///| Compute Square Root of a number
///
/// # Examples
///
/// ```moonbit
/// assert_eq!(sqrt(0), 0);
/// assert_eq!(sqrt(1), 1);
/// assert_eq!(sqrt(2), 1.4142135623730951);
/// assert_eq!(sqrt(3), 1.7320508075688772);
/// ```
///
/// # Special Cases
///
/// 1. sqrt(NaN) = NaN
/// 2. sqrt(x) = NaN if x < 0
/// 3. sqrt(+inf) = +inf
/// 4. sqrt(-inf) = NaN
///
/// # Accuracy
///
/// 0 ulp.
pub fn sqrt(x : Double) -> Double {
  x.sqrt()
}

///|
test "sqrt" {
  fn assert_sqrt_ulp!(input, expect) {
    assert_ulp!(expect, sqrt(input), SQRT_MAX_ULP)
  }

  assert_sqrt_ulp!(-0.8, @double.not_a_number)
  assert_sqrt_ulp!(-0.7, @double.not_a_number)
  assert_sqrt_ulp!(-0, -0)
  assert_sqrt_ulp!(-0.7853981633974483, @double.not_a_number)
  assert_sqrt_ulp!(0, 0)
  assert_sqrt_ulp!(0.1, 0.31622776601683794)
  assert_sqrt_ulp!(0.2, 0.4472135954999579)
  assert_sqrt_ulp!(0.3, 0.5477225575051661)
  assert_sqrt_ulp!(0.4, 0.6324555320336759)
  assert_sqrt_ulp!(0.5, 0.7071067811865476)
  assert_sqrt_ulp!(0.6, 0.7745966692414834)
  assert_sqrt_ulp!(0.7, 0.8366600265340756)
  assert_sqrt_ulp!(0.8, 0.8944271909999159)
  assert_sqrt_ulp!(0.9, 0.9486832980505138)
  assert_sqrt_ulp!(1, 1)
  assert_sqrt_ulp!(3.141592653589793, 1.7724538509055159)
  assert_sqrt_ulp!(1.5707963267948966, 1.2533141373155001)
  assert_sqrt_ulp!(0.7853981633974483, 0.8862269254527579)
  assert_sqrt_ulp!(-1, @double.not_a_number)
  assert_sqrt_ulp!(-2, @double.not_a_number)
  assert_sqrt_ulp!(-3, @double.not_a_number)
  assert_sqrt_ulp!(-4, @double.not_a_number)
  assert_sqrt_ulp!(-5, @double.not_a_number)
  assert_sqrt_ulp!(-6, @double.not_a_number)
  assert_sqrt_ulp!(-7, @double.not_a_number)
  assert_sqrt_ulp!(-8, @double.not_a_number)
  assert_sqrt_ulp!(-9, @double.not_a_number)
  assert_sqrt_ulp!(1, 1)
  assert_sqrt_ulp!(2, 1.4142135623730951)
  assert_sqrt_ulp!(3, 1.7320508075688772)
  assert_sqrt_ulp!(4, 2)
  assert_sqrt_ulp!(5, 2.23606797749979)
  assert_sqrt_ulp!(6, 2.449489742783178)
  assert_sqrt_ulp!(7, 2.6457513110645907)
  assert_sqrt_ulp!(8, 2.8284271247461903)
  assert_sqrt_ulp!(9, 3)
  assert_sqrt_ulp!(10, 3.1622776601683795)
  assert_sqrt_ulp!(100, 10)
  assert_sqrt_ulp!(1000, 31.622776601683793)
  assert_sqrt_ulp!(10000, 100)
  assert_sqrt_ulp!(2.5, 1.5811388300841898)
  assert_sqrt_ulp!(3.4, 1.8439088914585775)
  assert_sqrt_ulp!(5.3, 2.3021728866442674)
  assert_sqrt_ulp!(6.2, 2.4899799195977463)
  assert_sqrt_ulp!(7.1, 2.6645825188948455)
  assert_sqrt_ulp!(8.9, 2.9832867780352594)
  assert_sqrt_ulp!(9.8, 3.1304951684997055)
  assert_sqrt_ulp!(10.7, 3.271085446759225)
  assert_sqrt_ulp!(101.6, 10.079682534683322)
  assert_sqrt_ulp!(1.542, 1.241772926102031)
  assert_sqrt_ulp!(2.846, 1.6870091878825082)
  assert_sqrt_ulp!(7.881, 2.8073118814980282)
  assert_sqrt_ulp!(3.772, 1.9421637418096342)
  assert_sqrt_ulp!(0, 0)
  assert_sqrt_ulp!(-0, -0)
  assert_sqrt_ulp!(@double.not_a_number, @double.not_a_number)
  assert_sqrt_ulp!(@double.infinity, @double.infinity)
  assert_sqrt_ulp!(@double.neg_infinity, @double.not_a_number)
}