I've long liked Bob Jenkins' hash function for its speed and distribution properties. AFAICT, jsf32 is based on the same design theory, and should fit into your constraints (I think -- I'm not a WebGL person):http://www.pcg-random.org/posts/bob-jenkins-small-prng-passes-practrand.html …
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Is xorshift32 appropriate? Might be worth a look
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Maybe the one under 32-bit Generators onhttps://web.archive.org/web/20190712003931/http://xoshiro.di.unimi.it/ ? Otherwise you may look at counter-based random number generators
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since you have 16x16->32 multiplies you can emulate 32x32->64 with them and so do even 64x64->64 but maybe you don't really need it to be that good (and slow :P)
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