//! Automatic differentiation through discrete operations
//!
//! This module provides differentiable approximations for discrete operations
//! that are traditionally non-differentiable, such as sorting, top-k selection,
//! and other discrete combinatorial operations. These approximations enable
//! gradient-based optimization of neural networks containing discrete operations.

// Framework infrastructure - components designed for future use
#![allow(dead_code)]
use std::collections::HashMap;
use torsh_core::error::Result;
use torsh_core::DeviceType;
use torsh_tensor::{creation, Tensor};

/// Configuration for discrete operation differentiation
#[derive(Debug, Clone)]
pub struct DiscreteConfig {
    /// Temperature parameter for softmax-based approximations
    pub temperature: f32,
    /// Whether to use straight-through estimator
    pub straight_through: bool,
    /// Variance reduction technique for stochastic gradients
    pub variance_reduction: VarianceReduction,
    /// Regularization strength for smooth approximations
    pub regularization: f32,
    /// Number of samples for stochastic approximations
    pub num_samples: usize,
}

impl Default for DiscreteConfig {
    fn default() -> Self {
        Self {
            temperature: 1.0,
            straight_through: false,
            variance_reduction: VarianceReduction::ControlVariates,
            regularization: 1e-6,
            num_samples: 100,
        }
    }
}

/// Variance reduction techniques for stochastic gradients
#[derive(Debug, Clone, PartialEq)]
pub enum VarianceReduction {
    /// No variance reduction
    None,
    /// Control variates method
    ControlVariates,
    /// Importance sampling
    ImportanceSampling,
    /// Rao-Blackwellization
    RaoBlackwell,
}

/// Differentiable approximation to the sorting operation
pub struct DifferentiableSort {
    config: DiscreteConfig,
}

impl DifferentiableSort {
    pub fn new(config: DiscreteConfig) -> Self {
        Self { config }
    }

    /// Smooth approximation to sorting using bitonic sort-like operations
    pub fn smooth_sort(&self, input: &Tensor) -> Result<Tensor> {
        let mut sorted = input.clone();
        let n = input.shape().dims()[input.shape().dims().len() - 1] as f32;

        // Use temperature-scaled softmax to approximate sorting
        let temperature = self.config.temperature;

        // Create differentiable comparison operations
        for stage in 0..(n.log2().ceil() as usize) {
            for substage in 0..=stage {
                sorted = self.smooth_compare_and_swap(&sorted, stage, substage, temperature)?;
            }
        }

        Ok(sorted)
    }

    /// Straight-through estimator for sorting
    pub fn straight_through_sort(&self, input: &Tensor) -> Result<(Tensor, Tensor)> {
        // Forward pass: exact sorting
        let sorted = self.exact_sort(input)?;

        // Backward pass: identity gradient (straight-through)
        let grad_fn = if self.config.straight_through {
            Some(input.clone()) // Pass gradients straight through
        } else {
            None
        };

        Ok((sorted, grad_fn.unwrap_or_else(|| input.clone())))
    }

    /// Stochastic approximation using Gumbel-based sorting
    pub fn gumbel_sort(&self, input: &Tensor) -> Result<Tensor> {
        let shape = input.shape();
        let gumbel_noise = self.sample_gumbel(&shape)?;

        // Add Gumbel noise and use soft sorting
        let noisy_input = input.add(&gumbel_noise)?;
        let temperature = self.config.temperature;

        self.soft_sort(&noisy_input, temperature)
    }

    fn smooth_compare_and_swap(
        &self,
        input: &Tensor,
        stage: usize,
        substage: usize,
        temperature: f32,
    ) -> Result<Tensor> {
        // Implement smooth compare-and-swap operations for bitonic sort
        let n = input.shape().dims()[input.shape().dims().len() - 1] as usize;
        let stride = 1 << (stage - substage);
        let mut result = input.clone();

        for i in (0..n).step_by(stride * 2) {
            for j in 0..stride {
                let idx1 = i + j;
                let idx2 = i + j + stride;

                if idx2 < n {
                    result = self.smooth_compare_pair(&result, idx1, idx2, temperature)?;
                }
            }
        }

        Ok(result)
    }

    fn smooth_compare_pair(
        &self,
        input: &Tensor,
        idx1: usize,
        idx2: usize,
        temperature: f32,
    ) -> Result<Tensor> {
        // Extract values at the two indices
        let val1 = input.select(0, idx1 as i64)?;
        let val2 = input.select(0, idx2 as i64)?;

        // Compute smooth min/max using softmax
        let diff = val1.sub(&val2)?;
        let scaled_diff = diff.div_scalar(temperature)?;
        let sigmoid = scaled_diff.sigmoid()?;

        // Smooth interpolation: min_val + sigmoid * (max_val - min_val)
        let min_val = val1.minimum(&val2)?;
        let max_val = val1.maximum(&val2)?;
        let range = max_val.sub(&min_val)?;
        let _smooth_result = min_val.add(&sigmoid.mul(&range)?)?;

        // Update the tensor with smooth results - simplified approach
        let result = input.clone();
        // Note: index_put_ is not available, using a simplified approach
        // In a complete implementation, you would need proper tensor indexing update

        Ok(result)
    }

    fn exact_sort(&self, input: &Tensor) -> Result<Tensor> {
        // Implement exact sorting using standard sort algorithm
        let mut data = input.to_vec()?;
        data.sort_by(|a, b| a.partial_cmp(b).unwrap_or(std::cmp::Ordering::Equal));
        Tensor::from_vec(data, input.shape().dims())
    }

    fn sample_gumbel(&self, shape: &torsh_core::shape::Shape) -> Result<Tensor> {
        // Sample from Gumbel(0, 1) distribution
        let uniform = creation::randn::<f32>(shape.dims())?;
        let eps = 1e-20;
        let log_uniform = uniform.add_scalar(eps)?.log()?;
        let neg_log_uniform = log_uniform.neg()?;
        neg_log_uniform.add_scalar(eps)?.log()?.neg()
    }

    fn soft_sort(&self, input: &Tensor, temperature: f32) -> Result<Tensor> {
        // Implement soft sorting using optimal transport
        let n = input.shape().dims()[input.shape().dims().len() - 1] as f32;

        // Create target positions (uniform distribution)
        let positions = creation::arange(0.0, n, 1.0)?;
        let normalized_positions = positions.div_scalar(n - 1.0)?;

        // Use Sinkhorn algorithm for optimal transport-based soft sorting
        self.sinkhorn_sort(input, &normalized_positions, temperature)
    }

    fn sinkhorn_sort(&self, input: &Tensor, targets: &Tensor, temperature: f32) -> Result<Tensor> {
        // Simplified Sinkhorn algorithm for soft sorting
        let n = input.shape().dims()[input.shape().dims().len() - 1];
        let max_iters = 50;

        // Compute cost matrix: |input[i] - target[j]|
        let mut transport_matrix = Tensor::zeros(&[n, n], DeviceType::Cpu)?;

        for i in 0..n {
            for j in 0..n {
                let input_val = input.select(0, i as i64)?;
                let target_val = targets.select(0, j as i64)?;
                let cost = input_val.sub(&target_val)?;
                let cost = cost.abs()?;
                let _scaled_cost = cost.div_scalar(temperature)?.neg()?;
                // Note: index_put_ method may not be available, using placeholder
                // transport_matrix.index_put_(&[i as i32, j as i32], &scaled_cost.exp()?)?;
            }
        }

        // Sinkhorn iterations
        for _ in 0..max_iters {
            // Row normalization
            let row_sums = transport_matrix.sum_dim(&[1], true)?;
            transport_matrix = transport_matrix.div(&row_sums)?;

            // Column normalization
            let col_sums = transport_matrix.sum_dim(&[0], true)?;
            transport_matrix = transport_matrix.div(&col_sums)?;
        }

        // Apply transport matrix to get sorted result
        transport_matrix.matmul(input)
    }
}

/// Differentiable top-k operation
pub struct DifferentiableTopK {
    config: DiscreteConfig,
    k: usize,
}

impl DifferentiableTopK {
    pub fn new(k: usize, config: DiscreteConfig) -> Self {
        Self { config, k }
    }

    /// Smooth approximation to top-k using sparsemax
    pub fn smooth_top_k(&self, input: &Tensor) -> Result<Tensor> {
        let temperature = self.config.temperature;

        // Manual softmax implementation to avoid broadcasting issues
        let input_data = input.data()?;
        let shape = input.shape().dims().to_vec();

        // Apply temperature scaling
        let mut scaled_data: Vec<f32> = input_data.iter().map(|&x| x / temperature).collect();

        // Numerical stability: subtract max
        let max_val = scaled_data
            .iter()
            .cloned()
            .fold(f32::NEG_INFINITY, f32::max);
        for x in &mut scaled_data {
            *x -= max_val;
        }

        // Compute softmax
        let exp_data: Vec<f32> = scaled_data.iter().map(|&x| x.exp()).collect();
        let exp_sum: f32 = exp_data.iter().sum();
        let softmax_data: Vec<f32> = exp_data.iter().map(|&x| x / exp_sum).collect();

        // Create softmax tensor with preserved shape
        let softmax = Tensor::from_data(softmax_data, shape, input.device())?;

        self.sparsemax_project(&softmax, self.k)
    }

    /// Gumbel-based top-k approximation
    pub fn gumbel_top_k(&self, input: &Tensor) -> Result<Tensor> {
        let gumbel_noise = self.sample_gumbel(&input.shape())?;
        let noisy_input = input.add(&gumbel_noise)?;

        // Use smooth approximation on noisy input
        self.smooth_top_k(&noisy_input)
    }

    /// Straight-through estimator for top-k
    pub fn straight_through_top_k(&self, input: &Tensor) -> Result<(Tensor, Tensor)> {
        // Forward: exact top-k
        let top_k_values = self.exact_top_k(input)?;

        // Backward: straight-through gradients
        let grad_input = if self.config.straight_through {
            input.clone()
        } else {
            // Use subgradient: gradient only for top-k elements
            self.create_top_k_mask(input)?.mul(&input)?
        };

        Ok((top_k_values, grad_input))
    }

    /// Entmax-based relaxation of top-k
    pub fn entmax_top_k(&self, input: &Tensor, alpha: f32) -> Result<Tensor> {
        // Entmax provides a natural relaxation of top-k selection
        self.entmax(input, alpha)
    }

    fn sparsemax_project(&self, input: &Tensor, k: usize) -> Result<Tensor> {
        // Project onto the k-dimensional simplex (sparsemax)
        let n = input.shape().dims()[input.shape().dims().len() - 1] as usize;

        if k >= n {
            return Ok(input.clone());
        }

        // Sort in descending order and find threshold
        let sorted = self.sort_descending(input)?;
        let mut cumsum = 0.0;
        let mut threshold;

        for i in 0..k {
            let val = sorted.select(0, i as i64)?.to_vec()?[0];
            cumsum += val;
            threshold = val - (cumsum - 1.0) / ((i + 1) as f32);
            if threshold >= 0.0 {
                break;
            }
        }

        // Apply thresholding
        // Placeholder for clamp_min - method not available
        let clamped = input.clone(); // Simplified implementation
        Ok(clamped)
    }

    fn entmax(&self, input: &Tensor, alpha: f32) -> Result<Tensor> {
        // Entmax transformation - generalizes softmax and sparsemax
        if alpha == 1.0 {
            return input.softmax(-1);
        }

        // Simplified entmax implementation
        let scaled = input.pow_scalar(alpha - 1.0)?;
        let sum = scaled.sum_dim(&[-1], true)?;
        scaled.div(&sum)
    }

    fn exact_top_k(&self, input: &Tensor) -> Result<Tensor> {
        // Implement exact top-k using partial sort
        let mut data = input.to_vec()?;
        let k = self.k.min(data.len());

        // Use partial sort to get top k elements
        data.select_nth_unstable_by(k, |a, b| {
            b.partial_cmp(a).unwrap_or(std::cmp::Ordering::Equal)
        });

        // Take only the first k elements (which are now the largest)
        data.truncate(k);

        // Sort the top k elements in descending order
        data.sort_by(|a, b| b.partial_cmp(a).unwrap_or(std::cmp::Ordering::Equal));

        Tensor::from_vec(data, &[k])
    }

    fn create_top_k_mask(&self, input: &Tensor) -> Result<Tensor> {
        // Create binary mask for top-k elements
        let threshold = self.find_kth_largest(input, self.k)?;
        let mask_bool = input.ge_scalar(threshold)?;

        // Convert boolean mask to f32
        let mask_data: Vec<f32> = mask_bool
            .to_vec()?
            .iter()
            .map(|&b| if b { 1.0 } else { 0.0 })
            .collect();
        Tensor::from_vec(mask_data, input.shape().dims())
    }

    fn find_kth_largest(&self, input: &Tensor, k: usize) -> Result<f32> {
        // Find the k-th largest element using quickselect algorithm
        let mut data = input.to_vec()?;

        if k == 0 || k > data.len() {
            return Err(torsh_core::error::TorshError::InvalidArgument(format!(
                "k={} is out of range for tensor of length {}",
                k,
                data.len()
            )));
        }

        // Use select_nth_unstable for O(n) average case
        let (_left, &mut kth, _right) = data.select_nth_unstable_by(k - 1, |a, b| {
            b.partial_cmp(a).unwrap_or(std::cmp::Ordering::Equal)
        });

        Ok(kth)
    }

    fn sort_descending(&self, input: &Tensor) -> Result<Tensor> {
        // Sort tensor in descending order
        let mut data = input.to_vec()?;
        data.sort_by(|a, b| b.partial_cmp(a).unwrap_or(std::cmp::Ordering::Equal));
        Tensor::from_vec(data, input.shape().dims())
    }

    fn sample_gumbel(&self, shape: &torsh_core::shape::Shape) -> Result<Tensor> {
        // Sample from Gumbel(0, 1) distribution
        let uniform = creation::randn::<f32>(shape.dims())?;
        let eps = 1e-20;
        let log_uniform = uniform.add_scalar(eps)?.log()?;
        let neg_log_uniform = log_uniform.neg()?;
        neg_log_uniform.add_scalar(eps)?.log()?.neg()
    }
}

/// Differentiable argmax operation
pub struct DifferentiableArgmax {
    config: DiscreteConfig,
}

impl DifferentiableArgmax {
    pub fn new(config: DiscreteConfig) -> Self {
        Self { config }
    }

    /// Smooth approximation using soft argmax
    pub fn soft_argmax(&self, input: &Tensor) -> Result<Tensor> {
        let temperature = self.config.temperature;

        // Get the input data and compute softmax manually to avoid broadcasting issues
        let input_data = input.data()?;
        let _n = input.shape().dims()[input.shape().dims().len() - 1];

        // Apply temperature scaling and softmax
        let mut scaled_data: Vec<f32> = input_data.iter().map(|&x| x / temperature).collect();

        // Numerical stability: subtract max
        let max_val = scaled_data
            .iter()
            .cloned()
            .fold(f32::NEG_INFINITY, f32::max);
        for x in &mut scaled_data {
            *x -= max_val;
        }

        // Compute exp and sum for normalization
        let exp_data: Vec<f32> = scaled_data.iter().map(|&x| x.exp()).collect();
        let exp_sum: f32 = exp_data.iter().sum();

        // Compute weighted average of indices
        let mut weighted_sum = 0.0;
        for (i, &exp_val) in exp_data.iter().enumerate() {
            let probability = exp_val / exp_sum;
            weighted_sum += (i as f32) * probability;
        }

        // Return as scalar tensor
        Tensor::scalar(weighted_sum)
    }

    /// Gumbel-based argmax approximation
    pub fn gumbel_argmax(&self, input: &Tensor) -> Result<Tensor> {
        let gumbel_noise = self.sample_gumbel(&input.shape())?;
        let noisy_input = input.add(&gumbel_noise)?;

        self.soft_argmax(&noisy_input)
    }

    /// Straight-through estimator for argmax
    pub fn straight_through_argmax(&self, input: &Tensor) -> Result<(Tensor, Tensor)> {
        // Forward: exact argmax
        let argmax_result = self.exact_argmax(input)?;

        // Backward: straight-through or one-hot gradient
        let grad_input = if self.config.straight_through {
            input.clone()
        } else {
            // Create one-hot vector at argmax position
            self.create_one_hot_at_argmax(input)?
        };

        Ok((argmax_result, grad_input))
    }

    fn exact_argmax(&self, input: &Tensor) -> Result<Tensor> {
        // Find the index of the maximum element
        let data = input.to_vec()?;

        if data.is_empty() {
            return Err(torsh_core::error::TorshError::InvalidArgument(
                "Cannot find argmax of empty tensor".to_string(),
            ));
        }

        let (argmax_idx, _) = data
            .iter()
            .enumerate()
            .max_by(|(_, a), (_, b)| a.partial_cmp(b).unwrap_or(std::cmp::Ordering::Equal))
            .expect("data is checked to be non-empty");

        Tensor::scalar(argmax_idx as f32)
    }

    fn create_one_hot_at_argmax(&self, input: &Tensor) -> Result<Tensor> {
        // Create one-hot vector at argmax position
        let argmax_result = self.exact_argmax(input)?;
        let argmax_idx = argmax_result.to_vec()?[0] as usize;
        let n = input.shape().dims()[input.shape().dims().len() - 1];

        // Create one-hot vector
        let mut one_hot = vec![0.0f32; n];
        if argmax_idx < n {
            one_hot[argmax_idx] = 1.0;
        }

        Tensor::from_vec(one_hot, &[n])
    }

    fn sample_gumbel(&self, shape: &torsh_core::shape::Shape) -> Result<Tensor> {
        // Sample from Gumbel(0, 1) distribution
        let uniform = creation::randn::<f32>(shape.dims())?;
        let eps = 1e-20;
        let log_uniform = uniform.add_scalar(eps)?.log()?;
        let neg_log_uniform = log_uniform.neg()?;
        neg_log_uniform.add_scalar(eps)?.log()?.neg()
    }
}

/// Registry for custom discrete operations
pub struct DiscreteOpRegistry {
    operations: HashMap<String, Box<dyn DiscreteOperation>>,
}

/// Trait for custom discrete operations
pub trait DiscreteOperation: Send + Sync {
    /// Forward pass of the discrete operation
    fn forward(&self, inputs: &[&Tensor], config: &DiscreteConfig) -> Result<Tensor>;

    /// Backward pass with gradient approximation
    fn backward(
        &self,
        grad_output: &Tensor,
        inputs: &[&Tensor],
        config: &DiscreteConfig,
    ) -> Result<Vec<Tensor>>;

    /// Name of the operation
    fn name(&self) -> &str;
}

impl DiscreteOpRegistry {
    pub fn new() -> Self {
        Self {
            operations: HashMap::new(),
        }
    }

    pub fn register<T: DiscreteOperation + 'static>(&mut self, operation: T) {
        self.operations
            .insert(operation.name().to_string(), Box::new(operation));
    }

    pub fn get(&self, name: &str) -> Option<&dyn DiscreteOperation> {
        self.operations.get(name).map(|op| op.as_ref())
    }

    pub fn list_operations(&self) -> Vec<&str> {
        self.operations.keys().map(|s| s.as_str()).collect()
    }
}

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

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

    #[test]
    fn test_smooth_sort() {
        let config = DiscreteConfig::default();
        let sorter = DifferentiableSort::new(config);

        let input = Tensor::from_vec(vec![3.0, 1.0, 4.0, 1.0, 5.0], &[5]).unwrap();
        let result = sorter.smooth_sort(&input).unwrap();

        // Should approximate sorted order
        assert_eq!(result.shape().dims(), &[5]);
    }

    #[test]
    fn test_soft_argmax() {
        let config = DiscreteConfig::default();
        let argmax = DifferentiableArgmax::new(config);

        let input = Tensor::from_vec(vec![1.0, 3.0, 2.0], &[3]).unwrap();
        let result = argmax.soft_argmax(&input).unwrap();

        // Should be close to index 1 (the argmax)
        let value = result.to_vec().unwrap()[0];
        assert!(
            value > 0.5 && value < 2.5,
            "Expected value between 0.5 and 2.5, got {}",
            value
        );
    }

    #[test]
    fn test_top_k_approximation() {
        let config = DiscreteConfig::default();
        let top_k = DifferentiableTopK::new(2, config);

        let input = Tensor::from_vec(vec![1.0, 5.0, 3.0, 2.0, 4.0], &[5]).unwrap();
        let result = top_k.smooth_top_k(&input).unwrap();

        // Should approximate selecting top-2 elements
        assert_eq!(result.shape().dims(), &[5]);
    }

    #[test]
    fn test_gumbel_sampling() {
        let config = DiscreteConfig::default();
        let sorter = DifferentiableSort::new(config);

        let shape = Shape::new(vec![10]);
        let gumbel_samples = sorter.sample_gumbel(&shape).unwrap();

        // Check that we get the right shape
        assert_eq!(gumbel_samples.shape().dims(), &[10]);
    }

    #[test]
    fn test_straight_through_gradients() {
        let mut config = DiscreteConfig::default();
        config.straight_through = true;

        let argmax = DifferentiableArgmax::new(config);
        let input = Tensor::from_vec(vec![1.0, 3.0, 2.0], &[3]).unwrap();

        let (_forward, backward) = argmax.straight_through_argmax(&input).unwrap();

        // Backward should be the same as input for straight-through
        assert_eq!(backward.shape(), input.shape());
    }

    #[test]
    fn test_variance_reduction_config() {
        let config = DiscreteConfig {
            variance_reduction: VarianceReduction::ControlVariates,
            num_samples: 200,
            ..Default::default()
        };

        assert_eq!(
            config.variance_reduction,
            VarianceReduction::ControlVariates
        );
        assert_eq!(config.num_samples, 200);
    }

    #[test]
    fn test_operation_registry() {
        struct DummyOp;

        impl DiscreteOperation for DummyOp {
            fn forward(&self, _inputs: &[&Tensor], _config: &DiscreteConfig) -> Result<Tensor> {
                Ok(Tensor::zeros(&[1], torsh_core::DeviceType::Cpu)?)
            }

            fn backward(
                &self,
                _grad_output: &Tensor,
                _inputs: &[&Tensor],
                _config: &DiscreteConfig,
            ) -> Result<Vec<Tensor>> {
                Ok(vec![])
            }

            fn name(&self) -> &str {
                "dummy"
            }
        }

        let mut registry = DiscreteOpRegistry::new();
        registry.register(DummyOp);

        assert!(registry.get("dummy").is_some());
        assert_eq!(registry.list_operations(), vec!["dummy"]);
    }
}
