Folding Function

A folding function is a function that maps the integers onto the nonnegative integers . This type of function arises naturally in situations where it is desirable to remove the sign of an integer (for example, to show that , or when encoding signed integers using a technique that works only for nonnegative integers (for example, in data compression).

The usual function folding function is given by

(1)

with inverse

(2)

0		1		2		3		4		5		6		7
0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15

computes the mapping shown above.

Another variant may be defined by

(3)

with inverse

(4)

0	1		2		3		4		5		6		7		8
0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15

computes the mapping shown above.