# 3.14. NumExts

The NumExts interface collect together various numeric operations that have proven to be commonly useful

 ``` -- Going between Doubles and Floats: doubleToFloat :: Double -> Float floatToDouble :: Float -> Double showHex :: Integral a => a -> ShowS showOct :: Integral a => a -> ShowS showBin :: Integral a => a -> ShowS showIntAtBase :: Integral a => a -- base -> (a -> Char) -- digit to char -> a -- number to show. -> ShowS showListWith :: (a -> ShowS) -> [a] -> ShowS ```

Notes:

• If doubleToFloat is applied to a Double that is within the representable range for Float, the result may be the next higher or lower representable Float value. If the Double is out of range, the result is undefined.

• No loss of precision occurs in the other direction with floatToDouble, the floating value remains unchanged.

• showOct, showHex and showBin will prefix 0o, 0x and 0b, respectively. Like Numeric.showInt, these show functions work on positive numbers only.

• showIntAtBase is the more general function for converting a number at some base into a series of characters. The above show* functions use it, for instance, here's how showHex could be defined  ```showHex :: Integral a => a -> ShowS showHex n r = showString "0x" \$ showIntAtBase 16 (toChrHex) n r where toChrHex d | d < 10 = chr (ord '0' + fromIntegral d) | otherwise = chr (ord 'a' + fromIntegral (d - 10))```

• showListWith is strictly speaking not a 'NumExts' kind of function, but it's sometimes useful in conjunction with the other show* functions that NumExts exports. It is the non-overloaded version of showList, allowing you to supply the shows function to use per list element. For instance,  `putStrLn (NumExts.showListWith NumExts.showHex [0..16])`
will print out the elements of [1..16] in hexadecimal form.