| /* mpfr_sinh -- hyperbolic sine |
| |
| Copyright 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009 Free Software Foundation, Inc. |
| Contributed by the Arenaire and Cacao 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 2.1 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.LIB. If not, 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, mp_rnd_t rnd_mode) |
| { |
| mpfr_t x; |
| int inexact; |
| |
| MPFR_LOG_FUNC (("x[%#R]=%R rnd=%d", xt, xt, rnd_mode), |
| ("y[%#R]=%R inexact=%d", y, 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; |
| mp_exp_t d; |
| mp_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, GMP_RNDD)); |
| if (MPFR_OVERFLOW (flags)) |
| /* exp(x) does overflow */ |
| { |
| /* sinh(x) = 2 * sinh(x/2) * cosh(x/2) */ |
| mpfr_div_2ui (ti, x, 1, GMP_RNDD); /* exact */ |
| |
| /* t <- cosh(x/2): error(t) <= 1 ulp(t) */ |
| MPFR_BLOCK (flags, mpfr_cosh (t, ti, GMP_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, GMP_RNDD); |
| |
| /* multiplication below, error(t) <= 5 ulp(t) */ |
| MPFR_BLOCK (flags, mpfr_mul (t, t, ti, GMP_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, GMP_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, GMP_RNDU); /* 1/exp(x) */ |
| mpfr_sub (t, t, ti, GMP_RNDN); /* exp(x) - 1/exp(x) */ |
| mpfr_div_2ui (t, t, 1, GMP_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); |
| } |
