from math import add, mul, div, sub, sqrt

# Example of using the API for elementwise addition of two SIMD vectors
x = SIMD([1, 2, 3, 4], 4)  # First SIMD vector
y = SIMD([5, 6, 7, 8], 4)  # Second SIMD vector
result = add(x, y)  # Elementwise addition

Overview

The provided math API facilitates a variety of mathematical operations optimized for Single Instruction, Multiple Data (SIMD) processing. SIMD enables parallel processing of vectorized data, significantly enhancing computational efficiency for specific tasks. This API is designed to support operations on vectors, offering a suite of functions from basic arithmetic to more complex mathematical functions.

Key Features

• SIMD Support: Efficiently processes multiple data points in a single instruction, optimizing performance for vectorized computations.
• Broad Functionality: Includes basic arithmetic (addition, subtraction, multiplication, division), bit manipulation, and advanced mathematical functions (square root, trigonometric functions, exponentials).
• Type Flexibility: Supports a variety of data types, ensuring compatibility with different numeric representations.
• Precision Control: Functions like round, floor, ceil, and truncate provide precise control over numeric approximations.
• Vector Operations: Capable of elementwise operations, comparison, logical operations, and reduction functions across vectors.

Use Cases

• Scientific Computing: Accelerates calculations in physics simulations, statistical models, and mathematical research.
• Image Processing: Enhances performance in tasks like filtering, transformation, and analysis of pixel data.
• Financial Modeling: Optimizes complex financial simulations and risk assessments through efficient numeric computations.
• Machine Learning: Speeds up operations in neural networks, particularly in matrix multiplications and transformations.

Considerations

• Vector Alignment: Ensure data is appropriately aligned for SIMD operations to avoid performance degradation.
• Data Type Compatibility: Pay attention to function requirements regarding data types to prevent unexpected results or errors.
• Error Handling: Some operations might not handle exceptions like division by zero or overflow internally; user validation may be necessary.

Compatibility

This API is designed for environments that support SIMD operations. Compatibility may vary depending on the underlying hardware and the programming language's runtime environment. It's essential to verify support on the target platform for optimal performance.