amari_gpu/

shaders.rs

//! WebGPU compute shader library for mathematical operations
//!
//! This module contains optimized WGSL compute shaders for various mathematical
//! domains including tropical algebra, automatic differentiation, and fusion systems.

use std::collections::HashMap;

/// Shader library managing all mathematical compute shaders
pub struct ShaderLibrary {
    shaders: HashMap<String, &'static str>,
}

impl ShaderLibrary {
    /// Create new shader library with all mathematical shaders
    pub fn new() -> Self {
        let mut shaders = HashMap::new();

        // Tropical algebra shaders
        shaders.insert(
            "tropical_matrix_multiply".to_string(),
            TROPICAL_MATRIX_MULTIPLY,
        );
        shaders.insert("tropical_vector_add".to_string(), TROPICAL_VECTOR_ADD);
        shaders.insert(
            "tropical_neural_network".to_string(),
            TROPICAL_NEURAL_NETWORK,
        );

        // Dual number shaders
        shaders.insert("dual_forward_ad".to_string(), DUAL_FORWARD_AD);
        shaders.insert("dual_batch_gradient".to_string(), DUAL_BATCH_GRADIENT);
        shaders.insert("dual_chain_rule".to_string(), DUAL_CHAIN_RULE);

        // Fusion system shaders
        shaders.insert("tropical_dual_clifford".to_string(), TROPICAL_DUAL_CLIFFORD);
        shaders.insert("fusion_attention".to_string(), FUSION_ATTENTION);

        // Information geometry shaders
        shaders.insert("fisher_information".to_string(), FISHER_INFORMATION);
        shaders.insert("kl_divergence_batch".to_string(), KL_DIVERGENCE_BATCH);

        // Cellular automata shaders
        shaders.insert("ca_evolution".to_string(), CA_EVOLUTION);
        shaders.insert("ca_self_assembly".to_string(), CA_SELF_ASSEMBLY);
        shaders.insert("rule_application".to_string(), RULE_APPLICATION);
        shaders.insert("energy_calculation".to_string(), ENERGY_CALCULATION);
        shaders.insert("neighbor_extraction".to_string(), NEIGHBOR_EXTRACTION);

        // Enumerative geometry shaders
        shaders.insert("intersection_theory".to_string(), INTERSECTION_THEORY);
        shaders.insert("schubert_calculus".to_string(), SCHUBERT_CALCULUS);

        // Holographic memory shaders
        shaders.insert("holographic_batch_bind".to_string(), HOLOGRAPHIC_BATCH_BIND);
        shaders.insert(
            "holographic_batch_similarity".to_string(),
            HOLOGRAPHIC_BATCH_SIMILARITY,
        );
        shaders.insert("holographic_bundle_all".to_string(), HOLOGRAPHIC_BUNDLE_ALL);
        shaders.insert(
            "holographic_resonator_step".to_string(),
            HOLOGRAPHIC_RESONATOR_STEP,
        );

        // Topology shaders
        shaders.insert(
            "topology_distance_matrix".to_string(),
            TOPOLOGY_DISTANCE_MATRIX,
        );
        shaders.insert(
            "topology_morse_critical".to_string(),
            TOPOLOGY_MORSE_CRITICAL,
        );
        shaders.insert(
            "topology_boundary_matrix".to_string(),
            TOPOLOGY_BOUNDARY_MATRIX,
        );
        shaders.insert(
            "topology_matrix_reduction".to_string(),
            TOPOLOGY_MATRIX_REDUCTION,
        );

        Self { shaders }
    }

    /// Get shader source by name
    pub fn get_shader(&self, name: &str) -> Option<&'static str> {
        self.shaders.get(name).copied()
    }

    /// List all available shaders
    pub fn list_shaders(&self) -> Vec<String> {
        self.shaders.keys().cloned().collect()
    }
}

impl Default for ShaderLibrary {
    fn default() -> Self {
        Self::new()
    }
}

/// Tropical algebra shader collection
pub const TROPICAL_SHADERS: &[(&str, &str)] = &[
    ("tropical_matrix_multiply", TROPICAL_MATRIX_MULTIPLY),
    ("tropical_vector_add", TROPICAL_VECTOR_ADD),
    ("tropical_neural_network", TROPICAL_NEURAL_NETWORK),
];

/// Dual number shader collection
pub const DUAL_SHADERS: &[(&str, &str)] = &[
    ("dual_forward_ad", DUAL_FORWARD_AD),
    ("dual_batch_gradient", DUAL_BATCH_GRADIENT),
    ("dual_chain_rule", DUAL_CHAIN_RULE),
];

/// Fusion system shader collection
pub const FUSION_SHADERS: &[(&str, &str)] = &[
    ("tropical_dual_clifford", TROPICAL_DUAL_CLIFFORD),
    ("fusion_attention", FUSION_ATTENTION),
];

/// Holographic memory shader collection
pub const HOLOGRAPHIC_SHADERS: &[(&str, &str)] = &[
    ("holographic_batch_bind", HOLOGRAPHIC_BATCH_BIND),
    ("holographic_batch_similarity", HOLOGRAPHIC_BATCH_SIMILARITY),
    ("holographic_bundle_all", HOLOGRAPHIC_BUNDLE_ALL),
    ("holographic_resonator_step", HOLOGRAPHIC_RESONATOR_STEP),
];

// =====================================================================
// TROPICAL ALGEBRA SHADERS
// =====================================================================

/// Tropical (max-plus) matrix multiplication: C = A ⊗ B where ⊗ is tropical product
const TROPICAL_MATRIX_MULTIPLY: &str = r#"
@group(0) @binding(0) var<storage, read> matrix_a: array<f32>;
@group(0) @binding(1) var<storage, read> matrix_b: array<f32>;
@group(0) @binding(2) var<storage, read_write> result: array<f32>;
@group(0) @binding(3) var<storage, read> dimensions: array<u32>; // [M, N, K]

@compute @workgroup_size(16, 16)
fn main(@builtin(global_invocation_id) global_id: vec3<u32>) {
    let M = dimensions[0];
    let N = dimensions[1];
    let K = dimensions[2];

    let row = global_id.x;
    let col = global_id.y;

    if (row >= M || col >= N) {
        return;
    }

    // Tropical matrix multiplication: (A ⊗ B)[i,j] = max_k(A[i,k] + B[k,j])
    var max_val = -3.4028235e+38; // -infinity in tropical algebra

    for (var k = 0u; k < K; k = k + 1u) {
        let a_val = matrix_a[row * K + k];
        let b_val = matrix_b[k * N + col];

        // Tropical multiplication: a ⊗ b = a + b
        let tropical_product = a_val + b_val;

        // Tropical addition: max operation
        if (tropical_product > max_val) {
            max_val = tropical_product;
        }
    }

    result[row * N + col] = max_val;
}
"#;

/// Tropical vector addition: c = a ⊕ b where ⊕ is max operation
const TROPICAL_VECTOR_ADD: &str = r#"
@group(0) @binding(0) var<storage, read> vector_a: array<f32>;
@group(0) @binding(1) var<storage, read> vector_b: array<f32>;
@group(0) @binding(2) var<storage, read_write> result: array<f32>;

@compute @workgroup_size(256)
fn main(@builtin(global_invocation_id) global_id: vec3<u32>) {
    let idx = global_id.x;

    if (idx >= arrayLength(&vector_a)) {
        return;
    }

    // Tropical addition: a ⊕ b = max(a, b)
    result[idx] = max(vector_a[idx], vector_b[idx]);
}
"#;

/// Tropical neural network layer computation
const TROPICAL_NEURAL_NETWORK: &str = r#"
@group(0) @binding(0) var<storage, read> input: array<f32>;
@group(0) @binding(1) var<storage, read> weights: array<f32>;
@group(0) @binding(2) var<storage, read> bias: array<f32>;
@group(0) @binding(3) var<storage, read_write> output: array<f32>;
@group(0) @binding(4) var<storage, read> dimensions: array<u32>; // [batch_size, input_size, output_size]

@compute @workgroup_size(16, 16)
fn main(@builtin(global_invocation_id) global_id: vec3<u32>) {
    let batch_idx = global_id.x;
    let output_idx = global_id.y;

    let batch_size = dimensions[0];
    let input_size = dimensions[1];
    let output_size = dimensions[2];

    if (batch_idx >= batch_size || output_idx >= output_size) {
        return;
    }

    // Tropical neural network: max-plus linear transformation
    var max_val = -3.4028235e+38; // -infinity

    for (var i = 0u; i < input_size; i = i + 1u) {
        let input_val = input[batch_idx * input_size + i];
        let weight_val = weights[i * output_size + output_idx];

        // Tropical multiplication: input ⊗ weight = input + weight
        let product = input_val + weight_val;

        // Tropical addition: max operation
        if (product > max_val) {
            max_val = product;
        }
    }

    // Add bias (tropical addition = max)
    let bias_val = bias[output_idx];
    let final_result = max(max_val, bias_val);

    output[batch_idx * output_size + output_idx] = final_result;
}
"#;

// =====================================================================
// DUAL NUMBER SHADERS (AUTOMATIC DIFFERENTIATION)
// =====================================================================

/// Forward-mode automatic differentiation for dual numbers
const DUAL_FORWARD_AD: &str = r#"
struct DualNumber {
    real: f32,
    dual: f32, // derivative part
}

@group(0) @binding(0) var<storage, read> input_dual: array<DualNumber>;
@group(0) @binding(1) var<storage, read> operation_params: array<f32>;
@group(0) @binding(2) var<storage, read_write> output_dual: array<DualNumber>;

@compute @workgroup_size(256)
fn main(@builtin(global_invocation_id) global_id: vec3<u32>) {
    let idx = global_id.x;

    if (idx >= arrayLength(&input_dual)) {
        return;
    }

    let x = input_dual[idx];
    let op_type = u32(operation_params[0]); // Operation type

    var result: DualNumber;

    // Forward-mode AD for different operations
    switch (op_type) {
        case 0u: { // sin(x): (sin(x), cos(x) * dx)
            result.real = sin(x.real);
            result.dual = cos(x.real) * x.dual;
        }
        case 1u: { // exp(x): (exp(x), exp(x) * dx)
            let exp_val = exp(x.real);
            result.real = exp_val;
            result.dual = exp_val * x.dual;
        }
        case 2u: { // x^2: (x^2, 2x * dx)
            result.real = x.real * x.real;
            result.dual = 2.0 * x.real * x.dual;
        }
        case 3u: { // log(x): (log(x), (1/x) * dx)
            result.real = log(x.real);
            result.dual = x.dual / x.real;
        }
        default: { // identity
            result = x;
        }
    }

    output_dual[idx] = result;
}
"#;

/// Batch gradient computation for multiple functions
const DUAL_BATCH_GRADIENT: &str = r#"
struct DualNumber {
    real: f32,
    dual: f32,
}

@group(0) @binding(0) var<storage, read> input_batch: array<DualNumber>;
@group(0) @binding(1) var<storage, read> function_params: array<f32>;
@group(0) @binding(2) var<storage, read_write> gradients: array<f32>;
@group(0) @binding(3) var<storage, read> batch_info: array<u32>; // [batch_size, function_dim]

@compute @workgroup_size(16, 16)
fn main(@builtin(global_invocation_id) global_id: vec3<u32>) {
    let batch_idx = global_id.x;
    let var_idx = global_id.y;

    let batch_size = batch_info[0];
    let function_dim = batch_info[1];

    if (batch_idx >= batch_size || var_idx >= function_dim) {
        return;
    }

    let input_idx = batch_idx * function_dim + var_idx;
    let x = input_batch[input_idx];

    // Compute gradient of composite function f(g(x)) where g is parameterized
    let param_idx = var_idx % 4u; // Assume up to 4 parameters per function
    let param = function_params[param_idx];

    // Example: f(x) = param * x^2 + sin(x), gradient = 2 * param * x + cos(x)
    let gradient = 2.0 * param * x.real + cos(x.real);

    gradients[input_idx] = gradient * x.dual;
}
"#;

/// Chain rule implementation for complex function compositions
const DUAL_CHAIN_RULE: &str = r#"
struct DualNumber {
    real: f32,
    dual: f32,
}

@group(0) @binding(0) var<storage, read> inner_function: array<DualNumber>;
@group(0) @binding(1) var<storage, read> outer_params: array<f32>;
@group(0) @binding(2) var<storage, read_write> composed_result: array<DualNumber>;

@compute @workgroup_size(256)
fn main(@builtin(global_invocation_id) global_id: vec3<u32>) {
    let idx = global_id.x;

    if (idx >= arrayLength(&inner_function)) {
        return;
    }

    let u = inner_function[idx]; // u = g(x), du/dx
    let outer_type = u32(outer_params[0]);

    var result: DualNumber;

    // Chain rule: d/dx[f(g(x))] = f'(g(x)) * g'(x) = f'(u) * du/dx
    switch (outer_type) {
        case 0u: { // f(u) = sin(u)
            result.real = sin(u.real);
            result.dual = cos(u.real) * u.dual; // cos(u) * du/dx
        }
        case 1u: { // f(u) = u^3
            result.real = u.real * u.real * u.real;
            result.dual = 3.0 * u.real * u.real * u.dual; // 3u^2 * du/dx
        }
        case 2u: { // f(u) = exp(u)
            let exp_u = exp(u.real);
            result.real = exp_u;
            result.dual = exp_u * u.dual; // exp(u) * du/dx
        }
        default: { // f(u) = u (identity)
            result = u;
        }
    }

    composed_result[idx] = result;
}
"#;

// =====================================================================
// FUSION SYSTEM SHADERS
// =====================================================================

/// TropicalDualClifford operations for LLM evaluation
const TROPICAL_DUAL_CLIFFORD: &str = r#"
struct TropicalNumber {
    value: f32, // Tropical number value
}

struct DualNumber {
    real: f32,
    dual: f32,
}

struct Multivector {
    coeffs: array<f32, 8>, // 3D Clifford algebra: 8 basis elements
}

struct TropicalDualClifford {
    tropical: TropicalNumber,
    dual: DualNumber,
    clifford: Multivector,
}

@group(0) @binding(0) var<storage, read> input_batch: array<TropicalDualClifford>;
@group(0) @binding(1) var<storage, read> operation_params: array<f32>;
@group(0) @binding(2) var<storage, read_write> output_batch: array<TropicalDualClifford>;

@compute @workgroup_size(64)
fn main(@builtin(global_invocation_id) global_id: vec3<u32>) {
    let idx = global_id.x;

    if (idx >= arrayLength(&input_batch)) {
        return;
    }

    let tdc = input_batch[idx];
    let op_type = u32(operation_params[0]);

    var result: TropicalDualClifford;

    switch (op_type) {
        case 0u: { // LLM attention computation
            // Combine tropical path selection with dual gradients and geometric transformations
            result.tropical.value = max(tdc.tropical.value, operation_params[1]);
            result.dual.real = tdc.dual.real * operation_params[2];
            result.dual.dual = tdc.dual.dual * operation_params[2];

            // Geometric rotation in Clifford algebra
            let angle = operation_params[3];
            let cos_half = cos(angle * 0.5);
            let sin_half = sin(angle * 0.5);

            // Simple rotation around e12 plane
            result.clifford.coeffs[0] = cos_half * tdc.clifford.coeffs[0]; // scalar
            result.clifford.coeffs[1] = tdc.clifford.coeffs[1]; // e1
            result.clifford.coeffs[2] = tdc.clifford.coeffs[2]; // e2
            result.clifford.coeffs[3] = tdc.clifford.coeffs[3]; // e3
            result.clifford.coeffs[4] = sin_half * tdc.clifford.coeffs[0]; // e12
            result.clifford.coeffs[5] = tdc.clifford.coeffs[5]; // e13
            result.clifford.coeffs[6] = tdc.clifford.coeffs[6]; // e23
            result.clifford.coeffs[7] = tdc.clifford.coeffs[7]; // e123
        }
        default: {
            result = tdc;
        }
    }

    output_batch[idx] = result;
}
"#;

/// Fusion attention mechanism using tropical algebra
const FUSION_ATTENTION: &str = r#"
@group(0) @binding(0) var<storage, read> queries: array<f32>;
@group(0) @binding(1) var<storage, read> keys: array<f32>;
@group(0) @binding(2) var<storage, read> values: array<f32>;
@group(0) @binding(3) var<storage, read_write> attention_output: array<f32>;
@group(0) @binding(4) var<storage, read> dimensions: array<u32>; // [seq_len, d_model]

@compute @workgroup_size(16, 16)
fn main(@builtin(global_invocation_id) global_id: vec3<u32>) {
    let seq_pos = global_id.x;
    let feature_idx = global_id.y;

    let seq_len = dimensions[0];
    let d_model = dimensions[1];

    if (seq_pos >= seq_len || feature_idx >= d_model) {
        return;
    }

    // Tropical attention: use max-plus algebra instead of softmax
    var max_score = -3.4028235e+38; // -infinity
    var best_key_idx = 0u;

    // Find the key with maximum tropical attention score
    for (var key_idx = 0u; key_idx < seq_len; key_idx = key_idx + 1u) {
        var score = -3.4028235e+38;

        // Compute tropical dot product: sum becomes max, product becomes sum
        for (var d = 0u; d < d_model; d = d + 1u) {
            let q = queries[seq_pos * d_model + d];
            let k = keys[key_idx * d_model + d];

            // Tropical multiplication: q ⊗ k = q + k
            let tropical_product = q + k;

            // Tropical sum: max operation
            if (tropical_product > score) {
                score = tropical_product;
            }
        }

        if (score > max_score) {
            max_score = score;
            best_key_idx = key_idx;
        }
    }

    // Tropical attention: select value from best key (winner-takes-all)
    attention_output[seq_pos * d_model + feature_idx] =
        values[best_key_idx * d_model + feature_idx];
}
"#;

// =====================================================================
// HOLOGRAPHIC MEMORY SHADERS
// =====================================================================

/// Batch binding operation for holographic memory
/// Computes key ⊛ value for multiple pairs using Clifford geometric product
pub const HOLOGRAPHIC_BATCH_BIND: &str = r#"
// TropicalDualClifford representation for GPU
// We use a simplified 8-dimensional Clifford representation
struct TDC {
    // Tropical component (max element)
    tropical: f32,
    // Dual component (real and dual parts)
    dual_real: f32,
    dual_dual: f32,
    // Clifford algebra coefficients (8D: scalar, 3 vectors, 3 bivectors, pseudoscalar)
    clifford: array<f32, 8>,
    // Padding for alignment
    _padding: array<f32, 5>,
}

@group(0) @binding(0) var<storage, read> keys: array<TDC>;
@group(0) @binding(1) var<storage, read> values: array<TDC>;
@group(0) @binding(2) var<storage, read_write> results: array<TDC>;
@group(0) @binding(3) var<uniform> params: vec4<u32>; // [count, 0, 0, 0]

// Storage order is [1, e1, e2, e3, e12, e13, e23, e123].
// Convert to/from bitmask order for Euclidean Cl(3,0):
// scalar=0, e1=1, e2=2, e12=3, e3=4, e13=5, e23=6, e123=7.
fn storage_to_mask(idx: u32) -> u32 {
    switch idx {
        case 0u: { return 0u; }
        case 1u: { return 1u; }
        case 2u: { return 2u; }
        case 3u: { return 4u; }
        case 4u: { return 3u; }
        case 5u: { return 5u; }
        case 6u: { return 6u; }
        default: { return 7u; }
    }
}

fn mask_to_storage(mask: u32) -> u32 {
    switch mask {
        case 0u: { return 0u; }
        case 1u: { return 1u; }
        case 2u: { return 2u; }
        case 3u: { return 4u; }
        case 4u: { return 3u; }
        case 5u: { return 5u; }
        case 6u: { return 6u; }
        default: { return 7u; }
    }
}

fn blade_product_sign(storage_i: u32, storage_j: u32) -> f32 {
    let a = storage_to_mask(storage_i);
    let b = storage_to_mask(storage_j);
    var swaps = 0u;

    for (var bit = 0u; bit < 3u; bit = bit + 1u) {
        if (((a >> bit) & 1u) == 1u) {
            let lower_mask = (1u << bit) - 1u;
            swaps = swaps + countOneBits(b & lower_mask);
        }
    }

    if ((swaps & 1u) == 0u) {
        return 1.0;
    }
    return -1.0;
}

fn blade_product_index(storage_i: u32, storage_j: u32) -> u32 {
    let a = storage_to_mask(storage_i);
    let b = storage_to_mask(storage_j);
    return mask_to_storage(a ^ b);
}

fn read_clifford(v: TDC, idx: u32) -> f32 {
    switch idx {
        case 0u: { return v.clifford[0]; }
        case 1u: { return v.clifford[1]; }
        case 2u: { return v.clifford[2]; }
        case 3u: { return v.clifford[3]; }
        case 4u: { return v.clifford[4]; }
        case 5u: { return v.clifford[5]; }
        case 6u: { return v.clifford[6]; }
        default: { return v.clifford[7]; }
    }
}

fn add_clifford(result_ptr: ptr<function, TDC>, idx: u32, value: f32) {
    switch idx {
        case 0u: { (*result_ptr).clifford[0] = (*result_ptr).clifford[0] + value; }
        case 1u: { (*result_ptr).clifford[1] = (*result_ptr).clifford[1] + value; }
        case 2u: { (*result_ptr).clifford[2] = (*result_ptr).clifford[2] + value; }
        case 3u: { (*result_ptr).clifford[3] = (*result_ptr).clifford[3] + value; }
        case 4u: { (*result_ptr).clifford[4] = (*result_ptr).clifford[4] + value; }
        case 5u: { (*result_ptr).clifford[5] = (*result_ptr).clifford[5] + value; }
        case 6u: { (*result_ptr).clifford[6] = (*result_ptr).clifford[6] + value; }
        default: { (*result_ptr).clifford[7] = (*result_ptr).clifford[7] + value; }
    }
}

@compute @workgroup_size(64)
fn main(@builtin(global_invocation_id) global_id: vec3<u32>) {
    let idx = global_id.x;
    let count = params[0];

    if (idx >= count) {
        return;
    }

    let key = keys[idx];
    let value = values[idx];

    var result: TDC;

    // Binding uses geometric product on Clifford components
    // result = key * value (geometric product)
    result.clifford[0] = 0.0;
    result.clifford[1] = 0.0;
    result.clifford[2] = 0.0;
    result.clifford[3] = 0.0;
    result.clifford[4] = 0.0;
    result.clifford[5] = 0.0;
    result.clifford[6] = 0.0;
    result.clifford[7] = 0.0;

    for (var i = 0u; i < 8u; i = i + 1u) {
        for (var j = 0u; j < 8u; j = j + 1u) {
            let target_idx = blade_product_index(i, j);
            let sign = blade_product_sign(i, j);
            let contribution = sign * read_clifford(key, i) * read_clifford(value, j);
            add_clifford(&result, target_idx, contribution);
        }
    }

    // Tropical: max of both (binding produces new tropical value)
    result.tropical = max(key.tropical, value.tropical);

    // Dual: product rule for dual numbers
    result.dual_real = key.dual_real * value.dual_real;
    result.dual_dual = key.dual_real * value.dual_dual + key.dual_dual * value.dual_real;

    results[idx] = result;
}
"#;

/// Batch similarity computation for holographic vectors
/// Computes pairwise similarities using inner product with reverse: <A B̃>₀
pub const HOLOGRAPHIC_BATCH_SIMILARITY: &str = r#"
struct TDC {
    tropical: f32,
    dual_real: f32,
    dual_dual: f32,
    clifford: array<f32, 8>,
    _padding: array<f32, 5>,
}

@group(0) @binding(0) var<storage, read> vectors_a: array<TDC>;
@group(0) @binding(1) var<storage, read> vectors_b: array<TDC>;
@group(0) @binding(2) var<storage, read_write> similarities: array<f32>;
@group(0) @binding(3) var<uniform> params: vec4<u32>; // [count_a, count_b, mode, 0]
                                                          // mode: 0=pairwise (a[i] vs b[i]), 1=matrix (all pairs)

// Compute reverse of multivector (flip sign of grades 2 and 3)
fn reverse_sign(grade: u32) -> f32 {
    switch grade {
        case 0u, 1u, 2u, 3u: { return 1.0; }
        default: { return -1.0; }
    }
}

// Compute scalar product <A B̃>₀ - the proper inner product for similarity
fn scalar_product_with_reverse(a: TDC, b: TDC) -> f32 {
    return a.clifford[0] * b.clifford[0] * reverse_sign(0u)
         + a.clifford[1] * b.clifford[1] * reverse_sign(1u)
         + a.clifford[2] * b.clifford[2] * reverse_sign(2u)
         + a.clifford[3] * b.clifford[3] * reverse_sign(3u)
         + a.clifford[4] * b.clifford[4] * reverse_sign(4u)
         + a.clifford[5] * b.clifford[5] * reverse_sign(5u)
         + a.clifford[6] * b.clifford[6] * reverse_sign(6u)
         + a.clifford[7] * b.clifford[7] * reverse_sign(7u);
}

fn norm(v: TDC) -> f32 {
    let sum = v.clifford[0] * v.clifford[0]
            + v.clifford[1] * v.clifford[1]
            + v.clifford[2] * v.clifford[2]
            + v.clifford[3] * v.clifford[3]
            + v.clifford[4] * v.clifford[4]
            + v.clifford[5] * v.clifford[5]
            + v.clifford[6] * v.clifford[6]
            + v.clifford[7] * v.clifford[7];
    return sqrt(sum);
}

@compute @workgroup_size(256)
fn main(@builtin(global_invocation_id) global_id: vec3<u32>) {
    let idx = global_id.x;
    let count_a = params[0];
    let count_b = params[1];
    let mode = params[2];

    if (mode == 0u) {
        // Pairwise mode: similarities[i] = sim(a[i], b[i])
        if (idx >= count_a) {
            return;
        }

        let a = vectors_a[idx];
        let b = vectors_b[idx];

        let norm_a = norm(a);
        let norm_b = norm(b);

        if (norm_a < 1e-10 || norm_b < 1e-10) {
            similarities[idx] = 0.0;
            return;
        }

        let inner = scalar_product_with_reverse(a, b);
        similarities[idx] = inner / (norm_a * norm_b);
    } else {
        // Matrix mode: similarities[i * count_b + j] = sim(a[i], b[j])
        let total = count_a * count_b;
        if (idx >= total) {
            return;
        }

        let i = idx / count_b;
        let j = idx % count_b;

        let a = vectors_a[i];
        let b = vectors_b[j];

        let norm_a = norm(a);
        let norm_b = norm(b);

        if (norm_a < 1e-10 || norm_b < 1e-10) {
            similarities[idx] = 0.0;
            return;
        }

        let inner = scalar_product_with_reverse(a, b);
        similarities[idx] = inner / (norm_a * norm_b);
    }
}
"#;

/// Bundle all vectors into a superposition (weighted average)
pub const HOLOGRAPHIC_BUNDLE_ALL: &str = r#"
struct TDC {
    tropical: f32,
    dual_real: f32,
    dual_dual: f32,
    clifford: array<f32, 8>,
    _padding: array<f32, 5>,
}

@group(0) @binding(0) var<storage, read> vectors: array<TDC>;
@group(0) @binding(1) var<storage, read_write> result: array<TDC>; // Single output
@group(0) @binding(2) var<uniform> params: vec4<f32>; // [count, beta, normalize, 0]

// Workgroup shared memory for parallel reduction
var<workgroup> shared_clifford: array<array<f32, 8>, 64>;
var<workgroup> shared_tropical: array<f32, 64>;
var<workgroup> shared_dual_real: array<f32, 64>;
var<workgroup> shared_dual_dual: array<f32, 64>;

@compute @workgroup_size(64)
fn main(
    @builtin(global_invocation_id) global_id: vec3<u32>,
    @builtin(local_invocation_id) local_id: vec3<u32>,
    @builtin(workgroup_id) workgroup_id: vec3<u32>
) {
    let idx = global_id.x;
    let local_idx = local_id.x;
    let count = u32(params.x);
    let beta = params.y;
    let do_normalize = params.z > 0.5;

    // Initialize shared memory
    for (var i = 0u; i < 8u; i = i + 1u) {
        shared_clifford[local_idx][i] = 0.0;
    }
    shared_tropical[local_idx] = -3.4028235e+38; // -inf for tropical
    shared_dual_real[local_idx] = 0.0;
    shared_dual_dual[local_idx] = 0.0;

    // Load data into shared memory
    if (idx < count) {
        let v = vectors[idx];
        for (var i = 0u; i < 8u; i = i + 1u) {
            shared_clifford[local_idx][i] = v.clifford[i];
        }
        shared_tropical[local_idx] = v.tropical;
        shared_dual_real[local_idx] = v.dual_real;
        shared_dual_dual[local_idx] = v.dual_dual;
    }

    workgroupBarrier();

    // Parallel reduction
    for (var stride = 32u; stride > 0u; stride = stride / 2u) {
        if (local_idx < stride && local_idx + stride < 64u) {
            // Bundle Clifford components (sum/average)
            for (var i = 0u; i < 8u; i = i + 1u) {
                shared_clifford[local_idx][i] += shared_clifford[local_idx + stride][i];
            }
            // Tropical: take max
            shared_tropical[local_idx] = max(shared_tropical[local_idx], shared_tropical[local_idx + stride]);
            // Dual: sum
            shared_dual_real[local_idx] += shared_dual_real[local_idx + stride];
            shared_dual_dual[local_idx] += shared_dual_dual[local_idx + stride];
        }
        workgroupBarrier();
    }

    // Thread 0 writes result
    if (local_idx == 0u) {
        var final_result: TDC;

        // Average the Clifford components
        let scale = 1.0 / f32(count);
        for (var i = 0u; i < 8u; i = i + 1u) {
            final_result.clifford[i] = shared_clifford[0][i] * scale;
        }

        final_result.tropical = shared_tropical[0];
        final_result.dual_real = shared_dual_real[0] * scale;
        final_result.dual_dual = shared_dual_dual[0] * scale;

        // Optionally normalize
        if (do_normalize) {
            var norm_sq = 0.0;
            for (var i = 0u; i < 8u; i = i + 1u) {
                norm_sq += final_result.clifford[i] * final_result.clifford[i];
            }
            let norm = sqrt(norm_sq);
            if (norm > 1e-10) {
                let inv_norm = 1.0 / norm;
                for (var i = 0u; i < 8u; i = i + 1u) {
                    final_result.clifford[i] *= inv_norm;
                }
            }
        }

        result[workgroup_id.x] = final_result;
    }
}
"#;

/// Resonator cleanup step - computes similarities against codebook
pub const HOLOGRAPHIC_RESONATOR_STEP: &str = r#"
struct TDC {
    tropical: f32,
    dual_real: f32,
    dual_dual: f32,
    clifford: array<f32, 8>,
    _padding: array<f32, 5>,
}

struct ResonatorOutput {
    cleaned: TDC,
    best_index: u32,
    best_similarity: f32,
    _padding: array<f32, 2>,
}

@group(0) @binding(0) var<storage, read> input: TDC;
@group(0) @binding(1) var<storage, read> codebook: array<TDC>;
@group(0) @binding(2) var<storage, read_write> output: ResonatorOutput;
@group(0) @binding(3) var<uniform> params: vec4<u32>; // [codebook_size, max_iterations, 0, 0]

fn reverse_sign(grade: u32) -> f32 {
    switch grade {
        case 0u, 1u, 2u, 3u: { return 1.0; }
        default: { return -1.0; }
    }
}

fn scalar_product_with_reverse(a: TDC, b: TDC) -> f32 {
    return a.clifford[0] * b.clifford[0] * reverse_sign(0u)
         + a.clifford[1] * b.clifford[1] * reverse_sign(1u)
         + a.clifford[2] * b.clifford[2] * reverse_sign(2u)
         + a.clifford[3] * b.clifford[3] * reverse_sign(3u)
         + a.clifford[4] * b.clifford[4] * reverse_sign(4u)
         + a.clifford[5] * b.clifford[5] * reverse_sign(5u)
         + a.clifford[6] * b.clifford[6] * reverse_sign(6u)
         + a.clifford[7] * b.clifford[7] * reverse_sign(7u);
}

fn norm(v: TDC) -> f32 {
    let sum = v.clifford[0] * v.clifford[0]
            + v.clifford[1] * v.clifford[1]
            + v.clifford[2] * v.clifford[2]
            + v.clifford[3] * v.clifford[3]
            + v.clifford[4] * v.clifford[4]
            + v.clifford[5] * v.clifford[5]
            + v.clifford[6] * v.clifford[6]
            + v.clifford[7] * v.clifford[7];
    return sqrt(sum);
}

fn similarity(a: TDC, b: TDC) -> f32 {
    let norm_a = norm(a);
    let norm_b = norm(b);
    if (norm_a < 1e-10 || norm_b < 1e-10) {
        return 0.0;
    }
    return scalar_product_with_reverse(a, b) / (norm_a * norm_b);
}

// Workgroup shared memory for parallel max finding
var<workgroup> shared_best_sim: array<f32, 256>;
var<workgroup> shared_best_idx: array<u32, 256>;

@compute @workgroup_size(256)
fn main(
    @builtin(global_invocation_id) global_id: vec3<u32>,
    @builtin(local_invocation_id) local_id: vec3<u32>
) {
    let idx = global_id.x;
    let local_idx = local_id.x;
    let codebook_size = params[0];

    // Initialize
    shared_best_sim[local_idx] = -2.0; // Below minimum similarity
    shared_best_idx[local_idx] = 0u;

    // Each thread computes similarity for one codebook entry
    if (idx < codebook_size) {
        let sim = similarity(input, codebook[idx]);
        shared_best_sim[local_idx] = sim;
        shared_best_idx[local_idx] = idx;
    }

    workgroupBarrier();

    // Parallel reduction to find max
    for (var stride = 128u; stride > 0u; stride = stride / 2u) {
        if (local_idx < stride && local_idx + stride < 256u) {
            if (shared_best_sim[local_idx + stride] > shared_best_sim[local_idx]) {
                shared_best_sim[local_idx] = shared_best_sim[local_idx + stride];
                shared_best_idx[local_idx] = shared_best_idx[local_idx + stride];
            }
        }
        workgroupBarrier();
    }

    // Thread 0 writes result
    if (local_idx == 0u) {
        let best_idx = shared_best_idx[0];
        output.cleaned = codebook[best_idx];
        output.best_index = best_idx;
        output.best_similarity = shared_best_sim[0];
    }
}
"#;

// =====================================================================
// INFORMATION GEOMETRY SHADERS
// =====================================================================

/// Fisher information matrix computation
const FISHER_INFORMATION: &str = r#"
@group(0) @binding(0) var<storage, read> probability_params: array<f32>;
@group(0) @binding(1) var<storage, read> data_points: array<f32>;
@group(0) @binding(2) var<storage, read_write> fisher_matrix: array<f32>;
@group(0) @binding(3) var<storage, read> dimensions: array<u32>; // [n_params, n_data]

@compute @workgroup_size(16, 16)
fn main(@builtin(global_invocation_id) global_id: vec3<u32>) {
    let param_i = global_id.x;
    let param_j = global_id.y;

    let n_params = dimensions[0];
    let n_data = dimensions[1];

    if (param_i >= n_params || param_j >= n_params) {
        return;
    }

    // Fisher Information Matrix: I[i,j] = E[∂²log p(x|θ)/∂θᵢ∂θⱼ]
    var fisher_element = 0.0;

    for (var data_idx = 0u; data_idx < n_data; data_idx = data_idx + 1u) {
        let x = data_points[data_idx];

        // Gaussian log-likelihood example: log p(x|μ,σ) = -½log(2πσ²) - (x-μ)²/(2σ²)
        let mu = probability_params[0];
        let sigma = probability_params[1];
        let sigma_sq = sigma * sigma;

        var d2_log_p = 0.0;

        if (param_i == 0u && param_j == 0u) { // ∂²/∂μ²
            d2_log_p = -1.0 / sigma_sq;
        } else if (param_i == 1u && param_j == 1u) { // ∂²/∂σ²
            let diff = x - mu;
            d2_log_p = -1.0 / sigma_sq + 3.0 * diff * diff / (sigma_sq * sigma_sq);
        } else if ((param_i == 0u && param_j == 1u) || (param_i == 1u && param_j == 0u)) { // ∂²/∂μ∂σ
            let diff = x - mu;
            d2_log_p = 2.0 * diff / (sigma_sq * sigma);
        }

        fisher_element += -d2_log_p; // Fisher = -E[Hessian of log-likelihood]
    }

    fisher_matrix[param_i * n_params + param_j] = fisher_element / f32(n_data);
}
"#;

/// Batch KL divergence computation
const KL_DIVERGENCE_BATCH: &str = r#"
@group(0) @binding(0) var<storage, read> distribution_p: array<f32>;
@group(0) @binding(1) var<storage, read> distribution_q: array<f32>;
@group(0) @binding(2) var<storage, read_write> kl_divergences: array<f32>;
@group(0) @binding(3) var<storage, read> batch_info: array<u32>; // [batch_size, dist_size]

@compute @workgroup_size(256)
fn main(@builtin(global_invocation_id) global_id: vec3<u32>) {
    let batch_idx = global_id.x;
    let batch_size = batch_info[0];
    let dist_size = batch_info[1];

    if (batch_idx >= batch_size) {
        return;
    }

    // KL divergence: D_KL(P||Q) = Σ P(x) log(P(x)/Q(x))
    var kl_div = 0.0;

    for (var i = 0u; i < dist_size; i = i + 1u) {
        let p_i = distribution_p[batch_idx * dist_size + i];
        let q_i = distribution_q[batch_idx * dist_size + i];

        if (p_i > 1e-10 && q_i > 1e-10) { // Avoid log(0)
            kl_div += p_i * log(p_i / q_i);
        }
    }

    kl_divergences[batch_idx] = kl_div;
}
"#;

// =====================================================================
// CELLULAR AUTOMATA SHADERS
// =====================================================================

/// Cellular automata evolution step
pub const CA_EVOLUTION: &str = r#"
@group(0) @binding(0) var<storage, read> current_state: array<u32>;
@group(0) @binding(1) var<storage, read_write> next_state: array<u32>;
@group(0) @binding(2) var<storage, read> rules: array<u32>;
@group(0) @binding(3) var<storage, read> dimensions: array<u32>; // [width, height]

@compute @workgroup_size(16, 16)
fn main(@builtin(global_invocation_id) global_id: vec3<u32>) {
    let x = global_id.x;
    let y = global_id.y;

    let width = dimensions[0];
    let height = dimensions[1];

    if (x >= width || y >= height) {
        return;
    }

    let idx = y * width + x;
    let current_cell = current_state[idx];

    // Count alive neighbors (Moore neighborhood)
    var alive_neighbors = 0u;

    for (var dy = 0u; dy < 3u; dy = dy + 1u) {
        for (var dx = 0u; dx < 3u; dx = dx + 1u) {
            if (dx == 1u && dy == 1u) { continue; } // Skip center cell

            let nx = (x + dx + width - 1u) % width; // Wrap around
            let ny = (y + dy + height - 1u) % height;
            let neighbor_idx = ny * width + nx;

            if (current_state[neighbor_idx] == 1u) {
                alive_neighbors = alive_neighbors + 1u;
            }
        }
    }

    // Conway's Game of Life rules (can be customized via rules buffer)
    var new_state = 0u;

    if (current_cell == 1u) { // Currently alive
        if (alive_neighbors == 2u || alive_neighbors == 3u) {
            new_state = 1u; // Survive
        }
    } else { // Currently dead
        if (alive_neighbors == 3u) {
            new_state = 1u; // Birth
        }
    }

    next_state[idx] = new_state;
}
"#;

/// Rule application for geometric algebra cellular automata
pub const RULE_APPLICATION: &str = r#"
struct GpuCellData {
    scalar: f32,
    e1: f32,
    e2: f32,
    e3: f32,
    e12: f32,
    e13: f32,
    e23: f32,
    e123: f32,
    generation: f32,
    neighborhood_size: f32,
    rule_type: f32,
    boundary_condition: f32,
    padding: array<f32, 4>,
}

struct GpuRuleConfig {
    rule_type: f32,
    threshold: f32,
    damping_factor: f32,
    energy_conservation: f32,
    time_step: f32,
    spatial_scale: f32,
    geometric_weight: f32,
    nonlinear_factor: f32,
    boundary_type: f32,
    neighborhood_radius: f32,
    evolution_speed: f32,
    stability_factor: f32,
    padding: array<f32, 4>,
}

@group(0) @binding(0) var<storage, read> cells: array<GpuCellData>;
@group(0) @binding(1) var<storage, read> rules: array<GpuRuleConfig>;
@group(0) @binding(2) var<storage, read_write> output: array<GpuCellData>;

@compute @workgroup_size(256)
fn rule_application_main(@builtin(global_invocation_id) global_id: vec3<u32>) {
    let idx = global_id.x;

    if (idx >= arrayLength(&cells)) {
        return;
    }

    let cell = cells[idx];
    let rule = rules[0]; // Use first rule for now

    var new_cell = cell;

    // Apply damping factor
    new_cell.scalar = cell.scalar * (1.0 - rule.damping_factor);
    new_cell.e1 = cell.e1 * (1.0 - rule.damping_factor);
    new_cell.e2 = cell.e2 * (1.0 - rule.damping_factor);
    new_cell.e3 = cell.e3 * (1.0 - rule.damping_factor);
    new_cell.e12 = cell.e12 * (1.0 - rule.damping_factor);
    new_cell.e13 = cell.e13 * (1.0 - rule.damping_factor);
    new_cell.e23 = cell.e23 * (1.0 - rule.damping_factor);
    new_cell.e123 = cell.e123 * (1.0 - rule.damping_factor);

    // Apply threshold
    if (abs(new_cell.scalar) < rule.threshold) {
        new_cell.scalar = 0.0;
    }

    output[idx] = new_cell;
}
"#;

/// Energy calculation for cellular automata
pub const ENERGY_CALCULATION: &str = r#"
struct GpuCellData {
    scalar: f32,
    e1: f32,
    e2: f32,
    e3: f32,
    e12: f32,
    e13: f32,
    e23: f32,
    e123: f32,
    generation: f32,
    neighborhood_size: f32,
    rule_type: f32,
    boundary_condition: f32,
    padding: array<f32, 4>,
}

@group(0) @binding(0) var<storage, read> cells: array<GpuCellData>;
@group(0) @binding(1) var<storage, read_write> total_energy: array<f32>;

@compute @workgroup_size(1)
fn energy_calculation_main(@builtin(global_invocation_id) global_id: vec3<u32>) {
    var energy = 0.0;

    // Sum the squared magnitudes of all multivector components
    for (var i = 0u; i < arrayLength(&cells); i = i + 1u) {
        let cell = cells[i];
        energy += cell.scalar * cell.scalar;
        energy += cell.e1 * cell.e1;
        energy += cell.e2 * cell.e2;
        energy += cell.e3 * cell.e3;
        energy += cell.e12 * cell.e12;
        energy += cell.e13 * cell.e13;
        energy += cell.e23 * cell.e23;
        energy += cell.e123 * cell.e123;
    }

    total_energy[0] = energy;
}
"#;

/// Neighbor extraction for cellular automata
pub const NEIGHBOR_EXTRACTION: &str = r#"
struct GpuCellData {
    scalar: f32,
    e1: f32,
    e2: f32,
    e3: f32,
    e12: f32,
    e13: f32,
    e23: f32,
    e123: f32,
    generation: f32,
    neighborhood_size: f32,
    rule_type: f32,
    boundary_condition: f32,
    padding: array<f32, 4>,
}

@group(0) @binding(0) var<storage, read> cells: array<GpuCellData>;
@group(0) @binding(1) var<uniform> params: array<f32, 4>; // [width, height, total_cells, padding]
@group(0) @binding(2) var<storage, read_write> neighborhoods: array<GpuCellData>;

@compute @workgroup_size(256)
fn neighbor_extraction_main(@builtin(global_invocation_id) global_id: vec3<u32>) {
    let idx = global_id.x;
    let width = u32(params[0]);
    let height = u32(params[1]);
    let total_cells = u32(params[2]);

    if (idx >= total_cells) {
        return;
    }

    // Calculate 2D position from linear index
    let x = idx % width;
    let y = idx / width;

    // Moore neighborhood: 8 neighbors
    let offsets = array<vec2<i32>, 8>(
        vec2<i32>(-1, -1), vec2<i32>(0, -1), vec2<i32>(1, -1),
        vec2<i32>(-1,  0),                   vec2<i32>(1,  0),
        vec2<i32>(-1,  1), vec2<i32>(0,  1), vec2<i32>(1,  1)
    );

    // Extract neighbors with wrapping boundaries
    for (var i = 0u; i < 8u; i = i + 1u) {
        let offset = offsets[i];
        let nx = (i32(x) + offset.x + i32(width)) % i32(width);
        let ny = (i32(y) + offset.y + i32(height)) % i32(height);
        let neighbor_idx = u32(ny) * width + u32(nx);

        // Store neighbor in output array
        neighborhoods[idx * 8u + i] = cells[neighbor_idx];
    }
}
"#;

/// Self-assembly pattern formation
const CA_SELF_ASSEMBLY: &str = r#"
@group(0) @binding(0) var<storage, read> particles: array<f32>; // [x, y, type, energy]
@group(0) @binding(1) var<storage, read_write> new_particles: array<f32>;
@group(0) @binding(2) var<storage, read> assembly_rules: array<f32>;
@group(0) @binding(3) var<storage, read> simulation_params: array<u32>; // [n_particles, grid_size]

@compute @workgroup_size(64)
fn main(@builtin(global_invocation_id) global_id: vec3<u32>) {
    let particle_idx = global_id.x;
    let n_particles = simulation_params[0];
    let grid_size = simulation_params[1];

    if (particle_idx >= n_particles) {
        return;
    }

    let base_idx = particle_idx * 4u;
    let x = particles[base_idx];
    let y = particles[base_idx + 1u];
    let particle_type = particles[base_idx + 2u];
    let energy = particles[base_idx + 3u];

    // Self-assembly based on local interactions
    var new_x = x;
    var new_y = y;
    var new_energy = energy;

    // Calculate forces from nearby particles
    var force_x = 0.0;
    var force_y = 0.0;

    for (var other_idx = 0u; other_idx < n_particles; other_idx = other_idx + 1u) {
        if (other_idx == particle_idx) { continue; }

        let other_base = other_idx * 4u;
        let other_x = particles[other_base];
        let other_y = particles[other_base + 1u];
        let other_type = particles[other_base + 2u];

        let dx = other_x - x;
        let dy = other_y - y;
        let distance = sqrt(dx * dx + dy * dy);

        if (distance < 5.0 && distance > 0.1) { // Interaction range
            let interaction_strength = assembly_rules[u32(particle_type) * 4u + u32(other_type)];

            // Attractive/repulsive force based on particle types
            let force_magnitude = interaction_strength / (distance * distance);
            force_x += force_magnitude * dx / distance;
            force_y += force_magnitude * dy / distance;
        }
    }

    // Update position based on forces
    new_x += force_x * 0.1; // time step
    new_y += force_y * 0.1;

    // Keep within bounds
    new_x = clamp(new_x, 0.0, f32(grid_size));
    new_y = clamp(new_y, 0.0, f32(grid_size));

    // Energy dissipation
    new_energy = energy * 0.99;

    new_particles[base_idx] = new_x;
    new_particles[base_idx + 1u] = new_y;
    new_particles[base_idx + 2u] = particle_type;
    new_particles[base_idx + 3u] = new_energy;
}
"#;

// =====================================================================
// ENUMERATIVE GEOMETRY SHADERS
// =====================================================================

/// Intersection theory computations
pub const INTERSECTION_THEORY: &str = r#"
struct RationalNumber {
    numerator: i32,
    denominator: i32,
}

@group(0) @binding(0) var<storage, read> chow_class_a: array<RationalNumber>;
@group(0) @binding(1) var<storage, read> chow_class_b: array<RationalNumber>;
@group(0) @binding(2) var<storage, read_write> intersection_result: array<RationalNumber>;
@group(0) @binding(3) var<storage, read> geometry_params: array<u32>; // [dimension, degree_a, degree_b]

fn gcd(a: u32, b: u32) -> u32 {
    if (b == 0u) { return a; }
    return gcd(b, a % b);
}

fn add_rationals(a: RationalNumber, b: RationalNumber) -> RationalNumber {
    let num = a.numerator * b.denominator + b.numerator * a.denominator;
    let den = a.denominator * b.denominator;
    let g = gcd(u32(abs(num)), u32(abs(den)));

    return RationalNumber(num / i32(g), den / i32(g));
}

fn multiply_rationals(a: RationalNumber, b: RationalNumber) -> RationalNumber {
    let num = a.numerator * b.numerator;
    let den = a.denominator * b.denominator;
    let g = gcd(u32(abs(num)), u32(abs(den)));

    return RationalNumber(num / i32(g), den / i32(g));
}

@compute @workgroup_size(256)
fn main(@builtin(global_invocation_id) global_id: vec3<u32>) {
    let idx = global_id.x;

    if (idx >= arrayLength(&chow_class_a)) {
        return;
    }

    let dimension = geometry_params[0];
    let degree_a = geometry_params[1];
    let degree_b = geometry_params[2];

    // Intersection product in Chow ring: A · B
    // For simplicity, implement as pointwise multiplication for this example
    let a = chow_class_a[idx];
    let b = chow_class_b[idx];

    // Check degree compatibility (degree_a + degree_b ≤ dimension)
    if (degree_a + degree_b <= dimension) {
        intersection_result[idx] = multiply_rationals(a, b);
    } else {
        intersection_result[idx] = RationalNumber(0, 1); // Zero class
    }
}
"#;

/// Schubert calculus computations
const SCHUBERT_CALCULUS: &str = r#"
@group(0) @binding(0) var<storage, read> partition_a: array<u32>;
@group(0) @binding(1) var<storage, read> partition_b: array<u32>;
@group(0) @binding(2) var<storage, read_write> littlewood_coeff: array<u32>;
@group(0) @binding(3) var<storage, read> grassmann_params: array<u32>; // [n, k]

@compute @workgroup_size(128)
fn main(@builtin(global_invocation_id) global_id: vec3<u32>) {
    let coeff_idx = global_id.x;

    let n = grassmann_params[0]; // Dimension of ambient space
    let k = grassmann_params[1]; // Dimension of subspaces

    if (coeff_idx >= arrayLength(&littlewood_coeff)) {
        return;
    }

    // Schubert calculus: compute Littlewood-Richardson coefficients
    // This is a simplified version - full LR coefficients require more complex algorithms

    let max_parts = min(arrayLength(&partition_a), arrayLength(&partition_b));
    var coefficient = 0u;

    // Simplified intersection number computation
    for (var i = 0u; i < max_parts; i = i + 1u) {
        let part_a = partition_a[i];
        let part_b = partition_b[i];

        // Check compatibility with Grassmannian Gr(k, n)
        if (part_a <= n - k && part_b <= n - k) {
            coefficient += part_a * part_b;
        }
    }

    littlewood_coeff[coeff_idx] = coefficient;
}
"#;

// =====================================================================
// TOPOLOGY SHADERS
// =====================================================================

/// Topology shader collection
pub const TOPOLOGY_SHADERS: &[(&str, &str)] = &[
    ("topology_distance_matrix", TOPOLOGY_DISTANCE_MATRIX),
    ("topology_morse_critical", TOPOLOGY_MORSE_CRITICAL),
    ("topology_boundary_matrix", TOPOLOGY_BOUNDARY_MATRIX),
    ("topology_matrix_reduction", TOPOLOGY_MATRIX_REDUCTION),
];

/// Distance matrix computation for Rips filtration
pub const TOPOLOGY_DISTANCE_MATRIX: &str = r#"
struct Point {
    x: f32,
    y: f32,
    z: f32,
    w: f32,
}

@group(0) @binding(0)
var<storage, read> points: array<Point>;

@group(0) @binding(1)
var<storage, read_write> distances: array<f32>;

@compute @workgroup_size(8, 8)
fn main(@builtin(global_invocation_id) global_id: vec3<u32>) {
    let i = global_id.x;
    let j = global_id.y;
    let num_points = arrayLength(&points);

    if (i >= num_points || j >= num_points) {
        return;
    }

    let idx = i * num_points + j;

    if (i == j) {
        distances[idx] = 0.0;
        return;
    }

    let pi = points[i];
    let pj = points[j];

    let dx = pi.x - pj.x;
    let dy = pi.y - pj.y;
    let dz = pi.z - pj.z;
    let dw = pi.w - pj.w;

    // Euclidean distance (supports up to 4D)
    distances[idx] = sqrt(dx * dx + dy * dy + dz * dz + dw * dw);
}
"#;

/// Morse critical point detection on 2D height function grid
pub const TOPOLOGY_MORSE_CRITICAL: &str = r#"
struct CriticalPoint {
    x: u32,
    y: u32,
    critical_type: u32,  // 0=min, 1=saddle, 2=max
    value: f32,
}

@group(0) @binding(0)
var<storage, read> values: array<f32>;

@group(0) @binding(1)
var<uniform> dims: vec2<u32>;  // width, height

@group(0) @binding(2)
var<storage, read_write> critical_points: array<CriticalPoint>;

@group(0) @binding(3)
var<storage, read_write> counter: atomic<u32>;

fn get_value(x: u32, y: u32) -> f32 {
    return values[y * dims.x + x];
}

@compute @workgroup_size(16, 16)
fn main(@builtin(global_invocation_id) global_id: vec3<u32>) {
    // Interior points only (offset by 1)
    let x = global_id.x + 1u;
    let y = global_id.y + 1u;

    if (x >= dims.x - 1u || y >= dims.y - 1u) {
        return;
    }

    let v = get_value(x, y);

    // Get 8-neighbors
    let n0 = get_value(x - 1u, y - 1u);
    let n1 = get_value(x, y - 1u);
    let n2 = get_value(x + 1u, y - 1u);
    let n3 = get_value(x - 1u, y);
    let n4 = get_value(x + 1u, y);
    let n5 = get_value(x - 1u, y + 1u);
    let n6 = get_value(x, y + 1u);
    let n7 = get_value(x + 1u, y + 1u);

    // Count neighbors lower/higher than center
    var lower_count = 0u;
    var upper_count = 0u;

    if (n0 < v) { lower_count += 1u; } else if (n0 > v) { upper_count += 1u; }
    if (n1 < v) { lower_count += 1u; } else if (n1 > v) { upper_count += 1u; }
    if (n2 < v) { lower_count += 1u; } else if (n2 > v) { upper_count += 1u; }
    if (n3 < v) { lower_count += 1u; } else if (n3 > v) { upper_count += 1u; }
    if (n4 < v) { lower_count += 1u; } else if (n4 > v) { upper_count += 1u; }
    if (n5 < v) { lower_count += 1u; } else if (n5 > v) { upper_count += 1u; }
    if (n6 < v) { lower_count += 1u; } else if (n6 > v) { upper_count += 1u; }
    if (n7 < v) { lower_count += 1u; } else if (n7 > v) { upper_count += 1u; }

    var critical_type = 3u;  // 3 = not critical

    if (lower_count == 8u) {
        critical_type = 2u;  // Maximum
    } else if (upper_count == 8u) {
        critical_type = 0u;  // Minimum
    } else if (lower_count > 0u && upper_count > 0u) {
        // Check for saddle by counting sign changes around boundary
        var signs = array<bool, 8>(
            n0 > v, n1 > v, n2 > v, n3 > v, n4 > v, n5 > v, n6 > v, n7 > v
        );

        var changes = 0u;
        if (signs[0] != signs[1]) { changes += 1u; }
        if (signs[1] != signs[2]) { changes += 1u; }
        if (signs[2] != signs[4]) { changes += 1u; }
        if (signs[4] != signs[7]) { changes += 1u; }
        if (signs[7] != signs[6]) { changes += 1u; }
        if (signs[6] != signs[5]) { changes += 1u; }
        if (signs[5] != signs[3]) { changes += 1u; }
        if (signs[3] != signs[0]) { changes += 1u; }

        if (changes >= 4u) {
            critical_type = 1u;  // Saddle
        }
    }

    if (critical_type < 3u) {
        let idx = atomicAdd(&counter, 1u);
        critical_points[idx] = CriticalPoint(x, y, critical_type, v);
    }
}
"#;

/// Boundary matrix construction for simplicial complex (sparse format)
pub const TOPOLOGY_BOUNDARY_MATRIX: &str = r#"
struct Simplex {
    vertices: array<u32, 8>,  // Max 7-simplex
    dimension: u32,
    filtration_time: f32,
    padding: array<u32, 2>,
}

struct MatrixEntry {
    row: u32,
    col: u32,
    value: i32,
    padding: u32,
}

@group(0) @binding(0)
var<storage, read> simplices: array<Simplex>;

@group(0) @binding(1)
var<storage, read_write> boundary_entries: array<MatrixEntry>;

@group(0) @binding(2)
var<storage, read_write> entry_counter: atomic<u32>;

@compute @workgroup_size(256)
fn main(@builtin(global_invocation_id) global_id: vec3<u32>) {
    let simplex_idx = global_id.x;
    if (simplex_idx >= arrayLength(&simplices)) {
        return;
    }

    let s = simplices[simplex_idx];
    if (s.dimension == 0u) {
        return;  // 0-simplices have no boundary
    }

    // Generate boundary faces with alternating signs
    let dim = s.dimension;
    for (var i = 0u; i <= dim; i++) {
        let sign = select(-1, 1, i % 2u == 0u);

        // Allocate entry atomically
        let entry_idx = atomicAdd(&entry_counter, 1u);

        // Compute hash of face (for row index)
        var face_hash = 0u;
        for (var j = 0u; j <= dim; j++) {
            if (j != i) {
                face_hash = face_hash * 31u + s.vertices[j];
            }
        }

        boundary_entries[entry_idx] = MatrixEntry(face_hash, simplex_idx, sign, 0u);
    }
}
"#;

/// Parallel matrix reduction for homology computation
pub const TOPOLOGY_MATRIX_REDUCTION: &str = r#"
// Parallel column reduction using GPU
// Finds pivot rows for each column

@group(0) @binding(0)
var<storage, read_write> matrix: array<i32>;

@group(0) @binding(1)
var<uniform> dims: vec2<u32>;  // rows, cols

@group(0) @binding(2)
var<storage, read_write> pivots: array<u32>;

@compute @workgroup_size(256)
fn main(@builtin(global_invocation_id) global_id: vec3<u32>) {
    let col = global_id.x;
    let rows = dims.x;
    let cols = dims.y;

    if (col >= cols) {
        return;
    }

    // Find lowest non-zero in column (pivot row)
    var pivot_row = rows;  // rows means no pivot
    for (var row = 0u; row < rows; row++) {
        let idx = row * cols + col;
        if (matrix[idx] != 0) {
            pivot_row = row;
        }
    }

    pivots[col] = pivot_row;
}
"#;

#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    fn test_shader_library_creation() {
        let library = ShaderLibrary::new();
        let shaders = library.list_shaders();

        // Should have shaders for all mathematical domains
        assert!(shaders.contains(&"tropical_matrix_multiply".to_string()));
        assert!(shaders.contains(&"dual_forward_ad".to_string()));
        assert!(shaders.contains(&"tropical_dual_clifford".to_string()));
        assert!(shaders.contains(&"fisher_information".to_string()));
        assert!(shaders.contains(&"ca_evolution".to_string()));
        assert!(shaders.contains(&"intersection_theory".to_string()));

        // Holographic memory shaders
        assert!(shaders.contains(&"holographic_batch_bind".to_string()));
        assert!(shaders.contains(&"holographic_batch_similarity".to_string()));
        assert!(shaders.contains(&"holographic_bundle_all".to_string()));
        assert!(shaders.contains(&"holographic_resonator_step".to_string()));
    }

    #[test]
    fn test_shader_retrieval() {
        let library = ShaderLibrary::new();

        let shader = library.get_shader("tropical_matrix_multiply");
        assert!(shader.is_some());
        assert!(shader.unwrap().contains("@compute"));
        assert!(shader.unwrap().contains("tropical"));
    }

    #[test]
    fn test_shader_constants() {
        assert_eq!(TROPICAL_SHADERS.len(), 3);
        assert_eq!(DUAL_SHADERS.len(), 3);
        assert_eq!(FUSION_SHADERS.len(), 2);
        assert_eq!(HOLOGRAPHIC_SHADERS.len(), 4);
    }

    #[test]
    fn test_holographic_shaders() {
        // Verify holographic shaders contain expected WGSL patterns
        assert!(HOLOGRAPHIC_BATCH_BIND.contains("@compute"));
        assert!(HOLOGRAPHIC_BATCH_BIND.contains("blade_product_sign"));

        assert!(HOLOGRAPHIC_BATCH_SIMILARITY.contains("@compute"));
        assert!(HOLOGRAPHIC_BATCH_SIMILARITY.contains("similarity"));

        assert!(HOLOGRAPHIC_BUNDLE_ALL.contains("@compute"));
        assert!(HOLOGRAPHIC_BUNDLE_ALL.contains("workgroupBarrier"));

        assert!(HOLOGRAPHIC_RESONATOR_STEP.contains("@compute"));
        assert!(HOLOGRAPHIC_RESONATOR_STEP.contains("codebook"));
    }
}