mirror of
https://github.com/vale981/arb
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117 lines
3.1 KiB
C
117 lines
3.1 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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long
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fmpr_sqrt(fmpr_t y, const fmpr_t x, long prec, fmpr_rnd_t rnd)
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{
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long shift, man_shift, r, bc;
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fmpz_t rem;
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if (fmpr_is_special(x))
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{
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if (fmpr_is_zero(x))
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fmpr_zero(y);
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else if (fmpr_is_pos_inf(x))
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fmpr_pos_inf(y);
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else
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fmpr_nan(y);
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return FMPR_RESULT_EXACT;
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}
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if (fmpr_sgn(x) < 0)
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{
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fmpr_nan(y);
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return FMPR_RESULT_EXACT;
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}
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/* special case: 4^n */
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/* TODO: process all small exact square roots efficiently */
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if (fmpz_is_one(fmpr_manref(x)) && fmpz_is_even(fmpr_expref(x)))
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{
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r = fmpr_set_round(y, x, prec, rnd);
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fmpz_tdiv_q_2exp(fmpr_expref(y), fmpr_expref(y), 1);
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return r;
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}
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fmpz_set(fmpr_expref(y), fmpr_expref(x));
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man_shift = 0;
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bc = fmpz_bits(fmpr_manref(x));
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if (fmpz_is_odd(fmpr_expref(y)))
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{
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fmpz_sub_ui(fmpr_expref(y), fmpr_expref(y), 1UL);
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man_shift += 1;
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bc += 1;
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}
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shift = FLINT_MAX(4, 2 * prec - bc + 4);
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shift += shift & 1;
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fmpz_init(rem);
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fmpz_mul_2exp(fmpr_manref(y), fmpr_manref(x), shift + man_shift);
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fmpz_sqrtrem(fmpr_manref(y), rem, fmpr_manref(y));
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if (!fmpz_is_zero(rem) && rnd != FMPR_RND_FLOOR && rnd != FMPR_RND_DOWN)
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{
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fmpz_mul_2exp(fmpr_manref(y), fmpr_manref(y), 1);
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fmpz_add_ui(fmpr_manref(y), fmpr_manref(y), 1UL);
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shift += 2;
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}
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fmpz_clear(rem);
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fmpz_sub_ui(fmpr_expref(y), fmpr_expref(y), shift);
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fmpz_tdiv_q_2exp(fmpr_expref(y), fmpr_expref(y), 1);
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return _fmpr_normalise(fmpr_manref(y), fmpr_expref(y), prec, rnd);
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}
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/*
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if exp & 1:
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exp -= 1
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man <<= 1
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bc += 1
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elif man == 1:
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return normalize1(sign, man, exp//2, bc, prec, rnd)
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shift = max(4, 2*prec-bc+4)
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shift += shift & 1
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if rnd in 'fd':
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man = isqrt(man<<shift)
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else:
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man, rem = sqrtrem(man<<shift)
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# Perturb up
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if rem:
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man = (man<<1)+1
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shift += 2
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return from_man_exp(man, (exp-shift)//2, prec, rnd)
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*/
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