How Can I Efficiently Convert 32-bit Floating-Point Numbers to 16-bit for Network Transmission?

32-bit to 16-bit Floating Point Conversion:

Background:
You seek a library or algorithm that can seamlessly convert between 32-bit and 16-bit floating-point numbers. The goal is to reduce the size of 32-bit floats for transmission over the network, acknowledging the potential loss of precision.

Solution:

Branchless Conversion:
The provided solution leverages a branchless conversion technique that utilizes the fact that -true == ~0. This enables efficient conversions without the use of conditional jumps or complex logic.

Accuracy:
To ensure accurate rounding, the algorithm performs bit-wise operations and employs a tie-breaking bias. This ensures that values are rounded correctly, even with significant differences in precision between the input and output formats.

Simplified Logic:
The provided code includes simplified if statements as comments above each branchless select to enhance clarity. Additionally, all incoming NaN (Not-a-Number) values are converted to the base quiet NaN for speed and consistency.

Usage:
You can use the encode_flt16 function to convert from 32-bit or 64-bit floats to 16-bit floating-point format. To decode the 16-bit floats back to 32-bit or 64-bit representation, you can use the decode_flt16 function.

Optimized for Network Transmission:
The generated 16-bit floats are suitable for network transmission due to their reduced size, effectively optimizing data transfer speed.

Additional Features:

Extensive Format Support:
The provided algorithm supports conversion between 32-bit and 16-bit half-precision IEEE formats, as per your request.

Cross-Platform Compatibility:
The solution is designed to work across multiple platforms, offering portability for your application.

Caution:

Loss of Precision:
As mentioned in your query, converting from 32-bit to 16-bit floating-point numbers may result in significant precision loss. The algorithm can only approximate the original values to the best of its ability within the 16-bit format.

Alternative Approach:

Linearization for Non-Logarithmic Values:
If your values do not require logarithmic resolution approaching zero, you could consider linearizing them to a fixed-point format for faster processing. However, this technique is not the focus of the provided solution.

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