/*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8   -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8                                       :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â                                                                              â
â  Musl Libc                                                                   â
â  Copyright Â© 2005-2014 Rich Felker, et al.                                   â
â                                                                              â
â  Permission is hereby granted, free of charge, to any person obtaining       â
â  a copy of this software and associated documentation files (the             â
â  "Software"), to deal in the Software without restriction, including         â
â  without limitation the rights to use, copy, modify, merge, publish,         â
â  distribute, sublicense, and/or sell copies of the Software, and to          â
â  permit persons to whom the Software is furnished to do so, subject to       â
â  the following conditions:                                                   â
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â  The above copyright notice and this permission notice shall be              â
â  included in all copies or substantial portions of the Software.             â
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â  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,             â
â  EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF          â
â  MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.      â
â  IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY        â
â  CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,        â
â  TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE           â
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â                                                                              â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#include "libc/tinymath/kernel.internal.h"

asm(".ident\t\"\\n\\n\
fdlibm (fdlibm license)\\n\
Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.\"");
asm(".ident\t\"\\n\\n\
Musl libc (MIT License)\\n\
Copyright 2005-2014 Rich Felker, et. al.\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off

/* origin: FreeBSD /usr/src/lib/msun/src/k_sin.c */
/*
 * ====================================================
 * 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.
 * ====================================================
 */
/* __sin( x, y, iy)
 * kernel sin function on ~[-pi/4, pi/4] (except on -0), 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. Callers must return sin(-0) = -0 without calling here since our
 *         odd polynomial is not evaluated in a way that preserves -0.
 *         Callers may do the optimization sin(x) ~ x for tiny x.
 *      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))
 */

#define S1 -1.66666666666666324348e-01
#define S2  8.33333333332248946124e-03
#define S3 -1.98412698298579493134e-04
#define S4  2.75573137070700676789e-06
#define S5 -2.50507602534068634195e-08
#define S6  1.58969099521155010221e-10

double __sin(double x, double y, int iy)
{
	double_t z,r,v,w;
	z = x*x;
	w = z*z;
	r = S2 + z*(S3 + z*S4) + z*w*(S5 + z*S6);
	v = z*x;
	if (iy == 0)
		return x + v*(S1 + z*r);
	else
		return x - ((z*(0.5*y - v*r) - y) - v*S1);
}
