(SC22WG11.419) pi and LIA

[uunet!cwi.nl!Dik.Winter]

One comment about this:
 > 1.  Trig functions with preselected bases other than "radians".
 > David says:
...
 > > The "trigd" functions are a common Fortran extension, and the trigpi
 > > functions less so, although they have been provided in Sun's libraries
 > > for C and Fortran since 1988.   They are just the TRIGFF functions
 > > prescribed in LIA-2, with u fixed at 360 and 2 respectively; 
...
 > I agree with the latter part of this.  The two base-specific functions can
 > be coded with more efficiency, more reliability, and, in the case of 
 > <trig>pi(x) higher guaranteed accuracy.   That makes these functions more
 > desirable than TRIGFF and suggests that they be recommended for use OVER
 > TRIGFF where appropriate!

I disagree.  In Ada TRIGFF has been standardized.  Coding is barely more
work than a single argument function.  What you do is an exact reduction
of the first argument mod the second argument (which can be done using
IEEE arithmetic).  [Perhaps you wish to reduce to one half or one quarter
of this range; that does not matter.]  Once you have done that you can
nearly reduce to the single argument case.  If for instance your base
approximation for sin(x) uses a polynomial approximation for (sin(x)-x)/x
you easily find a good approximation for the sin with arbitrary second
argument.  One caveat:  you should never code sin(x) through sin(x,pi*2).

I think Peter Tang has done some coding in this area (as I did).

dik
--
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