Branchless opt

.gas-snapshot

@@ -28,11 +28,11 @@ AuthTest:testSetOwnerWithPermissiveAuthority(address,address) (runs: 256, μ: 13
 Bytes32AddressLibTest:testFillLast12Bytes() (gas: 223)
 Bytes32AddressLibTest:testFromLast20Bytes() (gas: 191)
 CREATE3Test:testDeployERC20() (gas: 853111)
-CREATE3Test:testDeployERC20(bytes32,string,string,uint8) (runs: 256, μ: 923845, ~: 921961)
+CREATE3Test:testDeployERC20(bytes32,string,string,uint8) (runs: 256, μ: 924106, ~: 921961)
 CREATE3Test:testFailDoubleDeployDifferentBytecode() (gas: 9079256848778914174)
-CREATE3Test:testFailDoubleDeployDifferentBytecode(bytes32,bytes,bytes) (runs: 256, μ: 5062195514745832485, ~: 8937393460516727435)
+CREATE3Test:testFailDoubleDeployDifferentBytecode(bytes32,bytes,bytes) (runs: 256, μ: 5097107207950975695, ~: 8937393460516727446)
 CREATE3Test:testFailDoubleDeploySameBytecode() (gas: 9079256848778906218)
-CREATE3Test:testFailDoubleDeploySameBytecode(bytes32,bytes) (runs: 256, μ: 5027837975401088877, ~: 8937393460516728677)
+CREATE3Test:testFailDoubleDeploySameBytecode(bytes32,bytes) (runs: 256, μ: 5062749668606232091, ~: 8937393460516728689)
 DSTestPlusTest:testBound() (gas: 14214)
 DSTestPlusTest:testBound(uint256,uint256,uint256) (runs: 256, μ: 2787, ~: 2793)
 DSTestPlusTest:testBrutalizeMemory() (gas: 823)
@@ -115,8 +115,8 @@ ERC1155Test:testSafeTransferFromToEOA() (gas: 93167)
 ERC1155Test:testSafeTransferFromToEOA(uint256,uint256,bytes,uint256,address,bytes) (runs: 256, μ: 93478, ~: 97450)
 ERC1155Test:testSafeTransferFromToERC1155Recipient() (gas: 739583)
 ERC1155Test:testSafeTransferFromToERC1155Recipient(uint256,uint256,bytes,uint256,bytes) (runs: 256, μ: 769591, ~: 765729)
-ERC20Invariants:invariantBalanceSum() (runs: 256, calls: 3840, reverts: 2388)
-ERC20Test:invariantMetadata() (runs: 256, calls: 3840, reverts: 2606)
+ERC20Invariants:invariantBalanceSum (runs: 256, calls: 3840, reverts: 2388)
+ERC20Test:invariantMetadata (runs: 256, calls: 3840, reverts: 2560)
 ERC20Test:testApprove() (gas: 31058)
 ERC20Test:testApprove(address,uint256) (runs: 256, μ: 30424, ~: 31280)
 ERC20Test:testBurn() (gas: 56970)
@@ -137,16 +137,16 @@ ERC20Test:testFailTransferFromInsufficientBalance(address,uint256,uint256) (runs
 ERC20Test:testFailTransferInsufficientBalance() (gas: 52806)
 ERC20Test:testFailTransferInsufficientBalance(address,uint256,uint256) (runs: 256, μ: 51720, ~: 55310)
 ERC20Test:testInfiniteApproveTransferFrom() (gas: 89793)
-ERC20Test:testMetadata(string,string,uint8) (runs: 256, μ: 870618, ~: 863277)
+ERC20Test:testMetadata(string,string,uint8) (runs: 256, μ: 868512, ~: 863173)
 ERC20Test:testMint() (gas: 53746)
 ERC20Test:testMint(address,uint256) (runs: 256, μ: 52214, ~: 53925)
 ERC20Test:testPermit() (gas: 63193)
 ERC20Test:testPermit(uint248,address,uint256,uint256) (runs: 256, μ: 62584, ~: 63517)
 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)
+ERC20Test:testTransferFrom(address,uint256,uint256) (runs: 256, μ: 86308, ~: 92841)
+ERC4626Test:invariantMetadata (runs: 256, calls: 3840, reverts: 2881)
 ERC4626Test:testFailDepositWithNoApproval() (gas: 13357)
 ERC4626Test:testFailDepositWithNotEnoughApproval() (gas: 86993)
 ERC4626Test:testFailDepositZero() (gas: 7780)
@@ -163,7 +163,7 @@ ERC4626Test:testSingleDepositWithdraw(uint128) (runs: 256, μ: 201569, ~: 201579
 ERC4626Test:testSingleMintRedeem(uint128) (runs: 256, μ: 201484, ~: 201494)
 ERC4626Test:testVaultInteractionsForSomeoneElse() (gas: 286247)
 ERC4626Test:testWithdrawZero() (gas: 52462)
-ERC721Test:invariantMetadata() (runs: 256, calls: 3840, reverts: 2170)
+ERC721Test:invariantMetadata (runs: 256, calls: 3840, reverts: 2170)
 ERC721Test:testApprove() (gas: 78427)
 ERC721Test:testApprove(address,uint256) (runs: 256, μ: 78637, ~: 78637)
 ERC721Test:testApproveAll() (gas: 31063)
@@ -240,17 +240,17 @@ 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:testDifferentiallyFuzzSqrt(uint256) (runs: 256, μ: 13819, ~: 4231)
 FixedPointMathLibTest:testDivWadDown() (gas: 841)
-FixedPointMathLibTest:testDivWadDown(uint256,uint256) (runs: 256, μ: 718, ~: 820)
+FixedPointMathLibTest:testDivWadDown(uint256,uint256) (runs: 256, μ: 717, ~: 820)
 FixedPointMathLibTest:testDivWadDownEdgeCases() (gas: 446)
 FixedPointMathLibTest:testDivWadUp() (gas: 1003)
-FixedPointMathLibTest:testDivWadUp(uint256,uint256) (runs: 256, μ: 809, ~: 972)
+FixedPointMathLibTest:testDivWadUp(uint256,uint256) (runs: 256, μ: 807, ~: 972)
 FixedPointMathLibTest:testDivWadUpEdgeCases() (gas: 462)
-FixedPointMathLibTest:testFailDivWadDownOverflow(uint256,uint256) (runs: 256, μ: 443, ~: 419)
+FixedPointMathLibTest:testFailDivWadDownOverflow(uint256,uint256) (runs: 256, μ: 444, ~: 419)
 FixedPointMathLibTest:testFailDivWadDownZeroDenominator() (gas: 342)
 FixedPointMathLibTest:testFailDivWadDownZeroDenominator(uint256) (runs: 256, μ: 397, ~: 397)
-FixedPointMathLibTest:testFailDivWadUpOverflow(uint256,uint256) (runs: 256, μ: 398, ~: 374)
+FixedPointMathLibTest:testFailDivWadUpOverflow(uint256,uint256) (runs: 256, μ: 399, ~: 374)
 FixedPointMathLibTest:testFailDivWadUpZeroDenominator() (gas: 342)
 FixedPointMathLibTest:testFailDivWadUpZeroDenominator(uint256) (runs: 256, μ: 396, ~: 396)
 FixedPointMathLibTest:testFailMulDivDownOverflow(uint256,uint256,uint256) (runs: 256, μ: 437, ~: 414)
@@ -274,12 +274,12 @@ FixedPointMathLibTest:testMulWadUp() (gas: 981)
 FixedPointMathLibTest:testMulWadUp(uint256,uint256) (runs: 256, μ: 835, ~: 1073)
 FixedPointMathLibTest:testMulWadUpEdgeCases() (gas: 959)
 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:testSqrtBackHashedSingle() (gas: 58937)
-LibStringTest:testDifferentiallyFuzzToString(uint256,bytes) (runs: 256, μ: 20749, ~: 8925)
+FixedPointMathLibTest:testSqrt() (gas: 600)
+FixedPointMathLibTest:testSqrt(uint256) (runs: 256, μ: 990, ~: 1038)
+FixedPointMathLibTest:testSqrtBack(uint256) (runs: 256, μ: 14665, ~: 340)
+FixedPointMathLibTest:testSqrtBackHashed(uint256) (runs: 256, μ: 56528, ~: 56940)
+FixedPointMathLibTest:testSqrtBackHashedSingle() (gas: 56448)
+LibStringTest:testDifferentiallyFuzzToString(uint256,bytes) (runs: 256, μ: 21006, ~: 9531)
 LibStringTest:testToString() (gas: 10047)
 LibStringTest:testToStringDirty() (gas: 8123)
 LibStringTest:testToStringOverwrite() (gas: 484)
@@ -310,7 +310,7 @@ OwnedTest:testCallFunctionAsNonOwner(address) (runs: 256, μ: 16238, ~: 16257)
 OwnedTest:testCallFunctionAsOwner() (gas: 10479)
 OwnedTest:testSetOwner() (gas: 13035)
 OwnedTest:testSetOwner(address) (runs: 256, μ: 13151, ~: 13170)
-ReentrancyGuardTest:invariantReentrancyStatusAlways1() (runs: 256, calls: 3840, reverts: 319)
+ReentrancyGuardTest:invariantReentrancyStatusAlways1 (runs: 256, calls: 3840, reverts: 319)
 ReentrancyGuardTest:testFailUnprotectedCall() (gas: 46147)
 ReentrancyGuardTest:testNoReentrancy() (gas: 7515)
 ReentrancyGuardTest:testProtectedCall() (gas: 33467)
@@ -446,7 +446,7 @@ SignedWadMathTest:testFailWadDivZeroDenominator(int256) (runs: 256, μ: 296, ~:
 SignedWadMathTest:testFailWadMulOverflow(int256,int256) (runs: 256, μ: 323, ~: 296)
 SignedWadMathTest:testWadDiv(uint256,uint256,bool,bool) (runs: 256, μ: 5696, ~: 5664)
 SignedWadMathTest:testWadMul(uint256,uint256,bool,bool) (runs: 256, μ: 5720, ~: 5688)
-WETHInvariants:invariantTotalSupplyEqualsBalance() (runs: 256, calls: 3840, reverts: 1908)
+WETHInvariants:invariantTotalSupplyEqualsBalance (runs: 256, calls: 3840, reverts: 1908)
 WETHTest:testDeposit() (gas: 63535)
 WETHTest:testDeposit(uint256) (runs: 256, μ: 62792, ~: 65880)
 WETHTest:testFallbackDeposit() (gas: 63249)

src/utils/FixedPointMathLib.sol

@@ -172,24 +172,14 @@ library FixedPointMathLib {
             // This segment is to get a reasonable initial estimate for the Babylonian method. With a bad
             // start, the correct # of bits increases ~linearly each iteration instead of ~quadratically.
 
+            // Let y = x / 2**r, where r = lg2(x/65536).
             // We check y >= 2^(k + 8) but shift right by k bits
             // each branch to ensure that if x >= 256, then y >= 256.
-            if iszero(lt(y, 0x10000000000000000000000000000000000)) {
-                y := shr(128, y)
-                z := shl(64, z)
-            }
-            if iszero(lt(y, 0x1000000000000000000)) {
-                y := shr(64, y)
-                z := shl(32, z)
-            }
-            if iszero(lt(y, 0x10000000000)) {
-                y := shr(32, y)
-                z := shl(16, z)
-            }
-            if iszero(lt(y, 0x1000000)) {
-                y := shr(16, y)
-                z := shl(8, z)
-            }
+            let r := shl(7, gt(x, 0xffffffffffffffffffffffffffffffffff))
+            r := or(r, shl(6, gt(shr(r, x), 0xffffffffffffffffff)))
+            r := or(r, shl(5, gt(shr(r, x), 0xffffffffff)))
+            r := or(r, shl(4, gt(shr(r, x), 0xffffff)))
+            z := shl(shr(1, r), z)
 
             // Goal was to get z*z*y within a small factor of x. More iterations could
             // get y in a tighter range. Currently, we will have y in [256, 256*2^16).
@@ -207,7 +197,7 @@ library FixedPointMathLib {
             // sqrt(y) using sqrt(65536) * 181/1024 * (a + 1) = 181/4 * (y + 65536)/65536 = 181 * (y + 65536)/2^18.
 
             // There is no overflow risk here since y < 2^136 after the first branch above.
-            z := shr(18, mul(z, add(y, 65536))) // A mul() is saved from starting z at 181.
+            z := shr(18, mul(z, add(shr(r, x), 65536))) // A mul() is saved from starting z at 181.
 
             // Given the worst case multiplicative error of 2.84 above, 7 iterations should be enough.
             z := shr(1, add(z, div(x, z)))