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

[Albert Chan]

(04-12-2021 12:20 PM)Albert Chan Wrote:  And, accuracy affect both edges, not just the "zero" side.

An example, with both edge goes to +∞

>>> Q = require 'quad'
>>> f = function(x) return 1/sqrt(1-x*x) end

lua> Q.qthsh(Q.count(f), -1, 1), Q.n
3.141592644894014       59
lua> Q.quad(Q.count(f), -1, 1), Q.n
3.1415926047697873     115

This is not due to default 0.0 vs previous point.
The function has sharp edges. With x in (-1,1), f(x) never returned inf.
With IEEE double, this is the highest it goes:

lua> f(1 - 0x1p-53)
67108864

There is no zero edge here, and midpoint of (-1,1) is exactly 0.
Interpolate from the edges, qthsh use more accurate points.