From c6c80c906c0ec7d36f7bca3808b615c6113891f6 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E5=88=98=E8=88=AA=E5=AE=87?= <3364451258@qq.com>
Date: Tue, 16 Jun 2026 23:40:52 +0800
Subject: [PATCH] =?UTF-8?q?feat:=20Reed-Solomon=20=E7=BA=A0=E9=94=99?=
 =?UTF-8?q?=E7=BC=96=E7=A0=81=20+=20=E6=95=B0=E6=8D=AE=E4=BA=A4=E9=94=99?=
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---
 core/src/ecc/reed_solomon.rs | 145 ++++++++++++++++++++++++++++++++++-
 1 file changed, 144 insertions(+), 1 deletion(-)

diff --git a/core/src/ecc/reed_solomon.rs b/core/src/ecc/reed_solomon.rs
index 928e124..0d6c4a2 100644
--- a/core/src/ecc/reed_solomon.rs
+++ b/core/src/ecc/reed_solomon.rs
@@ -1 +1,144 @@
-// FIXME: Reed-Solomon 编码器 — Task 4
+use crate::ecc::galois;
+
+/// 计算多项式相乘: a(x) * b(x) in GF(2⁸)
+fn poly_mul(a: &[u8], b: &[u8]) -> Vec<u8> {
+    let mut result = vec![0u8; a.len() + b.len() - 1];
+    for (i, &ai) in a.iter().enumerate() {
+        for (j, &bj) in b.iter().enumerate() {
+            result[i + j] = galois::add(result[i + j], galois::mul(ai, bj));
+        }
+    }
+    result
+}
+
+/// 构造 RS 生成多项式: ∏ᵢ₌₀ⁿ⁻¹ (x - αⁱ)
+/// 参数 n: 纠错码字数
+fn generator_polynomial(n: u8) -> Vec<u8> {
+    let mut g = vec![1u8]; // 从 g(x) = 1 开始
+    for i in 0..n {
+        // g(x) *= (x + αⁱ)  in GF(2⁸) — 注意加法和减法相同
+        let factor = vec![1u8, galois::pow(2, i as usize)];
+        g = poly_mul(&g, &factor);
+    }
+    g
+}
+
+/// 多项式长除法: message(x) * xⁿ ÷ generator(x)，返回余数（即纠错码字）
+/// data: 数据码字
+/// ec_count: 纠错码字数量
+pub fn compute_ec(data: &[u8], ec_count: u8) -> Vec<u8> {
+    let gen = generator_polynomial(ec_count);
+    // 构造被除数: data 后接 ec_count 个零
+    let mut dividend = vec![0u8; data.len() + ec_count as usize];
+    dividend[..data.len()].copy_from_slice(data);
+
+    // 多项式长除法
+    for i in 0..data.len() {
+        let coef = dividend[i];
+        if coef != 0 {
+            for (j, &g) in gen.iter().enumerate() {
+                dividend[i + j] = galois::add(dividend[i + j], galois::mul(coef, g));
+            }
+        }
+    }
+
+    // 余数 = 最后 ec_count 个系数
+    dividend[data.len()..].to_vec()
+}
+
+/// 对一组数据块生成纠错码字并交错排列
+/// blocks: 每个数据块的内容
+/// ec_count: 每块纠错码字数
+/// 返回: 数据码字交错 + 纠错码字交错
+pub fn interleave(blocks: &[Vec<u8>], ec_count: u8) -> Vec<u8> {
+    // 数据码字交错：取每块第1个，再取每块第2个...
+    let max_data = blocks.iter().map(|b| b.len()).max().unwrap_or(0);
+    let mut result = Vec::new();
+
+    for i in 0..max_data {
+        for block in blocks.iter() {
+            if i < block.len() {
+                result.push(block[i]);
+            }
+        }
+    }
+
+    // 对每个块计算 EC
+    let ec_blocks: Vec<Vec<u8>> = blocks
+        .iter()
+        .map(|b| compute_ec(b, ec_count))
+        .collect();
+
+    // EC 码字交错
+    for i in 0..ec_count as usize {
+        for ec in ec_blocks.iter() {
+            result.push(ec[i]);
+        }
+    }
+
+    result
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn test_generator_polynomial_degree() {
+        let g = generator_polynomial(7);
+        // 7 个纠错码字 → 生成多项式应为 7 次，共 8 个系数
+        assert_eq!(g.len(), 8);
+        // 首项系数应为 1 (x⁷ 的系数)
+        assert_eq!(g[0], 1);
+    }
+
+    #[test]
+    fn test_compute_ec_zero_data() {
+        // 全零数据 + EC → EC 应全零
+        let ec = compute_ec(&vec![0u8; 19], 7);
+        assert_eq!(ec, vec![0u8; 7]);
+    }
+
+    #[test]
+    fn test_compute_ec_length() {
+        let data = vec![
+            1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19,
+        ];
+        let ec = compute_ec(&data, 10);
+        // EC 码字数量应等于 ec_count
+        assert_eq!(ec.len(), 10);
+    }
+
+    #[test]
+    fn test_compute_ec_nonzero() {
+        // 非零数据应产生非零 EC
+        let data = vec![
+            0x10, 0x20, 0x0C, 0x56, 0x61, 0x80, 0xEC, 0x11, 0xEC, 0x11, 0xEC, 0x11, 0xEC, 0x11,
+            0xEC, 0x11, 0xA3, 0x12, 0xD3,
+        ];
+        let ec = compute_ec(&data, 7);
+        assert_eq!(ec.len(), 7);
+        // 非零数据 + 非零多项式 → EC 不应全零
+        assert!(ec.iter().any(|&x| x != 0));
+    }
+
+    #[test]
+    fn test_interleave_basic() {
+        let b1 = vec![1, 2, 3];
+        let b2 = vec![4, 5];
+        // 数据交错: 1, 4, 2, 5, 3
+        // EC 交错: b1_ec[0], b2_ec[0], b1_ec[1], b2_ec[1], ...
+        let result = interleave(&[b1, b2], 2);
+        // 前 5 个是数据交错
+        assert_eq!(&result[..5], &[1, 4, 2, 5, 3]);
+    }
+
+    #[test]
+    fn test_interleave_single_block() {
+        let b1 = vec![10, 20, 30];
+        let result = interleave(&[b1.clone()], 3);
+        // 单个块: 数据直接输出 + 3 个 EC
+        assert_eq!(&result[..3], &[10, 20, 30]);
+        assert_eq!(result.len(), 6); // 3 data + 3 ec
+    }
+}