cl-num-utils and utf8

I find Unicode math symbols very useful for mixing a bit of math and text — even though they don't even begin to approach the flexibility of LaTeX, all editors and browsers should be able to render them by now. When writing Lisp code, I only use them in docstrings. For example, cl-num-utils contains comments like this:

(defclass interval/infinite-left ()
  ()
  (:documentation "Left endpoint is -∞."))

Anton Vodonosov has recently reported that this causes a problem when the default external format is not utf8, also suggesting that I include an :encoding clause in the system definition. I have just pushed this change and I hope that this fixes the issue for everyone.

I appreciate the work Anton and others have put into cl-test-grid. I usually use a single implementation (the latest released SBCL), but I strive to make my code compatible with all implementations. This is much easier to achieve with cl-test-grid.

Chebyshev polynomials in cl-num-utils

I just pushed an update to the cl-num-utils repository, merging a branch which implements function approximation with Chebyshev polynomials.

For example,

(defun myfun (x)
  "Function that we want to approximate."
  (expt x -2))

(defparameter *myapprox* (chebyshev-approximate #'myfun (interval 2 10) 8)
  "Chebyshev approximation for MYFUN on the interval [2,10], using 8 Chebyshev
  polynomials.")

(myfun 5d0)            ; 0.04d0
(funcall *myapprox* 5) ; 0.04018023309369832d0

Approximation with Chebyshev polynomials is very fast and stable because it does not require a matrix inversion (Chebyshev polynomials are orthogonal), and thus it is a very nice procedure if you want to approximate a "smooth" function that is expensive to evaluate.

I also extended the interval code in cl-num-utils, now it handles open and infinite endpoints. This extension is experimental and not all functions understand it at the moment, but you can use my new extended-reals library to denote infinites, for example

(chebyshev-approximate #'sqrt (interval 0 (xr:inf)) 10)

would approximate \(x\mapsto\sqrt{x}\) on \([0,\infty)\). I will blog about extended-reals soon.

updates to let-plus

I have just pushed some updates to the let-plus Github repository. The most important change is the handling of ignored values — let+ used to ignore nil, for example

(let+ (((a nil b) '(1 2 3)))   ; OLD SYNTAX, NO LONGER VALID
  ...)

would ignore the second element of the list. The implementation of let+ would simply replace nil with gensyms in the AST and declare them ignored. This caused some unexpected problems, for example in

(let+ (((a nil &optional (c nil c?)) '(1 2 3))) ; OLD SYNTAX, NO LONGER VALID
  ...)

nil is a value, not a placeholder for a variable. I could have extended let+ to work handle this, but that would have required destructuring the lambda lists internally instead of simply relying on destructuring-bind. Being lazy, I decided to change the syntax. From now on, users should use &ign to ignore variables. For example,

(let+ ((#(a &ign b) (vector 1 2 3)))
  (list a b)) ; => (1 3), no warning about the middle element not being used

The change is incompatible with the previous version (nil is no longer understood as being ignored and will most likely cause an error during macroexpansion), so you need to update your code if you are using let+. I am sorry about any inconvenience this may cause.

I also extended let+ to understand nesting in more places (when applicable, mostly for read-only forms). For example,

(let+ (((&slots-r/o ((&complex a b) bar))
        (make-instance 'foo :bar (complex 1 2))))
  (list 1 2)) ; => (1 2)

As usual, bug reports are welcome.