orbital.math
Interface Real

All Superinterfaces:

Arithmetic, java.lang.Comparable, Complex, Normed, Scalar

All Known Subinterfaces:

Integer, Rational

public interface Real
extends Complex, java.lang.Comparable

Representation of a real number a∈R.

Of course, the machine prevents us from handling real numbers at all. This class provides rational decimal numbers up to machine precision, instead. In fact, the class Real is limited to decimals and does not even feel that any irrational numbers could possibly exist as well. But for we are patient humans, we wisely nod and satisfy ourselfes with decimal numbers.

Author:

André Platzer

See Also:

ValueFactory.valueOf(double), ValueFactory.valueOf(float), ValueFactory.valueOf(java.math.BigDecimal)

Invariants:

(this is Comparable ∧ ◇abnormal(¬Comparable)) ∨ □abnormal(Comparable)

Stereotype:

data-type

Field Summary

static Predicate	hasType Checks whether the given number is in the set of reals and not a subset.
static Predicate	isa Checks whether the given number is in the set of reals.

Fields inherited from interface orbital.math.Arithmetic

numerical

Method Summary

Real	add(Real b)
int	compareTo(java.lang.Object o) Compares this object with the specified object for order.
Real	divide(Real b)
double	doubleValue() Returns the value of the specified real as a double.
float	floatValue() Returns the value of the specified real as a float.
Real	multiply(Real b)
Real	power(Real b) Return ab.
Real	subtract(Real b)

Methods inherited from interface orbital.math.Complex

add, arg, conjugate, divide, equals, hashCode, im, isInfinite, isNaN, multiply, norm, power, re, subtract

Methods inherited from interface orbital.math.Arithmetic

add, divide, equals, inverse, isOne, isZero, minus, multiply, one, power, scale, subtract, toString, valueFactory, zero

Field Detail

isa

static final Predicate isa

Checks whether the given number is in the set of reals. return whether v is real (or rational or an integer).

hasType

static final Predicate hasType

Checks whether the given number is in the set of reals and not a subset.

To be precise, for all numbers with machine precision can only be rational. Nevertheless, we model the difference between (machine precision) reals and explicit fractional numbers as Rationals with numerator and denominator.

return whether v∈R\Q is real, but not rational and thus irrational (for machine dimensions).

Method Detail

compareTo

int compareTo(java.lang.Object o)

Compares this object with the specified object for order.

Specified by:

compareTo in interface java.lang.Comparable

Returns:

a negative integer, zero, or a positive integer as this object is less than, equal to, or greater than the specified object.

Throws:

java.lang.ClassCastException - if the specified object's type prevents it from being compared to this Object.

See Also:

Comparable.compareTo(Object)

Preconditions:

this and o have comparable types

Postconditions:

∀e1,e2∈class (e1.compareTo((Object)e2)==0) ⇔ (e1.equals((Object)e2), i.e. compareTo is consistent with equals.

floatValue

float floatValue()

Returns the value of the specified real as a float. This may involve rounding. Similar to the double-to-float narrowing primitive conversion as defined in The Java Language Specification: if this real has too great a magnitude to represent as a float, it will be converted to Float.NEGATIVE_INFINITY or Float.POSITIVE_INFINITY as appropriate.

Returns:

the numeric value represented by this object after conversion to type float.

doubleValue

double doubleValue()

Returns the value of the specified real as a double. This may involve rounding. Similar to the double-to-float narrowing primitive conversion as defined in The Java Language Specification: if this real has too great a magnitude to represent as a double, it will be converted to Double.NEGATIVE_INFINITY or Double.POSITIVE_INFINITY as appropriate.

Returns:

the numeric value represented by this object after conversion to type double.

add

Real add(Real b)

subtract

Real subtract(Real b)

multiply

Real multiply(Real b)

divide

Real divide(Real b)

power

Real power(Real b)

Return a^b.

Postconditions:

(b != 0 → RES instanceof Real)