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https://github.com/cryb-to/cryb-to.git
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104 lines
3.4 KiB
C
104 lines
3.4 KiB
C
/*
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* Copyright (c) 2017 Dag-Erling Smørgrav
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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* 3. The name of the author may not be used to endorse or promote
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* products derived from this software without specific prior written
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* permission.
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*
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* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
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* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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* SUCH DAMAGE.
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*/
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#include "cryb/impl.h"
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#include <stddef.h>
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#include <stdint.h>
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#include <cryb/assert.h>
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#include <cryb/endian.h>
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#include <cryb/mpi.h>
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#include "cryb_mpi_impl.h"
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/*
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* Compute the greatest common denominator of the absolute values of A and
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* B and store the result in X. This is an iterative implementation of
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* Stein's binary GCD algorithm.
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*
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* TODO: replace with Lehmer's GCD algorithm, which should be
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* significantly faster for large inputs.
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*/
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int
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mpi_gcd_abs(cryb_mpi *X, const cryb_mpi *A, const cryb_mpi *B)
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{
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cryb_mpi TA = CRYB_MPI_ZERO, TB = CRYB_MPI_ZERO;
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unsigned int ashift, bshift;
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/* GCD(x, x) = x */
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if (A == B || mpi_eq(A, B)) {
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if (X != A && X != B && mpi_copy(X, A) != 0)
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return (-1);
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X->neg = 0;
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return (0);
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}
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/* GCD(x, 0) = 0 */
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if (A->msb == 0 || B->msb == 0) {
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mpi_zero(X);
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return (0);
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}
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/* Stein's algorithm is destructive, so we operate on copies */
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if (mpi_copy(&TA, A) != 0 || mpi_copy(&TB, B) != 0)
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goto fail;
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/* reduce each operand to its greatest odd denominator */
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/* neither operand is zero, and mpi_rshift() cannot fail */
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ashift = mpi_lsb(&TA) - 1;
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if ((bshift = mpi_lsb(&TB) - 1) < ashift)
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ashift = bshift;
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(void)mpi_rshift(&TA, ashift);
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(void)mpi_rshift(&TB, ashift);
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while (TA.msb != 0) {
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/* mpi_rshift() cannot fail */
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if ((TA.words[0] & 1) == 0)
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(void)mpi_rshift(&TA, mpi_lsb(&TA) - 1);
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if ((TB.words[0] & 1) == 0)
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(void)mpi_rshift(&TB, mpi_lsb(&TB) - 1);
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if (mpi_cmp_abs(&TA, &TB) < 0)
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mpi_swap(&TA, &TB);
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/* mpi_sub_abs() cannot fail in this case */
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(void)mpi_sub_abs(&TA, &TA, &TB);
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/* mpi_rshift() cannot fail */
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assert((TA.words[0] & 1) == 0);
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(void)mpi_rshift(&TA, 1);
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}
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/* undo the initial reduction to greatest odd denominator */
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if (mpi_copy(X, &TB) != 0 ||
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mpi_lshift(X, ashift) != 0)
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goto fail;
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X->neg = 0;
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return (0);
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fail:
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mpi_destroy(&TA);
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mpi_destroy(&TB);
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return (-1);
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}
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