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Cookbook/Numbers

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

Contents

1 Rounding numbers

Problem Solution Examples
rounding round 
round 3.4      --> 3
round 3.5      --> 4
find the nearest integer greaterthan or equal to x ceiling 
ceiling 3.1    --> 4
find the nearest integer less than or equal to x floor 
floor 3.5      --> 3

2 Taking logarithms 

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

3 Generating random numbers 

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

4 Binary representation of numbers 

import Data.Bits
import Data.List (foldl')
 
-- Extract a range of bits, most-significant first
bitRange :: Bits a => a -> Int -> Int -> [Bool]
bitRange n lo hi = foldl' (\l -> \x -> testBit n x : l) [] [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

5 Using complex numbers

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