newlib: update

git-svn-id: svn://kolibrios.org@1906 a494cfbc-eb01-0410-851d-a64ba20cac60
2011-03-11 18:52:24 +00:00
parent a316fa7c9d
commit 2336060a0c
297 changed files with 26930 additions and 2094 deletions
@@ -0,0 +1,161 @@
+/*							cbrtl.c
+ *
+ *	Cube root, long double precision
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, cbrtl();
+ *
+ * y = cbrtl( 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
+ *    IEEE     .125,8        80000      7.0e-20     2.2e-20
+ *    IEEE    exp(+-707)    100000      7.0e-20     2.4e-20
+ *
+ */
+
+
+/*
+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 "cephes_mconf.h"
+#else
+#include "mconf.h"
+#endif
+
+static const long double CBRT2  = 1.2599210498948731647672L;
+static const long double CBRT4  = 1.5874010519681994747517L;
+static const long double CBRT2I = 0.79370052598409973737585L;
+static const long double CBRT4I = 0.62996052494743658238361L;
+
+#ifndef __MINGW32__
+
+#ifdef ANSIPROT
+extern long double frexpl ( long double, int * );
+extern long double ldexpl ( long double, int );
+extern int isnanl ( long double );
+#else
+long double frexpl(), ldexpl();
+extern int isnanl();
+#endif
+
+#ifdef INFINITIES
+extern long double INFINITYL;
+#endif
+
+#endif /* __MINGW32__ */
+
+long double cbrtl(x)
+long double x;
+{
+int e, rem, sign;
+long double z;
+
+#ifdef __MINGW32__
+if (!isfinite (x) || x == 0.0L)
+	return(x);
+#else     
+
+#ifdef NANS
+if(isnanl(x))
+	return(x);
+#endif
+#ifdef INFINITIES
+if( x == INFINITYL)
+	return(x);
+if( x == -INFINITYL)
+	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 = frexpl( x, &e );
+
+/* Approximate cube root of number between .5 and 1,
+ * peak relative error = 1.2e-6
+ */
+x = (((( 1.3584464340920900529734e-1L * x
+       - 6.3986917220457538402318e-1L) * x
+       + 1.2875551670318751538055e0L) * x
+       - 1.4897083391357284957891e0L) * x
+       + 1.3304961236013647092521e0L) * x
+       + 3.7568280825958912391243e-1L;
+
+/* 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;
+	}
+else
+	{ /* argument less than 1 */
+	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 = ldexpl( x, e );
+
+/* Newton iteration */
+
+x -= ( x - (z/(x*x)) )*0.3333333333333333333333L;
+x -= ( x - (z/(x*x)) )*0.3333333333333333333333L;
+
+if( sign < 0 )
+	x = -x;
+return(x);
+}