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From "Phil Steitz" <p...@steitz.com>
Subject [math] Complex dilemmas
Date Thu, 05 Jun 2003 06:25:52 GMT
I had planned to submit "my" Complex classes as part of the iniital 
submission and I have been tearing this stuff apart and putting it back 
together again for the past several weeks,adding layers of abstraction 
and then tearing them away,  never quite ending in a satisfied state.

So.. I am asking for a little help.

Here are the decisions that I would like to confirm/discuss:

1. Complex is a concrete, immutable class.  The only methods belonging 
to Complex itself are things that it makes sense to apply to a single 
Complex number -- e.g., arg, modulus, re, im, etc.

2. Imaginary is a concrete, immutable class.  It's raison d'etre is to 
support more efficient, more accurate and in some cases more natural 
computations when dealing with complex numbers with no real parts.

3. ComplexUtils is a collection of static methods supporting 
mathematical operations involving Complex, Imaginary and Double operands 
-- e.g., plus(Complex,Complex), plus(Complex,Imaginary), 
plus(Complex,double), etc.

4. All use C9x Annex G:IEC 559-compatible complex arithmetic for 
arithmetic operations / infinity/NaN semantics/branch cuts/topolog, as 
defined here
http://std.dkuug.dk/JTC1/SC22/open/n2620/n2620.txt

5. ExpandableComplexArray is an array class with "in place" operations 
supported by ComplexUtils -- things like

times: (ExpandableComplexArray,int,Complex) |-> Complex or
times: (ExpandableComplexArray,Complex) |-> ExpandableComplexArray

To put this in perspective vis a vis the other stuff out there, here are 
some comparisons/observiations:

The existing library that I like the most is Visual Numerics
http://www.vni.com/corner/garage/grande/jsr/api/Complex.html

This one class combines Complex, ComplexUtils and Imaginary above. It 
also implements the C9x Annex G value semantics. The mathematical scope 
of the methods defined there is roughly equivalent to what I have in 
mind (really just what is in the C spec), though I would drop a few 
things, pull the operations out into ComplexUtils, add proj to support 
spherical semantics (as defined here: 
http://java.sun.com/people/darcy/complex-proposal.html#general) and add 
the Imaginary and ExpandableComplexArray classes.

Colt 
http://hoschek.home.cern.ch/hoschek/colt/V1.0.3/doc/com/imsl/math/Complex.html
is very similar to VNI.  Most importantly, it advertises the same C9x 
Annex G value semantics.

So...from a functionality and computational semantics standpoint, it 
seems clear that implementing the basic C9x function set with signed 
zero and the Annex G semantics is the right thing to do.  This will keep 
us interoperable with and allow easy migration from VNI or Colt.

What I need help confirming is the organization of the classes above. 
Please remember that these things will be used in computationally 
intense scenarios embedded in complex code. We need the syntax to be as 
simple as possible and the level of indirection to be minimal.

Phil


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