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/* @(#)s_sin.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/*
FUNCTION
<<sin>>, <<sinf>>, <<cos>>, <<cosf>>---sine or cosine
INDEX
sin
INDEX
sinf
INDEX
cos
INDEX
cosf
SYNOPSIS
#include <math.h>
double sin(double <[x]>);
float sinf(float <[x]>);
double cos(double <[x]>);
float cosf(float <[x]>);
DESCRIPTION
<<sin>> and <<cos>> compute (respectively) the sine and cosine
of the argument <[x]>. Angles are specified in radians.
<<sinf>> and <<cosf>> are identical, save that they take and
return <<float>> values.
RETURNS
The sine or cosine of <[x]> is returned.
PORTABILITY
<<sin>> and <<cos>> are ANSI C.
<<sinf>> and <<cosf>> are extensions.
QUICKREF
sin ansi pure
sinf - pure
*/
/* sin(x)
* Return sine function of x.
*
* kernel function:
* __kernel_sin ... sine function on [-pi/4,pi/4]
* __kernel_cos ... cose function on [-pi/4,pi/4]
* __ieee754_rem_pio2 ... argument reduction routine
*
* Method.
* Let S,C and T denote the sin, cos and tan respectively on
* [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
* in [-pi/4 , +pi/4], and let n = k mod 4.
* We have
*
* n sin(x) cos(x) tan(x)
* ----------------------------------------------------------
* 0 S C T
* 1 C -S -1/T
* 2 -S -C T
* 3 -C S -1/T
* ----------------------------------------------------------
*
* Special cases:
* Let trig be any of sin, cos, or tan.
* trig(+-INF) is NaN, with signals;
* trig(NaN) is that NaN;
*
* Accuracy:
* TRIG(x) returns trig(x) nearly rounded
*/
#include "fdlibm.h"
#ifndef _DOUBLE_IS_32BITS
#ifdef __STDC__
double sin(double x)
#else
double sin(x)
double x;
#endif
{
double y[2],z=0.0;
__int32_t n,ix;
/* High word of x. */
GET_HIGH_WORD(ix,x);
/* |x| ~< pi/4 */
ix &= 0x7fffffff;
if(ix <= 0x3fe921fb) return __kernel_sin(x,z,0);
/* sin(Inf or NaN) is NaN */
else if (ix>=0x7ff00000) return x-x;
/* argument reduction needed */
else {
n = __ieee754_rem_pio2(x,y);
switch(n&3) {
case 0: return __kernel_sin(y[0],y[1],1);
case 1: return __kernel_cos(y[0],y[1]);
case 2: return -__kernel_sin(y[0],y[1],1);
default:
return -__kernel_cos(y[0],y[1]);
}
}
}
#endif /* _DOUBLE_IS_32BITS */
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