efee5258bc
The MPFR library is a C library for multiple-precision floating-point computations with exact rounding (also called correct rounding). It is based on the GMP multiple-precision library and should replace the MPF class in further releases of GMP. GCC >= 4.2 requires MPFR.
183 lines
6.1 KiB
C
183 lines
6.1 KiB
C
/* mpfr_sinh -- hyperbolic sine
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Copyright 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011 Free Software Foundation, Inc.
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Contributed by the Arenaire and Cacao projects, INRIA.
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This file is part of the GNU MPFR Library.
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The GNU MPFR Library is free software; you can redistribute it and/or modify
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it under the terms of the GNU Lesser General Public License as published by
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the Free Software Foundation; either version 3 of the License, or (at your
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option) any later version.
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The GNU MPFR Library is distributed in the hope that it will be useful, but
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WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
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License for more details.
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You should have received a copy of the GNU Lesser General Public License
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along with the GNU MPFR Library; see the file COPYING.LESSER. If not, see
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http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
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51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */
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#define MPFR_NEED_LONGLONG_H
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#include "mpfr-impl.h"
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/* The computation of sinh is done by
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sinh(x) = 1/2 [e^(x)-e^(-x)] */
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int
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mpfr_sinh (mpfr_ptr y, mpfr_srcptr xt, mpfr_rnd_t rnd_mode)
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{
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mpfr_t x;
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int inexact;
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MPFR_LOG_FUNC (("x[%#R]=%R rnd=%d", xt, xt, rnd_mode),
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("y[%#R]=%R inexact=%d", y, y, inexact));
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if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (xt)))
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{
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if (MPFR_IS_NAN (xt))
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{
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MPFR_SET_NAN (y);
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MPFR_RET_NAN;
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}
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else if (MPFR_IS_INF (xt))
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{
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MPFR_SET_INF (y);
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MPFR_SET_SAME_SIGN (y, xt);
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MPFR_RET (0);
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}
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else /* xt is zero */
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{
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MPFR_ASSERTD (MPFR_IS_ZERO (xt));
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MPFR_SET_ZERO (y); /* sinh(0) = 0 */
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MPFR_SET_SAME_SIGN (y, xt);
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MPFR_RET (0);
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}
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}
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/* sinh(x) = x + x^3/6 + ... so the error is < 2^(3*EXP(x)-2) */
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MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, xt, -2 * MPFR_GET_EXP(xt), 2, 1,
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rnd_mode, {});
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MPFR_TMP_INIT_ABS (x, xt);
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{
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mpfr_t t, ti;
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mpfr_exp_t d;
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mpfr_prec_t Nt; /* Precision of the intermediary variable */
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long int err; /* Precision of error */
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MPFR_ZIV_DECL (loop);
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MPFR_SAVE_EXPO_DECL (expo);
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MPFR_GROUP_DECL (group);
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MPFR_SAVE_EXPO_MARK (expo);
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/* compute the precision of intermediary variable */
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Nt = MAX (MPFR_PREC (x), MPFR_PREC (y));
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/* the optimal number of bits : see algorithms.ps */
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Nt = Nt + MPFR_INT_CEIL_LOG2 (Nt) + 4;
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/* If x is near 0, exp(x) - 1/exp(x) = 2*x+x^3/3+O(x^5) */
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if (MPFR_GET_EXP (x) < 0)
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Nt -= 2*MPFR_GET_EXP (x);
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/* initialise of intermediary variables */
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MPFR_GROUP_INIT_2 (group, Nt, t, ti);
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/* First computation of sinh */
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MPFR_ZIV_INIT (loop, Nt);
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for (;;)
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{
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MPFR_BLOCK_DECL (flags);
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/* compute sinh */
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MPFR_BLOCK (flags, mpfr_exp (t, x, MPFR_RNDD));
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if (MPFR_OVERFLOW (flags))
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/* exp(x) does overflow */
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{
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/* sinh(x) = 2 * sinh(x/2) * cosh(x/2) */
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mpfr_div_2ui (ti, x, 1, MPFR_RNDD); /* exact */
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/* t <- cosh(x/2): error(t) <= 1 ulp(t) */
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MPFR_BLOCK (flags, mpfr_cosh (t, ti, MPFR_RNDD));
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if (MPFR_OVERFLOW (flags))
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/* when x>1 we have |sinh(x)| >= cosh(x/2), so sinh(x)
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overflows too */
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{
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inexact = mpfr_overflow (y, rnd_mode, MPFR_SIGN (xt));
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MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, MPFR_FLAGS_OVERFLOW);
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break;
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}
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/* ti <- sinh(x/2): , error(ti) <= 1 ulp(ti)
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cannot overflow because 0 < sinh(x) < cosh(x) when x > 0 */
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mpfr_sinh (ti, ti, MPFR_RNDD);
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/* multiplication below, error(t) <= 5 ulp(t) */
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MPFR_BLOCK (flags, mpfr_mul (t, t, ti, MPFR_RNDD));
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if (MPFR_OVERFLOW (flags))
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{
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inexact = mpfr_overflow (y, rnd_mode, MPFR_SIGN (xt));
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MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, MPFR_FLAGS_OVERFLOW);
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break;
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}
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/* doubling below, exact */
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MPFR_BLOCK (flags, mpfr_mul_2ui (t, t, 1, MPFR_RNDN));
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if (MPFR_OVERFLOW (flags))
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{
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inexact = mpfr_overflow (y, rnd_mode, MPFR_SIGN (xt));
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MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, MPFR_FLAGS_OVERFLOW);
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break;
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}
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/* we have lost at most 3 bits of precision */
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err = Nt - 3;
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if (MPFR_LIKELY (MPFR_CAN_ROUND (t, err, MPFR_PREC (y),
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rnd_mode)))
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{
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inexact = mpfr_set4 (y, t, rnd_mode, MPFR_SIGN (xt));
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break;
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}
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err = Nt; /* double the precision */
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}
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else
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{
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d = MPFR_GET_EXP (t);
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mpfr_ui_div (ti, 1, t, MPFR_RNDU); /* 1/exp(x) */
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mpfr_sub (t, t, ti, MPFR_RNDN); /* exp(x) - 1/exp(x) */
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mpfr_div_2ui (t, t, 1, MPFR_RNDN); /* 1/2(exp(x) - 1/exp(x)) */
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/* it may be that t is zero (in fact, it can only occur when te=1,
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and thus ti=1 too) */
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if (MPFR_IS_ZERO (t))
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err = Nt; /* double the precision */
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else
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{
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/* calculation of the error */
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d = d - MPFR_GET_EXP (t) + 2;
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/* error estimate: err = Nt-(__gmpfr_ceil_log2(1+pow(2,d)));*/
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err = Nt - (MAX (d, 0) + 1);
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if (MPFR_LIKELY (MPFR_CAN_ROUND (t, err, MPFR_PREC (y),
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rnd_mode)))
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{
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inexact = mpfr_set4 (y, t, rnd_mode, MPFR_SIGN (xt));
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break;
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}
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}
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}
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/* actualisation of the precision */
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Nt += err;
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MPFR_ZIV_NEXT (loop, Nt);
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MPFR_GROUP_REPREC_2 (group, Nt, t, ti);
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}
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MPFR_ZIV_FREE (loop);
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MPFR_GROUP_CLEAR (group);
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MPFR_SAVE_EXPO_FREE (expo);
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}
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return mpfr_check_range (y, inexact, rnd_mode);
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}
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