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

/*							asin.c
 *
 *	Inverse circular sine
 *
 *
 *
 * SYNOPSIS:
 *
 * double x, y, asin();
 *
 * y = asin( x );
 *
 *
 *
 * DESCRIPTION:
 *
 * Returns radian angle between -pi/2 and +pi/2 whose sine is x.
 *
 * A rational function of the form x + x**3 P(x**2)/Q(x**2)
 * is used for |x| in the interval [0, 0.5].  If |x| > 0.5 it is
 * transformed by the identity
 *
 *    asin(x) = pi/2 - 2 asin( sqrt( (1-x)/2 ) ).
 *
 *
 * ACCURACY:
 *
 *                      Relative error:
 * arithmetic   domain     # trials      peak         rms
 *    DEC      -1, 1        40000       2.6e-17     7.1e-18
 *    IEEE     -1, 1        10^6        1.9e-16     5.4e-17
 *
 *
 * ERROR MESSAGES:
 *
 *   message         condition      value returned
 * asin domain        |x| > 1           NAN
 *
 */
/*							acos()
 *
 *	Inverse circular cosine
 *
 *
 *
 * SYNOPSIS:
 *
 * double x, y, acos();
 *
 * y = acos( x );
 *
 *
 *
 * DESCRIPTION:
 *
 * Returns radian angle between 0 and pi whose cosine
 * is x.
 *
 * Analytically, acos(x) = pi/2 - asin(x).  However if |x| is
 * near 1, there is cancellation error in subtracting asin(x)
 * from pi/2.  Hence if x < -0.5,
 *
 *    acos(x) =	 pi - 2.0 * asin( sqrt((1+x)/2) );
 *
 * or if x > +0.5,
 *
 *    acos(x) =	 2.0 * asin(  sqrt((1-x)/2) ).
 *
 *
 * ACCURACY:
 *
 *                      Relative error:
 * arithmetic   domain     # trials      peak         rms
 *    DEC       -1, 1       50000       3.3e-17     8.2e-18
 *    IEEE      -1, 1       10^6        2.2e-16     6.5e-17
 *
 *
 * ERROR MESSAGES:
 *
 *   message         condition      value returned
 * asin domain        |x| > 1           NAN
 */

/*							asin.c	*/

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

#include "mconf.h"

/* arcsin(x)  =  x + x^3 P(x^2)/Q(x^2)
   0 <= x <= 0.625
   Peak relative error = 1.2e-18  */
#if UNK
static double P[6] = {
    4.253011369004428248960E-3, -6.019598008014123785661E-1,
    5.444622390564711410273E0,  -1.626247967210700244449E1,
    1.956261983317594739197E1,  -8.198089802484824371615E0,
};
static double Q[5] = {
    /* 1.000000000000000000000E0, */
    -1.474091372988853791896E1, 7.049610280856842141659E1,
    -1.471791292232726029859E2, 1.395105614657485689735E2,
    -4.918853881490881290097E1,
};
#endif
#if DEC
static short P[24] = {
    0036213, 0056330, 0057244, 0053234, 0140032, 0015011, 0114762, 0160255,
    0040656, 0035130, 0136121, 0067313, 0141202, 0014616, 0170474, 0101731,
    0041234, 0100076, 0151674, 0111310, 0141003, 0025540, 0033165, 0077246,
};
static short Q[20] = {
    /* 0040200,0000000,0000000,0000000, */
    0141153, 0155310, 0055360, 0072530, 0041614, 0177001, 0027764,
    0101237, 0142023, 0026733, 0064653, 0133266, 0042013, 0101264,
    0023775, 0176351, 0141504, 0140420, 0050660, 0036543,
};
#endif
#if IBMPC
static short P[24] = {
    0x8ad3, 0x0bd4, 0x6b9b, 0x3f71, 0x5c16, 0x333e, 0x4341, 0xbfe3,
    0x2dd9, 0x178a, 0xc74b, 0x4015, 0x907b, 0xde27, 0x4331, 0xc030,
    0x9259, 0xda77, 0x9007, 0x4033, 0xafd5, 0x06ce, 0x656c, 0xc020,
};
static short Q[20] = {
    /* 0x0000,0x0000,0x0000,0x3ff0, */
    0x0eab, 0x0b5e, 0x7b59, 0xc02d, 0x9054, 0x25fe, 0x9fc0,
    0x4051, 0x76d7, 0x6d35, 0x65bb, 0xc062, 0xbf9d, 0x84ff,
    0x7056, 0x4061, 0x07ac, 0x0a36, 0x9822, 0xc048,
};
#endif
#if MIEEE
static short P[24] = {
    0x3f71, 0x6b9b, 0x0bd4, 0x8ad3, 0xbfe3, 0x4341, 0x333e, 0x5c16,
    0x4015, 0xc74b, 0x178a, 0x2dd9, 0xc030, 0x4331, 0xde27, 0x907b,
    0x4033, 0x9007, 0xda77, 0x9259, 0xc020, 0x656c, 0x06ce, 0xafd5,
};
static short Q[20] = {
    /* 0x3ff0,0x0000,0x0000,0x0000, */
    0xc02d, 0x7b59, 0x0b5e, 0x0eab, 0x4051, 0x9fc0, 0x25fe,
    0x9054, 0xc062, 0x65bb, 0x6d35, 0x76d7, 0x4061, 0x7056,
    0x84ff, 0xbf9d, 0xc048, 0x9822, 0x0a36, 0x07ac,
};
#endif

/* arcsin(1-x) = pi/2 - sqrt(2x)(1+R(x))
   0 <= x <= 0.5
   Peak relative error = 4.2e-18  */
#if UNK
static double R[5] = {
    2.967721961301243206100E-3, -5.634242780008963776856E-1,
    6.968710824104713396794E0,  -2.556901049652824852289E1,
    2.853665548261061424989E1,
};
static double S[4] = {
    /* 1.000000000000000000000E0, */
    -2.194779531642920639778E1,
    1.470656354026814941758E2,
    -3.838770957603691357202E2,
    3.424398657913078477438E2,
};
#endif
#if DEC
static short R[20] = {
    0036102, 0077034, 0142164, 0174103, 0140020, 0036222, 0147711,
    0044173, 0040736, 0177655, 0153631, 0171523, 0141314, 0106525,
    0060015, 0055474, 0041344, 0045422, 0003630, 0040344,
};
static short S[16] = {
    /* 0040200,0000000,0000000,0000000, */
    0141257, 0112425, 0132772, 0166136, 0042023, 0010315, 0075523, 0175020,
    0142277, 0170104, 0126203, 0017563, 0042253, 0034115, 0102662, 0022757,
};
#endif
#if IBMPC
static short R[20] = {
    0x9f08, 0x988e, 0x4fc3, 0x3f68, 0x290f, 0x59f9, 0x0792,
    0xbfe2, 0x3e6a, 0xbaf3, 0xdff5, 0x401b, 0xab68, 0xac01,
    0x91aa, 0xc039, 0x081d, 0x40f3, 0x8962, 0x403c,
};
static short S[16] = {
    /* 0x0000,0x0000,0x0000,0x3ff0, */
    0x5d8c, 0xb6bf, 0xf2a2, 0xc035, 0x7f42, 0xaf6a, 0x6219, 0x4062,
    0x63ee, 0x9590, 0xfe08, 0xc077, 0x44be, 0xb0b6, 0x6709, 0x4075,
};
#endif
#if MIEEE
static short R[20] = {
    0x3f68, 0x4fc3, 0x988e, 0x9f08, 0xbfe2, 0x0792, 0x59f9,
    0x290f, 0x401b, 0xdff5, 0xbaf3, 0x3e6a, 0xc039, 0x91aa,
    0xac01, 0xab68, 0x403c, 0x8962, 0x40f3, 0x081d,
};
static short S[16] = {
    /* 0x3ff0,0x0000,0x0000,0x0000, */
    0xc035, 0xf2a2, 0xb6bf, 0x5d8c, 0x4062, 0x6219, 0xaf6a, 0x7f42,
    0xc077, 0xfe08, 0x9590, 0x63ee, 0x4075, 0x6709, 0xb0b6, 0x44be,
};
#endif

/* pi/2 = PIO2 + MOREBITS.  */
#ifdef DEC
#define MOREBITS 5.721188726109831840122E-18
#else
#define MOREBITS 6.123233995736765886130E-17
#endif

#ifdef ANSIPROT
extern double polevl(double, void *, int);
extern double p1evl(double, void *, int);
extern double sqrt(double);
double asin(double);
#else
double sqrt(), polevl(), p1evl();
double asin();
#endif
extern double PIO2, PIO4, NAN;

double asin(x) double x;
{
  double a, p, z, zz;
  short sign;

  if (x > 0) {
    sign = 1;
    a = x;
  } else {
    sign = -1;
    a = -x;
  }

  if (a > 1.0) {
    mtherr("asin", DOMAIN);
    return (NAN);
  }

  if (a > 0.625) {
    /* arcsin(1-x) = pi/2 - sqrt(2x)(1+R(x))  */
    zz = 1.0 - a;
    p = zz * polevl(zz, R, 4) / p1evl(zz, S, 4);
    zz = sqrt(zz + zz);
    z = PIO4 - zz;
    zz = zz * p - MOREBITS;
    z = z - zz;
    z = z + PIO4;
  } else {
    if (a < 1.0e-8) {
      return (x);
    }
    zz = a * a;
    z = zz * polevl(zz, P, 5) / p1evl(zz, Q, 5);
    z = a * z + a;
  }
  if (sign < 0)
    z = -z;
  return (z);
}

double acos(x) double x;
{
  double z;

  if ((x < -1.0) || (x > 1.0)) {
    mtherr("acos", DOMAIN);
    return (NAN);
  }
  if (x > 0.5) {
    return (2.0 * asin(sqrt(0.5 - 0.5 * x)));
  }
  z = PIO4 - asin(x);
  z = z + MOREBITS;
  z = z + PIO4;
  return (z);
}