import math
def root(x: float) -> float:
return math.sqrt(x)
def floor_of(x: float) -> int:
return math.floor(x)
def ceil_of(x: float) -> int:
return math.ceil(x)
def hypot(a: float, b: float) -> float:
# math.sqrt composed in a larger expression.
return math.sqrt(a * a + b * b)
def floor_neg(x: float) -> int:
return math.floor(x)