Thursday 19 April 2007
Ignoring folders with TODO Bundle in TextMate
Wednesday 11 April 2007
The Joys Of Floating Point Numbers
double pi = 3.1415926535897932384626433832795; double val = sqrt(pi) * sqrt(pi); printf("pi = %f\n", pi); printf("val = %f\n", val);which yields
pi = 3.141593 val = 3.141593Which is what we expected!
val
is the same as pi (the square is the inverse of the square root as we all know). However, the following C snippet shows the problem we run into:
if (val == pi) { printf ("pi == val\n"); } else { printf ("pi != val\n"); }which yields
pi != valSo two apparently equal values are not equal any more! Where is the problem? It is in the precision of
printf()
, of course. We modify the first snippet so the printf()
calls print the floating point values to more significant places
printf("pi = %.16f\n", pi); printf("val = %.16f\n", val);and now we get
pi = 3.1415926535897931 val = 3.1415926535897927So how do we resolve this? Instead of comparing floating point values directly, we calculate their difference and make sure it is below a small value, for example
1e-9
:
if (abs(val - pi) < 1e-9) { printf ("pi == val\n"); } else { printf ("pi != val\n"); }which now gives us
pi == valI guess most programmers are aware about the problems with floating point numbers and I have also known about the problem for a long time. What made me stumble, however, was that I trusted the printed value - which was inaccurate. As far as I know, there is no generic solution to the problem with floating point inaccuracies. You will get away with comparing whether the difference between two floating point values is smaller than a given value for comparing. In Ruby, you could hack the built in
Float
class with the following:
class Float def ==(value) self - value < 0.01 end endThis allows us to compare floating point values “fuzzily”:
>> Math.sqrt(2) ** 2 == 2.0 => false >> require 'floathack' => true >> Math.sqrt(2) ** 2 == 2.0 => trueHowever, I do not think that this is a good idea! Overwriting the
==
operator of the Float
as above breaks its transitivity, i.e. we get the following (in-)equalities
1.99 == 2.00 == 2.01 but 1.99 != 2.01
Another idea would be only to compare the first n numbers after the point, e.g. consider 3.1415926535897931 to be 3.141 for n = 2. However, this does not help us if a floating point error gives us two values just next to a “boundary”, i.e. a result of 1.999 would not be considered correct if 2.001 was expected and we only cared about the result being “sufficiently close” to the expected value.
So be careful when using floating point values are checking two of them for equality. Trouble will strike and most probably find some way to trick you into wasting time.
An extensive, academic - and arguably dry - discussion of the implications of floating point arithmetics can be found in What Every Computer Scientist Should Know About Floating-Point Arithmetic, by David Goldberg.
Saturday 7 April 2007
SQLite gotcha
SQLite is great. No, really, I do mean it. If you ever need to work on structured data and editing it from the outside is a must, then SQLite is worth checking out and might be a superior choice to XML and will be a superior choice to your own proprietary format.
I cannot speak about performance - there are some outdated claims that SQLite is faster than postgres and mysql for the most common operations; but those benchmarks don't feature a single join, and that's where database implementation gets interesting and hard. I just cannot believe that SQLite stands up to any full scale DBMS.
I spent a few hours chasing down a bug in my own code after realising that I've been utterly stupid and put my parameters in the wrong order into my parameter list.
To boil it down, this is what happens in SQLite if I compare an integer field with a string in a WHERE part of a statement:
sqlite> CREATE TABLE my_favourite_numbers (number integer);
sqlite> SELECT * FROM my_favourite_numbers WHERE number = "foo";
sqlite>
You get no result. No error is thrown, like in Postgres:
# CREATE TABLE my_favourite_numbers (number integer);
# SELECT * FROM my_favourite_numbers WHERE number = 'bla';
ERROR: invalid input syntax for integer: "bla"
I know now what to look out for in the future.
Friday 6 April 2007
First Post
- programming
- computers in the widest sense
- computer science (prepare for some math, hehe).