[libre-riscv-dev] [isa-dev] Re: FP transcendentals (trigonometry, root/exp/log) proposal
hendrik at topoi.pooq.com
Thu Aug 8 20:14:57 BST 2019
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.
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