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Diffstat (limited to 'libm/double/ellpe.c')
| -rw-r--r-- | libm/double/ellpe.c | 195 |
1 files changed, 195 insertions, 0 deletions
diff --git a/libm/double/ellpe.c b/libm/double/ellpe.c new file mode 100644 index 000000000..9b2438e0e --- /dev/null +++ b/libm/double/ellpe.c @@ -0,0 +1,195 @@ +/* ellpe.c + * + * Complete elliptic integral of the second kind + * + * + * + * SYNOPSIS: + * + * double m1, y, ellpe(); + * + * y = ellpe( m1 ); + * + * + * + * DESCRIPTION: + * + * Approximates the integral + * + * + * pi/2 + * - + * | | 2 + * E(m) = | sqrt( 1 - m sin t ) dt + * | | + * - + * 0 + * + * Where m = 1 - m1, using the approximation + * + * P(x) - x log x Q(x). + * + * Though there are no singularities, the argument m1 is used + * rather than m for compatibility with ellpk(). + * + * E(1) = 1; E(0) = pi/2. + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * DEC 0, 1 13000 3.1e-17 9.4e-18 + * IEEE 0, 1 10000 2.1e-16 7.3e-17 + * + * + * ERROR MESSAGES: + * + * message condition value returned + * ellpe domain x<0, x>1 0.0 + * + */ + +/* ellpe.c */ + +/* Elliptic integral of second kind */ + +/* +Cephes Math Library, Release 2.8: June, 2000 +Copyright 1984, 1987, 1989, 2000 by Stephen L. Moshier +*/ + +#include <math.h> + +#ifdef UNK +static double P[] = { + 1.53552577301013293365E-4, + 2.50888492163602060990E-3, + 8.68786816565889628429E-3, + 1.07350949056076193403E-2, + 7.77395492516787092951E-3, + 7.58395289413514708519E-3, + 1.15688436810574127319E-2, + 2.18317996015557253103E-2, + 5.68051945617860553470E-2, + 4.43147180560990850618E-1, + 1.00000000000000000299E0 +}; +static double Q[] = { + 3.27954898576485872656E-5, + 1.00962792679356715133E-3, + 6.50609489976927491433E-3, + 1.68862163993311317300E-2, + 2.61769742454493659583E-2, + 3.34833904888224918614E-2, + 4.27180926518931511717E-2, + 5.85936634471101055642E-2, + 9.37499997197644278445E-2, + 2.49999999999888314361E-1 +}; +#endif + +#ifdef DEC +static unsigned short P[] = { +0035041,0001364,0141572,0117555, +0036044,0066032,0130027,0033404, +0036416,0053617,0064456,0102632, +0036457,0161100,0061177,0122612, +0036376,0136251,0012403,0124162, +0036370,0101316,0151715,0131613, +0036475,0105477,0050317,0133272, +0036662,0154232,0024645,0171552, +0037150,0126220,0047054,0030064, +0037742,0162057,0167645,0165612, +0040200,0000000,0000000,0000000 +}; +static unsigned short Q[] = { +0034411,0106743,0115771,0055462, +0035604,0052575,0155171,0045540, +0036325,0030424,0064332,0167756, +0036612,0052366,0063006,0115175, +0036726,0070430,0004533,0124654, +0037011,0022741,0030675,0030711, +0037056,0174452,0127062,0132122, +0037157,0177750,0142041,0072523, +0037277,0177777,0173137,0002627, +0037577,0177777,0177777,0101101 +}; +#endif + +#ifdef IBMPC +static unsigned short P[] = { +0x53ee,0x986f,0x205e,0x3f24, +0xe6e0,0x5602,0x8d83,0x3f64, +0xd0b3,0xed25,0xcaf1,0x3f81, +0xf4b1,0x0c4f,0xfc48,0x3f85, +0x750e,0x22a0,0xd795,0x3f7f, +0xb671,0xda79,0x1059,0x3f7f, +0xf6d7,0xea19,0xb167,0x3f87, +0xbe6d,0x4534,0x5b13,0x3f96, +0x8607,0x09c5,0x1592,0x3fad, +0xbd71,0xfdf4,0x5c85,0x3fdc, +0x0000,0x0000,0x0000,0x3ff0 +}; +static unsigned short Q[] = { +0x2b66,0x737f,0x31bc,0x3f01, +0x296c,0xbb4f,0x8aaf,0x3f50, +0x5dfe,0x8d1b,0xa622,0x3f7a, +0xd350,0xccc0,0x4a9e,0x3f91, +0x7535,0x012b,0xce23,0x3f9a, +0xa639,0x2637,0x24bc,0x3fa1, +0x568a,0x55c6,0xdf25,0x3fa5, +0x2eaa,0x1884,0xfffd,0x3fad, +0xe0b3,0xfecb,0xffff,0x3fb7, +0xf048,0xffff,0xffff,0x3fcf +}; +#endif + +#ifdef MIEEE +static unsigned short P[] = { +0x3f24,0x205e,0x986f,0x53ee, +0x3f64,0x8d83,0x5602,0xe6e0, +0x3f81,0xcaf1,0xed25,0xd0b3, +0x3f85,0xfc48,0x0c4f,0xf4b1, +0x3f7f,0xd795,0x22a0,0x750e, +0x3f7f,0x1059,0xda79,0xb671, +0x3f87,0xb167,0xea19,0xf6d7, +0x3f96,0x5b13,0x4534,0xbe6d, +0x3fad,0x1592,0x09c5,0x8607, +0x3fdc,0x5c85,0xfdf4,0xbd71, +0x3ff0,0x0000,0x0000,0x0000 +}; +static unsigned short Q[] = { +0x3f01,0x31bc,0x737f,0x2b66, +0x3f50,0x8aaf,0xbb4f,0x296c, +0x3f7a,0xa622,0x8d1b,0x5dfe, +0x3f91,0x4a9e,0xccc0,0xd350, +0x3f9a,0xce23,0x012b,0x7535, +0x3fa1,0x24bc,0x2637,0xa639, +0x3fa5,0xdf25,0x55c6,0x568a, +0x3fad,0xfffd,0x1884,0x2eaa, +0x3fb7,0xffff,0xfecb,0xe0b3, +0x3fcf,0xffff,0xffff,0xf048 +}; +#endif + +#ifdef ANSIPROT +extern double polevl ( double, void *, int ); +extern double log ( double ); +#else +double polevl(), log(); +#endif + +double ellpe(x) +double x; +{ + +if( (x <= 0.0) || (x > 1.0) ) + { + if( x == 0.0 ) + return( 1.0 ); + mtherr( "ellpe", DOMAIN ); + return( 0.0 ); + } +return( polevl(x,P,10) - log(x) * (x * polevl(x,Q,9)) ); +} |