HMath.Constants¶
Module index · Numerical conventions
Description
Constants with machine-readable provenance and uncertainty. Mathematical decimal literals carry an absolute truncation bound of 10^-50; conversion to Float/Double adds the target format's rounding error. Physical values are the CODATA 2022 adjustment (NIST SRD 121), not an unversioned latest-value promise.
On this page¶
| API | Purpose |
|---|---|
| piConstant | The circle constant pi at the target Floating precision. |
| eConstant | Euler number exp(1) at the target Floating precision. |
| tau | One full turn in radians, 2*pi, at target Floating precision. |
| goldenRatio | Golden ratio (1+sqrt 5)/2 at the target Floating precision. |
| eulerMascheroni | Euler-Mascheroni constant from the stored 50-decimal-place literal, rounded to the chosen Floating type. |
| catalanConstant | Catalan constant from a 50-decimal-place literal, rounded to the target Floating type; distinct from the integer Catalan-number sequence. |
| aperyConstant | Apery constant zeta(3), from a 50-decimal-place literal rounded to the chosen Floating type. |
| sqrt2 | Positive square root of two in the target Floating type. |
| sqrt3 | Positive square root of three in the target Floating type. |
| ln2 | Natural logarithm of two in the target Floating type. |
| ln10 | Natural logarithm of ten in the target Floating type. |
| infinity | Positive IEEE infinity (1/0) for a RealFloat type. |
| nan | IEEE not-a-number (0/0) for a RealFloat type. |
| Constant | Exact stored decimal Rational with name,unit,provenance,measurement uncertainty,and separate approximation bound. constantAs converts the value without its metadata. |
| Constant | Declaration and type contract below. |
| constantName | Human-readable name of this mathematical or physical constant. |
| constantValue | Exact Rational representation of the stored decimal value; measurement/approximation uncertainties are separate fields. |
| standardUncertainty | Absolute one-standard-deviation measurement uncertainty; zero for definitions. |
| approximationBound | Absolute decimal truncation bound, separate from measurement uncertainty. |
| constantUnit | Display unit string; mathematical dimensionless constants use 1. |
| constantSource | Provenance URL and adjustment/definition identifier for the stored value. |
| constantAs | Convert a Constant record's exact stored Rational decimal to the target Fractional type. |
| mathematicalConstants | Catalog of mathematical constants with names, Rational decimal values, source URLs, and absolute decimal truncation bounds of 10^-50. |
| physicalConstants | Catalog of supported physical constants, retaining unit, source, standard measurement uncertainty, and approximation-bound metadata. |
| speedOfLight | Speed of light in vacuum: stored value 299792458 m s^-1, absolute standard uncertainty 0, from CODATA 2022. |
| planckConstant | Planck constant: stored value 6.62607015e-34 J s, absolute standard uncertainty 0, from CODATA 2022. |
| elementaryCharge | Elementary charge: stored value 1.602176634e-19 C, absolute standard uncertainty 0, from CODATA 2022. |
| boltzmannConstant | Boltzmann constant: stored value 1.380649e-23 J K^-1, absolute standard uncertainty 0, from CODATA 2022. |
| avogadroConstant | Avogadro constant: stored value 6.02214076e23 mol^-1, absolute standard uncertainty 0, from CODATA 2022. |
| gravitationalConstant | Newtonian constant of gravitation: stored value 6.67430e-11 m^3 kg^-1 s^-2, absolute standard uncertainty 0.00015e-11, from CODATA 2022. |
| electronMass | Electron mass: stored value 9.1093837139e-31 kg, absolute standard uncertainty 0.0000000028e-31, from CODATA 2022. |
| astronomicalUnit | IAU 2012 exact astronomical unit: 149597870700 metres, with zero measurement uncertainty and approximation bound. |
| NumericLimits | Format limits and precision metadata derived from RealFloat or the explicit 16-bit format definition. |
| NumericLimits | Declaration and type contract below. |
| minimumNormal | Smallest positive normal value of the represented floating format. |
| minimumSubnormal | Smallest positive subnormal value of the represented floating format. |
| maximumFinite | Largest finite positive value of the represented floating format. |
| machineEpsilon | Gap between one and its next larger representable value. |
| significandDigits | Number of radix digits in the floating significand. |
| minimumExponent | Lower exponent bound returned by RealFloat.floatRange. |
| maximumExponent | Upper exponent bound returned by RealFloat.floatRange. |
| numericLimits | Derived from RealFloat radixdigitsrange, not hardcoded for Double. |
| integerLimits | Given a bounded integral type witness, return its exact (minimum,maximum) as Integers. |
Documentation
piConstant
piConstant :: Floating a => a Source #
The circle constant pi at the target Floating precision. Example: piConstant :: Double. For decimal provenance and an approximation bound, use mathematicalConstants.
eConstant
eConstant :: Floating a => a Source #
Euler number exp(1) at the target Floating precision. Use mathematicalConstants for rational decimal provenance.
goldenRatio
goldenRatio :: Floating a => a Source #
Golden ratio (1+sqrt 5)/2 at the target Floating precision.
eulerMascheroni
eulerMascheroni :: Floating a => a Source #
Euler-Mascheroni constant from the stored 50-decimal-place literal, rounded to the chosen Floating type. Provenance is in mathematicalConstants.
catalanConstant
catalanConstant :: Floating a => a Source #
Catalan constant from a 50-decimal-place literal, rounded to the target Floating type; distinct from the integer Catalan-number sequence.
aperyConstant
aperyConstant :: Floating a => a Source #
Apery constant zeta(3), from a 50-decimal-place literal rounded to the chosen Floating type.
infinity
infinity :: RealFloat a => a Source #
Positive IEEE infinity (1/0) for a RealFloat type. This value is intentionally non-finite and is rejected by checked finite-input APIs.
nan
nan :: RealFloat a => a Source #
IEEE not-a-number (0/0) for a RealFloat type. NaN is not equal to itself; use isNaN to inspect it.
Constant
Exact stored decimal Rational with name,unit,provenance,measurement uncertainty,and separate approximation bound. constantAs converts the value without its metadata.
Constructors
| Constant | |
Fields
| |
constantAs
constantAs :: Fractional a => Constant -> a Source #
Convert a Constant record's exact stored Rational decimal to the target Fractional type. The result omits its uncertainty metadata; retain the record when reporting measurements.
mathematicalConstants
mathematicalConstants :: [Constant] Source #
Catalog of mathematical constants with names, Rational decimal values, source URLs, and absolute decimal truncation bounds of 10^-50. Measurement uncertainties are zero; target Float/Double conversion adds rounding error.
physicalConstants
physicalConstants :: [Constant] Source #
Catalog of supported physical constants, retaining unit, source, standard measurement uncertainty, and approximation-bound metadata. Values use CODATA 2022 except the IAU-defined astronomical unit.
speedOfLight
speedOfLight :: Constant Source #
Speed of light in vacuum: stored value 299792458 m s^-1, absolute standard uncertainty 0, from CODATA 2022. Returns a Constant metadata record; use constantAs for a numeric conversion.
planckConstant
planckConstant :: Constant Source #
Planck constant: stored value 6.62607015e-34 J s, absolute standard uncertainty 0, from CODATA 2022. Returns a Constant metadata record; use constantAs for a numeric conversion.
elementaryCharge
elementaryCharge :: Constant Source #
Elementary charge: stored value 1.602176634e-19 C, absolute standard uncertainty 0, from CODATA 2022. Returns a Constant metadata record; use constantAs for a numeric conversion.
boltzmannConstant
boltzmannConstant :: Constant Source #
Boltzmann constant: stored value 1.380649e-23 J K^-1, absolute standard uncertainty 0, from CODATA 2022. Returns a Constant metadata record; use constantAs for a numeric conversion.
avogadroConstant
avogadroConstant :: Constant Source #
Avogadro constant: stored value 6.02214076e23 mol^-1, absolute standard uncertainty 0, from CODATA 2022. Returns a Constant metadata record; use constantAs for a numeric conversion.
gravitationalConstant
gravitationalConstant :: Constant Source #
Newtonian constant of gravitation: stored value 6.67430e-11 m^3 kg^-1 s^-2, absolute standard uncertainty 0.00015e-11, from CODATA 2022. Returns a Constant metadata record; use constantAs for a numeric conversion.
electronMass
electronMass :: Constant Source #
Electron mass: stored value 9.1093837139e-31 kg, absolute standard uncertainty 0.0000000028e-31, from CODATA 2022. Returns a Constant metadata record; use constantAs for a numeric conversion.
astronomicalUnit
astronomicalUnit :: Constant Source #
IAU 2012 exact astronomical unit: 149597870700 metres, with zero measurement uncertainty and approximation bound. Returns a Constant record with its source URL.
NumericLimits
data NumericLimits a Source #
Format limits and precision metadata derived from RealFloat or the explicit 16-bit format definition.
Constructors
| NumericLimits | |
Fields
| |
Instances
| Show a => Show (NumericLimits a) Source # | |
Defined in HMath.Numeric Methods showsPrec :: Int -> NumericLimits a -> ShowS # show :: NumericLimits a -> String # showList :: [NumericLimits a] -> ShowS # | |
| Eq a => Eq (NumericLimits a) Source # | |
Defined in HMath.Numeric Methods (==) :: NumericLimits a -> NumericLimits a -> Bool # (/=) :: NumericLimits a -> NumericLimits a -> Bool # | |
numericLimits
numericLimits :: RealFloat a => a -> NumericLimits a Source #
Derived from RealFloat radixdigitsrange, not hardcoded for Double.