416 lines
10 KiB
C
416 lines
10 KiB
C
/*
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* This file comes from the cephes math library, which was
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* released under the GPLV2+ license as a part of the Debian labplot
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* package (I've included the GPLV2 license reference here to make
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* this clear) - Keith Packard <keithp@keithp.com>
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*
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* Cephes Math Library Release 2.0: April, 1987
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* Copyright 1984, 1987 by Stephen L. Moshier
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* Direct inquiries to 30 Frost Street, Cambridge, MA 02140
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 2 of the License, or
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* (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful, but
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* WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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* General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License along
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* with this program; if not, write to the Free Software Foundation, Inc.,
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* 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA.
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*/
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/* i0.c
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*
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* Modified Bessel function of order zero
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*
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*
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*
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* SYNOPSIS:
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*
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* double x, y, i0();
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*
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* y = i0( x );
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*
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*
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*
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* DESCRIPTION:
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*
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* Returns modified Bessel function of order zero of the
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* argument.
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*
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* The function is defined as i0(x) = j0( ix ).
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*
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* The range is partitioned into the two intervals [0,8] and
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* (8, infinity). Chebyshev polynomial expansions are employed
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* in each interval.
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*
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*
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*
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* ACCURACY:
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*
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* Relative error:
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* arithmetic domain # trials peak rms
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* DEC 0,30 6000 8.2e-17 1.9e-17
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* IEEE 0,30 30000 5.8e-16 1.4e-16
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*
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*/
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/* i0e.c
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*
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* Modified Bessel function of order zero,
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* exponentially scaled
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*
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*
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*
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* SYNOPSIS:
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*
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* double x, y, i0e();
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*
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* y = i0e( x );
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*
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*
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*
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* DESCRIPTION:
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*
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* Returns exponentially scaled modified Bessel function
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* of order zero of the argument.
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*
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* The function is defined as i0e(x) = exp(-|x|) j0( ix ).
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*
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*
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*
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* ACCURACY:
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*
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* Relative error:
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* arithmetic domain # trials peak rms
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* IEEE 0,30 30000 5.4e-16 1.2e-16
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* See i0().
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*
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*/
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/* i0.c */
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/*
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Cephes Math Library Release 2.0: April, 1987
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Copyright 1984, 1987 by Stephen L. Moshier
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Direct inquiries to 30 Frost Street, Cambridge, MA 02140
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*/
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#include <math.h>
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#include "mconf.h"
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#include "cephes.h"
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/* Chebyshev coefficients for exp(-x) I0(x)
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* in the interval [0,8].
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*
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* lim(x->0){ exp(-x) I0(x) } = 1.
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*/
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#ifdef UNK
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static double A[] =
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{
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-4.41534164647933937950E-18,
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3.33079451882223809783E-17,
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-2.43127984654795469359E-16,
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1.71539128555513303061E-15,
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-1.16853328779934516808E-14,
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7.67618549860493561688E-14,
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-4.85644678311192946090E-13,
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2.95505266312963983461E-12,
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-1.72682629144155570723E-11,
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9.67580903537323691224E-11,
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-5.18979560163526290666E-10,
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2.65982372468238665035E-9,
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-1.30002500998624804212E-8,
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6.04699502254191894932E-8,
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-2.67079385394061173391E-7,
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1.11738753912010371815E-6,
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-4.41673835845875056359E-6,
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1.64484480707288970893E-5,
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-5.75419501008210370398E-5,
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1.88502885095841655729E-4,
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-5.76375574538582365885E-4,
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1.63947561694133579842E-3,
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-4.32430999505057594430E-3,
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1.05464603945949983183E-2,
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-2.37374148058994688156E-2,
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4.93052842396707084878E-2,
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-9.49010970480476444210E-2,
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1.71620901522208775349E-1,
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-3.04682672343198398683E-1,
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6.76795274409476084995E-1
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};
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#endif
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#ifdef DEC
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static unsigned short A[] = {
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0121642,0162671,0004646,0103567,
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0022431,0115424,0135755,0026104,
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0123214,0023533,0110365,0156635,
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0023767,0033304,0117662,0172716,
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0124522,0100426,0012277,0157531,
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0025254,0155062,0054461,0030465,
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0126010,0131143,0013560,0153604,
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0026517,0170577,0006336,0114437,
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0127227,0162253,0152243,0052734,
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0027724,0142766,0061641,0160200,
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0130416,0123760,0116564,0125262,
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0031066,0144035,0021246,0054641,
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0131537,0053664,0060131,0102530,
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0032201,0155664,0165153,0020652,
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0132617,0061434,0074423,0176145,
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0033225,0174444,0136147,0122542,
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0133624,0031576,0056453,0020470,
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0034211,0175305,0172321,0041314,
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0134561,0054462,0147040,0165315,
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0035105,0124333,0120203,0162532,
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0135427,0013750,0174257,0055221,
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0035726,0161654,0050220,0100162,
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0136215,0131361,0000325,0041110,
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0036454,0145417,0117357,0017352,
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0136702,0072367,0104415,0133574,
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0037111,0172126,0072505,0014544,
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0137302,0055601,0120550,0033523,
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0037457,0136543,0136544,0043002,
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0137633,0177536,0001276,0066150,
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0040055,0041164,0100655,0010521
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};
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#endif
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#ifdef IBMPC
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static unsigned short A[] = {
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0xd0ef,0x2134,0x5cb7,0xbc54,
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0xa589,0x977d,0x3362,0x3c83,
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0xbbb4,0x721e,0x84eb,0xbcb1,
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0x5eba,0x93f6,0xe6d8,0x3cde,
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0xfbeb,0xc297,0x5022,0xbd0a,
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0x2627,0x4b26,0x9b46,0x3d35,
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0x1af0,0x62ee,0x164c,0xbd61,
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0xd324,0xe19b,0xfe2f,0x3d89,
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0x6abc,0x7a94,0xfc95,0xbdb2,
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0x3c10,0xcc74,0x98be,0x3dda,
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0x9556,0x13ae,0xd4fe,0xbe01,
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0xcb34,0xa454,0xd903,0x3e26,
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0x30ab,0x8c0b,0xeaf6,0xbe4b,
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0x6435,0x9d4d,0x3b76,0x3e70,
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0x7f8d,0x8f22,0xec63,0xbe91,
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0xf4ac,0x978c,0xbf24,0x3eb2,
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0x6427,0xcba5,0x866f,0xbed2,
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0x2859,0xbe9a,0x3f58,0x3ef1,
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0x1d5a,0x59c4,0x2b26,0xbf0e,
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0x7cab,0x7410,0xb51b,0x3f28,
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0xeb52,0x1f15,0xe2fd,0xbf42,
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0x100e,0x8a12,0xdc75,0x3f5a,
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0xa849,0x201a,0xb65e,0xbf71,
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0xe3dd,0xf3dd,0x9961,0x3f85,
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0xb6f0,0xf121,0x4e9e,0xbf98,
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0xa32d,0xcea8,0x3e8a,0x3fa9,
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0x06ea,0x342d,0x4b70,0xbfb8,
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0x88c0,0x77ac,0xf7ac,0x3fc5,
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0xcd8d,0xc057,0x7feb,0xbfd3,
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0xa22a,0x9035,0xa84e,0x3fe5,
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};
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#endif
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#ifdef MIEEE
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static unsigned short A[] = {
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0xbc54,0x5cb7,0x2134,0xd0ef,
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0x3c83,0x3362,0x977d,0xa589,
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0xbcb1,0x84eb,0x721e,0xbbb4,
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0x3cde,0xe6d8,0x93f6,0x5eba,
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0xbd0a,0x5022,0xc297,0xfbeb,
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0x3d35,0x9b46,0x4b26,0x2627,
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0xbd61,0x164c,0x62ee,0x1af0,
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0x3d89,0xfe2f,0xe19b,0xd324,
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0xbdb2,0xfc95,0x7a94,0x6abc,
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0x3dda,0x98be,0xcc74,0x3c10,
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0xbe01,0xd4fe,0x13ae,0x9556,
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0x3e26,0xd903,0xa454,0xcb34,
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0xbe4b,0xeaf6,0x8c0b,0x30ab,
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0x3e70,0x3b76,0x9d4d,0x6435,
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0xbe91,0xec63,0x8f22,0x7f8d,
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0x3eb2,0xbf24,0x978c,0xf4ac,
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0xbed2,0x866f,0xcba5,0x6427,
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0x3ef1,0x3f58,0xbe9a,0x2859,
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0xbf0e,0x2b26,0x59c4,0x1d5a,
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0x3f28,0xb51b,0x7410,0x7cab,
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0xbf42,0xe2fd,0x1f15,0xeb52,
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0x3f5a,0xdc75,0x8a12,0x100e,
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0xbf71,0xb65e,0x201a,0xa849,
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0x3f85,0x9961,0xf3dd,0xe3dd,
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0xbf98,0x4e9e,0xf121,0xb6f0,
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0x3fa9,0x3e8a,0xcea8,0xa32d,
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0xbfb8,0x4b70,0x342d,0x06ea,
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0x3fc5,0xf7ac,0x77ac,0x88c0,
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0xbfd3,0x7feb,0xc057,0xcd8d,
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0x3fe5,0xa84e,0x9035,0xa22a
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};
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#endif
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/* Chebyshev coefficients for exp(-x) sqrt(x) I0(x)
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* in the inverted interval [8,infinity].
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*
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* lim(x->inf){ exp(-x) sqrt(x) I0(x) } = 1/sqrt(2pi).
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*/
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#ifdef UNK
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static double B[] =
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{
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-7.23318048787475395456E-18,
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-4.83050448594418207126E-18,
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4.46562142029675999901E-17,
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3.46122286769746109310E-17,
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-2.82762398051658348494E-16,
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-3.42548561967721913462E-16,
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1.77256013305652638360E-15,
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3.81168066935262242075E-15,
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-9.55484669882830764870E-15,
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-4.15056934728722208663E-14,
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1.54008621752140982691E-14,
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3.85277838274214270114E-13,
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7.18012445138366623367E-13,
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-1.79417853150680611778E-12,
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-1.32158118404477131188E-11,
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-3.14991652796324136454E-11,
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1.18891471078464383424E-11,
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4.94060238822496958910E-10,
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3.39623202570838634515E-9,
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2.26666899049817806459E-8,
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2.04891858946906374183E-7,
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2.89137052083475648297E-6,
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6.88975834691682398426E-5,
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3.36911647825569408990E-3,
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8.04490411014108831608E-1
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};
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#endif
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#ifdef DEC
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static unsigned short B[] = {
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0122005,0066672,0123124,0054311,
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0121662,0033323,0030214,0104602,
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0022515,0170300,0113314,0020413,
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0022437,0117350,0035402,0007146,
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0123243,0000135,0057220,0177435,
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0123305,0073476,0144106,0170702,
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0023777,0071755,0017527,0154373,
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0024211,0052214,0102247,0033270,
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0124454,0017763,0171453,0012322,
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0125072,0166316,0075505,0154616,
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0024612,0133770,0065376,0025045,
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0025730,0162143,0056036,0001632,
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0026112,0015077,0150464,0063542,
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0126374,0101030,0014274,0065457,
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0127150,0077271,0125763,0157617,
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0127412,0104350,0040713,0120445,
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0027121,0023765,0057500,0001165,
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0030407,0147146,0003643,0075644,
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0031151,0061445,0044422,0156065,
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0031702,0132224,0003266,0125551,
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0032534,0000076,0147153,0005555,
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0033502,0004536,0004016,0026055,
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0034620,0076433,0142314,0171215,
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0036134,0146145,0013454,0101104,
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0040115,0171425,0062500,0047133
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};
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#endif
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#ifdef IBMPC
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static unsigned short B[] = {
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0x8b19,0x54ca,0xadb7,0xbc60,
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0x9130,0x6611,0x46da,0xbc56,
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0x8421,0x12d9,0xbe18,0x3c89,
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0x41cd,0x0760,0xf3dd,0x3c83,
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0x1fe4,0xabd2,0x600b,0xbcb4,
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0xde38,0xd908,0xaee7,0xbcb8,
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0xfb1f,0xa3ea,0xee7d,0x3cdf,
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0xe6d7,0x9094,0x2a91,0x3cf1,
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0x629a,0x7e65,0x83fe,0xbd05,
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0xbb32,0xcf68,0x5d99,0xbd27,
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0xc545,0x0d5f,0x56ff,0x3d11,
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0xc073,0x6b83,0x1c8c,0x3d5b,
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0x8cec,0xfa26,0x4347,0x3d69,
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0x8d66,0x0317,0x9043,0xbd7f,
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0x7bf2,0x357e,0x0fd7,0xbdad,
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0x7425,0x0839,0x511d,0xbdc1,
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0x004f,0xabe8,0x24fe,0x3daa,
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0x6f75,0xc0f4,0xf9cc,0x3e00,
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0x5b87,0xa922,0x2c64,0x3e2d,
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0xd56d,0x80d6,0x5692,0x3e58,
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0x616e,0xd9cd,0x8007,0x3e8b,
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0xc586,0xc101,0x412b,0x3ec8,
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0x9e52,0x7899,0x0fa3,0x3f12,
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0x9049,0xa2e5,0x998c,0x3f6b,
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0x09cb,0xaca8,0xbe62,0x3fe9
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};
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#endif
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#ifdef MIEEE
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static unsigned short B[] = {
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0xbc60,0xadb7,0x54ca,0x8b19,
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0xbc56,0x46da,0x6611,0x9130,
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0x3c89,0xbe18,0x12d9,0x8421,
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0x3c83,0xf3dd,0x0760,0x41cd,
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0xbcb4,0x600b,0xabd2,0x1fe4,
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0xbcb8,0xaee7,0xd908,0xde38,
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0x3cdf,0xee7d,0xa3ea,0xfb1f,
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0x3cf1,0x2a91,0x9094,0xe6d7,
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0xbd05,0x83fe,0x7e65,0x629a,
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0xbd27,0x5d99,0xcf68,0xbb32,
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0x3d11,0x56ff,0x0d5f,0xc545,
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0x3d5b,0x1c8c,0x6b83,0xc073,
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0x3d69,0x4347,0xfa26,0x8cec,
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0xbd7f,0x9043,0x0317,0x8d66,
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0xbdad,0x0fd7,0x357e,0x7bf2,
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0xbdc1,0x511d,0x0839,0x7425,
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0x3daa,0x24fe,0xabe8,0x004f,
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0x3e00,0xf9cc,0xc0f4,0x6f75,
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0x3e2d,0x2c64,0xa922,0x5b87,
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0x3e58,0x5692,0x80d6,0xd56d,
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0x3e8b,0x8007,0xd9cd,0x616e,
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0x3ec8,0x412b,0xc101,0xc586,
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0x3f12,0x0fa3,0x7899,0x9e52,
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0x3f6b,0x998c,0xa2e5,0x9049,
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0x3fe9,0xbe62,0xaca8,0x09cb
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};
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#endif
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double i0(double x)
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{
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double y;
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if( x < 0 )
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x = -x;
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if( x <= 8.0 )
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{
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y = (x/2.0) - 2.0;
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return( exp(x) * chbevl( y, A, 30 ) );
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}
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return( exp(x) * chbevl( 32.0/x - 2.0, B, 25 ) / sqrt(x) );
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}
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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) );
|
||
|
||
}
|