def f(x):
    """pointless sample function"""
    if x < 0:
        return 0
    else:
        x-=1
        return f(x)


def power(x,y,tot=1):
    """raise to the power - no square optimisation (lisp-like)"""
    if y > 0:
        tot = x*tot
        return power(x,y-1,tot)
    else:
        return 1



#
# Note this would be faster if the optimisation removed
# the unneccessary loading and saving of "x"
# before each loop
# 
def quickpower(x, y):
    """raise to the power - with square optimisation"""
    if y%2 == 1:
        return quickpower( quickpower(x,(y-1)/2), 2)
    elif y == 2:
        return x*x
    elif y > 0:
        return quickpower( quickpower(x,y//2) , 2 )
    else:
        return 1



def gcd(a,b):
    """greatest common devisor - Euclid"""
    if b > a:
        c=a
        a=b
        b=a
    if b > 0:
        return gcd(b,a%b)
    return a


def gcd_dijkstra(m, n):
    """greatest common devisor - Dijkstra"""
    if m > n:
        return gcd_dijkstra(m-n, n)
    elif n > m:
        return gcd_dijkstra(m, n-m)
    return m


def fact(x,tot=1):
    """Factorial (lisp-like)"""
    if x > 1:
        return fact(x-1,tot*x)
    return tot    



# This could be much faster because 
# data and search_for are not modified
# But we still end up doing
# 
# LOAD_FAST data
# LOAD_FAST search_for
# ...
# SAVE_FAST search_for
# SAVE_FAST data
# 
# before doing our
# JUMP_ABSOLUTE <Label>
# (or something like that) - those four ops could be optimised away though
#
def binary_search(data,search_for,start,end):
    """Simple binary search or ordered list"""
    if start > end:
       return -1
    mid = start + (end - start)//2
    a = data[mid]
    if a > search_for:
       return binary_search(data, search_for, start, mid-1)
    elif a < search_for:
       return binary_search(data, search_for, mid+1, end)
    else:
       return mid


#  This is currently not optimised well
#  - the double recurrsion in a single statement is not removed
# 
def ackermann(m,n):
    """Ackermann-Peter function (doesn't get properly optimised)"""
    if m >0 and n>0:
        return ackermann(m-1,ackermann(m,n-1))
    elif m == 0:
        return n+1
    else:
        return ackermann(m-1,1)