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

[Nigel (UK)]

I'd like to ask a question about the exp_sinh_opt_d split-point program on pages 31-32 of the qthsh.pdf booklet. On page 32, above the table, it says

Quote: If the sign of \(h\) changes from negative to positive, then \(d\) is multiplied by \(2^{k-1}\).
If the sign of \(h\) changes from positive to negative, then \(d\) is divided by \(2^{k-1}\).

This fits in with what the table below shows - for this function, \(h\) changes from negative to positive as \(r\) increases, so \(d\) (initially 1) gets set to 32. The text below the table confirms that \(d=32\) is the value estimated by the method.

However, rather than checking directly how the sign of \(h\) changes, the program tests if (fabs(lfl) < fabs(lfr)), which isn't obviously the same thing. Indeed, for the data in the table this test is true, which means that the code returns \(d = 1/32\) rather than \(d = 32\).

Am I misunderstanding the code, or the text? Sorry if the answer is obvious - it's late here, but I've looked at it for a while and I remain confused!

Nigel (UK)