path: root/lib/libcrypto/bn/bn_div.c

/* $OpenBSD: bn_div.c,v 1.25 2017/01/29 17:49:22 beck Exp $ */
/* 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/opensslconf.h>

#include <openssl/bn.h>
#include <openssl/err.h>

#include "bn_lcl.h"

#if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM) \
    && !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>
    */
#undef bn_div_words
#  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)
   /*
    * Same story here, but it's 128-bit by 64-bit division. Wow!
    *					<appro@fy.chalmers.se>
    */
#  undef bn_div_words
#  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 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_internal(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor,
    BN_CTX *ctx, int ct)
{
	int norm_shift, i, loop;
	BIGNUM *tmp, wnum, *snum, *sdiv, *res;
	BN_ULONG *resp, *wnump;
	BN_ULONG d0, d1;
	int num_n, div_n;
	int no_branch = 0;

	/* 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) {
		BNerror(BN_R_NOT_INITIALIZED);
		return 0;
	}

	bn_check_top(num);

	if (ct)
		no_branch = 1;

	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)) {
		BNerror(BN_R_DIV_BY_ZERO);
		return (0);
	}

	if (!no_branch && 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 (tmp == NULL || snum == NULL || 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;

	if (no_branch) {
		/* 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 */
	wnum.flags = snum->flags | BN_FLG_STATIC_DATA;

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

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

	if (!no_branch) {
		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_DIV2W) && !defined(bn_div_words)
			q = (BN_ULONG)(((((BN_ULLONG)n0) << BN_BITS2)|n1)/d0);
#else
			q = bn_div_words(n0, n1, d0);
#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);
#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);
	}
	if (no_branch)
		bn_correct_top(res);
	BN_CTX_end(ctx);
	return (1);

err:
	bn_check_top(rm);
	BN_CTX_end(ctx);
	return (0);
}

int
BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor,
    BN_CTX *ctx)
{
	int ct = ((BN_get_flags(num, BN_FLG_CONSTTIME) != 0) ||
	    (BN_get_flags(divisor, BN_FLG_CONSTTIME) != 0));

	return BN_div_internal(dv, rm, num, divisor, ctx, ct);
}

int
BN_div_nonct(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor,
    BN_CTX *ctx)
{
	return BN_div_internal(dv, rm, num, divisor, ctx, 0);
}

int
BN_div_ct(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor,
    BN_CTX *ctx)
{
	return BN_div_internal(dv, rm, num, divisor, ctx, 1);
}