glsl hash testing

hash.md

just gathering the comments from https://www.shadertoy.com/view/WttXWX in a place I can actually find, which also has more markdown :)

OK, results are in: as 32 bit RNGs, the 3-round Wellons function here is marked as weak in just 2 tests, with no failures. The 2-round Wellons function has 4 weaks and 1 failure, the murmurhash derivative only slightly worse with 5 weaks and 1 failure. Jenkins and Wang have many failures (Wang fails almost everything) so aren't really in the running.

http://webhome.phy.duke.edu/~rgb/General/dieharder.php http://simul.iro.umontreal.ca/testu01/guideshorttestu01.pdf p 88-157 https://github.com/umontreal-simul/latticetester

Individual tests (just the negative results from the 50 or so tests):

// --- choose one:
//#define hashi(x)   lowbias32(x)
  #define hashi(x)   triple32(x) 

  #define hash(x)  ( float( hashi(x) ) / float( 0xffffffffU ) )

//bias: 0.17353355999581582 ( very probably the best of its kind )
uint lowbias32(uint x)
{
    x ^= x >> 16;
    x *= 0x7feb352dU;
    x ^= x >> 15;
    x *= 0x846ca68bU;
    x ^= x >> 16;
    return x;
}

// bias: 0.020888578919738908 = minimal theoretic limit
uint triple32(uint x)
{
    x ^= x >> 17;
    x *= 0xed5ad4bbU;
    x ^= x >> 11;
    x *= 0xac4c1b51U;
    x ^= x >> 15;
    x *= 0x31848babU;
    x ^= x >> 14;
    return x;
}

wellons2 (lowbias32)

TEST					RESULT
diehard_opso	0	2097152	100	0.00000001	FAILED
sts_serial	15	100000	100	0.99636479	WEAK
rgb_minimum_distance	4	10000	1000	0.99754988	WEAK
rgb_permutations	3	100000	100	0.99946899	WEAK
rgb_lagged_sum	5	1000000	100	0.99575897	WEAK

wellons3 (triple32)

TEST					RESULT
diehard_parking_lot	0	12000	100	0.99650356	WEAK
rgb_minimum_distance	5	10000	1000	0.00125775	WEAK

murmur

TEST					RESULT
diehard_craps	0	200000	100	0.00012089	WEAK
marsaglia_tsang_gcd	0	10000000	100	0.00000000	FAILED
sts_serial	6	100000	100	0.99932034	WEAK
rgb_bitdist	5	100000	100	0.99933401	WEAK
rgb_permutations	5	100000	100	0.99646826	WEAK
rgb_lagged_sum	18	1000000	100	0.99788947	WEAK

glsl-sine hash

Using the sine hash from https://www.shadertoy.com/view/ltyBWm (which visually looks fine) and using to generate 16-bit random numbers, C++ code:

float sinhash(uint x, uint y) {
  float seed = 71.33*x+852.381*y;
  return fmod(fabs(38351.43*sin(14.13*seed)),1.0);
}

uint sinhash(uint n) {
  float x = sinhash(n >> 16, n & 0xffff);
  return uint(x*0x10000);
}

Result is not awful, but not great:

TEST					RESULT
diehard_operm5	0	1000000	100	0.00000000	FAILED
diehard_squeeze	0	100000	100	0.00000000	FAILED
diehard_runs	0	100000	100	0.99996083	WEAK
marsaglia_tsang_gcd	0	10000000	100	0.00000000	FAILED
marsaglia_tsang_gcd	0	10000000	100	0.00000000	FAILED
sts_runs	2	100000	100	0.00000004	FAILED
sts_serial	3	100000	100	0.00021384	WEAK
sts_serial	13	100000	100	0.00145147	WEAK
rgb_bitdist	4	100000	100	0.00050052	WEAK
rgb_bitdist	8	100000	100	0.00000000	FAILED
rgb_lagged_sum	0	1000000	100	0.00000000	FAILED
rgb_lagged_sum	1	1000000	100	0.00000000	FAILED
rgb_lagged_sum	2	1000000	100	0.00000000	FAILED
rgb_lagged_sum	3	1000000	100	0.00000000	FAILED
rgb_lagged_sum	4	1000000	100	0.00000000	FAILED
rgb_lagged_sum	5	1000000	100	0.00000000	FAILED
rgb_lagged_sum	6	1000000	100	0.00000000	FAILED
					<more failures>

Very similar results from the "official" sine hash:

float hash(vec2 p)
{
    return fract(sin(dot(p, vec2(12.9898, 78.233))) * 43758.5453);
}

TEST					RESULT
diehard_operm5	0	1000000	100	0.00000000	FAILED
diehard_dna	0	2097152	100	0.00144687	WEAK
diehard_squeeze	0	100000	100	0.00000012	FAILED
diehard_runs	0	100000	100	0.00000000	FAILED
diehard_runs	0	100000	100	0.00000029	FAILED
diehard_craps	0	200000	100	0.00000003	FAILED
sts_serial	1	100000	100	0.00273519	WEAK
sts_serial	9	100000	100	0.99532417	WEAK
sts_serial	10	100000	100	0.99710812	WEAK
rgb_permutations	3	100000	100	0.00008555	WEAK
rgb_permutations	4	100000	100	0.00175526	WEAK
rgb_lagged_sum	0	1000000	100	0.00000000	FAILED
rgb_lagged_sum	1	1000000	100	0.00000008	FAILED
rgb_lagged_sum	2	1000000	100	0.00000000	FAILED
rgb_lagged_sum	3	1000000	100	0.00000000	FAILED
rgb_lagged_sum	4	1000000	100	0.00000000	FAILED
rgb_lagged_sum	5	1000000	100	0.00000000	FAILED
					<more failures>

LCG

OK, some more results for a 32-bit linear congruential generator, this one is from Numerical Recipes:

uint lcg(uint) {
  static uint value = 1;
  value *= 1664525U;
  value += 1013904223U;
  return value;
}

TEST					RESULT
diehard_rank_6x8	0	100000	100	0.00000000	FAILED
diehard_bitstream	0	2097152	100	0.00000000	FAILED
diehard_opso	0	2097152	100	0.00000000	FAILED
diehard_oqso	0	2097152	100	0.00000000	FAILED
diehard_dna	0	2097152	100	0.00000000	FAILED
diehard_count_1s_str	0	256000	100	0.00000000	FAILED
diehard_count_1s_byt	0	256000	100	0.00000000	FAILED
diehard_parking_lot	0	12000	100	0.99983528	WEAK
marsaglia_tsang_gcd	0	10000000	100	0.00000000	FAILED
marsaglia_tsang_gcd	0	10000000	100	0.00000000	FAILED
sts_serial	2	100000	100	0.00001211	WEAK
sts_serial	3	100000	100	0.00000001	FAILED
sts_serial	3	100000	100	0.00001378	WEAK
sts_serial	4	100000	100	0.00000000	FAILED
sts_serial	4	100000	100	0.00000492	WEAK
sts_serial	5	100000	100	0.00000000	FAILED
					<more sts_serial failures>
rgb_bitdist	1	100000	100	0.00000000	FAILED
rgb_bitdist	2	100000	100	0.00000000	FAILED
					<more rgb_bitdist failures>
rgb_minimum_distance	2	10000	1000	0.00000000	FAILED
rgb_minimum_distance	3	10000	1000	0.00292069	WEAK
rgb_minimum_distance	4	10000	1000	0.00000000	FAILED
rgb_minimum_distance	5	10000	1000	0.00000004	FAILED
rgb_lagged_sum	11	1000000	100	0.99708426	WEAK
rgb_lagged_sum	13	1000000	100	0.99998108	WEAK
rgb_lagged_sum	22	1000000	100	0.99964562	WEAK
dab_bytedistrib	0	51200000	1	1.00000000	FAILED
dab_dct	256	50000	1	0.00000000	FAILED
dab_filltree2	0	5000000	1	0.00000000	FAILED
dab_filltree2	1	5000000	1	0.00000000	FAILED
dab_monobit2	12	65000000	1	1.00000000	FAILED