A mathematical model must be transparent traceable and demonstrably continuously improvable, without having to be entirely re-qualified.
[EU legal requirement]

A mathematical model must be easy to integrate on any hardware and software, and consistently deliver mathematically correct results.
[simplicity and quality requirement]

Date: May 2021

PRODUCT BRIEF – paceval.
mathematical engine, Version 4.01

Computing Excellence

Calculation Speed Calculates ‘real-time’, in milliseconds. In repeated calculations even faster as we use caching methods. Exact speed is dependent on hardware capacities and function complexity.
Data Volume No limits by paceval. The limit values ​​are determined by the hardware system or development environment used.

Dependent on Compiler:

long double 80 bits (or 128 bit on IBM POWER and special versions) value area
1.1E +/- 4932
19 digits (or 31 digits on IBM POWER and special versions)
double 64 bits value area
1.7E +/- 308
16 digits
float 32 bits value area
3.4E +/- 38
7 digits
Accuracy optimization Trusted Interval Computation, TINC™ (paceval. specific Interval arithmetic) putting bounds on rounding errors and measurement errors of the computation system to yield reliable results.
Formula length and numbers of variables No limits by paceval. The limit values ​​are determined by the hardware system or development environment used.


Computing Excellence
Supported terms in closed-form expressions and interval arithmetic

       + Allows the definition of up to 1000 custom user functions.

Elementary arithmetic
Addition Sign +
Subtraction Sign
Multiplication Sign *
Division Sign /
Logical operators returning Boolean values either 0 (for false) or 1 (for true)
Negation NOT()
AND Operator Conjunction AND
OR Operator Disjunction OR
XOR Operator Exclusive Disjunction XOR
NAND Operator NAND
NOR Operator NOR
XNOR Operator XNOR
Annotation: For the operands, 0 is false and all other values ​​are true.
Relational operators
less than. greater than, not equal to <, >, <>
equal to, greater than or equal to, less than or equal to =, >=, <=
Factorial Sign !
Factorial Function (paceval. specific) fac()
π (~3.1415384626433832795) pi
Euler’s number (~2.718281828459045235) e
Circle Bracket Open Character (
Circle Bracket Close Character )
Variables as symbolic names for values A paceval. identifier must start with a letter (A-Z) or (a-z); subsequent characters can also be digits (0-9).
Power Sign ^
Square Function sqr()
Square Root Function sqrt()
Exponential Function exp()
Logarithm Function lg()
Natural Logarithm Function ln()
Standard Logistic Sigmoid Function sig()
Trigonometric functions
Sine Function sin()
Cosine Function cos()
Tangent Function tan()
Cotangent Function cot()
Inverse trigonometric functions
Arc Sine Function asin()
Arc Cosine Function acos()
Arc Tangent Function atan()
Arc Cotangent Function acot()
Hyperbolic functions
Hyperbolic Sine Function sinh()
Hyperbolic Cosine Function cosh()
Hyperbolic Tangent Function tanh()
Hyperbolic Cotangent Function coth()
Inverse hyperbolic functions
Area Hyperbolic Sine Function arsinh()
Area Hyperbolic Cosine Function arcosh()
Area Hyperbolic Tangent Function artanh()
Area Hyperbolic Cotangent Function arcoth()
Numerical manipulations
Sign Function sgn()
Absolute Value Function abs()
Rounding Value Function round()
Ceiling Value Function ceil()
Floor Value Function floor()
Other Numerical manipulations (paceval. specific)
Greater Than Zero Function ispos()
Greater Than Zero Or Zero Function isposq()
Less Than Zero Function isneg()
Less Than Zero Or Zero Function isnegq()
Is Zero Function isnull()


small and safe
Use cases, security and size

Watchdog and System monitoring applications

Large hardware systems with many small subsystems and processors or sensors (e.g. cars, automation, etc.) can be monitored by a mathematical model that is implemented by a finite-state machine processed by paceval.

Black-box testing, Boundary and Stress testing

To identify and quickly fix anomalies in system and software / hardware applications, paceval. can be used to define and create black box test cases based on a mathematical model. Usually this mathematical model is derived from the specification or is already part of the specification for the application.

Internet of Things applications Calculations on computers and servers are increasingly changing into self-computing (intelligent) things. Fast and trustworthy calculations help you to improve your development cycles and overall schedules, which leads to lower costs and broad support for various (hardware) systems.
Pattern matching algorithms You can easily create your own pattern matching algorithms that identify patterns and regularities in data.
Safety Concept With a special technique we can quickly monitor whether data manipulation, i. H. Hack, your mathematical models will take place.
Object code footprint Only a few hundred of kilobytes in size; exact size depends on your compiler, development environment and operating system.
Memory usage footprint Only a few hundred kilobytes in size; exact size depends on your compiler, development environment and mathematical model.

easy handling fast implementation
Handling and integration

Programming language Written in standard C/C++ as defined per ISO
Supported operating system Any; operates best on 16bit and above, e.g. Linux, Windows, iOS, macOS, Android, as well as
proprietary or specialized operating systems
Supported development environment Any; you just need a suitable compiler for the integration in your target development environment, e.g. Golang, C++, Python, Object Pascal, Fortran, Visual Basic, Java, C#, Perl, Ruby or PHP, see https://github.com/paceval. Enables a low code/no code approach.
Integration concept Integrate a paceval. library simply with text files into your software.
Commands Just use the standard mathematical notations when using paceval.



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