skyformat99/ieee754-packing

Packing and unpacking <float> and <double> using std c++ only

ieee754-packing

When it comes to serializing float and double in C/C++, the accepted wisdom is to stream them as text, or use some sort of library. I always thought this is unsatisfactory. Text can take up a lot of space, and it is sometimes impractical to use libraries. Besides, why the code bloat, when all you want to do is serialize some numbers!

The code in ieee-packing.hpp serializes single and double precision floating point numbers using only well definied C++ features. As such, it should work on any hardware that supports 64bit integers. If __STDC_IEC_559__ is defined, then the hardware already uses ieee754 formatted numbers, and they are bitcase (safely) to unsigned integer types. Otherwise, the code uses the standard library routines std::frexp and std::ldexp to extract the mantissa and exponent, to produce an ieee754 bitpattern. Although this works with denormalized (i.e., very very tiny) numbers, it cannot be expected to be more accurate than std::numeric_limits<T>::epsilon().

ieee754 uses 8 and 11 bits for the exponents of (respectively) floats and doubles. If your hardware does not use this many bits in its representation, then there will be a further loss of precision. This will be indicated by a failure in one of the test cases.

Note the packed result is an unsigned integer in the byte order of your platform. Thus, when swapping numbers between little endian and big endian systems, it is imperative to fix the byte order. For example, use the macros in <endian.h>.

testing

make test
./test

example

#include <iostream>
#include "ieee-packing.hpp"

int main(int, char**)
{
   double value  = M_PI;
   auto packed   = pack_f64(value);
   auto unpacked = unpack_f64(packed);

   printf("   Number is:      %f\n", value);
   printf("   Number (hex):   %a\n", value);
   printf("   Packed value:   0x%016lx\n", packed);
   printf("   Unpacked (hex): %a\n", unpacked);
   printf("   Error:          %a\n", fabs(value - unpacked)); // 0.0
}

Output is:

   Number is:      3.141593
   Number (hex):   0x1.921fb54442d18p+1
   Packed value:   0x400921fb54442d18
   Unpacked (hex): 0x1.921fb54442d18p+1
   Error:          0x0p+0