Hash functions take an input and produce an output within a defined range. The input is called a hash value. Figure 6-6 shows the basic format along with a classic hash function. The x mod 10 function can easily be used to ensure that, regardless of the positive integer hash value input, the result will always reside between 0 (zero) and 9. With a hash value input of 11, the output will be 1. This is commonly spoken as, "Eleven is hashed to one."

Figure 6-6. A hashing function maps the hash value input to a defined range. Part a shows the general hashing algorithm structure; part b shows a classic hashing algorithm. Regardless of the positive integer input, the output will always be between 0 and 9.

A good hash function will yield evenly dispersed outputs. For example, regardless of the hash value, any output is just as likely to occur as any other output. More specifically, if the output range is between 0 and 9, looking at actual outputs, there are just as many 0 values as 1, 2, 3 ... 9 values. Figure 6-7 shows a histogram depicting this near-perfect result.