Echidna testing and flat fee introduction

.gitignore

@@ -4,24 +4,27 @@
 *.swp
 *.swo
 
-#Buidler files
+# Buidler files
 cache
 artifacts
 node_modules/
 output/
 
-#Truffle files
+# Truffle files
 .infuraKey
 .secret
 build/
 
-#Solidity-coverage
+# Solidity-coverage
 coverage/
 .coverage_contracts/
 coverage.json
 
 # Yarn
 yarn-error.log
 
-#NPM
+# NPM
 package-lock.json
+
+# Crytic
+crytic-export/

contracts/echidna/YieldMath.yaml

@@ -0,0 +1,8 @@
+seqLen: 50
+testLimit: 20000
+prefix: "crytic_"
+deployer: "0x41414141"
+sender: ["0x42424242", "0x43434343"]
+cryticArgs: ["--compile-force-framework", "Buidler"]
+coverage: true
+checkAsserts: true

contracts/echidna/YieldMathEchidna.sol

@@ -0,0 +1,227 @@
+// SPDX-License-Identifier: GPL-3.0-or-later
+pragma solidity ^0.6.10;
+import "../pool/YieldMath.sol"; // 64 bits
+import "../pool/Math64x64.sol";
+import "@nomiclabs/buidler/console.sol";
+
+
+contract YieldMathEchidna {
+    uint128 constant internal precision = 1e12;
+    int128 constant internal k = int128(uint256((1 << 64)) / 126144000); // 1 / Seconds in 4 years, in 64.64
+    int128 constant internal g = int128(uint256((95 << 64)) / 100); // All constants are `ufixed`, to divide them they must be converted to uint256
+
+    uint128 minDaiReserves = 10**21; // $1000
+    uint128 minYDaiReserves = minDaiReserves + 1;
+    uint128 minTrade = minDaiReserves / 1000; // $1
+    uint128 minTimeTillMaturity = 0;
+    uint128 maxDaiReserves = 10**27; // $1B
+    uint128 maxYDaiReserves = maxDaiReserves + 1; // $1B
+    uint128 maxTrade = maxDaiReserves / 10;
+    uint128 maxTimeTillMaturity = 126144000;
+
+    constructor() public {}
+
+    /// @dev Bali Overflow-protected addition, from OpenZeppelin
+    function add(uint128 a, uint128 b)
+        internal pure returns (uint128)
+    {
+        uint128 c = a + b;
+        require(c >= a, "Pool: Dai reserves too high");
+        return c;
+    }
+    /// @dev Bali Overflow-protected substraction, from OpenZeppelin
+    function sub(uint128 a, uint128 b) internal pure returns (uint128) {
+        require(b <= a, "Pool: yDai reserves too low");
+        uint128 c = a - b;
+        return c;
+    }
+
+    function testSellYDaiAndReverse(uint128 daiReserves, uint128 yDAIReserves, uint128 yDaiIn, uint128 timeTillMaturity)
+        public view returns (bool)
+    {
+        require(daiReserves > yDAIReserves);
+        daiReserves = minDaiReserves + daiReserves % maxDaiReserves;
+        yDAIReserves = minYDaiReserves + yDAIReserves % maxYDaiReserves;
+        timeTillMaturity = minTimeTillMaturity + timeTillMaturity % maxTimeTillMaturity;
+
+        uint128 yDaiOut = _sellYDaiAndReverse(daiReserves, yDAIReserves, yDaiIn, timeTillMaturity);
+        assert(yDaiOut <= yDaiIn);
+    }
+
+    function testBuyYDaiAndReverse(uint128 daiReserves, uint128 yDAIReserves, uint128 yDaiOut, uint128 timeTillMaturity)
+        public view returns (bool)
+    {
+        require(daiReserves > yDAIReserves);
+        daiReserves = minDaiReserves + daiReserves % maxDaiReserves;
+        yDAIReserves = minYDaiReserves + yDAIReserves % maxYDaiReserves;
+        timeTillMaturity = minTimeTillMaturity + timeTillMaturity % maxTimeTillMaturity;
+
+        uint128 yDaiIn = _buyYDaiAndReverse(daiReserves, yDAIReserves, yDaiOut, timeTillMaturity);
+        assert(yDaiOut <= yDaiIn);
+    }
+
+    function testSellDaiAndReverse(uint128 daiReserves, uint128 yDAIReserves, uint128 daiIn, uint128 timeTillMaturity)
+        public view returns (bool)
+    {
+        require(daiReserves > yDAIReserves);
+        daiReserves = minDaiReserves + daiReserves % maxDaiReserves;
+        yDAIReserves = minYDaiReserves + yDAIReserves % maxYDaiReserves;
+        timeTillMaturity = minTimeTillMaturity + timeTillMaturity % maxTimeTillMaturity;
+
+        console.log(daiIn);
+        uint128 daiOut = _sellDaiAndReverse(daiReserves, yDAIReserves, daiIn, timeTillMaturity);
+        // assert(daiOut <= daiIn);
+        // console.log(daiOut);
+        return(daiOut <= daiIn);
+    }
+
+    function testBuyDaiAndReverse(uint128 daiReserves, uint128 yDAIReserves, uint128 daiOut, uint128 timeTillMaturity)
+        public view returns (bool)
+    {
+        require(daiReserves > yDAIReserves);
+        daiReserves = minDaiReserves + daiReserves % maxDaiReserves;
+        yDAIReserves = minYDaiReserves + yDAIReserves % maxYDaiReserves;
+        timeTillMaturity = minTimeTillMaturity + timeTillMaturity % maxTimeTillMaturity;
+
+        uint128 daiIn = _buyYDaiAndReverse(daiReserves, yDAIReserves, daiOut, timeTillMaturity);
+        assert(daiOut <= daiIn);
+    }
+
+    function testLiquidityDaiOutForYDaiIn(uint128 daiReserves, uint128 yDAIReserves, uint128 yDaiIn, uint128 timeTillMaturity)
+        public view returns (bool)
+    {
+        if (daiReserves > yDAIReserves) return true;
+        daiReserves = minDaiReserves + daiReserves % maxDaiReserves;
+        yDAIReserves = minYDaiReserves + yDAIReserves % maxYDaiReserves;
+        timeTillMaturity = minTimeTillMaturity + timeTillMaturity % maxTimeTillMaturity;
+
+        uint128 reserves_0 = _initialReservesValue(daiReserves, yDAIReserves, timeTillMaturity);
+        uint128 daiOut= YieldMath.daiOutForYDaiIn(daiReserves, yDAIReserves, yDaiIn, timeTillMaturity, k, g);
+        uint128 reserves_1 = _initialReservesValue(sub(daiReserves, daiOut), add(yDAIReserves, yDaiIn), sub(timeTillMaturity, 1));
+        assert(reserves_0 < reserves_1);
+        return reserves_0 < reserves_1;
+    }
+
+    function testLiquidityDaiInForYDaiOut(uint128 daiReserves, uint128 yDAIReserves, uint128 yDaiOut, uint128 timeTillMaturity)
+        public view returns (bool)
+    {
+        if (daiReserves > yDAIReserves - yDaiOut) return true;
+        daiReserves = minDaiReserves + daiReserves % maxDaiReserves;
+        yDAIReserves = minYDaiReserves + yDAIReserves % maxYDaiReserves;
+        timeTillMaturity = minTimeTillMaturity + timeTillMaturity % maxTimeTillMaturity;
+
+        uint128 reserves_0 = _initialReservesValue(daiReserves, yDAIReserves, timeTillMaturity);
+        uint128 daiIn= YieldMath.daiInForYDaiOut(daiReserves, yDAIReserves, yDaiOut, timeTillMaturity, k, g);
+        uint128 reserves_1 = _initialReservesValue(add(daiReserves, daiIn), sub(yDAIReserves, yDaiOut), sub(timeTillMaturity, 1));
+        assert(reserves_0 < reserves_1);
+        return reserves_0 < reserves_1;
+    }
+
+    function testLiquidityYDaiOutForDaiIn(uint128 daiReserves, uint128 yDAIReserves, uint128 daiIn, uint128 timeTillMaturity)
+        public view returns (bool)
+    {
+        if (daiReserves + daiIn > yDAIReserves) return true;
+        daiReserves = minDaiReserves + daiReserves % maxDaiReserves;
+        yDAIReserves = minYDaiReserves + yDAIReserves % maxYDaiReserves;
+        timeTillMaturity = minTimeTillMaturity + timeTillMaturity % maxTimeTillMaturity;
+
+        uint128 reserves_0 = _initialReservesValue(daiReserves, yDAIReserves, timeTillMaturity);
+        uint128 yDaiOut= YieldMath.yDaiOutForDaiIn(daiReserves, yDAIReserves, daiIn, timeTillMaturity, k, g);
+        uint128 reserves_1 = _initialReservesValue(add(daiReserves, daiIn), sub(yDAIReserves, yDaiOut), sub(timeTillMaturity, 1));
+        assert(reserves_0 < reserves_1);
+        return reserves_0 < reserves_1;
+    }
+
+    function testLiquidityYDaiInForDaiOut(uint128 daiReserves, uint128 yDAIReserves, uint128 daiOut, uint128 timeTillMaturity)
+        public view returns (bool)
+    {
+        if (daiReserves > yDAIReserves) return true;
+        daiReserves = minDaiReserves + daiReserves % maxDaiReserves;
+        yDAIReserves = minYDaiReserves + yDAIReserves % maxYDaiReserves;
+        timeTillMaturity = minTimeTillMaturity + timeTillMaturity % maxTimeTillMaturity;
+
+        uint128 reserves_0 = _initialReservesValue(daiReserves, yDAIReserves, timeTillMaturity);
+        uint128 yDaiIn= YieldMath.yDaiInForDaiOut(daiReserves, yDAIReserves, daiOut, timeTillMaturity, k, g);
+        uint128 reserves_1 = _initialReservesValue(sub(daiReserves, daiOut), add(yDAIReserves, yDaiIn), sub(timeTillMaturity, 1));
+        assert(reserves_0 < reserves_1);
+        return reserves_0 < reserves_1;
+    }
+
+    /*
+    function testLog2MonotonicallyGrows(uint128 x) internal view {
+        uint128 z1= YieldMath.log_2(x);
+        uint128 z2= YieldMath.log_2(x + 1);
+        assert(z2 >= z1);
+    }
+
+    function testLog2PrecisionLossRoundsDown(uint128 x) internal view {
+        uint128 z1 = YieldMath.log_2(x);
+        uint128 z2= YieldMath.log_2(x);
+        assert(z2 >= z1);portugal
+    }
+
+    function testPow2PrecisionLossRoundsDown(uint128 x) internal view {
+        uint128 z1 = YieldMath.pow_2(x);
+        uint128 z2= YieldMath.pow_2(x);
+        assert(z2 >= z1);
+    } */
+
+    /**
+     * Estimate in DAI the value of reserves at protocol initialization time.
+     *
+     * @param daiReserves DAI reserves amount
+     * @param yDAIReserves yDAI reserves amount
+     * @param timeTillMaturity time till maturity in seconds
+     * @return estimated value of reserves
+     */
+    function _initialReservesValue (
+        uint128 daiReserves, uint128 yDAIReserves, uint128 timeTillMaturity)
+        internal pure returns (uint128)
+    {
+        // a = (1 - k * timeTillMaturity)
+        int128 a = Math64x64.sub (0x10000000000000000, Math64x64.mul (k, Math64x64.fromUInt (timeTillMaturity)));
+        require (a > 0);
+
+        uint256 sum =
+        uint256 (YieldMath.pow (daiReserves, uint128 (a), 0x10000000000000000)) +
+        uint256 (YieldMath.pow (yDAIReserves, uint128 (a), 0x10000000000000000)) >> 1;
+        require (sum < 0x100000000000000000000000000000000);
+
+        uint256 result = uint256 (YieldMath.pow (uint128 (sum), 0x10000000000000000, uint128 (a))) << 1;
+        require (result < 0x100000000000000000000000000000000);
+
+        return uint128 (result);
+    }
+
+    /// @dev Sell yDai and sell the obtained Dai back for yDai
+    function _sellYDaiAndReverse(uint128 daiReserves, uint128 yDAIReserves, uint128 yDaiIn, uint128 timeTillMaturity)
+        internal pure returns (uint128)
+    {
+        uint128 daiAmount = YieldMath.daiOutForYDaiIn(daiReserves, yDAIReserves, yDaiIn, timeTillMaturity, k, g);
+        return YieldMath.yDaiOutForDaiIn(sub(daiReserves, daiAmount), add(yDAIReserves, yDaiIn), daiAmount, timeTillMaturity, k, g);
+    }
+
+    /// @dev Buy yDai and sell it back
+    function _buyYDaiAndReverse(uint128 daiReserves, uint128 yDAIReserves, uint128 yDaiOut, uint128 timeTillMaturity)
+        internal pure returns (uint128)
+    {
+        uint128 daiAmount = YieldMath.daiInForYDaiOut(daiReserves, yDAIReserves, yDaiOut, timeTillMaturity, k, g);
+        return YieldMath.yDaiInForDaiOut(add(daiReserves, daiAmount), sub(yDAIReserves, yDaiOut), daiAmount, timeTillMaturity, k, g);
+    }
+
+    /// @dev Sell yDai and sell the obtained Dai back for yDai
+    function _sellDaiAndReverse(uint128 daiReserves, uint128 yDAIReserves, uint128 daiIn, uint128 timeTillMaturity)
+        internal pure returns (uint128)
+    {
+        uint128 yDaiAmount = YieldMath.yDaiOutForDaiIn(daiReserves, yDAIReserves, daiIn, timeTillMaturity, k, g);
+        return YieldMath.daiOutForYDaiIn(add(daiReserves, daiIn), sub(yDAIReserves, yDaiAmount), yDaiAmount, timeTillMaturity, k, g);
+    }
+
+    /// @dev Buy yDai and sell it back
+    function _buyDaiAndReverse(uint128 daiReserves, uint128 yDAIReserves, uint128 daiOut, uint128 timeTillMaturity)
+        internal pure returns (uint128)
+    {
+        uint128 yDaiAmount = YieldMath.yDaiInForDaiOut(daiReserves, yDAIReserves, daiOut, timeTillMaturity, k, g);
+        return YieldMath.daiInForYDaiOut(sub(daiReserves, daiOut), add(yDAIReserves, yDaiAmount), yDaiAmount, timeTillMaturity, k, g);
+    }
+}

contracts/echidna/YieldMathEchidnaWrapper.sol

@@ -0,0 +1,40 @@
+// SPDX-License-Identifier: GPL-3.0-or-later
+pragma solidity ^0.6.10;
+import "./YieldMathEchidna.sol";
+
+contract YieldMathEchidnaWrapper is YieldMathEchidna {
+
+    /// @dev Sell yDai and sell the obtained Dai back for yDai
+    function sellYDaiAndReverse(uint128 daiReserves, uint128 yDAIReserves, uint128 yDaiIn, uint128 timeTillMaturity)
+        public pure returns (uint128)
+    {
+        _sellYDaiAndReverse(daiReserves, yDAIReserves, yDaiIn, timeTillMaturity);
+    }
+
+    /// @dev Buy yDai and sell it back
+    function buyYDaiAndReverse(uint128 daiReserves, uint128 yDAIReserves, uint128 yDaiOut, uint128 timeTillMaturity)
+        public pure returns (uint128)
+    {
+        _buyYDaiAndReverse(daiReserves, yDAIReserves, yDaiOut, timeTillMaturity);
+    }
+
+    /// @dev Sell yDai and sell the obtained Dai back for yDai
+    function sellDaiAndReverse(uint128 daiReserves, uint128 yDAIReserves, uint128 daiIn, uint128 timeTillMaturity)
+        public pure returns (uint128)
+    {
+        _sellDaiAndReverse(daiReserves, yDAIReserves, daiIn, timeTillMaturity);
+    }
+
+    /// @dev Buy yDai and sell it back
+    function buyDaiAndReverse(uint128 daiReserves, uint128 yDAIReserves, uint128 daiOut, uint128 timeTillMaturity)
+        public pure returns (uint128)
+    {
+        _buyDaiAndReverse(daiReserves, yDAIReserves, daiOut, timeTillMaturity);
+    }
+
+    function initialReservesValue (uint128 daiReserves, uint128 yDAIReserves, uint128 timeTillMaturity)
+        public pure returns (uint128)
+    {
+        _initialReservesValue (daiReserves, yDAIReserves, timeTillMaturity);
+    }
+}