From 575e234b005d45dbcdf2afb274df56aac995ef2a Mon Sep 17 00:00:00 2001 From: Hans-Christoph Steiner Date: Thu, 13 Dec 2007 04:10:52 +0000 Subject: imported jsarlo's DSP windowing objects from http://crca.ucsd.edu/~jsarlo/pd/windowing.tar.gz which has a date of 2002-04-06 svn path=/trunk/externals/windowing/; revision=9090 --- i0.c | 409 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 409 insertions(+) create mode 100644 i0.c (limited to 'i0.c') diff --git a/i0.c b/i0.c new file mode 100644 index 0000000..b6a00f4 --- /dev/null +++ b/i0.c @@ -0,0 +1,409 @@ +/* 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 +#include "mconf.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 + +double chbevl(double x, double array[], int n) +{ +double b0, b1, b2, *p; +int i; + +p = array; +b0 = *p++; +b1 = 0.0; +i = n - 1; + +do + { + b2 = b1; + b1 = b0; + b0 = x * b1 - b2 + *p++; + } +while( --i ); + +return( 0.5*(b0-b2) ); +} + +double i0(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(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) ); + +} -- cgit v1.2.1