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[robve]

(06-19-2024 02:01 AM)robve Wrote:  My improved Newton implementation:
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Previously in that post I showed the results for 64 bit float (double). I also have results for 128 bit floats (long double) and updated to the most recent implementations:

  tvmperfcomp-newton-hybrid-128bit.pdf (Size: 34.47 KB / Downloads: 3)
Hybrid has lower FVerror overall. It is hard to argue that the difference in accuracy is due to roundoff alone.

The implementations aren't using any tricks or special prep. They take the same initial guess, then Hybrid performs one Newton step to get the next point and iterates Secant until convergence without retrying (g=0). Two case for Newton are shown (g=0) and with one retry (g=1) after overshooting to try to find the root.

- Rob