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