from complex import ComplexFloat64

# Initialize two complex numbers
a = ComplexFloat64(re=3.0, im=4.0)
b = ComplexFloat64(re=5.0, im=-2.0)

# Perform basic operations
c = a + b  # Add two complex numbers
d = a * b  # Multiply two complex numbers
e = -a     # Negate a complex number
f = a.norm()  # Get the magnitude of a complex number

print(f"Addition: {c}, Multiplication: {d}, Negation: {e}, Magnitude: {f}")

Overview

The ComplexSIMD component from the complex package offers a sophisticated way to represent and manipulate complex numbers leveraging SIMD (Single Instruction, Multiple Data) capabilities. This component is designed to efficiently handle complex mathematical operations, particularly beneficial for high-performance computing tasks.

Key Features

• SIMD Optimization: Utilizes SIMD for parallel processing of complex numbers, enhancing computational efficiency.
• Basic Arithmetic Operations: Supports addition, multiplication, and negation of complex numbers.
• Magnitude Calculations: Provides methods to calculate the magnitude (norm) and squared magnitude (squared_norm) of complex numbers.
• Fused Operations: Includes fused multiply-add (fma) and squared-add (squared_add) operations for advanced computational tasks.

Use Cases

• Signal Processing: Ideal for applications in signal processing where complex numbers are frequently used to represent signals.
• Quantum Computing Simulations: Can be utilized in simulations of quantum systems, where complex numbers play a crucial role.
• Electrical Engineering: Useful for electrical engineers working with phasors, impedances, and other complex-valued entities.
• Scientific Research: Supports complex mathematical operations required in physics, engineering, and other scientific disciplines.

Considerations

• Precision and Performance: Choose the appropriate data type (ComplexFloat32 or ComplexFloat64) based on the required precision and performance trade-offs.
• SIMD Width Compatibility: Ensure the hardware supports the SIMD width used by the complex numbers for optimal performance.

Compatibility

The ComplexSIMD component is designed to be versatile, but its performance benefits are most pronounced on platforms that support SIMD instructions. The choice between ComplexFloat32 and ComplexFloat64 should be made based on the precision requirements of the application and the underlying hardware capabilities.