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

/* mpfr_log -- natural logarithm of a floating-point number | |

Copyright 1999, 2000, 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 computation of log(x) is done using the formula : | |

if we want p bits of the result, | |

pi | |

log(x) ~ ------------ - m log 2 | |

2 AG(1,4/s) | |

where s = x 2^m > 2^(p/2) | |

More precisely, if F(x) = int(1/sqrt(1-(1-x^2)*sin(t)^2), t=0..PI/2), | |

then for s>=1.26 we have log(s) < F(4/s) < log(s)*(1+4/s^2) | |

from which we deduce pi/2/AG(1,4/s)*(1-4/s^2) < log(s) < pi/2/AG(1,4/s) | |

so the relative error 4/s^2 is < 4/2^p i.e. 4 ulps. | |

*/ | |

int | |

mpfr_log (mpfr_ptr r, mpfr_srcptr a, mp_rnd_t rnd_mode) | |

{ | |

int inexact; | |

mp_prec_t p, q; | |

mpfr_t tmp1, tmp2; | |

mp_limb_t *tmp1p, *tmp2p; | |

MPFR_SAVE_EXPO_DECL (expo); | |

MPFR_ZIV_DECL (loop); | |

MPFR_TMP_DECL(marker); | |

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

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

/* Special cases */ | |

if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (a))) | |

{ | |

/* If a is NaN, the result is NaN */ | |

if (MPFR_IS_NAN (a)) | |

{ | |

MPFR_SET_NAN (r); | |

MPFR_RET_NAN; | |

} | |

/* check for infinity before zero */ | |

else if (MPFR_IS_INF (a)) | |

{ | |

if (MPFR_IS_NEG (a)) | |

/* log(-Inf) = NaN */ | |

{ | |

MPFR_SET_NAN (r); | |

MPFR_RET_NAN; | |

} | |

else /* log(+Inf) = +Inf */ | |

{ | |

MPFR_SET_INF (r); | |

MPFR_SET_POS (r); | |

MPFR_RET (0); | |

} | |

} | |

else /* a is zero */ | |

{ | |

MPFR_ASSERTD (MPFR_IS_ZERO (a)); | |

MPFR_SET_INF (r); | |

MPFR_SET_NEG (r); | |

MPFR_RET (0); /* log(0) is an exact -infinity */ | |

} | |

} | |

/* If a is negative, the result is NaN */ | |

else if (MPFR_UNLIKELY (MPFR_IS_NEG (a))) | |

{ | |

MPFR_SET_NAN (r); | |

MPFR_RET_NAN; | |

} | |

/* If a is 1, the result is 0 */ | |

else if (MPFR_UNLIKELY (MPFR_GET_EXP (a) == 1 && mpfr_cmp_ui (a, 1) == 0)) | |

{ | |

MPFR_SET_ZERO (r); | |

MPFR_SET_POS (r); | |

MPFR_RET (0); /* only "normal" case where the result is exact */ | |

} | |

q = MPFR_PREC (r); | |

/* use initial precision about q+lg(q)+5 */ | |

p = q + 5 + 2 * MPFR_INT_CEIL_LOG2 (q); | |

/* % ~(mp_prec_t)BITS_PER_MP_LIMB ; | |

m=q; while (m) { p++; m >>= 1; } */ | |

/* if (MPFR_LIKELY(p % BITS_PER_MP_LIMB != 0)) | |

p += BITS_PER_MP_LIMB - (p%BITS_PER_MP_LIMB); */ | |

MPFR_TMP_MARK(marker); | |

MPFR_SAVE_EXPO_MARK (expo); | |

MPFR_ZIV_INIT (loop, p); | |

for (;;) | |

{ | |

mp_size_t size; | |

long m; | |

mp_exp_t cancel; | |

/* Calculus of m (depends on p) */ | |

m = (p + 1) / 2 - MPFR_GET_EXP (a) + 1; | |

/* All the mpfr_t needed have a precision of p */ | |

size = (p-1)/BITS_PER_MP_LIMB+1; | |

MPFR_TMP_INIT (tmp1p, tmp1, p, size); | |

MPFR_TMP_INIT (tmp2p, tmp2, p, size); | |

mpfr_mul_2si (tmp2, a, m, GMP_RNDN); /* s=a*2^m, err<=1 ulp */ | |

mpfr_div (tmp1, __gmpfr_four, tmp2, GMP_RNDN);/* 4/s, err<=2 ulps */ | |

mpfr_agm (tmp2, __gmpfr_one, tmp1, GMP_RNDN); /* AG(1,4/s),err<=3 ulps */ | |

mpfr_mul_2ui (tmp2, tmp2, 1, GMP_RNDN); /* 2*AG(1,4/s), err<=3 ulps */ | |

mpfr_const_pi (tmp1, GMP_RNDN); /* compute pi, err<=1ulp */ | |

mpfr_div (tmp2, tmp1, tmp2, GMP_RNDN); /* pi/2*AG(1,4/s), err<=5ulps */ | |

mpfr_const_log2 (tmp1, GMP_RNDN); /* compute log(2), err<=1ulp */ | |

mpfr_mul_si (tmp1, tmp1, m, GMP_RNDN); /* compute m*log(2),err<=2ulps */ | |

mpfr_sub (tmp1, tmp2, tmp1, GMP_RNDN); /* log(a), err<=7ulps+cancel */ | |

if (MPFR_LIKELY (MPFR_IS_PURE_FP (tmp1) && MPFR_IS_PURE_FP (tmp2))) | |

{ | |

cancel = MPFR_GET_EXP (tmp2) - MPFR_GET_EXP (tmp1); | |

MPFR_LOG_MSG (("canceled bits=%ld\n", (long) cancel)); | |

MPFR_LOG_VAR (tmp1); | |

if (MPFR_UNLIKELY (cancel < 0)) | |

cancel = 0; | |

/* we have 7 ulps of error from the above roundings, | |

4 ulps from the 4/s^2 second order term, | |

plus the canceled bits */ | |

if (MPFR_LIKELY (MPFR_CAN_ROUND (tmp1, p-cancel-4, q, rnd_mode))) | |

break; | |

/* VL: I think it is better to have an increment that it isn't | |

too low; in particular, the increment must be positive even | |

if cancel = 0 (can this occur?). */ | |

p += cancel >= 8 ? cancel : 8; | |

} | |

else | |

{ | |

/* TODO: find why this case can occur and what is best to do | |

with it. */ | |

p += 32; | |

} | |

MPFR_ZIV_NEXT (loop, p); | |

} | |

MPFR_ZIV_FREE (loop); | |

inexact = mpfr_set (r, tmp1, rnd_mode); | |

/* We clean */ | |

MPFR_TMP_FREE(marker); | |

MPFR_SAVE_EXPO_FREE (expo); | |

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

} |