js: programmatic

programmatic.js

//fixed point example
var programmatic = {
	tolerance: 0.0001,
	isCloseEnough: function(x, y) {
		return Math.abs((x - y) / x) / x < this.tolerance;
	},
	fixedPoint: function(f) {
		return function(firstGuess) {
			var iterate = function(guess) {
				var next = f(guess);
				if(programmatic.isCloseEnough(guess, next)) {
					return next;
				} else {
					return iterate(next);
				}
				return next;
			};
			return iterate(firstGuess);
		};
	},
	averageDamp: function(f) {
		return function(x) {
			return(x + f(x)) / 2;
		};
	}
};

// square root using fixed point 1
function sqrt(x) {
	return programmatic.fixedPoint(function(y) { return (y +  x / y) / 2; })(1.0);
}

// square root using fixed point and averageDamp
function sqrt2(x) {
	return programmatic.fixedPoint(programmatic.averageDamp(function(y) { return x / y; }))(1.0);
}

// og loop average
function avg(nums) {
	var t = 0;
	for(i = 0; i < nums.length; i++) {
		t += nums[i];
	}
	return t / nums.length;
}

// recursive average
function avg(nums) {
	function sum(n) {
		if(n && n.length > 0) {
			return n[0] + sum(n.slice(1));
		} else {
			return 0;
		}
	}
	return sum(nums) / nums.length;
}