Class RealFloat

java.lang.Object

java.lang.Number

org.episteme.core.mathematics.numbers.real.Real

org.episteme.core.mathematics.numbers.real.RealFloat

All Implemented Interfaces:

Serializable, Comparable<Real>, AbelianGroup<Real>, AbelianMonoid<Real>, Group<Real>, Magma<Real>, Monoid<Real>, Field<Real>, FieldElement<Real>, Ring<Real>, RingElement<Real>, Semiring<Real>, Set<Real>

public final class RealFloat
extends Real

Real number backed by a 32-bit float. Package-private implementation detail.

Since:

1.0

Author:

Silvere Martin-Michiellot, Gemini AI (Google DeepMind)

See Also:

• Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
static final Ring<RealFloat>	RING

Fields inherited from class Real

E, HALF_PI, LN10, LN2, NaN, NEGATIVE_INFINITY, ONE, PI, POSITIVE_INFINITY, TWO, TWO_PI, ZERO

Method Summary

Modifier and Type	Method	Description
Real	abs()
Real	acos()	Returns the arccosine of this number.
Real	acosh()	Returns the inverse hyperbolic cosine of this number.
Real	add(Real other)	Returns the sum of this element and another.
Real	asin()	Returns the arcsine of this number.
Real	asinh()	Returns the inverse hyperbolic sine of this number.
Real	atan()	Returns the arctangent of this number.
Real	atan2(Real x)	Returns the angle theta from the conversion of rectangular coordinates (x, y) to polar coordinates (r, theta).
Real	atanh()	Returns the inverse hyperbolic tangent of this number.
BigDecimal	bigDecimalValue()
Real	cbrt()	Returns the cube root of this number.
Real	ceil()	Returns the smallest (closest to negative infinity) double value that is greater than or equal to the argument and is equal to a mathematical integer.
int	characteristic()	Returns the characteristic of this field.
int	compareTo(Real other)
Real	cos()	Returns the cosine of this number (in radians).
Real	cosh()	Returns the hyperbolic cosine of this number.
static RealFloat	create(float value)
Real	divide(Real other)	Returns this element divided by another.
double	doubleValue()
boolean	equals(Object obj)
Real	exp()	Returns e raised to this number.
Real	floor()	Returns the largest (closest to positive infinity) double value that is less than or equal to the argument and is equal to a mathematical integer.
int	hashCode()
Real	hypot(Real y)	Returns sqrt(x^2 + y^2) without intermediate overflow or underflow.
Real	inverse()	Returns the multiplicative inverse of this element.
boolean	isFast()
boolean	isInfinite()
boolean	isNaN()
boolean	isOne()	Checks if this element is the multiplicative identity (one).
boolean	isZero()	Checks if this element is the additive identity (zero).
Real	log()	Returns the natural logarithm of this number.
Real	log10()	Returns the base-10 logarithm of this number.
Real	multiply(Real other)	Returns the product of this element and another.
Real	negate()	Returns the additive inverse of this element.
Real	pow(double exponent)	Returns this number raised to a power.
Real	pow(int exp)
Real	pow(Real exp)
Real	round()	Returns the closest long to the argument, with ties rounding to positive infinity.
Real	sin()	Returns the sine of this number (in radians).
Real	sinh()	Returns the hyperbolic sine of this number.
Real	sqrt()
Real	subtract(Real other)	Returns the difference of this element and another.
Real	tan()	Returns the tangent of this number (in radians).
Real	tanh()	Returns the hyperbolic tangent of this number.
Real	toDegrees()	Converts an angle measured in radians to an approximately equivalent angle measured in degrees.
Real	toRadians()	Converts an angle measured in degrees to an approximately equivalent angle measured in radians.
String	toString()

Methods inherited from class Real

add, contains, description, eE, floatValue, getScalarRing, halfPiE, intValue, inverse, isEmpty, isHighPrecision, isMultiplicationCommutative, isNegative, isPositive, ln10E, ln2E, longValue, max, min, mod, multiply, nanE, negate, negativeInfinityE, of, of, of, of, of, of, one, oneE, operate, piE, positiveInfinityE, remainder, ring, sign, twoE, twoPiE, valueOf, zero, zeroE

Methods inherited from class Number

byteValue, shortValue

Methods inherited from class Object

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

Methods inherited from interface AbelianGroup

isCommutative, subtract

Methods inherited from interface AbelianMonoid

identity, isCommutative

Methods inherited from interface Field

divide, hasUnity

Methods inherited from interface Monoid

isAssociative

Methods inherited from interface Semiring

pow

Field Details

RING

public static final Ring<RealFloat> RING

Method Details

create

public static RealFloat create(float value)

add

public Real add(Real other)

Description copied from interface: RingElement

Returns the sum of this element and another.

Specified by:

add in interface RingElement<Real>

Specified by:

add in class Real

Parameters:

other - the element to add

Returns:

this + other

subtract

public Real subtract(Real other)

Description copied from interface: RingElement

Returns the difference of this element and another.

Default implementation: this.add(other.negate())

Specified by:

subtract in interface RingElement<Real>

Specified by:

subtract in class Real

Parameters:

other - the element to subtract

Returns:

this - other

multiply

public Real multiply(Real other)

Description copied from interface: RingElement

Returns the product of this element and another.

Specified by:

multiply in interface RingElement<Real>

Specified by:

multiply in class Real

Parameters:

other - the element to multiply

Returns:

this * other

divide

public Real divide(Real other)

Description copied from interface: FieldElement

Returns this element divided by another.

Default implementation: this.multiply(other.inverse())

Specified by:

divide in interface FieldElement<Real>

Specified by:

divide in class Real

Parameters:

other - the divisor

Returns:

this / other

negate

public Real negate()

Description copied from interface: RingElement

Returns the additive inverse of this element.

Specified by:

negate in interface RingElement<Real>

Specified by:

negate in class Real

Returns:

-this

abs

public Real abs()

Specified by:

abs in class Real

inverse

public Real inverse()

Description copied from interface: FieldElement

Returns the multiplicative inverse of this element.

For any non-zero element e: e.multiply(e.inverse()) = e.one()

Specified by:

inverse in interface FieldElement<Real>

Specified by:

inverse in class Real

Returns:

1/this

sqrt

public Real sqrt()

Specified by:

sqrt in class Real

pow

public Real pow(int exp)

Specified by:

pow in class Real

pow

public Real pow(Real exp)

Specified by:

pow in class Real

isZero

public boolean isZero()

Description copied from interface: RingElement

Checks if this element is the additive identity (zero).

Specified by:

isZero in interface RingElement<Real>

Specified by:

isZero in class Real

Returns:

true if this equals zero()

isOne

public boolean isOne()

Description copied from interface: RingElement

Checks if this element is the multiplicative identity (one).

Specified by:

isOne in interface RingElement<Real>

Specified by:

isOne in class Real

Returns:

true if this equals one()

isNaN

public boolean isNaN()

Specified by:

isNaN in class Real

isInfinite

public boolean isInfinite()

Specified by:

isInfinite in class Real

isFast

public boolean isFast()

Overrides:

isFast in class Real

doubleValue

public double doubleValue()

Specified by:

doubleValue in class Real

bigDecimalValue

public BigDecimal bigDecimalValue()

Specified by:

bigDecimalValue in class Real

compareTo

public int compareTo(Real other)

Specified by:

compareTo in interface Comparable<Real>

Specified by:

compareTo in class Real

equals

public boolean equals(Object obj)

Specified by:

equals in class Real

hashCode

public int hashCode()

Specified by:

hashCode in class Real

toString

public String toString()

Specified by:

toString in class Real

pow

public Real pow(double exponent)

Description copied from class: Real

Returns this number raised to a power.

Specified by:

pow in class Real

Parameters:

exponent - the exponent

Returns:

this^exponent

exp

public Real exp()

Description copied from class: Real

Returns e raised to this number.

Specified by:

exp in class Real

Returns:

e^this

log

public Real log()

Description copied from class: Real

Returns the natural logarithm of this number.

Specified by:

log in class Real

Returns:

ln(this)

log10

public Real log10()

Description copied from class: Real

Returns the base-10 logarithm of this number.

Specified by:

log10 in class Real

Returns:

log₁₀(this)

sin

public Real sin()

Description copied from class: Real

Returns the sine of this number (in radians).

Specified by:

sin in class Real

Returns:

sin(this)

cos

public Real cos()

Description copied from class: Real

Returns the cosine of this number (in radians).

Specified by:

cos in class Real

Returns:

cos(this)

tan

public Real tan()

Description copied from class: Real

Returns the tangent of this number (in radians).

Specified by:

tan in class Real

Returns:

tan(this)

asin

public Real asin()

Description copied from class: Real

Returns the arcsine of this number.

Specified by:

asin in class Real

Returns:

arcsin(this) in radians

acos

public Real acos()

Description copied from class: Real

Returns the arccosine of this number.

Specified by:

acos in class Real

Returns:

arccos(this) in radians

atan

public Real atan()

Description copied from class: Real

Returns the arctangent of this number.

Specified by:

atan in class Real

Returns:

arctan(this) in radians

atan2

public Real atan2(Real x)

Description copied from class: Real

Returns the angle theta from the conversion of rectangular coordinates (x, y) to polar coordinates (r, theta).

Specified by:

atan2 in class Real

Parameters:

x - the abscissa coordinate

Returns:

the theta component of the point (r, theta)

sinh

public Real sinh()

Description copied from class: Real

Returns the hyperbolic sine of this number.

Specified by:

sinh in class Real

Returns:

sinh(this)

cosh

public Real cosh()

Description copied from class: Real

Returns the hyperbolic cosine of this number.

Specified by:

cosh in class Real

Returns:

cosh(this)

tanh

public Real tanh()

Description copied from class: Real

Returns the hyperbolic tangent of this number.

Specified by:

tanh in class Real

Returns:

tanh(this)

asinh

public Real asinh()

Description copied from class: Real

Returns the inverse hyperbolic sine of this number.

Specified by:

asinh in class Real

Returns:

asinh(this)

acosh

public Real acosh()

Description copied from class: Real

Returns the inverse hyperbolic cosine of this number.

Specified by:

acosh in class Real

Returns:

acosh(this)

atanh

public Real atanh()

Description copied from class: Real

Returns the inverse hyperbolic tangent of this number.

Specified by:

atanh in class Real

Returns:

atanh(this)

cbrt

public Real cbrt()

Description copied from class: Real

Returns the cube root of this number.

Specified by:

cbrt in class Real

Returns:

cbrt(this)

hypot

public Real hypot(Real y)

Description copied from class: Real

Returns sqrt(x^2 + y^2) without intermediate overflow or underflow.

Specified by:

hypot in class Real

Parameters:

y - the other value

Returns:

sqrt(this^2 + y^2)

ceil

public Real ceil()

Description copied from class: Real

Returns the smallest (closest to negative infinity) double value that is greater than or equal to the argument and is equal to a mathematical integer.

Specified by:

ceil in class Real

Returns:

ceil(this)

floor

public Real floor()

Description copied from class: Real

Returns the largest (closest to positive infinity) double value that is less than or equal to the argument and is equal to a mathematical integer.

Specified by:

floor in class Real

Returns:

floor(this)

round

public Real round()

Description copied from class: Real

Returns the closest long to the argument, with ties rounding to positive infinity.

Specified by:

round in class Real

Returns:

round(this)

toDegrees

public Real toDegrees()

Description copied from class: Real

Converts an angle measured in radians to an approximately equivalent angle measured in degrees.

Overrides:

toDegrees in class Real

Returns:

this converted to degrees

toRadians

public Real toRadians()

Description copied from class: Real

Converts an angle measured in degrees to an approximately equivalent angle measured in radians.

Overrides:

toRadians in class Real

Returns:

this converted to radians

characteristic

public int characteristic()

Description copied from interface: Field

Returns the characteristic of this field.

The characteristic is the smallest positive integer n such that:
1 + 1 + ... + 1 (n times) = 0
If no such n exists, the characteristic is 0.

Examples:

• char(â„š) = char(ℝ) = char(â„‚) = 0
• char(𝔽ₚ) = p (for prime p)

Specified by:

characteristic in interface Field<Real>

Overrides:

characteristic in class Real

Returns:

the characteristic (0 for infinite fields, p for finite fields)