| 1 | /* Round towards positive infinity. |
| 2 | Copyright (C) 2007, 2010-2011 Free Software Foundation, Inc. |
| 3 | |
| 4 | This program is free software: you can redistribute it and/or modify |
| 5 | it under the terms of the GNU Lesser General Public License as published by |
| 6 | the Free Software Foundation; either version 3 of the License, or |
| 7 | (at your option) any later version. |
| 8 | |
| 9 | This program 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 <http://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 | #undef MIN |
| 29 | |
| 30 | #ifdef USE_LONG_DOUBLE |
| 31 | # define FUNC ceill |
| 32 | # define DOUBLE long double |
| 33 | # define MANT_DIG LDBL_MANT_DIG |
| 34 | # define MIN LDBL_MIN |
| 35 | # define L_(literal) literal##L |
| 36 | #elif ! defined USE_FLOAT |
| 37 | # define FUNC ceil |
| 38 | # define DOUBLE double |
| 39 | # define MANT_DIG DBL_MANT_DIG |
| 40 | # define MIN DBL_MIN |
| 41 | # define L_(literal) literal |
| 42 | #else /* defined USE_FLOAT */ |
| 43 | # define FUNC ceilf |
| 44 | # define DOUBLE float |
| 45 | # define MANT_DIG FLT_MANT_DIG |
| 46 | # define MIN FLT_MIN |
| 47 | # define L_(literal) literal##f |
| 48 | #endif |
| 49 | |
| 50 | /* -0.0. See minus-zero.h. */ |
| 51 | #if defined __hpux || defined __sgi || defined __ICC |
| 52 | # define MINUS_ZERO (-MIN * MIN) |
| 53 | #else |
| 54 | # define MINUS_ZERO L_(-0.0) |
| 55 | #endif |
| 56 | |
| 57 | /* 2^(MANT_DIG-1). */ |
| 58 | static const DOUBLE TWO_MANT_DIG = |
| 59 | /* Assume MANT_DIG <= 5 * 31. |
| 60 | Use the identity |
| 61 | n = floor(n/5) + floor((n+1)/5) + ... + floor((n+4)/5). */ |
| 62 | (DOUBLE) (1U << ((MANT_DIG - 1) / 5)) |
| 63 | * (DOUBLE) (1U << ((MANT_DIG - 1 + 1) / 5)) |
| 64 | * (DOUBLE) (1U << ((MANT_DIG - 1 + 2) / 5)) |
| 65 | * (DOUBLE) (1U << ((MANT_DIG - 1 + 3) / 5)) |
| 66 | * (DOUBLE) (1U << ((MANT_DIG - 1 + 4) / 5)); |
| 67 | |
| 68 | DOUBLE |
| 69 | FUNC (DOUBLE x) |
| 70 | { |
| 71 | /* The use of 'volatile' guarantees that excess precision bits are dropped |
| 72 | at each addition step and before the following comparison at the caller's |
| 73 | site. It is necessary on x86 systems where double-floats are not IEEE |
| 74 | compliant by default, to avoid that the results become platform and compiler |
| 75 | option dependent. 'volatile' is a portable alternative to gcc's |
| 76 | -ffloat-store option. */ |
| 77 | volatile DOUBLE y = x; |
| 78 | volatile DOUBLE z = y; |
| 79 | |
| 80 | if (z > L_(0.0)) |
| 81 | { |
| 82 | /* Avoid rounding errors for values near 2^k, where k >= MANT_DIG-1. */ |
| 83 | if (z < TWO_MANT_DIG) |
| 84 | { |
| 85 | /* Round to the next integer (nearest or up or down, doesn't matter). */ |
| 86 | z += TWO_MANT_DIG; |
| 87 | z -= TWO_MANT_DIG; |
| 88 | /* Enforce rounding up. */ |
| 89 | if (z < y) |
| 90 | z += L_(1.0); |
| 91 | } |
| 92 | } |
| 93 | else if (z < L_(0.0)) |
| 94 | { |
| 95 | /* For -1 < x < 0, return -0.0 regardless of the current rounding |
| 96 | mode. */ |
| 97 | if (z > L_(-1.0)) |
| 98 | z = MINUS_ZERO; |
| 99 | /* Avoid rounding errors for values near -2^k, where k >= MANT_DIG-1. */ |
| 100 | else if (z > - TWO_MANT_DIG) |
| 101 | { |
| 102 | /* Round to the next integer (nearest or up or down, doesn't matter). */ |
| 103 | z -= TWO_MANT_DIG; |
| 104 | z += TWO_MANT_DIG; |
| 105 | /* Enforce rounding up. */ |
| 106 | if (z < y) |
| 107 | z += L_(1.0); |
| 108 | } |
| 109 | } |
| 110 | return z; |
| 111 | } |