new mpfr_sinh_cosh function

git-svn-id: svn://scm.gforge.inria.fr/svn/mpfr/trunk@4864 280ebfd0-de03-0410-8827-d642c229c3f4

1 files changed, 144 insertions, 0 deletions

diff --git a/sinh_cosh.c b/sinh_cosh.c
new file mode 100644
index 000000000..d9ebf31a1
--- /dev/null
+++ b/sinh_cosh.c
@@ -0,0 +1,144 @@
+/* mpfr_sinh_cosh -- hyperbolic sine and cosine
+
+Copyright 2001, 2002, 2003, 2004, 2005, 2006, 2007 Free Software Foundation, Inc.
+Contributed by the Arenaire and Cacao projects, INRIA.
+
+This file is part of the MPFR Library.
+
+The 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 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 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 */
+        }
+    }
+
+  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 (;;) {
+      /* compute sinh_cosh */
+      mpfr_clear_flags ();
+      mpfr_exp (s, x, GMP_RNDD);        /* exp(x) */
+      /* exp(x) can overflow! */
+      /* BUG/TODO/FIXME: exp can overflow but sinh or cosh may be 
+	 representable! */
+      if (MPFR_UNLIKELY (mpfr_overflow_p ())) {
+        inexact_ch = mpfr_overflow (ch, rnd_mode, MPFR_SIGN_POS);
+        inexact_sh = mpfr_overflow (sh, rnd_mode, MPFR_SIGN (xt));
+        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;
+}