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

   Copyright (C) 1999 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, write to the Free

   Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA

   02111-1307 USA.  */

#include "quadmath-imp.h"

static const __float128 c[] = {

#define ONE c[0]

 1.00000000000000000000000000000000000E+00Q, /* 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-01Q, /* bffe0000000000000000000000000000 */

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

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

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

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

/* 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-01Q, /* bffdfffffffffffffffffffffffffffb */

 4.16666666666666666666666666651287795E-02Q, /* 3ffa5555555555555555555555516f30 */

-1.38888888888888888888888742314300284E-03Q, /* bff56c16c16c16c16c16c16a463dfd0d */

 2.48015873015873015867694002851118210E-05Q, /* 3fefa01a01a01a01a0195cebe6f3d3a5 */

-2.75573192239858811636614709689300351E-07Q, /* bfe927e4fb7789f5aa8142a22044b51f */

 2.08767569877762248667431926878073669E-09Q, /* 3fe21eed8eff881d1e9262d7adff4373 */

-1.14707451049343817400420280514614892E-11Q, /* bfda9397496922a9601ed3d4ca48944b */

 4.77810092804389587579843296923533297E-14Q, /* 3fd2ae5f8197cbcdcaf7c3fb4523414c */

/* 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-01Q, /* bffc5555555555555555555555555555 */

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

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

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

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

};

#define SINCOSQ_COS_HI 0

#define SINCOSQ_COS_LO 1

#define SINCOSQ_SIN_HI 2

#define SINCOSQ_SIN_LO 3

extern const __float128 __sincosq_table[];

__float128

__quadmath_kernel_cosq (__float128 x, __float128 y)

{

  __float128 h, l, z, sin_l, cos_l_m1;

  int64_t ix;

  uint32_t tix, hix, index;

  GET_FLT128_MSW64 (ix, x);

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

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

  if (tix < 0x3ffc3000)                 /* |x| < 0.1484375 */

    {

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

         polynomial of degree 16.  */

      if (tix < 0x3fc60000)             /* |x| < 2^-57 */

        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 = 0x3ffe - (tix >> 16);

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

      x = fabsq (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;

        }

      SET_FLT128_WORDS64(h, ((uint64_t)hix) << 32, 0);

      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 __sincosq_table [index + SINCOSQ_COS_HI]

             + (__sincosq_table [index + SINCOSQ_COS_LO]

                - (__sincosq_table [index + SINCOSQ_SIN_HI] * sin_l

                   - __sincosq_table [index + SINCOSQ_COS_HI] * cos_l_m1));

    }

}