Imported gcc-4.4.3

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

diff --git a/mpfr/asin.c b/mpfr/asin.c
new file mode 100644 (file)
index 0000000..4ad8d8d
--- /dev/null
+++ b/mpfr/asin.c
@@ -0,0 +1,121 @@
+/* mpfr_asin -- arc-sinus of a floating-point number
+
+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, and was contributed by Mathieu Dutour.
+
+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. */
+
+#include "mpfr-impl.h"
+
+int
+mpfr_asin (mpfr_ptr asin, mpfr_srcptr x, mp_rnd_t rnd_mode)
+{
+  mpfr_t xp;
+  int compared, inexact;
+  mp_prec_t prec;
+  mp_exp_t xp_exp;
+  MPFR_SAVE_EXPO_DECL (expo);
+  MPFR_ZIV_DECL (loop);
+
+  MPFR_LOG_FUNC (("x[%#R]=%R rnd=%d", x, x, rnd_mode),
+                 ("asin[%#R]=%R inexact=%d", asin, asin, inexact));
+
+  /* Special cases */
+  if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
+    {
+      if (MPFR_IS_NAN (x) || MPFR_IS_INF (x))
+        {
+          MPFR_SET_NAN (asin);
+          MPFR_RET_NAN;
+        }
+      else /* x = 0 */
+        {
+          MPFR_ASSERTD (MPFR_IS_ZERO (x));
+          MPFR_SET_ZERO (asin);
+          MPFR_SET_SAME_SIGN (asin, x);
+          MPFR_RET (0); /* exact result */
+        }
+    }
+
+  /* asin(x) = x + x^3/6 + ... so the error is < 2^(3*EXP(x)-2) */
+  MPFR_FAST_COMPUTE_IF_SMALL_INPUT (asin, x, -2 * MPFR_GET_EXP (x), 2, 1,
+                                    rnd_mode, {});
+
+  /* Set x_p=|x| (x is a normal number) */
+  mpfr_init2 (xp, MPFR_PREC (x));
+  inexact = mpfr_abs (xp, x, GMP_RNDN);
+  MPFR_ASSERTD (inexact == 0);
+
+  compared = mpfr_cmp_ui (xp, 1);
+
+  if (MPFR_UNLIKELY (compared >= 0))
+    {
+      mpfr_clear (xp);
+      if (compared > 0)                  /* asin(x) = NaN for |x| > 1 */
+        {
+          MPFR_SET_NAN (asin);
+          MPFR_RET_NAN;
+        }
+      else                              /* x = 1 or x = -1 */
+        {
+          if (MPFR_IS_POS (x)) /* asin(+1) = Pi/2 */
+            inexact = mpfr_const_pi (asin, rnd_mode);
+          else /* asin(-1) = -Pi/2 */
+            {
+              inexact = -mpfr_const_pi (asin, MPFR_INVERT_RND(rnd_mode));
+              MPFR_CHANGE_SIGN (asin);
+            }
+          mpfr_div_2ui (asin, asin, 1, rnd_mode); /* May underflow */
+          return inexact;
+        }
+    }
+
+  MPFR_SAVE_EXPO_MARK (expo);
+
+  /* Compute exponent of 1 - ABS(x) */
+  mpfr_ui_sub (xp, 1, xp, GMP_RNDD);
+  MPFR_ASSERTD (MPFR_GET_EXP (xp) <= 0);
+  MPFR_ASSERTD (MPFR_GET_EXP (x) <= 0);
+  xp_exp = 2 - MPFR_GET_EXP (xp);
+
+  /* Set up initial prec */
+  prec = MPFR_PREC (asin) + 10 + xp_exp;
+
+  /* use asin(x) = atan(x/sqrt(1-x^2)) */
+  MPFR_ZIV_INIT (loop, prec);
+  for (;;)
+    {
+      mpfr_set_prec (xp, prec);
+      mpfr_sqr (xp, x, GMP_RNDN);
+      mpfr_ui_sub (xp, 1, xp, GMP_RNDN);
+      mpfr_sqrt (xp, xp, GMP_RNDN);
+      mpfr_div (xp, x, xp, GMP_RNDN);
+      mpfr_atan (xp, xp, GMP_RNDN);
+      if (MPFR_LIKELY (MPFR_CAN_ROUND (xp, prec - xp_exp,
+                                       MPFR_PREC (asin), rnd_mode)))
+        break;
+      MPFR_ZIV_NEXT (loop, prec);
+    }
+  MPFR_ZIV_FREE (loop);
+  inexact = mpfr_set (asin, xp, rnd_mode);
+
+  mpfr_clear (xp);
+
+  MPFR_SAVE_EXPO_FREE (expo);
+  return mpfr_check_range (asin, inexact, rnd_mode);
+}