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/* @(#)s_tan.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
        <<tan>>, <<tanf>>---tangent
 
INDEX
tan
INDEX
tanf
 
ANSI_SYNOPSIS
        #include <math.h>
        double tan(double <[x]>);
        float tanf(float <[x]>);
 
TRAD_SYNOPSIS
        #include <math.h>
        double tan(<[x]>)
        double <[x]>;
 
        float tanf(<[x]>)
        float <[x]>;
 
 
DESCRIPTION
<<tan>> computes the tangent of the argument <[x]>.
Angles are specified in radians.
 
<<tanf>> is identical, save that it takes and returns <<float>> values.
 
RETURNS
The tangent of <[x]> is returned.
 
PORTABILITY
<<tan>> is ANSI. <<tanf>> is an extension.
*/
 
/* tan(x)
 * Return tangent function of x.
 *
 * kernel function:
 *      __kernel_tan            ... tangent 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 tan(double x)
#else
        double tan(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_tan(x,z,1);
 
    /* tan(Inf or NaN) is NaN */
        else if (ix>=0x7ff00000) return x-x;            /* NaN */
 
    /* argument reduction needed */
        else {
            n = __ieee754_rem_pio2(x,y);
            return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /*   1 -- n even
                                                        -1 -- n odd */
        }
}
 
#endif /* _DOUBLE_IS_32BITS */

Line No.	Rev	Author	Line
1	1010	ivang
2			`/* @(#)s_tan.c 5.1 93/09/24 */`
3			`/*`
4			`* ====================================================`
5			`* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.`
6			`*`
7			`* Developed at SunPro, a Sun Microsystems, Inc. business.`
8			`* Permission to use, copy, modify, and distribute this`
9			`* software is freely granted, provided that this notice`
10			`* is preserved.`
11			`* ====================================================`
12			`*/`
13
14
15			`/*`
16
17			`FUNCTION`
18			`<<tan>>, <<tanf>>---tangent`
19
20			`INDEX`
21			`tan`
22			`INDEX`
23			`tanf`
24
25			`ANSI_SYNOPSIS`
26			`#include <math.h>`
27			`double tan(double <[x]>);`
28			`float tanf(float <[x]>);`
29
30			`TRAD_SYNOPSIS`
31			`#include <math.h>`
32			`double tan(<[x]>)`
33			`double <[x]>;`
34
35			`float tanf(<[x]>)`
36			`float <[x]>;`
37
38
39			`DESCRIPTION`
40			`<<tan>> computes the tangent of the argument <[x]>.`
41			`Angles are specified in radians.`
42
43			`<<tanf>> is identical, save that it takes and returns <<float>> values.`
44
45			`RETURNS`
46			`The tangent of <[x]> is returned.`
47
48			`PORTABILITY`
49			`<<tan>> is ANSI. <<tanf>> is an extension.`
50			`*/`
51
52			`/* tan(x)`
53			`* Return tangent function of x.`
54			`*`
55			`* kernel function:`
56			`* __kernel_tan ... tangent function on [-pi/4,pi/4]`
57			`* __ieee754_rem_pio2 ... argument reduction routine`
58			`*`
59			`* Method.`
60			`* Let S,C and T denote the sin, cos and tan respectively on`
61			`* [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2`
62			`* in [-pi/4 , +pi/4], and let n = k mod 4.`
63			`* We have`
64			`*`
65			`* n sin(x) cos(x) tan(x)`
66			`* ----------------------------------------------------------`
67			`* 0 S C T`
68			`* 1 C -S -1/T`
69			`* 2 -S -C T`
70			`* 3 -C S -1/T`
71			`* ----------------------------------------------------------`
72			`*`
73			`* Special cases:`
74			`* Let trig be any of sin, cos, or tan.`
75			`* trig(+-INF) is NaN, with signals;`
76			`* trig(NaN) is that NaN;`
77			`*`
78			`* Accuracy:`
79			`* TRIG(x) returns trig(x) nearly rounded`
80			`*/`
81
82			`#include "fdlibm.h"`
83
84			`#ifndef _DOUBLE_IS_32BITS`
85
86			`#ifdef __STDC__`
87			`double tan(double x)`
88			`#else`
89			`double tan(x)`
90			`double x;`
91			`#endif`
92			`{`
93			`double y[2],z=0.0;`
94			`__int32_t n,ix;`
95
96			`/* High word of x. */`
97			`GET_HIGH_WORD(ix,x);`
98
99			`/* \|x\| ~< pi/4 */`
100			`ix &= 0x7fffffff;`
101			`if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1);`
102
103			`/* tan(Inf or NaN) is NaN */`
104			`else if (ix>=0x7ff00000) return x-x; /* NaN */`
105
106			`/* argument reduction needed */`
107			`else {`
108			`n = __ieee754_rem_pio2(x,y);`
109			`return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even`
110			`-1 -- n odd */`
111			`}`
112			`}`
113
114			`#endif /* _DOUBLE_IS_32BITS */`

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