⚡️ Optimize gas consumption for mulDivUp and mulDivDown (#306)

Co-authored-by: t11s <greenfeatherhelp@gmail.com>

Author: MerlinEgalite

.gas-snapshot

@@ -146,22 +146,22 @@ ERC20Test:testTransfer() (gas: 60272)
 ERC20Test:testTransfer(address,uint256) (runs: 256, μ: 58773, ~: 60484)
 ERC20Test:testTransferFrom() (gas: 83777)
 ERC20Test:testTransferFrom(address,uint256,uint256) (runs: 256, μ: 86464, ~: 92841)
-ERC4626Test:invariantMetadata() (runs: 256, calls: 3840, reverts: 2881)
+ERC4626Test:invariantMetadata() (runs: 256, calls: 3840, reverts: 2885)
 ERC4626Test:testFailDepositWithNoApproval() (gas: 13357)
 ERC4626Test:testFailDepositWithNotEnoughApproval() (gas: 86993)
 ERC4626Test:testFailDepositZero() (gas: 7780)
 ERC4626Test:testFailMintWithNoApproval() (gas: 13296)
 ERC4626Test:testFailRedeemWithNoShareAmount() (gas: 32342)
-ERC4626Test:testFailRedeemWithNotEnoughShareAmount() (gas: 203638)
+ERC4626Test:testFailRedeemWithNotEnoughShareAmount() (gas: 203631)
 ERC4626Test:testFailRedeemZero() (gas: 7967)
 ERC4626Test:testFailWithdrawWithNoUnderlyingAmount() (gas: 32289)
-ERC4626Test:testFailWithdrawWithNotEnoughUnderlyingAmount() (gas: 203615)
-ERC4626Test:testMetadata(string,string) (runs: 256, μ: 1479572, ~: 1471277)
+ERC4626Test:testFailWithdrawWithNotEnoughUnderlyingAmount() (gas: 203595)
+ERC4626Test:testMetadata(string,string) (runs: 256, μ: 1489261, ~: 1481501)
 ERC4626Test:testMintZero() (gas: 54595)
-ERC4626Test:testMultipleMintDepositRedeemWithdraw() (gas: 411940)
-ERC4626Test:testSingleDepositWithdraw(uint128) (runs: 256, μ: 201569, ~: 201579)
-ERC4626Test:testSingleMintRedeem(uint128) (runs: 256, μ: 201484, ~: 201494)
-ERC4626Test:testVaultInteractionsForSomeoneElse() (gas: 286247)
+ERC4626Test:testMultipleMintDepositRedeemWithdraw() (gas: 411747)
+ERC4626Test:testSingleDepositWithdraw(uint128) (runs: 256, μ: 201526, ~: 201536)
+ERC4626Test:testSingleMintRedeem(uint128) (runs: 256, μ: 201451, ~: 201461)
+ERC4626Test:testVaultInteractionsForSomeoneElse() (gas: 286209)
 ERC4626Test:testWithdrawZero() (gas: 52462)
 ERC721Test:invariantMetadata() (runs: 256, calls: 3840, reverts: 2170)
 ERC721Test:testApprove() (gas: 78427)
@@ -240,44 +240,44 @@ ERC721Test:testTransferFromApproveAll() (gas: 92898)
 ERC721Test:testTransferFromApproveAll(uint256,address) (runs: 256, μ: 93182, ~: 93182)
 ERC721Test:testTransferFromSelf() (gas: 64776)
 ERC721Test:testTransferFromSelf(uint256,address) (runs: 256, μ: 65061, ~: 65061)
-FixedPointMathLibTest:testDifferentiallyFuzzSqrt(uint256) (runs: 256, μ: 13827, ~: 4181)
-FixedPointMathLibTest:testDivWadDown() (gas: 841)
-FixedPointMathLibTest:testDivWadDown(uint256,uint256) (runs: 256, μ: 718, ~: 820)
-FixedPointMathLibTest:testDivWadDownEdgeCases() (gas: 446)
-FixedPointMathLibTest:testDivWadUp() (gas: 1003)
-FixedPointMathLibTest:testDivWadUp(uint256,uint256) (runs: 256, μ: 809, ~: 972)
-FixedPointMathLibTest:testDivWadUpEdgeCases() (gas: 462)
-FixedPointMathLibTest:testFailDivWadDownOverflow(uint256,uint256) (runs: 256, μ: 443, ~: 419)
-FixedPointMathLibTest:testFailDivWadDownZeroDenominator() (gas: 342)
-FixedPointMathLibTest:testFailDivWadDownZeroDenominator(uint256) (runs: 256, μ: 397, ~: 397)
-FixedPointMathLibTest:testFailDivWadUpOverflow(uint256,uint256) (runs: 256, μ: 398, ~: 374)
-FixedPointMathLibTest:testFailDivWadUpZeroDenominator() (gas: 342)
-FixedPointMathLibTest:testFailDivWadUpZeroDenominator(uint256) (runs: 256, μ: 396, ~: 396)
-FixedPointMathLibTest:testFailMulDivDownOverflow(uint256,uint256,uint256) (runs: 256, μ: 437, ~: 414)
-FixedPointMathLibTest:testFailMulDivDownZeroDenominator() (gas: 338)
-FixedPointMathLibTest:testFailMulDivDownZeroDenominator(uint256,uint256) (runs: 256, μ: 395, ~: 395)
-FixedPointMathLibTest:testFailMulDivUpOverflow(uint256,uint256,uint256) (runs: 256, μ: 460, ~: 437)
-FixedPointMathLibTest:testFailMulDivUpZeroDenominator() (gas: 339)
-FixedPointMathLibTest:testFailMulDivUpZeroDenominator(uint256,uint256) (runs: 256, μ: 438, ~: 438)
-FixedPointMathLibTest:testFailMulWadDownOverflow(uint256,uint256) (runs: 256, μ: 424, ~: 387)
-FixedPointMathLibTest:testFailMulWadUpOverflow(uint256,uint256) (runs: 256, μ: 401, ~: 364)
-FixedPointMathLibTest:testMulDivDown() (gas: 1883)
-FixedPointMathLibTest:testMulDivDown(uint256,uint256,uint256) (runs: 256, μ: 691, ~: 793)
-FixedPointMathLibTest:testMulDivDownEdgeCases() (gas: 707)
-FixedPointMathLibTest:testMulDivUp() (gas: 2295)
-FixedPointMathLibTest:testMulDivUp(uint256,uint256,uint256) (runs: 256, μ: 835, ~: 1054)
-FixedPointMathLibTest:testMulDivUpEdgeCases() (gas: 845)
-FixedPointMathLibTest:testMulWadDown() (gas: 844)
-FixedPointMathLibTest:testMulWadDown(uint256,uint256) (runs: 256, μ: 686, ~: 810)
-FixedPointMathLibTest:testMulWadDownEdgeCases() (gas: 843)
-FixedPointMathLibTest:testMulWadUp() (gas: 981)
-FixedPointMathLibTest:testMulWadUp(uint256,uint256) (runs: 256, μ: 835, ~: 1073)
-FixedPointMathLibTest:testMulWadUpEdgeCases() (gas: 959)
+FixedPointMathLibTest:testDifferentiallyFuzzSqrt(uint256) (runs: 256, μ: 13830, ~: 4181)
+FixedPointMathLibTest:testDivWadDown() (gas: 820)
+FixedPointMathLibTest:testDivWadDown(uint256,uint256) (runs: 256, μ: 713, ~: 813)
+FixedPointMathLibTest:testDivWadDownEdgeCases() (gas: 439)
+FixedPointMathLibTest:testDivWadUp() (gas: 943)
+FixedPointMathLibTest:testDivWadUp(uint256,uint256) (runs: 256, μ: 795, ~: 952)
+FixedPointMathLibTest:testDivWadUpEdgeCases() (gas: 442)
+FixedPointMathLibTest:testFailDivWadDownOverflow(uint256,uint256) (runs: 256, μ: 441, ~: 419)
+FixedPointMathLibTest:testFailDivWadDownZeroDenominator() (gas: 332)
+FixedPointMathLibTest:testFailDivWadDownZeroDenominator(uint256) (runs: 256, μ: 387, ~: 387)
+FixedPointMathLibTest:testFailDivWadUpOverflow(uint256,uint256) (runs: 256, μ: 396, ~: 374)
+FixedPointMathLibTest:testFailDivWadUpZeroDenominator() (gas: 332)
+FixedPointMathLibTest:testFailDivWadUpZeroDenominator(uint256) (runs: 256, μ: 386, ~: 386)
+FixedPointMathLibTest:testFailMulDivDownOverflow(uint256,uint256,uint256) (runs: 256, μ: 434, ~: 414)
+FixedPointMathLibTest:testFailMulDivDownZeroDenominator() (gas: 328)
+FixedPointMathLibTest:testFailMulDivDownZeroDenominator(uint256,uint256) (runs: 256, μ: 385, ~: 385)
+FixedPointMathLibTest:testFailMulDivUpOverflow(uint256,uint256,uint256) (runs: 256, μ: 457, ~: 437)
+FixedPointMathLibTest:testFailMulDivUpZeroDenominator() (gas: 329)
+FixedPointMathLibTest:testFailMulDivUpZeroDenominator(uint256,uint256) (runs: 256, μ: 428, ~: 428)
+FixedPointMathLibTest:testFailMulWadDownOverflow(uint256,uint256) (runs: 256, μ: 421, ~: 387)
+FixedPointMathLibTest:testFailMulWadUpOverflow(uint256,uint256) (runs: 256, μ: 398, ~: 364)
+FixedPointMathLibTest:testMulDivDown() (gas: 1813)
+FixedPointMathLibTest:testMulDivDown(uint256,uint256,uint256) (runs: 256, μ: 686, ~: 786)
+FixedPointMathLibTest:testMulDivDownEdgeCases() (gas: 686)
+FixedPointMathLibTest:testMulDivUp() (gas: 2095)
+FixedPointMathLibTest:testMulDivUp(uint256,uint256,uint256) (runs: 256, μ: 821, ~: 1034)
+FixedPointMathLibTest:testMulDivUpEdgeCases() (gas: 785)
+FixedPointMathLibTest:testMulWadDown() (gas: 823)
+FixedPointMathLibTest:testMulWadDown(uint256,uint256) (runs: 256, μ: 681, ~: 803)
+FixedPointMathLibTest:testMulWadDownEdgeCases() (gas: 822)
+FixedPointMathLibTest:testMulWadUp() (gas: 921)
+FixedPointMathLibTest:testMulWadUp(uint256,uint256) (runs: 256, μ: 821, ~: 1053)
+FixedPointMathLibTest:testMulWadUpEdgeCases() (gas: 899)
 FixedPointMathLibTest:testRPow() (gas: 2164)
 FixedPointMathLibTest:testSqrt() (gas: 2580)
 FixedPointMathLibTest:testSqrt(uint256) (runs: 256, μ: 997, ~: 1013)
 FixedPointMathLibTest:testSqrtBack(uint256) (runs: 256, μ: 15210, ~: 340)
-FixedPointMathLibTest:testSqrtBackHashed(uint256) (runs: 256, μ: 59040, ~: 59500)
+FixedPointMathLibTest:testSqrtBackHashed(uint256) (runs: 256, μ: 59034, ~: 59500)
 FixedPointMathLibTest:testSqrtBackHashedSingle() (gas: 58937)
 LibStringTest:testDifferentiallyFuzzToString(uint256,bytes) (runs: 256, μ: 20749, ~: 8925)
 LibStringTest:testToString() (gas: 10047)

src/utils/FixedPointMathLib.sol

@@ -9,6 +9,8 @@ library FixedPointMathLib {
                     SIMPLIFIED FIXED POINT OPERATIONS
     //////////////////////////////////////////////////////////////*/
 
+    uint256 internal constant MAX_UINT256 = 2**256 - 1;
+
     uint256 internal constant WAD = 1e18; // The scalar of ETH and most ERC20s.
 
     function mulWadDown(uint256 x, uint256 y) internal pure returns (uint256) {
@@ -37,16 +39,13 @@ library FixedPointMathLib {
         uint256 denominator
     ) internal pure returns (uint256 z) {
         assembly {
-            // Store x * y in z for now.
-            z := mul(x, y)
-
-            // Equivalent to require(denominator != 0 && (x == 0 || (x * y) / x == y))
-            if iszero(and(iszero(iszero(denominator)), or(iszero(x), eq(div(z, x), y)))) {
+            // Equivalent to require(denominator != 0 && (y == 0 || x <= type(uint256).max / y))
+            if iszero(mul(denominator, iszero(mul(y, gt(x, div(MAX_UINT256, y)))))) {
                 revert(0, 0)
             }
 
-            // Divide z by the denominator.
-            z := div(z, denominator)
+            // Divide x * y by the denominator.
+            z := div(mul(x, y), denominator)
         }
     }
 
@@ -56,18 +55,14 @@ library FixedPointMathLib {
         uint256 denominator
     ) internal pure returns (uint256 z) {
         assembly {
-            // Store x * y in z for now.
-            z := mul(x, y)
-
-            // Equivalent to require(denominator != 0 && (x == 0 || (x * y) / x == y))
-            if iszero(and(iszero(iszero(denominator)), or(iszero(x), eq(div(z, x), y)))) {
+            // Equivalent to require(denominator != 0 && (y == 0 || x <= type(uint256).max / y))
+            if iszero(mul(denominator, iszero(mul(y, gt(x, div(MAX_UINT256, y)))))) {
                 revert(0, 0)
             }
 
-            // First, divide z - 1 by the denominator and add 1.
-            // We allow z - 1 to underflow if z is 0, because we multiply the
-            // end result by 0 if z is zero, ensuring we return 0 if z is zero.
-            z := mul(iszero(iszero(z)), add(div(sub(z, 1), denominator), 1))
+            // If x * y modulo the denominator is strictly greater than 0,
+            // 1 is added to round up the division of x * y by the denominator.
+            z := add(gt(mod(mul(x, y), denominator), 0), div(mul(x, y), denominator))
         }
     }