1 files changed, 308 insertions, 0 deletions
diff --git a/euler-golf/js/cx.js b/euler-golf/js/cx.js
new file mode 100644
index 0000000..371415d
--- /dev/null
+++ b/euler-golf/js/cx.js
@@ -0,0 +1,308 @@
+// http://www.russellcottrell.com/fractalsEtc/cx.js
+
+class cx {
+  static degrees(d) {
+    cx._RD = d ? Math.PI / 180 : 1;
+  }
+  // Math.PI/180 for degrees, 1 for radians
+  // applies to i/o (constructor, get/set arg, and toString etc.)
+
+  constructor(x, y, polar) {
+    if (!polar) {
+      this.re = x;
+      this.im = y;
+    } else {
+      y *= cx._RD; // may be radians or degrees
+      this.re = x * Math.cos(y);
+      this.im = x * Math.sin(y);
+    }
+  }
+
+  get abs() {
+    return Math.sqrt(this.re * this.re + this.im * this.im);
+  }
+
+  set abs(r) {
+    var theta = this._arg;
+    this.re = r * Math.cos(theta);
+    this.im = r * Math.sin(theta);
+  }
+
+  get arg() {
+    // returns radians or degrees, non-negative
+    return (
+      ((Math.atan2(this.im, this.re) + 2 * Math.PI) % (2 * Math.PI)) / cx._RD
+    );
+  }
+
+  set arg(theta) {
+    // may be radians or degrees
+    var r = this.abs;
+    this.re = r * Math.cos(theta * cx._RD);
+    this.im = r * Math.sin(theta * cx._RD);
+  }
+
+  get _arg() {
+    // internal; returns radians
+    return Math.atan2(this.im, this.re);
+  }
+
+  static get i() {
+    return new cx(0, 1);
+  }
+
+  static set i(x) {
+    throw new Error("i is read-only");
+  }
+
+  toString(polar) {
+    if (!polar)
+      return (
+        this.re.toString() +
+        (this.im >= 0 ? " + " : " - ") +
+        Math.abs(this.im).toString() +
+        "i"
+      );
+    else return this.abs.toString() + " cis " + this.arg.toString();
+  }
+
+  toPrecision(n, polar) {
+    if (!polar)
+      return (
+        this.re.toPrecision(n) +
+        (this.im >= 0 ? " + " : " - ") +
+        Math.abs(this.im).toPrecision(n) +
+        "i"
+      );
+    else return this.abs.toPrecision(n) + " cis " + this.arg.toPrecision(n);
+  }
+
+  toPrecis(n, polar) {
+    // trims trailing zeros
+    if (!polar)
+      return (
+        parseFloat(this.re.toPrecision(n)).toString() +
+        (this.im >= 0 ? " + " : " - ") +
+        parseFloat(Math.abs(this.im).toPrecision(n)).toString() +
+        "i"
+      );
+    else
+      return (
+        parseFloat(this.abs.toPrecision(n)).toString() +
+        " cis " +
+        parseFloat(this.arg.toPrecision(n)).toString()
+      );
+  }
+
+  toFixed(n, polar) {
+    if (!polar)
+      return (
+        this.re.toFixed(n) +
+        (this.im >= 0 ? " + " : " - ") +
+        Math.abs(this.im).toFixed(n) +
+        "i"
+      );
+    else return this.abs.toFixed(n) + " cis " + this.arg.toFixed(n);
+  }
+
+  toExponential(n, polar) {
+    if (!polar)
+      return (
+        this.re.toExponential(n) +
+        (this.im >= 0 ? " + " : " - ") +
+        Math.abs(this.im).toExponential(n) +
+        "i"
+      );
+    else return this.abs.toExponential(n) + " cis " + this.arg.toExponential(n);
+  }
+
+  static getReals(c, d) {
+    // when c or d may be simple or complex
+    var x, y, u, v;
+    if (c instanceof cx) {
+      x = c.re;
+      y = c.im;
+    } else {
+      x = c;
+      y = 0;
+    }
+    if (d instanceof cx) {
+      u = d.re;
+      v = d.im;
+    } else {
+      u = d;
+      v = 0;
+    }
+    return [x, y, u, v];
+  }
+
+  static conj(c) {
+    return new cx(c.re, -c.im);
+  }
+
+  static neg(c) {
+    return new cx(-c.re, -c.im);
+  }
+
+  static add(c, d) {
+    var a = cx.getReals(c, d);
+    var x = a[0];
+    var y = a[1];
+    var u = a[2];
+    var v = a[3];
+    return new cx(x + u, y + v);
+  }
+
+  static sub(c, d) {
+    var a = cx.getReals(c, d);
+    var x = a[0];
+    var y = a[1];
+    var u = a[2];
+    var v = a[3];
+    return new cx(x - u, y - v);
+  }
+
+  static mult(c, d) {
+    var a = cx.getReals(c, d);
+    var x = a[0];
+    var y = a[1];
+    var u = a[2];
+    var v = a[3];
+    return new cx(x * u - y * v, x * v + y * u);
+  }
+
+  static div(c, d) {
+    var a = cx.getReals(c, d);
+    var x = a[0];
+    var y = a[1];
+    var u = a[2];
+    var v = a[3];
+    return new cx(
+      (x * u + y * v) / (u * u + v * v),
+      (y * u - x * v) / (u * u + v * v)
+    );
+  }
+
+  static pow(c, int) {
+    if (Number.isInteger(int) && int >= 0) {
+      var r = Math.pow(c.abs, int);
+      var theta = int * c._arg;
+      return new cx(r * Math.cos(theta), r * Math.sin(theta));
+    } else return NaN;
+  }
+
+  static root(c, int, k) {
+    if (!k) k = 0;
+    if (
+      Number.isInteger(int) &&
+      int >= 2 &&
+      Number.isInteger(k) &&
+      k >= 0 &&
+      k < int
+    ) {
+      var r = Math.pow(c.abs, 1 / int);
+      var theta = (c._arg + 2 * k * Math.PI) / int;
+      return new cx(r * Math.cos(theta), r * Math.sin(theta));
+    } else return NaN;
+  }
+
+  static log(c) {
+    return new cx(Math.log(c.abs), c._arg);
+  }
+
+  static exp(c) {
+    var r = Math.exp(c.re);
+    var theta = c.im;
+    return new cx(r * Math.cos(theta), r * Math.sin(theta));
+  }
+
+  static sin(c) {
+    var a = c.re;
+    var b = c.im;
+    return new cx(Math.sin(a) * Math.cosh(b), Math.cos(a) * Math.sinh(b));
+  }
+
+  static cos(c) {
+    var a = c.re;
+    var b = c.im;
+    return new cx(Math.cos(a) * Math.cosh(b), -Math.sin(a) * Math.sinh(b));
+  }
+
+  static tan(c) {
+    return cx.div(cx.sin(c), cx.cos(c));
+  }
+
+  static asin(c, k) {
+    if (!k) k = 0;
+    var ic = cx.mult(cx.i, c);
+    var c2 = cx.pow(c, 2);
+    return cx.mult(
+      cx.neg(cx.i),
+      cx.log(cx.add(ic, cx.root(cx.sub(1, c2), 2, k)))
+    );
+  }
+
+  static acos(c, k) {
+    if (!k) k = 0;
+    var c2 = cx.pow(c, 2);
+    return cx.mult(
+      cx.neg(cx.i),
+      cx.log(cx.add(c, cx.mult(cx.i, cx.root(cx.sub(1, c2), 2, k))))
+    );
+  }
+
+  static atan(c) {
+    return cx.mult(
+      cx.div(cx.i, 2),
+      cx.log(cx.div(cx.add(cx.i, c), cx.sub(cx.i, c)))
+    );
+  }
+
+  static sinh(c) {
+    var a = c.re;
+    var b = c.im;
+    return new cx(Math.sinh(a) * Math.cos(b), Math.cosh(a) * Math.sin(b));
+  }
+
+  static cosh(c) {
+    var a = c.re;
+    var b = c.im;
+    return new cx(Math.cosh(a) * Math.cos(b), Math.sinh(a) * Math.sin(b));
+  }
+
+  static tanh(c) {
+    return cx.div(cx.sinh(c), cx.cosh(c));
+  }
+
+  static asinh(c, k) {
+    if (!k) k = 0;
+    var c2 = cx.pow(c, 2);
+    return cx.log(cx.add(c, cx.root(cx.add(c2, 1), 2, k)));
+  }
+
+  static acosh(c, k) {
+    if (!k) k = 0;
+    var c2 = cx.pow(c, 2);
+    return cx.log(cx.add(c, cx.root(cx.sub(c2, 1), 2, k)));
+  }
+
+  static atanh(c) {
+    return cx.mult(cx.div(1, 2), cx.log(cx.div(cx.add(1, c), cx.sub(1, c))));
+  }
+
+  static copy(c) {
+    return new cx(c.re, c.im);
+  }
+
+  static eq(c, d, epsilon) {
+    if (!epsilon) {
+      if (c.re == d.re && c.im == d.im) return true;
+    } else {
+      if (Math.abs(c.re - d.re) < epsilon && Math.abs(c.im - d.im) < epsilon)
+        return true;
+    }
+    return false;
+  }
+}
+
+cx.degrees(true); // need to call this