1 /* mpf_sqrt_ui -- Compute the square root of an unsigned integer.
2
3 Copyright 1993, 1994, 1996, 2000, 2001, 2004, 2005, 2015 Free Software
4 Foundation, Inc.
5
6 This file is part of the GNU MP Library.
7
8 The GNU MP Library is free software; you can redistribute it and/or modify
9 it under the terms of either:
10
11 * the GNU Lesser General Public License as published by the Free
12 Software Foundation; either version 3 of the License, or (at your
13 option) any later version.
14
15 or
16
17 * the GNU General Public License as published by the Free Software
18 Foundation; either version 2 of the License, or (at your option) any
19 later version.
20
21 or both in parallel, as here.
22
23 The GNU MP Library is distributed in the hope that it will be useful, but
24 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
25 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
26 for more details.
27
28 You should have received copies of the GNU General Public License and the
29 GNU Lesser General Public License along with the GNU MP Library. If not,
30 see https://www.gnu.org/licenses/. */
31
32 #include <stdio.h> /* for NULL */
33 #include "gmp-impl.h"
34
35
36 /* As usual the aim is to produce PREC(r) limbs of result with the high limb
37 non-zero. That high limb will end up floor(sqrt(u)), and limbs below are
38 produced by padding the input with zeros, two for each desired result
39 limb, being 2*(prec-1) for a total 2*prec-1 limbs passed to mpn_sqrtrem.
40 The way mpn_sqrtrem calculates floor(sqrt(x)) ensures the root is correct
41 to the intended accuracy, ie. truncated to prec limbs.
42
43 With nails, u might be two limbs, in which case a total 2*prec limbs is
44 passed to mpn_sqrtrem (still giving a prec limb result). If uhigh is
45 zero we adjust back to 2*prec-1, since mpn_sqrtrem requires the high
46 non-zero. 2*prec limbs are always allocated, even when uhigh is zero, so
47 the store of uhigh can be done without a conditional.
48
49 u==0 is a special case so the rest of the code can assume the result is
50 non-zero (ie. will have a non-zero high limb on the result).
51
52 Not done:
53
54 No attempt is made to identify perfect squares. It's considered this can
55 be left to an application if it might occur with any frequency. As it
56 stands, mpn_sqrtrem does its normal amount of work on a perfect square
57 followed by zero limbs, though of course only an mpn_sqrtrem1 would be
58 actually needed. We also end up leaving our mpf result with lots of low
59 trailing zeros, slowing down subsequent operations.
60
61 We're not aware of any optimizations that can be made using the fact the
62 input has lots of trailing zeros (apart from the perfect square
63 case). */
64
65
66 /* 1 if we (might) need two limbs for u */
67 #define U2 (GMP_NUMB_BITS < BITS_PER_ULONG)
68
69 void
mpf_sqrt_ui(mpf_ptr r,unsigned long int u)70 mpf_sqrt_ui (mpf_ptr r, unsigned long int u)
71 {
72 mp_size_t rsize, zeros;
73 mp_ptr tp;
74 mp_size_t prec;
75 TMP_DECL;
76
77 if (UNLIKELY (u <= 1))
78 {
79 SIZ (r) = EXP (r) = u;
80 *PTR (r) = u;
81 return;
82 }
83
84 TMP_MARK;
85
86 prec = PREC (r);
87 zeros = 2 * prec - 2;
88 rsize = zeros + 1 + U2;
89
90 tp = TMP_ALLOC_LIMBS (rsize);
91
92 MPN_ZERO (tp, zeros);
93 tp[zeros] = u & GMP_NUMB_MASK;
94
95 #if U2
96 {
97 mp_limb_t uhigh = u >> GMP_NUMB_BITS;
98 tp[zeros + 1] = uhigh;
99 rsize -= (uhigh == 0);
100 }
101 #endif
102
103 mpn_sqrtrem (PTR (r), NULL, tp, rsize);
104
105 SIZ (r) = prec;
106 EXP (r) = 1;
107 TMP_FREE;
108 }
109