peteroupc.github.io/autodist.html at master · peteroupc/peteroupc.github.io · GitHub

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<head>
<title>Code Generator for Discrete Distributions</title>
<meta charset=utf-8>
</head>
<h2>Code Generator for Discrete Distributions</h2>
<p>This page generates standalone programming code that samples from a discrete distribution, or instructions to choose a random number by flipping a real coin or rolling a real die.  That is, the code or instructions are designed to choose an integer in [0, n) at random where each of the n integers has a separate probability of occurring.  The idea for a code generator like this came from Leydold et al. (2001).  The generator supports generating JavaScript code, Ruby code, or coin-flipping instructions.</p>

<p>The code generator is powered by the recently presented Fast Loaded Dice Roller (Saad et al. 2020) and by the Fast Dice Roller (Lumbroso 2013).  The code generator is also powered by JavaScript, at least the kind supported by modern Web browsers.  Accordingly, the generator requires JavaScript (active scripting) to be enabled in the browser settings.</p>
<form action='javascript:void(null)'>
<p>In the text box below, enter one of the following:
<ul>
<li>A comma-separated list of integer weights.  Each weight must be 0 or greater.  Spaces can appear at the beginning and end of the value as well as around the commas.  In the following example <code>10, 30, 40</code>, 0 is chosen with probability (10/(10+30+40)) and 1 is chosen with probability (30/(10+30+40)).
<li>A dice specification of the following form: [XX]dYY[+ZZ], where XX is the number of dice, YY is the number of faces per die, and ZZ is a number to add to the final die roll.  Examples: d20, d6, 2d10, 4d8+25.  Up to 99 dice and 100 faces per die are supported.  Note, however, that with high numbers of faces and dice, the code generation may take so long to build that the browser may time out.
</ul>
<br><input type=text id=probabilities /><br>
Name of generator: <input type=text id=genname value="discrete_gen"/><br>
Language of generated code: <select id=genlang>
<option value='javascript'>JavaScript</option>
<option value='ruby'>Ruby</option>
<option value='coinflip'>Coin Flipping (start at 0)</option>
<option value='coinflip1'>Coin Flipping (start at 1)</option>
<option value='dieroll'>Die Rolling (start at 0)</option>
<option value='dieroll1'>Die Rolling (start at 1)</option>
</select>
<div style='color: red' id=error>&nbsp;</div>
<div>The generated code will appear below.  No rights are claimed to the code generated by this page (it can be used and distributed freely).</div>
<textarea rows=30 cols=40 id=code></textarea>
</form>
<p>This is an <a href="https://github.com/peteroupc/peteroupc.github.io/blob/master/autodist.html">open-source generator</a> written by Peter Occil.  Any copyright to this page is released to the Public Domain.  In case this is not possible, this page is also licensed under <a href="https://creativecommons.org/publicdomain/zero/1.0/">Creative Commons Zero</a>.  If you have comments or issues on this generator, send them to the <a href="https://github.com/peteroupc/peteroupc.github.io/issues">GitHub issues page</a>.</p>

<h3>About the Coin-Flipping and Die-Rolling Instructions</h3>

<p>This generator supports generating instructions that choose a nonuniform random number by flipping a real coin or rolling a real six-sided die.</p>
<ul>
<li>The coin-flipping instructions were generated by running the Fast Loaded Dice Roller on fixed sequences of coin flip results (such as H/T/T/H/H).  For dice specifications, the coin-flipping instructions were generated similarly to the die-rolling instructions instead, because it's considerably faster than checking all sequences with the Fast Loaded Dice Roller.
<li>The die-rolling instructions implement a variant of the "greedy simulation" process described in B. Kloeckner, "<a href="https://perso.math.u-pem.fr/kloeckner.benoit/papiers/DiceSimulation.pdf">Simulating a dice with a dice</a>", 2008, except it supports any nonuniform discrete distribution (within reason), that is, the output die can be a loaded die, not just a fair one.  The die-rolling instructions allow a nonuniform random number to be chosen by rolling a real (fair) six-sided die.</li>
</ul>

<h3>References</h3>

<p>Saad, F.A., Freer C.E., et al. "The Fast Loaded Dice Roller: A Near-Optimal Exact Sampler for Discrete Probability Distributions", in _AISTATS 2020_ 108.</p>
<p>Leydold, et al., "An Automatic Code Generator for Nonuniform Random Variate Generation", 2001.</p>
<p>Lumbroso, J., "<a href='https://arxiv.org/abs/1304.1916'>Optimal Discrete Uniform Generation from Coin Flips, and Applications</a>", arXiv:1304.1916 [cs.DS]</p>
<script>
function times(n) {
  let x=[]
  for(let i=0;i<n;i++){
    x.push(i)
  }
  return x
}
function min(a) {
  let x=a[0]
  for(let i=1;i<a.length;i++){
    x=Math.min(x, a[i])
  }
  return x
}
function maxval(a) {
  let x=a[0]
  for(let i=1;i<a.length;i++){
    x=Math.max(x, a[i])
  }
  return x
}
function sum(a) {
  let x=0
  for(let i=0;i<a.length;i++){
    x+=a[i]
  }
  return x
}
function zeros(n) {
  let x=[]
  for(let i=0;i<n;i++){
    x.push(0)
  }
  return x
}

function fdrruby(name, v) {
   name=name||"discrete_gen"
   ret="def "+name+"()\n"
        if (v==1) {
           ret += "return 0\n"
        } else if(v==2) {
           // Special case of 2 items with equal probability
           ret += "  return rand(2)\n"
        } else {
        ret += "  x = 1\n"
        ret += "  y = 0\n"
        ret += "  while true\n"
        ret += "    x = (x << 1)\n"
        ret += "    y = rand(2) + (y << 1)\n"
        ret += "    if x > "+(v-1)+"\n"
        ret += "      return y if y <= "+(v-1)+"\n"
        ret += "      x -= "+(v)+"\n"
        ret += "      y -= "+(v)+"\n"
        ret += "    end\n"
        ret += "  end\n"
        }
        ret+="end\n"
       return ret
}

function fdr(name, v) {
   name=name||"discrete_gen"
   ret="function "+name+"() {\n"
        if (v==1) {
           ret += "return 0\n"
        } else if(v==2) {
           // Special case of 2 items with equal probability
           ret += "  return Math.random() < 0.5 ? 0 : 1;\n"
        } else {
        ret += "  let x = 1;\n"
        ret += "  let y = 0;\n"
        ret += "  while (true) {\n"
        ret += "    x = (x * 2);\n"
        ret += "    y = (Math.random() < 0.5 ? 0 : 1) + (y * 2);\n"
        ret += "    if (x > "+(v-1)+") {\n"
        ret += "      if (y <= "+(v-1)+") { return y; }\n"
        ret += "      x -= "+(v)+";\n"
        ret += "      y -= "+(v)+";\n"
        ret += "    }\n"
        ret += "  }\n"
        }
        ret+="}\n"
       return ret
}

function codegenruby(fldr,name,offset) {
   name=name||"discrete_gen"
   ret="def "+name+"()\n"
        if (fldr[0]==null) {
           ret += "return " + (fldr[2]+(offset||0)) + "\n"
        } else if(fldr[0][0].length==1) {
           // Special case of 2 items with equal probability
           ret += "  return rand(2) == 0 ? " +(fldr[0][1][0]-1+(offset||0)) +" : " +
              (fldr[0][2][0]-1+(offset||0))+"\n"
        } else {
        ret += "  table = ["
        for (let i=0;i<fldr[0].length;i++){
            if(i > 0) {
                ret += ", "
            }
            ret += "["+fldr[0][i]+"]"
        }
        ret += "]\n\n"
        ret += "  x = 0\n"
        ret += "  y = 0\n"
        ret += "  while true\n"
        ret += "    x = rand(2) + (x * 2)\n"
        ret += "    leaves = table[0][y]\n"
        ret += "    if x < leaves\n"
        if (fldr[2]<fldr[1]) {
          // No rejection leaf
          if (offset && offset!=0) {
            ret += "        return (table[x + 1][y] - 1) + " + (offset||0) + "\n"
            } else {
            ret += "        return table[x + 1][y] - 1\n"
            }
        } else {
          ret += "        label = table[x + 1][y]\n"
          ret += "        if label <= "+fldr[1]+"\n"
          if (offset && offset!=0) {
             ret += "            return (label - 1) + " + (offset||0) + "\n"
          } else {
             ret += "            return label - 1\n"
          }
          ret += "        end\n"
          ret += "        x = 0\n"
          ret += "        y = 0\n"
        }
        ret += "    else\n"
        ret += "        x -= leaves\n"
        ret += "        y += 1\n"
        ret += "    end\n"
        ret += "  end\n"
        }
        ret+="end\n"
       return ret
}

function codegen(fldr,name,offset) {
   name=name||"discrete_gen"
   ret="var "+name+" = (function() {\n"
        if (fldr[0]==null) {
           ret += "return function(){\n"
           ret += "  return " + (fldr[2]+(offset||0)) + "\n"
        } else if(fldr[0][0].length==1) {
           // Special case of 2 items with equal probability
           ret += "return function(){\n"
           ret += "  return Math.random() < 0.5 ? " +((fldr[0][1][0]-1)+(offset||0)) +" : " +
              ((fldr[0][2][0]-1)+(offset||0))+"\n"
        } else {
        ret += "var table = ["
        for (let i=0;i<fldr[0].length;i++){
            if(i > 0) {
                ret += ", "
            }
            ret += "["+fldr[0][i]+"]"
        }
        ret += "]\n\n"
        ret += "return function(){\n"
        ret += "  let x = 0\n"
        ret += "  let y = 0\n"
        ret += "  while (true) {\n"
        ret += "    x = (Math.random() < 0.5 ? 0 : 1) + (x * 2)\n"
        ret += "    let leaves = table[0][y]\n"
        ret += "    if(x < leaves){\n"
        if (fldr[2]<fldr[1]) {
          // No rejection leaf
          if (offset && offset!=0) {
              ret += "        return (table[x + 1][y] - 1) + " + (offset||0) + "\n"
          } else {
              ret += "        return table[x + 1][y] - 1\n"
          }
        } else {
          ret += "        let label = table[x + 1][y]\n"
          ret += "        if (label <= "+fldr[1]+") {\n"
          if (offset && offset!=0) {
             ret += "            return (label - 1) + " + (offset||0) + "\n"
          } else {
             ret += "            return label - 1\n"
          }
          ret += "        }\n"
          ret += "        x = 0\n"
          ret += "        y = 0\n"
        }
        ret += "    } else {\n"
        ret += "        x -= leaves\n"
        ret += "        y += 1\n"
        ret += "}}\n"
        }
        ret+="}})();\n"
       return ret
}

function fldrResult(table,coinresult,max){
  let i=0
  let x=0
  let y=0
  let numcoins=0
  while(true){
     x=(coinresult&1)+x*2
     coinresult>>=1
     numcoins+=1
     let leaves=table[0][y]
     if(x<leaves){
        let label=table[x+1][y]
        if(label<=max)
           return [label-1,numcoins]
        // Rejected
        return null
     } else {
        x-=leaves
        y+=1
     }
  }
}

function headstails(coinresult,coins,truecoins){
  let ret=[]
  for(var i=0;i<coins;i+=1){
    if (i<truecoins)
      ret.push((coinresult&1)==1 ? "H" : "T")
    else
      ret.push("X")
    coinresult>>=1
  }
  return ret.join("/")
}

function dieroll(dice,truecoins){
  let ret=[]
  for(var i=0;i<truecoins;i+=1){
    if (i<dice.length)
      ret.push((Number(dice[i])+1)+"")
    else
      ret.push("X")
  }
  return ret.join("/")
}

function cointoss(dice,truecoins){
  let ret=[]
  for(var i=0;i<truecoins;i+=1){
    if (i<dice.length)
      ret.push(("TH").charAt(Number(dice[i]))+"")
    else
      ret.push("X")
  }
  return ret.join("/")
}

function chancenote(weights,offset){
  let wmax=weights[0]
  let wmin=weights[0]
  let ret=""
  for(var i=0;i<weights.length;i++){
    wmax=Math.max(wmax,weights[i])
    wmin=Math.min(wmin,weights[i])
  }
  if(wmax==wmin) {
    ret+="With these instructions, there is an equal chance of " +
         "getting any whole number from " +
         (offset||0) + " through " + ((weights.length-1)+(offset||0))+".\n"
  } else {
    ret+="With these instructions, the chance of getting:\n\n"
    let wsum=sum(weights)
    for(var i=0;i<weights.length;i++){
      let pct=Math.floor((weights[i]/wsum)*10000)/100.0
      let w=weights[i]
      if (w == 0) {
         ret+="- "+(i+(offset||0)) + " is 0 (0%).\n"
      } else {
         let wgcd=gcd(w,wsum)
         ret+="- "+(i+(offset||0)) + " is "+(weights[i]/wgcd)+"/"+(wsum/wgcd)
         if(pct/100.0 == (weights[i]/wsum)) {
           ret+=" ("+pct+"%).\n"
         } else {
           ret+=" (about "+pct+"%).\n"
         }
       }
    }
  }
  return ret
}

function fldrTable(data,offset,weights){
  if(!data || !data[0]){
    return "The result is "+(offset||0)+".\n\n"
  }
  let table=data[0]
  let max=data[1]
  let coins=table[0].length
  let ret="Flip a coin"+(coins>1 ? " up to "+coins+" times" : "")+".  If you get:\n\n"
  let results={}
  let items=[]
  let quick1=0
  let quick2=0
  let quick3=0
  let quick4=0
  let quick5=0
  let reject=false
  let x=0
  //console.log("fldrtable")
  for (var i=0;i<2**coins;i+=1){
     if((quick1 & (1<<(i&1)))!=0)continue;
     if((quick2 & (1<<(i&3)))!=0)continue;
     if((quick3 & (1<<(i&0x07)))!=0)continue;
     if((quick4 & (1<<(i&0x0f)))!=0)continue;
     if((quick5 & (1<<(i&0x1f)))!=0)continue;
     //if(x%10000==0)console.log([x,i])
     //x+=1
     let r=fldrResult(table,i,max)
     if(r!=null){
        let res=headstails(i,coins,r[1])
        if (!results[res]){
           if(r[1]==1)quick1|=1<<(i&0x01);
           if(r[1]==2)quick2|=1<<(i&0x03);
           if(r[1]==3)quick3|=1<<(i&0x07);
           if(r[1]==4)quick4|=1<<(i&0x0F);
           if(r[1]==5)quick5|=1<<(i&0x1f);
           //console.log([r[1],quick1,quick2,quick3,quick4,quick5])
           items.push("- "+res+", the result is "+(r[0]+(offset||0))+".")
           results[res]=true
        }
     } else {
       reject=true
     }
  }
  ret+=items.sort().reverse().join("\n")+"\n"
  if(reject){
    ret+="- Anything else, start over.\n"
  }
  ret+="\n"
  ret+="T = Tails (or 1, 2, or 3 on a six-sided die).\n"
  ret+="H = Heads (or 4, 5, or 6 on a six-sided die).\n"
  ret+="X = Either T or H.\n\n"
  ret+=chancenote(weights,offset)+"\n"
  return ret
}

function ceilingToPowerOf2Or3Or6(x) {
  let power2=2
  let power3=3
  let power6=6
  while(x>power2) {
    power2*=2
  }
  while(x>power3) {
    power3*=3
  }
  while(x>power6) {
    power6*=6
  }
  return Math.min(Math.min(power2,power3), power6)
}

function ceilingToPowerOf2(x) {
  let power2=2
  while(x>power2) {
    power2*=2
  }
  return power2
}

function rational(x,y) {
  if(typeof y=="undefined")y=1
  if(typeof BigInt!="undefined") {
    return [BigInt(x),BigInt(y)]
  } else {
    return [x,y]
  }
}

function rationalpow(rat,y) {
  if(y>Number.MAX_SAFE_INTEGER)throw new Error("unsupported y")
  var n=Number(y)
  var j=rational(1)
  var m=rat
  while(n>0){
    if(n%2==1){
       j=rationalmul(j,m)
    }
    n=Math.floor(n/2)
    m=rationalmul(m,m)
  }
  return j
}

function rationalmul(rat,rat2) {
  return [rat[0]*rat2[0],rat[1]*rat2[1]]
}

function rationaladd(rat,rat2) {
  return [rat[0]*rat2[1]+rat[1]*rat2[0],rat[1]*rat2[1]]
}

function rationalabssub(rat,rat2) {
  let r=rat[0]*rat2[1]-rat[1]*rat2[0]
  if(r<0)r=-r
  return [r,rat[1]*rat2[1]]
}

function rationaldiv(rat,rat2) {
  return [rat[0]*rat2[1],rat[1]*rat2[0]]
}

function rationalcmp(rat,rat2) {
  if(typeof rat2=="number")rat2=rational(rat2)
  s=rat[0]*rat2[1]-rat[1]*rat2[0]
  return s<0 ? -1 : (s==0 ? 0 : 1)
}

function rationalsum(a) {
  let x=rational(0)
  for(let i=0;i<a.length;i++){
    x=rationaladd(x,a[i])
  }
  return x
}

function rationalnum(rat) {
  return Number(rat[0])/Number(rat[1])
}

function dicetable(weights, offset, srcFaces) {
  // Reference: Benoît Kloeckner, "Simulating a dice with a dice", 2008.
  // Extended to allow the output die to have an arbitrary discrete
  // distribution (loaded dice), not just a uniform distribution (fair dice).
  // This requires only a trivial modification to the greedy simulation
  // process in that paper.
  if(weights.length<2){
    return "The result is "+(offset||0)+".\n\n"
  }
  let origweights=weights
  let wgcd=weightsgcd(weights)
  weights=weights.map(o=>o/wgcd)
  // Notice that this method works for any number of faces
  // if the sum of weights adjusts so that every prime number
  // dividing that sum also divides 'srcFaces' (see Lemma 3 of
  // Kloeckner's paper).
  if(srcFaces==null)srcFaces=6
  let dstWords=[];
  for(var i=0;i<weights.length;i++) { dstWords.push([]) }
  let dstWeights=[];
  for(var i=0;i<weights.length;i++) { dstWeights.push(rational(0)) }
  let srcWord=0
  let srcWordCount=1
  let onen=1
  let wsum=sum(weights)
  if(typeof BigInt!="undefined"){
    srcFaces=BigInt(srcFaces)
    srcWordCount=BigInt(srcWord)
    srcWord=BigInt(srcWordCount)
    onen=BigInt(onen)
  }
  let dstFaces=weights.length // Max. number of outcomes
  // Make the sum of weights a power of all prime factors of srcFaces,
  // or a power of 6 if srcFaces==6, to give
  // the simulation a bounded running time (see Lemma 3 of
  // Kloeckner's paper).  Assumes srcFaces is either 2 or 6.
  // This is similar to an idea used by the
  // Fast Loaded Dice Roller, where it changes the weight table
  // to make the sum of weights a power of 2, by adding a
  // rejection event.
  let wsp2or3=(srcFaces==6) ? ceilingToPowerOf2Or3Or6(wsum) :
        ceilingToPowerOf2(wsum)
  if(wsum!=wsp2or3) {
     // Add a "rejection" weight
     let newWeights=[]
     for(var i=0;i<weights.length;i++) { newWeights.push(weights[i]) }
     let newWeight = wsp2or3-wsum
     wsum+=newWeight
     newWeights.push(newWeight)
     dstWords.push([])
     dstWeights.push(rational(0))
     weights=newWeights
  }
  while (true) {
    let wordsAddedInAll=true
    for (var i=0;i<dstWords.length;i++){
      let wordsAdded=0
      //console.log([srcWord,srcFaces**srcWordCount])
      if(srcWord+onen==srcWord){
        return "Accuracy error detected, so the die-rolling instructions could not be created."
      }
      while(srcWord<srcFaces**srcWordCount) {
        let t=srcWord
        let wordToAdd=[]
        for (var j=0;j<srcWordCount;j++){
          wordToAdd.push(t%srcFaces)
          t=t/srcFaces
          if(typeof BigInt=="undefined"){
             t=Math.floor(t)
          }
        }
        let newWeight=rationaladd(
              dstWeights[i],
              rationalpow(rational(1,srcFaces),srcWordCount))
        // Instead of 1/k (as in the paper), we check whether
        // newWeight is greater than the face's corresponding probability
        if (rationalcmp(newWeight,rational(weights[i],wsum))>0) {
           if(wordsAdded>0) {
              wordsAddedInAll=false
           }
           break
        }
        dstWeights[i]=newWeight
        srcWord+=onen
        wordsAdded+=1
        wordToAdd=wordToAdd.reverse()
        dstWords[i].push(wordToAdd)
      }
    }
    // Stop if all the faces are filled with words and their
    // "weights" sum to 1.
    let minWordsLength=-1
    for(var i=0;i<weights.length;i++){
      if(weights[i]>0) {
        if (minWordsLength==-1)
           minWordsLength=dstWords[i].length
        else
           minWordsLength=Math.min(minWordsLength,dstWords[i].length)
      }
    }
    var dw=rationalsum(dstWeights)
    if(minWordsLength>0 && rationalcmp(dw,1)==0) {
      break
    }
    srcWord*=srcFaces
    srcWordCount+=onen
  }
  let coins=0
  for(var i=0;i<dstWords.length;i++){
    for(var j=0;j<dstWords[i].length;j++){
      coins=Math.max(coins,dstWords[i][j].length)
    }
  }
  let ret=(srcFaces==2 ? "Flip a coin" : "Roll a "+srcFaces+"-sided die")
  ret+=(coins>1 ? " up to "+coins+" times" : "")+".  If you get:\n\n"
  let results={}
  let items=[]
  let reject=false
  for(var i=0;i<dstWords.length;i++){
    for(var j=0;j<dstWords[i].length;j++){
      if(dstWords[i][j].length>0 && i < dstFaces) {
        items.push("- "+(srcFaces==2 ? cointoss : dieroll)(dstWords[i][j],coins)+", the result is "+(i+(offset||0))+".")
      }
    }
  }
  items=items.sort()
  if(srcFaces==2)items=items.reverse()
  ret+=items.join("\n")+"\n"
  if(sum(dstWeights)<1 || dstFaces < dstWeights.length){
    ret+="- Anything else, start over.\n"
  }
  ret+="\n"
  if(srcFaces==2) {
    ret+="T = Tails (or 1, 2, or 3 on a six-sided die).\n"
    ret+="H = Heads (or 4, 5, or 6 on a six-sided die).\n"
    ret+="X = Either T or H.\n\n"
  } else {
    ret+="X = Any die roll.\n\n"
  }
  ret+=chancenote(origweights,offset)+"\n"
  return ret
}

function gcd(a, b) {
  if(a==0||b==0)return 0
  while(true){
    var c=Math.floor(a/b)
    var d=a-b*c
    a=b
    b=d
    if(b==0)return a
  }
}

function weightsgcd(weights){
  var lastgcd=-1
  for(var i=0;i<weights.length;i++){
    if(weights[i]!=0){
      if(lastgcd<0){
        lastgcd=weights[i]
      } else {
        lastgcd=gcd(lastgcd,weights[i])
      }
    }
  }
  return Math.max(1, lastgcd)
}

function fldr(weights) {
        // Initialize data for Fast Loaded Dice Roller
        let n = weights.length
        let weightBits = 0
        // Find GCD of all weights, to optimize the table's size
        let wgcd = weightsgcd(weights)
        weights=weights.map(o=>o/wgcd)
        let totalWeights = sum(weights)
        if(totalWeights==0)return null
        if(totalWeights < 0)
            throw new Error("Sum of weights is negative")
        let minWeight = min(weights)
        if(minWeight<0)return null
        let realLabels=null
        let rejectionLabel=n
        if(minWeight==0) {
          // Some weights are zero
          newWeights=[]
          realLabels=[]
          for(let i=0;i<weights.length;i++){
             if(weights[i]!=0) {
               newWeights.push(weights[i])
               realLabels.push(i + 1)
             }
          }
          realLabels.push(rejectionLabel + 1)
          weights=newWeights
          n=weights.length
        }
        if(weights.length==1) {
          // Degenerate case
          return [null, -1, realLabels ? (realLabels[0]-1) : 0]
        }
        let tmp = (totalWeights-1)
        while(tmp > 0) {
            tmp = Math.floor(tmp/2)
            weightBits += 1
        }
        let maxLeaf = 0
        let lasta = Math.pow(2, weightBits) - totalWeights
        let leavesAndLabels = times(n+2).map(o=>zeros(weightBits))
        let shift = weightBits - 1
        for (let j=0;j<weightBits;j++){
            let level = 1
            for (let i=0;i<n+1;i++){
                let ai = (i==n) ? lasta : weights[i]
                if (ai < 0) { return null; }
                let leaf = Math.floor(ai/Math.pow(2, shift)) & 1
                if (leaf > 0) {
                    // NOTE: Labels start at 1
                    leavesAndLabels[0][j] += leaf
                    label = realLabels ? realLabels[i] : i + 1
                    leavesAndLabels[level][j] = label
                    maxLeaf = Math.max(maxLeaf, label - 1)
                    level += 1
               }
            }
            shift -= 1
        }
        return [leavesAndLabels, rejectionLabel, maxLeaf]
}

function sameweights(x){
  if(x.length<2)return true
  for(var i=1;i<x.length;i++){
    if(x[i]!=x[0])return false
  }
  return true
}

function binco(n, i) {
      // A robust form of the binomial coefficient that
      // returns NaN if the result would exceed MAX_SAFE_INTEGER.
      // Except in certain trivial cases, also returns NaN
      // if either argument exceeds MAX_SAFE_INTEGER.
      if(i === 0 || i === n) {
        return 1;
      } else if(isNaN(n) || isNaN(i) || n > 9007199254740991 ||
         i > 9007199254740991) {
        return 0.0 / 0.0;
      } else if(i === 1) {
        return n;
      } else if(i > n || n < 0 || i < 0) {
        return 0;
      } else if(n - 1 === i) {
        return n;
      } else if(n < binco._fact.length) {
        return binco._fact[n] / (binco._fact[i] * binco._fact[n - i]);
      } else if(n / 2 < i && n - i !== i) {
        return binco(n, n - i);
      } else {
        var bc = binco(n - 1, i - 1);
        if(isNaN(bc))return bc;
        if(bc % i === 0) {
          var ret = bc / i * n;
          if(ret <= 9007199254740991)return ret;
        } else {
          var tret = bc * n;
          if(tret <= 9007199254740991)return tret / i;
        }
        var bc2 = binco(n - 1, i);
        bc2 += bc;
        if(bc2 <= 9007199254740991)return bc2;
        return 0.0 / 0.0;
      }
}
binco._fact = [1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880,
      3628800, 39916800, 479001600, 6227020800, 87178291200,
      1307674368000, 20922789888000, 355687428096000,
      6402373705728000];

var changefunc=function() {
     var curval=document.getElementById("probabilities").value+"|"+
        document.getElementById("genname").value+"|"+
        document.getElementById("genlang").value
     if(currentValue==curval)return
     currentValue=curval
     var weights=document.getElementById("probabilities").value
     if(weights.length==0)return
     var genname=document.getElementById("genname").value
     var glang=document.getElementById("genlang").value
     var d20test=(/^\s*(\d\d?)?d(\d+?)(?:\+(\d+))?\s*$/).exec(weights)
     //console.log(d20test)
     var weightints=[]
     var code=""
     if(d20test) {
        let numdice=d20test[1]==null ? 1 : parseInt(d20test[1],10)
        let numfaces=parseInt(d20test[2],10)
        let bonus=d20test[3]==null ? 0 : parseInt(d20test[3],10)
        if(numfaces>100 || numfaces<2) {
            document.getElementById("error").innerHTML="This generator supports "+
               "only 2 through 100 die faces."
            return
        }
        if(numdice>99) {
            document.getElementById("error").innerHTML="This generator does not "+
               "support die numbers greater than 99."
            return
        }
        if(bonus>Number.MAX_SAFE_INTEGER) {
            document.getElementById("error").innerHTML="This generator does not "+
               "support bonuses greater than "+Number.MAX_SAFE_INTEGER+"."
            return
        }
        weightints=[]
        for(var i=0;i<=numdice*numfaces;i++){
          var p=i
          var lim=Math.floor(((p+1)-numdice)/numfaces)
          //console.log(lim)
          if(lim<0) {
             weightints.push(0)
          } else {
             var weight=0
             for(var j=0;j<=lim;j++){
                weight+=Math.pow(-1,j) * binco(numdice, j) * binco(p - numfaces*j - 1, numdice-1)
             }
             weightints.push(weight)
          }
        }
        var data=fldr(weightints)
        if(!data && document.getElementById("probabilities").value!="") {
          document.getElementById("error").innerHTML="Failed to generate code for these weights."
          return
        }
        //console.log([weightints,bonus])
        if (glang=="javascript")code=codegen(data,genname,bonus)
        if (glang=="ruby")code=codegenruby(data,genname,bonus)
        if (glang=="coinflip")code=dicetable(weightints,bonus,2)
        if (glang=="coinflip1")code=dicetable(weightints,bonus+1,2)
        if (glang=="dieroll")code=dicetable(weightints,bonus)
        if (glang=="dieroll1")code=dicetable(weightints,bonus+1)
     } else {
        genname=genname.replace(/[^A-Za-z0-9_]+/g,"_")
          .replace(/^[0-9]/,"_")
        weights=weights.replace(/^\s+/g,"")
        weights=weights.replace(/\s+$/g,"")
        weights=weights.replace(/,\s*$/g,"")
        weights=weights.split(/\s*,\s*/)
        for(var i=0;i<weights.length;i++){
          if(!(/^\d+$/).test(weights[i])) {
            document.getElementById("error").innerHTML="Not a valid list of integer weights."
            return
          }
          num=Number.parseInt(weights[i],10)
          if(num>Number.MAX_SAFE_INTEGER) {
            document.getElementById("error").innerHTML="This generator does not "+
               "support weights greater than "+Number.MAX_SAFE_INTEGER+"."
            return
          }
          weightints.push(num)
        }
        if(weightints.length==0)return
        if(sum(weightints)>Number.MAX_SAFE_INTEGER){
            document.getElementById("error").innerHTML="This generator does not "+
               "support a sum of weights greater than "+Number.MAX_SAFE_INTEGER+"."
            return
       }
     if(sameweights(weightints) && (glang=="javascript" || glang=="ruby")) {
       // All weights are the same
       if (glang=="javascript")code=fdr(data,weightints.length)
       if (glang=="ruby")code=fdrruby(data,weightints.length)
     } else {
       var data=fldr(weightints)
       if(!data && document.getElementById("probabilities").value!="") {
         document.getElementById("error").innerHTML="Failed to generate code for these weights."
         return
       }
       if (glang=="javascript")code=codegen(data,genname)
       if (glang=="ruby")code=codegenruby(data,genname)
       if (glang=="coinflip")code=fldrTable(data,0,weightints)
       if (glang=="coinflip1")code=fldrTable(data,1,weightints)
       if (glang=="dieroll")code=dicetable(weightints,0)
       if (glang=="dieroll1")code=dicetable(weightints,1)
     }
     }
     document.getElementById("code").value=code
     document.getElementById("error").innerHTML=""
  }

var currentValue = null
document.getElementById("probabilities").addEventListener(
   "change",
  changefunc)
window.setInterval(function() {
  changefunc()
}, 200)

</script>