{ "contractName": "BigDiv", "abi": [], "metadata": "{\"compiler\":{\"version\":\"0.5.17+commit.d19bba13\"},\"language\":\"Solidity\",\"output\":{\"abi\":[],\"devdoc\":{\"details\":\"Results may be off by 1 + 0.000001% for 2x1 calls and 2 + 0.00001% for 2x2 calls. Do not use if your contract expects very small result values to be accurate.\",\"methods\":{},\"title\":\"Reduces the size of terms before multiplication, to avoid an overflow, and then restores the proper size after division.\"},\"userdoc\":{\"methods\":{},\"notice\":\"This effectively allows us to overflow values in the numerator and/or denominator of a fraction, so long as the end result does not overflow as well.\"}},\"settings\":{\"compilationTarget\":{\"/home/circleci/repo/contracts/math/BigDiv.sol\":\"BigDiv\"},\"evmVersion\":\"istanbul\",\"libraries\":{},\"optimizer\":{\"enabled\":true,\"runs\":200},\"remappings\":[]},\"sources\":{\"/home/circleci/repo/contracts/math/BigDiv.sol\":{\"keccak256\":\"0xf695ffefeaf1c536baecf7684f56cc089e54d8a852d6ff299b7cb02313d821f7\",\"urls\":[\"bzz-raw://90052e8d9837cf9529de377bee6bf5ccf33f640b586fd05539f4543863f4b474\",\"dweb:/ipfs/QmPoWhkbMZm1pYjPEkzKG3aSpPHaMnwqqXRs7gbFrH62Fk\"]},\"@openzeppelin/contracts-ethereum-package/contracts/math/SafeMath.sol\":{\"keccak256\":\"0x640b6dee7a4b830bdfd52b5031a07fc2b12209f5b2e29e5d364a7d37f69d8076\",\"urls\":[\"bzz-raw://31113152e1ddb78fe7a4197f247591ca894e93f916867beb708d8e747b6cc74f\",\"dweb:/ipfs/QmbZaJyXdpsYGykVhHH9qpVGQg9DGCxE2QufbCUy3daTgq\"]}},\"version\":1}", "bytecode": "0x60556023600b82828239805160001a607314601657fe5b30600052607381538281f3fe73000000000000000000000000000000000000000030146080604052600080fdfea265627a7a7231582044d54bc7459af0091e9b889e4ce43305bc218fbb3c8276da45db36205346567164736f6c63430005110032", "deployedBytecode": "0x73000000000000000000000000000000000000000030146080604052600080fdfea265627a7a7231582044d54bc7459af0091e9b889e4ce43305bc218fbb3c8276da45db36205346567164736f6c63430005110032", "sourceMap": "581:6113:6:-;;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": "581:6113:6:-;;;;;;;;", "source": "pragma solidity ^0.5.0;\n\nimport \"@openzeppelin/contracts-ethereum-package/contracts/math/SafeMath.sol\";\n\n/**\n * @title Reduces the size of terms before multiplication, to avoid an overflow, and then\n * restores the proper size after division.\n * @notice This effectively allows us to overflow values in the numerator and/or denominator\n * of a fraction, so long as the end result does not overflow as well.\n * @dev Results may be off by 1 + 0.000001% for 2x1 calls and 2 + 0.00001% for 2x2 calls.\n * Do not use if your contract expects very small result values to be accurate.\n */\nlibrary BigDiv {\n using SafeMath for uint;\n\n /// @notice The max possible value\n uint private constant MAX_UINT = 2**256 - 1;\n\n /// @notice When multiplying 2 terms <= this value the result won't overflow\n uint private constant MAX_BEFORE_SQUARE = 2**128 - 1;\n\n /// @notice The max error target is off by 1 plus up to 0.000001% error\n /// for bigDiv2x1 and that `* 2` for bigDiv2x2\n uint private constant MAX_ERROR = 100000000;\n\n /// @notice A larger error threshold to use when multiple rounding errors may apply\n uint private constant MAX_ERROR_BEFORE_DIV = MAX_ERROR * 2;\n\n /**\n * @notice Returns the approx result of `a * b / d` so long as the result is <= MAX_UINT\n * @param _numA the first numerator term\n * @param _numB the second numerator term\n * @param _den the denominator\n * @return the approx result with up to off by 1 + MAX_ERROR, rounding down if needed\n */\n function bigDiv2x1(\n uint _numA,\n uint _numB,\n uint _den\n ) internal pure returns (uint) {\n if (_numA == 0 || _numB == 0) {\n // would div by 0 or underflow if we don't special case 0\n return 0;\n }\n\n uint value;\n\n if (MAX_UINT / _numA >= _numB) {\n // a*b does not overflow, return exact math\n value = _numA * _numB;\n value /= _den;\n return value;\n }\n\n // Sort numerators\n uint numMax = _numB;\n uint numMin = _numA;\n if (_numA > _numB) {\n numMax = _numA;\n numMin = _numB;\n }\n\n value = numMax / _den;\n if (value > MAX_ERROR) {\n // _den is small enough to be MAX_ERROR or better w/o a factor\n value = value.mul(numMin);\n return value;\n }\n\n // formula = ((a / f) * b) / (d / f)\n // factor >= a / sqrt(MAX) * (b / sqrt(MAX))\n uint factor = numMin - 1;\n factor /= MAX_BEFORE_SQUARE;\n factor += 1;\n uint temp = numMax - 1;\n temp /= MAX_BEFORE_SQUARE;\n temp += 1;\n if (MAX_UINT / factor >= temp) {\n factor *= temp;\n value = numMax / factor;\n if (value > MAX_ERROR_BEFORE_DIV) {\n value = value.mul(numMin);\n temp = _den - 1;\n temp /= factor;\n temp = temp.add(1);\n value /= temp;\n return value;\n }\n }\n\n // formula: (a / (d / f)) * (b / f)\n // factor: b / sqrt(MAX)\n factor = numMin - 1;\n factor /= MAX_BEFORE_SQUARE;\n factor += 1;\n value = numMin / factor;\n temp = _den - 1;\n temp /= factor;\n temp += 1;\n temp = numMax / temp;\n value = value.mul(temp);\n return value;\n }\n\n /**\n * @notice Returns the approx result of `a * b / d` so long as the result is <= MAX_UINT\n * @param _numA the first numerator term\n * @param _numB the second numerator term\n * @param _den the denominator\n * @return the approx result with up to off by 1 + MAX_ERROR, rounding down if needed\n * @dev roundUp is implemented by first rounding down and then adding the max error to the result\n */\n function bigDiv2x1RoundUp(\n uint _numA,\n uint _numB,\n uint _den\n ) internal pure returns (uint) {\n // first get the rounded down result\n uint value = bigDiv2x1(_numA, _numB, _den);\n\n if (value == 0) {\n // when the value rounds down to 0, assume up to an off by 1 error\n return 1;\n }\n\n // round down has a max error of MAX_ERROR, add that to the result\n // for a round up error of <= MAX_ERROR\n uint temp = value - 1;\n temp /= MAX_ERROR;\n temp += 1;\n if (MAX_UINT - value < temp) {\n // value + error would overflow, return MAX\n return MAX_UINT;\n }\n\n value += temp;\n\n return value;\n }\n\n /**\n * @notice Returns the approx result of `a * b / (c * d)` so long as the result is <= MAX_UINT\n * @param _numA the first numerator term\n * @param _numB the second numerator term\n * @param _denA the first denominator term\n * @param _denB the second denominator term\n * @return the approx result with up to off by 2 + MAX_ERROR*10 error, rounding down if needed\n * @dev this uses bigDiv2x1 and adds additional rounding error so the max error of this\n * formula is larger\n */\n function bigDiv2x2(\n uint _numA,\n uint _numB,\n uint _denA,\n uint _denB\n ) internal pure returns (uint) {\n if (MAX_UINT / _denA >= _denB) {\n // denA*denB does not overflow, use bigDiv2x1 instead\n return bigDiv2x1(_numA, _numB, _denA * _denB);\n }\n\n if (_numA == 0 || _numB == 0) {\n // would div by 0 or underflow if we don't special case 0\n return 0;\n }\n\n // Sort denominators\n uint denMax = _denB;\n uint denMin = _denA;\n if (_denA > _denB) {\n denMax = _denA;\n denMin = _denB;\n }\n\n uint value;\n\n if (MAX_UINT / _numA >= _numB) {\n // a*b does not overflow, use `a / d / c`\n value = _numA * _numB;\n value /= denMin;\n value /= denMax;\n return value;\n }\n\n // `ab / cd` where both `ab` and `cd` would overflow\n\n // Sort numerators\n uint numMax = _numB;\n uint numMin = _numA;\n if (_numA > _numB) {\n numMax = _numA;\n numMin = _numB;\n }\n\n // formula = (a/d) * b / c\n uint temp = numMax / denMin;\n if (temp > MAX_ERROR_BEFORE_DIV) {\n return bigDiv2x1(temp, numMin, denMax);\n }\n\n // formula: ((a/f) * b) / d then either * f / c or / c * f\n // factor >= a / sqrt(MAX) * (b / sqrt(MAX))\n uint factor = numMin - 1;\n factor /= MAX_BEFORE_SQUARE;\n factor += 1;\n temp = numMax - 1;\n temp /= MAX_BEFORE_SQUARE;\n temp += 1;\n if (MAX_UINT / factor >= temp) {\n factor *= temp;\n\n value = numMax / factor;\n if (value > MAX_ERROR_BEFORE_DIV) {\n value = value.mul(numMin);\n value /= denMin;\n if (value > 0 && MAX_UINT / value >= factor) {\n value *= factor;\n value /= denMax;\n return value;\n }\n }\n }\n\n // formula: (a/f) * b / ((c*d)/f)\n // factor >= c / sqrt(MAX) * (d / sqrt(MAX))\n factor = denMin;\n factor /= MAX_BEFORE_SQUARE;\n temp = denMax;\n // + 1 here prevents overflow of factor*temp\n temp /= MAX_BEFORE_SQUARE + 1;\n factor *= temp;\n return bigDiv2x1(numMax / factor, numMin, MAX_UINT);\n }\n}\n", "sourcePath": "/home/circleci/repo/contracts/math/BigDiv.sol", "ast": { "absolutePath": "/home/circleci/repo/contracts/math/BigDiv.sol", "exportedSymbols": { "BigDiv": [ 4982 ] }, "id": 4983, "nodeType": "SourceUnit", "nodes": [ { "id": 4447, "literals": [ "solidity", "^", "0.5", ".0" ], "nodeType": "PragmaDirective", "src": "0:23:6" }, { "absolutePath": "@openzeppelin/contracts-ethereum-package/contracts/math/SafeMath.sol", "file": "@openzeppelin/contracts-ethereum-package/contracts/math/SafeMath.sol", "id": 4448, "nodeType": "ImportDirective", "scope": 4983, "sourceUnit": 6070, "src": "25:78:6", "symbolAliases": [], "unitAlias": "" }, { "baseContracts": [], "contractDependencies": [], "contractKind": "library", "documentation": "@title Reduces the size of terms before multiplication, to avoid an overflow, and then\nrestores the proper size after division.\n@notice This effectively allows us to overflow values in the numerator and/or denominator\nof a fraction, so long as the end result does not overflow as well.\n@dev Results may be off by 1 + 0.000001% for 2x1 calls and 2 + 0.00001% for 2x2 calls.\nDo not use if your contract expects very small result values to be accurate.", "fullyImplemented": true, "id": 4982, "linearizedBaseContracts": [ 4982 ], "name": "BigDiv", "nodeType": "ContractDefinition", "nodes": [ { "id": 4451, "libraryName": { "contractScope": null, "id": 4449, "name": "SafeMath", "nodeType": "UserDefinedTypeName", "referencedDeclaration": 6069, "src": "606:8:6", "typeDescriptions": { "typeIdentifier": "t_contract$_SafeMath_$6069", "typeString": "library SafeMath" } }, "nodeType": "UsingForDirective", "src": "600:24:6", "typeName": { "id": 4450, "name": "uint", "nodeType": "ElementaryTypeName", "src": "619:4:6", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } }, { "constant": true, "id": 4458, "name": "MAX_UINT", "nodeType": "VariableDeclaration", "scope": 4982, "src": "665:43:6", "stateVariable": true, "storageLocation": 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"t_uint256", "typeString": "uint256" } }, "src": "3007:13:6", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "3000:20:6", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 4677, "nodeType": "ExpressionStatement", "src": "3000:20:6" }, { "expression": { "argumentTypes": null, "id": 4683, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "argumentTypes": null, "id": 4678, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4496, "src": "3026:5:6", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "=", "rightHandSide": { "argumentTypes": null, "arguments": [ { "argumentTypes": null, "id": 4681, "name": "temp", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4573, "src": "3044:4:6", "typeDescriptions": { 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"isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "argumentTypes": null, "id": 4968, "name": "factor", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4869, "src": "6616:6:6", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "*=", "rightHandSide": { "argumentTypes": null, "id": 4969, "name": "temp", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4852, "src": "6626:4:6", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "6616:14:6", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 4971, "nodeType": "ExpressionStatement", "src": "6616:14:6" }, { "expression": { "argumentTypes": null, "arguments": [ { "argumentTypes": null, "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 4975, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "argumentTypes": null, "id": 4973, "name": "numMax", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4831, "src": "6653:6:6", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "/", "rightExpression": { "argumentTypes": null, "id": 4974, "name": "factor", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4869, "src": "6662:6:6", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "6653:15:6", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "argumentTypes": null, "id": 4976, "name": "numMin", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4835, "src": "6670:6:6", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "argumentTypes": null, "id": 4977, "name": "MAX_UINT", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4458, "src": "6678:8:6", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } ], "expression": { "argumentTypes": [ { "typeIdentifier": "t_uint256", "typeString": "uint256" }, { "typeIdentifier": "t_uint256", "typeString": "uint256" }, { "typeIdentifier": "t_uint256", "typeString": "uint256" } ], "id": 4972, "name": "bigDiv2x1", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4688, "src": "6643:9:6", "typeDescriptions": { "typeIdentifier": "t_function_internal_pure$_t_uint256_$_t_uint256_$_t_uint256_$returns$_t_uint256_$", "typeString": "function (uint256,uint256,uint256) pure returns (uint256)" } }, "id": 4978, "isConstant": false, "isLValue": false, "isPure": false, "kind": "functionCall", "lValueRequested": false, "names": [], "nodeType": "FunctionCall", "src": "6643:44:6", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "functionReturnParameters": 4756, "id": 4979, "nodeType": "Return", "src": "6636:51:6" } ] }, "documentation": "@notice Returns the approx result of `a * b / (c * d)` so long as the result is <= MAX_UINT\n@param _numA the first numerator term\n@param _numB the second numerator term\n@param _denA the first denominator term\n@param _denB the second denominator term\n@return the approx result with up to off by 2 + MAX_ERROR*10 error, rounding down if needed\n@dev this uses bigDiv2x1 and adds additional rounding error so the max error of this\nformula is larger", "id": 4981, "implemented": true, "kind": "function", "modifiers": [], "name": "bigDiv2x2", "nodeType": "FunctionDefinition", "parameters": { "id": 4753, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 4746, "name": "_numA", "nodeType": "VariableDeclaration", "scope": 4981, "src": "4664:10:6", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 4745, "name": "uint", "nodeType": "ElementaryTypeName", "src": "4664:4:6", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "value": null, "visibility": "internal" }, { "constant": false, "id": 4748, "name": "_numB", "nodeType": "VariableDeclaration", "scope": 4981, "src": "4680:10:6", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 4747, "name": "uint", "nodeType": "ElementaryTypeName", "src": "4680:4:6", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "value": null, "visibility": "internal" }, { "constant": false, "id": 4750, "name": "_denA", "nodeType": "VariableDeclaration", "scope": 4981, "src": "4696:10:6", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 4749, "name": "uint", "nodeType": "ElementaryTypeName", "src": "4696:4:6", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "value": null, "visibility": "internal" }, { "constant": false, "id": 4752, "name": "_denB", "nodeType": "VariableDeclaration", "scope": 4981, "src": "4712:10:6", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 4751, "name": "uint", "nodeType": "ElementaryTypeName", "src": "4712:4:6", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "value": null, "visibility": "internal" } ], "src": "4658:68:6" }, "returnParameters": { "id": 4756, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 4755, "name": "", "nodeType": "VariableDeclaration", "scope": 4981, "src": "4750:4:6", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 4754, "name": "uint", "nodeType": "ElementaryTypeName", "src": "4750:4:6", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "value": null, "visibility": "internal" } ], "src": "4749:6:6" }, "scope": 4982, "src": "4640:2052:6", "stateMutability": "pure", "superFunction": null, "visibility": "internal" } ], "scope": 4983, "src": "581:6113:6" } ], "src": "0:6695:6" }, "legacyAST": { "absolutePath": "/home/circleci/repo/contracts/math/BigDiv.sol", "exportedSymbols": { "BigDiv": [ 4982 ] }, "id": 4983, "nodeType": "SourceUnit", "nodes": [ { "id": 4447, "literals": [ "solidity", "^", "0.5", ".0" ], "nodeType": "PragmaDirective", "src": "0:23:6" }, { "absolutePath": "@openzeppelin/contracts-ethereum-package/contracts/math/SafeMath.sol", "file": "@openzeppelin/contracts-ethereum-package/contracts/math/SafeMath.sol", "id": 4448, "nodeType": "ImportDirective", "scope": 4983, "sourceUnit": 6070, "src": "25:78:6", "symbolAliases": [], "unitAlias": "" }, { "baseContracts": [], "contractDependencies": [], "contractKind": "library", "documentation": "@title Reduces the size of terms before multiplication, to avoid an overflow, and then\nrestores the proper size after division.\n@notice This effectively allows us to overflow values in the numerator and/or denominator\nof a fraction, so long as the end result does not overflow as well.\n@dev Results may be off by 1 + 0.000001% for 2x1 calls and 2 + 0.00001% for 2x2 calls.\nDo not use if your contract expects very small result values to be accurate.", "fullyImplemented": true, "id": 4982, "linearizedBaseContracts": [ 4982 ], "name": "BigDiv", "nodeType": "ContractDefinition", "nodes": [ { "id": 4451, "libraryName": { "contractScope": null, "id": 4449, "name": "SafeMath", "nodeType": "UserDefinedTypeName", "referencedDeclaration": 6069, "src": "606:8:6", "typeDescriptions": { "typeIdentifier": "t_contract$_SafeMath_$6069", "typeString": "library SafeMath" } }, "nodeType": "UsingForDirective", "src": "600:24:6", "typeName": { "id": 4450, "name": "uint", "nodeType": "ElementaryTypeName", "src": "619:4:6", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } }, { "constant": true, "id": 4458, "name": "MAX_UINT", "nodeType": "VariableDeclaration", "scope": 4982, "src": "665:43:6", "stateVariable": true, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 4452, "name": "uint", "nodeType": "ElementaryTypeName", "src": "665:4:6", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "value": { "argumentTypes": null, "commonType": { "typeIdentifier": "t_rational_115792089237316195423570985008687907853269984665640564039457584007913129639935_by_1", "typeString": "int_const 1157...(70 digits omitted)...9935" }, "id": 4457, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "leftExpression": { "argumentTypes": null, "commonType": { "typeIdentifier": "t_rational_115792089237316195423570985008687907853269984665640564039457584007913129639936_by_1", "typeString": "int_const 1157...(70 digits omitted)...9936" }, "id": 4455, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "leftExpression": { "argumentTypes": null, "hexValue": "32", "id": 4453, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "698:1:6", "subdenomination": null, "typeDescriptions": { "typeIdentifier": "t_rational_2_by_1", "typeString": "int_const 2" }, "value": "2" }, "nodeType": "BinaryOperation", "operator": "**", "rightExpression": { "argumentTypes": null, "hexValue": "323536", "id": 4454, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "701:3:6", "subdenomination": null, "typeDescriptions": { "typeIdentifier": "t_rational_256_by_1", "typeString": "int_const 256" }, "value": "256" }, "src": "698:6:6", "typeDescriptions": { "typeIdentifier": "t_rational_115792089237316195423570985008687907853269984665640564039457584007913129639936_by_1", "typeString": "int_const 1157...(70 digits omitted)...9936" } }, "nodeType": "BinaryOperation", "operator": "-", "rightExpression": { "argumentTypes": null, "hexValue": "31", "id": 4456, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "707:1:6", "subdenomination": null, "typeDescriptions": { "typeIdentifier": "t_rational_1_by_1", "typeString": "int_const 1" }, "value": "1" }, "src": "698:10:6", "typeDescriptions": { "typeIdentifier": "t_rational_115792089237316195423570985008687907853269984665640564039457584007913129639935_by_1", "typeString": "int_const 1157...(70 digits omitted)...9935" } }, "visibility": "private" }, { "constant": true, "id": 4465, "name": "MAX_BEFORE_SQUARE", "nodeType": "VariableDeclaration", "scope": 4982, "src": "792:52:6", "stateVariable": true, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 4459, "name": "uint", "nodeType": "ElementaryTypeName", "src": "792:4:6", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "value": { "argumentTypes": null, "commonType": { "typeIdentifier": "t_rational_340282366920938463463374607431768211455_by_1", "typeString": "int_const 3402...(31 digits omitted)...1455" }, "id": 4464, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "leftExpression": { "argumentTypes": null, "commonType": { "typeIdentifier": "t_rational_340282366920938463463374607431768211456_by_1", "typeString": "int_const 3402...(31 digits omitted)...1456" }, "id": 4462, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "leftExpression": { "argumentTypes": null, "hexValue": "32", "id": 4460, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "834:1:6", "subdenomination": null, "typeDescriptions": { "typeIdentifier": "t_rational_2_by_1", "typeString": "int_const 2" }, "value": "2" }, "nodeType": "BinaryOperation", "operator": "**", "rightExpression": { "argumentTypes": null, "hexValue": "313238", "id": 4461, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "837:3:6", "subdenomination": null, "typeDescriptions": { "typeIdentifier": "t_rational_128_by_1", "typeString": "int_const 128" }, "value": "128" }, "src": "834:6:6", "typeDescriptions": { "typeIdentifier": "t_rational_340282366920938463463374607431768211456_by_1", "typeString": "int_const 3402...(31 digits omitted)...1456" } }, "nodeType": "BinaryOperation", "operator": "-", "rightExpression": { "argumentTypes": null, "hexValue": "31", "id": 4463, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "843:1:6", "subdenomination": null, "typeDescriptions": { "typeIdentifier": "t_rational_1_by_1", "typeString": "int_const 1" }, "value": "1" }, "src": "834:10:6", "typeDescriptions": { "typeIdentifier": "t_rational_340282366920938463463374607431768211455_by_1", "typeString": "int_const 3402...(31 digits omitted)...1455" } }, "visibility": "private" }, { "constant": true, "id": 4468, "name": "MAX_ERROR", "nodeType": "VariableDeclaration", "scope": 4982, "src": "972:43:6", "stateVariable": true, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 4466, "name": "uint", "nodeType": "ElementaryTypeName", "src": "972:4:6", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "value": { "argumentTypes": null, "hexValue": "313030303030303030", "id": 4467, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "1006:9:6", "subdenomination": null, "typeDescriptions": { "typeIdentifier": "t_rational_100000000_by_1", "typeString": "int_const 100000000" }, "value": "100000000" }, "visibility": "private" }, { "constant": true, "id": 4473, "name": "MAX_ERROR_BEFORE_DIV", "nodeType": "VariableDeclaration", "scope": 4982, "src": "1106:58:6", "stateVariable": true, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 4469, "name": "uint", "nodeType": "ElementaryTypeName", "src": "1106:4:6", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "value": { "argumentTypes": null, "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 4472, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "leftExpression": { "argumentTypes": null, "id": 4470, "name": "MAX_ERROR", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4468, "src": "1151:9:6", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "*", "rightExpression": { "argumentTypes": null, "hexValue": "32", "id": 4471, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "1163:1:6", "subdenomination": null, "typeDescriptions": { "typeIdentifier": "t_rational_2_by_1", "typeString": "int_const 2" }, "value": "2" }, "src": "1151:13:6", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "private" }, { "body": { "id": 4687, "nodeType": "Block", "src": "1579:1493:6", "statements": [ { "condition": { "argumentTypes": null, "commonType": { "typeIdentifier": "t_bool", "typeString": "bool" }, "id": 4490, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "argumentTypes": null, "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 4486, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "argumentTypes": null, "id": 4484, "name": "_numA", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4475, "src": "1589:5:6", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "==", "rightExpression": { "argumentTypes": null, "hexValue": "30", "id": 4485, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "1598:1:6", "subdenomination": null, "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "src": "1589:10:6", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "nodeType": "BinaryOperation", "operator": "||", "rightExpression": { "argumentTypes": null, "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 4489, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "argumentTypes": null, "id": 4487, "name": "_numB", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4477, "src": "1603:5:6", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "==", "rightExpression": { "argumentTypes": null, "hexValue": "30", "id": 4488, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "1612:1:6", "subdenomination": null, "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "src": "1603:10:6", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "src": "1589:24:6", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "falseBody": null, "id": 4494, "nodeType": "IfStatement", "src": "1585:117:6", "trueBody": { "id": 4493, "nodeType": "Block", "src": "1615:87:6", "statements": [ { "expression": { "argumentTypes": null, "hexValue": "30", "id": 4491, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "1694:1:6", "subdenomination": null, "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "functionReturnParameters": 4483, "id": 4492, "nodeType": "Return", "src": "1687:8:6" } ] } }, { "assignments": [ 4496 ], "declarations": [ { "constant": false, "id": 4496, "name": "value", "nodeType": "VariableDeclaration", "scope": 4687, "src": "1708:10:6", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 4495, "name": "uint", "nodeType": "ElementaryTypeName", "src": "1708:4:6", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "value": null, "visibility": "internal" } ], "id": 4497, "initialValue": null, "nodeType": "VariableDeclarationStatement", "src": "1708:10:6" }, { "condition": { "argumentTypes": null, "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 4502, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "argumentTypes": null, "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 4500, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "argumentTypes": null, "id": 4498, "name": "MAX_UINT", "nodeType": 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"typeString": "uint256" } }, "id": 4971, "nodeType": "ExpressionStatement", "src": "6616:14:6" }, { "expression": { "argumentTypes": null, "arguments": [ { "argumentTypes": null, "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 4975, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "argumentTypes": null, "id": 4973, "name": "numMax", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4831, "src": "6653:6:6", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "/", "rightExpression": { "argumentTypes": null, "id": 4974, "name": "factor", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4869, "src": "6662:6:6", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "6653:15:6", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "argumentTypes": null, "id": 4976, "name": "numMin", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4835, "src": "6670:6:6", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "argumentTypes": null, "id": 4977, "name": "MAX_UINT", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4458, "src": "6678:8:6", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } ], "expression": { "argumentTypes": [ { "typeIdentifier": "t_uint256", "typeString": "uint256" }, { "typeIdentifier": "t_uint256", "typeString": "uint256" }, { "typeIdentifier": "t_uint256", "typeString": "uint256" } ], "id": 4972, "name": "bigDiv2x1", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4688, "src": "6643:9:6", "typeDescriptions": { "typeIdentifier": "t_function_internal_pure$_t_uint256_$_t_uint256_$_t_uint256_$returns$_t_uint256_$", "typeString": "function (uint256,uint256,uint256) pure returns (uint256)" } }, "id": 4978, "isConstant": false, "isLValue": false, "isPure": false, "kind": "functionCall", "lValueRequested": false, "names": [], "nodeType": "FunctionCall", "src": "6643:44:6", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "functionReturnParameters": 4756, "id": 4979, "nodeType": "Return", "src": "6636:51:6" } ] }, "documentation": "@notice Returns the approx result of `a * b / (c * d)` so long as the result is <= MAX_UINT\n@param _numA the first numerator term\n@param _numB the second numerator term\n@param _denA the first denominator term\n@param _denB the second denominator term\n@return the approx result with up to off by 2 + MAX_ERROR*10 error, rounding down if needed\n@dev this uses bigDiv2x1 and adds additional rounding error so the max error of this\nformula is larger", "id": 4981, "implemented": true, "kind": "function", "modifiers": [], "name": "bigDiv2x2", "nodeType": "FunctionDefinition", "parameters": { "id": 4753, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 4746, "name": "_numA", "nodeType": "VariableDeclaration", "scope": 4981, "src": "4664:10:6", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 4745, "name": "uint", "nodeType": "ElementaryTypeName", "src": "4664:4:6", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "value": null, "visibility": "internal" }, { "constant": false, "id": 4748, "name": "_numB", "nodeType": "VariableDeclaration", "scope": 4981, "src": "4680:10:6", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 4747, "name": "uint", "nodeType": "ElementaryTypeName", "src": "4680:4:6", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "value": null, "visibility": "internal" }, { "constant": false, "id": 4750, "name": "_denA", "nodeType": "VariableDeclaration", "scope": 4981, "src": "4696:10:6", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 4749, "name": "uint", "nodeType": "ElementaryTypeName", "src": "4696:4:6", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "value": null, "visibility": "internal" }, { "constant": false, "id": 4752, "name": "_denB", "nodeType": "VariableDeclaration", "scope": 4981, "src": "4712:10:6", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 4751, "name": "uint", "nodeType": "ElementaryTypeName", "src": "4712:4:6", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "value": null, "visibility": "internal" } ], "src": "4658:68:6" }, "returnParameters": { "id": 4756, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 4755, "name": "", "nodeType": "VariableDeclaration", "scope": 4981, "src": "4750:4:6", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 4754, "name": "uint", "nodeType": "ElementaryTypeName", "src": "4750:4:6", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "value": null, "visibility": "internal" } ], "src": "4749:6:6" }, "scope": 4982, "src": "4640:2052:6", "stateMutability": "pure", "superFunction": null, "visibility": "internal" } ], "scope": 4983, "src": "581:6113:6" } ], "src": "0:6695:6" }, "compiler": { "name": "solc", "version": "0.5.17+commit.d19bba13.Emscripten.clang" }, "networks": {}, "schemaVersion": "3.3.0", "updatedAt": "2020-12-11T05:03:09.344Z", "devdoc": { "details": "Results may be off by 1 + 0.000001% for 2x1 calls and 2 + 0.00001% for 2x2 calls. Do not use if your contract expects very small result values to be accurate.", "methods": {}, "title": "Reduces the size of terms before multiplication, to avoid an overflow, and then restores the proper size after division." }, "userdoc": { "methods": {}, "notice": "This effectively allows us to overflow values in the numerator and/or denominator of a fraction, so long as the end result does not overflow as well." } }