mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
333 lines
9.5 KiB
C
333 lines
9.5 KiB
C
/*=============================================================================
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This file is part of ARB.
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ARB 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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ARB 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 ARB; 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 Fredrik Johansson
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******************************************************************************/
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#include "fmpr.h"
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static __inline__ int
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rounds_up(fmpr_rnd_t rnd, int negative)
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{
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if (rnd == FMPR_RND_DOWN) return 0;
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if (rnd == FMPR_RND_UP) return 1;
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if (rnd == FMPR_RND_FLOOR) return negative;
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return !negative;
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}
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#define MUL_STACK_ALLOC 40
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/* requires xn >= yn, xman and yman both normalised and odd */
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static long
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_fmpr_mul_large(fmpz_t zman, fmpz_t zexp,
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mp_srcptr xman, mp_size_t xn, const fmpz_t xexp,
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mp_srcptr yman, mp_size_t yn, const fmpz_t yexp,
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int negative, long prec, fmpr_rnd_t rnd)
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{
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long zn, alloc, lead, bc, ret;
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mp_limb_t tmp_stack[MUL_STACK_ALLOC];
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mp_ptr tmp;
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zn = xn + yn;
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alloc = zn + 1; /* may need one extra temp limb for rounding carry */
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if (alloc > MUL_STACK_ALLOC)
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tmp = flint_malloc(alloc * sizeof(mp_limb_t));
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else
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tmp = tmp_stack;
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mpn_mul(tmp, xman, xn, yman, yn);
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zn = zn - (tmp[zn-1] == 0);
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count_leading_zeros(lead, tmp[zn-1]);
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bc = zn * FLINT_BITS - lead;
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if (bc <= prec)
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{
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if (zn == 1)
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{
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if (!negative)
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fmpz_set_ui(zman, tmp[0]);
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else
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fmpz_neg_ui(zman, tmp[0]);
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}
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else
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{
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fmpz_set_mpn_large(zman, tmp, zn, negative);
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}
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fmpz_add_inline(zexp, xexp, yexp);
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ret = FMPR_RESULT_EXACT;
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}
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else
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{
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long cut_limb, cut_bit, shift, trail_limbs, trail_bits;
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mp_limb_t cy;
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mp_ptr res;
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shift = bc - prec;
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cut_limb = shift / FLINT_BITS;
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cut_bit = shift % FLINT_BITS;
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/* cut off at the rounding bit */
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tmp[cut_limb] &= ~(((mp_limb_t) 1UL << cut_bit) - 1UL);
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if (rounds_up(rnd, negative))
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{
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cy = mpn_add_1(tmp + cut_limb,
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tmp + cut_limb, zn - cut_limb, (1UL << cut_bit));
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tmp[zn] = cy;
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zn += cy;
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}
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/* remove trailing zero limbs */
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trail_limbs = 0;
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while (tmp[cut_limb + trail_limbs] == 0)
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trail_limbs++;
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res = tmp + (cut_limb + trail_limbs);
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zn -= (cut_limb + trail_limbs);
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count_trailing_zeros(trail_bits, res[0]);
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ret = (trail_limbs * FLINT_BITS) + trail_bits - cut_bit;
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shift = (cut_limb + trail_limbs) * FLINT_BITS + trail_bits;
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fmpz_set_mpn_rshift(zman, res, zn, trail_bits, negative);
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fmpz_add2_fmpz_si_inline(zexp, xexp, yexp, shift);
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}
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if (alloc > MUL_STACK_ALLOC)
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flint_free(tmp);
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return ret;
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}
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static void
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_fmpr_mul_special(fmpr_t z, const fmpr_t x, const fmpr_t y)
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{
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if (fmpr_is_zero(x))
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{
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if (!fmpr_is_special(y) || fmpr_is_zero(y))
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fmpr_zero(z);
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else
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fmpr_nan(z);
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return;
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}
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if (fmpr_is_zero(y))
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{
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if (!fmpr_is_special(x))
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fmpr_zero(z);
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else
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fmpr_nan(z);
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return;
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}
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if ((fmpr_is_inf(x) && (fmpr_is_inf(y) || !fmpr_is_special(y))) ||
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(fmpr_is_inf(y) && !fmpr_is_special(x)))
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{
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if (fmpr_sgn(x) == fmpr_sgn(y))
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fmpr_pos_inf(z);
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else
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fmpr_neg_inf(z);
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return;
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}
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fmpr_nan(z);
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}
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long
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fmpr_mul(fmpr_t z, const fmpr_t x, const fmpr_t y, long prec, fmpr_rnd_t rnd)
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{
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__mpz_struct *xmpz, *ympz;
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long xn, yn;
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int negative;
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fmpz u, v;
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if (fmpr_is_special(x) || fmpr_is_special(y))
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{
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_fmpr_mul_special(z, x, y);
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return FMPR_RESULT_EXACT;
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}
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u = *fmpr_manref(x);
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v = *fmpr_manref(y);
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if (!COEFF_IS_MPZ(u))
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{
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if (!COEFF_IS_MPZ(v))
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{
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mp_limb_t hi, lo;
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negative = (u ^ v) < 0;
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u = FLINT_ABS(u);
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v = FLINT_ABS(v);
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umul_ppmm(hi, lo, u, v);
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if (hi == 0)
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{
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/* 1 limb */
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long lead, trail, bc, shift, ret;
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count_leading_zeros(lead, lo);
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bc = FLINT_BITS - lead;
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shift = 0;
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ret = FMPR_RESULT_EXACT;
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if (bc > prec)
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{
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shift = bc - prec;
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lo = (lo >> shift) + rounds_up(rnd, negative);
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count_trailing_zeros(trail, lo);
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lo >>= trail;
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shift += trail;
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ret = trail;
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}
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if (!negative)
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fmpz_set_ui(fmpr_manref(z), lo);
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else
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fmpz_neg_ui(fmpr_manref(z), lo);
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fmpz_add2_fmpz_si_inline(fmpr_expref(z), fmpr_expref(x), fmpr_expref(y), shift);
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return ret;
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}
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else
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{
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/* 2 limbs */
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long lead, trail, bc, shift, ret;
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count_leading_zeros(lead, hi);
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bc = 2 * FLINT_BITS - lead;
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shift = 0;
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ret = FMPR_RESULT_EXACT;
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if (bc > prec)
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{
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shift = bc - prec;
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/* round */
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if (shift < FLINT_BITS)
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{
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lo = (lo >> shift) | (hi << (FLINT_BITS - shift));
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hi >>= shift;
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}
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else
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{
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lo = hi >> (shift - FLINT_BITS);
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hi = 0;
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}
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if (rounds_up(rnd, negative))
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add_ssaaaa(hi, lo, hi, lo, 0, 1);
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/* remove trailing zeros */
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if (lo == 0)
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{
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count_trailing_zeros(trail, hi);
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hi >>= trail;
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shift += FLINT_BITS + trail;
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ret = FLINT_BITS + trail;
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if (!negative)
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fmpz_set_ui(fmpr_manref(z), hi);
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else
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fmpz_neg_ui(fmpr_manref(z), hi);
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}
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else
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{
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count_trailing_zeros(trail, lo);
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if (trail != 0)
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{
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lo = (lo >> trail) | (hi << (FLINT_BITS - trail));
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hi >>= trail;
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shift += trail;
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}
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ret = trail;
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if (!negative)
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fmpz_set_uiui(fmpr_manref(z), hi, lo);
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else
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fmpz_neg_uiui(fmpr_manref(z), hi, lo);
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}
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}
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else
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{
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if (!negative)
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fmpz_set_uiui(fmpr_manref(z), hi, lo);
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else
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fmpz_neg_uiui(fmpr_manref(z), hi, lo);
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}
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fmpz_add2_fmpz_si_inline(fmpr_expref(z), fmpr_expref(x), fmpr_expref(y), shift);
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return ret;
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}
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}
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else
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{
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mp_limb_t t;
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ympz = COEFF_TO_PTR(v);
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yn = ympz->_mp_size;
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negative = (yn < 0) ^ (u < 0);
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t = FLINT_ABS(u);
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yn = FLINT_ABS(yn);
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return _fmpr_mul_large(fmpr_manref(z), fmpr_expref(z),
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ympz->_mp_d, yn, fmpr_expref(y),
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&t, 1, fmpr_expref(x), negative, prec, rnd);
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}
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}
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else
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{
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xmpz = COEFF_TO_PTR(u);
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xn = xmpz->_mp_size;
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if (!COEFF_IS_MPZ(v))
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{
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mp_limb_t t;
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negative = (xn < 0) ^ (v < 0);
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t = FLINT_ABS(v);
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xn = FLINT_ABS(xn);
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return _fmpr_mul_large(fmpr_manref(z), fmpr_expref(z),
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xmpz->_mp_d, xn, fmpr_expref(x),
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&t, 1, fmpr_expref(y), negative, prec, rnd);
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}
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else
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{
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ympz = COEFF_TO_PTR(v);
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yn = ympz->_mp_size;
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negative = (xn ^ yn) < 0;
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xn = FLINT_ABS(xn);
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yn = FLINT_ABS(yn);
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if (xn >= yn)
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return _fmpr_mul_large(fmpr_manref(z), fmpr_expref(z),
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xmpz->_mp_d, xn, fmpr_expref(x),
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ympz->_mp_d, yn, fmpr_expref(y), negative, prec, rnd);
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else
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return _fmpr_mul_large(fmpr_manref(z), fmpr_expref(z),
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ympz->_mp_d, yn, fmpr_expref(y),
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xmpz->_mp_d, xn, fmpr_expref(x), negative, prec, rnd);
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}
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}
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}
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