Fix IEEE 754 Conversion and ULP Calculation in Float64 Binary Conversion

[0xbryer]

This contribution resolves a critical issue in the binary_to_float64 function and ULP calculation logic, ensuring compliance with the IEEE 754 standard and improving code clarity and correctness.

Key Changes

1. Sign Bit Handling:
   The previous implementation overlooked the sign bit in the IEEE 754 format, always treating numbers as positive. This fix incorporates proper sign handling, allowing accurate conversion of both positive and negative numbers.

2. Mantissa Length Correction:
   The function previously processed a 53-bit mantissa instead of the standard 52 bits (with an implicit leading bit). This fix ensures the mantissa length adheres to the standard by truncating excess bits and appending the hidden leading bit correctly.

3. ULP Calculation Refinement:
   The code introduced ambiguity by reassigning ulp to different meanings. This fix separates ULP distance (difference between r_plus and r_minus) from the ULP error calculation, improving code readability and maintaining semantic consistency.

4. Improved Code Robustness:
   The revised implementation ensures better handling of edge cases and simplifies logic for future maintenance.

Why This Matters

• The IEEE 754 floating-point format is foundational in many numerical computations. Misrepresenting values can lead to cascading inaccuracies in applications relying on this function.
• Proper ULP calculation is crucial for numerical precision, particularly in applications like cryptography, scientific simulations, and performance benchmarking.

Testing and Validation

• The updated function has been tested with a variety of inputs, including boundary cases for positive and negative numbers.
• Results were validated against expected values, ensuring compliance with the IEEE 754 standard and correct ULP computation.

This fix not only addresses the immediate issue but also lays a more solid foundation for further improvements and ensures reliability in precision-critical scenarios.