<![CDATA[size : 6861
uploaded_on : Sat Jun 20 00:00:00 1998
modified_on : Wed Dec 8 14:03:37 1999
title : Complex Numbers
org_filename : Cmplxclc.pas
author : Reinout Raymakers
authoremail : reinoutr@sci.kun.nl
description : Unit for working with complex numbers
keywords :
tested : Borland Pascal 7.0
submitted_by : The CKB Crew
submitted_by_email : ckb@netalive.org
uploaded_by : nobody
modified_by : nobody
owner : nobody
lang : pas
file-type : text/plain
category : pascal-alg-maths
__END_OF_HEADER__
Unit CmplxClc; { CMPLXCLC.PAS unit version 1.0 Reinout Raymakers 1997 }
{$N+,E+}
{ This unit implements a full set of functions to work with complex numbers
in Turbo Pascal. The type Complex is defined as a pointer to be able to use
the type as a return value for functions. Values of complex numbers first
have to be assigned to a variable using CDef, before you can use them in
calculations...
Two examples of how to work with this unit:
The Complex calculation (2.3 + 4.1i) + cos (-9.1 + 0.7i) can be done
in several ways:
1) An extended but understandable one:
var A, B, C, D : Complex
....
New(A);
New(B);
A := CDef(2.3,4.1);
B := CDef(-9.1,0.7);
C := CCos(B);
D := CAdd(A,C);
....
2) A compact but not very readable form:
var D : Complex;
....
New(D);
D := CAdd(CDef(2.3,4.1),CCos(CDef(-9.1,0.7));
....
In other words: you can do every step seperatly, but also implement
all the functions in one line of code....
P.S. Whether or not it is always necessary to first declare the
variables with the New command is not clear to me....
Try it out and see what works best..... (I'm not used to
working with pointers....)
You are free to use or change this unit in any way you like, but I would
appreciate it, if you mailed me your suggestions / changes / bugs or
anything else you want changed....
Reinout Raymakers
Nolensstraat 12
5344 SK Oss
The Netherlands
reinoutr@sci.kun.nl
RR, 24 December 1997
Other units created by me : - Full support unit for 256 color PCX files
Projects that I'm still working on: - True color (24 bit) PCX files unit
- Export routines for GIF / BMP formats
}
Interface
Type ComplexValue = Record
R : Double; { Real part }
I : Double; { Complex part }
end;
Complex = ^ComplexValue;
Const iValue : ComplexValue = (R: 0.0 ;I: 1.0);
i : Complex = @iValue;
_2iValue : ComplexValue = (R: 0.0 ;I: 2.0);
_2i : Complex = @_2iValue;
_1Value : ComplexValue = (R: 1.0 ;I: 0.0);
_1 : Complex = @_1Value;
_2Value : ComplexValue = (R: 2.0 ;I: 0.0);
_2 : Complex = @_2Value;
Function CDef(R, I : Real) : Complex; { CDef := R + Ii }
{ Remarks: - All functions marked with 'B' are basic functions, that are
defined by only using the standard calculations provided by
Turbo Pascal. All other functions are defined in terms of
these basic functions and add no (mathematical) functionality
to the unit.
- Note that the CArg function has a non-defined situation, in
which case it gives '666' as an answer (an impossible value
for an argument).
}
Function CAbsSqr(C : Complex) : Real; { ( Abs C )^2 } {B}
Function CAbs(C : Complex) : Real; { Abs C } {B}
Function CReal(C : Complex) : Real; { Real C } {B}
Function Re(C : Complex) : Real; { Real C }
Function CImag(C : Complex) : Real; { Imag C } {B}
Function Im(C : Complex) : Real; { Imag C }
Function CArg(C : Complex) : Real; { Arg C } {B}
Function CConj(C : Complex) : Complex; { Conj C } {B}
Function CMin(C : Complex) : Complex; { - C } {B}
Function CAdd(C1,C2 : Complex) : Complex; { C1 + C2 } {B}
Function CSub(C1,C2 : Complex) : Complex; { C1 - C2 } {B}
Function CMul(C1,C2 : Complex) : Complex; { C1 * C2 } {B}
Function CDiv(C1,C2 : Complex) : Complex; { C1 / C2 } {B}
Function CExp(C : Complex) : Complex; { e^C } {B}
Function CLn(C : Complex) : Complex; { Ln C } {B}
Function CPow(C1, C2 : Complex) : Complex; { C1^C2 }
Function CSqr(C : Complex) : Complex; { C^2 }
Function CLog(C1, C2 : Complex) : Complex; { C1 Log C2 }
Function CRt(C1, C2 : Complex) : Complex; { C1 √ C2 }
Function CSqrt(C : Complex) : Complex; { √ C }
Function CSin(C : Complex) : Complex; { Sin C }
Function CCos(C : Complex) : Complex; { Cos C }
Function CTan(C : Complex) : Complex; { Tan C }
Function CCot(C : Complex) : Complex; { Cot C (COT = 1 / TAN) }
Function CSec(C : Complex) : Complex; { Sec C (SEC = 1 / COS) }
Function CCsc(C : Complex) : Complex; { Csc C (CSC = 1 / SIN) }
Function CASin(C : Complex) : Complex; { ArcSin C }
Function CACos(C : Complex) : Complex; { ArcCos C }
Function CATan(C : Complex) : Complex; { ArcTan C }
Function CACot(C : Complex) : Complex; { ArcCot C }
Function CASec(C : Complex) : Complex; { ArcSec C }
Function CACsc(C : Complex) : Complex; { ArcCsc C }
Function CSinh(C : Complex) : Complex; { Sinh C }
Function CCosh(C : Complex) : Complex; { Cosh C }
Function CTanh(C : Complex) : Complex; { Tanh C }
Function CCoth(C : Complex) : Complex; { Coth C }
Function CSech(C : Complex) : Complex; { Sech C }
Function CCsch(C : Complex) : Complex; { Csch C }
Function CASinh(C : Complex) : Complex; { ArcSinh C }
Function CACosh(C : Complex) : Complex; { ArcCosh C }
Function CATanh(C : Complex) : Complex; { ArcTanh C }
Function CACoth(C : Complex) : Complex; { ArcCoth C }
Function CASech(C : Complex) : Complex; { ArcSech C }
Function CACsch(C : Complex) : Complex; { ArcCsch C }
Implementation
Function CDef;
var U : Complex;
begin
New(U);
U^.R := R;
U^.I := I;
CDef := U;
end; { Fill the complex number with the values of R en I }
Function CAbsSqr;
begin
CAbsSqr := C^.R * C^.R + C^.I * C^.I;
end; { Absolute value of C squared }
Function CAbs;
begin
CAbs := Sqrt( C^.R * C^.R + C^.I * C^.I );
end; { Absolute value of C }
Function CReal;
begin
CReal := C^.R;
end; { Real part of C }
Function Re;
begin
Re := CReal(C);
end; { Real part of C }
Function CImag;
begin
CImag := C^.I;
end; { Imaginairy part of C }
Function Im;
begin
Im := CImag(C);
end; { Imaginairy part of C }
Function CArg;
var A, B : Real;
begin
A := C^.R;
B := C^.I;
if (A > 0) then
begin
if (B > 0)
or (B < 0) then CArg := ArcTan(B/A);
if (B = 0) then CArg := 0;
end; { if }
if (A < 0) then
begin
if (B > 0) then CArg := ArcTan(B/A) + Pi;
if (B < 0) then CArg := ArcTan(B/A) - Pi;
if (B = 0) then CArg := Pi;
end; { if }
if (A = 0) then
begin
if (B > 0) then CArg := Pi / 2;
if (B < 0)
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