acosf.c File Reference

#include "libm.h"
#include "libm_util.h"
#include "libm_inlines.h"
#include "libm_errno.h"

Include dependency graph for acosf.c:

Go to the source code of this file.

Macros
#define	USE_VALF_WITH_FLAGS
#define	USE_NANF_WITH_FLAGS
#define	USE_HANDLE_ERRORF

Functions
float FN_PROTOTYPE()	acosf (float x)

Macro Definition Documentation

USE_HANDLE_ERRORF

#define USE_HANDLE_ERRORF

Definition at line 32 of file acosf.c.

USE_NANF_WITH_FLAGS

#define USE_NANF_WITH_FLAGS

Definition at line 31 of file acosf.c.

USE_VALF_WITH_FLAGS

#define USE_VALF_WITH_FLAGS

Definition at line 30 of file acosf.c.

Function Documentation

acosf()

float FN_PROTOTYPE() acosf

(

float

x

)

Definition at line 47 of file acosf.c.

{
  /* Computes arccos(x).
     The argument is first reduced by noting that arccos(x)
     is invalid for abs(x) > 1. For denormal and small
     arguments arccos(x) = pi/2 to machine accuracy.
     Remaining argument ranges are handled as follows.
     For abs(x) <= 0.5 use
     arccos(x) = pi/2 - arcsin(x)
     = pi/2 - (x + x^3*R(x^2))
     where R(x^2) is a rational minimax approximation to
     (arcsin(x) - x)/x^3.
     For abs(x) > 0.5 exploit the identity:
     arccos(x) = pi - 2*arcsin(sqrt(1-x)/2)
     together with the above rational approximation, and
     reconstruct the terms carefully.
  */
 
  /* Some constants and split constants. */
 
  static const float
    piby2      = 1.5707963705e+00F; /* 0x3fc90fdb */
  static const double
    pi         = 3.1415926535897933e+00, /* 0x400921fb54442d18 */
    piby2_head = 1.5707963267948965580e+00, /* 0x3ff921fb54442d18 */
    piby2_tail = 6.12323399573676603587e-17; /* 0x3c91a62633145c07 */
 
  float u, y, s = 0.0F, r;
  int xexp, xnan, transform = 0;
 
  unsigned int ux, aux, xneg;
 
  GET_BITS_SP32(x, ux);
  aux = ux & ~SIGNBIT_SP32;
  xneg = (ux & SIGNBIT_SP32);
  xnan = (aux > PINFBITPATT_SP32);
  xexp = (int)((ux & EXPBITS_SP32) >> EXPSHIFTBITS_SP32) - EXPBIAS_SP32;
 
  /* Special cases */
 
  if (xnan)
    {
      return _handle_errorf("acosf", OP_ACOS, ux|0x00400000, _DOMAIN, 0,
                           EDOM, x, 0.0F, 1);
    }
  else if (xexp < -26)
    /* y small enough that arccos(x) = pi/2 */
    return valf_with_flags(piby2, AMD_F_INEXACT);
  else if (xexp >= 0)
    { /* abs(x) >= 1.0 */
      if (x == 1.0F)
        return 0.0F;
      else if (x == -1.0F)
        return valf_with_flags((float)pi, AMD_F_INEXACT);
      else
        return _handle_errorf("acosf", OP_ACOS, INDEFBITPATT_SP32, _DOMAIN,
                             AMD_F_INVALID, EDOM, x, 0.0F, 1);
    }
 
  if (xneg) y = -x;
  else y = x;
 
  transform = (xexp >= -1); /* abs(x) >= 0.5 */
 
  if (transform)
    { /* Transform y into the range [0,0.5) */
      r = 0.5F*(1.0F - y);
      /* VC++ intrinsic call */
      _mm_store_ss(&s, _mm_sqrt_ss(_mm_load_ss(&r)));
      y = s;
    }
  else
    r = y*y;
 
  /* Use a rational approximation for [0.0, 0.5] */
 
  u=r*(0.184161606965100694821398249421F +
       (-0.0565298683201845211985026327361F +
    (-0.0133819288943925804214011424456F -
     0.00396137437848476485201154797087F*r)*r)*r)/
    (1.10496961524520294485512696706F -
     0.836411276854206731913362287293F*r);
 
  if (transform)
    {
      /* Reconstruct acos carefully in transformed region */
      if (xneg)
        return (float)(pi - 2.0*(s+(y*u - piby2_tail)));
      else
    {
      float c, s1;
      unsigned int us;
      GET_BITS_SP32(s, us);
      PUT_BITS_SP32(0xffff0000 & us, s1);
      c = (r-s1*s1)/(s+s1);
          return 2.0F*s1 + (2.0F*c+2.0F*y*u);
    }
    }
  else
    return (float)(piby2_head - (x - (piby2_tail - x*u)));
}