{ "contractName": "RealMath", "abi": [], "metadata": "{\"compiler\":{\"version\":\"0.5.16+commit.9c3226ce\"},\"language\":\"Solidity\",\"output\":{\"abi\":[],\"devdoc\":{\"methods\":{}},\"userdoc\":{\"methods\":{},\"notice\":\"RealMath: fixed-point math library, based on fractional and integer parts. Using uint256 as real216x40, which isn't in Solidity yet. Internally uses the wider uint256 for some math. * Note that for addition, subtraction, and mod (%), you should just use the built-in Solidity operators. Functions for these operations are not provided. \"}},\"settings\":{\"compilationTarget\":{\"@daostack/infra/contracts/libs/RealMath.sol\":\"RealMath\"},\"evmVersion\":\"istanbul\",\"libraries\":{},\"optimizer\":{\"enabled\":true,\"runs\":200},\"remappings\":[]},\"sources\":{\"@daostack/infra/contracts/libs/RealMath.sol\":{\"keccak256\":\"0x3ee79c4b483da327916ac36f9d5cc6a1f2f0363db3ad06793ec67f46e1f653db\",\"urls\":[\"bzz-raw://19b423aa16b93e414c50ca513caabc0f1cb835f31deec82d85d9bb31c0f8d5fb\",\"dweb:/ipfs/QmS8gjtT3jxxoNAosJf6QSStFAE2KZLhNA1Qq9MXwT2CnN\"]}},\"version\":1}", "bytecode": "0x60556023600b82828239805160001a607314601657fe5b30600052607381538281f3fe73000000000000000000000000000000000000000030146080604052600080fdfea265627a7a723158202cf11dd469410d9c368202d205bb618131e6b27384f07f9997f2e6de7662c59064736f6c63430005100032", "deployedBytecode": "0x73000000000000000000000000000000000000000030146080604052600080fdfea265627a7a723158202cf11dd469410d9c368202d205bb618131e6b27384f07f9997f2e6de7662c59064736f6c63430005100032", "sourceMap": "390:2427:63:-;;132:2:-1;166:7;155:9;146:7;137:37;255:7;249:14;246:1;241:23;235:4;232:33;222:2;;269:9;222:2;293:9;290:1;283:20;323:4;314:7;306:22;347:7;338;331:24", "deployedSourceMap": "390:2427:63:-;;;;;;;;", "source": "pragma solidity ^0.5.4;\n\n/**\n * RealMath: fixed-point math library, based on fractional and integer parts.\n * Using uint256 as real216x40, which isn't in Solidity yet.\n * Internally uses the wider uint256 for some math.\n *\n * Note that for addition, subtraction, and mod (%), you should just use the\n * built-in Solidity operators. Functions for these operations are not provided.\n *\n */\n\n\nlibrary RealMath {\n\n /**\n * How many total bits are there?\n */\n uint256 constant private REAL_BITS = 256;\n\n /**\n * How many fractional bits are there?\n */\n uint256 constant private REAL_FBITS = 40;\n\n /**\n * What's the first non-fractional bit\n */\n uint256 constant private REAL_ONE = uint256(1) << REAL_FBITS;\n\n /**\n * Raise a real number to any positive integer power\n */\n function pow(uint256 realBase, uint256 exponent) internal pure returns (uint256) {\n\n uint256 tempRealBase = realBase;\n uint256 tempExponent = exponent;\n\n // Start with the 0th power\n uint256 realResult = REAL_ONE;\n while (tempExponent != 0) {\n // While there are still bits set\n if ((tempExponent & 0x1) == 0x1) {\n // If the low bit is set, multiply in the (many-times-squared) base\n realResult = mul(realResult, tempRealBase);\n }\n // Shift off the low bit\n tempExponent = tempExponent >> 1;\n if (tempExponent != 0) {\n // Do the squaring\n tempRealBase = mul(tempRealBase, tempRealBase);\n }\n }\n\n // Return the final result.\n return realResult;\n }\n\n /**\n * Create a real from a rational fraction.\n */\n function fraction(uint216 numerator, uint216 denominator) internal pure returns (uint256) {\n return div(uint256(numerator) * REAL_ONE, uint256(denominator) * REAL_ONE);\n }\n\n /**\n * Multiply one real by another. Truncates overflows.\n */\n function mul(uint256 realA, uint256 realB) private pure returns (uint256) {\n // When multiplying fixed point in x.y and z.w formats we get (x+z).(y+w) format.\n // So we just have to clip off the extra REAL_FBITS fractional bits.\n uint256 res = realA * realB;\n require(res/realA == realB, \"RealMath mul overflow\");\n return (res >> REAL_FBITS);\n }\n\n /**\n * Divide one real by another real. Truncates overflows.\n */\n function div(uint256 realNumerator, uint256 realDenominator) private pure returns (uint256) {\n // We use the reverse of the multiplication trick: convert numerator from\n // x.y to (x+z).(y+w) fixed point, then divide by denom in z.w fixed point.\n return uint256((uint256(realNumerator) * REAL_ONE) / uint256(realDenominator));\n }\n\n}\n", "sourcePath": "@daostack/infra/contracts/libs/RealMath.sol", "ast": { "absolutePath": "@daostack/infra/contracts/libs/RealMath.sol", "exportedSymbols": { "RealMath": [ 16577 ] }, "id": 16578, "nodeType": "SourceUnit", "nodes": [ { "id": 16425, "literals": [ "solidity", "^", "0.5", ".4" ], "nodeType": "PragmaDirective", "src": "0:23:63" }, { "baseContracts": [], "contractDependencies": [], "contractKind": "library", "documentation": "RealMath: fixed-point math library, based on fractional and integer parts.\nUsing uint256 as real216x40, which isn't in Solidity yet.\nInternally uses the wider uint256 for some math.\n * Note that for addition, subtraction, and mod (%), you should just use the\nbuilt-in Solidity operators. 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