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/* @(#)s_tan.c 5.1 93/09/24 */
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/* @(#)s_tan.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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<<tan>>, <<tanf>>---tangent
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<<tan>>, <<tanf>>---tangent
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INDEX
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INDEX
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tan
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tan
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INDEX
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INDEX
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tanf
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tanf
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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 tan(double <[x]>);
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double tan(double <[x]>);
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float tanf(float <[x]>);
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float tanf(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 tan(<[x]>)
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double tan(<[x]>)
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double <[x]>;
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double <[x]>;
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float tanf(<[x]>)
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float tanf(<[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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<<tan>> computes the tangent of the argument <[x]>.
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<<tan>> computes the tangent of the argument <[x]>.
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Angles are specified in radians.
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Angles are specified in radians.
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<<tanf>> is identical, save that it takes and returns <<float>> values.
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<<tanf>> is identical, save that it takes and returns <<float>> values.
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RETURNS
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RETURNS
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The tangent of <[x]> is returned.
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The tangent of <[x]> is returned.
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PORTABILITY
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PORTABILITY
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<<tan>> is ANSI. <<tanf>> is an extension.
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<<tan>> is ANSI. <<tanf>> is an extension.
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*/
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*/
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/* tan(x)
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/* tan(x)
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* Return tangent function of x.
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* Return tangent 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_tan ... tangent function on [-pi/4,pi/4]
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* __kernel_tan ... tangent 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 tan(double x)
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double tan(double x)
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#else
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#else
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double tan(x)
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double tan(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_tan(x,z,1);
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if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1);
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/* tan(Inf or NaN) is NaN */
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/* tan(Inf or NaN) is NaN */
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else if (ix>=0x7ff00000) return x-x; /* NaN */
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else if (ix>=0x7ff00000) return x-x; /* NaN */
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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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return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even
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return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even
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-1 -- n odd */
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-1 -- n odd */
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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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