Imported gcc-4.4.3

[msp430-gcc.git] / mpfr / exp2.c

diff --git a/mpfr/exp2.c b/mpfr/exp2.c
new file mode 100644 (file)
index 0000000..ee14fc0
--- /dev/null
+++ b/mpfr/exp2.c
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+/* mpfr_exp2 -- power of 2 function 2^y
+
+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 y = 2^z is done by                           *
+ *     y = exp(z*log(2)). The result is exact iff z is an integer. */
+
+int
+mpfr_exp2 (mpfr_ptr y, mpfr_srcptr x, mp_rnd_t rnd_mode)
+{
+  int inexact;
+  long xint;
+  mpfr_t xfrac;
+  MPFR_SAVE_EXPO_DECL (expo);
+
+  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))
+        {
+          if (MPFR_IS_POS (x))
+            MPFR_SET_INF (y);
+          else
+            MPFR_SET_ZERO (y);
+          MPFR_SET_POS (y);
+          MPFR_RET (0);
+        }
+      else /* 2^0 = 1 */
+        {
+          MPFR_ASSERTD (MPFR_IS_ZERO(x));
+          return mpfr_set_ui (y, 1, rnd_mode);
+        }
+    }
+
+  /* since the smallest representable non-zero float is 1/2*2^__gmpfr_emin,
+     if x < __gmpfr_emin - 1, the result is either 1/2*2^__gmpfr_emin or 0 */
+  MPFR_ASSERTN (MPFR_EMIN_MIN >= LONG_MIN + 2);
+  if (MPFR_UNLIKELY (mpfr_cmp_si (x, __gmpfr_emin - 1) < 0))
+    {
+      mp_rnd_t rnd2 = rnd_mode;
+      /* in round to nearest mode, round to zero when x <= __gmpfr_emin-2 */
+      if (rnd_mode == GMP_RNDN &&
+          mpfr_cmp_si_2exp (x, __gmpfr_emin - 2, 0) <= 0)
+        rnd2 = GMP_RNDZ;
+      return mpfr_underflow (y, rnd2, 1);
+    }
+
+  MPFR_ASSERTN (MPFR_EMAX_MAX <= LONG_MAX);
+  if (MPFR_UNLIKELY (mpfr_cmp_si (x, __gmpfr_emax) >= 0))
+    return mpfr_overflow (y, rnd_mode, 1);
+
+  /* We now know that emin - 1 <= x < emax. */
+
+  MPFR_SAVE_EXPO_MARK (expo);
+
+  /* 2^x = 1 + x*log(2) + O(x^2) for x near zero, and for |x| <= 1 we have
+     |2^x - 1| <= x < 2^EXP(x). If x > 0 we must round away from 0 (dir=1);
+     if x < 0 we must round towards 0 (dir=0). */
+  MPFR_SMALL_INPUT_AFTER_SAVE_EXPO (y, __gmpfr_one, - MPFR_GET_EXP (x), 0,
+                                    MPFR_SIGN(x) > 0, rnd_mode, expo, {});
+
+  xint = mpfr_get_si (x, GMP_RNDZ);
+  mpfr_init2 (xfrac, MPFR_PREC (x));
+  mpfr_sub_si (xfrac, x, xint, GMP_RNDN); /* exact */
+
+  if (MPFR_IS_ZERO (xfrac))
+    {
+      mpfr_set_ui (y, 1, GMP_RNDN);
+      inexact = 0;
+    }
+  else
+    {
+      /* Declaration of the intermediary variable */
+      mpfr_t t;
+
+      /* Declaration of the size variable */
+      mp_prec_t Ny = MPFR_PREC(y);              /* target precision */
+      mp_prec_t Nt;                             /* working precision */
+      mp_exp_t err;                             /* error */
+      MPFR_ZIV_DECL (loop);
+
+      /* compute the precision of intermediary variable */
+      /* the optimal number of bits : see algorithms.tex */
+      Nt = Ny + 5 + MPFR_INT_CEIL_LOG2 (Ny);
+
+      /* initialise of intermediary variable */
+      mpfr_init2 (t, Nt);
+
+      /* First computation */
+      MPFR_ZIV_INIT (loop, Nt);
+      for (;;)
+        {
+          /* compute exp(x*ln(2))*/
+          mpfr_const_log2 (t, GMP_RNDU);       /* ln(2) */
+          mpfr_mul (t, xfrac, t, GMP_RNDU);    /* xfrac * ln(2) */
+          err = Nt - (MPFR_GET_EXP (t) + 2);   /* Estimate of the error */
+          mpfr_exp (t, t, GMP_RNDN);           /* exp(xfrac * ln(2)) */
+
+          if (MPFR_LIKELY (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_set (y, t, rnd_mode);
+
+      mpfr_clear (t);
+    }
+
+  mpfr_clear (xfrac);
+  mpfr_clear_flags ();
+  mpfr_mul_2si (y, y, xint, GMP_RNDN); /* exact or overflow */
+  /* Note: We can have an overflow only when t was rounded up to 2. */
+  MPFR_ASSERTD (MPFR_IS_PURE_FP (y) || inexact > 0);
+  MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, __gmpfr_flags);
+  MPFR_SAVE_EXPO_FREE (expo);
+  return mpfr_check_range (y, inexact, rnd_mode);
+}