a *= b not equivalent to a = a*b

[Peter Otten]

mlz wrote:

> I've been playing with the binomial function, and found that in the below
> code, rs *= x does not behave the same way as rs = rs * x. When I set FAIL
> to True, I get a different result.  Both results are below.
> 
> I had read that the two were equivalent. What am I missing?
> 
> thanks,
>   -= miles =-
> 
> 
> #!/usr/bin/python2
> 
> import sys
> FAIL= True if len(sys.argv)>1 else False
> 
> def bin(n,k):
>     rs=1
>     k=min(k,n-k)
>     
>     for i in range(1,k+1):
>         if FAIL: rs *= (n-(i-1))/i  # these should be the same,

This is evaluated as

rs = rs * ((n - (i - 1)) / i)

>         else: rs = rs * (n-(i-1))/i  #  but apparently are not

while this is evaluated as

rs = (rs * (n - (i - 1))/i

so the two expressions do not really result in the same calculation. A 
simpler example:

>>> (2*2)/3
1
>>> 2*(2/3)
0

Now "hide" the the order of evaluation:

>>> a, b = 2, 3
>>> a *= a/b
>>> a
0
>>> a, b = 2, 3
>>> a = a*a/b
>>> a
1

>     return rs
>         
>         
> for n in range(10):
>     for k in range(n+1):
>         print bin(n,k),
>     print''
>        
> ------------------- output -------------------------
> 
> 
> $ pascal2
> 1
> 1 1
> 1 2 1
> 1 3 3 1
> 1 4 6 4 1
> 1 5 10 10 5 1
> 1 6 15 20 15 6 1
> 1 7 21 35 35 21 7 1
> 1 8 28 56 70 56 28 8 1
> 1 9 36 84 126 126 84 36 9 1
> 
> $ pascal2 fail
> 1
> 1 1
> 1 2 1
> 1 3 3 1
> 1 4 4 4 1
> 1 5 10 10 5 1
> 1 6 12 12 12 6 1
> 1 7 21 21 21 21 7 1
> 1 8 24 48 48 48 24 8 1
> 1 9 36 72 72 72 72 36 9 1