Not just for cryptography

[Don]

Era Scarecrow wrote:
>> From: Sean Kelly <sean at invisibleduck.org>
>>
>> bearophile wrote:
>>> Another little story for people that think the
>> multi-precision integers are mostly good for cryptography:
>> http://dobbscodetalk.com/index.php?option=com_content&task=view&id=614&Itemid=
>>
>> Avoiding computation overflow is never a bad thing :)
> 
>  There's an idea...
> 
>  I have a feature request. Please give me heads or tails on what you think. implementing it hopefully won't break any code, and i don't know of a single compiler/language the is protected against this.
> 
>  When using math operations hopefully the compiler can take the types and increase them by 1 (32 to 64bit), and then when you do comparisons immediately following those you can compare against the larger non-overflow version vs the one that can overflow. (but if you don't do a compare, it would probably only keep the 32bit version anyways).

Actually that's (sort of) implemented in most hardware (X86, for 
instance). The overflow flag is set if you get an int overflow (signed 
ints). The carry flag is set if you get a uint overflow.

There are several branch instructions which make use of it.

>  Internally (Assembly) it would look something like this.
>  if (a+b > 0){
> ...
> }
> --becomes
>  xor edx,edx        ;clear upper 32bits
>  mov eax, [esp-12]  ;int a
>  add eax, [esp-8]   ;int b
>  adc edx, 0         ;add with carry

> 
> --then following the compare 
> 
>  cmp edx,0
>  jg inside_if  ;jump if greater than 0. More likely?
>  jb outside_if ;below 0, so it's false
>  cmp eax,0
>  jbe outside_if
> inside_if:
> ;{...}
> outside_if:

mov eax, [esp-12];
add eax, [esp-8];
jo error;
jbe outside_if;

error: throw IntegerOverflowException.

Could be added in debug builds, at least.