Comparison between Binary and Decimal Floating-Point Numbers
Nicolas Brisebarre, Christoph Lauter, Marc Mezzarobba, Jean‐Michel Muller · IEEE Transactions on Computers · 2015
We introduce an algorithm to compare a binary floating-point (FP) number and a decimal FP number, assuming the “binary encoding” of the decimal formats is used, and with a special emphasis on the basic interchange formats specified by the IEEE 754-2008 standard for FP arithmetic. It is a two-step algorithm: a first pass, based on the exponents only, quickly eliminates most cases, then, when the first pass does not suffice, a more accurate second pass is performed. We provide an implementation of several variants of our algorithm, and compare them.