Imported gcc-4.4.3

[msp430-gcc.git] / mpfr / asinh.c

diff --git a/mpfr/asinh.c b/mpfr/asinh.c
new file mode 100644 (file)
index 0000000..2bb7c47
--- /dev/null
+++ b/mpfr/asinh.c
@@ -0,0 +1,117 @@
+/* mpfr_asinh -- inverse 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 asinh is done by  *
+ *    asinh = ln(x + sqrt(x^2 + 1))     */
+
+int
+mpfr_asinh (mpfr_ptr y, mpfr_srcptr x, mp_rnd_t rnd_mode)
+{
+  int inexact;
+  int signx, neg;
+  mp_prec_t Ny, Nt;
+  mpfr_t t; /* auxiliary variables */
+  mp_exp_t err;
+  MPFR_SAVE_EXPO_DECL (expo);
+  MPFR_ZIV_DECL (loop);
+
+  MPFR_LOG_FUNC (("x[%#R]=%R rnd=%d", x, x, rnd_mode),
+                 ("y[%#R]=%R inexact=%d", y, y, inexact));
+
+  if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
+    {
+      if (MPFR_IS_NAN (x))
+        {
+          MPFR_SET_NAN (y);
+          MPFR_RET_NAN;
+        }
+      else if (MPFR_IS_INF (x))
+        {
+          MPFR_SET_INF (y);
+          MPFR_SET_SAME_SIGN (y, x);
+          MPFR_RET (0);
+        }
+      else /* x is necessarily 0 */
+        {
+          MPFR_ASSERTD (MPFR_IS_ZERO (x));
+          MPFR_SET_ZERO (y);   /* asinh(0) = 0 */
+          MPFR_SET_SAME_SIGN (y, x);
+          MPFR_RET (0);
+        }
+    }
+
+  /* asinh(x) = x - x^3/6 + ... so the error is < 2^(3*EXP(x)-2) */
+  MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, x, -2 * MPFR_GET_EXP (x), 2, 0,
+                                    rnd_mode, {});
+
+  Ny = MPFR_PREC (y);   /* Precision of output variable */
+
+  signx = MPFR_SIGN (x);
+  neg = MPFR_IS_NEG (x);
+
+  /* General case */
+
+  /* compute the precision of intermediary variable */
+  /* the optimal number of bits : see algorithms.tex */
+  Nt = Ny + 4 + MPFR_INT_CEIL_LOG2 (Ny);
+
+  MPFR_SAVE_EXPO_MARK (expo);
+
+  /* initialize intermediary variables */
+  mpfr_init2 (t, Nt);
+
+  /* First computation of asinh */
+  MPFR_ZIV_INIT (loop, Nt);
+  for (;;)
+    {
+      /* compute asinh */
+      mpfr_mul (t, x, x, GMP_RNDD);                    /* x^2 */
+      mpfr_add_ui (t, t, 1, GMP_RNDD);                 /* x^2+1 */
+      mpfr_sqrt (t, t, GMP_RNDN);                      /* sqrt(x^2+1) */
+      (neg ? mpfr_sub : mpfr_add) (t, t, x, GMP_RNDN); /* sqrt(x^2+1)+x */
+      mpfr_log (t, t, GMP_RNDN);                       /* ln(sqrt(x^2+1)+x)*/
+
+      if (MPFR_LIKELY (MPFR_IS_PURE_FP (t)))
+        {
+          /* error estimate -- see algorithms.tex */
+          err = Nt - (MAX (4 - MPFR_GET_EXP (t), 0) + 1);
+          if (MPFR_LIKELY (MPFR_IS_ZERO (t)
+                           || MPFR_CAN_ROUND (t, err, Ny, rnd_mode)))
+            break;
+        }
+
+      /* actualisation of the precision */
+      MPFR_ZIV_NEXT (loop, Nt);
+      mpfr_set_prec (t, Nt);
+    }
+  MPFR_ZIV_FREE (loop);
+
+  inexact = mpfr_set4 (y, t, rnd_mode, signx);
+
+  mpfr_clear (t);
+
+  MPFR_SAVE_EXPO_FREE (expo);
+  return mpfr_check_range (y, inexact, rnd_mode);
+}