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Diffstat (limited to 'Build/source/libs/mpfr/mpfr-src/src/log1p.c')
-rw-r--r-- | Build/source/libs/mpfr/mpfr-src/src/log1p.c | 158 |
1 files changed, 158 insertions, 0 deletions
diff --git a/Build/source/libs/mpfr/mpfr-src/src/log1p.c b/Build/source/libs/mpfr/mpfr-src/src/log1p.c new file mode 100644 index 00000000000..6ef0e866ca8 --- /dev/null +++ b/Build/source/libs/mpfr/mpfr-src/src/log1p.c @@ -0,0 +1,158 @@ +/* mpfr_log1p -- Compute log(1+x) + +Copyright 2001-2015 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 log1p is done by + log1p(x)=log(1+x) */ + +int +mpfr_log1p (mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t rnd_mode) +{ + int comp, inexact; + mpfr_exp_t ex; + MPFR_SAVE_EXPO_DECL (expo); + + MPFR_LOG_FUNC + (("x[%Pu]=%.*Rg rnd=%d", mpfr_get_prec (x), mpfr_log_prec, x, rnd_mode), + ("y[%Pu]=%.*Rg inexact=%d", mpfr_get_prec (y), mpfr_log_prec, y, + inexact)); + + if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x))) + { + if (MPFR_IS_NAN (x)) + { + MPFR_SET_NAN (y); + MPFR_RET_NAN; + } + /* check for inf or -inf (result is not defined) */ + else if (MPFR_IS_INF (x)) + { + if (MPFR_IS_POS (x)) + { + MPFR_SET_INF (y); + MPFR_SET_POS (y); + MPFR_RET (0); + } + else + { + MPFR_SET_NAN (y); + MPFR_RET_NAN; + } + } + else /* x is zero */ + { + MPFR_ASSERTD (MPFR_IS_ZERO (x)); + MPFR_SET_ZERO (y); /* log1p(+/- 0) = +/- 0 */ + MPFR_SET_SAME_SIGN (y, x); + MPFR_RET (0); + } + } + + ex = MPFR_GET_EXP (x); + if (ex < 0) /* -0.5 < x < 0.5 */ + { + /* For x > 0, abs(log(1+x)-x) < x^2/2. + For x > -0.5, abs(log(1+x)-x) < x^2. */ + if (MPFR_IS_POS (x)) + MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, x, - ex - 1, 0, 0, rnd_mode, {}); + else + MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, x, - ex, 0, 1, rnd_mode, {}); + } + + comp = mpfr_cmp_si (x, -1); + /* log1p(x) is undefined for x < -1 */ + if (MPFR_UNLIKELY(comp <= 0)) + { + if (comp == 0) + /* x=0: log1p(-1)=-inf (divide-by-zero exception) */ + { + MPFR_SET_INF (y); + MPFR_SET_NEG (y); + mpfr_set_divby0 (); + MPFR_RET (0); + } + MPFR_SET_NAN (y); + MPFR_RET_NAN; + } + + MPFR_SAVE_EXPO_MARK (expo); + + /* General case */ + { + /* Declaration of the intermediary variable */ + mpfr_t t; + /* Declaration of the size variable */ + mpfr_prec_t Ny = MPFR_PREC(y); /* target precision */ + mpfr_prec_t Nt; /* working precision */ + mpfr_exp_t err; /* error */ + MPFR_ZIV_DECL (loop); + + /* compute the precision of intermediary variable */ + /* the optimal number of bits : see algorithms.tex */ + Nt = Ny + MPFR_INT_CEIL_LOG2 (Ny) + 6; + + /* if |x| is smaller than 2^(-e), we will loose about e bits + in log(1+x) */ + if (MPFR_EXP(x) < 0) + Nt += -MPFR_EXP(x); + + /* initialise of intermediary variable */ + mpfr_init2 (t, Nt); + + /* First computation of log1p */ + MPFR_ZIV_INIT (loop, Nt); + for (;;) + { + /* compute log1p */ + inexact = mpfr_add_ui (t, x, 1, MPFR_RNDN); /* 1+x */ + /* if inexact = 0, then t = x+1, and the result is simply log(t) */ + if (inexact == 0) + { + inexact = mpfr_log (y, t, rnd_mode); + goto end; + } + mpfr_log (t, t, MPFR_RNDN); /* log(1+x) */ + + /* the error is bounded by (1/2+2^(1-EXP(t))*ulp(t) (cf algorithms.tex) + if EXP(t)>=2, then error <= ulp(t) + if EXP(t)<=1, then error <= 2^(2-EXP(t))*ulp(t) */ + err = Nt - MAX (0, 2 - MPFR_GET_EXP (t)); + + if (MPFR_LIKELY (MPFR_CAN_ROUND (t, err, Ny, rnd_mode))) + break; + + /* increase the precision */ + MPFR_ZIV_NEXT (loop, Nt); + mpfr_set_prec (t, Nt); + } + inexact = mpfr_set (y, t, rnd_mode); + + end: + MPFR_ZIV_FREE (loop); + mpfr_clear (t); + } + + MPFR_SAVE_EXPO_FREE (expo); + return mpfr_check_range (y, inexact, rnd_mode); +} |