Import http://www.mpfr.org/mpfr-current/mpfr-3.1.5.tar.xz

1 files changed, 164 insertions, 0 deletions

diff --git a/mpfr/src/pow_ui.c b/mpfr/src/pow_ui.c
new file mode 100644
index 0000000000..061b54cbb7
--- /dev/null
+++ b/mpfr/src/pow_ui.c
@@ -0,0 +1,164 @@
+/* mpfr_pow_ui-- compute the power of a floating-point
+                                  by a machine integer
+
+Copyright 1999-2016 Free Software Foundation, Inc.
+Contributed by the AriC and Caramba 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 3 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.LESSER.  If not, see
+http://www.gnu.org/licenses/ or 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"
+
+/* sets y to x^n, and return 0 if exact, non-zero otherwise */
+int
+mpfr_pow_ui (mpfr_ptr y, mpfr_srcptr x, unsigned long int n, mpfr_rnd_t rnd)
+{
+  unsigned long m;
+  mpfr_t res;
+  mpfr_prec_t prec, err;
+  int inexact;
+  mpfr_rnd_t rnd1;
+  MPFR_SAVE_EXPO_DECL (expo);
+  MPFR_ZIV_DECL (loop);
+  MPFR_BLOCK_DECL (flags);
+
+  MPFR_LOG_FUNC
+    (("x[%Pu]=%.*Rg n=%lu rnd=%d",
+      mpfr_get_prec (x), mpfr_log_prec, x, n, rnd),
+     ("y[%Pu]=%.*Rg inexact=%d",
+      mpfr_get_prec (y), mpfr_log_prec, y, inexact));
+
+  /* x^0 = 1 for any x, even a NaN */
+  if (MPFR_UNLIKELY (n == 0))
+    return mpfr_set_ui (y, 1, rnd);
+
+  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))
+        {
+          /* Inf^n = Inf, (-Inf)^n = Inf for n even, -Inf for n odd */
+          if (MPFR_IS_NEG (x) && (n & 1) == 1)
+            MPFR_SET_NEG (y);
+          else
+            MPFR_SET_POS (y);
+          MPFR_SET_INF (y);
+          MPFR_RET (0);
+        }
+      else /* x is zero */
+        {
+          MPFR_ASSERTD (MPFR_IS_ZERO (x));
+          /* 0^n = 0 for any n */
+          MPFR_SET_ZERO (y);
+          if (MPFR_IS_POS (x) || (n & 1) == 0)
+            MPFR_SET_POS (y);
+          else
+            MPFR_SET_NEG (y);
+          MPFR_RET (0);
+        }
+    }
+  else if (MPFR_UNLIKELY (n <= 2))
+    {
+      if (n < 2)
+        /* x^1 = x */
+        return mpfr_set (y, x, rnd);
+      else
+        /* x^2 = sqr(x) */
+        return mpfr_sqr (y, x, rnd);
+    }
+
+  /* Augment exponent range */
+  MPFR_SAVE_EXPO_MARK (expo);
+
+  /* setup initial precision */
+  prec = MPFR_PREC (y) + 3 + GMP_NUMB_BITS
+    + MPFR_INT_CEIL_LOG2 (MPFR_PREC (y));
+  mpfr_init2 (res, prec);
+
+  rnd1 = MPFR_IS_POS (x) ? MPFR_RNDU : MPFR_RNDD; /* away */
+
+  MPFR_ZIV_INIT (loop, prec);
+  for (;;)
+    {
+      int i;
+
+      for (m = n, i = 0; m; i++, m >>= 1)
+        ;
+      /* now 2^(i-1) <= n < 2^i */
+      MPFR_ASSERTD (prec > (mpfr_prec_t) i);
+      err = prec - 1 - (mpfr_prec_t) i;
+      /* First step: compute square from x */
+      MPFR_BLOCK (flags,
+                  inexact = mpfr_mul (res, x, x, MPFR_RNDU);
+                  MPFR_ASSERTD (i >= 2);
+                  if (n & (1UL << (i-2)))
+                    inexact |= mpfr_mul (res, res, x, rnd1);
+                  for (i -= 3; i >= 0 && !MPFR_BLOCK_EXCEP; i--)
+                    {
+                      inexact |= mpfr_mul (res, res, res, MPFR_RNDU);
+                      if (n & (1UL << i))
+                        inexact |= mpfr_mul (res, res, x, rnd1);
+                    });
+      /* let r(n) be the number of roundings: we have r(2)=1, r(3)=2,
+         and r(2n)=2r(n)+1, r(2n+1)=2r(n)+2, thus r(n)=n-1.
+         Using Higham's method, to each rounding corresponds a factor
+         (1-theta) with 0 <= theta <= 2^(1-p), thus at the end the
+         absolute error is bounded by (n-1)*2^(1-p)*res <= 2*(n-1)*ulp(res)
+         since 2^(-p)*x <= ulp(x). Since n < 2^i, this gives a maximal
+         error of 2^(1+i)*ulp(res).
+      */
+      if (MPFR_LIKELY (inexact == 0
+                       || MPFR_OVERFLOW (flags) || MPFR_UNDERFLOW (flags)
+                       || MPFR_CAN_ROUND (res, err, MPFR_PREC (y), rnd)))
+        break;
+      /* Actualisation of the precision */
+      MPFR_ZIV_NEXT (loop, prec);
+      mpfr_set_prec (res, prec);
+    }
+  MPFR_ZIV_FREE (loop);
+
+  if (MPFR_UNLIKELY (MPFR_OVERFLOW (flags) || MPFR_UNDERFLOW (flags)))
+    {
+      mpz_t z;
+
+      /* Internal overflow or underflow. However the approximation error has
+       * not been taken into account. So, let's solve this problem by using
+       * mpfr_pow_z, which can handle it. This case could be improved in the
+       * future, without having to use mpfr_pow_z.
+       */
+      MPFR_LOG_MSG (("Internal overflow or underflow,"
+                     " let's use mpfr_pow_z.\n", 0));
+      mpfr_clear (res);
+      MPFR_SAVE_EXPO_FREE (expo);
+      mpz_init (z);
+      mpz_set_ui (z, n);
+      inexact = mpfr_pow_z (y, x, z, rnd);
+      mpz_clear (z);
+      return inexact;
+    }
+
+  inexact = mpfr_set (y, res, rnd);
+  mpfr_clear (res);
+
+  MPFR_SAVE_EXPO_FREE (expo);
+  return mpfr_check_range (y, inexact, rnd);
+}