Internals of floating point numbers in Ruby.

Basics of floating point numbers

Links:

• https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html

Endianess

Endianess is the sequential order in which bytes are arragned in a machine.

The macro WORDS_BIGENDIAN from gcc can be used for telling whether the machine you are on is using big-endian or little-endian encoding.

Link:

Ruby floating point numbers

Most of the functionality for 32-bit and 64-bit floating point numbers (the majority types found in scientific computing code) are handled by Ruby.

The RFloat struct contains the value for the floating point number. The definition can be found in the internal.h file here.

This is what it looks like:

struct RFloat {
    struct RBasic basic;
    double float_value;
};

As can be seen, Ruby always stores numbers as double which is 64-bits long on most machines. To access the double value of a Float Ruby object, one can use the RFLOAT_VALUE(VALUE v) macro that ultimately calls the rb_float_value_inline function present in internal.h file. There is no way to have 32-bit or 16-bit floating point numbers in Ruby.

In Ruby, the numeric.c file contains the code for working with floats.

Ruby uses a technique called ‘FLONUM’ for speeding up 64-bit floating point calculations. The proposal for this can be found here. It basically reduces the overhead of object creation by giving the same treatment to floats as is given to 64-bit integers (treating the VALUE pointer as the value itself).

Links:

• http://patshaughnessy.net/2014/1/9/how-big-is-a-bignum
• https://www.slideshare.net/burkelibbey/ruby-internals
• http://gnu.huihoo.org/autoconf-2.13/html_node/autoconf_36.html

The IEEE formats

Ruby uses the IEEE 754 format by default. If a machine does not contain the headers required for this format, Ruby defines them here.