chromium / native_client / nacl-gcc / f80d6b9ee7f94755c697ffb7194fb01dd0c537dd / . / mpfr-2.4.1 / acos.c

/* mpfr_acos -- arc-cosinus of a floating-point number | |

Copyright 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009 Free Software Foundation, Inc. | |

Contributed by the Arenaire and Cacao projects, INRIA. | |

This file is part of the GNU MPFR Library, and was contributed by Mathieu Dutour. | |

The GNU 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 GNU 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 GNU MPFR Library; see the file COPYING.LIB. If not, write to | |

the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, | |

MA 02110-1301, USA. */ | |

#include "mpfr-impl.h" | |

int | |

mpfr_acos (mpfr_ptr acos, mpfr_srcptr x, mp_rnd_t rnd_mode) | |

{ | |

mpfr_t xp, arcc, tmp; | |

mp_exp_t supplement; | |

mp_prec_t prec; | |

int sign, compared, inexact; | |

MPFR_SAVE_EXPO_DECL (expo); | |

MPFR_ZIV_DECL (loop); | |

MPFR_LOG_FUNC (("x[%#R]=%R rnd=%d", x, x, rnd_mode), | |

("acos[%#R]=%R inexact=%d", acos, acos, inexact)); | |

/* Singular cases */ | |

if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x))) | |

{ | |

if (MPFR_IS_NAN (x) || MPFR_IS_INF (x)) | |

{ | |

MPFR_SET_NAN (acos); | |

MPFR_RET_NAN; | |

} | |

else /* necessarily x=0 */ | |

{ | |

MPFR_ASSERTD(MPFR_IS_ZERO(x)); | |

/* acos(0)=Pi/2 */ | |

inexact = mpfr_const_pi (acos, rnd_mode); | |

mpfr_div_2ui (acos, acos, 1, rnd_mode); /* exact */ | |

MPFR_RET (inexact); | |

} | |

} | |

/* Set x_p=|x| */ | |

sign = MPFR_SIGN (x); | |

mpfr_init2 (xp, MPFR_PREC (x)); | |

mpfr_abs (xp, x, GMP_RNDN); /* Exact */ | |

compared = mpfr_cmp_ui (xp, 1); | |

if (MPFR_UNLIKELY (compared >= 0)) | |

{ | |

mpfr_clear (xp); | |

if (compared > 0) /* acos(x) = NaN for x > 1 */ | |

{ | |

MPFR_SET_NAN(acos); | |

MPFR_RET_NAN; | |

} | |

else | |

{ | |

if (MPFR_IS_POS_SIGN (sign)) /* acos(+1) = 0 */ | |

return mpfr_set_ui (acos, 0, rnd_mode); | |

else /* acos(-1) = Pi */ | |

return mpfr_const_pi (acos, rnd_mode); | |

} | |

} | |

MPFR_SAVE_EXPO_MARK (expo); | |

/* Compute the supplement */ | |

mpfr_ui_sub (xp, 1, xp, GMP_RNDD); | |

if (MPFR_IS_POS_SIGN (sign)) | |

supplement = 2 - 2 * MPFR_GET_EXP (xp); | |

else | |

supplement = 2 - MPFR_GET_EXP (xp); | |

mpfr_clear (xp); | |

prec = MPFR_PREC (acos) + 10 + supplement; | |

/* VL: The following change concerning prec comes from r3145 | |

"Optimize mpfr_acos by choosing a better initial precision." | |

but it doesn't seem to be correct and leads to problems (assertion | |

failure or very important inefficiency) with tiny arguments. | |

Therefore, I've disabled it. */ | |

/* If x ~ 2^-N, acos(x) ~ PI/2 - x - x^3/6 | |

If Prec < 2*N, we can't round since x^3/6 won't be counted. */ | |

#if 0 | |

if (MPFR_PREC (acos) >= MPFR_PREC (x) && MPFR_GET_EXP (x) < 0) | |

{ | |

mpfr_uexp_t pmin = (mpfr_uexp_t) (-2 * MPFR_GET_EXP (x)) + 5; | |

MPFR_ASSERTN (pmin <= MPFR_PREC_MAX); | |

if (prec < pmin) | |

prec = pmin; | |

} | |

#endif | |

mpfr_init2 (tmp, prec); | |

mpfr_init2 (arcc, prec); | |

MPFR_ZIV_INIT (loop, prec); | |

for (;;) | |

{ | |

/* acos(x) = Pi/2 - asin(x) = Pi/2 - atan(x/sqrt(1-x^2)) */ | |

mpfr_sqr (tmp, x, GMP_RNDN); | |

mpfr_ui_sub (tmp, 1, tmp, GMP_RNDN); | |

mpfr_sqrt (tmp, tmp, GMP_RNDN); | |

mpfr_div (tmp, x, tmp, GMP_RNDN); | |

mpfr_atan (arcc, tmp, GMP_RNDN); | |

mpfr_const_pi (tmp, GMP_RNDN); | |

mpfr_div_2ui (tmp, tmp, 1, GMP_RNDN); | |

mpfr_sub (arcc, tmp, arcc, GMP_RNDN); | |

if (MPFR_LIKELY (MPFR_CAN_ROUND (arcc, prec-supplement, | |

MPFR_PREC (acos), rnd_mode))) | |

break; | |

MPFR_ZIV_NEXT (loop, prec); | |

mpfr_set_prec (tmp, prec); | |

mpfr_set_prec (arcc, prec); | |

} | |

MPFR_ZIV_FREE (loop); | |

inexact = mpfr_set (acos, arcc, rnd_mode); | |

mpfr_clear (tmp); | |

mpfr_clear (arcc); | |

MPFR_SAVE_EXPO_FREE (expo); | |

return mpfr_check_range (acos, inexact, rnd_mode); | |

} |