perf wExp

src/irm/libraries/ErrorsLib.sol

@@ -4,5 +4,6 @@ pragma solidity ^0.8.0;
 library ErrorsLib {
     string internal constant MAX_INT128_EXCEEDED = "max int128 exceeded";
     string internal constant INPUT_TOO_LARGE = "input too large";
+    string internal constant WEXP_OVERFLOW = "wExp overflow";
     string internal constant NOT_MORPHO = "not Morpho";
 }

src/irm/libraries/MathLib.sol

@@ -2,6 +2,7 @@
 pragma solidity ^0.8.0;
 
 import {WAD, MathLib as MorphoMathLib} from "morpho-blue/libraries/MathLib.sol";
+import {ErrorsLib} from "./ErrorsLib.sol";
 
 int256 constant WAD_INT = int256(WAD);
 
@@ -15,29 +16,31 @@ library MathLib {
     int256 private constant LN2_INT = 0.693147180559945309 ether;
 
     /// @dev Returns an approximation of exp.
-    /// @dev Expects input between -ln(2**256) and ln(2**256).
     function wExp(int256 x) internal pure returns (uint256) {
         unchecked {
+            // Revert if x > ln(2^256-1) ~ 177.
+            require(x <= 177.44567822334599921 ether, ErrorsLib.WEXP_OVERFLOW);
+
             // Decompose x as x = q * ln(2) + r with q an integer and -ln(2) < r < ln(2).
             int256 q = x / LN2_INT;
-            // Safe unchecked * because |q * LN2_INT| <= x.
+            // Safe unchecked because |q * LN2_INT| <= x.
             int256 r = x - q * LN2_INT;
 
             // Compute e^r.
             int256 firstTerm = WAD_INT;
             int256 secondTerm = r;
-            // Safe unchecked * because |r| < 1.
+            // Safe unchecked because |r| < 1.
             int256 thirdTerm = r.wMulDown(r) / 2;
-            // Safe unchecked * because |r| < 1.
+            // Safe unchecked because |r| < 1.
             int256 fourthTerm = thirdTerm.wMulDown(r) / 3;
-            // Safe unchecked * because |r| < 1.
-            int256 fifthTerm = fourthTerm.wMulDown(r) / 12;
-            // Safe unchecked + because expR < 2.
+            // Safe unchecked because |r| < 1.
+            int256 fifthTerm = fourthTerm.wMulDown(r) / 4;
+            // Safe unchecked because expR < 2 and the sum is positive.
             uint256 expR = uint256(firstTerm + secondTerm + thirdTerm + fourthTerm + fifthTerm);
 
             // Return e^x = 2^q * e^r.
-            if (q >= 0) return (1 << uint256(q)) * expR;
-            else return expR / (1 << uint256(-q));
+            if (q >= 0) return expR << uint256(q);
+            else return expR >> uint256(-q);
         }
     }
 

test/irm/MathLibTest.sol

@@ -9,13 +9,35 @@ contract MathLibTest is Test {
     using MathLib for uint256;
 
     function testWExp() public {
+        assertApproxEqRel(MathLib.wExp(-14 ether), 0.00000083131 ether, 0.01 ether);
+        assertApproxEqRel(MathLib.wExp(-13 ether), 0.00000226033 ether, 0.01 ether);
+        assertApproxEqRel(MathLib.wExp(-12 ether), 0.00000614421 ether, 0.01 ether);
+        assertApproxEqRel(MathLib.wExp(-11 ether), 0.00001670164 ether, 0.01 ether);
+        assertApproxEqRel(MathLib.wExp(-10 ether), 0.00004539992 ether, 0.01 ether);
+        assertApproxEqRel(MathLib.wExp(-9 ether), 0.0001234098 ether, 0.01 ether);
+        assertApproxEqRel(MathLib.wExp(-8 ether), 0.00033546262 ether, 0.01 ether);
+        assertApproxEqRel(MathLib.wExp(-7 ether), 0.00091188196 ether, 0.01 ether);
+        assertApproxEqRel(MathLib.wExp(-6 ether), 0.00247875217 ether, 0.01 ether);
+        assertApproxEqRel(MathLib.wExp(-5 ether), 0.00673794699 ether, 0.01 ether);
+        assertApproxEqRel(MathLib.wExp(-4 ether), 0.01831563888 ether, 0.01 ether);
         assertApproxEqRel(MathLib.wExp(-3 ether), 0.04978706836 ether, 0.01 ether);
         assertApproxEqRel(MathLib.wExp(-2 ether), 0.13533528323 ether, 0.01 ether);
         assertApproxEqRel(MathLib.wExp(-1 ether), 0.36787944117 ether, 0.01 ether);
         assertEq(MathLib.wExp(0 ether), 1.0 ether);
         assertApproxEqRel(MathLib.wExp(1 ether), 2.71828182846 ether, 0.01 ether);
         assertApproxEqRel(MathLib.wExp(2 ether), 7.38905609893 ether, 0.01 ether);
         assertApproxEqRel(MathLib.wExp(3 ether), 20.0855369232 ether, 0.01 ether);
+        assertApproxEqRel(MathLib.wExp(4 ether), 54.5981500331 ether, 0.01 ether);
+        assertApproxEqRel(MathLib.wExp(5 ether), 148.413159103 ether, 0.01 ether);
+        assertApproxEqRel(MathLib.wExp(6 ether), 403.428793493 ether, 0.01 ether);
+        assertApproxEqRel(MathLib.wExp(7 ether), 1096.63315843 ether, 0.01 ether);
+        assertApproxEqRel(MathLib.wExp(8 ether), 2980.95798704 ether, 0.01 ether);
+        assertApproxEqRel(MathLib.wExp(9 ether), 8103.08392758 ether, 0.01 ether);
+        assertApproxEqRel(MathLib.wExp(10 ether), 22026.4657948 ether, 0.01 ether);
+        assertApproxEqRel(MathLib.wExp(11 ether), 59874.1417152 ether, 0.01 ether);
+        assertApproxEqRel(MathLib.wExp(12 ether), 162754.791419 ether, 0.01 ether);
+        assertApproxEqRel(MathLib.wExp(13 ether), 442413.392009 ether, 0.01 ether);
+        assertApproxEqRel(MathLib.wExp(14 ether), 1202604.28416 ether, 0.01 ether);
     }
 
     function testWExp(int256 x) public {
@@ -31,6 +53,17 @@ contract MathLibTest is Test {
         x = bound(x, -3 ether, 3 ether);
         assertApproxEqRel(MathLib.wExp(x), wExpRef(x), 0.03 ether);
     }
+
+    function testWExpRevertTooSmall(int256 x) public {
+        vm.assume(x <= -178 ether);
+        assertEq(MathLib.wExp(x), 0);
+    }
+
+    function testWExpRevertTooBig(int256 x) public {
+        vm.assume(x >= 178 ether);
+        vm.expectRevert();
+        MathLib.wExp(x);
+    }
 }
 
 function wExpRef(int256 x) pure returns (uint256) {