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From: be@dde.uucp (Bjorn Engsig)
Newsgroups: comp.lang.c,sci.math.num-analysis
Subject: Power (Re: all those :-)
Keywords: No need, No good, NO! (This is new; read it!)
Message-ID: <302@Aragorn.dde.uucp>
Date: 18 Jan 88 09:30:12 GMT
Organization: Dansk Data Elektronik A/S, Herlev, Denmark
Lines: 42

A short resume for sci.math.num-analysis readers:
-- A lot of people have written pro et contra for the inclusion
-- of a power (which power? most don't bother :-) operator in the
-- C programming language.  The discussion has been on which symbol
-- to use for power, where to put it in the operator hierarchy, and
-- wether it should have integer or real exponents.  C currently includes
-- a pow function with real exponents, defined for nonnegative mantissa
-- only.

Let me start to comment on power with integer exponents.

Pick up any first grade textbook on numerical analysis, and you will
be told NEVER to use a power function like that.  First, if you need to
calculate  x ** n (fortran notation), you will most often need
x ** (n-1)  etc. as well, and it should be calculated using recursion,
to optimize calculation time.  Second, you should bear in mind,
that using ordinary polynmials is often a bad practice in numerical 
computation, since they are higly unorthogonal (i.e. similar, try to
graph  x ** 9  and  x ** 10  for  x  between  0  and  1.).  If you are
doing computations with polynomials involved, you will normally pick a
set of orthogonal polynomials, such as the chebychef polynomials.
These kinds of polynomials are always calculated by recursion for speed
and accuracy.

Thus: Power with integer exponent is not needed!

Next, the power with real exponent, which we have as the pow() function,
is according to my knowledge not very heavily used.  If a lot of people
can come up with a lot of REAL application, where the call of pow()
really makes their code look ugly compared with an infix operator, one
MIGTH consider the inclusion of the operator.  However, a lot of non
numerics will definately use this operator for integer exponention, and
they will not understand why they can't square -2.0, and why their
progam is using that much CPU time.

Thus: Power with real exponent is not good!

-- 
Bjorn Engsig, E-mail:  ..!uunet!mcvax!diku!dde!be  or  be@dde.uucp
--
Hofstadters Law: It always take longer than you expect, even if you take into
		 account Hofstadters Law.