1. Introduction
1.1. Benchmark suite
The benchmark routines for this benchmark suite
have been developed under Mathematica 5. It is freely available under the
following link:
Click here to download the Mathematica
notebook for this benchmark test.
Note:
Please run the benchmark suite only with a fresh loaded Mathematica
kernel, don't run it more then once during the same session and make sure that
no other programs are running in the background which might disturb the
performance measurement. Only if these requirements are guaranteed then the
resulting timings are comparable.
1.2. Latest results
This is the latest version of Mathematica timing tests; (further
results are welcome: stefan@steinhaus-net.de).
New results:
Toshiba Satellite U500-1DV, Intel Core i5 M430, 2.27 GHz
(1.066 GHz FSB), 4 GB DRR3 RAM, Win. 7 Home Premium (64 Bit) [25]
1.3. The benchmark functions
The intention of the benchmark suite is to
cover the timings of functions from every important The functions used in this benchmark suite
have been grouped by mathematical topic groups. The following topics are
covered:
- Miscellaneous operations
- Integer computations
- Floating point computations
- Symbolic computations
- Graphics
- Animations
1.3.1. Miscellaneous operations
The section miscellaneous operations covers typical data
manipulation operations.
- 150 times doing the following steps: Creation of a
1.000x1.000 random matrix, take the absolute values of this matrix, transposes
the matrix, flattens it to a list and resizes it to a 500x2.000 matrix
- Sorting of 20.000.000 random values.
1.3.2. Integer computations
The section of integer computations covers operations with
integere numbers as input and output most especially in terms of number theory.
- Computation of the factorial of 2.200.001 (2.200.001!)
- Check of the first 5.000.000 numbers of the form x^2-1
whether they are Mersenne
Prime numbers
- Computation of the first 260 Euler numbers of the
polynomial n
- 150 times computing a 1.000x1.000 Toeplitz matrix
1.3.3. Floating point computations
The section of floating point computations covers several
functions from simple math., Linear Algebra, Analysis and Statistics which have
to work with floating point numbers.
- Calculate Pi on 3.000.000 digits behind the comma.
- Creates a 1.500x1.500 random matrix and computes the
Eigenvalues of it.
- Creates a 800x800 random matrix and computes an orthogonal
and normalized set of it.
- Numerical integration of 6 triple integrals.
- Creates 2^23 random values, calculates the FFT followed by
inverse FFT.
- Creates a table with 1.920 random values with 3 factor
columns and calculates a 3 way ANOVA with 4 levels.
1.3.4. Symbolic computations
The symbolic computation section covers simple but time
intensive symbolic computations.
- Creates a polynomial with more then 3.000 terms and
expands it.
- Computation of a multidimensional Laplace transformation.
1.3.5. Graphics
The graphics section covers complex 2D and 3D graphics.
- Computation of a 8 level
Koch snowflake.
- Computation of an graphics array containing 9
Mandelbrot graphics. Each graphic symbolizes a zoom into the previous Mandelbrot graphic.
- Computation of an
graphics array with 3D parametric pipes
and Klein bottles.
1.3.6. Animation
This section covers only a short excursion into the subject
of animated graphics.
- Animation of a 3D heat mountain.