Boolean-0.2.3: Generalized booleans and numbers

Copyright(c) Jan Bracker 2013
LicenseBSD3
Maintainerjbra@informatik.uni-kiel.de
Stabilityexperimental
Safe HaskellSafe-Inferred
LanguageHaskell98

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.

Synopsis

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.

Associated Types

type IntegerOf a Source

The accociated integer type of the number.

Methods

fromIntegerB :: IntegerOf a -> a Source

Construct the number from the associated integer.

Instances

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

toIntegerB

Methods

quot :: a -> a -> a Source

Integer division truncated towards zero.

rem :: a -> a -> a Source

Integer reminder, satisfying: (x quot y) * y + (x rem y) == x

div :: a -> a -> a Source

Integer division truncated toward negative infinity.

mod :: a -> a -> a Source

Integer modulus, satisfying: (x div y) * y + (x mod y) == x

quotRem :: a -> a -> (a, a) Source

Simultaneous quot and rem.

divMod :: a -> a -> (a, a) Source

Simultaneous div and mod.

toIntegerB :: a -> IntegerOf a Source

Create a integer from this integral.

Instances

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

properFraction, round, ceiling, floor

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:

  • n is an integral number with the same sign as x; and
  • f is a fraction with the same type and sign as x, and with absolute value less than 1.

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 x returns the integer nearest x between zero and x

round :: (IntegerOf a ~ IntegerOf b, IntegralB b) => a -> b Source

round x returns the nearest integer to x; the even integer if x is equidistant between two integers

ceiling :: (IntegerOf a ~ IntegerOf b, IntegralB b) => a -> b Source

ceiling x returns the least integer not less than x

floor :: (IntegerOf a ~ IntegerOf b, IntegralB b) => a -> b Source

floor x returns the greatest integer not greater than x.

Instances

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.

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.

atan2 :: a -> a -> a Source

a version of arctangent taking two real floating-point arguments. For real floating x and y, atan2 y x computes the angle (from the positive x-axis) of the vector from the origin to the point (x,y). atan2 y x returns a value in the range [-pi, pi]. It follows the Common Lisp semantics for the origin when signed zeroes are supported. atan2 y 1, with y 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.