--- /dev/null
+/* 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);
+}
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