I am writing a program for an embedded hardware that only supports 32-bit single-precision floating-point arithmetic. The algorithm I am implementing, however, requires a 64-bit double-precision addition and comparison. I am trying to emulate double datatype using a tuple of two floats. So a double d will be emulated as a struct containing the tuple: (float d.hi, float d.low).
The comparison should be straightforward using a lexicographic ordering. The addition however is a bit tricky because I am not sure which base should I use. Should it be FLT_MAX? And how can I detect a carry?
How can this be done?
Edit (Clarity): I need the extra significant digits rather than the extra range.
double-float is a technique that uses pairs of single-precision numbers to achieve almost twice the precision of single precision arithmetic accompanied by a slight reduction of the single precision exponent range (due to intermediate underflow and overflow at the far ends of the range). The basic algorithms were developed by T.J. Dekker and William Kahan in the 1970s. Below I list two fairly recent papers that show how these techniques can be adapted to GPUs, however much of the material covered in these papers is applicable independent of platform so should be useful for the task at hand.
https://hal.archives-ouvertes.fr/hal-00021443
Guillaume Da Graça, David Defour
Implementation of float-float operators on graphics hardware,
7th conference on Real Numbers and Computers, RNC7.
http://andrewthall.org/papers/df64_qf128.pdf
Andrew Thall
Extended-Precision Floating-Point Numbers for GPU Computation.