If Gosper's Appendix to HAKMEM interests you, you may want to read some of the continued fraction papers by Oskar Mencer and his collaborators Michael Flynn, Ma

If Gosper's Appendix to HAKMEM interests you, you may want to read some of the continued fraction papers by Oskar Mencer and his collaborators Michael Flynn, Martin Morf, and Wayne Luk. Suffice it to say, continued fractions can be used to replace floating point arithmetic (including some mathematical functions) directly. See, for example, https://www.researchgate.net/publication/2412477 https://www.researchgate.net/publication/2412477.