[racket] Math library ready for testing

Friends don't let friends program drunk.

On Fri, Dec 7, 2012 at 8:31 PM, Michael Wilber <mwilber at uccs.edu> wrote:
> This is such an exciting time to be a Racket programmer! Thanks for all
> your work, Neil.
>
> During winter break once I'm finished with grad school apps, I'll
> convert my final Signals and Systems Matlab project to racket/math to
> get a feel for the library.
>
> One note off-hand: I really don't like the (array #[#[#[...]]]) syntax.
> In Matlab, a 2D array is just:
>     [1 2; 3 4]
> That's 10 characters. In Python, the equivalent array is (including whitespace):
>     [[1, 2], [3, 4]]
> But in Racket, the equivalent array is:
>     (array #[#[1 1] #[3 4]])
> This syntax, especially the visual weight of all the hash marks #[#[,
> makes it harder for me to visually scan the line and see the actual
> array values. To see this, note that I miscopied one of the numbers
> when I wrote the racket array. How many seconds did it take you to find
> my mistake? Now imagine doing that at 3AM when drunk and you get an idea
> of my reason for saying this. This is the kind of syntax that will trip
> up undergraduates who are trying to debug their programs.
>
> Another syntax might be something akin to vectors: #[[1 2] [3 4]]
>
> Or just (array (1 2) (3 4))
>
> Or maybe using a : or something to separate rows for 2D arrays?
> (array 1 2 : 3 4)
>
> (array 1 0 0 0 0 0
>      : 0 1 0 0 0 0
>      : 0 0 1 0 0 0
>      : 0 0 0 1 0 0
>      : 0 0 0 0 1 0
>      : 0 0 0 0 0 1)
>
> All of these feel much less "racket-y," but they would eliminate all the
> visual cruft.
>
>
> Neil Toronto <neil.toronto at gmail.com> writes:
>> I've just pushed the last commits that make the new math library ready
>> for wider testing. Almost everything ready for use is documented, the
>> tests keep passing, and everything *seems* to work.
>>
>> We (the Racket development team) need people to use the heck out of it,
>> to find the majority of the remaining logic and design errors before the
>> next release. This is a big chunk of new code - ~20k lines in ~100
>> nontrivial files - so the more eyes, the better.
>>
>> If all you have time for is checking documentation, we'll take it. The
>> latest docs are here:
>>
>>      http://pre.racket-lang.org/docs/html/math/
>>
>> The nightly builds are here:
>>
>>      http://pre.racket-lang.org/installers/
>>
>> For Windows and Mac, the nightlies should include two new libraries used
>> by `math/bigfloat': libgmp and libmpfr. Linux users almost certainly
>> already have them; many packages (e.g. gcc) depend on libmpfr.
>>
>> If you prefer to build from source, clone the git repository here:
>>
>>      https://github.com/plt/racket
>>
>> If you're building on Windows or Mac, you can download pre-built libgmp
>> and libmpfr from here:
>>
>>      http://download.racket-lang.org/libs/10/
>>
>> ************
>>
>> Once you have a pre-release build, do (require math), and away you go!
>>
>> Well, it's probably not obvious where to start. The following are the
>> modules that `math' re-exports, and for some, what needs testing. Please
>> feel free to skim. In decreasing order of attention they need:
>>
>> (require math/array)
>>
>>    NumPy/SciPy/Repa-like arrays, Typed-Racket-style. Provides a
>>    covariant `Array' type and several mutable subtypes, array literals,
>>    functional constructors, pointwise operations with automatic
>>    broadcasting in SciPy/NumPy or permissive mode, slicing, indexing
>>    tricks, folds, easy arbitrary transformations, and parallel FFT.
>>
>>    This one needs a lot of usability testing. In particular...
>>
>>    We're trying something that's been done only once before, in
>>    Haskell's Repa: by default, arrays' elements are *non-strict*,
>>    meaning that they're recomputed when referenced. Cool things about
>>    this: pretty much everything can in principle be parallelized, and
>>    most intermediate arrays use almost no memory. But it requires more
>>    thought from users about when arrays should be made strict (computed
>>    and stored all at once). If it totally sucks, we can change it. If
>>    it's a worthwhile imposition, we'll leave it. If it's a wash, we
>>    could parameterize the default behavior.
>>
>>    Also, I've been considering allowing negative axis numbers and row
>>    indexes. Need feedback on how helpful it would be vs. confusing and
>>    error-hiding.
>>
>>    Lastly, I'm looking for a dual of `array-axis-reduce' (a kind of
>>    fold) that makes it easy to write `list-array->array', the inverse of
>>    the existing `array->list-array'. If you're into functional design
>>    puzzles, give this one a shot.
>>
>> (require math/bigfloat)
>>
>>    Floating-point numbers with arbitrarily large precision and
>>    large exponents. Also elementary and special functions, whose results
>>    are proved to be correct in many theses and dissertations. This is a
>>    Racket interface to MPFR (www.mpfr.org).
>>
>>    This module needs platform-specific testing.
>>
>>    I think we've verified that `math/bigfloat' works on all the
>>    supported 64-bit platforms, but not whether it works on supported
>>    32-bit platforms. It should. ;)
>>
>>    There's an error in the current nightly build, which causes an
>>    infinite loop when libmpfr isn't installed and a bigfloat function is
>>    applied. I just pushed a fix; it should fail properly tomorrow.
>>
>> (require math/distributions)
>>
>>    Probability distributions: discrete, integer-valued and real-valued.
>>    Distribution objects can compute pdfs, cdfs and inverse cdfs,
>>    optionally in log space, and for cdfs and inverse cdfs, optionally
>>    for upper tails. They can also generate samples.
>>
>>    Design ideas are welcome. More distributions are planned. Let me know
>>    which you need, and I'll concentrate on those first.
>>
>>    Watch out, R. Our gamma cdf is more accurate.
>>
>> (require math/special-functions)
>>
>>    Non-elementary functions like gamma, erf, zeta, Lambert W, and
>>    incomplete gamma and beta integrals. Most of these should be fairly
>>    accurate; i.e. they compute answers with apparently < 5 ulps error
>>    for the majority of their domains. But floating-point domains are
>>    huge, so the more use, the better.
>>
>> (require math/number-theory)
>>
>>    Number theory! Chinese Remainder solutions, coprimality and primality
>>    testing, factorization, congruence arithmetic parameterized on a
>>    current modulus, integer nth roots, multiplicative functions, common
>>    number sequences (Bernoulli, Eulerian, tangent, etc.), combinatorics,
>>    primitive roots, and more.
>>
>>    Please thank Jens Axel Søgaard, who wrote this module, for his
>>    excellent work.
>>
>> (require math/statistics)
>>
>>    Functions to compute summary values for collections of data, and to
>>    manage weighted samples. Every function for which it makes sense
>>    accepts weighted values, including the O(1)-space running statistics
>>    update.
>>
>>    I'm in the middle of documenting this. I'll get around to documenting
>>    correlation, kth-value order statistics (via quickselect), and
>>    counting/binning at least by Dec. 18.
>>
>> (require math/flonum)
>>
>>    Re-exports `racket/flonum' along with many more floating-point
>>    goodies. If you're a floating-point nut, you'll love it. If you're
>>    not, at least check out `flsum'. If you're doing statistics, look
>>    into log-space arithmetic (`lg+' and friends).
>>
>> (require math/base)
>>
>>    Re-exports `racket/math'; also exports some more constants like
>>    gamma.0 (Euler-Mascheroni), a bit more float-complex support, inverse
>>    hyperbolic functions, large random numbers, error measurement.
>>
>> Lastly, there's `math/matrix', which is currently not re-exported by
>> `math' because I haven't reviewed it yet. This is more from Jens Axel,
>> and if it's like his other fine work, it's correct and well-tested. I'll
>> probably get to it by Christmas.
>>
>> To sum up, there are 8 modules that need pounding on, and we need YOU to
>> do some pounding. If you're not terribly busy, please pick one that
>> looks interesting/fun/useful, and try it out.
>>
>> Thanks!
>>
>> Neil ⊥
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