
sl@0: 					break;
sl@0: 				q--;
sl@0: 				rem += d0;
sl@0: 				if (rem < d0) break; /* don't let rem overflow */
sl@0: 				if (t2l < d1) t2h--; t2l -= d1;
sl@0: 				}
sl@0: #endif /* !BN_LLONG */
sl@0: 			}
sl@0: #endif /* !BN_DIV3W */
sl@0: 
sl@0: 		l0=bn_mul_words(tmp->d,sdiv->d,div_n,q);
sl@0: 		tmp->d[div_n]=l0;
sl@0: 		wnum.d--;
sl@0: 		/* ingore top values of the bignums just sub the two 
sl@0: 		 * BN_ULONG arrays with bn_sub_words */
sl@0: 		if (bn_sub_words(wnum.d, wnum.d, tmp->d, div_n+1))
sl@0: 			{
sl@0: 			/* Note: As we have considered only the leading
sl@0: 			 * two BN_ULONGs in the calculation of q, sdiv * q
sl@0: 			 * might be greater than wnum (but then (q-1) * sdiv
sl@0: 			 * is less or equal than wnum)
sl@0: 			 */
sl@0: 			q--;
sl@0: 			if (bn_add_words(wnum.d, wnum.d, sdiv->d, div_n))
sl@0: 				/* we can't have an overflow here (assuming
sl@0: 				 * that q != 0, but if q == 0 then tmp is
sl@0: 				 * zero anyway) */
sl@0: 				(*wnump)++;
sl@0: 			}
sl@0: 		/* store part of the result */
sl@0: 		*resp = q;
sl@0: 		}
sl@0: 	bn_correct_top(snum);
sl@0: 	if (rm != NULL)
sl@0: 		{
sl@0: 		/* Keep a copy of the neg flag in num because if rm==num
sl@0: 		 * BN_rshift() will overwrite it.
sl@0: 		 */
sl@0: 		int neg = num->neg;
sl@0: 		BN_rshift(rm,snum,norm_shift);
sl@0: 		if (!BN_is_zero(rm))
sl@0: 			rm->neg = neg;
sl@0: 		bn_check_top(rm);
sl@0: 		}
sl@0: 	BN_CTX_end(ctx);
sl@0: 	return(1);
sl@0: err:
sl@0: 	bn_check_top(rm);
sl@0: 	BN_CTX_end(ctx);
sl@0: 	return(0);
sl@0: 	}
sl@0: 
sl@0: /* BN_div_no_branch is a special version of BN_div. It does not contain
sl@0:  * branches that may leak sensitive information.
sl@0:  */
sl@0: static int BN_div_no_branch(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, 
sl@0: 	const BIGNUM *divisor, BN_CTX *ctx)
sl@0: 	{
sl@0: 	int norm_shift,i,loop;
sl@0: 	BIGNUM *tmp,wnum,*snum,*sdiv,*res;
sl@0: 	BN_ULONG *resp,*wnump;
sl@0: 	BN_ULONG d0,d1;
sl@0: 	int num_n,div_n;
sl@0: 
sl@0: 	bn_check_top(dv);
sl@0: 	bn_check_top(rm);
sl@0: 	bn_check_top(num);
sl@0: 	bn_check_top(divisor);
sl@0: 
sl@0: 	if (BN_is_zero(divisor))
sl@0: 		{
sl@0: 		BNerr(BN_F_BN_DIV_NO_BRANCH,BN_R_DIV_BY_ZERO);
sl@0: 		return(0);
sl@0: 		}
sl@0: 
sl@0: 	BN_CTX_start(ctx);
sl@0: 	tmp=BN_CTX_get(ctx);
sl@0: 	snum=BN_CTX_get(ctx);
sl@0: 	sdiv=BN_CTX_get(ctx);
sl@0: 	if (dv == NULL)
sl@0: 		res=BN_CTX_get(ctx);
sl@0: 	else	res=dv;
sl@0: 	if (sdiv == NULL || res == NULL) goto err;
sl@0: 
sl@0: 	/* First we normalise the numbers */
sl@0: 	norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2);
sl@0: 	if (!(BN_lshift(sdiv,divisor,norm_shift))) goto err;
sl@0: 	sdiv->neg=0;
sl@0: 	norm_shift+=BN_BITS2;
sl@0: 	if (!(BN_lshift(snum,num,norm_shift))) goto err;
sl@0: 	snum->neg=0;
sl@0: 
sl@0: 	/* Since we don't know whether snum is larger than sdiv,
sl@0: 	 * we pad snum with enough zeroes without changing its
sl@0: 	 * value. 
sl@0: 	 */
sl@0: 	if (snum->top <= sdiv->top+1) 
sl@0: 		{
sl@0: 		if (bn_wexpand(snum, sdiv->top + 2) == NULL) goto err;
sl@0: 		for (i = snum->top; i < sdiv->top + 2; i++) snum->d[i] = 0;
sl@0: 		snum->top = sdiv->top + 2;
sl@0: 		}
sl@0: 	else
sl@0: 		{
sl@0: 		if (bn_wexpand(snum, snum->top + 1) == NULL) goto err;
sl@0: 		snum->d[snum->top] = 0;
sl@0: 		snum->top ++;
sl@0: 		}
sl@0: 
sl@0: 	div_n=sdiv->top;
sl@0: 	num_n=snum->top;
sl@0: 	loop=num_n-div_n;
sl@0: 	/* Lets setup a 'window' into snum
sl@0: 	 * This is the part that corresponds to the current
sl@0: 	 * 'area' being divided */
sl@0: 	wnum.neg   = 0;
sl@0: 	wnum.d     = &(snum->d[loop]);
sl@0: 	wnum.top   = div_n;
sl@0: 	/* only needed when BN_ucmp messes up the values between top and max */
sl@0: 	wnum.dmax  = snum->dmax - loop; /* so we don't step out of bounds */
sl@0: 
sl@0: 	/* Get the top 2 words of sdiv */
sl@0: 	/* div_n=sdiv->top; */
sl@0: 	d0=sdiv->d[div_n-1];
sl@0: 	d1=(div_n == 1)?0:sdiv->d[div_n-2];
sl@0: 
sl@0: 	/* pointer to the 'top' of snum */
sl@0: 	wnump= &(snum->d[num_n-1]);
sl@0: 
sl@0: 	/* Setup to 'res' */
sl@0: 	res->neg= (num->neg^divisor->neg);
sl@0: 	if (!bn_wexpand(res,(loop+1))) goto err;
sl@0: 	res->top=loop-1;
sl@0: 	resp= &(res->d[loop-1]);
sl@0: 
sl@0: 	/* space for temp */
sl@0: 	if (!bn_wexpand(tmp,(div_n+1))) goto err;
sl@0: 
sl@0: 	/* if res->top == 0 then clear the neg value otherwise decrease
sl@0: 	 * the resp pointer */
sl@0: 	if (res->top == 0)
sl@0: 		res->neg = 0;
sl@0: 	else
sl@0: 		resp--;
sl@0: 
sl@0: 	for (i=0; i<loop-1; i++, wnump--, resp--)
sl@0: 		{
sl@0: 		BN_ULONG q,l0;
sl@0: 		/* the first part of the loop uses the top two words of
sl@0: 		 * snum and sdiv to calculate a BN_ULONG q such that
sl@0: 		 * | wnum - sdiv * q | < sdiv */
sl@0: #if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM)
sl@0: 		BN_ULONG bn_div_3_words(BN_ULONG*,BN_ULONG,BN_ULONG);
sl@0: 		q=bn_div_3_words(wnump,d1,d0);
sl@0: #else
sl@0: 		BN_ULONG n0,n1,rem=0;
sl@0: 
sl@0: 		n0=wnump[0];
sl@0: 		n1=wnump[-1];
sl@0: 		if (n0 == d0)
sl@0: 			q=BN_MASK2;
sl@0: 		else 			/* n0 < d0 */
sl@0: 			{
sl@0: #ifdef BN_LLONG
sl@0: 			BN_ULLONG t2;
sl@0: 
sl@0: #if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
sl@0: 			q=(BN_ULONG)(((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0);
sl@0: #else
sl@0: 			q=bn_div_words(n0,n1,d0);
sl@0: #ifdef BN_DEBUG_LEVITTE
sl@0: 			fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
sl@0: X) -> 0x%08X\n",
sl@0: 				n0, n1, d0, q);
sl@0: #endif
sl@0: #endif
sl@0: 
sl@0: #ifndef REMAINDER_IS_ALREADY_CALCULATED
sl@0: 			/*
sl@0: 			 * rem doesn't have to be BN_ULLONG. The least we
sl@0: 			 * know it's less that d0, isn't it?
sl@0: 			 */
sl@0: 			rem=(n1-q*d0)&BN_MASK2;
sl@0: #endif
sl@0: 			t2=(BN_ULLONG)d1*q;
sl@0: 
sl@0: 			for (;;)
sl@0: 				{
sl@0: 				if (t2 <= ((((BN_ULLONG)rem)<<BN_BITS2)|wnump[-2]))
sl@0: 					break;
sl@0: 				q--;
sl@0: 				rem += d0;
sl@0: 				if (rem < d0) break; /* don't let rem overflow */
sl@0: 				t2 -= d1;
sl@0: 				}
sl@0: #else /* !BN_LLONG */
sl@0: 			BN_ULONG t2l,t2h,ql,qh;
sl@0: 
sl@0: 			q=bn_div_words(n0,n1,d0);
sl@0: #ifdef BN_DEBUG_LEVITTE
sl@0: 			fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
sl@0: X) -> 0x%08X\n",
sl@0: 				n0, n1, d0, q);
sl@0: #endif
sl@0: #ifndef REMAINDER_IS_ALREADY_CALCULATED
sl@0: 			rem=(n1-q*d0)&BN_MASK2;
sl@0: #endif
sl@0: 
sl@0: #if defined(BN_UMULT_LOHI)
sl@0: 			BN_UMULT_LOHI(t2l,t2h,d1,q);
sl@0: #elif defined(BN_UMULT_HIGH)
sl@0: 			t2l = d1 * q;
sl@0: 			t2h = BN_UMULT_HIGH(d1,q);
sl@0: #else
sl@0: 			t2l=LBITS(d1); t2h=HBITS(d1);
sl@0: 			ql =LBITS(q);  qh =HBITS(q);
sl@0: 			mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */
sl@0: #endif
sl@0: 
sl@0: 			for (;;)
sl@0: 				{
sl@0: 				if ((t2h < rem) ||
sl@0: 					((t2h == rem) && (t2l <= wnump[-2])))
sl@0: 					break;
sl@0: 				q--;
sl@0: 				rem += d0;
sl@0: 				if (rem < d0) break; /* don't let rem overflow */
sl@0: 				if (t2l < d1) t2h--; t2l -= d1;
sl@0: 				}
sl@0: #endif /* !BN_LLONG */
sl@0: 			}
sl@0: #endif /* !BN_DIV3W */
sl@0: 
sl@0: 		l0=bn_mul_words(tmp->d,sdiv->d,div_n,q);
sl@0: 		tmp->d[div_n]=l0;
sl@0: 		wnum.d--;
sl@0: 		/* ingore top values of the bignums just sub the two 
sl@0: 		 * BN_ULONG arrays with bn_sub_words */
sl@0: 		if (bn_sub_words(wnum.d, wnum.d, tmp->d, div_n+1))
sl@0: 			{
sl@0: 			/* Note: As we have considered only the leading
sl@0: 			 * two BN_ULONGs in the calculation of q, sdiv * q
sl@0: 			 * might be greater than wnum (but then (q-1) * sdiv
sl@0: 			 * is less or equal than wnum)
sl@0: 			 */
sl@0: 			q--;
sl@0: 			if (bn_add_words(wnum.d, wnum.d, sdiv->d, div_n))
sl@0: 				/* we can't have an overflow here (assuming
sl@0: 				 * that q != 0, but if q == 0 then tmp is
sl@0: 				 * zero anyway) */
sl@0: 				(*wnump)++;
sl@0: 			}
sl@0: 		/* store part of the result */
sl@0: 		*resp = q;
sl@0: 		}
sl@0: 	bn_correct_top(snum);
sl@0: 	if (rm != NULL)
sl@0: 		{
sl@0: 		/* Keep a copy of the neg flag in num because if rm==num
sl@0: 		 * BN_rshift() will overwrite it.
sl@0: 		 */
sl@0: 		int neg = num->neg;
sl@0: 		BN_rshift(rm,snum,norm_shift);
sl@0: 		if (!BN_is_zero(rm))
sl@0: 			rm->neg = neg;
sl@0: 		bn_check_top(rm);
sl@0: 		}
sl@0: 	bn_correct_top(res);
sl@0: 	BN_CTX_end(ctx);
sl@0: 	return(1);
sl@0: err:
sl@0: 	bn_check_top(rm);
sl@0: 	BN_CTX_end(ctx);
sl@0: 	return(0);
sl@0: 	}
sl@0: 
sl@0: #endif