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Diffstat (limited to 'Build/source/libs/mpfr/mpfr-3.1.2/src/log.c')
| -rw-r--r-- | Build/source/libs/mpfr/mpfr-3.1.2/src/log.c | 171 |
1 files changed, 171 insertions, 0 deletions
diff --git a/Build/source/libs/mpfr/mpfr-3.1.2/src/log.c b/Build/source/libs/mpfr/mpfr-3.1.2/src/log.c new file mode 100644 index 00000000000..0244ab569f8 --- /dev/null +++ b/Build/source/libs/mpfr/mpfr-3.1.2/src/log.c @@ -0,0 +1,171 @@ +/* mpfr_log -- natural logarithm of a floating-point number + +Copyright 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013 Free Software Foundation, Inc. +Contributed by the AriC 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; + MPFR_SAVE_EXPO_DECL (expo); + MPFR_ZIV_DECL (loop); + MPFR_GROUP_DECL(group); + + MPFR_LOG_FUNC + (("a[%Pu]=%.*Rg rnd=%d", mpfr_get_prec (a), mpfr_log_prec, a, rnd_mode), + ("r[%Pu]=%.*Rg inexact=%d", mpfr_get_prec (r), mpfr_log_prec, 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_set_divby0 (); + 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_SAVE_EXPO_MARK (expo); + MPFR_GROUP_INIT_2 (group, p, tmp1, tmp2); + + MPFR_ZIV_INIT (loop, p); + for (;;) + { + long m; + mpfr_exp_t cancel; + + /* Calculus of m (depends on p) */ + m = (p + 1) / 2 - MPFR_GET_EXP (a) + 1; + + 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_GROUP_REPREC_2 (group, p, tmp1, tmp2); + } + MPFR_ZIV_FREE (loop); + inexact = mpfr_set (r, tmp1, rnd_mode); + /* We clean */ + MPFR_GROUP_CLEAR (group); + + MPFR_SAVE_EXPO_FREE (expo); + return mpfr_check_range (r, inexact, rnd_mode); +} |