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Diffstat (limited to 'src/sinh_cosh.c')
| -rw-r--r-- | src/sinh_cosh.c | 157 |
1 files changed, 157 insertions, 0 deletions
diff --git a/src/sinh_cosh.c b/src/sinh_cosh.c new file mode 100644 index 000000000..af83fff68 --- /dev/null +++ b/src/sinh_cosh.c @@ -0,0 +1,157 @@ +/* mpfr_sinh_cosh -- hyperbolic sine and cosine + +Copyright 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010 Free Software Foundation, Inc. +Contributed by the Arenaire 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" + +#define INEXPOS(y) ((y) == 0 ? 0 : (((y) > 0) ? 1 : 2)) +#define INEX(y,z) (INEXPOS(y) | (INEXPOS(z) << 2)) + + /* The computations are done by + cosh(x) = 1/2 [e^(x)+e^(-x)] + sinh(x) = 1/2 [e^(x)-e^(-x)] + Adapted from mpfr_sinh.c */ + +int +mpfr_sinh_cosh (mpfr_ptr sh, mpfr_ptr ch, mpfr_srcptr xt, mpfr_rnd_t rnd_mode) +{ + mpfr_t x; + int inexact_sh, inexact_ch; + + MPFR_ASSERTN (sh != ch); + + MPFR_LOG_FUNC (("x[%#R]=%R rnd=%d", xt, xt, rnd_mode), + ("sh[%#R]=%R ch[%#R]=%R", sh, sh, ch, ch)); + + if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (xt))) + { + if (MPFR_IS_NAN (xt)) + { + MPFR_SET_NAN (ch); + MPFR_SET_NAN (sh); + MPFR_RET_NAN; + } + else if (MPFR_IS_INF (xt)) + { + MPFR_SET_INF (sh); + MPFR_SET_SAME_SIGN (sh, xt); + MPFR_SET_INF (ch); + MPFR_SET_POS (ch); + MPFR_RET (0); + } + else /* xt is zero */ + { + MPFR_ASSERTD (MPFR_IS_ZERO (xt)); + MPFR_SET_ZERO (sh); /* sinh(0) = 0 */ + MPFR_SET_SAME_SIGN (sh, xt); + inexact_sh = 0; + inexact_ch = mpfr_set_ui (ch, 1, rnd_mode); /* cosh(0) = 1 */ + return INEX(inexact_sh,inexact_ch); + } + } + + /* Warning: if we use MPFR_FAST_COMPUTE_IF_SMALL_INPUT here, make sure + that the code also works in case of overlap (see sin_cos.c) */ + + MPFR_TMP_INIT_ABS (x, xt); + + { + mpfr_t s, c, ti; + mpfr_exp_t d; + mpfr_prec_t N; /* Precision of the intermediary variables */ + 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 */ + N = MPFR_PREC (ch); + N = MAX (N, MPFR_PREC (sh)); + /* the optimal number of bits : see algorithms.ps */ + N = N + MPFR_INT_CEIL_LOG2 (N) + 4; + + /* initialise of intermediary variables */ + MPFR_GROUP_INIT_3 (group, N, s, c, ti); + + /* First computation of sinh_cosh */ + MPFR_ZIV_INIT (loop, N); + for (;;) + { + MPFR_BLOCK_DECL (flags); + + /* compute sinh_cosh */ + MPFR_BLOCK (flags, mpfr_exp (s, x, MPFR_RNDD)); + if (MPFR_OVERFLOW (flags)) + /* exp(x) does overflow */ + { + /* since cosh(x) >= exp(x), cosh(x) overflows too */ + inexact_ch = mpfr_overflow (ch, rnd_mode, MPFR_SIGN_POS); + /* sinh(x) may be representable */ + inexact_sh = mpfr_sinh (sh, xt, rnd_mode); + MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, MPFR_FLAGS_OVERFLOW); + break; + } + d = MPFR_GET_EXP (s); + mpfr_ui_div (ti, 1, s, MPFR_RNDU); /* 1/exp(x) */ + mpfr_add (c, s, ti, MPFR_RNDU); /* exp(x) + 1/exp(x) */ + mpfr_sub (s, s, ti, MPFR_RNDN); /* exp(x) - 1/exp(x) */ + mpfr_div_2ui (c, c, 1, MPFR_RNDN); /* 1/2(exp(x) + 1/exp(x)) */ + mpfr_div_2ui (s, s, 1, MPFR_RNDN); /* 1/2(exp(x) - 1/exp(x)) */ + + /* it may be that s is zero (in fact, it can only occur when exp(x)=1, + and thus ti=1 too) */ + if (MPFR_IS_ZERO (s)) + err = N; /* double the precision */ + else + { + /* calculation of the error */ + d = d - MPFR_GET_EXP (s) + 2; + /* error estimate: err = N-(__gmpfr_ceil_log2(1+pow(2,d)));*/ + err = N - (MAX (d, 0) + 1); + if (MPFR_LIKELY (MPFR_CAN_ROUND (s, err, MPFR_PREC (sh), + rnd_mode) && \ + MPFR_CAN_ROUND (c, err, MPFR_PREC (ch), + rnd_mode))) + { + inexact_sh = mpfr_set4 (sh, s, rnd_mode, MPFR_SIGN (xt)); + inexact_ch = mpfr_set (ch, c, rnd_mode); + break; + } + } + /* actualisation of the precision */ + N += err; + MPFR_ZIV_NEXT (loop, N); + MPFR_GROUP_REPREC_3 (group, N, s, c, ti); + } + MPFR_ZIV_FREE (loop); + MPFR_GROUP_CLEAR (group); + MPFR_SAVE_EXPO_FREE (expo); + } + + /* now, let's raise the flags if needed */ + inexact_sh = mpfr_check_range (sh, inexact_sh, rnd_mode); + inexact_ch = mpfr_check_range (ch, inexact_ch, rnd_mode); + + return INEX(inexact_sh,inexact_ch); +} |