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Diffstat (limited to 'log.c')
-rw-r--r-- | log.c | 174 |
1 files changed, 0 insertions, 174 deletions
diff --git a/log.c b/log.c deleted file mode 100644 index c657a6ac2..000000000 --- a/log.c +++ /dev/null @@ -1,174 +0,0 @@ -/* mpfr_log -- natural logarithm of a floating-point number - -Copyright 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010 Free Software Foundation, Inc. -Contributed by the Arenaire and Caramel 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 3 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.LESSER. If not, see -http://www.gnu.org/licenses/ or 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, mpfr_rnd_t rnd_mode) -{ - int inexact; - mpfr_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); - /* % ~(mpfr_prec_t)GMP_NUMB_BITS ; - m=q; while (m) { p++; m >>= 1; } */ - /* if (MPFR_LIKELY(p % GMP_NUMB_BITS != 0)) - p += GMP_NUMB_BITS - (p%GMP_NUMB_BITS); */ - - MPFR_TMP_MARK(marker); - MPFR_SAVE_EXPO_MARK (expo); - - MPFR_ZIV_INIT (loop, p); - for (;;) - { - mp_size_t size; - long m; - mpfr_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)/GMP_NUMB_BITS+1; - MPFR_TMP_INIT (tmp1p, tmp1, p, size); - MPFR_TMP_INIT (tmp2p, tmp2, p, size); - - mpfr_mul_2si (tmp2, a, m, MPFR_RNDN); /* s=a*2^m, err<=1 ulp */ - mpfr_div (tmp1, __gmpfr_four, tmp2, MPFR_RNDN);/* 4/s, err<=2 ulps */ - mpfr_agm (tmp2, __gmpfr_one, tmp1, MPFR_RNDN); /* AG(1,4/s),err<=3 ulps */ - mpfr_mul_2ui (tmp2, tmp2, 1, MPFR_RNDN); /* 2*AG(1,4/s), err<=3 ulps */ - mpfr_const_pi (tmp1, MPFR_RNDN); /* compute pi, err<=1ulp */ - mpfr_div (tmp2, tmp1, tmp2, MPFR_RNDN); /* pi/2*AG(1,4/s), err<=5ulps */ - mpfr_const_log2 (tmp1, MPFR_RNDN); /* compute log(2), err<=1ulp */ - mpfr_mul_si (tmp1, tmp1, m, MPFR_RNDN); /* compute m*log(2),err<=2ulps */ - mpfr_sub (tmp1, tmp2, tmp1, MPFR_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); -} |