// CARRY Fibonacci + Taylor Construction Braid (FTB) Research Module
// RESEARCH HYPOTHESIS: Evaluates mapping of Fibonacci recurrence + Taylor operator expansions to B3 braids.
//
// Formally labeled: RESEARCH_HYPOTHESIS (unproven quantum algorithm until validated).

use std::fmt;
use crate::quantum::core::Gate;

/// Research status tag for experimental constructions.
#[derive(Debug, Clone, Copy, PartialEq, Eq)]
pub enum ResearchStatus {
    ResearchHypothesis,
    ValidatedTheorem,
    UnprovenCandidate,
}

impl fmt::Display for ResearchStatus {
    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
        match self {
            ResearchStatus::ResearchHypothesis => write!(f, "RESEARCH_HYPOTHESIS"),
            ResearchStatus::ValidatedTheorem => write!(f, "VALIDATED_THEOREM"),
            ResearchStatus::UnprovenCandidate => write!(f, "UNPROVEN_CANDIDATE"),
        }
    }
}

/// Fibonacci-Taylor Braid (FTB) Construction Object.
#[derive(Debug, Clone)]
pub struct FibonacciTaylorBraid {
    pub order_n: usize,
    pub time_t: f64,
    pub status: ResearchStatus,
    pub fibonacci_sequence: Vec<u64>,
    pub taylor_coefficients: Vec<f64>,
    pub braid_word: Vec<String>,
}

impl FibonacciTaylorBraid {
    pub fn new(order_n: usize, time_t: f64) -> Self {
        // 1. Compute Fibonacci recurrence F[n] = F[n-1] + F[n-2]
        let mut fib = vec![1, 1];
        for i in 2..order_n.max(2) {
            let next = fib[i - 1] + fib[i - 2];
            fib.push(next);
        }

        // 2. Compute Taylor expansion coefficients: c_k = t^k / k!
        // CE-3 fix: stop accumulating once the term would overflow f64 or
        // becomes negligible (|term| < 1e-15), to prevent Inf gate angles.
        let mut taylor = Vec::new();
        let mut factorial = 1.0f64;
        let mut t_pow = 1.0f64;
        for k in 0..order_n {
            if k > 0 {
                factorial *= k as f64;
                t_pow *= time_t;
            }
            let term = t_pow / factorial;
            if !term.is_finite() {
                // Truncate series here; further terms would be Inf or NaN.
                break;
            }
            taylor.push(term);
            if term.abs() < 1e-15 {
                // Series has converged; remaining terms are negligible.
                break;
            }
        }

        // 3. Construct braid generator sequence in B3 group: sigma_1, sigma_2
        let mut braid_word = Vec::new();
        for k in 0..order_n {
            let fib_val = fib[k % fib.len()];
            if fib_val % 2 == 0 {
                braid_word.push(format!("sigma_1^{}", k + 1));
            } else {
                braid_word.push(format!("sigma_2^{}", k + 1));
            }
        }

        Self {
            order_n,
            time_t,
            status: ResearchStatus::ResearchHypothesis,
            fibonacci_sequence: fib,
            taylor_coefficients: taylor,
            braid_word,
        }
    }

    /// Map FTB braid word onto a sequence of single and two-qubit quantum gates.
    pub fn synthesize_circuit_gates(&self, target_q1: usize, target_q2: usize) -> Vec<Gate> {
        let mut gates = Vec::new();

        for (k, coeff) in self.taylor_coefficients.iter().enumerate() {
            let angle = coeff * (self.fibonacci_sequence[k % self.fibonacci_sequence.len()] as f64);
            if k % 2 == 0 {
                gates.push(Gate::rx(target_q1, angle));
                gates.push(Gate::cnot(target_q1, target_q2));
            } else {
                gates.push(Gate::rz(target_q2, angle));
                gates.push(Gate::cz(target_q1, target_q2));
            }
        }

        gates
    }
}