JuliaFloat32

julia.spad line 94 [edit on github]

JuliaFloat32 implements 32 bits floating point arithmetic using Julia Float32 type. Bear in mind that, like JuliaInt64, the internal representation depends on the underlying Lisp implementation, so the usual pure arithmetic operations occur there. For other functions like sqrt, log, exp, transcendental functions etc. the computation is performed at machine level (generally in C language, or even using assembly language).

0: %

from AbelianMonoid

1: %

from MagmaWithUnit

*: (%, %) -> %

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

<=: (%, %) -> Boolean

from PartialOrder

<: (%, %) -> Boolean

from PartialOrder

=: (%, %) -> Boolean

from BasicType

>=: (%, %) -> Boolean

from PartialOrder

>: (%, %) -> Boolean

from PartialOrder

^: (%, %) -> %

from ElementaryFunctionCategory

^: (%, Fraction Integer) -> %

from RadicalCategory

^: (%, 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

catalan: () -> %

catalan() return the Catalan's constant.

ceiling: % -> %

from RealNumberSystem

characteristic: () -> NonNegativeInteger

from NonAssociativeRing

coerce: % -> %

from Algebra %

coerce: % -> OutputForm

from CoercibleTo OutputForm

coerce: Fraction Integer -> %

from Algebra Fraction Integer

coerce: Integer -> %

from NonAssociativeRing

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

convert: DoubleFloat -> %

from ConvertibleFrom DoubleFloat

convert: JuliaFloat64 -> %

from ConvertibleFrom JuliaFloat64

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

differentiate: % -> %

from DifferentialRing

differentiate: (%, NonNegativeInteger) -> %

from DifferentialRing

digits: () -> PositiveInteger

from FloatingPointSystem

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

from EuclideanDomain

euclideanSize: % -> NonNegativeInteger

from EuclideanDomain

eulerGamma: () -> %

eulerGamma() returns the Euler's constant gamma (γ).

exp: % -> %

from ElementaryFunctionCategory

exp: () -> %

exp() returns the JuliaFloat32 ℯ (%e or exp(1)).

expm1: % -> %

expm1(x) computes accurately e^x-1.

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

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

goldenRation: () -> %

goldenRation() returns the golden ratio.

inv: % -> %

from DivisionRing

jf32: DoubleFloat -> %

jf32(x) coerces x to a Julia Float32.

jf32: Integer -> %

jf32(i) coerces i to a Julia Float32.

jf32: JuliaFloat64 -> %

jf32(x) coerces x to a Julia Float32.

jlApply: (String, %) -> %

jlApply(func, x) applies func to argument x.

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

jlApply(func, x, y) applies func to arguments x and y.

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

jlApply(func, x, y, z) applies func to arguments x, y and z.

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.

jlCApply: (String, JuliaSymbol, %) -> %

jlCApply(lib, func, x) applies the C function func from the library lib to argument x. For example: example{jlCApply(“libm.so.6”,jsym(sqrt),jf32(2.0))}

jlCApply: (String, JuliaSymbol, %, %) -> %

jlCApply(lib, func, x, y) applies the C function func from the library lib to arguments x and y. For example: example{jlCApply(“libopenlibm”, jsym(pow),2.7,3.0)} OpenLibm library is provided by Julia.

jlCApply: (String, JuliaSymbol, %, %, %) -> %

jlCApply(lib, func, x, y, z) applies the C function func from the library lib to arguments x, y and z. For example if you have the GNU Scientific Library (GSl-2.8) installed: example{jlCApply(“libgsl.so.28”,jsym(gsl_hypot3),2.0,7.0,9.0)}

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.

log2: % -> %

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

log: % -> %

from ElementaryFunctionCategory

mantissa: % -> Integer

from FloatingPointSystem

max: (%, %) -> %

from OrderedSet

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

from FloatingPointSystem

min: (%, %) -> %

from OrderedSet

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

from FloatingPointSystem

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

from EuclideanDomain

nan: () -> %

nan() returns the Julia Float32 NaN (not a number) constant.

negative?: % -> Boolean

from OrderedRing

negativeInfinity: () -> %

negativeInfinity() returns the Julia Float32 negtive infinity constant.

norm: % -> %

from RealNumberSystem

nrand: () -> %

nrand() returns a 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

positiveInfinity: () -> %

positiveInfinity() returns the Julia Float32 positive infinity constant.

precision: () -> 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(x) stringify(x) using default format. See jlF32Format(String).

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

ArcHyperbolicFunctionCategory

ArcTrigonometricFunctionCategory

BasicType

BiModule(%, %)

BiModule(Fraction Integer, Fraction Integer)

CancellationAbelianMonoid

canonicalsClosed

canonicalUnitNormal

CharacteristicZero

CoercibleFrom Fraction Integer

CoercibleFrom Integer

CoercibleTo OutputForm

CommutativeRing

CommutativeStar

Comparable

ConvertibleFrom DoubleFloat

ConvertibleFrom JuliaFloat64

ConvertibleTo DoubleFloat

ConvertibleTo Float

ConvertibleTo InputForm

ConvertibleTo Pattern Float

ConvertibleTo String

DifferentialRing

DivisionRing

ElementaryFunctionCategory

EntireRing

EuclideanDomain

Field

FloatingPointSystem

GcdDomain

HyperbolicFunctionCategory

IntegralDomain

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