| /* mpfr_ui_pow_ui -- compute the power beetween two 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. */ |
| |
| #include "mpfr-impl.h" |
| |
| int |
| mpfr_ui_pow_ui (mpfr_ptr x, unsigned long int y, unsigned long int n, |
| mp_rnd_t rnd) |
| { |
| mp_exp_t err; |
| unsigned long m; |
| mpfr_t res; |
| mp_prec_t prec; |
| int size_n; |
| int inexact; |
| MPFR_ZIV_DECL (loop); |
| MPFR_SAVE_EXPO_DECL (expo); |
| |
| if (MPFR_UNLIKELY (n <= 1)) |
| { |
| if (n == 1) |
| return mpfr_set_ui (x, y, rnd); /* y^1 = y */ |
| else |
| return mpfr_set_ui (x, 1, rnd); /* y^0 = 1 for any y */ |
| } |
| else if (MPFR_UNLIKELY (y <= 1)) |
| { |
| if (y == 1) |
| return mpfr_set_ui (x, 1, rnd); /* 1^n = 1 for any n > 0 */ |
| else |
| return mpfr_set_ui (x, 0, rnd); /* 0^n = 0 for any n > 0 */ |
| } |
| |
| for (size_n = 0, m = n; m; size_n++, m >>= 1); |
| |
| MPFR_SAVE_EXPO_MARK (expo); |
| prec = MPFR_PREC (x) + 3 + size_n; |
| mpfr_init2 (res, prec); |
| |
| MPFR_ZIV_INIT (loop, prec); |
| for (;;) |
| { |
| int i = size_n; |
| |
| inexact = mpfr_set_ui (res, y, GMP_RNDU); |
| err = 1; |
| /* now 2^(i-1) <= n < 2^i: i=1+floor(log2(n)) */ |
| for (i -= 2; i >= 0; i--) |
| { |
| inexact |= mpfr_mul (res, res, res, GMP_RNDU); |
| err++; |
| if (n & (1UL << i)) |
| inexact |= mpfr_mul_ui (res, res, y, GMP_RNDU); |
| } |
| /* since the loop is executed floor(log2(n)) times, |
| we have err = 1+floor(log2(n)). |
| Since prec >= MPFR_PREC(x) + 4 + floor(log2(n)), prec > err */ |
| err = prec - err; |
| |
| if (MPFR_LIKELY (inexact == 0 |
| || MPFR_CAN_ROUND (res, err, MPFR_PREC (x), rnd))) |
| break; |
| |
| /* Actualisation of the precision */ |
| MPFR_ZIV_NEXT (loop, prec); |
| mpfr_set_prec (res, prec); |
| } |
| MPFR_ZIV_FREE (loop); |
| |
| inexact = mpfr_set (x, res, rnd); |
| |
| mpfr_clear (res); |
| |
| MPFR_SAVE_EXPO_FREE (expo); |
| return mpfr_check_range (x, inexact, rnd); |
| } |