danrosher commented on PR #940:
URL: https://github.com/apache/solr/pull/940#issuecomment-1191522782
Thanks for looking into this more @madrob .
I wasn't aware of SloppyMath. If we assume Math.acos correct, then to get
the same accuracy with FastInvTrig to within 40cm, I've tested it takes 17
terms, which after running a benchmark means that:
```
Benchmark (num_points) Mode Cnt Score
Error Units
FastInvTrigBenchmark.acosBM10 2000000 avgt 2 44.149
ms/op
FastInvTrigBenchmark.acosBM17 2000000 avgt 2 67.977
ms/op
FastInvTrigBenchmark.fastMathAcosBM 2000000 avgt 2 252.578
ms/op
FastInvTrigBenchmark.haversineBM 2000000 avgt 2 288.209
ms/op
FastInvTrigBenchmark.mathAcosBM 2000000 avgt 2 300.509
ms/op
FastInvTrigBenchmark.mathAsin 2000000 avgt 2 320.407
ms/op
FastInvTrigBenchmark.sloppyAsin 2000000 avgt 2 50.152
ms/op
FastInvTrigBenchmark.sloppyHaversinMeters 2000000 avgt 2 134.309
ms/op
FastInvTrigBenchmark.sloppyHaversinSortKey 2000000 avgt 2 82.845
ms/op
```
So then:
SloppyMath.HaversinSortKey is 1.9x slower than FastInvTrig with 10 terms
(as you found)
SloppyMath.HaversinSortKey is 1.2x slower than FastInvTrig with 17 terms
However I also noticed that SloppyMath has an asin implementation, and with
pi/2-asin(x) = acos(x)
https://www.wolframalpha.com/input?i2d=true&i=%5C%2840%29Divide%5Bpi%2C2%5D-asin%5C%2840%29x%5C%2841%29%5C%2841%29-acos%5C%2840%29x%5C%2841%29
after adding this into the benchmark, using nvector and this identity ^ for
acos then:
FastInvTrig with 17 terms is 1.3x slower than SloppyMath.asin !
The caveat is that SloppyMath.asin uses more memory for caching values I
think.
So I'm wondering now whether to abandon the FastInvTrig series expansion,
and use SloppyMath.asin for NVector? What do you think ?
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