/* Quad-precision floating point sine on <-pi/4,pi/4>.

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

   This file is part of the GNU C Library.

   Contributed 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 <float.h>

#include <math.h>

#include <math_private.h>

#include <math-underflow.h>

static const long double c[] = {

#define ONE c[0]

 1.00000000000000000000000000000000000E+00L, /* 3fff0000000000000000000000000000 */

/* 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, /* bffe0000000000000000000000000000 */

 4.16666666666666666666666666556146073E-02L, /* 3ffa5555555555555555555555395023 */

-1.38888888888888888888309442601939728E-03L, /* bff56c16c16c16c16c16a566e42c0375 */

 2.48015873015862382987049502531095061E-05L, /* 3fefa01a01a019ee02dcf7da2d6d5444 */

-2.75573112601362126593516899592158083E-07L, /* bfe927e4f5dce637cb0b54908754bde0 */

/* sin x ~ ONE * x + x^3 ( SIN1 + SIN2 * x^2 + ... + SIN7 * x^12 + SIN8 * x^14 )

   x in <0,0.1484375>  */

#define SIN1 c[6]

#define SIN2 c[7]

#define SIN3 c[8]

#define SIN4 c[9]

#define SIN5 c[10]

#define SIN6 c[11]

#define SIN7 c[12]

#define SIN8 c[13]

-1.66666666666666666666666666666666538e-01L, /* bffc5555555555555555555555555550 */

 8.33333333333333333333333333307532934e-03L, /* 3ff811111111111111111111110e7340 */

-1.98412698412698412698412534478712057e-04L, /* bff2a01a01a01a01a01a019e7a626296 */

 2.75573192239858906520896496653095890e-06L, /* 3fec71de3a556c7338fa38527474b8f5 */

-2.50521083854417116999224301266655662e-08L, /* bfe5ae64567f544e16c7de65c2ea551f */

 1.60590438367608957516841576404938118e-10L, /* 3fde6124613a811480538a9a41957115 */

-7.64716343504264506714019494041582610e-13L, /* bfd6ae7f3d5aef30c7bc660b060ef365 */

 2.81068754939739570236322404393398135e-15L, /* 3fce9510115aabf87aceb2022a9a9180 */

/* 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, /* bffc5555555555555555555555555555 */

 8.33333333333333333333333333146298442E-03L, /* 3ff81111111111111111111110fe195d */

-1.98412698412698412697726277416810661E-04L, /* bff2a01a01a01a01a019e7121e080d88 */

 2.75573192239848624174178393552189149E-06L, /* 3fec71de3a556c640c6aaa51aa02ab41 */

-2.50521016467996193495359189395805639E-08L, /* bfe5ae644ee90c47dc71839de75b2787 */

};

#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_sinl(long double x, long double y, int iy)

{

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

  int64_t ix;

  uint32_t tix, hix, index;

  double xhi, hhi;

  xhi = ldbl_high (x);

  EXTRACT_WORDS64 (ix, xhi);

  tix = ((uint64_t)ix) >> 32;

  tix &= ~0x80000000;			/* tix = |x|'s high 32 bits */

  if (tix < 0x3fc30000)			/* |x| < 0.1484375 */

    {

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

	 polynomial of degree 17.  */

      if (tix < 0x3c600000)		/* |x| < 2^-57 */

	{

	  math_check_force_underflow (x);

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

	}

      z = x * x;

      return x + (x * (z*(SIN1+z*(SIN2+z*(SIN3+z*(SIN4+

		       z*(SIN5+z*(SIN6+z*(SIN7+z*SIN8)))))))));

    }

  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

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

      int six = tix;

      tix = ((six - 0x3ff00000) >> 4) + 0x3fff0000;

      index = 0x3ffe - (tix >> 16);

      hix = (tix + (0x200 << index)) & (0xfffffc00 << index);

      x = fabsl (x);

      switch (index)

	{

	case 0: index = ((45 << 10) + hix - 0x3ffe0000) >> 8; break;

	case 1: index = ((13 << 11) + hix - 0x3ffd0000) >> 9; break;

	default:

	case 2: index = (hix - 0x3ffc3000) >> 10; break;

	}

      hix = (hix << 4) & 0x3fffffff;

/*

    The following should work for double but generates the wrong index.

    For now the code above converts double to ieee extended to compute

    the index back to double for the h value.

      index = 0x3fe - (tix >> 20);

      hix = (tix + (0x2000 << index)) & (0xffffc000 << index);

      x = fabsl (x);

      switch (index)

	{

	case 0: index = ((45 << 14) + hix - 0x3fe00000) >> 12; break;

	case 1: index = ((13 << 15) + hix - 0x3fd00000) >> 13; break;

	default:

	case 2: index = (hix - 0x3fc30000) >> 14; break;

	}

*/

      INSERT_WORDS64 (hhi, ((uint64_t)hix) << 32);

      h = hhi;

      if (iy)

	l = (ix < 0 ? -y : y) - (h - x);

      else

	l = x - h;

      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))));

      z = __sincosl_table [index + SINCOSL_SIN_HI]

	  + (__sincosl_table [index + SINCOSL_SIN_LO]

	     + (__sincosl_table [index + SINCOSL_SIN_HI] * cos_l_m1)

	     + (__sincosl_table [index + SINCOSL_COS_HI] * sin_l));

      return (ix < 0) ? -z : z;

    }

}