1/* mpf_sqrt_ui -- Compute the square root of an unsigned integer.
2
3Copyright 1993, 1994, 1996, 2000, 2001, 2004, 2005, 2015 Free Software
4Foundation, Inc.
5
6This file is part of the GNU MP Library.
7
8The GNU MP Library is free software; you can redistribute it and/or modify
9it 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
15or
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
21or both in parallel, as here.
22
23The GNU MP Library is distributed in the hope that it will be useful, but
24WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
25or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
26for more details.
27
28You should have received copies of the GNU General Public License and the
29GNU Lesser General Public License along with the GNU MP Library.  If not,
30see 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
69void
70mpf_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