Appendix D. Half-Precision

As half-precision floating-point numbers were only added to IEEE 754 in 2008, today's programming platforms often still only have limited support for them. It is very easy to include at least decoding support for them even without such support. An example of a small decoder for half-precision floating-point numbers in the C language is shown in Figure 3. A similar program for Python is in Figure 4; this code assumes that the 2-byte value has already been decoded as an (unsigned short) integer in network byte order (as would be done by the pseudocode in Appendix C).

#include <math.h>

double decode_half(unsigned char *halfp) {
  int half = (halfp[0] << 8) + halfp[1];
  int exp = (half >> 10) & 0x1f;
  int mant = half & 0x3ff;
  double val;
  if (exp == 0) val = ldexp(mant, -24);
  else if (exp != 31) val = ldexp(mant + 1024, exp - 25);
  else val = mant == 0 ? INFINITY : NAN;
  return half & 0x8000 ? -val : val;
}

Figure 3: C Code for a Half-Precision Decoder

import struct
from math import ldexp

def decode_single(single):
    return struct.unpack("!f", struct.pack("!I", single))[0]

def decode_half(half):
    valu = (half & 0x7fff) << 13 | (half & 0x8000) << 16
    if ((half & 0x7c00) != 0x7c00):
        return ldexp(decode_single(valu), 112)
    return decode_single(valu | 0x7f800000)

Figure 4: Python Code for a Half-Precision Decoder