topos 0.13.0

An autodiff compiler stack in Rust.
Documentation 
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use std::ops::{Add, Mul};

use crate::{GemmTask, Shape, Tape, Tensor, init};

use super::{executed_f32, executed_f64, gemm_f32, strides_for};

/// Computes the product of two row-major matrices in the logical
/// path's accumulation order: the reference every case compares to,
/// within a tolerance, since the kernel packs and sums in its own
/// order.
fn reference<Element: Copy + Add<Output = Element> + Mul<Output = Element>>(
    a: &[Element],
    b: &[Element],
    m: usize,
    k: usize,
    n: usize,
) -> Vec<Element> {
    let mut elements = Vec::with_capacity(m * n);
    for row in 0..m {
        for column in 0..n {
            let mut total = a[row * k] * b[column];
            for step in 1..k {
                total = total + a[row * k + step] * b[step * n + column];
            }
            elements.push(total);
        }
    }
    elements
}

/// Returns distinct, sign-varied row-major values for a matrix.
fn varied(rows: usize, columns: usize, seed: i64) -> Vec<f64> {
    (0..(rows * columns) as i64)
        .map(|index| ((index * 7 + seed * 13) % 23 - 11) as f64 / 4.0)
        .collect()
}

/// A buffer holding a logical matrix under one stride form.
struct Form {
    buffer: Vec<f64>,
    strides: [usize; 2],
}

/// One stride-form builder of the grid.
type FormBuilder = fn(&[f64], usize, usize) -> Form;

/// Returns the logical matrix stored contiguously.
fn contiguous(logical: &[f64], _rows: usize, columns: usize) -> Form {
    Form {
        buffer: logical.to_vec(),
        strides: [columns, 1],
    }
}

/// Returns the logical matrix stored as its transpose, read back
/// through a transposed view's strides.
fn transposed(logical: &[f64], rows: usize, columns: usize) -> Form {
    let mut buffer = vec![0.0; rows * columns];
    for row in 0..rows {
        for column in 0..columns {
            buffer[column * rows + row] = logical[row * columns + column];
        }
    }
    Form {
        buffer,
        strides: [1, rows],
    }
}

/// Returns the logical matrix stored with three padding elements per
/// row: a narrowed window's wide leading dimension.
fn narrowed(logical: &[f64], rows: usize, columns: usize) -> Form {
    let padded = columns + 3;
    let mut buffer = vec![0.0; rows * padded];
    for row in 0..rows {
        buffer[row * padded..row * padded + columns]
            .copy_from_slice(&logical[row * columns..(row + 1) * columns]);
    }
    Form {
        buffer,
        strides: [padded, 1],
    }
}

/// Asserts elementwise closeness under the k-scaled tolerance of the
/// design note (the kernel reorders sums; it must not change them).
fn assert_close_f64(actual: &[f64], expected: &[f64], k: usize) {
    let tolerance = 8.0 * f64::EPSILON * (k as f64).sqrt();
    for (actual, expected) in actual.iter().zip(expected) {
        assert!(
            (actual - expected).abs() <= tolerance * (1.0 + expected.abs()),
            "{actual} differs from {expected} beyond tolerance (k = {k})"
        );
    }
}

/// The `f32` twin of [`assert_close_f64`].
fn assert_close_f32(actual: &[f32], expected: &[f32], k: usize) {
    let tolerance = 8.0 * f32::EPSILON * (k as f32).sqrt();
    for (actual, expected) in actual.iter().zip(expected) {
        assert!(
            (actual - expected).abs() <= tolerance * (1.0 + expected.abs()),
            "{actual} differs from {expected} beyond tolerance (k = {k})"
        );
    }
}

/// The shape grid: squares, rectangles, primes, and GEMV shapes.
const SHAPES: [(usize, usize, usize); 9] = [
    (1, 1, 1),
    (2, 3, 4),
    (5, 8, 13),
    (16, 16, 16),
    (63, 64, 65),
    (100, 127, 3),
    (128, 100, 64),
    (1, 64, 128),
    (64, 128, 1),
];

#[test]
fn every_stride_form_matches_the_reference_f64() {
    let forms: [FormBuilder; 3] = [contiguous, transposed, narrowed];
    for (m, k, n) in SHAPES {
        let left = varied(m, k, 1);
        let right = varied(k, n, 2);
        let expected = reference(&left, &right, m, k, n);
        for left_form in forms {
            for right_form in forms {
                let a = left_form(&left, m, k);
                let b = right_form(&right, k, n);
                let task = GemmTask::new(&a.buffer, a.strides, &b.buffer, b.strides, m, k, n);
                let product = executed_f64(&task).expect("the mapping accepts this form");
                assert_close_f64(&product, &expected, k);
            }
        }
    }
}

#[test]
fn every_stride_form_matches_the_reference_f32() {
    for (m, k, n) in SHAPES {
        let left: Vec<f32> = varied(m, k, 3).iter().map(|&value| value as f32).collect();
        let right: Vec<f32> = varied(k, n, 4).iter().map(|&value| value as f32).collect();
        let expected = reference(&left, &right, m, k, n);
        let task = GemmTask::new(&left, [k, 1], &right, [n, 1], m, k, n);
        let product = executed_f32(&task).expect("the mapping accepts contiguous operands");
        assert_close_f32(&product, &expected, k);

        let mut transposed_right = vec![0.0_f32; k * n];
        for row in 0..k {
            for column in 0..n {
                transposed_right[column * k + row] = right[row * n + column];
            }
        }
        let task = GemmTask::new(&left, [k, 1], &transposed_right, [1, k], m, k, n);
        let product = executed_f32(&task).expect("the mapping accepts a transposed operand");
        assert_close_f32(&product, &expected, k);
    }
}

#[test]
fn broadcast_strides_decline_to_the_built_in_paths() {
    let row = varied(1, 8, 1);
    let right = varied(8, 4, 2);
    // A stride-0 row axis declines conservatively, mirroring the
    // cblas arm; relaxing it is a recorded experiment, not a bet.
    let task = GemmTask::new(&row, [0, 1], &right, [4, 1], 3, 8, 4);
    assert_eq!(executed_f64(&task), None);
}

#[test]
fn the_threshold_declines_small_tasks() {
    let left = varied(2, 2, 1);
    let right = varied(2, 2, 2);
    let task = GemmTask::new(&left, [2, 1], &right, [2, 1], 2, 2, 2);
    let left32: Vec<f32> = left.iter().map(|&value| value as f32).collect();
    let right32: Vec<f32> = right.iter().map(|&value| value as f32).collect();
    let task32 = GemmTask::new(&left32, [2, 1], &right32, [2, 1], 2, 2, 2);
    assert_eq!(super::gemm_f64(&task), None);
    assert_eq!(gemm_f32(&task32), None);
}

#[test]
fn unaddressable_offsets_decline_without_allocating() {
    // The pure eligibility arithmetic, exercised directly: a furthest
    // element offset beyond `isize` declines before any pointer math
    // could see it, and no giant operand needs to exist to prove it.
    assert_eq!(strides_for([0, 1], 4, 4), None);
    assert_eq!(strides_for([1, 0], 4, 4), None);
    assert_eq!(strides_for([usize::MAX / 2, 1], 3, 4), None);
    assert_eq!(strides_for([1, usize::MAX / 2], 4, 3), None);
    assert_eq!(strides_for([4, 1], 4, 4), Some([4, 1]));
    assert_eq!(strides_for([1, 4], 4, 4), Some([1, 4]));
}

#[test]
fn repeated_products_answer_bitwise_identically() {
    // The kernel is single-threaded with fixed blocking per version
    // and detected instruction set; per the house rule its run-to-run
    // determinism is verified, not assumed. The observed answer is
    // recorded in notes/simd-backend.md.
    let size = 1024;
    let left = varied(size, size, 5);
    let right = varied(size, size, 6);
    let task = GemmTask::new(&left, [size, 1], &right, [size, 1], size, size, size);
    let first = executed_f64(&task).expect("a plain square product");
    let second = executed_f64(&task).expect("a plain square product");
    let first_bits: Vec<u64> = first.iter().map(|value| value.to_bits()).collect();
    let second_bits: Vec<u64> = second.iter().map(|value| value.to_bits()).collect();
    assert_eq!(first_bits, second_bits);
}

#[test]
fn training_runs_through_the_backend_end_to_end() {
    // A batch-64 regression whose products sit above the threshold,
    // so forward and backward (transposed views included) route
    // through the kernel against the real tape — on any platform,
    // which is the point of this backend.
    let tape = Tape::new();
    let inputs = tape.input(Tensor::filled([64, 8], 0.5_f64));
    let targets = tape.input(Tensor::filled([64, 1], 1.0_f64));
    let mut initializer = init::uniform(11, 0.3);
    let weights = tape.parameter(initializer(&Shape::new([8, 64])));
    let output_weights = tape.parameter(initializer(&Shape::new([64, 1])));
    let hidden = inputs.matmul(weights).tanh();
    let prediction = hidden.matmul(output_weights);
    let error = prediction - targets;
    let loss = (error * error).sum();
    let loss_symbol = loss.symbol();

    let network = tape.into_network();
    let mut parameters = network.parameters();
    let mut last_loss = f64::INFINITY;
    for _ in 0..50 {
        let run = network.forward(&parameters, []);
        last_loss = run.of(loss_symbol).scalar();
        let gradients = run.backward(loss_symbol).parameters(&parameters);
        parameters = parameters.step(&gradients, |weight, gradient| {
            weight.clone() - Tensor::filled(gradient.shape(), 0.001) * gradient.clone()
        });
    }
    assert!(
        last_loss < 1.0,
        "training through the backend did not converge: {last_loss}"
    );
}