Re: Radians Or Degrees?

MitchAlsup1 wrote:

Michael S wrote:
 

To make it less tempting, you could try to push for inclusion of
rsqrt() into basic set. Long overdue, IMHO.

 Many Newton-Raphson iterations converge more rapidly with RSQRT than
with SQRT, for reasons I never looked that deeply into.

The classic NR iteration for rsqrt() uses only fmul & fadd/fsub, while the naive sqrt() version needs a divide in every iteration.
Personally I prefer to use the y = rsqrt(x) form and then just multiply by x in the end:
   y = sqrt(x) = x/sqrt(x) = rsqrt(x)*x
In order to get the rounding correct from this form you can probably just square the final result and compare this with the original input?

 

Right now, I can't think of any other transcendental that I really want
to elevate to higher status. It seems to me that elevation of log2(x)
and of 2**x will do no harm, but I am not sure about usefulness.

 Ln2 and EXP2 are the basis of My 66000 log and EXP families, performed in
HW function unit.
 Ln2 has the property that a binade [1..2) maps directly to another binade
[2..4); exp2 has a similar property. Ln2 is easier to get good accuracy
from than Ln or Log as a starting point. But in any event:: you are always within a high precision multiply of the correct result = round(53×106);

Exactly the same reasoning I used to compute rsqrt() over the [1.0 - 4.0> range, or (simplifying the exp logic) over [0.5 - 2.0> so that the last exp bit maps to the first vs second half of the range. Back before we got approximate rsqrt() lookup opcodes, I wrote code that took the last exp bit and the first n mantissa bits and looked up an optimal starting point for that value + 0.5 ulp. Getting 11-12 bits this way means approximatly correct float after a single iteration and useful double after two.
Terje
--
- <Terje.Mathisen at tmsw.no>
"almost all programming can be viewed as an exercise in caching"