# Subversion RepositoriesKolibri OS

Rev
1. /* Copyright (C) 1994 DJ Delorie, see COPYING.DJ for details */
2. /* @(#)k_tan.c 5.1 93/09/24 */
3. /*
4.  * ====================================================
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. #if defined(LIBM_SCCS) && !defined(lint)
15. static char rcsid[] = "\$Id: k_tan.c,v 1.6 1994/08/18 23:06:16 jtc Exp \$";
16. #endif
17.
18. /* __kernel_tan( x, y, k )
19.  * kernel tan function on [-pi/4, pi/4], pi/4 ~ 0.7854
20.  * Input x is assumed to be bounded by ~pi/4 in magnitude.
21.  * Input y is the tail of x.
22.  * Input k indicates whether tan (if k=1) or
23.  * -1/tan (if k= -1) is returned.
24.  *
25.  * Algorithm
26.  *      1. Since tan(-x) = -tan(x), we need only to consider positive x.
27.  *      2. if x < 2^-28 (hx<0x3e300000 0), return x with inexact if x!=0.
28.  *      3. tan(x) is approximated by a odd polynomial of degree 27 on
29.  *         [0,0.67434]
30.  *                               3             27
31.  *              tan(x) ~ x + T1*x + ... + T13*x
32.  *         where
33.  *
34.  *              |tan(x)         2     4            26   |     -59.2
35.  *              |----- - (1+T1*x +T2*x +.... +T13*x    )| <= 2
36.  *              |  x                                    |
37.  *
38.  *         Note: tan(x+y) = tan(x) + tan'(x)*y
39.  *                        ~ tan(x) + (1+x*x)*y
40.  *         Therefore, for better accuracy in computing tan(x+y), let
41.  *                   3      2      2       2       2
42.  *              r = x *(T2+x *(T3+x *(...+x *(T12+x *T13))))
43.  *         then
44.  *                                  3    2
45.  *              tan(x+y) = x + (T1*x + (x *(r+y)+y))
46.  *
47.  *      4. For x in [0.67434,pi/4],  let y = pi/4 - x, then
48.  *              tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y))
49.  *                     = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y)))
50.  */
51.
52. #include "math.h"
53. #include "math_private.h"
54. #ifdef __STDC__
55. static const double
56. #else
57. static double
58. #endif
59. one   =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
60. pio4  =  7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */
61. pio4lo=  3.06161699786838301793e-17, /* 0x3C81A626, 0x33145C07 */
62. T[] =  {
63.   3.33333333333334091986e-01, /* 0x3FD55555, 0x55555563 */
64.   1.33333333333201242699e-01, /* 0x3FC11111, 0x1110FE7A */
65.   5.39682539762260521377e-02, /* 0x3FABA1BA, 0x1BB341FE */
66.   2.18694882948595424599e-02, /* 0x3F9664F4, 0x8406D637 */
67.   8.86323982359930005737e-03, /* 0x3F8226E3, 0xE96E8493 */
68.   3.59207910759131235356e-03, /* 0x3F6D6D22, 0xC9560328 */
69.   1.45620945432529025516e-03, /* 0x3F57DBC8, 0xFEE08315 */
70.   5.88041240820264096874e-04, /* 0x3F4344D8, 0xF2F26501 */
71.   2.46463134818469906812e-04, /* 0x3F3026F7, 0x1A8D1068 */
72.   7.81794442939557092300e-05, /* 0x3F147E88, 0xA03792A6 */
73.   7.14072491382608190305e-05, /* 0x3F12B80F, 0x32F0A7E9 */
74.  -1.85586374855275456654e-05, /* 0xBEF375CB, 0xDB605373 */
75.   2.59073051863633712884e-05, /* 0x3EFB2A70, 0x74BF7AD4 */
76. };
77.
78. #ifdef __STDC__
79.         double __kernel_tan(double x, double y, int iy)
80. #else
81.         double __kernel_tan(x, y, iy)
82.         double x,y; int iy;
83. #endif
84. {
85.         double z,r,v,w,s;
86.         int32_t ix,hx;
87.         GET_HIGH_WORD(hx,x);
88.         ix = hx&0x7fffffff;     /* high word of |x| */
89.         if(ix<0x3e300000)                       /* x < 2**-28 */
90.             {if((int)x==0) {                    /* generate inexact */
91.                 u_int32_t low;
92.                 GET_LOW_WORD(low,x);
93.                 if(((ix|low)|(iy+1))==0) return one/fabs(x);
94.                 else return (iy==1)? x: -one/x;
95.             }
96.             }
97.         if(ix>=0x3FE59428) {                    /* |x|>=0.6744 */
98.             if(hx<0) {x = -x; y = -y;}
99.             z = pio4-x;
100.             w = pio4lo-y;
101.             x = z+w; y = 0.0;
102.         }
103.         z       =  x*x;
104.         w       =  z*z;
105.     /* Break x^5*(T[1]+x^2*T[2]+...) into
106.      *    x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +
107.      *    x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))
108.      */
109.         r = T[1]+w*(T[3]+w*(T[5]+w*(T[7]+w*(T[9]+w*T[11]))));
110.         v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12])))));
111.         s = z*x;
112.         r = y + z*(s*(r+v)+y);
113.         r += T[0]*s;
114.         w = x+r;
115.         if(ix>=0x3FE59428) {
116.             v = (double)iy;
117.             return (double)(1-((hx>>30)&2))*(v-2.0*(x-(w*w/(w+v)-r)));
118.         }
119.         if(iy==1) return w;
120.         else {          /* if allow error up to 2 ulp,
121.                            simply return -1.0/(x+r) here */
122.      /*  compute -1.0/(x+r) accurately */
123.             double a,t;
124.             z  = w;
125.             SET_LOW_WORD(z,0);
126.             v  = r-(z - x);     /* z+v = r+x */
127.             t = a  = -1.0/w;    /* a = -1.0/w */
128.             SET_LOW_WORD(t,0);
129.             s  = 1.0+t*z;
130.             return t+a*(s+t*v);
131.         }
132. }
133.