1 files changed, 515 insertions, 0 deletions
diff --git a/libm/double/j1.c b/libm/double/j1.c
new file mode 100644
index 000000000..95e46ea79
--- /dev/null
+++ b/libm/double/j1.c
@@ -0,0 +1,515 @@
+/*							j1.c
+ *
+ *	Bessel function of order one
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, j1();
+ *
+ * y = j1( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of order one of the argument.
+ *
+ * The domain is divided into the intervals [0, 8] and
+ * (8, infinity). In the first interval a 24 term Chebyshev
+ * expansion is used. In the second, the asymptotic
+ * trigonometric representation is employed using two
+ * rational functions of degree 5/5.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Absolute error:
+ * arithmetic   domain      # trials      peak         rms
+ *    DEC       0, 30       10000       4.0e-17     1.1e-17
+ *    IEEE      0, 30       30000       2.6e-16     1.1e-16
+ *
+ *
+ */
+/*							y1.c
+ *
+ *	Bessel function of second kind of order one
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, y1();
+ *
+ * y = y1( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of the second kind of order one
+ * of the argument.
+ *
+ * The domain is divided into the intervals [0, 8] and
+ * (8, infinity). In the first interval a 25 term Chebyshev
+ * expansion is used, and a call to j1() is required.
+ * In the second, the asymptotic trigonometric representation
+ * is employed using two rational functions of degree 5/5.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Absolute error:
+ * arithmetic   domain      # trials      peak         rms
+ *    DEC       0, 30       10000       8.6e-17     1.3e-17
+ *    IEEE      0, 30       30000       1.0e-15     1.3e-16
+ *
+ * (error criterion relative when |y1| > 1).
+ *
+ */
+
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1984, 1987, 1989, 2000 by Stephen L. Moshier
+*/
+
+/*
+#define PIO4 .78539816339744830962
+#define THPIO4 2.35619449019234492885
+#define SQ2OPI .79788456080286535588
+*/
+
+#include <math.h>
+
+#ifdef UNK
+static double RP[4] = {
+-8.99971225705559398224E8,
+ 4.52228297998194034323E11,
+-7.27494245221818276015E13,
+ 3.68295732863852883286E15,
+};
+static double RQ[8] = {
+/* 1.00000000000000000000E0,*/
+ 6.20836478118054335476E2,
+ 2.56987256757748830383E5,
+ 8.35146791431949253037E7,
+ 2.21511595479792499675E10,
+ 4.74914122079991414898E12,
+ 7.84369607876235854894E14,
+ 8.95222336184627338078E16,
+ 5.32278620332680085395E18,
+};
+#endif
+#ifdef DEC
+static unsigned short RP[16] = {
+0147526,0110742,0063322,0077052,
+0051722,0112720,0065034,0061530,
+0153604,0052227,0033147,0105650,
+0055121,0055025,0032276,0022015,
+};
+static unsigned short RQ[32] = {
+/*0040200,0000000,0000000,0000000,*/
+0042433,0032610,0155604,0033473,
+0044572,0173320,0067270,0006616,
+0046637,0045246,0162225,0006606,
+0050645,0004773,0157577,0053004,
+0052612,0033734,0001667,0176501,
+0054462,0054121,0173147,0121367,
+0056237,0002777,0121451,0176007,
+0057623,0136253,0131601,0044710,
+};
+#endif
+#ifdef IBMPC
+static unsigned short RP[16] = {
+0x4fc5,0x4cda,0xd23c,0xc1ca,
+0x8c6b,0x0d43,0x52ba,0x425a,
+0xf175,0xe6cc,0x8a92,0xc2d0,
+0xc482,0xa697,0x2b42,0x432a,
+};
+static unsigned short RQ[32] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0x86e7,0x1b70,0x66b1,0x4083,
+0x01b2,0x0dd7,0x5eda,0x410f,
+0xa1b1,0xdc92,0xe954,0x4193,
+0xeac1,0x7bef,0xa13f,0x4214,
+0xffa8,0x8076,0x46fb,0x4291,
+0xf45f,0x3ecc,0x4b0a,0x4306,
+0x3f81,0xf465,0xe0bf,0x4373,
+0x2939,0x7670,0x7795,0x43d2,
+};
+#endif
+#ifdef MIEEE
+static unsigned short RP[16] = {
+0xc1ca,0xd23c,0x4cda,0x4fc5,
+0x425a,0x52ba,0x0d43,0x8c6b,
+0xc2d0,0x8a92,0xe6cc,0xf175,
+0x432a,0x2b42,0xa697,0xc482,
+};
+static unsigned short RQ[32] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0x4083,0x66b1,0x1b70,0x86e7,
+0x410f,0x5eda,0x0dd7,0x01b2,
+0x4193,0xe954,0xdc92,0xa1b1,
+0x4214,0xa13f,0x7bef,0xeac1,
+0x4291,0x46fb,0x8076,0xffa8,
+0x4306,0x4b0a,0x3ecc,0xf45f,
+0x4373,0xe0bf,0xf465,0x3f81,
+0x43d2,0x7795,0x7670,0x2939,
+};
+#endif
+
+#ifdef UNK
+static double PP[7] = {
+ 7.62125616208173112003E-4,
+ 7.31397056940917570436E-2,
+ 1.12719608129684925192E0,
+ 5.11207951146807644818E0,
+ 8.42404590141772420927E0,
+ 5.21451598682361504063E0,
+ 1.00000000000000000254E0,
+};
+static double PQ[7] = {
+ 5.71323128072548699714E-4,
+ 6.88455908754495404082E-2,
+ 1.10514232634061696926E0,
+ 5.07386386128601488557E0,
+ 8.39985554327604159757E0,
+ 5.20982848682361821619E0,
+ 9.99999999999999997461E-1,
+};
+#endif
+#ifdef DEC
+static unsigned short PP[28] = {
+0035507,0144542,0061543,0024326,
+0037225,0145105,0017766,0022661,
+0040220,0043766,0010254,0133255,
+0040643,0113047,0142611,0151521,
+0041006,0144344,0055351,0074261,
+0040646,0156520,0120574,0006416,
+0040200,0000000,0000000,0000000,
+};
+static unsigned short PQ[28] = {
+0035425,0142330,0115041,0165514,
+0037214,0177352,0145105,0052026,
+0040215,0072515,0141207,0073255,
+0040642,0056427,0137222,0106405,
+0041006,0062716,0166427,0165450,
+0040646,0133352,0035425,0123304,
+0040200,0000000,0000000,0000000,
+};
+#endif
+#ifdef IBMPC
+static unsigned short PP[28] = {
+0x651b,0x4c6c,0xf92c,0x3f48,
+0xc4b6,0xa3fe,0xb948,0x3fb2,
+0x96d6,0xc215,0x08fe,0x3ff2,
+0x3a6a,0xf8b1,0x72c4,0x4014,
+0x2f16,0x8b5d,0xd91c,0x4020,
+0x81a2,0x142f,0xdbaa,0x4014,
+0x0000,0x0000,0x0000,0x3ff0,
+};
+static unsigned short PQ[28] = {
+0x3d69,0x1344,0xb89b,0x3f42,
+0xaa83,0x5948,0x9fdd,0x3fb1,
+0xeed6,0xb850,0xaea9,0x3ff1,
+0x51a1,0xf7d2,0x4ba2,0x4014,
+0xfd65,0xdda2,0xccb9,0x4020,
+0xb4d9,0x4762,0xd6dd,0x4014,
+0x0000,0x0000,0x0000,0x3ff0,
+};
+#endif
+#ifdef MIEEE
+static unsigned short PP[28] = {
+0x3f48,0xf92c,0x4c6c,0x651b,
+0x3fb2,0xb948,0xa3fe,0xc4b6,
+0x3ff2,0x08fe,0xc215,0x96d6,
+0x4014,0x72c4,0xf8b1,0x3a6a,
+0x4020,0xd91c,0x8b5d,0x2f16,
+0x4014,0xdbaa,0x142f,0x81a2,
+0x3ff0,0x0000,0x0000,0x0000,
+};
+static unsigned short PQ[28] = {
+0x3f42,0xb89b,0x1344,0x3d69,
+0x3fb1,0x9fdd,0x5948,0xaa83,
+0x3ff1,0xaea9,0xb850,0xeed6,
+0x4014,0x4ba2,0xf7d2,0x51a1,
+0x4020,0xccb9,0xdda2,0xfd65,
+0x4014,0xd6dd,0x4762,0xb4d9,
+0x3ff0,0x0000,0x0000,0x0000,
+};
+#endif
+
+#ifdef UNK
+static double QP[8] = {
+ 5.10862594750176621635E-2,
+ 4.98213872951233449420E0,
+ 7.58238284132545283818E1,
+ 3.66779609360150777800E2,
+ 7.10856304998926107277E2,
+ 5.97489612400613639965E2,
+ 2.11688757100572135698E2,
+ 2.52070205858023719784E1,
+};
+static double QQ[7] = {
+/* 1.00000000000000000000E0,*/
+ 7.42373277035675149943E1,
+ 1.05644886038262816351E3,
+ 4.98641058337653607651E3,
+ 9.56231892404756170795E3,
+ 7.99704160447350683650E3,
+ 2.82619278517639096600E3,
+ 3.36093607810698293419E2,
+};
+#endif
+#ifdef DEC
+static unsigned short QP[32] = {
+0037121,0037723,0055605,0151004,
+0040637,0066656,0031554,0077264,
+0041627,0122714,0153170,0161466,
+0042267,0061712,0036520,0140145,
+0042461,0133315,0131573,0071176,
+0042425,0057525,0147500,0013201,
+0042123,0130122,0061245,0154131,
+0041311,0123772,0064254,0172650,
+};
+static unsigned short QQ[28] = {
+/*0040200,0000000,0000000,0000000,*/
+0041624,0074603,0002112,0101670,
+0042604,0007135,0010162,0175565,
+0043233,0151510,0157757,0172010,
+0043425,0064506,0112006,0104276,
+0043371,0164125,0032271,0164242,
+0043060,0121425,0122750,0136013,
+0042250,0005773,0053472,0146267,
+};
+#endif
+#ifdef IBMPC
+static unsigned short QP[32] = {
+0xba40,0x6b70,0x27fa,0x3faa,
+0x8fd6,0xc66d,0xedb5,0x4013,
+0x1c67,0x9acf,0xf4b9,0x4052,
+0x180d,0x47aa,0xec79,0x4076,
+0x6e50,0xb66f,0x36d9,0x4086,
+0x02d0,0xb9e8,0xabea,0x4082,
+0xbb0b,0x4c54,0x760a,0x406a,
+0x9eb5,0x4d15,0x34ff,0x4039,
+};
+static unsigned short QQ[28] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0x5077,0x6089,0x8f30,0x4052,
+0x5f6f,0xa20e,0x81cb,0x4090,
+0xfe81,0x1bfd,0x7a69,0x40b3,
+0xd118,0xd280,0xad28,0x40c2,
+0x3d14,0xa697,0x3d0a,0x40bf,
+0x1781,0xb4bd,0x1462,0x40a6,
+0x5997,0x6ae7,0x017f,0x4075,
+};
+#endif
+#ifdef MIEEE
+static unsigned short QP[32] = {
+0x3faa,0x27fa,0x6b70,0xba40,
+0x4013,0xedb5,0xc66d,0x8fd6,
+0x4052,0xf4b9,0x9acf,0x1c67,
+0x4076,0xec79,0x47aa,0x180d,
+0x4086,0x36d9,0xb66f,0x6e50,
+0x4082,0xabea,0xb9e8,0x02d0,
+0x406a,0x760a,0x4c54,0xbb0b,
+0x4039,0x34ff,0x4d15,0x9eb5,
+};
+static unsigned short QQ[28] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0x4052,0x8f30,0x6089,0x5077,
+0x4090,0x81cb,0xa20e,0x5f6f,
+0x40b3,0x7a69,0x1bfd,0xfe81,
+0x40c2,0xad28,0xd280,0xd118,
+0x40bf,0x3d0a,0xa697,0x3d14,
+0x40a6,0x1462,0xb4bd,0x1781,
+0x4075,0x017f,0x6ae7,0x5997,
+};
+#endif
+
+#ifdef UNK
+static double YP[6] = {
+ 1.26320474790178026440E9,
+-6.47355876379160291031E11,
+ 1.14509511541823727583E14,
+-8.12770255501325109621E15,
+ 2.02439475713594898196E17,
+-7.78877196265950026825E17,
+};
+static double YQ[8] = {
+/* 1.00000000000000000000E0,*/
+ 5.94301592346128195359E2,
+ 2.35564092943068577943E5,
+ 7.34811944459721705660E7,
+ 1.87601316108706159478E10,
+ 3.88231277496238566008E12,
+ 6.20557727146953693363E14,
+ 6.87141087355300489866E16,
+ 3.97270608116560655612E18,
+};
+#endif
+#ifdef DEC
+static unsigned short YP[24] = {
+0047626,0112763,0013715,0133045,
+0152026,0134552,0142033,0024411,
+0053720,0045245,0102210,0077565,
+0155347,0000321,0136415,0102031,
+0056463,0146550,0055633,0032605,
+0157054,0171012,0167361,0054265,
+};
+static unsigned short YQ[32] = {
+/*0040200,0000000,0000000,0000000,*/
+0042424,0111515,0044773,0153014,
+0044546,0005405,0171307,0075774,
+0046614,0023575,0047105,0063556,
+0050613,0143034,0101533,0156026,
+0052541,0175367,0166514,0114257,
+0054415,0014466,0134350,0171154,
+0056164,0017436,0025075,0022101,
+0057534,0103614,0103663,0121772,
+};
+#endif
+#ifdef IBMPC
+static unsigned short YP[24] = {
+0xb6c5,0x62f9,0xd2be,0x41d2,
+0x6521,0x5883,0xd72d,0xc262,
+0x0fef,0xb091,0x0954,0x42da,
+0xb083,0x37a1,0xe01a,0xc33c,
+0x66b1,0x0b73,0x79ad,0x4386,
+0x2b17,0x5dde,0x9e41,0xc3a5,
+};
+static unsigned short YQ[32] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0x7ac2,0xa93f,0x9269,0x4082,
+0xef7f,0xbe58,0xc160,0x410c,
+0xacee,0xa9c8,0x84ef,0x4191,
+0x7b83,0x906b,0x78c3,0x4211,
+0x9316,0xfda9,0x3f5e,0x428c,
+0x1e4e,0xd71d,0xa326,0x4301,
+0xa488,0xc547,0x83e3,0x436e,
+0x747f,0x90f6,0x90f1,0x43cb,
+};
+#endif
+#ifdef MIEEE
+static unsigned short YP[24] = {
+0x41d2,0xd2be,0x62f9,0xb6c5,
+0xc262,0xd72d,0x5883,0x6521,
+0x42da,0x0954,0xb091,0x0fef,
+0xc33c,0xe01a,0x37a1,0xb083,
+0x4386,0x79ad,0x0b73,0x66b1,
+0xc3a5,0x9e41,0x5dde,0x2b17,
+};
+static unsigned short YQ[32] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0x4082,0x9269,0xa93f,0x7ac2,
+0x410c,0xc160,0xbe58,0xef7f,
+0x4191,0x84ef,0xa9c8,0xacee,
+0x4211,0x78c3,0x906b,0x7b83,
+0x428c,0x3f5e,0xfda9,0x9316,
+0x4301,0xa326,0xd71d,0x1e4e,
+0x436e,0x83e3,0xc547,0xa488,
+0x43cb,0x90f1,0x90f6,0x747f,
+};
+#endif
+
+
+#ifdef UNK
+static double Z1 = 1.46819706421238932572E1;
+static double Z2 = 4.92184563216946036703E1;
+#endif
+
+#ifdef DEC
+static unsigned short DZ1[] = {0041152,0164532,0006114,0010540};
+static unsigned short DZ2[] = {0041504,0157663,0001625,0020621};
+#define Z1 (*(double *)DZ1)
+#define Z2 (*(double *)DZ2)
+#endif
+
+#ifdef IBMPC
+static unsigned short DZ1[] = {0x822c,0x4189,0x5d2b,0x402d};
+static unsigned short DZ2[] = {0xa432,0x6072,0x9bf6,0x4048};
+#define Z1 (*(double *)DZ1)
+#define Z2 (*(double *)DZ2)
+#endif
+
+#ifdef MIEEE
+static unsigned short DZ1[] = {0x402d,0x5d2b,0x4189,0x822c};
+static unsigned short DZ2[] = {0x4048,0x9bf6,0x6072,0xa432};
+#define Z1 (*(double *)DZ1)
+#define Z2 (*(double *)DZ2)
+#endif
+
+#ifdef ANSIPROT
+extern double polevl ( double, void *, int );
+extern double p1evl ( double, void *, int );
+extern double log ( double );
+extern double sin ( double );
+extern double cos ( double );
+extern double sqrt ( double );
+double j1 ( double );
+#else
+double polevl(), p1evl(), log(), sin(), cos(), sqrt();
+double j1();
+#endif
+extern double TWOOPI, THPIO4, SQ2OPI;
+
+double j1(x)
+double x;
+{
+double w, z, p, q, xn;
+
+w = x;
+if( x < 0 )
+	w = -x;
+
+if( w <= 5.0 )
+	{
+	z = x * x;	
+	w = polevl( z, RP, 3 ) / p1evl( z, RQ, 8 );
+	w = w * x * (z - Z1) * (z - Z2);
+	return( w );
+	}
+
+w = 5.0/x;
+z = w * w;
+p = polevl( z, PP, 6)/polevl( z, PQ, 6 );
+q = polevl( z, QP, 7)/p1evl( z, QQ, 7 );
+xn = x - THPIO4;
+p = p * cos(xn) - w * q * sin(xn);
+return( p * SQ2OPI / sqrt(x) );
+}
+
+
+extern double MAXNUM;
+
+double y1(x)
+double x;
+{
+double w, z, p, q, xn;
+
+if( x <= 5.0 )
+	{
+	if( x <= 0.0 )
+		{
+		mtherr( "y1", DOMAIN );
+		return( -MAXNUM );
+		}
+	z = x * x;
+	w = x * (polevl( z, YP, 5 ) / p1evl( z, YQ, 8 ));
+	w += TWOOPI * ( j1(x) * log(x)  -  1.0/x );
+	return( w );
+	}
+
+w = 5.0/x;
+z = w * w;
+p = polevl( z, PP, 6)/polevl( z, PQ, 6 );
+q = polevl( z, QP, 7)/p1evl( z, QQ, 7 );
+xn = x - THPIO4;
+p = p * sin(xn) + w * q * cos(xn);
+return( p * SQ2OPI / sqrt(x) );
+}