source/libs/mpfr/mpfr-3.1.3/src/ui_pow_ui.c

   1 /*  mpfr_ui_pow_ui -- compute the power beetween two machine integer
   2
   3 Copyright 1999-2015 Free Software Foundation, Inc.
   4 Contributed by the AriC and Caramel projects, INRIA.
   5
   6 This file is part of the GNU MPFR Library.
   7
   8 The GNU MPFR Library is free software; you can redistribute it and/or modify
   9 it under the terms of the GNU Lesser General Public License as published by
  10 the Free Software Foundation; either version 3 of the License, or (at your
  11 option) any later version.
  12
  13 The GNU MPFR Library is distributed in the hope that it will be useful, but
  14 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
  15 or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
  16 License for more details.
  17
  18 You should have received a copy of the GNU Lesser General Public License
  19 along with the GNU MPFR Library; see the file COPYING.LESSER.  If not, see
  20 http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
  21 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */
  22
  23 #include "mpfr-impl.h"
  24
  25 int
  26 mpfr_ui_pow_ui (mpfr_ptr x, unsigned long int y, unsigned long int n,
  27                 mpfr_rnd_t rnd)
  28 {
  29   mpfr_exp_t err;
  30   unsigned long m;
  31   mpfr_t res;
  32   mpfr_prec_t prec;
  33   int size_n;
  34   int inexact;
  35   MPFR_ZIV_DECL (loop);
  36   MPFR_SAVE_EXPO_DECL (expo);
  37
  38   if (MPFR_UNLIKELY (n <= 1))
  39     {
  40       if (n == 1)
  41         return mpfr_set_ui (x, y, rnd);     /* y^1 = y */
  42       else
  43         return mpfr_set_ui (x, 1, rnd);     /* y^0 = 1 for any y */
  44     }
  45   else if (MPFR_UNLIKELY (y <= 1))
  46     {
  47       if (y == 1)
  48         return mpfr_set_ui (x, 1, rnd);     /* 1^n = 1 for any n > 0 */
  49       else
  50         return mpfr_set_ui (x, 0, rnd);     /* 0^n = 0 for any n > 0 */
  51     }
  52
  53   for (size_n = 0, m = n; m; size_n++, m >>= 1);
  54
  55   MPFR_SAVE_EXPO_MARK (expo);
  56   prec = MPFR_PREC (x) + 3 + size_n;
  57   mpfr_init2 (res, prec);
  58
  59   MPFR_ZIV_INIT (loop, prec);
  60   for (;;)
  61     {
  62       int i = size_n;
  63
  64       inexact = mpfr_set_ui (res, y, MPFR_RNDU);
  65       err = 1;
  66       /* now 2^(i-1) <= n < 2^i: i=1+floor(log2(n)) */
  67       for (i -= 2; i >= 0; i--)
  68         {
  69           inexact |= mpfr_mul (res, res, res, MPFR_RNDU);
  70           err++;
  71           if (n & (1UL << i))
  72             inexact |= mpfr_mul_ui (res, res, y, MPFR_RNDU);
  73         }
  74       /* since the loop is executed floor(log2(n)) times,
  75          we have err = 1+floor(log2(n)).
  76          Since prec >= MPFR_PREC(x) + 4 + floor(log2(n)), prec > err */
  77       err = prec - err;
  78
  79       if (MPFR_LIKELY (inexact == 0
  80                        || MPFR_CAN_ROUND (res, err, MPFR_PREC (x), rnd)))
  81         break;
  82
  83       /* Actualisation of the precision */
  84       MPFR_ZIV_NEXT (loop, prec);
  85       mpfr_set_prec (res, prec);
  86     }
  87   MPFR_ZIV_FREE (loop);
  88
  89   inexact = mpfr_set (x, res, rnd);
  90
  91   mpfr_clear (res);
  92
  93   MPFR_SAVE_EXPO_FREE (expo);
  94   return mpfr_check_range (x, inexact, rnd);
  95 }