Beispiel #1
0
CFLOAT
M_DECL_FUNC (__cproj) (CFLOAT x)
{
  if (isinf (__real__ x) || isinf (__imag__ x))
    {
      CFLOAT res;

      __real__ res = INFINITY;
      __imag__ res = M_COPYSIGN (0, __imag__ x);

      return res;
    }

  return x;
}
Beispiel #2
0
CFLOAT
M_DECL_FUNC (__casin) (CFLOAT x)
{
  CFLOAT res;

  if (isnan (__real__ x) || isnan (__imag__ x))
    {
      if (__real__ x == 0)
	{
	  res = x;
	}
      else if (isinf (__real__ x) || isinf (__imag__ x))
	{
	  __real__ res = M_NAN;
	  __imag__ res = M_COPYSIGN (M_HUGE_VAL, __imag__ x);
	}
      else
	{
	  __real__ res = M_NAN;
	  __imag__ res = M_NAN;
	}
    }
  else
    {
      CFLOAT y;

      __real__ y = -__imag__ x;
      __imag__ y = __real__ x;

      y = M_SUF (__casinh) (y);

      __real__ res = __imag__ y;
      __imag__ res = -__real__ y;
    }

  return res;
}
Beispiel #3
0
CFLOAT
M_DECL_FUNC (__csin) (CFLOAT x)
{
  CFLOAT retval;
  int negate = signbit (__real__ x);
  int rcls = fpclassify (__real__ x);
  int icls = fpclassify (__imag__ x);

  __real__ x = M_FABS (__real__ x);

  if (__glibc_likely (icls >= FP_ZERO))
    {
      /* Imaginary part is finite.  */
      if (__glibc_likely (rcls >= FP_ZERO))
	{
	  /* Real part is finite.  */
	  const int t = (int) ((M_MAX_EXP - 1) * M_MLIT (M_LN2));
	  FLOAT sinix, cosix;

	  if (__glibc_likely (__real__ x > M_MIN))
	    {
	      M_SINCOS (__real__ x, &sinix, &cosix);
	    }
	  else
	    {
	      sinix = __real__ x;
	      cosix = 1;
	    }

	  if (negate)
	    sinix = -sinix;

	  if (M_FABS (__imag__ x) > t)
	    {
	      FLOAT exp_t = M_EXP (t);
	      FLOAT ix = M_FABS (__imag__ x);
	      if (signbit (__imag__ x))
		cosix = -cosix;
	      ix -= t;
	      sinix *= exp_t / 2;
	      cosix *= exp_t / 2;
	      if (ix > t)
		{
		  ix -= t;
		  sinix *= exp_t;
		  cosix *= exp_t;
		}
	      if (ix > t)
		{
		  /* Overflow (original imaginary part of x > 3t).  */
		  __real__ retval = M_MAX * sinix;
		  __imag__ retval = M_MAX * cosix;
		}
	      else
		{
		  FLOAT exp_val = M_EXP (ix);
		  __real__ retval = exp_val * sinix;
		  __imag__ retval = exp_val * cosix;
		}
	    }
	  else
	    {
	      __real__ retval = M_COSH (__imag__ x) * sinix;
	      __imag__ retval = M_SINH (__imag__ x) * cosix;
	    }

	  math_check_force_underflow_complex (retval);
	}
      else
	{
	  if (icls == FP_ZERO)
	    {
	      /* Imaginary part is 0.0.  */
	      __real__ retval = __real__ x - __real__ x;
	      __imag__ retval = __imag__ x;
	    }
	  else
	    {
	      __real__ retval = M_NAN;
	      __imag__ retval = M_NAN;

	      feraiseexcept (FE_INVALID);
	    }
	}
    }
  else if (icls == FP_INFINITE)
    {
      /* Imaginary part is infinite.  */
      if (rcls == FP_ZERO)
	{
	  /* Real part is 0.0.  */
	  __real__ retval = M_COPYSIGN (0, negate ? -1 : 1);
	  __imag__ retval = __imag__ x;
	}
      else if (rcls > FP_ZERO)
	{
	  /* Real part is finite.  */
	  FLOAT sinix, cosix;

	  if (__glibc_likely (__real__ x > M_MIN))
	    {
	      M_SINCOS (__real__ x, &sinix, &cosix);
	    }
	  else
	    {
	      sinix = __real__ x;
	      cosix = 1;
	    }

	  __real__ retval = M_COPYSIGN (M_HUGE_VAL, sinix);
	  __imag__ retval = M_COPYSIGN (M_HUGE_VAL, cosix);

	  if (negate)
	    __real__ retval = -__real__ retval;
	  if (signbit (__imag__ x))
	    __imag__ retval = -__imag__ retval;
	}
      else
	{
	  __real__ retval = __real__ x - __real__ x;
	  __imag__ retval = M_HUGE_VAL;
	}
    }
  else
    {
      if (rcls == FP_ZERO)
	__real__ retval = M_COPYSIGN (0, negate ? -1 : 1);
      else
	__real__ retval = M_NAN;
      __imag__ retval = M_NAN;
    }

  return retval;
}
Beispiel #4
0
CFLOAT
M_DECL_FUNC (__catanh) (CFLOAT x)
{
  CFLOAT res;
  int rcls = fpclassify (__real__ x);
  int icls = fpclassify (__imag__ x);

  if (__glibc_unlikely (rcls <= FP_INFINITE || icls <= FP_INFINITE))
    {
      if (icls == FP_INFINITE)
	{
	  __real__ res = M_COPYSIGN (0, __real__ x);
	  __imag__ res = M_COPYSIGN (M_MLIT (M_PI_2), __imag__ x);
	}
      else if (rcls == FP_INFINITE || rcls == FP_ZERO)
	{
	  __real__ res = M_COPYSIGN (0, __real__ x);
	  if (icls >= FP_ZERO)
	    __imag__ res = M_COPYSIGN (M_MLIT (M_PI_2), __imag__ x);
	  else
	    __imag__ res = M_NAN;
	}
      else
	{
	  __real__ res = M_NAN;
	  __imag__ res = M_NAN;
	}
    }
  else if (__glibc_unlikely (rcls == FP_ZERO && icls == FP_ZERO))
    {
      res = x;
    }
  else
    {
      if (M_FABS (__real__ x) >= 16 / M_EPSILON
	  || M_FABS (__imag__ x) >= 16 / M_EPSILON)
	{
	  __imag__ res = M_COPYSIGN (M_MLIT (M_PI_2), __imag__ x);
	  if (M_FABS (__imag__ x) <= 1)
	    __real__ res = 1 / __real__ x;
	  else if (M_FABS (__real__ x) <= 1)
	    __real__ res = __real__ x / __imag__ x / __imag__ x;
	  else
	    {
	      FLOAT h = M_HYPOT (__real__ x / 2, __imag__ x / 2);
	      __real__ res = __real__ x / h / h / 4;
	    }
	}
      else
	{
	  if (M_FABS (__real__ x) == 1
	      && M_FABS (__imag__ x) < M_EPSILON * M_EPSILON)
	    __real__ res = (M_COPYSIGN (M_LIT (0.5), __real__ x)
			    * ((FLOAT) M_MLIT (M_LN2)
			       - M_LOG (M_FABS (__imag__ x))));
	  else
	    {
	      FLOAT i2 = 0;
	      if (M_FABS (__imag__ x) >= M_EPSILON * M_EPSILON)
		i2 = __imag__ x * __imag__ x;

	      FLOAT num = 1 + __real__ x;
	      num = i2 + num * num;

	      FLOAT den = 1 - __real__ x;
	      den = i2 + den * den;

	      FLOAT f = num / den;
	      if (f < M_LIT (0.5))
		__real__ res = M_LIT (0.25) * M_LOG (f);
	      else
		{
		  num = 4 * __real__ x;
		  __real__ res = M_LIT (0.25) * M_LOG1P (num / den);
		}
	    }

	  FLOAT absx, absy, den;

	  absx = M_FABS (__real__ x);
	  absy = M_FABS (__imag__ x);
	  if (absx < absy)
	    {
	      FLOAT t = absx;
	      absx = absy;
	      absy = t;
	    }

	  if (absy < M_EPSILON / 2)
	    {
	      den = (1 - absx) * (1 + absx);
	      if (den == 0)
		den = 0;
	    }
	  else if (absx >= 1)
	    den = (1 - absx) * (1 + absx) - absy * absy;
	  else if (absx >= M_LIT (0.75) || absy >= M_LIT (0.5))
	    den = -M_SUF (__x2y2m1) (absx, absy);
	  else
	    den = (1 - absx) * (1 + absx) - absy * absy;

	  __imag__ res = M_LIT (0.5) * M_ATAN2 (2 * __imag__ x, den);
	}

      math_check_force_underflow_complex (res);
    }

  return res;
}
Beispiel #5
0
CFLOAT
M_DECL_FUNC (__cacosh) (CFLOAT x)
{
  CFLOAT res;
  int rcls = fpclassify (__real__ x);
  int icls = fpclassify (__imag__ x);

  if (rcls <= FP_INFINITE || icls <= FP_INFINITE)
    {
      if (icls == FP_INFINITE)
	{
	  __real__ res = M_HUGE_VAL;

	  if (rcls == FP_NAN)
	    __imag__ res = M_NAN;
	  else
	    __imag__ res = M_COPYSIGN ((rcls == FP_INFINITE
					? (__real__ x < 0
					   ? M_MLIT (M_PI) - M_MLIT (M_PI_4)
					   : M_MLIT (M_PI_4))
					: M_MLIT (M_PI_2)), __imag__ x);
	}
      else if (rcls == FP_INFINITE)
	{
	  __real__ res = M_HUGE_VAL;

	  if (icls >= FP_ZERO)
	    __imag__ res = M_COPYSIGN (signbit (__real__ x)
				       ? M_MLIT (M_PI) : 0, __imag__ x);
	  else
	    __imag__ res = M_NAN;
	}
      else
	{
	  __real__ res = M_NAN;
	  __imag__ res = M_NAN;
	}
    }
  else if (rcls == FP_ZERO && icls == FP_ZERO)
    {
      __real__ res = 0;
      __imag__ res = M_COPYSIGN (M_MLIT (M_PI_2), __imag__ x);
    }
  else
    {
      CFLOAT y;

      __real__ y = -__imag__ x;
      __imag__ y = __real__ x;

      y = M_SUF (__kernel_casinh) (y, 1);

      if (signbit (__imag__ x))
	{
	  __real__ res = __real__ y;
	  __imag__ res = -__imag__ y;
	}
      else
	{
	  __real__ res = -__real__ y;
	  __imag__ res = __imag__ y;
	}
    }

  return res;
}
Beispiel #6
0
CFLOAT
M_DECL_FUNC (__csqrt) (CFLOAT x)
{
  CFLOAT res;
  int rcls = fpclassify (__real__ x);
  int icls = fpclassify (__imag__ x);

  if (__glibc_unlikely (rcls <= FP_INFINITE || icls <= FP_INFINITE))
    {
      if (icls == FP_INFINITE)
	{
	  __real__ res = M_HUGE_VAL;
	  __imag__ res = __imag__ x;
	}
      else if (rcls == FP_INFINITE)
	{
	  if (__real__ x < 0)
	    {
	      __real__ res = icls == FP_NAN ? M_NAN : 0;
	      __imag__ res = M_COPYSIGN (M_HUGE_VAL, __imag__ x);
	    }
	  else
	    {
	      __real__ res = __real__ x;
	      __imag__ res = (icls == FP_NAN
			      ? M_NAN : M_COPYSIGN (0, __imag__ x));
	    }
	}
      else
	{
	  __real__ res = M_NAN;
	  __imag__ res = M_NAN;
	}
    }
  else
    {
      if (__glibc_unlikely (icls == FP_ZERO))
	{
	  if (__real__ x < 0)
	    {
	      __real__ res = 0;
	      __imag__ res = M_COPYSIGN (M_SQRT (-__real__ x), __imag__ x);
	    }
	  else
	    {
	      __real__ res = M_FABS (M_SQRT (__real__ x));
	      __imag__ res = M_COPYSIGN (0, __imag__ x);
	    }
	}
      else if (__glibc_unlikely (rcls == FP_ZERO))
	{
	  FLOAT r;
	  if (M_FABS (__imag__ x) >= 2 * M_MIN)
	    r = M_SQRT (M_LIT (0.5) * M_FABS (__imag__ x));
	  else
	    r = M_LIT (0.5) * M_SQRT (2 * M_FABS (__imag__ x));

	  __real__ res = r;
	  __imag__ res = M_COPYSIGN (r, __imag__ x);
	}
      else
	{
	  FLOAT d, r, s;
	  int scale = 0;

	  if (M_FABS (__real__ x) > M_MAX / 4)
	    {
	      scale = 1;
	      __real__ x = M_SCALBN (__real__ x, -2 * scale);
	      __imag__ x = M_SCALBN (__imag__ x, -2 * scale);
	    }
	  else if (M_FABS (__imag__ x) > M_MAX / 4)
	    {
	      scale = 1;
	      if (M_FABS (__real__ x) >= 4 * M_MIN)
		__real__ x = M_SCALBN (__real__ x, -2 * scale);
	      else
		__real__ x = 0;
	      __imag__ x = M_SCALBN (__imag__ x, -2 * scale);
	    }
	  else if (M_FABS (__real__ x) < 2 * M_MIN
		   && M_FABS (__imag__ x) < 2 * M_MIN)
	    {
	      scale = -((M_MANT_DIG + 1) / 2);
	      __real__ x = M_SCALBN (__real__ x, -2 * scale);
	      __imag__ x = M_SCALBN (__imag__ x, -2 * scale);
	    }

	  d = M_HYPOT (__real__ x, __imag__ x);
	  /* Use the identity   2  Re res  Im res = Im x
	     to avoid cancellation error in  d +/- Re x.  */
	  if (__real__ x > 0)
	    {
	      r = M_SQRT (M_LIT (0.5) * (d + __real__ x));
	      if (scale == 1 && M_FABS (__imag__ x) < 1)
		{
		  /* Avoid possible intermediate underflow.  */
		  s = __imag__ x / r;
		  r = M_SCALBN (r, scale);
		  scale = 0;
		}
	      else
		s = M_LIT (0.5) * (__imag__ x / r);
	    }
	  else
	    {
	      s = M_SQRT (M_LIT (0.5) * (d - __real__ x));
	      if (scale == 1 && M_FABS (__imag__ x) < 1)
		{
		  /* Avoid possible intermediate underflow.  */
		  r = M_FABS (__imag__ x / s);
		  s = M_SCALBN (s, scale);
		  scale = 0;
		}
	      else
		r = M_FABS (M_LIT (0.5) * (__imag__ x / s));
	    }

	  if (scale)
	    {
	      r = M_SCALBN (r, scale);
	      s = M_SCALBN (s, scale);
	    }

	  math_check_force_underflow (r);
	  math_check_force_underflow (s);

	  __real__ res = r;
	  __imag__ res = M_COPYSIGN (s, __imag__ x);
	}
    }

  return res;
}
Beispiel #7
0
CFLOAT
M_DECL_FUNC (__cexp) (CFLOAT x)
{
  CFLOAT retval;
  int rcls = fpclassify (__real__ x);
  int icls = fpclassify (__imag__ x);

  if (__glibc_likely (rcls >= FP_ZERO))
    {
      /* Real part is finite.  */
      if (__glibc_likely (icls >= FP_ZERO))
	{
	  /* Imaginary part is finite.  */
	  const int t = (int) ((M_MAX_EXP - 1) * M_MLIT (M_LN2));
	  FLOAT sinix, cosix;

	  if (__glibc_likely (M_FABS (__imag__ x) > M_MIN))
	    {
	      M_SINCOS (__imag__ x, &sinix, &cosix);
	    }
	  else
	    {
	      sinix = __imag__ x;
	      cosix = 1;
	    }

	  if (__real__ x > t)
	    {
	      FLOAT exp_t = M_EXP (t);
	      __real__ x -= t;
	      sinix *= exp_t;
	      cosix *= exp_t;
	      if (__real__ x > t)
		{
		  __real__ x -= t;
		  sinix *= exp_t;
		  cosix *= exp_t;
		}
	    }
	  if (__real__ x > t)
	    {
	      /* Overflow (original real part of x > 3t).  */
	      __real__ retval = M_MAX * cosix;
	      __imag__ retval = M_MAX * sinix;
	    }
	  else
	    {
	      FLOAT exp_val = M_EXP (__real__ x);
	      __real__ retval = exp_val * cosix;
	      __imag__ retval = exp_val * sinix;
	    }
	  math_check_force_underflow_complex (retval);
	}
      else
	{
	  /* If the imaginary part is +-inf or NaN and the real part
	     is not +-inf the result is NaN + iNaN.  */
	  __real__ retval = M_NAN;
	  __imag__ retval = M_NAN;

	  feraiseexcept (FE_INVALID);
	}
    }
  else if (__glibc_likely (rcls == FP_INFINITE))
    {
      /* Real part is infinite.  */
      if (__glibc_likely (icls >= FP_ZERO))
	{
	  /* Imaginary part is finite.  */
	  FLOAT value = signbit (__real__ x) ? 0 : M_HUGE_VAL;

	  if (icls == FP_ZERO)
	    {
	      /* Imaginary part is 0.0.  */
	      __real__ retval = value;
	      __imag__ retval = __imag__ x;
	    }
	  else
	    {
	      FLOAT sinix, cosix;

	      if (__glibc_likely (M_FABS (__imag__ x) > M_MIN))
		{
		  M_SINCOS (__imag__ x, &sinix, &cosix);
		}
	      else
		{
		  sinix = __imag__ x;
		  cosix = 1;
		}

	      __real__ retval = M_COPYSIGN (value, cosix);
	      __imag__ retval = M_COPYSIGN (value, sinix);
	    }
	}
      else if (signbit (__real__ x) == 0)
	{
	  __real__ retval = M_HUGE_VAL;
	  __imag__ retval = __imag__ x - __imag__ x;
	}
      else
	{
	  __real__ retval = 0;
	  __imag__ retval = M_COPYSIGN (0, __imag__ x);
	}
    }
  else
    {
      /* If the real part is NaN the result is NaN + iNaN unless the
	 imaginary part is zero.  */
      __real__ retval = M_NAN;
      if (icls == FP_ZERO)
	__imag__ retval = __imag__ x;
      else
	{
	  __imag__ retval = M_NAN;

	  if (rcls != FP_NAN || icls != FP_NAN)
	    feraiseexcept (FE_INVALID);
	}
    }

  return retval;
}
Beispiel #8
0
CFLOAT
M_DECL_FUNC (__clog) (CFLOAT x)
{
  CFLOAT result;
  int rcls = fpclassify (__real__ x);
  int icls = fpclassify (__imag__ x);

  if (__glibc_unlikely (rcls == FP_ZERO && icls == FP_ZERO))
    {
      /* Real and imaginary part are 0.0.  */
      __imag__ result = signbit (__real__ x) ? (FLOAT) M_MLIT (M_PI) : 0;
      __imag__ result = M_COPYSIGN (__imag__ result, __imag__ x);
      /* Yes, the following line raises an exception.  */
      __real__ result = -1 / M_FABS (__real__ x);
    }
  else if (__glibc_likely (rcls != FP_NAN && icls != FP_NAN))
    {
      /* Neither real nor imaginary part is NaN.  */
      FLOAT absx = M_FABS (__real__ x), absy = M_FABS (__imag__ x);
      int scale = 0;

      if (absx < absy)
	{
	  FLOAT t = absx;
	  absx = absy;
	  absy = t;
	}

      if (absx > M_MAX / 2)
	{
	  scale = -1;
	  absx = M_SCALBN (absx, scale);
	  absy = (absy >= M_MIN * 2 ? M_SCALBN (absy, scale) : 0);
	}
      else if (absx < M_MIN && absy < M_MIN)
	{
	  scale = M_MANT_DIG;
	  absx = M_SCALBN (absx, scale);
	  absy = M_SCALBN (absy, scale);
	}

      if (absx == 1 && scale == 0)
	{
	  __real__ result = M_LOG1P (absy * absy) / 2;
	  math_check_force_underflow_nonneg (__real__ result);
	}
      else if (absx > 1 && absx < 2 && absy < 1 && scale == 0)
	{
	  FLOAT d2m1 = (absx - 1) * (absx + 1);
	  if (absy >= M_EPSILON)
	    d2m1 += absy * absy;
	  __real__ result = M_LOG1P (d2m1) / 2;
	}
      else if (absx < 1
	       && absx >= M_LIT (0.5)
	       && absy < M_EPSILON / 2
	       && scale == 0)
	{
	  FLOAT d2m1 = (absx - 1) * (absx + 1);
	  __real__ result = M_LOG1P (d2m1) / 2;
	}
      else if (absx < 1
	       && absx >= M_LIT (0.5)
	       && scale == 0
	       && absx * absx + absy * absy >= M_LIT (0.5))
	{
	  FLOAT d2m1 = M_SUF (__x2y2m1) (absx, absy);
	  __real__ result = M_LOG1P (d2m1) / 2;
	}
      else
	{
	  FLOAT d = M_HYPOT (absx, absy);
	  __real__ result = M_LOG (d) - scale * (FLOAT) M_MLIT (M_LN2);
	}

      __imag__ result = M_ATAN2 (__imag__ x, __real__ x);
    }
  else
    {
      __imag__ result = M_NAN;
      if (rcls == FP_INFINITE || icls == FP_INFINITE)
	/* Real or imaginary part is infinite.  */
	__real__ result = M_HUGE_VAL;
      else
	__real__ result = M_NAN;
    }

  return result;
}
Beispiel #9
0
CFLOAT
M_DECL_FUNC (__ctanh) (CFLOAT x)
{
  CFLOAT res;

  if (__glibc_unlikely (!isfinite (__real__ x) || !isfinite (__imag__ x)))
    {
      if (isinf (__real__ x))
	{
	  __real__ res = M_COPYSIGN (1, __real__ x);
	  if (isfinite (__imag__ x) && M_FABS (__imag__ x) > 1)
	    {
	      FLOAT sinix, cosix;
	      M_SINCOS (__imag__ x, &sinix, &cosix);
	      __imag__ res = M_COPYSIGN (0, sinix * cosix);
	    }
	  else
	    __imag__ res = M_COPYSIGN (0, __imag__ x);
	}
      else if (__imag__ x == 0)
	{
	  res = x;
	}
      else
	{
	  __real__ res = M_NAN;
	  __imag__ res = M_NAN;

	  if (isinf (__imag__ x))
	    feraiseexcept (FE_INVALID);
	}
    }
  else
    {
      FLOAT sinix, cosix;
      FLOAT den;
      const int t = (int) ((M_MAX_EXP - 1) * M_MLIT (M_LN2) / 2);

      /* tanh(x+iy) = (sinh(2x) + i*sin(2y))/(cosh(2x) + cos(2y))
	 = (sinh(x)*cosh(x) + i*sin(y)*cos(y))/(sinh(x)^2 + cos(y)^2).  */

      if (__glibc_likely (M_FABS (__imag__ x) > M_MIN))
	{
	  M_SINCOS (__imag__ x, &sinix, &cosix);
	}
      else
	{
	  sinix = __imag__ x;
	  cosix = 1;
	}

      if (M_FABS (__real__ x) > t)
	{
	  /* Avoid intermediate overflow when the imaginary part of
	     the result may be subnormal.  Ignoring negligible terms,
	     the real part is +/- 1, the imaginary part is
	     sin(y)*cos(y)/sinh(x)^2 = 4*sin(y)*cos(y)/exp(2x).  */
	  FLOAT exp_2t = M_EXP (2 * t);

	  __real__ res = M_COPYSIGN (1, __real__ x);
	  __imag__ res = 4 * sinix * cosix;
	  __real__ x = M_FABS (__real__ x);
	  __real__ x -= t;
	  __imag__ res /= exp_2t;
	  if (__real__ x > t)
	    {
	      /* Underflow (original real part of x has absolute value
		 > 2t).  */
	      __imag__ res /= exp_2t;
	    }
	  else
	    __imag__ res /= M_EXP (2 * __real__ x);
	}
      else
	{
	  FLOAT sinhrx, coshrx;
	  if (M_FABS (__real__ x) > M_MIN)
	    {
	      sinhrx = M_SINH (__real__ x);
	      coshrx = M_COSH (__real__ x);
	    }
	  else
	    {
	      sinhrx = __real__ x;
	      coshrx = 1;
	    }

	  if (M_FABS (sinhrx) > M_FABS (cosix) * M_EPSILON)
	    den = sinhrx * sinhrx + cosix * cosix;
	  else
	    den = cosix * cosix;
	  __real__ res = sinhrx * coshrx / den;
	  __imag__ res = sinix * cosix / den;
	}
      math_check_force_underflow_complex (res);
    }

  return res;
}