A unit of measurement.

A dimensional quantity.

A dimensional quantity, stored as an ExactPi' multiple of its value in its dimension's SI coherent unit.

The name is an abbreviation for scaled quantity.

Encodes whether a unit is a metric unit, that is, whether it can be combined with a metric prefix to form a related unit.

Represents a physical dimension in the basis of the 7 SI base dimensions, where the respective dimensions are represented by type variables using the following convention:

• l: Length
• m: Mass
• t: Time
• i: Electric current
• th: Thermodynamic temperature
• n: Amount of substance
• j: Luminous intensity

For the equivalent term-level representation, see Dimension'

Multiplication of dimensions corresponds to adding of the base dimensions' exponents.

Division of dimensions corresponds to subtraction of the base dimensions' exponents.

Powers of dimensions corresponds to multiplication of the base dimensions' exponents by the exponent.

We limit ourselves to integer powers of Dimensionals as fractional powers make little physical sense.

Roots of dimensions corresponds to division of the base dimensions' exponents by the order of the root.

The reciprocal of a dimension is defined as the result of dividing DOne by it, or of negating each of the base dimensions' exponents.

A physical dimension, encoded as 7 integers, representing a factorization of the dimension into the 7 SI base dimensions. By convention they are stored in the same order as in the Dimension data kind.

Dimensional values inhabit this class, which allows access to a term-level representation of their dimension.

A KnownDimension is one for which we can construct a term-level representation. Each validly constructed type of kind Dimension has a KnownDimension instance.

While KnownDimension is a constraint synonym, the presence of KnownDimension d in a context allows use of dimension :: Proxy d -> Dimension'.

Forms a possibly scaled SQuantity by multipliying a number and a unit.

Divides a possibly scaled SQuantity by a Unit of the same physical dimension, obtaining the numerical value of the quantity expressed in that unit.

Multiplies two Quantitys or two Units.

The intimidating type signature captures the similarity between these operations and ensures that composite Units are NonMetric.

Divides one Quantity by another or one Unit by another.

The intimidating type signature captures the similarity between these operations and ensures that composite Units are NotPrefixable.

Adds two possibly scaled SQuantitys, preserving any scale factor.

Use in conjunction with changeRepRound to combine quantities with differing scale factors.

Subtracts one possibly scaled SQuantity from another, preserving any scale factor.

Use in conjunction with changeRepRound to combine quantities with differing scale factors.

Negates the value of a possibly scaled SQuantity, preserving any scale factor.

Takes the absolute value of a possibly scaled SQuantity, preserving any scale factor.

The standard two argument arctangent function. Since it interprets its two arguments in comparison with one another, the input may have any dimension.

The standard two argument arctangent function. Since it interprets its two arguments in comparison with one another, the input may have any dimension.

Applies *~ to all values in a functor.

Applies /~ to all values in a functor.

The sum of all elements in a list.

The arithmetic mean of all elements in a list.

Rescales a fixed point quantity, accomodating changes both in its scale factor and its representation type.

Note that this uses an arbitrary precision representation of pi, which may be quite slow.

Rescales a fixed point quantity, accomodating changes both in its scale factor and its representation type.

Expected to outperform rescale when a FiniteBits context is available for the source and destination representation types.

Approximately rescales a fixed point quantity, accomodating changes both in its scale factor and its representation type.

Uses approximate arithmetic by way of an intermediate Double representation.

Approximately rescales a fixed point quantity, accomodating changes both in its scale factor and its representation type.

Uses approximate arithmetic by way of an intermediate Floating type, to which a proxy must be supplied.

A KnownVariant is one whose term-level Dimensional values we can represent with an associated data family instance and manipulate with certain functions, not all of which are exported from the package.

Each validly constructed type of kind Variant has a KnownVariant instance.

Convenient conversion between numerical types while retaining dimensional information.

Convenient conversion to types with Integral representations using round.

Convenient conversion from exactly represented values while retaining dimensional information.

The type-level dimension of dimensionless values.

The constant for zero is polymorphic, allowing it to express zero Length or Capacitance or Velocity etc, in addition to the Dimensionless value zero.

The least positive representable value in a given fixed-point scaled quantity type.

Twice pi.

For background on tau see http://tauday.com/tau-manifesto (but also feel free to review http://www.thepimanifesto.com).

A polymorphic Unit which can be used in place of the coherent SI base unit of any dimension. This allows polymorphic quantity creation and destruction without exposing the Dimensional constructor.

The unit one has dimension DOne and is the base unit of dimensionless values.

As detailed in 7.10 "Values of quantities expressed simply as numbers: the unit one, symbol 1" of [1] the unit one generally does not appear in expressions. However, for us it is necessary to use one as we would any other unit to perform the "boxing" of dimensionless values.

Forms a new atomic Unit by specifying its UnitName and its definition as a multiple of another Unit.

Use this variant when the scale factor of the resulting unit is irrational or Approximate. See mkUnitQ for when it is rational and mkUnitZ for when it is an integer.

Note that supplying zero as a definining quantity is invalid, as the library relies upon units forming a group under multiplication.

Supplying negative defining quantities is allowed and handled gracefully, but is discouraged on the grounds that it may be unexpected by other readers.

Forms a new atomic Unit by specifying its UnitName and its definition as a multiple of another Unit.

Use this variant when the scale factor of the resulting unit is rational. See mkUnitZ for when it is an integer and mkUnitR for the general case.

For more information see mkUnitR.

Forms a new atomic Unit by specifying its UnitName and its definition as a multiple of another Unit.

Use this variant when the scale factor of the resulting unit is an integer. See mkUnitQ for when it is rational and mkUnitR for the general case.

For more information see mkUnitR.

Extracts the UnitName of a Unit.

Extracts the exact value of a Unit, expressed in terms of the SI coherent derived unit (see siUnit) of the same Dimension.

Note that the actual value may in some cases be approximate, for example if the unit is defined by experiment.

Discards potentially unwanted type level information about a Unit.

Attempts to convert a Unit which may or may not be Metric to one which is certainly Metric.

Forms the exact version of a Unit.

A dimensionless number with n fractional bits, using a representation of type a.

A binary scale factor.

A single-turn angle represented as a signed 8-bit integer.

A single-turn angle represented as a signed 16-bit integer.

A single-turn angle represented as a signed 32-bit integer.