Editing Hash function (section)

=== Radix conversion hashing ===
Analogous to the way an ASCII or [[EBCDIC]] character string representing a decimal number is converted to a numeric quantity for computing, a variable-length string can be converted as {{math|''x''<sub>''k''&minus;1</sub>a<sup>''k''−1</sup> + ''x''<sub>''k''&minus;2</sub>a<sup>''k''−2</sup> + &ctdot; + ''x''<sub>1</sub>''a'' + ''x''<sub>0</sub>}}. This is simply a polynomial in a [[radix]] {{math|1=''a''&nbsp;&gt;&nbsp;1}} that takes the components {{math|(''x''<sub>0</sub>,''x''<sub>1</sub>,...,''x''<sub>''k''−1</sub>)}} as the characters of the input string of length {{math|''k''}}. It can be used directly as the hash code, or a hash function applied to it to map the potentially large value to the hash table size. The value of {{math|''a''}} is usually a prime number large enough to hold the number of different characters in the character set of potential keys. Radix conversion hashing of strings minimizes the number of collisions.<ref>{{cite conference |last1=Ramakrishna |first1=M. V. |last2=Zobel |first2=Justin |date=1997 |url=https://citeseer.ist.psu.edu/viewdoc/download?doi=10.1.1.18.7520&rep=rep1&type=pdf |title=Performance in Practice of String Hashing Functions |book-title=Database Systems for Advanced Applications '97 |conference=DASFAA 1997 |pages=215–224 |citeseerx=10.1.1.18.7520 |doi=10.1142/9789812819536_0023 |isbn=981-02-3107-5 |s2cid=8250194 |access-date=2021-12-06}}</ref> Available data sizes may restrict the maximum length of string that can be hashed with this method.  For example, a 128-bit word will hash only a 26-character alphabetic string (ignoring case) with a radix of 29; a printable ASCII string is limited to 9 characters using radix 97 and a 64-bit word.  However, alphabetic keys are usually of modest length, because keys must be stored in the hash table. Numeric character strings are usually not a problem; 64 bits can count up to {{math|10<sup>19</sup>}}, or 19 decimal digits with radix 10.