This page is meant to give a summary of how to use complex numbers in ZPL programs. At this point, complex numbers are not fully implemented, but have been prototyped in order to allow users to do simple computations using them. If you find any bugs or inconsistencies in our implementation of complex numbers, pleae let us know at zpl-bugs@cs.washington.edu.
ZPL supports three varieties of complex numbers:
complex, dcomplex, and
qcomplex. All three of these data types have
real and imaginary components, but with differing amounts of
precision, namely float, double, and
quad, respsectively (on platforms that don't support
quad precision, double is used instead).
Complex variables and arrays of complex variables can be
declared of any of the complex types in the usual manner. Complex
constants can also be declared in the standard way using ZPL's
record initialization syntax (identical to C's) to initialize the
values. For example, the following declaration would create a
double precision representation of i: constant
I:dcomplex = {0,1};.
At the present, assignment (:=), equality
(=), inequality (!=), addition
(+), subtraction (-), multiplication
(*), division (/), plus-gets
(+=) and minus-gets (-=) are supported
on all combinations of complex and real values. In addition,
ZPL's (@), wrap, reflect, flood
(>>), and remap (<##,
>##) operators work on complex values as expected.
Plus and multiplication reductions and scans
(+<<, *<<, +||,
*||) are implemented for complex values for
seq, pvm, and mpi installations. Currently,
times-gets (*=) and divide-gets (/=) are
not implemented. In addition, none of ZPL's standard math library
routines support complex values.
Unfortunately, warnings are currently not generated for using complex values with unimplemented operations. Instead, the operation will be applied to the real component of the complex value only.
Known bug: complex assignments that use the same complex
variable on the LHS and RHS in such a way that assignment to the
imaginary component requires using its real component as well will
currently not work. For example, a := a + b; will
work since the imaginary assignment of a depends only
on the imaginary component of a. However, a :=
a * b; will not work since the imaginary assignment of
a depends on the real component of a.
If this causes problems for you, please mail us at the address
above.
In addition, the user can access a complex number's real and
imaginary components by treating the complex variable as though it
was a record with fields named re and
im, respectively. For example a.im :=
0 would set the imaginary component of a to
0.
Text I/O with the console and files is supported for complex
values. The default I/O for complex variables is:
realval + imagvali. As
with any text I/O, this control string may be over-ridden. One
difference from traditional scalar I/O is that two control strings
should be specified to refer to the real and imaginary parts in
that order. For example, to write a complex variable using the
(realval,imagval),
one would use: writeln("(%f,%f)":cmplxvar);
It is our intention to support additional operations on complex variables such as the other shortcut assignment operations (*=, /=), scans, reductions, etc. Our implementation of these features may be somewhat demand-driven, so if you require them, please let us know at the address below.
If you have further questions about complex types in ZPL, please don't hesitate to contact us at zpl-info@cs.washington.edu.