Checking for overflows, revisited once

Pascal Cuoq - 12th Feb 2012

I do not have any solution I am 100% happy with to the overflow dilemma in the previous post. Here is one of the solutions that does not make me 100% happy.

The first (partial) solution is: program so that overflows correspond exactly to unwanted circumstances (and then it becomes meaningful to verify the absence of overflows. There are great automatic tools for that. Have you heard of them?)

“Program so that…” sounds abstract but it may be as simple as using larger integer types that won't overflow for all intermediate computations:

  s = (int)((long long) u1 - (long long)u2); 

Then the desired property (variable s contains the mathematical difference of u1 and u2) entirely rests on the final conversion from long long to int.

This solution doesn't apply in the common situation where the code is already written and gratuitous changes to it are prohibited. Also you need to have an integer type large enough to contain all intermediate computations without overflows. In this example unsigned int is 32-bit and long long is 64-bit but the standard does not prevent unsigned int to be 64-bit and the same size as long long in which case the conversion from unsigned int to long long could overflow. Rte would only insert additional assertions for the two intermediate conversions that we have added in the assignment. This wouldn't help; it would only make things worse.

“Won't the generated code be less efficient?” you rightly ask. That all depends on the compiler. Optimizing compilers have no trouble at all optimizing the above assignment so that it uses only one 32-bit subtraction. On the Linux workstation on which I tried this both clang -m32 -O0 and gcc -m32 -O0 did. It is amusing because the code generated by both compilers with -O0 is ugly (gratuitously moving registers to memory and then to registers again) but even with optimizations disabled they still both get the fact that it is only necessary to compute the least significant 32 bits of the result.

With optimizations both Clang and GCC generate clean code that naturally still uses a single 32-bit subtraction:

$ gcc -S -O2 -m32 t.c 
$ cat t.s 
	pushl	%ebp 
	movl	%esp  %ebp 
	movl	8(%ebp)  %eax 
        subl	12(%ebp)  %eax 
	popl	%ebp 

As an anecdote when generating x86-64 code (and therefore having 64-bit subtraction available as a single instruction with only the drawback of a slightly larger encoding) gcc -O0 keeps using 32-bit subtraction but clang -O0 uses 64-bit subtraction. This does not reveal anything about the compilers: it does not make sense to compare for efficiency the code they generate with optimization disabled.

That's all for this post.

Pascal Cuoq
12th Feb 2012