1 /* Round according to the current rounding mode. 2 Copyright (C) 2007, 2010-2021 Free Software Foundation, Inc. 3 4 This file is free software: you can redistribute it and/or modify 5 it under the terms of the GNU Lesser General Public License as 6 published by the Free Software Foundation; either version 3 of the 7 License, or (at your option) any later version. 8 9 This file is distributed in the hope that it will be useful, 10 but WITHOUT ANY WARRANTY; without even the implied warranty of 11 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 12 GNU Lesser General Public License for more details. 13 14 You should have received a copy of the GNU Lesser General Public License 15 along with this program. If not, see <https://www.gnu.org/licenses/>. */ 16 17 #if ! defined USE_LONG_DOUBLE 18 # include <config.h> 19 #endif 20 21 /* Specification. */ 22 #include <math.h> 23 24 #include <float.h> 25 #include <stdlib.h> 26 27 #undef MIN 28 29 #ifdef USE_LONG_DOUBLE 30 # define RINT rintl 31 # define DOUBLE long double 32 # define MANT_DIG LDBL_MANT_DIG 33 # define MIN LDBL_MIN 34 # define L_(literal) literal##L 35 #elif ! defined USE_FLOAT 36 # define RINT rint 37 # define DOUBLE double 38 # define MANT_DIG DBL_MANT_DIG 39 # define MIN DBL_MIN 40 # define L_(literal) literal 41 #else /* defined USE_FLOAT */ 42 # define RINT rintf 43 # define DOUBLE float 44 # define MANT_DIG FLT_MANT_DIG 45 # define MIN FLT_MIN 46 # define L_(literal) literal##f 47 #endif 48 49 /* -0.0. See minus-zero.h. */ 50 #if defined __hpux || defined __sgi || defined __ICC 51 # define MINUS_ZERO (-MIN * MIN) 52 #else 53 # define MINUS_ZERO L_(-0.0) 54 #endif 55 56 /* MSVC with option -fp:strict refuses to compile constant initializers that 57 contain floating-point operations. Pacify this compiler. */ 58 #if defined _MSC_VER && !defined __clang__ 59 # pragma fenv_access (off) 60 #endif 61 62 DOUBLE 63 RINT (DOUBLE x) /* */ 64 { 65 /* 2^(MANT_DIG-1). */ 66 static const DOUBLE TWO_MANT_DIG = 67 /* Assume MANT_DIG <= 5 * 31. 68 Use the identity 69 n = floor(n/5) + floor((n+1)/5) + ... + floor((n+4)/5). */ 70 (DOUBLE) (1U << ((MANT_DIG - 1) / 5)) 71 * (DOUBLE) (1U << ((MANT_DIG - 1 + 1) / 5)) 72 * (DOUBLE) (1U << ((MANT_DIG - 1 + 2) / 5)) 73 * (DOUBLE) (1U << ((MANT_DIG - 1 + 3) / 5)) 74 * (DOUBLE) (1U << ((MANT_DIG - 1 + 4) / 5)); 75 76 /* The use of 'volatile' guarantees that excess precision bits are dropped at 77 each addition step and before the following comparison at the caller's 78 site. It is necessary on x86 systems where double-floats are not IEEE 79 compliant by default, to avoid that the results become platform and 80 compiler option dependent. 'volatile' is a portable alternative to gcc's 81 -ffloat-store option. */ 82 volatile DOUBLE z = x; 83 84 /* Consider the current rounding mode, cf. 85 <https://pubs.opengroup.org/onlinepubs/9699919799/basedefs/float.h.html>. 86 This implementation supports only rounds-to-nearest. */ 87 if (FLT_ROUNDS != 1) 88 abort (); 89 90 if (z > L_(0.0)) 91 { 92 /* Avoid rounding error for x = 0.5 - 2^(-MANT_DIG-1). */ 93 if (z < L_(0.5)) 94 z = L_(0.0); 95 /* Avoid rounding errors for values near 2^k, where k >= MANT_DIG-1. */ 96 else if (z < TWO_MANT_DIG) 97 { 98 /* Round to the next integer. */ 99 z += TWO_MANT_DIG; 100 z -= TWO_MANT_DIG; 101 } 102 } 103 else if (z < L_(0.0)) 104 { 105 /* Avoid rounding error for x = -(0.5 - 2^(-MANT_DIG-1)). */ 106 if (z > - L_(0.5)) 107 z = MINUS_ZERO; 108 /* Avoid rounding errors for values near -2^k, where k >= MANT_DIG-1. */ 109 else if (z > -TWO_MANT_DIG) 110 { 111 /* Round to the next integer. */ 112 z -= TWO_MANT_DIG; 113 z += TWO_MANT_DIG; 114 } 115 } 116 return z; 117 }