Archive for May, 2009

Loops in Ocaml

Following on from my look at basic looping syntax in various languages I thought I’d take a look at various methods of looping in Ocaml to make amends for the Ocaml solution.

gcd is the same as in the previous post.

let rec gcd a b =
  if b = 0 then a
  else gcd b (a mod b);;

Using one function for one loop is nicer than cramming both into one which felt too much like coding using if and goto.

Most of the solutions use the following recursive function.

let count_for_denom denom =
  let rec loop num count =
    if num >= (denom/2+1) then count
    else loop (num+1) (count + if gcd num denom = 1 then 1 else 0)
    loop (denom/3+1) 0;;

The first solution is a pure recursive function. This is really just mental masturbation – needlessly exchanging loops for more verbose recursion.

let solve_it max_denom =
  let rec loop denom count =
    if denom > max_denom then count
    else loop (denom+1) count+count_for_denom denom
    loop 5 0;;

Printf.printf "%d solutions\n" (solve_it 10000);;

$ time ./a.out
XXX solutions

real    0m1.138s
user    0m1.108s
sys     0m0.000s

Functional programming includes a bunch of higher level functions such as map and fold. In a strict language it would be wasteful to construct a list before iterating over it with one of these higher-order functions.

How about a fold-like function that folds over a range of numbers?

let collector s e acc f =
  let rec loop s acc =
    if s > e then acc
    else loop (s+1) (f acc s)
  in loop s acc;;

Printf.printf "%d solutions\n"
  (collector 5 1000 0 (fun acc denom -> acc+count_for_denom denom));;

Here is one with a reference and a for next loop. I think this is quite nice – I like that Ocaml is a pragmatic language and includes this kind of stuff.

let count = ref 0 in
  for i = 5 to 1000 do
    count := !count + count_for_denom i
  Printf.printf "%d solutions\n" !count;;

And finally the pure nested for loop solution which is about 20% faster than the recursive versions.

let count = ref 0 in
  for i = 5 to 10000 do
    for j = (i/3+1) to (i/2) do
      if gcd i j == 1 then count := !count + 1
  Printf.printf "%d solutions\n" !count;;

$ time ./a.out
XXX solutions

real    0m0.934s
user    0m0.928s
sys     0m0.004s

So, is there anything I missed? What other types of loops are there in Ocaml?


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Okay, this post is going to be quite long. I’m going to start with a basic problem I was solving in emacs lisp. From there I’ll segue into thinking about looping syntax and finally I’ll do a bit of benchmarking as I’ve got the code already and people seem to like that (the scheme, ocaml, c++ speed comparison is by far the most popular post on this blog followed by this).

Futzing around with Project Euler is something I do for fun. Most recently I was looking at problem 73 – count the reduced proper fractions with a denominator less than or equal to 10,000 between 1/3 and 1/2.

Emacs Lisp Solution

Emacs Lisp is usually my default language for doing this kind of thing as I’m already in my text editor and there is a REPL to experiment with.

First of all, it is clear that I’m going to need a function to calculate the greatest common divisor. I found an imperative Pascal implementation of Euclid’s algorithm here. A brief aside – I searched for Pascal deliberately as I generally find it very clear. Does anyone else do that?

(defun gcd (a b)
  (while (not (= b 0))
    (let ((tmp b))
      (setq b (% a b))
      (setq a tmp)))

Thinking ahead, I’ll probably know what the gcd is before we call make-fraction as only fractions with a gcd of 1 will be actually counted amongst the solutions. I’ve therefore made gcd an optional parameter as a nod to efficiency.

(defsubst make-fraction (num denom &optional gcd)
  (unless gcd (setq gcd (gcd num denom)))
  (cons (/ num gcd) (/ denom gcd)))

I like the flexibility that lisp-like languages give you to name your functions too.

(defsubst more-than-1/3 (frac)
  (let ((num (car frac))
        (denom (cdr frac)))
    (> (* num 3) denom)))

(defsubst less-than-1/2 (frac)
  (let ((num (car frac))
        (denom (cdr frac)))
    (< (* num 2) denom)))

(defsubst within-range (frac)
  (and (more-than-1/3 frac) (less-than-1/2 frac)))

We only check fractions between 1/3 and 1/2 as to do all fractions with a denominator <= 10,000 would take far too long.

(defun solve-it (max-denom)
  (insert (format-time-string "\n\nStarted at: %H:%M:%S\n\n"))
  (let (num denom frac max gcd solutions)
    (setq solutions 0)
    (setq denom 2)
    (while (<= denom max-denom)
      (setq num (/ denom 3))
      (setq max (1+ (/ denom 2)))
      (while (<= num max)
        (setq gcd (gcd num denom))
        (when (= gcd 1)
          (setq frac (make-fraction num denom gcd))
          (when (within-range frac)
            ;; (insert (format "%s\n" frac))
            (incf solutions)))
        (incf num))
      (incf denom)
      (when (= (% denom 50) 0)
        (insert (format "Denom: %d Solutions: %d\n" denom solutions)))
      (sit-for 0))
    (insert (format "\n%d solutions\n" solutions))
    (insert (format-time-string "Finished at: %H:%M:%S\n"))))

After I wrote this, I realised I didn’t need to construct and destruct my fraction type so simplified to the following:

(defun solve-it (max-denom)
  (insert (format-time-string "\n\nStarted at: %H:%M:%S\n"))
  (let (num denom frac max solutions)
    (setq solutions 0)
    (setq denom 5)
    (while (<= denom max-denom)
      (setq num (1+ (/ denom 3)))
      (setq max (/ denom 2))
      (while (<= num max)
        (when (= (gcd num denom) 1)
          (incf solutions))
        (incf num))
      (incf denom))
    (insert (format "%d solutions\n" solutions))
    (insert (format-time-string "Finished at: %H:%M:%S\n"))))

(solve-it 10000)

;; Started at: 22:14:35
;; 5066251 solutions
;; Finished at: 22:15:45

70 seconds. Okay.

The most annoying thing is the primitive looping constructs. while is the basic and obvious built-in. It also has a slew of macros beginning with doXXX including dotimes and dolist not to mention the mighty common lisp loop macro.

I don’t know loop (but I’m going to learn it), but after messing about with do* for a few minutes, I realised it wasn’t the looping construct for me.

(do* ((i 5 (if (> j 10) (+ i 1) i))
      (j (+ i 1) (if (> j 10) (+ i 1) (+ j 1))))
    ((> i 10))
  (insert (format "[%d %d]" i j)))


Now, the great thing about lisp is supposed to be that if you don’t like the syntax you can add your own with macros. Unfortunately, I haven’t got around to that yet as a bunch of people have already designed most of the syntax I like.

Scheme Solution

When I read some of the earlier posts on this blog, it seems that scheme has got some nice generator syntax (aka eager comprehensions) for handling nested loops.

There are a nice set of posts on eager comprehensions here.

I took print-ln from the portable scheme post and gcd from SICP.

#lang scheme/base

(require srfi/42)

(define (print-ln . args)
  (for-each display args)

(define (gcd a b)
  (if (= b 0) a
      (gcd b (remainder a b))))

(define (solve-it max-denom)
  (sum-ec (:range denom 2 (+ max-denom 1))
          (:range num (+ (floor (/ denom 3)) 1) (ceiling (/ denom 2)))
          (if (= (gcd num denom) 1) 1 0)))

(print-ln "There are " (solve-it 10000) " solutions")

Yikes, mzscheme is much quicker than emacs-lisp. That surprised me. A factor of 10 I would have expected, a factor of 50 not so much.

$ time mzscheme frac.scm
There are XXX solutions

real    0m1.413s
user    0m1.404s
sys     0m0.004s

Perl Solution

use strict;
use warnings;

use POSIX qw(floor ceil);

sub gcd
    my ($n1, $n2) = @_;
    until ($n2 == 0) {
        my $tmp = $n2;
        $n2 = $n1 % $n2;
        $n1 = $tmp;
    return $n1;

The nested loop actually looks okay to me in perl although not as nice as the srfi-42 eager comprehensions.

sub solve_it
    my $max_denom = $_[0];
    my $solutions = 0;
    foreach my $denom (5..$max_denom) {
        my $max = ceil($denom / 2) - 1;
        foreach my $num ((1 + floor($denom / 3))..$max) {
            if (gcd($num, $denom) == 1) {
    return $solutions;

printf "There are %d solutions\n", solve_it(10000);

The performance of my perl is pretty bad too.

$ time perl frac.pl
There are XXX solutions

real    0m47.026s
user    0m46.963s
sys     0m0.008s

Ocaml Solution

let rec gcd a b =
  if b = 0 then a
  else gcd b (a mod b);;

let solve_it max_denom =
  let rec loop num denom solutions =
    if denom > max_denom then solutions
    else if num >= (denom/2+1) then
      loop ((denom+1)/3+1) (denom+1) solutions
    else begin
      if gcd num denom = 1 then begin
        (* Printf.printf "%d/%d\n" num denom; *)
        loop (num+1) denom (solutions+1)
      end else
        loop (num+1) denom solutions
    loop ((5/3)+1) 5 0;;

Printf.printf "There are %d solutions\n" (solve_it 1000);;

Oh dear, I seem to have an awful accent when programming ocaml. I’ll need to work on that.

$ time ./a.out
There are XXX solutions

real    0m1.071s
user    0m1.060s
sys     0m0.004s

So, Conclusions

For this particular task (looping and integer math) Emacs Lisp is slow, but not that slow compared with another scripting language. I really like the scheme looping constructs and mzscheme is surprisingly quick (again, just for this tiny thing), not too far from the ocaml – although again I should emphasise that the ocaml is a terrible hack. And finally, I need to learn how to use loop properly.

All comments welcome.

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Useful Blog Comments

Nachopp demonstrates some emacs lisp that inserts a commonly used find command in a shell buffer. And Ian Eure has a great follow-up comment which demonstrates the more typical way of defining emacs lisp functions; talks about alternatives such as abbrev mode and yasnippet and finally mentions the best solution, the built-in rgrep.

Defining C++ styles

David Ha has a gallery of some of the built-in C++ styles. None of the styles suit me exactly so I have accreted a fair amount of C++ configuration code over the years. I must admit, I haven’t audited for ages so I’m not sure which bits are necessary and which are not.

(defconst *my-cc-style*
  '((c-basic-offset . 4)
    (c-comment-only-line-offset . 0)
    (c-hanging-braces-alist . ((brace-list-open)
                               (substatement-open after)
                               (block-close . c-snug-do-while)))
    (c-cleanup-list . (brace-else-brace))
    (c-offsets-alist . ((statement-block-intro . +)
                        (knr-argdecl-intro     . 0)
                        (substatement-open     . 0)
                        (substatement-label    . 0)
                        (innamespace           . 0)
                        (case-label            . +)
                        (statement-cont        . +)))))

(defun my-c-initialization-hook ()
  (define-key c-mode-base-map "\C-m" 'c-context-line-break)
  (define-key c-mode-base-map (kbd "RET") 'newline-and-indent)
  (define-key c-mode-base-map [f7] 'run-compile))

(add-hook 'c-initialization-hook 'my-c-initialization-hook)
(setq c-offsets-alist '((member-init-intro . ++)))

(c-add-style "PERSONAL" *my-cc-style*)

(defun my-c-mode-common-hook ()
  (c-set-style "PERSONAL")
  (setq tab-width 4
        indent-tabs-mode nil
        c-hungry-delete-key t)
  (c-toggle-auto-newline 1))

(add-hook 'c-mode-common-hook 'my-c-mode-common-hook)

The most useful commands for finding out which of the variables to set are C-c C-o (c-set-offset) and C-c C-s (c-show-syntactic-information)

This is kinda interesting where Ronnie Collinson (from the NotThinking blog)
removes the *compilation* buffer if the compile is successful. It isn’t something I personally would use as I like the feedback, but I wasn’t previously thinking about compilation-finish-functions and I have a few ideas of things I would like to run after a successful compile.

Perennial Emacs Blog Topics

There are a few perennial blog topics in the emacs world – I mentioned a smooth scrolling post in my links from 2009/17 and here is Da Zhang’s take (does anyone like the default behaviour by the way?). I included a link to a post on the incredibly useful mark ring in emacs-links-2009-09 and here is another from yesterday.

Proposed solutions – fix the smooth scrolling behaviour so it works nicely out of the box and… well, perhaps blogs are not a great way of educating the masses after all. Pity.

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Some time ago, I wrote about doing batch processing of text with an external process running, e.g. Perl. Similarly, emacs-lisp has a lot of functionality for manipulating text.

The Problem

I have a file like this:

John James,Admin,other data,...
Dave Jones,Sales,...
Lisa Sims,IT,...

I want to convert it into the following1:

AND name IN ("Dave Jones", "John James", "Lisa Sims")
AND dept IN ("Admin", "IT", "Sales")

The Solution

First of all I need a helper function that converts lisp lists into a quoted comma-separated list.

(defun make-csv (seq)
  (mapconcat (lambda (e) (format "\"%s\"" e)) seq ", "))

And then I can iterate over the text with re-search-forward, collecting the matched strings. At the end, I’ll output the collected strings. in a sql clause fragment.

(defun process-lines (&optional begin end)
  (interactive "r")
  (goto-char begin)
  (let (names depts)
    (while (re-search-forward "\\([^,]+\\),\\([^\n,]+\\)" end t)
      (push (match-string 1) names)
      (push (match-string 2) depts)
    (insert (format (concat "\n"
                            "AND name IN (%s)\n"
                            "AND dept IN (%s)\n")
                    (make-csv (sort names #'string-lessp))
                    (make-csv (sort depts #'string-lessp))))))

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1. Okay, you got me, I don’t really want to convert it into this. But for the purpose of the example, this will do. Exercise for the reader – how can I convert it into sql that will efficiently extract just the lines I want?

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When writing a muse file it always annoyed me when I have written (for example) a-really-long-variable somewhere else in the file and then when I type =a-rea and press M-/ it fails to expand.

The way to fix this behaviour is by setting dabbrev-abbrev-skip-leading-regexp

(setq dabbrev-abbrev-skip-leading-regexp "[=*]")

(Edit: fixed the first regex per Billy’s comment below. Thanks)

Okay, you think, this doesn’t affect me – I don’t use muse (why not?) How about if you’re writing some html/xml.

(setq dabbrev-abbrev-skip-leading-regexp "[^ ]*[<>=*]")

Now <strong>long-word- completes as you would expect.

There is also dabbrev-abbrev-char-regexp if you want even more control over what should be considered a match.

Also, I’m no longer using autocomplete as I find vanilla dabbrev nicer to use.

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A little while ago we were talking about clients and servers. And I’ve finally got back to the interesting thing which is playing with emacs networking.

The comment from Gabriel nicely pointed out emacs’ low-level socket facilities.

(open-network-stream) which is synchronous and
(make-network-process) which can be asynchronous if the parameter is set. I haven’t been able to make the last one work, but check it out yourself.

So, er, I’m not 100% sure how to simulate a crappy internet connection. Maybe making my server pause 2 seconds between line reads will be sufficient.

sub process_request
    while () {
        print STDERR "Received [$_]\n";
        last if /quit/i;
        sleep 2;

I’m also interested (or perhaps curious?) in when the connection is made and broken.

sub post_accept_hook
    print STDERR "Accepted new connection\n";

sub post_process_request_hook
    print STDERR "Client disconnected\n";

Did I mention I think Perl’s bad press is a little unfair?

So what I need now is a basic API for connecting, disconnecting and sending messages. make-network-process makes a process as you can probably infer from the name and for my purposes a single client is enough so I make a wrapper to get the current process. Layering in this way means I can add any error handling at the appropriate point later on. And also it should be fairly easy to generalise client-process to choose between different connections.

(defconst client-process-name "*client*")
(defsubst client-process () (get-process client-process-name))

For maximum asynchronicity we add a sentinel function that will be called back when the connection has completed, either successfully or unsuccessfully.

It turns out that a perl-style chomp function is really handy!

(defun chomp (str)
  (if (and (stringp str) (string-match "\r?\n$" str))
      (replace-match "" t nil str)

(defun client-notify-connect (&rest args)
  (message (format "Connection message [%s]" (mapcar #'chomp args))))

I added a fairly hacky (sit-for 1) after opening the client as otherwise I could send messages before it was ready due to the sentinel and nowait. Future versions will probably get the sentinel to set an "opened" variable which will determine whether the send message and close functions work.

(defun client-open (host port)
  (make-network-process :name client-process-name
                        :host host
                        :service port
                        :nowait t
                        :sentinel #'client-notify-connect)
  (sit-for 1))

Closing the connection is a simple matter of deleting the process. I confirmed this against my test perl server.

(defun client-close ()
  (delete-process (client-process)))
(defun client-send-string (str)
  (process-send-string (client-process) (concat str "\r\n")))

My test program simply sends 10 hello messages to the server at the same time as inserting 10 hellos in the buffer. The fact that the buffer insertions completed almost instantaneously whereas the server took around 20 seconds to display the messages indicates there is some degree of separation.

  (client-open 'local 8080)
  (dotimes (var 10)
    (client-send-string (format "Hello %s" var))
    (insert (format "Hello %s\n" var)))

Next time I’ll look at setting up a filter to receive messages that the server sends back. Any questions or comments let me know.

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A few weeks ago when I was talking about autocomplete and dabbrevone of my commenters asked if I had tried hippie-expand. My response was no, but I should take a look as it might allow me to input buffer names more quickly which is something I often need to do.

Following the recipe from the emacs wiki, I tried this:

(global-set-key [(meta f5)] (make-hippie-expand-function
                               try-complete-file-name) t))

After some experimentation, the limitation is obvious. I usually want to complete the entire filename including the path but I can’t remember what the path begins with.

The next thing I thought about was removing *Messages* and *Buffer List* from dabbrev-ignored-buffer-names. Unfortunately, I still need to complete from the beginning of the path but this is generally useful so I’m going to keep it. Really, I want to be able to select any part of the filename and complete from that. Sounds like a job for ido.

First I need a method that returns all buffer names and filenames.

(defun get-files-and-buffers ()
  (let ((res '()))
    (dolist (buffer (buffer-list) res)
      (let ((buffername (buffer-name buffer))
            (filename (buffer-file-name buffer)))
        (unless (string-match "^ *\\*.*\\*$" buffername)
          (push buffername res))
        (when filename (push filename res))))))

Then I can use ido to select between them which is perfect.

(defun insert-file-or-buffer-name (&optional initial)
  (let ((name (ido-completing-read "File/Buffer Name: "
                                   nil nil initial)))
    (when (and (stringp name) (> (length name) 0))
      (insert name))))

(global-set-key (kbd "<f2> i b") 'insert-file-or-buffer-name)

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