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/* mpfr_atan -- arc-tangent of a floating-point number
Copyright (C) 2001 Free Software Foundation.
This file is part of the MPFR Library, and was contributed by Mathieu Dutour.
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"
#define CST 2.27 /* CST=1+ln(2.4)/ln(2) */
#define CST2 1.45 /* CST2=1/ln(2) */
int mpfr_atan_aux _PROTO((mpfr_ptr, mpz_srcptr, int, int));
#undef B
#define A
#define A1 1
#define A2 2
#define C
#define C1 3
#define C2 2
#define NO_FACTORIAL
#define GENERIC mpfr_atan_aux
#include "generic.c"
#undef C
#undef C1
#undef C2
#undef A
#undef A1
#undef A2
#undef NO_FACTORIAL
#undef GENERIC
int
#if __STDC__
mpfr_atan (mpfr_ptr arctangent, mpfr_srcptr x, mp_rnd_t rnd_mode)
#else
mpfr_atan (arctangent, x, rnd_mode)
mpfr_ptr arctangent;
mpfr_srcptr x;
mp_rnd_t rnd_mode;
#endif
{
mpfr_t Pisur2;
mpfr_t xp;
mpfr_t arctgt;
int comparaison, signe, suplement;
mpfr_t t_arctan;
int i;
mpz_t ukz;
mpfr_t ukf;
mpfr_t sk,Ak;
mpz_t square;
mpfr_t tmp_arctan;
mpfr_t tmp, tmp2;
#ifdef DEBUG
mpfr_t tst;
#endif
int twopoweri;
int Prec;
int prec_x;
int prec_arctan;
int good = 0;
int realprec;
int estimated_delta;
/* calculation of the floor */
int exptol;
int N0;
int logn;
/* Trivial cases */
if (MPFR_IS_NAN(x))
{
MPFR_SET_NAN(arctangent);
return 1;
}
if (MPFR_IS_INF(x))
{
if (MPFR_SIGN(x) > 0) /* arctan(+inf) = Pi/2 */
mpfr_const_pi (arctangent, rnd_mode);
else /* arctan(-inf) = -Pi/2 */
{
if (rnd_mode == GMP_RNDU)
rnd_mode = GMP_RNDD;
else if (rnd_mode == GMP_RNDD)
rnd_mode = GMP_RNDU;
mpfr_const_pi (arctangent, rnd_mode);
}
MPFR_EXP(arctangent)--;
return 1; /* inexact */
}
if (!MPFR_NOTZERO(x))
{
mpfr_set_ui(arctangent, 0, GMP_RNDN);
return 0; /* exact result */
}
signe = MPFR_SIGN(x);
prec_arctan = MPFR_PREC(arctangent);
/* Set x_p=|x| */
mpfr_init2(xp, MPFR_PREC(x));
mpfr_set(xp, x, rnd_mode);
if (signe == -1)
MPFR_CHANGE_SIGN(xp);
/* Other simple case arctang(-+1)=-+pi/4 */
comparaison=mpfr_cmp_ui(xp, 1);
if (comparaison == 0) {
mpfr_init2(Pisur2, prec_arctan);
mpfr_const_pi(Pisur2, rnd_mode);
mpfr_div_2exp(arctangent, Pisur2, 2, rnd_mode);
if (signe == -1)
MPFR_CHANGE_SIGN(arctangent);
mpfr_clear(Pisur2);
mpfr_clear(xp);
return 0; /* Result correct */
}
if (comparaison > 0)
suplement = 1;
else
suplement = 2-MPFR_EXP(xp);
prec_x = _mpfr_ceil_log2 ((double) MPFR_PREC(x) / BITS_PER_MP_LIMB);
logn = _mpfr_ceil_log2 ((double) prec_x);
if (logn < 2) logn = 2;
realprec = prec_arctan + _mpfr_ceil_log2((double) prec_arctan) + 4;
mpz_init(ukz);
mpz_init(square);
while (!good){
N0 = _mpfr_ceil_log2((double) realprec + suplement + CST);
estimated_delta = 1 + suplement + _mpfr_ceil_log2((double) (3*N0-2));
Prec = realprec+estimated_delta;
/* Initialisation */
mpfr_init2(sk,Prec);
mpfr_init2(ukf, Prec);
mpfr_init2(t_arctan, Prec);
mpfr_init2(tmp_arctan, Prec);
mpfr_init2(tmp, Prec);
mpfr_init2(tmp2, Prec);
mpfr_init2(Ak, Prec);
mpfr_init2(arctgt, Prec);
#ifdef DEBUG
/* Tests */
mpfr_init2(tst, realprec);
#endif
if (comparaison > 0)
{
mpfr_init2(Pisur2, Prec);
mpfr_const_pi(Pisur2, GMP_RNDD);
mpfr_div_2exp(Pisur2, Pisur2, 1, GMP_RNDD);
mpfr_ui_div(sk, 1, xp, GMP_RNDD);
}
else
mpfr_set(sk, xp, GMP_RNDN);
/* Assignation */
mpfr_set_ui(tmp_arctan, 0, GMP_RNDN);
twopoweri = 1;
for(i = 0; i <= N0; i++){
mpfr_mul_2exp(tmp, sk, twopoweri, GMP_RNDD);
/* Calculation of trunc(tmp) --> mpz */
mpfr_trunc(ukf, tmp);
exptol=mpz_set_fr(ukz, ukf);
if (exptol>0)
mpz_mul_2exp(ukz, ukz, exptol);
else
mpz_tdiv_q_2exp(ukz, ukz, (unsigned long int) (-exptol));
/* Calculation of arctan(Ak) */
mpz_mul(square, ukz, ukz);
mpz_neg(square, square);
mpfr_atan_aux(t_arctan, square, 2*twopoweri, N0 - i);
mpfr_set_z(Ak, ukz, GMP_RNDD);
mpfr_div_2exp(Ak, Ak, twopoweri, GMP_RNDD);
mpfr_mul(t_arctan, t_arctan, Ak, GMP_RNDD);
/* Addition and iteration */
mpfr_add(tmp_arctan, tmp_arctan, t_arctan, GMP_RNDD);
if (i<N0)
{
mpfr_sub(tmp, sk, Ak, GMP_RNDD);
mpfr_mul(tmp2, sk, Ak, GMP_RNDU);
mpfr_add_ui(tmp2, tmp2, 1, GMP_RNDU);
mpfr_div(sk, tmp, tmp2, GMP_RNDD);
twopoweri <<= 1;
}
}
if (comparaison > 0)
{
mpfr_sub(arctgt, Pisur2, tmp_arctan, GMP_RNDD);
if (signe == -1)
MPFR_CHANGE_SIGN(arctgt);
}
else
{
mpfr_set(arctgt, tmp_arctan, GMP_RNDD);
if (signe == -1)
MPFR_CHANGE_SIGN(arctgt);
}
#ifdef DEBUG
mpfr_set(tst, arctgt, rnd_mode);
#endif
if (mpfr_can_round(arctgt, realprec, GMP_RNDD, rnd_mode, MPFR_PREC(arctangent)))
{
mpfr_set(arctangent, arctgt, rnd_mode);
good = 1;
realprec += 1;
}
else
{
realprec += _mpfr_ceil_log2 ((double) realprec);
}
mpfr_clear(sk);
mpfr_clear(ukf);
mpfr_clear(t_arctan);
mpfr_clear(tmp_arctan);
mpfr_clear(tmp);
mpfr_clear(tmp2);
mpfr_clear(Ak);
mpfr_clear(arctgt);
#ifdef DEBUG
mpfr_clear(tst);
#endif
if (comparaison > 0)
mpfr_clear(Pisur2);
}
mpfr_clear(xp);
mpz_clear(ukz);
mpz_clear(square);
return 1; /* inexact result */
}
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