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

[Allen Baum]

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. Since many of the trig functions
required input reduction of X mod pi ( or 2pi of .5pi - don't recall) -
that could be pretty far out without ~99 digits of pi to reduce it, and
even if it was perfectly reduced, one LSB of X.xxxxxxxxE 99 is not a small
number, so accuracy at the end of the scale is a bit nebulous.

On Thu, Aug 8, 2019 at 8:58 AM 'MitchAlsup' via RISC-V ISA Dev <
isa-dev at groups.riscv.org> wrote:

>
> We are talking about all of this without a point of reference.
>
> Here is what I do know about correctly rounded transcendentals::
>
> My technology for performing transcendentals in an FMAC unit performs a
> power series polynomial calculation.
>
> I can achieve 14 cycle LN2, EXP2 and 19 cycle SIN, COS faithfully rounded
> with coefficient tables which are (essentially) the same size as the
> FDIV/FSQRT seed tables for Newton-Raphson (or Goldschmidt) iterations. FDIV
> will end up at 17 cycles and FSQRT at 23 cycles. This is exactly what
> Opteron FDIV/FSQRT performance was (oh so onog ago).
>
> If you impose the correctly rounded requirement::
> a) the size of the coefficient tables grows by 3.5× and
> b) the number of cycles to compute grows by 1.8×
> c) the power to compute grows by 2.5×
> For a gain of accuracy of about 0.005 ULP
>
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