feat: Scaffold StableSwap invariant curve math

contracts/tradeflow/src/utils/math.rs

@@ -0,0 +1,110 @@
+use soroban_sdk::Env;
+use super::fixed_point::*;
+
+/// Calculates the amount out for a StableSwap invariant curve
+/// 
+/// The StableSwap invariant (similar to Curve Finance) concentrates liquidity around the $1.00 peg
+/// for stablecoin pairs, drastically reducing slippage compared to constant-product AMMs.
+/// 
+/// The invariant formula is: A * (x + y) + x * y = k
+/// where A is the amplification coefficient that determines how "stable" the pool behaves.
+/// 
+/// # Parameters:
+/// - `amount_in`: Amount of tokens being deposited
+/// - `reserve_in`: Current reserve of the input token
+/// - `reserve_out`: Current reserve of the output token  
+/// - `amplification_coefficient`: Amplification parameter A (higher = more stable, less slippage)
+/// 
+/// # Returns:
+/// - `u128`: Amount of output tokens (dummy value for now)
+/// 
+/// # Newton-Raphson Method:
+/// The StableSwap curve requires solving a polynomial equation that cannot be expressed
+/// in closed form. We use the Newton-Raphson iterative method to find the root:
+/// 
+/// 1. Start with an initial guess for the output amount
+/// 2. Iteratively refine using: x_{n+1} = x_n - f(x_n) / f'(x_n)
+/// 3. Where f(x) is the invariant equation and f'(x) is its derivative
+/// 4. Continue until the change between iterations is below a tolerance threshold
+/// 
+/// The invariant we need to solve is:
+/// A * (x + y) + x * y = A * (x_new + y_new) + x_new * y_new
+/// 
+/// Where x_new = x + amount_in and y_new = y - amount_out
+/// 
+/// This expands to a quadratic in terms of amount_out, which we solve iteratively.
+pub fn calculate_stableswap_amount_out(
+    _env: &Env,
+    amount_in: u128,
+    reserve_in: u128,
+    reserve_out: u128,
+    amplification_coefficient: u128,
+) -> u128 {
+    // Input validation - prevent division by zero and negative scenarios
+    if reserve_in == 0 || reserve_out == 0 {
+        panic!("Reserves cannot be zero");
+    }
+
+    if amount_in == 0 {
+        return 0;
+    }
+
+    if amplification_coefficient == 0 {
+        panic!("Amplification coefficient cannot be zero");
+    }
+
+    // TODO: Implement actual Newton-Raphson solver in future phase
+    // For now, return a dummy value as specified in requirements
+
+    // The dummy value is calculated as a simple proportion of the input
+    // This is NOT the correct StableSwap calculation, just a placeholder
+    let dummy_output = mul_div_down(_env, amount_in, reserve_out, reserve_in + amount_in);
+
+    dummy_output
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn test_stableswap_basic() {
+        let env = Env::default();
+
+        // Test basic scenario
+        let amount_in = 1000;
+        let reserve_in = 10000;
+        let reserve_out = 10000;
+        let amplification = 100; // Typical amplification coefficient
+
+        let result = calculate_stableswap_amount_out(&env, amount_in, reserve_in, reserve_out, amplification);
+
+        // Should return some positive amount (dummy calculation for now)
+        assert!(result > 0);
+        assert!(result < reserve_out); // Cannot withdraw more than reserve
+    }
+
+    #[test]
+    #[should_panic(expected = "Reserves cannot be zero")]
+    fn test_stableswap_zero_reserves() {
+        let env = Env::default();
+
+        calculate_stableswap_amount_out(&env, 1000, 0, 10000, 100);
+    }
+
+    #[test]
+    fn test_stableswap_zero_input() {
+        let env = Env::default();
+
+        let result = calculate_stableswap_amount_out(&env, 0, 10000, 10000, 100);
+        assert_eq!(result, 0);
+    }
+
+    #[test]
+    #[should_panic(expected = "Amplification coefficient cannot be zero")]
+    fn test_stableswap_zero_amplification() {
+        let env = Env::default();
+
+        calculate_stableswap_amount_out(&env, 1000, 10000, 10000, 0);
+    }
+}

contracts/tradeflow/src/utils/mod.rs

@@ -1 +1,2 @@
 pub mod fixed_point;
+pub mod math;