source: Dev/trunk/src/client/dojox/math/_base.js @ 532

// AMD-ID "dojox/math/_base"
define(["dojo", "dojox"], function(dojo, dojox) {
        dojo.getObject("math", true, dojox);

        var m = dojox.math;
        dojo.mixin(dojox.math, {
                toRadians: function(/* Number */n){
                        // summary:
                        //              Convert the passed number to radians.
                        return (n*Math.PI)/180; // Number
                },
                toDegrees: function(/* Number */n){
                        // summary:
                        //              Convert the passed number to degrees.
                        return (n*180)/Math.PI; // Number
                },
                degreesToRadians: function(/* Number */n){
                        // summary:
                        //              Deprecated.  Use dojox.math.toRadians.
                        return m.toRadians(n);  // Number
                },
                radiansToDegrees: function(/* Number */n){
                        // summary:
                        //              Deprecated.  Use dojox.math.toDegrees.
                        return m.toDegrees(n);  // Number
                },

                _gamma: function(z){
                        // summary:
                        //              Compute the gamma function for the passed number.
                        //              Approximately 14 digits of precision with non-integers.
                        var answer = 1; // 0!
                        // gamma(n+1) = n * gamma(n)
                        while (--z >= 1){
                                answer *= z;
                        }
                        if(z == 0){ return answer; } // normal integer quick return
                        if(Math.floor(z) == z){ return NaN; } // undefined at nonpositive integers since sin() below will return 0
                        // assert: z < 1, remember this z is really z-1
                        if(z == -0.5){ return Math.sqrt(Math.PI); } // popular gamma(1/2)
                        if(z < -0.5){ // remember this z is really z-1
                                return Math.PI / (Math.sin(Math.PI * (z + 1)) * this._gamma(-z)); // reflection
                        }
                        // assert: -0.5 < z < 1
                        // Spouge approximation algorithm
                        var a = 13;
                        // c[0] = sqrt(2*PI) / exp(a)
                        // var kfact = 1
                        // for (var k=1; k < a; k++){
                        //              c[k] = pow(-k + a, k - 0.5) * exp(-k) / kfact
                        //              kfact *= -k  // (-1)^(k-1) * (k-1)!
                        // }
                        var c = [ // precomputed from the above algorithm
                                         5.6658056015186327e-6,
                                         1.2743717663379679,
                                        -4.9374199093155115,
                                         7.8720267032485961,
                                        -6.6760503749436087,
                                         3.2525298444485167,
                                        -9.1852521441026269e-1,
                                         1.4474022977730785e-1,
                                        -1.1627561382389853e-2,
                                         4.0117980757066622e-4,
                                        -4.2652458386405744e-6,
                                         6.6651913290336086e-9,
                                        -1.5392547381874824e-13
                                ];
                        var sum = c[0];
                        for (var k=1; k < a; k++){
                                sum += c[k] / (z + k);
                        }
                        return answer * Math.pow(z + a, z + 0.5) / Math.exp(z) * sum;
                },

                factorial: function(/* Number */n){
                        // summary:
                        //              Return the factorial of n
                        return this._gamma(n+1);        // Number
                },

                permutations: function(/* Number */n, /* Number */k){
                        // summary:
                        //              TODO
                        if(n==0 || k==0){
                                return 1;       // Number
                        }
                        return this.factorial(n) / this.factorial(n-k);
                },

                combinations: function(/* Number */n, /* Number */r){
                        // summary:
                        //              TODO
                        if(n==0 || r==0){
                                return 1;       // Number
                        }
                        return this.factorial(n) / (this.factorial(n-r) * this.factorial(r));   // Number
                },

                bernstein: function(/* Number */t, /* Number */n, /* Number */ i){
                        // summary:
                        //              TODO
                        return this.combinations(n, i) * Math.pow(t, i) * Math.pow(1-t, n-i);   // Number
                },

                gaussian: function(){
                        // summary:
                        //              Return a random number based on the Gaussian algo.
                        var k=2;
                        do{
                                var i=2*Math.random()-1;
                                var j=2*Math.random()-1;
                                k = i*i+j*j;
                        }while(k>=1);
                        return i * Math.sqrt((-2*Math.log(k))/k);       // Number
                },

                // create a range of numbers
                range: function(/* Number */a, /* Number? */b, /* Number? */step){
                        // summary:
                        //              Create a range of numbers based on the parameters.
                        if(arguments.length<2){
                                b=a,a=0;
                        }
                        var range=[], s=step||1, i;
                        if(s>0){
                                for(i=a; i<b; i+=s){
                                        range.push(i);
                                }
                        }else{
                                if(s<0){
                                        for(i=a; i>b; i+=s){
                                                range.push(i);
                                        }
                                }else{
                                        throw new Error("dojox.math.range: step must not be zero.");
                                }
                        }
                        return range;   // Array
                },

                distance: function(/* Array */a, /* Array */b){
                        // summary:
                        //              Calculate the distance between point A and point B
                        return Math.sqrt(Math.pow(b[0]-a[0],2)+Math.pow(b[1]-a[1],2));  // Number
                },

                midpoint: function(/* Array */a, /* Array */b){
                        // summary:
                        //              Calculate the midpoint between points A and B.  A and B may be multidimensional.
                        if(a.length!=b.length){
                                console.error("dojox.math.midpoint: Points A and B are not the same dimensionally.", a, b);
                        }
                        var m=[];
                        for(var i=0; i<a.length; i++){
                                m[i]=(a[i]+b[i])/2;
                        }
                        return m;       // Array
                }
        });

        return dojox.math;
});