Add StableHLO complex sqrt to stablehlo-complex-math-expander pass #2679
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As in the title.
The existing implementation of
sqrt
on complex inputs uses polar form of complex sqrt which is inaccurate/incorrect on about 28 % of uniformly distributed samples over all complex plane. The JAX complex sqrt accuracy statistics is as follows:This PR provides an algorithm for complex sqrt that is accurate up to 3/6 ULP difference error on complex samples. The corresponding JAX complex sqrt accuracy statistics is as follows:
It is interesting to note that although the same algorithm is used for both CUDA and CPU platforms, then the expected maximal ULP difference is 4 (obtained from applying the algorithm to numpy arrays). Hence