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/* Extended-precision floating point cosine on <-pi/4,pi/4>.
Copyright (C) 1999-2022 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
<https://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));
}
}
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