research!rsc

My post “Floating-Point Printing and Parsing Can Be Simple And Fast”depends on fast unrounded scaling, defined as:
⟨
x

Introduction
A floating point number
f

These are the posts in the “Floating Point Formatting” series,which started in 2011 and continued in 2026.
“Floating Point to Decimal Conversion is Easy” (2011)
“Pulling a New Proof from Knuth’s Fixed-Point Printer” (2026)

Introduction
Donald Knuth wrote his 1989 paper “A Simple Program Whose Proof Isn’t”as part of a tribute to Edsger Dijkstra on the occasion of Dijkstra’s 60th birthday.Today’s post is a reply to Knuth’s paper on the occasion of Knuth’s 88th birthday.
In his paper, Knuth posed the problemof converting 16-bit fixed-point binary fractions to decimal fractions,aiming for the shortest decimal that converts back to the original 16-bit binary fraction.Knuth gives a program named P2 that leaves digits in...