| /* Round towards positive infinity. |
| Copyright (C) 2007, 2010-2020 Free Software Foundation, Inc. |
| |
| This program is free software: you can redistribute it and/or modify |
| it under the terms of the GNU General Public License as published by |
| the Free Software Foundation; either version 3 of the License, or |
| (at your option) any later version. |
| |
| This program is distributed in the hope that it will be useful, |
| but WITHOUT ANY WARRANTY; without even the implied warranty of |
| MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
| GNU General Public License for more details. |
| |
| You should have received a copy of the GNU General Public License |
| along with this program. If not, see <https://www.gnu.org/licenses/>. */ |
| |
| /* Written by Bruno Haible <bruno@clisp.org>, 2007. */ |
| |
| #if ! defined USE_LONG_DOUBLE |
| # include <config.h> |
| #endif |
| |
| /* Specification. */ |
| #include <math.h> |
| |
| #include <float.h> |
| |
| #undef MIN |
| |
| #ifdef USE_LONG_DOUBLE |
| # define FUNC ceill |
| # define DOUBLE long double |
| # define MANT_DIG LDBL_MANT_DIG |
| # define MIN LDBL_MIN |
| # define L_(literal) literal##L |
| #elif ! defined USE_FLOAT |
| # define FUNC ceil |
| # define DOUBLE double |
| # define MANT_DIG DBL_MANT_DIG |
| # define MIN DBL_MIN |
| # define L_(literal) literal |
| #else /* defined USE_FLOAT */ |
| # define FUNC ceilf |
| # define DOUBLE float |
| # define MANT_DIG FLT_MANT_DIG |
| # define MIN FLT_MIN |
| # define L_(literal) literal##f |
| #endif |
| |
| /* -0.0. See minus-zero.h. */ |
| #if defined __hpux || defined __sgi || defined __ICC |
| # define MINUS_ZERO (-MIN * MIN) |
| #else |
| # define MINUS_ZERO L_(-0.0) |
| #endif |
| |
| /* MSVC with option -fp:strict refuses to compile constant initializers that |
| contain floating-point operations. Pacify this compiler. */ |
| #ifdef _MSC_VER |
| # pragma fenv_access (off) |
| #endif |
| |
| /* 2^(MANT_DIG-1). */ |
| static const DOUBLE TWO_MANT_DIG = |
| /* Assume MANT_DIG <= 5 * 31. |
| Use the identity |
| n = floor(n/5) + floor((n+1)/5) + ... + floor((n+4)/5). */ |
| (DOUBLE) (1U << ((MANT_DIG - 1) / 5)) |
| * (DOUBLE) (1U << ((MANT_DIG - 1 + 1) / 5)) |
| * (DOUBLE) (1U << ((MANT_DIG - 1 + 2) / 5)) |
| * (DOUBLE) (1U << ((MANT_DIG - 1 + 3) / 5)) |
| * (DOUBLE) (1U << ((MANT_DIG - 1 + 4) / 5)); |
| |
| DOUBLE |
| FUNC (DOUBLE x) |
| { |
| /* The use of 'volatile' guarantees that excess precision bits are dropped |
| at each addition step and before the following comparison at the caller's |
| site. It is necessary on x86 systems where double-floats are not IEEE |
| compliant by default, to avoid that the results become platform and compiler |
| option dependent. 'volatile' is a portable alternative to gcc's |
| -ffloat-store option. */ |
| volatile DOUBLE y = x; |
| volatile DOUBLE z = y; |
| |
| if (z > L_(0.0)) |
| { |
| /* Avoid rounding errors for values near 2^k, where k >= MANT_DIG-1. */ |
| if (z < TWO_MANT_DIG) |
| { |
| /* Round to the next integer (nearest or up or down, doesn't matter). */ |
| z += TWO_MANT_DIG; |
| z -= TWO_MANT_DIG; |
| /* Enforce rounding up. */ |
| if (z < y) |
| z += L_(1.0); |
| } |
| } |
| else if (z < L_(0.0)) |
| { |
| /* For -1 < x < 0, return -0.0 regardless of the current rounding |
| mode. */ |
| if (z > L_(-1.0)) |
| z = MINUS_ZERO; |
| /* Avoid rounding errors for values near -2^k, where k >= MANT_DIG-1. */ |
| else if (z > - TWO_MANT_DIG) |
| { |
| /* Round to the next integer (nearest or up or down, doesn't matter). */ |
| z -= TWO_MANT_DIG; |
| z += TWO_MANT_DIG; |
| /* Enforce rounding up. */ |
| if (z < y) |
| z += L_(1.0); |
| } |
| } |
| return z; |
| } |