standards/83845: [ patch ] add log2() and log2f() support for libm

[David Schultz]

The following reply was made to PR standards/83845; it has been noted by GNATS.

From: David Schultz <das at FreeBSD.ORG>
To: Roman Bogorodskiy <bogorodskiy at gmail.com>
Cc: FreeBSD-gnats-submit at FreeBSD.ORG
Subject: Re: standards/83845: [ patch ] add log2() and log2f() support for libm
Date: Thu, 21 Jul 2005 14:07:08 -0400

 On Thu, Jul 21, 2005, Roman Bogorodskiy wrote:
 > 	Add e_log2.c and e_log2f.c files based on e_log.c and e_logf.c 
 > 	respectively which adds support of C99 funtions log2() and log2f().
 > 
 > 	The idea is simple:
 > 
 > 	log(N) to base A is equal to logN/logA, that way, log2(x) = log(x)/log(2).
 > 	So after some simplifications and deviding result by precalculated value of
 > 	log(2) we can compute the value of the logarithm of argument x to base 2.
 
 Though this seems like a reasonable approach, it leads to
 significant rounding errors since it requires dividing an inexact
 result (ln(x) rounded to 52 bits) by another inexact quantity
 (ln(2) rounded to 52 bits).  For instance, I suspect that if you
 computed log2(2), log2(4), log2(8), log2(16), ... using your
 implementation, the results would not always be exact.
 Technically speaking I don't think they are required to be exact,
 but common sense suggests that they ought to be.
 
 A more minor objection is that log2() can be computed more quickly
 than log(), but this impelementation does it less quickly.  This
 isn't such a big deal, though; I'm more concerned about the
 problem that accuracy guarantees will be significantly weaker than
 for other routines in libm.
 
 --David