Re: TOMS748 question

From: Shriramana Sharma (samjnaa_at_[hidden])
Date: 2021-01-28 12:27:41

Another question:

https://github.com/boostorg/math/blob/develop/include/boost/math/tools/toms748_solve.hpp#L352

Can you elucidate which step from the original paper this quadratic
step corresponds to? IIANM the whole implementation is based on the
algorithm 4.2 of the paper and not 4.1, because e and fe don't figure
in 4.1 and the secant step on L347 is 4.2.1 same as 4.1.1. But I don't
see a separate compulsory quadratic step after 4.2.1 other than the
quadratic/ipzero branch at 4.2.3, however this code seems to have such
a compulsory step ie a step without the option of ipzero.

L380 starts the branch at 4.2.3 and L402 starts the branch at 4.2.5,
but apart from that I don't see anything in the steps given in the
paper to indicate a non-branching quadratic step beforehand.

Or maybe I'm missing something. Please clarify. Thanks!