atan.c

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#include "libm.h"
#include "libm_util.h"
 
#define USE_VAL_WITH_FLAGS
#define USE_NAN_WITH_FLAGS
#define USE_HANDLE_ERROR
#include "libm_inlines.h"
#undef USE_VAL_WITH_FLAGS
#undef USE_NAN_WITH_FLAGS
#undef USE_HANDLE_ERROR
 
#include "libm_errno.h"
 
#ifdef _MSC_VER
#pragma function(atan)
#endif
 
double FN_PROTOTYPE(atan)(double x)
{
 
  /* Some constants and split constants. */
 
  static double piby2 = 1.5707963267948966e+00; /* 0x3ff921fb54442d18 */
  double chi, clo, v, s, q, z;
 
  /* Find properties of argument x. */
 
  unsigned long long ux, aux, xneg;
  GET_BITS_DP64(x, ux);
  aux = ux & ~SIGNBIT_DP64;
  xneg = (ux != aux);
 
  if (xneg) v = -x;
  else v = x;
 
  /* Argument reduction to range [-7/16,7/16] */
 
  if (aux > 0x4003800000000000) /* v > 39./16. */
    {
 
      if (aux > PINFBITPATT_DP64)
        {
          /* x is NaN */
          return _handle_error("atan", OP_ATAN, ux|0x0008000000000000, _DOMAIN, 0,
                              EDOM, x, 0.0, 1);
        }
      else if (v > 0x4370000000000000)
    { /* abs(x) > 2^56 => arctan(1/x) is
         insignificant compared to piby2 */
      if (xneg)
            return val_with_flags(-piby2, AMD_F_INEXACT);
      else
            return val_with_flags(piby2, AMD_F_INEXACT);
    }
 
      x = -1.0/v;
      /* (chi + clo) = arctan(infinity) */
      chi = 1.57079632679489655800e+00; /* 0x3ff921fb54442d18 */
      clo = 6.12323399573676480327e-17; /* 0x3c91a62633145c06 */
    }
  else if (aux > 0x3ff3000000000000) /* 39./16. > v > 19./16. */
    {
      x = (v-1.5)/(1.0+1.5*v);
      /* (chi + clo) = arctan(1.5) */
      chi = 9.82793723247329054082e-01; /* 0x3fef730bd281f69b */
      clo = 1.39033110312309953701e-17; /* 0x3c7007887af0cbbc */
    }
  else if (aux > 0x3fe6000000000000) /* 19./16. > v > 11./16. */
    {
      x = (v-1.0)/(1.0+v);
      /* (chi + clo) = arctan(1.) */
      chi = 7.85398163397448278999e-01; /* 0x3fe921fb54442d18 */
      clo = 3.06161699786838240164e-17; /* 0x3c81a62633145c06 */
    }
  else if (aux > 0x3fdc000000000000) /* 11./16. > v > 7./16. */
    {
      x = (2.0*v-1.0)/(2.0+v);
      /* (chi + clo) = arctan(0.5) */
      chi = 4.63647609000806093515e-01; /* 0x3fddac670561bb4f */
      clo = 2.26987774529616809294e-17; /* 0x3c7a2b7f222f65e0 */
    }
  else  /* v < 7./16. */
    {
      x = v;
      chi = 0.0;
      clo = 0.0;
    }
 
  /* Core approximation: Remez(4,4) on [-7/16,7/16] */
 
  s = x*x;
  q = x*s*
       (0.268297920532545909e0 +
    (0.447677206805497472e0 +
     (0.220638780716667420e0 +
      (0.304455919504853031e-1 +
        0.142316903342317766e-3*s)*s)*s)*s)/
       (0.804893761597637733e0 +
    (0.182596787737507063e1 +
     (0.141254259931958921e1 +
      (0.424602594203847109e0 +
        0.389525873944742195e-1*s)*s)*s)*s);
 
  z = chi - ((q - clo) - x);
 
  if (xneg) z = -z;
  return z;
}