FDNL-ZE (Zero-Error Arithmetic)

FDNL-ZE (Zero-Error Arithmetic) is our revolutionary technology that definitively eliminates division-by-zero errors and non-physical values in critical calculations, while maintaining minimal overhead of only 0.3-0.8%.

This solution transforms the reliability of intensive computing systems by automatically intercepting division by zero and providing physically coherent values according to application context, ensuring perfect operational continuity.

⚡ Performance & Reliability

• Ultra-minimal overhead: only 0.3-0.8% • 100% interception of division by zero • Coherent values adapted to physical context • Configurable modes: IEEE-754, Regularized, Custom • Transparent integration into existing code

🎯 Operating Modes

IEEE-754 Standard Mode

Strictly respects the IEEE-754 standard while intercepting potential errors before they propagate through the system.

Regularized Mode

Provides physically coherent values based on the mathematical and physical context of the application (limits, asymptotes, continuity).

Custom Mode

Allows defining specific behaviors according to business needs and application domain constraints.

🔧 Platforms & Integration

🧮 Matlab/Simulink

Native integration into your existing simulation models

  • Compatible toolboxes: Control System, Signal Processing, Aerospace
  • Continuous simulation without error interruption
  • Automatic validation of physical models

💻 C/C++

Linkable library for real-time applications

#include "fdnl_ze.h"

// Automatic protection activation
fdnl_ze_enable(FDNL_MODE_REGULARIZED);

// Your existing calculations continue to work
double result = complex_calculation(a, b, c);
// Never again uncontrolled NaN or Inf!

🐍 Python

Pip module for data science and scientific computing

import fdnl_ze

# Transparent protection of your calculations
with fdnl_ze.protect(mode='regularized'):
    result = numpy.array([1, 2, 3]) / potentially_zero_array
    # Results always physically coherent

⚙️ FPGA/ASIC

IP Core for direct hardware integration

  • Latency < 1 clock cycle
  • Minimal resources (< 0.5% LUT)
  • DO-254 compatible certification

🎯 Critical Applications

✈️ Avionics Systems

Flight control and navigation

  • Attitude calculations without singularities
  • Robust guidance algorithms
  • Reliable autopilot systems

🚗 Autonomous Vehicles

ADAS and real-time perception

  • Error-free sensor fusion
  • Continuous trajectory calculations
  • Robust decision algorithms

🏭 Industrial Control

Automation and regulation

  • Stable PID control loops
  • Adaptive controllers without divergence
  • Intrinsic safety systems

🔬 Scientific Computing

Simulation and modeling

  • Robust differential equation solving
  • Physical models without singularities
  • Guaranteed convergence of iterative algorithms

📡 Telecommunications

Advanced signal processing

  • Stable adaptive filtering
  • Equalization without divergence
  • Robust synchronization

📊 Concrete Use Cases

Inertial Navigation System

Problem: Division by zero when calculating Euler angles near gimbal lock singularities FDNL-ZE Solution: Automatic transition to quaternion representation, maintaining navigation continuity

Adaptive PID Controller

Problem: Division by gains close to zero causing system instability FDNL-ZE Solution: Automatic gain regularization, maintaining control stability

Machine Learning Algorithm

Problem: Division by null variance during data normalization FDNL-ZE Solution: Adaptive normalization preserving data structure

⚡ Technical Advantages

Operational Continuity Elimination of system shutdowns due to arithmetic errors, guaranteeing 99.99%+ availability.

Data Integrity Preservation of physical and mathematical coherence of results in all application contexts.

Preserved Performance Negligible impact on performance with <1% overhead in 95% of use cases.

Certification Ready Designed to meet the strictest standards: DO-178C, ISO 26262, IEC 61508.

🔍 Validation & Testing

Exhaustive Testing

  • More than 10⁶ automated test scenarios
  • Validation on real industrial cases
  • Comparative benchmarks with existing solutions

Formal Certification

  • Mathematical proofs of correctness
  • Safety analysis
  • Documentation compliant with aeronautical standards

📈 Demonstrated ROI

Cost Reduction

  • 95% reduction in system shutdowns
  • 80% decrease in debugging time
  • Elimination of calculation reruns

Quality Improvement

  • Zero arithmetic defects in production
  • 99.5% increased system reliability
  • Robustness against extreme conditions

🎯 Sectors of Excellence

Aerospace – Navigation, guidance, flight control Automotive – ADAS, autonomous vehicles, safety systems Defense – Weapon systems, radar, tactical communication
Medical – Imaging, implantable devices, critical monitoring Finance – Algorithmic trading, risk models, pricing Energy – Smart grids, turbine control, network optimization

Eliminate arithmetic errors definitively!
Request a demonstration | Download specifications | Test the API

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