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/* mpfr_exp -- exponential of a floating-point number
Copyright 1999, 2001, 2002, 2003, 2004 Free Software Foundation, Inc.
This file is part of the MPFR Library.
The MPFR Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation; either version 2.1 of the License, or (at your
option) any later version.
The MPFR Library is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
License for more details.
You should have received a copy of the GNU Lesser General Public License
along with the MPFR Library; see the file COPYING.LIB. If not, write to
the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
MA 02111-1307, USA. */
#include <stdio.h>
#include <stddef.h>
#include <limits.h>
#define MPFR_NEED_LONGLONG_H
#include "mpfr-impl.h"
static int
mpfr_exp_rational (mpfr_ptr y, mpz_srcptr p, int r, int m)
{
int n, i, k, j, l;
mpz_t *P, *S;
mpz_t *ptoj;
int diff, expo;
int precy = MPFR_PREC(y);
int *mult;
int prec_i_have;
int *nb_terms;
int accu;
TMP_DECL (marker);
TMP_MARK (marker);
MPFR_ASSERTN((size_t) m < sizeof(int) * CHAR_BIT - 1);
n = 1 << m;
P = (mpz_t*) TMP_ALLOC((m+1) * sizeof(mpz_t));
S = (mpz_t*) TMP_ALLOC((m+1) * sizeof(mpz_t));
ptoj = (mpz_t*) TMP_ALLOC((m+1) * sizeof(mpz_t)); /* ptoj[i] = mantissa^(2^i) */
mult = (int*) TMP_ALLOC((m+1) * sizeof(int));
nb_terms = (int*) TMP_ALLOC((m+1) * sizeof(int));
mult[0] = 0;
for (i = 0; i <= m; i++)
{
mpz_init (P[i]);
mpz_init (S[i]);
mpz_init (ptoj[i]);
}
mpz_set (ptoj[0], p);
for (i = 1; i < m; i++)
mpz_mul (ptoj[i], ptoj[i-1], ptoj[i-1]);
mpz_set_ui (P[0], 1);
mpz_set_ui (S[0], 1);
k = 0;
nb_terms[0] = 1;
prec_i_have = 0;
for (i = 1; (prec_i_have < precy) && (i < n); i++)
{
/* invariant: P[0]*P[1]*...*P[k] equals i! */
k++;
nb_terms[k] = 1;
mpz_set_ui (P[k], i + 1);
mpz_set (S[k], P[k]);
j = i + 1;
l = 0;
while ((j & 1) == 0)
{
MPFR_ASSERTN((size_t) l < sizeof(int) * CHAR_BIT - 1);
mpz_mul (S[k], S[k], ptoj[l]);
mpz_mul (S[k-1], S[k-1], P[k]);
mpz_mul_2exp (S[k-1], S[k-1], r * (1 << l));
mpz_add (S[k-1], S[k-1], S[k]);
mpz_mul (P[k-1], P[k-1], P[k]);
nb_terms[k-1] = nb_terms[k-1] + nb_terms[k];
mult[k] = mult[k-1] + (1 << l) * (r >> 2)
+ mpz_sizeinbase (P[k], 2) - 1;
prec_i_have = mult[k];
/* since mult[k] >= mult[k-1] + nbits(P[k]),
we have P[0]*...*P[k] <= 2^mult[k] = 2^prec_i_have */
l++;
j >>= 1;
k--;
}
}
/* accumulate all products in P[0] */
l = 0;
accu = 0;
while (k > 0)
{
mpz_mul (S[k], S[k], ptoj[MPFR_INT_CEIL_LOG2 (nb_terms[k])]);
mpz_mul (S[k-1], S[k-1], P[k]);
accu += nb_terms[k];
mpz_mul_2exp (S[k-1], S[k-1], r * accu);
mpz_add (S[k-1], S[k-1], S[k]);
mpz_mul (P[k-1], P[k-1], P[k]);
l++;
k--;
}
/* P[0] now equals i! */
diff = mpz_sizeinbase (S[0], 2) - 2 * precy;
expo = diff;
if (diff >= 0)
mpz_div_2exp (S[0], S[0], diff);
else
mpz_mul_2exp (S[0], S[0], -diff);
diff = mpz_sizeinbase(P[0], 2) - precy;
expo -= diff;
if (diff > 0)
mpz_div_2exp (P[0], P[0], diff);
else
mpz_mul_2exp (P[0], P[0], -diff);
mpz_tdiv_q (S[0], S[0], P[0]);
mpfr_set_z (y, S[0], GMP_RNDD);
MPFR_SET_EXP (y, MPFR_GET_EXP (y) + expo);
mpfr_div_2ui (y, y, r * (i - 1), GMP_RNDN);
for (i = 0; i <= m; i++)
{
mpz_clear (P[i]);
mpz_clear (S[i]);
mpz_clear (ptoj[i]);
}
TMP_FREE (marker);
return 0;
}
#define shift (BITS_PER_MP_LIMB/2)
int
mpfr_exp_3 (mpfr_ptr y, mpfr_srcptr x, mp_rnd_t rnd_mode)
{
mpfr_t t;
mpfr_t x_copy;
int i, k;
mpz_t uk;
mpfr_t tmp;
int ttt;
int twopoweri;
int Prec;
int loop;
int prec_x;
int shift_x = 0;
int good = 0;
int realprec = 0;
int iter;
int logn, inexact = 0;
/* decompose x */
/* we first write x = 1.xxxxxxxxxxxxx
----- k bits -- */
/* FIXME: Can I replace this with MPFR_INT_CEIL_LOG2? */
prec_x = __gmpfr_ceil_log2 ((double) (MPFR_PREC(x)) / BITS_PER_MP_LIMB);
if (prec_x < 0)
prec_x = 0;
logn = MPFR_INT_CEIL_LOG2 (prec_x + MPFR_PREC (y));
if (logn < 2)
logn = 2;
ttt = MPFR_GET_EXP (x);
mpfr_init2 (x_copy, MPFR_PREC(x));
mpfr_set (x_copy, x, GMP_RNDD);
/* we shift to get a number less than 1 */
if (ttt > 0)
{
shift_x = ttt;
mpfr_div_2ui (x_copy, x, ttt, GMP_RNDN);
ttt = MPFR_GET_EXP (x_copy);
}
MPFR_ASSERTD(ttt <= 0);
/* the following code assumes BITS_PER_MP_LIMB is a power of two */
MPFR_ASSERTN((BITS_PER_MP_LIMB & (BITS_PER_MP_LIMB - 1)) == 0);
realprec = MPFR_PREC(y) + logn;
mpz_init (uk);
while (!good)
{
Prec = realprec + shift + 2 + shift_x;
k = __gmpfr_ceil_log2 ((double) Prec / BITS_PER_MP_LIMB);
/* now we have to extract */
mpfr_init2 (t, Prec);
mpfr_init2 (tmp, Prec);
mpfr_set_ui (tmp, 1, GMP_RNDN);
twopoweri = BITS_PER_MP_LIMB;
iter = (k <= prec_x) ? k : prec_x;
for (i = 0; i <= iter; i++)
{
mpfr_extract (uk, x_copy, i);
if (i)
mpfr_exp_rational (t, uk, twopoweri - ttt, k - i + 1);
else
{
/* particular case: we have to compute with x/2^., then
do squarings (this is faster) */
mpfr_exp_rational (t, uk, shift + twopoweri - ttt, k + 1);
for (loop = 0 ; loop < shift; loop++)
mpfr_mul (t, t, t, GMP_RNDD);
}
mpfr_mul (tmp, tmp, t, GMP_RNDD);
MPFR_ASSERTN(twopoweri <= INT_MAX/2);
twopoweri <<= 1;
}
mpfr_clear (t);
for (loop = 0 ; loop < shift_x; loop++)
mpfr_mul (tmp, tmp, tmp, GMP_RNDD);
if (mpfr_can_round (tmp, realprec, GMP_RNDD, GMP_RNDZ,
MPFR_PREC(y) + (rnd_mode == GMP_RNDN)))
{
inexact = mpfr_set (y, tmp, rnd_mode);
good = 1;
}
else
realprec += 3 * logn;
mpfr_clear (tmp);
}
mpz_clear (uk);
mpfr_clear (x_copy);
return inexact;
}
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