1 files changed, 129 insertions, 0 deletions
diff --git a/libm/float/log2f.c b/libm/float/log2f.c
new file mode 100644
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+/*							log2f.c
+ *
+ *	Base 2 logarithm
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, log2f();
+ *
+ * y = log2f( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the base 2 logarithm of x.
+ *
+ * The argument is separated into its exponent and fractional
+ * parts.  If the exponent is between -1 and +1, the base e
+ * logarithm of the fraction is approximated by
+ *
+ *     log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x).
+ *
+ * Otherwise, setting  z = 2(x-1)/x+1),
+ * 
+ *     log(x) = z + z**3 P(z)/Q(z).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      exp(+-88)   100000      1.1e-7      2.4e-8
+ *    IEEE      0.5, 2.0    100000      1.1e-7      3.0e-8
+ *
+ * In the tests over the interval [exp(+-88)], the logarithms
+ * of the random arguments were uniformly distributed.
+ *
+ * ERROR MESSAGES:
+ *
+ * log singularity:  x = 0; returns MINLOGF/log(2)
+ * log domain:       x < 0; returns MINLOGF/log(2)
+ */
+
+/*
+Cephes Math Library Release 2.2:  June, 1992
+Copyright 1984, 1992 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include <math.h>
+static char fname[] = {"log2"};
+
+/* Coefficients for log(1+x) = x - x**2/2 + x**3 P(x)
+ * 1/sqrt(2) <= x < sqrt(2)
+ */
+
+static float P[] = {
+ 7.0376836292E-2,
+-1.1514610310E-1,
+ 1.1676998740E-1,
+-1.2420140846E-1,
+ 1.4249322787E-1,
+-1.6668057665E-1,
+ 2.0000714765E-1,
+-2.4999993993E-1,
+ 3.3333331174E-1
+};
+
+#define LOG2EA 0.44269504088896340735992
+#define SQRTH 0.70710678118654752440
+extern float MINLOGF, LOGE2F;
+
+float frexpf(float, int *), polevlf(float, float *, int);
+
+float log2f(float xx)
+{
+float x, y, z;
+int e;
+
+x = xx;
+/* Test for domain */
+if( x <= 0.0 )
+	{
+	if( x == 0.0 )
+		mtherr( fname, SING );
+	else
+		mtherr( fname, DOMAIN );
+	return( MINLOGF/LOGE2F );
+	}
+
+/* separate mantissa from exponent */
+x = frexpf( x, &e );
+
+
+/* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */
+
+if( x < SQRTH )
+	{
+	e -= 1;
+	x = 2.0*x - 1.0;
+	}	
+else
+	{
+	x = x - 1.0;
+	}
+
+z = x*x;
+y = x * ( z * polevlf( x, P, 8 ) );
+y = y - 0.5 * z;   /*  y - 0.5 * x**2  */
+
+
+/* Multiply log of fraction by log2(e)
+ * and base 2 exponent by 1
+ *
+ * ***CAUTION***
+ *
+ * This sequence of operations is critical and it may
+ * be horribly defeated by some compiler optimizers.
+ */
+z = y * LOG2EA;
+z += x * LOG2EA;
+z += y;
+z += x;
+z += (float )e;
+return( z );
+}