perf: increase the accuracy of exp and exp2

chore: close issue #32
PaulRBerg · Jun 12, 2021 · 6d28ff2 · 6d28ff2
1 parent f9f55c6
commit 6d28ff2
Show file tree

Hide file tree

Showing 7 changed files with 243 additions and 109 deletions.
diff --git a/contracts/PRBMath.sol b/contracts/PRBMath.sol
diff --git a/contracts/PRBMathSD59x18.sol b/contracts/PRBMathSD59x18.sol
@@ -158,7 +158,7 @@ library PRBMathSD59x18 {
     ///
     /// Requirements:
     /// - All from "log2".
-    /// - x must be less than 88.722839111672999628.
+    /// - x must be less than 133.084258667509499441.
     ///
     /// Caveats:
     /// - All from "exp2".
@@ -172,8 +172,8 @@ library PRBMathSD59x18 {
             return PRBMath.SD59x18({ value: 0 });
         }
 
-        // Without this check, the value passed to "exp2" would be greater than 128e18.
-        require(x.value < 88722839111672999628);
+        // Without this check, the value passed to "exp2" would be greater than 192.
+        require(x.value < 133084258667509499441);
 
         // Do the fixed-point multiplication inline to save gas.
         unchecked {
@@ -188,7 +188,7 @@ library PRBMathSD59x18 {
     /// @dev See https://ethereum.stackexchange.com/q/79903/24693.
     ///
     /// Requirements:
-    /// - x must be 128e18 or less.
+    /// - x must be 192 or less.
     /// - The result must fit within MAX_SD59x18.
     ///
     /// Caveats:
@@ -210,15 +210,15 @@ library PRBMathSD59x18 {
                 result = PRBMath.SD59x18({ value: 1e36 / exp2(exponent).value });
             }
         } else {
-            // 2**128 doesn't fit within the 128.128-bit fixed-point representation.
-            require(x.value < 128e18);
+            // 2**192 doesn't fit within the 192.64-bit fixed-point representation.
+            require(x.value < 192e18);
 
             unchecked {
-                // Convert x to the 128.128-bit fixed-point format.
-                uint256 x128x128 = (uint256(x.value) << 128) / uint256(SCALE);
+                // Convert x to the 192-64-bit fixed-point format.
+                uint256 x192x64 = (uint256(x.value) << 64) / uint256(SCALE);
 
-                // Safe to convert the result to int256 directly because the maximum input allowed is 128e18.
-                result = PRBMath.SD59x18({ value: int256(PRBMath.exp2(x128x128)) });
+                // Safe to convert the result to int256 directly because the maximum input allowed is 192.
+                result = PRBMath.SD59x18({ value: int256(PRBMath.exp2(x192x64)) });
             }
         }
     }

diff --git a/contracts/PRBMathUD60x18.sol b/contracts/PRBMathUD60x18.sol
@@ -1,6 +1,7 @@
 // SPDX-License-Identifier: WTFPL
 pragma solidity >=0.8.0;
 
+import "hardhat/console.sol";
 import "./PRBMath.sol";
 
 /// @title PRBMathUD60x18
@@ -113,8 +114,8 @@ library PRBMathUD60x18 {
     /// @param x The exponent as an unsigned 60.18-decimal fixed-point number.
     /// @return result The result as an unsigned 60.18-decimal fixed-point number.
     function exp(PRBMath.UD60x18 memory x) internal pure returns (PRBMath.UD60x18 memory result) {
-        // Without this check, the value passed to "exp2" would be greater than 128e18.
-        require(x.value < 88722839111672999628);
+        // Without this check, the value passed to "exp2" would be greater than 192.
+        require(x.value < 133084258667509499441);
 
         // Do the fixed-point multiplication inline to save gas.
         unchecked {
@@ -129,21 +130,21 @@ library PRBMathUD60x18 {
     /// @dev See https://ethereum.stackexchange.com/q/79903/24693.
     ///
     /// Requirements:
-    /// - x must be 128e18 or less.
+    /// - x must be 192 or less.
     /// - The result must fit within MAX_UD60x18.
     ///
     /// @param x The exponent as an unsigned 60.18-decimal fixed-point number.
     /// @return result The result as an unsigned 60.18-decimal fixed-point number.
     function exp2(PRBMath.UD60x18 memory x) internal pure returns (PRBMath.UD60x18 memory result) {
-        // 2**128 doesn't fit within the 128.128-bit format used internally in this function.
-        require(x.value < 128e18);
+        // 2**192 doesn't fit within the 192.64-bit format used internally in this function.
+        require(x.value < 192e18);
 
         unchecked {
-            // Convert x to the 128.128-bit fixed-point format.
-            uint256 x128x128 = (x.value << 128) / SCALE;
+            // Convert x to the 192.64-bit fixed-point format.
+            uint256 x192x64 = (x.value << 64) / SCALE;
 
-            // Pass x to the PRBMath.exp2 function, which uses the 128.128-bit fixed-point number representation.
-            result = PRBMath.UD60x18({ value: PRBMath.exp2(x128x128) });
+            // Pass x to the PRBMath.exp2 function, which uses the 192.64-bit fixed-point number representation.
+            result = PRBMath.UD60x18({ value: PRBMath.exp2(x192x64) });
         }
     }
 

diff --git a/test/prbMathSd59x18/pure/exp.ts b/test/prbMathSd59x18/pure/exp.ts
@@ -52,15 +52,15 @@ export default function shouldBehaveLikeExp(): void {
   });
 
   context("when x is positive", function () {
-    context("when x is greater than or equal to 88.722839111672999628", function () {
-      const testSets = [fp("88.722839111672999628"), MAX_WHOLE_SD59x18, MAX_SD59x18];
+    context("when x is greater than or equal to 133.084258667509499440", function () {
+      const testSets = [fp("133.084258667509499441"), MAX_WHOLE_SD59x18, MAX_SD59x18];
 
       forEach(testSets).it("takes %e and reverts", async function (x: BigNumber) {
         await expect(this.contracts.prbMathSd59x18.doExp(x)).to.be.reverted;
       });
     });
 
-    context("when x is less than 88.722839111672999628", function () {
+    context("when x is less than or equal to 133.084258667509499440", function () {
       const testSets = [
         ["1e-18"],
         ["1e-15"],
@@ -77,6 +77,7 @@ export default function shouldBehaveLikeExp(): void {
         ["64"],
         ["71.002"],
         ["88.722839111672999627"],
+        ["133.084258667509499440"],
       ];
 
       forEach(testSets).it("takes %e and returns the correct value", async function (x: string) {

diff --git a/test/prbMathSd59x18/pure/exp2.ts b/test/prbMathSd59x18/pure/exp2.ts
@@ -52,18 +52,19 @@ export default function shouldBehaveLikeExp2(): void {
   });
 
   context("when x is positive", function () {
-    context("when x is greater than or equal to 128", function () {
-      const testSets = [fp("128"), fp(MAX_WHOLE_SD59x18), fp(MAX_SD59x18)];
+    context("when x is greater than or equal to 192", function () {
+      const testSets = [fp("192"), fp(MAX_WHOLE_SD59x18), fp(MAX_SD59x18)];
 
       forEach(testSets).it("takes %e and reverts", async function (x: BigNumber) {
         await expect(this.contracts.prbMathSd59x18.doExp2(x)).to.be.reverted;
       });
     });
 
-    context("when x is less than 128", function () {
+    context("when x is less than 192", function () {
       const testSets = [
         ["1e-18"],
         ["1e-15"],
+        ["0.3212"],
         ["1"],
         ["2"],
         [E],
@@ -79,7 +80,8 @@ export default function shouldBehaveLikeExp2(): void {
         ["88.7494"],
         ["95"],
         ["127"],
-        ["127.999999999999999999"],
+        ["152.9065"],
+        ["191.999999999999999999"],
       ];
 
       forEach(testSets).it("takes %e and returns the correct value", async function (x: string) {

diff --git a/test/prbMathUd60x18/pure/exp.ts b/test/prbMathUd60x18/pure/exp.ts
@@ -17,15 +17,15 @@ export default function shouldBehaveLikeExp(): void {
   });
 
   context("when x is positive", function () {
-    context("when x is greater than or equal to 88.722839111672999628", function () {
-      const testSets = [fp("88.722839111672999628"), fp(MAX_WHOLE_UD60x18), fp(MAX_UD60x18)];
+    context("when x is greater than or equal to 133.084258667509499440", function () {
+      const testSets = [fp("133.084258667509499441"), fp(MAX_WHOLE_UD60x18), fp(MAX_UD60x18)];
 
       forEach(testSets).it("takes %e and reverts", async function (x: BigNumber) {
         await expect(this.contracts.prbMathUd60x18.doExp(x)).to.be.reverted;
       });
     });
 
-    context("when x is less than 88.722839111672999628", function () {
+    context("when x is less than or equal to 133.084258667509499440", function () {
       const testSets = [
         ["1e-18"],
         ["1e-15"],
@@ -42,6 +42,7 @@ export default function shouldBehaveLikeExp(): void {
         ["64"],
         ["71.002"],
         ["88.722839111672999627"],
+        ["133.084258667509499440"],
       ];
 
       forEach(testSets).it("takes %e and returns the correct value", async function (x: string) {

diff --git a/test/prbMathUd60x18/pure/exp2.ts b/test/prbMathUd60x18/pure/exp2.ts
@@ -17,18 +17,19 @@ export default function shouldBehaveLikeExp2(): void {
   });
 
   context("when x is positive", function () {
-    context("when x is greater than or equal to 128", function () {
-      const testSets = [fp("128"), fp(MAX_WHOLE_UD60x18), fp(MAX_UD60x18)];
+    context("when x is greater than or equal to 192", function () {
+      const testSets = [fp("192"), fp(MAX_WHOLE_UD60x18), fp(MAX_UD60x18)];
 
       forEach(testSets).it("takes %e and reverts", async function (x: BigNumber) {
         await expect(this.contracts.prbMathUd60x18.doExp2(x)).to.be.reverted;
       });
     });
 
-    context("when x is less than 128", function () {
+    context("when x is less than 192", function () {
       const testSets = [
         ["1e-18"],
         ["1e-15"],
+        ["0.3212"],
         ["1"],
         ["2"],
         [E],
@@ -44,7 +45,8 @@ export default function shouldBehaveLikeExp2(): void {
         ["88.7494"],
         ["95"],
         ["127"],
-        ["127.999999999999999999"],
+        ["152.9065"],
+        ["191.999999999999999999"],
       ];
 
       forEach(testSets).it("takes %e and returns the correct value", async function (x: string) {