| Copyright | (c) Jan Bracker 2013 |
|---|---|
| License | BSD3 |
| Maintainer | jbra@informatik.uni-kiel.de |
| Stability | experimental |
| Safe Haskell | Safe |
| Language | Haskell98 |
Data.Boolean.Numbers
Description
A generalized version of the class hirarchy for numbers. All functions that would break a potential deep embedding are removed or generalized to support deep embeddings.
The class hierarchy for numeric types keeps as close as possible to the
Prelude hierarchy. A great part of the default implementation and comments
are copied and adopted from Prelude.
- class Num a => NumB a where
- type IntegerOf a
- class (NumB a, OrdB a) => IntegralB a where
- class (NumB a, OrdB a, Fractional a) => RealFracB a where
- class (Boolean (BooleanOf a), RealFracB a, Floating a) => RealFloatB a where
- evenB :: (IfB a, EqB a, IntegralB a) => a -> BooleanOf a
- oddB :: (IfB a, EqB a, IntegralB a) => a -> BooleanOf a
- fromIntegralB :: (IntegerOf a ~ IntegerOf b, IntegralB a, NumB b) => a -> b
Documentation
class Num a => NumB a where Source #
An extension of Num that supplies the integer type of a
given number type and a way to create that number from the
integer.
Minimal complete definition
class (NumB a, OrdB a) => IntegralB a where Source #
A deep embedded version of Integral.
Integral numbers, supporting integer division.
Minimal complete definition is either quotRem and divMod
or the other four functions. Besides that toIntegerB always
has to be implemented.
Minimal complete definition
class (NumB a, OrdB a, Fractional a) => RealFracB a where Source #
Deep embedded version of RealFloat.
Extracting components of fractions.
Minimal complete definition: properFraction,
round, floor and ceiling.
Minimal complete definition
Methods
properFraction :: (IntegerOf a ~ IntegerOf b, IntegralB b) => a -> (b, a) Source #
The function properFraction takes a real fractional number x
and returns a pair (n,f) such that x = n+f, and:
nis an integral number with the same sign asx; andfis a fraction with the same type and sign asx, and with absolute value less than1.
The default definitions of the ceiling, floor, truncate
and round functions are in terms of properFraction.
truncate :: (IntegerOf a ~ IntegerOf b, IntegralB b) => a -> b Source #
truncate xx between zero and x
round :: (IntegerOf a ~ IntegerOf b, IntegralB b) => a -> b Source #
round xx;
the even integer if x is equidistant between two integers
ceiling :: (IntegerOf a ~ IntegerOf b, IntegralB b) => a -> b Source #
ceiling xx
floor :: (IntegerOf a ~ IntegerOf b, IntegralB b) => a -> b Source #
floor xx.
class (Boolean (BooleanOf a), RealFracB a, Floating a) => RealFloatB a where Source #
Deep embedded version of RealFloat.
Efficient, machine-independent access to the components of a
floating-point number.
A complete definition has to define all functions.
Minimal complete definition
Methods
isNaN :: a -> BooleanOf a Source #
true if the argument is an IEEE "not-a-number" (NaN) value.
isInfinite :: a -> BooleanOf a Source #
true if the argument is an IEEE infinity or negative infinity.
isNegativeZero :: a -> BooleanOf a Source #
true if the argument is an IEEE negative zero.
isIEEE :: a -> BooleanOf a Source #
true if the argument is an IEEE floating point number.
a version of arctangent taking two real floating-point arguments.
For real floating x and y, atan2 y x(x,y). atan2 y x-pi,
pi]. It follows the Common Lisp semantics for the origin when
signed zeroes are supported. atan2 y 1y in a type
that is RealFloatB, should return the same value as atan y
Instances
evenB :: (IfB a, EqB a, IntegralB a) => a -> BooleanOf a Source #
Variant of even for generalized booleans.
oddB :: (IfB a, EqB a, IntegralB a) => a -> BooleanOf a Source #
Variant of odd for generalized booleans.
fromIntegralB :: (IntegerOf a ~ IntegerOf b, IntegralB a, NumB b) => a -> b Source #
Variant of fromIntegral for generalized booleans.