series

fn series(comptime T: type, abs: T) T {
    const numerator = [_]T{
        23531376880.410759688572007674451636754734846804940,
        42919803642.649098768957899047001988850926355848959,
        35711959237.355668049440185451547166705960488635843,
        17921034426.037209699919755754458931112671403265390,
        6039542586.3520280050642916443072979210699388420708,
        1439720407.3117216736632230727949123939715485786772,
        248874557.86205415651146038641322942321632125127801,
        31426415.585400194380614231628318205362874684987640,
        2876370.6289353724412254090516208496135991145378768,
        186056.26539522349504029498971604569928220784236328,
        8071.6720023658162106380029022722506138218516325024,
        210.82427775157934587250973392071336271166969580291,
        2.5066282746310002701649081771338373386264310793408,
    };
    const denominator = [_]T{
        0.0,
        39916800.0,
        120543840.0,
        150917976.0,
        105258076.0,
        45995730.0,
        13339535.0,
        2637558.0,
        357423.0,
        32670.0,
        1925.0,
        66.0,
        1.0,
    };
    var num: T = 0;
    var den: T = 0;
    // split to avoid overflow
    if (abs < 8) {
        // big abs would overflow here
        for (0..numerator.len) |i| {
            num = num * abs + numerator[numerator.len - 1 - i];
            den = den * abs + denominator[numerator.len - 1 - i];
        }
    } else {
        // small abs would overflow here
        for (0..numerator.len) |i| {
            num = num / abs + numerator[i];
            den = den / abs + denominator[i];
        }
    }
    return num / den;
}