atanf.c

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MIT License
-----------
 
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#include "libm.h"
#include "libm_util.h"
 
#define USE_VALF_WITH_FLAGS
#define USE_NAN_WITH_FLAGS
#define USE_HANDLE_ERRORF
#include "libm_inlines.h"
#undef USE_VALF_WITH_FLAGS
#undef USE_NAN_WITH_FLAGS
#undef USE_HANDLE_ERRORF
 
#include "libm_errno.h"
 
#ifdef _MSC_VER
// Disable "C4163: not available as intrinsic function" warning that older
// compilers may issue here.
#pragma warning(disable:4163)
#pragma function(atanf)
#endif
 
float FN_PROTOTYPE(atanf)(float fx)
{
 
  /* Some constants and split constants. */
 
  static double piby2 = 1.5707963267948966e+00; /* 0x3ff921fb54442d18 */
 
  double c, v, s, q, z;
  unsigned int xnan;
 
  double x = fx;
 
  /* Find properties of argument fx. */
 
  unsigned long long ux, aux, xneg;
 
  GET_BITS_DP64(x, ux);
  aux = ux & ~SIGNBIT_DP64;
  xneg = ux & SIGNBIT_DP64;
 
  v = x;
  if (xneg) v = -x;
 
  /* Argument reduction to range [-7/16,7/16] */
 
  if (aux < 0x3fdc000000000000) /* v < 7./16. */
    {
      x = v;
      c = 0.0;
    }
  else if (aux < 0x3fe6000000000000) /* v < 11./16. */
    {
      x = (2.0*v-1.0)/(2.0+v);
      /* c = arctan(0.5) */
      c = 4.63647609000806093515e-01; /* 0x3fddac670561bb4f */
    }
  else if (aux < 0x3ff3000000000000) /* v < 19./16. */
    {
      x = (v-1.0)/(1.0+v);
      /* c = arctan(1.) */
      c = 7.85398163397448278999e-01; /* 0x3fe921fb54442d18 */
    }
  else if (aux < 0x4003800000000000) /* v < 39./16. */
    {
      x = (v-1.5)/(1.0+1.5*v);
      /* c = arctan(1.5) */
      c = 9.82793723247329054082e-01; /* 0x3fef730bd281f69b */
    }
  else
    {
 
      xnan = (aux > PINFBITPATT_DP64);
 
      if (xnan)
        {
          /* x is NaN */
          unsigned int uhx;
          GET_BITS_SP32(fx, uhx);
          return _handle_errorf("atanf", OP_ATAN, uhx|0x00400000, _DOMAIN,
                               0, EDOM, fx, 0.0F, 1);
        }
      else if (v > 0x4c80000000000000)
    { /* abs(x) > 2^26 => arctan(1/x) is
         insignificant compared to piby2 */
      if (xneg)
            return valf_with_flags((float)-piby2, AMD_F_INEXACT);
      else
            return valf_with_flags((float)piby2, AMD_F_INEXACT);
    }
 
      x = -1.0/v;
      /* c = arctan(infinity) */
      c = 1.57079632679489655800e+00; /* 0x3ff921fb54442d18 */
    }
 
  /* Core approximation: Remez(2,2) on [-7/16,7/16] */
 
  s = x*x;
  q = x*s*
    (0.296528598819239217902158651186e0 +
     (0.192324546402108583211697690500e0 +
       0.470677934286149214138357545549e-2*s)*s)/
    (0.889585796862432286486651434570e0 +
     (0.111072499995399550138837673349e1 +
       0.299309699959659728404442796915e0*s)*s);
 
  z = c - (q - x);
 
  if (xneg) z = -z;
  return (float)z;
}