time stretch bugfix (#727)

crates/hyperdrive-math/src/utils.rs

@@ -2,15 +2,15 @@ use ethers::types::{I256, U256};
 use fixed_point::FixedPoint;
 use fixed_point_macros::{fixed, uint256};
 
-pub fn get_time_stretch(mut rate: FixedPoint, position_duration: FixedPoint) -> FixedPoint {
+pub fn get_time_stretch(rate: FixedPoint, position_duration: FixedPoint) -> FixedPoint {
     let seconds_in_a_year = FixedPoint::from(U256::from(60 * 60 * 24 * 365));
-    let annualized_time = position_duration / seconds_in_a_year;
-    rate = (U256::from(rate) * uint256!(100)).into();
     // Calculate the benchmark time stretch. This time stretch is tuned for
     // a position duration of 1 year.
-    let time_stretch = fixed!(1e18) / (fixed!(5.24592e18) / (fixed!(0.04665e18) * rate));
+    let time_stretch = fixed!(5.24592e18)
+        / (fixed!(0.04665e18) * FixedPoint::from(U256::from(rate) * uint256!(100)));
+    let time_stretch = fixed!(1e18) / time_stretch;
     // if the position duration is 1 year, we can return the benchmark
-    if annualized_time == fixed!(1e18) {
+    if position_duration == seconds_in_a_year {
         return time_stretch;
     }
 
@@ -33,6 +33,8 @@ pub fn get_time_stretch(mut rate: FixedPoint, position_duration: FixedPoint) ->
     // p = ratio ** timeStretch
     //          =>
     // timeStretch = ln(p) / ln(ratio)
+    let target_spot_price =
+        fixed!(1e18) / (fixed!(1e18) + rate.mul_div_down(position_duration, seconds_in_a_year));
     let benchmark_reserve_ratio = fixed!(1e18)
         / calculate_initial_bond_reserves(
             fixed!(1e18),
@@ -41,16 +43,12 @@ pub fn get_time_stretch(mut rate: FixedPoint, position_duration: FixedPoint) ->
             seconds_in_a_year,
             time_stretch,
         );
-    let target_spot_price = fixed!(1e18) / (fixed!(1e18) * annualized_time);
     // target spot price and benchmark reserve ratio will have negative ln,
     // but since we are dividing them we can cast to positive before converting types
     // TODO: implement FixedPoint `neg` pub fn to support "-"
-    let new_time_stretch = U256::from(FixedPoint::from(-FixedPoint::ln(I256::from(
-        target_spot_price,
-    )))) / U256::from(FixedPoint::from(-FixedPoint::ln(I256::from(
-        benchmark_reserve_ratio,
-    ))));
-    new_time_stretch.into()
+    let new_time_stretch = FixedPoint::from(-FixedPoint::ln(I256::from(target_spot_price)))
+        / FixedPoint::from(-FixedPoint::ln(I256::from(benchmark_reserve_ratio)));
+    new_time_stretch
 }
 
 pub fn get_effective_share_reserves(
@@ -117,15 +115,18 @@ mod tests {
         let chain = TestChainWithMocks::new(1).await?;
         let mock = chain.mock_hyperdrive_math();
         // Fuzz the rust and solidity implementations against each other.
-        let apr = fixed!(0.05e18); // 5%
-        let seconds_in_a_year = U256::from(60 * 60 * 24 * 365);
+        let seconds_in_ten_years = U256::from(10 * 60 * 60 * 24 * 365);
+        let seconds_in_a_day = U256::from(60 * 60 * 24);
         let mut rng = thread_rng();
         for _ in 0..*FAST_FUZZ_RUNS {
             // Get the current state of the mock contract
-            let state = rng.gen::<State>();
-            let actual_t = get_time_stretch(apr, seconds_in_a_year.into());
+            let position_duration = rng.gen_range(
+                FixedPoint::from(seconds_in_a_day)..=FixedPoint::from(seconds_in_ten_years),
+            );
+            let apr = rng.gen_range(fixed!(0.001e18)..=fixed!(10.0e18));
+            let actual_t = get_time_stretch(apr, position_duration);
             match mock
-                .calculate_time_stretch(apr.into(), seconds_in_a_year)
+                .calculate_time_stretch(apr.into(), position_duration.into())
                 .call()
                 .await
             {