/* Compute cosine of argument.

   Copyright (C) 2017-2018 Free Software Foundation, Inc.

   This file is part of the GNU C Library.

   The GNU C Library is free software; you can redistribute it and/or

   modify it under the terms of the GNU Lesser General Public

   License as published by the Free Software Foundation; either

   version 2.1 of the License, or (at your option) any later version.

   The GNU C Library is distributed in the hope that it will be useful,

   but WITHOUT ANY WARRANTY; without even the implied warranty of

   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU

   Lesser General Public License for more details.

   You should have received a copy of the GNU Lesser General Public

   License along with the GNU C Library; if not, see

   <http://www.gnu.org/licenses/>.  */

#include <errno.h>

#include <math.h>

#include <math_private.h>

#include <libm-alias-float.h>

#include "s_sincosf.h"

#ifndef COSF

# define COSF_FUNC __cosf

#else

# define COSF_FUNC COSF

#endif

float

COSF_FUNC (float x)

{

  double theta = x;

  double abstheta = fabs (theta);

  if (isless (abstheta, M_PI_4))

    {

      double cx;

      if (abstheta >= 0x1p-5)

	{

	  const double theta2 = theta * theta;

	  /* Chebyshev polynomial of the form for cos:

	   * 1 + x^2 (C0 + x^2 (C1 + x^2 (C2 + x^2 (C3 + x^2 * C4)))).  */

	  cx = C3 + theta2 * C4;

	  cx = C2 + theta2 * cx;

	  cx = C1 + theta2 * cx;

	  cx = C0 + theta2 * cx;

	  cx = 1. + theta2 * cx;

	  return cx;

	}

      else if (abstheta >= 0x1p-27)

	{

	  /* A simpler Chebyshev approximation is close enough for this range:

	   * 1 + x^2 (CC0 + x^3 * CC1).  */

	  const double theta2 = theta * theta;

	  cx = CC0 + theta * theta2 * CC1;

	  cx = 1.0 + theta2 * cx;

	  return cx;

	}

      else

	{

	  /* For small enough |theta|, this is close enough.  */

	  return 1.0 - abstheta;

	}

    }

  else /* |theta| >= Pi/4.  */

    {

      if (isless (abstheta, 9 * M_PI_4))

	{

	  /* There are cases where FE_UPWARD rounding mode can

	     produce a result of abstheta * inv_PI_4 == 9,

	     where abstheta < 9pi/4, so the domain for

	     pio2_table must go to 5 (9 / 2 + 1).  */

	  unsigned int n = (abstheta * inv_PI_4) + 1;

	  theta = abstheta - pio2_table[n / 2];

	  return reduced_cos (theta, n);

	}

      else if (isless (abstheta, INFINITY))

	{

	  if (abstheta < 0x1p+23)

	    {

	      unsigned int n = ((unsigned int) (abstheta * inv_PI_4)) + 1;

	      double x = n / 2;

	      theta = (abstheta - x * PI_2_hi) - x * PI_2_lo;

	      /* Argument reduction needed.  */

	      return reduced_cos (theta, n);

	    }

	  else /* |theta| >= 2^23.  */

	    {

	      x = fabsf (x);

	      int exponent;

	      GET_FLOAT_WORD (exponent, x);

	      exponent = (exponent >> FLOAT_EXPONENT_SHIFT)

			 - FLOAT_EXPONENT_BIAS;

	      exponent += 3;

	      exponent /= 28;

	      double a = invpio4_table[exponent] * x;

	      double b = invpio4_table[exponent + 1] * x;

	      double c = invpio4_table[exponent + 2] * x;

	      double d = invpio4_table[exponent + 3] * x;

	      uint64_t l = a;

	      l &= ~0x7;

	      a -= l;

	      double e = a + b;

	      l = e;

	      e = a - l;

	      if (l & 1)

		{

		  e -= 1.0;

		  e += b;

		  e += c;

		  e += d;

		  e *= M_PI_4;

		  return reduced_cos (e, l + 1);

		}

	      else

		{

		  e += b;

		  e += c;

		  e += d;

		  if (e <= 1.0)

		    {

		      e *= M_PI_4;

		      return reduced_cos (e, l + 1);

		    }

		  else

		    {

		      l++;

		      e -= 2.0;

		      e *= M_PI_4;

		      return reduced_cos (e, l + 1);

		    }

		}

	    }

	}

      else

	{

	  int32_t ix;

	  GET_FLOAT_WORD (ix, abstheta);

	  /* cos(Inf or NaN) is NaN.  */

	  if (ix == 0x7f800000) /* Inf.  */

	    __set_errno (EDOM);

	  return x - x;

	}

    }

}

#ifndef COSF

libm_alias_float (__cos, cos)

#endif