RandomInt function that can evenly process the entire range of MIN and MAX_SAFE_INTEGER

Question

Requirements and Background

I need a generic function randomIntthat can handle a range of values ​​up Number.MIN_SAFE_INTEGERto Number.MAX_SAFE_INTEGERand that the return values ​​are evenly distributed .

So, I started with MDN and looked at the page Math.random. They give an example that seems to be evenly distributed.

// Returns a random integer between min (included) and max (excluded)
// Using Math.round() will give you a non-uniform distribution!
function getRandomInt(min, max) {
  return Math.floor(Math.random() * (max - min)) + min;
}

But he comes with the following note.

Note that since numbers in JavaScript are IEEE 754 floating point numbers rounded to the nearest and even behavior, the ranges declared for the function given below (with the exception of one for Math.random () itself) are not exact. If extremely large boundaries are selected (2 ^ 53 or higher), it is possible in extremely rare cases to calculate the usually excluded upper limit.

I want to use the range - (2 ^ 53 - 1) and 2 ^ 53 - 1, so I think this note does not apply. Then I notice max - min: this will be a problem for the larger ranges that I indicated:

Example - Maximum Range

Number.MAX_SAFE_INTEGER - Number.MIN_SAFE_INTEGER > Number.MAX_SAFE_INTEGER

Solution 1 - not a solution

Disconnect I go and play a little and come up with the following code based on the MDN example and my requirements.

Number.MAX_SAFE_INTEGER = Number.MAX_SAFE_INTEGER || 9007199254740991;

Number.MIN_SAFE_INTEGER = Number.MIN_SAFE_INTEGER || -Number.MAX_SAFE_INTEGER;

Number.toInteger = Number.toInteger || function (inputArg) {
    var number = +inputArg,
        val = 0;

    if (number === number) {
        if (!number || number === Infinity || number === -Infinity) {
            val = number;
        } else {
            val = (number > 0 || -1) * Math.floor(Math.abs(number));
        }
    }

    return val;
};

function clampSafeInt(number) {
    return Math.min(Math.max(Number.toInteger(number), Number.MIN_SAFE_INTEGER), Number.MAX_SAFE_INTEGER);
}

// Returns a random integer between min (included) and max (included)
// Using Math.round() will give you a non-uniform distribution!
function randomInt(min, max) {
    var tmp,
        val;

    if (arguments.length === 1) {
        max = min;
        min = 0;
    }

    min = clampSafeInt(min);
    max = clampSafeInt(max);
    if (min > max) {
        tmp = min;
        min = max;
        max = tmp;
    }

    tmp = max - min + 1;
    if (tmp > Number.MAX_SAFE_INTEGER) {
        throw new RangeError('Difference of max and min is greater than Number.MAX_SAFE_INTEGER: ' + tmp);
    } else {
        val = Math.floor(Math.random() * tmp) + min;
    }
    
    return val;
}

console.log(randomInt(Number.MIN_SAFE_INTEGER, Number.MAX_SAFE_INTEGER));

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Number.MAX_SAFE_INTEGER = Number.MAX_SAFE_INTEGER || 9007199254740991;

Number.MIN_SAFE_INTEGER = Number.MIN_SAFE_INTEGER || -Number.MAX_SAFE_INTEGER;

Number.toInteger = Number.toInteger || function (inputArg) {
    var number = +inputArg,
        val = 0;

    if (number === number) {
        if (!number || number === Infinity || number === -Infinity) {
            val = number;
        } else {
            val = (number > 0 || -1) * Math.floor(Math.abs(number));
        }
    }

    return val;
};

function clampSafeInt(number) {
    return Math.min(Math.max(Number.toInteger(number), Number.MIN_SAFE_INTEGER), Number.MAX_SAFE_INTEGER);
}

// Returns a random integer between min (included) and max (included)
// Using Math.round() will give you a non-uniform distribution!
function randomInt(min, max) {
    var tmp,
        val;

    if (arguments.length === 1) {
        max = min;
        min = 0;
    }

    min = clampSafeInt(min);
    max = clampSafeInt(max);
    if (min > max) {
        tmp = min;
        min = max;
        max = tmp;
    }

    tmp = max - min + 1;
    if (tmp > Number.MAX_SAFE_INTEGER) {
        if (Math.floor(Math.random() * 2)) {
            val = Math.floor(Math.random() * (max - 0 + 1)) + 0;
        } else {
            val = Math.floor(Math.random() * (0 - min + 1)) + min;
        }
    } else {
        val = Math.floor(Math.random() * tmp) + min;
    }
    
    return val;
}

console.log(randomInt(Number.MIN_SAFE_INTEGER, Number.MAX_SAFE_INTEGER));

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function getData() {
  var x = {},
    c = 1000000,
    min = -20,
    max = 20,
    q,
    i;

  for (i = 0; i < c; i += 1) {
    if (Math.floor(Math.random() * 2)) {
      q = Math.floor(Math.random() * (max - 0 + 1)) + 0;
    } else {
      q = Math.floor(Math.random() * (1 - min + 1)) + min;
    }

    if (!x[q]) {
      x[q] = 1;
    } else {
      x[q] += 1;
    }
  };

  return Object.keys(x).sort(function(x, y) {
    return x - y;
  }).map(function(key, index) {
    return {
      'q': +key,
      'p': (x[key] / c) * 100
    };
  });
}

var data = getData(),
  margin = {
    top: 20,
    right: 20,
    bottom: 30,
    left: 50
  },
  width = 960 - margin.left - margin.right,
  height = 500 - margin.top - margin.bottom,
  x = d3.scale.linear().range([0, width]),
  y = d3.scale.linear().range([height, 0]),
  xAxis = d3.svg.axis().scale(x).orient("bottom"),
  yAxis = d3.svg.axis().scale(y).orient("left"),
  line = d3.svg.line().x(function(d) {
    return x(d.q);
  }).y(function(d) {
    return y(d.p);
  }),
  svg = d3.select("body").append("svg")
  .attr("width", width + margin.left + margin.right)
  .attr("height", height + margin.top + margin.bottom)
  .append("g")
  .attr("transform", "translate(" + margin.left + "," + margin.top + ")");

x.domain(d3.extent(data, function(d) {
  return d.q;
}));

y.domain(d3.extent(data, function(d) {
  return d.p;
}));

svg.append("g")
  .attr("class", "x axis")
  .attr("transform", "translate(0," + height + ")")
  .call(xAxis);

svg.append("g")
  .attr("class", "y axis")
  .call(yAxis);

svg.append("path")
  .datum(data)
  .attr("class", "line")
  .attr("d", line);

body {
  font: 10px sans-serif;
}
.axis path,
.axis line {
  fill: none;
  stroke: #000;
  shape-rendering: crispEdges;
}
.line {
  fill: none;
  stroke: steelblue;
  stroke-width: 1.5px;
}

<script src="https://cdnjs.cloudflare.com/ajax/libs/d3/3.4.11/d3.min.js"></script>

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3 -

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Number.MAX_SAFE_INTEGER = Number.MAX_SAFE_INTEGER || 9007199254740991;

Number.MIN_SAFE_INTEGER = Number.MIN_SAFE_INTEGER || -Number.MAX_SAFE_INTEGER;

Number.toInteger = Number.toInteger || function (inputArg) {
    var number = +inputArg,
        val = 0;

    if (number === number) {
        if (!number || number === Infinity || number === -Infinity) {
            val = number;
        } else {
            val = (number > 0 || -1) * Math.floor(Math.abs(number));
        }
    }

    return val;
};

function clampSafeInt(number) {
    return Math.min(Math.max(Number.toInteger(number), Number.MIN_SAFE_INTEGER), Number.MAX_SAFE_INTEGER);
}

var boxMullerRandom = (function () {
    var phase = 0,
        RAND_MAX,
        array,
        random,
        x1, x2, w, z;

    if (crypto && crypto.getRandomValues) {
        RAND_MAX = Math.pow(2, 32) - 1;
        array = new Uint32Array(1);
        random = function () {
            crypto.getRandomValues(array);

            return array[0] / RAND_MAX;
        };
    } else {
        random = Math.random;
    }

    return function () {
        if (!phase) {
            do {
                x1 = 2.0 * random() - 1.0;
                x2 = 2.0 * random() - 1.0;
                w = x1 * x1 + x2 * x2;
            } while (w >= 1.0);

            w = Math.sqrt((-2.0 * Math.log(w)) / w);
            z = x1 * w;
        } else {
            z = x2 * w;
        }

        phase ^= 1;

        return z;
    }
}());

function rejectionSample(stdev, mean, from, to) {
    var retVal;
    
    do {
        retVal = (boxMullerRandom() * stdev) + mean;
    } while (retVal < from || to < retVal);

    return retVal;
}

function randomInt(min, max) {
    var tmp,
        val;

    if (arguments.length === 1) {
        max = min;
        min = 0;
    }

    min = clampSafeInt(min);
    max = clampSafeInt(max);
    if (min > max) {
        tmp = min;
        min = max;
        max = tmp;
    }

    tmp = {};
    tmp.mean = (min / 2) + (max / 2);
    tmp.variance = (Math.pow(min - tmp.mean, 2) + Math.pow(max - tmp.mean, 2)) / 2;
    tmp.deviation = Math.sqrt(tmp.variance);
    console.log(tmp);
    return Math.floor(rejectionSample(tmp.deviation, tmp.mean, min, max + 1));
}

console.log(randomInt(Number.MIN_SAFE_INTEGER, Number.MAX_SAFE_INTEGER));

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, ( ). - Number.MAX_SAFE_INTEGER. console.log(tmp);

{mean: 0, variance: 8.112963841460666e+31, deviation: 9007199254740991} 

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Number.MAX_SAFE_INTEGER = Number.MAX_SAFE_INTEGER || 9007199254740991;

Number.MIN_SAFE_INTEGER = Number.MIN_SAFE_INTEGER || -Number.MAX_SAFE_INTEGER;

Number.toInteger = Number.toInteger || function(inputArg) {
  var number = +inputArg,
    val = 0;

  if (number === number) {
    if (!number || number === Infinity || number === -Infinity) {
      val = number;
    } else {
      val = (number > 0 || -1) * Math.floor(Math.abs(number));
    }
  }

  return val;
};

function clampSafeInt(number) {
  return Math.min(Math.max(Number.toInteger(number), Number.MIN_SAFE_INTEGER), Number.MAX_SAFE_INTEGER);
}

var boxMullerRandom = (function() {
  var phase = 0,
    RAND_MAX,
    array,
    random,
    x1, x2, w, z;

  if (crypto && crypto.getRandomValues) {
    RAND_MAX = Math.pow(2, 32) - 1;
    array = new Uint32Array(1);
    random = function() {
      crypto.getRandomValues(array);

      return array[0] / RAND_MAX;
    };
  } else {
    random = Math.random;
  }

  return function() {
    if (!phase) {
      do {
        x1 = 2.0 * random() - 1.0;
        x2 = 2.0 * random() - 1.0;
        w = x1 * x1 + x2 * x2;
      } while (w >= 1.0);

      w = Math.sqrt((-2.0 * Math.log(w)) / w);
      z = x1 * w;
    } else {
      z = x2 * w;
    }

    phase ^= 1;

    return z;
  }
}());

function rejectionSample(stdev, mean, from, to) {
  var retVal;

  do {
    retVal = (boxMullerRandom() * stdev) + mean;
  } while (retVal < from || to < retVal);

  return retVal;
}

function randomInt(min, max) {
  var tmp,
    val;

  if (arguments.length === 1) {
    max = min;
    min = 0;
  }

  min = clampSafeInt(min);
  max = clampSafeInt(max);
  if (min > max) {
    tmp = min;
    min = max;
    max = tmp;
  }

  tmp = {};
  tmp.mean = (min / 2) + (max / 2);
  tmp.variance = (Math.pow(min - tmp.mean, 2) + Math.pow(max - tmp.mean, 2)) / 2;
  tmp.deviation = Math.sqrt(tmp.variance);

  return Math.floor(rejectionSample(tmp.deviation, tmp.mean, min, max + 1));
}

function getData() {
  var x = {},
    c = 1000000,
    q,
    i;

  for (i = 0; i < c; i += 1) {
    q = randomInt(-9, 3);
    if (!x[q]) {
      x[q] = 1;
    } else {
      x[q] += 1;
    }
  };

  return Object.keys(x).sort(function(x, y) {
    return x - y;
  }).map(function(key) {
    return {
      'q': +key,
      'p': x[key] / c
    };
  });
}

var data = getData(),
  margin = {
    top: 20,
    right: 20,
    bottom: 30,
    left: 50
  },
  width = 960 - margin.left - margin.right,
  height = 500 - margin.top - margin.bottom,
  x = d3.scale.linear().range([0, width]),
  y = d3.scale.linear().range([height, 0]),
  xAxis = d3.svg.axis().scale(x).orient("bottom"),
  yAxis = d3.svg.axis().scale(y).orient("left"),
  line = d3.svg.line().x(function(d) {
    return x(d.q);
  }).y(function(d) {
    return y(d.p);
  }),
  svg = d3.select("body").append("svg")
  .attr("width", width + margin.left + margin.right)
  .attr("height", height + margin.top + margin.bottom)
  .append("g")
  .attr("transform", "translate(" + margin.left + "," + margin.top + ")");

x.domain(d3.extent(data, function(d) {
  return d.q;
}));

y.domain(d3.extent(data, function(d) {
  return d.p;
}));

svg.append("g")
  .attr("class", "x axis")
  .attr("transform", "translate(0," + height + ")")
  .call(xAxis);

svg.append("g")
  .attr("class", "y axis")
  .call(yAxis);

svg.append("path")
  .datum(data)
  .attr("class", "line")
  .attr("d", line);

body {
  font: 10px sans-serif;
}
.axis path,
.axis line {
  fill: none;
  stroke: #000;
  shape-rendering: crispEdges;
}
.line {
  fill: none;
  stroke: steelblue;
  stroke-width: 1.5px;
}

<script src="https://cdnjs.cloudflare.com/ajax/libs/d3/3.4.11/d3.min.js"></script>

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Answer 1

, , , , - BigNumber. , BigNumber, .

console.log(window);
Number.MAX_SAFE_INTEGER = Number.MAX_SAFE_INTEGER || 9007199254740991;

Number.MIN_SAFE_INTEGER = Number.MIN_SAFE_INTEGER || -Number.MAX_SAFE_INTEGER;

Number.toInteger = Number.toInteger || function (inputArg) {
    var number = +inputArg,
        val = 0;

    if (number === number) {
        if (!number || number === Infinity || number === -Infinity) {
            val = number;
        } else {
            val = (number > 0 || -1) * Math.floor(Math.abs(number));
        }
    }

    return val;
};

function clampSafeInt(number) {
    return Math.min(Math.max(Number.toInteger(number), Number.MIN_SAFE_INTEGER), Number.MAX_SAFE_INTEGER);
}

// Returns a random integer between min (included) and max (included)
// Using Math.round() will give you a non-uniform distribution!
function randomInt(min, max) {
    var tmp,
    val;

    if (arguments.length === 1) {
        max = min;
        min = 0;
    }

    min = clampSafeInt(min);
    max = clampSafeInt(max);
    if (min > max) {
        tmp = min;
        min = max;
        max = tmp;
    }

    tmp = max - min + 1;
    if (tmp > Number.MAX_SAFE_INTEGER) {
        tmp = new Big(max).minus(min).plus(1);
        val = Math.floor(tmp.times(Math.random())) + min;
    } else {
        val = Math.floor(Math.random() * tmp) + min;
    }

    return val;
}

console.log(randomInt(Number.MIN_SAFE_INTEGER, Number.MAX_SAFE_INTEGER));

<script src="https://rawgithub.com/MikeMcl/big.js/master/big.min.js"></script>

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Answer 2

Math.random() , 26 ? , .

function random53() {
    var hi, lo, sign = 0;

    while (true) {
        hi = Math.floor(67108864 * Math.random());
        lo = Math.floor(67108864 * Math.random());

        if (hi >= 33554432) {
            sign = -1;
            hi -= 33554432;

            // Gotta throw out negative zero!
            if (0 === hi && 0 === lo) { continue; }
        }
        return sign * (hi * 67108864) + lo;
    }
}