floating is a simple command-line tool for exploring IEEE754 floating-point formats.
It can show you the bit strings of single-precision (binary32) and double-precision (binary64) floats. It can also show you a number's floating-point neighbors, i.e., the next or previous values.
You can give floating a bit string as an integer and it will tell you the floating-point value.
It should compile cleanly on any Linux system with a relatively recent gcc.
Run make or, optionally, make install. Default installtion location is /usr/local/bin, but
this can be changed in the Makefile.
Calling floating with the -h flag shows the help:
./floating -- show binary representation of an IEEE754 floating-point number
Usage:
./floating [options] <number>
where <number> can be in decimal (3.14), hex (0x42), exponential (1.4E-12), or
binary exponent (0x1.4p+1) form.
Options:
-d use double-precision binary64 format
-f show a few interesting IEEE754 facts
-i treat the input as an integer bit string, then interpret as float
-P increment the given number to the next floating-point value (Plus)
-M decrement the given number to the previous floating-point value (Minus)
NB: to enter a negative value, use '--' to stop processing arguments, e.g.,
./floating -d -- -3.14
The single-precision representation of 1.25 is exact:
In contrast, 0.1 is non-terminating in base-2 and so must be approximated:
We can use binary exponent form to describe the approximation exactly:
Positive infinity is represented by all exponent bits set and all mantissa bits off, which we can express with the integer 0x7800000:
Adding one to this value (-P) gives us the first NaN in the sequence:
Javier Lombillo javier@asymptotic.org May 2021