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-rw-r--r--libm/double/ellpk.c234
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diff --git a/libm/double/ellpk.c b/libm/double/ellpk.c
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--- a/libm/double/ellpk.c
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-/* ellpk.c
- *
- * Complete elliptic integral of the first kind
- *
- *
- *
- * SYNOPSIS:
- *
- * double m1, y, ellpk();
- *
- * y = ellpk( 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
- * DEC 0,1 16000 3.5e-17 1.1e-17
- * IEEE 0,1 30000 2.5e-16 6.8e-17
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * ellpk domain x<0, x>1 0.0
- *
- */
-
-/* ellpk.c */
-
-
-/*
-Cephes Math Library, Release 2.8: June, 2000
-Copyright 1984, 1987, 2000 by Stephen L. Moshier
-*/
-
-#include <math.h>
-
-#ifdef DEC
-static unsigned short P[] =
-{
-0035020,0127576,0040430,0051544,
-0036025,0070136,0042703,0153716,
-0036402,0122614,0062555,0077777,
-0036441,0102130,0072334,0025172,
-0036341,0043320,0117242,0172076,
-0036312,0146456,0077242,0154141,
-0036420,0003467,0013727,0035407,
-0036564,0137263,0110651,0020237,
-0036775,0001330,0144056,0020305,
-0037305,0144137,0157521,0141734,
-0040261,0071027,0173721,0147572
-};
-static unsigned short Q[] =
-{
-0034366,0130371,0103453,0077633,
-0035557,0122745,0173515,0113016,
-0036302,0124470,0167304,0074473,
-0036575,0132403,0117226,0117576,
-0036703,0156271,0047124,0147733,
-0036766,0137465,0002053,0157312,
-0037031,0014423,0154274,0176515,
-0037107,0177747,0143216,0016145,
-0037217,0177777,0172621,0074000,
-0037377,0177777,0177776,0156435,
-0040000,0000000,0000000,0000000
-};
-static unsigned short ac1[] = {0040261,0071027,0173721,0147572};
-#define C1 (*(double *)ac1)
-#endif
-
-#ifdef IBMPC
-static unsigned short P[] =
-{
-0x0a6d,0xc823,0x15ef,0x3f22,
-0x7afa,0xc8b8,0xae0b,0x3f62,
-0xb000,0x8cad,0x54b1,0x3f80,
-0x854f,0x0e9b,0x308b,0x3f84,
-0x5e88,0x13d4,0x28da,0x3f7c,
-0x5b0c,0xcfd4,0x59a5,0x3f79,
-0xe761,0xe2fa,0x00e6,0x3f82,
-0x2414,0x7235,0x97d6,0x3f8e,
-0xc419,0x1905,0xa05b,0x3f9f,
-0x387c,0xfbea,0xb90b,0x3fb8,
-0x39ef,0xfefa,0x2e42,0x3ff6
-};
-static unsigned short Q[] =
-{
-0x6ff3,0x30e5,0xd61f,0x3efe,
-0xb2c2,0xbee9,0xf4bc,0x3f4d,
-0x8f27,0x1dd8,0x5527,0x3f78,
-0xd3f0,0x73d2,0xb6a0,0x3f8f,
-0x99fb,0x29ca,0x7b97,0x3f98,
-0x7bd9,0xa085,0xd7e6,0x3f9e,
-0x9faa,0x7b17,0x2322,0x3fa3,
-0xc38d,0xf8d1,0xfffc,0x3fa8,
-0x2f00,0xfeb2,0xffff,0x3fb1,
-0xdba4,0xffff,0xffff,0x3fbf,
-0x0000,0x0000,0x0000,0x3fe0
-};
-static unsigned short ac1[] = {0x39ef,0xfefa,0x2e42,0x3ff6};
-#define C1 (*(double *)ac1)
-#endif
-
-#ifdef MIEEE
-static unsigned short P[] =
-{
-0x3f22,0x15ef,0xc823,0x0a6d,
-0x3f62,0xae0b,0xc8b8,0x7afa,
-0x3f80,0x54b1,0x8cad,0xb000,
-0x3f84,0x308b,0x0e9b,0x854f,
-0x3f7c,0x28da,0x13d4,0x5e88,
-0x3f79,0x59a5,0xcfd4,0x5b0c,
-0x3f82,0x00e6,0xe2fa,0xe761,
-0x3f8e,0x97d6,0x7235,0x2414,
-0x3f9f,0xa05b,0x1905,0xc419,
-0x3fb8,0xb90b,0xfbea,0x387c,
-0x3ff6,0x2e42,0xfefa,0x39ef
-};
-static unsigned short Q[] =
-{
-0x3efe,0xd61f,0x30e5,0x6ff3,
-0x3f4d,0xf4bc,0xbee9,0xb2c2,
-0x3f78,0x5527,0x1dd8,0x8f27,
-0x3f8f,0xb6a0,0x73d2,0xd3f0,
-0x3f98,0x7b97,0x29ca,0x99fb,
-0x3f9e,0xd7e6,0xa085,0x7bd9,
-0x3fa3,0x2322,0x7b17,0x9faa,
-0x3fa8,0xfffc,0xf8d1,0xc38d,
-0x3fb1,0xffff,0xfeb2,0x2f00,
-0x3fbf,0xffff,0xffff,0xdba4,
-0x3fe0,0x0000,0x0000,0x0000
-};
-static unsigned short ac1[] = {
-0x3ff6,0x2e42,0xfefa,0x39ef
-};
-#define C1 (*(double *)ac1)
-#endif
-
-#ifdef UNK
-static double P[] =
-{
- 1.37982864606273237150E-4,
- 2.28025724005875567385E-3,
- 7.97404013220415179367E-3,
- 9.85821379021226008714E-3,
- 6.87489687449949877925E-3,
- 6.18901033637687613229E-3,
- 8.79078273952743772254E-3,
- 1.49380448916805252718E-2,
- 3.08851465246711995998E-2,
- 9.65735902811690126535E-2,
- 1.38629436111989062502E0
-};
-
-static double Q[] =
-{
- 2.94078955048598507511E-5,
- 9.14184723865917226571E-4,
- 5.94058303753167793257E-3,
- 1.54850516649762399335E-2,
- 2.39089602715924892727E-2,
- 3.01204715227604046988E-2,
- 3.73774314173823228969E-2,
- 4.88280347570998239232E-2,
- 7.03124996963957469739E-2,
- 1.24999999999870820058E-1,
- 4.99999999999999999821E-1
-};
-static double C1 = 1.3862943611198906188E0; /* log(4) */
-#endif
-
-#ifdef ANSIPROT
-extern double polevl ( double, void *, int );
-extern double p1evl ( double, void *, int );
-extern double log ( double );
-#else
-double polevl(), p1evl(), log();
-#endif
-extern double MACHEP, MAXNUM;
-
-double ellpk(x)
-double x;
-{
-
-if( (x < 0.0) || (x > 1.0) )
- {
- mtherr( "ellpk", DOMAIN );
- return( 0.0 );
- }
-
-if( x > MACHEP )
- {
- return( polevl(x,P,10) - log(x) * polevl(x,Q,10) );
- }
-else
- {
- if( x == 0.0 )
- {
- mtherr( "ellpk", SING );
- return( MAXNUM );
- }
- else
- {
- return( C1 - 0.5 * log(x) );
- }
- }
-}