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"source": "pragma solidity ^0.4.15;\n\n\n/// @title Math library - Allows calculation of logarithmic and exponential functions\n/// @author Alan Lu - \n/// @author Stefan George - \nlibrary Math {\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 constant\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 var (lower, 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 constant\n returns (uint)\n {\n var (lower, 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 constant\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 (safeToAdd(lower, uint(zpow)))\n upper = lower + uint(zpow);\n else\n upper = 2**256-1;\n return;\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;\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 constant\n returns (int)\n {\n var (lower, upper) = log2Bounds(x);\n return ((upper - lower) / 2 + lower) * int(ONE) / int(LOG2_E);\n }\n\n /// @dev Returns estimate of log2(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 log2(x) in fixed point\n function log2(uint x, EstimationMode estimationMode)\n public\n constant\n returns (int)\n {\n var (lower, 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 /// @dev Returns bounds for value of log2(x) given x\n /// @param x logarithm argument in fixed point\n /// @return {\n /// \"lower\": \"lower bound of log2(x) in fixed point\",\n /// \"upper\": \"upper bound of log2(x) in fixed point\"\n /// }\n function log2Bounds(uint x)\n public\n constant\n returns (int lower, int upper)\n {\n require(x > 0);\n // compute ⌊log₂x⌋\n lower = floorLog2(x);\n\n uint y;\n if (lower < 0)\n y = x << uint(-lower);\n else\n y = x >> uint(lower);\n\n lower *= int(ONE);\n\n // y = x * 2^(-⌊log₂x⌋)\n // so 1 <= y < 2\n // and log₂x = ⌊log₂x⌋ + log₂y\n for (int m = 1; m <= 64; m++) {\n if(y == ONE) {\n break;\n }\n y = y * y / ONE;\n if(y >= 2 * ONE) {\n lower += int(ONE >> m);\n y /= 2;\n }\n }\n\n return (lower, lower + 4);\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)\n public\n constant\n returns (int lo)\n {\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)\n hi = mid;\n else\n 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[] nums)\n public\n constant\n returns (int max)\n {\n require(nums.length > 0);\n max = -2**255;\n for (uint i = 0; i < nums.length; i++)\n if (nums[i] > max)\n max = 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)\n public\n constant\n returns (bool)\n {\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)\n public\n constant\n returns (bool)\n {\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)\n public\n constant\n returns (bool)\n {\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)\n public\n constant\n returns (uint)\n {\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)\n public\n constant\n returns (uint)\n {\n require(safeToSub(a, b));\n return a - b;\n }\n\n /// @dev Returns product if no overflow occurred\n /// @param a First factor\n /// @param b Second factor\n /// @return Product\n function mul(uint a, uint b)\n public\n constant\n returns (uint)\n {\n require(safeToMul(a, b));\n return a * b;\n }\n\n 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3559, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7930:1:11", "subdenomination": null, "typeDescriptions": { "typeIdentifier": "t_rational_4_by_1", "typeString": "int_const 4" }, "value": "4" }, "src": "7922:9:11", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" } } ], "id": 3561, "isConstant": false, "isInlineArray": false, "isLValue": false, "isPure": false, "lValueRequested": false, "nodeType": "TupleExpression", "src": "7914:18:11", "typeDescriptions": { "typeIdentifier": "t_tuple$_t_int256_$_t_int256_$", "typeString": "tuple(int256,int256)" } }, "functionReturnParameters": 3469, "id": 3562, "nodeType": "Return", "src": "7907:25:11" } ] }, "documentation": "@dev Returns bounds for value of log2(x) given x\n @param x logarithm argument in fixed point\n @return {\n \"lower\": \"lower bound of log2(x) in fixed point\",\n \"upper\": \"upper bound of log2(x) in fixed point\"\n }", "id": 3564, "implemented": true, "isConstructor": false, "isDeclaredConst": true, "modifiers": [], "name": "log2Bounds", "nodeType": "FunctionDefinition", "parameters": { "id": 3464, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 3463, "name": "x", "nodeType": "VariableDeclaration", "scope": 3564, "src": "7211:6:11", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 3462, "name": "uint", "nodeType": "ElementaryTypeName", "src": "7211:4:11", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "value": null, "visibility": "internal" } ], "src": "7210:8:11" }, "payable": false, "returnParameters": { "id": 3469, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 3466, "name": "lower", "nodeType": "VariableDeclaration", "scope": 3564, "src": "7268:9:11", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" }, "typeName": { "id": 3465, "name": "int", "nodeType": "ElementaryTypeName", "src": "7268:3:11", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" } }, "value": null, "visibility": "internal" }, { "constant": false, "id": 3468, "name": "upper", "nodeType": "VariableDeclaration", "scope": 3564, "src": "7279:9:11", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" }, "typeName": { "id": 3467, "name": "int", "nodeType": "ElementaryTypeName", "src": "7279:3:11", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" } }, "value": null, "visibility": "internal" } ], "src": "7267:22:11" }, "scope": 3954, "src": "7191:748:11", "stateMutability": "view", "superFunction": null, "visibility": "public" }, { "body": { "id": 3639, "nodeType": "Block", "src": "8141:404:11", "statements": [ { "expression": { "argumentTypes": null, "id": 3574, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "argumentTypes": null, "id": 3571, "name": "lo", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 3569, "src": "8151:2:11", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" } }, "nodeType": "Assignment", "operator": "=", "rightHandSide": { "argumentTypes": null, "id": 3573, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "nodeType": "UnaryOperation", "operator": "-", "prefix": true, "src": "8156:3:11", "subExpression": { "argumentTypes": null, "hexValue": "3634", "id": 3572, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "8157:2:11", "subdenomination": null, "typeDescriptions": { "typeIdentifier": "t_rational_64_by_1", "typeString": "int_const 64" }, "value": "64" }, "typeDescriptions": { "typeIdentifier": "t_rational_-64_by_1", "typeString": "int_const -64" } }, "src": "8151:8:11", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" } }, "id": 3575, "nodeType": "ExpressionStatement", "src": "8151:8:11" }, { "assignments": [ 3577 ], "declarations": [ { "constant": false, "id": 3577, "name": "hi", "nodeType": "VariableDeclaration", "scope": 3640, "src": "8169:6:11", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" }, "typeName": { "id": 3576, "name": "int", "nodeType": "ElementaryTypeName", "src": "8169:3:11", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" } }, "value": null, "visibility": "internal" } ], "id": 3579, "initialValue": { "argumentTypes": null, "hexValue": "313933", "id": 3578, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "8178:3:11", "subdenomination": null, "typeDescriptions": { "typeIdentifier": "t_rational_193_by_1", "typeString": "int_const 193" }, "value": "193" }, "nodeType": "VariableDeclarationStatement", "src": "8169:12:11" }, { "assignments": [ 3581 ], "declarations": [ { "constant": false, "id": 3581, "name": "mid", "nodeType": "VariableDeclaration", "scope": 3640, "src": "8284:7:11", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" }, "typeName": { "id": 3580, "name": "int", "nodeType": "ElementaryTypeName", "src": "8284:3:11", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" } }, "value": null, "visibility": "internal" } ], "id": 3588, "initialValue": { "argumentTypes": null, "commonType": { "typeIdentifier": "t_int256", "typeString": "int256" }, "id": 3587, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "argumentTypes": null, 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"nodeType": "TupleExpression", "src": "8294:9:11", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" } }, "nodeType": "BinaryOperation", "operator": ">>", "rightExpression": { "argumentTypes": null, "hexValue": "31", "id": 3586, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "8307:1:11", "subdenomination": null, "typeDescriptions": { "typeIdentifier": "t_rational_1_by_1", "typeString": "int_const 1" }, "value": "1" }, "src": "8294:14:11", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" } }, "nodeType": "VariableDeclarationStatement", "src": "8284:24:11" }, { "body": { "id": 3637, "nodeType": "Block", "src": "8339:200:11", "statements": [ { "condition": { "argumentTypes": null, "commonType": { "typeIdentifier": "t_bool", "typeString": "bool" }, "id": 3618, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, 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"typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "src": "8357:7:11", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "nodeType": "BinaryOperation", "operator": "&&", "rightExpression": { "argumentTypes": null, "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 3605, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "argumentTypes": null, "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 3603, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "argumentTypes": null, "id": 3598, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 3566, "src": "8368:1:11", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "<<", "rightExpression": { "argumentTypes": 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"argumentTypes": null, "hexValue": "323535", "id": 3658, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "8808:3:11", "subdenomination": null, "typeDescriptions": { "typeIdentifier": "t_rational_255_by_1", "typeString": "int_const 255" }, "value": "255" }, "src": "8804:7:11", "typeDescriptions": { "typeIdentifier": "t_rational_-57896044618658097711785492504343953926634992332820282019728792003956564819968_by_1", "typeString": "int_const -578...(70 digits omitted)...9968" } }, "src": "8798:13:11", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" } }, "id": 3661, "nodeType": "ExpressionStatement", "src": "8798:13:11" }, { "body": { "condition": { "argumentTypes": null, "commonType": { "typeIdentifier": "t_int256", "typeString": "int256" }, "id": 3677, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "argumentTypes": null, "baseExpression": { "argumentTypes": null, "id": 3673, "name": "nums", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 3643, "src": "8876:4:11", "typeDescriptions": { "typeIdentifier": "t_array$_t_int256_$dyn_memory_ptr", "typeString": "int256[] memory" } }, "id": 3675, "indexExpression": { "argumentTypes": null, "id": 3674, "name": "i", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 3663, "src": "8881:1:11", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "isConstant": false, "isLValue": true, "isPure": false, "lValueRequested": false, "nodeType": "IndexAccess", "src": "8876:7:11", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" } }, "nodeType": "BinaryOperation", "operator": ">", "rightExpression": { "argumentTypes": null, "id": 3676, "name": "max", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 3646, "src": "8886:3:11", 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"overloadedDeclarations": [], "referencedDeclaration": 3663, "src": "8838:1:11", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "<", "rightExpression": { "argumentTypes": null, "expression": { "argumentTypes": null, "id": 3667, "name": "nums", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 3643, "src": "8842:4:11", "typeDescriptions": { "typeIdentifier": "t_array$_t_int256_$dyn_memory_ptr", "typeString": "int256[] memory" } }, "id": 3668, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "memberName": "length", "nodeType": "MemberAccess", "referencedDeclaration": null, "src": "8842:11:11", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "8838:15:11", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 3685, "initializationExpression": { "assignments": [ 3663 ], 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"t_uint256", "typeString": "uint256" } }, "src": "10407:5:11", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "functionReturnParameters": 3768, "id": 3779, "nodeType": "Return", "src": "10400:12:11" } ] }, "documentation": "@dev Returns difference if no overflow occurred\n @param a Minuend\n @param b Subtrahend\n @return Difference", "id": 3781, "implemented": true, "isConstructor": false, "isDeclaredConst": true, "modifiers": [], "name": "sub", "nodeType": "FunctionDefinition", "parameters": { "id": 3765, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 3762, "name": "a", "nodeType": "VariableDeclaration", "scope": 3781, "src": "10281:6:11", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 3761, "name": "uint", "nodeType": "ElementaryTypeName", "src": "10281:4:11", "typeDescriptions": { "typeIdentifier": "t_uint256", 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"10346:4:11", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "value": null, "visibility": "internal" } ], "src": "10345:6:11" }, "scope": 3954, "src": "10268:151:11", "stateMutability": "view", "superFunction": null, "visibility": "public" }, { "body": { "id": 3801, "nodeType": "Block", "src": "10651:63:11", "statements": [ { "expression": { "argumentTypes": null, "arguments": [ { "argumentTypes": null, "arguments": [ { "argumentTypes": null, "id": 3792, "name": "a", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 3783, "src": "10679:1:11", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "argumentTypes": null, "id": 3793, "name": "b", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 3785, "src": "10682:1:11", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } ], "expression": { "argumentTypes": [ { "typeIdentifier": 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"name": "b", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 3785, "src": "10706:1:11", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "10702:5:11", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "functionReturnParameters": 3789, "id": 3800, "nodeType": "Return", "src": "10695:12:11" } ] }, "documentation": "@dev Returns product if no overflow occurred\n @param a First factor\n @param b Second factor\n @return Product", "id": 3802, "implemented": true, "isConstructor": false, "isDeclaredConst": true, "modifiers": [], "name": "mul", "nodeType": "FunctionDefinition", "parameters": { "id": 3786, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 3783, "name": "a", "nodeType": "VariableDeclaration", "scope": 3802, "src": "10576:6:11", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 3782, "name": "uint", "nodeType": "ElementaryTypeName", "src": "10576:4:11", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "value": null, "visibility": "internal" }, { "constant": false, "id": 3785, "name": "b", "nodeType": "VariableDeclaration", "scope": 3802, "src": "10584:6:11", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 3784, "name": "uint", "nodeType": "ElementaryTypeName", "src": "10584:4:11", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "value": null, "visibility": "internal" } ], "src": "10575:16:11" }, "payable": false, "returnParameters": { "id": 3789, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 3788, "name": "", "nodeType": "VariableDeclaration", "scope": 3802, "src": "10641:4:11", "stateVariable": false, "storageLocation": "default", 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"11005:5:11", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" } }, "nodeType": "BinaryOperation", "operator": ">=", "rightExpression": { "argumentTypes": null, "id": 3817, "name": "a", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 3804, "src": "11014:1:11", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" } }, "src": "11005:10:11", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "src": "10995:20:11", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } } ], "id": 3820, "isConstant": false, "isInlineArray": false, "isLValue": false, "isPure": false, "lValueRequested": false, "nodeType": "TupleExpression", "src": "10994:22:11", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "nodeType": "BinaryOperation", "operator": "||", "rightExpression": { "argumentTypes": null, "components": [ { "argumentTypes": null, "commonType": { 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