127 lines
3.5 KiB
C
127 lines
3.5 KiB
C
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/*=============================================================================
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This file is part of FLINT.
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FLINT is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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FLINT is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with FLINT; if not, write to the Free Software
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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=============================================================================*/
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/******************************************************************************
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Copyright (C) 2012 William Hart
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******************************************************************************/
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#include <gmp.h>
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#include "flint.h"
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#include "ulong_extras.h"
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#include "fmpz.h"
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void fmpz_xgcd_partial(fmpz_t co2, fmpz_t co1,
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fmpz_t r2, fmpz_t r1, const fmpz_t L)
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{
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fmpz_t q, r;
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slong aa2, aa1, bb2, bb1, rr1, rr2, qq, bb, t1, t2, t3, i;
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slong bits, bits1, bits2;
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fmpz_init(q); fmpz_init(r);
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fmpz_zero(co2);
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fmpz_set_si(co1, -1);
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while (!fmpz_is_zero(r1) && fmpz_cmp(r1, L) > 0)
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{
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bits2 = fmpz_bits(r2);
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bits1 = fmpz_bits(r1);
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bits = FLINT_MAX(bits2, bits1) - FLINT_BITS + 1;
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if (bits < 0) bits = 0;
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fmpz_tdiv_q_2exp(r, r2, bits);
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rr2 = fmpz_get_ui(r);
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fmpz_tdiv_q_2exp(r, r1, bits);
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rr1 = fmpz_get_ui(r);
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fmpz_tdiv_q_2exp(r, L, bits);
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bb = fmpz_get_ui(r);
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aa2 = 0; aa1 = 1;
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bb2 = 1; bb1 = 0;
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for (i = 0; rr1 != 0 && rr1 > bb; i++)
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{
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qq = rr2 / rr1;
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t1 = rr2 - qq*rr1;
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t2 = aa2 - qq*aa1;
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t3 = bb2 - qq*bb1;
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if (i & 1)
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{
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if (t1 < -t3 || rr1 - t1 < t2 - aa1) break;
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} else
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{
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if (t1 < -t2 || rr1 - t1 < t3 - bb1) break;
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}
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rr2 = rr1; rr1 = t1;
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aa2 = aa1; aa1 = t2;
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bb2 = bb1; bb1 = t3;
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}
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if (i == 0)
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{
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fmpz_fdiv_qr(q, r2, r2, r1);
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fmpz_swap(r2, r1);
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fmpz_submul(co2, co1, q);
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fmpz_swap(co2, co1);
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} else
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{
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fmpz_mul_si(r, r2, bb2);
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if (aa2 >= 0)
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fmpz_addmul_ui(r, r1, aa2);
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else
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fmpz_submul_ui(r, r1, -aa2);
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fmpz_mul_si(r1, r1, aa1);
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if (bb1 >= 0)
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fmpz_addmul_ui(r1, r2, bb1);
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else
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fmpz_submul_ui(r1, r2, -bb1);
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fmpz_set(r2, r);
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fmpz_mul_si(r, co2, bb2);
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if (aa2 >= 0)
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fmpz_addmul_ui(r, co1, aa2);
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else
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fmpz_submul_ui(r, co1, -aa2);
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fmpz_mul_si(co1, co1, aa1);
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if (bb1 >= 0)
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fmpz_addmul_ui(co1, co2, bb1);
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else
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fmpz_submul_ui(co1, co2, -bb1);
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fmpz_set(co2, r);
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if (fmpz_sgn(r1) < 0) { fmpz_neg(co1, co1); fmpz_neg(r1, r1); }
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if (fmpz_sgn(r2) < 0) { fmpz_neg(co2, co2); fmpz_neg(r2, r2); }
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}
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}
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if (fmpz_sgn(r2) < 0)
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{
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fmpz_neg(co2, co2); fmpz_neg(co1, co1);
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fmpz_neg(r2, r2);
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}
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fmpz_clear(q); fmpz_clear(r);
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}
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