# PRODUCT BRIEF – paceval.

## Computing

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. Limits are set by the hardware system or development environment you use.
Accuracy Dependent on Compiler:

 long double 80 bits -1.1E-4932.. 1.1E-4932 value area 19 digits double 64 bits -1.7E-308.. 1.7E+308 value area 15 digits float 32 bits -3.4E-38.. 3.4E-38 value area 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. Limits are set by the hardware system or development environment you use.

## Supported terms in closed-form expressions>> and interval arithmetic>>

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
 Factorial Sign ! Factorial Function (paceval. specific) fac()
Constants
 π (~3.1415384626433832795) pi Euler’s number (~2.718281828459045235) e
Brackets
 Circle Bracket Open Character ( Circle Bracket Close Character )
Variables
 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).
Exponentiation
 Power Sign ^ Square Function sqr() Square Root Function sqrt() Exponential Function exp()
Logarithm
 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()

## Use cases, security and size

 Watchdog and System monitoring applications Big hardware systems with many small sub-systems and processors or sensors (e.g. cars, automation,..) can be connected monitored through a mathematical model implemented by a finite-state machine being processed by paceval. Black-box testing, Boundary and Stress testing To identify and quickly solve 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 changing more and more to self computing (intelligent) things. Fast and trusted calculations will help you to improve your development cycles and overall timelines leading to lower costs and broad support of diverse (hardware) systems. Pattern matching algorithms You can easily create your own pattern matching algorithms identifying patterns and regularities in data. Safety Concept With a special technique, we are able to monitor quickly if data manipulation, i.e. hacking, of your mathematical models takes 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.

## Handling and integration

 Programming language Written in standard C/C++ as defined per ISO Supported operating system Any; operates best on 16bit and above Supported development environment Any; you just need a suitable compiler for the integration in your target development environment, e.g. C++, Python, Object Pascal, Fortran, Visual Basic, Java, C#, Perl, Ruby or PHP. Integration concept Integrate a paceval. library simply with text files into your software. Commands Just use the standard mathematical notations when using paceval.