[thirdparty/openssl.git] / crypto / bn / bn_div.c

/* crypto/bn/bn_div.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 <openssl/bn.h>
#include "cryptlib.h"
#include "bn_lcl.h"


/* The old slow way */
#if 0
int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, const BIGNUM *d,
	   BN_CTX *ctx)
	{
	int i,nm,nd;
	int ret = 0;
	BIGNUM *D;

	bn_check_top(m);
	bn_check_top(d);
	if (BN_is_zero(d))
		{
		BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO);
		return(0);
		}

	if (BN_ucmp(m,d) < 0)
		{
		if (rem != NULL)
			{ if (BN_copy(rem,m) == NULL) return(0); }
		if (dv != NULL) BN_zero(dv);
		return(1);
		}

	BN_CTX_start(ctx);
	D = BN_CTX_get(ctx);
	if (dv == NULL) dv = BN_CTX_get(ctx);
	if (rem == NULL) rem = BN_CTX_get(ctx);
	if (D == NULL || dv == NULL || rem == NULL)
		goto end;

	nd=BN_num_bits(d);
	nm=BN_num_bits(m);
	if (BN_copy(D,d) == NULL) goto end;
	if (BN_copy(rem,m) == NULL) goto end;

	/* The next 2 are needed so we can do a dv->d[0]|=1 later
	 * since BN_lshift1 will only work once there is a value :-) */
	BN_zero(dv);
	bn_wexpand(dv,1);
	dv->top=1;

	if (!BN_lshift(D,D,nm-nd)) goto end;
	for (i=nm-nd; i>=0; i--)
		{
		if (!BN_lshift1(dv,dv)) goto end;
		if (BN_ucmp(rem,D) >= 0)
			{
			dv->d[0]|=1;
			if (!BN_usub(rem,rem,D)) goto end;
			}
/* CAN IMPROVE (and have now :=) */
		if (!BN_rshift1(D,D)) goto end;
		}
	rem->neg=BN_is_zero(rem)?0:m->neg;
	dv->neg=m->neg^d->neg;
	ret = 1;
 end:
	BN_CTX_end(ctx);
	return(ret);
	}

#else

#if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM) \
    && !defined(PEDANTIC) && !defined(BN_DIV3W)
# if defined(__GNUC__) && __GNUC__>=2
#  if defined(__i386) || defined (__i386__)
   /*
    * There were two reasons for implementing this template:
    * - GNU C generates a call to a function (__udivdi3 to be exact)
    *   in reply to ((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0 (I fail to
    *   understand why...);
    * - divl doesn't only calculate quotient, but also leaves
    *   remainder in %edx which we can definitely use here:-)
    *
    *					<appro@fy.chalmers.se>
    */
#  define bn_div_words(n0,n1,d0)		\
	({  asm volatile (			\
		"divl	%4"			\
		: "=a"(q), "=d"(rem)		\
		: "a"(n1), "d"(n0), "g"(d0)	\
		: "cc");			\
	    q;					\
	})
#  define REMAINDER_IS_ALREADY_CALCULATED
#  elif defined(__x86_64) && defined(SIXTY_FOUR_BIT_LONG)
   /*
    * Same story here, but it's 128-bit by 64-bit division. Wow!
    *					<appro@fy.chalmers.se>
    */
#  define bn_div_words(n0,n1,d0)		\
	({  asm volatile (			\
		"divq	%4"			\
		: "=a"(q), "=d"(rem)		\
		: "a"(n1), "d"(n0), "g"(d0)	\
		: "cc");			\
	    q;					\
	})
#  define REMAINDER_IS_ALREADY_CALCULATED
#  endif /* __<cpu> */
# endif /* __GNUC__ */
#endif /* OPENSSL_NO_ASM */


/* BN_div[_no_branch] computes  dv := num / divisor,  rounding towards
 * zero, and sets up rm  such that  dv*divisor + rm = num  holds.
 * Thus:
 *     dv->neg == num->neg ^ divisor->neg  (unless the result is zero)
 *     rm->neg == num->neg                 (unless the remainder is zero)
 * If 'dv' or 'rm' is NULL, the respective value is not returned.
 */
static int BN_div_no_branch(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num,
        const BIGNUM *divisor, BN_CTX *ctx);
int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor,
	   BN_CTX *ctx)
	{
	int norm_shift,i;
	size_t loop;
	BIGNUM *tmp,wnum,*snum,*sdiv,*res;
	BN_ULONG *resp,*wnump;
	BN_ULONG d0,d1;
	size_t num_n,div_n;

	/* Invalid zero-padding would have particularly bad consequences
	 * in the case of 'num', so don't just rely on bn_check_top() for this one
	 * (bn_check_top() works only for BN_DEBUG builds) */
	if (num->top > 0 && num->d[num->top - 1] == 0)
		{
		BNerr(BN_F_BN_DIV,BN_R_NOT_INITIALIZED);
		return 0;
		}

	bn_check_top(num);

	if ((BN_get_flags(num, BN_FLG_CONSTTIME) != 0) || (BN_get_flags(divisor, BN_FLG_CONSTTIME) != 0))
		{
		return BN_div_no_branch(dv, rm, num, divisor, ctx);
		}

	bn_check_top(dv);
	bn_check_top(rm);
	/* bn_check_top(num); */ /* 'num' has been checked already */
	bn_check_top(divisor);

	if (BN_is_zero(divisor))
		{
		BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO);
		return(0);
		}

	if (BN_ucmp(num,divisor) < 0)
		{
		if (rm != NULL)
			{ if (BN_copy(rm,num) == NULL) return(0); }
		if (dv != NULL) BN_zero(dv);
		return(1);
		}

	BN_CTX_start(ctx);
	tmp=BN_CTX_get(ctx);
	snum=BN_CTX_get(ctx);
	sdiv=BN_CTX_get(ctx);
	if (dv == NULL)
		res=BN_CTX_get(ctx);
	else	res=dv;
	if (sdiv == NULL || res == NULL) goto err;

	/* First we normalise the numbers */
	norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2);
	if (!(BN_lshift(sdiv,divisor,norm_shift))) goto err;
	sdiv->neg=0;
	norm_shift+=BN_BITS2;
	if (!(BN_lshift(snum,num,norm_shift))) goto err;
	snum->neg=0;
	div_n=sdiv->top;
	num_n=snum->top;
	loop=num_n-div_n;
	/* Lets setup a 'window' into snum
	 * This is the part that corresponds to the current
	 * 'area' being divided */
	wnum.neg   = 0;
	wnum.d     = &(snum->d[loop]);
	wnum.top   = div_n;
	/* only needed when BN_ucmp messes up the values between top and max */
	wnum.dmax  = snum->dmax - loop; /* so we don't step out of bounds */

	/* Get the top 2 words of sdiv */
	/* div_n=sdiv->top; */
	d0=sdiv->d[div_n-1];
	d1=(div_n == 1)?0:sdiv->d[div_n-2];

	/* pointer to the 'top' of snum */
	wnump= &(snum->d[num_n-1]);

	/* Setup to 'res' */
	res->neg= (num->neg^divisor->neg);
	if (!bn_wexpand(res,(loop+1))) goto err;
	res->top=loop;
	resp= &(res->d[loop-1]);

	/* space for temp */
	if (!bn_wexpand(tmp, div_n+1)) goto err;

	if (BN_ucmp(&wnum,sdiv) >= 0)
		{
		/* If BN_DEBUG_RAND is defined BN_ucmp changes (via
		 * bn_pollute) the const bignum arguments =>
		 * clean the values between top and max again */
		bn_clear_top2max(&wnum);
		bn_sub_words(wnum.d, wnum.d, sdiv->d, div_n);
		*resp=1;
		}
	else
		res->top--;
	/* if res->top == 0 then clear the neg value otherwise decrease
	 * the resp pointer */
	if (res->top == 0)
		res->neg = 0;
	else
		resp--;

	for (i=0; i<loop-1; i++, wnump--, resp--)
		{
		BN_ULONG q,l0;
		/* the first part of the loop uses the top two words of
		 * snum and sdiv to calculate a BN_ULONG q such that
		 * | wnum - sdiv * q | < sdiv */
#if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM)
		BN_ULONG bn_div_3_words(BN_ULONG*,BN_ULONG,BN_ULONG);
		q=bn_div_3_words(wnump,d1,d0);
#else
		BN_ULONG n0,n1,rem=0;

		n0=wnump[0];
		n1=wnump[-1];
		if (n0 == d0)
			q=BN_MASK2;
		else 			/* n0 < d0 */
			{
#ifdef BN_LLONG
			BN_ULLONG t2;

#if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
			q=(BN_ULONG)(((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0);
#else
			q=bn_div_words(n0,n1,d0);
#ifdef BN_DEBUG_LEVITTE
			fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
X) -> 0x%08X\n",
				n0, n1, d0, q);
#endif
#endif

#ifndef REMAINDER_IS_ALREADY_CALCULATED
			/*
			 * rem doesn't have to be BN_ULLONG. The least we
			 * know it's less that d0, isn't it?
			 */
			rem=(n1-q*d0)&BN_MASK2;
#endif
			t2=(BN_ULLONG)d1*q;

			for (;;)
				{
				if (t2 <= ((((BN_ULLONG)rem)<<BN_BITS2)|wnump[-2]))
					break;
				q--;
				rem += d0;
				if (rem < d0) break; /* don't let rem overflow */
				t2 -= d1;
				}
#else /* !BN_LLONG */
			BN_ULONG t2l,t2h;

			q=bn_div_words(n0,n1,d0);
#ifdef BN_DEBUG_LEVITTE
			fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
X) -> 0x%08X\n",
				n0, n1, d0, q);
#endif
#ifndef REMAINDER_IS_ALREADY_CALCULATED
			rem=(n1-q*d0)&BN_MASK2;
#endif

#if defined(BN_UMULT_LOHI)
			BN_UMULT_LOHI(t2l,t2h,d1,q);
#elif defined(BN_UMULT_HIGH)
			t2l = d1 * q;
			t2h = BN_UMULT_HIGH(d1,q);
#else
			{
			BN_ULONG ql, qh;
			t2l=LBITS(d1); t2h=HBITS(d1);
			ql =LBITS(q);  qh =HBITS(q);
			mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */
			}
#endif

			for (;;)
				{
				if ((t2h < rem) ||
					((t2h == rem) && (t2l <= wnump[-2])))
					break;
				q--;
				rem += d0;
				if (rem < d0) break; /* don't let rem overflow */
				if (t2l < d1) t2h--; t2l -= d1;
				}
#endif /* !BN_LLONG */
			}
#endif /* !BN_DIV3W */

		l0=bn_mul_words(tmp->d,sdiv->d,div_n,q);
		tmp->d[div_n]=l0;
		wnum.d--;
		/* ingore top values of the bignums just sub the two 
		 * BN_ULONG arrays with bn_sub_words */
		if (bn_sub_words(wnum.d, wnum.d, tmp->d, div_n+1))
			{
			/* Note: As we have considered only the leading
			 * two BN_ULONGs in the calculation of q, sdiv * q
			 * might be greater than wnum (but then (q-1) * sdiv
			 * is less or equal than wnum)
			 */
			q--;
			if (bn_add_words(wnum.d, wnum.d, sdiv->d, div_n))
				/* we can't have an overflow here (assuming
				 * that q != 0, but if q == 0 then tmp is
				 * zero anyway) */
				(*wnump)++;
			}
		/* store part of the result */
		*resp = q;
		}
	bn_correct_top(snum);
	if (rm != NULL)
		{
		/* Keep a copy of the neg flag in num because if rm==num
		 * BN_rshift() will overwrite it.
		 */
		int neg = num->neg;
		BN_rshift(rm,snum,norm_shift);
		if (!BN_is_zero(rm))
			rm->neg = neg;
		bn_check_top(rm);
		}
	BN_CTX_end(ctx);
	return(1);
err:
	bn_check_top(rm);
	BN_CTX_end(ctx);
	return(0);
	}


/* BN_div_no_branch is a special version of BN_div. It does not contain
 * branches that may leak sensitive information.
 */
static int BN_div_no_branch(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, 
	const BIGNUM *divisor, BN_CTX *ctx)
	{
	int norm_shift,i,loop;
	BIGNUM *tmp,wnum,*snum,*sdiv,*res;
	BN_ULONG *resp,*wnump;
	BN_ULONG d0,d1;
	size_t num_n,div_n;

	bn_check_top(dv);
	bn_check_top(rm);
	/* bn_check_top(num); */ /* 'num' has been checked in BN_div() */
	bn_check_top(divisor);

	if (BN_is_zero(divisor))
		{
		BNerr(BN_F_BN_DIV_NO_BRANCH,BN_R_DIV_BY_ZERO);
		return(0);
		}

	BN_CTX_start(ctx);
	tmp=BN_CTX_get(ctx);
	snum=BN_CTX_get(ctx);
	sdiv=BN_CTX_get(ctx);
	if (dv == NULL)
		res=BN_CTX_get(ctx);
	else	res=dv;
	if (sdiv == NULL || res == NULL) goto err;

	/* First we normalise the numbers */
	norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2);
	if (!(BN_lshift(sdiv,divisor,norm_shift))) goto err;
	sdiv->neg=0;
	norm_shift+=BN_BITS2;
	if (!(BN_lshift(snum,num,norm_shift))) goto err;
	snum->neg=0;

	/* Since we don't know whether snum is larger than sdiv,
	 * we pad snum with enough zeroes without changing its
	 * value. 
	 */
	if (snum->top <= sdiv->top+1) 
		{
		if (bn_wexpand(snum, sdiv->top + 2) == NULL) goto err;
		for (i = snum->top; i < sdiv->top + 2; i++) snum->d[i] = 0;
		snum->top = sdiv->top + 2;
		}
	else
		{
		if (bn_wexpand(snum, snum->top + 1) == NULL) goto err;
		snum->d[snum->top] = 0;
		snum->top ++;
		}

	div_n=sdiv->top;
	num_n=snum->top;
	loop=num_n-div_n;
	/* Lets setup a 'window' into snum
	 * This is the part that corresponds to the current
	 * 'area' being divided */
	wnum.neg   = 0;
	wnum.d     = &(snum->d[loop]);
	wnum.top   = div_n;
	/* only needed when BN_ucmp messes up the values between top and max */
	wnum.dmax  = snum->dmax - loop; /* so we don't step out of bounds */

	/* Get the top 2 words of sdiv */
	/* div_n=sdiv->top; */
	d0=sdiv->d[div_n-1];
	d1=(div_n == 1)?0:sdiv->d[div_n-2];

	/* pointer to the 'top' of snum */
	wnump= &(snum->d[num_n-1]);

	/* Setup to 'res' */
	res->neg= (num->neg^divisor->neg);
	if (!bn_wexpand(res,loop+1U)) goto err;
	res->top=loop-1;
	resp= &(res->d[loop-1]);

	/* space for temp */
	if (!bn_wexpand(tmp,div_n+1U)) goto err;

	/* if res->top == 0 then clear the neg value otherwise decrease
	 * the resp pointer */
	if (res->top == 0)
		res->neg = 0;
	else
		resp--;

	for (i=0; i<loop-1; i++, wnump--, resp--)
		{
		BN_ULONG q,l0;
		/* the first part of the loop uses the top two words of
		 * snum and sdiv to calculate a BN_ULONG q such that
		 * | wnum - sdiv * q | < sdiv */
#if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM)
		BN_ULONG bn_div_3_words(BN_ULONG*,BN_ULONG,BN_ULONG);
		q=bn_div_3_words(wnump,d1,d0);
#else
		BN_ULONG n0,n1,rem=0;

		n0=wnump[0];
		n1=wnump[-1];
		if (n0 == d0)
			q=BN_MASK2;
		else 			/* n0 < d0 */
			{
#ifdef BN_LLONG
			BN_ULLONG t2;

#if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
			q=(BN_ULONG)(((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0);
#else
			q=bn_div_words(n0,n1,d0);
#ifdef BN_DEBUG_LEVITTE
			fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
X) -> 0x%08X\n",
				n0, n1, d0, q);
#endif
#endif

#ifndef REMAINDER_IS_ALREADY_CALCULATED
			/*
			 * rem doesn't have to be BN_ULLONG. The least we
			 * know it's less that d0, isn't it?
			 */
			rem=(n1-q*d0)&BN_MASK2;
#endif
			t2=(BN_ULLONG)d1*q;

			for (;;)
				{
				if (t2 <= ((((BN_ULLONG)rem)<<BN_BITS2)|wnump[-2]))
					break;
				q--;
				rem += d0;
				if (rem < d0) break; /* don't let rem overflow */
				t2 -= d1;
				}
#else /* !BN_LLONG */
			BN_ULONG t2l,t2h;

			q=bn_div_words(n0,n1,d0);
#ifdef BN_DEBUG_LEVITTE
			fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
X) -> 0x%08X\n",
				n0, n1, d0, q);
#endif
#ifndef REMAINDER_IS_ALREADY_CALCULATED
			rem=(n1-q*d0)&BN_MASK2;
#endif

#if defined(BN_UMULT_LOHI)
			BN_UMULT_LOHI(t2l,t2h,d1,q);
#elif defined(BN_UMULT_HIGH)
			t2l = d1 * q;
			t2h = BN_UMULT_HIGH(d1,q);
#else
			{
			BN_ULONG ql, qh;
			t2l=LBITS(d1); t2h=HBITS(d1);
			ql =LBITS(q);  qh =HBITS(q);
			mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */
			}
#endif

			for (;;)
				{
				if ((t2h < rem) ||
					((t2h == rem) && (t2l <= wnump[-2])))
					break;
				q--;
				rem += d0;
				if (rem < d0) break; /* don't let rem overflow */
				if (t2l < d1) t2h--; t2l -= d1;
				}
#endif /* !BN_LLONG */
			}
#endif /* !BN_DIV3W */

		l0=bn_mul_words(tmp->d,sdiv->d,div_n,q);
		tmp->d[div_n]=l0;
		wnum.d--;
		/* ingore top values of the bignums just sub the two 
		 * BN_ULONG arrays with bn_sub_words */
		if (bn_sub_words(wnum.d, wnum.d, tmp->d, div_n+1))
			{
			/* Note: As we have considered only the leading
			 * two BN_ULONGs in the calculation of q, sdiv * q
			 * might be greater than wnum (but then (q-1) * sdiv
			 * is less or equal than wnum)
			 */
			q--;
			if (bn_add_words(wnum.d, wnum.d, sdiv->d, div_n))
				/* we can't have an overflow here (assuming
				 * that q != 0, but if q == 0 then tmp is
				 * zero anyway) */
				(*wnump)++;
			}
		/* store part of the result */
		*resp = q;
		}
	bn_correct_top(snum);
	if (rm != NULL)
		{
		/* Keep a copy of the neg flag in num because if rm==num
		 * BN_rshift() will overwrite it.
		 */
		int neg = num->neg;
		BN_rshift(rm,snum,norm_shift);
		if (!BN_is_zero(rm))
			rm->neg = neg;
		bn_check_top(rm);
		}
	bn_correct_top(res);
	BN_CTX_end(ctx);
	return(1);
err:
	bn_check_top(rm);
	BN_CTX_end(ctx);
	return(0);
	}

#endif
Commit	Line	Data
d02b48c6	1	/* crypto/bn/bn_div.c */
58964a49	2	/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
d02b48c6 RE	3	* All rights reserved.
	4	*
	5	* This package is an SSL implementation written
	6	* by Eric Young (eay@cryptsoft.com).
	7	* The implementation was written so as to conform with Netscapes SSL.
	8	*
	9	* This library is free for commercial and non-commercial use as long as
	10	* the following conditions are aheared to. The following conditions
	11	* apply to all code found in this distribution, be it the RC4, RSA,
	12	* lhash, DES, etc., code; not just the SSL code. The SSL documentation
	13	* included with this distribution is covered by the same copyright terms
	14	* except that the holder is Tim Hudson (tjh@cryptsoft.com).
	15	*
	16	* Copyright remains Eric Young's, and as such any Copyright notices in
	17	* the code are not to be removed.
	18	* If this package is used in a product, Eric Young should be given attribution
	19	* as the author of the parts of the library used.
	20	* This can be in the form of a textual message at program startup or
	21	* in documentation (online or textual) provided with the package.
	22	*
	23	* Redistribution and use in source and binary forms, with or without
	24	* modification, are permitted provided that the following conditions
	25	* are met:
	26	* 1. Redistributions of source code must retain the copyright
	27	* notice, this list of conditions and the following disclaimer.
	28	* 2. Redistributions in binary form must reproduce the above copyright
	29	* notice, this list of conditions and the following disclaimer in the
	30	* documentation and/or other materials provided with the distribution.
	31	* 3. All advertising materials mentioning features or use of this software
	32	* must display the following acknowledgement:
	33	* "This product includes cryptographic software written by
	34	* Eric Young (eay@cryptsoft.com)"
	35	* The word 'cryptographic' can be left out if the rouines from the library
	36	* being used are not cryptographic related :-).
	37	* 4. If you include any Windows specific code (or a derivative thereof) from
	38	* the apps directory (application code) you must include an acknowledgement:
	39	* "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
	40	*
	41	* THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
	42	* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
	43	* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
	44	* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
	45	* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
	46	* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
	47	* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
	48	* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
	49	* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
	50	* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
	51	* SUCH DAMAGE.
	52	*
	53	* The licence and distribution terms for any publically available version or
	54	* derivative of this code cannot be changed. i.e. this code cannot simply be
	55	* copied and put under another distribution licence
	56	* [including the GNU Public Licence.]
	57	*/
	58
	59	#include <stdio.h>
84c15db5	60	#include <openssl/bn.h>
d02b48c6 RE	61	#include "cryptlib.h"
	62	#include "bn_lcl.h"
	63
78a0c1f1	64
d02b48c6	65	/* The old slow way */
4a6222d7	66	#if 0
0bde1089 UM	67	int BN_div(BIGNUM dv, BIGNUM rem, const BIGNUM m, const BIGNUM d,
0bde1089 UM	68	BN_CTX *ctx)
d02b48c6 RE	69	{
d02b48c6 RE	70	int i,nm,nd;
9b141126	71	int ret = 0;
d02b48c6 RE	72	BIGNUM *D;
d02b48c6 RE	73
dfeab068 RE	74	bn_check_top(m);
dfeab068 RE	75	bn_check_top(d);
d02b48c6 RE	76	if (BN_is_zero(d))
	77	{
	78	BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO);
	79	return(0);
	80	}
	81
	82	if (BN_ucmp(m,d) < 0)
	83	{
	84	if (rem != NULL)
	85	{ if (BN_copy(rem,m) == NULL) return(0); }
	86	if (dv != NULL) BN_zero(dv);
	87	return(1);
	88	}
	89
9b141126 UM	90	BN_CTX_start(ctx);
	91	D = BN_CTX_get(ctx);
	92	if (dv == NULL) dv = BN_CTX_get(ctx);
	93	if (rem == NULL) rem = BN_CTX_get(ctx);
	94	if (D == NULL \|\| dv == NULL \|\| rem == NULL)
	95	goto end;
d02b48c6 RE	96
	97	nd=BN_num_bits(d);
	98	nm=BN_num_bits(m);
9b141126 UM	99	if (BN_copy(D,d) == NULL) goto end;
9b141126 UM	100	if (BN_copy(rem,m) == NULL) goto end;
d02b48c6 RE	101
	102	/* The next 2 are needed so we can do a dv->d[0]\|=1 later
	103	* since BN_lshift1 will only work once there is a value :-) */
	104	BN_zero(dv);
dfeab068	105	bn_wexpand(dv,1);
d02b48c6 RE	106	dv->top=1;
d02b48c6 RE	107
9b141126	108	if (!BN_lshift(D,D,nm-nd)) goto end;
d02b48c6 RE	109	for (i=nm-nd; i>=0; i--)
d02b48c6 RE	110	{
9b141126	111	if (!BN_lshift1(dv,dv)) goto end;
d02b48c6 RE	112	if (BN_ucmp(rem,D) >= 0)
	113	{
	114	dv->d[0]\|=1;
9b141126	115	if (!BN_usub(rem,rem,D)) goto end;
d02b48c6 RE	116	}
d02b48c6 RE	117	/* CAN IMPROVE (and have now :=) */
9b141126	118	if (!BN_rshift1(D,D)) goto end;
d02b48c6 RE	119	}
	120	rem->neg=BN_is_zero(rem)?0:m->neg;
	121	dv->neg=m->neg^d->neg;
9b141126 UM	122	ret = 1;
	123	end:
	124	BN_CTX_end(ctx);
	125	return(ret);
d02b48c6 RE	126	}
	127
	128	#else
	129
cf1b7d96 RL	130	#if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM) \
cf1b7d96 RL	131	&& !defined(PEDANTIC) && !defined(BN_DIV3W)
4a6222d7	132	# if defined(__GNUC__) && __GNUC__>=2
5dd955dc	133	# if defined(__i386) \|\| defined (__i386__)
4a6222d7 UM	134	/*
	135	* There were two reasons for implementing this template:
	136	* - GNU C generates a call to a function (__udivdi3 to be exact)
	137	* in reply to ((((BN_ULLONG)n0)<<BN_BITS2)\|n1)/d0 (I fail to
	138	* understand why...);
	139	* - divl doesn't only calculate quotient, but also leaves
	140	* remainder in %edx which we can definitely use here:-)
	141	*
	142	* <appro@fy.chalmers.se>
	143	*/
	144	# define bn_div_words(n0,n1,d0) \
	145	({ asm volatile ( \
	146	"divl %4" \
	147	: "=a"(q), "=d"(rem) \
	148	: "a"(n1), "d"(n0), "g"(d0) \
	149	: "cc"); \
	150	q; \
	151	})
	152	# define REMAINDER_IS_ALREADY_CALCULATED
2f98abbc AP	153	# elif defined(__x86_64) && defined(SIXTY_FOUR_BIT_LONG)
	154	/*
	155	* Same story here, but it's 128-bit by 64-bit division. Wow!
	156	* <appro@fy.chalmers.se>
	157	*/
	158	# define bn_div_words(n0,n1,d0) \
	159	({ asm volatile ( \
	160	"divq %4" \
	161	: "=a"(q), "=d"(rem) \
	162	: "a"(n1), "d"(n0), "g"(d0) \
	163	: "cc"); \
	164	q; \
	165	})
	166	# define REMAINDER_IS_ALREADY_CALCULATED
4a6222d7 UM	167	# endif /* __<cpu> */
4a6222d7 UM	168	# endif /* __GNUC__ */
cf1b7d96	169	#endif /* OPENSSL_NO_ASM */
4a6222d7	170
78a0c1f1	171
55525742 AP	172	/* BN_div[_no_branch] computes dv := num / divisor, rounding towards
55525742 AP	173	* zero, and sets up rm such that dv*divisor + rm = num holds.
78a0c1f1 BM	174	* Thus:
	175	* dv->neg == num->neg ^ divisor->neg (unless the result is zero)
	176	* rm->neg == num->neg (unless the remainder is zero)
	177	* If 'dv' or 'rm' is NULL, the respective value is not returned.
	178	*/
55525742 AP	179	static int BN_div_no_branch(BIGNUM dv, BIGNUM rm, const BIGNUM *num,
55525742 AP	180	const BIGNUM divisor, BN_CTX ctx);
84c15db5 BL	181	int BN_div(BIGNUM dv, BIGNUM rm, const BIGNUM num, const BIGNUM divisor,
84c15db5 BL	182	BN_CTX *ctx)
d02b48c6	183	{
4d6e1e4f BL	184	int norm_shift,i;
4d6e1e4f BL	185	size_t loop;
d02b48c6 RE	186	BIGNUM tmp,wnum,snum,sdiv,res;
	187	BN_ULONG resp,wnump;
	188	BN_ULONG d0,d1;
4d6e1e4f	189	size_t num_n,div_n;
d02b48c6	190
f8d6be3f BM	191	/* Invalid zero-padding would have particularly bad consequences
	192	* in the case of 'num', so don't just rely on bn_check_top() for this one
	193	* (bn_check_top() works only for BN_DEBUG builds) */
	194	if (num->top > 0 && num->d[num->top - 1] == 0)
	195	{
	196	BNerr(BN_F_BN_DIV,BN_R_NOT_INITIALIZED);
	197	return 0;
	198	}
	199
	200	bn_check_top(num);
	201
b002265e	202	if ((BN_get_flags(num, BN_FLG_CONSTTIME) != 0) \|\| (BN_get_flags(divisor, BN_FLG_CONSTTIME) != 0))
bd31fb21 BM	203	{
	204	return BN_div_no_branch(dv, rm, num, divisor, ctx);
	205	}
	206
8215e7a9 NL	207	bn_check_top(dv);
8215e7a9 NL	208	bn_check_top(rm);
f8d6be3f	209	/* bn_check_top(num); / / 'num' has been checked already */
dfeab068 RE	210	bn_check_top(divisor);
dfeab068 RE	211
58964a49	212	if (BN_is_zero(divisor))
d02b48c6 RE	213	{
	214	BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO);
	215	return(0);
	216	}
	217
	218	if (BN_ucmp(num,divisor) < 0)
	219	{
	220	if (rm != NULL)
	221	{ if (BN_copy(rm,num) == NULL) return(0); }
	222	if (dv != NULL) BN_zero(dv);
	223	return(1);
	224	}
	225
9b141126 UM	226	BN_CTX_start(ctx);
9b141126 UM	227	tmp=BN_CTX_get(ctx);
9b141126 UM	228	snum=BN_CTX_get(ctx);
9b141126 UM	229	sdiv=BN_CTX_get(ctx);
d02b48c6	230	if (dv == NULL)
9b141126	231	res=BN_CTX_get(ctx);
d02b48c6	232	else res=dv;
7f7b8d68	233	if (sdiv == NULL \|\| res == NULL) goto err;
d02b48c6 RE	234
	235	/* First we normalise the numbers */
	236	norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2);
9cdf87f1	237	if (!(BN_lshift(sdiv,divisor,norm_shift))) goto err;
d02b48c6 RE	238	sdiv->neg=0;
d02b48c6 RE	239	norm_shift+=BN_BITS2;
9cdf87f1	240	if (!(BN_lshift(snum,num,norm_shift))) goto err;
d02b48c6 RE	241	snum->neg=0;
	242	div_n=sdiv->top;
	243	num_n=snum->top;
	244	loop=num_n-div_n;
d02b48c6 RE	245	/* Lets setup a 'window' into snum
	246	* This is the part that corresponds to the current
	247	* 'area' being divided */
9e989810 GT	248	wnum.neg = 0;
	249	wnum.d = &(snum->d[loop]);
	250	wnum.top = div_n;
9e989810 GT	251	/* only needed when BN_ucmp messes up the values between top and max */
9e989810 GT	252	wnum.dmax = snum->dmax - loop; /* so we don't step out of bounds */
d02b48c6 RE	253
d02b48c6 RE	254	/* Get the top 2 words of sdiv */
5c0c2280	255	/* div_n=sdiv->top; */
d02b48c6 RE	256	d0=sdiv->d[div_n-1];
	257	d1=(div_n == 1)?0:sdiv->d[div_n-2];
	258
	259	/* pointer to the 'top' of snum */
	260	wnump= &(snum->d[num_n-1]);
	261
	262	/* Setup to 'res' */
	263	res->neg= (num->neg^divisor->neg);
58964a49	264	if (!bn_wexpand(res,(loop+1))) goto err;
dfeab068	265	res->top=loop;
d02b48c6 RE	266	resp= &(res->d[loop-1]);
	267
	268	/* space for temp */
4d6e1e4f	269	if (!bn_wexpand(tmp, div_n+1)) goto err;
d02b48c6 RE	270
	271	if (BN_ucmp(&wnum,sdiv) >= 0)
	272	{
9e989810 GT	273	/* If BN_DEBUG_RAND is defined BN_ucmp changes (via
	274	* bn_pollute) the const bignum arguments =>
	275	* clean the values between top and max again */
	276	bn_clear_top2max(&wnum);
9e989810	277	bn_sub_words(wnum.d, wnum.d, sdiv->d, div_n);
d02b48c6	278	*resp=1;
d02b48c6 RE	279	}
	280	else
	281	res->top--;
9e989810 GT	282	/* if res->top == 0 then clear the neg value otherwise decrease
9e989810 GT	283	* the resp pointer */
80d89e6a BM	284	if (res->top == 0)
80d89e6a BM	285	res->neg = 0;
bd31fb21 BM	286	else
	287	resp--;
	288
	289	for (i=0; i<loop-1; i++, wnump--, resp--)
	290	{
	291	BN_ULONG q,l0;
	292	/* the first part of the loop uses the top two words of
	293	* snum and sdiv to calculate a BN_ULONG q such that
	294	* \| wnum - sdiv * q \| < sdiv */
	295	#if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM)
	296	BN_ULONG bn_div_3_words(BN_ULONG*,BN_ULONG,BN_ULONG);
	297	q=bn_div_3_words(wnump,d1,d0);
	298	#else
	299	BN_ULONG n0,n1,rem=0;
	300
	301	n0=wnump[0];
	302	n1=wnump[-1];
	303	if (n0 == d0)
	304	q=BN_MASK2;
	305	else /* n0 < d0 */
	306	{
	307	#ifdef BN_LLONG
	308	BN_ULLONG t2;
	309
	310	#if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
	311	q=(BN_ULONG)(((((BN_ULLONG)n0)<<BN_BITS2)\|n1)/d0);
	312	#else
	313	q=bn_div_words(n0,n1,d0);
	314	#ifdef BN_DEBUG_LEVITTE
	315	fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
	316	X) -> 0x%08X\n",
	317	n0, n1, d0, q);
	318	#endif
	319	#endif
	320
	321	#ifndef REMAINDER_IS_ALREADY_CALCULATED
	322	/*
	323	* rem doesn't have to be BN_ULLONG. The least we
	324	* know it's less that d0, isn't it?
	325	*/
	326	rem=(n1-q*d0)&BN_MASK2;
	327	#endif
	328	t2=(BN_ULLONG)d1*q;
	329
	330	for (;;)
	331	{
	332	if (t2 <= ((((BN_ULLONG)rem)<<BN_BITS2)\|wnump[-2]))
	333	break;
	334	q--;
	335	rem += d0;
	336	if (rem < d0) break; /* don't let rem overflow */
	337	t2 -= d1;
	338	}
	339	#else /* !BN_LLONG */
56c7754c	340	BN_ULONG t2l,t2h;
bd31fb21 BM	341
	342	q=bn_div_words(n0,n1,d0);
	343	#ifdef BN_DEBUG_LEVITTE
	344	fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
	345	X) -> 0x%08X\n",
	346	n0, n1, d0, q);
	347	#endif
	348	#ifndef REMAINDER_IS_ALREADY_CALCULATED
	349	rem=(n1-q*d0)&BN_MASK2;
	350	#endif
	351
	352	#if defined(BN_UMULT_LOHI)
	353	BN_UMULT_LOHI(t2l,t2h,d1,q);
	354	#elif defined(BN_UMULT_HIGH)
	355	t2l = d1 * q;
	356	t2h = BN_UMULT_HIGH(d1,q);
	357	#else
56c7754c DSH	358	{
56c7754c DSH	359	BN_ULONG ql, qh;
bd31fb21 BM	360	t2l=LBITS(d1); t2h=HBITS(d1);
	361	ql =LBITS(q); qh =HBITS(q);
	362	mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1q; /
56c7754c	363	}
bd31fb21 BM	364	#endif
	365
	366	for (;;)
	367	{
	368	if ((t2h < rem) \|\|
	369	((t2h == rem) && (t2l <= wnump[-2])))
	370	break;
	371	q--;
	372	rem += d0;
	373	if (rem < d0) break; /* don't let rem overflow */
	374	if (t2l < d1) t2h--; t2l -= d1;
	375	}
	376	#endif /* !BN_LLONG */
	377	}
	378	#endif /* !BN_DIV3W */
	379
	380	l0=bn_mul_words(tmp->d,sdiv->d,div_n,q);
	381	tmp->d[div_n]=l0;
	382	wnum.d--;
	383	/* ingore top values of the bignums just sub the two
	384	* BN_ULONG arrays with bn_sub_words */
	385	if (bn_sub_words(wnum.d, wnum.d, tmp->d, div_n+1))
	386	{
	387	/* Note: As we have considered only the leading
	388	* two BN_ULONGs in the calculation of q, sdiv * q
	389	* might be greater than wnum (but then (q-1) * sdiv
	390	* is less or equal than wnum)
	391	*/
	392	q--;
	393	if (bn_add_words(wnum.d, wnum.d, sdiv->d, div_n))
	394	/* we can't have an overflow here (assuming
	395	* that q != 0, but if q == 0 then tmp is
	396	* zero anyway) */
	397	(*wnump)++;
	398	}
	399	/* store part of the result */
	400	*resp = q;
	401	}
	402	bn_correct_top(snum);
	403	if (rm != NULL)
	404	{
	405	/* Keep a copy of the neg flag in num because if rm==num
	406	* BN_rshift() will overwrite it.
	407	*/
	408	int neg = num->neg;
	409	BN_rshift(rm,snum,norm_shift);
	410	if (!BN_is_zero(rm))
	411	rm->neg = neg;
	412	bn_check_top(rm);
	413	}
	414	BN_CTX_end(ctx);
	415	return(1);
	416	err:
	417	bn_check_top(rm);
	418	BN_CTX_end(ctx);
	419	return(0);
	420	}
	421
	422
	423	/* BN_div_no_branch is a special version of BN_div. It does not contain
	424	* branches that may leak sensitive information.
	425	*/
55525742	426	static int BN_div_no_branch(BIGNUM dv, BIGNUM rm, const BIGNUM *num,
bd31fb21 BM	427	const BIGNUM divisor, BN_CTX ctx)
	428	{
	429	int norm_shift,i,loop;
	430	BIGNUM tmp,wnum,snum,sdiv,res;
	431	BN_ULONG resp,wnump;
	432	BN_ULONG d0,d1;
4d6e1e4f	433	size_t num_n,div_n;
bd31fb21 BM	434
	435	bn_check_top(dv);
	436	bn_check_top(rm);
f8d6be3f	437	/* bn_check_top(num); / / 'num' has been checked in BN_div() */
bd31fb21 BM	438	bn_check_top(divisor);
	439
	440	if (BN_is_zero(divisor))
	441	{
24a8c25a	442	BNerr(BN_F_BN_DIV_NO_BRANCH,BN_R_DIV_BY_ZERO);
bd31fb21 BM	443	return(0);
	444	}
	445
	446	BN_CTX_start(ctx);
	447	tmp=BN_CTX_get(ctx);
	448	snum=BN_CTX_get(ctx);
	449	sdiv=BN_CTX_get(ctx);
	450	if (dv == NULL)
	451	res=BN_CTX_get(ctx);
	452	else res=dv;
	453	if (sdiv == NULL \|\| res == NULL) goto err;
	454
	455	/* First we normalise the numbers */
	456	norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2);
	457	if (!(BN_lshift(sdiv,divisor,norm_shift))) goto err;
	458	sdiv->neg=0;
	459	norm_shift+=BN_BITS2;
	460	if (!(BN_lshift(snum,num,norm_shift))) goto err;
	461	snum->neg=0;
	462
	463	/* Since we don't know whether snum is larger than sdiv,
	464	* we pad snum with enough zeroes without changing its
	465	* value.
	466	*/
	467	if (snum->top <= sdiv->top+1)
	468	{
	469	if (bn_wexpand(snum, sdiv->top + 2) == NULL) goto err;
	470	for (i = snum->top; i < sdiv->top + 2; i++) snum->d[i] = 0;
	471	snum->top = sdiv->top + 2;
	472	}
	473	else
	474	{
	475	if (bn_wexpand(snum, snum->top + 1) == NULL) goto err;
	476	snum->d[snum->top] = 0;
	477	snum->top ++;
	478	}
	479
	480	div_n=sdiv->top;
	481	num_n=snum->top;
	482	loop=num_n-div_n;
	483	/* Lets setup a 'window' into snum
	484	* This is the part that corresponds to the current
	485	* 'area' being divided */
	486	wnum.neg = 0;
	487	wnum.d = &(snum->d[loop]);
	488	wnum.top = div_n;
	489	/* only needed when BN_ucmp messes up the values between top and max */
	490	wnum.dmax = snum->dmax - loop; /* so we don't step out of bounds */
	491
	492	/* Get the top 2 words of sdiv */
	493	/* div_n=sdiv->top; */
	494	d0=sdiv->d[div_n-1];
	495	d1=(div_n == 1)?0:sdiv->d[div_n-2];
	496
	497	/* pointer to the 'top' of snum */
	498	wnump= &(snum->d[num_n-1]);
	499
	500	/* Setup to 'res' */
	501	res->neg= (num->neg^divisor->neg);
4d6e1e4f	502	if (!bn_wexpand(res,loop+1U)) goto err;
bd31fb21 BM	503	res->top=loop-1;
	504	resp= &(res->d[loop-1]);
	505
	506	/* space for temp */
4d6e1e4f	507	if (!bn_wexpand(tmp,div_n+1U)) goto err;
bd31fb21 BM	508
	509	/* if res->top == 0 then clear the neg value otherwise decrease
	510	* the resp pointer */
	511	if (res->top == 0)
	512	res->neg = 0;
9e989810 GT	513	else
9e989810 GT	514	resp--;
d02b48c6	515
9e989810	516	for (i=0; i<loop-1; i++, wnump--, resp--)
d02b48c6	517	{
0dd25e36	518	BN_ULONG q,l0;
9e989810 GT	519	/* the first part of the loop uses the top two words of
	520	* snum and sdiv to calculate a BN_ULONG q such that
	521	* \| wnum - sdiv * q \| < sdiv */
cf1b7d96	522	#if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM)
500230ee	523	BN_ULONG bn_div_3_words(BN_ULONG*,BN_ULONG,BN_ULONG);
0bbd0352	524	q=bn_div_3_words(wnump,d1,d0);
0dd25e36	525	#else
4c22909e	526	BN_ULONG n0,n1,rem=0;
d02b48c6	527
d02b48c6 RE	528	n0=wnump[0];
	529	n1=wnump[-1];
	530	if (n0 == d0)
	531	q=BN_MASK2;
4a6222d7 UM	532	else /* n0 < d0 */
	533	{
	534	#ifdef BN_LLONG
	535	BN_ULLONG t2;
	536
4c22909e	537	#if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
8e1589ec	538	q=(BN_ULONG)(((((BN_ULLONG)n0)<<BN_BITS2)\|n1)/d0);
0dd25e36	539	#else
dfeab068	540	q=bn_div_words(n0,n1,d0);
3c801fa4 RL	541	#ifdef BN_DEBUG_LEVITTE
	542	fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
	543	X) -> 0x%08X\n",
	544	n0, n1, d0, q);
	545	#endif
0dd25e36	546	#endif
0dd25e36	547
fe7cd164	548	#ifndef REMAINDER_IS_ALREADY_CALCULATED
4a6222d7 UM	549	/*
	550	* rem doesn't have to be BN_ULLONG. The least we
	551	* know it's less that d0, isn't it?
	552	*/
	553	rem=(n1-q*d0)&BN_MASK2;
4c22909e	554	#endif
4a6222d7 UM	555	t2=(BN_ULLONG)d1*q;
	556
	557	for (;;)
	558	{
	559	if (t2 <= ((((BN_ULLONG)rem)<<BN_BITS2)\|wnump[-2]))
	560	break;
	561	q--;
	562	rem += d0;
	563	if (rem < d0) break; /* don't let rem overflow */
	564	t2 -= d1;
	565	}
	566	#else /* !BN_LLONG */
56c7754c	567	BN_ULONG t2l,t2h;
0dd25e36	568
4a6222d7	569	q=bn_div_words(n0,n1,d0);
3c801fa4 RL	570	#ifdef BN_DEBUG_LEVITTE
	571	fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
	572	X) -> 0x%08X\n",
	573	n0, n1, d0, q);
	574	#endif
fe7cd164	575	#ifndef REMAINDER_IS_ALREADY_CALCULATED
4a6222d7	576	rem=(n1-q*d0)&BN_MASK2;
4c22909e	577	#endif
4a6222d7	578
2f98abbc AP	579	#if defined(BN_UMULT_LOHI)
	580	BN_UMULT_LOHI(t2l,t2h,d1,q);
	581	#elif defined(BN_UMULT_HIGH)
4a6222d7 UM	582	t2l = d1 * q;
4a6222d7 UM	583	t2h = BN_UMULT_HIGH(d1,q);
fb81ac5e	584	#else
56c7754c DSH	585	{
56c7754c DSH	586	BN_ULONG ql, qh;
4a6222d7 UM	587	t2l=LBITS(d1); t2h=HBITS(d1);
	588	ql =LBITS(q); qh =HBITS(q);
	589	mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1q; /
56c7754c	590	}
fb81ac5e	591	#endif
0dd25e36	592
4a6222d7 UM	593	for (;;)
	594	{
	595	if ((t2h < rem) \|\|
	596	((t2h == rem) && (t2l <= wnump[-2])))
	597	break;
	598	q--;
	599	rem += d0;
	600	if (rem < d0) break; /* don't let rem overflow */
	601	if (t2l < d1) t2h--; t2l -= d1;
	602	}
	603	#endif /* !BN_LLONG */
d02b48c6	604	}
4c22909e	605	#endif /* !BN_DIV3W */
4a6222d7	606
58964a49	607	l0=bn_mul_words(tmp->d,sdiv->d,div_n,q);
d02b48c6	608	tmp->d[div_n]=l0;
9e989810 GT	609	wnum.d--;
	610	/* ingore top values of the bignums just sub the two
	611	* BN_ULONG arrays with bn_sub_words */
	612	if (bn_sub_words(wnum.d, wnum.d, tmp->d, div_n+1))
d02b48c6	613	{
9e989810 GT	614	/* Note: As we have considered only the leading
	615	* two BN_ULONGs in the calculation of q, sdiv * q
	616	* might be greater than wnum (but then (q-1) * sdiv
	617	* is less or equal than wnum)
	618	*/
d02b48c6	619	q--;
9e989810 GT	620	if (bn_add_words(wnum.d, wnum.d, sdiv->d, div_n))
	621	/* we can't have an overflow here (assuming
	622	* that q != 0, but if q == 0 then tmp is
	623	* zero anyway) */
	624	(*wnump)++;
d02b48c6	625	}
9e989810 GT	626	/* store part of the result */
9e989810 GT	627	*resp = q;
d02b48c6	628	}
a8aa764d	629	bn_correct_top(snum);
d02b48c6 RE	630	if (rm != NULL)
d02b48c6 RE	631	{
3d2e469c DSH	632	/* Keep a copy of the neg flag in num because if rm==num
	633	* BN_rshift() will overwrite it.
	634	*/
	635	int neg = num->neg;
d02b48c6	636	BN_rshift(rm,snum,norm_shift);
78a0c1f1	637	if (!BN_is_zero(rm))
3d2e469c	638	rm->neg = neg;
d870740c	639	bn_check_top(rm);
d02b48c6	640	}
d1e7d1d9	641	bn_correct_top(res);
9b141126	642	BN_CTX_end(ctx);
d02b48c6 RE	643	return(1);
d02b48c6 RE	644	err:
8215e7a9	645	bn_check_top(rm);
4a6222d7	646	BN_CTX_end(ctx);
d02b48c6 RE	647	return(0);
	648	}
	649
	650	#endif