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Diffstat (limited to 'Build/source/libs/mpfr/mpfr-3.1.2/src/pow_ui.c')
| -rw-r--r-- | Build/source/libs/mpfr/mpfr-3.1.2/src/pow_ui.c | 164 |
1 files changed, 164 insertions, 0 deletions
diff --git a/Build/source/libs/mpfr/mpfr-3.1.2/src/pow_ui.c b/Build/source/libs/mpfr/mpfr-3.1.2/src/pow_ui.c new file mode 100644 index 00000000000..377aee1cec2 --- /dev/null +++ b/Build/source/libs/mpfr/mpfr-3.1.2/src/pow_ui.c @@ -0,0 +1,164 @@ +/* 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, 2010, 2011, 2012, 2013 Free Software Foundation, Inc. +Contributed by the AriC and Caramel 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); +} |