safe-react/build/contracts/GnosisMath.json

{
  "contractName": "GnosisMath",
  "abi": [
    {
      "constant": true,
      "inputs": [],
      "name": "LN2",
      "outputs": [
        {
          "name": "",
          "type": "uint256"
        }
      ],
      "payable": false,
      "stateMutability": "view",
      "type": "function"
    },
    {
      "constant": true,
      "inputs": [],
      "name": "LOG2_E",
      "outputs": [
        {
          "name": "",
          "type": "uint256"
        }
      ],
      "payable": false,
      "stateMutability": "view",
      "type": "function"
    },
    {
      "constant": true,
      "inputs": [],
      "name": "ONE",
      "outputs": [
        {
          "name": "",
          "type": "uint256"
        }
      ],
      "payable": false,
      "stateMutability": "view",
      "type": "function"
    },
    {
      "constant": true,
      "inputs": [
        {
          "name": "x",
          "type": "int256"
        }
      ],
      "name": "exp",
      "outputs": [
        {
          "name": "",
          "type": "uint256"
        }
      ],
      "payable": false,
      "stateMutability": "pure",
      "type": "function"
    },
    {
      "constant": true,
      "inputs": [
        {
          "name": "x",
          "type": "uint256"
        }
      ],
      "name": "ln",
      "outputs": [
        {
          "name": "",
          "type": "int256"
        }
      ],
      "payable": false,
      "stateMutability": "pure",
      "type": "function"
    },
    {
      "constant": true,
      "inputs": [
        {
          "name": "x",
          "type": "uint256"
        }
      ],
      "name": "floorLog2",
      "outputs": [
        {
          "name": "lo",
          "type": "int256"
        }
      ],
      "payable": false,
      "stateMutability": "pure",
      "type": "function"
    },
    {
      "constant": true,
      "inputs": [
        {
          "name": "nums",
          "type": "int256[]"
        }
      ],
      "name": "max",
      "outputs": [
        {
          "name": "maxNum",
          "type": "int256"
        }
      ],
      "payable": false,
      "stateMutability": "pure",
      "type": "function"
    }
  ],
  "metadata": "{\"compiler\":{\"version\":\"0.5.8+commit.23d335f2\"},\"language\":\"Solidity\",\"output\":{\"abi\":[{\"constant\":true,\"inputs\":[],\"name\":\"LN2\",\"outputs\":[{\"name\":\"\",\"type\":\"uint256\"}],\"payable\":false,\"stateMutability\":\"view\",\"type\":\"function\"},{\"constant\":true,\"inputs\":[],\"name\":\"LOG2_E\",\"outputs\":[{\"name\":\"\",\"type\":\"uint256\"}],\"payable\":false,\"stateMutability\":\"view\",\"type\":\"function\"},{\"constant\":true,\"inputs\":[{\"name\":\"x\",\"type\":\"uint256\"}],\"name\":\"ln\",\"outputs\":[{\"name\":\"\",\"type\":\"int256\"}],\"payable\":false,\"stateMutability\":\"pure\",\"type\":\"function\"},{\"constant\":true,\"inputs\":[{\"name\":\"x\",\"type\":\"uint256\"}],\"name\":\"floorLog2\",\"outputs\":[{\"name\":\"lo\",\"type\":\"int256\"}],\"payable\":false,\"stateMutability\":\"pure\",\"type\":\"function\"},{\"constant\":true,\"inputs\":[],\"name\":\"ONE\",\"outputs\":[{\"name\":\"\",\"type\":\"uint256\"}],\"payable\":false,\"stateMutability\":\"view\",\"type\":\"function\"},{\"constant\":true,\"inputs\":[{\"name\":\"nums\",\"type\":\"int256[]\"}],\"name\":\"max\",\"outputs\":[{\"name\":\"maxNum\",\"type\":\"int256\"}],\"payable\":false,\"stateMutability\":\"pure\",\"type\":\"function\"},{\"constant\":true,\"inputs\":[{\"name\":\"x\",\"type\":\"int256\"}],\"name\":\"exp\",\"outputs\":[{\"name\":\"\",\"type\":\"uint256\"}],\"payable\":false,\"stateMutability\":\"pure\",\"type\":\"function\"}],\"devdoc\":{\"author\":\"Alan Lu - <alan.lu@gnosis.pm>Stefan George - <stefan@gnosis.pm>\",\"methods\":{\"exp(int256)\":{\"details\":\"Returns natural exponential function value of given x\",\"params\":{\"x\":\"x\"},\"return\":\"e**x\"},\"floorLog2(uint256)\":{\"details\":\"Returns base 2 logarithm value of given x\",\"params\":{\"x\":\"x\"},\"return\":\"logarithmic value\"},\"ln(uint256)\":{\"details\":\"Returns natural logarithm value of given x\",\"params\":{\"x\":\"x\"},\"return\":\"ln(x)\"},\"max(int256[])\":{\"details\":\"Returns maximum of an array\",\"params\":{\"nums\":\"Numbers to look through\"},\"return\":\"Maximum number\"}},\"title\":\"Math library - Allows calculation of logarithmic and exponential functions\"},\"userdoc\":{\"methods\":{}}},\"settings\":{\"compilationTarget\":{\"@gnosis.pm/util-contracts/contracts/Math.sol\":\"GnosisMath\"},\"evmVersion\":\"petersburg\",\"libraries\":{},\"optimizer\":{\"enabled\":true,\"runs\":500},\"remappings\":[]},\"sources\":{\"@gnosis.pm/util-contracts/contracts/Math.sol\":{\"keccak256\":\"0x857768cd0d460e33778dcde29e997b539640bbf37ea23832213b2e5039147ea5\",\"urls\":[\"bzzr://628f7e63a0d6a092aad389b70cc55d6d9c10cd9753f3644d5ea9dc75a3314a8e\"]}},\"version\":1}",
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  "source": "pragma solidity ^0.5.2;\n\n/// @title Math library - Allows calculation of logarithmic and exponential functions\n/// @author Alan Lu - <alan.lu@gnosis.pm>\n/// @author Stefan George - <stefan@gnosis.pm>\nlibrary GnosisMath {\n    /*\n     *  Constants\n     */\n    // This is equal to 1 in our calculations\n    uint public constant ONE = 0x10000000000000000;\n    uint public constant LN2 = 0xb17217f7d1cf79ac;\n    uint public constant LOG2_E = 0x171547652b82fe177;\n\n    /*\n     *  Public functions\n     */\n    /// @dev Returns natural exponential function value of given x\n    /// @param x x\n    /// @return e**x\n    function exp(int x) public pure returns (uint) {\n        // revert if x is > MAX_POWER, where\n        // MAX_POWER = int(mp.floor(mp.log(mpf(2**256 - 1) / ONE) * ONE))\n        require(x <= 2454971259878909886679);\n        // return 0 if exp(x) is tiny, using\n        // MIN_POWER = int(mp.floor(mp.log(mpf(1) / ONE) * ONE))\n        if (x < -818323753292969962227) return 0;\n        // Transform so that e^x -> 2^x\n        x = x * int(ONE) / int(LN2);\n        // 2^x = 2^whole(x) * 2^frac(x)\n        //       ^^^^^^^^^^ is a bit shift\n        // so Taylor expand on z = frac(x)\n        int shift;\n        uint z;\n        if (x >= 0) {\n            shift = x / int(ONE);\n            z = uint(x % int(ONE));\n        } else {\n            shift = x / int(ONE) - 1;\n            z = ONE - uint(-x % int(ONE));\n        }\n        // 2^x = 1 + (ln 2) x + (ln 2)^2/2! x^2 + ...\n        //\n        // Can generate the z coefficients using mpmath and the following lines\n        // >>> from mpmath import mp\n        // >>> mp.dps = 100\n        // >>> ONE =  0x10000000000000000\n        // >>> print('\\n'.join(hex(int(mp.log(2)**i / mp.factorial(i) * ONE)) for i in range(1, 7)))\n        // 0xb17217f7d1cf79ab\n        // 0x3d7f7bff058b1d50\n        // 0xe35846b82505fc5\n        // 0x276556df749cee5\n        // 0x5761ff9e299cc4\n        // 0xa184897c363c3\n        uint zpow = z;\n        uint result = ONE;\n        result += 0xb17217f7d1cf79ab * zpow / ONE;\n        zpow = zpow * z / ONE;\n        result += 0x3d7f7bff058b1d50 * zpow / ONE;\n        zpow = zpow * z / ONE;\n        result += 0xe35846b82505fc5 * zpow / ONE;\n        zpow = zpow * z / ONE;\n        result += 0x276556df749cee5 * zpow / ONE;\n        zpow = zpow * z / ONE;\n        result += 0x5761ff9e299cc4 * zpow / ONE;\n        zpow = zpow * z / ONE;\n        result += 0xa184897c363c3 * zpow / ONE;\n        zpow = zpow * z / ONE;\n        result += 0xffe5fe2c4586 * zpow / ONE;\n        zpow = zpow * z / ONE;\n        result += 0x162c0223a5c8 * zpow / ONE;\n        zpow = zpow * z / ONE;\n        result += 0x1b5253d395e * zpow / ONE;\n        zpow = zpow * z / ONE;\n        result += 0x1e4cf5158b * zpow / ONE;\n        zpow = zpow * z / ONE;\n        result += 0x1e8cac735 * zpow / ONE;\n        zpow = zpow * z / ONE;\n        result += 0x1c3bd650 * zpow / ONE;\n        zpow = zpow * z / ONE;\n        result += 0x1816193 * zpow / ONE;\n        zpow = zpow * z / ONE;\n        result += 0x131496 * zpow / ONE;\n        zpow = zpow * z / ONE;\n        result += 0xe1b7 * zpow / ONE;\n        zpow = zpow * z / ONE;\n        result += 0x9c7 * zpow / ONE;\n        if (shift >= 0) {\n            if (result >> (256 - shift) > 0) return (2 ** 256 - 1);\n            return result << shift;\n        } else return result >> (-shift);\n    }\n\n    /// @dev Returns natural logarithm value of given x\n    /// @param x x\n    /// @return ln(x)\n    function ln(uint x) public pure returns (int) {\n        require(x > 0);\n        // binary search for floor(log2(x))\n        int ilog2 = floorLog2(x);\n        int z;\n        if (ilog2 < 0) z = int(x << uint(-ilog2));\n        else z = int(x >> uint(ilog2));\n        // z = x * 2^-⌊log₂x⌋\n        // so 1 <= z < 2\n        // and ln z = ln x - ⌊log₂x⌋/log₂e\n        // so just compute ln z using artanh series\n        // and calculate ln x from that\n        int term = (z - int(ONE)) * int(ONE) / (z + int(ONE));\n        int halflnz = term;\n        int termpow = term * term / int(ONE) * term / int(ONE);\n        halflnz += termpow / 3;\n        termpow = termpow * term / int(ONE) * term / int(ONE);\n        halflnz += termpow / 5;\n        termpow = termpow * term / int(ONE) * term / int(ONE);\n        halflnz += termpow / 7;\n        termpow = termpow * term / int(ONE) * term / int(ONE);\n        halflnz += termpow / 9;\n        termpow = termpow * term / int(ONE) * term / int(ONE);\n        halflnz += termpow / 11;\n        termpow = termpow * term / int(ONE) * term / int(ONE);\n        halflnz += termpow / 13;\n        termpow = termpow * term / int(ONE) * term / int(ONE);\n        halflnz += termpow / 15;\n        termpow = termpow * term / int(ONE) * term / int(ONE);\n        halflnz += termpow / 17;\n        termpow = termpow * term / int(ONE) * term / int(ONE);\n        halflnz += termpow / 19;\n        termpow = termpow * term / int(ONE) * term / int(ONE);\n        halflnz += termpow / 21;\n        termpow = termpow * term / int(ONE) * term / int(ONE);\n        halflnz += termpow / 23;\n        termpow = termpow * term / int(ONE) * term / int(ONE);\n        halflnz += termpow / 25;\n        return (ilog2 * int(ONE)) * int(ONE) / int(LOG2_E) + 2 * halflnz;\n    }\n\n    /// @dev Returns base 2 logarithm value of given x\n    /// @param x x\n    /// @return logarithmic value\n    function floorLog2(uint x) public pure returns (int lo) {\n        lo = -64;\n        int hi = 193;\n        // I use a shift here instead of / 2 because it floors instead of rounding towards 0\n        int mid = (hi + lo) >> 1;\n        while ((lo + 1) < hi) {\n            if (mid < 0 && x << uint(-mid) < ONE || mid >= 0 && x >> uint(mid) < ONE) hi = mid;\n            else lo = mid;\n            mid = (hi + lo) >> 1;\n        }\n    }\n\n    /// @dev Returns maximum of an array\n    /// @param nums Numbers to look through\n    /// @return Maximum number\n    function max(int[] memory nums) public pure returns (int maxNum) {\n        require(nums.length > 0);\n        maxNum = -2 ** 255;\n        for (uint i = 0; i < nums.length; i++) if (nums[i] > maxNum) maxNum = nums[i];\n    }\n\n    /// @dev Returns whether an add operation causes an overflow\n    /// @param a First addend\n    /// @param b Second addend\n    /// @return Did no overflow occur?\n    function safeToAdd(uint a, uint b) internal pure returns (bool) {\n        return a + b >= a;\n    }\n\n    /// @dev Returns whether a subtraction operation causes an underflow\n    /// @param a Minuend\n    /// @param b Subtrahend\n    /// @return Did no underflow occur?\n    function safeToSub(uint a, uint b) internal pure returns (bool) {\n        return a >= b;\n    }\n\n    /// @dev Returns whether a multiply operation causes an overflow\n    /// @param a First factor\n    /// @param b Second factor\n    /// @return Did no overflow occur?\n    function safeToMul(uint a, uint b) internal pure returns (bool) {\n        return b == 0 || a * b / b == a;\n    }\n\n    /// @dev Returns sum if no overflow occurred\n    /// @param a First addend\n    /// @param b Second addend\n    /// @return Sum\n    function add(uint a, uint b) internal pure returns (uint) {\n        require(safeToAdd(a, b));\n        return a + b;\n    }\n\n    /// @dev Returns difference if no overflow occurred\n    /// @param a Minuend\n    /// @param b Subtrahend\n    /// @return Difference\n    function sub(uint a, uint b) internal pure returns (uint) {\n        require(safeToSub(a, b));\n        return a - 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