--- /dev/null
+/* mpfr_pow_ui-- compute the power of a floating-point
+ by a machine integer
+
+Copyright 1999, 2000, 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"
+
+/* 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, mp_rnd_t rnd)
+{
+ unsigned long m;
+ mpfr_t res;
+ mp_prec_t prec, err;
+ int inexact;
+ mp_rnd_t rnd1;
+ MPFR_SAVE_EXPO_DECL (expo);
+ MPFR_ZIV_DECL (loop);
+ MPFR_BLOCK_DECL (flags);
+
+ MPFR_LOG_FUNC (("x[%#R]=%R n=%lu rnd=%d", x, x, n, rnd),
+ ("y[%#R]=%R inexact=%d", y, 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 + BITS_PER_MP_LIMB
+ + MPFR_INT_CEIL_LOG2 (MPFR_PREC (y));
+ mpfr_init2 (res, prec);
+
+ rnd1 = MPFR_IS_POS (x) ? GMP_RNDU : GMP_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, GMP_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, GMP_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);
+}
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