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/*
Copyright (C) 2012 Fredrik Johansson
This file is part of Arb.
Arb is free software: you can redistribute it and/or modify it under
the terms of the GNU Lesser General Public License (LGPL) as published
by the Free Software Foundation; either version 2.1 of the License, or
(at your option) any later version. See <http://www.gnu.org/licenses/>.
*/
#include "fmpr.h"
static void
_fmpr_div_special(fmpr_t z, const fmpr_t x, const fmpr_t y)
{
if ((fmpr_is_zero(x) && !fmpr_is_zero(y) && !fmpr_is_nan(y)) ||
(fmpr_is_inf(y) && !fmpr_is_special(x)))
{
fmpr_zero(z);
}
else if (fmpr_is_zero(y) || (fmpr_is_special(x) && fmpr_is_special(y)) ||
fmpr_is_nan(x) || fmpr_is_nan(y))
{
fmpr_nan(z);
}
else if (fmpr_sgn(x) == fmpr_sgn(y))
fmpr_pos_inf(z);
else
fmpr_neg_inf(z);
}
static __inline__ int
low_bits_are_zero(const fmpz_t u, int bits)
{
fmpz f = *u;
mp_limb_t low;
if (!COEFF_IS_MPZ(f))
low = FLINT_ABS(f);
else
low = COEFF_TO_PTR(f)->_mp_d[0];
return (low & ((UWORD(1) << bits) - 1)) == 0;
}
slong
fmpr_div(fmpr_t z, const fmpr_t x, const fmpr_t y, slong prec, fmpr_rnd_t rnd)
{
if (fmpr_is_special(x) || fmpr_is_special(y))
{
_fmpr_div_special(z, x, y);
return FMPR_RESULT_EXACT;
}
/* division by power of two <=> shift exponents */
if (fmpz_is_pm1(fmpr_manref(y)))
{
if (fmpz_is_one(fmpr_manref(y)))
fmpz_set(fmpr_manref(z), fmpr_manref(x));
else
fmpz_neg(fmpr_manref(z), fmpr_manref(x));
fmpz_sub(fmpr_expref(z), fmpr_expref(x), fmpr_expref(y));
return _fmpr_normalise(fmpr_manref(z), fmpr_expref(z), prec, rnd);
}
else
{
slong xbits, ybits, extra, extra_pad, extra_control;
int negative;
fmpz_t t, u;
/* todo: work out exact needed shift */
xbits = fmpz_bits(fmpr_manref(x));
ybits = fmpz_bits(fmpr_manref(y));
extra = prec - xbits + ybits;
extra = FLINT_MAX(extra, 0);
extra_pad = 32;
extra_control = 24;
extra += extra_pad;
fmpz_init(t);
fmpz_init(u);
fmpz_mul_2exp(t, fmpr_manref(x), extra);
fmpz_tdiv_q(u, t, fmpr_manref(y));
if (low_bits_are_zero(u, extra_control))
{
fmpz_t v;
fmpz_init(v);
fmpz_mul(v, u, fmpr_manref(y));
negative = fmpz_sgn(fmpr_manref(x)) != fmpz_sgn(fmpr_manref(y));
if (!fmpz_equal(t, v))
{
if (negative)
fmpz_sub_ui(u, u, 1);
else
fmpz_add_ui(u, u, 1);
}
fmpz_clear(v);
}
fmpz_swap(fmpr_manref(z), u);
fmpz_clear(t);
fmpz_clear(u);
fmpz_sub(fmpr_expref(z), fmpr_expref(x), fmpr_expref(y));
fmpz_sub_ui(fmpr_expref(z), fmpr_expref(z), extra);
return _fmpr_normalise(fmpr_manref(z), fmpr_expref(z), prec, rnd);
}
}
slong
fmpr_div_ui(fmpr_t z, const fmpr_t x, ulong y, slong prec, fmpr_rnd_t rnd)
{
fmpr_t t; slong r;
fmpr_init(t);
fmpr_set_ui(t, y);
r = fmpr_div(z, x, t, prec, rnd);
fmpr_clear(t);
return r;
}
slong
fmpr_ui_div(fmpr_t z, ulong x, const fmpr_t y, slong prec, fmpr_rnd_t rnd)
{
fmpr_t t; slong r;
fmpr_init(t);
fmpr_set_ui(t, x);
r = fmpr_div(z, t, y, prec, rnd);
fmpr_clear(t);
return r;
}
slong
fmpr_div_si(fmpr_t z, const fmpr_t x, slong y, slong prec, fmpr_rnd_t rnd)
{
fmpr_t t; slong r;
fmpr_init(t);
fmpr_set_si(t, y);
r = fmpr_div(z, x, t, prec, rnd);
fmpr_clear(t);
return r;
}
slong
fmpr_si_div(fmpr_t z, slong x, const fmpr_t y, slong prec, fmpr_rnd_t rnd)
{
fmpr_t t; slong r;
fmpr_init(t);
fmpr_set_si(t, x);
r = fmpr_div(z, t, y, prec, rnd);
fmpr_clear(t);
return r;
}
slong
fmpr_div_fmpz(fmpr_t z, const fmpr_t x, const fmpz_t y, slong prec, fmpr_rnd_t rnd)
{
fmpr_t t; slong r;
fmpr_init(t);
fmpr_set_fmpz(t, y);
r = fmpr_div(z, x, t, prec, rnd);
fmpr_clear(t);
return r;
}
slong
fmpr_fmpz_div(fmpr_t z, const fmpz_t x, const fmpr_t y, slong prec, fmpr_rnd_t rnd)
{
fmpr_t t; slong r;
fmpr_init(t);
fmpr_set_fmpz(t, x);
r = fmpr_div(z, t, y, prec, rnd);
fmpr_clear(t);
return r;
}
slong
fmpr_fmpz_div_fmpz(fmpr_t z, const fmpz_t x, const fmpz_t y, slong prec, fmpr_rnd_t rnd)
{
fmpr_t t, u; slong r;
fmpr_init(t);
fmpr_init(u);
fmpr_set_fmpz(t, x);
fmpr_set_fmpz(u, y);
r = fmpr_div(z, t, u, prec, rnd);
fmpr_clear(t);
fmpr_clear(u);
return r;
}
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