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Diffstat (limited to 'mpfr/src/acosh.c')
| -rw-r--r-- | mpfr/src/acosh.c | 158 |
1 files changed, 158 insertions, 0 deletions
diff --git a/mpfr/src/acosh.c b/mpfr/src/acosh.c new file mode 100644 index 0000000000..75e931d189 --- /dev/null +++ b/mpfr/src/acosh.c @@ -0,0 +1,158 @@ +/* mpfr_acosh -- inverse hyperbolic cosine + +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 acosh is done by * + * acosh= ln(x + sqrt(x^2-1)) */ + +int +mpfr_acosh (mpfr_ptr y, mpfr_srcptr x , mpfr_rnd_t rnd_mode) +{ + MPFR_SAVE_EXPO_DECL (expo); + int inexact; + int comp; + + 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)); + + /* Deal with special cases */ + if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x))) + { + /* Nan, or zero or -Inf */ + if (MPFR_IS_INF (x) && MPFR_IS_POS (x)) + { + MPFR_SET_INF (y); + MPFR_SET_POS (y); + MPFR_RET (0); + } + else /* Nan, or zero or -Inf */ + { + MPFR_SET_NAN (y); + MPFR_RET_NAN; + } + } + comp = mpfr_cmp_ui (x, 1); + if (MPFR_UNLIKELY (comp < 0)) + { + MPFR_SET_NAN (y); + MPFR_RET_NAN; + } + else if (MPFR_UNLIKELY (comp == 0)) + { + MPFR_SET_ZERO (y); /* acosh(1) = 0 */ + MPFR_SET_POS (y); + MPFR_RET (0); + } + MPFR_SAVE_EXPO_MARK (expo); + + /* General case */ + { + /* Declaration of the intermediary variables */ + mpfr_t t; + /* Declaration of the size variables */ + mpfr_prec_t Ny = MPFR_PREC(y); /* Precision of output variable */ + mpfr_prec_t Nt; /* Precision of the intermediary variable */ + mpfr_exp_t err, exp_te, d; /* Precision of error */ + MPFR_ZIV_DECL (loop); + + /* compute the precision of intermediary variable */ + /* the optimal number of bits : see algorithms.tex */ + Nt = Ny + 4 + MPFR_INT_CEIL_LOG2 (Ny); + + /* initialization of intermediary variables */ + mpfr_init2 (t, Nt); + + /* First computation of acosh */ + MPFR_ZIV_INIT (loop, Nt); + for (;;) + { + MPFR_BLOCK_DECL (flags); + + /* compute acosh */ + MPFR_BLOCK (flags, mpfr_mul (t, x, x, MPFR_RNDD)); /* x^2 */ + if (MPFR_OVERFLOW (flags)) + { + mpfr_t ln2; + mpfr_prec_t pln2; + + /* As x is very large and the precision is not too large, we + assume that we obtain the same result by evaluating ln(2x). + We need to compute ln(x) + ln(2) as 2x can overflow. TODO: + write a proof and add an MPFR_ASSERTN. */ + mpfr_log (t, x, MPFR_RNDN); /* err(log) < 1/2 ulp(t) */ + pln2 = Nt - MPFR_PREC_MIN < MPFR_GET_EXP (t) ? + MPFR_PREC_MIN : Nt - MPFR_GET_EXP (t); + mpfr_init2 (ln2, pln2); + mpfr_const_log2 (ln2, MPFR_RNDN); /* err(ln2) < 1/2 ulp(t) */ + mpfr_add (t, t, ln2, MPFR_RNDN); /* err <= 3/2 ulp(t) */ + mpfr_clear (ln2); + err = 1; + } + else + { + exp_te = MPFR_GET_EXP (t); + mpfr_sub_ui (t, t, 1, MPFR_RNDD); /* x^2-1 */ + if (MPFR_UNLIKELY (MPFR_IS_ZERO (t))) + { + /* This means that x is very close to 1: x = 1 + t with + t < 2^(-Nt). We have: acosh(x) = sqrt(2t) (1 - eps(t)) + with 0 < eps(t) < t / 12. */ + mpfr_sub_ui (t, x, 1, MPFR_RNDD); /* t = x - 1 */ + mpfr_mul_2ui (t, t, 1, MPFR_RNDN); /* 2t */ + mpfr_sqrt (t, t, MPFR_RNDN); /* sqrt(2t) */ + err = 1; + } + else + { + d = exp_te - MPFR_GET_EXP (t); + mpfr_sqrt (t, t, MPFR_RNDN); /* sqrt(x^2-1) */ + mpfr_add (t, t, x, MPFR_RNDN); /* sqrt(x^2-1)+x */ + mpfr_log (t, t, MPFR_RNDN); /* ln(sqrt(x^2-1)+x) */ + + /* error estimate -- see algorithms.tex */ + err = 3 + MAX (1, d) - MPFR_GET_EXP (t); + /* error is bounded by 1/2 + 2^err <= 2^(max(0,1+err)) */ + err = MAX (0, 1 + err); + } + } + + if (MPFR_LIKELY (MPFR_CAN_ROUND (t, Nt - err, Ny, rnd_mode))) + break; + + /* reactualisation of the precision */ + MPFR_ZIV_NEXT (loop, Nt); + mpfr_set_prec (t, Nt); + } + MPFR_ZIV_FREE (loop); + + inexact = mpfr_set (y, t, rnd_mode); + + mpfr_clear (t); + } + + MPFR_SAVE_EXPO_FREE (expo); + return mpfr_check_range (y, inexact, rnd_mode); +} |