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

/*							pow.c
 *
 *	Power function
 *
 *
 *
 * SYNOPSIS:
 *
 * double x, y, z, pow();
 *
 * z = pow( x, y );
 *
 *
 *
 * DESCRIPTION:
 *
 * Computes x raised to the yth power.  Analytically,
 *
 *      x**y  =  exp( y log(x) ).
 *
 * Following Cody and Waite, this program uses a lookup table
 * of 2**-i/16 and pseudo extended precision arithmetic to
 * obtain an extra three bits of accuracy in both the logarithm
 * and the exponential.
 *
 *
 *
 * ACCURACY:
 *
 *                      Relative error:
 * arithmetic   domain     # trials      peak         rms
 *    IEEE     -26,26       30000      4.2e-16      7.7e-17
 *    DEC      -26,26       60000      4.8e-17      9.1e-18
 * 1/26 < x < 26, with log(x) uniformly distributed.
 * -26 < y < 26, y uniformly distributed.
 *    IEEE     0,8700       30000      1.5e-14      2.1e-15
 * 0.99 < x < 1.01, 0 < y < 8700, uniformly distributed.
 *
 *
 * ERROR MESSAGES:
 *
 *   message         condition      value returned
 * pow overflow     x**y > MAXNUM      INFINITY
 * pow underflow   x**y < 1/MAXNUM       0.0
 * pow domain      x<0 and y noninteger  0.0
 *
 */

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

#include "mconf.h"
static char fname[] = {"pow"};

#define SQRTH 0.70710678118654752440

#ifdef UNK
static double P[] = {4.97778295871696322025E-1, 3.73336776063286838734E0,
                     7.69994162726912503298E0, 4.66651806774358464979E0};
static double Q[] = {
    /* 1.00000000000000000000E0, */
    9.33340916416696166113E0, 2.79999886606328401649E1,
    3.35994905342304405431E1, 1.39995542032307539578E1};
/* 2^(-i/16), IEEE precision */
static double A[] = {1.00000000000000000000E0,  9.57603280698573700036E-1,
                     9.17004043204671215328E-1, 8.78126080186649726755E-1,
                     8.40896415253714502036E-1, 8.05245165974627141736E-1,
                     7.71105412703970372057E-1, 7.38413072969749673113E-1,
                     7.07106781186547572737E-1, 6.77127773468446325644E-1,
                     6.48419777325504820276E-1, 6.20928906036742001007E-1,
                     5.94603557501360513449E-1, 5.69394317378345782288E-1,
                     5.45253866332628844837E-1, 5.22136891213706877402E-1,
                     5.00000000000000000000E-1};
static double B[] = {0.00000000000000000000E0,    1.64155361212281360176E-17,
                     4.09950501029074826006E-17,  3.97491740484881042808E-17,
                     -4.83364665672645672553E-17, 1.26912513974441574796E-17,
                     1.99100761573282305549E-17,  -1.52339103990623557348E-17,
                     0.00000000000000000000E0};
static double R[] = {1.49664108433729301083E-5, 1.54010762792771901396E-4,
                     1.33335476964097721140E-3, 9.61812908476554225149E-3,
                     5.55041086645832347466E-2, 2.40226506959099779976E-1,
                     6.93147180559945308821E-1};

#define douba(k) A[k]
#define doubb(k) B[k]
#define MEXP 16383.0
#ifdef DENORMAL
#define MNEXP -17183.0
#else
#define MNEXP -16383.0
#endif
#endif

#ifdef DEC
static unsigned short P[] = {
    0037776, 0156313, 0175332, 0163602, 0040556, 0167577, 0052366, 0174245,
    0040766, 0062753, 0175707, 0055564, 0040625, 0052035, 0131344, 0155636,
};
static unsigned short Q[] = {
    /*0040200,0000000,0000000,0000000,*/
    0041025, 0052644, 0154404, 0105155, 0041337, 0177772, 0007016, 0047646,
    0041406, 0062740, 0154273, 0020020, 0041137, 0177054, 0106127, 0044555,
};
static unsigned short A[] = {
    0040200, 0000000, 0000000, 0000000, 0040165, 0022575, 0012444, 0103314,
    0040152, 0140306, 0163735, 0022071, 0040140, 0146336, 0166052, 0112341,
    0040127, 0042374, 0145326, 0116553, 0040116, 0022214, 0012437, 0102201,
    0040105, 0063452, 0010525, 0003333, 0040075, 0004243, 0117530, 0006067,
    0040065, 0002363, 0031771, 0157145, 0040055, 0054076, 0165102, 0120513,
    0040045, 0177326, 0124661, 0050471, 0040036, 0172462, 0060221, 0120422,
    0040030, 0033760, 0050615, 0134251, 0040021, 0141723, 0071653, 0010703,
    0040013, 0112701, 0161752, 0105727, 0040005, 0125303, 0063714, 0044173,
    0040000, 0000000, 0000000, 0000000};
static unsigned short B[] = {
    0000000, 0000000, 0000000, 0000000, 0021473, 0040265, 0153315, 0140671,
    0121074, 0062627, 0042146, 0176454, 0121413, 0003524, 0136332, 0066212,
    0121767, 0046404, 0166231, 0012553, 0121257, 0015024, 0002357, 0043574,
    0021736, 0106532, 0043060, 0056206, 0121310, 0020334, 0165705, 0035326,
    0000000, 0000000, 0000000, 0000000};

static unsigned short R[] = {
    0034173, 0014076, 0137624, 0115771, 0035041, 0076763, 0003744,
    0111311, 0035656, 0141766, 0041127, 0074351, 0036435, 0112533,
    0073611, 0116664, 0037143, 0054106, 0134040, 0152223, 0037565,
    0176757, 0176026, 0025551, 0040061, 0071027, 0173721, 0147572};

/*
static double R[] = {
0.14928852680595608186e-4,
0.15400290440989764601e-3,
0.13333541313585784703e-2,
0.96181290595172416964e-2,
0.55504108664085595326e-1,
0.24022650695909537056e0,
0.69314718055994529629e0
};
*/
#define douba(k) (*(double *)&A[(k) << 2])
#define doubb(k) (*(double *)&B[(k) << 2])
#define MEXP 2031.0
#define MNEXP -2031.0
#endif

#ifdef IBMPC
static unsigned short P[] = {
    0x5cf0, 0x7f5b, 0xdb99, 0x3fdf, 0xdf15, 0xea9e, 0xddef, 0x400d,
    0xeb6f, 0x7f78, 0xccbd, 0x401e, 0x9b74, 0xb65c, 0xaa83, 0x4012,
};
static unsigned short Q[] = {
    /*0x0000,0x0000,0x0000,0x3ff0,*/
    0x914e, 0x9b20, 0xaab4, 0x4022, 0xc9f5, 0x41c1, 0xffff, 0x403b,
    0x6402, 0x1b17, 0xccbc, 0x4040, 0xe92e, 0x918a, 0xffc5, 0x402b,
};
static unsigned short A[] = {
    0x0000, 0x0000, 0x0000, 0x3ff0, 0x90da, 0xa2a4, 0xa4af, 0x3fee, 0xa487,
    0xdcfb, 0x5818, 0x3fed, 0x529c, 0xdd85, 0x199b, 0x3fec, 0xd3ad, 0x995a,
    0xe89f, 0x3fea, 0xf090, 0x82a3, 0xc491, 0x3fe9, 0xa0db, 0x422a, 0xace5,
    0x3fe8, 0x0187, 0x73eb, 0xa114, 0x3fe7, 0x3bcd, 0x667f, 0xa09e, 0x3fe6,
    0x5429, 0xdd48, 0xab07, 0x3fe5, 0x2a27, 0xd536, 0xbfda, 0x3fe4, 0x3422,
    0x4c12, 0xdea6, 0x3fe3, 0xb715, 0x0a31, 0x06fe, 0x3fe3, 0x6238, 0x6e75,
    0x387a, 0x3fe2, 0x517b, 0x3c7d, 0x72b8, 0x3fe1, 0x890f, 0x6cf9, 0xb558,
    0x3fe0, 0x0000, 0x0000, 0x0000, 0x3fe0};
static unsigned short B[] = {
    0x0000, 0x0000, 0x0000, 0x0000, 0x3707, 0xd75b, 0xed02, 0x3c72, 0xcc81,
    0x345d, 0xa1cd, 0x3c87, 0x4b27, 0x5686, 0xe9f1, 0x3c86, 0x6456, 0x13b2,
    0xdd34, 0xbc8b, 0x42e2, 0xafec, 0x4397, 0x3c6d, 0x82e4, 0xd231, 0xf46a,
    0x3c76, 0x8a76, 0xb9d7, 0x9041, 0xbc71, 0x0000, 0x0000, 0x0000, 0x0000};
static unsigned short R[] = {0x937f, 0xd7f2, 0x6307, 0x3eef, 0x9259, 0x60fc,
                             0x2fbe, 0x3f24, 0xef1d, 0xc84a, 0xd87e, 0x3f55,
                             0x33b7, 0x6ef1, 0xb2ab, 0x3f83, 0x1a92, 0xd704,
                             0x6b08, 0x3fac, 0xc56d, 0xff82, 0xbfbd, 0x3fce,
                             0x39ef, 0xfefa, 0x2e42, 0x3fe6};

#define douba(k) (*(double *)&A[(k) << 2])
#define doubb(k) (*(double *)&B[(k) << 2])
#define MEXP 16383.0
#ifdef DENORMAL
#define MNEXP -17183.0
#else
#define MNEXP -16383.0
#endif
#endif

#ifdef MIEEE
static unsigned short P[] = {0x3fdf, 0xdb99, 0x7f5b, 0x5cf0, 0x400d, 0xddef,
                             0xea9e, 0xdf15, 0x401e, 0xccbd, 0x7f78, 0xeb6f,
                             0x4012, 0xaa83, 0xb65c, 0x9b74};
static unsigned short Q[] = {0x4022, 0xaab4, 0x9b20, 0x914e, 0x403b, 0xffff,
                             0x41c1, 0xc9f5, 0x4040, 0xccbc, 0x1b17, 0x6402,
                             0x402b, 0xffc5, 0x918a, 0xe92e};
static unsigned short A[] = {
    0x3ff0, 0x0000, 0x0000, 0x0000, 0x3fee, 0xa4af, 0xa2a4, 0x90da, 0x3fed,
    0x5818, 0xdcfb, 0xa487, 0x3fec, 0x199b, 0xdd85, 0x529c, 0x3fea, 0xe89f,
    0x995a, 0xd3ad, 0x3fe9, 0xc491, 0x82a3, 0xf090, 0x3fe8, 0xace5, 0x422a,
    0xa0db, 0x3fe7, 0xa114, 0x73eb, 0x0187, 0x3fe6, 0xa09e, 0x667f, 0x3bcd,
    0x3fe5, 0xab07, 0xdd48, 0x5429, 0x3fe4, 0xbfda, 0xd536, 0x2a27, 0x3fe3,
    0xdea6, 0x4c12, 0x3422, 0x3fe3, 0x06fe, 0x0a31, 0xb715, 0x3fe2, 0x387a,
    0x6e75, 0x6238, 0x3fe1, 0x72b8, 0x3c7d, 0x517b, 0x3fe0, 0xb558, 0x6cf9,
    0x890f, 0x3fe0, 0x0000, 0x0000, 0x0000};
static unsigned short B[] = {
    0x0000, 0x0000, 0x0000, 0x0000, 0x3c72, 0xed02, 0xd75b, 0x3707, 0x3c87,
    0xa1cd, 0x345d, 0xcc81, 0x3c86, 0xe9f1, 0x5686, 0x4b27, 0xbc8b, 0xdd34,
    0x13b2, 0x6456, 0x3c6d, 0x4397, 0xafec, 0x42e2, 0x3c76, 0xf46a, 0xd231,
    0x82e4, 0xbc71, 0x9041, 0xb9d7, 0x8a76, 0x0000, 0x0000, 0x0000, 0x0000};
static unsigned short R[] = {0x3eef, 0x6307, 0xd7f2, 0x937f, 0x3f24, 0x2fbe,
                             0x60fc, 0x9259, 0x3f55, 0xd87e, 0xc84a, 0xef1d,
                             0x3f83, 0xb2ab, 0x6ef1, 0x33b7, 0x3fac, 0x6b08,
                             0xd704, 0x1a92, 0x3fce, 0xbfbd, 0xff82, 0xc56d,
                             0x3fe6, 0x2e42, 0xfefa, 0x39ef};

#define douba(k) (*(double *)&A[(k) << 2])
#define doubb(k) (*(double *)&B[(k) << 2])
#define MEXP 16383.0
#ifdef DENORMAL
#define MNEXP -17183.0
#else
#define MNEXP -16383.0
#endif
#endif

/* log2(e) - 1 */
#define LOG2EA 0.44269504088896340736

#define F W
#define Fa Wa
#define Fb Wb
#define G W
#define Ga Wa
#define Gb u
#define H W
#define Ha Wb
#define Hb Wb

#ifdef ANSIPROT
extern double floor(double);
extern double fabs(double);
extern double frexp(double, int *);
extern double ldexp(double, int);
extern double polevl(double, void *, int);
extern double p1evl(double, void *, int);
extern double powi(double, int);
extern int signbit(double);
extern int isnan(double);
extern int isfinite(double);
static double reduc(double);
#else
double floor(), fabs(), frexp(), ldexp();
double polevl(), p1evl(), powi();
int signbit(), isnan(), isfinite();
static double reduc();
#endif
extern double MAXNUM;
#ifdef INFINITIES
extern double INFINITY;
#endif
#ifdef NANS
extern double NAN;
#endif
#ifdef MINUSZERO
extern double NEGZERO;
#endif

double pow(x, y) double x, y;
{
  double w, z, W, Wa, Wb, ya, yb, u;
  /* double F, Fa, Fb, G, Ga, Gb, H, Ha, Hb */
  double aw, ay, wy;
  int e, i, nflg, iyflg, yoddint;

  if (y == 0.0)
    return (1.0);
#ifdef NANS
  if (isnan(x))
    return (x);
  if (isnan(y))
    return (y);
#endif
  if (y == 1.0)
    return (x);

#ifdef INFINITIES
  if (!isfinite(y) && (x == 1.0 || x == -1.0)) {
    mtherr("pow", DOMAIN);
#ifdef NANS
    return (NAN);
#else
    return (INFINITY);
#endif
  }
#endif

  if (x == 1.0)
    return (1.0);

  if (y >= MAXNUM) {
#ifdef INFINITIES
    if (x > 1.0)
      return (INFINITY);
#else
    if (x > 1.0)
      return (MAXNUM);
#endif
    if (x > 0.0 && x < 1.0)
      return (0.0);
    if (x < -1.0) {
#ifdef INFINITIES
      return (INFINITY);
#else
      return (MAXNUM);
#endif
    }
    if (x > -1.0 && x < 0.0)
      return (0.0);
  }
  if (y <= -MAXNUM) {
    if (x > 1.0)
      return (0.0);
#ifdef INFINITIES
    if (x > 0.0 && x < 1.0)
      return (INFINITY);
#else
    if (x > 0.0 && x < 1.0)
      return (MAXNUM);
#endif
    if (x < -1.0)
      return (0.0);
#ifdef INFINITIES
    if (x > -1.0 && x < 0.0)
      return (INFINITY);
#else
    if (x > -1.0 && x < 0.0)
      return (MAXNUM);
#endif
  }
  if (x >= MAXNUM) {
#if INFINITIES
    if (y > 0.0)
      return (INFINITY);
#else
    if (y > 0.0)
      return (MAXNUM);
#endif
    return (0.0);
  }
  /* Set iyflg to 1 if y is an integer.  */
  iyflg = 0;
  w = floor(y);
  if (w == y)
    iyflg = 1;

  /* Test for odd integer y.  */
  yoddint = 0;
  if (iyflg) {
    ya = fabs(y);
    ya = floor(0.5 * ya);
    yb = 0.5 * fabs(w);
    if (ya != yb)
      yoddint = 1;
  }

  if (x <= -MAXNUM) {
    if (y > 0.0) {
#ifdef INFINITIES
      if (yoddint)
        return (-INFINITY);
      return (INFINITY);
#else
      if (yoddint)
        return (-MAXNUM);
      return (MAXNUM);
#endif
    }
    if (y < 0.0) {
#ifdef MINUSZERO
      if (yoddint)
        return (NEGZERO);
#endif
      return (0.0);
    }
  }

  nflg = 0; /* flag = 1 if x<0 raised to integer power */
  if (x <= 0.0) {
    if (x == 0.0) {
      if (y < 0.0) {
#ifdef MINUSZERO
        if (signbit(x) && yoddint)
          return (-INFINITY);
#endif
#ifdef INFINITIES
        return (INFINITY);
#else
        return (MAXNUM);
#endif
      }
      if (y > 0.0) {
#ifdef MINUSZERO
        if (signbit(x) && yoddint)
          return (NEGZERO);
#endif
        return (0.0);
      }
      return (1.0);
    } else {
      if (iyflg == 0) { /* noninteger power of negative number */
        mtherr(fname, DOMAIN);
#ifdef NANS
        return (NAN);
#else
        return (0.0L);
#endif
      }
      nflg = 1;
    }
  }

  /* Integer power of an integer.  */

  if (iyflg) {
    i = w;
    w = floor(x);
    if ((w == x) && (fabs(y) < 32768.0)) {
      w = powi(x, (int)y);
      return (w);
    }
  }

  if (nflg)
    x = fabs(x);

  /* For results close to 1, use a series expansion.  */
  w = x - 1.0;
  aw = fabs(w);
  ay = fabs(y);
  wy = w * y;
  ya = fabs(wy);
  if ((aw <= 1.0e-3 && ay <= 1.0) || (ya <= 1.0e-3 && ay >= 1.0)) {
    z = (((((w * (y - 5.) / 720. + 1. / 120.) * w * (y - 4.) + 1. / 24.) * w *
               (y - 3.) +
           1. / 6.) *
              w * (y - 2.) +
          0.5) *
         w * (y - 1.)) *
            wy +
        wy + 1.;
    goto done;
  }
/* These are probably too much trouble.  */
#if 0
w = y * log(x);
if (aw > 1.0e-3 && fabs(w) < 1.0e-3)
  {
    z = ((((((
    w/7. + 1.)*w/6. + 1.)*w/5. + 1.)*w/4. + 1.)*w/3. + 1.)*w/2. + 1.)*w + 1.;
    goto done;
  }

if(ya <= 1.0e-3 && aw <= 1.0e-4)
  {
    z = (((((
	     wy*1./720.
	     + (-w*1./48. + 1./120.) )*wy
	    + ((w*17./144. - 1./12.)*w + 1./24.) )*wy
	   + (((-w*5./16. + 7./24.)*w - 1./4.)*w + 1./6.) )*wy
	  + ((((w*137./360. - 5./12.)*w + 11./24.)*w - 1./2.)*w + 1./2.) )*wy
	 + (((((-w*1./6. + 1./5.)*w - 1./4)*w + 1./3.)*w -1./2.)*w ) )*wy
	   + wy + 1.0;
    goto done;
  }
#endif

  /* separate significand from exponent */
  x = frexp(x, &e);

#if 0
/* For debugging, check for gross overflow. */
if( (e * y)  > (MEXP + 1024) )
	goto overflow;
#endif

  /* Find significand of x in antilog table A[]. */
  i = 1;
  if (x <= douba(9))
    i = 9;
  if (x <= douba(i + 4))
    i += 4;
  if (x <= douba(i + 2))
    i += 2;
  if (x >= douba(1))
    i = -1;
  i += 1;

  /* Find (x - A[i])/A[i]
   * in order to compute log(x/A[i]):
   *
   * log(x) = log( a x/a ) = log(a) + log(x/a)
   *
   * log(x/a) = log(1+v),  v = x/a - 1 = (x-a)/a
   */
  x -= douba(i);
  x -= doubb(i / 2);
  x /= douba(i);

  /* rational approximation for log(1+v):
   *
   * log(1+v)  =  v  -  v**2/2  +  v**3 P(v) / Q(v)
   */
  z = x * x;
  w = x * (z * polevl(x, P, 3) / p1evl(x, Q, 4));
  w = w - ldexp(z, -1); /*  w - 0.5 * z  */

  /* Convert to base 2 logarithm:
   * multiply by log2(e)
   */
  w = w + LOG2EA * w;
  /* Note x was not yet added in
   * to above rational approximation,
   * so do it now, while multiplying
   * by log2(e).
   */
  z = w + LOG2EA * x;
  z = z + x;

  /* Compute exponent term of the base 2 logarithm. */
  w = -i;
  w = ldexp(w, -4); /* divide by 16 */
  w += e;
  /* Now base 2 log of x is w + z. */

  /* Multiply base 2 log by y, in extended precision. */

  /* separate y into large part ya
   * and small part yb less than 1/16
   */
  ya = reduc(y);
  yb = y - ya;

  F = z * y + w * yb;
  Fa = reduc(F);
  Fb = F - Fa;

  G = Fa + w * ya;
  Ga = reduc(G);
  Gb = G - Ga;

  H = Fb + Gb;
  Ha = reduc(H);
  w = ldexp(Ga + Ha, 4);

  /* Test the power of 2 for overflow */
  if (w > MEXP) {
#ifndef INFINITIES
    mtherr(fname, OVERFLOW);
#endif
#ifdef INFINITIES
    if (nflg && yoddint)
      return (-INFINITY);
    return (INFINITY);
#else
    if (nflg && yoddint)
      return (-MAXNUM);
    return (MAXNUM);
#endif
  }

  if (w < (MNEXP - 1)) {
#ifndef DENORMAL
    mtherr(fname, UNDERFLOW);
#endif
#ifdef MINUSZERO
    if (nflg && yoddint)
      return (NEGZERO);
#endif
    return (0.0);
  }

  e = w;
  Hb = H - Ha;

  if (Hb > 0.0) {
    e += 1;
    Hb -= 0.0625;
  }

  /* Now the product y * log2(x)  =  Hb + e/16.0.
   *
   * Compute base 2 exponential of Hb,
   * where -0.0625 <= Hb <= 0.
   */
  z = Hb * polevl(Hb, R, 6); /*    z  =  2**Hb - 1    */

  /* Express e/16 as an integer plus a negative number of 16ths.
   * Find lookup table entry for the fractional power of 2.
   */
  if (e < 0)
    i = 0;
  else
    i = 1;
  i = e / 16 + i;
  e = 16 * i - e;
  w = douba(e);
  z = w + w * z;   /*    2**-e * ( 1 + (2**Hb-1) )    */
  z = ldexp(z, i); /* multiply by integer power of 2 */

done:

  /* Negate if odd integer power of negative number */
  if (nflg && yoddint) {
#ifdef MINUSZERO
    if (z == 0.0)
      z = NEGZERO;
    else
#endif
      z = -z;
  }
  return (z);
}

/* Find a multiple of 1/16 that is within 1/16 of x. */
static double reduc(x) double x;
{
  double t;

  t = ldexp(x, 4);
  t = floor(t);
  t = ldexp(t, -4);
  return (t);
}