Add incomplet long double math support to libmingwex.a

winsup/mingw/mingwex/math/cbrt.c

@@ -0,0 +1,162 @@
+/*							cbrt.c
+ *
+ *	Cube root
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, cbrt();
+ *
+ * y = cbrt( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the cube root of the argument, which may be negative.
+ *
+ * Range reduction involves determining the power of 2 of
+ * the argument.  A polynomial of degree 2 applied to the
+ * mantissa, and multiplication by the cube root of 1, 2, or 4
+ * approximates the root to within about 0.1%.  Then Newton's
+ * iteration is used three times to converge to an accurate
+ * result.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC        -10,10     200000      1.8e-17     6.2e-18
+ *    IEEE       0,1e308     30000      1.5e-16     5.0e-17
+ *
+ */
+/*							cbrt.c  */
+
+/*
+Cephes Math Library Release 2.2:  January, 1991
+Copyright 1984, 1991 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+/*
+  Modified for mingwex.a 
+  2002-07-01  Danny Smith  <dannysmith@users.sourceforge.net>
+ */
+#ifdef __MINGW32__
+#include <math.h>
+#include "cephes_mconf.h"
+#else
+#include "mconf.h"
+#endif
+
+
+static const double CBRT2  = 1.2599210498948731647672;
+static const double CBRT4  = 1.5874010519681994747517;
+static const double CBRT2I = 0.79370052598409973737585;
+static const double CBRT4I = 0.62996052494743658238361;
+
+#ifndef __MINGW32__
+#ifdef ANSIPROT
+extern double frexp ( double, int * );
+extern double ldexp ( double, int );
+extern int isnan ( double );
+extern int isfinite ( double );
+#else
+double frexp(), ldexp();
+int isnan(), isfinite();
+#endif
+#endif
+
+double cbrt(x)
+double x;
+{
+int e, rem, sign;
+double z;
+
+#ifdef __MINGW32__
+if (!isfinite (x) || x == 0 )
+  return x;
+#else
+
+#ifdef NANS
+if( isnan(x) )
+  return x;
+#endif
+#ifdef INFINITIES
+if( !isfinite(x) )
+  return x;
+#endif
+if( x == 0 )
+	return( x );
+
+#endif /* __MINGW32__ */
+
+if( x > 0 )
+	sign = 1;
+else
+	{
+	sign = -1;
+	x = -x;
+	}
+
+z = x;
+/* extract power of 2, leaving
+ * mantissa between 0.5 and 1
+ */
+x = frexp( x, &e );
+
+/* Approximate cube root of number between .5 and 1,
+ * peak relative error = 9.2e-6
+ */
+x = (((-1.3466110473359520655053e-1  * x
+      + 5.4664601366395524503440e-1) * x
+      - 9.5438224771509446525043e-1) * x
+      + 1.1399983354717293273738e0 ) * x
+      + 4.0238979564544752126924e-1;
+
+/* exponent divided by 3 */
+if( e >= 0 )
+	{
+	rem = e;
+	e /= 3;
+	rem -= 3*e;
+	if( rem == 1 )
+		x *= CBRT2;
+	else if( rem == 2 )
+		x *= CBRT4;
+	}
+
+
+/* argument less than 1 */
+
+else
+	{
+	e = -e;
+	rem = e;
+	e /= 3;
+	rem -= 3*e;
+	if( rem == 1 )
+		x *= CBRT2I;
+	else if( rem == 2 )
+		x *= CBRT4I;
+	e = -e;
+	}
+
+/* multiply by power of 2 */
+x = ldexp( x, e );
+
+/* Newton iteration */
+x -= ( x - (z/(x*x)) )*0.33333333333333333333;
+#ifdef DEC
+x -= ( x - (z/(x*x)) )/3.0;
+#else
+x -= ( x - (z/(x*x)) )*0.33333333333333333333;
+#endif
+
+if( sign < 0 )
+	x = -x;
+return(x);
+}