{
    "Function": "ln",
    "File": "contracts/staking/libs/LibFixedMath.sol",
    "Parent Contracts": [],
    "High-Level Calls": [],
    "Internal Calls": [
        "revert(string)",
        "revert(string)"
    ],
    "Library Calls": [],
    "Low-Level Calls": [],
    "Code": "function ln(int256 x) internal pure returns (int256 r) {\n        if (x > LN_MAX_VAL) {\n            revert(\"out-of-bounds\");\n        }\n        if (x <= 0) {\n            revert(\"too-small\");\n        }\n        if (x == FIXED_1) {\n            return 0;\n        }\n        if (x <= LN_MIN_VAL) {\n            return EXP_MIN_VAL;\n        }\n\n        int256 y;\n        int256 z;\n        int256 w;\n\n        // Rewrite the input as a quotient of negative natural exponents and a single residual q, such that 1 < q < 2\n        // For example: log(0.3) = log(e^-1 * e^-0.25 * 1.0471028872385522)\n        //              = 1 - 0.25 - log(1 + 0.0471028872385522)\n        // e ^ -32\n        if (x <= int256(0x00000000000000000000000000000000000000000001c8464f76164760000000)) {\n            r -= int256(0x0000000000000000000000000000001000000000000000000000000000000000); // - 32\n            x =\n                (x * FIXED_1) /\n                int256(0x00000000000000000000000000000000000000000001c8464f76164760000000); // / e ^ -32\n        }\n        // e ^ -16\n        if (x <= int256(0x00000000000000000000000000000000000000f1aaddd7742e90000000000000)) {\n            r -= int256(0x0000000000000000000000000000000800000000000000000000000000000000); // - 16\n            x =\n                (x * FIXED_1) /\n                int256(0x00000000000000000000000000000000000000f1aaddd7742e90000000000000); // / e ^ -16\n        }\n        // e ^ -8\n        if (x <= int256(0x00000000000000000000000000000000000afe10820813d78000000000000000)) {\n            r -= int256(0x0000000000000000000000000000000400000000000000000000000000000000); // - 8\n            x =\n                (x * FIXED_1) /\n                int256(0x00000000000000000000000000000000000afe10820813d78000000000000000); // / e ^ -8\n        }\n        // e ^ -4\n        if (x <= int256(0x0000000000000000000000000000000002582ab704279ec00000000000000000)) {\n            r -= int256(0x0000000000000000000000000000000200000000000000000000000000000000); // - 4\n            x =\n                (x * FIXED_1) /\n                int256(0x0000000000000000000000000000000002582ab704279ec00000000000000000); // / e ^ -4\n        }\n        // e ^ -2\n        if (x <= int256(0x000000000000000000000000000000001152aaa3bf81cc000000000000000000)) {\n            r -= int256(0x0000000000000000000000000000000100000000000000000000000000000000); // - 2\n            x =\n                (x * FIXED_1) /\n                int256(0x000000000000000000000000000000001152aaa3bf81cc000000000000000000); // / e ^ -2\n        }\n        // e ^ -1\n        if (x <= int256(0x000000000000000000000000000000002f16ac6c59de70000000000000000000)) {\n            r -= int256(0x0000000000000000000000000000000080000000000000000000000000000000); // - 1\n            x =\n                (x * FIXED_1) /\n                int256(0x000000000000000000000000000000002f16ac6c59de70000000000000000000); // / e ^ -1\n        }\n        // e ^ -0.5\n        if (x <= int256(0x000000000000000000000000000000004da2cbf1be5828000000000000000000)) {\n            r -= int256(0x0000000000000000000000000000000040000000000000000000000000000000); // - 0.5\n            x =\n                (x * FIXED_1) /\n                int256(0x000000000000000000000000000000004da2cbf1be5828000000000000000000); // / e ^ -0.5\n        }\n        // e ^ -0.25\n        if (x <= int256(0x0000000000000000000000000000000063afbe7ab2082c000000000000000000)) {\n            r -= int256(0x0000000000000000000000000000000020000000000000000000000000000000); // - 0.25\n            x =\n                (x * FIXED_1) /\n                int256(0x0000000000000000000000000000000063afbe7ab2082c000000000000000000); // / e ^ -0.25\n        }\n        // e ^ -0.125\n        if (x <= int256(0x0000000000000000000000000000000070f5a893b608861e1f58934f97aea57d)) {\n            r -= int256(0x0000000000000000000000000000000010000000000000000000000000000000); // - 0.125\n            x =\n                (x * FIXED_1) /\n                int256(0x0000000000000000000000000000000070f5a893b608861e1f58934f97aea57d); // / e ^ -0.125\n        }\n        // `x` is now our residual in the range of 1 <= x <= 2 (or close enough).\n\n        // Add the taylor series for log(1 + z), where z = x - 1\n        z = y = x - FIXED_1;\n        w = (y * y) / FIXED_1;\n        r += (z * (0x100000000000000000000000000000000 - y)) / 0x100000000000000000000000000000000;\n        z = (z * w) / FIXED_1; // add y^01 / 01 - y^02 / 02\n        r += (z * (0x0aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa - y)) / 0x200000000000000000000000000000000;\n        z = (z * w) / FIXED_1; // add y^03 / 03 - y^04 / 04\n        r += (z * (0x099999999999999999999999999999999 - y)) / 0x300000000000000000000000000000000;\n        z = (z * w) / FIXED_1; // add y^05 / 05 - y^06 / 06\n        r += (z * (0x092492492492492492492492492492492 - y)) / 0x400000000000000000000000000000000;\n        z = (z * w) / FIXED_1; // add y^07 / 07 - y^08 / 08\n        r += (z * (0x08e38e38e38e38e38e38e38e38e38e38e - y)) / 0x500000000000000000000000000000000;\n        z = (z * w) / FIXED_1; // add y^09 / 09 - y^10 / 10\n        r += (z * (0x08ba2e8ba2e8ba2e8ba2e8ba2e8ba2e8b - y)) / 0x600000000000000000000000000000000;\n        z = (z * w) / FIXED_1; // add y^11 / 11 - y^12 / 12\n        r += (z * (0x089d89d89d89d89d89d89d89d89d89d89 - y)) / 0x700000000000000000000000000000000;\n        z = (z * w) / FIXED_1; // add y^13 / 13 - y^14 / 14\n        r += (z * (0x088888888888888888888888888888888 - y)) / 0x800000000000000000000000000000000; // add y^15 / 15 - y^16 / 16\n    }"
}