Updated SC2039 (markdown)

SC2039.md

@@ -57,6 +57,60 @@ POSIX:
 while [ $((test)) -ne 0 ]; do foo; : $((next)); done
 ```
 
+### Arithmetic exponentiation
+
+Bash:
+
+```Bash
+printf "%s\n" "$(( 2**63 ))"
+```
+
+POSIX:
+
+The POSIX standard does not allow for exponents.  However, you can replicate them completely built-in using a POSIX compatible function.  As an example, the `pow` function from [here](http://unix.stackexchange.com/a/7925).
+
+```sh
+pow () {
+    set $1 $2 1
+    while [ $2 -gt 0 ]; do
+      set $1 $(($2-1)) $(($1*$3))
+    done
+    echo $3
+}
+```
+
+To compare:
+
+```sh
+$ echo "$(( 2**62 ))"
+4611686018427387904
+$ pow 2 62
+4611686018427387904
+```
+
+Alternatively, if you don't mind using an external program, you can use `bc`.  Be aware though: `bash` and other programs may abide by a certain maximum integer that `bc` does not (for `bash` that's: 64-bit signed long int, failing back to 32-bit signed long int).  
+
+Example:
+
+```Bash
+# Note the overflow that gives a negative number
+$ echo "$(( 2**63 ))"
+-9223372036854775808
+
+# No such problem
+$ echo 2^63 | bc
+9223372036854775808
+
+# 'bc' just keeps on going
+$ echo 2^1280 | bc
+20815864389328798163850480654728171077230524494533409610638224700807\
+21611934672059602447888346464836968484322790856201558276713249664692\
+98162798132113546415258482590187784406915463666993231671009459188410\
+95379622423387354295096957733925002768876520583464697770622321657076\
+83317005651120933244966378183760369413644440628104205339687097746591\
+6057756101739472373801429441421111406337458176
+```
+
 ### standalone `((..))`
 
 Bash: