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Diffstat (limited to 'libm/ldouble/ellpkl.c')
| -rw-r--r-- | libm/ldouble/ellpkl.c | 203 |
1 files changed, 203 insertions, 0 deletions
diff --git a/libm/ldouble/ellpkl.c b/libm/ldouble/ellpkl.c new file mode 100644 index 000000000..dd42ac861 --- /dev/null +++ b/libm/ldouble/ellpkl.c @@ -0,0 +1,203 @@ +/* ellpkl.c + * + * Complete elliptic integral of the first kind + * + * + * + * SYNOPSIS: + * + * long double m1, y, ellpkl(); + * + * y = ellpkl( m1 ); + * + * + * + * DESCRIPTION: + * + * Approximates the integral + * + * + * + * pi/2 + * - + * | | + * | dt + * K(m) = | ------------------ + * | 2 + * | | sqrt( 1 - m sin t ) + * - + * 0 + * + * where m = 1 - m1, using the approximation + * + * P(x) - log x Q(x). + * + * The argument m1 is used rather than m so that the logarithmic + * singularity at m = 1 will be shifted to the origin; this + * preserves maximum accuracy. + * + * K(0) = pi/2. + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE 0,1 10000 1.1e-19 3.3e-20 + * + * ERROR MESSAGES: + * + * message condition value returned + * ellpkl domain x<0, x>1 0.0 + * + */ + +/* ellpkl.c */ + + +/* +Cephes Math Library, Release 2.3: October, 1995 +Copyright 1984, 1987, 1995 by Stephen L. Moshier +*/ + +#include <math.h> + +#if UNK +static long double P[13] = { + 1.247539729154838838628E-6L, + 2.149421654232011240659E-4L, + 2.265267575136470585139E-3L, + 6.723088676584254248821E-3L, + 8.092066790639263075808E-3L, + 5.664069509748147028621E-3L, + 4.579865994050801042865E-3L, + 5.797368411662027645234E-3L, + 8.767698209432225911803E-3L, + 1.493761594388688915057E-2L, + 3.088514457872042326871E-2L, + 9.657359027999314232753E-2L, + 1.386294361119890618992E0L, +}; +static long double Q[12] = { + 5.568631677757315398993E-5L, + 1.036110372590318802997E-3L, + 5.500459122138244213579E-3L, + 1.337330436245904844528E-2L, + 2.033103735656990487115E-2L, + 2.522868345512332304268E-2L, + 3.026786461242788135379E-2L, + 3.738370118296930305919E-2L, + 4.882812208418620146046E-2L, + 7.031249999330222751046E-2L, + 1.249999999999978263154E-1L, + 4.999999999999999999924E-1L, +}; +static long double C1 = 1.386294361119890618834L; /* log(4) */ +#endif +#if IBMPC +static short P[] = { +0xf098,0xad01,0x2381,0xa771,0x3feb, XPD +0xd6ed,0xea22,0x1922,0xe162,0x3ff2, XPD +0x3733,0xe2f1,0xe226,0x9474,0x3ff6, XPD +0x3031,0x3c9d,0x5aff,0xdc4d,0x3ff7, XPD +0x9a46,0x4310,0x968e,0x8494,0x3ff8, XPD +0xbe4c,0x3ff2,0xa8a7,0xb999,0x3ff7, XPD +0xf35c,0x0eaf,0xb355,0x9612,0x3ff7, XPD +0xbc56,0x8fd4,0xd9dd,0xbdf7,0x3ff7, XPD +0xc01e,0x867f,0x6444,0x8fa6,0x3ff8, XPD +0x4ba3,0x6392,0xe6fd,0xf4bc,0x3ff8, XPD +0x62c3,0xbb12,0xd7bc,0xfd02,0x3ff9, XPD +0x08fe,0x476c,0x5fdf,0xc5c8,0x3ffb, XPD +0x79ad,0xd1cf,0x17f7,0xb172,0x3fff, XPD +}; +static short Q[] = { +0x96a4,0x8474,0xba33,0xe990,0x3ff0, XPD +0xe5a7,0xa50e,0x1854,0x87ce,0x3ff5, XPD +0x8999,0x72e3,0x3205,0xb43d,0x3ff7, XPD +0x3255,0x13eb,0xb438,0xdb1b,0x3ff8, XPD +0xb717,0x497f,0x4691,0xa68d,0x3ff9, XPD +0x30be,0x8c6b,0x624b,0xceac,0x3ff9, XPD +0xa858,0x2a0d,0x5014,0xf7f4,0x3ff9, XPD +0x8615,0xbfa6,0xa6df,0x991f,0x3ffa, XPD +0x103c,0xa076,0xff37,0xc7ff,0x3ffa, XPD +0xf508,0xc515,0xffff,0x8fff,0x3ffb, XPD +0x1af5,0xfffb,0xffff,0xffff,0x3ffb, XPD +0x0000,0x0000,0x0000,0x8000,0x3ffe, XPD +}; +static unsigned short ac1[] = { +0x79ac,0xd1cf,0x17f7,0xb172,0x3fff, XPD +}; +#define C1 (*(long double *)ac1) +#endif + +#ifdef MIEEE +static long P[39] = { +0x3feb0000,0xa7712381,0xad01f098, +0x3ff20000,0xe1621922,0xea22d6ed, +0x3ff60000,0x9474e226,0xe2f13733, +0x3ff70000,0xdc4d5aff,0x3c9d3031, +0x3ff80000,0x8494968e,0x43109a46, +0x3ff70000,0xb999a8a7,0x3ff2be4c, +0x3ff70000,0x9612b355,0x0eaff35c, +0x3ff70000,0xbdf7d9dd,0x8fd4bc56, +0x3ff80000,0x8fa66444,0x867fc01e, +0x3ff80000,0xf4bce6fd,0x63924ba3, +0x3ff90000,0xfd02d7bc,0xbb1262c3, +0x3ffb0000,0xc5c85fdf,0x476c08fe, +0x3fff0000,0xb17217f7,0xd1cf79ad, +}; +static long Q[36] = { +0x3ff00000,0xe990ba33,0x847496a4, +0x3ff50000,0x87ce1854,0xa50ee5a7, +0x3ff70000,0xb43d3205,0x72e38999, +0x3ff80000,0xdb1bb438,0x13eb3255, +0x3ff90000,0xa68d4691,0x497fb717, +0x3ff90000,0xceac624b,0x8c6b30be, +0x3ff90000,0xf7f45014,0x2a0da858, +0x3ffa0000,0x991fa6df,0xbfa68615, +0x3ffa0000,0xc7ffff37,0xa076103c, +0x3ffb0000,0x8fffffff,0xc515f508, +0x3ffb0000,0xffffffff,0xfffb1af5, +0x3ffe0000,0x80000000,0x00000000, +}; +static unsigned long ac1[] = { +0x3fff0000,0xb17217f7,0xd1cf79ac +}; +#define C1 (*(long double *)ac1) +#endif + + +#ifdef ANSIPROT +extern long double polevll ( long double, void *, int ); +extern long double logl ( long double ); +#else +long double polevll(), logl(); +#endif +extern long double MACHEPL, MAXNUML; + +long double ellpkl(x) +long double x; +{ + +if( (x < 0.0L) || (x > 1.0L) ) + { + mtherr( "ellpkl", DOMAIN ); + return( 0.0L ); + } + +if( x > MACHEPL ) + { + return( polevll(x,P,12) - logl(x) * polevll(x,Q,11) ); + } +else + { + if( x == 0.0L ) + { + mtherr( "ellpkl", SING ); + return( MAXNUML ); + } + else + { + return( C1 - 0.5L * logl(x) ); + } + } +} |