From a5692e1d0a176dc2320b2b030accad86091e286e Mon Sep 17 00:00:00 2001
From: Harry Sarson <harry.sarson@hotmail.co.uk>
Date: Sun, 23 Apr 2017 13:13:23 +0100
Subject: [PATCH] Extension of pow function to support Infinite exponents.

---
 lib/function/arithmetic/pow.js       | 17 +++++++++++++++++
 test/function/arithmetic/pow.test.js | 25 +++++++++++++++++++++++++
 2 files changed, 42 insertions(+)

diff --git a/lib/function/arithmetic/pow.js b/lib/function/arithmetic/pow.js
index 9ed92827d..47553248c 100644
--- a/lib/function/arithmetic/pow.js
+++ b/lib/function/arithmetic/pow.js
@@ -120,6 +120,23 @@ function factory (type, config, load, typed) {
       // Unable to express y as a fraction, so continue on
     }
 
+
+    // x^Infinity === 0 if -1 < x < 1
+    // A real number 0 is returned instead of complex(0)
+    if ((x*x < 1 && y ===  Infinity) ||
+        (x*x > 1 && y === -Infinity)) {
+      return 0;
+    }
+
+    // **for predictable mode** x^Infinity === NaN if x < -1
+    // N.B. this behavour is different from `Math.pow` which gives
+    // (-2)^Infinity === Infinity
+    if (config.predictable &&
+        ((x < -1 &&          y ===  Infinity) ||
+         (x > -1 && x < 0 && y === -Infinity))) {
+      return NaN;
+    }
+
     if (isInteger(y) || x >= 0 || config.predictable) {
       return Math.pow(x, y);
     }
diff --git a/test/function/arithmetic/pow.test.js b/test/function/arithmetic/pow.test.js
index 10897da97..267f1842c 100644
--- a/test/function/arithmetic/pow.test.js
+++ b/test/function/arithmetic/pow.test.js
@@ -131,6 +131,31 @@ describe('pow', function() {
     assert.throws(function () {pow(1, 2, 3)}, /TypeError: Too many arguments in function pow \(expected: 2, actual: 3\)/);
   });
 
+  it('should handle infitie exponents', function() {
+    var Ptbl = mathPredictable;
+
+     // TODO replace isNaN with complexInfinity when complex.js updates
+
+
+    assert.equal(math.pow( 3,  Infinity), Infinity);
+    assert.equal(math.pow( 3, -Infinity), 0);
+    assert(isNaN(Ptbl.pow(-3,  Infinity)));
+    assert(      math.pow(-3,  Infinity).isNaN());
+    assert.equal(math.pow(-3, -Infinity), 0);
+
+    assert.equal(math.pow( 0.3,  Infinity), 0);
+    assert.equal(math.pow( 0.3, -Infinity), Infinity);
+    assert.equal(math.pow(-0.3,  Infinity), 0);
+    assert(isNaN(Ptbl.pow(-0.3, -Infinity)));
+    assert(      math.pow(-0.3, -Infinity).isNaN());
+
+    assert.equal(math.pow( Infinity,  Infinity), Infinity);
+    assert.equal(math.pow( Infinity, -Infinity), 0); // https://www.wolframalpha.com/input/?i=infinity%5E(-infinity)
+    assert(isNaN(Ptbl.pow(-Infinity,  Infinity)));
+    assert(      math.pow(-Infinity,  Infinity).isNaN());
+    assert.equal(math.pow(-Infinity, -Infinity), 0);
+  });
+
   it('should exponentiate a complex number to the given power', function() {
     approx.deepEqual(pow(complex(3, 0), 2), complex(9, 0));
     approx.deepEqual(pow(complex(0, 2), 2), complex(-4, 0));