Joseph Wright skrev:
> Hello all,
> Those of you who take an interest in the LaTeX3 SVN may have noticed
> that I've just added the beginnings of a 'l3fp' module as part of expl3.
> This is intended to provide a set of floating point functions for LaTeX3.
> In terms of input range, I've gone for -999999999.999999999 to
> +999999999.999999999. This should be sufficient for a wide range of
> purposes (for example, if you convert a dimen into a floating point
> number in units pt then you are safe for any dimen TeX can handle).
I was as confused by this as J.Fine, but it now seems clear that you've
implemented a fixed point arithmetic package that possibly will become
a floating point arithmetic package.
> The design of the internals of the package is loosely following the
> well-known fp package. However, that package is rather slow, at least
> partly as it handles 18 digits either side of the decimal. The approach
> in l3fp currently delivers addition, subtraction, multiplication and
> division much faster than fp does (between about 8 and 15 times as fast
> for a large number of repeated calculations). I hope this makes the
> module fast enough for practical use.
> The next phase is to add some more complex functions. I'm planning to
> cover trigonometry, exponential/ln and roots, plus a pseudo-random
> number generator
That most standard libraries primarily provide a "uniform in $[0,1]$"
(or some open variation of that interval) PRNG doesn't mean it is the
most natural form of a PRNG. It is entirely reasonable for an l3 core
PRNG to primarily produce random bits or random integers, which could
then be converted to random floats if anyone asks for it; it's easier
than going the other way.
> and a few utility functions. They may take a while:
> getting it right is not that easy.
> Feedback on the module is very welcome, for example on which functions
> to provide, bugs (there are bound to be some), etc.
There are some standard floating-point arithmetic modules for MetaPost,
which could perhaps provide inspiration, but on closer inspection those
seem to rely on built-in primitives for logarithm and exponent (of
course, one can then take a look in mp.web to see how Knuth implemented
those while avoiding overflow and such, but the level of indirection is
then pretty high).
Two Meta*-ish operations which could well be useful in LaTeX are
"Pythagorean addition" (known as hypot in the C library I think) and
"Pythagorean subtraction" (given one side and the hypothenuse, find the