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add efficient prefix-sums and reductions #22

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programmerjake merged 1 commit from programmerjake/fayalite:add-prefix-sum-and-reduce into master 2025-03-03 07:12:31 +00:00
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1
crates/fayalite/src/util.rs
View file

@ -29,4 +29,5 @@ pub use misc::{
}; };
pub mod job_server; pub mod job_server;
pub mod prefix_sum;
pub mod ready_valid; pub mod ready_valid;

839
crates/fayalite/src/util/prefix_sum.rs Normal file
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@ -0,0 +1,839 @@
// SPDX-License-Identifier: LGPL-3.0-or-later
// See Notices.txt for copyright information
// code derived from:
// https://web.archive.org/web/20250303054010/https://git.libre-soc.org/?p=nmutil.git;a=blob;f=src/nmutil/prefix_sum.py;hb=effeb28e5848392adddcdad1f6e7a098f2a44c9c
use crate::intern::{Intern, Interned, Memoize};
use std::{borrow::Cow, num::NonZeroUsize};
#[derive(Copy, Clone, PartialEq, Eq, PartialOrd, Ord, Hash, Debug)]
pub struct PrefixSumOp {
pub lhs_index: usize,
pub rhs_and_dest_index: NonZeroUsize,
pub row: u32,
}
#[derive(Clone, PartialEq, Eq, Hash, Debug)]
#[non_exhaustive]
pub struct DiagramConfig {
pub space: Cow<'static, str>,
pub vertical_bar: Cow<'static, str>,
pub plus: Cow<'static, str>,
pub slant: Cow<'static, str>,
pub connect: Cow<'static, str>,
pub no_connect: Cow<'static, str>,
pub padding: usize,
}
impl DiagramConfig {
pub const fn new() -> Self {
Self {
space: Cow::Borrowed(" "),
vertical_bar: Cow::Borrowed("|"),
plus: Cow::Borrowed("\u{2295}"), // ⊕
slant: Cow::Borrowed(r"\"),
connect: Cow::Borrowed("\u{25CF}"), // ●
no_connect: Cow::Borrowed("X"),
padding: 1,
}
}
pub fn draw(self, ops: impl IntoIterator<Item = PrefixSumOp>, item_count: usize) -> String {
#[derive(Copy, Clone, Debug)]
struct DiagramCell {
slant: bool,
plus: bool,
tee: bool,
}
let mut ops_by_row: Vec<Vec<PrefixSumOp>> = Vec::new();
let mut last_row = 0;
ops.into_iter().for_each(|op| {
assert!(
op.lhs_index < op.rhs_and_dest_index.get(),
"invalid PrefixSumOp! lhs_index must be less \
than rhs_and_dest_index: {op:?}",
);
assert!(
op.row >= last_row,
"invalid PrefixSumOp! row must \
not decrease (row last was: {last_row}): {op:?}",
);
let ops = if op.row > last_row || ops_by_row.is_empty() {
ops_by_row.push(vec![]);
ops_by_row.last_mut().expect("just pushed")
} else {
ops_by_row
.last_mut()
.expect("just checked if ops_by_row is empty")
};
if let Some(last) = ops.last() {
assert!(
op.rhs_and_dest_index < last.rhs_and_dest_index,
"invalid PrefixSumOp! rhs_and_dest_index must strictly \
decrease in a row:\nthis op: {op:?}\nlast op: {last:?}",
);
}
ops.push(op);
last_row = op.row;
});
let blank_row = || {
vec![
DiagramCell {
slant: false,
plus: false,
tee: false
};
item_count
]
};
let mut cells = vec![blank_row()];
for ops in ops_by_row {
let max_distance = ops
.iter()
.map(
|&PrefixSumOp {
lhs_index,
rhs_and_dest_index,
..
}| { rhs_and_dest_index.get() - lhs_index },
)
.max()
.expect("ops is known to be non-empty");
cells.extend((0..max_distance).map(|_| blank_row()));
for op in ops {
let mut y = cells.len() - 1;
assert!(
op.rhs_and_dest_index.get() < item_count,
"invalid PrefixSumOp! rhs_and_dest_index must be \
less than item_count ({item_count}): {op:?}",
);
let mut x = op.rhs_and_dest_index.get();
cells[y][x].plus = true;
x -= 1;
y -= 1;
while op.lhs_index < x {
cells[y][x].slant = true;
x -= 1;
y -= 1;
}
cells[y][x].tee = true;
}
}
let mut retval = String::new();
let mut row_text = vec![String::new(); 2 * self.padding + 1];
for cells_row in cells {
for cell in cells_row {
// top padding
for y in 0..self.padding {
// top left padding
for x in 0..self.padding {
row_text[y] += if x == y && (cell.plus || cell.slant) {
&self.slant
} else {
&self.space
};
}
// top vertical bar
row_text[y] += &self.vertical_bar;
// top right padding
for _ in 0..self.padding {
row_text[y] += &self.space;
}
}
// center left padding
for _ in 0..self.padding {
row_text[self.padding] += &self.space;
}
// center
row_text[self.padding] += if cell.plus {
&self.plus
} else if cell.tee {
&self.connect
} else if cell.slant {
&self.no_connect
} else {
&self.vertical_bar
};
// center right padding
for _ in 0..self.padding {
row_text[self.padding] += &self.space;
}
let bottom_padding_start = self.padding + 1;
let bottom_padding_last = self.padding * 2;
// bottom padding
for y in bottom_padding_start..=bottom_padding_last {
// bottom left padding
for _ in 0..self.padding {
row_text[y] += &self.space;
}
// bottom vertical bar
row_text[y] += &self.vertical_bar;
// bottom right padding
for x in bottom_padding_start..=bottom_padding_last {
row_text[y] += if x == y && (cell.tee || cell.slant) {
&self.slant
} else {
&self.space
};
}
}
}
for line in &mut row_text {
retval += line.trim_end();
retval += "\n";
line.clear();
}
}
retval
}
}
impl Default for DiagramConfig {
fn default() -> Self {
Self::new()
}
}
impl PrefixSumOp {
pub fn diagram(ops: impl IntoIterator<Item = Self>, item_count: usize) -> String {
Self::diagram_with_config(ops, item_count, DiagramConfig::new())
}
pub fn diagram_with_config(
ops: impl IntoIterator<Item = Self>,
item_count: usize,
config: DiagramConfig,
) -> String {
config.draw(ops, item_count)
}
}
#[derive(Copy, Clone, PartialEq, Eq, Hash, Debug)]
pub enum PrefixSumAlgorithm {
/// Uses the algorithm from:
/// https://en.wikipedia.org/wiki/Prefix_sum#Algorithm_1:_Shorter_span,_more_parallel
LowLatency,
/// Uses the algorithm from:
/// https://en.wikipedia.org/wiki/Prefix_sum#Algorithm_2:_Work-efficient
WorkEfficient,
}
impl PrefixSumAlgorithm {
fn ops_impl(self, item_count: usize) -> Vec<PrefixSumOp> {
let mut retval = Vec::new();
let mut distance = 1;
let mut row = 0;
while distance < item_count {
let double_distance = distance
.checked_mul(2)
.expect("prefix-sum item_count is too big");
let (start, step) = match self {
Self::LowLatency => (distance, 1),
Self::WorkEfficient => (double_distance - 1, double_distance),
};
for rhs_and_dest_index in (start..item_count).step_by(step).rev() {
let Some(rhs_and_dest_index) = NonZeroUsize::new(rhs_and_dest_index) else {
unreachable!();
};
let lhs_index = rhs_and_dest_index.get() - distance;
retval.push(PrefixSumOp {
lhs_index,
rhs_and_dest_index,
row,
});
}
distance = double_distance;
row += 1;
}
match self {
Self::LowLatency => {}
Self::WorkEfficient => {
distance /= 2;
while distance >= 1 {
let start = distance
.checked_mul(3)
.expect("prefix-sum item_count is too big")
- 1;
for rhs_and_dest_index in (start..item_count).step_by(distance * 2).rev() {
let Some(rhs_and_dest_index) = NonZeroUsize::new(rhs_and_dest_index) else {
unreachable!();
};
let lhs_index = rhs_and_dest_index.get() - distance;
retval.push(PrefixSumOp {
lhs_index,
rhs_and_dest_index,
row,
});
}
row += 1;
distance /= 2;
}
}
}
retval
}
pub fn ops(self, item_count: usize) -> Interned<[PrefixSumOp]> {
#[derive(Copy, Clone, PartialEq, Eq, Hash, Debug)]
struct MyMemoize(PrefixSumAlgorithm);
impl Memoize for MyMemoize {
type Input = usize;
type InputOwned = usize;
type Output = Interned<[PrefixSumOp]>;
fn inner(self, item_count: &Self::Input) -> Self::Output {
Intern::intern_owned(self.0.ops_impl(*item_count))
}
}
MyMemoize(self).get_owned(item_count)
}
pub fn run<T>(self, items: impl IntoIterator<Item = T>, f: impl FnMut(&T, &T) -> T) -> Vec<T> {
let mut items = Vec::from_iter(items);
self.run_on_slice(&mut items, f);
items
}
pub fn run_on_slice<T>(self, items: &mut [T], mut f: impl FnMut(&T, &T) -> T) -> &mut [T] {
self.ops(items.len()).into_iter().for_each(
|PrefixSumOp {
lhs_index,
rhs_and_dest_index,
row: _,
}| {
items[rhs_and_dest_index.get()] =
f(&items[lhs_index], &items[rhs_and_dest_index.get()]);
},
);
items
}
pub fn filtered_ops(
self,
item_live_out_flags: impl IntoIterator<Item = bool>,
) -> Vec<PrefixSumOp> {
let mut item_live_out_flags = Vec::from_iter(item_live_out_flags);
let prefix_sum_ops = self.ops(item_live_out_flags.len());
let mut ops_live_flags = vec![false; prefix_sum_ops.len()];
for (
op_index,
&PrefixSumOp {
lhs_index,
rhs_and_dest_index,
row: _,
},
) in prefix_sum_ops.iter().enumerate().rev()
{
let live = item_live_out_flags[rhs_and_dest_index.get()];
item_live_out_flags[lhs_index] |= live;
ops_live_flags[op_index] = live;
}
prefix_sum_ops
.into_iter()
.zip(ops_live_flags)
.filter_map(|(op, live)| live.then_some(op))
.collect()
}
pub fn reduce_ops(self, item_count: usize) -> Interned<[PrefixSumOp]> {
#[derive(Copy, Clone, PartialEq, Eq, Hash, Debug)]
struct MyMemoize(PrefixSumAlgorithm);
impl Memoize for MyMemoize {
type Input = usize;
type InputOwned = usize;
type Output = Interned<[PrefixSumOp]>;
fn inner(self, item_count: &Self::Input) -> Self::Output {
let mut item_live_out_flags = vec![false; *item_count];
let Some(last_item_live_out_flag) = item_live_out_flags.last_mut() else {
return Interned::default();
};
*last_item_live_out_flag = true;
Intern::intern_owned(self.0.filtered_ops(item_live_out_flags))
}
}
MyMemoize(self).get_owned(item_count)
}
}
pub fn reduce_ops(item_count: usize) -> Interned<[PrefixSumOp]> {
PrefixSumAlgorithm::LowLatency.reduce_ops(item_count)
}
pub fn reduce<T>(items: impl IntoIterator<Item = T>, mut f: impl FnMut(T, T) -> T) -> Option<T> {
let mut items: Vec<_> = items.into_iter().map(Some).collect();
for op in reduce_ops(items.len()) {
let (Some(lhs), Some(rhs)) = (
items[op.lhs_index].take(),
items[op.rhs_and_dest_index.get()].take(),
) else {
unreachable!();
};
items[op.rhs_and_dest_index.get()] = Some(f(lhs, rhs));
}
items.last_mut().and_then(Option::take)
}
#[cfg(test)]
mod tests {
use super::*;
fn input_strings() -> [String; 9] {
std::array::from_fn(|i| String::from_utf8(vec![b'a' + i as u8]).unwrap())
}
#[test]
fn test_prefix_sum_strings() {
let input = input_strings();
let expected: Vec<String> = input
.iter()
.scan(String::new(), |l, r| {
*l += r;
Some(l.clone())
})
.collect();
println!("expected: {expected:?}");
assert_eq!(
*PrefixSumAlgorithm::WorkEfficient
.run_on_slice(&mut input.clone(), |l, r| l.to_string() + r),
*expected
);
assert_eq!(
*PrefixSumAlgorithm::LowLatency
.run_on_slice(&mut input.clone(), |l, r| l.to_string() + r),
*expected
);
}
#[test]
fn test_reduce_string() {
let input = input_strings();
let expected = input.clone().into_iter().reduce(|l, r| l + &r);
assert_eq!(reduce(input, |l, r| l + &r), expected);
}
fn op(lhs_index: usize, rhs_and_dest_index: usize, row: u32) -> PrefixSumOp {
PrefixSumOp {
lhs_index,
rhs_and_dest_index: NonZeroUsize::new(rhs_and_dest_index).expect("should be non-zero"),
row,
}
}
#[test]
fn test_reduce_ops_9() {
let expected = vec![
op(7, 8, 0),
op(5, 6, 0),
op(3, 4, 0),
op(1, 2, 0),
op(6, 8, 1),
op(2, 4, 1),
op(4, 8, 2),
op(0, 8, 3),
];
println!("expected: {expected:#?}");
let ops = reduce_ops(9);
println!("ops: {ops:#?}");
assert_eq!(*ops, *expected);
}
#[test]
fn test_reduce_ops_8() {
let expected = vec![
op(6, 7, 0),
op(4, 5, 0),
op(2, 3, 0),
op(0, 1, 0),
op(5, 7, 1),
op(1, 3, 1),
op(3, 7, 2),
];
println!("expected: {expected:#?}");
let ops = reduce_ops(8);
println!("ops: {ops:#?}");
assert_eq!(*ops, *expected);
}
#[test]
fn test_count_ones() {
for width in 0..=10u32 {
for v in 0..1u32 << width {
let expected = v.count_ones();
assert_eq!(
reduce((0..width).map(|i| (v >> i) & 1), |l, r| l + r).unwrap_or(0),
expected,
"v={v:#X}"
);
}
}
}
#[track_caller]
fn test_diagram(ops: impl IntoIterator<Item = PrefixSumOp>, item_count: usize, expected: &str) {
let text = PrefixSumOp::diagram_with_config(
ops,
item_count,
DiagramConfig {
plus: Cow::Borrowed("@"),
..Default::default()
},
);
println!("text:\n{text}\n");
assert_eq!(text, expected);
}
#[test]
fn test_work_efficient_diagram_16() {
let item_count = 16;
test_diagram(
PrefixSumAlgorithm::WorkEfficient.ops(item_count),
item_count,
&r"
| | | | | | | | | | | | | | | |
● | ● | ● | ● | ● | ● | ● | ● |
|\ | |\ | |\ | |\ | |\ | |\ | |\ | |\ |
| \| | \| | \| | \| | \| | \| | \| | \|
| @ | @ | @ | @ | @ | @ | @ | @
| |\ | | | |\ | | | |\ | | | |\ | |
| | \| | | | \| | | | \| | | | \| |
| | X | | | X | | | X | | | X |
| | |\ | | | |\ | | | |\ | | | |\ |
| | | \| | | | \| | | | \| | | | \|
| | | @ | | | @ | | | @ | | | @
| | | |\ | | | | | | | |\ | | | |
| | | | \| | | | | | | | \| | | |
| | | | X | | | | | | | X | | |
| | | | |\ | | | | | | | |\ | | |
| | | | | \| | | | | | | | \| | |
| | | | | X | | | | | | | X | |
| | | | | |\ | | | | | | | |\ | |
| | | | | | \| | | | | | | | \| |
| | | | | | X | | | | | | | X |
| | | | | | |\ | | | | | | | |\ |
| | | | | | | \| | | | | | | | \|
| | | | | | | @ | | | | | | | @
| | | | | | | |\ | | | | | | | |
| | | | | | | | \| | | | | | | |
| | | | | | | | X | | | | | | |
| | | | | | | | |\ | | | | | | |
| | | | | | | | | \| | | | | | |
| | | | | | | | | X | | | | | |
| | | | | | | | | |\ | | | | | |
| | | | | | | | | | \| | | | | |
| | | | | | | | | | X | | | | |
| | | | | | | | | | |\ | | | | |
| | | | | | | | | | | \| | | | |
| | | | | | | | | | | X | | | |
| | | | | | | | | | | |\ | | | |
| | | | | | | | | | | | \| | | |
| | | | | | | | | | | | X | | |
| | | | | | | | | | | | |\ | | |
| | | | | | | | | | | | | \| | |
| | | | | | | | | | | | | X | |
| | | | | | | | | | | | | |\ | |
| | | | | | | | | | | | | | \| |
| | | | | | | | | | | | | | X |
| | | | | | | | | | | | | | |\ |
| | | | | | | | | | | | | | | \|
| | | | | | | ● | | | | | | | @
| | | | | | | |\ | | | | | | | |
| | | | | | | | \| | | | | | | |
| | | | | | | | X | | | | | | |
| | | | | | | | |\ | | | | | | |
| | | | | | | | | \| | | | | | |
| | | | | | | | | X | | | | | |
| | | | | | | | | |\ | | | | | |
| | | | | | | | | | \| | | | | |
| | | | | | | | | | X | | | | |
| | | | | | | | | | |\ | | | | |
| | | | | | | | | | | \| | | | |
| | | ● | | | ● | | | @ | | | |
| | | |\ | | | |\ | | | |\ | | | |
| | | | \| | | | \| | | | \| | | |
| | | | X | | | X | | | X | | |
| | | | |\ | | | |\ | | | |\ | | |
| | | | | \| | | | \| | | | \| | |
| ● | ● | @ | ● | @ | ● | @ | |
| |\ | |\ | |\ | |\ | |\ | |\ | |\ | |
| | \| | \| | \| | \| | \| | \| | \| |
| | @ | @ | @ | @ | @ | @ | @ |
| | | | | | | | | | | | | | | |
"[1..], // trim newline at start
);
}
#[test]
fn test_low_latency_diagram_16() {
let item_count = 16;
test_diagram(
PrefixSumAlgorithm::LowLatency.ops(item_count),
item_count,
&r"
| | | | | | | | | | | | | | | |
● ● ● ● ● ● ● ● ● ● ● ● ● ● ● |
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |
| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \|
● @ @ @ @ @ @ @ @ @ @ @ @ @ @ @
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ | |
| \| \| \| \| \| \| \| \| \| \| \| \| \| \| |
| X X X X X X X X X X X X X X |
| |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |
| | \| \| \| \| \| \| \| \| \| \| \| \| \| \|
● ● @ @ @ @ @ @ @ @ @ @ @ @ @ @
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ | | | |
| \| \| \| \| \| \| \| \| \| \| \| \| | | |
| X X X X X X X X X X X X | | |
| |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ | | |
| | \| \| \| \| \| \| \| \| \| \| \| \| | |
| | X X X X X X X X X X X X | |
| | |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ | |
| | | \| \| \| \| \| \| \| \| \| \| \| \| |
| | | X X X X X X X X X X X X |
| | | |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |
| | | | \| \| \| \| \| \| \| \| \| \| \| \|
● ● ● ● @ @ @ @ @ @ @ @ @ @ @ @
|\ |\ |\ |\ |\ |\ |\ |\ | | | | | | | |
| \| \| \| \| \| \| \| \| | | | | | | |
| X X X X X X X X | | | | | | |
| |\ |\ |\ |\ |\ |\ |\ |\ | | | | | | |
| | \| \| \| \| \| \| \| \| | | | | | |
| | X X X X X X X X | | | | | |
| | |\ |\ |\ |\ |\ |\ |\ |\ | | | | | |
| | | \| \| \| \| \| \| \| \| | | | | |
| | | X X X X X X X X | | | | |
| | | |\ |\ |\ |\ |\ |\ |\ |\ | | | | |
| | | | \| \| \| \| \| \| \| \| | | | |
| | | | X X X X X X X X | | | |
| | | | |\ |\ |\ |\ |\ |\ |\ |\ | | | |
| | | | | \| \| \| \| \| \| \| \| | | |
| | | | | X X X X X X X X | | |
| | | | | |\ |\ |\ |\ |\ |\ |\ |\ | | |
| | | | | | \| \| \| \| \| \| \| \| | |
| | | | | | X X X X X X X X | |
| | | | | | |\ |\ |\ |\ |\ |\ |\ |\ | |
| | | | | | | \| \| \| \| \| \| \| \| |
| | | | | | | X X X X X X X X |
| | | | | | | |\ |\ |\ |\ |\ |\ |\ |\ |
| | | | | | | | \| \| \| \| \| \| \| \|
| | | | | | | | @ @ @ @ @ @ @ @
| | | | | | | | | | | | | | | |
"[1..], // trim newline at start
);
}
#[test]
fn test_work_efficient_diagram_9() {
let item_count = 9;
test_diagram(
PrefixSumAlgorithm::WorkEfficient.ops(item_count),
item_count,
&r"
| | | | | | | | |
● | ● | ● | ● | |
|\ | |\ | |\ | |\ | |
| \| | \| | \| | \| |
| @ | @ | @ | @ |
| |\ | | | |\ | | |
| | \| | | | \| | |
| | X | | | X | |
| | |\ | | | |\ | |
| | | \| | | | \| |
| | | @ | | | @ |
| | | |\ | | | | |
| | | | \| | | | |
| | | | X | | | |
| | | | |\ | | | |
| | | | | \| | | |
| | | | | X | | |
| | | | | |\ | | |
| | | | | | \| | |
| | | | | | X | |
| | | | | | |\ | |
| | | | | | | \| |
| | | ● | | | @ |
| | | |\ | | | | |
| | | | \| | | | |
| | | | X | | | |
| | | | |\ | | | |
| | | | | \| | | |
| ● | ● | @ | ● |
| |\ | |\ | |\ | |\ |
| | \| | \| | \| | \|
| | @ | @ | @ | @
| | | | | | | | |
"[1..], // trim newline at start
);
}
#[test]
fn test_low_latency_diagram_9() {
let item_count = 9;
test_diagram(
PrefixSumAlgorithm::LowLatency.ops(item_count),
item_count,
&r"
| | | | | | | | |
● ● ● ● ● ● ● ● |
|\ |\ |\ |\ |\ |\ |\ |\ |
| \| \| \| \| \| \| \| \|
● @ @ @ @ @ @ @ @
|\ |\ |\ |\ |\ |\ |\ | |
| \| \| \| \| \| \| \| |
| X X X X X X X |
| |\ |\ |\ |\ |\ |\ |\ |
| | \| \| \| \| \| \| \|
● ● @ @ @ @ @ @ @
|\ |\ |\ |\ |\ | | | |
| \| \| \| \| \| | | |
| X X X X X | | |
| |\ |\ |\ |\ |\ | | |
| | \| \| \| \| \| | |
| | X X X X X | |
| | |\ |\ |\ |\ |\ | |
| | | \| \| \| \| \| |
| | | X X X X X |
| | | |\ |\ |\ |\ |\ |
| | | | \| \| \| \| \|
● | | | @ @ @ @ @
|\ | | | | | | | |
| \| | | | | | | |
| X | | | | | | |
| |\ | | | | | | |
| | \| | | | | | |
| | X | | | | | |
| | |\ | | | | | |
| | | \| | | | | |
| | | X | | | | |
| | | |\ | | | | |
| | | | \| | | | |
| | | | X | | | |
| | | | |\ | | | |
| | | | | \| | | |
| | | | | X | | |
| | | | | |\ | | |
| | | | | | \| | |
| | | | | | X | |
| | | | | | |\ | |
| | | | | | | \| |
| | | | | | | X |
| | | | | | | |\ |
| | | | | | | | \|
| | | | | | | | @
| | | | | | | | |
"[1..], // trim newline at start
);
}
#[test]
fn test_reduce_diagram_16() {
let item_count = 16;
test_diagram(
reduce_ops(item_count),
item_count,
&r"
| | | | | | | | | | | | | | | |
● | ● | ● | ● | ● | ● | ● | ● |
|\ | |\ | |\ | |\ | |\ | |\ | |\ | |\ |
| \| | \| | \| | \| | \| | \| | \| | \|
| @ | @ | @ | @ | @ | @ | @ | @
| |\ | | | |\ | | | |\ | | | |\ | |
| | \| | | | \| | | | \| | | | \| |
| | X | | | X | | | X | | | X |
| | |\ | | | |\ | | | |\ | | | |\ |
| | | \| | | | \| | | | \| | | | \|
| | | @ | | | @ | | | @ | | | @
| | | |\ | | | | | | | |\ | | | |
| | | | \| | | | | | | | \| | | |
| | | | X | | | | | | | X | | |
| | | | |\ | | | | | | | |\ | | |
| | | | | \| | | | | | | | \| | |
| | | | | X | | | | | | | X | |
| | | | | |\ | | | | | | | |\ | |
| | | | | | \| | | | | | | | \| |
| | | | | | X | | | | | | | X |
| | | | | | |\ | | | | | | | |\ |
| | | | | | | \| | | | | | | | \|
| | | | | | | @ | | | | | | | @
| | | | | | | |\ | | | | | | | |
| | | | | | | | \| | | | | | | |
| | | | | | | | X | | | | | | |
| | | | | | | | |\ | | | | | | |
| | | | | | | | | \| | | | | | |
| | | | | | | | | X | | | | | |
| | | | | | | | | |\ | | | | | |
| | | | | | | | | | \| | | | | |
| | | | | | | | | | X | | | | |
| | | | | | | | | | |\ | | | | |
| | | | | | | | | | | \| | | | |
| | | | | | | | | | | X | | | |
| | | | | | | | | | | |\ | | | |
| | | | | | | | | | | | \| | | |
| | | | | | | | | | | | X | | |
| | | | | | | | | | | | |\ | | |
| | | | | | | | | | | | | \| | |
| | | | | | | | | | | | | X | |
| | | | | | | | | | | | | |\ | |
| | | | | | | | | | | | | | \| |
| | | | | | | | | | | | | | X |
| | | | | | | | | | | | | | |\ |
| | | | | | | | | | | | | | | \|
| | | | | | | | | | | | | | | @
| | | | | | | | | | | | | | | |
"[1..], // trim newline at start
);
}
#[test]
fn test_reduce_diagram_9() {
let item_count = 9;
test_diagram(
reduce_ops(item_count),
item_count,
&r"
| | | | | | | | |
| ● | ● | ● | ● |
| |\ | |\ | |\ | |\ |
| | \| | \| | \| | \|
| | @ | @ | @ | @
| | |\ | | | |\ | |
| | | \| | | | \| |
| | | X | | | X |
| | | |\ | | | |\ |
| | | | \| | | | \|
| | | | @ | | | @
| | | | |\ | | | |
| | | | | \| | | |
| | | | | X | | |
| | | | | |\ | | |
| | | | | | \| | |
| | | | | | X | |
| | | | | | |\ | |
| | | | | | | \| |
| | | | | | | X |
| | | | | | | |\ |
| | | | | | | | \|
● | | | | | | | @
|\ | | | | | | | |
| \| | | | | | | |
| X | | | | | | |
| |\ | | | | | | |
| | \| | | | | | |
| | X | | | | | |
| | |\ | | | | | |
| | | \| | | | | |
| | | X | | | | |
| | | |\ | | | | |
| | | | \| | | | |
| | | | X | | | |
| | | | |\ | | | |
| | | | | \| | | |
| | | | | X | | |
| | | | | |\ | | |
| | | | | | \| | |
| | | | | | X | |
| | | | | | |\ | |
| | | | | | | \| |
| | | | | | | X |
| | | | | | | |\ |
| | | | | | | | \|
| | | | | | | | @
| | | | | | | | |
"[1..], // trim newline at start
);
}
}