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gather simd into diffxi

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Magnus Ulimoen
2019-12-14 00:29:54 +01:00
parent dd3e7cfb31
commit 0106ba5fbd
2 changed files with 264 additions and 271 deletions
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54
src/operators.rs
View File

@@ -11,5 +11,59 @@ pub trait UpwindOperator: SbpOperator {
fn disseta(prev: ArrayView2<f32>, fut: ArrayViewMut2<f32>);
}
#[macro_export]
macro_rules! diff_op_1d {
($self: ty, $name: ident, $BLOCK: expr, $DIAG: expr, $symmetric: expr) => {
impl $self {
fn $name(prev: ArrayView1<f32>, mut fut: ArrayViewMut1<f32>) {
assert_eq!(prev.shape(), fut.shape());
let nx = prev.shape()[0];
assert!(nx >= 2 * $BLOCK.len());
let dx = 1.0 / (nx - 1) as f32;
let idx = 1.0 / dx;
let block = ::ndarray::arr2($BLOCK);
let diag = ::ndarray::arr1($DIAG);
let first_elems = prev.slice(::ndarray::s!(..block.len_of(::ndarray::Axis(1))));
for (bl, f) in block.outer_iter().zip(&mut fut) {
let diff = first_elems.dot(&bl);
*f = diff * idx;
}
// The window needs to be aligned to the diagonal elements,
// based on the block size
let window_elems_to_skip =
block.len_of(::ndarray::Axis(0)) - ((diag.len() - 1) / 2);
for (window, f) in prev
.windows(diag.len())
.into_iter()
.skip(window_elems_to_skip)
.zip(fut.iter_mut().skip(block.len_of(::ndarray::Axis(0))))
.take(nx - 2 * block.len_of(::ndarray::Axis(0)))
{
let diff = diag.dot(&window);
*f = diff * idx;
}
let last_elems = prev.slice(::ndarray::s!(nx - block.len_of(::ndarray::Axis(1))..;-1));
for (bl, f) in block.outer_iter()
.zip(&mut fut.slice_mut(s![nx - block.len_of(::ndarray::Axis(0))..;-1]))
{
let diff = if $symmetric {
bl.dot(&last_elems)
} else {
-bl.dot(&last_elems)
};
*f = diff * idx;
}
}
}
};
}
mod upwind4;
pub use upwind4::Upwind4;

481
src/operators/upwind4.rs
View File

@@ -1,11 +1,21 @@
use super::{SbpOperator, UpwindOperator};
use ndarray::{arr1, arr2, s, ArrayView1, ArrayView2, ArrayViewMut1, ArrayViewMut2};
/// Simdtype used in diffeta_simd
type SimdT = packed_simd::f32x8;
use crate::diff_op_1d;
use ndarray::{s, ArrayView1, ArrayView2, ArrayViewMut1, ArrayViewMut2, Axis};
pub struct Upwind4 {}
/// Simdtype used in diff_simd_col
type SimdT = packed_simd::f32x8;
diff_op_1d!(Upwind4, diff_1d, Upwind4::BLOCK, Upwind4::DIAG, false);
diff_op_1d!(
Upwind4,
diss_1d,
Upwind4::DISS_BLOCK,
Upwind4::DISS_DIAG,
true
);
impl Upwind4 {
#[rustfmt::skip]
const HBLOCK: &'static [f32] = &[
@@ -23,171 +33,141 @@ impl Upwind4 {
[ 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],
];
const DISS_BLOCK: [[f32; 7]; 4] = [
[
-3.0 / 49.0,
9.0 / 49.0,
-9.0 / 49.0,
3.0 / 49.0,
0.0,
0.0,
0.0,
],
[
3.0 / 61.0,
-11.0 / 61.0,
15.0 / 61.0,
-9.0 / 61.0,
2.0 / 61.0,
0.0,
0.0,
],
[
-3.0 / 41.0,
15.0 / 41.0,
-29.0 / 41.0,
27.0 / 41.0,
-12.0 / 41.0,
2.0 / 41.0,
0.0,
],
[
3.0 / 149.0,
-27.0 / 149.0,
81.0 / 149.0,
-117.0 / 149.0,
90.0 / 149.0,
-36.0 / 149.0,
6.0 / 149.0,
],
#[rustfmt::skip]
const DISS_BLOCK: &'static [[f32; 7]; 4] = &[
[-3.0 / 49.0, 9.0 / 49.0, -9.0 / 49.0, 3.0 / 49.0, 0.0, 0.0, 0.0],
[ 3.0 / 61.0, -11.0 / 61.0, 15.0 / 61.0, -9.0 / 61.0, 2.0 / 61.0, 0.0, 0.0],
[-3.0 / 41.0, 15.0 / 41.0, -29.0 / 41.0, 27.0 / 41.0, -12.0 / 41.0, 2.0 / 41.0, 0.0],
[3.0 / 149.0, -27.0 / 149.0, 81.0 / 149.0, -117.0 / 149.0, 90.0 / 149.0, -36.0 / 149.0, 6.0 / 149.0],
];
const DISS_DIAG: [f32; 7] = [
1.0 / 24.0,
-1.0 / 4.0,
5.0 / 8.0,
-5.0 / 6.0,
5.0 / 8.0,
-1.0 / 4.0,
1.0 / 24.0,
#[rustfmt::skip]
const DISS_DIAG: &'static [f32; 7] = &[
1.0 / 24.0, -1.0 / 4.0, 5.0 / 8.0, -5.0 / 6.0, 5.0 / 8.0, -1.0 / 4.0, 1.0 / 24.0
];
#[inline(never)]
fn diff_simd(prev: &[f32], fut: &mut [f32]) {
fn diff_simd_row(prev: ArrayView2<f32>, mut fut: ArrayViewMut2<f32>) {
use packed_simd::{f32x8, u32x8};
assert_eq!(prev.len(), fut.len());
assert!(prev.len() >= 2 * Self::BLOCK.len());
let nx = prev.len();
assert_eq!(prev.shape(), fut.shape());
assert!(prev.len_of(Axis(1)) >= 2 * Self::BLOCK.len());
assert!(prev.len() >= f32x8::lanes());
// The prev array must have contigous last dimension
assert_eq!(prev.strides()[1], 1);
let nx = prev.len_of(Axis(1));
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()
};
for j in 0..prev.len_of(Axis(0)) {
//use std::slice;
//let prev = unsafe { slice::from_raw_parts(prev.slice(s![j, ..]).as_ptr(), nx) };
let prev = prev.slice(s![j, ..]);
let prev = prev.as_slice_memory_order().unwrap();
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 first_elems = unsafe { f32x8::from_slice_unaligned_unchecked(prev) };
let block = {
let bl = Self::BLOCK;
[
f32x8::new(
bl[0][0], bl[0][1], bl[0][2], bl[0][3], bl[0][4], bl[0][5], bl[0][6], 0.0,
),
f32x8::new(
bl[1][0], bl[1][1], bl[1][2], bl[1][3], bl[1][4], bl[1][5], bl[1][6], 0.0,
),
f32x8::new(
bl[2][0], bl[2][1], bl[2][2], bl[2][3], bl[2][4], bl[2][5], bl[2][6], 0.0,
),
f32x8::new(
bl[3][0], bl[3][1], bl[3][2], bl[3][3], bl[3][4], bl[3][5], bl[3][6], 0.0,
),
]
};
fut[(j, 0)] = idx * (block[0] * first_elems).sum();
fut[(j, 1)] = idx * (block[1] * first_elems).sum();
fut[(j, 2)] = idx * (block[2] * first_elems).sum();
fut[(j, 3)] = idx * (block[3] * first_elems).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();
let diag = {
let diag = Self::DIAG;
f32x8::new(
diag[0], diag[1], diag[2], diag[3], diag[4], diag[5], diag[6], 0.0,
)
};
for (f, p) in fut
.slice_mut(s![j, ..])
.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));
fut[(j, nx - 4)] = -idx * (block[3] * last_elems).sum();
fut[(j, nx - 3)] = -idx * (block[2] * last_elems).sum();
fut[(j, nx - 2)] = -idx * (block[1] * last_elems).sum();
fut[(j, nx - 1)] = -idx * (block[0] * last_elems).sum();
}
}
#[inline(never)]
fn diffeta_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);
fn diff_simd_col(prev: ArrayView2<f32>, mut fut: ArrayViewMut2<f32>) {
use std::slice;
assert_eq!(prev.shape(), fut.shape());
assert_eq!(prev.stride_of(Axis(0)), 1);
assert_eq!(prev.stride_of(Axis(0)), 1);
let ny = prev.len_of(Axis(0));
let nx = prev.len_of(Axis(1));
assert!(nx >= 2 * Self::BLOCK.len());
assert!(ny >= SimdT::lanes());
assert!(ny % SimdT::lanes() == 0);
let dy = 1.0 / (ny - 1) as f32;
let idy = 1.0 / dy;
let dx = 1.0 / (nx - 1) as f32;
let idx = 1.0 / dx;
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 j in (0..ny).step_by(SimdT::lanes()) {
let a = unsafe {
[
SimdT::from_slice_unaligned(slice::from_raw_parts(
prev.slice(s![j.., 0]).as_ptr(),
SimdT::lanes(),
)),
SimdT::from_slice_unaligned(slice::from_raw_parts(
prev.slice(s![j.., 1]).as_ptr(),
SimdT::lanes(),
)),
SimdT::from_slice_unaligned(slice::from_raw_parts(
prev.slice(s![j.., 2]).as_ptr(),
SimdT::lanes(),
)),
SimdT::from_slice_unaligned(slice::from_raw_parts(
prev.slice(s![j.., 3]).as_ptr(),
SimdT::lanes(),
)),
SimdT::from_slice_unaligned(slice::from_raw_parts(
prev.slice(s![j.., 4]).as_ptr(),
SimdT::lanes(),
)),
SimdT::from_slice_unaligned(slice::from_raw_parts(
prev.slice(s![j.., 5]).as_ptr(),
SimdT::lanes(),
)),
SimdT::from_slice_unaligned(slice::from_raw_parts(
prev.slice(s![j.., 6]).as_ptr(),
SimdT::lanes(),
)),
]
};
for (i, bl) in Self::BLOCK.iter().enumerate() {
let b = idy
let b = idx
* (a[0] * bl[0]
+ a[1] * bl[1]
+ a[2] * bl[2]
@@ -195,22 +175,24 @@ impl Upwind4 {
+ a[4] * bl[4]
+ a[5] * bl[5]
+ a[6] * bl[6]);
b.write_to_slice_unaligned(&mut fut[i * nx + j..]);
unsafe {
b.write_to_slice_unaligned(slice::from_raw_parts_mut(
fut.slice_mut(s![j.., i]).as_mut_ptr(),
SimdT::lanes(),
));
}
}
let mut a = a;
for i in Self::BLOCK.len()..ny - Self::BLOCK.len() {
for i in Self::BLOCK.len()..nx - 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 = [a[1], a[2], a[3], a[4], a[5], a[6], unsafe {
SimdT::from_slice_unaligned(slice::from_raw_parts(
prev.slice(s![j.., i + 3]).as_ptr(),
SimdT::lanes(),
))
}];
let b = idx
* (a[0] * Self::DIAG[0]
+ a[1] * Self::DIAG[1]
+ a[2] * Self::DIAG[2]
@@ -218,21 +200,49 @@ impl Upwind4 {
+ 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..]);
unsafe {
b.write_to_slice_unaligned(slice::from_raw_parts_mut(
fut.slice_mut(s![j.., i]).as_mut_ptr(),
SimdT::lanes(),
));
}
}
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..]),
];
let a = unsafe {
[
SimdT::from_slice_unaligned(slice::from_raw_parts(
prev.slice(s![j.., nx - 1]).as_ptr(),
SimdT::lanes(),
)),
SimdT::from_slice_unaligned(slice::from_raw_parts(
prev.slice(s![j.., nx - 2]).as_ptr(),
SimdT::lanes(),
)),
SimdT::from_slice_unaligned(slice::from_raw_parts(
prev.slice(s![j.., nx - 3]).as_ptr(),
SimdT::lanes(),
)),
SimdT::from_slice_unaligned(slice::from_raw_parts(
prev.slice(s![j.., nx - 4]).as_ptr(),
SimdT::lanes(),
)),
SimdT::from_slice_unaligned(slice::from_raw_parts(
prev.slice(s![j.., nx - 5]).as_ptr(),
SimdT::lanes(),
)),
SimdT::from_slice_unaligned(slice::from_raw_parts(
prev.slice(s![j.., nx - 6]).as_ptr(),
SimdT::lanes(),
)),
SimdT::from_slice_unaligned(slice::from_raw_parts(
prev.slice(s![j.., nx - 7]).as_ptr(),
SimdT::lanes(),
)),
]
};
for (i, bl) in Self::BLOCK.iter().enumerate() {
let b = -idy
let b = -idx
* (a[0] * bl[0]
+ a[1] * bl[1]
+ a[2] * bl[2]
@@ -240,50 +250,16 @@ impl Upwind4 {
+ a[4] * bl[4]
+ a[5] * bl[5]
+ a[6] * bl[6]);
b.write_to_slice_unaligned(&mut fut[(ny - 1 - i) * nx + j..]);
unsafe {
b.write_to_slice_unaligned(slice::from_raw_parts_mut(
fut.slice_mut(s![j.., nx - 1 - i]).as_mut_ptr(),
SimdT::lanes(),
));
}
}
}
}
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;
}
}
#[inline(never)]
fn diss_simd(prev: &[f32], fut: &mut [f32]) {
use packed_simd::{f32x8, u32x8};
@@ -456,69 +432,32 @@ impl Upwind4 {
}
}
}
fn diss(prev: ArrayView1<f32>, mut fut: ArrayViewMut1<f32>) {
assert_eq!(prev.shape(), fut.shape());
let nx = prev.shape()[0];
assert!(nx >= 2 * Self::DISS_BLOCK.len());
if let (Some(p), Some(f)) = (prev.as_slice(), fut.as_slice_mut()) {
Self::diss_simd(p, f);
return;
}
let dx = 1.0 / (nx - 1) as f32;
let idx = 1.0 / dx;
let diag = arr1(&Self::DISS_DIAG);
let block = arr2(&Self::DISS_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 diffxi(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)
match (prev.strides(), fut.strides()) {
([_, 1], [_, _]) => {
Self::diff_simd_row(prev, fut);
}
([1, _], [1, _]) if prev.len_of(Axis(0)) % SimdT::lanes() == 0 => {
Self::diff_simd_col(prev, fut);
}
([_, _], [_, _]) => {
// Fallback, work row by row
for (r0, r1) in prev.outer_iter().zip(fut.outer_iter_mut()) {
Self::diff_1d(r0, r1);
}
}
_ => unreachable!("Should only be two elements in the strides vectors"),
}
}
fn diffeta(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::diffeta_simd(p, f, nx, ny);
return;
}
}
// diffeta = transpose then use diffxi
fn diffeta(prev: ArrayView2<f32>, fut: ArrayViewMut2<f32>) {
// transpose then use diffxi
Self::diffxi(prev.reversed_axes(), fut.reversed_axes());
}
@@ -541,7 +480,7 @@ fn upwind4_test() {
target[i] = 1.0;
}
res.fill(0.0);
Upwind4::diff(source.view(), res.view_mut());
Upwind4::diff_1d(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));
@@ -567,7 +506,7 @@ fn upwind4_test() {
target[i] = 2.0 * x;
}
res.fill(0.0);
Upwind4::diff(source.view(), res.view_mut());
Upwind4::diff_1d(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));
@@ -593,7 +532,7 @@ fn upwind4_test() {
target[i] = 3.0 * x * x;
}
res.fill(0.0);
Upwind4::diff(source.view(), res.view_mut());
Upwind4::diff_1d(source.view(), res.view_mut());
approx::assert_abs_diff_eq!(&res, &target, epsilon = 1e-2);
{
@@ -620,7 +559,7 @@ impl UpwindOperator for Upwind4 {
assert_eq!(prev.shape(), fut.shape());
assert!(prev.shape()[1] >= 2 * Self::DISS_BLOCK.len());
for (r0, r1) in prev.outer_iter().zip(fut.outer_iter_mut()) {
Self::diss(r0, r1)
Self::diss_1d(r0, r1)
}
}