1 files changed, 319 insertions, 0 deletions
diff --git a/libm/ldouble/log10l.c b/libm/ldouble/log10l.c
new file mode 100644
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+++ b/libm/ldouble/log10l.c
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+/*							log10l.c
+ *
+ *	Common logarithm, long double precision
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, log10l();
+ *
+ * y = log10l( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the base 10 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     30000      9.0e-20     2.6e-20
+ *    IEEE     exp(+-10000)  30000      6.0e-20     2.3e-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 MINLOG
+ * log domain:       x < 0; returns MINLOG
+ */
+
+/*
+Cephes Math Library Release 2.2:  January, 1991
+Copyright 1984, 1991 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include <math.h>
+static char fname[] = {"log10l"};
+
+/* 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 = 6.2e-22
+ */
+#ifdef UNK
+static long double P[] = {
+ 4.9962495940332550844739E-1L,
+ 1.0767376367209449010438E1L,
+ 7.7671073698359539859595E1L,
+ 2.5620629828144409632571E2L,
+ 4.2401812743503691187826E2L,
+ 3.4258224542413922935104E2L,
+ 1.0747524399916215149070E2L,
+};
+static long double Q[] = {
+/* 1.0000000000000000000000E0,*/
+ 2.3479774160285863271658E1L,
+ 1.9444210022760132894510E2L,
+ 7.7952888181207260646090E2L,
+ 1.6911722418503949084863E3L,
+ 2.0307734695595183428202E3L,
+ 1.2695660352705325274404E3L,
+ 3.2242573199748645407652E2L,
+};
+#endif
+
+#ifdef IBMPC
+static short P[] = {
+0xfe72,0xce22,0xd7b9,0xffce,0x3ffd, XPD
+0xb778,0x0e34,0x2c71,0xac47,0x4002, XPD
+0xea8b,0xc751,0x96f8,0x9b57,0x4005, XPD
+0xfeaf,0x6a02,0x67fb,0x801a,0x4007, XPD
+0x6b5a,0xf252,0x51ff,0xd402,0x4007, XPD
+0x39ce,0x9f76,0x8704,0xab4a,0x4007, XPD
+0x1b39,0x740b,0x532e,0xd6f3,0x4005, XPD
+};
+static short Q[] = {
+/*0x0000,0x0000,0x0000,0x8000,0x3fff,*/
+0x2f3a,0xbf26,0x93d5,0xbbd6,0x4003, XPD
+0x13c8,0x031a,0x2d7b,0xc271,0x4006, XPD
+0x449d,0x1993,0xd933,0xc2e1,0x4008, XPD
+0x5b65,0x574e,0x8301,0xd365,0x4009, XPD
+0xa65d,0x3bd2,0xc043,0xfdd8,0x4009, XPD
+0x3b21,0xffea,0x1cf5,0x9eb2,0x4009, XPD
+0x545c,0xd708,0x7e62,0xa136,0x4007, XPD
+};
+#endif
+
+#ifdef MIEEE
+static long P[] = {
+0x3ffd0000,0xffced7b9,0xce22fe72,
+0x40020000,0xac472c71,0x0e34b778,
+0x40050000,0x9b5796f8,0xc751ea8b,
+0x40070000,0x801a67fb,0x6a02feaf,
+0x40070000,0xd40251ff,0xf2526b5a,
+0x40070000,0xab4a8704,0x9f7639ce,
+0x40050000,0xd6f3532e,0x740b1b39,
+};
+static long Q[] = {
+/*0x3fff0000,0x80000000,0x00000000,*/
+0x40030000,0xbbd693d5,0xbf262f3a,
+0x40060000,0xc2712d7b,0x031a13c8,
+0x40080000,0xc2e1d933,0x1993449d,
+0x40090000,0xd3658301,0x574e5b65,
+0x40090000,0xfdd8c043,0x3bd2a65d,
+0x40090000,0x9eb21cf5,0xffea3b21,
+0x40070000,0xa1367e62,0xd708545c,
+};
+#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,
+};
+/* log10(2) */
+#define L102A 0.3125L
+#define L102B -1.1470004336018804786261e-2L
+/* log10(e) */
+#define L10EA 0.5L
+#define L10EB -6.5705518096748172348871e-2L
+#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 LG102A[] = {0x0000,0x0000,0x0000,0xa000,0x3ffd, XPD};
+#define L102A *(long double *)LG102A
+static short LG102B[] = {0x0cee,0x8601,0xaf60,0xbbec,0xbff8, XPD};
+#define L102B *(long double *)LG102B
+static short LG10EA[] = {0x0000,0x0000,0x0000,0x8000,0x3ffe, XPD};
+#define L10EA *(long double *)LG10EA
+static short LG10EB[] = {0x39ab,0x235e,0x9d5b,0x8690,0xbffb, XPD};
+#define L10EB *(long double *)LG10EB
+#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 LG102A[] = {0x3ffd0000,0xa0000000,0x00000000};
+#define L102A *(long double *)LG102A
+static long LG102B[] = {0xbff80000,0xbbecaf60,0x86010cee};
+#define L102B *(long double *)LG102B
+static long LG10EA[] = {0x3ffe0000,0x80000000,0x00000000};
+#define L10EA *(long double *)LG10EA
+static long LG10EB[] = {0xbffb0000,0x86909d5b,0x235e39ab};
+#define L10EB *(long double *)LG10EB
+#endif
+
+
+#define SQRTH 0.70710678118654752440L
+#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 log10l(x)
+long double x;
+{
+long double y;
+VOLATILE long double z;
+int e;
+
+#ifdef NANS
+if( isnanl(x) )
+	return(x);
+#endif
+/* Test for domain */
+if( x <= 0.0L )
+	{
+	if( x == 0.0L )
+		{
+		mtherr( fname, SING );
+#ifdef INFINITIES
+		return(-INFINITYL);
+#else
+		return( -4.9314733889673399399914e3L );
+#endif
+		}
+	else
+		{
+		mtherr( fname, DOMAIN );
+#ifdef NANS
+		return(NANL);
+#else
+		return( -4.9314733889673399399914e3L );
+#endif
+		}
+	}
+#ifdef INFINITIES
+if( x == INFINITYL )
+	return(INFINITYL);
+#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;
+y = x * ( z * polevll( z, R, 3 ) / p1evll( z, S, 3 ) );
+goto done;
+}
+
+
+/* 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, 7 ) );
+y = y - ldexpl( z, -1 );   /* -0.5x^2 + ... */
+
+done:
+
+/* Multiply log of fraction by log10(e)
+ * and base 2 exponent by log10(2).
+ *
+ * ***CAUTION***
+ *
+ * This sequence of operations is critical and it may
+ * be horribly defeated by some compiler optimizers.
+ */
+z = y * (L10EB);
+z += x * (L10EB);
+z += e * (L102B);
+z += y * (L10EA);
+z += x * (L10EA);
+z += e * (L102A);
+
+return( z );
+}