/* origin: FreeBSD /usr/src/lib/msun/src/s_cbrtl.c */
/*-
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 * Copyright (c) 2009-2011, Bruce D. Evans, Steven G. Kargl, David Schultz.
 *
 * Developed at SunPro, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 * ====================================================
 *
 * The argument reduction and testing for exceptional cases was
 * written by Steven G. Kargl with input from Bruce D. Evans
 * and David A. Schultz.
 */

#include "libm.h"

#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
long double cbrtl(long double x) {
  return cbrt(x);
}
#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
static const unsigned B1 =
    709958130; /* B1 = (127-127.0/3-0.03306235651)*2**23 */

long double cbrtl(long double x) {
  union ldshape u = {x}, v;
  union {
    float f;
    uint32_t i;
  } uft;
  long double r, s, t, w;
  double_t dr, dt, dx;
  float_t ft;
  int e = u.i.se & 0x7fff;
  int sign = u.i.se & 0x8000;

  /*
   * If x = +-Inf, then cbrt(x) = +-Inf.
   * If x = NaN, then cbrt(x) = NaN.
   */
  if (e == 0x7fff)
    return x + x;
  if (e == 0) {
    /* Adjust subnormal numbers. */
    u.f *= 0x1p120;
    e = u.i.se & 0x7fff;
    /* If x = +-0, then cbrt(x) = +-0. */
    if (e == 0)
      return x;
    e -= 120;
  }
  e -= 0x3fff;
  u.i.se = 0x3fff;
  x = u.f;
  switch (e % 3) {
    case 1:
    case -2:
      x *= 2;
      e--;
      break;
    case 2:
    case -1:
      x *= 4;
      e -= 2;
      break;
  }
  v.f = 1.0;
  v.i.se = sign | (0x3fff + e / 3);

  /*
   * The following is the guts of s_cbrtf, with the handling of
   * special values removed and extra care for accuracy not taken,
   * but with most of the extra accuracy not discarded.
   */

  /* ~5-bit estimate: */
  uft.f = x;
  uft.i = (uft.i & 0x7fffffff) / 3 + B1;
  ft = uft.f;

  /* ~16-bit estimate: */
  dx = x;
  dt = ft;
  dr = dt * dt * dt;
  dt = dt * (dx + dx + dr) / (dx + dr + dr);

  /* ~47-bit estimate: */
  dr = dt * dt * dt;
  dt = dt * (dx + dx + dr) / (dx + dr + dr);

#if LDBL_MANT_DIG == 64
  /*
   * dt is cbrtl(x) to ~47 bits (after x has been reduced to 1 <= x < 8).
   * Round it away from zero to 32 bits (32 so that t*t is exact, and
   * away from zero for technical reasons).
   */
  t = dt + (0x1.0p32L + 0x1.0p-31L) - 0x1.0p32;
#elif LDBL_MANT_DIG == 113
  /*
   * Round dt away from zero to 47 bits.  Since we don't trust the 47,
   * add 2 47-bit ulps instead of 1 to round up.  Rounding is slow and
   * might be avoidable in this case, since on most machines dt will
   * have been evaluated in 53-bit precision and the technical reasons
   * for rounding up might not apply to either case in cbrtl() since
   * dt is much more accurate than needed.
   */
  t = dt + 0x2.0p-46 + 0x1.0p60L - 0x1.0p60;
#endif

  /*
   * Final step Newton iteration to 64 or 113 bits with
   * error < 0.667 ulps
   */
  s = t * t;             /* t*t is exact */
  r = x / s;             /* error <= 0.5 ulps; |r| < |t| */
  w = t + t;             /* t+t is exact */
  r = (r - t) / (w + r); /* r-t is exact; w+r ~= 3*t */
  t = t + t * r;         /* error <= 0.5 + 0.5/3 + epsilon */

  t *= v.f;
  return t;
}
#endif