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/*
Copyright (C) 2017 Fredrik Johansson
This file is part of FLINT.
FLINT 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 3 of the License, or
(at your option) any later version. See <https://www.gnu.org/licenses/>.
*/
#include <math.h>
#include "mag.h"
void
mag_neg_log(mag_t z, const mag_t x)
{
if (mag_is_special(x))
{
if (mag_is_zero(x))
mag_inf(z);
else
mag_zero(z);
}
else
{
double t;
fmpz exp = MAG_EXP(x);
if (!COEFF_IS_MPZ(exp))
{
if (exp >= 1)
{
mag_zero(z);
}
else if (exp > -(1000 - MAG_BITS))
{
t = ldexp(MAG_MAN(x), exp - MAG_BITS);
t = -mag_d_log_lower_bound(t);
mag_set_d(z, t);
}
else
{
/* -log(2^(exp-1) * (2*v)) = -exp*log(2) - log(2*v), 1 <= 2v < 2 */
t = MAG_MAN(x) * ldexp(1.0, 1 - MAG_BITS);
t = -mag_d_log_lower_bound(t);
t -= (exp - 1) * 0.69314718055994530942;
t *= (1 + 1e-13);
mag_set_d(z, t);
}
}
else if (fmpz_sgn(MAG_EXPREF(x)) > 0)
{
mag_zero(z);
}
else
{
mag_inv(z, x);
mag_log(z, z);
}
}
}
void
mag_neg_log_lower(mag_t z, const mag_t x)
{
if (mag_is_special(x))
{
if (mag_is_zero(x))
mag_inf(z);
else
mag_zero(z);
}
else
{
double t;
fmpz exp = MAG_EXP(x);
if (!COEFF_IS_MPZ(exp))
{
if (exp >= 1)
{
mag_zero(z);
}
else if (exp > -(1000 - MAG_BITS))
{
t = ldexp(MAG_MAN(x), exp - MAG_BITS);
t = -mag_d_log_upper_bound(t);
mag_set_d_lower(z, t);
}
else
{
/* -log(2^(exp-1) * (2*v)) = -exp*log(2) - log(2*v), 1 <= 2v < 2 */
t = MAG_MAN(x) * ldexp(1.0, 1 - MAG_BITS);
t = -mag_d_log_upper_bound(t);
t -= (exp - 1) * 0.69314718055994530942;
t *= (1 - 1e-13);
mag_set_d_lower(z, t);
}
}
else if (fmpz_sgn(MAG_EXPREF(x)) > 0)
{
mag_zero(z);
}
else
{
mag_inv_lower(z, x);
mag_log_lower(z, z);
}
}
}
void
mag_log(mag_t z, const mag_t x)
{
if (mag_is_special(x))
{
if (mag_is_zero(x))
mag_zero(z);
else
mag_inf(z);
}
else
{
double t;
fmpz exp = MAG_EXP(x);
if (!COEFF_IS_MPZ(exp))
{
if (exp <= 0 || (exp == 1 && MAG_MAN(x) == MAG_ONE_HALF))
{
mag_zero(z);
}
else if (exp < 1000) /* safely within the double range */
{
t = ldexp(MAG_MAN(x), exp - MAG_BITS);
t = mag_d_log_upper_bound(t);
mag_set_d(z, t);
}
else
{
/* log(2^(exp-1)*(2v)) = (exp-1)*log(2) + log(2v), 1 <= 2v < 2 */
t = MAG_MAN(x) * ldexp(1.0, 1 - MAG_BITS); /* exact */
t = mag_d_log_upper_bound(t);
t += (exp - 1.0) * 0.69314718055994530942;
t *= (1 + 1e-13); /* last step could have rounded down */
mag_set_d(z, t);
}
}
else if (fmpz_sgn(MAG_EXPREF(x)) < 0)
{
mag_zero(z);
}
else
{
/* log(2^exp) = exp*log(2), log(2) < 744261118/2^30 */
fmpz_t t;
fmpz_init(t);
fmpz_mul_ui(t, MAG_EXPREF(x), 744261118);
mag_set_fmpz(z, t);
mag_mul_2exp_si(z, z, -30);
fmpz_clear(t);
}
}
}
void
mag_log_lower(mag_t z, const mag_t x)
{
if (mag_is_special(x))
{
if (mag_is_zero(x))
mag_zero(z);
else
mag_inf(z);
}
else
{
double t;
fmpz exp = MAG_EXP(x);
if (!COEFF_IS_MPZ(exp))
{
if (exp <= 0 || (exp == 1 && MAG_MAN(x) == MAG_ONE_HALF))
{
mag_zero(z);
}
else if (exp < 1000)
{
t = ldexp(MAG_MAN(x), exp - MAG_BITS);
t = mag_d_log_lower_bound(t);
mag_set_d_lower(z, t);
}
else
{
/* log(2^(exp-1) * (2*v)) = exp*log(2) + log(2*v), 1 <= 2v < 2 */
t = MAG_MAN(x) * ldexp(1.0, 1 - MAG_BITS);
t = mag_d_log_lower_bound(t);
t += (exp - 1) * 0.69314718055994530942;
t *= (1 - 1e-13);
mag_set_d_lower(z, t);
}
}
else if (fmpz_sgn(MAG_EXPREF(x)) < 0)
{
mag_zero(z);
}
else
{
/* log(2^exp) = exp*log(2), log(2) > 744261117/2^30 */
fmpz_t t;
fmpz_init(t);
fmpz_sub_ui(t, MAG_EXPREF(x), 1); /* lower bound for x */
fmpz_mul_ui(t, t, 744261117);
mag_set_fmpz_lower(z, t);
mag_mul_2exp_si(z, z, -30);
fmpz_clear(t);
}
}
}