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 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 = (mp_ptr) TMP_ALLOC (tsize * BYTES_PER_MP_LIMB); 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