libkate: Format - floating point value

# Format - floating point value

Floating point values are stored as a series of digitized fixed point values in the Kate bitstream format. Several distinct streams of floating point values may be saved at the same time. A stream has a constant format (number of bits saved per value). Streams may be merged together (eg, merging 2 streams of V values yields a single stream of 2*V values). Streams stored together always have the same number of values.

When loading N streams, the bitstream format is as follows:

- 1 bit, being 1 if the streams are merged.

If the streams to load are merged, the different streams are stored as a single stream. In this case, N is set to 1, and the number of values is equal to the total number of values in all streams (eg, the original N times the number of values in a single stream).

Then, for each stream:

- 4bits being the number of zero bits in the high bits of the integer part of a number (`head').
- 4bits being the number of bits in the low bits of the fractional part of a number (`tail').

Then, for each value:

- if head is strictly positive, a bit representing the sign of the number.
- 32-(head+tail) bits, representing the middle bits of the absolute value of the number.

Each number may then be reconstructed by concatenating the given number of high zero bits (`head'), the middle bits, the given number of low zero bits (`tail'), and negating the number if the sign bit was 1.