/* Extended-precision floating point cosine on <-pi/4,pi/4>.

   Copyright (C) 1999-2018 Free Software Foundation, Inc.

   This file is part of the GNU C Library.

   Based on quad-precision cosine by Jakub Jelinek <jj@ultra.linux.cz>

   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 <math.h>

#include <math_private.h>

/* The polynomials have not been optimized for extended-precision and

   may contain more terms than needed.  */

static const long double c[] = {

#define ONE c[0]

 1.00000000000000000000000000000000000E+00L,

/* cos x ~ ONE + x^2 ( SCOS1 + SCOS2 * x^2 + ... + SCOS4 * x^6 + SCOS5 * x^8 )

   x in <0,1/256>  */

#define SCOS1 c[1]

#define SCOS2 c[2]

#define SCOS3 c[3]

#define SCOS4 c[4]

#define SCOS5 c[5]

-5.00000000000000000000000000000000000E-01L,

 4.16666666666666666666666666556146073E-02L,

-1.38888888888888888888309442601939728E-03L,

 2.48015873015862382987049502531095061E-05L,

-2.75573112601362126593516899592158083E-07L,

/* cos x ~ ONE + x^2 ( COS1 + COS2 * x^2 + ... + COS7 * x^12 + COS8 * x^14 )

   x in <0,0.1484375>  */

#define COS1 c[6]

#define COS2 c[7]

#define COS3 c[8]

#define COS4 c[9]

#define COS5 c[10]

#define COS6 c[11]

#define COS7 c[12]

#define COS8 c[13]

-4.99999999999999999999999999999999759E-01L,

 4.16666666666666666666666666651287795E-02L,

-1.38888888888888888888888742314300284E-03L,

 2.48015873015873015867694002851118210E-05L,

-2.75573192239858811636614709689300351E-07L,

 2.08767569877762248667431926878073669E-09L,

-1.14707451049343817400420280514614892E-11L,

 4.77810092804389587579843296923533297E-14L,

/* sin x ~ ONE * x + x^3 ( SSIN1 + SSIN2 * x^2 + ... + SSIN4 * x^6 + SSIN5 * x^8 )

   x in <0,1/256>  */

#define SSIN1 c[14]

#define SSIN2 c[15]

#define SSIN3 c[16]

#define SSIN4 c[17]

#define SSIN5 c[18]

-1.66666666666666666666666666666666659E-01L,

 8.33333333333333333333333333146298442E-03L,

-1.98412698412698412697726277416810661E-04L,

 2.75573192239848624174178393552189149E-06L,

-2.50521016467996193495359189395805639E-08L,

};

#define SINCOSL_COS_HI 0

#define SINCOSL_COS_LO 1

#define SINCOSL_SIN_HI 2

#define SINCOSL_SIN_LO 3

extern const long double __sincosl_table[];

long double

__kernel_cosl(long double x, long double y)

{

  long double h, l, z, sin_l, cos_l_m1;

  int index;

  if (signbit (x))

    {

      x = -x;

      y = -y;

    }

  if (x < 0.1484375L)

    {

      /* Argument is small enough to approximate it by a Chebyshev

	 polynomial of degree 16.  */

      if (x < 0x1p-33L)

	if (!((int)x)) return ONE;	/* generate inexact */

      z = x * x;

      return ONE + (z*(COS1+z*(COS2+z*(COS3+z*(COS4+

		    z*(COS5+z*(COS6+z*(COS7+z*COS8))))))));

    }

  else

    {

      /* So that we don't have to use too large polynomial,  we find

	 l and h such that x = l + h,  where fabsl(l) <= 1.0/256 with 83

	 possible values for h.  We look up cosl(h) and sinl(h) in

	 pre-computed tables,  compute cosl(l) and sinl(l) using a

	 Chebyshev polynomial of degree 10(11) and compute

	 cosl(h+l) = cosl(h)cosl(l) - sinl(h)sinl(l).  */

      index = (int) (128 * (x - (0.1484375L - 1.0L / 256.0L)));

      h = 0.1484375L + index / 128.0;

      index *= 4;

      l = y - (h - x);

      z = l * l;

      sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5)))));

      cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5))));

      return __sincosl_table [index + SINCOSL_COS_HI]

	     + (__sincosl_table [index + SINCOSL_COS_LO]

		- (__sincosl_table [index + SINCOSL_SIN_HI] * sin_l

		   - __sincosl_table [index + SINCOSL_COS_HI] * cos_l_m1));

    }

}