JuliaFloat

jobject.spad line 668 [edit on github]

JuliaFloat implements arbitrary precision floating point arithmetic using Julia BigFloats. Use the MPFR library: https://www.mpfr.org/

0: %

from AbelianMonoid

1: %

from MagmaWithUnit

*: (%, %) -> %

from Magma

*: (%, Fraction Integer) -> %

from RightModule Fraction Integer

*: (%, 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

/: (Integer, %) -> %

<=: (%, %) -> Boolean

from PartialOrder

<: (%, %) -> Boolean

from PartialOrder

=: (%, %) -> Boolean

from BasicType

>=: (%, %) -> Boolean

from PartialOrder

>: (%, %) -> Boolean

from PartialOrder

^: (%, %) -> %

from ElementaryFunctionCategory

^: (%, Fraction Integer) -> %

^: (%, Integer) -> %

from DivisionRing

^: (%, NonNegativeInteger) -> %

from MagmaWithUnit

^: (%, PositiveInteger) -> %

from Magma

~=: (%, %) -> Boolean

from BasicType

abs: % -> %

from OrderedRing

acos: % -> %

from ArcTrigonometricFunctionCategory

acosh: % -> %

from ArcHyperbolicFunctionCategory

acot: % -> %

from ArcTrigonometricFunctionCategory

acoth: % -> %

from ArcHyperbolicFunctionCategory

acsc: % -> %

from ArcTrigonometricFunctionCategory

acsch: % -> %

from ArcHyperbolicFunctionCategory

annihilate?: (%, %) -> Boolean

from Rng

antiCommutator: (%, %) -> %

from NonAssociativeSemiRng

asec: % -> %

from ArcTrigonometricFunctionCategory

asech: % -> %

from ArcHyperbolicFunctionCategory

asin: % -> %

from ArcTrigonometricFunctionCategory

asinh: % -> %

from ArcHyperbolicFunctionCategory

associates?: (%, %) -> Boolean

from EntireRing

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

from NonAssociativeRng

atan: % -> %

from ArcTrigonometricFunctionCategory

atan: (%, %) -> %

atan(x, y) computes the inverse tangent of x/y.

atanh: % -> %

from ArcHyperbolicFunctionCategory

base: () -> PositiveInteger

from FloatingPointSystem

bits: () -> PositiveInteger

from FloatingPointSystem

bits: PositiveInteger -> PositiveInteger

from FloatingPointSystem

ceiling: % -> %

from RealNumberSystem

characteristic: () -> NonNegativeInteger

from NonAssociativeRing

cis: % -> JuliaComplexFloat

cis(x) returns exp(%i*x) computed efficiently.

cispi: % -> JuliaComplexFloat

cispi(x) returns cis(%pi*x) computed efficiently.

coerce: % -> %

from Algebra %

coerce: % -> OutputForm

from CoercibleTo OutputForm

coerce: Float -> %

coerce: Fraction Integer -> %

from Algebra Fraction Integer

coerce: Integer -> %

from NonAssociativeRing

coerce: JuliaFloat64 -> %

commutator: (%, %) -> %

from NonAssociativeRng

convert: % -> DoubleFloat

from ConvertibleTo DoubleFloat

convert: % -> Float

from ConvertibleTo Float

convert: % -> InputForm

from ConvertibleTo InputForm

convert: % -> Pattern Float

from ConvertibleTo Pattern Float

convert: % -> String

from ConvertibleTo String

cos: % -> %

from TrigonometricFunctionCategory

cosh: % -> %

from HyperbolicFunctionCategory

cot: % -> %

from TrigonometricFunctionCategory

coth: % -> %

from HyperbolicFunctionCategory

csc: % -> %

from TrigonometricFunctionCategory

csch: % -> %

from HyperbolicFunctionCategory

D: % -> %

from DifferentialRing

D: (%, NonNegativeInteger) -> %

from DifferentialRing

decreasePrecision: Integer -> PositiveInteger

from FloatingPointSystem

differentiate: % -> %

from DifferentialRing

differentiate: (%, NonNegativeInteger) -> %

from DifferentialRing

digits: () -> PositiveInteger

from FloatingPointSystem

digits: PositiveInteger -> PositiveInteger

from FloatingPointSystem

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

from EuclideanDomain

euclideanSize: % -> NonNegativeInteger

from EuclideanDomain

exp10: % -> %

exp10(x) computes the base 10 exponential of x.

exp1: () -> %

exp1() returns the JuliaFloat ℯ (%e or exp(1)).

exp2: % -> %

exp2(x) computes the base 2 exponential of x.

exp: % -> %

from ElementaryFunctionCategory

exp: () -> %

exp() returns the JuliaFloat ℯ (%e or exp(1)).

expm1: % -> %

expm1(x) computes accurately ℯ^x-1. It avoids the loss of precision involved in the direct evaluation of exp(x)-1 for small values of x.

exponent: % -> Integer

from FloatingPointSystem

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

finite?: % -> Boolean

finite?(x) tests whether or not x is finite.

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

increasePrecision: Integer -> PositiveInteger

from FloatingPointSystem

integer?: % -> Boolean

integer?(x) tests whether or not x is an integer.

inv: % -> %

from DivisionRing

jfloat: Float -> %

jfloat: Fraction Integer -> %

jfloat: Integer -> %

jfloat: String -> %

jlAbout: % -> Void

from JuliaObjectType

jlApply: (String, %) -> %

from JuliaObjectType

jlApply: (String, %, %) -> %

from JuliaObjectType

jlApply: (String, %, %, %) -> %

from JuliaObjectType

jlApply: (String, %, %, %, %) -> %

from JuliaObjectType

jlApply: (String, %, %, %, %, %) -> %

from JuliaObjectType

jlApply: (String, %, %, %, %, %, %) -> %

from JuliaObjectType

jlApprox?: (%, %) -> Boolean

jlApprox?(x,y) computes inexact equality comparison with default parameters. Two numbers compare equal if their relative distance or their absolute distance is within tolerance bounds.

jlApprox?: (%, %, %) -> Boolean

jlApprox?(x,y,atol) computes inexact equality comparison with absolute tolerance atol. Two numbers compare equal if their relative distance or their absolute distance is within tolerance bounds.

jlId: % -> String

from JuliaObjectType

jllMPFRApply: (JuliaObject, %) -> %

jllMPFRApply(func,x) applies the function pointer func to x. It is expected that the C function modifies the first parameters for the returned value (provided by FriCAS and returned here) and and as a last parameter, the rounding mode. See MPFR. Uses Julia rounding mode, default to nearest. example{mpfr:=jlDlOpen “libmpfr”} example{sym:= jlDlSym(mpfr,jsym(mpfr_gamma))} example{val:=jfloat(“0.7”);} example{jllMPFRApply(sym,val)} => 1.29805533264755778568117117915281161778… example{jlDlClose(mpfr)}

jllMPFRApply: (JuliaObject, %, %) -> %

jllMPFRApply(func,x,y) applies the function pointer func to x and y. It is expected that the C function modifies the first parameters for the returned value (provided by FriCAS and returned here) and and as a last parameter, the rounding mode. See MPFR. Uses Julia rounding mode, default to nearest. example{mpfr:=j lDlOpen “libmpfr”} example{sym:= jlDlSym(mpfr,jsym(mpfr_pow))} example{val:=jfloat(“0.7”);} example{jllMPFRApply(sym,val, jfloat(2))} example{jlDlClose(mpfr)}

jllMPFRApply: (JuliaObject, %, %, %) -> %

jllMPFRApply(func,x,y,z) applies the function pointer func to x, y and z. It is expected that the C function modifies the first parameters for the returned value (provided by FriCAS and returned here) and as a last parameter, the rounding mode (the default mode is used here). See MPFR. Uses Julia rounding mode, default to nearest. example{mpfr:=j lDlOpen “libmpfr”} example{sym:= jlDlSym(mpfr,jsym(mpfr_fma))} example{val:=jfloat(“0.7”);} example{jllMPFRApply(sym,val, jfloat(2), jfloat(5))} example{jlDlClose(mpfr)}

jlRef: % -> SExpression

from JuliaObjectType

jlref: String -> %

from JuliaObjectType

jlType: % -> String

from JuliaObjectType

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

log10: % -> %

log10(x) computes the base 10 logarithm of x.

log1p: % -> %

log1p(x) computes accurately log(1+x)

log2: % -> %

log2(x) computes the base 2 logarithm of x.

log: % -> %

from ElementaryFunctionCategory

mantissa: % -> Integer

from FloatingPointSystem

max: (%, %) -> %

from OrderedSet

max: () -> % if

from FloatingPointSystem

min: (%, %) -> %

from OrderedSet

min: () -> % if

from FloatingPointSystem

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

from EuclideanDomain

mutable?: % -> Boolean

from JuliaObjectType

negative?: % -> Boolean

from OrderedRing

norm: % -> %

from RealNumberSystem

nothing?: % -> Boolean

from JuliaObjectType

nrand: () -> %

nrand() returns an normally distributed random number.

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

pi: () -> %

from TranscendentalFunctionCategory

plenaryPower: (%, PositiveInteger) -> %

from NonAssociativeAlgebra Fraction Integer

positive?: % -> Boolean

from OrderedRing

precision: % -> PositiveInteger

precision(x) returns the precision of x.

precision: (%, PositiveInteger) -> %

precision(x, p) returns a copy of x with precision p.

precision: () -> PositiveInteger

from FloatingPointSystem

precision: PositiveInteger -> PositiveInteger

from FloatingPointSystem

prime?: % -> Boolean

from UniqueFactorizationDomain

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

from PrincipalIdealDomain

quo: (%, %) -> %

from EuclideanDomain

recip: % -> Union(%, failed)

from MagmaWithUnit

rem: (%, %) -> %

from EuclideanDomain

retract: % -> Fraction Integer

from RetractableTo Fraction Integer

retract: % -> Integer

from RetractableTo Integer

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

sec: % -> %

from TrigonometricFunctionCategory

sech: % -> %

from HyperbolicFunctionCategory

sign: % -> Integer

from OrderedRing

sin: % -> %

from TrigonometricFunctionCategory

sinh: % -> %

from HyperbolicFunctionCategory

sizeLess?: (%, %) -> Boolean

from EuclideanDomain

smaller?: (%, %) -> Boolean

from Comparable

sqrt: % -> %

from RadicalCategory

squareFree: % -> Factored %

from UniqueFactorizationDomain

squareFreePart: % -> %

from UniqueFactorizationDomain

string: % -> String

string(fl) return the strings representation of fl.

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

from CancellationAbelianMonoid

tan: % -> %

from TrigonometricFunctionCategory

tanh: % -> %

from HyperbolicFunctionCategory

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

urand01: () -> %

urand01() returns an uniformly distributed random number contained in [0,1].

wholePart: % -> Integer

from RealNumberSystem

zero?: % -> Boolean

from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

Algebra %

Algebra Fraction Integer

Approximate

arbitraryPrecision

ArcHyperbolicFunctionCategory

ArcTrigonometricFunctionCategory

BasicType

BiModule(%, %)

BiModule(Fraction Integer, Fraction Integer)

CancellationAbelianMonoid

canonicalsClosed

canonicalUnitNormal

CharacteristicZero

CoercibleFrom Fraction Integer

CoercibleFrom Integer

CoercibleTo OutputForm

CommutativeRing

CommutativeStar

Comparable

ConvertibleTo DoubleFloat

ConvertibleTo Float

ConvertibleTo InputForm

ConvertibleTo Pattern Float

ConvertibleTo String

DifferentialRing

DivisionRing

ElementaryFunctionCategory

EntireRing

EuclideanDomain

Field

FloatingPointSystem

GcdDomain

HyperbolicFunctionCategory

IntegralDomain

JuliaObjectRing

JuliaObjectType

JuliaRing

JuliaType

LeftModule %

LeftModule Fraction Integer

LeftOreRing

Magma

MagmaWithUnit

Module %

Module Fraction Integer

Monoid

NonAssociativeAlgebra %

NonAssociativeAlgebra Fraction Integer

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

noZeroDivisors

OrderedAbelianGroup

OrderedAbelianMonoid

OrderedAbelianSemiGroup

OrderedCancellationAbelianMonoid

OrderedRing

OrderedSet

PartialOrder

PatternMatchable Float

PrincipalIdealDomain

RadicalCategory

RealConstant

RealNumberSystem

RetractableTo Fraction Integer

RetractableTo Integer

RightModule %

RightModule Fraction Integer

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

TranscendentalFunctionCategory

TrigonometricFunctionCategory

TwoSidedRecip

UniqueFactorizationDomain

unitsKnown