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

/* mpfr_sinh_cosh -- hyperbolic sine and cosine | |

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. | |

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. */ | |

#define MPFR_NEED_LONGLONG_H | |

#include "mpfr-impl.h" | |

/* The computations are done by | |

cosh(x) = 1/2 [e^(x)+e^(-x)] | |

sinh(x) = 1/2 [e^(x)-e^(-x)] | |

Adapted from mpfr_sinh.c */ | |

int | |

mpfr_sinh_cosh (mpfr_ptr sh, mpfr_ptr ch, mpfr_srcptr xt, mp_rnd_t rnd_mode) | |

{ | |

mpfr_t x; | |

int inexact, inexact_sh, inexact_ch; | |

MPFR_ASSERTN (sh != ch); | |

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

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

if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (xt))) | |

{ | |

if (MPFR_IS_NAN (xt)) | |

{ | |

MPFR_SET_NAN (ch); | |

MPFR_SET_NAN (sh); | |

MPFR_RET_NAN; | |

} | |

else if (MPFR_IS_INF (xt)) | |

{ | |

MPFR_SET_INF (sh); | |

MPFR_SET_SAME_SIGN (sh, xt); | |

MPFR_SET_INF (ch); | |

MPFR_SET_POS (ch); | |

MPFR_RET (0); | |

} | |

else /* xt is zero */ | |

{ | |

MPFR_ASSERTD (MPFR_IS_ZERO (xt)); | |

MPFR_SET_ZERO (sh); /* sinh(0) = 0 */ | |

MPFR_SET_SAME_SIGN (sh, xt); | |

return mpfr_set_ui (ch, 1, rnd_mode); /* cosh(0) = 1 */ | |

} | |

} | |

/* Warning: if we use MPFR_FAST_COMPUTE_IF_SMALL_INPUT here, make sure | |

that the code also works in case of overlap (see sin_cos.c) */ | |

MPFR_TMP_INIT_ABS (x, xt); | |

{ | |

mpfr_t s, c, ti; | |

mp_exp_t d; | |

mp_prec_t N; /* Precision of the intermediary variables */ | |

long int err; /* Precision of error */ | |

MPFR_ZIV_DECL (loop); | |

MPFR_SAVE_EXPO_DECL (expo); | |

MPFR_GROUP_DECL (group); | |

MPFR_SAVE_EXPO_MARK (expo); | |

/* compute the precision of intermediary variable */ | |

N = MPFR_PREC (ch); | |

N = MAX (N, MPFR_PREC (sh)); | |

N = MAX (N, MPFR_PREC (x)); | |

/* the optimal number of bits : see algorithms.ps */ | |

N = N + MPFR_INT_CEIL_LOG2 (N) + 4; | |

/* initialise of intermediary variables */ | |

MPFR_GROUP_INIT_3 (group, N, s, c, ti); | |

/* First computation of sinh_cosh */ | |

MPFR_ZIV_INIT (loop, N); | |

for (;;) | |

{ | |

MPFR_BLOCK_DECL (flags); | |

/* compute sinh_cosh */ | |

MPFR_BLOCK (flags, mpfr_exp (s, x, GMP_RNDD)); | |

if (MPFR_OVERFLOW (flags)) | |

/* exp(x) does overflow */ | |

{ | |

/* since cosh(x) >= exp(x), cosh(x) overflows too */ | |

inexact_ch = mpfr_overflow (ch, rnd_mode, MPFR_SIGN_POS); | |

/* sinh(x) may be representable */ | |

inexact_sh = mpfr_sinh (sh, xt, rnd_mode); | |

MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, MPFR_FLAGS_OVERFLOW); | |

break; | |

} | |

d = MPFR_GET_EXP (s); | |

mpfr_ui_div (ti, 1, s, GMP_RNDU); /* 1/exp(x) */ | |

mpfr_add (c, s, ti, GMP_RNDU); /* exp(x) + 1/exp(x) */ | |

mpfr_sub (s, s, ti, GMP_RNDN); /* exp(x) - 1/exp(x) */ | |

mpfr_div_2ui (c, c, 1, GMP_RNDN); /* 1/2(exp(x) + 1/exp(x)) */ | |

mpfr_div_2ui (s, s, 1, GMP_RNDN); /* 1/2(exp(x) - 1/exp(x)) */ | |

/* it may be that s is zero (in fact, it can only occur when exp(x)=1, | |

and thus ti=1 too) */ | |

if (MPFR_IS_ZERO (s)) | |

err = N; /* double the precision */ | |

else | |

{ | |

/* calculation of the error */ | |

d = d - MPFR_GET_EXP (s) + 2; | |

/* error estimate: err = N-(__gmpfr_ceil_log2(1+pow(2,d)));*/ | |

err = N - (MAX (d, 0) + 1); | |

if (MPFR_LIKELY (MPFR_CAN_ROUND (s, err, MPFR_PREC (sh), | |

rnd_mode) && \ | |

MPFR_CAN_ROUND (c, err, MPFR_PREC (ch), | |

rnd_mode))) | |

{ | |

inexact_sh = mpfr_set4 (sh, s, rnd_mode, MPFR_SIGN (xt)); | |

inexact_ch = mpfr_set (ch, c, rnd_mode); | |

break; | |

} | |

} | |

/* actualisation of the precision */ | |

N += err; | |

MPFR_ZIV_NEXT (loop, N); | |

MPFR_GROUP_REPREC_3 (group, N, s, c, ti); | |

} | |

MPFR_ZIV_FREE (loop); | |

MPFR_GROUP_CLEAR (group); | |

MPFR_SAVE_EXPO_FREE (expo); | |

} | |

/* now, let's raise the flags if needed */ | |

inexact = mpfr_check_range (sh, inexact_sh, rnd_mode); | |

inexact = mpfr_check_range (ch, inexact_ch, rnd_mode) || inexact; | |

return inexact; | |

} |