Modifies exp() and pow() and specs behaviour of z^inf and inf^z.

Previous behaviour was inconsistant and was not tested for. This
commit ensures that z^inf and inf^z return reasonable and consistant
values.

See rawify#24 for the dicussion on the behaviour which can be summaried as:

    z ^ Infinity === NaN
    Infinity ^ z === Infinity if Im(z) === 0 and Re(z) > 0
    Infinity ^ z === 0 if Re(z) < 0
    Infinity ^ 0 === 1
    Infinity ^ z === NaN otherwise

Author: harrysarson

complex.js

@@ -456,6 +456,18 @@
         return Complex['ONE'];
       }
 
+      if (!z.isFinite()) {
+        return Complex['NAN'];
+      }
+
+      if (!this.isFinite()) {
+        return z['re'] < 0
+          ? Complex['ZERO']
+          : z['im'] === 0 && z['re'] > 0 // should we epsilon ball here
+            ? Complex['INFINITY']
+            : Complex['NAN'];
+      }
+
       // If the exponent is real
       if (z['im'] === 0) {
 
@@ -549,9 +561,10 @@
 
       const tmp = Math.exp(this['re']);
 
-      if (this['im'] === 0) {
-        //return new Complex(tmp, 0);
+      if (!this.isFinite()) {
+        return Complex['NAN'];
       }
+
       return new Complex(
               tmp * Math.cos(this['im']),
               tmp * Math.sin(this['im']));
@@ -573,6 +586,10 @@
        = expm1(a)*cos(b) + cosm1(b) + j*exp(a)*sin(b)
        */
 
+      if (!this.isFinite()) {
+        return Complex['NAN'];
+      }
+
       const a = this['re'];
       const b = this['im'];
 

tests/complex.test.js

@@ -193,6 +193,14 @@ var functionTests = [{
     set: "3 + 2i",
     fn: "exp",
     expect: "-8.358532650935372 + 18.263727040666765i"
+  }, {
+    set: Infinity,
+    fn: "exp",
+    expect: "NaN"
+  }, {
+    set: Infinity,
+    fn: "expm1",
+    expect: "NaN"
   }, {
     set: "3 - 2i",
     fn: "exp",
@@ -403,8 +411,58 @@ var functionTests = [{
   }, {
     set: "0-0i",
     fn: "pow",
+    param: Infinity,
+    expect: "NaN"
+  }, {
+    set: "-1",
+    fn: "pow",
+    param: Infinity,
+    expect: "NaN"
+  }, {
+    set: "1",
+    fn: "pow",
+    param: Infinity,
+    expect: "NaN"
+  }, {
+    set: "4 - 7i",
+    fn: "pow",
+    param: Infinity,
+    expect: "NaN"
+  }, {
+    set: "-5.9 + 8i",
+    fn: "pow",
+    param: Infinity,
+    expect: "NaN"
+  }, {
+    set: Infinity,
+    fn: "pow",
     param: 0,
     expect: "1"
+  }, {
+    set: Infinity,
+    fn: "pow",
+    param: -1,
+    expect: "0"
+  }, {
+    set: Infinity,
+    fn: "pow",
+    param: 1,
+    expect: "Infinity"
+  }, {
+    set: Infinity,
+    fn: "pow",
+    param: "-1.9 + 7i",
+    expect: "0"
+  }, {
+    set: Infinity,
+    fn: "pow",
+    param: "0.3",
+    expect: "Infinity"
+  }, {
+    set: Infinity,
+    fn: "pow",
+    param: "88",
+    expect: "Infinity"
   }, {
     set: "1 + 4i",
     fn: "sqrt",