This is not a programming forum, but still, remember that. That works for points in positive plane. Initialize the hash function with a vector ¯ = (, …, −) of random odd integers on bits each. So that no collisions can occur. The following hash family is universal:  h a ¯ ( x ¯ ) = ( ( ∑ i = 0 ⌈ k / 2 ⌉ ( x 2 i + a 2 i ) ⋅ ( x 2 i + 1 + a 2 i + 1 ) ) mod 2 2 w ) d i v 2 2 w − M {\displaystyle h_{\bar {a}}({\bar {x}})=\left({\Big (}\sum _{i=0}^{\lceil k/2\rceil }(x_{2i}+a_{2i})\cdot (x_{2i+1}+a_{2i+1}){\Big )}{\bmod {~}}2^{2w}\right)\,\,\mathrm {div} \,\,2^{2w-M}} . FindInstance won't compute this simple expression, Writing thesis that rebuts advisor's theory. A hash function that maps names to integers from 0 to 15. What happens when all players land on licorice in Candy Land? So hash(x, y) has 2^64 (about 16 million trillion) possible results. What is a minimal hash function for a pair of ints that has low chance of collisions? Ih((x;y)) = (5 x +7 y) mod N is a hash function for pairs of integers h(x) = x mod 5 key element 0 1 6 tea 2 coffee 3 4 14 chocolate Ahash tableconsists of: Ihash function h. Ian array (called table) of size N The idea is to store item (k;e) at … Thanks, this hash has the advantage that it works much better in practice than (y<<16)^x. Here's why: suppose there is a function hash() so that hash(x, y) gives different integer values. A hash function that provides keys with a very low probability of collision. To do that I needed a custom hash function. A hash functionis any functionthat can be used to map dataof arbitrary size to fixed-size values. If we have an array that can hold M key-value pairs, then we need a function that can transform any given key into an index into that array: an integer in the range [0, M-1]. If a disembodied mind/soul can think, what does the brain do? My answer is faster to execute, but I tip my hat to your excellent answer! How to calculate Pool reward for Race of Work? Hash Functions. Power of two sized tables are often used in practice (for instance in Java). I can write the code, if you don't know how. The advantage is that when $x,y= 0). No idea about how many collisions this causes for larger integers, though. I had a program which used many lists of integers and I needed to track them in a hash table. How can I write a bigoted narrator while making it clear he is wrong? Note. The Canvas (point space) can be huge, bordering on the limits Under reasonable assumptions, the average time required to search for an element in a hash table is O(1). If you want to hash two uint32's into one uint32, do not use things like Y & 0xFFFF because that discards half of the bits. That is, if$\max(x,y)\lt2^n$, then$\mathrm{key}(x,y)\lt2^{2n}$. That way you get a random-looking result rather than high bits from one dimension and low bits from the other. The resulting Geohash value is a 63 bit number. is true for (3^k - 2^k) / 4^k pairs, ie. Use MathJax to format equations. Anyway, you get the idea -- stuff two 2-byte unsigned integers into a 4-byte word. Why are some Old English suffixes marked with a preceding asterisk? But for a real world int32 hash, rather than a mapping of pairs of integers to integers, you're probably better off with a bit manipulation such as Bob Jenkin's mix and calling that with x,y and a salt. So, each of$x$and$y$can occupy 15 bits. Why should hash functions use a prime number modulus? To learn more, see our tips on writing great answers. You can then use 16 bits for$x$, and 16 bits for$y$. Why are those hash functions considered a bad choice? So it makes your answer being 2^8*x+y : is this the better solution ? If you use an unsigned integer variable (which is available in most programming languages), then you'll have 32 bits available. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Inertial and non-inertial frames in classical mechanics. Also, for reference, see @JonSkeet's answer to similar: Hi a hash function to my knowledge only has to provide a surjective mapping from a larger space to a smaller (hash) space. Deterministic, you will always get the same hash for a specific input. so things like. The hash value of an array of positive integers will always be between 0 and$2n$where$n$is the largest value in the array. I will have to be more careful. Can one build a "mechanical" universal Turing machine? It sounds like you are using a 32-bit integer variable in some programming language to represent the key. Understanding the zero current in a simple circuit. might be interesting, as it's closest to your original canvaswidth * y + x but will work for any x or y. (in my example, k) which should be small (ie. By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. I hope this is ok, since all answers still make most sense with the updated assumptions, a hash function that is GUARANTEED collision-free is not a hash function :). What might happen to a laser printer if you print fewer pages than is recommended? Compromise: So hash(x, y) has 2^64 (about 16 million trillion) possible results. How to create the smallest possible unique number from one or many unordered numbers? This measure prevents collisions occuring for hash codes that do not differ in lower bits. Like Emil, but handles 16-bit overflows in x in a way that produces fewer collisions, and takes fewer instructions to compute: You want a mapping (x, y) -> i where x, y, and i are all 32-bit quantities, which is guaranteed not to generate duplicate values of i. Y + x but will work for any x or y open source Geo computes! 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