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

/* mpfr_csc - cosecant function. | |

Copyright 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. | |

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. */ | |

/* the cosecant is defined by csc(x) = 1/sin(x). | |

csc (NaN) = NaN. | |

csc (+Inf) = csc (-Inf) = NaN. | |

csc (+0) = +Inf. | |

csc (-0) = -Inf. | |

*/ | |

#define FUNCTION mpfr_csc | |

#define INVERSE mpfr_sin | |

#define ACTION_NAN(y) do { MPFR_SET_NAN(y); MPFR_RET_NAN; } while (1) | |

#define ACTION_INF(y) do { MPFR_SET_NAN(y); MPFR_RET_NAN; } while (1) | |

#define ACTION_ZERO(y,x) do { MPFR_SET_SAME_SIGN(y,x); MPFR_SET_INF(y); \ | |

MPFR_RET(0); } while (1) | |

/* near x=0, we have csc(x) = 1/x + x/6 + ..., more precisely we have | |

|csc(x) - 1/x| <= 0.2 for |x| <= 1. The analysis is similar to that for | |

gamma(x) near x=0 (see gamma.c), except here the error term has the same | |

sign as 1/x, thus |csc(x)| >= |1/x|. Then: | |

(i) either x is a power of two, then 1/x is exactly representable, and | |

as long as 1/2*ulp(1/x) > 0.2, we can conclude; | |

(ii) otherwise assume x has <= n bits, and y has <= n+1 bits, then | |

|y - 1/x| >= 2^(-2n) ufp(y), where ufp means unit in first place. | |

Since |csc(x) - 1/x| <= 0.2, if 2^(-2n) ufp(y) >= 0.4, then | |

|y - csc(x)| >= 2^(-2n-1) ufp(y), and rounding 1/x gives the correct result. | |

If x < 2^E, then y > 2^(-E), thus ufp(y) > 2^(-E-1). | |

A sufficient condition is thus EXP(x) <= -2 MAX(PREC(x),PREC(Y)). */ | |

#define ACTION_TINY(y,x,r) \ | |

if (MPFR_EXP(x) <= -2 * (mp_exp_t) MAX(MPFR_PREC(x), MPFR_PREC(y))) \ | |

{ \ | |

int signx = MPFR_SIGN(x); \ | |

inexact = mpfr_ui_div (y, 1, x, r); \ | |

if (inexact == 0) /* x is a power of two */ \ | |

{ /* result always 1/x, except when rounding away from zero */ \ | |

if (rnd_mode == GMP_RNDU) \ | |

{ \ | |

if (signx > 0) \ | |

mpfr_nextabove (y); /* 2^k + epsilon */ \ | |

inexact = 1; \ | |

} \ | |

else if (rnd_mode == GMP_RNDD) \ | |

{ \ | |

if (signx < 0) \ | |

mpfr_nextbelow (y); /* -2^k - epsilon */ \ | |

inexact = -1; \ | |

} \ | |

else /* round to zero, or nearest */ \ | |

inexact = -signx; \ | |

} \ | |

MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, __gmpfr_flags); \ | |

goto end; \ | |

} | |

#include "gen_inverse.h" |