/* 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

EXPORT_C 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);

EXPORT_C int BN_div(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;

	int num_n,div_n;

	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);

	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,ql,qh;

			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

			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;

	int num_n,div_n;

	bn_check_top(dv);

	bn_check_top(rm);

	bn_check_top(num);

	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+1))) goto err;

	res->top=loop-1;

	resp= &(res->d[loop-1]);

	/* space for temp */

	if (!bn_wexpand(tmp,(div_n+1))) 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