Merge remote-tracking branch 'origin/develop' into develop

HISTORY.md

@@ -1,5 +1,11 @@
 # History
 
+## not yet released, version 3.12.1
+
+- Fixed #804
+  - Improved handling of powers of `Infinity`. Thanks @HarrySarson.
+  - Fixed wrong formatting of complex NaN.
+
 
 ## 2017-04-17, version 3.12.1
 

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);
     }

lib/type/complex/Complex.js

@@ -78,18 +78,18 @@ function factory (type, config, load, typed, math) {
       }
     } else {
       // complex value
-      if (im > 0) {
+      if (im < 0) {
+        if (im == -1) {
+          str = strRe + ' - i';
+        } else {
+          str = strRe + ' - ' + (/[\d-.]/.test(strIm.charAt(0)) ? strIm.substring(1) : strIm) + 'i';
+        }
+      } else {
         if (im == 1) {
           str = strRe + ' + i';
         } else {
           str = strRe + ' + ' + strIm + 'i';
         }
-      } else {
-        if (im == -1) {
-          str = strRe + ' - i';
-        } else {
-          str = strRe + ' - ' + strIm.substring(1) + 'i';
-        }
       }
     }
     return str;

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));

test/function/string/format.test.js

@@ -27,6 +27,10 @@ describe('format', function() {
     assert.equal(math.format(math.divide(math.complex(2,5),3), 5), '0.66667 + 1.6667i');
     assert.equal(math.format(math.divide(math.complex(2,5),3), {notation: 'fixed'}), '1 + 2i');
     assert.equal(math.format(math.divide(math.complex(2,5),3), {notation: 'fixed', precision: 1}), '0.7 + 1.7i');
+
+    assert.equal(math.format(math.complex(NaN , NaN)), 'NaN + NaNi');
+    assert.equal(math.format(math.complex(Infinity, Infinity)), 'Infinity + Infinityi');
+    assert.equal(math.format(math.complex(Infinity, -Infinity)), 'Infinity - Infinityi');
   });
 
   describe('precision', function() {