# Cookbook/Numbers

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

## 1 Rounding numbers

Problem Solution Examples
rounding round
```round 3.4      --> 3
round 3.5      --> 4```
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```

## 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 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```