How Are Unlimited Precision Integers Accomplished?

[Martin v. Loewis]

Michael Chermside <mcherm at destiny.com> writes:

>          2**( 15 * (2**MAXINT) ) - 1
[...]
>  >>> big = 1L << (2**31 - 1)
>  >>> big <<= 15
>  >>> big += 1
>  >>> big <<= 45
>  >>>
> 
> As you can see, it should have overflowed (I thought) in line 3.

I really cannot see why that should overflow. Performing

big = 1L << (2**31 - 1)
big <<= 15

is the same as performing

big = 1L << (2**31 + 14)

which is roughly

2**(15 * (2**27))

So this is *much* less than 2**( 15 * (2**MAXINT) ) - 1.

On any 32-bit machine, the memory needed to store the largest large
integer exceeeds the amount of memory that the processor can
address. For a 64-bit machine, the same is true if MAXINT is 2**63-1.

Regards,
Martin