lib/mpi/mpi-div.c - kernel/msm - Gitiles

 /* mpi-div.c  -  MPI functions
  *	Copyright (C) 1994, 1996 Free Software Foundation, Inc.
  *	Copyright (C) 1998, 1999, 2000, 2001 Free Software Foundation, Inc.
  *
  * This file is part of GnuPG.
  *
  * GnuPG is free software; you can redistribute it and/or modify
  * it under the terms of the GNU General Public License as published by
  * the Free Software Foundation; either version 2 of the License, or
  * (at your option) any later version.
  *
  * GnuPG is distributed in the hope that it will be useful,
  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  * GNU General Public License for more details.
  *
  * You should have received a copy of the GNU General Public License
  * along with this program; if not, write to the Free Software
  * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
  *
  * Note: This code is heavily based on the GNU MP Library.
  *	 Actually it's the same code with only minor changes in the
  *	 way the data is stored; this is to support the abstraction
  *	 of an optional secure memory allocation which may be used
  *	 to avoid revealing of sensitive data due to paging etc.
  *	 The GNU MP Library itself is published under the LGPL;
  *	 however I decided to publish this code under the plain GPL.
  */

 #include <linux/string.h>
 #include "mpi-internal.h"
 #include "longlong.h"

 int mpi_fdiv_r(MPI rem, MPI dividend, MPI divisor)
 {
 	int rc = -ENOMEM;
 	int divisor_sign = divisor->sign;
 	MPI temp_divisor = NULL;

 	/* We need the original value of the divisor after the remainder has been
 	 * preliminary calculated.      We have to copy it to temporary space if it's
 	 * the same variable as REM.  */
 	if (rem == divisor) {
 		if (mpi_copy(&temp_divisor, divisor) < 0)
 			goto nomem;
 		divisor = temp_divisor;
 	}

 	if (mpi_tdiv_qr(NULL, rem, dividend, divisor) < 0)
 		goto nomem;
 	if (((divisor_sign ? 1 : 0) ^ (dividend->sign ? 1 : 0)) && rem->nlimbs)
 		if (mpi_add(rem, rem, divisor) < 0)
 			goto nomem;

 	rc = 0;

 nomem:
 	if (temp_divisor)
 		mpi_free(temp_divisor);
 	return rc;
 }

 /****************
  * Division rounding the quotient towards -infinity.
  * The remainder gets the same sign as the denominator.
  * rem is optional
  */

 ulong mpi_fdiv_r_ui(MPI rem, MPI dividend, ulong divisor)
 {
 	mpi_limb_t rlimb;

 	rlimb = mpihelp_mod_1(dividend->d, dividend->nlimbs, divisor);
 	if (rlimb && dividend->sign)
 		rlimb = divisor - rlimb;

 	if (rem) {
 		rem->d[0] = rlimb;
 		rem->nlimbs = rlimb ? 1 : 0;
 	}
 	return rlimb;
 }

 int mpi_fdiv_q(MPI quot, MPI dividend, MPI divisor)
 {
 	MPI tmp = mpi_alloc(mpi_get_nlimbs(quot));
 	if (!tmp)
 		return -ENOMEM;
 	mpi_fdiv_qr(quot, tmp, dividend, divisor);
 	mpi_free(tmp);
 	return 0;
 }

 int mpi_fdiv_qr(MPI quot, MPI rem, MPI dividend, MPI divisor)
 {
 	int divisor_sign = divisor->sign;
 	MPI temp_divisor = NULL;

 	if (quot == divisor || rem == divisor) {
 		if (mpi_copy(&temp_divisor, divisor) < 0)
 			return -ENOMEM;
 		divisor = temp_divisor;
 	}

 	if (mpi_tdiv_qr(quot, rem, dividend, divisor) < 0)
 		goto nomem;

 	if ((divisor_sign ^ dividend->sign) && rem->nlimbs) {
 		if (mpi_sub_ui(quot, quot, 1) < 0)
 			goto nomem;
 		if (mpi_add(rem, rem, divisor) < 0)
 			goto nomem;
 	}

 	if (temp_divisor)
 		mpi_free(temp_divisor);

 	return 0;

 nomem:
 	mpi_free(temp_divisor);
 	return -ENOMEM;
 }

 /* If den == quot, den needs temporary storage.
  * If den == rem, den needs temporary storage.
  * If num == quot, num needs temporary storage.
  * If den has temporary storage, it can be normalized while being copied,
  *   i.e no extra storage should be allocated.
  */

 int mpi_tdiv_r(MPI rem, MPI num, MPI den)
 {
 	return mpi_tdiv_qr(NULL, rem, num, den);
 }

 int mpi_tdiv_qr(MPI quot, MPI rem, MPI num, MPI den)
 {
 	int rc = -ENOMEM;
 	mpi_ptr_t np, dp;
 	mpi_ptr_t qp, rp;
 	mpi_size_t nsize = num->nlimbs;
 	mpi_size_t dsize = den->nlimbs;
 	mpi_size_t qsize, rsize;
 	mpi_size_t sign_remainder = num->sign;
 	mpi_size_t sign_quotient = num->sign ^ den->sign;
 	unsigned normalization_steps;
 	mpi_limb_t q_limb;
 	mpi_ptr_t marker[5];
 	int markidx = 0;

 	if (!dsize)
 		return -EINVAL;

 	memset(marker, 0, sizeof(marker));

 	/* Ensure space is enough for quotient and remainder.
 	 * We need space for an extra limb in the remainder, because it's
 	 * up-shifted (normalized) below.  */
 	rsize = nsize + 1;
 	if (mpi_resize(rem, rsize) < 0)
 		goto nomem;

 	qsize = rsize - dsize;	/* qsize cannot be bigger than this.  */
 	if (qsize <= 0) {
 		if (num != rem) {
 			rem->nlimbs = num->nlimbs;
 			rem->sign = num->sign;
 			MPN_COPY(rem->d, num->d, nsize);
 		}
 		if (quot) {
 			/* This needs to follow the assignment to rem, in case the
 			 * numerator and quotient are the same.  */
 			quot->nlimbs = 0;
 			quot->sign = 0;
 		}
 		return 0;
 	}

 	if (quot)
 		if (mpi_resize(quot, qsize) < 0)
 			goto nomem;

 	/* Read pointers here, when reallocation is finished.  */
 	np = num->d;
 	dp = den->d;
 	rp = rem->d;

 	/* Optimize division by a single-limb divisor.  */
 	if (dsize == 1) {
 		mpi_limb_t rlimb;
 		if (quot) {
 			qp = quot->d;
 			rlimb = mpihelp_divmod_1(qp, np, nsize, dp[0]);
 			qsize -= qp[qsize - 1] == 0;
 			quot->nlimbs = qsize;
 			quot->sign = sign_quotient;
 		} else
 			rlimb = mpihelp_mod_1(np, nsize, dp[0]);
 		rp[0] = rlimb;
 		rsize = rlimb != 0 ? 1 : 0;
 		rem->nlimbs = rsize;
 		rem->sign = sign_remainder;
 		return 0;
 	}

 	if (quot) {
 		qp = quot->d;
 		/* Make sure QP and NP point to different objects.  Otherwise the
 		 * numerator would be gradually overwritten by the quotient limbs.  */
 		if (qp == np) {	/* Copy NP object to temporary space.  */
 			np = marker[markidx++] = mpi_alloc_limb_space(nsize);
 			if (!np)
 				goto nomem;
 			MPN_COPY(np, qp, nsize);
 		}
 	} else			/* Put quotient at top of remainder. */
 		qp = rp + dsize;

 	count_leading_zeros(normalization_steps, dp[dsize - 1]);

 	/* Normalize the denominator, i.e. make its most significant bit set by
 	 * shifting it NORMALIZATION_STEPS bits to the left.  Also shift the
 	 * numerator the same number of steps (to keep the quotient the same!).
 	 */
 	if (normalization_steps) {
 		mpi_ptr_t tp;
 		mpi_limb_t nlimb;

 		/* Shift up the denominator setting the most significant bit of
 		 * the most significant word.  Use temporary storage not to clobber
 		 * the original contents of the denominator.  */
 		tp = marker[markidx++] = mpi_alloc_limb_space(dsize);
 		if (!tp)
 			goto nomem;
 		mpihelp_lshift(tp, dp, dsize, normalization_steps);
 		dp = tp;

 		/* Shift up the numerator, possibly introducing a new most
 		 * significant word.  Move the shifted numerator in the remainder
 		 * meanwhile.  */
 		nlimb = mpihelp_lshift(rp, np, nsize, normalization_steps);
 		if (nlimb) {
 			rp[nsize] = nlimb;
 			rsize = nsize + 1;
 		} else
 			rsize = nsize;
 	} else {
 		/* The denominator is already normalized, as required.  Copy it to
 		 * temporary space if it overlaps with the quotient or remainder.  */
 		if (dp == rp || (quot && (dp == qp))) {
 			mpi_ptr_t tp;

 			tp = marker[markidx++] = mpi_alloc_limb_space(dsize);
 			if (!tp)
 				goto nomem;
 			MPN_COPY(tp, dp, dsize);
 			dp = tp;
 		}

 		/* Move the numerator to the remainder.  */
 		if (rp != np)
 			MPN_COPY(rp, np, nsize);

 		rsize = nsize;
 	}

 	q_limb = mpihelp_divrem(qp, 0, rp, rsize, dp, dsize);

 	if (quot) {
 		qsize = rsize - dsize;
 		if (q_limb) {
 			qp[qsize] = q_limb;
 			qsize += 1;
 		}

 		quot->nlimbs = qsize;
 		quot->sign = sign_quotient;
 	}

 	rsize = dsize;
 	MPN_NORMALIZE(rp, rsize);

 	if (normalization_steps && rsize) {
 		mpihelp_rshift(rp, rp, rsize, normalization_steps);
 		rsize -= rp[rsize - 1] == 0 ? 1 : 0;
 	}

 	rem->nlimbs = rsize;
 	rem->sign = sign_remainder;

 	rc = 0;
 nomem:
 	while (markidx)
 		mpi_free_limb_space(marker[--markidx]);
 	return rc;
 }

 int mpi_tdiv_q_2exp(MPI w, MPI u, unsigned count)
 {
 	mpi_size_t usize, wsize;
 	mpi_size_t limb_cnt;

 	usize = u->nlimbs;
 	limb_cnt = count / BITS_PER_MPI_LIMB;
 	wsize = usize - limb_cnt;
 	if (limb_cnt >= usize)
 		w->nlimbs = 0;
 	else {
 		mpi_ptr_t wp;
 		mpi_ptr_t up;

 		if (RESIZE_IF_NEEDED(w, wsize) < 0)
 			return -ENOMEM;
 		wp = w->d;
 		up = u->d;

 		count %= BITS_PER_MPI_LIMB;
 		if (count) {
 			mpihelp_rshift(wp, up + limb_cnt, wsize, count);
 			wsize -= !wp[wsize - 1];
 		} else {
 			MPN_COPY_INCR(wp, up + limb_cnt, wsize);
 		}

 		w->nlimbs = wsize;
 	}
 	return 0;
 }

 /****************
  * Check whether dividend is divisible by divisor
  * (note: divisor must fit into a limb)
  */
 int mpi_divisible_ui(MPI dividend, ulong divisor)
 {
 	return !mpihelp_mod_1(dividend->d, dividend->nlimbs, divisor);
 }
	/* mpi-div.c - MPI functions
	* Copyright (C) 1994, 1996 Free Software Foundation, Inc.
	* Copyright (C) 1998, 1999, 2000, 2001 Free Software Foundation, Inc.
	*
	* This file is part of GnuPG.
	*
	* GnuPG is free software; you can redistribute it and/or modify
	* it under the terms of the GNU General Public License as published by
	* the Free Software Foundation; either version 2 of the License, or
	* (at your option) any later version.
	*
	* GnuPG is distributed in the hope that it will be useful,
	* but WITHOUT ANY WARRANTY; without even the implied warranty of
	* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
	* GNU General Public License for more details.
	*
	* You should have received a copy of the GNU General Public License
	* along with this program; if not, write to the Free Software
	* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
	*
	* Note: This code is heavily based on the GNU MP Library.
	* Actually it's the same code with only minor changes in the
	* way the data is stored; this is to support the abstraction
	* of an optional secure memory allocation which may be used
	* to avoid revealing of sensitive data due to paging etc.
	* The GNU MP Library itself is published under the LGPL;
	* however I decided to publish this code under the plain GPL.
	*/

	#include <linux/string.h>
	#include "mpi-internal.h"
	#include "longlong.h"

	int mpi_fdiv_r(MPI rem, MPI dividend, MPI divisor)
	{
	int rc = -ENOMEM;
	int divisor_sign = divisor->sign;
	MPI temp_divisor = NULL;

	/* We need the original value of the divisor after the remainder has been
	* preliminary calculated. We have to copy it to temporary space if it's
	* the same variable as REM. */
	if (rem == divisor) {
	if (mpi_copy(&temp_divisor, divisor) < 0)
	goto nomem;
	divisor = temp_divisor;
	}

	if (mpi_tdiv_qr(NULL, rem, dividend, divisor) < 0)
	goto nomem;
	if (((divisor_sign ? 1 : 0) ^ (dividend->sign ? 1 : 0)) && rem->nlimbs)
	if (mpi_add(rem, rem, divisor) < 0)
	goto nomem;

	rc = 0;

	nomem:
	if (temp_divisor)
	mpi_free(temp_divisor);
	return rc;
	}

	/****************
	* Division rounding the quotient towards -infinity.
	* The remainder gets the same sign as the denominator.
	* rem is optional
	*/

	ulong mpi_fdiv_r_ui(MPI rem, MPI dividend, ulong divisor)
	{
	mpi_limb_t rlimb;

	rlimb = mpihelp_mod_1(dividend->d, dividend->nlimbs, divisor);
	if (rlimb && dividend->sign)
	rlimb = divisor - rlimb;

	if (rem) {
	rem->d[0] = rlimb;
	rem->nlimbs = rlimb ? 1 : 0;
	}
	return rlimb;
	}

	int mpi_fdiv_q(MPI quot, MPI dividend, MPI divisor)
	{
	MPI tmp = mpi_alloc(mpi_get_nlimbs(quot));
	if (!tmp)
	return -ENOMEM;
	mpi_fdiv_qr(quot, tmp, dividend, divisor);
	mpi_free(tmp);
	return 0;
	}

	int mpi_fdiv_qr(MPI quot, MPI rem, MPI dividend, MPI divisor)
	{
	int divisor_sign = divisor->sign;
	MPI temp_divisor = NULL;

	if (quot == divisor \|\| rem == divisor) {
	if (mpi_copy(&temp_divisor, divisor) < 0)
	return -ENOMEM;
	divisor = temp_divisor;
	}

	if (mpi_tdiv_qr(quot, rem, dividend, divisor) < 0)
	goto nomem;

	if ((divisor_sign ^ dividend->sign) && rem->nlimbs) {
	if (mpi_sub_ui(quot, quot, 1) < 0)
	goto nomem;
	if (mpi_add(rem, rem, divisor) < 0)
	goto nomem;
	}

	if (temp_divisor)
	mpi_free(temp_divisor);

	return 0;

	nomem:
	mpi_free(temp_divisor);
	return -ENOMEM;
	}

	/* If den == quot, den needs temporary storage.
	* If den == rem, den needs temporary storage.
	* If num == quot, num needs temporary storage.
	* If den has temporary storage, it can be normalized while being copied,
	* i.e no extra storage should be allocated.
	*/

	int mpi_tdiv_r(MPI rem, MPI num, MPI den)
	{
	return mpi_tdiv_qr(NULL, rem, num, den);
	}

	int mpi_tdiv_qr(MPI quot, MPI rem, MPI num, MPI den)
	{
	int rc = -ENOMEM;
	mpi_ptr_t np, dp;
	mpi_ptr_t qp, rp;
	mpi_size_t nsize = num->nlimbs;
	mpi_size_t dsize = den->nlimbs;
	mpi_size_t qsize, rsize;
	mpi_size_t sign_remainder = num->sign;
	mpi_size_t sign_quotient = num->sign ^ den->sign;
	unsigned normalization_steps;
	mpi_limb_t q_limb;
	mpi_ptr_t marker[5];
	int markidx = 0;

	if (!dsize)
	return -EINVAL;

	memset(marker, 0, sizeof(marker));

	/* Ensure space is enough for quotient and remainder.
	* We need space for an extra limb in the remainder, because it's
	* up-shifted (normalized) below. */
	rsize = nsize + 1;
	if (mpi_resize(rem, rsize) < 0)
	goto nomem;

	qsize = rsize - dsize; /* qsize cannot be bigger than this. */
	if (qsize <= 0) {
	if (num != rem) {
	rem->nlimbs = num->nlimbs;
	rem->sign = num->sign;
	MPN_COPY(rem->d, num->d, nsize);
	}
	if (quot) {
	/* This needs to follow the assignment to rem, in case the
	* numerator and quotient are the same. */
	quot->nlimbs = 0;
	quot->sign = 0;
	}
	return 0;
	}

	if (quot)
	if (mpi_resize(quot, qsize) < 0)
	goto nomem;

	/* Read pointers here, when reallocation is finished. */
	np = num->d;
	dp = den->d;
	rp = rem->d;

	/* Optimize division by a single-limb divisor. */
	if (dsize == 1) {
	mpi_limb_t rlimb;
	if (quot) {
	qp = quot->d;
	rlimb = mpihelp_divmod_1(qp, np, nsize, dp[0]);
	qsize -= qp[qsize - 1] == 0;
	quot->nlimbs = qsize;
	quot->sign = sign_quotient;
	} else
	rlimb = mpihelp_mod_1(np, nsize, dp[0]);
	rp[0] = rlimb;
	rsize = rlimb != 0 ? 1 : 0;
	rem->nlimbs = rsize;
	rem->sign = sign_remainder;
	return 0;
	}

	if (quot) {
	qp = quot->d;
	/* Make sure QP and NP point to different objects. Otherwise the
	* numerator would be gradually overwritten by the quotient limbs. */
	if (qp == np) { /* Copy NP object to temporary space. */
	np = marker[markidx++] = mpi_alloc_limb_space(nsize);
	if (!np)
	goto nomem;
	MPN_COPY(np, qp, nsize);
	}
	} else /* Put quotient at top of remainder. */
	qp = rp + dsize;

	count_leading_zeros(normalization_steps, dp[dsize - 1]);

	/* Normalize the denominator, i.e. make its most significant bit set by
	* shifting it NORMALIZATION_STEPS bits to the left. Also shift the
	* numerator the same number of steps (to keep the quotient the same!).
	*/
	if (normalization_steps) {
	mpi_ptr_t tp;
	mpi_limb_t nlimb;

	/* Shift up the denominator setting the most significant bit of
	* the most significant word. Use temporary storage not to clobber
	* the original contents of the denominator. */
	tp = marker[markidx++] = mpi_alloc_limb_space(dsize);
	if (!tp)
	goto nomem;
	mpihelp_lshift(tp, dp, dsize, normalization_steps);
	dp = tp;

	/* Shift up the numerator, possibly introducing a new most
	* significant word. Move the shifted numerator in the remainder
	* meanwhile. */
	nlimb = mpihelp_lshift(rp, np, nsize, normalization_steps);
	if (nlimb) {
	rp[nsize] = nlimb;
	rsize = nsize + 1;
	} else
	rsize = nsize;
	} else {
	/* The denominator is already normalized, as required. Copy it to
	* temporary space if it overlaps with the quotient or remainder. */
	if (dp == rp \|\| (quot && (dp == qp))) {
	mpi_ptr_t tp;

	tp = marker[markidx++] = mpi_alloc_limb_space(dsize);
	if (!tp)
	goto nomem;
	MPN_COPY(tp, dp, dsize);
	dp = tp;
	}

	/* Move the numerator to the remainder. */
	if (rp != np)
	MPN_COPY(rp, np, nsize);

	rsize = nsize;
	}

	q_limb = mpihelp_divrem(qp, 0, rp, rsize, dp, dsize);

	if (quot) {
	qsize = rsize - dsize;
	if (q_limb) {
	qp[qsize] = q_limb;
	qsize += 1;
	}

	quot->nlimbs = qsize;
	quot->sign = sign_quotient;
	}

	rsize = dsize;
	MPN_NORMALIZE(rp, rsize);

	if (normalization_steps && rsize) {
	mpihelp_rshift(rp, rp, rsize, normalization_steps);
	rsize -= rp[rsize - 1] == 0 ? 1 : 0;
	}

	rem->nlimbs = rsize;
	rem->sign = sign_remainder;

	rc = 0;
	nomem:
	while (markidx)
	mpi_free_limb_space(marker[--markidx]);
	return rc;
	}

	int mpi_tdiv_q_2exp(MPI w, MPI u, unsigned count)
	{
	mpi_size_t usize, wsize;
	mpi_size_t limb_cnt;

	usize = u->nlimbs;
	limb_cnt = count / BITS_PER_MPI_LIMB;
	wsize = usize - limb_cnt;
	if (limb_cnt >= usize)
	w->nlimbs = 0;
	else {
	mpi_ptr_t wp;
	mpi_ptr_t up;

	if (RESIZE_IF_NEEDED(w, wsize) < 0)
	return -ENOMEM;
	wp = w->d;
	up = u->d;

	count %= BITS_PER_MPI_LIMB;
	if (count) {
	mpihelp_rshift(wp, up + limb_cnt, wsize, count);
	wsize -= !wp[wsize - 1];
	} else {
	MPN_COPY_INCR(wp, up + limb_cnt, wsize);
	}

	w->nlimbs = wsize;
	}
	return 0;
	}

	/****************
	* Check whether dividend is divisible by divisor
	* (note: divisor must fit into a limb)
	*/
	int mpi_divisible_ui(MPI dividend, ulong divisor)
	{
	return !mpihelp_mod_1(dividend->d, dividend->nlimbs, divisor);
	}