--- /dev/null
+/* mpfr_sinh_cosh -- hyperbolic sine and cosine
+
+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 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, mp_rnd_t rnd_mode)
+{
+ mpfr_t x;
+ int inexact, 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 inexact=%d", sh, sh, ch, ch, inexact));
+
+ 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);
+ return mpfr_set_ui (ch, 1, rnd_mode); /* cosh(0) = 1 */
+ }
+ }
+
+ /* 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;
+ mp_exp_t d;
+ mp_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));
+ N = MAX (N, MPFR_PREC (x));
+ /* 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, GMP_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, GMP_RNDU); /* 1/exp(x) */
+ mpfr_add (c, s, ti, GMP_RNDU); /* exp(x) + 1/exp(x) */
+ mpfr_sub (s, s, ti, GMP_RNDN); /* exp(x) - 1/exp(x) */
+ mpfr_div_2ui (c, c, 1, GMP_RNDN); /* 1/2(exp(x) + 1/exp(x)) */
+ mpfr_div_2ui (s, s, 1, GMP_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 = mpfr_check_range (sh, inexact_sh, rnd_mode);
+ inexact = mpfr_check_range (ch, inexact_ch, rnd_mode) || inexact;
+
+ return inexact;
+}
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