Dan Baruth, Dr. rer. nat.
IGING, Los Angeles

Using computer graphics to analyze mathematical functions allows instant visualization of their characteristics. Furthermore, optimal gauging of approximations as well as detection of programming errors are facilitated.  Analyses of complex functions, their singularities in particular, yield intriguing 3D structures -- See example in Graphical Analyses below.

In some cases the 80-bit x87 FPU registers can not contain accumulating rounding errors. To overcome this difficulty, large (48-byte) Virtual Floating Point Registers were introduced (see example below). They can also be used to test the precision of "native 80-bit" results.

These tools, methods and algorithms were created for the development of reliable libraries of Transcendental Functions and can be used to analyze practically any mathematical formula.  Hence, we offer to independently study the behaviour of mathematical functions embedded in a client's software-driven system.  For details, please contact x87@iging.com.


Graphical Analyses

Bessel Functions

J_ν(x)  -  Error analysis
J₁₀₀₀₀(x≤ 9990)  -  Debye's asymptotic expansion
J_1000000(x)  -  Fixed large index and large arguments

Riemann Zeta Function

ζ(x)  -  Real Function Analysis
ζ(z)  -  Complex Singularity Image

Virtual Floating Point Registers

Introduction to Virtual Registers
Evaluating ₁F₁(-n;½;x)