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 SpeedCalculates ‘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 VolumeNo limits by paceval. The limit values ​​are determined by the hardware system or development environment used.

Dependent on Compiler:

long double80 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)
double64 bitsvalue area
1.7E +/- 308
16 digits
float32 bitsvalue area
3.4E +/- 38
7 digits
Accuracy optimizationTrusted 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 variablesNo 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)
AND Operator ConjunctionAND
OR Operator DisjunctionOR
XOR Operator Exclusive DisjunctionXOR
NOR OperatorNOR
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 valuesA paceval. identifier must start with a letter (A-Z) or (a-z); subsequent characters can also be digits (0-9).
Power Sign^
Square Functionsqr()
Square Root Functionsqrt()
Exponential Functionexp()
Logarithm Functionlg()
Natural Logarithm Functionln()
Standard Logistic Sigmoid Functionsig()
Trigonometric functions
Sine Functionsin()
Cosine Functioncos()
Tangent Functiontan()
Cotangent Functioncot()
Inverse trigonometric functions
Arc Sine Functionasin()
Arc Cosine Functionacos()
Arc Tangent Functionatan()
Arc Cotangent Functionacot()
Hyperbolic functions
Hyperbolic Sine Functionsinh()
Hyperbolic Cosine Functioncosh()
Hyperbolic Tangent Functiontanh()
Hyperbolic Cotangent Functioncoth()
Inverse hyperbolic functions
Area Hyperbolic Sine Functionarsinh()
Area Hyperbolic Cosine Functionarcosh()
Area Hyperbolic Tangent Functionartanh()
Area Hyperbolic Cotangent Functionarcoth()
Numerical manipulations
Sign Functionsgn()
Absolute Value Functionabs()
Rounding Value Functionround()
Ceiling Value Functionceil()
Floor Value Functionfloor()
Other Numerical manipulations (paceval. specific)
Greater Than Zero Functionispos()
Greater Than Zero Or Zero Functionisposq()
Less Than Zero Functionisneg()
Less Than Zero Or Zero Functionisnegq()
Is Zero Functionisnull()


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 applicationsCalculations 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 algorithmsYou can easily create your own pattern matching algorithms that identify patterns and regularities in data.
Safety ConceptWith a special technique we can quickly monitor whether data manipulation, i. H. Hack, your mathematical models will take place.
Object code footprintOnly a few hundred of kilobytes in size; exact size depends on your compiler, development environment and operating system.
Memory usage footprintOnly 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 languageWritten in standard C/C++ as defined per ISO
Supported operating systemAny; operates best on 16bit and above, e.g. Linux, Windows, iOS, macOS, Android, as well as
proprietary or specialized operating systems
Supported development environmentAny; 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 conceptIntegrate a paceval. library simply with text files into your software.
CommandsJust use the standard mathematical notations when using paceval.



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