1) Here are a couple of famous scholarly articles somewhat relevant to
 our current discussion:

  William D Clinger
  "How to Read Floating Point Numbers Accurately"
  
https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.45.4152&rep=rep1&type=pdf

  Guy L Steele and Jon L White
  "How to Print Floating-Point Numbers Accurately"
  https://lists.nongnu.org/archive/html/gcl-devel/2012-10/pdfkieTlklRzN.pdf


2) I dug up an old example of a simple, obvious algorithm that fails miserably
 at a somewhat-related task, namely normalizing a longitude so that it falls
 in the half-open interval [-180, 180). It fails due to inevitable 
floating-point
 rounding errors. Also included is a simple (slightly less obvious) algorithm
 that performs much better.

 The self-compiling C++ source is here:
   
https://www.av8n.com/cgit/FPU/plain/pv180.c?id=67067c555e1d1e281a008d440e189db709ec3ec3
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