pow

pub fn pow(comptime T: type, x: T, y: T) T {
    if (@typeInfo(T) == .int) {
        return math.powi(T, x, y) catch unreachable;
    }

    if (T != f32 and T != f64) {
        @compileError("pow not implemented for " ++ @typeName(T));
    }

    // pow(x, +-0) = 1      for all x
    // pow(1, y) = 1        for all y
    if (y == 0 or x == 1) {
        return 1;
    }

    // pow(nan, y) = nan    for all y
    // pow(x, nan) = nan    for all x
    if (math.isNan(x) or math.isNan(y)) {
        @branchHint(.unlikely);
        return math.nan(T);
    }

    // pow(x, 1) = x        for all x
    if (y == 1) {
        return x;
    }

    if (x == 0) {
        if (y < 0) {
            // pow(+-0, y) = +-inf  for y an odd integer
            if (isOddInteger(y)) {
                return math.copysign(math.inf(T), x);
            }
            // pow(+-0, y) = +inf   for y an even integer
            else {
                return math.inf(T);
            }
        } else {
            if (isOddInteger(y)) {
                return x;
            } else {
                return 0;
            }
        }
    }

    if (math.isInf(y)) {
        // pow(-1, inf) = 1     for all x
        if (x == -1) {
            return 1.0;
        }
        // pow(x, +inf) = +0    for |x| < 1
        // pow(x, -inf) = +0    for |x| > 1
        else if ((@abs(x) < 1) == math.isPositiveInf(y)) {
            return 0;
        }
        // pow(x, -inf) = +inf  for |x| < 1
        // pow(x, +inf) = +inf  for |x| > 1
        else {
            return math.inf(T);
        }
    }

    if (math.isInf(x)) {
        if (math.isNegativeInf(x)) {
            return pow(T, 1 / x, -y);
        }
        // pow(+inf, y) = +0    for y < 0
        else if (y < 0) {
            return 0;
        }
        // pow(+inf, y) = +0    for y > 0
        else if (y > 0) {
            return math.inf(T);
        }
    }

    // special case sqrt
    if (y == 0.5) {
        return @sqrt(x);
    }

    if (y == -0.5) {
        return 1 / @sqrt(x);
    }

    const r1 = math.modf(@abs(y));
    var yi = r1.ipart;
    var yf = r1.fpart;

    if (yf != 0 and x < 0) {
        return math.nan(T);
    }
    if (yi >= 1 << (@typeInfo(T).float.bits - 1)) {
        return @exp(y * @log(x));
    }

    // a = a1 * 2^ae
    var a1: T = 1.0;
    var ae: i32 = 0;

    // a *= x^yf
    if (yf != 0) {
        if (yf > 0.5) {
            yf -= 1;
            yi += 1;
        }
        a1 = @exp(yf * @log(x));
    }

    // a *= x^yi
    const r2 = math.frexp(x);
    var xe = r2.exponent;
    var x1 = r2.significand;

    var i = @as(std.meta.Int(.signed, @typeInfo(T).float.bits), @intFromFloat(yi));
    while (i != 0) : (i >>= 1) {
        const overflow_shift = math.floatExponentBits(T) + 1;
        if (xe < -(1 << overflow_shift) or (1 << overflow_shift) < xe) {
            // catch xe before it overflows the left shift below
            // Since i != 0 it has at least one bit still set, so ae will accumulate xe
            // on at least one more iteration, ae += xe is a lower bound on ae
            // the lower bound on ae exceeds the size of a float exp
            // so the final call to Ldexp will produce under/overflow (0/Inf)
            ae += xe;
            break;
        }
        if (i & 1 == 1) {
            a1 *= x1;
            ae += xe;
        }
        x1 *= x1;
        xe <<= 1;
        if (x1 < 0.5) {
            x1 += x1;
            xe -= 1;
        }
    }

    // a *= a1 * 2^ae
    if (y < 0) {
        a1 = 1 / a1;
        ae = -ae;
    }

    return math.scalbn(a1, ae);
}