Random Numbers, including Surreal Decimals

surrealDecimals.js

// random number between -1 and 1 with 0 most common result, linearly decreasing
function triangle() { return Math.random() + Math.random() - 1.0 }

// random number between -1.5 and 1.5 with 0 most common, roughly following the bell curve
function bell() { return Math.random() + Math.random() + Math.random()  - 1.5 }

// random number between -1.5e-300 and 1.5e+300 with 50% of the numbers between -0.75 and 0.75 
function wild() { return (Math.random() + Math.random() + Math.random()  - 1.5) / (Math.random()+1e-300) }

// show distribution counts after 10,000 runs.
// Example: testDistr(wild, 6);
function testDistr(fcn,k) { 
  var count={},sum=0,total=0; for(x=0; x<10000; ++x) { 
    var r; 
    ++total; 
    sum += r = Math.round(k * fcn()) ; 
    count[r] = 1 + (count[r]||0); 
  }; 
  var results = {count:count, sum:sum, total:total}; 
  if (typeof console != "undefined" && typeof JSON != "undefined") console.log(JSON.stringify(results, null, "  ")); 
  return results;  
}

// Find the maximum, minimum, and what percentage are less than range 
function testBounds(count,range) { 
  var total = 0, sum = 0, max=-Infinity, min=Infinity; 
  for (x in count) { 
    if (!isNaN(x)) {
      x=x-0; total += count[x]; 
      if (x>max) max=x;
      if (x<min) min=x; 
      if (Math.abs(x) <= range) sum += count[x] 
    }
  } 
  return [max,min, 100 * sum / total] 
}

/*
One way to quickly generate a random binary number is by looking at the decimal digits in math.random() and replace 0-4 with '1' and 5-9 with '1':

0.8430419054348022
becomes
  1000001010001011

0.5513009827118367
becomes
  1100001101001011
etc
*/

function toBinary(r) {
 return r.split("").map(function(digit) { return digit >= "5" ? 1 : 0 })
}

function randomToBinary() {
  return toBinary(Math.random().toString().substring(2))
}

// Note: always starts with "0." in binary form
function randomAsBinary() {
  return Math.random().toString(2).substring(2)
}

 
/**
For a surreal-like decimal expansion, you need a random binary number.
*Even* bits tell you whether to stop or continue, *odd* bits tell you whether to go right or left on the tree:

    > 0... => 0.0 [50%] Stop
    > 100... => -0.5 [12.5%] Go, Left, Stop
    > 110... => 0.5 [12.5%] Go, Right, Stop
    > 11000... => 0.25 [<3.125%] Go, Right, Go, Left, Stop
    > 11010... => 0.75 [<3.125%] Go, Right, Go, Right, Stop
    > 1100100... => 0.125
    > 1100110... => 0.375
    > 1101100... => 0.625
    > 1101110... => 0.875
    > etc

*/

function toSurrealDecimal(list) { 
  list= list!=null ? list.slice().reverse() : randomToBinary(); 
  var exp=0.5, sign, num=0; 
  list.pop();
  while (list.length && list.pop()) { 
    sign=list.length && list.pop() ? -1 : 1; 
    num += sign*exp; 
    exp *= 0.5; 
  } 
  return num; 
}

function randomSurreal() { return toSurrealDecimal(randomToBinary()) }

// Add a wild integer and a random surreal decimal

function randomSurrealWild() { return Math.round(wild()*6) + randomSurreal() }

// Usage:

results = testDistr(randomSurrealWild, 1.0)

testBounds(results.count, 6)
[94307, -127684, 62.49]

testBounds(results.count, 6*1.5)
[94307, -127684, 73.79]

testBounds(results.count, 6*4.5)
[94307, -127684, 90.83]