Imported gcc-4.4.3

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

diff --git a/mpfr/atanh.c b/mpfr/atanh.c
new file mode 100644 (file)
index 0000000..b0183ad
--- /dev/null
+++ b/mpfr/atanh.c
@@ -0,0 +1,127 @@
+/* mpfr_atanh -- Inverse Hyperbolic Tangente
+
+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 atanh is done by
+       atanh= 1/2*ln(x+1)-1/2*ln(1-x)   */
+
+int
+mpfr_atanh (mpfr_ptr y, mpfr_srcptr xt , mp_rnd_t rnd_mode)
+{
+  int inexact;
+  mpfr_t x, t, te;
+  mp_prec_t Nx, Ny, Nt;
+  mp_exp_t err;
+  MPFR_ZIV_DECL (loop);
+  MPFR_SAVE_EXPO_DECL (expo);
+
+  MPFR_LOG_FUNC (("x[%#R]=%R rnd=%d", xt, xt, rnd_mode),
+                 ("y[%#R]=%R inexact=%d", y, y, inexact));
+
+  /* Special cases */
+  if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (xt)))
+    {
+      /* atanh(NaN) = NaN, and atanh(+/-Inf) = NaN since tanh gives a result
+         between -1 and 1 */
+      if (MPFR_IS_NAN (xt) || MPFR_IS_INF (xt))
+        {
+          MPFR_SET_NAN (y);
+          MPFR_RET_NAN;
+        }
+      else /* necessarily xt is 0 */
+        {
+          MPFR_ASSERTD (MPFR_IS_ZERO (xt));
+          MPFR_SET_ZERO (y);   /* atanh(0) = 0 */
+          MPFR_SET_SAME_SIGN (y,xt);
+          MPFR_RET (0);
+        }
+    }
+
+  /* atanh (x) = NaN as soon as |x| > 1, and arctanh(+/-1) = +/-Inf */
+  if (MPFR_UNLIKELY (MPFR_EXP (xt) > 0))
+    {
+      if (MPFR_EXP (xt) == 1 && mpfr_powerof2_raw (xt))
+        {
+          MPFR_SET_INF (y);
+          MPFR_SET_SAME_SIGN (y, xt);
+          MPFR_RET (0);
+        }
+      MPFR_SET_NAN (y);
+      MPFR_RET_NAN;
+    }
+
+  /* atanh(x) = x + x^3/3 + ... so the error is < 2^(3*EXP(x)-1) */
+  MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, xt, -2 * MPFR_GET_EXP (xt), 1, 1,
+                                    rnd_mode, {});
+
+  MPFR_SAVE_EXPO_MARK (expo);
+
+  /* Compute initial precision */
+  Nx = MPFR_PREC (xt);
+  MPFR_TMP_INIT_ABS (x, xt);
+  Ny = MPFR_PREC (y);
+  Nt = MAX (Nx, Ny);
+  /* the optimal number of bits : see algorithms.ps */
+  Nt = Nt + MPFR_INT_CEIL_LOG2 (Nt) + 4;
+
+  /* initialise of intermediary variable */
+  mpfr_init2 (t, Nt);
+  mpfr_init2 (te, Nt);
+
+  /* First computation of cosh */
+  MPFR_ZIV_INIT (loop, Nt);
+  for (;;)
+    {
+      /* compute atanh */
+      mpfr_ui_sub (te, 1, x, GMP_RNDU);   /* (1-xt)*/
+      mpfr_add_ui (t,  x, 1, GMP_RNDD);   /* (xt+1)*/
+      mpfr_div (t, t, te, GMP_RNDN);      /* (1+xt)/(1-xt)*/
+      mpfr_log (t, t, GMP_RNDN);          /* ln((1+xt)/(1-xt))*/
+      mpfr_div_2ui (t, t, 1, GMP_RNDN);   /* (1/2)*ln((1+xt)/(1-xt))*/
+
+      /* error estimate: see algorithms.tex */
+      /* FIXME: this does not correspond to the value in algorithms.tex!!! */
+      /* err=Nt-__gmpfr_ceil_log2(1+5*pow(2,1-MPFR_EXP(t)));*/
+      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;
+
+      /* reactualisation of the precision */
+      MPFR_ZIV_NEXT (loop, Nt);
+      mpfr_set_prec (t, Nt);
+      mpfr_set_prec (te, Nt);
+    }
+  MPFR_ZIV_FREE (loop);
+
+  inexact = mpfr_set4 (y, t, rnd_mode, MPFR_SIGN (xt));
+
+  mpfr_clear(t);
+  mpfr_clear(te);
+
+  MPFR_SAVE_EXPO_FREE (expo);
+  return mpfr_check_range (y, inexact, rnd_mode);
+}
+