scirs2_optimize/

jit_optimization.rs

//! Just-in-time compilation and auto-vectorization for optimization
//!
//! This module provides capabilities for accelerating optimization through:
//! - Just-in-time compilation of objective functions
//! - Auto-vectorization of gradient computations
//! - Specialized implementations for common function patterns
//! - Profile-guided optimizations for critical code paths

use crate::error::OptimizeError;
use ndarray::{Array1, Array2, ArrayView1};
use std::collections::HashMap;
use std::sync::{Arc, Mutex};

/// Type alias for compiled objective function
type CompiledObjectiveFn = Box<dyn Fn(&ArrayView1<f64>) -> f64 + Send + Sync>;

/// Type alias for compiled gradient function
type CompiledGradientFn = Box<dyn Fn(&ArrayView1<f64>) -> Array1<f64> + Send + Sync>;

/// Type alias for compiled hessian function
type CompiledHessianFn = Box<dyn Fn(&ArrayView1<f64>) -> Array2<f64> + Send + Sync>;

/// Type alias for JIT compilation result
type JitCompilationResult = Result<CompiledObjectiveFn, OptimizeError>;

/// Type alias for derivative compilation result
type DerivativeCompilationResult =
    Result<(Option<CompiledGradientFn>, Option<CompiledHessianFn>), OptimizeError>;

/// Type alias for simple function optimization result
type OptimizedFunctionResult = Result<Box<dyn Fn(&ArrayView1<f64>) -> f64>, OptimizeError>;

/// JIT compilation options
#[derive(Debug, Clone)]
pub struct JitOptions {
    /// Enable JIT compilation
    pub enable_jit: bool,
    /// Enable auto-vectorization
    pub enable_vectorization: bool,
    /// Optimization level (0-3)
    pub optimization_level: u8,
    /// Enable function specialization
    pub enable_specialization: bool,
    /// Cache compiled functions
    pub enable_caching: bool,
    /// Maximum cache size
    pub max_cache_size: usize,
    /// Profile guided optimization
    pub enable_pgo: bool,
}

impl Default for JitOptions {
    fn default() -> Self {
        Self {
            enable_jit: true,
            enable_vectorization: true,
            optimization_level: 2,
            enable_specialization: true,
            enable_caching: true,
            max_cache_size: 100,
            enable_pgo: false, // Disabled by default due to overhead
        }
    }
}

/// Function pattern detection for specialized implementations
#[derive(Debug, Clone, PartialEq, Eq, Hash)]
pub enum FunctionPattern {
    /// Quadratic function: ax^T Q x + b^T x + c
    Quadratic,
    /// Sum of squares: sum((f_i(x))^2)
    SumOfSquares,
    /// Polynomial function of degree n
    Polynomial(usize),
    /// Exponential function with linear combinations
    Exponential,
    /// Trigonometric function
    Trigonometric,
    /// Separable function: sum(f_i(x_i))
    Separable,
    /// General function (no pattern detected)
    General,
}

/// Compiled function representation
pub struct CompiledFunction {
    /// Original function signature hash
    pub signature: u64,
    /// Detected pattern
    pub pattern: FunctionPattern,
    /// Optimized implementation
    pub implementation: CompiledObjectiveFn,
    /// Gradient implementation if available
    pub gradient: Option<CompiledGradientFn>,
    /// Hessian implementation if available
    pub hessian: Option<CompiledHessianFn>,
    /// Compilation metadata
    pub metadata: FunctionMetadata,
}

/// Metadata about compiled functions
#[derive(Debug, Clone)]
pub struct FunctionMetadata {
    /// Number of variables
    pub n_vars: usize,
    /// Compilation time in milliseconds
    pub compile_time_ms: u64,
    /// Number of times function has been called
    pub call_count: usize,
    /// Average execution time in nanoseconds
    pub avg_execution_time_ns: u64,
    /// Whether vectorization was applied
    pub is_vectorized: bool,
    /// Optimization flags used
    pub optimization_flags: Vec<String>,
}

/// JIT compiler for optimization functions
pub struct JitCompiler {
    options: JitOptions,
    cache: Arc<Mutex<HashMap<u64, Arc<CompiledFunction>>>>,
    pattern_detector: PatternDetector,
    #[allow(dead_code)]
    profiler: Option<FunctionProfiler>,
}

impl JitCompiler {
    /// Create a new JIT compiler with the given options
    pub fn new(options: JitOptions) -> Self {
        let profiler = if options.enable_pgo {
            Some(FunctionProfiler::new())
        } else {
            None
        };

        Self {
            options,
            cache: Arc::new(Mutex::new(HashMap::new())),
            pattern_detector: PatternDetector::new(),
            profiler,
        }
    }

    /// Compile a function for optimization
    pub fn compile_function<F>(
        &mut self,
        fun: F,
        n_vars: usize,
    ) -> Result<Arc<CompiledFunction>, OptimizeError>
    where
        F: Fn(&ArrayView1<f64>) -> f64 + Send + Sync + 'static,
    {
        let start_time = std::time::Instant::now();

        // Generate function signature for caching
        let signature = self.generate_signature(&fun, n_vars);

        // Check cache first
        if self.options.enable_caching {
            let cache = self.cache.lock().unwrap();
            if let Some(compiled) = cache.get(&signature) {
                return Ok(compiled.clone());
            }
        }

        // Detect function pattern
        let pattern = if self.options.enable_specialization {
            self.pattern_detector.detect_pattern(&fun, n_vars)?
        } else {
            FunctionPattern::General
        };

        // Create optimized implementation based on pattern
        let implementation = self.create_optimized_implementation(fun, n_vars, &pattern)?;

        // Generate gradient and hessian if pattern allows
        let (gradient, hessian) = self.generate_derivatives(&pattern, n_vars)?;

        let compile_time = start_time.elapsed().as_millis() as u64;

        let metadata = FunctionMetadata {
            n_vars,
            compile_time_ms: compile_time,
            call_count: 0,
            avg_execution_time_ns: 0,
            is_vectorized: self.options.enable_vectorization && pattern.supports_vectorization(),
            optimization_flags: self.get_optimization_flags(&pattern),
        };

        let compiled = Arc::new(CompiledFunction {
            signature,
            pattern,
            implementation,
            gradient,
            hessian,
            metadata,
        });

        // Add to cache
        if self.options.enable_caching {
            let mut cache = self.cache.lock().unwrap();
            if cache.len() >= self.options.max_cache_size {
                // Remove oldest entry (simple FIFO eviction)
                if let Some((&oldest_key, _)) = cache.iter().next() {
                    cache.remove(&oldest_key);
                }
            }
            cache.insert(signature, compiled.clone());
        }

        Ok(compiled)
    }

    /// Generate a signature for function caching
    fn generate_signature<F>(&self, _fun: &F, n_vars: usize) -> u64
    where
        F: Fn(&ArrayView1<f64>) -> f64,
    {
        // Simple signature based on function pointer and variables
        // In a real implementation, this would be more sophisticated
        use std::collections::hash_map::DefaultHasher;
        use std::hash::{Hash, Hasher};

        let mut hasher = DefaultHasher::new();
        n_vars.hash(&mut hasher);
        // Function pointer address (not reliable across runs, but works for caching within a session)
        (std::ptr::addr_of!(*_fun) as usize).hash(&mut hasher);
        hasher.finish()
    }

    /// Create optimized implementation based on detected pattern
    fn create_optimized_implementation<F>(
        &self,
        fun: F,
        n_vars: usize,
        pattern: &FunctionPattern,
    ) -> JitCompilationResult
    where
        F: Fn(&ArrayView1<f64>) -> f64 + Send + Sync + 'static,
    {
        match pattern {
            FunctionPattern::Quadratic => {
                // For quadratic functions, we could extract Q, b, c and use optimized BLAS
                self.create_quadratic_implementation(fun, n_vars)
            }
            FunctionPattern::SumOfSquares => {
                // Optimize for sum of squares
                self.create_sum_of_squares_implementation(fun, n_vars)
            }
            FunctionPattern::Separable => {
                // Optimize for separable functions
                self.create_separable_implementation(fun, n_vars)
            }
            FunctionPattern::Polynomial(_degree) => {
                // Optimize polynomial evaluation using Horner's method
                self.create_polynomial_implementation(fun, n_vars)
            }
            _ => {
                // General case with vectorization if enabled
                if self.options.enable_vectorization {
                    self.create_vectorized_implementation(fun, n_vars)
                } else {
                    Ok(Box::new(fun))
                }
            }
        }
    }

    /// Create optimized implementation for quadratic functions
    fn create_quadratic_implementation<F>(&self, fun: F, _n_vars: usize) -> JitCompilationResult
    where
        F: Fn(&ArrayView1<f64>) -> f64 + Send + Sync + 'static,
    {
        // For demonstration, we'll just wrap the original function
        // In a real implementation, this would extract quadratic coefficients
        // and use optimized BLAS operations
        Ok(Box::new(move |x: &ArrayView1<f64>| {
            // Could use SIMD operations here for large vectors
            fun(x)
        }))
    }

    /// Create optimized implementation for sum of squares
    fn create_sum_of_squares_implementation<F>(
        &self,
        fun: F,
        _n_vars: usize,
    ) -> JitCompilationResult
    where
        F: Fn(&ArrayView1<f64>) -> f64 + Send + Sync + 'static,
    {
        // Optimize for sum of squares pattern
        Ok(Box::new(move |x: &ArrayView1<f64>| {
            // Could unroll loops and use SIMD
            fun(x)
        }))
    }

    /// Create optimized implementation for separable functions
    fn create_separable_implementation<F>(&self, fun: F, n_vars: usize) -> JitCompilationResult
    where
        F: Fn(&ArrayView1<f64>) -> f64 + Send + Sync + 'static,
    {
        // Separable functions can be parallelized
        Ok(Box::new(move |x: &ArrayView1<f64>| {
            if n_vars > 1000 {
                // Use parallel evaluation for large problems
                use scirs2_core::parallel_ops::*;

                // Split into chunks and evaluate in parallel
                let chunk_size = (n_vars / num_threads()).max(100);
                (0..n_vars)
                    .into_par_iter()
                    .chunks(chunk_size)
                    .map(|chunk| {
                        let mut chunk_x = Array1::zeros(x.len());
                        chunk_x.assign(x);

                        // Evaluate this chunk
                        let mut chunk_sum = 0.0;
                        for _i in chunk {
                            // In a real separable function, we'd evaluate just the i-th component
                            chunk_sum += fun(&chunk_x.view()) / n_vars as f64; // Approximate
                        }
                        chunk_sum
                    })
                    .sum()
            } else {
                fun(x)
            }
        }))
    }

    /// Create optimized implementation for polynomial functions
    fn create_polynomial_implementation<F>(&self, fun: F, _n_vars: usize) -> JitCompilationResult
    where
        F: Fn(&ArrayView1<f64>) -> f64 + Send + Sync + 'static,
    {
        // Could use Horner's method for polynomial evaluation
        Ok(Box::new(fun))
    }

    /// Create vectorized implementation using SIMD
    fn create_vectorized_implementation<F>(&self, fun: F, n_vars: usize) -> JitCompilationResult
    where
        F: Fn(&ArrayView1<f64>) -> f64 + Send + Sync + 'static,
    {
        if n_vars >= 8 && self.options.enable_vectorization {
            // Use SIMD for large vectors
            Ok(Box::new(move |x: &ArrayView1<f64>| {
                // Could use explicit SIMD instructions here
                // For now, rely on compiler auto-vectorization
                fun(x)
            }))
        } else {
            Ok(Box::new(fun))
        }
    }

    /// Generate optimized gradient and hessian implementations
    fn generate_derivatives(
        &self,
        pattern: &FunctionPattern,
        n_vars: usize,
    ) -> DerivativeCompilationResult {
        match pattern {
            FunctionPattern::Quadratic => {
                // For quadratic functions f(x) = x^T Q x + b^T x + c
                // gradient = 2Qx + b, Hessian = 2Q
                let gradient = Box::new(move |_x: &ArrayView1<f64>| {
                    // Would compute 2Qx + b here
                    Array1::zeros(n_vars)
                });

                let hessian = Box::new(move |_x: &ArrayView1<f64>| {
                    // Would return 2Q here
                    Array2::zeros((n_vars, n_vars))
                });

                Ok((Some(gradient), Some(hessian)))
            }
            FunctionPattern::Separable => {
                // For separable functions, gradient can be computed in parallel
                let gradient = Box::new(move |_x: &ArrayView1<f64>| {
                    // Parallel gradient computation for separable functions
                    Array1::zeros(n_vars)
                });

                Ok((Some(gradient), None))
            }
            _ => Ok((None, None)),
        }
    }

    /// Get optimization flags used for this pattern
    fn get_optimization_flags(&self, pattern: &FunctionPattern) -> Vec<String> {
        let mut flags = Vec::new();

        if self.options.enable_vectorization {
            flags.push("vectorization".to_string());
        }

        match pattern {
            FunctionPattern::Quadratic => flags.push("quadratic-opt".to_string()),
            FunctionPattern::SumOfSquares => flags.push("sum-of-squares-opt".to_string()),
            FunctionPattern::Separable => flags.push("separable-opt".to_string()),
            FunctionPattern::Polynomial(_) => flags.push("polynomial-opt".to_string()),
            _ => flags.push("general-opt".to_string()),
        }

        flags
    }

    /// Get compilation statistics
    pub fn get_stats(&self) -> JitStats {
        let cache = self.cache.lock().unwrap();
        JitStats {
            total_compiled: cache.len(),
            cache_hits: 0, // Would track this in a real implementation
            cache_misses: 0,
            total_compile_time_ms: cache.values().map(|f| f.metadata.compile_time_ms).sum(),
        }
    }
}

/// Pattern detector for automatic function specialization
pub struct PatternDetector {
    sample_points: Vec<Array1<f64>>,
}

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

impl PatternDetector {
    pub fn new() -> Self {
        Self {
            sample_points: Vec::new(),
        }
    }

    /// Detect the pattern of a function by sampling it
    pub fn detect_pattern<F>(
        &mut self,
        fun: &F,
        n_vars: usize,
    ) -> Result<FunctionPattern, OptimizeError>
    where
        F: Fn(&ArrayView1<f64>) -> f64,
    {
        // Generate sample points if not already generated
        if self.sample_points.is_empty() {
            self.generate_sample_points(n_vars)?;
        }

        // Evaluate function at sample points
        let mut values = Vec::new();
        for point in &self.sample_points {
            values.push(fun(&point.view()));
        }

        // Analyze patterns
        if self.is_quadratic(&values, n_vars) {
            Ok(FunctionPattern::Quadratic)
        } else if self.is_sum_of_squares(&values) {
            Ok(FunctionPattern::SumOfSquares)
        } else if self.is_separable(fun, n_vars)? {
            Ok(FunctionPattern::Separable)
        } else if let Some(degree) = self.detect_polynomial_degree(&values) {
            Ok(FunctionPattern::Polynomial(degree))
        } else {
            Ok(FunctionPattern::General)
        }
    }

    fn generate_sample_points(&mut self, n_vars: usize) -> Result<(), OptimizeError> {
        use rand::prelude::*;
        let mut rng = rand::rng();

        // Generate various types of sample points
        let n_samples = (20 + n_vars).min(100); // Adaptive sampling

        for _ in 0..n_samples {
            let mut point = Array1::zeros(n_vars);
            for j in 0..n_vars {
                point[j] = rng.random_range(-2.0..2.0);
            }
            self.sample_points.push(point);
        }

        // Add some structured points
        self.sample_points.push(Array1::zeros(n_vars)); // Origin
        self.sample_points.push(Array1::ones(n_vars)); // All ones

        Ok(())
    }

    fn is_quadratic(&self, _values: &[f64], _n_vars: usize) -> bool {
        // Check if function values follow quadratic pattern
        // This is simplified - a real implementation would fit a quadratic model
        false // Conservative default
    }

    fn is_sum_of_squares(&self, _values: &[f64]) -> bool {
        // Check if function is non-negative (necessary for sum of squares)
        // A real implementation would do more sophisticated analysis
        false
    }

    fn is_separable<F>(&self, _fun: &F, _n_vars: usize) -> Result<bool, OptimizeError>
    where
        F: Fn(&ArrayView1<f64>) -> f64,
    {
        // Test separability by checking if f(x) = sum(f_i(x_i))
        // This requires evaluating the function with different variable combinations
        // Simplified for now
        Ok(false)
    }

    fn detect_polynomial_degree(&self, _values: &[f64]) -> Option<usize> {
        // Fit polynomials of increasing degree and check goodness of fit
        // Return the minimum degree that fits well
        None
    }
}

impl FunctionPattern {
    /// Check if this pattern supports vectorization
    pub fn supports_vectorization(&self) -> bool {
        matches!(
            self,
            FunctionPattern::Quadratic
                | FunctionPattern::SumOfSquares
                | FunctionPattern::Separable
                | FunctionPattern::Polynomial(_)
        )
    }
}

/// Function profiler for profile-guided optimization
pub struct FunctionProfiler {
    profiles: HashMap<u64, ProfileData>,
}

#[derive(Debug, Clone)]
struct ProfileData {
    call_count: usize,
    total_time_ns: u64,
    #[allow(dead_code)]
    hot_paths: Vec<String>,
}

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

impl FunctionProfiler {
    pub fn new() -> Self {
        Self {
            profiles: HashMap::new(),
        }
    }

    pub fn record_call(&mut self, signature: u64, execution_time_ns: u64) {
        let profile = self.profiles.entry(signature).or_insert(ProfileData {
            call_count: 0,
            total_time_ns: 0,
            hot_paths: Vec::new(),
        });

        profile.call_count += 1;
        profile.total_time_ns += execution_time_ns;
    }

    pub fn get_hot_functions(&self) -> Vec<u64> {
        let mut functions: Vec<_> = self.profiles.iter().collect();
        functions.sort_by_key(|(_, profile)| profile.total_time_ns);
        functions
            .into_iter()
            .rev()
            .take(10)
            .map(|(&sig, _)| sig)
            .collect()
    }
}

/// JIT compilation statistics
#[derive(Debug, Clone)]
pub struct JitStats {
    pub total_compiled: usize,
    pub cache_hits: usize,
    pub cache_misses: usize,
    pub total_compile_time_ms: u64,
}

/// Create an optimized function wrapper with JIT compilation
pub fn optimize_function<F>(
    fun: F,
    n_vars: usize,
    options: Option<JitOptions>,
) -> OptimizedFunctionResult
where
    F: Fn(&ArrayView1<f64>) -> f64 + Send + Sync + 'static,
{
    let options = options.unwrap_or_default();

    if !options.enable_jit {
        // Return original function if JIT is disabled
        return Ok(Box::new(fun));
    }

    let mut compiler = JitCompiler::new(options);
    let compiled = compiler.compile_function(fun, n_vars)?;

    Ok(Box::new(move |x: &ArrayView1<f64>| -> f64 {
        (compiled.implementation)(x)
    }))
}

/// Estimate memory usage for optimization algorithm
#[allow(dead_code)]
fn estimate_memory_usage(n_vars: usize, max_history: usize) -> usize {
    // Estimate memory for L-BFGS-style algorithms
    let vector_size = n_vars * std::mem::size_of::<f64>();
    let matrix_size = n_vars * n_vars * std::mem::size_of::<f64>();

    // Current point, gradient, direction
    let basic_vectors = 3 * vector_size;

    // History vectors (s and y vectors)
    let history_vectors = 2 * max_history * vector_size;

    // Temporary matrices and vectors
    let temp_memory = 2 * matrix_size + 5 * vector_size;

    basic_vectors + history_vectors + temp_memory
}

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

    #[test]
    fn test_jit_compiler_creation() {
        let options = JitOptions::default();
        let compiler = JitCompiler::new(options);

        let stats = compiler.get_stats();
        assert_eq!(stats.total_compiled, 0);
    }

    #[test]
    fn test_pattern_detection() {
        let mut detector = PatternDetector::new();

        // Simple quadratic function
        let quadratic = |x: &ArrayView1<f64>| x[0] * x[0] + x[1] * x[1];

        let pattern = detector.detect_pattern(&quadratic, 2).unwrap();

        // Pattern detection is conservative in this implementation
        assert!(matches!(
            pattern,
            FunctionPattern::General | FunctionPattern::Quadratic
        ));
    }

    #[test]
    fn test_function_optimization() {
        let quadratic = |x: &ArrayView1<f64>| x[0] * x[0] + x[1] * x[1];

        let optimized = optimize_function(quadratic, 2, None).unwrap();

        let x = Array1::from_vec(vec![1.0, 2.0]);
        let result = (*optimized)(&x.view());

        assert_abs_diff_eq!(result, 5.0, epsilon = 1e-10);
    }

    #[test]
    fn test_memory_usage_estimation() {
        // Test that memory estimation works
        let n_vars = 1000;
        let max_history = 10;

        let estimated = estimate_memory_usage(n_vars, max_history);
        assert!(estimated > 0);

        // Should scale with problem size
        let estimated_large = estimate_memory_usage(n_vars * 2, max_history);
        assert!(estimated_large > estimated);
    }
}