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3.2.0 • Public • Published


A fast deterministic random helper library for Javascript.

Included distributions are


  • A fast tested internal PRNG.
  • Many distribution options - illustrated on the test page.
  • Quasi random walks and fill patterns.
  • Random mix, shuffle and 'antisorting' functions.


<script src='Fdrandom.js'></script>
double_value  =     // 0 to 0.999999999999998
signed_int_value = Fdrandom.i32()   // -2147483648 to 2147483647
unsigned_int_value = Fdrandom.ui32()// 0 to 4294967295
let apot = Fdrandom.pot(seed) //a seeded clone of Fdrandom
int_val = apot.i32()
let hpot= Fdrandom.hotpot() //an unpredicatably seeded clone
arandhex = hpot.mixof("0123456789abcdef","0x",8)

Method list

Equal Distribution Prngs

Method Speed % Notes
next 100 Standard randoms with 48bit resolution
f48 100 Alias of next (0 to 0.999999999999998)
dbl 50 Same as next/f48 with 53 bits resolution
f24 90 Safe values for Float32array (0 to 0.99999994)
i32 80 32 bit signed integer values
ui32 80 32 bit unsigned integer values
rbit 150 0 or 1
rpole 140 -1 or 1
range 90 Uniformly distributed numbers in range
irange 70 Uniformly distributed integers (inclusive)
vrange 30 Middle/end loaded numbers in range
zrange 5 Dynamically distributed numbers in range

Normal Distribution Prngs

Method Speed % Notes
gaus 20 Fast high quality gaussians
cauchy 10 Cauchy distribution
usum 25@n=4 Custom uniform sum
gnorm 30 Normal curve shaped game distribution
gcauchy 15 Cauchy curve shaped game distribution

Other Distributions

Method Speed % Notes
qskip 30 Low discrepancy floats (custom spaced)
qxskip 20 Curious discrepancy (see chart)
qhop 10 Curious discrepancy (see chart)
qtrip 10 Curious discrepancy (see chart)
fillr1 30 HQ Line staggered fill pattern
fillr2 25 HQ Square staggered fill pattern
fillr3 20 HQ Cube staggered fill pattern
ggrad 50 Linear gradient distribution
ngrad 50 Normal gradient distribution
gspill 50 Linear with drop off distribution
ghorn 50 Like normal but peaked dist.
gbands 50 Triangular approximation with bands.
gpick 50 Custom variance, sharp or smooth.
gskew 50 Smooth skewed range middle average.
gbowl 50 Bowl shaped distribution
gthorn 30 Thorn shaped distribution
gteat 30 Teat shaped distribution
gtrapez 50 Trapezoid distribution
uigless 50 Unsigned 1/4 bit density game dist.
uigmore 50 Unsigned 3/4 bit density game dist.
igmmode 50 Signed multi modal game dist.
igbrist 50 Signed bristly game dist.

Random Pick and Mix

Method Speed % Notes
mixof fast Make a mix of elements or chars length n
mixup fast Randomly mix up order of elements in an array or string
antisort medium Specialy mix up order of elements in an array.
aindex medium Return an antisorting index of array
aresult Report the minimum delta achieved by antisort


Method Speed % Notes
pot 0.005 Clone and seed Fdrandom object (pot)
hotpot 0.005 Clone Fdrandom using seeds from browser crypto
repot 5>0.5% Resets or reseeds an existing pot
getstate 5% Gets an array containing state of a pot
setstate 5% Sets state of pot with array (no reseeding)
version prints version
checkfloat checks float math is compliant for expected output


Method Notes
bulk returns an array filled with the supplied function
within runs a generator up to n times

A compact api reference is here

Speed & Quality

The percentages in the above tables are very rough as VM performance varies. Fdrandoms default method:f48 runs at about same speed as both Firefox and Chromes native Math.random in 2017.

f48 and 'dbl' have no detectable bias across over 10^16 outputs and each has at least 48 bits of resolution which are tested as passing G Marsaglias old but quite substantial diehard test suite.

Math.random on Chrome had detectable statistical bias and only 32 bits of resolution in 2016. Firefoxs Math.random was using its slow cryptographic PRNG but in 2017 is updated to a good quality PRNG faster than fdrandoms.

f48 algorithm is informed by J.Baagoe's PRNG Alea which seems to be the fastest form of high quality prng for vanilla javascript to date. f48 uses different multipliers in a slightly adjusted mechanism to output 16 more bits of resolution per number than Alea v0.8 while achieving similar speed.

Seeding Pots

Fdrandom.repot(seed) will reset or reseed a pot.
Fdrandom.pot(seed) returns a clone of Fdrandom seeded by numbers and strings in all elements of the object seed. To maximally seed the prng requires 9 or 10 completely unpredicatable 50 bit numbers or hundres of text characters. Practical seeding can be achieved by sending an array containing public user strings, or private unique ids, or a single number or nothing depending on the level of uniqueness desired.

Fdrandom.hotpot(seed) returns an unpredictable clone which includes seeds from browser crypto if available, and date and Math.random if not available.

Seeding pots with same data or setting same state produces identical random number streams. Any difference in seeds should result in very different streams.

Seeding digests all elements of any array or object up 1000 deep and strings up to 100,000 char. It could be used with repot() to effectively hash objects but is somewhat slow for that.

'Pot'ing is a relatively slow operation (about 50,000 op/s) as the Fdrandom object gets cloned for each pot. 'Repot'ing with a new seed is much faster. 'repot' without a seed resets to first potted state and is very fast. (or is a static 'hot' (indeterminable) instance for speed and convienience. Note that methods like gaus(), gskip(), zrange() and aresult() require an independant instance (pot or hotpot) for full continuity of results.


i32 returns number values equivalent to signed 32 bit integers

ui32 returns number values of unsigned int values

f48 alias next returns JS Numbers with 48 bits of precision in range 0 to 0.999999999999998

dbl returns JS Numbers with all 53 bits of their mantissa utilised (0 to 0.9999999999999999).

f24 is designed to be cast to float32 arrays sometime, this is the only reason to use it (for opengl etc). f24 has 48 bits of precision but scales short of 1 enough to not round-up when cast into float32 array. Because the float32 type only has 24 bits of practical precision, this can introduce a tiny but noticable bias to the sum of millions of output values.

Benchmarking and Testing

Diehard reports for the generators are in the directory reports

The drafts directory contains messy code and node scripts used to discover and test the generators and methods.


oneToTenFloat = p.range(1,10)    //end is not (quite) inclusive
oneToTenInteger=p.irange(1,10)   //end is inclusive
minusOneToOne_FlatDist =p.lrange(0,1,0.5) //loaded range. 
minusOneToOne_EndBias =p.lrange(0,1,0.4)  //First param sets a loading factor
twoToFive_MidBias = p.lrange(2,5,0.6) //0= High ends, 0.5=Flat, 1=High Mid
rangeInUnknownDist = p.zrange(0,1) //0to1 in a dynamicly changing distribution
random0or1 = p.rbit()   //random bit
random0or1 = p.rpole()  //random -1 or 1
gaussianNormal = p.gaus()
gaussianMath = p.gaus(stndev,mean) //default stndv=1, mean=0
uniformSum = p.usum(n)             //add n*( -0.5 > 0.5 ) randoms
uniformSum = p.usum(n,stndev,mean) //scale to stnd deviation and mean
cauchy = p.cauchy(scale,mean) //cauchy distribution tends towards excessive values 
limitedcauchy = p.within(-10,10,function(){return p.cauchy(scale,mean)},13) 
//'within' calls the callback up to 13 times, until value is in range.
//if never in range returns range(-10,10) 
normGame = gnorm()      //approx gaussian shape range -1 to 1
normGame = gnorm(2,4.5) //same shape range 2 to 4.5
cauchyGame = gcauchy(2,4.5) //cauchy shape range 2 to 4.5
oftenMid = gpick()      //sharp peak in middle, range -1 to 1
oftenMid = gpick(p,q)  //same shape over range p to q
oftenMid = gpick(p,q,s)  //s=sharpness : 0 flat, <0 sharper, >0 blunter  

See the Charts for gaming distributions


inray =["0","1","2","3","4","5","6","sha","la","la"] 
instr ="0123456789abcdef" 
//mixup(in,[out=in],[in_start=0],[in_fin=len]) //mixes inplace or add to out
p.mixup(inray,2,4) //mixes up elements 2 to 4
p.mixup(instr,2,4) //mixes up chars at 2 to 4
//return in a string mixed up chars from 2 to 4
newstr = p.mixup(instr,"",2,4) 
//mixes up chars at 2 to 4 onto end of outray
//all inray mixed onto end of outstr
//mixof (in,[out=intype],[n=1],[in_st=0],[in_fn=len])
hexstr = p.mixof(instr,"0x",8)   //like mixup but mix*of* 
decstr = p.mixof(inray,"",8,3,7) //string of 8 elements 3 to 7  
mxdarr = p.mixof(inray)          //1 element of all
mxdarr = p.mixof(instr,[],2)     //2 of instr as array
//eg. make a random uuid:
UUIDv4 = h.mixof(instr,8) +
   "-" + h.mixof(instr,4) + 
   "-4"+ h.mixof(instr,3) +
   "-" + h.mixof(instr,h.mixof("89ab",1),3) +
   "-" + h.mixof(instr,12); 
playShuffleIndex= p.aindex(medialist)    //antisorting index same length as input
playListCopied= p.antisort(medialist,[]) //a playlist shuffled by its antisort
hardShuffleIndex= p.aindex(100)          //a generic antisort-index 100 long
//bulk results in array
arrayOfFunc= p.bulk(100 ,p.irange ,1 ,6) //array of 100 dicerolls


While sorting entails moving the most similar items together into a simple incremental pattern, "antisorting" could mean the opposite - to arrange the most similar items to not be placed close to each other.

Functions antisort and aindex are designed for this:

  • antisort(inarray, ..opts) quasi-randomly shuffles arrays out of order.
  • aindex(array or length, ..opts) returns an 'antisorted index' for accessing arrays out of order.

The functions can re-arrange by elements input indices (which works on any pre-ordered arrays of the same length), or by elements numeric values such as song quality ratings, ages or sizes (which works on the particular distribution of those values). The output is quite randomly shuffled or indexed except items of similar value (or source position) are not placed next to each other. The algorithm used is basically a random shuffle followed by dithered checking and swapping values until all are separated.

File contains more notes on antisorting.

Version History

  • 3.2.0 - Improve zrange, state resetting is changed.
  • 3.1.0 - Add ngrad distribution (half bell shape)
  • 3.0.0 - Add new quasi-random and game distributions and retire some. Faster gnorm.
  • 2.8.0 - object seeding tweaked
  • 2.7.0 - added 'R' fill patterns of Martin Roberts. From Article
  • 2.6.0 - added cauchy and gcauchy functions, and 'within' helper
  • 2.5.0 - tweaked zrange to have drifting average
  • 2.4.0 - created zrange, a dynamic distribution generator
  • 2.3.2 - improved usum. Made hot() static, added hotpot()s
  • 2.3.0 - tweaked seeding slightly
  • 2.2.0 - made hot pots non static and tweaked rbit and rpole
  • 2.0.3 - improved aindex parameters
  • 2.0.1 - augmented aresult()
  • 2.0.0 - added antisorting
  • 1.4.1 - revised seeding


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