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

/* mpfr_coth - Hyperbolic cotangent 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 hyperbolic cotangent is defined by coth(x) = 1/tanh(x) | |

coth (NaN) = NaN. | |

coth (+Inf) = 1 | |

coth (-Inf) = -1 | |

coth (+0) = +0. | |

coth (-0) = -0. | |

*/ | |

#define FUNCTION mpfr_coth | |

#define INVERSE mpfr_tanh | |

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

#define ACTION_INF(y) return mpfr_set_si (y, MPFR_IS_POS(x) ? 1 : -1, rnd_mode) | |

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

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

/* We know |coth(x)| > 1, thus if the approximation z is such that | |

1 <= z <= 1 + 2^(-p) where p is the target precision, then the | |

result is either 1 or nextabove(1) = 1 + 2^(1-p). */ | |

#define ACTION_SPECIAL \ | |

if (MPFR_GET_EXP(z) == 1) /* 1 <= |z| < 2 */ \ | |

{ \ | |

/* the following is exact by Sterbenz theorem */ \ | |

mpfr_sub_si (z, z, MPFR_SIGN(z) > 0 ? 1 : -1, GMP_RNDN); \ | |

if (MPFR_IS_ZERO(z) || MPFR_GET_EXP(z) <= - (mp_exp_t) precy) \ | |

{ \ | |

mpfr_add_si (z, z, MPFR_SIGN(z) > 0 ? 1 : -1, GMP_RNDN); \ | |

break; \ | |

} \ | |

} | |

/* The analysis is adapted from that for mpfr_csc: | |

near x=0, coth(x) = 1/x + x/3 + ..., more precisely we have | |

|coth(x) - 1/x| <= 0.32 for |x| <= 1. Like for csc, the error term has | |

the same sign as 1/x, thus |coth(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) > 0.32, 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 |coth(x) - 1/x| <= 0.32, if 2^(-2n) ufp(y) >= 0.64, then | |

|y - coth(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) + 1 <= -2 MAX(PREC(x),PREC(Y)). */ | |

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

if (MPFR_EXP(x) + 1 <= -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" |