How to Convert 32-bit Floating Point Numbers to 16-bit with Minimal Precision Loss?

32-bit to 16-bit Floating Point Conversion

Problem:
Convert 32-bit floating point numbers to 16-bit floating point numbers while minimizing precision loss. The converted values will be transmitted over a network, making size reduction a priority.

Solution:
This article introduces three solutions:

1. Encode IEEE 16-bit Floating Point:

   • Uses a cross-platform library that supports IEEE 16-bit floating point format.
   • This method is suitable for precise conversion between 32-bit and 16-bit floating point numbers.

   • Sample code:

     <code class="cpp">auto encodedValue = encode_flt16(floatValue);
     auto decodedValue = decode_flt16(encodedValue);</code>

2. Linear Conversion to Fixed Point:

   • Linearly maps the input 32-bit floating point number to a 16-bit fixed point format.
   • This method is faster than IEEE conversion but less precise, especially around zero.

   • Sample code:

     <code class="cpp">// Assuming 8-bit mantissa
     uint16_t fixedPointValue = (uint16_t)(floatValue * (1 << 8));
     float decodedValue = (float)fixedPointValue / (1 << 8);</code>

3. Round-to-Nearest Conversion:

   • Converts the 32-bit floating point number to a 16-bit floating point number using rounding to the nearest value.
   • This method provides a balance between speed and precision.

   • Sample code:

     <code class="cpp">// Assuming float16 type supports binary32 conversion
     float16 float16Value = float16(floatValue);</code>

Select the conversion method based on the specific requirements of your application, such as precision and performance.

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