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//! Implements portable horizontal float vector arithmetic reductions.
macro_rules! impl_reduction_float_arithmetic {
([$elem_ty:ident; $elem_count:expr]: $id:ident | $test_tt:tt) => {
impl $id {
/// Horizontal sum of the vector elements.
///
/// The intrinsic performs a tree-reduction of the vector elements.
/// That is, for an 8 element vector:
///
/// > ((x0 + x1) + (x2 + x3)) + ((x4 + x5) + (x6 + x7))
///
/// If one of the vector element is `NaN` the reduction returns
/// `NaN`. The resulting `NaN` is not required to be equal to any
/// of the `NaN`s in the vector.
#[inline]
pub fn sum(self) -> $elem_ty {
#[cfg(not(target_arch = "aarch64"))]
{
use crate::llvm::simd_reduce_add_ordered;
unsafe { simd_reduce_add_ordered(self.0, 0 as $elem_ty) }
}
#[cfg(target_arch = "aarch64")]
{
// FIXME: broken on AArch64
// https://github.com/rust-lang-nursery/packed_simd/issues/15
let mut x = self.extract(0) as $elem_ty;
for i in 1..$id::lanes() {
x += self.extract(i) as $elem_ty;
}
x
}
}
/// Horizontal product of the vector elements.
///
/// The intrinsic performs a tree-reduction of the vector elements.
/// That is, for an 8 element vector:
///
/// > ((x0 * x1) * (x2 * x3)) * ((x4 * x5) * (x6 * x7))
///
/// If one of the vector element is `NaN` the reduction returns
/// `NaN`. The resulting `NaN` is not required to be equal to any
/// of the `NaN`s in the vector.
#[inline]
pub fn product(self) -> $elem_ty {
#[cfg(not(target_arch = "aarch64"))]
{
use crate::llvm::simd_reduce_mul_ordered;
unsafe { simd_reduce_mul_ordered(self.0, 1 as $elem_ty) }
}
#[cfg(target_arch = "aarch64")]
{
// FIXME: broken on AArch64
// https://github.com/rust-lang-nursery/packed_simd/issues/15
let mut x = self.extract(0) as $elem_ty;
for i in 1..$id::lanes() {
x *= self.extract(i) as $elem_ty;
}
x
}
}
}
impl crate::iter::Sum for $id {
#[inline]
fn sum<I: Iterator<Item = $id>>(iter: I) -> $id {
iter.fold($id::splat(0.), crate::ops::Add::add)
}
}
impl crate::iter::Product for $id {
#[inline]
fn product<I: Iterator<Item = $id>>(iter: I) -> $id {
iter.fold($id::splat(1.), crate::ops::Mul::mul)
}
}
impl<'a> crate::iter::Sum<&'a $id> for $id {
#[inline]
fn sum<I: Iterator<Item = &'a $id>>(iter: I) -> $id {
iter.fold($id::splat(0.), |a, b| crate::ops::Add::add(a, *b))
}
}
impl<'a> crate::iter::Product<&'a $id> for $id {
#[inline]
fn product<I: Iterator<Item = &'a $id>>(iter: I) -> $id {
iter.fold($id::splat(1.), |a, b| crate::ops::Mul::mul(a, *b))
}
}
test_if! {
$test_tt:
paste::item! {
// Comparisons use integer casts within mantissa^1 range.
#[allow(clippy::float_cmp)]
pub mod [<$id _reduction_float_arith>] {
use super::*;
fn alternating(x: usize) -> $id {
let mut v = $id::splat(1 as $elem_ty);
for i in 0..$id::lanes() {
if i % x == 0 {
v = v.replace(i, 2 as $elem_ty);
}
}
v
}
#[cfg_attr(not(target_arch = "wasm32"), test)]
#[cfg_attr(target_arch = "wasm32", wasm_bindgen_test)]
fn sum() {
let v = $id::splat(0 as $elem_ty);
assert_eq!(v.sum(), 0 as $elem_ty);
let v = $id::splat(1 as $elem_ty);
assert_eq!(v.sum(), $id::lanes() as $elem_ty);
let v = alternating(2);
assert_eq!(
v.sum(),
($id::lanes() / 2 + $id::lanes()) as $elem_ty
);
}
#[cfg_attr(not(target_arch = "wasm32"), test)]
#[cfg_attr(target_arch = "wasm32", wasm_bindgen_test)]
fn product() {
let v = $id::splat(0 as $elem_ty);
assert_eq!(v.product(), 0 as $elem_ty);
let v = $id::splat(1 as $elem_ty);
assert_eq!(v.product(), 1 as $elem_ty);
let f = match $id::lanes() {
64 => 16,
32 => 8,
16 => 4,
_ => 2,
};
let v = alternating(f);
assert_eq!(
v.product(),
(2_usize.pow(($id::lanes() / f) as u32)
as $elem_ty)
);
}
#[cfg_attr(not(target_arch = "wasm32"), test)]
#[cfg_attr(target_arch = "wasm32", wasm_bindgen_test)]
#[allow(unreachable_code)]
fn sum_nan() {
// FIXME: https://bugs.llvm.org/show_bug.cgi?id=36732
// https://github.com/rust-lang-nursery/packed_simd/issues/6
return;
let n0 = crate::$elem_ty::NAN;
let v0 = $id::splat(-3.0);
for i in 0..$id::lanes() {
let mut v = v0.replace(i, n0);
// If the vector contains a NaN the result is NaN:
assert!(
v.sum().is_nan(),
"nan at {} => {} | {:?}",
i,
v.sum(),
v
);
for j in 0..i {
v = v.replace(j, n0);
assert!(v.sum().is_nan());
}
}
let v = $id::splat(n0);
assert!(v.sum().is_nan(), "all nans | {:?}", v);
}
#[cfg_attr(not(target_arch = "wasm32"), test)]
#[cfg_attr(target_arch = "wasm32", wasm_bindgen_test)]
#[allow(unreachable_code)]
fn product_nan() {
// FIXME: https://bugs.llvm.org/show_bug.cgi?id=36732
// https://github.com/rust-lang-nursery/packed_simd/issues/6
return;
let n0 = crate::$elem_ty::NAN;
let v0 = $id::splat(-3.0);
for i in 0..$id::lanes() {
let mut v = v0.replace(i, n0);
// If the vector contains a NaN the result is NaN:
assert!(
v.product().is_nan(),
"nan at {} => {} | {:?}",
i,
v.product(),
v
);
for j in 0..i {
v = v.replace(j, n0);
assert!(v.product().is_nan());
}
}
let v = $id::splat(n0);
assert!(v.product().is_nan(), "all nans | {:?}", v);
}
#[cfg_attr(not(target_arch = "wasm32"), test)]
#[cfg_attr(target_arch = "wasm32", wasm_bindgen_test)]
#[allow(unused, dead_code)]
fn sum_roundoff() {
// Performs a tree-reduction
fn tree_reduce_sum(a: &[$elem_ty]) -> $elem_ty {
assert!(!a.is_empty());
if a.len() == 1 {
a[0]
} else if a.len() == 2 {
a[0] + a[1]
} else {
let mid = a.len() / 2;
let (left, right) = a.split_at(mid);
tree_reduce_sum(left) + tree_reduce_sum(right)
}
}
let mut start = crate::$elem_ty::EPSILON;
let mut scalar_reduction = 0. as $elem_ty;
let mut v = $id::splat(0. as $elem_ty);
for i in 0..$id::lanes() {
let c = if i % 2 == 0 { 1e3 } else { -1. };
start *= ::core::$elem_ty::consts::PI * c;
scalar_reduction += start;
v = v.replace(i, start);
}
let simd_reduction = v.sum();
let mut a = [0. as $elem_ty; $id::lanes()];
v.write_to_slice_unaligned(&mut a);
let tree_reduction = tree_reduce_sum(&a);
// tolerate 1 ULP difference:
let red_bits = simd_reduction.to_bits();
let tree_bits = tree_reduction.to_bits();
assert!(
if red_bits > tree_bits {
red_bits - tree_bits
} else {
tree_bits - red_bits
} < 2,
"vector: {:?} | simd_reduction: {:?} | \
tree_reduction: {} | scalar_reduction: {}",
v,
simd_reduction,
tree_reduction,
scalar_reduction
);
}
#[cfg_attr(not(target_arch = "wasm32"), test)]
#[cfg_attr(target_arch = "wasm32", wasm_bindgen_test)]
#[allow(unused, dead_code)]
fn product_roundoff() {
use ::core::convert::TryInto;
// Performs a tree-reduction
fn tree_reduce_product(a: &[$elem_ty]) -> $elem_ty {
assert!(!a.is_empty());
if a.len() == 1 {
a[0]
} else if a.len() == 2 {
a[0] * a[1]
} else {
let mid = a.len() / 2;
let (left, right) = a.split_at(mid);
tree_reduce_product(left)
* tree_reduce_product(right)
}
}
let mut start = crate::$elem_ty::EPSILON;
let mut scalar_reduction = 1. as $elem_ty;
let mut v = $id::splat(0. as $elem_ty);
for i in 0..$id::lanes() {
let c = if i % 2 == 0 { 1e3 } else { -1. };
start *= ::core::$elem_ty::consts::PI * c;
scalar_reduction *= start;
v = v.replace(i, start);
}
let simd_reduction = v.product();
let mut a = [0. as $elem_ty; $id::lanes()];
v.write_to_slice_unaligned(&mut a);
let tree_reduction = tree_reduce_product(&a);
// FIXME: Too imprecise, even only for product(f32x8).
// Figure out how to narrow this down.
let ulp_limit = $id::lanes() / 2;
let red_bits = simd_reduction.to_bits();
let tree_bits = tree_reduction.to_bits();
assert!(
if red_bits > tree_bits {
red_bits - tree_bits
} else {
tree_bits - red_bits
} < ulp_limit.try_into().unwrap(),
"vector: {:?} | simd_reduction: {:?} | \
tree_reduction: {} | scalar_reduction: {}",
v,
simd_reduction,
tree_reduction,
scalar_reduction
);
}
}
}
}
};
}