1 /* mpf_sqrt -- Compute the square root of a float.
2
3 Copyright 1993, 1994, 1996, 2000, 2001, 2004, 2005 Free Software Foundation,
4 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 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 MP 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 MP Library. If not, see http://www.gnu.org/licenses/. */
20
21 #include <stdio.h> /* for NULL */
22 #include "gmp.h"
23 #include "gmp-impl.h"
24
25
26 /* As usual, the aim is to produce PREC(r) limbs of result, with the high
27 limb non-zero. This is accomplished by applying mpn_sqrtrem to either
28 2*prec or 2*prec-1 limbs, both such sizes resulting in prec limbs.
29
30 The choice between 2*prec or 2*prec-1 limbs is based on the input
31 exponent. With b=2^GMP_NUMB_BITS the limb base then we can think of
32 effectively taking out a factor b^(2k), for suitable k, to get to an
33 integer input of the desired size ready for mpn_sqrtrem. It must be an
34 even power taken out, ie. an even number of limbs, so the square root
35 gives factor b^k and the radix point is still on a limb boundary. So if
36 EXP(r) is even we'll get an even number of input limbs 2*prec, or if
37 EXP(r) is odd we get an odd number 2*prec-1.
38
39 Further limbs below the 2*prec or 2*prec-1 used don't affect the result
40 and are simply truncated. This can be seen by considering an integer x,
41 with s=floor(sqrt(x)). s is the unique integer satisfying s^2 <= x <
42 (s+1)^2. Notice that adding a fraction part to x (ie. some further bits)
43 doesn't change the inequality, s remains the unique solution. Working
44 suitable factors of 2 into this argument lets it apply to an intended
45 precision at any position for any x, not just the integer binary point.
46
47 If the input is smaller than 2*prec or 2*prec-1, then we just pad with
48 zeros, that of course being our usual interpretation of short inputs.
49 The effect is to extend the root beyond the size of the input (for
50 instance into fractional limbs if u is an integer). */
51
52 void
mpf_sqrt(mpf_ptr r,mpf_srcptr u)53 mpf_sqrt (mpf_ptr r, mpf_srcptr u)
54 {
55 mp_size_t usize;
56 mp_ptr up, tp;
57 mp_size_t prec, tsize;
58 mp_exp_t uexp, expodd;
59 TMP_DECL;
60
61 usize = u->_mp_size;
62 if (usize <= 0)
63 {
64 if (usize < 0)
65 SQRT_OF_NEGATIVE;
66 r->_mp_size = 0;
67 r->_mp_exp = 0;
68 return;
69 }
70
71 TMP_MARK;
72
73 uexp = u->_mp_exp;
74 prec = r->_mp_prec;
75 up = u->_mp_d;
76
77 expodd = (uexp & 1);
78 tsize = 2 * prec - expodd;
79 r->_mp_size = prec;
80 r->_mp_exp = (uexp + expodd) / 2; /* ceil(uexp/2) */
81
82 /* root size is ceil(tsize/2), this will be our desired "prec" limbs */
83 ASSERT ((tsize + 1) / 2 == prec);
84
85 tp = TMP_ALLOC_LIMBS (tsize);
86
87 if (usize > tsize)
88 {
89 up += usize - tsize;
90 usize = tsize;
91 MPN_COPY (tp, up, tsize);
92 }
93 else
94 {
95 MPN_ZERO (tp, tsize - usize);
96 MPN_COPY (tp + (tsize - usize), up, usize);
97 }
98
99 mpn_sqrtrem (r->_mp_d, NULL, tp, tsize);
100
101 TMP_FREE;
102 }
103