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/* mpfr_cbrt -- cube root function.
Copyright 2002 Free Software Foundation.
Contributed by the Spaces project, INRIA Lorraine.
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. If not, write to
the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
MA 02111-1307, USA. */
#include <stdio.h>
#include <stdlib.h>
#include "gmp.h"
#include "gmp-impl.h"
#include "mpfr.h"
#include "mpfr-impl.h"
/* The computation of y=x^(1/3) is done by
Case exp-log y=e^((1/3)*log(x))
Case Newton y / y_{k+1}=(1/3)[(x/(y_k^2))+2y_k]
*/
int
#if __STDC__
mpfr_cbrt (mpfr_ptr y, mpfr_srcptr x , mp_rnd_t rnd_mode)
#else
mpfr_cbrt (y, x, rnd_mode)
mpfr_ptr y;
mpfr_srcptr x;
mp_rnd_t rnd_mode;
#endif
{
/****** Declaration ******/
/* Variable of Intermediary Calculation*/
mpfr_t t1,t2,t;
int round;
int boucle;
long int exp_t;
ldiv_t epsilon;
int tau=2;
int ktau=0;
int i;
mp_prec_t Nx; /* Precision of input variable */
mp_prec_t Ny; /* Precision of output variable */
mp_prec_t Nt; /* Precision of Intermediary Calculation variable */
mp_prec_t Ntemp; /* Precision of Intermediary Calculation variable */
mp_prec_t err; /* Precision of error */
/* Gestion des NaN */
if (MPFR_IS_NAN(x)) { MPFR_SET_NAN(y); return 1; }
MPFR_CLEAR_NAN(y);
/* Gestion des infinies*/
if (MPFR_IS_INF(x)){
MPFR_SET_INF(y);
if(MPFR_SIGN(x) > 0) {
if (MPFR_SIGN(y) < 0) MPFR_CHANGE_SIGN(y);}
else{
if (MPFR_SIGN(y) < 0) MPFR_CHANGE_SIGN(y);}
return 1;
}
MPFR_CLEAR_INF(y);
/*Gestion du cas 0*/
if(!MPFR_NOTZERO(x)){
MPFR_SET_ZERO(y); /* cbrt(+/- 0) = +/- 0 */
if(MPFR_SIGN(x) > 0){
if (MPFR_SIGN(y) < 0) MPFR_CHANGE_SIGN(y);
}
else{
if (MPFR_SIGN(y) > 0) MPFR_CHANGE_SIGN(y);
}
return 0;
}
/* Initialisation of the Precision */
Nx=MPFR_PREC(x);
Ny=MPFR_PREC(y);
/* compute the size of intermediary variable */
if(Ny>=Nx)
Nt=Ny;
else
Nt=Nx;
/* Calcul du nombre d'iteration necessaire pour newton*/
/* t0=2, t{k+1}=2.t{k}-1 k / tk>n */
while(tau<=Nt){
tau=2*tau-1;
ktau++;
}
/* Calcul de la taille des variable temporaire */
Ntemp=0;
for(i=0;i<ktau;i++){
Ntemp=10*(Ntemp)+17;
epsilon=ldiv(Ntemp,3);
Ntemp=epsilon.quot+1;
}
Nt=Nt+(int)_mpfr_ceil_log2((double)Nt)+(int)_mpfr_ceil_log2((double)Ntemp);
mpfr_init2(t1,Nt);
mpfr_init2(t2,Nt);
mpfr_init2(t,Nt);
mpfr_set(t,x,GMP_RNDN);
/* normalisation de la valeur de t */
/* tel que t= (m/2^r) x 2^(3e') avec e=3e'-r exposant et m mantisse de t*/
exp_t=(int)MPFR_EXP(t);
epsilon=ldiv(exp_t,3);
mpfr_div_2exp(t,t,MPFR_EXP(t),GMP_RNDN);
mpfr_div_2exp(t,t,(3-epsilon.rem),GMP_RNDN);
/*Gestion des negatifs*/
if(MPFR_SIGN(x)<0) MPFR_CHANGE_SIGN(t);
boucle=1;
while(boucle==1){
/* compute cbrt */
/*mpfr_log(t,x,GMP_RNDN);*/ /* ln(x) */
/*mpfr_div_ui(t,t,3,GMP_RNDN);*/ /* ln(x)/3 */
/*mpfr_exp(t,t,GMP_RNDN);*/ /* exp(ln(x)/3)*/
mpfr_set_d(t1,0.75,GMP_RNDN);
for(i=0;i<ktau;i++){
mpfr_mul_2exp(t2,t1,1,GMP_RNDN); /*2x*/
mpfr_mul(t1,t1,t1,GMP_RNDN); /*x^2*/
mpfr_div(t1,t,t1,GMP_RNDN); /*N/x^2*/
mpfr_add(t1,t1,t2,GMP_RNDN); /*2x+N/x^2*/
mpfr_div_ui(t1,t1,3,GMP_RNDN); /*(1/3)[2x+N/x^2]*/
}
err=Nt-1-(int)_mpfr_ceil_log2((double)Nt);
round=mpfr_can_round(t1,err,GMP_RNDN,rnd_mode,Ny);
if(round == 1){
/*Gestion des negatifs*/
if(MPFR_SIGN(x)<0) MPFR_CHANGE_SIGN(t1);
mpfr_mul_2exp(t1,t1,(epsilon.quot+1),GMP_RNDN);
mpfr_set(y,t1,rnd_mode);
boucle=0;
}
else{
Nt=Nt+10;
/* re-initialise of intermediary variable */
mpfr_set_prec(t1,Nt);
mpfr_set_prec(t2,Nt);
boucle=1;
}
}
mpfr_clear(t1);
mpfr_clear(t2);
mpfr_clear(t);
return(1);
}
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