A much more interesting example is this (in Maxima)

fpprec:16
sin (bfloat(2)^10000)

-6.104079172368958b-1

which is correct to 16 decimal places.

  Making this work by adding in more terms in the taylor series for
sine would be a very bad idea.

Instead, the sine routine first compute pi to 10016  or more decimal
places.

I assume mpfr does such things. I hope you do such things in python
numerics.

RJF



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