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(Complex numbers)
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! Examples
 
! Examples
 
|-
 
|-
| rounding
+
| rounding a given number
 
| [http://haskell.org/ghc/docs/latest/html/libraries/base/Prelude.html#v:round round]
 
| [http://haskell.org/ghc/docs/latest/html/libraries/base/Prelude.html#v:round round]
 
|<haskell>
 
|<haskell>
 
round 3.4 --> 3
 
round 3.4 --> 3
 
round 3.5 --> 4
 
round 3.5 --> 4
  +
round 2.5 --> 2
 
</haskell>
 
</haskell>
 
|-
 
|-
| finding the nearest integer greater than or equal to <code>x</code>
+
| finding the nearest integer greater than or equal to a given number
 
| [http://haskell.org/ghc/docs/latest/html/libraries/base/Prelude.html#v%3Aceiling ceiling]
 
| [http://haskell.org/ghc/docs/latest/html/libraries/base/Prelude.html#v%3Aceiling ceiling]
 
|<haskell>
 
|<haskell>
Line 23: Line 24:
 
</haskell>
 
</haskell>
 
|-
 
|-
| finding the nearest integer less than or equal to <code>x</code>
+
| finding the nearest integer less than or equal to a given number
 
| [http://haskell.org/ghc/docs/latest/html/libraries/base/Prelude.html#v%3Afloor floor]
 
| [http://haskell.org/ghc/docs/latest/html/libraries/base/Prelude.html#v%3Afloor floor]
 
|<haskell>
 
|<haskell>
 
floor 3.0 --> 3
 
floor 3.0 --> 3
 
floor 3.9 --> 3
 
floor 3.9 --> 3
  +
</haskell>
  +
|-
  +
| finding the nearest integer between zero and a given number
  +
| [http://haskell.org/ghc/docs/latest/html/libraries/base/Prelude.html#v%3Atruncate truncate]
  +
|<haskell>
  +
truncate 3.0 --> 3
  +
truncate 3.9 --> 3
  +
truncate (negate 3.0) --> -3
  +
truncate (negate 3.9) --> -3
 
</haskell>
 
</haskell>
 
|}
 
|}
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<haskell>
 
<haskell>
 
import Data.Bits
 
import Data.Bits
import Data.List (foldl')
 
   
 
-- Extract a range of bits, most-significant first
 
-- Extract a range of bits, most-significant first
 
bitRange :: Bits a => a -> Int -> Int -> [Bool]
 
bitRange :: Bits a => a -> Int -> Int -> [Bool]
bitRange n lo hi = foldl' (\l -> \x -> testBit n x : l) [] [lo..hi]
+
bitRange n lo hi = reverse . map (testBit n) [lo..hi]
   
 
-- Extract all bits, most-significant first
 
-- Extract all bits, most-significant first
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| [http://haskell.org/ghc/docs/latest/html/libraries/base/Data-Complex.html#v%3A%3A%2B (:+)]
 
| [http://haskell.org/ghc/docs/latest/html/libraries/base/Data-Complex.html#v%3A%3A%2B (:+)]
 
|<haskell>
 
|<haskell>
import Complex
+
import Data.Complex
 
1.0 :+ 0.0 --> 1.0 :+ 0.0
 
1.0 :+ 0.0 --> 1.0 :+ 0.0
 
</haskell>
 
</haskell>
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| [http://haskell.org/ghc/docs/latest/html/libraries/base/Data-Complex.html#v%3AmkPolar mkPolar]
 
| [http://haskell.org/ghc/docs/latest/html/libraries/base/Data-Complex.html#v%3AmkPolar mkPolar]
 
|<haskell>
 
|<haskell>
import Complex
+
import Data.Complex
 
mkPolar 1.0 pi --> (-1.0) :+ 1.2246063538223773e-16
 
mkPolar 1.0 pi --> (-1.0) :+ 1.2246063538223773e-16
  +
</haskell>
  +
|-
  +
| adding complex numbers
  +
|
  +
|<haskell>
  +
import Data.Complex
  +
(1 :+ 1) + (2 :+ 2) --> 3.0 :+ 3.0
 
</haskell>
 
</haskell>
 
|}
 
|}

Latest revision as of 10:14, 13 December 2009

Numbers in Haskell can be of the type
Int, Integer, Float, Double, or Rational
.

Contents

[edit] 1 Rounding numbers

Problem Solution Examples
rounding a given number round
round 3.4      --> 3
round 3.5      --> 4
round 2.5      --> 2
finding the nearest integer greater than or equal to a given number ceiling
ceiling 3.0    --> 3
ceiling 3.1    --> 4
finding the nearest integer less than or equal to a given number floor
floor 3.0      --> 3
floor 3.9      --> 3
finding the nearest integer between zero and a given number truncate
truncate 3.0           -->  3
truncate 3.9           -->  3
truncate (negate 3.0)  --> -3
truncate (negate 3.9)  --> -3

[edit] 2 Taking logarithms

log 2.718281828459045  --> 1.0
logBase 10 10000       --> 4.0

[edit] 3 Generating random numbers

import System.Random
 
main = do
  gen <- getStdGen
  let ns = randoms gen :: [Int]
  print $ take 10 ns

[edit] 4 Binary representation of numbers

import Data.Bits
 
-- Extract a range of bits, most-significant first
bitRange :: Bits a => a -> Int -> Int -> [Bool]
bitRange n lo hi = reverse . map (testBit n) [lo..hi]
 
-- Extract all bits, most-significant first
bits :: Bits a => a -> [Bool]
bits n = bitRange n 0 (bitSize n - 1)
 
-- Display a number in binary, including leading zeroes.
-- c.f. Numeric.showHex
showBits :: Bits a => a -> ShowS
showBits = showString . map (\b -> if b then '1' else '0') . bits

[edit] 5 Using complex numbers

Problem Solution Examples
creating a complex number from real and imaginary rectangular components (:+)
import Data.Complex
1.0 :+ 0.0        --> 1.0 :+ 0.0
creating a complex number from polar components mkPolar
import Data.Complex
mkPolar 1.0 pi    --> (-1.0) :+ 1.2246063538223773e-16
adding complex numbers
import Data.Complex
(1 :+ 1) + (2 :+ 2) --> 3.0 :+ 3.0