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

/*							tan.c
 *
 *	Circular tangent
 *
 *
 *
 * SYNOPSIS:
 *
 * double x, y, tan();
 *
 * y = tan( x );
 *
 *
 *
 * DESCRIPTION:
 *
 * Returns the circular tangent of the radian argument x.
 *
 * Range reduction is modulo pi/4.  A rational function
 *       x + x**3 P(x**2)/Q(x**2)
 * is employed in the basic interval [0, pi/4].
 *
 *
 *
 * ACCURACY:
 *
 *                      Relative error:
 * arithmetic   domain     # trials      peak         rms
 *    DEC      +-1.07e9      44000      4.1e-17     1.0e-17
 *    IEEE     +-1.07e9      30000      2.9e-16     8.1e-17
 *
 * ERROR MESSAGES:
 *
 *   message         condition          value returned
 * tan total loss   x > 1.073741824e9     0.0
 *
 */
/*							cot.c
 *
 *	Circular cotangent
 *
 *
 *
 * SYNOPSIS:
 *
 * double x, y, cot();
 *
 * y = cot( x );
 *
 *
 *
 * DESCRIPTION:
 *
 * Returns the circular cotangent of the radian argument x.
 *
 * Range reduction is modulo pi/4.  A rational function
 *       x + x**3 P(x**2)/Q(x**2)
 * is employed in the basic interval [0, pi/4].
 *
 *
 *
 * ACCURACY:
 *
 *                      Relative error:
 * arithmetic   domain     # trials      peak         rms
 *    IEEE     +-1.07e9      30000      2.9e-16     8.2e-17
 *
 *
 * ERROR MESSAGES:
 *
 *   message         condition          value returned
 * cot total loss   x > 1.073741824e9       0.0
 * cot singularity  x = 0                  INFINITY
 *
 */

/*
Cephes Math Library Release 2.8:  June, 2000
yright 1984, 1995, 2000 by Stephen L. Moshier
*/

#include "mconf.h"

#ifdef UNK
static double P[] = {-1.30936939181383777646E4, 1.15351664838587416140E6,
                     -1.79565251976484877988E7};
static double Q[] = {
    /* 1.00000000000000000000E0,*/
    1.36812963470692954678E4, -1.32089234440210967447E6,
    2.50083801823357915839E7, -5.38695755929454629881E7};
static double DP1 = 7.853981554508209228515625E-1;
static double DP2 = 7.94662735614792836714E-9;
static double DP3 = 3.06161699786838294307E-17;
static double lossth = 1.073741824e9;
#endif

#ifdef DEC
static unsigned short P[] = {0143514, 0113306, 0111171, 0174674,
                             0045214, 0147545, 0027744, 0167346,
                             0146210, 0177526, 0114514, 0105660};
static unsigned short Q[] = {
    /*0040200,0000000,0000000,0000000,*/
    0043525, 0142457, 0072633, 0025617, 0145241, 0036742, 0140525, 0162256,
    0046276, 0146176, 0013526, 0143573, 0146515, 0077401, 0162762, 0150607};
/*  7.853981629014015197753906250000E-1 */
static unsigned short P1[] = {
    0040111,
    0007732,
    0120000,
    0000000,
};
/*  4.960467869796758577649598009884E-10 */
static unsigned short P2[] = {
    0030410,
    0055060,
    0100000,
    0000000,
};
/*  2.860594363054915898381331279295E-18 */
static unsigned short P3[] = {
    0021523,
    0011431,
    0105056,
    0001560,
};
#define DP1 *(double *)P1
#define DP2 *(double *)P2
#define DP3 *(double *)P3
static double lossth = 1.073741824e9;
#endif

#ifdef IBMPC
static unsigned short P[] = {0x3f38, 0xd24f, 0x92d8, 0xc0c9, 0x9ddd, 0xa5fc,
                             0x99ec, 0x4131, 0x9176, 0xd329, 0x1fea, 0xc171};
static unsigned short Q[] = {
    /*0x0000,0x0000,0x0000,0x3ff0,*/
    0x6572, 0xeeb3, 0xb8a5, 0x40ca, 0xbc96, 0x582a, 0x27bc, 0xc134,
    0xd8ef, 0xc2ea, 0xd98f, 0x4177, 0x5a31, 0x3cbe, 0xafe0, 0xc189};
/*
  7.85398125648498535156E-1,
  3.77489470793079817668E-8,
  2.69515142907905952645E-15,
*/
static unsigned short P1[] = {0x0000, 0x4000, 0x21fb, 0x3fe9};
static unsigned short P2[] = {0x0000, 0x0000, 0x442d, 0x3e64};
static unsigned short P3[] = {0x5170, 0x98cc, 0x4698, 0x3ce8};
#define DP1 *(double *)P1
#define DP2 *(double *)P2
#define DP3 *(double *)P3
static double lossth = 1.073741824e9;
#endif

#ifdef MIEEE
static unsigned short P[] = {0xc0c9, 0x92d8, 0xd24f, 0x3f38, 0x4131, 0x99ec,
                             0xa5fc, 0x9ddd, 0xc171, 0x1fea, 0xd329, 0x9176};
static unsigned short Q[] = {0x40ca, 0xb8a5, 0xeeb3, 0x6572, 0xc134, 0x27bc,
                             0x582a, 0xbc96, 0x4177, 0xd98f, 0xc2ea, 0xd8ef,
                             0xc189, 0xafe0, 0x3cbe, 0x5a31};
static unsigned short P1[] = {0x3fe9, 0x21fb, 0x4000, 0x0000};
static unsigned short P2[] = {0x3e64, 0x442d, 0x0000, 0x0000};
static unsigned short P3[] = {
    0x3ce8,
    0x4698,
    0x98cc,
    0x5170,
};
#define DP1 *(double *)P1
#define DP2 *(double *)P2
#define DP3 *(double *)P3
static double lossth = 1.073741824e9;
#endif

#ifdef ANSIPROT
extern double polevl(double, void *, int);
extern double p1evl(double, void *, int);
extern double floor(double);
extern double ldexp(double, int);
extern int isnan(double);
extern int isfinite(double);
static double tancot(double, int);
#else
double polevl(), p1evl(), floor(), ldexp();
static double tancot();
int isnan(), isfinite();
#endif
extern double PIO4;
extern double INFINITY;
extern double NAN;

double tan(x) double x;
{
#ifdef MINUSZERO
  if (x == 0.0)
    return (x);
#endif
#ifdef NANS
  if (isnan(x))
    return (x);
  if (!isfinite(x)) {
    mtherr("tan", DOMAIN);
    return (NAN);
  }
#endif
  return (tancot(x, 0));
}

double cot(x) double x;
{

  if (x == 0.0) {
    mtherr("cot", SING);
    return (INFINITY);
  }
  return (tancot(x, 1));
}

static double tancot(xx, cotflg) double xx;
int cotflg;
{
  double x, y, z, zz;
  int j, sign;

  /* make argument positive but save the sign */
  if (xx < 0) {
    x = -xx;
    sign = -1;
  } else {
    x = xx;
    sign = 1;
  }

  if (x > lossth) {
    if (cotflg)
      mtherr("cot", TLOSS);
    else
      mtherr("tan", TLOSS);
    return (0.0);
  }

  /* compute x mod PIO4 */
  y = floor(x / PIO4);

  /* strip high bits of integer part */
  z = ldexp(y, -3);
  z = floor(z);        /* integer part of y/8 */
  z = y - ldexp(z, 3); /* y - 16 * (y/16) */

  /* integer and fractional part modulo one octant */
  j = z;

  /* map zeros and singularities to origin */
  if (j & 1) {
    j += 1;
    y += 1.0;
  }

  z = ((x - y * DP1) - y * DP2) - y * DP3;

  zz = z * z;

  if (zz > 1.0e-14)
    y = z + z * (zz * polevl(zz, P, 2) / p1evl(zz, Q, 4));
  else
    y = z;

  if (j & 2) {
    if (cotflg)
      y = -y;
    else
      y = -1.0 / y;
  } else {
    if (cotflg)
      y = 1.0 / y;
  }

  if (sign < 0)
    y = -y;

  return (y);
}