1 files changed, 335 insertions, 0 deletions
diff --git a/libm/double/k1.c b/libm/double/k1.c
new file mode 100644
index 000000000..a96305355
--- /dev/null
+++ b/libm/double/k1.c
@@ -0,0 +1,335 @@
+/*							k1.c
+ *
+ *	Modified Bessel function, third kind, order one
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, k1();
+ *
+ * y = k1( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Computes the modified Bessel function of the third kind
+ * of order one of the argument.
+ *
+ * The range is partitioned into the two intervals [0,2] and
+ * (2, infinity).  Chebyshev polynomial expansions are employed
+ * in each interval.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       0, 30        3300       8.9e-17     2.2e-17
+ *    IEEE      0, 30       30000       1.2e-15     1.6e-16
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * k1 domain          x <= 0          MAXNUM
+ *
+ */
+/*							k1e.c
+ *
+ *	Modified Bessel function, third kind, order one,
+ *	exponentially scaled
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, k1e();
+ *
+ * y = k1e( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns exponentially scaled modified Bessel function
+ * of the third kind of order one of the argument:
+ *
+ *      k1e(x) = exp(x) * k1(x).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      0, 30       30000       7.8e-16     1.2e-16
+ * See k1().
+ *
+ */
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1984, 1987, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+/* Chebyshev coefficients for x(K1(x) - log(x/2) I1(x))
+ * in the interval [0,2].
+ * 
+ * lim(x->0){ x(K1(x) - log(x/2) I1(x)) } = 1.
+ */
+
+#ifdef UNK
+static double A[] =
+{
+-7.02386347938628759343E-18,
+-2.42744985051936593393E-15,
+-6.66690169419932900609E-13,
+-1.41148839263352776110E-10,
+-2.21338763073472585583E-8,
+-2.43340614156596823496E-6,
+-1.73028895751305206302E-4,
+-6.97572385963986435018E-3,
+-1.22611180822657148235E-1,
+-3.53155960776544875667E-1,
+ 1.52530022733894777053E0
+};
+#endif
+
+#ifdef DEC
+static unsigned short A[] = {
+0122001,0110501,0164746,0151255,
+0124056,0165213,0150034,0147377,
+0126073,0124026,0167207,0001044,
+0130033,0030735,0141061,0033116,
+0131676,0020350,0121341,0107175,
+0133443,0046631,0062031,0070716,
+0135065,0067427,0026435,0164022,
+0136344,0112234,0165752,0006222,
+0137373,0015622,0017016,0155636,
+0137664,0150333,0125730,0067240,
+0040303,0036411,0130200,0043120
+};
+#endif
+
+#ifdef IBMPC
+static unsigned short A[] = {
+0xda56,0x3d3c,0x3228,0xbc60,
+0x99e0,0x7a03,0xdd51,0xbce5,
+0xe045,0xddd0,0x7502,0xbd67,
+0x26ca,0xb846,0x663b,0xbde3,
+0x31d0,0x145c,0xc41d,0xbe57,
+0x2e3a,0x2c83,0x69b3,0xbec4,
+0xbd02,0xe5a3,0xade2,0xbf26,
+0x4192,0x9d7d,0x9293,0xbf7c,
+0xdb74,0x43c1,0x6372,0xbfbf,
+0x0dd4,0x757b,0x9a1b,0xbfd6,
+0x08ca,0x3610,0x67a1,0x3ff8
+};
+#endif
+
+#ifdef MIEEE
+static unsigned short A[] = {
+0xbc60,0x3228,0x3d3c,0xda56,
+0xbce5,0xdd51,0x7a03,0x99e0,
+0xbd67,0x7502,0xddd0,0xe045,
+0xbde3,0x663b,0xb846,0x26ca,
+0xbe57,0xc41d,0x145c,0x31d0,
+0xbec4,0x69b3,0x2c83,0x2e3a,
+0xbf26,0xade2,0xe5a3,0xbd02,
+0xbf7c,0x9293,0x9d7d,0x4192,
+0xbfbf,0x6372,0x43c1,0xdb74,
+0xbfd6,0x9a1b,0x757b,0x0dd4,
+0x3ff8,0x67a1,0x3610,0x08ca
+};
+#endif
+
+
+
+/* Chebyshev coefficients for exp(x) sqrt(x) K1(x)
+ * in the interval [2,infinity].
+ *
+ * lim(x->inf){ exp(x) sqrt(x) K1(x) } = sqrt(pi/2).
+ */
+
+#ifdef UNK
+static double B[] =
+{
+-5.75674448366501715755E-18,
+ 1.79405087314755922667E-17,
+-5.68946255844285935196E-17,
+ 1.83809354436663880070E-16,
+-6.05704724837331885336E-16,
+ 2.03870316562433424052E-15,
+-7.01983709041831346144E-15,
+ 2.47715442448130437068E-14,
+-8.97670518232499435011E-14,
+ 3.34841966607842919884E-13,
+-1.28917396095102890680E-12,
+ 5.13963967348173025100E-12,
+-2.12996783842756842877E-11,
+ 9.21831518760500529508E-11,
+-4.19035475934189648750E-10,
+ 2.01504975519703286596E-9,
+-1.03457624656780970260E-8,
+ 5.74108412545004946722E-8,
+-3.50196060308781257119E-7,
+ 2.40648494783721712015E-6,
+-1.93619797416608296024E-5,
+ 1.95215518471351631108E-4,
+-2.85781685962277938680E-3,
+ 1.03923736576817238437E-1,
+ 2.72062619048444266945E0
+};
+#endif
+
+#ifdef DEC
+static unsigned short B[] = {
+0121724,0061352,0013041,0150076,
+0022245,0074324,0016172,0173232,
+0122603,0030250,0135670,0165221,
+0023123,0165362,0023561,0060124,
+0123456,0112436,0141654,0073623,
+0024022,0163557,0077564,0006753,
+0124374,0165221,0131014,0026524,
+0024737,0017512,0144250,0175451,
+0125312,0021456,0123136,0076633,
+0025674,0077720,0020125,0102607,
+0126265,0067543,0007744,0043701,
+0026664,0152702,0033002,0074202,
+0127273,0055234,0120016,0071733,
+0027712,0133200,0042441,0075515,
+0130346,0057000,0015456,0074470,
+0031012,0074441,0051636,0111155,
+0131461,0136444,0177417,0002101,
+0032166,0111743,0032176,0021410,
+0132674,0001224,0076555,0027060,
+0033441,0077430,0135226,0106663,
+0134242,0065610,0167155,0113447,
+0035114,0131304,0043664,0102163,
+0136073,0045065,0171465,0122123,
+0037324,0152767,0147401,0017732,
+0040456,0017275,0050061,0062120,
+};
+#endif
+
+#ifdef IBMPC
+static unsigned short B[] = {
+0x3a08,0x42c4,0x8c5d,0xbc5a,
+0x5ed3,0x838f,0xaf1a,0x3c74,
+0x1d52,0x1777,0x6615,0xbc90,
+0x2c0b,0x44ee,0x7d5e,0x3caa,
+0x8ef2,0xd875,0xd2a3,0xbcc5,
+0x81bd,0xefee,0x5ced,0x3ce2,
+0x85ab,0x3641,0x9d52,0xbcff,
+0x1f65,0x5915,0xe3e9,0x3d1b,
+0xcfb3,0xd4cb,0x4465,0xbd39,
+0xb0b1,0x040a,0x8ffa,0x3d57,
+0x88f8,0x61fc,0xadec,0xbd76,
+0x4f10,0x46c0,0x9ab8,0x3d96,
+0xce7b,0x9401,0x6b53,0xbdb7,
+0x2f6a,0x08a4,0x56d0,0x3dd9,
+0xcf27,0x0365,0xcbc0,0xbdfc,
+0xd24e,0x2a73,0x4f24,0x3e21,
+0xe088,0x9fe1,0x37a4,0xbe46,
+0xc461,0x668f,0xd27c,0x3e6e,
+0xa5c6,0x8fad,0x8052,0xbe97,
+0xd1b6,0x1752,0x2fe3,0x3ec4,
+0xb2e5,0x1dcd,0x4d71,0xbef4,
+0x908e,0x88f6,0x9658,0x3f29,
+0xb48a,0xbe66,0x6946,0xbf67,
+0x23fb,0xf9e0,0x9abe,0x3fba,
+0x2c8a,0xaa06,0xc3d7,0x4005
+};
+#endif
+
+#ifdef MIEEE
+static unsigned short B[] = {
+0xbc5a,0x8c5d,0x42c4,0x3a08,
+0x3c74,0xaf1a,0x838f,0x5ed3,
+0xbc90,0x6615,0x1777,0x1d52,
+0x3caa,0x7d5e,0x44ee,0x2c0b,
+0xbcc5,0xd2a3,0xd875,0x8ef2,
+0x3ce2,0x5ced,0xefee,0x81bd,
+0xbcff,0x9d52,0x3641,0x85ab,
+0x3d1b,0xe3e9,0x5915,0x1f65,
+0xbd39,0x4465,0xd4cb,0xcfb3,
+0x3d57,0x8ffa,0x040a,0xb0b1,
+0xbd76,0xadec,0x61fc,0x88f8,
+0x3d96,0x9ab8,0x46c0,0x4f10,
+0xbdb7,0x6b53,0x9401,0xce7b,
+0x3dd9,0x56d0,0x08a4,0x2f6a,
+0xbdfc,0xcbc0,0x0365,0xcf27,
+0x3e21,0x4f24,0x2a73,0xd24e,
+0xbe46,0x37a4,0x9fe1,0xe088,
+0x3e6e,0xd27c,0x668f,0xc461,
+0xbe97,0x8052,0x8fad,0xa5c6,
+0x3ec4,0x2fe3,0x1752,0xd1b6,
+0xbef4,0x4d71,0x1dcd,0xb2e5,
+0x3f29,0x9658,0x88f6,0x908e,
+0xbf67,0x6946,0xbe66,0xb48a,
+0x3fba,0x9abe,0xf9e0,0x23fb,
+0x4005,0xc3d7,0xaa06,0x2c8a
+};
+#endif
+
+#ifdef ANSIPROT
+extern double chbevl ( double, void *, int );
+extern double exp ( double );
+extern double i1 ( double );
+extern double log ( double );
+extern double sqrt ( double );
+#else
+double chbevl(), exp(), i1(), log(), sqrt();
+#endif
+extern double PI;
+extern double MINLOG, MAXNUM;
+
+double k1(x)
+double x;
+{
+double y, z;
+
+z = 0.5 * x;
+if( z <= 0.0 )
+	{
+	mtherr( "k1", DOMAIN );
+	return( MAXNUM );
+	}
+
+if( x <= 2.0 )
+	{
+	y = x * x - 2.0;
+	y =  log(z) * i1(x)  +  chbevl( y, A, 11 ) / x;
+	return( y );
+	}
+
+return(  exp(-x) * chbevl( 8.0/x - 2.0, B, 25 ) / sqrt(x) );
+}
+
+
+
+
+double k1e( x )
+double x;
+{
+double y;
+
+if( x <= 0.0 )
+	{
+	mtherr( "k1e", DOMAIN );
+	return( MAXNUM );
+	}
+
+if( x <= 2.0 )
+	{
+	y = x * x - 2.0;
+	y =  log( 0.5 * x ) * i1(x)  +  chbevl( y, A, 11 ) / x;
+	return( y * exp(x) );
+	}
+
+return(  chbevl( 8.0/x - 2.0, B, 25 ) / sqrt(x) );
+}