Zig 0.17.0-dev (Split by item)

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sqrt64

sqrt.sqrt64

fn sqrt64(z: Complex(f64)) Complex(f64)

File

lib/std/math/complex/sqrt.zig:73

Code

fn sqrt64(z: Complex(f64)) Complex(f64) {
    // may encounter overflow for im,re >= DBL_MAX / (1 + sqrt(2))
    const threshold = 0x1.a827999fcef32p+1022;

    var x = z.re;
    var y = z.im;

    if (x == 0 and y == 0) {
        return Complex(f64).init(0, y);
    }
    if (math.isInf(y)) {
        return Complex(f64).init(math.inf(f64), y);
    }
    if (math.isNan(x)) {
        // raise invalid if y is not nan
        const t = (y - y) / (y - y);
        return Complex(f64).init(x, t);
    }
    if (math.isInf(x)) {
        // sqrt(inf + i nan)    = inf + nan i
        // sqrt(inf + iy)       = inf + i0
        // sqrt(-inf + i nan)   = nan +- inf i
        // sqrt(-inf + iy)      = 0 + inf i
        if (math.signbit(x)) {
            return Complex(f64).init(@abs(y - y), math.copysign(x, y));
        } else {
            return Complex(f64).init(x, math.copysign(y - y, y));
        }
    }

    // y = nan special case is handled fine below

    // scale to avoid overflow
    var scale = false;
    if (@abs(x) >= threshold or @abs(y) >= threshold) {
        x *= 0.25;
        y *= 0.25;
        scale = true;
    }

    var result: Complex(f64) = undefined;
    if (x >= 0) {
        const t = @sqrt((x + math.hypot(x, y)) * 0.5);
        result = Complex(f64).init(t, y / (2.0 * t));
    } else {
        const t = @sqrt((-x + math.hypot(x, y)) * 0.5);
        result = Complex(f64).init(@abs(y) / (2.0 * t), math.copysign(t, y));
    }

    if (scale) {
        result.re *= 2;
        result.im *= 2;
    }

    return result;
}