uClibc now has a math library. muahahahaha!

 -Erik

1 files changed, 228 insertions, 0 deletions

diff --git a/libm/float/j0f.c b/libm/float/j0f.c
new file mode 100644
index 000000000..2b0d4a5a4
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+++ b/libm/float/j0f.c
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+/*							j0f.c
+ *
+ *	Bessel function of order zero
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, j0f();
+ *
+ * y = j0f( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of order zero of the argument.
+ *
+ * The domain is divided into the intervals [0, 2] and
+ * (2, infinity). In the first interval the following polynomial
+ * approximation is used:
+ *
+ *
+ *        2         2         2
+ * (w - r  ) (w - r  ) (w - r  ) P(w)
+ *       1         2         3   
+ *
+ *            2
+ * where w = x  and the three r's are zeros of the function.
+ *
+ * In the second interval, the modulus and phase are approximated
+ * by polynomials of the form Modulus(x) = sqrt(1/x) Q(1/x)
+ * and Phase(x) = x + 1/x R(1/x^2) - pi/4.  The function is
+ *
+ *   j0(x) = Modulus(x) cos( Phase(x) ).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Absolute error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      0, 2        100000      1.3e-7      3.6e-8
+ *    IEEE      2, 32       100000      1.9e-7      5.4e-8
+ *
+ */
+/*							y0f.c
+ *
+ *	Bessel function of the second kind, order zero
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, y0f();
+ *
+ * y = y0f( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of the second kind, of order
+ * zero, of the argument.
+ *
+ * The domain is divided into the intervals [0, 2] and
+ * (2, infinity). In the first interval a rational approximation
+ * R(x) is employed to compute
+ *
+ *                  2         2         2
+ * y0(x)  =  (w - r  ) (w - r  ) (w - r  ) R(x)  +  2/pi ln(x) j0(x).
+ *                 1         2         3   
+ *
+ * Thus a call to j0() is required.  The three zeros are removed
+ * from R(x) to improve its numerical stability.
+ *
+ * In the second interval, the modulus and phase are approximated
+ * by polynomials of the form Modulus(x) = sqrt(1/x) Q(1/x)
+ * and Phase(x) = x + 1/x S(1/x^2) - pi/4.  Then the function is
+ *
+ *   y0(x) = Modulus(x) sin( Phase(x) ).
+ *
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *  Absolute error, when y0(x) < 1; else relative error:
+ *
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      0,  2       100000      2.4e-7      3.4e-8
+ *    IEEE      2, 32       100000      1.8e-7      5.3e-8
+ *
+ */
+
+/*
+Cephes Math Library Release 2.2:  June, 1992
+Copyright 1984, 1987, 1989, 1992 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+
+#include <math.h>
+
+static float MO[8] = {
+-6.838999669318810E-002f,
+ 1.864949361379502E-001f,
+-2.145007480346739E-001f,
+ 1.197549369473540E-001f,
+-3.560281861530129E-003f,
+-4.969382655296620E-002f,
+-3.355424622293709E-006f,
+ 7.978845717621440E-001f
+};
+
+static float PH[8] = {
+ 3.242077816988247E+001f,
+-3.630592630518434E+001f,
+ 1.756221482109099E+001f,
+-4.974978466280903E+000f,
+ 1.001973420681837E+000f,
+-1.939906941791308E-001f,
+ 6.490598792654666E-002f,
+-1.249992184872738E-001f
+};
+
+static float YP[5] = {
+ 9.454583683980369E-008f,
+-9.413212653797057E-006f,
+ 5.344486707214273E-004f,
+-1.584289289821316E-002f,
+ 1.707584643733568E-001f
+};
+
+float YZ1 =  0.43221455686510834878f;
+float YZ2 = 22.401876406482861405f;
+float YZ3 = 64.130620282338755553f;
+
+static float DR1 =  5.78318596294678452118f;
+/*
+static float DR2 = 30.4712623436620863991;
+static float DR3 = 74.887006790695183444889;
+*/
+
+static float JP[5] = {
+-6.068350350393235E-008f,
+ 6.388945720783375E-006f,
+-3.969646342510940E-004f,
+ 1.332913422519003E-002f,
+-1.729150680240724E-001f
+};
+extern float PIO4F;
+
+
+float polevlf(float, float *, int);
+float logf(float), sinf(float), cosf(float), sqrtf(float);
+
+float j0f( float xx )
+{
+float x, w, z, p, q, xn;
+
+
+if( xx < 0 )
+	x = -xx;
+else
+	x = xx;
+
+if( x <= 2.0f )
+	{
+	z = x * x;
+	if( x < 1.0e-3f )
+		return( 1.0f - 0.25f*z );
+
+	p = (z-DR1) * polevlf( z, JP, 4);
+	return( p );
+	}
+
+q = 1.0f/x;
+w = sqrtf(q);
+
+p = w * polevlf( q, MO, 7);
+w = q*q;
+xn = q * polevlf( w, PH, 7) - PIO4F;
+p = p * cosf(xn + x);
+return(p);
+}
+
+/*							y0() 2	*/
+/* Bessel function of second kind, order zero	*/
+
+/* Rational approximation coefficients YP[] are used for x < 6.5.
+ * The function computed is  y0(x)  -  2 ln(x) j0(x) / pi,
+ * whose value at x = 0 is  2 * ( log(0.5) + EUL ) / pi
+ * = 0.073804295108687225 , EUL is Euler's constant.
+ */
+
+static float TWOOPI =  0.636619772367581343075535f; /* 2/pi */
+extern float MAXNUMF;
+
+float y0f( float xx )
+{
+float x, w, z, p, q, xn;
+
+
+x = xx;
+if( x <= 2.0f )
+	{
+	if( x <= 0.0f )
+		{
+		mtherr( "y0f", DOMAIN );
+		return( -MAXNUMF );
+		}
+	z = x * x;
+/*	w = (z-YZ1)*(z-YZ2)*(z-YZ3) * polevlf( z, YP, 4);*/
+	w = (z-YZ1) * polevlf( z, YP, 4);
+	w += TWOOPI * logf(x) * j0f(x);
+	return( w );
+	}
+
+q = 1.0f/x;
+w = sqrtf(q);
+
+p = w * polevlf( q, MO, 7);
+w = q*q;
+xn = q * polevlf( w, PH, 7) - PIO4F;
+p = p * sinf(xn + x);
+return( p );
+}