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I mean, he's using relative tolerance, not absolute. Most common arithmetic operations should be well behaved w.r.t. relative tolerance, unless you're using denormalised numbers.


relative tolerance is not always enough, especially near 0. This classic article gives a nice overview of absolute, relative, ulp-based and other methods for comparison of float numbers: https://randomascii.wordpress.com/2012/02/25/comparing-float...


> especially near 0

Yes, these are denormalised numbers. They aren't as well behaved.




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