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implementation categories, exact rationals

This page is part of the web mail archives of SRFI 77 from before July 7th, 2015. The new archives for SRFI 77 contain all messages, not just those from before July 7th, 2015.

 | Most implementations of Scheme fall into one of the following
 | categories:
 |     * fixnums only (now rare except in toy implementations)
 |     * fixnums and flonums only
 |     * exact rationals and flonums only (no imaginary numbers)
 |     * the complete numeric tower 

SCM, Guile, and SCM-Mac (and one presumes Galapagos and WinSCM) have
fixnums, bignums, and real and complex flonums.  SCM and its
derivatives have a large installed base.  In particular, Guile is part
of every Fedora GNU/Linux installation.  This category should be
included in your list.

 | This SRFI proposes to revise section 6.2 ("Numbers") of R5RS by:
 |     * requiring a Scheme implementation to provide the full tower,
 |       including exact rationals of arbitrary precision, exact
 |       rectangular complex numbers with rational real and imaginary
 |       parts, and inexact real and complex arithmetic

What is the rationale for mandating exact rationals?  Over 15 years I
have written numerical Scheme code for everything from symbolic
algebra to Galois fields to linear systems to optics simulations
without needing exact rationals.

A case could be made if (expt -26. 1/3) returned -2.9624960684073702;
but I know of no Scheme implementation that does so.