crates/fayalite/src/util.rs

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

crates/fayalite/src/util/prefix_sum.rs

@@ -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
+        );
+    }
+}