All entries for May 2019

May 30, 2019

Black and white

Quick 'philosophy of programming' entry this time. General solutions to common programming probelms are often called 'design patterns' (e.g. the wiki articleor the book which started the name). The idea of these is to have language independent (as far as possible) 'patterns', like clothing patterns, which can be tweaked to fit a specific situation. A lot of these patterns seem obvious, which is good, and since they're developed and tested by many people they can be very valuable in showing you questions you hadn't even thought of.

This weeks topic is perhaps too simple to really call a pattern, but it is a very useful thing to keep in mind when doing anything that deals with restricting function which exists, but should not be allowed. For example, forms which take user information often disallow anything except numbers in a 'telephone' field. A code I work on has a lot of user-specifiable options, but as the programmer I know that some are incompatible where it might not be obvious to the user - and I want to either warn or abort if these are used together.

There are two general approaches to things like this, and which you choose depends on many things. You have to maintain some kind of list to check against, but you can choose to use either the "blacklist" or the "whitelist". The former, the "blacklist" is a list of the things which aren't allowed, and anything not in the list is OK. The "whitelist" approach means keeping a list of the things which are allowed, and anything not in the list is excluded.

Sometimes the choice is fairly easy, because one method is a much, much simpler list. For instance, in the phone number example, it is fair easier to use the whitelist, allowing only '1234567890', but nothing else. If you try the other way, you might think to exclude letters, but what about Greek or Cyrillic characters? On the other hand, this is a source of deep annoyance if you forget any needed character - in the example I just gave, one could not put any spaces in, which is annoying, nor brackets or the '+' symbol.

A classic example of the poorly-thought out whitelist is in name fields which often exclude characters like the apostrophe, annoying the Scots and the Dutch for eternity. And what about accented letters, or the German ess-tsett. With a whitelist, you need to be sure you've caught everything, or people will be, rightly, upset. For a user-name on a website, and for a password, it is probably fine to allow any ASCII or Unicode character and set up your systems to handle them, leaving far less upset without any real cost to you.

On the other hand, with a blacklist, anything not forbidden is permitted. These are generally used in cases where certain characters have a function and so must be excluded, even if this annoys. So, for instance, in most programming languages variable names may not start with a number, nor contain a comment character.

Apart from the length of the lists, the two methods trade off this annoyance to your user, who must wait until you fix the omission (with a whitelist) against potential unknown failures and security risk (with a blacklist). Imagine the 'incompatible features' problem with both methods. If I use a whitelist, and forget to allow some pairing, my worst case is that I will likely be asked (somewhat irately) why X and Y can't be used together. I realise they can be, I update the code and I make a new release version to fix the omission and everybody is happy. If I use a blacklist and forget that some X and Y don't work together, my worst case is that one day I have to tell somebody that their last n years of research is all invalid, because the simulation they ran didn't work as expected, and since nothing actually went wrong they didn't know. Worse still, would be having to tell them that their fascinating effect is just a code error, and it's my fault.

In some cases, only one or other list type is really viable. For instance, virus scanners keep a list of 'tells' for malicious code, because even though they let things slip through until their lists update, they could never describe all of the 'allowed' code. App permissions (on better, more granular systems) are a whitelist - you give an app the permissions you choose, and only those.

So as a general rules of thumb:

  • If only one method is viable, obviously use that
  • If one or other list is going to be much much shorter, you have better chances of getting it right, so use that method
  • If it is really important not to let things slip through, use a carefully managed, kept up to date, whitelist. If possible, put it into a file or something, so that updates just require sending out new definitions, not modifying the entire code
  • If it's really important not to get accidental exclusions (false positives) use a, similarly carefully managed, kept up to date etc, blacklist
  • In some cases, combine the two. Programming languages generally have a set of allowed characters (a whitelist) and small blacklists for specific contexts such as the first character of a name.

As well as the literal 'blacklist' and 'whitelist' there is a more general principle here - do I selectively forbid, or selectively allow? Do I stop somebody doing this thing here, here and perhaps here, or do I only permit them to do it there and there. If you find the 'here's' or 'there's' proliferating, re-examine whether you're doing it the right way around. In safety or security critical situations, you almost always must allow only what is permitted. If you find yourself trying to plug up security holes with ever growing blacklists, you should probably change tack and think about what should be allowed instead.

May 15, 2019

Datastructures – Linked lists part 1

Back to data structures this month with the linked list. Linked lists are a way of holding data that allows you to add and remove items quickly and easily.

Why not arrays?

First question: why is adding and removing items from an array not quick and/or easy? The problem with adding items is quite simple - arrays have a fixed size so eventually you will run out of spaces in your array to store items. When this happens you have to do something to allocate additional space. Many languages have a function called "realloc" or similar that tries to extend the length of your array but it can only do that if there is unused memory space "above" the location of your array because the array elements have to be arranged one after the other in memory. The concept of "space above" is a bit complex in general and depends on details of your OS etc. but as a general idea if you allocate two arrays then they are placed one after the other in the computer's underlying memory so if you try to realloc the first array then there won't be any space between it and the second array to grow it in. If you can't grow your array like this then you have to allocate new memory to store the bigger array and copy the existing elements in. If you keep adding items then this continual growing of your array can be quite expensive, although this can be mitigated by always growing your array by more elements than you immediately need.

Removing items has the opposite problem. Since arrays are required to be contiguous (can't have gaps in them) you can't just "remove" an item you have to either flag it as empty and ignore it when going through your array in future or take all of the items above the removed element and move them down to pack everything up. The first approach has three problems

  1. You have to use additional memory to flag items as being empty or not
  2. If you are both adding and removing items from your array then since you don't actually recover memory when you remove an item your total memory requirements will grow without bounds
  3. Depending on your algorithm you might have more difficulty getting optimal performance if you have to do fundamentally different things for empty and non-empty array elements

The second approach avoids those problems but on average involves copying half of the elements in your array every time you remove an item which can also be quite expensive.

It is quite possible to build a container based on arrays that you can add and remove items from that has good general performance (C++ std::vector is a good example of one) but they always have to make tradeoffs and if you are doing a lot of adding and removing of arbitrary elements it might be better to use a data structure other than an array.

Linked lists

The idea of a linked list is quite simple. Each element in a linked list is like a link in a chain - linked to the item after them, so you go through the linked list by taking the first item then going to the next item and the next etc. until you reach the end. This is generally implemented using pointers in what are often called "self referential structures", that is structures that contain pointers to themselves. These are easy enough to implement in either C/C++ or Fortran.

struct llitem{
  struct llitem *prev, *next;

TYPE :: llitem
  TYPE(llitem), POINTER :: next, prev
END TYPE llitem

These are more or less normal types but there is one more important rule: self referential structures can contain only pointers to their own type, not actual instances of their own type (try removing the *s in C or the POINTER attribute in Fortran and it will fail to compile). This is because types, much like arrays, are laid out contiguously in memory so they can only contain things that the compiler knows the length of and if you have a type that contains an instance of itself then there would be an infinite regression problem because you don't know how big it is until you have finished creating it and you can't create it until you know how big it is. Pointers are all of a fixed size so they work OK.

The structure as given is for what is technically called a doubly linked list because it contains links both to the next item and the previous item in the list. A singly linked list has each item linked only to the next item in the list. Doubly linked lists have some substantial advantages over singly linked lists, notably that you can go through it from either end, but also you can remove an item from the list needing only the item itself (and the list that it is held in if you have several).

Creating linked lists

Creating a linked list is quite easy. You hold a simple pointer to the first element in the list (generally called the head item) and then you simply create the list going down from that. The key thing is that you have to hook up the prev and next links as you go. This isn't too difficult and looks like


struct llitem{
  int value;
  struct llitem *next;
  struct llitem *prev;

void init_ll(struct llitem * l)
  l-> value = -1;
  l->next = NULL;
  l->prev = NULL;

int main(int argc, char** argv)
  struct llitem *head, *current;
  int i;

  head = malloc(sizeof(struct llitem));
  head->value = 1;
  current = head;
  for (i=0;i<10;++i){
    current->next = malloc(sizeof(struct llitem)); /*Create the next element*/
    init_ll(current->next); /*Initialise it to nullify pointers*/
    current->next->value = current->value + 1; /*Simple counter*/
    current->next->prev = current; /*It's previous pointer should be the current item*/
    current = current->next; /*Now move onwards so the newly created particle is now current*/

  current = head;
    printf("%i\n", current->value);
    current = current->next;


  TYPE :: llitem
    INTEGER :: value = -1
    TYPE(llitem), POINTER :: next => NULL()
    TYPE(llitem), POINTER :: prev => NULL()
  END TYPE llitem

  TYPE(llitem), POINTER :: head, current
  INTEGER :: i

  ALLOCATE(head) !Create the head
  head%value = 1
  current => head
  DO i = 1, 10
    ALLOCATE(current%next) !Create the next element
    current%next%value = current%value + 1
    current%next%prev => current !The next element's previous is the current element
    current => current%next !Now move onwards so the newly created particle is now current

  current => head
    PRINT *,current%value
    current => current%next


This example also shows how you how to step through the linked list from the head, simply by having a "current" pointer that starts at head and is then incremented by setting current = current->next (or current => current%next in Fortran). This can look a bit odd but it isn't that hard to understand. I start by manually creating the "head" element, using either ALLOCATE or malloc. Once I have a head element I then loop through, each time using the same ALLOCATE or malloc command on the "current->next" pointer, creating a new item every time. In C I then call the ll_init function to setup the values of the struct (in Fortran this is done for me since I gave the elements of my TYPE default values). After this the prev and next pointers are both NULL. This is correct for the next pointer becuase my new item is the last item in the list (it won't be next iteration but right now it is), but I have to set the prev pointer. If my new item is the next element in the chain from my current element then the previous element in the chain from my new element must be my current element so I set that up. After that I just have to repeat until I have added enough items.

Part 2 of this will be in a couple of weeks and will describe how you remove and item from a linked list and how to add new items to the middle of a linked list.

May 01, 2019

The Numba "stencil" directive

After a bit of a delay we're getting the blog posts going again with a mention of a slightly odd bit of the Python Numba compiler - the stencil directive. The purpose of Numba is to produce compiled code from Python source that should run at a reasonable fraction of the speed of classical C/Fortran etc. codes. In general it produces codes that is about 20-40% as fast as C or Fortran code, so typically only about 1-2% as fast as the computer can theoretically operate. In general, the more that you can tell Numba in advance about how you are going to use your data the more options it has to optimise the code as it compiles it. The "stencil" directive is used to indicate to Numba that you are going to operate on an array by moving a stencil across it and updating each point using data from neighbouring points.

This is a fairly common thing to want to do and crops up in algorithms from image smoothing to numerical solutions to differential equations so this is a useful bit of the library. As a simple example consider the simplest possible image smoothing algorithm. For each pixel in the image P(i,j) replace the value with the average of the surrounding pixels, so

P'(i,j) = 1/4 * (P(i+1,j) + P(i-1,j) + P(i,j+1) + P(i,j-1))

Note that the left hand side of this equation is P' not P, so when we calculate the average for each pixel using the original values surrounding it not the values that have already been through the averaging process. After you have finished you copy P' to P. There is then one last thing that you have to worry about: what do you do when you reach the edge of the array? Since you are using adjacent cells you have to do something or you will read outside your array. Numba's stencil operator at present only has two options: set the outer cells to be zero or some other constant value. In general, this will mean that you want to have an outer strip of cells added around your image otherwise your image will get smaller as it smooths. These outer cells are often called ghost or guard cells and are also common in numerical solution of differential equations for representing boundary conditions. The code for doing all this in Python is quite simple

def blur(A):
    s = A.shape
    B = np.zeros((s[0],s[1]))
    for i in range(1,s[0]-1): #Range only over the inner cells
        for j in range(1,s[1]-1): #Range only over the inner cells
             B[i, j] = 0.25 * (A[i-1,j] + A[i+1,j] + A[i,j-1] + A[i,j+1])
    return B

This code takes a numpy array and iterates over all but the outer strip of cells in every direction, averages and returns the value. Each call to this function smooths your image a bit (by a radius of about 1 pixel) so in general you'll want to call it several times to smooth your image as much as you want. Running this algorithm on a stock image of 1529 x 2250 pixels on a 3.4GHz processor takes about 3.3 seconds per iteration using the pure Python implementation and 0.006 seconds by using the Numba @njit decorator. For testing we ran 100 iterations of the pure Python code and 1000 iterations of the Numba code. If run to the same number of iterations, the results in both cases is the same

Circuit board image before smoothingCircuit board image after smoothing 1000 times

The simple equivalent using stencil is

def blur(A):
    return 0.25 * (A[-1,0] + A[1,0] + A[0,-1] + A[0,1])

You can see how i-1 becomes just -1 and similarly for other parameters in the stencil, and you can also see how this operation now becomes a one-liner so it's much easier to write. Unfortunately the performance is much worse than the @njit version too taking about 0.22 seconds per iteration, although that is still some 10x faster than the native python performance. Fortunately performance can be improved by calling the stencil from a Numba jit-ed function, so for example

def inner_blur(A):
    return 0.25 * (A[-1,0] + A[1,0] + A[0,-1] + A[0,1])

def blur(A):
    return inner_blur(A)

The result from this method gives performance that is indistinguishable from that of the direct Numba jit version and is still rather shorter. Since these stencils lay out the data dependency you can also set parallel=True in the @njit call and this can be quite succesful but tends to work better for more complex stencils. In this particular case despite showing the Python interpreter apparently using 6 cores solidly the execution speed slows down by a factor of 3.

May 2019

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