Looking for TVM contributions

[Albert Chan]

(06-18-2024 03:27 AM)robve Wrote:  Let me illustrate with the "time reversed" TVM problem, which is essentially the same. The forward npmt() is best for this TVM example (the backward npmt() line is fatter):
./tvm 5 '?' -369494.09 17500 540000
3/0 i%= 11.9999997132 y=-2.05654941965e-08
4/0 i%= 11.9999997132 y= 0
4, 11.9999997132285614%, 0
s=0.567426862982966185 r=-0.43257313701703376

./tvm -5 '?' -540000 17500 369494.09
3/0 i%= 11.9999997132 y=-2.05764081329e-08
4/0 i%= 11.9999997132 y=-7.27595761418e-12
5/0 i%= 11.9999997132 y= 2.91038304567e-11
5, 11.9999997132285596%, 0
s=1.76234166063797959 r=0.762341660637979479

The |s| and |r| values are closer in the forward than in the backward npmt().

I think both time direction are equally good here.
1 ULP difference, may even be caused by scaling by 100 for percentage!

If I have to pick one, I would go for r = expm1(log1p(i)*n) to be positive. (== i*n > 0)
We can map positive to negative without too much error, but not the other way.

lua> i, n = .1, 100
lua> r1, r2 = EFF(i,n), EFF(i,-n)
lua> r1, r2
13779.612339822266      -0.9999274342840985
lua> -r2/(1+r2), -r1/(1+r1)
13779.612339813315      -0.9999274342840985

But, there are many things going on ... this is only 1 factor out of many.
See solve for n example, https://www.hpmuseum.org/forum/thread-21...#pid187533