/* 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

 #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_correct_top(res);

 	BN_CTX_end(ctx);

 	return(1);

 err:

 	bn_check_top(rm);

 	BN_CTX_end(ctx);

 	return(0);

 	}

 #endif