CocoRoboDesktop/pdf1.js/node_modules/cephes/cephes/ellpk.c

/*							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 "mconf.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));
    }
  }
}