[libre-riscv-dev] [isa-dev] Re: FP transcendentals (trigonometry, root/exp/log) proposal

[Hendrik Boom]

On Thu, Aug 08, 2019 at 11:36:20AM -0700, Allen Baum wrote:
> For what it's worth, the HP calculator algorithms had Prof. Kahan as a
> consultant (and HP had exclusive rights for the decimal versions of the
> algorithm; I think Intel had rights to the binary versions).
>
> Their accuracy requirements were that the result was accurate to with +/-1
> bit of the *input* argument, which gives quite a bit of leeway when the
> slope of the function is extremely steep.

That's a very practical way of determining numerical accuracy of 
calculations -- getting the exact function value for an argument close 
the one provided.

It's surprising, but this backward correctness reasoning has 
substantial theoretical support.  It's the entire concept betweem 
Dijkstra's "A Discipline of Programming", which discusses how this kind 
of backwards reasoning can even be used in the synthesis of programs.

-- hendrik