uClibc now has a math library. muahahahaha!

 -Erik

1 files changed, 292 insertions, 0 deletions

diff --git a/libm/ldouble/logl.c b/libm/ldouble/logl.c
new file mode 100644
index 000000000..d6367eb19
--- /dev/null
+++ b/libm/ldouble/logl.c
@@ -0,0 +1,292 @@
+/*							logl.c
+ *
+ *	Natural logarithm, long double precision
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, logl();
+ *
+ * y = logl( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the base e (2.718...) logarithm of x.
+ *
+ * The argument is separated into its exponent and fractional
+ * parts.  If the exponent is between -1 and +1, the 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      0.5, 2.0    150000      8.71e-20    2.75e-20
+ *    IEEE     exp(+-10000) 100000      5.39e-20    2.34e-20
+ *
+ * In the tests over the interval exp(+-10000), the logarithms
+ * of the random arguments were uniformly distributed over
+ * [-10000, +10000].
+ *
+ * ERROR MESSAGES:
+ *
+ * log singularity:  x = 0; returns -INFINITYL
+ * log domain:       x < 0; returns NANL
+ */
+
+/*
+Cephes Math Library Release 2.7:  May, 1998
+Copyright 1984, 1990, 1998 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+/* Coefficients for log(1+x) = x - x**2/2 + x**3 P(x)/Q(x)
+ * 1/sqrt(2) <= x < sqrt(2)
+ * Theoretical peak relative error = 2.32e-20
+ */
+#ifdef UNK
+static long double P[] = {
+ 4.5270000862445199635215E-5L,
+ 4.9854102823193375972212E-1L,
+ 6.5787325942061044846969E0L,
+ 2.9911919328553073277375E1L,
+ 6.0949667980987787057556E1L,
+ 5.7112963590585538103336E1L,
+ 2.0039553499201281259648E1L,
+};
+static long double Q[] = {
+/* 1.0000000000000000000000E0,*/
+ 1.5062909083469192043167E1L,
+ 8.3047565967967209469434E1L,
+ 2.2176239823732856465394E2L,
+ 3.0909872225312059774938E2L,
+ 2.1642788614495947685003E2L,
+ 6.0118660497603843919306E1L,
+};
+#endif
+
+#ifdef IBMPC
+static short P[] = {
+0x51b9,0x9cae,0x4b15,0xbde0,0x3ff0, XPD
+0x19cf,0xf0d4,0xc507,0xff40,0x3ffd, XPD
+0x9942,0xa7d2,0xfa37,0xd284,0x4001, XPD
+0x4add,0x65ce,0x9c5c,0xef4b,0x4003, XPD
+0x8445,0x619a,0x75c3,0xf3cc,0x4004, XPD
+0x81ab,0x3cd0,0xacba,0xe473,0x4004, XPD
+0x4cbf,0xcc18,0x016c,0xa051,0x4003, XPD
+};
+static short Q[] = {
+/*0x0000,0x0000,0x0000,0x8000,0x3fff,*/
+0xb8b7,0x81f1,0xacf4,0xf101,0x4002, XPD
+0xbc31,0x09a4,0x5a91,0xa618,0x4005, XPD
+0xaeec,0xe7da,0x2c87,0xddc3,0x4006, XPD
+0x2bde,0x4845,0xa2ee,0x9a8c,0x4007, XPD
+0x3120,0x4703,0x89f2,0xd86d,0x4006, XPD
+0x7347,0x3224,0x8223,0xf079,0x4004, XPD
+};
+#endif
+
+#ifdef MIEEE
+static long P[] = {
+0x3ff00000,0xbde04b15,0x9cae51b9,
+0x3ffd0000,0xff40c507,0xf0d419cf,
+0x40010000,0xd284fa37,0xa7d29942,
+0x40030000,0xef4b9c5c,0x65ce4add,
+0x40040000,0xf3cc75c3,0x619a8445,
+0x40040000,0xe473acba,0x3cd081ab,
+0x40030000,0xa051016c,0xcc184cbf,
+};
+static long Q[] = {
+/*0x3fff0000,0x80000000,0x00000000,*/
+0x40020000,0xf101acf4,0x81f1b8b7,
+0x40050000,0xa6185a91,0x09a4bc31,
+0x40060000,0xddc32c87,0xe7daaeec,
+0x40070000,0x9a8ca2ee,0x48452bde,
+0x40060000,0xd86d89f2,0x47033120,
+0x40040000,0xf0798223,0x32247347,
+};
+#endif
+
+/* Coefficients for log(x) = z + z^3 P(z^2)/Q(z^2),
+ * where z = 2(x-1)/(x+1)
+ * 1/sqrt(2) <= x < sqrt(2)
+ * Theoretical peak relative error = 6.16e-22
+ */
+
+#ifdef UNK
+static long double R[4] = {
+ 1.9757429581415468984296E-3L,
+-7.1990767473014147232598E-1L,
+ 1.0777257190312272158094E1L,
+-3.5717684488096787370998E1L,
+};
+static long double S[4] = {
+/* 1.00000000000000000000E0L,*/
+-2.6201045551331104417768E1L,
+ 1.9361891836232102174846E2L,
+-4.2861221385716144629696E2L,
+};
+static long double C1 = 6.9314575195312500000000E-1L;
+static long double C2 = 1.4286068203094172321215E-6L;
+#endif
+#ifdef IBMPC
+static short R[] = {
+0x6ef4,0xf922,0x7763,0x817b,0x3ff6, XPD
+0x15fd,0x1af9,0xde8f,0xb84b,0xbffe, XPD
+0x8b96,0x4f8d,0xa53c,0xac6f,0x4002, XPD
+0x8932,0xb4e3,0xe8ae,0x8ede,0xc004, XPD
+};
+static short S[] = {
+/*0x0000,0x0000,0x0000,0x8000,0x3fff,*/
+0x7ce4,0x1fc9,0xbdc5,0xd19b,0xc003, XPD
+0x0af3,0x0d10,0x716f,0xc19e,0x4006, XPD
+0x4d7d,0x0f55,0x5d06,0xd64e,0xc007, XPD
+};
+static short sc1[] = {0x0000,0x0000,0x0000,0xb172,0x3ffe, XPD};
+#define C1 (*(long double *)sc1)
+static short sc2[] = {0x4f1e,0xcd5e,0x8e7b,0xbfbe,0x3feb, XPD};
+#define C2 (*(long double *)sc2)
+#endif
+#ifdef MIEEE
+static long R[12] = {
+0x3ff60000,0x817b7763,0xf9226ef4,
+0xbffe0000,0xb84bde8f,0x1af915fd,
+0x40020000,0xac6fa53c,0x4f8d8b96,
+0xc0040000,0x8edee8ae,0xb4e38932,
+};
+static long S[9] = {
+/*0x3fff0000,0x80000000,0x00000000,*/
+0xc0030000,0xd19bbdc5,0x1fc97ce4,
+0x40060000,0xc19e716f,0x0d100af3,
+0xc0070000,0xd64e5d06,0x0f554d7d,
+};
+static long sc1[] = {0x3ffe0000,0xb1720000,0x00000000};
+#define C1 (*(long double *)sc1)
+static long sc2[] = {0x3feb0000,0xbfbe8e7b,0xcd5e4f1e};
+#define C2 (*(long double *)sc2)
+#endif
+
+
+#define SQRTH 0.70710678118654752440L
+extern long double MINLOGL;
+#ifdef ANSIPROT
+extern long double frexpl ( long double, int * );
+extern long double ldexpl ( long double, int );
+extern long double polevll ( long double, void *, int );
+extern long double p1evll ( long double, void *, int );
+extern int isnanl ( long double );
+#else
+long double frexpl(), ldexpl(), polevll(), p1evll(), isnanl();
+#endif
+#ifdef INFINITIES
+extern long double INFINITYL;
+#endif
+#ifdef NANS
+extern long double NANL;
+#endif
+
+long double logl(x)
+long double x;
+{
+long double y, z;
+int e;
+
+#ifdef NANS
+if( isnanl(x) )
+	return(x);
+#endif
+#ifdef INFINITIES
+if( x == INFINITYL )
+	return(x);
+#endif
+/* Test for domain */
+if( x <= 0.0L )
+	{
+	if( x == 0.0L )
+		{
+#ifdef INFINITIES
+		return( -INFINITYL );
+#else
+		mtherr( "logl", SING );
+		return( MINLOGL );
+#endif
+		}
+	else
+		{
+#ifdef NANS
+		return( NANL );
+#else
+		mtherr( "logl", DOMAIN );
+		return( MINLOGL );
+#endif
+		}
+	}
+
+/* separate mantissa from exponent */
+
+/* Note, frexp is used so that denormal numbers
+ * will be handled properly.
+ */
+x = frexpl( x, &e );
+
+/* logarithm using log(x) = z + z**3 P(z)/Q(z),
+ * where z = 2(x-1)/x+1)
+ */
+if( (e > 2) || (e < -2) )
+{
+if( x < SQRTH )
+	{ /* 2( 2x-1 )/( 2x+1 ) */
+	e -= 1;
+	z = x - 0.5L;
+	y = 0.5L * z + 0.5L;
+	}	
+else
+	{ /*  2 (x-1)/(x+1)   */
+	z = x - 0.5L;
+	z -= 0.5L;
+	y = 0.5L * x  + 0.5L;
+	}
+x = z / y;
+z = x*x;
+z = x * ( z * polevll( z, R, 3 ) / p1evll( z, S, 3 ) );
+z = z + e * C2;
+z = z + x;
+z = z + e * C1;
+return( z );
+}
+
+
+/* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */
+
+if( x < SQRTH )
+	{
+	e -= 1;
+	x = ldexpl( x, 1 ) - 1.0L; /*  2x - 1  */
+	}	
+else
+	{
+	x = x - 1.0L;
+	}
+z = x*x;
+y = x * ( z * polevll( x, P, 6 ) / p1evll( x, Q, 6 ) );
+y = y + e * C2;
+z = y - ldexpl( z, -1 );   /*  y - 0.5 * z  */
+/* Note, the sum of above terms does not exceed x/4,
+ * so it contributes at most about 1/4 lsb to the error.
+ */
+z = z + x;
+z = z + e * C1; /* This sum has an error of 1/2 lsb. */
+return( z );
+}