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============================================================ */

#include "libm_amd.h"
#include "libm_util_amd.h"

#define USE_REMAINDER_PIBY2F_INLINE
#define USE_VALF_WITH_FLAGS
#define USE_NANF_WITH_FLAGS
#define USE_HANDLE_ERRORF
#include "libm_inlines_amd.h"
#undef USE_VALF_WITH_FLAGS
#undef USE_NANF_WITH_FLAGS
#undef USE_REMAINDER_PIBY2F_INLINE
#undef USE_HANDLE_ERRORF

/* tan(x) approximation valid on the interval [-pi/4,pi/4].
   If recip is true return -1/tan(x) instead. */
static inline double
tanf_piby4(double x, int recip)
{
  double r, t;

  /* Core Remez [1,2] approximation to tan(x) on the
     interval [0,pi/4]. */
  r = x * x;
  t = x +
      x * r *
          (0.385296071263995406715129e0 - 0.172032480471481694693109e-1 * r) /
          (0.115588821434688393452299e+1 +
           (-0.51396505478854532132342e0 + 0.1844239256901656082986661e-1 * r) *
               r);

  if (recip)
    return -1.0 / t;
  else
    return t;
}

float FN_PROTOTYPE(mth_i_tan)(float x)
{
  double r, dx;
  int region, xneg;

  __UINT8_T ux, ax;

  dx = x;

  GET_BITS_DP64(dx, ux);
  ax = (ux & ~SIGNBIT_DP64);

  if (ax <= 0x3fe921fb54442d18) /* abs(x) <= pi/4 */
  {
    if (ax < 0x3f80000000000000) /* abs(x) < 2.0^(-7) */
    {
      if (ax < 0x3f20000000000000) /* abs(x) < 2.0^(-13) */
      {
        if (ax == 0x0000000000000000)
          return x;
        else
          return valf_with_flags(x, AMD_F_INEXACT);
      } else
        return (float)(dx + dx * dx * dx * 0.333333333333333333);
    } else
      return (float)tanf_piby4(x, 0);
  } else if ((ux & EXPBITS_DP64) == EXPBITS_DP64) {
    /* x is either NaN or infinity */
    if (ux & MANTBITS_DP64) {
      /* x is NaN */
      return x + x; /* Raise invalid if it is a signalling NaN */
    } else {
      /* x is infinity. Return a NaN */
      return nanf_with_flags(AMD_F_INVALID);
    }
  }

  xneg = (int)(ux >> 63);

  if (xneg)
    dx = -dx;

  if (dx < 5.0e5) {
    /* For these size arguments we can just carefully subtract the
       appropriate multiple of pi/2, using extra precision where
       dx is close to an exact multiple of pi/2 */
    static const double twobypi =
                            6.36619772367581382433e-01, /* 0x3fe45f306dc9c883 */
        piby2_1 = 1.57079632673412561417e+00,           /* 0x3ff921fb54400000 */
        piby2_1tail = 6.07710050650619224932e-11,       /* 0x3dd0b4611a626331 */
        piby2_2 = 6.07710050630396597660e-11,           /* 0x3dd0b4611a600000 */
        piby2_2tail = 2.02226624879595063154e-21,       /* 0x3ba3198a2e037073 */
        piby2_3 = 2.02226624871116645580e-21,           /* 0x3ba3198a2e000000 */
        piby2_3tail = 8.47842766036889956997e-32;       /* 0x397b839a252049c1 */
    double t, rhead, rtail;
    int npi2;
    __UINT8_T uy, xexp, expdiff;
    xexp = ax >> EXPSHIFTBITS_DP64;
    /* How many pi/2 is dx a multiple of? */
    if (ax <= 0x400f6a7a2955385e) /* 5pi/4 */
    {
      if (ax <= 0x4002d97c7f3321d2) /* 3pi/4 */
        npi2 = 1;
      else
        npi2 = 2;
    } else if (ax <= 0x401c463abeccb2bb) /* 9pi/4 */
    {
      if (ax <= 0x4015fdbbe9bba775) /* 7pi/4 */
        npi2 = 3;
      else
        npi2 = 4;
    } else
      npi2 = (int)(dx * twobypi + 0.5);
    /* Subtract the multiple from dx to get an extra-precision remainder */
    rhead = dx - npi2 * piby2_1;
    rtail = npi2 * piby2_1tail;
    GET_BITS_DP64(rhead, uy);
    expdiff = xexp - ((uy & EXPBITS_DP64) >> EXPSHIFTBITS_DP64);
    if (expdiff > 15) {
      /* The remainder is pretty small compared with dx, which
         implies that dx is a near multiple of pi/2
         (dx matches the multiple to at least 15 bits) */
      t = rhead;
      rtail = npi2 * piby2_2;
      rhead = t - rtail;
      rtail = npi2 * piby2_2tail - ((t - rhead) - rtail);
      if (expdiff > 48) {
        /* dx matches a pi/2 multiple to at least 48 bits */
        t = rhead;
        rtail = npi2 * piby2_3;
        rhead = t - rtail;
        rtail = npi2 * piby2_3tail - ((t - rhead) - rtail);
      }
    }
    r = rhead - rtail;
    region = npi2 & 3;
  } else {
    /* Reduce x into range [-pi/4,pi/4] */
    __remainder_piby2f_inline(ax, &r, &region);
  }

  if (xneg)
    return (float)-tanf_piby4(r, region & 1);
  else
    return (float)tanf_piby4(r, region & 1);
}