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/* 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);
}
}
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