1/* mpf_pow_ui -- Compute b^e.
2
3Copyright 1998, 1999, 2001, 2012, 2015 Free Software Foundation, Inc.
4
5This file is part of the GNU MP Library.
6
7The GNU MP Library is free software; you can redistribute it and/or modify
8it under the terms of either:
9
10  * the GNU Lesser General Public License as published by the Free
11    Software Foundation; either version 3 of the License, or (at your
12    option) any later version.
13
14or
15
16  * the GNU General Public License as published by the Free Software
17    Foundation; either version 2 of the License, or (at your option) any
18    later version.
19
20or both in parallel, as here.
21
22The GNU MP Library is distributed in the hope that it will be useful, but
23WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
24or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
25for more details.
26
27You should have received copies of the GNU General Public License and the
28GNU Lesser General Public License along with the GNU MP Library.  If not,
29see https://www.gnu.org/licenses/.  */
30
31#include "gmp-impl.h"
32#include "longlong.h"
33
34/* This uses a plain right-to-left square-and-multiply algorithm.
35
36   FIXME: When popcount(e) is not too small, it would probably speed things up
37   to use a k-ary sliding window algorithm.  */
38
39void
40mpf_pow_ui (mpf_ptr r, mpf_srcptr b, unsigned long int e)
41{
42  mpf_t t;
43  int cnt;
44
45  if (e <= 1)
46    {
47      if (e == 0)
48	mpf_set_ui (r, 1);
49      else
50	mpf_set (r, b);
51      return;
52    }
53
54  count_leading_zeros (cnt, (mp_limb_t) e);
55  cnt = GMP_LIMB_BITS - 1 - cnt;
56
57  /* Increase computation precision as a function of the exponent.  Adding
58     log2(popcount(e) + log2(e)) bits should be sufficient, but we add log2(e),
59     i.e. much more.  With mpf's rounding of precision to whole limbs, this
60     will be excessive only when limbs are artificially small.  */
61  mpf_init2 (t, mpf_get_prec (r) + cnt);
62
63  mpf_set (t, b);		/* consume most significant bit */
64  while (--cnt > 0)
65    {
66      mpf_mul (t, t, t);
67      if ((e >> cnt) & 1)
68	mpf_mul (t, t, b);
69    }
70
71  /* Do the last iteration specially in order to save a copy operation.  */
72  if (e & 1)
73    {
74      mpf_mul (t, t, t);
75      mpf_mul (r, t, b);
76    }
77  else
78    {
79      mpf_mul (r, t, t);
80    }
81
82  mpf_clear (t);
83}
84