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From: jaroslav@warwick.UUCP (Jaroslav Stark)
Newsgroups: net.micro.mac
Subject: SANE trigonometric functions
Message-ID: <269@euclid.warwick.UUCP>
Date: Mon, 7-Apr-86 10:26:47 EST
Article-I.D.: euclid.269
Posted: Mon Apr  7 10:26:47 1986
Date-Received: Thu, 10-Apr-86 00:35:03 EST
Organization: Maths Institute, Warwick University, UK
Lines: 22

Does anybody out there know just how accurate the SANE trigonometric
functions are??? The apple manuals go to great length to specify the 
accuracy of the arithmetic functions, but say nothing about the 
transcendental ones. 

The specific question I need to answer is : what is the maximum
error in sin(x) where  0 <= x <= pi ( and x is extended precision).
Some experimentation suggests that in fact the error is confined to 
the least significant bit of the mantissa (i.e. 63 bit accuracy), but
I need GUARANTEED error bounds.

Any help would be much appreciated, including pointers to where the 
information might be found.

Many Thanks

Jaroslav Stark
Math. Institute
U. of Warwick
U.K.

e-mail: ...seismo!mcvax!ukc!warwick!jaroslav