{ "contractName": "Math", "abi": [], "metadata": "{\"compiler\":{\"version\":\"0.8.19+commit.7dd6d404\"},\"language\":\"Solidity\",\"output\":{\"abi\":[],\"devdoc\":{\"details\":\"Standard math utilities missing in the Solidity language.\",\"kind\":\"dev\",\"methods\":{},\"version\":1},\"userdoc\":{\"kind\":\"user\",\"methods\":{},\"version\":1}},\"settings\":{\"compilationTarget\":{\"@openzeppelin/contracts/utils/math/Math.sol\":\"Math\"},\"evmVersion\":\"paris\",\"libraries\":{},\"metadata\":{\"bytecodeHash\":\"ipfs\"},\"optimizer\":{\"enabled\":true,\"runs\":25},\"remappings\":[]},\"sources\":{\"@openzeppelin/contracts/utils/math/Math.sol\":{\"keccak256\":\"0xa1e8e83cd0087785df04ac79fb395d9f3684caeaf973d9e2c71caef723a3a5d6\",\"license\":\"MIT\",\"urls\":[\"bzz-raw://33bbf48cc069be677705037ba7520c22b1b622c23b33e1a71495f2d36549d40b\",\"dweb:/ipfs/Qmct36zWXv3j7LZB83uwbg7TXwnZSN1fqHNDZ93GG98bGz\"]}},\"version\":1}", "bytecode": "0x60566037600b82828239805160001a607314602a57634e487b7160e01b600052600060045260246000fd5b30600052607381538281f3fe73000000000000000000000000000000000000000030146080604052600080fdfea2646970667358221220056b324ae2f3719c85e74de1b1307a51c1afdcb264f08e91abdbe14c6b6c94aa64736f6c63430008130033", "deployedBytecode": "0x73000000000000000000000000000000000000000030146080604052600080fdfea2646970667358221220056b324ae2f3719c85e74de1b1307a51c1afdcb264f08e91abdbe14c6b6c94aa64736f6c63430008130033", "immutableReferences": {}, "generatedSources": [], "deployedGeneratedSources": [], "sourceMap": "202:12302:22:-:0;;;;;;;;;;;;;;;-1:-1:-1;;;202:12302:22;;;;;;;;;;;;;;;;;", "deployedSourceMap": "202:12302:22:-:0;;;;;;;;", "source": "// SPDX-License-Identifier: MIT\n// OpenZeppelin Contracts (last updated v4.8.0) (utils/math/Math.sol)\n\npragma solidity ^0.8.0;\n\n/**\n * @dev Standard math utilities missing in the Solidity language.\n */\nlibrary Math {\n enum Rounding {\n Down, // Toward negative infinity\n Up, // Toward infinity\n Zero // Toward zero\n }\n\n /**\n * @dev Returns the largest of two numbers.\n */\n function max(uint256 a, uint256 b) internal pure returns (uint256) {\n return a > b ? a : b;\n }\n\n /**\n * @dev Returns the smallest of two numbers.\n */\n function min(uint256 a, uint256 b) internal pure returns (uint256) {\n return a < b ? a : b;\n }\n\n /**\n * @dev Returns the average of two numbers. The result is rounded towards\n * zero.\n */\n function average(uint256 a, uint256 b) internal pure returns (uint256) {\n // (a + b) / 2 can overflow.\n return (a & b) + (a ^ b) / 2;\n }\n\n /**\n * @dev Returns the ceiling of the division of two numbers.\n *\n * This differs from standard division with `/` in that it rounds up instead\n * of rounding down.\n */\n function ceilDiv(uint256 a, uint256 b) internal pure returns (uint256) {\n // (a + b - 1) / b can overflow on addition, so we distribute.\n return a == 0 ? 0 : (a - 1) / b + 1;\n }\n\n /**\n * @notice Calculates floor(x * y / denominator) with full precision. Throws if result overflows a uint256 or denominator == 0\n * @dev Original credit to Remco Bloemen under MIT license (https://xn--2-umb.com/21/muldiv)\n * with further edits by Uniswap Labs also under MIT license.\n */\n function mulDiv(\n uint256 x,\n uint256 y,\n uint256 denominator\n ) internal pure returns (uint256 result) {\n unchecked {\n // 512-bit multiply [prod1 prod0] = x * y. Compute the product mod 2^256 and mod 2^256 - 1, then use\n // use the Chinese Remainder Theorem to reconstruct the 512 bit result. The result is stored in two 256\n // variables such that product = prod1 * 2^256 + prod0.\n uint256 prod0; // Least significant 256 bits of the product\n uint256 prod1; // Most significant 256 bits of the product\n assembly {\n let mm := mulmod(x, y, not(0))\n prod0 := mul(x, y)\n prod1 := sub(sub(mm, prod0), lt(mm, prod0))\n }\n\n // Handle non-overflow cases, 256 by 256 division.\n if (prod1 == 0) {\n return prod0 / denominator;\n }\n\n // Make sure the result is less than 2^256. Also prevents denominator == 0.\n require(denominator > prod1);\n\n ///////////////////////////////////////////////\n // 512 by 256 division.\n ///////////////////////////////////////////////\n\n // Make division exact by subtracting the remainder from [prod1 prod0].\n uint256 remainder;\n assembly {\n // Compute remainder using mulmod.\n remainder := mulmod(x, y, denominator)\n\n // Subtract 256 bit number from 512 bit number.\n prod1 := sub(prod1, gt(remainder, prod0))\n prod0 := sub(prod0, remainder)\n }\n\n // Factor powers of two out of denominator and compute largest power of two divisor of denominator. Always >= 1.\n // See https://cs.stackexchange.com/q/138556/92363.\n\n // Does not overflow because the denominator cannot be zero at this stage in the function.\n uint256 twos = denominator & (~denominator + 1);\n assembly {\n // Divide denominator by twos.\n denominator := div(denominator, twos)\n\n // Divide [prod1 prod0] by twos.\n prod0 := div(prod0, twos)\n\n // Flip twos such that it is 2^256 / twos. If twos is zero, then it becomes one.\n twos := add(div(sub(0, twos), twos), 1)\n }\n\n // Shift in bits from prod1 into prod0.\n prod0 |= prod1 * twos;\n\n // Invert denominator mod 2^256. Now that denominator is an odd number, it has an inverse modulo 2^256 such\n // that denominator * inv = 1 mod 2^256. Compute the inverse by starting with a seed that is correct for\n // four bits. That is, denominator * inv = 1 mod 2^4.\n uint256 inverse = (3 * denominator) ^ 2;\n\n // Use the Newton-Raphson iteration to improve the precision. Thanks to Hensel's lifting lemma, this also works\n // in modular arithmetic, doubling the correct bits in each step.\n inverse *= 2 - denominator * inverse; // inverse mod 2^8\n inverse *= 2 - denominator * inverse; // inverse mod 2^16\n inverse *= 2 - denominator * inverse; // inverse mod 2^32\n inverse *= 2 - denominator * inverse; // inverse mod 2^64\n inverse *= 2 - denominator * inverse; // inverse mod 2^128\n inverse *= 2 - denominator * inverse; // inverse mod 2^256\n\n // Because the division is now exact we can divide by multiplying with the modular inverse of denominator.\n // This will give us the correct result modulo 2^256. Since the preconditions guarantee that the outcome is\n // less than 2^256, this is the final result. We don't need to compute the high bits of the result and prod1\n // is no longer required.\n result = prod0 * inverse;\n return result;\n }\n }\n\n /**\n * @notice Calculates x * y / denominator with full precision, following the selected rounding direction.\n */\n function mulDiv(\n uint256 x,\n uint256 y,\n uint256 denominator,\n Rounding rounding\n ) internal pure returns (uint256) {\n uint256 result = mulDiv(x, y, denominator);\n if (rounding == Rounding.Up && mulmod(x, y, denominator) > 0) {\n result += 1;\n }\n return result;\n }\n\n /**\n * @dev Returns the square root of a number. If the number is not a perfect square, the value is rounded down.\n *\n * Inspired by Henry S. Warren, Jr.'s \"Hacker's Delight\" (Chapter 11).\n */\n function sqrt(uint256 a) internal pure returns (uint256) {\n if (a == 0) {\n return 0;\n }\n\n // For our first guess, we get the biggest power of 2 which is smaller than the square root of the target.\n //\n // We know that the \"msb\" (most significant bit) of our target number `a` is a power of 2 such that we have\n // `msb(a) <= a < 2*msb(a)`. This value can be written `msb(a)=2**k` with `k=log2(a)`.\n //\n // This can be rewritten `2**log2(a) <= a < 2**(log2(a) + 1)`\n // → `sqrt(2**k) <= sqrt(a) < sqrt(2**(k+1))`\n // → `2**(k/2) <= sqrt(a) < 2**((k+1)/2) <= 2**(k/2 + 1)`\n //\n // Consequently, `2**(log2(a) / 2)` is a good first approximation of `sqrt(a)` with at least 1 correct bit.\n uint256 result = 1 << (log2(a) >> 1);\n\n // At this point `result` is an estimation with one bit of precision. We know the true value is a uint128,\n // since it is the square root of a uint256. Newton's method converges quadratically (precision doubles at\n // every iteration). We thus need at most 7 iteration to turn our partial result with one bit of precision\n // into the expected uint128 result.\n unchecked {\n result = (result + a / result) >> 1;\n result = (result + a / result) >> 1;\n result = (result + a / result) >> 1;\n result = (result + a / result) >> 1;\n result = (result + a / result) >> 1;\n result = (result + a / result) >> 1;\n result = (result + a / result) >> 1;\n return min(result, a / result);\n }\n }\n\n /**\n * @notice Calculates sqrt(a), following the selected rounding direction.\n */\n function sqrt(uint256 a, Rounding rounding) internal pure returns (uint256) {\n unchecked {\n uint256 result = sqrt(a);\n return result + (rounding == Rounding.Up && result * result < a ? 1 : 0);\n }\n }\n\n /**\n * @dev Return the log in base 2, rounded down, of a positive value.\n * Returns 0 if given 0.\n */\n function log2(uint256 value) internal pure returns (uint256) {\n uint256 result = 0;\n unchecked {\n if (value >> 128 > 0) {\n value >>= 128;\n result += 128;\n }\n if (value >> 64 > 0) {\n value >>= 64;\n result += 64;\n }\n if (value >> 32 > 0) {\n value >>= 32;\n result += 32;\n }\n if (value >> 16 > 0) {\n value >>= 16;\n result += 16;\n }\n if (value >> 8 > 0) {\n value >>= 8;\n result += 8;\n }\n if (value >> 4 > 0) {\n value >>= 4;\n result += 4;\n }\n if (value >> 2 > 0) {\n value >>= 2;\n result += 2;\n }\n if (value >> 1 > 0) {\n result += 1;\n }\n }\n return result;\n }\n\n /**\n * @dev Return the log in base 2, following the selected rounding direction, of a positive value.\n * Returns 0 if given 0.\n */\n function log2(uint256 value, Rounding rounding) internal pure returns (uint256) {\n unchecked {\n uint256 result = log2(value);\n return result + (rounding == Rounding.Up && 1 << result < value ? 1 : 0);\n }\n }\n\n /**\n * @dev Return the log in base 10, rounded down, of a positive value.\n * Returns 0 if given 0.\n */\n function log10(uint256 value) internal pure returns (uint256) {\n uint256 result = 0;\n unchecked {\n if (value >= 10**64) {\n value /= 10**64;\n result += 64;\n }\n if (value >= 10**32) {\n value /= 10**32;\n result += 32;\n }\n if (value >= 10**16) {\n value /= 10**16;\n result += 16;\n }\n if (value >= 10**8) {\n value /= 10**8;\n result += 8;\n }\n if (value >= 10**4) {\n value /= 10**4;\n result += 4;\n }\n if (value >= 10**2) {\n value /= 10**2;\n result += 2;\n }\n if (value >= 10**1) {\n result += 1;\n }\n }\n return result;\n }\n\n /**\n * @dev Return the log in base 10, following the selected rounding direction, of a positive value.\n * Returns 0 if given 0.\n */\n function log10(uint256 value, Rounding rounding) internal pure returns (uint256) {\n unchecked {\n uint256 result = log10(value);\n return result + (rounding == Rounding.Up && 10**result < value ? 1 : 0);\n }\n }\n\n /**\n * @dev Return the log in base 256, rounded down, of a positive value.\n * Returns 0 if given 0.\n *\n * Adding one to the result gives the number of pairs of hex symbols needed to represent `value` as a hex string.\n */\n function log256(uint256 value) internal pure returns (uint256) {\n uint256 result = 0;\n unchecked {\n if (value >> 128 > 0) {\n value >>= 128;\n result += 16;\n }\n if (value >> 64 > 0) {\n value >>= 64;\n result += 8;\n }\n if (value >> 32 > 0) {\n value >>= 32;\n result += 4;\n }\n if (value >> 16 > 0) {\n value >>= 16;\n result += 2;\n }\n if (value >> 8 > 0) {\n result += 1;\n }\n }\n return result;\n }\n\n /**\n * @dev Return the log in base 10, following the selected rounding direction, of a positive value.\n * Returns 0 if given 0.\n */\n function log256(uint256 value, Rounding rounding) internal pure returns (uint256) {\n unchecked {\n uint256 result = log256(value);\n return result + (rounding == Rounding.Up && 1 << (result * 8) < value ? 1 : 0);\n }\n }\n}\n", "sourcePath": "@openzeppelin/contracts/utils/math/Math.sol", "ast": { "absolutePath": "@openzeppelin/contracts/utils/math/Math.sol", "exportedSymbols": { "Math": [ 3203 ] }, 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"typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 2653, "nodeType": "ExpressionStatement", "src": "7630:35:22" }, { "expression": { "id": 2663, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 2654, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 2611, "src": "7679:6:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "=", "rightHandSide": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 2662, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "components": [ { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 2659, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 2655, "name": "result", "nodeType": "Identifier", 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"uint256" } } ], "id": 2671, "isConstant": false, "isInlineArray": false, "isLValue": false, "isPure": false, "lValueRequested": false, "nodeType": "TupleExpression", "src": "7737:21:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">>", "rightExpression": { "hexValue": "31", "id": 2672, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7762:1:22", "typeDescriptions": { "typeIdentifier": "t_rational_1_by_1", "typeString": "int_const 1" }, "value": "1" }, "src": "7737:26:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "7728:35:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 2675, "nodeType": "ExpressionStatement", "src": "7728:35:22" }, { "expression": { "id": 2685, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 2676, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 2611, "src": "7777:6:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "=", "rightHandSide": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 2684, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "components": [ { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 2681, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 2677, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 2611, "src": "7787:6:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "+", "rightExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 2680, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 2678, "name": "a", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 2598, "src": "7796:1:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "/", "rightExpression": { "id": 2679, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 2611, "src": "7800:6:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "7796:10:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "7787:19:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } ], "id": 2682, "isConstant": false, "isInlineArray": false, "isLValue": false, "isPure": false, "lValueRequested": false, "nodeType": "TupleExpression", "src": "7786:21:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">>", "rightExpression": { "hexValue": "31", "id": 2683, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7811:1:22", "typeDescriptions": { "typeIdentifier": "t_rational_1_by_1", "typeString": "int_const 1" }, "value": "1" }, "src": "7786:26:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "7777:35:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 2686, "nodeType": "ExpressionStatement", "src": "7777:35:22" }, { "expression": { "id": 2696, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 2687, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 2611, "src": "7826:6:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "=", "rightHandSide": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 2695, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "components": [ { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 2692, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 2688, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 2611, "src": "7836:6:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "+", "rightExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 2691, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 2689, "name": "a", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 2598, "src": "7845:1:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "/", "rightExpression": { "id": 2690, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 2611, "src": "7849:6:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "7845:10:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "7836:19:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } ], "id": 2693, "isConstant": false, "isInlineArray": false, "isLValue": false, "isPure": false, "lValueRequested": false, "nodeType": "TupleExpression", "src": "7835:21:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">>", "rightExpression": { "hexValue": "31", "id": 2694, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7860:1:22", "typeDescriptions": { "typeIdentifier": "t_rational_1_by_1", "typeString": "int_const 1" }, "value": "1" }, "src": "7835:26:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "7826:35:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 2697, "nodeType": "ExpressionStatement", "src": "7826:35:22" }, { "expression": { "arguments": [ { "id": 2699, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 2611, "src": "7886:6:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 2702, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 2700, "name": "a", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 2598, "src": "7894:1:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "/", "rightExpression": { "id": 2701, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 2611, "src": "7898:6:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "7894:10:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } ], "expression": { "argumentTypes": [ { "typeIdentifier": "t_uint256", "typeString": "uint256" }, { "typeIdentifier": "t_uint256", "typeString": "uint256" } ], "id": 2698, "name": "min", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 2381, "src": "7882:3:22", "typeDescriptions": { "typeIdentifier": "t_function_internal_pure$_t_uint256_$_t_uint256_$returns$_t_uint256_$", "typeString": "function (uint256,uint256) pure returns (uint256)" } }, "id": 2703, "isConstant": false, "isLValue": false, "isPure": false, "kind": "functionCall", "lValueRequested": false, "nameLocations": [], "names": [], "nodeType": "FunctionCall", "src": "7882:23:22", "tryCall": false, "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "functionReturnParameters": 2602, "id": 2704, "nodeType": "Return", "src": "7875:30:22" } ] } ] }, "documentation": { "id": 2596, "nodeType": "StructuredDocumentation", "src": "6067:208:22", "text": " @dev Returns the square root of a number. If the number is not a perfect square, the value is rounded down.\n Inspired by Henry S. Warren, Jr.'s \"Hacker's Delight\" (Chapter 11)." }, "id": 2707, "implemented": true, "kind": "function", "modifiers": [], "name": "sqrt", "nameLocation": "6289:4:22", "nodeType": "FunctionDefinition", "parameters": { "id": 2599, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 2598, "mutability": "mutable", "name": "a", "nameLocation": "6302:1:22", "nodeType": "VariableDeclaration", "scope": 2707, "src": "6294:9:22", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 2597, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "6294:7:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "src": "6293:11:22" }, "returnParameters": { "id": 2602, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 2601, "mutability": "mutable", "name": "", "nameLocation": "-1:-1:-1", 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{ "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 2901, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 2899, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "hexValue": "31", "id": 2897, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "9719:1:22", "typeDescriptions": { "typeIdentifier": "t_rational_1_by_1", "typeString": "int_const 1" }, "value": "1" }, "nodeType": "BinaryOperation", "operator": "<<", "rightExpression": { "id": 2898, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 2887, "src": "9724:6:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "9719:11:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "<", "rightExpression": { "id": 2900, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 2878, "src": "9733:5:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "9719:19:22", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "src": "9692:46:22", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "falseExpression": { "hexValue": "30", "id": 2904, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "9745:1:22", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "id": 2905, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "nodeType": "Conditional", "src": "9692:54:22", "trueExpression": { "hexValue": "31", "id": 2903, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "9741:1:22", "typeDescriptions": { "typeIdentifier": "t_rational_1_by_1", "typeString": "int_const 1" }, "value": "1" }, "typeDescriptions": { "typeIdentifier": "t_uint8", "typeString": "uint8" } } ], "id": 2906, "isConstant": false, "isInlineArray": false, "isLValue": false, "isPure": false, "lValueRequested": false, "nodeType": "TupleExpression", "src": "9691:56:22", "typeDescriptions": { "typeIdentifier": "t_uint8", "typeString": "uint8" } }, "src": "9682:65:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "functionReturnParameters": 2885, "id": 2908, "nodeType": "Return", "src": "9675:72:22" } ] } ] }, "documentation": { "id": 2876, "nodeType": "StructuredDocumentation", "src": "9372:142:22", "text": " @dev Return the log in base 2, following the selected rounding direction, of a positive value.\n Returns 0 if given 0." }, "id": 2911, "implemented": true, "kind": "function", "modifiers": [], "name": "log2", "nameLocation": "9528:4:22", "nodeType": "FunctionDefinition", "parameters": { "id": 2882, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 2878, "mutability": "mutable", "name": "value", "nameLocation": "9541:5:22", "nodeType": "VariableDeclaration", "scope": 2911, "src": "9533:13:22", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 2877, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "9533:7:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" }, { "constant": false, "id": 2881, "mutability": "mutable", "name": "rounding", "nameLocation": "9557:8:22", "nodeType": "VariableDeclaration", "scope": 2911, "src": "9548:17:22", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_enum$_Rounding_$2345", "typeString": "enum Math.Rounding" }, "typeName": { "id": 2880, "nodeType": "UserDefinedTypeName", "pathNode": { "id": 2879, "name": "Rounding", "nameLocations": [ "9548:8:22" ], "nodeType": "IdentifierPath", "referencedDeclaration": 2345, "src": "9548:8:22" }, "referencedDeclaration": 2345, "src": "9548:8:22", "typeDescriptions": { "typeIdentifier": "t_enum$_Rounding_$2345", "typeString": "enum Math.Rounding" } }, "visibility": "internal" } ], "src": "9532:34:22" }, "returnParameters": { "id": 2885, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 2884, "mutability": "mutable", "name": "", "nameLocation": "-1:-1:-1", "nodeType": "VariableDeclaration", "scope": 2911, "src": "9590:7:22", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 2883, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "9590:7:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "src": "9589:9:22" }, "scope": 3203, "src": "9519:245:22", "stateMutability": "pure", "virtual": false, "visibility": "internal" }, { "body": { "id": 3039, "nodeType": "Block", "src": "9951:828:22", "statements": [ { "assignments": [ 2920 ], "declarations": [ { "constant": false, "id": 2920, "mutability": "mutable", "name": "result", "nameLocation": "9969:6:22", "nodeType": "VariableDeclaration", "scope": 3039, "src": "9961:14:22", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 2919, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "9961:7:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "id": 2922, "initialValue": { "hexValue": "30", "id": 2921, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "9978:1:22", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "nodeType": "VariableDeclarationStatement", "src": "9961:18:22" }, { "id": 3036, "nodeType": "UncheckedBlock", "src": "9989:761:22", "statements": [ { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 2927, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 2923, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 2914, "src": "10017:5:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">=", "rightExpression": { "commonType": { "typeIdentifier": "t_rational_10000000000000000000000000000000000000000000000000000000000000000_by_1", "typeString": "int_const 1000...(57 digits omitted)...0000" }, "id": 2926, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "leftExpression": { "hexValue": "3130", "id": 2924, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10026:2:22", "typeDescriptions": { "typeIdentifier": "t_rational_10_by_1", "typeString": "int_const 10" }, "value": "10" }, "nodeType": "BinaryOperation", "operator": "**", "rightExpression": { "hexValue": "3634", "id": 2925, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10030:2:22", "typeDescriptions": { "typeIdentifier": "t_rational_64_by_1", "typeString": "int_const 64" }, "value": "64" }, "src": "10026:6:22", "typeDescriptions": { "typeIdentifier": "t_rational_10000000000000000000000000000000000000000000000000000000000000000_by_1", "typeString": "int_const 1000...(57 digits omitted)...0000" } }, "src": "10017:15:22", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 2939, "nodeType": "IfStatement", "src": "10013:99:22", "trueBody": { "id": 2938, "nodeType": "Block", "src": "10034:78:22", "statements": [ { "expression": { "id": 2932, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 2928, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 2914, "src": "10052:5:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "/=", "rightHandSide": { "commonType": { "typeIdentifier": "t_rational_10000000000000000000000000000000000000000000000000000000000000000_by_1", "typeString": "int_const 1000...(57 digits omitted)...0000" }, "id": 2931, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "leftExpression": { "hexValue": "3130", "id": 2929, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10061:2:22", "typeDescriptions": { "typeIdentifier": "t_rational_10_by_1", "typeString": "int_const 10" }, "value": "10" }, "nodeType": "BinaryOperation", "operator": "**", "rightExpression": { "hexValue": "3634", "id": 2930, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10065:2:22", "typeDescriptions": { "typeIdentifier": "t_rational_64_by_1", "typeString": "int_const 64" }, "value": "64" }, "src": "10061:6:22", "typeDescriptions": { "typeIdentifier": "t_rational_10000000000000000000000000000000000000000000000000000000000000000_by_1", "typeString": "int_const 1000...(57 digits omitted)...0000" } }, "src": "10052:15:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 2933, "nodeType": "ExpressionStatement", "src": "10052:15:22" }, { "expression": { "id": 2936, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 2934, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 2920, "src": "10085:6:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "+=", "rightHandSide": { "hexValue": "3634", "id": 2935, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10095:2:22", "typeDescriptions": { "typeIdentifier": "t_rational_64_by_1", "typeString": "int_const 64" }, "value": "64" }, "src": "10085:12:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 2937, "nodeType": "ExpressionStatement", "src": "10085:12:22" } ] } }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 2944, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 2940, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 2914, "src": "10129:5:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">=", "rightExpression": { "commonType": { "typeIdentifier": "t_rational_100000000000000000000000000000000_by_1", "typeString": "int_const 1000...(25 digits omitted)...0000" }, "id": 2943, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "leftExpression": { "hexValue": "3130", "id": 2941, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10138:2:22", "typeDescriptions": { "typeIdentifier": "t_rational_10_by_1", "typeString": "int_const 10" }, "value": "10" }, "nodeType": "BinaryOperation", "operator": "**", "rightExpression": { "hexValue": "3332", "id": 2942, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10142:2:22", "typeDescriptions": { "typeIdentifier": "t_rational_32_by_1", "typeString": "int_const 32" }, "value": "32" }, "src": "10138:6:22", "typeDescriptions": { "typeIdentifier": "t_rational_100000000000000000000000000000000_by_1", "typeString": "int_const 1000...(25 digits omitted)...0000" } }, "src": "10129:15:22", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 2956, "nodeType": "IfStatement", "src": "10125:99:22", "trueBody": { "id": 2955, "nodeType": "Block", "src": "10146:78:22", "statements": [ { "expression": { "id": 2949, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 2945, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 2914, "src": "10164:5:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "/=", "rightHandSide": { "commonType": { "typeIdentifier": "t_rational_100000000000000000000000000000000_by_1", "typeString": "int_const 1000...(25 digits omitted)...0000" }, "id": 2948, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "leftExpression": { "hexValue": "3130", "id": 2946, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10173:2:22", "typeDescriptions": { "typeIdentifier": "t_rational_10_by_1", "typeString": "int_const 10" }, "value": "10" }, "nodeType": "BinaryOperation", "operator": "**", "rightExpression": { "hexValue": "3332", "id": 2947, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10177:2:22", "typeDescriptions": { "typeIdentifier": "t_rational_32_by_1", "typeString": "int_const 32" }, "value": "32" }, "src": "10173:6:22", "typeDescriptions": { "typeIdentifier": "t_rational_100000000000000000000000000000000_by_1", "typeString": "int_const 1000...(25 digits omitted)...0000" } }, "src": "10164:15:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 2950, "nodeType": "ExpressionStatement", "src": "10164:15:22" }, { "expression": { "id": 2953, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 2951, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 2920, "src": "10197:6:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "+=", "rightHandSide": { "hexValue": "3332", "id": 2952, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10207:2:22", "typeDescriptions": { "typeIdentifier": "t_rational_32_by_1", "typeString": "int_const 32" }, "value": "32" }, "src": "10197:12:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 2954, "nodeType": "ExpressionStatement", "src": "10197:12:22" } ] } }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 2961, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 2957, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 2914, "src": "10241:5:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">=", "rightExpression": { "commonType": { "typeIdentifier": "t_rational_10000000000000000_by_1", "typeString": "int_const 10000000000000000" }, "id": 2960, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "leftExpression": { "hexValue": "3130", "id": 2958, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10250:2:22", "typeDescriptions": { "typeIdentifier": "t_rational_10_by_1", "typeString": "int_const 10" }, "value": "10" }, "nodeType": "BinaryOperation", "operator": "**", "rightExpression": { "hexValue": "3136", "id": 2959, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10254:2:22", "typeDescriptions": { "typeIdentifier": "t_rational_16_by_1", "typeString": "int_const 16" }, "value": "16" }, "src": "10250:6:22", "typeDescriptions": { "typeIdentifier": "t_rational_10000000000000000_by_1", "typeString": "int_const 10000000000000000" } }, "src": "10241:15:22", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 2973, "nodeType": "IfStatement", "src": "10237:99:22", "trueBody": { "id": 2972, "nodeType": "Block", "src": "10258:78:22", "statements": [ { "expression": { "id": 2966, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 2962, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 2914, "src": "10276:5:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "/=", "rightHandSide": { "commonType": { "typeIdentifier": "t_rational_10000000000000000_by_1", "typeString": "int_const 10000000000000000" }, "id": 2965, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "leftExpression": { "hexValue": "3130", "id": 2963, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10285:2:22", "typeDescriptions": { "typeIdentifier": "t_rational_10_by_1", "typeString": "int_const 10" }, "value": "10" }, "nodeType": "BinaryOperation", "operator": "**", "rightExpression": { "hexValue": "3136", "id": 2964, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10289:2:22", "typeDescriptions": { "typeIdentifier": "t_rational_16_by_1", "typeString": "int_const 16" }, "value": "16" }, "src": "10285:6:22", "typeDescriptions": { "typeIdentifier": "t_rational_10000000000000000_by_1", "typeString": "int_const 10000000000000000" } }, "src": "10276:15:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 2967, "nodeType": "ExpressionStatement", "src": "10276:15:22" }, { "expression": { "id": 2970, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 2968, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 2920, "src": "10309:6:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "+=", "rightHandSide": { "hexValue": "3136", "id": 2969, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10319:2:22", "typeDescriptions": { "typeIdentifier": "t_rational_16_by_1", "typeString": "int_const 16" }, "value": "16" }, "src": "10309:12:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 2971, "nodeType": "ExpressionStatement", "src": "10309:12:22" } ] } }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 2978, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 2974, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 2914, "src": "10353:5:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">=", "rightExpression": { "commonType": { "typeIdentifier": "t_rational_100000000_by_1", "typeString": "int_const 100000000" }, "id": 2977, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "leftExpression": { "hexValue": "3130", "id": 2975, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10362:2:22", "typeDescriptions": { "typeIdentifier": "t_rational_10_by_1", "typeString": "int_const 10" }, "value": "10" }, "nodeType": "BinaryOperation", "operator": "**", "rightExpression": { "hexValue": "38", "id": 2976, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10366:1:22", "typeDescriptions": { "typeIdentifier": "t_rational_8_by_1", "typeString": "int_const 8" }, "value": "8" }, "src": "10362:5:22", "typeDescriptions": { "typeIdentifier": "t_rational_100000000_by_1", "typeString": "int_const 100000000" } }, "src": "10353:14:22", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 2990, "nodeType": "IfStatement", "src": "10349:96:22", "trueBody": { "id": 2989, "nodeType": "Block", "src": "10369:76:22", "statements": [ { "expression": { "id": 2983, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 2979, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 2914, "src": "10387:5:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "/=", "rightHandSide": { "commonType": { "typeIdentifier": "t_rational_100000000_by_1", "typeString": "int_const 100000000" }, "id": 2982, "isConstant": false, 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"isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "hexValue": "3130", "id": 3062, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "11135:2:22", "typeDescriptions": { "typeIdentifier": "t_rational_10_by_1", "typeString": "int_const 10" }, "value": "10" }, "nodeType": "BinaryOperation", "operator": "**", "rightExpression": { "id": 3063, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 3052, "src": "11139:6:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "11135:10:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "<", "rightExpression": { "id": 3065, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 3043, "src": "11148:5:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "11135:18:22", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "src": "11108:45:22", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "falseExpression": { "hexValue": "30", "id": 3069, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "11160:1:22", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "id": 3070, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "nodeType": "Conditional", "src": "11108:53:22", "trueExpression": { "hexValue": "31", "id": 3068, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "11156:1:22", "typeDescriptions": { "typeIdentifier": "t_rational_1_by_1", "typeString": "int_const 1" }, "value": "1" }, "typeDescriptions": { "typeIdentifier": "t_uint8", "typeString": "uint8" } } ], "id": 3071, "isConstant": false, "isInlineArray": false, "isLValue": false, "isPure": false, "lValueRequested": false, "nodeType": "TupleExpression", "src": "11107:55:22", "typeDescriptions": { "typeIdentifier": "t_uint8", "typeString": "uint8" } }, "src": "11098:64:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "functionReturnParameters": 3050, "id": 3073, "nodeType": "Return", "src": "11091:71:22" } ] } ] }, "documentation": { "id": 3041, "nodeType": "StructuredDocumentation", "src": "10785:143:22", "text": " @dev Return the log in base 10, following the selected rounding direction, of a positive value.\n Returns 0 if given 0." }, "id": 3076, "implemented": true, "kind": "function", "modifiers": [], "name": "log10", "nameLocation": "10942:5:22", "nodeType": "FunctionDefinition", "parameters": { "id": 3047, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 3043, "mutability": "mutable", "name": "value", "nameLocation": "10956:5:22", "nodeType": "VariableDeclaration", "scope": 3076, "src": "10948:13:22", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 3042, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "10948:7:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" }, { "constant": false, "id": 3046, "mutability": "mutable", "name": "rounding", "nameLocation": "10972:8:22", "nodeType": "VariableDeclaration", "scope": 3076, "src": "10963:17:22", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_enum$_Rounding_$2345", "typeString": "enum Math.Rounding" }, "typeName": { "id": 3045, "nodeType": "UserDefinedTypeName", "pathNode": { "id": 3044, "name": "Rounding", "nameLocations": [ "10963:8:22" ], "nodeType": "IdentifierPath", "referencedDeclaration": 2345, "src": "10963:8:22" }, "referencedDeclaration": 2345, "src": "10963:8:22", "typeDescriptions": { "typeIdentifier": "t_enum$_Rounding_$2345", "typeString": "enum Math.Rounding" } }, "visibility": "internal" } ], "src": "10947:34:22" }, "returnParameters": { "id": 3050, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 3049, "mutability": "mutable", "name": "", "nameLocation": "-1:-1:-1", "nodeType": "VariableDeclaration", "scope": 3076, "src": "11005:7:22", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 3048, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "11005:7:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "src": "11004:9:22" }, "scope": 3203, "src": "10933:246:22", "stateMutability": "pure", "virtual": false, "visibility": "internal" }, { "body": { "id": 3162, "nodeType": "Block", "src": "11493:600:22", "statements": [ { "assignments": [ 3085 ], "declarations": [ { "constant": false, "id": 3085, "mutability": "mutable", "name": "result", "nameLocation": "11511:6:22", "nodeType": "VariableDeclaration", "scope": 3162, "src": "11503:14:22", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 3084, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "11503:7:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "id": 3087, "initialValue": { "hexValue": "30", "id": 3086, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "11520:1:22", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "nodeType": "VariableDeclarationStatement", "src": "11503:18:22" }, { "id": 3159, "nodeType": "UncheckedBlock", "src": "11531:533:22", "statements": [ { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 3092, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 3090, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 3088, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 3079, "src": "11559:5:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">>", "rightExpression": { "hexValue": "313238", "id": 3089, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "11568:3:22", "typeDescriptions": { "typeIdentifier": "t_rational_128_by_1", "typeString": "int_const 128" }, "value": "128" }, "src": "11559:12:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">", "rightExpression": { "hexValue": "30", "id": 3091, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "11574:1:22", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "src": "11559:16:22", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 3102, "nodeType": "IfStatement", "src": "11555:98:22", "trueBody": { "id": 3101, "nodeType": "Block", "src": "11577:76:22", "statements": [ { "expression": { "id": 3095, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 3093, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 3079, "src": "11595:5:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": ">>=", "rightHandSide": { "hexValue": "313238", "id": 3094, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "11605:3:22", "typeDescriptions": { "typeIdentifier": "t_rational_128_by_1", "typeString": "int_const 128" }, "value": "128" }, "src": "11595:13:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 3096, "nodeType": "ExpressionStatement", "src": "11595:13:22" }, { "expression": { "id": 3099, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 3097, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 3085, "src": "11626:6:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "+=", "rightHandSide": { "hexValue": "3136", "id": 3098, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "11636:2:22", "typeDescriptions": { "typeIdentifier": "t_rational_16_by_1", "typeString": "int_const 16" }, "value": "16" }, "src": "11626:12:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 3100, "nodeType": "ExpressionStatement", "src": "11626:12:22" } ] } }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 3107, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 3105, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 3103, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 3079, "src": "11670:5:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">>", "rightExpression": { "hexValue": "3634", "id": 3104, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "11679:2:22", "typeDescriptions": { "typeIdentifier": "t_rational_64_by_1", "typeString": "int_const 64" }, "value": "64" }, "src": "11670:11:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">", "rightExpression": { "hexValue": "30", "id": 3106, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "11684:1:22", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "src": "11670:15:22", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 3117, "nodeType": "IfStatement", "src": "11666:95:22", "trueBody": { "id": 3116, "nodeType": "Block", "src": "11687:74:22", "statements": [ { "expression": { "id": 3110, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 3108, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 3079, "src": "11705:5:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": ">>=", "rightHandSide": { "hexValue": "3634", "id": 3109, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "11715:2:22", "typeDescriptions": { "typeIdentifier": "t_rational_64_by_1", "typeString": "int_const 64" }, "value": "64" }, "src": "11705:12:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 3111, "nodeType": "ExpressionStatement", "src": "11705:12:22" }, { "expression": { "id": 3114, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 3112, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 3085, "src": "11735:6:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "+=", "rightHandSide": { "hexValue": "38", "id": 3113, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "11745:1:22", "typeDescriptions": { "typeIdentifier": "t_rational_8_by_1", "typeString": "int_const 8" }, "value": "8" }, "src": "11735:11:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 3115, "nodeType": "ExpressionStatement", "src": "11735:11:22" } ] } }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 3122, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 3120, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 3118, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 3079, "src": "11778:5:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">>", "rightExpression": { "hexValue": "3332", "id": 3119, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "11787:2:22", "typeDescriptions": { "typeIdentifier": "t_rational_32_by_1", "typeString": "int_const 32" }, "value": "32" }, "src": "11778:11:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">", "rightExpression": { "hexValue": "30", "id": 3121, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "11792:1:22", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "src": "11778:15:22", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 3132, "nodeType": "IfStatement", "src": "11774:95:22", "trueBody": { "id": 3131, "nodeType": "Block", "src": "11795:74:22", "statements": [ { "expression": { "id": 3125, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 3123, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 3079, "src": "11813:5:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": ">>=", "rightHandSide": { "hexValue": "3332", "id": 3124, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "11823:2:22", "typeDescriptions": { "typeIdentifier": "t_rational_32_by_1", "typeString": "int_const 32" }, "value": "32" }, "src": "11813:12:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 3126, "nodeType": "ExpressionStatement", "src": "11813:12:22" }, { "expression": { "id": 3129, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 3127, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 3085, "src": "11843:6:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "+=", "rightHandSide": { "hexValue": "34", "id": 3128, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "11853:1:22", "typeDescriptions": { "typeIdentifier": "t_rational_4_by_1", "typeString": "int_const 4" }, "value": "4" }, "src": "11843:11:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 3130, "nodeType": "ExpressionStatement", "src": "11843:11:22" } ] } }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 3137, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 3135, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 3133, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 3079, "src": "11886:5:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">>", "rightExpression": { "hexValue": "3136", "id": 3134, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "11895:2:22", "typeDescriptions": { "typeIdentifier": "t_rational_16_by_1", "typeString": "int_const 16" }, "value": "16" }, "src": "11886:11:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">", "rightExpression": { "hexValue": "30", "id": 3136, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "11900:1:22", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "src": "11886:15:22", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 3147, "nodeType": "IfStatement", "src": "11882:95:22", "trueBody": { "id": 3146, "nodeType": "Block", "src": "11903:74:22", "statements": [ { "expression": { "id": 3140, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 3138, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 3079, "src": "11921:5:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": ">>=", "rightHandSide": { "hexValue": "3136", "id": 3139, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "11931:2:22", "typeDescriptions": { "typeIdentifier": "t_rational_16_by_1", "typeString": "int_const 16" }, "value": "16" }, "src": "11921:12:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 3141, "nodeType": "ExpressionStatement", "src": "11921:12:22" }, { "expression": { "id": 3144, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 3142, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 3085, "src": "11951:6:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "+=", "rightHandSide": { "hexValue": "32", "id": 3143, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "11961:1:22", "typeDescriptions": { "typeIdentifier": "t_rational_2_by_1", "typeString": "int_const 2" }, "value": "2" }, "src": "11951:11:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 3145, "nodeType": "ExpressionStatement", "src": "11951:11:22" } ] } }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 3152, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 3150, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 3148, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 3079, "src": "11994:5:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">>", "rightExpression": { "hexValue": "38", "id": 3149, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "12003:1:22", "typeDescriptions": { "typeIdentifier": "t_rational_8_by_1", "typeString": "int_const 8" }, "value": "8" }, "src": "11994:10:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">", "rightExpression": { "hexValue": "30", "id": 3151, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "12007:1:22", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "src": "11994:14:22", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 3158, "nodeType": "IfStatement", "src": "11990:64:22", "trueBody": { "id": 3157, "nodeType": "Block", "src": "12010:44:22", "statements": [ { "expression": { "id": 3155, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 3153, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 3085, "src": "12028:6:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "+=", "rightHandSide": { "hexValue": "31", "id": 3154, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "12038:1:22", "typeDescriptions": { "typeIdentifier": "t_rational_1_by_1", "typeString": "int_const 1" }, "value": "1" }, "src": "12028:11:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 3156, "nodeType": "ExpressionStatement", "src": "12028:11:22" } ] } } ] }, { "expression": { "id": 3160, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 3085, "src": "12080:6:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "functionReturnParameters": 3083, "id": 3161, "nodeType": "Return", "src": "12073:13:22" } ] }, "documentation": { "id": 3077, "nodeType": "StructuredDocumentation", "src": "11185:240:22", "text": " @dev Return the log in base 256, rounded down, of a positive value.\n Returns 0 if given 0.\n Adding one to the result gives the number of pairs of hex symbols needed to represent `value` as a hex string." }, "id": 3163, "implemented": true, "kind": "function", "modifiers": [], "name": "log256", "nameLocation": "11439:6:22", "nodeType": "FunctionDefinition", "parameters": { "id": 3080, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 3079, "mutability": "mutable", "name": "value", "nameLocation": "11454:5:22", "nodeType": "VariableDeclaration", "scope": 3163, "src": "11446:13:22", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 3078, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "11446:7:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "src": "11445:15:22" }, "returnParameters": { "id": 3083, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 3082, "mutability": "mutable", "name": "", "nameLocation": "-1:-1:-1", "nodeType": "VariableDeclaration", "scope": 3163, "src": "11484:7:22", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 3081, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "11484:7:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "src": "11483:9:22" }, "scope": 3203, "src": "11430:663:22", "stateMutability": "pure", "virtual": false, "visibility": "internal" }, { "body": { "id": 3201, "nodeType": "Block", "src": "12329:173:22", "statements": [ { "id": 3200, "nodeType": "UncheckedBlock", "src": "12339:157:22", "statements": [ { "assignments": [ 3175 ], "declarations": [ { "constant": false, "id": 3175, "mutability": "mutable", "name": "result", "nameLocation": "12371:6:22", "nodeType": "VariableDeclaration", "scope": 3200, "src": "12363:14:22", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 3174, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "12363:7:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "id": 3179, "initialValue": { "arguments": [ { "id": 3177, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 3166, "src": "12387:5:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } ], "expression": { "argumentTypes": [ { "typeIdentifier": "t_uint256", "typeString": "uint256" } ], "id": 3176, "name": "log256", "nodeType": "Identifier", "overloadedDeclarations": [ 3163, 3202 ], "referencedDeclaration": 3163, "src": "12380:6:22", "typeDescriptions": { "typeIdentifier": "t_function_internal_pure$_t_uint256_$returns$_t_uint256_$", "typeString": "function (uint256) pure returns (uint256)" } }, "id": 3178, "isConstant": false, "isLValue": false, "isPure": false, "kind": "functionCall", "lValueRequested": false, "nameLocations": [], "names": [], "nodeType": "FunctionCall", "src": "12380:13:22", "tryCall": false, "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "VariableDeclarationStatement", "src": "12363:30:22" }, { "expression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 3198, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 3180, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 3175, "src": "12414:6:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "+", "rightExpression": { "components": [ { "condition": { "commonType": { "typeIdentifier": "t_bool", "typeString": "bool" }, "id": 3193, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "commonType": { "typeIdentifier": "t_enum$_Rounding_$2345", "typeString": "enum Math.Rounding" }, "id": 3184, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 3181, "name": "rounding", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 3169, "src": "12424:8:22", "typeDescriptions": { "typeIdentifier": "t_enum$_Rounding_$2345", "typeString": "enum Math.Rounding" } }, "nodeType": "BinaryOperation", "operator": "==", "rightExpression": { "expression": { "id": 3182, "name": "Rounding", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 2345, "src": "12436:8:22", "typeDescriptions": { "typeIdentifier": "t_type$_t_enum$_Rounding_$2345_$", "typeString": "type(enum Math.Rounding)" } }, "id": 3183, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "memberLocation": "12445:2:22", "memberName": "Up", "nodeType": "MemberAccess", "referencedDeclaration": 2343, "src": "12436:11:22", "typeDescriptions": { "typeIdentifier": "t_enum$_Rounding_$2345", "typeString": "enum Math.Rounding" } }, "src": "12424:23:22", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "nodeType": "BinaryOperation", "operator": "&&", "rightExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 3192, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 3190, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "hexValue": "31", "id": 3185, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "12451:1:22", "typeDescriptions": { "typeIdentifier": "t_rational_1_by_1", "typeString": "int_const 1" }, "value": "1" }, "nodeType": "BinaryOperation", "operator": "<<", "rightExpression": { "components": [ { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 3188, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 3186, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 3175, "src": "12457:6:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "*", "rightExpression": { "hexValue": "38", "id": 3187, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "12466:1:22", "typeDescriptions": { "typeIdentifier": "t_rational_8_by_1", "typeString": "int_const 8" }, "value": "8" }, "src": "12457:10:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } ], "id": 3189, "isConstant": false, "isInlineArray": false, "isLValue": false, "isPure": false, "lValueRequested": false, "nodeType": "TupleExpression", "src": "12456:12:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "12451:17:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "<", "rightExpression": { "id": 3191, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 3166, "src": "12471:5:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "12451:25:22", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "src": "12424:52:22", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "falseExpression": { "hexValue": "30", "id": 3195, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "12483:1:22", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "id": 3196, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "nodeType": "Conditional", "src": "12424:60:22", "trueExpression": { "hexValue": "31", "id": 3194, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "12479:1:22", "typeDescriptions": { "typeIdentifier": "t_rational_1_by_1", "typeString": "int_const 1" }, "value": "1" }, "typeDescriptions": { "typeIdentifier": "t_uint8", "typeString": "uint8" } } ], "id": 3197, "isConstant": false, "isInlineArray": false, "isLValue": false, "isPure": false, "lValueRequested": false, "nodeType": "TupleExpression", "src": "12423:62:22", "typeDescriptions": { "typeIdentifier": "t_uint8", "typeString": "uint8" } }, "src": "12414:71:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "functionReturnParameters": 3173, "id": 3199, "nodeType": "Return", "src": "12407:78:22" } ] } ] }, "documentation": { "id": 3164, "nodeType": "StructuredDocumentation", "src": "12099:143:22", "text": " @dev Return the log in base 10, following the selected rounding direction, of a positive value.\n Returns 0 if given 0." }, "id": 3202, "implemented": true, "kind": "function", "modifiers": [], "name": "log256", "nameLocation": "12256:6:22", "nodeType": "FunctionDefinition", "parameters": { "id": 3170, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 3166, "mutability": "mutable", "name": "value", "nameLocation": "12271:5:22", "nodeType": "VariableDeclaration", "scope": 3202, "src": "12263:13:22", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 3165, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "12263:7:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" }, { "constant": false, "id": 3169, "mutability": "mutable", "name": "rounding", "nameLocation": "12287:8:22", "nodeType": "VariableDeclaration", "scope": 3202, "src": "12278:17:22", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_enum$_Rounding_$2345", "typeString": "enum Math.Rounding" }, "typeName": { "id": 3168, "nodeType": "UserDefinedTypeName", "pathNode": { "id": 3167, "name": "Rounding", "nameLocations": [ "12278:8:22" ], "nodeType": "IdentifierPath", "referencedDeclaration": 2345, "src": "12278:8:22" }, "referencedDeclaration": 2345, "src": "12278:8:22", "typeDescriptions": { "typeIdentifier": "t_enum$_Rounding_$2345", "typeString": "enum Math.Rounding" } }, "visibility": "internal" } ], "src": "12262:34:22" }, "returnParameters": { "id": 3173, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 3172, "mutability": "mutable", "name": "", "nameLocation": "-1:-1:-1", "nodeType": "VariableDeclaration", "scope": 3202, "src": "12320:7:22", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 3171, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "12320:7:22", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "src": "12319:9:22" }, "scope": 3203, "src": "12247:255:22", "stateMutability": "pure", "virtual": false, "visibility": "internal" } ], "scope": 3204, "src": "202:12302:22", "usedErrors": [] } ], "src": "103:12402:22" }, "compiler": { "name": "solc", "version": "0.8.19+commit.7dd6d404.Emscripten.clang" }, "networks": {}, "schemaVersion": "3.4.12", "updatedAt": "2023-03-22T17:07:39.594Z", "devdoc": { "details": "Standard math utilities missing in the Solidity language.", "kind": "dev", "methods": {}, "version": 1 }, "userdoc": { "kind": "user", "methods": {}, "version": 1 } }