| /* origin: FreeBSD /usr/src/lib/msun/src/s_fmaf.c */ |
| /*- |
| * Copyright (c) 2005-2011 David Schultz <das@FreeBSD.ORG> |
| * All rights reserved. |
| * |
| * Redistribution and use in source and binary forms, with or without |
| * modification, are permitted provided that the following conditions |
| * are met: |
| * 1. Redistributions of source code must retain the above copyright |
| * notice, this list of conditions and the following disclaimer. |
| * 2. Redistributions in binary form must reproduce the above copyright |
| * notice, this list of conditions and the following disclaimer in the |
| * documentation and/or other materials provided with the distribution. |
| * |
| * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND |
| * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
| * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE |
| * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE |
| * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL |
| * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS |
| * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) |
| * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT |
| * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY |
| * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF |
| * SUCH DAMAGE. |
| */ |
| |
| use core::f32; |
| use core::ptr::read_volatile; |
| |
| use super::fenv::{ |
| feclearexcept, fegetround, feraiseexcept, fetestexcept, FE_INEXACT, FE_TONEAREST, FE_UNDERFLOW, |
| }; |
| |
| /* |
| * Fused multiply-add: Compute x * y + z with a single rounding error. |
| * |
| * A double has more than twice as much precision than a float, so |
| * direct double-precision arithmetic suffices, except where double |
| * rounding occurs. |
| */ |
| |
| /// Floating multiply add (f32) |
| /// |
| /// Computes `(x*y)+z`, rounded as one ternary operation: |
| /// Computes the value (as if) to infinite precision and rounds once to the result format, |
| /// according to the rounding mode characterized by the value of FLT_ROUNDS. |
| #[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)] |
| pub fn fmaf(x: f32, y: f32, mut z: f32) -> f32 { |
| let xy: f64; |
| let mut result: f64; |
| let mut ui: u64; |
| let e: i32; |
| |
| xy = x as f64 * y as f64; |
| result = xy + z as f64; |
| ui = result.to_bits(); |
| e = (ui >> 52) as i32 & 0x7ff; |
| /* Common case: The double precision result is fine. */ |
| if ( |
| /* not a halfway case */ |
| ui & 0x1fffffff) != 0x10000000 || |
| /* NaN */ |
| e == 0x7ff || |
| /* exact */ |
| (result - xy == z as f64 && result - z as f64 == xy) || |
| /* not round-to-nearest */ |
| fegetround() != FE_TONEAREST |
| { |
| /* |
| underflow may not be raised correctly, example: |
| fmaf(0x1p-120f, 0x1p-120f, 0x1p-149f) |
| */ |
| if e < 0x3ff - 126 && e >= 0x3ff - 149 && fetestexcept(FE_INEXACT) != 0 { |
| feclearexcept(FE_INEXACT); |
| // prevent `xy + vz` from being CSE'd with `xy + z` above |
| let vz: f32 = unsafe { read_volatile(&z) }; |
| result = xy + vz as f64; |
| if fetestexcept(FE_INEXACT) != 0 { |
| feraiseexcept(FE_UNDERFLOW); |
| } else { |
| feraiseexcept(FE_INEXACT); |
| } |
| } |
| z = result as f32; |
| return z; |
| } |
| |
| /* |
| * If result is inexact, and exactly halfway between two float values, |
| * we need to adjust the low-order bit in the direction of the error. |
| */ |
| let neg = ui >> 63 != 0; |
| let err = if neg == (z as f64 > xy) { |
| xy - result + z as f64 |
| } else { |
| z as f64 - result + xy |
| }; |
| if neg == (err < 0.0) { |
| ui += 1; |
| } else { |
| ui -= 1; |
| } |
| f64::from_bits(ui) as f32 |
| } |
| |
| #[cfg(test)] |
| mod tests { |
| #[test] |
| fn issue_263() { |
| let a = f32::from_bits(1266679807); |
| let b = f32::from_bits(1300234242); |
| let c = f32::from_bits(1115553792); |
| let expected = f32::from_bits(1501560833); |
| assert_eq!(super::fmaf(a, b, c), expected); |
| } |
| } |
