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/*
* k_sin.c
*
* Copyright (C) 1998-2015, ARM Limited, All Rights Reserved
* SPDX-License-Identifier: Apache-2.0
*
* Licensed under the Apache License, Version 2.0 (the "License"); you may
* not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
* WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*
* This file is part of the Optimized Routines project
*/
/* @(#)k_sin.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* __kernel_sin( x, y, iy)
* kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854
* Input x is assumed to be bounded by ~pi/4 in magnitude.
* Input y is the tail of x.
* Input iy indicates whether y is 0. (if iy=0, y assume to be 0).
*
* Algorithm
* 1. Since sin(-x) = -sin(x), we need only to consider positive x.
* 2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0.
* 3. sin(x) is approximated by a polynomial of degree 13 on
* [0,pi/4]
* 3 13
* sin(x) ~ x + S1*x + ... + S6*x
* where
*
* |sin(x) 2 4 6 8 10 12 | -58
* |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2
* | x |
*
* 4. sin(x+y) = sin(x) + sin'(x')*y
* ~ sin(x) + (1-x*x/2)*y
* For better accuracy, let
* 3 2 2 2 2
* r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
* then 3 2
* sin(x) = x + (S1*x + (x *(r-y/2)+y))
*/
#include "arm_math.h"
#include "math_private.h"
#include <math.h>
static const double
half = 0x1p-1, /* 5.00000000000000000000e-01 */
S1 = -0x1.5555555555549p-3, /* -1.66666666666666324348e-01 */
S[] = { 0x1.111111110f8a6p-7, /* 8.33333333332248946124e-03 */
-0x1.a01a019c161d5p-13, /* -1.98412698298579493134e-04 */
0x1.71de357b1fe7dp-19, /* 2.75573137070700676789e-06 */
-0x1.ae5e68a2b9cebp-26, /* -2.50507602534068634195e-08 */
0x1.5d93a5acfd57cp-33, /* 1.58969099521155010221e-10 */ };
double
ARM__kernel_sin(double x, double y, int iy)
{
double z,r,v;
int ix;
ix = __HI(x)&0x7fffffff; /* high word of x */
if(ix<0x3e400000) /* |x| < 2**-27 */
return DOUBLE_CHECKDENORM(x);
z = x*x;
v = z*x;
r = ARM__kernel_poly(S,5,z);
if(iy==0) return x+v*(S1+z*r);
else return x-((z*(half*y-v*r)-y)-v*S1);
}
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