asinf.c

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#include "libm.h"
#include "libm_util.h"
 
#define USE_VALF_WITH_FLAGS
#define USE_NANF_WITH_FLAGS
#define USE_HANDLE_ERRORF
#include "libm_inlines.h"
#undef USE_NANF_WITH_FLAGS
#undef USE_VALF_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(asinf)
#endif
 
float FN_PROTOTYPE(asinf)(float x)
{
  /* Computes arcsin(x).
     The argument is first reduced by noting that arcsin(x)
     is invalid for abs(x) > 1 and arcsin(-x) = -arcsin(x).
     For denormal and small arguments arcsin(x) = x to machine
     accuracy. Remaining argument ranges are handled as follows.
     For abs(x) <= 0.5 use
     arcsin(x) = 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:
      arcsin(x) = pi/2 - 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_tail  = 7.5497894159e-08F, /* 0x33a22168 */
    hpiby2_head = 7.8539812565e-01F, /* 0x3f490fda */
    piby2       = 1.5707963705e+00F; /* 0x3fc90fdb */
  float u, v, 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("asinf", OP_ASIN, ux|0x00400000, _DOMAIN, 0,
                           EDOM, x, 0.0F, 1);
    }
  else if (xexp < -14)
    /* y small enough that arcsin(x) = x */
    return valf_with_flags(x, AMD_F_INEXACT);
  else if (xexp >= 0)
    {
      /* abs(x) >= 1.0 */
      if (x == 1.0F)
        return valf_with_flags(piby2, AMD_F_INEXACT);
      else if (x == -1.0F)
        return valf_with_flags(-piby2, AMD_F_INEXACT);
      else
        return _handle_errorf("asinf", OP_ASIN, 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 asin carefully in transformed region */
      float c, s1, p, q;
      unsigned int us;
      GET_BITS_SP32(s, us);
      PUT_BITS_SP32(0xffff0000 & us, s1);
      c = (r-s1*s1)/(s+s1);
      p = 2.0F*s*u - (piby2_tail-2.0F*c);
      q = hpiby2_head - 2.0F*s1;
      v = hpiby2_head - (p-q);
    }
  else
    {
      /* Use a temporary variable to prevent VC++ rearranging
            y + y*u
         into
            y * (1 + u)
         and getting an incorrectly rounded result */
      float tmp;
      tmp = y * u;
      v = y + tmp;
    }
 
  if (xneg) return -v;
  else return v;
}