{
  "errors": {
    "Overflow()": "0x35278d12",
    "DivisionByZero()": "0x23d359a3",
    "OutOfRange()": "0x7db3aba7"
  },
  "ops": [
    {
      "name": "fromFixed18",
      "signature": "fromFixed18(int256)",
      "selector": "0x9aea0a13",
      "inputs": [
        "x"
      ],
      "notice": "Convert an 18-decimal fixed-point value to 127.128.",
      "domain": "|x| < 2^127",
      "reverts": "OutOfRange() if |x| >= 2^127"
    },
    {
      "name": "toFixed18",
      "signature": "toFixed18(int256)",
      "selector": "0xa2745c74",
      "inputs": [
        "x"
      ],
      "notice": "Convert a 127.128 value to 18-decimal fixed-point.",
      "domain": "any x",
      "reverts": "never"
    },
    {
      "name": "add",
      "signature": "add(int256,int256)",
      "selector": "0xa5f3c23b",
      "inputs": [
        "a",
        "b"
      ],
      "notice": "a + b. Reverts with Overflow on signed overflow.",
      "domain": "any a, b",
      "reverts": "Overflow() on signed overflow"
    },
    {
      "name": "sub",
      "signature": "sub(int256,int256)",
      "selector": "0xadefc37b",
      "inputs": [
        "a",
        "b"
      ],
      "notice": "a - b. Reverts with Overflow on signed overflow.",
      "domain": "any a, b",
      "reverts": "Overflow() on signed overflow"
    },
    {
      "name": "mul",
      "signature": "mul(int256,int256)",
      "selector": "0xbbe93d91",
      "inputs": [
        "a",
        "b"
      ],
      "notice": "floor(a * b / 2^128), the 127.128 product.",
      "domain": "any a, b",
      "reverts": "Overflow() when a·b / 2^128 does not fit in int256"
    },
    {
      "name": "div",
      "signature": "div(int256,int256)",
      "selector": "0x43509138",
      "inputs": [
        "a",
        "b"
      ],
      "notice": "a / b in 127.128, truncated toward zero.",
      "domain": "b != 0",
      "reverts": "DivisionByZero() when b == 0; Overflow() when the quotient does not fit"
    },
    {
      "name": "exp2",
      "signature": "exp2(int256)",
      "selector": "0xdbbb06d2",
      "inputs": [
        "x"
      ],
      "notice": "2^x.",
      "domain": "x < 127; returns 0 below -128",
      "reverts": "Overflow() for x >= 127"
    },
    {
      "name": "exp",
      "signature": "exp(int256)",
      "selector": "0xe46751e3",
      "inputs": [
        "x"
      ],
      "notice": "e^x, computed as 2^(x * log2(e)).",
      "domain": "x <= 88; returns 0 below -88",
      "reverts": "Overflow() for x > 88"
    },
    {
      "name": "exp10",
      "signature": "exp10(int256)",
      "selector": "0x4c0dafa2",
      "inputs": [
        "x"
      ],
      "notice": "10^x, computed as 2^(x * log2(10)).",
      "domain": "x·log2(10) < 127",
      "reverts": "Overflow() above that"
    },
    {
      "name": "log2",
      "signature": "log2(int256)",
      "selector": "0xe0d68737",
      "inputs": [
        "x"
      ],
      "notice": "log2(x) for x > 0.",
      "domain": "x > 0",
      "reverts": "OutOfRange() for x <= 0"
    },
    {
      "name": "ln",
      "signature": "ln(int256)",
      "selector": "0x8e6f2353",
      "inputs": [
        "x"
      ],
      "notice": "ln(x) = log2(x) * ln(2) for x > 0, scaled at 2^-192 before one rounding. Reverts with OutOfRange otherwise.",
      "domain": "x > 0",
      "reverts": "OutOfRange() for x <= 0"
    },
    {
      "name": "log10",
      "signature": "log10(int256)",
      "selector": "0xb47ca3c7",
      "inputs": [
        "x"
      ],
      "notice": "log10(x) = log2(x) / log2(10) for x > 0, scaled at 2^-192 before one rounding. Reverts with OutOfRange otherwise.",
      "domain": "x > 0",
      "reverts": "OutOfRange() for x <= 0"
    },
    {
      "name": "log2Up",
      "signature": "log2Up(int256)",
      "selector": "0xa1985bb6",
      "inputs": [
        "x"
      ],
      "notice": "ceil(log2(x)) for x > 0. Exact for powers of two.",
      "domain": "x > 0",
      "reverts": "OutOfRange() for x <= 0"
    },
    {
      "name": "sqrt",
      "signature": "sqrt(int256)",
      "selector": "0x665df460",
      "inputs": [
        "x"
      ],
      "notice": "sqrt(x) for x >= 0.",
      "domain": "x >= 0",
      "reverts": "OutOfRange() for x < 0"
    },
    {
      "name": "pow",
      "signature": "pow(int256,int256)",
      "selector": "0x92b0c5b2",
      "inputs": [
        "x",
        "y"
      ],
      "notice": "x^y = 2^(y * log2(x)) for x >= 0.",
      "domain": "x >= 0",
      "reverts": "OutOfRange() for x < 0; Overflow() when the result does not fit"
    },
    {
      "name": "cbrt",
      "signature": "cbrt(int256)",
      "selector": "0xd4b6188c",
      "inputs": [
        "x"
      ],
      "notice": "Cube root, defined for all x: cbrt(-x) = -cbrt(x).",
      "domain": "any x",
      "reverts": "Overflow() only at -2^255"
    },
    {
      "name": "gavg",
      "signature": "gavg(int256,int256)",
      "selector": "0xa13ed853",
      "inputs": [
        "a",
        "b"
      ],
      "notice": "Geometric mean sqrt(a * b). Reverts with OutOfRange if a * b < 0.",
      "domain": "a·b >= 0",
      "reverts": "OutOfRange() if a·b < 0; Overflow() if a·b does not fit"
    },
    {
      "name": "hypot",
      "signature": "hypot(int256,int256)",
      "selector": "0xc479210c",
      "inputs": [
        "a",
        "b"
      ],
      "notice": "sqrt(a^2 + b^2), checked.",
      "domain": "any a, b",
      "reverts": "Overflow() if a^2 + b^2 does not fit"
    },
    {
      "name": "inv",
      "signature": "inv(int256)",
      "selector": "0x3a02c983",
      "inputs": [
        "x"
      ],
      "notice": "1 / x. Reverts with DivisionByZero for x == 0.",
      "domain": "x != 0",
      "reverts": "DivisionByZero() for x == 0; Overflow() when 1/x does not fit"
    },
    {
      "name": "abs",
      "signature": "abs(int256)",
      "selector": "0x1b5ac4b5",
      "inputs": [
        "x"
      ],
      "notice": "|x|. Reverts with Overflow for x == -2^255, which has no positive.",
      "domain": "any x",
      "reverts": "Overflow() at -2^255"
    },
    {
      "name": "neg",
      "signature": "neg(int256)",
      "selector": "0x54a53dc1",
      "inputs": [
        "x"
      ],
      "notice": "-x. Reverts with Overflow for x == -2^255.",
      "domain": "any x",
      "reverts": "Overflow() at -2^255"
    },
    {
      "name": "sign",
      "signature": "sign(int256)",
      "selector": "0xae610b48",
      "inputs": [
        "x"
      ],
      "notice": "-1, 0 or 1 in 127.128.",
      "domain": "any x",
      "reverts": "never"
    },
    {
      "name": "min",
      "signature": "min(int256,int256)",
      "selector": "0x29aa9cbe",
      "inputs": [
        "a",
        "b"
      ],
      "notice": "Signed minimum.",
      "domain": "any a, b",
      "reverts": "never"
    },
    {
      "name": "max",
      "signature": "max(int256,int256)",
      "selector": "0x81fe5786",
      "inputs": [
        "a",
        "b"
      ],
      "notice": "Signed maximum.",
      "domain": "any a, b",
      "reverts": "never"
    },
    {
      "name": "clamp",
      "signature": "clamp(int256,int256,int256)",
      "selector": "0x7b8d0f0c",
      "inputs": [
        "x",
        "lo",
        "hi"
      ],
      "notice": "min(hi, max(lo, x)). If lo > hi the result is hi, as in the Huff.",
      "domain": "any x, lo, hi",
      "reverts": "never"
    },
    {
      "name": "avg",
      "signature": "avg(int256,int256)",
      "selector": "0xebf274be",
      "inputs": [
        "a",
        "b"
      ],
      "notice": "floor((a + b) / 2) without intermediate overflow.",
      "domain": "any a, b",
      "reverts": "never"
    },
    {
      "name": "zeroFloorSub",
      "signature": "zeroFloorSub(int256,int256)",
      "selector": "0xff78cf2d",
      "inputs": [
        "a",
        "b"
      ],
      "notice": "max(0, a - b), with the subtraction checked.",
      "domain": "any a, b",
      "reverts": "Overflow() if a - b does not fit"
    },
    {
      "name": "dist",
      "signature": "dist(int256,int256)",
      "selector": "0x2110b689",
      "inputs": [
        "a",
        "b"
      ],
      "notice": "|a - b|, checked.",
      "domain": "any a, b",
      "reverts": "Overflow() if a - b does not fit"
    },
    {
      "name": "lerp",
      "signature": "lerp(int256,int256,int256)",
      "selector": "0x84e13b60",
      "inputs": [
        "a",
        "b",
        "t"
      ],
      "notice": "a + t * (b - a), checked. t is not clamped to [0, 1].",
      "domain": "any a, b, t",
      "reverts": "Overflow() on any intermediate that does not fit"
    },
    {
      "name": "floor",
      "signature": "floor(int256)",
      "selector": "0xda3ff648",
      "inputs": [
        "x"
      ],
      "notice": "Largest integer <= x. Clearing the fraction bits of a two's complement word is a floor for both signs.",
      "domain": "any x",
      "reverts": "never"
    },
    {
      "name": "ceil",
      "signature": "ceil(int256)",
      "selector": "0x42fba7ae",
      "inputs": [
        "x"
      ],
      "notice": "Smallest integer >= x, as -floor(-x). Reverts with Overflow when that integer is 2^127, which does not fit.",
      "domain": "any x",
      "reverts": "Overflow() when the result is 2^127"
    },
    {
      "name": "frac",
      "signature": "frac(int256)",
      "selector": "0xae2785ac",
      "inputs": [
        "x"
      ],
      "notice": "x - floor(x), always in [0, 1).",
      "domain": "any x",
      "reverts": "never"
    },
    {
      "name": "round",
      "signature": "round(int256)",
      "selector": "0x58b4370b",
      "inputs": [
        "x"
      ],
      "notice": "Nearest integer, halves rounded up: floor(x + 1/2). Checked.",
      "domain": "any x",
      "reverts": "Overflow() when the result is 2^127"
    },
    {
      "name": "gcd",
      "signature": "gcd(int256,int256)",
      "selector": "0x63b03896",
      "inputs": [
        "a",
        "b"
      ],
      "notice": "gcd of the integer parts |floor(a)|, |floor(b)|, as a 127.128 integer.",
      "domain": "any a, b",
      "reverts": "never"
    },
    {
      "name": "factorial",
      "signature": "factorial(int256)",
      "selector": "0x5ad78e8a",
      "inputs": [
        "n"
      ],
      "notice": "floor(n)! for 0 <= n < 34. 33! is the largest that fits.",
      "domain": "0 <= n < 34",
      "reverts": "OutOfRange() outside that"
    },
    {
      "name": "pi",
      "signature": "pi(int256)",
      "selector": "0x929edbfb",
      "inputs": [
        "terms"
      ],
      "notice": "pi by Ramanujan's 1914 series, floor(terms) terms: 1/pi = (2 sqrt2 / 9801) sum_k (4k)! (1103 + 26390 k) / ((k!)^4 396^(4k)). Each term adds about eight digits: 7, 15, 23, 31, then 36 at five terms, the format's floor; more terms change nothing.",
      "domain": "0 <= terms < 8, an integer in 127.128",
      "reverts": "OutOfRange() outside that"
    },
    {
      "name": "lambertW0",
      "signature": "lambertW0(int256)",
      "selector": "0x6de23d34",
      "inputs": [
        "x"
      ],
      "notice": "Principal branch of the Lambert W function, W(x) e^W(x) = x, for x >= -1/e.",
      "domain": "x >= -1/e",
      "reverts": "OutOfRange() below -1/e"
    },
    {
      "name": "lambertWm1",
      "signature": "lambertWm1(int256)",
      "selector": "0xae94abc8",
      "inputs": [
        "x"
      ],
      "notice": "Secondary real branch of the Lambert W function, W(x) e^W(x) = x with W(x) <= -1, for -1/e <= x < 0.",
      "domain": "-1/e <= x < 0",
      "reverts": "OutOfRange() outside that"
    }
  ]
}