MachineFloat

fortmac.spad line 51 [edit on github]

A domain which models the floating point representation used by machines in the AXIOM-NAG link.

* : (%, %) -> %

from Magma

* : (%, Fraction(Integer)) -> %

from RightModule(Fraction(Integer))

* : (Fraction(Integer), %) -> %

from LeftModule(Fraction(Integer))

* : (Integer, %) -> %

from AbelianGroup

* : (NonNegativeInteger, %) -> %

from AbelianMonoid

* : (PositiveInteger, %) -> %

from AbelianSemiGroup

+ : (%, %) -> %

from AbelianSemiGroup

- : % -> %

from AbelianGroup

- : (%, %) -> %

from AbelianGroup

/ : (%, %) -> %

from Field

/ : (%, Integer) -> %

from FloatingPointSystem

0 : () -> %

from AbelianMonoid

1 : () -> %

from MagmaWithUnit

< : (%, %) -> Boolean

from PartialOrder

<= : (%, %) -> Boolean

from PartialOrder

= : (%, %) -> Boolean

from BasicType

> : (%, %) -> Boolean

from PartialOrder

>= : (%, %) -> Boolean

from PartialOrder

^ : (%, Fraction(Integer)) -> %

from RadicalCategory

^ : (%, Integer) -> %

from DivisionRing

^ : (%, NonNegativeInteger) -> %

from MagmaWithUnit

^ : (%, PositiveInteger) -> %

from Magma

abs : % -> %

from OrderedRing

annihilate? : (%, %) -> Boolean

from Rng

antiCommutator : (%, %) -> %

from NonAssociativeSemiRng

associates? : (%, %) -> Boolean

from EntireRing

associator : (%, %, %) -> %

from NonAssociativeRng

base : () -> PositiveInteger

base() returns the base of the model

base : PositiveInteger -> PositiveInteger

base(b) sets the base of the model to b

bits : () -> PositiveInteger

from FloatingPointSystem

ceiling : % -> %

from RealNumberSystem

changeBase : (Integer, Integer, PositiveInteger) -> %

changeBase(exp, man, base) is undocumented

characteristic : () -> NonNegativeInteger

from NonAssociativeRing

coerce : % -> %

from Algebra(%)

coerce : Float -> %

from CoercibleFrom(Float)

coerce : Fraction(Integer) -> %

from Algebra(Fraction(Integer))

coerce : Integer -> %

from NonAssociativeRing

coerce : MachineInteger -> %

coerce(u) transforms a MachineInteger into a MachineFloat

coerce : % -> Float

coerce(u) transforms a MachineFloat to a standard Float

coerce : % -> OutputForm

from CoercibleTo(OutputForm)

commutator : (%, %) -> %

from NonAssociativeRng

convert : % -> DoubleFloat

from ConvertibleTo(DoubleFloat)

convert : % -> Float

from ConvertibleTo(Float)

convert : % -> Pattern(Float)

from ConvertibleTo(Pattern(Float))

convert : % -> String

from ConvertibleTo(String)

digits : () -> PositiveInteger

from FloatingPointSystem

divide : (%, %) -> Record(quotient : %, remainder : %)

from EuclideanDomain

euclideanSize : % -> NonNegativeInteger

from EuclideanDomain

exponent : % -> Integer

exponent(u) returns the exponent of u

expressIdealMember : (List(%), %) -> Union(List(%), "failed")

from PrincipalIdealDomain

exquo : (%, %) -> Union(%, "failed")

from EntireRing

extendedEuclidean : (%, %) -> Record(coef1 : %, coef2 : %, generator : %)

from EuclideanDomain

extendedEuclidean : (%, %, %) -> Union(Record(coef1 : %, coef2 : %), "failed")

from EuclideanDomain

factor : % -> Factored(%)

from UniqueFactorizationDomain

float : (Integer, Integer) -> %

from FloatingPointSystem

float : (Integer, Integer, PositiveInteger) -> %

from FloatingPointSystem

floor : % -> %

from RealNumberSystem

fractionPart : % -> %

from RealNumberSystem

gcd : (%, %) -> %

from GcdDomain

gcd : List(%) -> %

from GcdDomain

gcdPolynomial : (SparseUnivariatePolynomial(%), SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%)

from GcdDomain

inv : % -> %

from DivisionRing

latex : % -> String

from SetCategory

lcm : (%, %) -> %

from GcdDomain

lcm : List(%) -> %

from GcdDomain

lcmCoef : (%, %) -> Record(llcm_res : %, coeff1 : %, coeff2 : %)

from LeftOreRing

leftPower : (%, NonNegativeInteger) -> %

from MagmaWithUnit

leftPower : (%, PositiveInteger) -> %

from Magma

leftRecip : % -> Union(%, "failed")

from MagmaWithUnit

mantissa : % -> Integer

mantissa(u) returns the mantissa of u

max : () -> % if % hasn't arbitraryExponent and % hasn't arbitraryPrecision

from FloatingPointSystem

max : (%, %) -> %

from OrderedSet

maximumExponent : () -> Integer

maximumExponent() returns the maximum exponent in the model

maximumExponent : Integer -> Integer

maximumExponent(e) sets the maximum exponent in the model to e

min : () -> % if % hasn't arbitraryExponent and % hasn't arbitraryPrecision

from FloatingPointSystem

min : (%, %) -> %

from OrderedSet

minimumExponent : () -> Integer

minimumExponent() returns the minimum exponent in the model

minimumExponent : Integer -> Integer

minimumExponent(e) sets the minimum exponent in the model to e

multiEuclidean : (List(%), %) -> Union(List(%), "failed")

from EuclideanDomain

negative? : % -> Boolean

from OrderedRing

norm : % -> %

from RealNumberSystem

nthRoot : (%, Integer) -> %

from RadicalCategory

one? : % -> Boolean

from MagmaWithUnit

opposite? : (%, %) -> Boolean

from AbelianMonoid

order : % -> Integer

from FloatingPointSystem

patternMatch : (%, Pattern(Float), PatternMatchResult(Float, %)) -> PatternMatchResult(Float, %)

from PatternMatchable(Float)

plenaryPower : (%, PositiveInteger) -> %

from NonAssociativeAlgebra(%)

positive? : % -> Boolean

from OrderedRing

precision : () -> PositiveInteger

precision() returns the number of digits in the model

precision : PositiveInteger -> PositiveInteger

precision(p) sets the number of digits in the model to p

prime? : % -> Boolean

from UniqueFactorizationDomain

principalIdeal : List(%) -> Record(coef : List(%), generator : %)

from PrincipalIdealDomain

quo : (%, %) -> %

from EuclideanDomain

recip : % -> Union(%, "failed")

from MagmaWithUnit

rem : (%, %) -> %

from EuclideanDomain

retract : % -> Float

from RetractableTo(Float)

retract : % -> Fraction(Integer)

from RetractableTo(Fraction(Integer))

retract : % -> Integer

from RetractableTo(Integer)

retractIfCan : % -> Union(Float, "failed")

from RetractableTo(Float)

retractIfCan : % -> Union(Fraction(Integer), "failed")

from RetractableTo(Fraction(Integer))

retractIfCan : % -> Union(Integer, "failed")

from RetractableTo(Integer)

rightPower : (%, NonNegativeInteger) -> %

from MagmaWithUnit

rightPower : (%, PositiveInteger) -> %

from Magma

rightRecip : % -> Union(%, "failed")

from MagmaWithUnit

round : % -> %

from RealNumberSystem

sample : () -> %

from AbelianMonoid

sign : % -> Integer

from OrderedRing

sizeLess? : (%, %) -> Boolean

from EuclideanDomain

smaller? : (%, %) -> Boolean

from Comparable

sqrt : % -> %

from RadicalCategory

squareFree : % -> Factored(%)

from UniqueFactorizationDomain

squareFreePart : % -> %

from UniqueFactorizationDomain

subtractIfCan : (%, %) -> Union(%, "failed")

from CancellationAbelianMonoid

toString : % -> String

from FloatingPointSystem

toString : (%, NonNegativeInteger) -> String

from FloatingPointSystem

truncate : % -> %

from RealNumberSystem

unit? : % -> Boolean

from EntireRing

unitCanonical : % -> %

from EntireRing

unitNormal : % -> Record(unit : %, canonical : %, associate : %)

from EntireRing

wholePart : % -> Integer

from RealNumberSystem

zero? : % -> Boolean

from AbelianMonoid

~= : (%, %) -> Boolean

from BasicType

Module(Fraction(Integer))

ConvertibleTo(Float)

PrincipalIdealDomain

PartialOrder

NonAssociativeSemiRing

OrderedAbelianGroup

BiModule(%, %)

canonicalUnitNormal

Rng

CoercibleFrom(Integer)

SemiRing

EntireRing

PatternMatchable(Float)

NonAssociativeAlgebra(Fraction(Integer))

unitsKnown

RadicalCategory

FortranMachineTypeCategory

NonAssociativeSemiRng

Field

noZeroDivisors

RetractableTo(Fraction(Integer))

OrderedSet

Magma

SemiGroup

RightModule(Fraction(Integer))

GcdDomain

LeftModule(%)

NonAssociativeRing

UniqueFactorizationDomain

CharacteristicZero

Algebra(%)

CommutativeRing

CoercibleFrom(Fraction(Integer))

DivisionRing

RetractableTo(Float)

LeftOreRing

CancellationAbelianMonoid

EuclideanDomain

Approximate

canonicalsClosed

Comparable

TwoSidedRecip

RetractableTo(Integer)

OrderedCancellationAbelianMonoid

OrderedAbelianMonoid

OrderedRing

RealNumberSystem

FloatingPointSystem

CommutativeStar

AbelianMonoid

MagmaWithUnit

RightModule(%)

RealConstant

ConvertibleTo(String)

ConvertibleTo(DoubleFloat)

OrderedAbelianSemiGroup

Module(%)

CoercibleTo(OutputForm)

ConvertibleTo(Pattern(Float))

SemiRng

Monoid

NonAssociativeAlgebra(%)

Algebra(Fraction(Integer))

BasicType

Ring

AbelianSemiGroup

IntegralDomain

SetCategory

LeftModule(Fraction(Integer))

NonAssociativeRng

BiModule(Fraction(Integer), Fraction(Integer))

CoercibleFrom(Float)

AbelianGroup