Cookbook/Numbers

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

Rounding numbers

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

Taking logarithms

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

Generating random numbers

import System.Random

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

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

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