C log function inaccurate (with fix) (many UNIX versions)

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2 total messages Started by Guido van Rossum Thu, 05 Jan 1984 20:20

#164

Author: Guido van Rossum
Date: Thu, 05 Jan 1984 20:20

21 lines
1427 bytes

One of my colleagues discovered that the log function the the mathematical
C library is quite inaccurate.  What's more, he also provided a change
to one of the coefficients which much improved it.  Here they are:

BAD:  p2 = -.963769093368686593e1;
GOOD: p2 = -.963769093377840513e1;
                       ^^^^^^^^

So now you should all go and fix your C library.
I found the same coefficients in UNIX V7 as in 4.2 BSD, so I suspect
they are probably in almost all other UNIXes around the world.

Related question: the source states
	"The coefficients are #2705 from Hart & Cheney. (19.38D)".
We cannot locate this reference in our institute's library.
Does someone know what this references, and give us a more precise pointer?

Guido van Rossum, {philabs,decvax}!mcvax!guido
Centre for Mathematics and Computer Science, (CWI, formerly MC), Amsterdam

(with thanks to Lambert Meertens)

Re: C log function inaccurate (with fix) (many UNIX versions)

#166

Author: Geoffrey Collyer
Date: Sat, 07 Jan 1984 22:37

41 lines
2164 bytes

DDT
	BAD:  p2 = -.963769093368686593e1;
	GOOD: p2 = -.963769093377840513e1;
	                       ^^^^^^^^

	Related question: the source states
		"The coefficients are #2705 from Hart & Cheney. (19.38D)".
	We cannot locate this reference in our institute's library.
	Does someone know what this references, and give us a more precise pointer?

	Guido van Rossum, {philabs,decvax}!mcvax!guido
	Centre for Mathematics and Computer Science, (CWI, formerly MC), Amsterdam
---
The oft-cited Hart & Cheney is

	Computer Approximations
	John F. Hart, E. W. Cheney, Charles L. Lawson, Hans J. Maehly,
	Charles K. Mesztenyi, John R. Rice, Henry G. Thacher, Jr.,
	Christoph Witzgall
	Robert E. Kreiger Publishing Company, 645 New York Avenue,
	Huntington, New York 11743, 1978
	Copyright 1968 by John Wiley & Sons, Inc.
	Original edition 1968
	Reprint 1978 with corrections
	Library of Congress: QA297.C64 1978
	ISBN 0-88275-642-7

This book appears to have been used as a source of coefficients
throughout the mathematical library (-lm).

The ``BAD'' p2 coefficient above is from table 2705 on p. 195.
p. 111 explains that this table is coefficients for computing
ln(x) as approximately z*(zP(z^2)/Q(z^2)), z=(x-1)/(x+1)
where x is on the range [1/sqrt(2), sqrt(2)]
and yields a precision of 19.38, where precision is defined as
``the range of validity of the approximation (-log10(maximum error))''
(p. 83).  I'm *certainly* no numerical analyst, but I read that to
mean that precision is the number of significant digits that may
be assumed to be correct.

Geoff Collyer, U. of Toronto

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