From 2ef53ce0691e14b4f836032a4fc133ecddde700f Mon Sep 17 00:00:00 2001
From: Pavel Panchekha <me@pavpanchekha.com>
Date: Mon, 11 Aug 2014 17:30:23 -0700
Subject: [PATCH] Changed calculation of math.sqrt to avoid numerical problems
 when re < 0

---
 lib/function/arithmetic/sqrt.js | 29 ++++++++++++++++++++---------
 1 file changed, 20 insertions(+), 9 deletions(-)

diff --git a/lib/function/arithmetic/sqrt.js b/lib/function/arithmetic/sqrt.js
index 0e65fd92b..0035eb987 100644
--- a/lib/function/arithmetic/sqrt.js
+++ b/lib/function/arithmetic/sqrt.js
@@ -52,17 +52,28 @@ module.exports = function (math) {
 
     if (isComplex(x)) {
       var r = Math.sqrt(x.re * x.re + x.im * x.im);
-      if (x.im >= 0) {
-        return new Complex(
-            0.5 * Math.sqrt(2.0 * (r + x.re)),
-            0.5 * Math.sqrt(2.0 * (r - x.re))
-        );
+
+      var re, im;
+
+      if (x.re >= 0) {
+        re = 0.5 * Math.sqrt(2.0 * (r + x.re));
       }
       else {
-        return new Complex(
-            0.5 * Math.sqrt(2.0 * (r + x.re)),
-            -0.5 * Math.sqrt(2.0 * (r - x.re))
-        );
+        re = Math.abs(x.im) / Math.sqrt(2 * (r - x.re));
+      }
+
+      if (x.re <= 0) {
+        im = 0.5 * Math.sqrt(2.0 * (r - x.re));
+      }
+      else {
+        im = Math.abs(x.im) / Math.sqrt(2 * (r + x.re));
+      }
+
+      if (x.im >= 0) {
+        return new Complex(re, im);
+      }
+      else {
+        return new Complex(re, -im);
       }
     }