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/* mpfr_exp -- exponential of a floating-point number
Copyright (C) 1999, 2001 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 "gmp.h"
#include "gmp-impl.h"
#include "mpfr.h"
#include "mpfr-impl.h"
static int mpfr_exp_rational _PROTO ((mpfr_ptr, mpz_srcptr, int, int));
int mpfr_exp3 _PROTO ((mpfr_ptr, mpfr_srcptr, mp_rnd_t));
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);
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++) {
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) {
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];
l++; j>>=1; k--;
}
}
l = 0;
accu = 0;
while (k > 0){
mpz_mul(S[k], S[k], ptoj[_mpfr_ceil_log2((double) 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--;
}
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_EXP(y) += expo;
mpfr_div_2exp(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_exp3 (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 -- */
prec_x = _mpfr_ceil_log2 ((double) (MPFR_PREC(x)) / BITS_PER_MP_LIMB);
if (prec_x < 0) prec_x = 0;
logn = _mpfr_ceil_log2 ((double) prec_x + MPFR_PREC(y));
if (logn < 2) logn = 2;
ttt = MPFR_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_mul_2exp(x_copy,x,-ttt, GMP_RNDN);
ttt = MPFR_EXP(x_copy);
}
realprec = MPFR_PREC(y)+logn;
mpz_init (uk);
while (!good){
Prec = realprec+shift+2+shift_x;
k = _mpfr_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;
if (k <= prec_x) iter = k; else iter= 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);
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, rnd_mode, MPFR_PREC(y)))
{
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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