Add some tests

Author: Vectorized

.gas-snapshot

@@ -241,40 +241,43 @@ ERC721Test:testTransferFromApproveAll(uint256,address) (runs: 256, μ: 93182, ~:
 ERC721Test:testTransferFromSelf() (gas: 64776)
 ERC721Test:testTransferFromSelf(uint256,address) (runs: 256, μ: 65061, ~: 65061)
 FixedPointMathLibTest:testDivWadDown() (gas: 864)
-FixedPointMathLibTest:testDivWadDown(uint256,uint256) (runs: 256, μ: 670, ~: 776)
-FixedPointMathLibTest:testDivWadDownEdgeCases() (gas: 423)
-FixedPointMathLibTest:testDivWadUp() (gas: 981)
+FixedPointMathLibTest:testDivWadDown(uint256,uint256) (runs: 256, μ: 714, ~: 820)
+FixedPointMathLibTest:testDivWadDownEdgeCases() (gas: 446)
+FixedPointMathLibTest:testDivWadUp() (gas: 1003)
 FixedPointMathLibTest:testDivWadUp(uint256,uint256) (runs: 256, μ: 845, ~: 1016)
-FixedPointMathLibTest:testDivWadUpEdgeCases() (gas: 482)
+FixedPointMathLibTest:testDivWadUpEdgeCases() (gas: 504)
 FixedPointMathLibTest:testFailDivWadDownOverflow(uint256,uint256) (runs: 256, μ: 423, ~: 397)
-FixedPointMathLibTest:testFailDivWadDownZeroDenominator() (gas: 362)
-FixedPointMathLibTest:testFailDivWadDownZeroDenominator(uint256) (runs: 256, μ: 419, ~: 419)
-FixedPointMathLibTest:testFailDivWadUpOverflow(uint256,uint256) (runs: 256, μ: 401, ~: 375)
+FixedPointMathLibTest:testFailDivWadDownZeroDenominator() (gas: 320)
+FixedPointMathLibTest:testFailDivWadDownZeroDenominator(uint256) (runs: 256, μ: 397, ~: 397)
+FixedPointMathLibTest:testFailDivWadUpOverflow(uint256,uint256) (runs: 256, μ: 423, ~: 397)
 FixedPointMathLibTest:testFailDivWadUpZeroDenominator() (gas: 342)
 FixedPointMathLibTest:testFailDivWadUpZeroDenominator(uint256) (runs: 256, μ: 396, ~: 396)
 FixedPointMathLibTest:testFailMulDivDownOverflow(uint256,uint256,uint256) (runs: 256, μ: 460, ~: 437)
 FixedPointMathLibTest:testFailMulDivDownZeroDenominator() (gas: 316)
 FixedPointMathLibTest:testFailMulDivDownZeroDenominator(uint256,uint256) (runs: 256, μ: 395, ~: 395)
-FixedPointMathLibTest:testFailMulDivUpOverflow(uint256,uint256,uint256) (runs: 256, μ: 482, ~: 459)
+FixedPointMathLibTest:testFailMulDivUpOverflow(uint256,uint256,uint256) (runs: 256, μ: 438, ~: 415)
 FixedPointMathLibTest:testFailMulDivUpZeroDenominator() (gas: 317)
-FixedPointMathLibTest:testFailMulDivUpZeroDenominator(uint256,uint256) (runs: 256, μ: 394, ~: 394)
-FixedPointMathLibTest:testFailMulWadDownOverflow(uint256,uint256) (runs: 256, μ: 380, ~: 342)
-FixedPointMathLibTest:testFailMulWadUpOverflow(uint256,uint256) (runs: 256, μ: 380, ~: 342)
+FixedPointMathLibTest:testFailMulDivUpZeroDenominator(uint256,uint256) (runs: 256, μ: 416, ~: 416)
+FixedPointMathLibTest:testFailMulWadDownOverflow(uint256,uint256) (runs: 256, μ: 425, ~: 387)
+FixedPointMathLibTest:testFailMulWadUpOverflow(uint256,uint256) (runs: 256, μ: 425, ~: 387)
 FixedPointMathLibTest:testMulDivDown() (gas: 1861)
 FixedPointMathLibTest:testMulDivDown(uint256,uint256,uint256) (runs: 256, μ: 669, ~: 771)
 FixedPointMathLibTest:testMulDivDownEdgeCases() (gas: 751)
 FixedPointMathLibTest:testMulDivUp() (gas: 2273)
 FixedPointMathLibTest:testMulDivUp(uint256,uint256,uint256) (runs: 256, μ: 835, ~: 1054)
-FixedPointMathLibTest:testMulDivUpEdgeCases() (gas: 846)
-FixedPointMathLibTest:testMulWadDown() (gas: 821)
+FixedPointMathLibTest:testMulDivUpEdgeCases() (gas: 823)
+FixedPointMathLibTest:testMulWadDown() (gas: 844)
 FixedPointMathLibTest:testMulWadDown(uint256,uint256) (runs: 256, μ: 683, ~: 810)
-FixedPointMathLibTest:testMulWadDownEdgeCases() (gas: 886)
+FixedPointMathLibTest:testMulWadDownEdgeCases() (gas: 843)
 FixedPointMathLibTest:testMulWadUp() (gas: 959)
 FixedPointMathLibTest:testMulWadUp(uint256,uint256) (runs: 256, μ: 806, ~: 1051)
 FixedPointMathLibTest:testMulWadUpEdgeCases() (gas: 1002)
 FixedPointMathLibTest:testRPow() (gas: 2142)
 FixedPointMathLibTest:testSqrt() (gas: 521)
-FixedPointMathLibTest:testSqrt(uint256) (runs: 256, μ: 1065, ~: 1113)
+FixedPointMathLibTest:testSqrt(uint256) (runs: 256, μ: 1043, ~: 1091)
+FixedPointMathLibTest:testSqrtBack(uint256) (runs: 256, μ: 16876, ~: 340)
+FixedPointMathLibTest:testSqrtBackHashed(uint256) (runs: 256, μ: 65176, ~: 65644)
+FixedPointMathLibTest:testSqrtBackHashedSingle() (gas: 65128)
 LibStringTest:testDifferentiallyFuzzToString(uint256,bytes) (runs: 256, μ: 21006, ~: 9531)
 LibStringTest:testToString() (gas: 10047)
 LibStringTest:testToStringDirty() (gas: 8123)

src/test/FixedPointMathLib.t.sol

@@ -274,4 +274,22 @@ contract FixedPointMathLibTest is DSTestPlus {
 
         assertTrue(root * root <= x && next * next > x);
     }
+
+    function testSqrtBack(uint256 x) public {
+        unchecked {
+            x >>= 128;
+            while (x != 0) {
+                assertEq(FixedPointMathLib.sqrt(x * x), x);
+                x >>= 1;
+            }
+        }
+    }
+
+    function testSqrtBackHashed(uint256 x) public {
+        testSqrtBack(uint256(keccak256(abi.encode(x))));
+    }
+
+    function testSqrtBackHashedSingle() public {
+        testSqrtBackHashed(123);
+    }
 }