1 files changed, 282 insertions, 0 deletions
diff --git a/js/complex.js b/js/complex.js
new file mode 100644
index 0000000..3f009bd
--- /dev/null
+++ b/js/complex.js
@@ -0,0 +1,282 @@
+/*
+    complex.js
+        Client-side complex numbers in JavaScript
+*/
+var complex = {};
+
+complex.i = [0, 1];
+complex.logi = [0, 0.682188177];
+complex.PI = [Math.PI, 0];
+complex.E = [Math.E, 0];
+
+complex.lnAccuracy = 20;
+
+
+complex.re = function (a)
+{
+    return a[0];
+}
+
+complex.im = function (a)
+{
+    return a[1];
+}
+
+// Create a complex number from a real number
+complex.reToC = function (a)
+{
+    return [a, 0];
+}
+
+complex.reC = function (a)
+{
+    return complex.reToC(complex.re(a));
+}
+
+complex.imC = function (a)
+{
+    return complex.reToC(complex.im(a));
+}
+
+
+
+complex.show = function (a)
+{
+    var im = complex.im(a);
+    var re = complex.re(a);
+    if (im == 1 && re == 0)
+        return "i";
+    if (im == 0)
+        return re.toString();
+    if (im == 1)
+        return re + " + i";
+    if (re == 0)
+        return im + "i";
+    return re + " + " + im + "i";
+}
+
+complex.add = function (a, b)
+{
+    return [complex.re(a) + complex.re(b), complex.im(a) + complex.im(b)];
+}
+
+complex.neg = function (a)
+{
+    return [-complex.re(a), -complex.im(a)];
+}
+
+complex.sub = function (a, b)
+{
+    return complex.add(a, complex.neg(b));
+}
+
+complex.mult = function (a, b)
+{
+    var a_Re, a_Im, b_Re, b_Im;
+    a_Re = complex.re(a);
+    a_Im = complex.im(a);
+    b_Re = complex.re(b);
+    b_Im = complex.im(b);
+    return [a_Re * b_Re - a_Im * b_Im, a_Re * b_Im + a_Im * b_Re];
+}
+
+complex.recip = function (a)
+{
+    var re = complex.re(a);
+    var im = complex.im(a);
+    var divBy = re*re + im*im;
+    return [re/divBy, -im/divBy]
+}
+
+complex.div = function (a, b)
+{
+    return complex.mult(a, complex.recip(b));
+}
+
+complex.exp = function (a)
+{
+    var re = complex.re(a);
+    var im = complex.im(a);
+    var expRe = Math.exp(re);
+    return [expRe * Math.cos(im), expRe * Math.sin(im)];
+}
+
+complex.theta = function (a)
+{
+    return Math.atan(complex.im(a) / complex.re(a));
+}
+
+complex.abs = function (a)
+{
+    var re = complex.re(a);
+    var im = complex.im(a);
+    return Math.sqrt(re*re + im*im);
+}
+
+complex.polar = function (a)
+{
+    return [complex.abs(a), complex.theta(a)];
+}
+
+complex.arg = function (a)
+{
+    var x = complex.re(a);
+    var y = complex.im(a);
+    var theta = complex.theta(a);
+    if (x > 0)
+        return theta;
+    if (x < 0 && y >= 0)
+        return theta + Math.PI;
+    if (x < 0 && y < 0)
+        return theta - Math.PI;
+    if (x == 0 && y > 0)
+        return Math.PI / 2;
+    if (x == 0 && y < 0)
+        return -Math.PI / 2;
+    return 1 / 0;
+}
+
+complex.ln = function (a)
+{
+    return [Math.log(complex.abs(a)), complex.arg(a)];
+}
+
+complex.log = function (base, a)
+{
+    return complex.div(complex.ln(a), complex.ln(base));
+}
+
+complex.pow = function (a, b)
+{
+    return complex.exp(complex.mult(b, complex.ln(a)));
+}
+
+complex.sin = function (a)
+{
+    var ia = complex.mult(complex.i, a);
+    return complex.mult([0, 0.5], complex.sub(complex.exp(complex.neg(ia)), complex.exp(ia)));
+}
+
+complex.cos = function (a)
+{
+    return complex.sin(complex.sub(complex.reToC(Math.PI / 2), a));
+}
+
+complex.tan = function (a)
+{
+    return complex.div(complex.sin(a), complex.cos(a));
+}
+
+complex.sqrt = function (a)
+{
+    return complex.pow(a, complex.reToC(0.5));
+}
+
+complex.sinh = function (a)
+{
+    return complex.mult([0.5, 0], complex.sub(complex.exp(a), complex.exp(complex.neg(a))));
+}
+
+complex.cosh = function (a)
+{
+    return complex.mult([0.5, 0], complex.add(complex.exp(a), complex.exp(complex.neg(a))))
+}
+
+complex.tanh = function (a)
+{
+    return complex.div(complex.sinh(a), complex.cosh(a));
+}
+
+complex.rpn = function (s)
+{
+    // complex.rpn :: String -> (Complex -> Complex)
+
+
+    var tokens = s.split(" ");
+
+    return function(x)
+    {
+        var token;
+        var stack = [];
+        for (var i = 0; i < tokens.length; i++)
+        {
+            token = tokens[i];
+            switch (token)
+            {
+            case "+":
+                stack.push(complex.add(stack.pop(), stack.pop()));
+                break;
+            case "*":
+                stack.push(complex.mult(stack.pop(), stack.pop()));
+                break;
+            case "-":
+                var val2 = stack.pop();
+                var val1 = stack.pop();
+                stack.push(complex.sub(val1, val2));
+                break;
+            case "/":
+                var val2 = stack.pop();
+                var val1 = stack.pop();
+                stack.push(complex.div(val1, val2));
+                break;
+            case "^":
+                var val2 = stack.pop();
+                var val1 = stack.pop();
+                stack.push(complex.pow(val1, val2));
+                break;
+            case "sqrt":
+                stack.push(complex.sqrt(stack.pop()));
+                break;
+            case "exp":
+                stack.push(complex.exp(stack.pop()));
+                break;
+            case "sin":
+                stack.push(complex.sin(stack.pop()));
+                break;
+            case "cos":
+                stack.push(complex.cos(stack.pop()));
+                break;
+            case "tan":
+                stack.push(complex.tan(stack.pop()));
+                break;
+            case "sinh":
+                stack.push(complex.sinh(stack.pop()));
+                break;
+            case "cosh":
+                stack.push(complex.cosh(stack.pop()));
+                break;
+            case "tanh":
+                stack.push(complex.tanh(stack.pop()));
+                break;
+            case "re":
+                stack.push(complex.reC(stack.pop()));
+                break;
+            case "im":
+                stack.push(complex.imC(stack.pop()));
+                break;
+            case "x":
+                stack.push(x);
+                break;
+            case "i":
+                stack.push(complex.i);
+                break;
+            case "e":
+                stack.push(complex.E);
+                break;
+            case "pi":
+                stack.push(complex.PI);
+                break;
+            default:
+                if (token[token.length-1] == "i")
+                {
+                    stack.push([0, parseFloat(token.substring(0, token.length-1))]);
+                }
+                else
+                {
+                    stack.push(complex.reToC(parseFloat(token)));
+                }
+            }
+        }
+        return stack.pop();
+    };
+}