1 /* Round towards negative infinity. 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 /* Written by Bruno Haible <bruno@clisp.org>, 2007. */ 18 19 #if ! defined USE_LONG_DOUBLE 20 # include <config.h> 21 #endif 22 23 /* Specification. */ 24 #include <math.h> 25 26 #include <float.h> 27 28 #ifdef USE_LONG_DOUBLE 29 # define FUNC floorl 30 # define DOUBLE long double 31 # define MANT_DIG LDBL_MANT_DIG 32 # define L_(literal) literal##L 33 #elif ! defined USE_FLOAT 34 # define FUNC floor 35 # define DOUBLE double 36 # define MANT_DIG DBL_MANT_DIG 37 # define L_(literal) literal 38 #else /* defined USE_FLOAT */ 39 # define FUNC floorf 40 # define DOUBLE float 41 # define MANT_DIG FLT_MANT_DIG 42 # define L_(literal) literal##f 43 #endif 44 45 /* MSVC with option -fp:strict refuses to compile constant initializers that 46 contain floating-point operations. Pacify this compiler. */ 47 #if defined _MSC_VER && !defined __clang__ 48 # pragma fenv_access (off) 49 #endif 50 51 /* 2^(MANT_DIG-1). */ 52 static const DOUBLE TWO_MANT_DIG = 53 /* Assume MANT_DIG <= 5 * 31. 54 Use the identity 55 n = floor(n/5) + floor((n+1)/5) + ... + floor((n+4)/5). */ 56 (DOUBLE) (1U << ((MANT_DIG - 1) / 5)) 57 * (DOUBLE) (1U << ((MANT_DIG - 1 + 1) / 5)) 58 * (DOUBLE) (1U << ((MANT_DIG - 1 + 2) / 5)) 59 * (DOUBLE) (1U << ((MANT_DIG - 1 + 3) / 5)) 60 * (DOUBLE) (1U << ((MANT_DIG - 1 + 4) / 5)); 61 62 DOUBLE 63 FUNC (DOUBLE x) /* */ 64 { 65 /* The use of 'volatile' guarantees that excess precision bits are dropped 66 at each addition step and before the following comparison at the caller's 67 site. It is necessary on x86 systems where double-floats are not IEEE 68 compliant by default, to avoid that the results become platform and compiler 69 option dependent. 'volatile' is a portable alternative to gcc's 70 -ffloat-store option. */ 71 volatile DOUBLE y = x; 72 volatile DOUBLE z = y; 73 74 if (z > L_(0.0)) 75 { 76 /* For 0 < x < 1, return +0.0 even if the current rounding mode is 77 FE_DOWNWARD. */ 78 if (z < L_(1.0)) 79 z = L_(0.0); 80 /* Avoid rounding errors for values near 2^k, where k >= MANT_DIG-1. */ 81 else if (z < TWO_MANT_DIG) 82 { 83 /* Round to the next integer (nearest or up or down, doesn't matter). */ 84 z += TWO_MANT_DIG; 85 z -= TWO_MANT_DIG; 86 /* Enforce rounding down. */ 87 if (z > y) 88 z -= L_(1.0); 89 } 90 } 91 else if (z < L_(0.0)) 92 { 93 /* Avoid rounding errors for values near -2^k, where k >= MANT_DIG-1. */ 94 if (z > - TWO_MANT_DIG) 95 { 96 /* Round to the next integer (nearest or up or down, doesn't matter). */ 97 z -= TWO_MANT_DIG; 98 z += TWO_MANT_DIG; 99 /* Enforce rounding down. */ 100 if (z > y) 101 z -= L_(1.0); 102 } 103 } 104 return z; 105 }