@gnosis.pm/pm-contracts

{ "contractName": "Fixed192x64Math", "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": "int256" }, { "name": "estimationMode", "type": "Fixed192x64Math.EstimationMode" } ], "name": "pow2", "outputs": [ { "name": "", "type": "uint256" } ], "payable": false, "stateMutability": "pure", "type": "function" }, { "constant": true, "inputs": [ { "name": "x", "type": "int256" } ], "name": "pow2Bounds", "outputs": [ { "name": "lower", "type": "uint256" }, { "name": "upper", "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": "estimationMode", "type": "Fixed192x64Math.EstimationMode" } ], "name": "binaryLog", "outputs": [ { "name": "", "type": "int256" } ], "payable": false, "stateMutability": "pure", "type": "function" }, { "constant": true, "inputs": [ { "name": "x", "type": "uint256" } ], "name": "log2Bounds", "outputs": [ { "name": "lower", "type": "int256" }, { "name": "upper", "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\":\"0.5.6+commit.b259423e\"},\"language\":\"Solidity\",\"output\":{\"abi\":[{\"constant\":true,\"inputs\":[],\"name\":\"LN2\",\"outputs\":[{\"name\":\"\",\"type\":\"uint256\"}],\"payable\":false,\"stateMutability\":\"view\",\"type\":\"function\"},{\"constant\":true,\"inputs\":[{\"name\":\"x\",\"type\":\"uint256\"},{\"name\":\"estimationMode\",\"type\":\"Fixed192x64Math.EstimationMode\"}],\"name\":\"binaryLog\",\"outputs\":[{\"name\":\"\",\"type\":\"int256\"}],\"payable\":false,\"stateMutability\":\"pure\",\"type\":\"function\"},{\"constant\":true,\"inputs\":[{\"name\":\"x\",\"type\":\"uint256\"}],\"name\":\"log2Bounds\",\"outputs\":[{\"name\":\"lower\",\"type\":\"int256\"},{\"name\":\"upper\",\"type\":\"int256\"}],\"payable\":false,\"stateMutability\":\"pure\",\"type\":\"function\"},{\"constant\":true,\"inputs\":[{\"name\":\"x\",\"type\":\"int256\"},{\"name\":\"estimationMode\",\"type\":\"Fixed192x64Math.EstimationMode\"}],\"name\":\"pow2\",\"outputs\":[{\"name\":\"\",\"type\":\"uint256\"}],\"payable\":false,\"stateMutability\":\"pure\",\"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\":\"x\",\"type\":\"int256\"}],\"name\":\"pow2Bounds\",\"outputs\":[{\"name\":\"lower\",\"type\":\"uint256\"},{\"name\":\"upper\",\"type\":\"uint256\"}],\"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\":{\"binaryLog(uint256,Fixed192x64Math.EstimationMode)\":{\"details\":\"Returns estimate of binaryLog(x) given x\",\"params\":{\"estimationMode\":\"whether to return a lower bound, upper bound, or a midpoint\",\"x\":\"logarithm argument in fixed point\"},\"return\":\"estimate of binaryLog(x) in fixed point\"},\"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)\"},\"log2Bounds(uint256)\":{\"details\":\"Returns bounds for value of binaryLog(x) given x\",\"params\":{\"x\":\"logarithm argument in fixed point\"},\"return\":\"{ \\\"lower\\\": \\\"lower bound of binaryLog(x) in fixed point\\\", \\\"upper\\\": \\\"upper bound of binaryLog(x) in fixed point\\\" }\"},\"max(int256[])\":{\"details\":\"Returns maximum of an array\",\"params\":{\"nums\":\"Numbers to look through\"},\"return\":\"Maximum number\"},\"pow2(int256,Fixed192x64Math.EstimationMode)\":{\"details\":\"Returns estimate of 2**x given x\",\"params\":{\"estimationMode\":\"whether to return a lower bound, upper bound, or a midpoint\",\"x\":\"exponent in fixed point\"},\"return\":\"estimate of 2**x in fixed point\"},\"pow2Bounds(int256)\":{\"details\":\"Returns bounds for value of 2**x given x\",\"params\":{\"x\":\"exponent in fixed point\"},\"return\":\"{ \\\"lower\\\": \\\"lower bound of 2**x in fixed point\\\", \\\"upper\\\": \\\"upper bound of 2**x in fixed point\\\" }\"}},\"title\":\"Fixed192x64Math library - Allows calculation of logarithmic and exponential functions\"},\"userdoc\":{\"methods\":{}}},\"settings\":{\"compilationTarget\":{\"@gnosis.pm/util-contracts/contracts/Fixed192x64Math.sol\":\"Fixed192x64Math\"},\"evmVersion\":\"petersburg\",\"libraries\":{},\"optimizer\":{\"enabled\":false,\"runs\":200},\"remappings\":[]},\"sources\":{\"@gnosis.pm/util-contracts/contracts/Fixed192x64Math.sol\":{\"keccak256\":\"0xad15b641bf8f5862034749b679ab91cb2c330c2ca997da4455863dc169ab82d4\",\"urls\":[\"bzzr://a37b3d23f367b7f0ba4669c417af754260f0dbedad21294079aed622222427f5\"]}},\"version\":1}", "bytecode": 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"source": "pragma solidity >=0.4.24 ^0.5.1;\n\n\n/// @title Fixed192x64Math library - Allows calculation of logarithmic and exponential functions\n/// @author Alan Lu - <alan.lu@gnosis.pm>\n/// @author Stefan George - <stefan@gnosis.pm>\nlibrary Fixed192x64Math {\n\n enum EstimationMode { LowerBound, UpperBound, Midpoint }\n\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)\n public\n pure\n returns (uint)\n {\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)\n return 0;\n\n // Transform so that e^x -> 2^x\n (uint lower, uint upper) = pow2Bounds(x * int(ONE) / int(LN2));\n return (upper - lower) / 2 + lower;\n }\n\n /// @dev Returns estimate of 2**x given x\n /// @param x exponent in fixed point\n /// @param estimationMode whether to return a lower bound, upper bound, or a midpoint\n /// @return estimate of 2**x in fixed point\n function pow2(int x, EstimationMode estimationMode)\n public\n pure\n returns (uint)\n {\n (uint lower, uint upper) = pow2Bounds(x);\n if(estimationMode == EstimationMode.LowerBound) {\n return lower;\n }\n if(estimationMode == EstimationMode.UpperBound) {\n return upper;\n }\n if(estimationMode == EstimationMode.Midpoint) {\n return (upper - lower) / 2 + lower;\n }\n revert();\n }\n\n /// @dev Returns bounds for value of 2**x given x\n /// @param x exponent in fixed point\n /// @return {\n /// \"lower\": \"lower bound of 2**x in fixed point\",\n /// \"upper\": \"upper bound of 2**x in fixed point\"\n /// }\n function pow2Bounds(int x)\n public\n pure\n returns (uint lower, uint upper)\n {\n // revert if x is > MAX_POWER, where\n // MAX_POWER = int(mp.floor(mp.log(mpf(2**256 - 1) / ONE, 2) * ONE))\n require(x <= 3541774862152233910271);\n // return 0 if exp(x) is tiny, using\n // MIN_POWER = int(mp.floor(mp.log(mpf(1) / ONE, 2) * ONE))\n if (x < -1180591620717411303424)\n return (0, 1);\n\n // 2^x = 2^(floor(x)) * 2^(x-floor(x))\n // ^^^^^^^^^^^^^^ is a bit shift of ceil(x)\n // so Taylor expand on z = x-floor(x), z in [0, 1)\n int shift;\n int z;\n if (x >= 0) {\n shift = x / int(ONE);\n z = x % int(ONE);\n }\n else {\n shift = (x+1) / int(ONE) - 1;\n z = x - (int(ONE) * shift);\n }\n assert(z >= 0);\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 // >>> coeffs = [mp.log(2)**i / mp.factorial(i) for i in range(1, 21)]\n // >>> shifts = [64 - int(mp.log(c, 2)) for c in coeffs]\n // >>> print('\\n'.join(hex(int(c * (1 << s))) + ', ' + str(s) for c, s in zip(coeffs, shifts)))\n int result = int(ONE) << 64;\n int zpow = z;\n result += 0xb17217f7d1cf79ab * zpow;\n zpow = zpow * z / int(ONE);\n result += 0xf5fdeffc162c7543 * zpow >> (66 - 64);\n zpow = zpow * z / int(ONE);\n result += 0xe35846b82505fc59 * zpow >> (68 - 64);\n zpow = zpow * z / int(ONE);\n result += 0x9d955b7dd273b94e * zpow >> (70 - 64);\n zpow = zpow * z / int(ONE);\n result += 0xaec3ff3c53398883 * zpow >> (73 - 64);\n zpow = zpow * z / int(ONE);\n result += 0xa184897c363c3b7a * zpow >> (76 - 64);\n zpow = zpow * z / int(ONE);\n result += 0xffe5fe2c45863435 * zpow >> (80 - 64);\n zpow = zpow * z / int(ONE);\n result += 0xb160111d2e411fec * zpow >> (83 - 64);\n zpow = zpow * z / int(ONE);\n result += 0xda929e9caf3e1ed2 * zpow >> (87 - 64);\n zpow = zpow * z / int(ONE);\n result += 0xf267a8ac5c764fb7 * zpow >> (91 - 64);\n zpow = zpow * z / int(ONE);\n result += 0xf465639a8dd92607 * zpow >> (95 - 64);\n zpow = zpow * z / int(ONE);\n result += 0xe1deb287e14c2f15 * zpow >> (99 - 64);\n zpow = zpow * z / int(ONE);\n result += 0xc0b0c98b3687cb14 * zpow >> (103 - 64);\n zpow = zpow * z / int(ONE);\n result += 0x98a4b26ac3c54b9f * zpow >> (107 - 64);\n zpow = zpow * z / int(ONE);\n result += 0xe1b7421d82010f33 * zpow >> (112 - 64);\n zpow = zpow * z / int(ONE);\n result += 0x9c744d73cfc59c91 * zpow >> (116 - 64);\n zpow = zpow * z / int(ONE);\n result += 0xcc2225a0e12d3eab * zpow >> (121 - 64);\n zpow = zpow * z / int(ONE);\n zpow = 0xfb8bb5eda1b4aeb9 * zpow >> (126 - 64);\n result += zpow;\n zpow = int(8 * ONE);\n\n shift -= 64;\n if (shift >= 0) {\n if (result >> (256-shift) == 0) {\n lower = uint(result) << shift;\n zpow <<= shift; // todo: is this safe?\n if (lower + uint(zpow) >= lower)\n upper = lower + uint(zpow);\n else\n upper = 2**256-1;\n return (lower, upper);\n }\n else\n return (2**256-1, 2**256-1);\n }\n zpow = (zpow >> (-shift)) + 1;\n lower = uint(result) >> (-shift);\n upper = lower + uint(zpow);\n return (lower, upper);\n }\n\n /// @dev Returns natural logarithm value of given x\n /// @param x x\n /// @return ln(x)\n function ln(uint x)\n public\n pure\n returns (int)\n {\n (int lower, int upper) = log2Bounds(x);\n return ((upper - lower) / 2 + lower) * int(ONE) / int(LOG2_E);\n }\n\n /// @dev Returns estimate of binaryLog(x) given x\n /// @param x logarithm argument in fixed point\n /// @param estimationMode whether to return a lower bound, upper bound, or a midpoint\n /// @return estimate of binaryLog(x) in fixed point\n function binaryLog(uint x, EstimationMode estimationMode)\n public\n pure\n returns (int)\n {\n (int lower, int upper) = log2Bounds(x);\n if(estimationMode == EstimationMode.LowerBound) {\n return lower;\n }\n if(estimationMode == EstimationMode.UpperBound) {\n return upper;\n }\n if(estimationMode == EstimationMode.Midpoint) {\n return (upper - lower) / 2 + lower;\n }\n revert();\n }\n\n 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