add cbrt in fonctionnality

git-svn-id: svn://scm.gforge.inria.fr/svn/mpfr/trunk@1723 280ebfd0-de03-0410-8827-d642c229c3f4

1 files changed, 197 insertions, 0 deletions

diff --git a/cbrt.c b/cbrt.c
new file mode 100644
index 000000000..5783db0dd
--- /dev/null
+++ b/cbrt.c
@@ -0,0 +1,197 @@
+/* mpfr_cbrt -- power function x^(1/3)
+
+Copyright (C) 1999 Free Software Foundation.
+
+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 Library General Public License as published by
+the Free Software Foundation; either version 2 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 Library General Public
+License for more details.
+
+You should have received a copy of the GNU Library 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 <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);
+
+   
+    
+}