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/* mpfr_sin_cos -- sine and cosine of a floating-point number
Copyright (C) 2000 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"
int mpfr_sin_aux _PROTO ((mpfr_ptr, mpz_srcptr, int, int));
int mpfr_cos_aux _PROTO ((mpfr_ptr, mpz_srcptr, int, int));
#undef A
#undef B
#define C
#define C1 3
#define C2 2
#define GENERIC mpfr_sin_aux
#include "generic.c"
#undef C
#undef C1
#undef C2
#undef GENERIC
#undef A
#undef B
#define C
#define C1 1
#define C2 2
#define GENERIC mpfr_cos_aux
#include "generic.c"
#define shift (BITS_PER_MP_LIMB / 2)
int
#if __STDC__
mpfr_sin_cos (mpfr_ptr sinus, mpfr_ptr cosinus, mpfr_srcptr x, mp_rnd_t rnd_mode)
#else
mpfr_sin_cos (sinus, cosinus, x, rnd_mode)
mpfr_ptr sinus;
mpfr_ptr cosinus;
mpfr_srcptr x;
mp_rnd_t rnd_mode;
#endif
{
mpfr_t t_sin, t_cos;
mpfr_t x_copy;
int i,k;
mpz_t uk;
mpz_t square;
mpfr_t tmp_sin, tmp_cos;
mpfr_t tmp;
mpfr_t inter;
int ttt;
int twopoweri;
int Prec;
int loop;
int prec_x;
int shift_x = 0;
int good = 0;
int realprec = 0, target_prec;
int iter;
int factor;
int logn;
int tmp_factor;
int tmpi;
if (sinus == cosinus) {
fprintf (stderr, "Error in mpfr_sin_cos: 1st and 2nd operands must be different\n");
exit (1);
}
if (MPFR_IS_NAN(x) || MPFR_IS_INF(x)) {
MPFR_SET_NAN(sinus);
MPFR_SET_NAN(cosinus);
return 1; /* inexact */
}
if (!MPFR_NOTZERO(x)) {
mpfr_set_ui(sinus, 0, GMP_RNDN);
mpfr_set_ui(cosinus, 1, GMP_RNDN);
return 0; /* exact results */
}
prec_x = _mpfr_ceil_log2 ((double) MPFR_PREC(x) / BITS_PER_MP_LIMB);
ttt = MPFR_EXP(x);
mpfr_init2(x_copy, MPFR_PREC(x));
mpfr_set(x_copy,x,GMP_RNDD);
mpz_init(square);
/* on fait le shift pour que le nombre soit inferieur a 1 */
if (ttt > 0)
{
shift_x = ttt;
mpfr_mul_2exp(x_copy,x,-ttt, GMP_RNDN);
ttt = MPFR_EXP(x_copy);
}
target_prec = MPFR_PREC(sinus);
if (MPFR_PREC(cosinus) > target_prec) target_prec = MPFR_PREC(cosinus);
logn = _mpfr_ceil_log2 ((double) target_prec);
if (logn < 2) logn = 2;
factor = logn;
realprec = target_prec + logn;
mpz_init (uk);
while (!good) {
Prec = realprec + 2*shift + 2 + shift_x + factor;
k = _mpfr_ceil_log2 ((double) Prec / BITS_PER_MP_LIMB);
/* now we extract */
mpfr_init2(t_sin, Prec);
mpfr_init2(t_cos, Prec);
mpfr_init2(tmp, Prec);
mpfr_init2(tmp_sin, Prec);
mpfr_init2(tmp_cos, Prec);
mpfr_init2(inter, Prec);
mpfr_set_ui(tmp_sin,0,GMP_RNDN);
mpfr_set_ui(tmp_cos,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)
{
mpz_mul (square, uk, uk);
mpz_neg (square, square);
mpfr_sin_aux (t_sin, square, 2*(twopoweri - ttt) + 2, k - i + 1);
mpfr_cos_aux (t_cos, square, 2*(twopoweri - ttt) + 2, k - i + 1);
mpfr_set_z (tmp, uk, GMP_RNDD);
mpfr_mul (t_sin, t_sin, tmp, GMP_RNDD);
mpfr_div_2exp (t_sin, t_sin, twopoweri - ttt, GMP_RNDD);
}
else
{
/* cas particulier : on est oblige de faire les calculs avec x/2^.
puis elever au carre (plus rapide) */
mpz_set (square, uk);
mpz_mul(square, square, square);
mpz_neg(square, square);
/* pour l'instant, shift = 0 ... */
/* ATTENTION, IL FAUT AUSSI MULTIPLIER LE DENOMINATEUR */
mpfr_sin_aux(t_sin,square, 2*(shift + twopoweri - ttt) + 2, k+1);
mpfr_cos_aux(t_cos,square, 2*(shift + twopoweri - ttt) + 2, k+1);
mpfr_set_z (tmp, uk, GMP_RNDD);
mpfr_mul(t_sin, t_sin, tmp,GMP_RNDD);
/* LA AUSSI, IL FAUT PENSER A DECALER DE twopoweri - ttt) */
mpfr_div_2exp(t_sin,t_sin, twopoweri - ttt + shift, GMP_RNDD);
for (loop= 0 ; loop < shift; loop++){
/* t_sin = sin(a)
t_cos = cos(a) */
/* on veut t_sin = 2 sin a cos a
et t_cos = 2 * cos^2 - 1 */
mpfr_mul(t_sin, t_sin, t_cos, GMP_RNDD);
mpfr_mul_2exp(t_sin, t_sin, 1, GMP_RNDD);
mpfr_mul(t_cos, t_cos, t_cos, GMP_RNDD);
mpfr_mul_2exp(t_cos, t_cos, 1, GMP_RNDD);
mpfr_sub_ui(t_cos, t_cos, 1, GMP_RNDD);
}
}
/* on utilise cos(a+b) = cos a cos b - sin a sin b
sin(a+b) = sin a cos b + cos a sin b */
/* Donnees :
tmp = cos(a)
tmp_sin = sin(a)
t_sin = sin(b)
t_cos = cos(b) */
mpfr_set(tmp, tmp_cos,GMP_RNDD);
/* inter = sin a sin b */
mpfr_mul(inter, tmp_sin, t_sin, GMP_RNDD);
/* tmp_cos = cos a cos b */
mpfr_mul(tmp_cos, tmp_cos, t_cos, GMP_RNDD);
/* tmp_cos = cos (a+b) */
mpfr_sub(tmp_cos, tmp_cos, inter, GMP_RNDD);
/* inter = cos a sin b */
mpfr_mul(inter, tmp, t_sin, GMP_RNDD);
/* tmp_sin = sin a cos b */
mpfr_mul(tmp_sin, tmp_sin, t_cos, GMP_RNDD);
/* tmp_sin = sin (a+b) */
mpfr_add(tmp_sin, tmp_sin, inter, GMP_RNDD);
twopoweri <<= 1;
}
tmp_factor= factor;
for (loop= 0 ; loop < shift_x; loop++){
mpfr_mul(tmp_sin, tmp_sin, tmp_cos, GMP_RNDD);
mpfr_mul_2exp(tmp_sin, tmp_sin, 1, GMP_RNDD);
mpfr_mul(tmp_cos, tmp_cos, tmp_cos, GMP_RNDD);
mpfr_mul_2exp(tmp_cos, tmp_cos, 1, GMP_RNDD);
tmpi = -MPFR_EXP(tmp_cos);
mpfr_set_ui(tmp, 1, GMP_RNDN);
mpfr_sub(tmp_cos, tmp_cos, tmp, GMP_RNDD);
/* rep\'erer si le nombre de chiffres obtenu est suffisant pour
avoir la bonne pr\'ecision. Le probl\`eme : comment faire ?
la pr\'ecision s'obtient en comparant
(Prec-factor) a la pr\'ecision obtenue r\'eellement, celle-ci
\'etant donn\'ee par Prec + MPFR_EXP(tmp_cos).
il faut donc comparer MPFR_EXP(tmp_cos) a factor */
tmp_factor -= -MPFR_EXP(tmp_cos) + tmpi;
if (tmp_factor <= 0)
{
factor += -tmp_factor + 5;
goto try_again;
}
}
if (mpfr_can_round(tmp_sin, realprec, GMP_RNDD, rnd_mode, MPFR_PREC(sinus)) &&
mpfr_can_round(tmp_cos, realprec, GMP_RNDD, rnd_mode, MPFR_PREC(cosinus))) {
mpfr_set(sinus, tmp_sin, rnd_mode);
mpfr_set(cosinus, tmp_cos, rnd_mode);
good = 1;
}
else {
realprec += 3*logn;
}
try_again:
mpfr_clear(t_sin);
mpfr_clear(t_cos);
mpfr_clear(tmp);
mpfr_clear(tmp_sin);
mpfr_clear(tmp_cos);
mpfr_clear(inter);
}
mpz_clear (uk);
mpz_clear (square);
mpfr_clear (x_copy);
return 1; /* inexact result */
}
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