glibc/sysdeps/ieee754/flt-32/s_cosf.c

/* 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