* Add Scilab square root algorithm.

* Need some further testing

1 files changed, 89 insertions, 2 deletions

diff --git a/src/elementaryFunctions/sqrt/csqrts.c b/src/elementaryFunctions/sqrt/csqrts.c
index f39b67f5..da7000e8 100644
--- a/src/elementaryFunctions/sqrt/csqrts.c
+++ b/src/elementaryFunctions/sqrt/csqrts.c
@@ -10,9 +10,96 @@
  *
  */
 
+#include <math.h>
 #include "sqrt.h"
+#include "lapack.h"
+#include "abs.h"
+#include "sign.h"
+#include "pythag.h"
+
+#define _sign(a, b) b >=0 ? a : -a
 
 floatComplex	csqrts(floatComplex in) {
-  /* FIXME : Dummy ... */
-  return in;
+  float RMax =  (float) getOverflowThreshold();
+  float BRMin = 2.0f * (float) getUnderflowThreshold();
+
+  float RealIn = creals(in);
+  float ImgIn = cimags(in);
+
+  float RealOut = 0;
+  float ImgOut = 0;
+
+  if(RealIn == 0)
+    {/* pure imaginary case */
+      if(dabss(ImgIn >= BRMin))
+	RealOut = ssqrts(0.5f * sabss(ImgIn));
+      else
+	RealOut = ssqrts(sabss(ImgIn)) * ssqrts(0.5);
+
+      ImgOut = _sign(1, ImgIn) * RealOut;
+    }
+  else if( sabss(RealIn) <= RMax && sabss(ImgIn) <= RMax)
+    {/* standard case : a (not zero) and b are finite */
+      float Temp = ssqrts(2.0f * (sabss(RealIn) + spythags(RealIn, ImgIn)));
+      /* overflow test */
+      if(Temp > RMax)
+	{/*     handle (spurious) overflow by scaling a and b */
+	  float RealTemp = RealIn / 16.0f;
+	  float ImgTemp = ImgIn / 16.0f;
+	  Temp = ssqrts(2.0f * (sabss(RealIn) + spythags(RealIn, ImgTemp)));
+	  if(RealTemp >= 0)
+	    {
+	      RealOut	= 2 * Temp;
+	      ImgOut	= 4 * ImgTemp / Temp;
+	    }
+	  else
+	    {
+	      RealOut	= 4 * sabss(ImgIn) / Temp;
+	      ImgOut	= _sign(2, ImgIn) * Temp;
+	    }
+	}
+      else if(RealIn >= 0) /* classic switch to get the stable formulas */
+	{
+	  RealOut	= 0.5f * Temp;
+	  ImgOut	= ImgIn / Temp;
+	}
+      else
+	{
+	  RealOut	= sabss(ImgIn) / Temp;
+	  ImgOut	= _sign(0.5f, ImgIn) * Temp;
+	}
+    }
+  else
+    {
+      /*
+      //Here we treat the special cases where a and b are +- 00 or NaN.
+      //The following is the treatment recommended by the C99 standard
+      //with the simplification of returning NaN + i NaN if the
+      //the real part or the imaginary part is NaN (C99 recommends
+      //something more complicated)
+      */
+
+      if(isnan(RealIn) == 1 || isnan(ImgIn) == 1)
+	{/* got NaN + i NaN */
+	  RealOut	= RealIn + ImgIn;
+	  ImgOut	= RealOut;
+	}
+      else if( dabss(ImgIn) > RMax)
+	{/* case a +- i oo -> result must be +oo +- i oo  for all a (finite or not) */
+	  RealOut	= sabss(ImgIn);
+	  ImgOut	= ImgIn;
+	}
+      else if(RealIn < -RMax)
+	{/* here a is -Inf and b is finite */
+	  RealOut	= 0;
+	  ImgOut	= _sign(1, ImgIn) * sabss(RealIn);
+	}
+      else
+	{/* here a is +Inf and b is finite */
+	  RealOut	= RealIn;
+	  ImgOut	= 0;
+	}
+    }
+
+  return FloatComplex(RealOut, ImgOut);
 }