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Diffstat (limited to 'src/sinh.c')
| -rw-r--r-- | src/sinh.c | 184 |
1 files changed, 184 insertions, 0 deletions
diff --git a/src/sinh.c b/src/sinh.c new file mode 100644 index 0000000..0349036 --- /dev/null +++ b/src/sinh.c @@ -0,0 +1,184 @@ +/* mpfr_sinh -- hyperbolic sine + +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 sinh is done by + sinh(x) = 1/2 [e^(x)-e^(-x)] */ + +int +mpfr_sinh (mpfr_ptr y, mpfr_srcptr xt, mpfr_rnd_t rnd_mode) +{ + mpfr_t x; + int inexact; + + MPFR_LOG_FUNC + (("x[%Pu]=%.*Rg rnd=%d", mpfr_get_prec (xt), mpfr_log_prec, xt, rnd_mode), + ("y[%Pu]=%.*Rg inexact=%d", + mpfr_get_prec (y), mpfr_log_prec, y, inexact)); + + if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (xt))) + { + if (MPFR_IS_NAN (xt)) + { + MPFR_SET_NAN (y); + MPFR_RET_NAN; + } + else if (MPFR_IS_INF (xt)) + { + MPFR_SET_INF (y); + MPFR_SET_SAME_SIGN (y, xt); + MPFR_RET (0); + } + else /* xt is zero */ + { + MPFR_ASSERTD (MPFR_IS_ZERO (xt)); + MPFR_SET_ZERO (y); /* sinh(0) = 0 */ + MPFR_SET_SAME_SIGN (y, xt); + MPFR_RET (0); + } + } + + /* sinh(x) = x + x^3/6 + ... so the error is < 2^(3*EXP(x)-2) */ + MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, xt, -2 * MPFR_GET_EXP(xt), 2, 1, + rnd_mode, {}); + + MPFR_TMP_INIT_ABS (x, xt); + + { + mpfr_t t, ti; + mpfr_exp_t d; + mpfr_prec_t Nt; /* Precision of the intermediary variable */ + long int err; /* Precision of error */ + MPFR_ZIV_DECL (loop); + MPFR_SAVE_EXPO_DECL (expo); + MPFR_GROUP_DECL (group); + + MPFR_SAVE_EXPO_MARK (expo); + + /* compute the precision of intermediary variable */ + Nt = MAX (MPFR_PREC (x), MPFR_PREC (y)); + /* the optimal number of bits : see algorithms.ps */ + Nt = Nt + MPFR_INT_CEIL_LOG2 (Nt) + 4; + /* If x is near 0, exp(x) - 1/exp(x) = 2*x+x^3/3+O(x^5) */ + if (MPFR_GET_EXP (x) < 0) + Nt -= 2*MPFR_GET_EXP (x); + + /* initialise of intermediary variables */ + MPFR_GROUP_INIT_2 (group, Nt, t, ti); + + /* First computation of sinh */ + MPFR_ZIV_INIT (loop, Nt); + for (;;) + { + MPFR_BLOCK_DECL (flags); + + /* compute sinh */ + MPFR_BLOCK (flags, mpfr_exp (t, x, MPFR_RNDD)); + if (MPFR_OVERFLOW (flags)) + /* exp(x) does overflow */ + { + /* sinh(x) = 2 * sinh(x/2) * cosh(x/2) */ + mpfr_div_2ui (ti, x, 1, MPFR_RNDD); /* exact */ + + /* t <- cosh(x/2): error(t) <= 1 ulp(t) */ + MPFR_BLOCK (flags, mpfr_cosh (t, ti, MPFR_RNDD)); + if (MPFR_OVERFLOW (flags)) + /* when x>1 we have |sinh(x)| >= cosh(x/2), so sinh(x) + overflows too */ + { + inexact = mpfr_overflow (y, rnd_mode, MPFR_SIGN (xt)); + MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, MPFR_FLAGS_OVERFLOW); + break; + } + + /* ti <- sinh(x/2): , error(ti) <= 1 ulp(ti) + cannot overflow because 0 < sinh(x) < cosh(x) when x > 0 */ + mpfr_sinh (ti, ti, MPFR_RNDD); + + /* multiplication below, error(t) <= 5 ulp(t) */ + MPFR_BLOCK (flags, mpfr_mul (t, t, ti, MPFR_RNDD)); + if (MPFR_OVERFLOW (flags)) + { + inexact = mpfr_overflow (y, rnd_mode, MPFR_SIGN (xt)); + MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, MPFR_FLAGS_OVERFLOW); + break; + } + + /* doubling below, exact */ + MPFR_BLOCK (flags, mpfr_mul_2ui (t, t, 1, MPFR_RNDN)); + if (MPFR_OVERFLOW (flags)) + { + inexact = mpfr_overflow (y, rnd_mode, MPFR_SIGN (xt)); + MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, MPFR_FLAGS_OVERFLOW); + break; + } + + /* we have lost at most 3 bits of precision */ + err = Nt - 3; + if (MPFR_LIKELY (MPFR_CAN_ROUND (t, err, MPFR_PREC (y), + rnd_mode))) + { + inexact = mpfr_set4 (y, t, rnd_mode, MPFR_SIGN (xt)); + break; + } + err = Nt; /* double the precision */ + } + else + { + d = MPFR_GET_EXP (t); + mpfr_ui_div (ti, 1, t, MPFR_RNDU); /* 1/exp(x) */ + mpfr_sub (t, t, ti, MPFR_RNDN); /* exp(x) - 1/exp(x) */ + mpfr_div_2ui (t, t, 1, MPFR_RNDN); /* 1/2(exp(x) - 1/exp(x)) */ + + /* it may be that t is zero (in fact, it can only occur when te=1, + and thus ti=1 too) */ + if (MPFR_IS_ZERO (t)) + err = Nt; /* double the precision */ + else + { + /* calculation of the error */ + d = d - MPFR_GET_EXP (t) + 2; + /* error estimate: err = Nt-(__gmpfr_ceil_log2(1+pow(2,d)));*/ + err = Nt - (MAX (d, 0) + 1); + if (MPFR_LIKELY (MPFR_CAN_ROUND (t, err, MPFR_PREC (y), + rnd_mode))) + { + inexact = mpfr_set4 (y, t, rnd_mode, MPFR_SIGN (xt)); + break; + } + } + } + + /* actualisation of the precision */ + Nt += err; + MPFR_ZIV_NEXT (loop, Nt); + MPFR_GROUP_REPREC_2 (group, Nt, t, ti); + } + MPFR_ZIV_FREE (loop); + MPFR_GROUP_CLEAR (group); + MPFR_SAVE_EXPO_FREE (expo); + } + + return mpfr_check_range (y, inexact, rnd_mode); +} |