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Project Notes

Error Function

Methods for calculating the Gauss error function in C with standard libraries and the GNU Scientific Library.

Notes

In mathematics, the error function is the probability that Y falls in the range [−x, x], where the random value Y is normally distributed with mean 0 and variance 1/2.

Error_Function

Using the C Standard Library

The erf.c example calculates the probability and area under the curve for a couple of sample values. It uses the erf() function from the C standard library, defined in header <math.h>.

The example requires linking with the math library (-lm). The Makefile is setup to compile and link the example, else it can be done by hand:

gcc erf.c -o erf -lm -Wall -O3 -std=gnu11

Installing the GNU Scientific Library

It is probably most common to install the GSL in precompiled form via a package managed. On Mac, I’d do that with brew install gsl - see the gsl homebrew fomula

But for now, I’m going to install from source as follows. NB: 1.15 is a pretty old version now.

wget ftp://ftp.gnu.org/gnu/gsl/gsl-1.15.tar.gz
tar xvzf gsl-1.15.tar.gz
rm gsl-1.15.tar.gz
cd gsl-1.15
./configure
make
sudo make install

All worked fine - installed to /usr/local/lib/libgsl* and /usr/local/include/gsl/, and can now be referenced with the help of pkg-config:

$ pkg-config --libs gsl
-L/usr/local/lib -lgsl -lgslcblas -lm

Using the GNU Scientific Library

The erf_gsl.c example repeats the calculation, but using functions from the GNU Scientific Library, namely:

Running the Examples

$ make
gcc -Wall -O3 -std=gnu11    erf.c  -lm -o erf
gcc -Wall -O3 -std=gnu11    erf_gsl.c  `pkg-config --libs gsl` -o erf_gsl
./erf
The probability that Normal(0, 1) random variable has a value between -0.25 and 0.25 is: 0.276326
The integral of a Normal(0, 1) distribution between -0.25 and 0.25 is: 0.197413
The probability that Normal(0, 1) random variable has a value between -1.96 and 1.96 is: 0.994426
The integral of a Normal(0, 1) distribution between -1.96 and 1.96 is: 0.950004
./erf_gsl
The probability that Normal(0, 1) random variable has a value between -0.25 and 0.25 is: 0.276326
The integral of a Normal(0, 1) distribution between -0.25 and 0.25 is: 0.197413
The probability that Normal(0, 1) random variable has a value between -1.96 and 1.96 is: 0.994426
The integral of a Normal(0, 1) distribution between -1.96 and 1.96 is: 0.950004

Credits and References

About LCK#118 c
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This page is a web-friendly rendering of my project notes shared in the LittleCodingKata GitHub repository.

LittleCodingKata is my collection of programming exercises, research and code toys broadly spanning things that relate to programming and software development (languages, frameworks and tools).

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