org.jmlspecs.samples.dbc
Class ComplexOps

java.lang.Object
  org.jmlspecs.samples.dbc.ComplexOps

All Implemented Interfaces:

Complex

Direct Known Subclasses:

Polar, Rectangular

public abstract strictfp class ComplexOps

extends Object

implements Complex

An abstract class that holds all of the common algorithms for complex numbers. Note that this class knows about both of its subclasses Rectangular and Polar.

Author:

Gary T. Leavens with help from Abelson and Sussman's Structure and Interpretation of Computer Programs

Class Specifications

Specifications inherited from class Object

represents objectState <- org.jmlspecs.lang.JMLDataGroup.IT; public represents _getClass <- \typeof(this);

Specifications inherited from interface Complex

axiom ( \forall double d, dd; dd > 0.0; d%dd > -dd&&d%dd < dd); axiom ( \forall double d, dd; ; d > -dd ==> d+dd > 0.0);

Model Field Summary

 

Model fields inherited from class java.lang.Object

_getClass, objectState, theString

 

Ghost Field Summary

 

Ghost fields inherited from class java.lang.Object

objectTimesFinalized, owner

 

Ghost fields inherited from interface org.jmlspecs.samples.dbc.Complex

tolerance

 

Constructor Summary

ComplexOps()

 

Model Method Summary

 

Model methods inherited from class java.lang.Object

hashValue

 

Model methods inherited from interface org.jmlspecs.samples.dbc.Complex

positiveRemainder, similarAngle

 

Method Summary
Complex	add(Complex b)           Return this + b (the sum of this and b).
Complex	div(Complex b)           Return this/b (the quotient of this by b).
boolean	equals(nullable Object o)           Return true if these are the same complex number.
int	hashCode()           Return a hashCode for this number.
Complex	mul(Complex b)           Return this * b (the product of this and b).
Complex	sub(Complex b)           Return this - b (the difference between this and b).

 

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, toString, wait, wait, wait

 

Methods inherited from interface org.jmlspecs.samples.dbc.Complex

angle, imaginaryPart, magnitude, realPart

 

Constructor Detail

ComplexOps

public ComplexOps()

add

public Complex add(Complex b)

Description copied from interface: Complex

Return this + b (the sum of this and b).

Specified by:

add in interface Complex

Specifications: (class)pure

Specifications inherited from overridden method add(Complex b) in interface Complex:
       (class)pure

requires_redundantly b != null;
ensures_redundantly \result != null;
ensures org.jmlspecs.models.JMLDouble.approximatelyEqualTo(this.realPart()+b.realPart(),\result .realPart(),0.0050);
ensures org.jmlspecs.models.JMLDouble.approximatelyEqualTo(this.imaginaryPart()+b.imaginaryPart(),\result .imaginaryPart(),0.0050);

sub

public Complex sub(Complex b)

Description copied from interface: Complex

Return this - b (the difference between this and b).

Specified by:

sub in interface Complex

Specifications: (class)pure

Specifications inherited from overridden method sub(Complex b) in interface Complex:
       (class)pure

requires_redundantly b != null;
ensures_redundantly \result != null;
ensures org.jmlspecs.models.JMLDouble.approximatelyEqualTo(this.realPart()-b.realPart(),\result .realPart(),0.0050);
ensures org.jmlspecs.models.JMLDouble.approximatelyEqualTo(this.imaginaryPart()-b.imaginaryPart(),\result .imaginaryPart(),0.0050);

mul

public Complex mul(Complex b)

Description copied from interface: Complex

Return this * b (the product of this and b).

Specified by:

mul in interface Complex

Specifications: (class)pure

Specifications inherited from overridden method mul(Complex b) in interface Complex:
       (class)pure

requires_redundantly b != null;
requires !java.lang.Double.isNaN(this.magnitude()*b.magnitude());
requires !java.lang.Double.isNaN(this.angle())&&!java.lang.Double.isNaN(b.angle());
ensures_redundantly \result != null;
ensures org.jmlspecs.models.JMLDouble.approximatelyEqualTo(this.magnitude()*b.magnitude(),\result .magnitude(),0.0050);
ensures this.similarAngle(this.angle()+b.angle(),\result .angle());

     also

requires_redundantly b != null;
requires java.lang.Double.isNaN(this.magnitude()*b.magnitude())||java.lang.Double.isNaN(this.angle())||java.lang.Double.isNaN(b.angle());
ensures java.lang.Double.isNaN(\result .realPart());
ensures \result .imaginaryPart() == 0.0;

div

public Complex div(Complex b)

Description copied from interface: Complex

Return this/b (the quotient of this by b).

Specified by:

div in interface Complex

Specifications: (class)pure

Specifications inherited from overridden method div(Complex b) in interface Complex:
       (class)pure

requires_redundantly b != null;
requires !java.lang.Double.isNaN(this.magnitude()/b.magnitude());
requires !java.lang.Double.isNaN(this.angle())&&!java.lang.Double.isNaN(b.angle());
ensures_redundantly \result != null;
ensures org.jmlspecs.models.JMLDouble.approximatelyEqualTo(this.magnitude()/b.magnitude(),\result .magnitude(),0.0050);
ensures this.similarAngle(this.angle()-b.angle(),\result .angle());

     also

requires_redundantly b != null;
requires java.lang.Double.isNaN(this.magnitude()/b.magnitude())||java.lang.Double.isNaN(this.angle())||java.lang.Double.isNaN(b.angle());
ensures java.lang.Double.isNaN(\result .realPart());
ensures \result .imaginaryPart() == 0.0;

equals

public boolean equals(nullable Object o)

Description copied from interface: Complex

Return true if these are the same complex number.

Specified by:

equals in interface Complex

Overrides:

equals in class Object

Specifications: (class)pure

Specifications inherited from overridden method equals(Object obj) in class Object:
       pure

public normal_behavior
requires obj != null;
ensures (* \result is true when obj is "equal to" this object *);

     also

public normal_behavior
requires this == obj;
ensures \result ;

     also

public code normal_behavior
requires obj != null;
ensures \result <==> this == obj;

     also

diverges false;
ensures obj == null ==> !\result ;

Specifications inherited from overridden method equals(Object o) in interface Complex:
       (class)pure

     also

ensures \result <==> o instanceof org.jmlspecs.samples.dbc.Complex&&this.realPart() == ((org.jmlspecs.samples.dbc.Complex)o).realPart()&&this.imaginaryPart() == ((org.jmlspecs.samples.dbc.Complex)o).imaginaryPart();
ensures \result <==> o instanceof org.jmlspecs.samples.dbc.Complex&&this.magnitude() == ((org.jmlspecs.samples.dbc.Complex)o).magnitude()&&this.angle() == ((org.jmlspecs.samples.dbc.Complex)o).angle();

hashCode

public int hashCode()

Description copied from interface: Complex

Return a hashCode for this number.

Specified by:

hashCode in interface Complex

Overrides:

hashCode in class Object

Specifications: (class)pure

Specifications inherited from overridden method in class Object:

public behavior
assignable objectState;
ensures (* \result is a hash code for this object *);

     also

public code normal_behavior
assignable \nothing;

Specifications inherited from overridden method in interface Complex:
       (class)pure