fix overflow/underflow bug in zeta(z) #129
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stevengj
commented
Oct 27, 2018
| @test 1e-12 > relerrc(zeta(3 + 99.69im), 1.09996958148566565003471336713642736202442134876588828500-0.00948220959478852115901654819402390826992494044787958181148im) | ||
| @test 1e-9 > relerrc(zeta(-3 + 99.69im), 10332.6267578711852982128675093428012860119184786399673520976+13212.8641740351391796168658602382583730208014957452167440726im) | ||
| @test 1e-13 > relerrc(zeta(-3 + 99.69im), 10332.6267578711852982128675093428012860119184786399673520976+13212.8641740351391796168658602382583730208014957452167440726im) |
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This PR also seems to have greatly improved the accuracy in this older test.
stevengj
commented
Oct 27, 2018
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| # issue #128 | ||
| @test 1e-13 > relerrc(zeta(.4 + 453.0im), 5.595631794716693 - 4.994584420588448im) | ||
| @test 1e-10 > relerrc(zeta(.4 + 4053.0im), -0.1248993234383550+0.9195498409364987im) |
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In general, our current zeta algorithm is problematic for very large imaginary arguments.
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It seems to be problematic for imaginary numbers greater than 10im, the issues start early.
My next task is to compute the fractional derivatives of zeta, so I will try look into this issue.
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Fixes #128.