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Diffstat (limited to 'src/expm1.c')
| -rw-r--r-- | src/expm1.c | 179 |
1 files changed, 179 insertions, 0 deletions
diff --git a/src/expm1.c b/src/expm1.c new file mode 100644 index 0000000..1961dd4 --- /dev/null +++ b/src/expm1.c @@ -0,0 +1,179 @@ +/* mpfr_expm1 -- Compute exp(x)-1 + +Copyright 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 expm1 is done by + expm1(x)=exp(x)-1 + */ + +int +mpfr_expm1 (mpfr_ptr y, mpfr_srcptr x , mpfr_rnd_t rnd_mode) +{ + int 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 (expm1(-inf)=-1) */ + else if (MPFR_IS_INF (x)) + { + if (MPFR_IS_POS (x)) + { + MPFR_SET_INF (y); + MPFR_SET_POS (y); + MPFR_RET (0); + } + else + return mpfr_set_si (y, -1, rnd_mode); + } + else + { + MPFR_ASSERTD (MPFR_IS_ZERO (x)); + MPFR_SET_ZERO (y); /* expm1(+/- 0) = +/- 0 */ + MPFR_SET_SAME_SIGN (y, x); + MPFR_RET (0); + } + } + + ex = MPFR_GET_EXP (x); + if (ex < 0) + { + /* For -1 < x < 0, abs(expm1(x)-x) < x^2/2. + For 0 < x < 1, abs(expm1(x)-x) < x^2. */ + if (MPFR_IS_POS (x)) + MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, x, - ex, 0, 1, rnd_mode, {}); + else + MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, x, - ex, 1, 0, rnd_mode, {}); + } + + MPFR_SAVE_EXPO_MARK (expo); + + if (MPFR_IS_NEG (x) && ex > 5) /* x <= -32 */ + { + mpfr_t minus_one, t; + mpfr_exp_t err; + + mpfr_init2 (minus_one, 2); + mpfr_init2 (t, 64); + mpfr_set_si (minus_one, -1, MPFR_RNDN); + mpfr_const_log2 (t, MPFR_RNDU); /* round upward since x is negative */ + mpfr_div (t, x, t, MPFR_RNDU); /* > x / ln(2) */ + err = mpfr_cmp_si (t, MPFR_EMIN_MIN >= -LONG_MAX ? + MPFR_EMIN_MIN : -LONG_MAX) <= 0 ? + - (MPFR_EMIN_MIN >= -LONG_MAX ? MPFR_EMIN_MIN : -LONG_MAX) : + - mpfr_get_si (t, MPFR_RNDU); + /* exp(x) = 2^(x/ln(2)) + <= 2^max(MPFR_EMIN_MIN,-LONG_MAX,ceil(x/ln(2)+epsilon)) + with epsilon > 0 */ + mpfr_clear (t); + MPFR_SMALL_INPUT_AFTER_SAVE_EXPO (y, minus_one, err, 0, 0, rnd_mode, + expo, { mpfr_clear (minus_one); }); + mpfr_clear (minus_one); + } + + /* 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, exp_te; /* 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 the + subtraction exp(x) - 1 */ + if (ex < 0) + Nt += - ex; + + /* initialize auxiliary variable */ + mpfr_init2 (t, Nt); + + /* First computation of expm1 */ + MPFR_ZIV_INIT (loop, Nt); + for (;;) + { + MPFR_BLOCK_DECL (flags); + + /* exp(x) may overflow and underflow */ + MPFR_BLOCK (flags, mpfr_exp (t, x, MPFR_RNDN)); + if (MPFR_OVERFLOW (flags)) + { + inexact = mpfr_overflow (y, rnd_mode, MPFR_SIGN_POS); + MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, MPFR_FLAGS_OVERFLOW); + break; + } + else if (MPFR_UNDERFLOW (flags)) + { + inexact = mpfr_set_si (y, -1, rnd_mode); + MPFR_ASSERTD (inexact == 0); + inexact = -1; + if (MPFR_IS_LIKE_RNDZ (rnd_mode, 1)) + { + inexact = 1; + mpfr_nexttozero (y); + } + break; + } + + exp_te = MPFR_GET_EXP (t); /* FIXME: exp(x) may overflow! */ + mpfr_sub_ui (t, t, 1, MPFR_RNDN); /* exp(x)-1 */ + + /* error estimate */ + /*err=Nt-(__gmpfr_ceil_log2(1+pow(2,MPFR_EXP(te)-MPFR_EXP(t))));*/ + err = Nt - (MAX (exp_te - MPFR_GET_EXP (t), 0) + 1); + + if (MPFR_LIKELY (MPFR_CAN_ROUND (t, err, Ny, rnd_mode))) + { + inexact = mpfr_set (y, t, rnd_mode); + break; + } + + /* increase the precision */ + MPFR_ZIV_NEXT (loop, Nt); + mpfr_set_prec (t, Nt); + } + MPFR_ZIV_FREE (loop); + + mpfr_clear (t); + } + + MPFR_SAVE_EXPO_FREE (expo); + return mpfr_check_range (y, inexact, rnd_mode); +} |