Fdrandom.js

A fast deterministic random helper library for Javascript.

Included distributions are

Features

• 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.

Usage

<script src='Fdrandom.js'></script>

double_value  = Fdrandom.next()     // 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

Instantiation

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

Helpers

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.

Fdrandom.hot() (or anypot.hot()) 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.

Precision/Types

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.

Examples

p=Fdrandom.pot()

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

Mixup/Pick:

inray =["0","1","2","3","4","5","6","sha","la","la"] 
instr ="0123456789abcdef" 
outray=[1,2,3]
outstr=""

//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
p.mixup(instr,outray,2,4) 

//all inray mixed onto end of outstr
p.mixup(inray,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:
h=p.hot()
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); 

//antisorting
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
...  

Antisorting

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 antisort.md 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