uClibc now has a math library. muahahahaha!

 -Erik

1 files changed, 324 insertions, 0 deletions

diff --git a/libm/double/asin.c b/libm/double/asin.c
new file mode 100644
index 000000000..1f83eccc8
--- /dev/null
+++ b/libm/double/asin.c
@@ -0,0 +1,324 @@
+/*							asin.c
+ *
+ *	Inverse circular sine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, asin();
+ *
+ * y = asin( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns radian angle between -pi/2 and +pi/2 whose sine is x.
+ *
+ * A rational function of the form x + x**3 P(x**2)/Q(x**2)
+ * is used for |x| in the interval [0, 0.5].  If |x| > 0.5 it is
+ * transformed by the identity
+ *
+ *    asin(x) = pi/2 - 2 asin( sqrt( (1-x)/2 ) ).
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC      -1, 1        40000       2.6e-17     7.1e-18
+ *    IEEE     -1, 1        10^6        1.9e-16     5.4e-17
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * asin domain        |x| > 1           NAN
+ *
+ */
+/*							acos()
+ *
+ *	Inverse circular cosine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, acos();
+ *
+ * y = acos( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns radian angle between 0 and pi whose cosine
+ * is x.
+ *
+ * Analytically, acos(x) = pi/2 - asin(x).  However if |x| is
+ * near 1, there is cancellation error in subtracting asin(x)
+ * from pi/2.  Hence if x < -0.5,
+ *
+ *    acos(x) =	 pi - 2.0 * asin( sqrt((1+x)/2) );
+ *
+ * or if x > +0.5,
+ *
+ *    acos(x) =	 2.0 * asin(  sqrt((1-x)/2) ).
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       -1, 1       50000       3.3e-17     8.2e-18
+ *    IEEE      -1, 1       10^6        2.2e-16     6.5e-17
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * asin domain        |x| > 1           NAN
+ */
+
+/*							asin.c	*/
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1984, 1995, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+/* arcsin(x)  =  x + x^3 P(x^2)/Q(x^2)
+   0 <= x <= 0.625
+   Peak relative error = 1.2e-18  */
+#if UNK
+static double P[6] = {
+ 4.253011369004428248960E-3,
+-6.019598008014123785661E-1,
+ 5.444622390564711410273E0,
+-1.626247967210700244449E1,
+ 1.956261983317594739197E1,
+-8.198089802484824371615E0,
+};
+static double Q[5] = {
+/* 1.000000000000000000000E0, */
+-1.474091372988853791896E1,
+ 7.049610280856842141659E1,
+-1.471791292232726029859E2,
+ 1.395105614657485689735E2,
+-4.918853881490881290097E1,
+};
+#endif
+#if DEC
+static short P[24] = {
+0036213,0056330,0057244,0053234,
+0140032,0015011,0114762,0160255,
+0040656,0035130,0136121,0067313,
+0141202,0014616,0170474,0101731,
+0041234,0100076,0151674,0111310,
+0141003,0025540,0033165,0077246,
+};
+static short Q[20] = {
+/* 0040200,0000000,0000000,0000000, */
+0141153,0155310,0055360,0072530,
+0041614,0177001,0027764,0101237,
+0142023,0026733,0064653,0133266,
+0042013,0101264,0023775,0176351,
+0141504,0140420,0050660,0036543,
+};
+#endif
+#if IBMPC
+static short P[24] = {
+0x8ad3,0x0bd4,0x6b9b,0x3f71,
+0x5c16,0x333e,0x4341,0xbfe3,
+0x2dd9,0x178a,0xc74b,0x4015,
+0x907b,0xde27,0x4331,0xc030,
+0x9259,0xda77,0x9007,0x4033,
+0xafd5,0x06ce,0x656c,0xc020,
+};
+static short Q[20] = {
+/* 0x0000,0x0000,0x0000,0x3ff0, */
+0x0eab,0x0b5e,0x7b59,0xc02d,
+0x9054,0x25fe,0x9fc0,0x4051,
+0x76d7,0x6d35,0x65bb,0xc062,
+0xbf9d,0x84ff,0x7056,0x4061,
+0x07ac,0x0a36,0x9822,0xc048,
+};
+#endif
+#if MIEEE
+static short P[24] = {
+0x3f71,0x6b9b,0x0bd4,0x8ad3,
+0xbfe3,0x4341,0x333e,0x5c16,
+0x4015,0xc74b,0x178a,0x2dd9,
+0xc030,0x4331,0xde27,0x907b,
+0x4033,0x9007,0xda77,0x9259,
+0xc020,0x656c,0x06ce,0xafd5,
+};
+static short Q[20] = {
+/* 0x3ff0,0x0000,0x0000,0x0000, */
+0xc02d,0x7b59,0x0b5e,0x0eab,
+0x4051,0x9fc0,0x25fe,0x9054,
+0xc062,0x65bb,0x6d35,0x76d7,
+0x4061,0x7056,0x84ff,0xbf9d,
+0xc048,0x9822,0x0a36,0x07ac,
+};
+#endif
+
+/* arcsin(1-x) = pi/2 - sqrt(2x)(1+R(x))
+   0 <= x <= 0.5
+   Peak relative error = 4.2e-18  */
+#if UNK
+static double R[5] = {
+ 2.967721961301243206100E-3,
+-5.634242780008963776856E-1,
+ 6.968710824104713396794E0,
+-2.556901049652824852289E1,
+ 2.853665548261061424989E1,
+};
+static double S[4] = {
+/* 1.000000000000000000000E0, */
+-2.194779531642920639778E1,
+ 1.470656354026814941758E2,
+-3.838770957603691357202E2,
+ 3.424398657913078477438E2,
+};
+#endif
+#if DEC
+static short R[20] = {
+0036102,0077034,0142164,0174103,
+0140020,0036222,0147711,0044173,
+0040736,0177655,0153631,0171523,
+0141314,0106525,0060015,0055474,
+0041344,0045422,0003630,0040344,
+};
+static short S[16] = {
+/* 0040200,0000000,0000000,0000000, */
+0141257,0112425,0132772,0166136,
+0042023,0010315,0075523,0175020,
+0142277,0170104,0126203,0017563,
+0042253,0034115,0102662,0022757,
+};
+#endif
+#if IBMPC
+static short R[20] = {
+0x9f08,0x988e,0x4fc3,0x3f68,
+0x290f,0x59f9,0x0792,0xbfe2,
+0x3e6a,0xbaf3,0xdff5,0x401b,
+0xab68,0xac01,0x91aa,0xc039,
+0x081d,0x40f3,0x8962,0x403c,
+};
+static short S[16] = {
+/* 0x0000,0x0000,0x0000,0x3ff0, */
+0x5d8c,0xb6bf,0xf2a2,0xc035,
+0x7f42,0xaf6a,0x6219,0x4062,
+0x63ee,0x9590,0xfe08,0xc077,
+0x44be,0xb0b6,0x6709,0x4075,
+};
+#endif
+#if MIEEE
+static short R[20] = {
+0x3f68,0x4fc3,0x988e,0x9f08,
+0xbfe2,0x0792,0x59f9,0x290f,
+0x401b,0xdff5,0xbaf3,0x3e6a,
+0xc039,0x91aa,0xac01,0xab68,
+0x403c,0x8962,0x40f3,0x081d,
+};
+static short S[16] = {
+/* 0x3ff0,0x0000,0x0000,0x0000, */
+0xc035,0xf2a2,0xb6bf,0x5d8c,
+0x4062,0x6219,0xaf6a,0x7f42,
+0xc077,0xfe08,0x9590,0x63ee,
+0x4075,0x6709,0xb0b6,0x44be,
+};
+#endif
+
+/* pi/2 = PIO2 + MOREBITS.  */
+#ifdef DEC
+#define MOREBITS 5.721188726109831840122E-18
+#else
+#define MOREBITS 6.123233995736765886130E-17
+#endif
+
+#ifdef ANSIPROT
+extern double polevl ( double, void *, int );
+extern double p1evl ( double, void *, int );
+extern double sqrt ( double );
+double asin ( double );
+#else
+double sqrt(), polevl(), p1evl();
+double asin();
+#endif
+extern double PIO2, PIO4, NAN;
+
+double asin(x)
+double x;
+{
+double a, p, z, zz;
+short sign;
+
+if( x > 0 )
+	{
+	sign = 1;
+	a = x;
+	}
+else
+	{
+	sign = -1;
+	a = -x;
+	}
+
+if( a > 1.0 )
+	{
+	mtherr( "asin", DOMAIN );
+	return( NAN );
+	}
+
+if( a > 0.625 )
+	{
+	/* arcsin(1-x) = pi/2 - sqrt(2x)(1+R(x))  */
+	zz = 1.0 - a;
+	p = zz * polevl( zz, R, 4)/p1evl( zz, S, 4);
+	zz = sqrt(zz+zz);
+	z = PIO4 - zz;
+	zz = zz * p - MOREBITS;
+	z = z - zz;
+	z = z + PIO4;
+	}
+else
+	{
+	if( a < 1.0e-8 )
+		{
+		return(x);
+		}
+	zz = a * a;
+	z = zz * polevl( zz, P, 5)/p1evl( zz, Q, 5);
+	z = a * z + a;
+	}
+if( sign < 0 )
+	z = -z;
+return(z);
+}
+
+
+
+double acos(x)
+double x;
+{
+double z;
+
+if( (x < -1.0) || (x > 1.0) )
+	{
+	mtherr( "acos", DOMAIN );
+	return( NAN );
+	}
+if( x > 0.5 )
+	{
+	return( 2.0 * asin(  sqrt(0.5 - 0.5*x) ) );
+	}
+z = PIO4 - asin(x);
+z = z + MOREBITS;
+z = z + PIO4;
+return( z );
+}