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.h" 34 #include "gmp-impl.h" 35 36 37 /* As usual the aim is to produce PREC(r) limbs of result with the high limb 38 non-zero. That high limb will end up floor(sqrt(u)), and limbs below are 39 produced by padding the input with zeros, two for each desired result 40 limb, being 2*(prec-1) for a total 2*prec-1 limbs passed to mpn_sqrtrem. 41 The way mpn_sqrtrem calculates floor(sqrt(x)) ensures the root is correct 42 to the intended accuracy, ie. truncated to prec limbs. 43 44 With nails, u might be two limbs, in which case a total 2*prec limbs is 45 passed to mpn_sqrtrem (still giving a prec limb result). If uhigh is 46 zero we adjust back to 2*prec-1, since mpn_sqrtrem requires the high 47 non-zero. 2*prec limbs are always allocated, even when uhigh is zero, so 48 the store of uhigh can be done without a conditional. 49 50 u==0 is a special case so the rest of the code can assume the result is 51 non-zero (ie. will have a non-zero high limb on the result). 52 53 Not done: 54 55 No attempt is made to identify perfect squares. It's considered this can 56 be left to an application if it might occur with any frequency. As it 57 stands, mpn_sqrtrem does its normal amount of work on a perfect square 58 followed by zero limbs, though of course only an mpn_sqrtrem1 would be 59 actually needed. We also end up leaving our mpf result with lots of low 60 trailing zeros, slowing down subsequent operations. 61 62 We're not aware of any optimizations that can be made using the fact the 63 input has lots of trailing zeros (apart from the perfect square 64 case). */ 65 66 67 /* 1 if we (might) need two limbs for u */ 68 #define U2 (GMP_NUMB_BITS < BITS_PER_ULONG) 69 70 void 71 mpf_sqrt_ui (mpf_ptr r, unsigned long int u) 72 { 73 mp_size_t rsize, zeros; 74 mp_ptr tp; 75 mp_size_t prec; 76 TMP_DECL; 77 78 if (UNLIKELY (u <= 1)) 79 { 80 SIZ (r) = EXP (r) = u; 81 *PTR (r) = u; 82 return; 83 } 84 85 TMP_MARK; 86 87 prec = PREC (r); 88 zeros = 2 * prec - 2; 89 rsize = zeros + 1 + U2; 90 91 tp = TMP_ALLOC_LIMBS (rsize); 92 93 MPN_ZERO (tp, zeros); 94 tp[zeros] = u & GMP_NUMB_MASK; 95 96 #if U2 97 { 98 mp_limb_t uhigh = u >> GMP_NUMB_BITS; 99 tp[zeros + 1] = uhigh; 100 rsize -= (uhigh == 0); 101 } 102 #endif 103 104 mpn_sqrtrem (PTR (r), NULL, tp, rsize); 105 106 SIZ (r) = prec; 107 EXP (r) = 1; 108 TMP_FREE; 109 } 110