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Attempt to implement bitburst-algorithm version of
BigMath.erfandBigMath.erfcThis pull request is a proof of concept, not meant to merge.
Considering the complexity of the implementation, (about 1/3 of math.rb code are about erf/erfc), I'm not sure if this improvement is worth maintaining.
Bit-burst algorithm implementation
Repeatedly apply Taylor expansion at increasing x.
x0 + x1 + x2 + ...f(x0)with Taylor expansion offat0f(x0 + x1)with Taylor expansion offatx0f(x0 + x1 + x2)with Taylor expansion offatx0 + x1Each Taylor expansion calculation uses binary-splitting method.
Details are described in source code comment.
Benchmark
Performance compared with initial implementation of erf/erfc (#357)
(multiplication-improvement(#407) exp-improvement(#433) pi-improvement(#434))