(PC-12xx~14xx) qthsh Tanh-Sinh quadrature

[Albert Chan]

(04-08-2021 01:32 PM)robve Wrote:  Using exp(t) in the inner loop instead of the strength-reduced expt recurrence should be the most accurate. Try it.

I did. It make no difference.

Same conclusion when I compared strength-reduced exp vs supposed more accurate expm1.
I even tried "improved u", when t get closer to 1. Again, no difference.

u = exp(1/t - t) = exp((1-t)*(1+1/t))

Think of this as Newton's method.
Once starting to converge, every iteration doubled accuracy.
In other words, correction term only required half precision. (guess had the other half)

Same with quadrature, required precision keep reducing.
Inaccuracy of strength-reduced expt does not contribute to the sum.