# Num

Basic numeric class. Minimal complete definition: all except negate or (-)
Extract the numerator of the ratio in reduced form: the numerator and denominator have no common factor and the denominator is positive.
Odds and ends, mostly functions for reading and showing RealFloat-like kind of values.
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Combinators for creating bijections from a subset of an arbitrary type to a range of Ints, , e.g. for using libraries that require Int IDs. Version 0.2.1
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Functions for finding prime numbers, checking whether a number is prime, finding the factors of a number etc. Version 0.2.1
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Instances of the numerical classes for a variety of different numbers: (computable) real numbers, arbitrary precision fixed numbers, arbitrary precision floating point numbers, differentiable numbers, symbolic numbers, natural numbers, interval arithmetic. Version 3000.0.0.0
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This package includes the Sieve of O'Neill and two generalizations of the Sieve of Eratosthenes.   The Sieve of O'Neill is a fully incremental primality sieve based on priority queues.  The other two are array based, and are not incremental.   One sieves the smallest prime factor,  and is useful if you want to factor a large quantity of small numbers.   The other sieves Euler's Totient, which is the number of positive integers relatively prime and less than a given number. Version 0.1.1
the value passed to the +RTS -N flag. This is the number of Haskell threads that can run truly simultaneously at any given time, and is typically set to the number of physical CPU cores on the machine.
Contains the number of entries in the colormap of the current window's current layer (0 in RGBA mode).
Contains Just the number of dials and buttons of an attached dial & button box or Nothing if there is none.
the current number of discarded tests
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Convert numbers to number words in a number of languages. Each language has its own module. The module name is based on one of the ISO 639 Alpha codes. Each module contains one or more cardinal functions and a struct function. The cardinal functions directly convert cardinal numbers to a string-like representation of their spoken form. The struct functions convert numbers to a polymorphic representation of their grammatical structure. All language modules are implemented using the numerals-base package. The use of this package is best understood with some examples. Because the results of conversion are polymorphic we need to choose a specific type. For these examples we'll use simple strings. But any type that has instances for Monoid and IsString will work. First some English number names, both British and US variants: >>> import qualified Text.Numeral.Language.EN as EN >>> EN.uk_cardinal 123 :: Maybe String Just &quot;one hundred and twenty-three&quot; >>> EN.us_cardinal (10^50 + 42) :: Maybe String Just &quot;one hundred quindecillion forty-two&quot; French, which contains some traces of a base 20 system: >>> import qualified Text.Numeral.Language.FR as FR >>> FR.cardinal (-99) :: Maybe String Just &quot;moins quatre-vingt-dix-neuf&quot; Conversions can fail. Alamblak, a language spoken by a few people in Papua New Guinea, has no representation for negative numbers: >>> import qualified Text.Numeral.Language.AMP as AMP >>> AMP.cardinal (-3) :: Maybe String Nothing Some languages have multiple scripts and methods for writing number names. Take Chinese for example, which can be written using Han characters or transcribed to the Latin script using Pinyin. Traditional Chinese characters: >>> import qualified Text.Numeral.Language.ZH as ZH >>> ZH.trad_cardinal 123456 :: Maybe String Just &quot;AŒ, CÛ~”Am&quot; Simplified characters for use in financial contexts: >>> ZH.finance_simpl_cardinal 123456 :: Maybe String Just &quot;þ0Âß†/ þF&quot; Transcribed using Pinyin: >>> ZH.pinyin_cardinal 123456 :: Maybe String Just &quot;shíèrwàn snqin sìbÎi wÔshí liù&quot; Using the struct functions you can see the grammatical structure of number names. Because the results of these functions are polymorphic you need to specify a specific type. >>> import qualified Text.Numeral.Language.NL as NL >>> NL.struct 123 :: Maybe Integer Just 123 >>> import Text.Numeral >>> NL.struct 123 :: Maybe Exp Just (Add (Lit 100) (Add (Lit 3) (Mul (Lit 2) (Lit 10)))) Compare with: >>> NL.cardinal 123 :: Maybe String Just &quot;honderddrieëntwintig&quot; 100 (honderd) + (3 (drie) + (ën) 2 (twin) * 10 (tig)) Version 0.3.0.1
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This package contains machinery to construct functions that convert numbers to number words. It allows you to write a function which converts a number like 142 to the string &quot;one hundred and forty-two&quot;. The documentation for the Text.Numeral module contains an high level overview of the package. If you just want to convert numbers to number words in a specific language you should probably use the numerals package. That package also contains numerous examples on how to use the functions in this package. Version 0.3
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Various floating point limit related constants. Version 0.1.0.0
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Revisiting the Numeric Classes The Prelude for Haskell 98 offers a well-considered set of numeric classes which covers the standard numeric types (Integer, Int, Rational, Float, Double, Complex) quite well. But they offer limited extensibility and have a few other flaws. In this proposal we will revisit these classes, addressing the following concerns: 1: The current Prelude defines no semantics for the fundamental operations. For instance, presumably addition should be associative (or come as close as feasible), but this is not mentioned anywhere. 2: There are some superfluous superclasses. For instance, Eq and Show are superclasses of Num. Consider the data type    data IntegerFunction a = IF (a -> Integer)  One can reasonably define all the methods of Algebra.Ring.C for IntegerFunction a (satisfying good semantics), but it is impossible to define non-bottom instances of Eq and Show. In general, superclass relationship should indicate some semantic connection between the two classes. 3: In a few cases, there is a mix of semantic operations and representation-specific operations. toInteger, toRational, and the various operations in RealFloating (decodeFloat, ...) are the main examples. 4: In some cases, the hierarchy is not finely-grained enough: Operations that are often defined independently are lumped together. For instance, in a financial application one might want a type &quot;Dollar&quot;, or in a graphics application one might want a type &quot;Vector&quot;. It is reasonable to add two Vectors or Dollars, but not, in general, reasonable to multiply them. But the programmer is currently forced to define a method for '(*)' when she defines a method for '(+)'. In specifying the semantics of type classes, I will state laws as follows: > (a + b) + c === a + (b + c) The intended meaning is extensional equality: The rest of the program should behave in the same way if one side is replaced with the other. Unfortunately, the laws are frequently violated by standard instances; the law above, for instance, fails for Float: > (1e20 + (-1e20)) + 1.0  = 1.0 > 1e20 + ((-1e20) + 1.0) = 0.0 For inexact number types like floating point types, thus these laws should be interpreted as guidelines rather than absolute rules. In particular, the compiler is not allowed to use them for optimization. Unless stated otherwise, default definitions should also be taken as laws. Thanks to Brian Boutel, Joe English, William Lee Irwin II, Marcin Kowalczyk, Ketil Malde, Tom Schrijvers, Ken Shan, and Henning Thielemann for helpful comments. Usage: Write modules in the following style: > [-# NoImplicitPrelude #-] > module MyModule where > ... various specific imports ... > import NumericPrelude Importing NumericPrelude is almost the same as > import NumericPrelude.Numeric > import NumericPrelude.Base   . Instead of the NoImplicitPrelude pragma you could also write import Prelude () but this will yield problems with numeric literals. There are two wrapper types that allow types to be used with both Haskell98 and NumericPrelude type classes that are initially implemented for only one of them. Scope & Limitations/TODO: * It might be desireable to split Ord up into Poset and Ord (a total ordering). This is not addressed here. * In some cases, this hierarchy may not yet be fine-grained enough. For instance, time spans (&quot;5 minutes&quot;) can be added to times (&quot;12:34&quot;), but two times are not addable. (&quot;12:34 + 8:23&quot;) As it stands, users have to use a different operator for adding time spans to times than for adding two time spans. Similar issues arise for vector space et al. This is a consciously-made tradeoff, but might be changed. This becomes most serious when dealing with quantities with units like length/distance^2, for which (*) as defined here is useless. (One way to see the issue: should   f x y = iterate (x *) y   have principal type   (Ring.C a) => a -> a -> [a]   or something like   (Ring.C a, Module a b) => a -> b -> [b]   ?) * I stuck with the Haskell 98 names. In some cases I find them lacking. Neglecting backwards compatibility, we have renamed classes as follows: Num           --> Additive, Ring, Absolute Integral      --> ToInteger, IntegralDomain, RealIntegral Fractional    --> Field Floating      --> Algebraic, Transcendental Real          --> ToRational RealFrac      --> RealRing, RealField RealFloat     --> RealTranscendental Additional standard libraries might include Enum, IEEEFloat (including the bulk of the functions in Haskell 98's RealFloat class), VectorSpace, Ratio, and Lattice. Version 0.3.0.2
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List based linear algebra, similtaneous linear equations, eigenvalues and eigenvectors, roots of polynomials, transcendent functions with arbitrary precision implemented by continued fractions, quantum operations, tensors Version 0.2