module math

// special cases are:
// sqrt(+inf) = +inf
// sqrt(±0) = ±0
// sqrt(x < 0) = nan
// sqrt(nan) = nan
[inline]
pub fn sqrt(a f64) f64 {
    mut x := a
    if x == 0.0 || is_nan(x) || is_inf(x, 1) {
        return x
    }
    if x < 0.0 {
        return nan()
    }
    z, ex := frexp(x)
    w := x
    // approximate square root of number between 0.5 and 1
    // relative error of approximation = 7.47e-3
    x = 4.173075996388649989089e-1 + 5.9016206709064458299663e-1 * z // adjust for odd powers of 2
    if (ex & 1) != 0 {
        x *= sqrt2
    }
    x = ldexp(x, ex >> 1)
    // newton iterations
    x = 0.5 * (x + w / x)
    x = 0.5 * (x + w / x)
    x = 0.5 * (x + w / x)
    return x
}

// sqrtf calculates square-root of the provided value. (float32)
[inline]
pub fn sqrtf(a f32) f32 {
    return f32(sqrt(a))
}

// sqrti calculates the integer square-root of the provided value. (i64)
pub fn sqrti(a i64) i64 {
    mut x := a
    mut q, mut r := i64(1), i64(0)
    for ; q <= x; {
        q <<= 2
    }
    for ; q > 1; {
        q >>= 2
        t := x - r - q
        r >>= 1
        if t >= 0 {
            x = t
            r += q
        }
    }
    return r
}