HyperScience

Org-mode Signature Code

I’ve been trying to learn a little elisp lately, and have written a useful routine that I thought someone might like. It’s interesting because it uses both elisp and org-mode tables.

Lately I have been setting up mu4e to read my personal email. As part of using that I wanted to have a signature that would generate a wise saying from a country, but to make it a bit more interesting I wanted the signature to choose a randomly selected saying from a different country each time I generated the signature.

I have an org-mode file that contains a two-column table. The first column contains the country and the second contains the quote.

#+NAME: SayingsTab
| Afghanistan           | Don't show me the palm tree, show me the dates                                      |
| Afghanistan           | No one says his own buttermilk is sour                                              |
| Afghanistan           | What you see in yourself is what you see in the world                               |
| Africa                | The tree that has been axed will never forget                                       |
| Albania               | Don't put gold buttons on a torn coat                                               |
| Albania               | Patience is the key to paradise                                                     |
| Albania               | When you have no companion, consult your walking stick                              |
| Algeria               | Do bad and remember, do good and forget                                             |
| America               | A pessimist is a person who has lived with an optimist                              |
| Armenia               | You cannot start a fast with baklava in your hand                                   |
| Australia             | There are none so deaf as those who will not hear                                   |
|-------------------------------------------------------------------------------------------------------------|
#+name: quote
#+begin_src elisp  :exports results :var sayings=SayingsTab
	(defun genquote()
      "Generate a random quote from an org-mode table.
  The table contains the country name in col 0 and the quote in col 1.
  Add more quotes to the table as needed, the function
 selects from the current number of rows."
	(interactive)
   (let ((selection  (nth (random (length sayings)) sayings)))
	  (message "As they say in %s, \"%s\"." (car selection) (cadr selection))))
   (genquote)
#+end_src

Running the source block here generates a random quote from the list in the table as a message. Hitting C-c C-c in the code will run it and generate a quote like

As they say in America, "A pessimist is a person who has lived with an optimist".

I like using the org-table because the new items can be sorted alphabetically, and its easy to add new sayings when I find them.

What I’d like to be able to do is to load the org table using an elisp function and then do the same thing as part of a signature-generating function. Currently I can’ do that, but I can read the text from a tab-delimited text file. Fortunately, I can generate the tabular data that can be read by elisp by putting the point at the table and using the M-x org-table-export command. I save the table to a tab-delimited file called sayings.txt whenever I add to the org-table.

Then in my init.el file, I define the following elisp function to generate an email signature using the data in the text file.

(defun signature()
   "Generates a random quote from a tab-delimited file for use as an email signature quote. 
	       Table of quotes is in ~/ownCloud/Org/sayings.txt
	       The tab-delimited table contains the country name in col 0 and the quote in col 1.
	       Add more quotes to the table as needed, the function
	       selects from the current number of rows."
   (interactive)
   (setq sayings (read-lines "~/ownCloud/Org/sayings.txt"))
   (setq sel (nth (random (length sayings)) sayings))
   (insert "\n-- \n" "John Doe \n \n" "john.doe@google.com \n" "Ph: 867 5309 \n")
   (insert "As they say in ")
   (insert (remove-trailing (car (split-string sel "\t" t))) ", '")
   (insert (remove-trailing (cadr (split-string sel "\t" t))) "'. \n")
   )

This should produce something like

-- 
John Doe 
john.doe@google.com 
Ph: 867 5309 
As they say in Malaysia, 'One buffalo brings mud and all the herd are smeared with it'. 

where the last line is the randomly generated quote. So then, when I’m editing my email, I just need to call the signature function when editing an email in mu4e and I get my signature with a new quote every time.

If you know how to read direct from the org-table, rather than from a text file, I’d love to know how you do it, as that would remove the need to update the table from time to time.

Maxima and IMaxima on Emacs

Sometimes (actually less frequently than I should) I try to do some maths. I tend to do more of it in teaching than in my research, as my research is mostly experimental and usually I’m using someone else’s maths. Most of my research calculations are numerical, and J works really well and efficiently for these sorts of things. However sometimes you need to use analytical maths, and when that happens and you forget the calculus you learned as an undergraduate, then computational algebra systems (CAS) can be very useful.

Probably the most well known CAS is mathematica, which became popular at the time when Macintosh GUI-based applications were coming out, but mathematica was at least in part the outgrowth of existing primarily text-based CASs such as Macsyma, Derive and others. Many of these started their lives as commercial packages, but were either discontinued because of mathematica’s dominance of the commercial space (like MathCad, which I used during my PhD) or were open-sourced. There are several open-source CASs around now, with the most common being maxima, SageMath and Fricas. Here I’m going to be talking about maxima.

Maxima is a descendent of Macsyma, a lisp-based CAS first written in the 1960s and released into the public domain. I have chosen this CAS, as it has good hooks into emacs, in particular a nice plugin that is part of the maxima package called imaxima.

There is another package called wxmaxima that contains a GUI interface to maxima, and many people use this because it has lots of nice icons and is easy to use. However, as an emacs user, I prefer to use the maxima REPL within an emacs buffer, and fortunately maxima comes with a file imaxima.el that allows all the power of maxima to be available from an emacs buffer.

Installation

First, install maxima itself. On linux systems, use your favourite package manager (eg apt on Debian systems). In my case, I use Manjaro, so I use pacman as the package manager. You can see the maxima-based packages using

pacman -Ss maxima

This produces

extra/maxima 5.46.0-2 [installed]
    A sophisticated computer algebra system
extra/maxima-ecl 5.46.0-2 [installed]
    ECL backend for Maxima
extra/maxima-fas 5.46.0-2
    Maxima FAS module for ECL
extra/maxima-sbcl 5.46.0-2 [installed]
   SBCL backend for Maxima

on my system. As I use sbcl, maxima-sbcl provides a back-end for that Lisp interpreter. Installation on my system is done typing

pacman -S maxima maxima-ecl maxima-sbcl

on the command line.

If you have the locate command installed (it can also be installed via pacman on Manjaro) then after typing

sudo updatedb

on the command line, followed by

locate imaxima.el

produces

/usr/share/emacs/site-lisp/maxima/imaxima.el

as an output. Then, to install imaxima, I put the following lines in my init.el file

;-----------------------------------------------------------------------
; imaxima - interactive computational algebra system
;-----------------------------------------------------------------------
(push "/usr/share/emacs/site-lisp" load-path)
(autoload 'imaxima "imaxima" "Maxima frontend" t)
(autoload 'imath "imath" "Interactive Math mode" t)
(setq imaxima-fnt-size "Large")

You may need to change the path based upon your locate command. These commands run the imaxima and imath functions that allow interactive use of imaxima and inline insertion of latex-quality equations in the output.

Examples

Once installed, typing M-x imaxima starts the interactive shell for imaxima. I’m not even going to try to make a maxima tutorial here, as there are already several available. Figure 1 contains an example of calculation of normal unit vectors for a vector function at a given location. Note that the equations are nicely typeset.

imaxima.png

Figure 1: Maxima session showing vector calculations

And of course no demo would be complete without the arbitrary plotting of a pretty 3D function, in this case a hyperboloid.

MaximaFuncPlot.png

Figure 2: Maxima with pretty plot

The M-x maxima command also works if the maxima package is installed (see next section), but the output is in text form, which is not as aesthetically appealing. The text below is the equivalent maxima output to that in Figure 1 for imaxima.

(%i92) r(t) := [t, cos(t), sin(t)];
(%o92)                    r(t) := [t, cos(t), sin(t)]
(%i93) limit(r(t), t, 2, plus);
(%o93)                        [2, cos(2), sin(2)]
(%i94) limit(r(t), t, 3, minus);
(%o94)                        [3, cos(3), sin(3)]
(%i95) diff(r(t), t);
(%o95)                       [1, - sin(t), cos(t)]
(%i96) define(rp(t), diff(r(t), t));
(%o96)                  rp(t) := [1, - sin(t), cos(t)]
(%i97) load(eigen);
(%o97)          /usr/share/maxima/5.46.0/share/matrix/eigen.mac
(%i98) uvect(rp(t));
                     1                           sin(t)
(%o98) [---------------------------, - ---------------------------, 
                2         2                    2         2
        sqrt(sin (t) + cos (t) + 1)    sqrt(sin (t) + cos (t) + 1)
                                                            cos(t)
                                                   ---------------------------]
                                                           2         2
                                                   sqrt(sin (t) + cos (t) + 1)
(%i99) trigsimp(%);
                             1       sin(t)   cos(t)
(%o99)                   [-------, - -------, -------]
                          sqrt(2)    sqrt(2)  sqrt(2)

It does the job, but the text is harder to read, at least for me, than the nicely typeset output.

Other Computer Algebra Systems

In addition to imaxima, there is a package on ELPA called maxima, which installs a major mode for editing maxima files. Also there is an interface to the Fricas CAS, called Frimacs, which I have not used, but which is worth investigating. Fricas is descended from Axiom, another commercial CAS, and is apparently strong at automatic integration of functions.

Conclusion

There is no question, these CASs can be very useful, either for learning algebra and calculus, or for using them in mathematics, physics and engineering applications. They can be used for anything from a simple calculator alternative (although M-x calc is much better for this) to a solver of integrals, derivatives and linear algebra problems, and for plotting of functions. Often the output of calculations is not simplified in the way one might expect when doing it by hand, but there are simplifying commands that can get around those limitations. It’s also a great tool when I can’t remember my integration techniques. I’ll be trying to use it more in my maths calculations in future now that it’s set up.

General Forth Words for GPIO On The STM32F103

This blog entry goes into the design of a Mecrisp Forth wordset that allows you to program the GPIO ports. This is typically one of the first things one learns to do on a microcontroller, and is usually taught by getting one or more LEDs to flash. We will hook up LEDs to the PC10 and PC8 pins of the STM32P103 board and write some code to get them to flash.

If one were to write a code to do this in an algol-derived programming language like C or the C-like language used in the Arduino programming environment, one would usually write code that involves calls to built-in libraries. For an Arduino, the code might look something like:

#define LED PC10
void setup() {
  // initialize digital pin LED_BUILTIN as an output.
  pinMode(LED, OUTPUT);
}
 
// the loop function runs over and over again forever
void loop() {
  digitalWrite(LED, HIGH);   // turn the LED on (HIGH is the voltage level)
  delay(200);                       // wait for 200 ms
  digitalWrite(LED, LOW);    // turn the LED off by making the voltage LOW
  delay(200);                       // wait for 200 ms
}

This code sets up port C pin 10 in the function setup as an output using a function called pinMode, and uses a separate function loop which, in turn, calls a function called digitalWrite to set the pin to high or low with a delay set by a call to the function delay, in this case of 200 ms. One may also need a function to turn on the clock to port C if it can’t already be assumed to be on.

Presumably one would include calls to these functions within a loop in a function main to complete the program. This is not too difficult to follow, if you ignore all the infrastructure like semicolons and explicit type declarations. And it’s nice to be able to call these pre-built functions, provided you can remember the function name someone else decided upon, and that you don’t want to do things that are not catered for in the function. For example, the pinMode function does not have an input parameter that allows you to set the clock speed of the GPIO pins, which is an option that is available on the chip. Of course you could write your own pinMode function, but perhaps other functions in the library would use the original pinMode function with a different clock speed. Because you didn’t write the code, you don’t easily know what was done in the library.

Forth encourages programmers to look at a problem like this differently. Rather than forcing the programmer’s application to always look like the syntax of the programming language, Forth makes it very easy for a programmer to make words that define a domain-specific language that is tailored to solving that particular problem. By combining the concept of the dictionary and the implicit passing of parameters on the stack, this domain-specific language can be made to look like a set of commands to the microcontroller that are set up to control any GPIO port. And with a little thought, they can be made quite general.

Pre-reading

Before we can make the generalised GPIO words, we need to make some words that allow us to save bit patterns to registers without changing the remaining bits in those registers. These nondestructive bit setting and resetting words were introduced previously here in a previous blog entry. It’s best to go through that and make sure you understand those words before going any further.

How to control GPIO

To get a GPIO port working you need to do three things:

  • Turn on the clock
    • This is done using the RCC_APB2ENR clock enabling register
  • Set the pin on the port to be an input or an output
    • This is done using the GPIOx_CRL (for pins 0-7 on a given port) or GPIOx_CRH (for pins 8 through 15).
  • Write or read the value of the bit(s) we are interested in, i.e.
    • Set or reset the bit in the GPIOx_ODR register to turn an output on or off, or
    • Read the value of the pin in the GPIOx_IDR register if you want to know if an input is on or off.

GPIO Registers and Where to Find Them

One of the neat things about the design of the registers in the STM32F103 chip is that each of the GPIO ports is separated by a consistent offset ($400) and each of the control registers for any port is at the same offset from the base address of that port. This consistency means that we are able to write generalised words that can be used to set any aspect of the behaviour of any of the GPIO pins on any of the ports.

The GPIO ports in the STM32F103 have addresses that can be found in the STM32F103 reference manual, in Section 3.3. All of ports A through E are in consecutive peripheral base addresses, as shown in the table below:

Port Base Address
A $4001 0800
B $4001 0C00
C $4001 1000
D $4001 1400
E $4001 1800

Each of these ports will have several registers, separated by 4 bytes from each other, that control the behaviour of these registers. In our GPIO library we will concentrate only on the most used of these registers, though once you know how to make the words, it will be easy to add words to change the other registers if necessary.

For the GPIO control we are interested in, we will be setting values in the registers GPIOx_CRL, GPIOx_CRH, GPIOx_IDR and GPIOx_ODR. Although there are other registers such as the GPIOx_BSRR set/reset register and the GPIOx_LOCKR lock register, I don’t use them, so won’t be using them in this wordset. I have also avoided the AFIO alternate function registers here, because we will come to them when using the timers later on.

In addition to the GPIO registers we also add the port clock setting register, RCC_APB2ENR that controls the clock of the five ports. By default, my Mecrisp has ports A, B and C switched on, so I don’t tend to set it. But for the sake of the exercise we will provide words that use that clock control register as well to turn on the ports.

Domain-specific Language Design

Before writing a Forth code, I like to imagine how I would call the words to operate the GPIO. This gives me a starting point for the implementation of the wordset itself, because I then know what the final words should look like. I would like to be able to use the same words to control any of the ports, which means that I would need to have a word that indicates the base address of the port, with words like GPIOA, GPIOB etc returning the base addresses of those ports. This allows me to write words that permit commands like GPIOA enable to enable the clock for GPIO port A.

Control commands based upon words like this would look something like

GPIOC enable  	\ enable port C
GPIOC 10 ppout 	\ set port to push-pull output (50 MHz)
GPIOC 10 GPon	\ turn on GPIOC pin 10
GPIOC 10 GPoff	\ turn off GPIOC pin 10

Words like this can then be included in more complex words such as lflashes to flash a particular pin a certain number of times

GPIOC 10 20 lflashes	\ flash GPIOC pin 10 20 times

and extended to do still more complex things like running light displays, all building upon these primitive port control words. At this point it’s worth comparing the Forth control method with the Arduino code at the start of this blog entry. Once the words have been made, the Forth code produces a direct command language available to the Forth user that looks a little like Forth, but a lot like a language designed to control GPIOs (albeit with an infix way of inputting data). In contrast, the Arduino code always carries the baggage of looking like the programming language it was implemented in. This is, I think, one of the strongest arguments for the use of Forth as a programming environment for microcontrollers. For some, the fact that the Arduino code always looks consistent with other Arduino code is an advantage because only one syntax needs to be learned. I have always thought the Forth way of doing things is cleaner-looking when done properly.

Building the Wordset

Now that we know the way we want to control the GPIO, we need to make words that allow us to develop those words. In other words, we are designing the application from the top down and implementing from the bottom up, once we know what the top-level words look like.

Initialising the Port(s)

The initialisation word switches on the clock for the port. This is done by setting bits in the RCC_APB2ENR register, shown in Fig. 1.

RCC_APB2ENR.png

Figure 1: RCC_APB2ENR Register

This register contains the clock enable bits for a number of peripherals, including all the GPIO ports. Notice that GPIOA through GPIOG are all consecutive (although the STM32F103RBT6 in the Olimex STM32P103 board that I am using only has ports A through E).

So to turn on the clock for a given port, we need to set bit 2 for port A, bit 3 for Port B etc. Assuming we are using the port address as the alias for PortA etc, we need a way to convert the address to the offset. We use the fact that the port addresses are $400 apart to subtract the address from port A’s address, divide by $400 and add 2 to determine the bit position we need to switch on.

First, we make constants for the base addresses of each port and for the RCC_APB2ENR register:

\ Address locations
$40010800 CONSTANT GPIOA 
$40010C00 CONSTANT GPIOB
$40011000 CONSTANT GPIOC
$40011400 CONSTANT GPIOD
$40021018 CONSTANT RCC_APB2ENR

Now we make the enable and disable words that allow us to set or reset the clock for a given port using the set_bits word we declared in the previous blog entry on non-destructive bit setting:

\ Application words 
: enable ( aPort -- ) 
  GPIOA - $400 / 2 + 
  RCC_APB2ENR SWAP 
  1 1 ROT
  set_bits ;         \ Turn on the clock
: disable ( aPort -- ) 
  GPIOA - $400 / 2 + \ Set location to shift to 
  RCC_APB2ENR SWAP
  0 1  ROT
  set_bits ;         \ Turn on the clock

This allows us to use commands like GPIOA enable or GPIOC disable to enable or disable any of the ports. One should be careful about disabling whole ports, as sometimes these ports can be used for other peripherals. For example, USART1 is driven by pins on GPIO port A and switching that off may stop Forth from communicating with the terminal program!

Once we can enable the port, we next have to be able to determine whether a pin is an input or an output. To do this, we need to declare the positions of the control registers for this particular port. Because the designers of the STM32F103 were nice enough to make the control register offsets the same for all the ports, we can define the registers as offsets from the base address.

\ Register offset definitions
\ NB aPort is the address of the port (eg GPIOA, as defined above) 
: CRL ( aPort -- aPort + CRL ) ;
: CRH ( aPort -- aPort + CRH ) $04 + ;
: IDR ( aPort -- aPort + IDR ) $08 + ;
: ODR ( aPort -- aPort + ODR ) $0C + ;

Thus, the commands GPIOA ODR will provide the address of the output data register for GPIOA, and GPIOE ODR provides the equivalent address for GPIOE. This means that you don’t need to declare constants for each of the registers of each of the ports separately.

To set a particular pin of a particular port to be an input or an output. To do this, we must set 4 bits: 2 CNF bits and 2 MODE bits. These 4 bits are indexed by 4 bits per pin, stretched over 2 registers – GPIOx_CRL for pins 0–7 and GPIOx_CRH for pins 8–15. The two lower MODE bits determine whether the pin is an input or an output while the CNF bits outline what kind of input or output the pin is. The arrangement is shown in Fig. 2 for the CRH register.

GPIOx_CRH.png

Figure 2: GPIOx_CRH register

MODE GPIO type
00 Input
01 10 MHz output
10 2 MHz output
11 50 MHz output
CNF GPIO type
If input
00 Analog
01 Floating
10 Pull up/pull-down
11 Reserved
If output
00 General purpose push/pull
01 General purpose open drain
10 Alternate function push/pull
11 Alternate function open drain

Any given pin of any given port can be set with any combination of these 4 bits, depending on how the GPIO is to operate. To make this work in a general way, I have made a word called GPset that takes the port address, pin number and the 4-bit string from the table above and uses our non-destructive set-bits word to set the appropriate 4 bits in the CRL or CRH register. We can then make words describing the type of input or output that you would like that pin to be, using the bit pattern with the call to GPset. The GPset word must choose whether the CRL or CRH register must be written to, based upon the pin number on the stack. This is done with an IF ... ELSE ... THEN statement.

: GPset ( aPort pin# porttype -- )
  \ Set a pin to output
  \ porttype is a 4-bit pattern
  >R 
  DUP 7 >
  IF 7 - SWAP CRH SWAP ELSE 1+ SWAP CRL SWAP THEN     
  4 * 1-
  R> 4 ROT  set_bits  ;
: ppout     ( aPort pin# -- ) %0011 GPset ; 	\ Set port pin to push-pull output, 50 MHz
: ppout2MHz ( aPort pin# -- ) %0010 GPset ; 	\ Set port pin to push-pull output, 2 MHz
: afout     ( aPort pin# -- ) %1011 GPset ; 	\ Set port pin to AF output, 50 MHz
: ppin      ( aPort pin# -- ) %1000 GPset ; 	\ Set port pin to push-pull input
: ain       ( aPort oun# -- ) %0000 GPset ; 	\ Set port pin to analog input

We can then issue commands like GPIOC 10 ppout to set pin 10 of GPIO port C to a 50 MHz push-pull output, or GPIOB 8 ppin to set pin 8 of GPIO port B to an input.

Once we can switch the ports on or off and declare the type of input or an output for a given pin of a given port, all that remains is to read from (for an input pin) or write to (for an output pin) the port. The reading or writing are done with the lower 16 bits of the IDR (for inputs) or ODR (for outputs) register. Again, we use set_bits for the setting, but for the reading we use LSHIFT for reading the port, using bitwise AND to set all the other bits to zero, leaving either a true (for a 1) or false (for a 0) at the bit position of interest.

: GPon ( aPort pin# -- )
  \ Turn on a pin for an output port
  SWAP ODR SWAP %1 1 ROT set_bits ;
: GPoff ( aPort pin# -- )
  \ Turn off a pin for an output port
  SWAP ODR SWAP %0 1 ROT set_bits ;
: GPon? ( aPort pin# -- fl )
  \ Check to see if an input is switched on
  SWAP IDR @ 1 SWAP LSHIFT AND = ;

And that’s pretty much all that’s needed to get a general-purpose GPIO wordset working that allows bits to be manipulated as needed. The remainder of the file provides a demonstration of the operation of this wordset in making simple LED flashing words. Set up a red LED and a 220 Ohm resistor going from pin 8 and pin 10 to ground. The setup for pin 10 is shown in Fig. 3.

GPIOLED.png

Figure 3: Setup for LED on Pin 10 of GPIOC

The setup here is done with the port driving pin 8 and pin 10 directly from the port. The port outputs can sink enough current to drive a LED, though it’s probably better to connect the anode to the +3.3V supply on the board and the ground-connection to the port. If you connect the ports this way, you can drive more current as the port is sinking to ground.

The rest of the code provides words that can flash an LED a given number of times using the lflashes word, or can flash the two outputs using the alternate word. Note that lflash is built upon GPon and GPoff, lflashes and alternate are built upon lflash. The ms word used here employs a software loop to generate the delay for the pin flash. It’s set up for a 72 MHz clock speed, and the delay multiple scale may need to be changed for a lower value if the clock speed is lower. In a future post we’ll work out how to make a more accurate timing word using the STM32F103’s built-in timers, but this is sufficient for illustration. The comments at the end of the code show you how this domain-specific GPIO language can be used to control input and output ports.

I hope this short example shows you how Forth can take some very simple primitive words and develop a language specifically tailored to a particular interactive programming task. The full source is reproduced below.

\ GPIO General Access Wordset
\ This is an example of how you can use Forth to make a language for 
\ operating your GPIO ports on the STM32F103 processor
\ Note that this particular code only deals with setting an entire
\ high or low part of a port to an input or an output
\ Also note that the ms word is highly dependent on the clock speed
\ Note that these words can be used with any of ports A, B, C and D
\ and can configure any output.
\
\ Sean O'Byrne 03/2022
\ Code released under terms of the Gnu Public Licence Version 3

\ Address locations
$40010800 CONSTANT GPIOA 
$40010C00 CONSTANT GPIOB
$40011000 CONSTANT GPIOC
$40011400 CONSTANT GPIOD
$40021018 CONSTANT RCC_APB2ENR

\ Register offset definitions
\ NB aPort is the address of the port (eg GPIOA, as defined above) 
: CRL ( aPort -- aPort + CRL ) ;
: CRH ( aPort -- aPort + CRH ) $04 + ;
: IDR ( aPort -- aPort + IDR ) $08 + ;
: ODR ( aPort -- aPort + ODR ) $0C + ;

\ Utility words

: ones ( n -- %11..1 )
  \ Generate a binary number consisting of n 1s
  1 SWAP 1- 0 ?DO 2 * 1 + LOOP ;

: pos_shift ( nbits pos -- nbits shift# )
  \ Determines the number of bits to shift given the position of the MSB
  \ and the number of bits
  OVER - 1+ ;

: not_mask ( nbits shift -- shift mask )
  \ Generate mask consisting of 1s everywhere but where we want to
  \ change bits
  SWAP ones OVER LSHIFT NOT ;

: set_bits ( addr %n nbits pos -- )
  \ Stores a bit pattern bits starting at a given bit position at address adr
  \ bits consists of nbits 1s and 0s at position pos in a 32-bit word.
  \ Non-intrusive for all other bits.
  \ Usage:
  \        GPIOC CRH %0011 4 7 set_bits
  \ This would place the 4-bit pattern %0011 at bit position 7 in GPIOC_CRH.
  \ The word b counts the bits (including leading zeros) in the binary number.
  \ Note that b can only be used interactively, not within a word definition.
 
  pos_shift \ Determine number of bits to shift pattern
  not_mask  \ Set bit pattern to AND with
  >R
  LSHIFT    \ Set bit pattern to OR with
  OVER @
  R>
  AND       \ AND with mask to get 0s at correct bit positions
  OR        \ OR with bit pattern to nonintrusively set
  SWAP ! ;  \ Store new bit pattern at address

\ Application words 
: enable ( aPort -- ) 
  GPIOA - $400 / 2 + 
  RCC_APB2ENR SWAP 
  1 1 ROT
  set_bits ;         \ Turn on the clock

: disable ( aPort -- ) 
  GPIOA - $400 / 2 + \ Set location to shift to 
  RCC_APB2ENR SWAP
  0 1  ROT
  set_bits ;         \ Turn on the clock

: GPset ( aPort pin# porttype -- )
  \ Set a pin to output
  \ porttype is a 4-bit pattern
  >R 
  DUP 7 >
  IF 7 - SWAP CRH SWAP ELSE 1+ SWAP CRL SWAP THEN     
  4 * 1-
  R> 4 ROT  set_bits  ;

: ppout     ( aPort pin# -- ) %0011 GPset ; 	\ Set port pin to push-pull output, 50 MHz
: ppout2MHz ( aPort pin# -- ) %0010 GPset ; 	\ Set port pin to push-pull output, 2 MHz
: afout     ( aPort pin# -- ) %1011 GPset ; 	\ Set port pin to AF output, 50 MHz
: ppin      ( aPort pin# -- ) %1000 GPset ; 	\ Set port pin to push-pull input
: ain       ( aPort pin# -- ) %0000 GPset ; 	\ Set port pin to analog input

: all_outputs ( aPort -- ) DUP CRH $33333333 SWAP ! CRL $33333333 SWAP ! ;
: all_inputs  ( aPort -- ) DUP CRH $88888888 SWAP ! CRL $88888888 SWAP ! ;

: GPon ( aPort pin# -- )
  \ Turn on a pin for an output port
  SWAP ODR SWAP %1 1 ROT set_bits ;

: GPoff ( aPort pin# -- )
  \ Turn off a pin for an output port
  SWAP ODR SWAP %0 1 ROT set_bits ;

: GPon? ( aPort pin# -- fl )
  \ Check to see if an input is switched on
  SWAP IDR @ 1 SWAP LSHIFT AND = ;

\ LED Flashing Routines
\ Here are some example words to make LEDs flash

\ Setup for LED flashing
GPIOC enable
GPIOC 10 ppout
GPIOC 8 ppout
0 GPIOC ODR H!

200 VARIABLE time \ flash delay time, in ms
12000 VARIABLE scale

\ Software ms loop 
: ms scale @ * 0 do loop ; \ change number to get accurate ms timing

: pulse ( n -- ) GPIOC 10 2dup GPon rot ms GPoff ;

: lflash ( aPort bit_pattern -- ) \ Flashes PC10 for the appropriate number of ms
  2DUP GPon time @ ms GPoff time @ ms ;

: lflashes ( aPort pin# n -- ) \ Flashes PC10 n times
  0 ?DO 2DUP lflash LOOP 2DROP ;

: alternate ( n -- )
  0 ?DO GPIOC 10 lflash time @ ms GPIOC 8 lflash time @ ms LOOP ;



\ Now you can try the following after hooking up an LED and resistor to 
\ port C pin 10 and another to port C pin 8...
\ Example usage below
\ GPIOC port_enable
\ GPIOC all_outputs
\ GPIOC 10 GPon
\ GPIOC 10 GPoff
\ GPIOC 10 lflash
\ GPIOC 8 lflash
\ GPIOC 10 20 lflashes

Hypersonic Tesla

As you might know, Tesla went and launched one of their roadster vehicles into space some time back. I’m still not sure why, but I guess it was because Elon Musk could.  So, in that spirit, because we have a facility that can generate hypersonic flow, my colleague Harald and I decided to see what it would look like if an alien decided to drive it back to Earth… So if you are curious, this is what a Tesla roadster would look like if it were entering the upper atmosphere at Mach 10.  Harald used a technique called colour schlieren to visualise the shock waves around the vehicle, and front-illuminated the vehicle so it looks like the vehicle rather than a shadow.  The colours near the end of the video have nothing to do with the hypersonic flow, but are either caused by the high temperature reacting with the paint on the car or is old rubidium that we used for previous experiments in the tunnel, still left over from those experiments.

The car was a little toy Matchbox Tesla Roadster model.  Just a bit of fun, but a nice illustration of how interesting and complex hypersonic flow can be, and a showcase for Harald’s talent!

 

Non-destructive Bit Setting in Mecrisp Stellaris Forth

Doing pretty much anything involving a peripheral on the STM32F103 microcontroller (or on most microcontrollers for that matter) involves putting ones or zeros into registers or reading the registers to see which bits are ones or zeros. The simplest way to do this is to write or read the number you want to write into the register. In Forth, this is done using the ! and @ words, respectively.

For example, $33333333 $40011000 ! stores the appropriate bit pattern to turn all the lower 8 pins of the general-purpose input-output port C (GPIOC) to be 50 MHz push-pull outputs, by setting all the bits of the GPIOC_CRL register located at address $40011000.

While this is easy to do, it has the disadvantage that whatever used to be in that register has now been obliterated by the $33333333. Often we just want to change the state of one pin of one of our GPIO ports without interfering with the others. This is particularly true of ports that operate more than 1 peripheral… you don’t want to lose your serial connection when changing a GPIO port.

So what we need is the ability to set 1 or more bits in a register without changing any of the others. An example of this sort of requirement is the setting of the GPIOx_CRH or GPIOx_CRL register to determine whether a particular pin in a GPIO port is an input or an output. This is done by setting 4 bits in this register. Which particular 4 bits to set, and indeed which of the CRL or CRH registers to set them in, will be different depending on the pin you want to set and the port containing that pin.

As an example, say that we want to set pin 10 of GPIO port C to be a push-pull output operating with a clock speed of 50 MHz. As it’s higher than pin 7, the appropriate register to set is GPIOC_CRH, located at $40011004 on the STM32F103 chip. The diagrammatic representation of this register, based upon the chip manual, is shown in the figure below

GPIOx_CRH.png

Each of pins 8 to 15 of the particular port (in this case port C) is controlled using 4 bits. The lower 2 bits are called mode bits and determine whether the port is an input or an output, and what speed it outputs to if it is the latter type. The upper two bits provide further characteristics of the input/output port. The lowest 4 bits control pin 8, the next higher 4 bits control pin 9 and so on.

For this case, if we want to set pin 10 to be a push-pull output at 50 MHz clock rate, we need to set bits 8-11 of this register to the binary number %0011. But we want to achieve this without changing the values of any of the other pins in this half of the port. The desired change in the port is shown below.

GPIOC_CRH_InitFinal.png

The x’s indicate either 0 or 1 values in that bit position.

Bitwise Logic

So if we want to set just these bits then we have to recall some bitwise Boolean logic operations. Specifically we will recall three important bitwise operations: NOT, AND and OR.

NOT is the simplest of these, as it only operates on single bits, reversing their value at every bit position. Thus, 0s become 1s and 1s become 0s. The truth table for the NOT operation looks like this:

Not.png

AND and OR both operate on two numbers, one bit at a time.

AndOr.png

In the case of AND, the only time a bit is not set to 0 is when both input bits are 1. Similarly, for OR, the only time a bit is not set to 1 is when both input bits are 0.

Looking at the truth table for AND, you can see that ANDing a bit with 0 always sets it to 0, while ANDing a bit with 1 leaves the original bit unchanged. Similarly, ORing a bit with 1 always sets it to 1 while ORing a bit with 0 leaves the original bit unchanged.

Thus, if I want to set a bit within a number to 1 while not changing the value of any of the other bits, I need to have a number of the same length with 0s everywhere except at the position that I need to set to 1.

To set a bit to 0, I need the opposite. I need to AND each bit with a 1 where I want to leave the bit unchanged and to AND with a 0 at the location of the bit I want to reset to 0. To do this conveniently, one typically puts a 1 at the location to reset, performs the NOT operation to all the bits, turning that bit to 0 and all the other bits in the number to 1s, then AND with the original value. By doing this, all the other bits are unchanged because they are being ANDed with 1 and the bit you wish to reset is always 0 regardless of whether it was a 0 or a 1 because you are ANDing that bit with 0. This takes a little concentration to get one’s head around, but it works.

Shifting a Bit Pattern in Forth

To get a particular pattern in the correct place we can use the Forth word LSHIFT ( pattern nshift -- ). A phrase like 1 10 LSHIFT would put a 1 on the stack and shift it to bit position 10, with 0s at every other bit position. Then ORing the register value with this number would ensure that there was a 1 at position 10 and 0s everywhere else. This is basically how a word is set. This can also be done for more than one 1. For example to set pins 10 and 11 to a 1, you would OR with a number made using %11 10 LSHIFT. Note that I’m assuming the Forth is in DECIMAL here. Any pattern of bits can be shifted using LSHIFT. The word always puts 0s in the new bit positions made by moving the bits to the left, and the bits on the right that are shifted out are lost.

Resetting a bit is a little more complicated. The first step is the same as for setting. Put a 1 at the position you want to change by using LSHIFT. However, now instead of using OR, you must use NOT to invert each bit so you have a zero at the reset bit positions and 1s everywhere else and then use AND to reset only those bits with a 0 at their location.

Setting and Resetting Bit Patterns

While setting or resetting single bits or strings of the same bits is not so complicated, there are a couple of extra complications when one wishes to use the same method to set a series of 0s and 1s. The first is that leading zeros are significant, unlike for numbers. The second is that the non-destructive replacement of bits needs to happen in two stages, as we will now illustrate.

The sequence of operations required to non-destructively set some bits in a register is shown in the diagram below:

GPIOC_CRH_Steps.png

Step 1 involves resetting all the bits occupied by the bit pattern to 0. If we have 4 bits that we need to set/reset, we shift 4 1s into the appropriate bit position using LSHIFT (in this case %1111 8 LSHIFT), then NOT the number to make those 4 bits zeros and all other bits 1s, then finally AND with the value in the register. This sets the 4 bits we want to modify to zeros while leaving the other bits unchanged, as shown in the first register diagram. After setting those bits to 0s, we put our bit pattern on the stack, shift it by the same number of places and then OR with the number currently in the register. After this second process, our bit pattern (%0011) is located in bits 8 through 11, while the other bits remain unchanged.

As we stated before, the zeros in a number like %0011 are significant in this case, because they contain information about the number of bits that need to be replaced. This causes difficulties with just using the stack to store these numbers because the leading zeros are lost. This means we will need to keep a separate record of the number of bits to mask out with our zeros in the first step.

The Forth Routines

Now that we know what to do, we just need to code it up. Firstly, a word that puts a given number of 1s on the stack, to be used and shifted to clear the bits we want to set. Given a number on the stack, we can generate 1s in a loop, noting that each binary place is generated by multiplying by 2. Thus we can multiply by 2 and add 1 in a loop to generate our string of 1s.

: ones ( n -- %11..1 )
  \ Generate a binary number consisting of n 1s
  1 SWAP 1- 0 ?DO 2 * 1 + LOOP ;

The next word works out how many places we need to shift our bit pattern to get it to the right starting point. This involves a design decision… do we work in terms of bit positions to shift, or in terms of the bit position of the most significant bit. These two are only the same when shifting single bits: otherwise the number of places to shift varies with the length of the binary string to be shifted. As I find it easier to operate in terms of the bit position of the most significant bit (MSB), we need a word that will use that information to determine the number of places to shift the bits. Note that to determine this, we need to keep track of the number of bits we are shifting (see previous discussion on significant bits). As such, we keep the number of bits as a separate number on the stack

: pos_shift ( nbits pos -- nbits shift# )
  \ Determines the number of bits to shift given the position of the MSB
  \ and the number of bits
  OVER - 1+ ;

Now we are able to make our bit-clearing mask, which I have called not_mask.

: not_mask ( nbits shift -- shift mask )
  \ Generate mask consisting of 1s everywhere but where we want to
  \ change bits
  SWAP ones OVER LSHIFT NOT ;

Our final utility word for setting/resetting a given bit pattern is called set_bits. This takes 4 arguments on the stack: addr %n nbits and pos. addr is the address of the register, %n is the binary bit pattern, nbits is an integer indicating the number of bits in the pattern and pos shows the location of the MSB of the number in the bit pattern.

: set_bits ( addr %n nbits pos -- )
  \ Stores a bit pattern bits starting at a given bit position at address adr
  \ bits consists of nbits 1s and 0s at position pos in a 32-bit word.
  \ Non-intrusive for all other bits.
  \ Usage:
  \        GPIOC CRH %0011 4 7 set_bits
  \ This would place the 4-bit pattern %0011 at bit position 7 in GPIOC_CRH.
  \ The word b counts the bits (including leading zeros) in the binary number.
  \ Note that b can only be used interactively, not within a word definition.
  
  pos_shift \ Determine number of bits to shift pattern
  not_mask  \ Set bit pattern to AND with
  >R
  LSHIFT    \ Set bit pattern to OR with
  OVER @
  R>
  AND       \ AND with mask to get 0s at correct bit positions
  OR        \ OR with bit pattern to nonintrusively set
  SWAP ! ;  \ Store new bit pattern at address

In this case, calling $40011004 %0011 4 11 set_bits would put the bit pattern %0011 in the place in GPIOC_CRH that sets pin 10 to be an output.

This routine is flexible enough to use with bit patterns of any length at any position.

In a later blog entry we will use these routines to generate a very general wordset for controlling the GPIO ports on the STM32F103.

An Icelandic Poem

A long time ago (1991 or so) I decided to learn Icelandic. Like most things I decided to do, I never really finished it. I can sort of pronounce Icelandic words, very slowly, and I remember a few words, learned a few songs, but never achieved anything like facility. I visited Iceland once, and had that terrible feeling you get as a foreigner that you are murdering someone else’s native tongue. Conversations with Icelanders never really lasted more than a sentence before the recipient would decide to end everyone’s misery and transition to perfect English instead.

I wanted to learn Icelandic because of Egil’s saga. If you don’t know, it’s a very old book detailing the history of a Viking called Egil Skallagrímsson, a poet and very violent man and his fights with everyone he knew. I still consider him one of the most interesting characters I ever read about, and recommend the book. He’s savage, unpleasant and arrogant, but strong and talented as a poet. He insults the king and then gets out of being killed by making a poem singing the king’s praises, called the head-ransom. Throughout the book he goes from being so vicious and hot-tempered that most people avoid him, to writing the most beautiful poem mourning his daughter’s death.

While the prose parts of Egil’s saga seemed to be well translated into English (at least I could follow them), the poetry did not seem to fare as well, seeming to lose subtelty and rhyme, and this was why I decided to learn Icelandic. I never really got to being able to translate the poems in Egil’s saga, but on my one trip to Iceland I got a book of more modern poems to read, intended for schoolchildren (I figured reading kids’ school books was a good way of learning the language). One of the poems in this book was by Hjálmar Jónsson, also known as Bólu-Hjálmar, and was called Mannslát.

Mínir vinir fara fjöld,
feigðin þessa heimtar köld.
Eg kem eftir, kannske í kvöld
með klofinn hjálm og rofinn skjöld,
brynju slitna, sundrað sverð og syndagjöld.

It’s one of the few poems that I remember. Bólu-Hjálmar was a farmer in the northwest of Iceland in the 1800s, and his poetry seemed mostly to be short and dealt with the harshness of what life was like on a farm in Iceland at the time, where food was scarce. He was called Bólu-Hjálmar because he lived on a farm called Bóla. His was a harsh, bitter but muscular poetry that I felt drawn to when I read it. Below is my rhyming translation of the poem above into english. To make it rhyme similarly some liberties were taken.

All my friends have left the fight
Frightened, left to fate's cold bite.
And I'll go too, perhaps tonight,
With cloven helm and riven shield,
Broken armour, sundered sword and sin's dark blight.

My translation is not quite the same (the last line is literally more like sin’s price, or the more biblical wages of sin, and there is no bite in the second line of the original), but hopefully my translation keeps the feeling of the Icelandic version. It’s an old man’s poem, and you get a sense of him, worn out but still struggling on in loneliness when everyone he knew is gone.

I found a few more of his poems on the internet, and would like to read more like them. And who knows… Maybe one day I’ll be able to read those poems in Egil’s saga properly.

New Daily Driver: the Odroid N2+

I have always had a soft spot for fanless ARM single-board computers (SBCs) because they are quiet, portable and consume very little power compared to a typical laptop or desktop machine. A typical desktop computer will consume from 100 to 500 Watts of power, while a typical laptop consumes 60 to 90 Watts. An ARM SBC can consume anything from 6 to 30 Watts, which is considerably less than either of the more common formats. They also have less in the way of hardware monitoring than intel-based CPUs, and can run linux, which is my preferred operating system.

Until fairly recently, however, these machines have been too slow to operate well as standard work computers because package availability was sloppy and memory and CPU availability were at the low end of what you would typically need to get the job done. Also graphic processor support, the bane of linux, is particularly bad for these devices, as they tend to have commercial GPU drivers (as phones are their main application market).

As I mostly use open-source software for my research, and my graphical needs are fairly simple, I have proved to my own satisfaction that I can use these boards to do real work, albeit with a performance penalty compared to a modern i5 or i7 intel chip laptop. My first arm machine was an Odroid XU4 which I brought with me on sabbatical and used for writing papers and reports over a 5-month period. The only problem I had with that machine was that it would get into funny states after updating the OS, and it required a fan. Subsequent to this, I purchased a Pinebook Pro, which I could use as a laptop but which was a slower than the XU4, making the experience a little too frustrating to persevere with in the longer term, though I still use it from time to time.

Now Hardkernal, the maker of the odroid machines, has a new ARM64 SBC which is more powerful than the XU4, the Odroid N2+. This device is marketed as an alternative to the Raspberry pi 4 (which I have not used), being more powerful and more expensive. I purchased mine for USD86 with a plastic case, wireless dongle, and 128 GB emmc card (note that if you are going to use a computer seriously, having as much solid state storage as possible is very helpful). The device comes with 4GB of memory which, as the old Rolls-Royce acceleration specs used to say, is `adequate’.

This device uses more power than the XU4, requiring 12V and 2 A, rather than 5V at 3A. But this is not so surprising given the extra speed of the newer device. It also is by default fanless, although a fan is available for high load applications. So far in using it for my work, the heatsink has not got much more than warm. Although the device can apparently be overclocked to 2.4 GHz, I have not attempted overclocking it.

Initially if you purchase the device from the hardkernel web site, the emmc chip comes with ubuntu mate installed as the recommended operating system. As I like manjaro better than ubuntu, after playing around a bit with the default I used etcher to implement a manjaro sway windowing environment that has been compiled specifically for this computer. After a successful install I noticed that the screen I was using with the N2+ (a QHD 32″ lenovo monitor) would flicker randomly, which was very irritating. In case it was a problem with the Wayland system, I installed manjaro XFCE, which uses X11 rather than Wayland, but when I tried the XFCE version of manjaro, the flickering still occurred. So after a couple of unsuccessful installs, I went back to the original Ubuntu mate installation, which does not cause the flicker problem on my monitor, presumably because hardkernel installed the correct graphics drivers.

I really like tiling window managers that you can control via the keyboard (hence my initial desire to use sway), so once I had mate installed and the default user account removed I installed i3. The i3 window manager seems to work really well under ubuntu, and I was able to set things up just the way I like them. One of the things I don’t like about ubuntu and other Debian-based distributions is the slow turnaround time, as several applications require very up-to-date versions to operate properly (like my University’s owncloud server). However I was pleasantly surprised this time that most programs installable by apt were able to work without causing me problems because of their age.

Here is a picture of what the configuration looks like. The image shows emacs, a translucent shell window (terminator, using powershell) and a web browser all open on the same workspace. The little icons on the bottom right show the other three workspaces that can be used.

Figure 1: i3 configuration

Because i3 is pretty lightweight compared to many window managers, the transition between workspaces and switching between applications is very fast. Using the emacs daemon makes editing very fast too. Once you get used to it, the keyboard-driven workflow associated with i3 and emacs is pretty hard to beat.

In total, with the blind alleys caused by trying the other distros, it took about 10 hours to completely set up the N2 the way I want it. Now I can use all the tools that I use on the intel laptop for my research work, and apart from taking a little longer to load programs, I don’t experience much lag at all compared to my i7 laptop. I was able to connect to my cloud service and to run all the codes I need to, either using snaps, apt, or in a couple of cases compiling from source. The experience is no worse than my usual linux installation experience (best described as me trying lots of permutations of random things based upon internet searches until something works). My existing i3 and emacs configurations were basically able to be transferred directly to the new computer with very few changes necessary. Because all my work in progress is on the cloud, this means that I can work on my project either on my laptop or on this SBC with seamless results, as I have the same applications installed on both machines.

In summary, I’m impressed. This blog post was written on it using emacs org2blog.  It’s possible that I might get bored or frustrated and stop using this machine for work, in which case it will be used as a lab device for transferring data from instruments, or as a connected diary device.  But at the moment I can’t much tell the difference between working on this machine and working on my laptop, and that’s a very good sign.  It’s really impressive how far ARM64 support has come in linux.  For a total outlay of less than AUD200, this is a really fun-to-use laptop replacement, provided you have access to a HDMI monitor and as long as you don’t mind shutting it down between moves (because it does not have a battery).  4GB is not a lot of memory, but in linux I have yet to reach a limit that affects my work in terms of available memory.

The small size of this machine means that, with a big rechargeable battery, it could be made into a very nice portable computer provided you have access to a TV or monitor with HDMI support, which is pretty much everything these days.  I have some ideas about form factors that I hope to have time to try out one day…

First Reproducible Research Paper

I have been playing around with reproducible research in org-mode. As an example for students, I have produced a paper written entirely in org-mode and containing all the required calculations within the document itself. The diagram was made using DITAA and the values were calculated and plotted using calls to elisp and python routines. The paper is formatted as if if were a paper in the Springer Journal Shock Waves, as I wanted to demonstrate the ease of using org-mode with a \(\LaTeX\) style for journal papers. It should be possible, though not necessarily straightforward, to change the style to suit whatever form of journal paper was required. I just chose this one because I like the Springer journal format and fonts.

The paper is on the eternal problem of whether your tea will be cooler after 10 minutes if you mix the milk and the tea immediately and then waiting 10 minutes or by waiting and then adding the tea. You’ll have to read the paper to find out the answer! This is a simple enough problem that allows for a demonstration of how equations and figures are generated and presented using the org-mode markup features.

It was an interesting experience to write this paper. It took me around 2 days of full-time work to get it up and running, but now that I’ve done it, the process should be much quicker for an actual paper. It was not always straightforward to get working either: I found the referencing of figures and tables was hit-and-miss. I’m not sure whether this is normal, or something to do with my configuration, but I often found myself looking at and compiling the .tex files produced by org to determine where my labels ended up and why they were sometimes not found. But eventually I did get it working.

My knowledge of python was not really good enough to allow me to do much in the way of calculating and plotting data, and I was not able to work out how to call a python routine to put numbers in a table. I therefore decided to do most of the table calculations in elisp, where the interface to the org-table is quite seamless. Although I find mathematics in lisp a little awkward, I was able to get it all working with a minimum of fuss, and elisp is pretty easy to debug in emacs.

It’s certainly very neat to be able to populate the text with computed numbers that can change whenever the input parameters for the paper change. And having the plots automatically update when the data is changed is also wonderful. For me, this is the way to properly write a paper, even though there is certainly more groundwork that needs to be done to get the paper written. It may not also work so well for papers where there is a lot of computational work, or where commercial gui-based software is used. But most of my papers contain only small calculations using scripting languages called from the command-line, and org-mode is perfect for that workflow.

An annoyance that I was not expecting is that for the Springer journal file, the abstract occurs in the preamble, so I could not just include a bunch of #+LATEX_HEADER: commands. Instead I needed to use a \input command to include the \(\LaTeX\) within the document.

My plan is for this paper to form a template for a document on how to set up emacs and org-mode from scratch in a new linux distribution, so any student gets a head-start in how to make a reproducible research paper. I could have added more bells and whistles, but I deliberately chose a minimal useful set to not cause unnecessary confusion.

Here is the pdf of the paper

Here is the org-mode file

Here is the bibliography file

Here is the \(\LaTeX\) header file

Because of the wordpress limits on file extensions I had to change all but the pdf file to a .txt extension.

Sometime soon I plan to write the installation from scratch document that allows one to go from a new installation of ubuntu to being able to produce this document.

Warp Speed in Mecrisp-Stellaris

Mecrisp-Stellaris Forth is an implementation of the Forth programming language for Arm Cortex microcontrollers. It is fast, small and elegant, and was clearly well designed. I use it in my teaching, and it’s my preferred implementation of the Forth programming language.

It can be downloaded from Sourceforge and has installation candidates for a wide range of microcontrollers. I use the STM32f103RB processor in the Olimex STM32p103 board, and sometimed the blue pill STM32f103 boards.

Out of the box, mecrisp uses the internal oscillator on the chip to run at 8 MHz. This is OK, but using the onboard PLL, you should be able to operate the chip at 72 MHz. That’s much more like it. I wanted to be able to do this, so started looking at the unofficial mecrisp guide, a site set up by Terry Porter to accumulate information about mecrisp, and about the closest thing it has to documentation. What I wanted to do was to start with the standard mecrisp forth for this processor, in a file called stm32f103rb.bin, and then add several words including this one, so I had some useful routines on the chip. Mecrisp forth makes this very easy by having two built-in words, compiletoflash and compiletoram. By running compiletoflash, any new word definitions are saved to flash rather than ram, allowing those words to be stored permanently as part of Forth. This is a really nice feature. There is also a word eraseflash that allows you to start from the original installed words, and someone has come up with a word called cornerstone that allows you to erase down to that point if you no longer need additional definitions.

If you have never seen Forth, it’s a stack-based interpreted programming environment that is conceptually quite simple. Numbers or addresses are passed on a stack as parameters to words (the equivalent of functions in other programming languages) to allow the words to perform the desired operations. Words are built from very simple building block words into more complex words by calling the primitive words in the desired order. New words can then call these words to do more complex things. Each time a new word is defined (in terms of existing words) it is compiled into a dictionary much as you would with a new word in English. As you are free to call the words whatever you like, you end up building a stack-based domain-specific programming language tailored to the problem you want to solve.

For example, you might make words that control a servo motor using pulsed-width-modulated timer. The primitive words would put the right numbers into the timing registers, and you would build your way up to having words that might address motors 1, 2, … n to turn a certain number of degrees. The program to turn the third motor by 30 degrees might look something like

3 motor 30 degrees turn

Words definitions tend to be short and closely linked to one another, because the overhead for defining a word is very small. Code tends to be fast, and takes up a small amount of memory, which is very advantageous when working with a microcontroller. You’ll see what I mean when I write the code further along.

So anyway, back to setting up the board to operate at high speed with the phase-locked loop. When I tried to use the word 72MHz as written, it would crash the board, and when that happens all the benefits of having an interactive programminh environment like Forth goes away. So I decided to move away from that code a little and start from scratch using the user manual for the STM32F103 chip. Upon looking up the appropriate registers, I was able to set the right bits in the registers that control the clocks on the chip, but it still crashed, producing a jumble of non-ascii characters on the screen and then not responding to typed text.

After many hours I worked out the problem: the original code was writing to the USART port (or serial port) 1, whereas on the STM32P103 the communications work on USART2. As the baud rate changes when the processor speed changes, the serial communication speed became all wrong, even though I thought I had fixed that (because I had fixed it for the wrong port). Once I realised this, it was a very easy fix to make the code work, and now I have 8MHz and 72MHz words that can change the speed of the processor on the fly, while keeping the baud rate at 115200 baud. Here’s the code:

8000000 variable clock-hz  \ the system clock is 8 MHz after reset

$40010000 constant AFIO
     AFIO $4 + constant AFIO_MAPR

$40013800 constant USART1
USART1 $08 + constant USART1_BRR
USART1 $0C + constant USART1_CR1
USART1 $10 + constant USART1_CR2

$40004400 constant USART2
USART2 $08 + constant USART2_BRR
USART2 $0C + constant USART2_CR1
USART2 $10 + constant USART2_CR2

$40021000 constant RCC
     RCC $00 + constant RCC_CR
     RCC $04 + constant RCC_CFGR
     RCC $10 + constant RCC_APB1RSTR
     RCC $14 + constant RCC_AHBENR
     RCC $18 + constant RCC_APB2ENR
     RCC $1C + constant RCC_APB1ENR

$40022000 constant FLASH
FLASH $0 + constant FLASH_ACR

$40010000 constant AFIO
AFIO $04 + constant AFIO_MAPR


: baud ( u -- u )  \ calculate baud rate divider, based on current clock rate
  clock-hz @ swap / ;

: 8MHz ( -- )  \ set the main clock back to 8 MHz, keep baud rate at 115200
  $0 RCC_CFGR !                   \ revert to HSI @ 8 MHz, no PLL
  $81 RCC_CR !                    \ turn off HSE and PLL, power-up value
  $18 FLASH_ACR !                 \ zero flash wait, enable half-cycle access
  8000000 clock-hz !  115200 baud USART2_BRR !  \ fix console baud rate
  $0 RCC_CFGR !                   \ remove PLL bits
  CR ." Reset to 115200 baud for 8 MHz clock speed" CR
;

: 72MHz ( -- )  \ set the main clock to 72 MHz, keep baud rate at 115200
\ Set to 8 MHz clock to start with, to make sure the PLL is off
  $0 RCC_CFGR !                   \ revert to HSI @ 8 MHz, no PLL
  $81 RCC_CR !                    \ turn off HSE and PLL, power-up value
  $18 FLASH_ACR !                 \ zero flash wait, enable half-cycle access
  8000000 clock-hz !  115200 baud USART2_BRR !  \ fix console baud rate
\  CR .USART2 
  $12 FLASH_ACR !                     \ two flash mem wait states
  16 bit RCC_CR bis!                  \ set HSEON
  begin 17 bit RCC_CR bit@ until      \ wait for HSERDY
  $0                                  \ start with 0
\  %111  24 lshift or                 \ operate the MCO from the PLL
  %111  18 lshift or                  \ PLL factor: 8 MHz * 9 = 72 MHz = HCLK
  %01   16 lshift or                  \ HSE clock is 8 MHz Xtal source for PLL
  %10   14 lshift or                  \ ADCPRE = PCLK2/6
  %100  8  lshift or                  \ PCLK1 = HCLK/2
              %10 or  RCC_CFGR !      \ PLL is the system clock
  24 bit RCC_CR bis!                  \ set PLLON
  begin 25 bit RCC_CR bit@ until      \ wait for PLLRDY

  72000000 clock-hz ! 115200 baud 2/ USART2_BRR !  \ fix console baud rate
  CR ." Reset to 115200 baud for 72 MHz clock speed" CR
;

Again, if you have never seen Forth, this might look a bit strange. The : character starts a new word definition, with the name of the word being the first word after the colon. A semicolon ; terminates the word definition. Then, if I load these definitions, I can simply type the name of the word 72MHz and the machine will start running at that speed. Backslashes indicate comments, as do the parentheses immediately after the word definition. These parentheses comments are special and are called stack constants because they remind the programmer of how many inputs need to be on the stack before the word is called, and how many remain after the word has finished running.

The constant definitions at the start of the code encode the addresses of various important registers. So after loading this file, if I were to type in AFIO_MAPR, then the address of the alternate function input-output register, $40010004 would be placed on the stack. One neat thing about Forth is how flexible it is in terms of its representation of words. For example, the word lshift is defined to take a number on the stack and shift its binary representation by a given number of bits to the left. This is like the C operator <<. So the code %011 24 lshift takes the number 3 (the % symbol represents a binary number) and shifts it left by 24 spaces, leaving the end result on the stack. So in the 72MHz word, we are able to shift the desired bit pattern into the correct locations as numbers and then logically OR the numbers together to give the number we want to put into the register to do what we want. The word that does the storing of the number into the register is ! (pronounced ‘store’). The word @ (pronounced ‘fetch’) gets the data from an address placed on the stack, so AFIO_MAPR @ would get the value currently stored in that register.

Now you may be thinking ‘lshift is a very unwieldy operator compared to <<‘. Well, one of the nice features of Forth is that if you don’t like it, you can change it easily, by defining : << ( n1 n2 --) lshift ; — again, the stuff between the parentheses in the definition is a stack comment and not code. Then you could type %011 24 << to get the same effect as lshift. The ease with which new words can be defined is either a great strength or a great weakness of the language, depending on your point of view. For some, it makes the language easily capable of conforming itself to the problem at hand. To others, it prevents the language from ever being properly standardised. Both points of view can be viewed as the correct one.

If you make a definition for a word init, mecrisp knows that it must, when stored in flash, execute the contents of that word when the controller is first booted. This allows a programmer to make a turnkey application that will run when the controller is switched on, and in this case if the word 72MHz is contained in the word init then it will be run on bootup, and the board will start running at full speed. Then, if the user wants to go back to 8 MHz operation, they can execute the 8MHz word interactively and the processor will drop back down to 8MHz.

Developing in Forth is very different to the C or arduino workflow commonly used for these microcontrollers. In the latter case, development is done on your pc, compiled to a binary program that is uploaded to the board if it compiles correctly, then executed, perhaps using a hardware debugger to ensure it’s doing what you thought it should be doing. In Forth, words are developed in RAM, tested in isolation and, when you are satisfied they work, are saved to flash from within the Forth interpreted environment. Development is done on the microcontroller via a serial terminal connection to a computer, but all the compiling is done in situ on the chip itself. In this way, you can use words like @ and ! to interrogate and change register settings in real time. Also, it’s very easy to write an assembler in Forth, allowing you to access the speed of assembly language from within Forth for those times when the overhead of the interpreter is too great (which with a processor as powerful as these is almost never, for my sorts of applications). When you get used to it, Forth can be a very powerful programming platform.

I’ve never really understood why this programming language never reached popularity in embedded programming circles. Forth has a reputation as a ‘forgotten’, or ‘old-fashioned’ language. People who say this forget how old C is. I guess C and its derivatives like arduino got a head start as a language that many programmers already knew from university courses, and I can see from an employer’s point of view it’s much easier to replace C programmers than Forth programmers — Forth code can be very idiosyncratic.

But for a small system like a microcontroller where codes are usually written by individuals or small teams, Forth’s interactivity and incremental debugging approach are very desirable characteristics. The biggest disadvantage, however, is that there is much less in the way of libraries for this language and, as in the case above, you end up doing everything at register level from scratch. Again, whether you find that an advantage or a disadvantage depends upon your viewpoint.

If you program microcontrollers and have not tried Forth, give mecrisp a try. I really enjoy programming microcontrollers this way. Who knows? You may, like me, never want to go back to the edit-compile-debug-upload-run way of doing things again!

Rearranging Tables in J

This blog entry was inspired by a need that I had to rearrange a comma-delimited text (csv) file for an administrative task, using the J programming language. I thought it was interesting enough (and difficult enough) to warrant describing here as a way to achieve these sorts of things in J. Being an array-based programming language, J has some features that make the algorithm different than what I would use in another language.

In this study, I had a very large table containing student names and the names of primary, joint and secondary supervisors for their projects. A primary supervisor is the person responsible for the supervision, a joint supervisor is an active supervisor who is not the primary supervisor and a secondary supervisor is an advisor who does not actively supervise the student on a regular basis.

For the purpose of workload balancing in our department, we want to make sure that individuals are not supervising too many students, so we need to monitor how many students are being supervised by any one person. As the data is keyed to students, this is a difficult thing to see from the csv file. For this reason, and because the students with projects change on a regular basis, I wanted a script that would take the csv data and extract the number of students supervised in each of the three categories for each academic. We then use a scoring system (1 point for primary, 0.5 points for joint and 0 points for secondary supervisions) to give a score to each academic involved in supervision. This is not as easy as it sounds.

Below I have put a (much simpler) sample data set like the actual one I had to use. Supervisors names have been changed and students are generic in this example.

Student ,Primary Supervisor,Joint Supervisor,Secondary Supervisor
Student Name1,Tony Stark,,"Jay Garrick, Steve Rogers"
Student Name2,Diana Prince  ,"Bruce Banner, Bruce Wayne",
Student Name3,Oliver Queen,"Eric Twinge,Peter Parker, Alan Scott ",
Student Name4,Alan Scott,Tony Stark,Peter Parker
Student Name5,Bruce Wayne,Dick Grayson,
Student Name6, Alan Scott,Diana Prince ,
Student Name7,Diana Prince  ," Diana PRINCE, Tony Stark",
Student Name8, Diana Prince,,Bruce Banner
Student Name9,Bruce Wayne,Dick Grayson,Peter Parker
Student Name10,Bruce banner,,James Howlett

A few things to note:

  • The first row describes the columns and the data starts at the second row
  • For any given student, there is not always a joint or a secondary supervisor
  • Although there is only one primary supervisor, there is often more than one secondary and/or joint supervisor for a given student, and there is always at least two supervisors on a supervisory panel.
  • People are not very consistent in data entry (see the capital surname, comma-delimited lists and different numbers of spaces before and after names. All these quirks have to be dealt with, otherwise there would be multiple names assigned to the same person.
  • Our data is a mixture of text and numbers, meaning that it can’t be represented by a simple array. In J, such data is dealt with using boxed data.

Because I like doing numerical work in J, but did not have much experience working with mixed data in boxes, I decided to try to implement this in J. What we want to have at the end of this code is a list of all the names of supervisors in the first column, and then a vector containing the numbers of primary-supervised students, joint-supervised students and secondary-supervised students for that academic, with the last column being the total score for that supervisors. If the score exceeds a certain value, we know not to assign a new student to that supervisor until they are finished supervising one of the others.

Before we begin in earnest, a caveat: I’m not a very experienced J programmer, so what I have done should not be considered in any way optimal, and an experienced J programmer would find much more efficient ways of doing this. But it was an interesting lesson for me in how to manipulate tabular mixed string and number data. I’ll go through each part of the code and describe it as we go along.

J uses terminology borrowed from english grammar: verbs are functions that operate on data, nouns are the data, and adverbs are modifiers that change the way their verb arguments operate. A conjunction is like an adverb but takes arguments on both sides to produce a new verb with some kind of modified behaviour. So when I talk about these parts of speech below in a J context, that’s what I mean. The vocabulary part of the J documentation goes into detail about the differences between these ways of operating.

clear ''
1!:44 '/home/xx/j902-user/projects/Supervision/'
load 'csv'
datafile =: readcsv 'SuperVision.csv'
headings =: 0{datafile
data     =: 1}. datafile
nstudents =: 0{$data NB. number of students

Primaries =: 1}"1 data
Joints =: 2}"1 data
Secondaries =: 3}"1 data

The clear '' verb clears all the variables that might have been defined elsewhere. This is very important for debugging, as it’s easy to get fooled that a change you made interactively is part of the code. By executing the script each time a change is made, this command guarantees you are starting with a clean slate.

1!:44 '...' is an example of a J ‘foreign’ verb, which executes an operating system call. They are all of the form a!:b with different values of a and b for different OS-specific applications. This one sets the working directory.

load 'csv' loads some libraries for dealing with comma-delimited files, allowing us to use the readcsv verb to open the file Supervision.csv, containing the data above. The remaining words read the data from the file 1}. datafile removes the first line, although in this case, the monadic ‘behead’ form (without the 1) would also work, as there is only one line of header data. The variables Primaries, Joints and Secondaries contain the unformatted list of names for the primary, joint and secondary supervisors.

The variable datafile looks like this…

┌──────────────┬──────────────────┬─────────────────────────────────────┬─────────────────────────┐
│Student       │Primary Supervisor│Joint Supervisor                     │Secondary Supervisor     │
├──────────────┼──────────────────┼─────────────────────────────────────┼─────────────────────────┤
│Student Name1 │Tony Stark        │                                     │Jay Garrick, Steve Rogers│
├──────────────┼──────────────────┼─────────────────────────────────────┼─────────────────────────┤
│Student Name2 │Diana Prince      │Bruce Banner, Bruce Wayne            │                         │
├──────────────┼──────────────────┼─────────────────────────────────────┼─────────────────────────┤
│Student Name3 │Oliver Queen      │Eric Twinge,Peter Parker, Alan Scott │                         │
├──────────────┼──────────────────┼─────────────────────────────────────┼─────────────────────────┤
│Student Name4 │Alan Scott        │Tony Stark                           │Peter Parker             │
├──────────────┼──────────────────┼─────────────────────────────────────┼─────────────────────────┤
│Student Name5 │Bruce Wayne       │Dick Grayson                         │                         │
├──────────────┼──────────────────┼─────────────────────────────────────┼─────────────────────────┤
│Student Name6 │ Alan Scott       │Diana Prince                         │                         │
├──────────────┼──────────────────┼─────────────────────────────────────┼─────────────────────────┤
│Student Name7 │Diana Prince      │ Diana PRINCE, Tony Stark            │                         │
├──────────────┼──────────────────┼─────────────────────────────────────┼─────────────────────────┤
│Student Name8 │ Diana Prince     │                                     │Bruce Banner             │
├──────────────┼──────────────────┼─────────────────────────────────────┼─────────────────────────┤
│Student Name9 │Bruce Wayne       │Dick Grayson                         │Peter Parker             │
├──────────────┼──────────────────┼─────────────────────────────────────┼─────────────────────────┤
│Student Name10│Bruce banner      │                                     │James Howlett            │
└──────────────┴──────────────────┴─────────────────────────────────────┴─────────────────────────┘

The next section of code provides the verbs and nouns used to rearrange the data and clean it up.

NB. General utility verbs
NB. The last two are taken from the j phrases collection
nub =: ~: # ] NB. unique names
RotateLeading =:  ] |.~ (+/)@(*./\ )@(' '&=) NB. Move leading spaces to end
RemoveTrailing =: #~ ([: +./\. ' '&~:) NB. Remove trailing spaces

NB. Arranging data verbs
   unify =: 3 : 0
tolower RotateLeading"1 > ,>(< ;._1) each ',', each y
)

Primaries =: unify 1}"1 data
Joints =: unify 2}"1 data
Secondaries =: unify 3}"1 data

nub produces a list of the unique items in an array. This is an example of tacit, or functional programming. It is equivalent to ~: y # y where y is the argument to the right of the list of verbs. ] selects the argument on the right of nub (i.e. y), while ~: finds the locations in the array y of its values as an array of 1s and 0s that is the same length as y. The ones indicate unique values, while the zeros indicate repeated values. This string of 1s and 0s, when passed to #, will provide a new array consisting only of the unique items. Such a collection of 3 verbs is known as a train in J. Tacit programming is very powerful, but I find it quite hard to implement. This verb nub is one that comes up very commonly in manipulation of arrays, and so is good to have in your library.

RotateLeading and RemoveTrailing are collections of verbs contained in the J Phrases book, and which I have lifted directly for this purpose. RotateLeading takes any leading spaces in each name and rotates them to the end of the character array. J can display the order in which verbs are executed in tree mode, as follows:

  ┌─ ]                         
  ├─ ~ ─── |.                  
  │           ┌─ / ─── +       
──┤     ┌─ @ ─┴─ \ ─── / ─── *.
  │     │                      
  └─ @ ─┤     ┌─ ' '           
        └─ & ─┴─ =      

Working our way from right to left along the tree, we first find all the characters in the name that are spaces, represent them as a list of 1s and 0s, then use *./\ to or each of the elements of that array progressively. +/ sums the remaining values to give the number of spaces at the start of the string. Then the |.~ rotates the string so that the leading spaces are sent to the end of the array. As a concrete example, take the string '___Hello__' where the underscores represent spaces. ' '&= produces 1 1 1 0 0 0 0 0 1 1. *./\ produces the progressive and-ing of each of these values in the array producing 1 1 1 0 0 0 0 0 0 0, i.e. a listing representing the leading spaces in the array as 1s. +/ then sums these to 3 and ] |. rotates the array by 3, placing the leading spaces at the end of the array. So we would end up, in this example, with 'Hello_____' as our final product. This is a really good example of the tacit and loopless way that J operates on arguments. There is no assumption made about the type of data that this verb operates on, and it uses the properties of the data itself to determine what needs to be done.

I’ll leave RemoveTrailing as an exercise for the reader, but it removes the trailing spaces from a string. So sequential application of RotateLeading and RemoveTrailing will remove all the spaces from the start and end of a string.

unify removes leading spaces from each name in the boxed array of names and transforms the text to lowercase. This allows names like Prince and PRINCE in the data to be treated the same and counted together. Otherwise it will look like they are two different supervisors. < and > are the box and unbox verbs respectively, which pack and unpack items stored in boxes. Boxes fulfil the task taken by structs in some other languages. unify also uses the ;. cut conjunction, which is a very powerful way of operating on patterns of data separated by some kind of delimiter (in this case, the commas separating lists of joint or secondary supervisors). So unify removes leading spaces, changes names to lowercase and separates out the names in the comma-delimited lists to produce a boxed list of names. If there are no names in an entry, then it produces an empty item.

NB. Now work on the data.
NB. Collections of unique supervisor lists and supervision numbers
NB. for each category of Primary, Joint and Secondary supervisors
GradeNub =: ([: /: nub) {  nub
PrimNub =: GradeNub Primaries
PrimNum =: (+/"1) -. (<"1 PrimNub)    (i."0 _) <"1 Primaries
JointNub =: GradeNub  Joints
JointNum =: (+/"1) -. (<"1 JointNub)    (i."0 _) <"1 Joints
SecNub =: GradeNub  Secondaries
SecNum =: (+/"1) -. (<"1 SecNub)    (i."0 _) <"1 Secondaries

In this part of the code GradeNub produces the unique supervisors in a given list of primary, joint or secondary supervisors and arranges them in alphabetical order starting with the first name. The sorting is done using the grade up /: verb. These are stored in nouns PrimNub, JointNub and SecNub. The PrimNum etc. nouns generate sums of the number of times each supervisor is named in this list, in the same position in the array as the name. +/ sums up and i. generates the indices of the instances of each name so it can be summed with +/. This idea of generating matrices of 1s and 0s for occurrences and summing over the array is common in J. I probably should have factored out the verb part of the code for the numbers as I did for the Nub words, but didn’t bother in this case.

If you have not seen J before you might wonder what the "0 _" and "1 things are. These are examples of the rank conjunctions (the underscore means infinity in J). Rank conjunctions tell the verbs before them (e.g. the +/ in +/"1) to operate on different subsections of a matrix. So while +/ would, by default, sums down columns of a 2-d matrix, +/"1 makes it sum down rows. Here’s a simple example:

3 4 $ i. 12 NB. Make a 3 x 4 array of the integers between 0 and 11
0 1  2  3
4 5  6  7
8 9 10 11
   +/ 3 4 $ i. 12 NB. Sum down columns
12 15 18 21
  (+/"1) 3 4 $ i. 12 NB. Sum along rows
6 22 38

Using infinity as one of the ranks (in "0 _", the verb is applied to the left noun at rank 0 and to the right noun at infinite rank) implies the highest possible rank that the data structure has. Rank is something that I find difficult to understand in J, as different verbs and conjunctions operate by default on different ranks. Mostly I just do lots of experimentation to ensure that I have the data being operated on in the right way. This, for me, is the most time-consuming part of programming in this language, although rank is one of the concepts that makes J a flexible and elegant way of expressing algorithms. One of the nice things about this language, as you can see from the vocabulary, is that there is a relatively small number of verbs and conjunctions in the language, but they can be combined using the rank concept in an amazing variety of ways. This means you don’t have so much to remember, but it also means that you have to understand those complex ways of interacting.

So by now our script has generated 6 arrays: 3 arrays of supervisors and 3 arrays containing the number of supervised students in each of the 3 supervision categories for each supervisor.

NB. Now make a list of the unique names with 
NB. numbers of primary, joint and secondary supervisions for each
NB. First, generate the unique list and sort in alphabetical order
TotalNames =: RemoveTrailing each <"1 GradeNub PrimNub,JointNub,SecNub

TotalNames accumulates the three lists of supervisors using , to string them together, and then finds the unique names in the accumulated list and removes the trailing space from each item in the list. This produces a single alphabetically ordered list of all the supervisors who showed up in any of the three supervision categories.

   TotalNames
┌┬──────────┬────────────┬───────────┬────────────┬────────────┬───────────┬─────────────┬───────────┬────────────┬─...
││alan scott│bruce banner│bruce wayne│diana prince│dick grayson│eric twinge│james howlett│jay garrick│oliver queen│pe...
└┴──────────┴────────────┴───────────┴────────────┴────────────┴───────────┴─────────────┴───────────┴────────────┴─...

Note that the first item is blank. This represents the cases where there is an empty item in one of the supervision lists.

NB. Now generate the numbers of each category of supervisions
NB. Note we add a 0 to the list of numbers because 
NB. if a name does not show up, the index 1 beyond the end 
NB. is generated, which corresponds to the name not being 
NB. on the list of primaries.
NumPrimNub =: ((RemoveTrailing each <"1 PrimNub) i. TotalNames){PrimNum,0
NumJointNub =: ((RemoveTrailing each <"1 JointNub) i. TotalNames){JointNum,0
NumSecNub =: ((RemoveTrailing each <"1 SecNub) i. TotalNames){SecNum,0

Having got the list of supervisors, we need to read the number of supervisions in each supervision category for each of the supervisors in the master list. This is done by the code generating the nouns NumPrimNub, NumJointNub and NumSecNub. The 0 is appended to the array because if a name does not occur in the array, i. references one past the end of the array. So we want to make sure that if a name does not occur in the array of names, we say that person is supervising 0 students.

NB. Now produce the Summary Tables
Score =: +/"1 (|: NumPrimNub,NumJointNub,:NumSecNub) (*"1) 1, 0.5,0
SupervisionMatrix =: (|: NumPrimNub,NumJointNub,:NumSecNub),"1 0  Score
Labels =: 'Name'; 'Primary'; 'Joint'; 'Secondary'; 'Score'
AlphaTable =: }. (TotalNames),"0 1 (<"0 SupervisionMatrix)
LeagueTable =: AlphaTable \: }. Score
AlphaSummary =: Labels,AlphaTable
LeagueSummary =: Labels,LeagueTable

Score produces an array of the of the number or primary, joint and secondary supervisions for each supervisor (|: NumPrimNub,NumJointNub,:NumSecNub) and multiplies this by the score for each type (1 0.5 0) and sums to produce an array containing the total supervision score for each supervisor in TotalNames.

SupervisionMatrix generates a matrix made up of the number of supervisions in each category, followed by a column for the total score. AlphaTable and LeagueTable then arrange the list of names with the matrix generated as SupervisionMatrix to make summaries in alphabetical and score order respectively. }. is used to remove the blank from the list of supervisors. As the matrix for supervisions is sparse, and there is no chance that there will be no blank fields in the table, it is safe to remove this from the matrix.

The final result of all this is the LeagueSummary, with all the supervisors and their supervisions and scores in decreasing order from highest score to lowest, with titles as the first row. Within each category of scores supervisors are ordered alphabetically.

┌─────────────┬───────┬─────┬─────────┬─────┐
│Name         │Primary│Joint│Secondary│Score│
├─────────────┼───────┼─────┼─────────┼─────┤
│diana prince │3      │2    │0        │4    │
├─────────────┼───────┼─────┼─────────┼─────┤
│alan scott   │2      │1    │0        │2.5  │
├─────────────┼───────┼─────┼─────────┼─────┤
│bruce wayne  │2      │1    │0        │2.5  │
├─────────────┼───────┼─────┼─────────┼─────┤
│tony stark   │1      │2    │0        │2    │
├─────────────┼───────┼─────┼─────────┼─────┤
│bruce banner │1      │1    │1        │1.5  │
├─────────────┼───────┼─────┼─────────┼─────┤
│dick grayson │0      │2    │0        │1    │
├─────────────┼───────┼─────┼─────────┼─────┤
│oliver queen │1      │0    │0        │1    │
├─────────────┼───────┼─────┼─────────┼─────┤
│eric twinge  │0      │1    │0        │0.5  │
├─────────────┼───────┼─────┼─────────┼─────┤
│peter parker │0      │1    │2        │0.5  │
├─────────────┼───────┼─────┼─────────┼─────┤
│james howlett│0      │0    │1        │0    │
├─────────────┼───────┼─────┼─────────┼─────┤
│jay garrick  │0      │0    │1        │0    │
├─────────────┼───────┼─────┼─────────┼─────┤
│steve rogers │0      │0    │1        │0    │
└─────────────┴───────┴─────┴─────────┴─────┘

It’s clear from this table that Wonder Woman is doing too much supervision and Wolverine, Flash and Captain America are not pulling their weight.

WriteSummary =: 3 : 0 
	FileName =. y 
	LeagueSummary writecsv FileName
)

This final verb allows the LeagueSummary to be saved to a different .csv file for later use, using the writecsv verb in the csv library.

So hopefully if you have not used J much, this might give a flavour of what can be done with it. As I said before, I am sure that someone with better skills than me could do this more efficiently, and I don’t think my code is a good advertisement for the terseness of J, but I was happy with being able to do this in an automated way, as it’s a lot of work to do such rearrangement manually and it has to be done on a reasonably regular basis. I welcome any comments on how this might be done better in J, or in another language for that matter.

NB. Here is the full J source code, and here is the csv data it operates on.