1 /* mpfr_ui_pow_ui -- compute the power between two machine integers
2
3 Copyright 1999-2023 Free Software Foundation, Inc.
4 Contributed by the AriC and Caramba 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 https://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 k, 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 MPFR_LOG_FUNC
39 (("k=%lu n=%lu rnd=%d", k, n, rnd),
40 ("y[%Pd]=%.*Rg inexact=%d",
41 mpfr_get_prec (x), mpfr_log_prec, x, inexact));
42
43 if (MPFR_UNLIKELY (n <= 1))
44 {
45 if (n == 1)
46 return mpfr_set_ui (x, k, rnd); /* k^1 = k */
47 else
48 return mpfr_set_ui (x, 1, rnd); /* k^0 = 1 for any k */
49 }
50 else if (MPFR_UNLIKELY (k <= 1))
51 {
52 if (k == 1)
53 return mpfr_set_ui (x, 1, rnd); /* 1^n = 1 for any n > 0 */
54 else
55 return mpfr_set_ui (x, 0, rnd); /* 0^n = 0 for any n > 0 */
56 }
57
58 for (size_n = 0, m = n; m != 0; size_n++, m >>= 1)
59 ;
60
61 MPFR_SAVE_EXPO_MARK (expo);
62 prec = MPFR_PREC (x) + 3 + size_n;
63 mpfr_init2 (res, prec);
64
65 MPFR_ZIV_INIT (loop, prec);
66 for (;;)
67 {
68 int i = size_n;
69 unsigned int inex_res;
70
71 inex_res = mpfr_set_ui (res, k, MPFR_RNDU);
72 err = 1;
73 /* now 2^(i-1) <= n < 2^i: i=1+floor(log2(n)) */
74 for (i -= 2; i >= 0; i--)
75 {
76 inex_res |= mpfr_sqr (res, res, MPFR_RNDU);
77 err++;
78 if (n & (1UL << i))
79 inex_res |= mpfr_mul_ui (res, res, k, MPFR_RNDU);
80 }
81
82 if (MPFR_UNLIKELY (MPFR_IS_INF (res)))
83 {
84 mpfr_t kf;
85 mpz_t z;
86 int size_k;
87 MPFR_BLOCK_DECL (flags);
88
89 /* Let's handle the overflow by calling mpfr_pow_z.
90 Alternatively, we could call mpfr_pow_ui; this would
91 need a bit shorter code below, but mpfr_pow_ui handles
92 the overflow by calling mpfr_pow_z, so that calling
93 mpfr_pow_z directly should be a bit more efficient. */
94
95 MPFR_ZIV_FREE (loop);
96 mpfr_clear (res);
97 for (size_k = 0, m = k; m != 0; size_k++, m >>= 1)
98 ;
99 mpfr_init2 (kf, size_k);
100 inexact = mpfr_set_ui (kf, k, MPFR_RNDN);
101 MPFR_ASSERTD (inexact == 0);
102 mpz_init (z);
103 mpz_set_ui (z, n);
104 MPFR_BLOCK (flags, inexact = mpfr_pow_z (x, kf, z, rnd););
105 mpz_clear (z);
106 mpfr_clear (kf);
107 MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, flags);
108 goto end;
109 }
110
111 /* since the loop is executed floor(log2(n)) times,
112 we have err = 1+floor(log2(n)).
113 Since prec >= MPFR_PREC(x) + 4 + floor(log2(n)), prec > err */
114 err = prec - err;
115
116 MPFR_LOG_VAR (res);
117 if (MPFR_LIKELY (!inex_res
118 || MPFR_CAN_ROUND (res, err, MPFR_PREC (x), rnd)))
119 break;
120
121 /* Actualisation of the precision */
122 MPFR_ZIV_NEXT (loop, prec);
123 mpfr_set_prec (res, prec);
124 }
125 MPFR_ZIV_FREE (loop);
126
127 inexact = mpfr_set (x, res, rnd);
128
129 mpfr_clear (res);
130
131 end:
132 MPFR_SAVE_EXPO_FREE (expo);
133 return mpfr_check_range (x, inexact, rnd);
134 }