11 /* __kernel_tan( x, y, k )
13  * Input x is assumed to be bounded by ~pi/4 in magnitude.
14  * Input y is the tail of x.
18  *	1. Since tan(-x) = -tan(x), we need only to consider positive x.
21  *	   Callers may do the optimization tan(x) ~ x for tiny x.
22  *	3. tan(x) is approximated by a odd polynomial of degree 27 on
24  *		  	         3             27
25  *	   	tan(x) ~ x + T1*x + ... + T13*x
28  * 	        |tan(x)         2     4            26   |     -59.2
29  * 	        |----- - (1+T1*x +T2*x +.... +T13*x    )| <= 2
30  * 	        |  x 					|
32  *	   Note: tan(x+y) = tan(x) + tan'(x)*y
33  *		          ~ tan(x) + (1+x*x)*y
34  *	   Therefore, for better accuracy in computing tan(x+y), let
35  *		     3      2      2       2       2
36  *		r = x *(T2+x *(T3+x *(...+x *(T12+x *T13))))
38  *		 		    3    2
39  *		tan(x+y) = x + (T1*x + (x *(r+y)+y))
41  *      4. For x in [0.67434,pi/4],  let y = pi/4 - x, then
42  *		tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y))
49 		 3.33333333333334091986e-01,	/* 3FD55555, 55555563 */
50 		 1.33333333333201242699e-01,	/* 3FC11111, 1110FE7A */
51 		 5.39682539762260521377e-02,	/* 3FABA1BA, 1BB341FE */
52 		 2.18694882948595424599e-02,	/* 3F9664F4, 8406D637 */
53 		 8.86323982359930005737e-03,	/* 3F8226E3, E96E8493 */
54 		 3.59207910759131235356e-03,	/* 3F6D6D22, C9560328 */
55 		 1.45620945432529025516e-03,	/* 3F57DBC8, FEE08315 */
56 		 5.88041240820264096874e-04,	/* 3F4344D8, F2F26501 */
57 		 2.46463134818469906812e-04,	/* 3F3026F7, 1A8D1068 */
58 		 7.81794442939557092300e-05,	/* 3F147E88, A03792A6 */
59 		 7.14072491382608190305e-05,	/* 3F12B80F, 32F0A7E9 */
61 		 2.59073051863633712884e-05,	/* 3EFB2A70, 74BF7AD4 */
62 /* one */	 1.00000000000000000000e+00,	/* 3FF00000, 00000000 */
63 /* pio4 */	 7.85398163397448278999e-01,	/* 3FE921FB, 54442D18 */
64 /* pio4lo */	 3.06161699786838301793e-17	/* 3C81A626, 33145C07 */
73 __kernel_tan(double x, double y, int iy) {  in __kernel_tan()  argument
77 	GET_HIGH_WORD(hx,x);  in __kernel_tan()
78 	ix = hx & 0x7fffffff;			/* high word of |x| */  in __kernel_tan()
79 	if (ix >= 0x3FE59428) {	/* |x| >= 0.6744 */  in __kernel_tan()
81 			x = -x;  in __kernel_tan()
84 		z = pio4 - x;  in __kernel_tan()
86 		x = z + w;  in __kernel_tan()
89 	z = x * x;  in __kernel_tan()
92 	 * Break x^5*(T[1]+x^2*T[2]+...) into  in __kernel_tan()
93 	 * x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +  in __kernel_tan()
94 	 * x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))  in __kernel_tan()
96 	r = T[1] + w * (T[3] + w * (T[5] + w * (T[7] + w * (T[9] +  in __kernel_tan()
100 	s = z * x;  in __kernel_tan()
103 	w = x + r;  in __kernel_tan()
107 			(v - 2.0 * (x - (w * w / (w + v) - r)));  in __kernel_tan()
114 		 * -1.0 / (x+r) here  in __kernel_tan()
116 		/* compute -1.0 / (x+r) accurately */  in __kernel_tan()
120 		v = r - (z - x);	/* z+v = r+x */  in __kernel_tan()