Re: [PATCH] Fold sqrt comparisons against constants

[Fergus Henderson <fjh at cs dot mu dot OZ dot AU>]

On 16-Mar-2003, Zack Weinberg <zack at codesourcery dot com> wrote:
> This looks good to me, but you should get a second opinion from
> someone who's more up on floating point issues.
> 
> As a followup, could you consider working out which of these
> optimizations are only safe under -ffast-math and which can be
> applied generally?  It looks to me like your example above is
> always safe, or at least could be made safe by adding NaN checks.

I think it has different rounding behaviour.
You may get situations arising where e.g.
sqrt(4.000000000000001) = 2.0 (because of rounding),
but 4.000000000000001 > 2.0 * 2.0.

For example, the following program prints more As than Bs.

	#include <math.h>
	#include <stdio.h>
	int main() {
		double sqr = 4.0;
		double rt = 2.0;
		double i;
		for (i = 1.0; i != 0.0; i /= 2) {
			double d = sqr + i;
			double sqrt_d = sqrt(d);
			printf("sqrt(%.30f) = %.30f\n", d, sqrt_d);
			if (sqrt_d <= rt) { printf("A\n"); }
			if (d <= rt * rt) { printf("B\n"); }
		}
		return 0;
	}

-- 
Fergus Henderson <fjh at cs dot mu dot oz dot au>  |  "I have always known that the pursuit
The University of Melbourne         |  of excellence is a lethal habit"
WWW: <http://www.cs.mu.oz.au/~fjh>  |     -- the last words of T. S. Garp.