How to Convert 32-bit Floating-Point Numbers to 16-bit Floating-Point Numbers?

32-bit to 16-bit Floating Point Conversion

Converting 32-bit floating-point numbers to 16-bit floating-point numbers is a common requirement when transmitting data over networks to minimize size. Here's an algorithm for such conversion:

1. Initialization:

• Define the following constants for 32-bit (float) and 16-bit (flt16) floating-point formats:

  • Significand bits (sig_bits): 23 for float, 10 for flt16
  • Exponent bits (exp_bits): 8 for float, 5 for flt16

2. Encoding:

• Convert the 32-bit floating-point number (value) to 16 bits using the encode_flt16() function, which rounds the result:

  <code class="cpp">uint16_t half_value = encode_flt16(value);</code>

3. Decoding to 32-bit Floating Point:

• To convert the 16-bit floating-point number back to 32-bit, use the decode_flt16() function:

  <code class="cpp">float decoded_value = decode_flt16(half_value);</code>

4. Considerations:

• The conversion introduces some rounding error due to the reduction in precision from 23 to 10 significand bits.
• This conversion is suitable for cases where reduced precision is acceptable while minimizing data size for transmission.
• If higher precision is required, consider using a different data format or compression technique.

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