/* ei.c
*
* Exponential integral
*
*
* SYNOPSIS:
*
* double x, y, ei();
*
* y = ei( x );
*
*
*
* DESCRIPTION:
*
* x
* - t
* | | e
* Ei(x) = -|- --- dt .
* | | t
* -
* -inf
*
* Not defined for x <= 0.
* See also md_expn.c.
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE 0,100 50000 8.6e-16 1.3e-16
*
*/
/*
Cephes Math Library Release 2.8: May, 1999
Copyright 1999 by Stephen L. Moshier
*/
#include "mconf.h"
#ifdef ANSIPROT
extern double md_log ( double );
extern double md_exp ( double );
extern double polevl ( double, void *, int );
extern double p1evl ( double, void *, int );
#else
extern double md_log(), md_exp(), polevl(), p1evl();
#endif
#define EUL 5.772156649015328606065e-1
/* 0 < x <= 2
Ei(x) - EUL - ln(x) = x A(x)/B(x)
Theoretical peak relative error 9.73e-18 */
#if UNK
static double A[6] = {
-5.350447357812542947283E0,
2.185049168816613393830E2,
-4.176572384826693777058E3,
5.541176756393557601232E4,
-3.313381331178144034309E5,
1.592627163384945414220E6,
};
static double B[6] = {
/* 1.000000000000000000000E0, */
-5.250547959112862969197E1,
1.259616186786790571525E3,
-1.756549581973534652631E4,
1.493062117002725991967E5,
-7.294949239640527645655E5,
1.592627163384945429726E6,
};
#endif
#if DEC
static short A[24] = {
0140653,0033335,0060230,0144217,
0042132,0100502,0035625,0167413,
0143202,0102224,0037176,0175403,
0044130,0071704,0077421,0170343,
0144641,0144504,0041200,0045154,
0045302,0064631,0047234,0142052,
};
static short B[24] = {
/* 0040200,0000000,0000000,0000000, */
0141522,0002634,0070442,0142614,
0042635,0071667,0146532,0027705,
0143611,0035375,0156025,0114015,
0044421,0147215,0106177,0046330,
0145062,0014556,0144216,0103725,
0045302,0064631,0047234,0142052,
};
#endif
#if IBMPC
static short A[24] = {
0x1912,0xac13,0x66db,0xc015,
0xbde1,0x4772,0x5028,0x406b,
0xdf60,0x87cf,0x5092,0xc0b0,
0x3e1c,0x8fe2,0x0e78,0x40eb,
0x094e,0x8850,0x3928,0xc114,
0x9885,0x29d3,0x4d33,0x4138,
};
static short B[24] = {
/* 0x0000,0x0000,0x0000,0x3ff0, */
0x58b1,0x8e24,0x40b3,0xc04a,
0x45f9,0xf9ab,0xae76,0x4093,
0xb302,0xbb82,0x275f,0xc0d1,
0xe99b,0xb18f,0x39d1,0x4102,
0xd0fb,0xd911,0x432d,0xc126,
0x9885,0x29d3,0x4d33,0x4138,
};
#endif
#if MIEEE
static short A[24] = {
0xc015,0x66db,0xac13,0x1912,
0x406b,0x5028,0x4772,0xbde1,
0xc0b0,0x5092,0x87cf,0xdf60,
0x40eb,0x0e78,0x8fe2,0x3e1c,
0xc114,0x3928,0x8850,0x094e,
0x4138,0x4d33,0x29d3,0x9885,
};
static short B[24] = {
/* 0x3ff0,0x0000,0x0000,0x0000, */
0xc04a,0x40b3,0x8e24,0x58b1,
0x4093,0xae76,0xf9ab,0x45f9,
0xc0d1,0x275f,0xbb82,0xb302,
0x4102,0x39d1,0xb18f,0xe99b,
0xc126,0x432d,0xd911,0xd0fb,
0x4138,0x4d33,0x29d3,0x9885,
};
#endif
#if 0
/* 0 < x <= 4
Ei(x) - EUL - ln(x) = x A(x)/B(x)
Theoretical peak relative error 4.75e-17 */
#if UNK
static double A[7] = {
-6.831869820732773831942E0,
2.920190530726774500309E2,
-1.195883839286649567993E4,
1.761045255472548975666E5,
-2.623034438354006526979E6,
1.472430336917880803157E7,
-8.205359388213261174960E7,
};
static double B[7] = {
/* 1.000000000000000000000E0, */
-7.731946237840033971071E1,
2.751808700543578450827E3,
-5.829268609072186897994E4,
7.916610857961870631379E5,
-6.873926904825733094076E6,
3.523770183971164032710E7,
-8.205359388213260785363E7,
};
#endif
#if DEC
static short A[28] = {
0140732,0117255,0072522,0071743,
0042222,0001160,0052302,0002334,
0143472,0155532,0101650,0155462,
0044453,0175041,0121220,0172022,
0145440,0014351,0140337,0157550,
0046140,0126317,0057202,0100233,
0146634,0100473,0036072,0067054,
};
static short B[28] = {
/* 0040200,0000000,0000000,0000000, */
0141632,0121620,0111247,0010115,
0043053,0176360,0067773,0027324,
0144143,0132257,0121644,0036204,
0045101,0043321,0057553,0151231,
0145721,0143215,0147505,0050610,
0046406,0065721,0072675,0152744,
0146634,0100473,0036072,0067052,
};
#endif
#if IBMPC
static short A[28] = {
0x4e7c,0xaeaa,0x53d5,0xc01b,
0x409b,0x0a98,0x404e,0x4072,
0x1b66,0x5075,0x5b6b,0xc0c7,
0x1e82,0x3452,0x7f44,0x4105,
0xfbed,0x381b,0x031d,0xc144,
0x5013,0xebd0,0x1599,0x416c,
0x4dc5,0x6787,0x9027,0xc193,
};
static short B[28] = {
/* 0x0000,0x0000,0x0000,0x3ff0, */
0xe20a,0x1254,0x5472,0xc053,
0x65db,0x0dff,0x7f9e,0x40a5,
0x8791,0xf474,0x7695,0xc0ec,
0x7a53,0x2bed,0x28da,0x4128,
0xaa31,0xb9e8,0x38d1,0xc15a,
0xbabd,0x2eb7,0xcd7a,0x4180,
0x4dc5,0x6787,0x9027,0xc193,
};
#endif
#if MIEEE
static short A[28] = {
0xc01b,0x53d5,0xaeaa,0x4e7c,
0x4072,0x404e,0x0a98,0x409b,
0xc0c7,0x5b6b,0x5075,0x1b66,
0x4105,0x7f44,0x3452,0x1e82,
0xc144,0x031d,0x381b,0xfbed,
0x416c,0x1599,0xebd0,0x5013,
0xc193,0x9027,0x6787,0x4dc5,
};
static short B[28] = {
/* 0x3ff0,0x0000,0x0000,0x0000, */
0xc053,0x5472,0x1254,0xe20a,
0x40a5,0x7f9e,0x0dff,0x65db,
0xc0ec,0x7695,0xf474,0x8791,
0x4128,0x28da,0x2bed,0x7a53,
0xc15a,0x38d1,0xb9e8,0xaa31,
0x4180,0xcd7a,0x2eb7,0xbabd,
0xc193,0x9027,0x6787,0x4dc5,
};
#endif
#endif /* 0 */
#if 0
/* 0 < x <= 8
Ei(x) - EUL - ln(x) = x A(x)/B(x)
Theoretical peak relative error 2.14e-17 */
#if UNK
static double A[9] = {
-1.111230942210860450145E1,
3.688203982071386319616E2,
-4.924786153494029574350E4,
1.050677503345557903241E6,
-3.626713709916703688968E7,
4.353499908839918635414E8,
-6.454613717232006895409E9,
3.408243056457762907071E10,
-1.995466674647028468613E11,
};
static double B[9] = {
/* 1.000000000000000000000E0, */
-1.356757648138514017969E2,
8.562181317107341736606E3,
-3.298257180413775117555E5,
8.543534058481435917210E6,
-1.542380618535140055068E8,
1.939251779195993632028E9,
-1.636096210465615015435E10,
8.396909743075306970605E10,
-1.995466674647028425886E11,
};
#endif
#if DEC
static short A[36] = {
0141061,0146004,0173357,0151553,
0042270,0064402,0147366,0126701,
0144100,0057734,0106615,0144356,
0045200,0040654,0003332,0004456,
0146412,0054440,0043130,0140263,
0047317,0113517,0033422,0065123,
0150300,0056313,0065235,0131147,
0050775,0167423,0146222,0075760,
0151471,0153642,0003442,0147667,
};
static short B[36] = {
/* 0040200,0000000,0000000,0000000, */
0142007,0126376,0166077,0043600,
0043405,0144271,0125461,0014364,
0144641,0006066,0175061,0164463,
0046002,0056456,0007370,0121657,
0147023,0013706,0156647,0177115,
0047747,0026504,0103144,0054507,
0150563,0146036,0007051,0177135,
0051234,0063625,0173266,0003111,
0151471,0153642,0003442,0147666,
};
#endif
#if IBMPC
static short A[36] = {
0xfa6d,0x9edd,0x3980,0xc026,
0xd5b8,0x59de,0x0d20,0x4077,
0xb91e,0x91b1,0x0bfb,0xc0e8,
0x4126,0x80db,0x0835,0x4130,
0x1816,0x08cb,0x4b24,0xc181,
0x4d4a,0xe6e2,0xf2e9,0x41b9,
0xb64d,0x6d53,0x0b99,0xc1f8,
0x4f7e,0x7992,0xbde2,0x421f,
0x59f7,0x40e4,0x3af4,0xc247,
};
static short B[36] = {
/* 0x0000,0x0000,0x0000,0x3ff0, */
0xe8f0,0xdd87,0xf59f,0xc060,
0x231e,0x3566,0xb917,0x40c0,
0x3d26,0xdf46,0x2186,0xc114,
0x1476,0xc1df,0x4ba5,0x4160,
0xffca,0xdbb4,0x62f8,0xc1a2,
0x8b29,0x90cc,0xe5a8,0x41dc,
0x3fcc,0xc1c5,0x7983,0xc20e,
0xc0c9,0xbed6,0x8cf2,0x4233,
0x59f7,0x40e4,0x3af4,0xc247,
};
#endif
#if MIEEE
static short A[36] = {
0xc026,0x3980,0x9edd,0xfa6d,
0x4077,0x0d20,0x59de,0xd5b8,
0xc0e8,0x0bfb,0x91b1,0xb91e,
0x4130,0x0835,0x80db,0x4126,
0xc181,0x4b24,0x08cb,0x1816,
0x41b9,0xf2e9,0xe6e2,0x4d4a,
0xc1f8,0x0b99,0x6d53,0xb64d,
0x421f,0xbde2,0x7992,0x4f7e,
0xc247,0x3af4,0x40e4,0x59f7,
};
static short B[36] = {
/* 0x3ff0,0x0000,0x0000,0x0000, */
0xc060,0xf59f,0xdd87,0xe8f0,
0x40c0,0xb917,0x3566,0x231e,
0xc114,0x2186,0xdf46,0x3d26,
0x4160,0x4ba5,0xc1df,0x1476,
0xc1a2,0x62f8,0xdbb4,0xffca,
0x41dc,0xe5a8,0x90cc,0x8b29,
0xc20e,0x7983,0xc1c5,0x3fcc,
0x4233,0x8cf2,0xbed6,0xc0c9,
0xc247,0x3af4,0x40e4,0x59f7,
};
#endif
#endif /* 0 */
/* 8 <= x <= 20
x md_exp(-x) Ei(x) - 1 = 1/x R(1/x)
Theoretical peak absolute error = 1.07e-17 */
#if UNK
static double A2[10] = {
-2.106934601691916512584E0,
1.732733869664688041885E0,
-2.423619178935841904839E-1,
2.322724180937565842585E-2,
2.372880440493179832059E-4,
-8.343219561192552752335E-5,
1.363408795605250394881E-5,
-3.655412321999253963714E-7,
1.464941733975961318456E-8,
6.176407863710360207074E-10,
};
static double B2[9] = {
/* 1.000000000000000000000E0, */
-2.298062239901678075778E-1,
1.105077041474037862347E-1,
-1.566542966630792353556E-2,
2.761106850817352773874E-3,
-2.089148012284048449115E-4,
1.708528938807675304186E-5,
-4.459311796356686423199E-7,
1.394634930353847498145E-8,
6.150865933977338354138E-10,
};
#endif
#if DEC
static short A2[40] = {
0140406,0154004,0035104,0173336,
0040335,0145071,0031560,0150165,
0137570,0026670,0176230,0055040,
0036676,0043416,0077122,0054476,
0035170,0150206,0034407,0175571,
0134656,0174121,0123231,0021751,
0034144,0136766,0036746,0121115,
0132704,0037632,0135077,0107300,
0031573,0126321,0117076,0004314,
0030451,0143233,0041352,0172464,
};
static short B2[36] = {
/* 0040200,0000000,0000000,0000000, */
0137553,0051122,0120721,0170437,
0037342,0050734,0175047,0032132,
0136600,0052311,0101406,0147050,
0036064,0171657,0120001,0071165,
0135133,0010043,0151244,0066340,
0034217,0051141,0026115,0043305,
0132757,0064120,0106341,0051217,
0031557,0114261,0060663,0135017,
0030451,0011337,0001344,0175542,
};
#endif
#if IBMPC
static short A2[40] = {
0x9edc,0x8748,0xdb00,0xc000,
0x1a0f,0x266e,0xb947,0x3ffb,
0x0b44,0x1f93,0x05b7,0xbfcf,
0x4b28,0xcfca,0xc8e1,0x3f97,
0xff6f,0xc720,0x1a10,0x3f2f,
0x247d,0x34d3,0xdf0a,0xbf15,
0xd44a,0xc7bc,0x97be,0x3eec,
0xf1d8,0x5747,0x87f3,0xbe98,
0xc119,0x33c7,0x759a,0x3e4f,
0x5ea6,0x685d,0x38d3,0x3e05,
};
static short B2[36] = {
/* 0x0000,0x0000,0x0000,0x3ff0, */
0x3e24,0x543a,0x6a4a,0xbfcd,
0xe68b,0x9f44,0x4a3b,0x3fbc,
0xd9c5,0x3060,0x0a99,0xbf90,
0x2e4f,0xf400,0x9e75,0x3f66,
0x8d9c,0x7a54,0x6204,0xbf2b,
0xa8d9,0x2589,0xea4c,0x3ef1,
0x2a52,0x119c,0xed0a,0xbe9d,
0x7742,0x2c36,0xf316,0x3e4d,
0x9f6c,0xe05c,0x225b,0x3e05,
};
#endif
#if MIEEE
static short A2[40] = {
0xc000,0xdb00,0x8748,0x9edc,
0x3ffb,0xb947,0x266e,0x1a0f,
0xbfcf,0x05b7,0x1f93,0x0b44,
0x3f97,0xc8e1,0xcfca,0x4b28,
0x3f2f,0x1a10,0xc720,0xff6f,
0xbf15,0xdf0a,0x34d3,0x247d,
0x3eec,0x97be,0xc7bc,0xd44a,
0xbe98,0x87f3,0x5747,0xf1d8,
0x3e4f,0x759a,0x33c7,0xc119,
0x3e05,0x38d3,0x685d,0x5ea6,
};
static short B2[36] = {
/* 0x3ff0,0x0000,0x0000,0x0000, */
0xbfcd,0x6a4a,0x543a,0x3e24,
0x3fbc,0x4a3b,0x9f44,0xe68b,
0xbf90,0x0a99,0x3060,0xd9c5,
0x3f66,0x9e75,0xf400,0x2e4f,
0xbf2b,0x6204,0x7a54,0x8d9c,
0x3ef1,0xea4c,0x2589,0xa8d9,
0xbe9d,0xed0a,0x119c,0x2a52,
0x3e4d,0xf316,0x2c36,0x7742,
0x3e05,0x225b,0xe05c,0x9f6c,
};
#endif
/* x > 20
x md_exp(-x) Ei(x) - 1 = 1/x A3(1/x)/B3(1/x)
Theoretical absolute error = 6.15e-17 */
#if UNK
static double A3[9] = {
-7.657847078286127362028E-1,
6.886192415566705051750E-1,
-2.132598113545206124553E-1,
3.346107552384193813594E-2,
-3.076541477344756050249E-3,
1.747119316454907477380E-4,
-6.103711682274170530369E-6,
1.218032765428652199087E-7,
-1.086076102793290233007E-9,
};
static double B3[9] = {
/* 1.000000000000000000000E0, */
-1.888802868662308731041E0,
1.066691687211408896850E0,
-2.751915982306380647738E-1,
3.930852688233823569726E-2,
-3.414684558602365085394E-3,
1.866844370703555398195E-4,
-6.345146083130515357861E-6,
1.239754287483206878024E-7,
-1.086076102793126632978E-9,
};
#endif
#if DEC
static short A3[36] = {
0140104,0005167,0071746,0115510,
0040060,0044531,0140741,0154556,
0137532,0060307,0126506,0071123,
0037011,0007173,0010405,0127224,
0136111,0117715,0003654,0175577,
0035067,0031340,0102657,0147714,
0133714,0147173,0167473,0136640,
0032402,0144407,0115547,0060114,
0130625,0042347,0156431,0113425,
};
static short B3[36] = {
/* 0040200,0000000,0000000,0000000, */
0140361,0142112,0155277,0067714,
0040210,0104532,0065676,0074326,
0137614,0162751,0142421,0131033,
0037041,0000772,0053236,0002632,
0136137,0144346,0100536,0153136,
0035103,0140270,0152211,0166215,
0133724,0164143,0145763,0021153,
0032405,0017033,0035333,0025736,
0130625,0042347,0156431,0077134,
};
#endif
#if IBMPC
static short A3[36] = {
0xd369,0xee7c,0x814e,0xbfe8,
0x3b2e,0x383c,0x092b,0x3fe6,
0xce4a,0xf5a8,0x4c18,0xbfcb,
0xb5d2,0x6220,0x21cf,0x3fa1,
0x9f70,0xa0f5,0x33f9,0xbf69,
0xf9f9,0x10b5,0xe65c,0x3f26,
0x77b4,0x7de7,0x99cf,0xbed9,
0xec09,0xf36c,0x5920,0x3e80,
0x32e3,0xfba3,0xa89c,0xbe12,
};
static short B3[36] = {
/* 0x0000,0x0000,0x0000,0x3ff0, */
0xedf9,0x5b57,0x3889,0xbffe,
0xcf1b,0x4d77,0x112b,0x3ff1,
0x3643,0x38a2,0x9cbd,0xbfd1,
0xc0b3,0x4ad3,0x203f,0x3fa4,
0xdacc,0xd02b,0xf91c,0xbf6b,
0x3d92,0x1a91,0x7817,0x3f28,
0x644d,0x797e,0x9d0c,0xbeda,
0x657c,0x675b,0xa3c3,0x3e80,
0x2fcb,0xfba3,0xa89c,0xbe12,
};
#endif
#if MIEEE
static short A3[36] = {
0xbfe8,0x814e,0xee7c,0xd369,
0x3fe6,0x092b,0x383c,0x3b2e,
0xbfcb,0x4c18,0xf5a8,0xce4a,
0x3fa1,0x21cf,0x6220,0xb5d2,
0xbf69,0x33f9,0xa0f5,0x9f70,
0x3f26,0xe65c,0x10b5,0xf9f9,
0xbed9,0x99cf,0x7de7,0x77b4,
0x3e80,0x5920,0xf36c,0xec09,
0xbe12,0xa89c,0xfba3,0x32e3,
};
static short B3[36] = {
/* 0x3ff0,0x0000,0x0000,0x0000, */
0xbffe,0x3889,0x5b57,0xedf9,
0x3ff1,0x112b,0x4d77,0xcf1b,
0xbfd1,0x9cbd,0x38a2,0x3643,
0x3fa4,0x203f,0x4ad3,0xc0b3,
0xbf6b,0xf91c,0xd02b,0xdacc,
0x3f28,0x7817,0x1a91,0x3d92,
0xbeda,0x9d0c,0x797e,0x644d,
0x3e80,0xa3c3,0x675b,0x657c,
0xbe12,0xa89c,0xfba3,0x2fcb,
};
#endif
/* 16 <= x <= 32
x md_exp(-x) Ei(x) - 1 = 1/x A4(1/x) / B4(1/x)
Theoretical absolute error = 1.22e-17 */
#if UNK
static double A4[8] = {
-2.458119367674020323359E-1,
-1.483382253322077687183E-1,
7.248291795735551591813E-2,
-1.348315687380940523823E-2,
1.342775069788636972294E-3,
-7.942465637159712264564E-5,
2.644179518984235952241E-6,
-4.239473659313765177195E-8,
};
static double B4[8] = {
/* 1.000000000000000000000E0, */
-1.044225908443871106315E-1,
-2.676453128101402655055E-1,
9.695000254621984627876E-2,
-1.601745692712991078208E-2,
1.496414899205908021882E-3,
-8.462452563778485013756E-5,
2.728938403476726394024E-6,
-4.239462431819542051337E-8,
};
#endif
#if DEC
static short A4[32] = {
0137573,0133037,0152607,0113356,
0137427,0162771,0145061,0126345,
0037224,0070754,0110451,0174104,
0136534,0164165,0072170,0063753,
0035660,0000016,0002560,0147751,
0134646,0110311,0123316,0047432,
0033461,0071250,0101031,0075202,
0132066,0012601,0077305,0170177,
};
static short B4[32] = {
/* 0040200,0000000,0000000,0000000, */
0137325,0155602,0162437,0030710,
0137611,0004316,0071344,0176361,
0037306,0106671,0011103,0155053,
0136603,0033412,0132530,0175171,
0035704,0021532,0015516,0166130,
0134661,0074162,0036741,0073466,
0033467,0021316,0003100,0171325,
0132066,0012541,0162202,0150160,
};
#endif
#if IBMPC
static short A4[] = {
0xf2de,0xfab0,0x76c3,0xbfcf,
0x359d,0x3946,0xfcbf,0xbfc2,
0x3f09,0x9225,0x8e3d,0x3fb2,
0x0cfd,0xae8f,0x9d0e,0xbf8b,
0x19fd,0xc0ae,0x0001,0x3f56,
0xc9e3,0x34d9,0xd219,0xbf14,
0x2f50,0x1043,0x2e55,0x3ec6,
0xbe10,0x2fd8,0xc2b0,0xbe66,
};
static short B4[] = {
/* 0x0000,0x0000,0x0000,0x3ff0, */
0xe639,0x5ca3,0xbb70,0xbfba,
0x9f9e,0xce5c,0x2119,0xbfd1,
0x7b45,0x2248,0xd1b7,0x3fb8,
0x1f4f,0x56ab,0x66e1,0xbf90,
0xdd8b,0x4369,0x846b,0x3f58,
0x2ee7,0x47bc,0x2f0e,0xbf16,
0x1e5b,0xc0c8,0xe459,0x3ec6,
0x5a0e,0x3c90,0xc2ac,0xbe66,
};
#endif
#if MIEEE
static short A4[32] = {
0xbfcf,0x76c3,0xfab0,0xf2de,
0xbfc2,0xfcbf,0x3946,0x359d,
0x3fb2,0x8e3d,0x9225,0x3f09,
0xbf8b,0x9d0e,0xae8f,0x0cfd,
0x3f56,0x0001,0xc0ae,0x19fd,
0xbf14,0xd219,0x34d9,0xc9e3,
0x3ec6,0x2e55,0x1043,0x2f50,
0xbe66,0xc2b0,0x2fd8,0xbe10,
};
static short B4[32] = {
/* 0x3ff0,0x0000,0x0000,0x0000, */
0xbfba,0xbb70,0x5ca3,0xe639,
0xbfd1,0x2119,0xce5c,0x9f9e,
0x3fb8,0xd1b7,0x2248,0x7b45,
0xbf90,0x66e1,0x56ab,0x1f4f,
0x3f58,0x846b,0x4369,0xdd8b,
0xbf16,0x2f0e,0x47bc,0x2ee7,
0x3ec6,0xe459,0xc0c8,0x1e5b,
0xbe66,0xc2ac,0x3c90,0x5a0e,
};
#endif
#if 0
/* 20 <= x <= 40
x md_exp(-x) Ei(x) - 1 = 1/x A4(1/x) / B4(1/x)
Theoretical absolute error = 1.78e-17 */
#if UNK
static double A4[8] = {
2.067245813525780707978E-1,
-5.153749551345223645670E-1,
1.928289589546695033096E-1,
-3.124468842857260044075E-2,
2.740283734277352539912E-3,
-1.377775664366875175601E-4,
3.803788980664744242323E-6,
-4.611038277393688031154E-8,
};
static double B4[8] = {
/* 1.000000000000000000000E0, */
-8.544436025219516861531E-1,
2.507436807692907385181E-1,
-3.647688090228423114064E-2,
3.008576950332041388892E-3,
-1.452926405348421286334E-4,
3.896007735260115431965E-6,
-4.611037642697098234083E-8,
};
#endif
#if DEC
static short A4[32] = {
0037523,0127633,0150301,0022031,
0140003,0167634,0170572,0170420,
0037505,0072364,0060672,0063220,
0136777,0172334,0057456,0102640,
0036063,0113125,0002476,0047251,
0135020,0074142,0042600,0043630,
0033577,0042230,0155372,0136105,
0132106,0005346,0165333,0114541,
};
static short B4[28] = {
/* 0040200,0000000,0000000,0000000, */
0140132,0136320,0160433,0131535,
0037600,0060571,0144452,0060214,
0137025,0064310,0024220,0176472,
0036105,0025613,0115762,0166605,
0135030,0054662,0035454,0061763,
0033602,0135163,0116430,0000066,
0132106,0005345,0020602,0137133,
};
#endif
#if IBMPC
static short A4[32] = {
0x2483,0x7a18,0x75f3,0x3fca,
0x5e22,0x9e2f,0x7df3,0xbfe0,
0x4cd2,0x8c37,0xae9e,0x3fc8,
0xd0b4,0x8be5,0xfe9b,0xbf9f,
0xc9d5,0xa0a7,0x72ca,0x3f66,
0x08f3,0x48b0,0x0f0c,0xbf22,
0x5789,0x1b5f,0xe893,0x3ecf,
0x732c,0xdd5b,0xc15c,0xbe68,
};
static short B4[28] = {
/* 0x0000,0x0000,0x0000,0x3ff0, */
0x766c,0x1c23,0x579a,0xbfeb,
0x4c11,0x3925,0x0c2f,0x3fd0,
0x1fa7,0x0512,0xad19,0xbfa2,
0x5db1,0x737e,0xa571,0x3f68,
0x8c7e,0x4765,0x0b36,0xbf23,
0x0007,0x73a3,0x574e,0x3ed0,
0x57cb,0xa430,0xc15c,0xbe68,
};
#endif
#if MIEEE
static short A4[32] = {
0x3fca,0x75f3,0x7a18,0x2483,
0xbfe0,0x7df3,0x9e2f,0x5e22,
0x3fc8,0xae9e,0x8c37,0x4cd2,
0xbf9f,0xfe9b,0x8be5,0xd0b4,
0x3f66,0x72ca,0xa0a7,0xc9d5,
0xbf22,0x0f0c,0x48b0,0x08f3,
0x3ecf,0xe893,0x1b5f,0x5789,
0xbe68,0xc15c,0xdd5b,0x732c,
};
static short B4[28] = {
/* 0x3ff0,0x0000,0x0000,0x0000, */
0xbfeb,0x579a,0x1c23,0x766c,
0x3fd0,0x0c2f,0x3925,0x4c11,
0xbfa2,0xad19,0x0512,0x1fa7,
0x3f68,0xa571,0x737e,0x5db1,
0xbf23,0x0b36,0x4765,0x8c7e,
0x3ed0,0x574e,0x73a3,0x0007,
0xbe68,0xc15c,0xa430,0x57cb,
};
#endif
#endif /* 0 */
/* 4 <= x <= 8
x md_exp(-x) Ei(x) - 1 = 1/x A5(1/x) / B5(1/x)
Theoretical absolute error = 2.20e-17 */
#if UNK
static double A5[8] = {
-1.373215375871208729803E0,
-7.084559133740838761406E-1,
1.580806855547941010501E0,
-2.601500427425622944234E-1,
2.994674694113713763365E-2,
-1.038086040188744005513E-3,
4.371064420753005429514E-5,
2.141783679522602903795E-6,
};
static double B5[8] = {
/* 1.000000000000000000000E0, */
8.585231423622028380768E-1,
4.483285822873995129957E-1,
7.687932158124475434091E-2,
2.449868241021887685904E-2,
8.832165941927796567926E-4,
4.590952299511353531215E-4,
-4.729848351866523044863E-6,
2.665195537390710170105E-6,
};
#endif
#if DEC
static short A5[32] = {
0140257,0142605,0076335,0113632,
0140065,0056535,0161231,0074311,
0040312,0053741,0004357,0076405,
0137605,0031142,0165503,0136705,
0036765,0051341,0053573,0007602,
0135610,0010143,0027643,0110522,
0034467,0052762,0062024,0120161,
0033417,0135620,0036500,0062647,
};
static short B[32] = {
/* 0040200,0000000,0000000,0000000, */
0040133,0144054,0031516,0004100,
0037745,0105522,0166622,0123146,
0037235,0071347,0157560,0157464,
0036710,0130565,0173747,0041670,
0035547,0103651,0106243,0101240,
0035360,0131267,0176263,0140257,
0133636,0132426,0102537,0102531,
0033462,0155665,0167503,0176350,
};
#endif
#if IBMPC
static short A5[32] = {
0xb2f3,0xaf9b,0xf8b0,0xbff5,
0x2f19,0xbc53,0xabab,0xbfe6,
0xefa1,0x211d,0x4afc,0x3ff9,
0x77b9,0x5d68,0xa64c,0xbfd0,
0x61f0,0x2aef,0xaa5c,0x3f9e,
0x722a,0x65f4,0x020c,0xbf51,
0x940e,0x4c82,0xeabe,0x3f06,
0x0cb5,0x07a8,0xf772,0x3ec1,
};
static short B5[32] = {
/* 0x0000,0x0000,0x0000,0x3ff0, */
0xc108,0x8669,0x7905,0x3feb,
0x54cd,0x5db2,0xb16a,0x3fdc,
0x1be7,0xfbee,0xae5c,0x3fb3,
0xe877,0xbefc,0x162e,0x3f99,
0x7054,0x3194,0xf0f5,0x3f4c,
0x7816,0xff96,0x1656,0x3f3e,
0xf0ab,0xd0ab,0xd6a2,0xbed3,
0x7f9d,0xbde8,0x5b76,0x3ec6,
};
#endif
#if MIEEE
static short A5[32] = {
0xbff5,0xf8b0,0xaf9b,0xb2f3,
0xbfe6,0xabab,0xbc53,0x2f19,
0x3ff9,0x4afc,0x211d,0xefa1,
0xbfd0,0xa64c,0x5d68,0x77b9,
0x3f9e,0xaa5c,0x2aef,0x61f0,
0xbf51,0x020c,0x65f4,0x722a,
0x3f06,0xeabe,0x4c82,0x940e,
0x3ec1,0xf772,0x07a8,0x0cb5,
};
static short B5[32] = {
/* 0x3ff0,0x0000,0x0000,0x0000, */
0x3feb,0x7905,0x8669,0xc108,
0x3fdc,0xb16a,0x5db2,0x54cd,
0x3fb3,0xae5c,0xfbee,0x1be7,
0x3f99,0x162e,0xbefc,0xe877,
0x3f4c,0xf0f5,0x3194,0x7054,
0x3f3e,0x1656,0xff96,0x7816,
0xbed3,0xd6a2,0xd0ab,0xf0ab,
0x3ec6,0x5b76,0xbde8,0x7f9d,
};
#endif
/* 2 <= x <= 4
x md_exp(-x) Ei(x) - 1 = 1/x A6(1/x) / B6(1/x)
Theoretical absolute error = 4.89e-17 */
#if UNK
static double A6[8] = {
1.981808503259689673238E-2,
-1.271645625984917501326E0,
-2.088160335681228318920E0,
2.755544509187936721172E0,
-4.409507048701600257171E-1,
4.665623805935891391017E-2,
-1.545042679673485262580E-3,
7.059980605299617478514E-5,
};
static double B6[7] = {
/* 1.000000000000000000000E0, */
1.476498670914921440652E0,
5.629177174822436244827E-1,
1.699017897879307263248E-1,
2.291647179034212017463E-2,
4.450150439728752875043E-3,
1.727439612206521482874E-4,
3.953167195549672482304E-5,
};
#endif
#if DEC
static short A6[32] = {
0036642,0054611,0061263,0000140,
0140242,0142510,0125732,0072035,
0140405,0122153,0037643,0104527,
0040460,0055327,0055550,0116240,
0137741,0142112,0070441,0103510,
0037077,0015234,0104750,0146765,
0135712,0101407,0107554,0020253,
0034624,0007373,0072621,0063735,
};
static short B6[28] = {
/* 0040200,0000000,0000000,0000000, */
0040274,0176750,0110025,0061006,
0040020,0015540,0021354,0155050,
0037455,0175274,0015257,0021112,
0036673,0135523,0016042,0117203,
0036221,0151221,0046352,0144174,
0035065,0021232,0117727,0152432,
0034445,0147317,0037300,0067123,
};
#endif
#if IBMPC
static short A6[32] = {
0x600c,0x2c56,0x4b31,0x3f94,
0x4e84,0x157b,0x58a9,0xbff4,
0x712b,0x67f4,0xb48d,0xc000,
0x1394,0xeb6d,0x0b5a,0x4006,
0x30e9,0x4e24,0x3889,0xbfdc,
0x19bf,0x913d,0xe353,0x3fa7,
0x8415,0xf1ed,0x5060,0xbf59,
0x2cfc,0x6eb2,0x81df,0x3f12,
};
static short B6[28] = {
/* 0x0000,0x0000,0x0000,0x3ff0, */
0xac41,0x1202,0x9fbd,0x3ff7,
0x9b45,0x045d,0x036c,0x3fe2,
0xe449,0x8355,0xbf57,0x3fc5,
0x53d0,0x6384,0x776a,0x3f97,
0x590f,0x299d,0x3a52,0x3f72,
0xfaa3,0x53fa,0xa453,0x3f26,
0x0dca,0xe7d8,0xb9d9,0x3f04,
};
#endif
#if MIEEE
static short A6[32] = {
0x3f94,0x4b31,0x2c56,0x600c,
0xbff4,0x58a9,0x157b,0x4e84,
0xc000,0xb48d,0x67f4,0x712b,
0x4006,0x0b5a,0xeb6d,0x1394,
0xbfdc,0x3889,0x4e24,0x30e9,
0x3fa7,0xe353,0x913d,0x19bf,
0xbf59,0x5060,0xf1ed,0x8415,
0x3f12,0x81df,0x6eb2,0x2cfc,
};
static short B6[28] = {
/* 0x3ff0,0x0000,0x0000,0x0000, */
0x3ff7,0x9fbd,0x1202,0xac41,
0x3fe2,0x036c,0x045d,0x9b45,
0x3fc5,0xbf57,0x8355,0xe449,
0x3f97,0x776a,0x6384,0x53d0,
0x3f72,0x3a52,0x299d,0x590f,
0x3f26,0xa453,0x53fa,0xfaa3,
0x3f04,0xb9d9,0xe7d8,0x0dca,
};
#endif
/* 32 <= x <= 64
x md_exp(-x) Ei(x) - 1 = 1/x A7(1/x) / B7(1/x)
Theoretical absolute error = 7.71e-18 */
#if UNK
static double A7[6] = {
1.212561118105456670844E-1,
-5.823133179043894485122E-1,
2.348887314557016779211E-1,
-3.040034318113248237280E-2,
1.510082146865190661777E-3,
-2.523137095499571377122E-5,
};
static double B7[5] = {
/* 1.000000000000000000000E0, */
-1.002252150365854016662E0,
2.928709694872224144953E-1,
-3.337004338674007801307E-2,
1.560544881127388842819E-3,
-2.523137093603234562648E-5,
};
#endif
#if DEC
static short A7[24] = {
0037370,0052437,0152524,0150125,
0140025,0011174,0050154,0131330,
0037560,0103253,0167464,0062245,
0136771,0005043,0174001,0023345,
0035705,0166762,0157300,0016451,
0134323,0123764,0157767,0134477,
};
static short B7[20] = {
/* 0040200,0000000,0000000,0000000, */
0140200,0044714,0064025,0060324,
0037625,0171457,0003712,0073131,
0137010,0127406,0150061,0141746,
0035714,0105462,0072356,0103712,
0134323,0123764,0156514,0077414,
};
#endif
#if IBMPC
static short A7[24] = {
0x9a0b,0xfaaa,0x0aa3,0x3fbf,
0x965b,0x8a0d,0xa24f,0xbfe2,
0x8c95,0x7de6,0x10d5,0x3fce,
0x24dd,0x7f00,0x2144,0xbf9f,
0x03a5,0x5bd8,0xbdbe,0x3f58,
0xf728,0x9bfe,0x74fe,0xbefa,
};
static short B7[20] = {
/* 0x0000,0x0000,0x0000,0x3ff0, */
0xac1a,0x8d02,0x0939,0xbff0,
0x4ecb,0xe0f9,0xbe65,0x3fd2,
0x387d,0xda06,0x15e0,0xbfa1,
0xd0f9,0x4e9d,0x9166,0x3f59,
0x8fe2,0x9ba9,0x74fe,0xbefa,
};
#endif
#if MIEEE
static short A7[24] = {
0x3fbf,0x0aa3,0xfaaa,0x9a0b,
0xbfe2,0xa24f,0x8a0d,0x965b,
0x3fce,0x10d5,0x7de6,0x8c95,
0xbf9f,0x2144,0x7f00,0x24dd,
0x3f58,0xbdbe,0x5bd8,0x03a5,
0xbefa,0x74fe,0x9bfe,0xf728,
};
static short B7[20] = {
/* 0x3ff0,0x0000,0x0000,0x0000, */
0xbff0,0x0939,0x8d02,0xac1a,
0x3fd2,0xbe65,0xe0f9,0x4ecb,
0xbfa1,0x15e0,0xda06,0x387d,
0x3f59,0x9166,0x4e9d,0xd0f9,
0xbefa,0x74fe,0x9ba9,0x8fe2,
};
#endif
double ei (x)
double x;
{
double f, w;
if (x <= 0.0)
{
mtherr("ei", DOMAIN);
return 0.0;
}
else if (x < 2.0)
{
/* Power series.
inf n
- x
Ei(x) = EUL + ln x + > ----
- n n!
n=1
*/
f = polevl(x,A,5) / p1evl(x,B,6);
/* f = polevl(x,A,6) / p1evl(x,B,7); */
/* f = polevl(x,A,8) / p1evl(x,B,9); */
return (EUL + md_log(x) + x * f);
}
else if (x < 4.0)
{
/* Asymptotic expansion.
1 2 6
x md_exp(-x) Ei(x) = 1 + --- + --- + ---- + ...
x 2 3
x x
*/
w = 1.0/x;
f = polevl(w,A6,7) / p1evl(w,B6,7);
return (md_exp(x) * w * (1.0 + w * f));
}
else if (x < 8.0)
{
w = 1.0/x;
f = polevl(w,A5,7) / p1evl(w,B5,8);
return (md_exp(x) * w * (1.0 + w * f));
}
else if (x < 16.0)
{
w = 1.0/x;
f = polevl(w,A2,9) / p1evl(w,B2,9);
return (md_exp(x) * w * (1.0 + w * f));
}
else if (x < 32.0)
{
w = 1.0/x;
f = polevl(w,A4,7) / p1evl(w,B4,8);
return (md_exp(x) * w * (1.0 + w * f));
}
else if (x < 64.0)
{
w = 1.0/x;
f = polevl(w,A7,5) / p1evl(w,B7,5);
return (md_exp(x) * w * (1.0 + w * f));
}
else
{
w = 1.0/x;
f = polevl(w,A3,8) / p1evl(w,B3,9);
return (md_exp(x) * w * (1.0 + w * f));
}
}