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 Re: Bug in l3fp for sines near 2pi Bruno Le Floch <[log in to unmask]> Thu, 7 Nov 2013 22:57:54 +0100 text/plain (39 lines) ```>> For the functions in radians, I would need >> to either store EMAX+16 decimals of pi, where EMAX is the maximal >> exponent and 16 is the precision of floating point numbers, or be able >> to compute them. Right now, I am cheating, using a fixed-precision >> value of 2pi (equal to twice \c_pi_fp). >> > > "fixed precision" makes me think of the LaTeX2e package fp, 18 places > before and after the decimal point. In using it I became alarmed at how > rapidly errors propagated inwards when exponents were involved. Indeed, sin(1e99) is currently completely wrong, as 1e99 is reduced modulo 6.283185307179588 rather than 2ð. It appears that many not-too-serious math libraries do this (with slightly more precise values of 2ð). The approach does not cause too much trouble, as identities such as sin(a+b)=sin(a)cos(b)+sin(b)cos(a) are preserved. Essentially, what it does is to stretch (or shrink) trigonometric functions so that they have a period equal to 6.283185307179588 rather than 2ð. I don't like this very much, so I will be looking into how to do proper argument reduction. >> Comments welcome on the addition of sind and friends (and similarly >> asind for arc-trigonometric functions, newly added), and on range >> reduction in radians. > > sind etc, and the inverse functions, are very welcome. (But as a student > of hyperbolic geometry, I especially look forward to the hyperbolic > functions and inverses!) Is this a jest, or would you actually use those functions? Hyperbolic functions are not too hard, now that I have added a few tools to manipulate extended precision numbers (basically, they're just a bunch of sums and products on the result of the exponential function). Their inverses are more tricky, and I can't promise them any time soon. Regards, Bruno ```