Exhaustive comparative testing of your primitives is the only true test of them. https://randomascii.wordpress.com/2014/01/27/theres-only-four-billion-floatsso-test-them-all/ … @BruceDawson0xB
Wonder if anyone's done automated VM spinup (eg AWS) to do exhaustive test of double functions?
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How many CPUs you want to spin up? With a million cores it might take a week or longer. Possible, but pricey.
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If the test isn't checking for strict equivalence, maybe you can get away with interval arithmetic over very small input ranges.
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I'd still expect around 2^53 different doubles for small ranges.
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A small range of 1000 double values means 1000x fewer cases to evaluate. Split the range if that's not enough.
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If you're talking about ranges you missed the whole point of this thread..
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A range of 1024 doubles only differs in low 10 bits. Plenty of trivial ways to discharge equivalence (ish) proof over such small ranges.
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For trig functions and at least 25% of doubles, low single input bit completely changes the output.
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Yeah. If you need 100% accurate rounding, things suck. But even saving 75% (in theory) would help on the million core.
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Would only work for unary functions, which are generally "easy" to give mathematical proofs for. Mostly not worth the cost.
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