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powl.c

/**
 * This file has no copyright assigned and is placed in the Public Domain.
 * This file is part of the w64 mingw-runtime package.
 * No warranty is given; refer to the file DISCLAIMER.PD within this package.
 */
#include "cephes_mconf.h"
#ifndef _SET_ERRNO
#define _SET_ERRNO(x)
#endif


/* Table size */
#define NXT 32
/* log2(Table size) */
#define LNXT 5

#ifdef UNK
/* log(1+x) =  x - .5x^2 + x^3 *  P(z)/Q(z)
 * on the domain  2^(-1/32) - 1  <=  x  <=  2^(1/32) - 1
 */
static uLD P[4] = {
  { { 8.3319510773868690346226E-4L } },
  { { 4.9000050881978028599627E-1L } },
  { { 1.7500123722550302671919E0L } },
  { { 1.4000100839971580279335E0L } }
};
static uLD Q[3] = {
  { { 5.2500282295834889175431E0L } },
  { { 8.4000598057587009834666E0L } },
  { { 4.2000302519914740834728E0L } }
};
/* A[i] = 2^(-i/32), rounded to IEEE long double precision.
 * If i is even, A[i] + B[i/2] gives additional accuracy.
 */
static uLD A[33] = {
  { { 1.0000000000000000000000E0L } },
  { { 9.7857206208770013448287E-1L } },
  { { 9.5760328069857364691013E-1L } },
  { { 9.3708381705514995065011E-1L } },
  { { 9.1700404320467123175367E-1L } },
  { { 8.9735453750155359320742E-1L } },
  { { 8.7812608018664974155474E-1L } },
  { { 8.5930964906123895780165E-1L } },
  { { 8.4089641525371454301892E-1L } },
  { { 8.2287773907698242225554E-1L } },
  { { 8.0524516597462715409607E-1L } },
  { { 7.8799042255394324325455E-1L } },
  { { 7.7110541270397041179298E-1L } },
  { { 7.5458221379671136985669E-1L } },
  { { 7.3841307296974965571198E-1L } },
  { { 7.2259040348852331001267E-1L } },
  { { 7.0710678118654752438189E-1L } },
  { { 6.9195494098191597746178E-1L } },
  { { 6.7712777346844636413344E-1L } },
  { { 6.6261832157987064729696E-1L } },
  { { 6.4841977732550483296079E-1L } },
  { { 6.3452547859586661129850E-1L } },
  { { 6.2092890603674202431705E-1L } },
  { { 6.0762367999023443907803E-1L } },
  { { 5.9460355750136053334378E-1L } },
  { { 5.8186242938878875689693E-1L } },
  { { 5.6939431737834582684856E-1L } },
  { { 5.5719337129794626814472E-1L } },
  { { 5.4525386633262882960438E-1L } },
  { { 5.3357020033841180906486E-1L } },
  { { 5.2213689121370692017331E-1L } },
  { { 5.1094857432705833910408E-1L } },
  { { 5.0000000000000000000000E-1L } }
};
static uLD B[17] = {
  { { 0.0000000000000000000000E0L } },
  { { 2.6176170809902549338711E-20L } },
  { { -1.0126791927256478897086E-20L } },
  { { 1.3438228172316276937655E-21L } },
  { { 1.2207982955417546912101E-20L } },
  { { -6.3084814358060867200133E-21L } },
  { { 1.3164426894366316434230E-20L } },
  { { -1.8527916071632873716786E-20L } },
  { { 1.8950325588932570796551E-20L } },
  { { 1.5564775779538780478155E-20L } },
  { { 6.0859793637556860974380E-21L } },
  { { -2.0208749253662532228949E-20L } },
  { { 1.4966292219224761844552E-20L } },
  { { 3.3540909728056476875639E-21L } },
  { { -8.6987564101742849540743E-22L } },
  { { -1.2327176863327626135542E-20L } },
  { { 0.0000000000000000000000E0L } }
};

/* 2^x = 1 + x P(x),
 * on the interval -1/32 <= x <= 0
 */
static uLD R[] = {
  { { 1.5089970579127659901157E-5L } },
  { { 1.5402715328927013076125E-4L } },
  { { 1.3333556028915671091390E-3L } },
  { { 9.6181291046036762031786E-3L } },
  { { 5.5504108664798463044015E-2L } },
  { { 2.4022650695910062854352E-1L } },
  { { 6.9314718055994530931447E-1L } }
};

#define douba(k) A[k].d
#define doubb(k) B[k].d
#define MEXP (NXT*16384.0L)
/* The following if denormal numbers are supported, else -MEXP: */
#ifdef DENORMAL
#define MNEXP (-NXT*(16384.0L+64.0L))
#else
#define MNEXP (-NXT*16384.0L)
#endif
/* log2(e) - 1 */
#define LOG2EA 0.44269504088896340735992L
#endif


#ifdef IBMPC
static const uLD P[] = {
  { { 0xb804,0xa8b7,0xc6f4,0xda6a,0x3ff4, 0, 0, 0 } },
  { { 0x7de9,0xcf02,0x58c0,0xfae1,0x3ffd, 0, 0, 0 } },
  { { 0x405a,0x3722,0x67c9,0xe000,0x3fff, 0, 0, 0 } },
  { { 0xcd99,0x6b43,0x87ca,0xb333,0x3fff, 0, 0, 0 } }
};
static const uLD Q[] = {
  { { 0x6307,0xa469,0x3b33,0xa800,0x4001, 0, 0, 0 } },
  { { 0xfec2,0x62d7,0xa51c,0x8666,0x4002, 0, 0, 0 } },
  { { 0xda32,0xd072,0xa5d7,0x8666,0x4001, 0, 0, 0 } }
};
static const uLD A[] = {
  { { 0x0000,0x0000,0x0000,0x8000,0x3fff, 0, 0, 0 } },
  { { 0x033a,0x722a,0xb2db,0xfa83,0x3ffe, 0, 0, 0 } },
  { { 0xcc2c,0x2486,0x7d15,0xf525,0x3ffe, 0, 0, 0 } },
  { { 0xf5cb,0xdcda,0xb99b,0xefe4,0x3ffe, 0, 0, 0 } },
  { { 0x392f,0xdd24,0xc6e7,0xeac0,0x3ffe, 0, 0, 0 } },
  { { 0x48a8,0x7c83,0x06e7,0xe5b9,0x3ffe, 0, 0, 0 } },
  { { 0xe111,0x2a94,0xdeec,0xe0cc,0x3ffe, 0, 0, 0 } },
  { { 0x3755,0xdaf2,0xb797,0xdbfb,0x3ffe, 0, 0, 0 } },
  { { 0x6af4,0xd69d,0xfcca,0xd744,0x3ffe, 0, 0, 0 } },
  { { 0xe45a,0xf12a,0x1d91,0xd2a8,0x3ffe, 0, 0, 0 } },
  { { 0x80e4,0x1f84,0x8c15,0xce24,0x3ffe, 0, 0, 0 } },
  { { 0x27a3,0x6e2f,0xbd86,0xc9b9,0x3ffe, 0, 0, 0 } },
  { { 0xdadd,0x5506,0x2a11,0xc567,0x3ffe, 0, 0, 0 } },
  { { 0x9456,0x6670,0x4cca,0xc12c,0x3ffe, 0, 0, 0 } },
  { { 0x36bf,0x580c,0xa39f,0xbd08,0x3ffe, 0, 0, 0 } },
  { { 0x9ee9,0x62fb,0xaf47,0xb8fb,0x3ffe, 0, 0, 0 } },
  { { 0x6484,0xf9de,0xf333,0xb504,0x3ffe, 0, 0, 0 } },
  { { 0x2590,0xd2ac,0xf581,0xb123,0x3ffe, 0, 0, 0 } },
  { { 0x4ac6,0x42a1,0x3eea,0xad58,0x3ffe, 0, 0, 0 } },
  { { 0x0ef8,0xea7c,0x5ab4,0xa9a1,0x3ffe, 0, 0, 0 } },
  { { 0x38ea,0xb151,0xd6a9,0xa5fe,0x3ffe, 0, 0, 0 } },
  { { 0x6819,0x0c49,0x4303,0xa270,0x3ffe, 0, 0, 0 } },
  { { 0x11ae,0x91a1,0x3260,0x9ef5,0x3ffe, 0, 0, 0 } },
  { { 0x5539,0xd54e,0x39b9,0x9b8d,0x3ffe, 0, 0, 0 } },
  { { 0xa96f,0x8db8,0xf051,0x9837,0x3ffe, 0, 0, 0 } },
  { { 0x0961,0xfef7,0xefa8,0x94f4,0x3ffe, 0, 0, 0 } },
  { { 0xc336,0xab11,0xd373,0x91c3,0x3ffe, 0, 0, 0 } },
  { { 0x53c0,0x45cd,0x398b,0x8ea4,0x3ffe, 0, 0, 0 } },
  { { 0xd6e7,0xea8b,0xc1e3,0x8b95,0x3ffe, 0, 0, 0 } },
  { { 0x8527,0x92da,0x0e80,0x8898,0x3ffe, 0, 0, 0 } },
  { { 0x7b15,0xcc48,0xc367,0x85aa,0x3ffe, 0, 0, 0 } },
  { { 0xa1d7,0xac2b,0x8698,0x82cd,0x3ffe, 0, 0, 0 } },
  { { 0x0000,0x0000,0x0000,0x8000,0x3ffe, 0, 0, 0 } }
};
static const uLD B[] = {
  { { 0x0000,0x0000,0x0000,0x0000,0x0000, 0, 0, 0 } },
  { { 0x1f87,0xdb30,0x18f5,0xf73a,0x3fbd, 0, 0, 0 } },
  { { 0xac15,0x3e46,0x2932,0xbf4a,0xbfbc, 0, 0, 0 } },
  { { 0x7944,0xba66,0xa091,0xcb12,0x3fb9, 0, 0, 0 } },
  { { 0xff78,0x40b4,0x2ee6,0xe69a,0x3fbc, 0, 0, 0 } },
  { { 0xc895,0x5069,0xe383,0xee53,0xbfbb, 0, 0, 0 } },
  { { 0x7cde,0x9376,0x4325,0xf8ab,0x3fbc, 0, 0, 0 } },
  { { 0xa10c,0x25e0,0xc093,0xaefd,0xbfbd, 0, 0, 0 } },
  { { 0x7d3e,0xea95,0x1366,0xb2fb,0x3fbd, 0, 0, 0 } },
  { { 0x5d89,0xeb34,0x5191,0x9301,0x3fbd, 0, 0, 0 } },
  { { 0x80d9,0xb883,0xfb10,0xe5eb,0x3fbb, 0, 0, 0 } },
  { { 0x045d,0x288c,0xc1ec,0xbedd,0xbfbd, 0, 0, 0 } },
  { { 0xeded,0x5c85,0x4630,0x8d5a,0x3fbd, 0, 0, 0 } },
  { { 0x9d82,0xe5ac,0x8e0a,0xfd6d,0x3fba, 0, 0, 0 } },
  { { 0x6dfd,0xeb58,0xaf14,0x8373,0xbfb9, 0, 0, 0 } },
  { { 0xf938,0x7aac,0x91cf,0xe8da,0xbfbc, 0, 0, 0 } },
  { { 0x0000,0x0000,0x0000,0x0000,0x0000, 0, 0, 0 } }
};
static const uLD R[] = {
  { { 0xa69b,0x530e,0xee1d,0xfd2a,0x3fee, 0, 0, 0 } },
  { { 0xc746,0x8e7e,0x5960,0xa182,0x3ff2, 0, 0, 0 } },
  { { 0x63b6,0xadda,0xfd6a,0xaec3,0x3ff5, 0, 0, 0 } },
  { { 0xc104,0xfd99,0x5b7c,0x9d95,0x3ff8, 0, 0, 0 } },
  { { 0xe05e,0x249d,0x46b8,0xe358,0x3ffa, 0, 0, 0 } },
  { { 0x5d1d,0x162c,0xeffc,0xf5fd,0x3ffc, 0, 0, 0 } },
  { { 0x79aa,0xd1cf,0x17f7,0xb172,0x3ffe, 0, 0, 0 } }
};

/* 10 byte sizes versus 12 byte */
#define douba(k) (A[(k)].ld)
#define doubb(k) (B[(k)].ld)
#define MEXP (NXT*16384.0L)
#ifdef DENORMAL
#define MNEXP (-NXT*(16384.0L+64.0L))
#else
#define MNEXP (-NXT*16384.0L)
#endif
static const
union
{
  unsigned short L[8];
  long double ld;
} log2ea = {{0xc2ef,0x705f,0xeca5,0xe2a8,0x3ffd, 0, 0, 0}};

#define LOG2EA (log2ea.ld)
/*
#define LOG2EA 0.44269504088896340735992L
*/
#endif

#ifdef MIEEE
static uLD P[] = {
  { { 0x3ff40000,0xda6ac6f4,0xa8b7b804, 0 } },
  { { 0x3ffd0000,0xfae158c0,0xcf027de9, 0 } },
  { { 0x3fff0000,0xe00067c9,0x3722405a, 0 } },
  { { 0x3fff0000,0xb33387ca,0x6b43cd99, 0 } }
};
static uLD Q[] = {
  { { 0x40010000,0xa8003b33,0xa4696307, 0 } },
  { { 0x40020000,0x8666a51c,0x62d7fec2, 0 } },
  { { 0x40010000,0x8666a5d7,0xd072da32, 0 } }
};
static uLD A[] = {
  { { 0x3fff0000,0x80000000,0x00000000, 0 } },
  { { 0x3ffe0000,0xfa83b2db,0x722a033a, 0 } },
  { { 0x3ffe0000,0xf5257d15,0x2486cc2c, 0 } },
  { { 0x3ffe0000,0xefe4b99b,0xdcdaf5cb, 0 } },
  { { 0x3ffe0000,0xeac0c6e7,0xdd24392f, 0 } },
  { { 0x3ffe0000,0xe5b906e7,0x7c8348a8, 0 } },
  { { 0x3ffe0000,0xe0ccdeec,0x2a94e111, 0 } },
  { { 0x3ffe0000,0xdbfbb797,0xdaf23755, 0 } },
  { { 0x3ffe0000,0xd744fcca,0xd69d6af4, 0 } },
  { { 0x3ffe0000,0xd2a81d91,0xf12ae45a, 0 } },
  { { 0x3ffe0000,0xce248c15,0x1f8480e4, 0 } },
  { { 0x3ffe0000,0xc9b9bd86,0x6e2f27a3, 0 } },
  { { 0x3ffe0000,0xc5672a11,0x5506dadd, 0 } },
  { { 0x3ffe0000,0xc12c4cca,0x66709456, 0 } },
  { { 0x3ffe0000,0xbd08a39f,0x580c36bf, 0 } },
  { { 0x3ffe0000,0xb8fbaf47,0x62fb9ee9, 0 } },
  { { 0x3ffe0000,0xb504f333,0xf9de6484, 0 } },
  { { 0x3ffe0000,0xb123f581,0xd2ac2590, 0 } },
  { { 0x3ffe0000,0xad583eea,0x42a14ac6, 0 } },
  { { 0x3ffe0000,0xa9a15ab4,0xea7c0ef8, 0 } },
  { { 0x3ffe0000,0xa5fed6a9,0xb15138ea, 0 } },
  { { 0x3ffe0000,0xa2704303,0x0c496819, 0 } },
  { { 0x3ffe0000,0x9ef53260,0x91a111ae, 0 } },
  { { 0x3ffe0000,0x9b8d39b9,0xd54e5539, 0 } },
  { { 0x3ffe0000,0x9837f051,0x8db8a96f, 0 } },
  { { 0x3ffe0000,0x94f4efa8,0xfef70961, 0 } },
  { { 0x3ffe0000,0x91c3d373,0xab11c336, 0 } },
  { { 0x3ffe0000,0x8ea4398b,0x45cd53c0, 0 } },
  { { 0x3ffe0000,0x8b95c1e3,0xea8bd6e7, 0 } },
  { { 0x3ffe0000,0x88980e80,0x92da8527, 0 } },
  { { 0x3ffe0000,0x85aac367,0xcc487b15, 0 } },
  { { 0x3ffe0000,0x82cd8698,0xac2ba1d7, 0 } },
  { { 0x3ffe0000,0x80000000,0x00000000, 0 } }
};
static uLD B[] = {
  { { 0x00000000,0x00000000,0x00000000, 0 } },
  { { 0x3fbd0000,0xf73a18f5,0xdb301f87, 0 } },
  { { 0xbfbc0000,0xbf4a2932,0x3e46ac15, 0 } },
  { { 0x3fb90000,0xcb12a091,0xba667944, 0 } },
  { { 0x3fbc0000,0xe69a2ee6,0x40b4ff78, 0 } },
  { { 0xbfbb0000,0xee53e383,0x5069c895, 0 } },
  { { 0x3fbc0000,0xf8ab4325,0x93767cde, 0 } },
  { { 0xbfbd0000,0xaefdc093,0x25e0a10c, 0 } },
  { { 0x3fbd0000,0xb2fb1366,0xea957d3e, 0 } },
  { { 0x3fbd0000,0x93015191,0xeb345d89, 0 } },
  { { 0x3fbb0000,0xe5ebfb10,0xb88380d9, 0 } },
  { { 0xbfbd0000,0xbeddc1ec,0x288c045d, 0 } },
  { { 0x3fbd0000,0x8d5a4630,0x5c85eded, 0 } },
  { { 0x3fba0000,0xfd6d8e0a,0xe5ac9d82, 0 } },
  { { 0xbfb90000,0x8373af14,0xeb586dfd, 0 } },
  { { 0xbfbc0000,0xe8da91cf,0x7aacf938, 0 } },
  { { 0x00000000,0x00000000,0x00000000, 0 } }
};
static uLD R[] = {
  { { 0x3fee0000,0xfd2aee1d,0x530ea69b, 0 } },
  { { 0x3ff20000,0xa1825960,0x8e7ec746, 0 } },
  { { 0x3ff50000,0xaec3fd6a,0xadda63b6, 0 } },
  { { 0x3ff80000,0x9d955b7c,0xfd99c104, 0 } },
  { { 0x3ffa0000,0xe35846b8,0x249de05e, 0 } },
  { { 0x3ffc0000,0xf5fdeffc,0x162c5d1d, 0 } },
  { { 0x3ffe0000,0xb17217f7,0xd1cf79aa, 0 } }
};

#define douba(k) (A[(k)].ld)
#define doubb(k) (B[(k)].ld)
#define MEXP (NXT*16384.0L)
#ifdef DENORMAL
#define MNEXP (-NXT*(16384.0L+64.0L))
#else
#define MNEXP (-NXT*16382.0L)
#endif
static uLD L[1] = [ {0x3ffd0000,0xe2a8eca5,0x705fc2ef, 0} };
#define LOG2EA (L[0].ld)
#endif


#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

static VOLATILE long double z;
static long double w, W, Wa, Wb, ya, yb, u;

static __inline__ long double reducl(long double);
extern long double __powil(long double, int);
extern long double powl(long double, long double);

/* No error checking. We handle Infs and zeros ourselves.  */
static __inline__ long double
__fast_ldexpl (long double x, int expn)
{
  long double res = 0.0L;
  __asm__ __volatile__ ("fscale"
          : "=t" (res)
          : "0" (x), "u" ((long double) expn));
  return res;
}

#define ldexpl  __fast_ldexpl

long double powl(long double x, long double y)
{
/*    double F, Fa, Fb, G, Ga, Gb, H, Ha, Hb */
      int i, nflg, iyflg, yoddint;
      long e;

      if (y == 0.0L)
            return (1.0L);

#ifdef NANS
      if (isnanl(x))
      {
            _SET_ERRNO (EDOM);
            return (x);
      }
      if (isnanl(y))
      {
            _SET_ERRNO (EDOM);
            return (y);
      }
#endif

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

      if (isinfl(y) && (x == -1.0L || x == 1.0L))
            return (y);

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

      if (y >= MAXNUML)
      {
            _SET_ERRNO (ERANGE);
#ifdef INFINITIES
            if (x > 1.0L)
                  return (INFINITYL);
#else
            if (x > 1.0L)
                  return (MAXNUML);
#endif
            if (x > 0.0L && x < 1.0L)
                  return (0.0L);
#ifdef INFINITIES
            if (x < -1.0L)
                  return (INFINITYL);
#else
            if (x < -1.0L)
                  return (MAXNUML);
#endif
            if (x > -1.0L && x < 0.0L)
                  return (0.0L);
      }
      if (y <= -MAXNUML)
      {
            _SET_ERRNO (ERANGE);
            if (x > 1.0L)
                  return (0.0L);
#ifdef INFINITIES
            if (x > 0.0L && x < 1.0L)
                  return (INFINITYL);
#else
            if (x > 0.0L && x < 1.0L)
                  return (MAXNUML);
#endif
            if (x < -1.0L)
                  return (0.0L);
#ifdef INFINITIES
            if (x > -1.0L && x < 0.0L)
                  return (INFINITYL);
#else
            if (x > -1.0L && x < 0.0L)
                  return (MAXNUML);
#endif
      }
      if (x >= MAXNUML)
      {
#if INFINITIES
            if (y > 0.0L)
                  return (INFINITYL);
#else
            if (y > 0.0L)
                  return (MAXNUML);
#endif
            return (0.0L);
      }

      w = floorl(y);
      /* Set iyflg to 1 if y is an integer.  */
      iyflg = 0;
      if (w == y)
            iyflg = 1;

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

      if (x <= -MAXNUML)
      {
            if (y > 0.0L)
            {
#ifdef INFINITIES
                  if (yoddint)
                        return (-INFINITYL);
                  return (INFINITYL);
#else
                  if (yoddint)
                        return (-MAXNUML);
                  return (MAXNUML);
#endif
            }
            if (y < 0.0L)
            {
#ifdef MINUSZERO
                  if (yoddint)
                        return (NEGZEROL);
#endif
                  return (0.0);
            }
      }


      nflg = 0;   /* flag = 1 if x<0 raised to integer power */
      if (x <= 0.0L)
      {
            if (x == 0.0L)
            {
                  if (y < 0.0)
                  {
#ifdef MINUSZERO
                        if (signbitl(x) && yoddint)
                              return (-INFINITYL);
#endif
#ifdef INFINITIES
                        return (INFINITYL);
#else
                        return (MAXNUML);
#endif
                  }
                  if (y > 0.0)
                  {
#ifdef MINUSZERO
                        if (signbitl(x) && yoddint)
                              return (NEGZEROL);
#endif
                        return (0.0);
                  }
                  if (y == 0.0L)
                        return (1.0L);  /*   0**0   */
                  else
                        return (0.0L);  /*   0**y   */
            }
            else
            {
                  if (iyflg == 0)
                  { /* noninteger power of negative number */
                        mtherr(fname, DOMAIN);
                        _SET_ERRNO (EDOM);
#ifdef NANS
                        return (NANL);
#else
                        return (0.0L);
#endif
                  }
                  nflg = 1;
            }
      }

/* Integer power of an integer.  */

      if (iyflg)
      {
            i = w;
            w = floorl(x);
            if ((w == x) && (fabsl(y) < 32768.0))
            {
                  w = __powil(x, (int) y);
                  return (w);
            }
      }

      if (nflg)
            x = fabsl(x);

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

      /* find significand in antilog table A[] */
      i = 1;
      if (x <= douba(17))
            i = 17;
      if (x <= douba(i + 8))
            i += 8;
      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 * polevll(x, P, 3) / p1evll(x, Q, 3) );
      w = w - ldexpl(z, -1);   /*  w - 0.5 * z  */

      /* Convert to base 2 logarithm:
       * multiply by log2(e) = 1 + LOG2EA
       */
      z = LOG2EA * w;
      z += w;
      z += LOG2EA * x;
      z += x;

      /* Compute exponent term of the base 2 logarithm. */
      w = -i;
      w = ldexpl(w, -LNXT);   /* divide by NXT */
      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/NXT
       */
      ya = reducl(y);
      yb = y - ya;

      /* (w+z)(ya+yb)
       * = w*ya + w*yb + z*y
       */
      F = z * y  +  w * yb;
      Fa = reducl(F);
      Fb = F - Fa;

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

      H = Fb + Gb;
      Ha = reducl(H);
      w = ldexpl(Ga + Ha, LNXT);

      /* Test the power of 2 for overflow */
      if (w > MEXP)
      {
            _SET_ERRNO (ERANGE);
            mtherr(fname, OVERFLOW);
            return (MAXNUML);
      }

      if (w < MNEXP)
      {
            _SET_ERRNO (ERANGE);
            mtherr(fname, UNDERFLOW);
            return (0.0L);
      }

      e = w;
      Hb = H - Ha;

      if (Hb > 0.0L)
      {
            e += 1;
            Hb -= (1.0L/NXT);  /*0.0625L;*/
      }

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

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

      if (nflg)
      {
      /* For negative x,
       * find out if the integer exponent
       * is odd or even.
       */
            w = ldexpl(y, -1);
            w = floorl(w);
            w = ldexpl(w, 1);
            if (w != y)
                  z = -z; /* odd exponent */
      }

      return (z);
}

static __inline__ long double
__convert_inf_to_maxnum(long double x)
{
      if (isinf(x))
            return (x > 0.0L ? MAXNUML : -MAXNUML);
      else
            return x;
}

/* Find a multiple of 1/NXT that is within 1/NXT of x. */
static long double reducl(long double x)
{
      long double t;

      /* If the call to ldexpl overflows, set it to MAXNUML.
         This avoids Inf - Inf = Nan result when calculating the 'small'
         part of a reduction.  Instead, the small part becomes Inf,
         causing under/overflow when adding it to the 'large' part.
         There must be a cleaner way of doing this. */
      t =  __convert_inf_to_maxnum (ldexpl( x, LNXT ));
      t = floorl(t);
      t = ldexpl(t, -LNXT);
      return (t);
}


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