# Programmer: Sriram Pemmaraju
# Date: 3/5/2015

# This function "rounds" a given floating point number to the nearest "half integer"
# provided the "half integer" is within distance 1/1000 and it returns that half integer. 
# Otherwise, the function returns None. By half integers, we mean elements in the set
# {...-1.5, -1. -0.5, 0, 0.5, 1, 1.5,...}
def nearHalfInteger(f):
    
    # We compute three candidates to compare f to
    # Note that we have to pay attention to whether
    # f is negative
    x = int(f)
    if x >= 0:
        y = x + 1/2
        z = x + 1
    else:
        y = x - 1/2
        z = x - 1
        
    # We check if there is candidate at distance <= 1/1000
    # and if so, return it.
    if abs(f - x) <= 1/1000:
        return x
    elif abs(f - y) <= 1/1000:
        return y
    elif abs(f - z) <= 1/1000:
        return z
    
    return None