FigurateNumbers.cs

public static class FigurateNumbers {
    public static ulong NthHexagonal(ulong value) => checked((2UL * NthSquare(value)) - value);
    public static ulong NthOblong(ulong value) => checked(value * (value + 1UL));
    public static ulong NthPentagonal(ulong value) => checked(((3UL * NthSquare(value)) - value) >> 1);
    public static ulong NthPhiCubic(ulong value) => unchecked((1UL + CubeRoot(value)) >> 1);
    public static ulong NthPhiSquare(ulong value) => unchecked((1UL + SquareRoot(value)) >> 1);
    public static ulong NthTriangular(ulong value) => checked(((value * (value + 1UL))) >> 1);
}
public static bool IsApproximatelyEqual(Func<ulong, ulong> x, Func<ulong, ulong> y, Func<ulong> randomNumberGenerator) {
    var result = true;

    for (var i = 0UL; (i < 9223372036854775808UL); i = NextPowerOfTwo(i)) { // monotonic testing
        var cube = NextCube(i);
        var square = NextSquare(i);

        for (var j = 1UL; (j < 11UL); ++j) {
            var cubeA = (cube + j);
            var cubeS = (cube - j);
            var identityA = (i + j);
            var identityS = (i - j);
            var squareA = (square + j);
            var squareS = (square - j);

            if (((x(cubeA) != y(cubeA)) || (x(cubeS) != y(cubeS))) || ((x(identityA) != y(identityA)) || (x(identityS) != y(identityS))) || ((x(squareA) != y(squareA)) || (x(squareS) != y(squareS)))) {
                result = false;
            }
        }
    }

    for (var i = 0UL; (i < 100000UL); ++i) { // midpoint testing
        var tempA = ((ulong.MaxValue >> 1) + i);
        var tempS = ((ulong.MaxValue >> 1) - i);

        if ((x(tempA) != y(tempA)) || (x(tempS) != y(tempS))) {
            result = false;
        }
    }

    for (var i = 0UL; (i < 100000000UL); ++i) { // uniformly distributed testing
        var temp = randomNumberGenerator();

        if (x(temp) != y(temp)) {
            result = false;
        }
    }

    return result;
}