from math import cos, sin, pi

def fpart(n): return n - int(n)
def min_max(a, b): return min(a, b), max(a, b)
def cos_sin(a): return cos(a), sin(a)
def bound_min_max(v, a, b): return max(a, min(b, v))
def dist2(x1, y1, x2=0, y2=0): return (x1 - x2)**2 + (y1 - y2)**2
def sign(x): return x<0 and -1 or x>0
def dprinc(a, b=0, c=2*pi): return ((a - b + c/2) % c) - c/2