# sign function
def sgn(x):
    if x>=0:
        return 1
    return -1

# check whether a number is an integer (with tolerance)
def isint_nonzero(x):
    if abs(x)<1e-11:
        return False
    return abs(round(x)-x)<1e-11

# check that a number is in an interval
def in_interval(x,a,b):
    return x>=a and x<=b