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SummationByParts/src/operators/upwind4.rs

389 lines
13 KiB
Rust
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use super::SbpOperator;
use ndarray::{arr1, arr2, s, ArrayView1, ArrayView2, ArrayViewMut1, ArrayViewMut2};
/// Simdtype used in diffy_simd
type SimdT = packed_simd::f32x8;
pub struct Upwind4 {}
impl Upwind4 {
const HBLOCK: &'static [f32] = &[49.0 / 144.0, 61.0 / 48.0, 41.0 / 48.0, 149.0 / 144.0];
const DIAG: &'static [f32] = &[
-1.0 / 24.0,
1.0 / 4.0,
-7.0 / 8.0,
0.0,
7.0 / 8.0,
-1.0 / 4.0,
1.0 / 24.0,
];
const BLOCK: &'static [[f32; 7]] = &[
[
-72.0 / 49.0_f32,
187.0 / 98.0,
-20.0 / 49.0,
-3.0 / 98.0,
0.0,
0.0,
0.0,
],
[
-187.0 / 366.0,
0.0,
69.0 / 122.0,
-16.0 / 183.0,
2.0 / 61.0,
0.0,
0.0,
],
[
20.0 / 123.0,
-69.0 / 82.0,
0.0,
227.0 / 246.0,
-12.0 / 41.0,
2.0 / 41.0,
0.0,
],
[
3.0 / 298.0,
16.0 / 149.0,
-227.0 / 298.0,
0.0,
126.0 / 149.0,
-36.0 / 149.0,
6.0 / 149.0,
],
];
#[inline(never)]
fn diff_simd(prev: &[f32], fut: &mut [f32]) {
use packed_simd::{f32x8, u32x8};
assert_eq!(prev.len(), fut.len());
assert!(prev.len() >= 2 * Self::BLOCK.len());
let nx = prev.len();
let dx = 1.0 / (nx - 1) as f32;
let idx = 1.0 / dx;
let first_elems = unsafe { f32x8::from_slice_unaligned_unchecked(prev) };
let block = [
f32x8::new(
Self::BLOCK[0][0],
Self::BLOCK[0][1],
Self::BLOCK[0][2],
Self::BLOCK[0][3],
Self::BLOCK[0][4],
Self::BLOCK[0][5],
Self::BLOCK[0][6],
0.0,
),
f32x8::new(
Self::BLOCK[1][0],
Self::BLOCK[1][1],
Self::BLOCK[1][2],
Self::BLOCK[1][3],
Self::BLOCK[1][4],
Self::BLOCK[1][5],
Self::BLOCK[1][6],
0.0,
),
f32x8::new(
Self::BLOCK[2][0],
Self::BLOCK[2][1],
Self::BLOCK[2][2],
Self::BLOCK[2][3],
Self::BLOCK[2][4],
Self::BLOCK[2][5],
Self::BLOCK[2][6],
0.0,
),
f32x8::new(
Self::BLOCK[3][0],
Self::BLOCK[3][1],
Self::BLOCK[3][2],
Self::BLOCK[3][3],
Self::BLOCK[3][4],
Self::BLOCK[3][5],
Self::BLOCK[3][6],
0.0,
),
];
unsafe {
*fut.get_unchecked_mut(0) = idx * (block[0] * first_elems).sum();
*fut.get_unchecked_mut(1) = idx * (block[1] * first_elems).sum();
*fut.get_unchecked_mut(2) = idx * (block[2] * first_elems).sum();
*fut.get_unchecked_mut(3) = idx * (block[3] * first_elems).sum()
};
let diag = f32x8::new(
Self::DIAG[0],
Self::DIAG[1],
Self::DIAG[2],
Self::DIAG[3],
Self::DIAG[4],
Self::DIAG[5],
Self::DIAG[6],
0.0,
);
for (f, p) in fut
.iter_mut()
.skip(block.len())
.zip(
prev.windows(f32x8::lanes())
.map(f32x8::from_slice_unaligned)
.skip(1),
)
.take(nx - 2 * block.len())
{
*f = idx * (p * diag).sum();
}
let last_elems = unsafe { f32x8::from_slice_unaligned_unchecked(&prev[nx - 8..]) }
.shuffle1_dyn(u32x8::new(7, 6, 5, 4, 3, 2, 1, 0));
unsafe {
*fut.get_unchecked_mut(nx - 4) = -idx * (block[3] * last_elems).sum();
*fut.get_unchecked_mut(nx - 3) = -idx * (block[2] * last_elems).sum();
*fut.get_unchecked_mut(nx - 2) = -idx * (block[1] * last_elems).sum();
*fut.get_unchecked_mut(nx - 1) = -idx * (block[0] * last_elems).sum();
}
}
#[inline(never)]
fn diffy_simd(prev: &[f32], fut: &mut [f32], nx: usize, ny: usize) {
assert!(ny >= 2 * Self::BLOCK.len());
assert!(nx >= SimdT::lanes());
assert!(nx % SimdT::lanes() == 0);
assert_eq!(prev.len(), fut.len());
assert_eq!(prev.len(), nx * ny);
let dy = 1.0 / (ny - 1) as f32;
let idy = 1.0 / dy;
for j in (0..nx).step_by(SimdT::lanes()) {
let a = [
SimdT::from_slice_unaligned(&prev[0 * nx + j..]),
SimdT::from_slice_unaligned(&prev[1 * nx + j..]),
SimdT::from_slice_unaligned(&prev[2 * nx + j..]),
SimdT::from_slice_unaligned(&prev[3 * nx + j..]),
SimdT::from_slice_unaligned(&prev[4 * nx + j..]),
SimdT::from_slice_unaligned(&prev[5 * nx + j..]),
SimdT::from_slice_unaligned(&prev[6 * nx + j..]),
];
for (i, bl) in Self::BLOCK.iter().enumerate() {
let b = idy
* (a[0] * bl[0]
+ a[1] * bl[1]
+ a[2] * bl[2]
+ a[3] * bl[3]
+ a[4] * bl[4]
+ a[5] * bl[5]
+ a[6] * bl[6]);
b.write_to_slice_unaligned(&mut fut[i * nx + j..]);
}
let mut a = a;
for i in Self::BLOCK.len()..ny - Self::BLOCK.len() {
// Push a onto circular buffer
a = [
a[1],
a[2],
a[3],
a[4],
a[5],
a[6],
SimdT::from_slice_unaligned(&prev[nx * (i + 3) + j..]),
];
let b = idy
* (a[0] * Self::DIAG[0]
+ a[1] * Self::DIAG[1]
+ a[2] * Self::DIAG[2]
+ a[3] * Self::DIAG[3]
+ a[4] * Self::DIAG[4]
+ a[5] * Self::DIAG[5]
+ a[6] * Self::DIAG[6]);
b.write_to_slice_unaligned(&mut fut[nx * i + j..]);
}
let a = [
SimdT::from_slice_unaligned(&prev[(ny - 1) * nx + j..]),
SimdT::from_slice_unaligned(&prev[(ny - 2) * nx + j..]),
SimdT::from_slice_unaligned(&prev[(ny - 3) * nx + j..]),
SimdT::from_slice_unaligned(&prev[(ny - 4) * nx + j..]),
SimdT::from_slice_unaligned(&prev[(ny - 5) * nx + j..]),
SimdT::from_slice_unaligned(&prev[(ny - 6) * nx + j..]),
SimdT::from_slice_unaligned(&prev[(ny - 7) * nx + j..]),
];
for (i, bl) in Self::BLOCK.iter().enumerate() {
let b = -idy
* (a[0] * bl[0]
+ a[1] * bl[1]
+ a[2] * bl[2]
+ a[3] * bl[3]
+ a[4] * bl[4]
+ a[5] * bl[5]
+ a[6] * bl[6]);
b.write_to_slice_unaligned(&mut fut[(ny - 1 - i) * nx + j..]);
}
}
}
fn diff(prev: ArrayView1<f32>, mut fut: ArrayViewMut1<f32>) {
assert_eq!(prev.shape(), fut.shape());
let nx = prev.shape()[0];
assert!(nx >= 2 * Self::BLOCK.len());
if let (Some(p), Some(f)) = (prev.as_slice(), fut.as_slice_mut()) {
Self::diff_simd(p, f);
return;
}
let dx = 1.0 / (nx - 1) as f32;
let idx = 1.0 / dx;
let diag = arr1(Self::DIAG);
let block = arr2(Self::BLOCK);
let first_elems = prev.slice(s!(..7));
for (bl, f) in block.outer_iter().zip(&mut fut) {
let diff = first_elems.dot(&bl);
*f = diff * idx;
}
for (window, f) in prev
.windows(diag.len())
.into_iter()
.skip(1)
.zip(fut.iter_mut().skip(4))
.take(nx - 8)
{
let diff = diag.dot(&window);
*f = diff * idx;
}
let last_elems = prev.slice(s!(nx - 7..;-1));
for (bl, f) in block.outer_iter().zip(&mut fut.slice_mut(s![nx - 4..;-1])) {
let diff = -bl.dot(&last_elems);
*f = diff * idx;
}
}
}
impl SbpOperator for Upwind4 {
fn diffx(prev: ArrayView2<f32>, mut fut: ArrayViewMut2<f32>) {
assert_eq!(prev.shape(), fut.shape());
assert!(prev.shape()[1] >= 2 * Self::BLOCK.len());
for (r0, r1) in prev.outer_iter().zip(fut.outer_iter_mut()) {
Self::diff(r0, r1)
}
}
fn diffy(prev: ArrayView2<f32>, mut fut: ArrayViewMut2<f32>) {
assert_eq!(prev.shape(), fut.shape());
assert!(prev.shape()[0] >= 2 * Self::BLOCK.len());
let nx = prev.shape()[1];
let ny = prev.shape()[0];
if nx >= SimdT::lanes() && nx % SimdT::lanes() == 0 {
if let (Some(p), Some(f)) = (prev.as_slice(), fut.as_slice_mut()) {
Self::diffy_simd(p, f, nx, ny);
return;
}
}
// diffy = transpose then use diffx
Self::diffx(prev.reversed_axes(), fut.reversed_axes());
}
fn h() -> &'static [f32] {
Self::HBLOCK
}
}
#[test]
fn upwind4_test() {
use ndarray::prelude::*;
let nx = 20;
let dx = 1.0 / (nx - 1) as f32;
let mut source: ndarray::Array1<f32> = ndarray::Array1::zeros(nx);
let mut res = ndarray::Array1::zeros(nx);
let mut target = ndarray::Array1::zeros(nx);
for i in 0..nx {
source[i] = i as f32 * dx;
target[i] = 1.0;
}
res.fill(0.0);
Upwind4::diff(source.view(), res.view_mut());
approx::assert_abs_diff_eq!(&res, &target, epsilon = 1e-4);
{
let source = source.to_owned().insert_axis(ndarray::Axis(0));
let mut res = res.to_owned().insert_axis(ndarray::Axis(0));
let target = target.to_owned().insert_axis(ndarray::Axis(0));
res.fill(0.0);
Upwind4::diffx(source.view(), res.view_mut());
approx::assert_abs_diff_eq!(&res, &target, epsilon = 1e-2);
}
{
let source = Array2::from_shape_fn((nx, 8), |(i, _)| source[i]);
let target = Array2::from_shape_fn((nx, 8), |(i, _)| target[i]);
let mut res = Array2::zeros((nx, 8));
res.fill(0.0);
Upwind4::diffy(source.view(), res.view_mut());
approx::assert_abs_diff_eq!(&res.to_owned(), &target.to_owned(), epsilon = 1e-2);
}
for i in 0..nx {
let x = i as f32 * dx;
source[i] = x * x;
target[i] = 2.0 * x;
}
res.fill(0.0);
Upwind4::diff(source.view(), res.view_mut());
approx::assert_abs_diff_eq!(&res, &target, epsilon = 1e-4);
{
let source = source.to_owned().insert_axis(ndarray::Axis(0));
let mut res = res.to_owned().insert_axis(ndarray::Axis(0));
let target = target.to_owned().insert_axis(ndarray::Axis(0));
res.fill(0.0);
Upwind4::diffx(source.view(), res.view_mut());
approx::assert_abs_diff_eq!(&res, &target, epsilon = 1e-2);
}
{
let source = Array2::from_shape_fn((nx, 8), |(i, _)| source[i]);
let target = Array2::from_shape_fn((nx, 8), |(i, _)| target[i]);
let mut res = Array2::zeros((nx, 8));
res.fill(0.0);
Upwind4::diffy(source.view(), res.view_mut());
approx::assert_abs_diff_eq!(&res.to_owned(), &target.to_owned(), epsilon = 1e-2);
}
for i in 0..nx {
let x = i as f32 * dx;
source[i] = x * x * x;
target[i] = 3.0 * x * x;
}
res.fill(0.0);
Upwind4::diff(source.view(), res.view_mut());
approx::assert_abs_diff_eq!(&res, &target, epsilon = 1e-2);
{
let source = source.to_owned().insert_axis(ndarray::Axis(0));
let mut res = res.to_owned().insert_axis(ndarray::Axis(0));
let target = target.to_owned().insert_axis(ndarray::Axis(0));
res.fill(0.0);
Upwind4::diffx(source.view(), res.view_mut());
approx::assert_abs_diff_eq!(&res, &target, epsilon = 1e-2);
}
{
let source = Array2::from_shape_fn((nx, 8), |(i, _)| source[i]);
let target = Array2::from_shape_fn((nx, 8), |(i, _)| target[i]);
let mut res = Array2::zeros((nx, 8));
res.fill(0.0);
Upwind4::diffy(source.view(), res.view_mut());
approx::assert_abs_diff_eq!(&res.to_owned(), &target.to_owned(), epsilon = 1e-2);
}
}
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