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number,\n /// where the least significant bit is at index 0 and the most significant bit is at index 255\n /// @dev The function satisfies the property:\n /// x >= 2**mostSignificantBit(x) and x < 2**(mostSignificantBit(x)+1)\n /// @param x the value for which to compute the most significant bit, must be greater than 0\n /// @return r the index of the most significant bit\n function mostSignificantBit(uint256 x) internal pure returns (uint8 r) {\n require(x > 0);\n\n if (x >= 0x100000000000000000000000000000000) {\n x >>= 128;\n r += 128;\n }\n if (x >= 0x10000000000000000) {\n x >>= 64;\n r += 64;\n }\n if (x >= 0x100000000) {\n x >>= 32;\n r += 32;\n }\n if (x >= 0x10000) {\n x >>= 16;\n r += 16;\n }\n if (x >= 0x100) {\n x >>= 8;\n r += 8;\n }\n if (x >= 0x10) {\n x >>= 4;\n r += 4;\n }\n if (x >= 0x4) {\n x >>= 2;\n r += 2;\n }\n if (x >= 0x2) r += 1;\n }\n\n /// @notice Returns the index of the least significant bit of the number,\n /// where the least significant bit is at index 0 and the most significant bit is at index 255\n /// @dev The function satisfies the property:\n /// (x & 2**leastSignificantBit(x)) != 0 and (x & (2**(leastSignificantBit(x)) - 1)) == 0)\n /// @param x the value for which to compute the least significant bit, must be greater than 0\n /// @return r the index of the least significant bit\n function leastSignificantBit(uint256 x) internal pure returns (uint8 r) {\n require(x > 0);\n\n r = 255;\n if (x & type(uint128).max > 0) {\n r -= 128;\n } else {\n x >>= 128;\n }\n if (x & type(uint64).max > 0) {\n r -= 64;\n } else {\n x >>= 64;\n }\n if (x & type(uint32).max > 0) {\n r -= 32;\n } else {\n x >>= 32;\n }\n if (x & type(uint16).max > 0) {\n r -= 16;\n } else {\n x >>= 16;\n }\n if (x & type(uint8).max > 0) {\n r -= 8;\n } else {\n x >>= 8;\n }\n if (x & 0xf > 0) {\n r -= 4;\n } else {\n x >>= 4;\n }\n if (x & 0x3 > 0) {\n r -= 2;\n } else {\n x >>= 2;\n }\n if (x & 0x1 > 0) r -= 1;\n }\n}\n", "sourcePath": 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"number", "lValueRequested": false, "nodeType": "Literal", "src": "1354:1:23", "subdenomination": null, "typeDescriptions": { "typeIdentifier": "t_rational_2_by_1", "typeString": "int_const 2" }, "value": "2" }, "src": "1349:6:23", "typeDescriptions": { "typeIdentifier": "t_uint8", "typeString": "uint8" } }, "id": 1988, "nodeType": "ExpressionStatement", "src": "1349:6:23" } ] } }, { "condition": { "argumentTypes": null, "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 1993, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "argumentTypes": null, "id": 1991, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 1889, "src": "1379:1:23", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">=", "rightExpression": { "argumentTypes": null, "hexValue": "307832", "id": 1992, "isConstant": false, 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true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "1394:1:23", "subdenomination": null, "typeDescriptions": { "typeIdentifier": "t_rational_1_by_1", "typeString": "int_const 1" }, "value": "1" }, "src": "1389:6:23", "typeDescriptions": { "typeIdentifier": "t_uint8", "typeString": "uint8" } }, "id": 1997, "nodeType": "ExpressionStatement", "src": "1389:6:23" } } ] }, "documentation": { "id": 1887, "nodeType": "StructuredDocumentation", "src": "209:457:23", "text": "@notice Returns the index of the most significant bit of the number,\n where the least significant bit is at index 0 and the most significant bit is at index 255\n @dev The function satisfies the property:\n x >= 2**mostSignificantBit(x) and x < 2**(mostSignificantBit(x)+1)\n @param x the value for which to compute the most significant bit, must be greater than 0\n @return r the index of the most significant bit" }, "id": 2000, "implemented": true, "kind": "function", "modifiers": [], "name": 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"tryCall": false, "typeDescriptions": { "typeIdentifier": "t_magic_meta_type_t_uint128", "typeString": "type(uint128)" } }, "id": 2023, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "memberName": "max", "nodeType": "MemberAccess", "referencedDeclaration": null, "src": "2025:17:23", "typeDescriptions": { "typeIdentifier": "t_uint128", "typeString": "uint128" } }, "src": "2021:21:23", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">", "rightExpression": { "argumentTypes": null, "hexValue": "30", "id": 2025, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "2045:1:23", "subdenomination": null, "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "src": "2021:25:23", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, 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