{
    "Function": "optimalLog",
    "File": "contracts/bancor/BancorFormula.sol",
    "Parent Contracts": [],
    "High-Level Calls": [],
    "Internal Calls": [],
    "Library Calls": [],
    "Low-Level Calls": [],
    "Code": "function optimalLog(uint256 x) internal pure returns (uint256) {\n        uint256 res = 0;\n\n        uint256 y;\n        uint256 z;\n        uint256 w;\n\n        if (x >= 0xd3094c70f034de4b96ff7d5b6f99fcd8) {\n            res += 0x40000000000000000000000000000000;\n            x = (x * FIXED_1) / 0xd3094c70f034de4b96ff7d5b6f99fcd8;\n        } // add 1 / 2^1\n        if (x >= 0xa45af1e1f40c333b3de1db4dd55f29a7) {\n            res += 0x20000000000000000000000000000000;\n            x = (x * FIXED_1) / 0xa45af1e1f40c333b3de1db4dd55f29a7;\n        } // add 1 / 2^2\n        if (x >= 0x910b022db7ae67ce76b441c27035c6a1) {\n            res += 0x10000000000000000000000000000000;\n            x = (x * FIXED_1) / 0x910b022db7ae67ce76b441c27035c6a1;\n        } // add 1 / 2^3\n        if (x >= 0x88415abbe9a76bead8d00cf112e4d4a8) {\n            res += 0x08000000000000000000000000000000;\n            x = (x * FIXED_1) / 0x88415abbe9a76bead8d00cf112e4d4a8;\n        } // add 1 / 2^4\n        if (x >= 0x84102b00893f64c705e841d5d4064bd3) {\n            res += 0x04000000000000000000000000000000;\n            x = (x * FIXED_1) / 0x84102b00893f64c705e841d5d4064bd3;\n        } // add 1 / 2^5\n        if (x >= 0x8204055aaef1c8bd5c3259f4822735a2) {\n            res += 0x02000000000000000000000000000000;\n            x = (x * FIXED_1) / 0x8204055aaef1c8bd5c3259f4822735a2;\n        } // add 1 / 2^6\n        if (x >= 0x810100ab00222d861931c15e39b44e99) {\n            res += 0x01000000000000000000000000000000;\n            x = (x * FIXED_1) / 0x810100ab00222d861931c15e39b44e99;\n        } // add 1 / 2^7\n        if (x >= 0x808040155aabbbe9451521693554f733) {\n            res += 0x00800000000000000000000000000000;\n            x = (x * FIXED_1) / 0x808040155aabbbe9451521693554f733;\n        } // add 1 / 2^8\n\n        z = y = x - FIXED_1;\n        w = (y * y) / FIXED_1;\n        res +=\n            (z * (0x100000000000000000000000000000000 - y)) /\n            0x100000000000000000000000000000000;\n        z = (z * w) / FIXED_1; // add y^01 / 01 - y^02 / 02\n        res +=\n            (z * (0x0aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa - y)) /\n            0x200000000000000000000000000000000;\n        z = (z * w) / FIXED_1; // add y^03 / 03 - y^04 / 04\n        res +=\n            (z * (0x099999999999999999999999999999999 - y)) /\n            0x300000000000000000000000000000000;\n        z = (z * w) / FIXED_1; // add y^05 / 05 - y^06 / 06\n        res +=\n            (z * (0x092492492492492492492492492492492 - y)) /\n            0x400000000000000000000000000000000;\n        z = (z * w) / FIXED_1; // add y^07 / 07 - y^08 / 08\n        res +=\n            (z * (0x08e38e38e38e38e38e38e38e38e38e38e - y)) /\n            0x500000000000000000000000000000000;\n        z = (z * w) / FIXED_1; // add y^09 / 09 - y^10 / 10\n        res +=\n            (z * (0x08ba2e8ba2e8ba2e8ba2e8ba2e8ba2e8b - y)) /\n            0x600000000000000000000000000000000;\n        z = (z * w) / FIXED_1; // add y^11 / 11 - y^12 / 12\n        res +=\n            (z * (0x089d89d89d89d89d89d89d89d89d89d89 - y)) /\n            0x700000000000000000000000000000000;\n        z = (z * w) / FIXED_1; // add y^13 / 13 - y^14 / 14\n        res +=\n            (z * (0x088888888888888888888888888888888 - y)) /\n            0x800000000000000000000000000000000; // add y^15 / 15 - y^16 / 16\n\n        return res;\n    }"
}