In a previous post about Integer numbers we have seen that Clojure for efficiency reasons tries to map the numbers to their Java basic types and that with the literals modifiers “N” for integers and “M” for decimals you can use BigIntegers and BigDecimals in place of the Long and Double.

Clojure in addition to the basic arithmetic operators (+, -, *) who leverage the speed of the Java platform basic types, it offers a series of operators that instead of throwing and exception when the type limit are crossed, it automatically promote the type to the higher capable counterpart. Those operators are +’, -‘ and *’ (like normal operators followed by a single quote. Lets see them in action.

For example:

;; this is bigger than java.lang.Long can represent
(+ 1 java.lang.Long/MAX_VALUE)
; ArithmeticException integer overflow  clojure.lang.Numbers.throwIntOverflow (Numbers.java:1388)

;; but with the auto-promotion operators you can write this as:
(+' 1 java.lang.Long/MAX_VALUE)
;=> 9223372036854775808N

(-' java.lang.Long/MAX_VALUE -1)
;=> 9223372036854775808N

(*' 2 java.lang.Long/MAX_VALUE)
;=> 18446744073709551614N

;; it preserves the basic type when possible
(type (+ 1 1))
;=> java.lang.Long
(type (+' 1 1))
;=> java.lang.Long

So if you expect that your operations might go beyond the Java’s Long limits, use the auto-promotion operator and avoid the arithmetics overflow.

Let’s calculate the factorial:

;;                  v--- auto promotion
(defn ! [x] (reduce *' (range 1 (inc x))))

(! 5)
;=> 120

(! 5000)
;=> 422857792660554352220106420023358440539078667 .... N
;=> (VERY BIG NUMBER)