1 files changed, 397 insertions, 0 deletions
diff --git a/libm/double/i0.c b/libm/double/i0.c
new file mode 100644
index 000000000..a4844ab7e
--- /dev/null
+++ b/libm/double/i0.c
@@ -0,0 +1,397 @@
+/*							i0.c
+ *
+ *	Modified Bessel function of order zero
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, i0();
+ *
+ * y = i0( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns modified Bessel function of order zero of the
+ * argument.
+ *
+ * The function is defined as i0(x) = j0( ix ).
+ *
+ * The range is partitioned into the two intervals [0,8] and
+ * (8, infinity).  Chebyshev polynomial expansions are employed
+ * in each interval.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       0,30         6000       8.2e-17     1.9e-17
+ *    IEEE      0,30        30000       5.8e-16     1.4e-16
+ *
+ */
+/*							i0e.c
+ *
+ *	Modified Bessel function of order zero,
+ *	exponentially scaled
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, i0e();
+ *
+ * y = i0e( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns exponentially scaled modified Bessel function
+ * of order zero of the argument.
+ *
+ * The function is defined as i0e(x) = exp(-|x|) j0( ix ).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      0,30        30000       5.4e-16     1.2e-16
+ * See i0().
+ *
+ */
+
+/*							i0.c		*/
+
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1984, 1987, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+/* Chebyshev coefficients for exp(-x) I0(x)
+ * in the interval [0,8].
+ *
+ * lim(x->0){ exp(-x) I0(x) } = 1.
+ */
+
+#ifdef UNK
+static double A[] =
+{
+-4.41534164647933937950E-18,
+ 3.33079451882223809783E-17,
+-2.43127984654795469359E-16,
+ 1.71539128555513303061E-15,
+-1.16853328779934516808E-14,
+ 7.67618549860493561688E-14,
+-4.85644678311192946090E-13,
+ 2.95505266312963983461E-12,
+-1.72682629144155570723E-11,
+ 9.67580903537323691224E-11,
+-5.18979560163526290666E-10,
+ 2.65982372468238665035E-9,
+-1.30002500998624804212E-8,
+ 6.04699502254191894932E-8,
+-2.67079385394061173391E-7,
+ 1.11738753912010371815E-6,
+-4.41673835845875056359E-6,
+ 1.64484480707288970893E-5,
+-5.75419501008210370398E-5,
+ 1.88502885095841655729E-4,
+-5.76375574538582365885E-4,
+ 1.63947561694133579842E-3,
+-4.32430999505057594430E-3,
+ 1.05464603945949983183E-2,
+-2.37374148058994688156E-2,
+ 4.93052842396707084878E-2,
+-9.49010970480476444210E-2,
+ 1.71620901522208775349E-1,
+-3.04682672343198398683E-1,
+ 6.76795274409476084995E-1
+};
+#endif
+
+#ifdef DEC
+static unsigned short A[] = {
+0121642,0162671,0004646,0103567,
+0022431,0115424,0135755,0026104,
+0123214,0023533,0110365,0156635,
+0023767,0033304,0117662,0172716,
+0124522,0100426,0012277,0157531,
+0025254,0155062,0054461,0030465,
+0126010,0131143,0013560,0153604,
+0026517,0170577,0006336,0114437,
+0127227,0162253,0152243,0052734,
+0027724,0142766,0061641,0160200,
+0130416,0123760,0116564,0125262,
+0031066,0144035,0021246,0054641,
+0131537,0053664,0060131,0102530,
+0032201,0155664,0165153,0020652,
+0132617,0061434,0074423,0176145,
+0033225,0174444,0136147,0122542,
+0133624,0031576,0056453,0020470,
+0034211,0175305,0172321,0041314,
+0134561,0054462,0147040,0165315,
+0035105,0124333,0120203,0162532,
+0135427,0013750,0174257,0055221,
+0035726,0161654,0050220,0100162,
+0136215,0131361,0000325,0041110,
+0036454,0145417,0117357,0017352,
+0136702,0072367,0104415,0133574,
+0037111,0172126,0072505,0014544,
+0137302,0055601,0120550,0033523,
+0037457,0136543,0136544,0043002,
+0137633,0177536,0001276,0066150,
+0040055,0041164,0100655,0010521
+};
+#endif
+
+#ifdef IBMPC
+static unsigned short A[] = {
+0xd0ef,0x2134,0x5cb7,0xbc54,
+0xa589,0x977d,0x3362,0x3c83,
+0xbbb4,0x721e,0x84eb,0xbcb1,
+0x5eba,0x93f6,0xe6d8,0x3cde,
+0xfbeb,0xc297,0x5022,0xbd0a,
+0x2627,0x4b26,0x9b46,0x3d35,
+0x1af0,0x62ee,0x164c,0xbd61,
+0xd324,0xe19b,0xfe2f,0x3d89,
+0x6abc,0x7a94,0xfc95,0xbdb2,
+0x3c10,0xcc74,0x98be,0x3dda,
+0x9556,0x13ae,0xd4fe,0xbe01,
+0xcb34,0xa454,0xd903,0x3e26,
+0x30ab,0x8c0b,0xeaf6,0xbe4b,
+0x6435,0x9d4d,0x3b76,0x3e70,
+0x7f8d,0x8f22,0xec63,0xbe91,
+0xf4ac,0x978c,0xbf24,0x3eb2,
+0x6427,0xcba5,0x866f,0xbed2,
+0x2859,0xbe9a,0x3f58,0x3ef1,
+0x1d5a,0x59c4,0x2b26,0xbf0e,
+0x7cab,0x7410,0xb51b,0x3f28,
+0xeb52,0x1f15,0xe2fd,0xbf42,
+0x100e,0x8a12,0xdc75,0x3f5a,
+0xa849,0x201a,0xb65e,0xbf71,
+0xe3dd,0xf3dd,0x9961,0x3f85,
+0xb6f0,0xf121,0x4e9e,0xbf98,
+0xa32d,0xcea8,0x3e8a,0x3fa9,
+0x06ea,0x342d,0x4b70,0xbfb8,
+0x88c0,0x77ac,0xf7ac,0x3fc5,
+0xcd8d,0xc057,0x7feb,0xbfd3,
+0xa22a,0x9035,0xa84e,0x3fe5,
+};
+#endif
+
+#ifdef MIEEE
+static unsigned short A[] = {
+0xbc54,0x5cb7,0x2134,0xd0ef,
+0x3c83,0x3362,0x977d,0xa589,
+0xbcb1,0x84eb,0x721e,0xbbb4,
+0x3cde,0xe6d8,0x93f6,0x5eba,
+0xbd0a,0x5022,0xc297,0xfbeb,
+0x3d35,0x9b46,0x4b26,0x2627,
+0xbd61,0x164c,0x62ee,0x1af0,
+0x3d89,0xfe2f,0xe19b,0xd324,
+0xbdb2,0xfc95,0x7a94,0x6abc,
+0x3dda,0x98be,0xcc74,0x3c10,
+0xbe01,0xd4fe,0x13ae,0x9556,
+0x3e26,0xd903,0xa454,0xcb34,
+0xbe4b,0xeaf6,0x8c0b,0x30ab,
+0x3e70,0x3b76,0x9d4d,0x6435,
+0xbe91,0xec63,0x8f22,0x7f8d,
+0x3eb2,0xbf24,0x978c,0xf4ac,
+0xbed2,0x866f,0xcba5,0x6427,
+0x3ef1,0x3f58,0xbe9a,0x2859,
+0xbf0e,0x2b26,0x59c4,0x1d5a,
+0x3f28,0xb51b,0x7410,0x7cab,
+0xbf42,0xe2fd,0x1f15,0xeb52,
+0x3f5a,0xdc75,0x8a12,0x100e,
+0xbf71,0xb65e,0x201a,0xa849,
+0x3f85,0x9961,0xf3dd,0xe3dd,
+0xbf98,0x4e9e,0xf121,0xb6f0,
+0x3fa9,0x3e8a,0xcea8,0xa32d,
+0xbfb8,0x4b70,0x342d,0x06ea,
+0x3fc5,0xf7ac,0x77ac,0x88c0,
+0xbfd3,0x7feb,0xc057,0xcd8d,
+0x3fe5,0xa84e,0x9035,0xa22a
+};
+#endif
+
+
+/* Chebyshev coefficients for exp(-x) sqrt(x) I0(x)
+ * in the inverted interval [8,infinity].
+ *
+ * lim(x->inf){ exp(-x) sqrt(x) I0(x) } = 1/sqrt(2pi).
+ */
+
+#ifdef UNK
+static double B[] =
+{
+-7.23318048787475395456E-18,
+-4.83050448594418207126E-18,
+ 4.46562142029675999901E-17,
+ 3.46122286769746109310E-17,
+-2.82762398051658348494E-16,
+-3.42548561967721913462E-16,
+ 1.77256013305652638360E-15,
+ 3.81168066935262242075E-15,
+-9.55484669882830764870E-15,
+-4.15056934728722208663E-14,
+ 1.54008621752140982691E-14,
+ 3.85277838274214270114E-13,
+ 7.18012445138366623367E-13,
+-1.79417853150680611778E-12,
+-1.32158118404477131188E-11,
+-3.14991652796324136454E-11,
+ 1.18891471078464383424E-11,
+ 4.94060238822496958910E-10,
+ 3.39623202570838634515E-9,
+ 2.26666899049817806459E-8,
+ 2.04891858946906374183E-7,
+ 2.89137052083475648297E-6,
+ 6.88975834691682398426E-5,
+ 3.36911647825569408990E-3,
+ 8.04490411014108831608E-1
+};
+#endif
+
+#ifdef DEC
+static unsigned short B[] = {
+0122005,0066672,0123124,0054311,
+0121662,0033323,0030214,0104602,
+0022515,0170300,0113314,0020413,
+0022437,0117350,0035402,0007146,
+0123243,0000135,0057220,0177435,
+0123305,0073476,0144106,0170702,
+0023777,0071755,0017527,0154373,
+0024211,0052214,0102247,0033270,
+0124454,0017763,0171453,0012322,
+0125072,0166316,0075505,0154616,
+0024612,0133770,0065376,0025045,
+0025730,0162143,0056036,0001632,
+0026112,0015077,0150464,0063542,
+0126374,0101030,0014274,0065457,
+0127150,0077271,0125763,0157617,
+0127412,0104350,0040713,0120445,
+0027121,0023765,0057500,0001165,
+0030407,0147146,0003643,0075644,
+0031151,0061445,0044422,0156065,
+0031702,0132224,0003266,0125551,
+0032534,0000076,0147153,0005555,
+0033502,0004536,0004016,0026055,
+0034620,0076433,0142314,0171215,
+0036134,0146145,0013454,0101104,
+0040115,0171425,0062500,0047133
+};
+#endif
+
+#ifdef IBMPC
+static unsigned short B[] = {
+0x8b19,0x54ca,0xadb7,0xbc60,
+0x9130,0x6611,0x46da,0xbc56,
+0x8421,0x12d9,0xbe18,0x3c89,
+0x41cd,0x0760,0xf3dd,0x3c83,
+0x1fe4,0xabd2,0x600b,0xbcb4,
+0xde38,0xd908,0xaee7,0xbcb8,
+0xfb1f,0xa3ea,0xee7d,0x3cdf,
+0xe6d7,0x9094,0x2a91,0x3cf1,
+0x629a,0x7e65,0x83fe,0xbd05,
+0xbb32,0xcf68,0x5d99,0xbd27,
+0xc545,0x0d5f,0x56ff,0x3d11,
+0xc073,0x6b83,0x1c8c,0x3d5b,
+0x8cec,0xfa26,0x4347,0x3d69,
+0x8d66,0x0317,0x9043,0xbd7f,
+0x7bf2,0x357e,0x0fd7,0xbdad,
+0x7425,0x0839,0x511d,0xbdc1,
+0x004f,0xabe8,0x24fe,0x3daa,
+0x6f75,0xc0f4,0xf9cc,0x3e00,
+0x5b87,0xa922,0x2c64,0x3e2d,
+0xd56d,0x80d6,0x5692,0x3e58,
+0x616e,0xd9cd,0x8007,0x3e8b,
+0xc586,0xc101,0x412b,0x3ec8,
+0x9e52,0x7899,0x0fa3,0x3f12,
+0x9049,0xa2e5,0x998c,0x3f6b,
+0x09cb,0xaca8,0xbe62,0x3fe9
+};
+#endif
+
+#ifdef MIEEE
+static unsigned short B[] = {
+0xbc60,0xadb7,0x54ca,0x8b19,
+0xbc56,0x46da,0x6611,0x9130,
+0x3c89,0xbe18,0x12d9,0x8421,
+0x3c83,0xf3dd,0x0760,0x41cd,
+0xbcb4,0x600b,0xabd2,0x1fe4,
+0xbcb8,0xaee7,0xd908,0xde38,
+0x3cdf,0xee7d,0xa3ea,0xfb1f,
+0x3cf1,0x2a91,0x9094,0xe6d7,
+0xbd05,0x83fe,0x7e65,0x629a,
+0xbd27,0x5d99,0xcf68,0xbb32,
+0x3d11,0x56ff,0x0d5f,0xc545,
+0x3d5b,0x1c8c,0x6b83,0xc073,
+0x3d69,0x4347,0xfa26,0x8cec,
+0xbd7f,0x9043,0x0317,0x8d66,
+0xbdad,0x0fd7,0x357e,0x7bf2,
+0xbdc1,0x511d,0x0839,0x7425,
+0x3daa,0x24fe,0xabe8,0x004f,
+0x3e00,0xf9cc,0xc0f4,0x6f75,
+0x3e2d,0x2c64,0xa922,0x5b87,
+0x3e58,0x5692,0x80d6,0xd56d,
+0x3e8b,0x8007,0xd9cd,0x616e,
+0x3ec8,0x412b,0xc101,0xc586,
+0x3f12,0x0fa3,0x7899,0x9e52,
+0x3f6b,0x998c,0xa2e5,0x9049,
+0x3fe9,0xbe62,0xaca8,0x09cb
+};
+#endif
+
+#ifdef ANSIPROT
+extern double chbevl ( double, void *, int );
+extern double exp ( double );
+extern double sqrt ( double );
+#else
+double chbevl(), exp(), sqrt();
+#endif
+
+double i0(x)
+double x;
+{
+double y;
+
+if( x < 0 )
+	x = -x;
+if( x <= 8.0 )
+	{
+	y = (x/2.0) - 2.0;
+	return( exp(x) * chbevl( y, A, 30 ) );
+	}
+
+return(  exp(x) * chbevl( 32.0/x - 2.0, B, 25 ) / sqrt(x) );
+
+}
+
+
+
+
+double i0e( x )
+double x;
+{
+double y;
+
+if( x < 0 )
+	x = -x;
+if( x <= 8.0 )
+	{
+	y = (x/2.0) - 2.0;
+	return( chbevl( y, A, 30 ) );
+	}
+
+return(  chbevl( 32.0/x - 2.0, B, 25 ) / sqrt(x) );
+
+}