1 /* From: @(#)k_tan.c 1.5 04/04/22 SMI */
2
3 /*
4 * ====================================================
5 * Copyright 2004 Sun Microsystems, Inc. All Rights Reserved.
6 * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans.
7 *
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 #include <sys/cdefs.h>
15 __FBSDID("$FreeBSD$");
16
17 /*
18 * ld128 version of k_tan.c. See ../src/k_tan.c for most comments.
19 */
20
21 #include "math.h"
22 #include "math_private.h"
23
24 /*
25 * Domain [-0.67434, 0.67434], range ~[-3.37e-36, 1.982e-37]
26 * |tan(x)/x - t(x)| < 2**-117.8 (XXX should be ~1e-37)
27 *
28 * See ../ld80/k_cosl.c for more details about the polynomial.
29 */
30 static const long double
31 T3 = 0x1.5555555555555555555555555553p-2L,
32 T5 = 0x1.1111111111111111111111111eb5p-3L,
33 T7 = 0x1.ba1ba1ba1ba1ba1ba1ba1b694cd6p-5L,
34 T9 = 0x1.664f4882c10f9f32d6bbe09d8bcdp-6L,
35 T11 = 0x1.226e355e6c23c8f5b4f5762322eep-7L,
36 T13 = 0x1.d6d3d0e157ddfb5fed8e84e27b37p-9L,
37 T15 = 0x1.7da36452b75e2b5fce9ee7c2c92ep-10L,
38 T17 = 0x1.355824803674477dfcf726649efep-11L,
39 T19 = 0x1.f57d7734d1656e0aceb716f614c2p-13L,
40 T21 = 0x1.967e18afcb180ed942dfdc518d6cp-14L,
41 T23 = 0x1.497d8eea21e95bc7e2aa79b9f2cdp-15L,
42 T25 = 0x1.0b132d39f055c81be49eff7afd50p-16L,
43 T27 = 0x1.b0f72d33eff7bfa2fbc1059d90b6p-18L,
44 T29 = 0x1.5ef2daf21d1113df38d0fbc00267p-19L,
45 T31 = 0x1.1c77d6eac0234988cdaa04c96626p-20L,
46 T33 = 0x1.cd2a5a292b180e0bdd701057dfe3p-22L,
47 T35 = 0x1.75c7357d0298c01a31d0a6f7d518p-23L,
48 T37 = 0x1.2f3190f4718a9a520f98f50081fcp-24L,
49 pio4 = 0x1.921fb54442d18469898cc51701b8p-1L,
50 pio4lo = 0x1.cd129024e088a67cc74020bbea60p-116L;
51
52 static const double
53 T39 = 0.000000028443389121318352, /* 0x1e8a7592977938.0p-78 */
54 T41 = 0.000000011981013102001973, /* 0x19baa1b1223219.0p-79 */
55 T43 = 0.0000000038303578044958070, /* 0x107385dfb24529.0p-80 */
56 T45 = 0.0000000034664378216909893, /* 0x1dc6c702a05262.0p-81 */
57 T47 = -0.0000000015090641701997785, /* -0x19ecef3569ebb6.0p-82 */
58 T49 = 0.0000000029449552300483952, /* 0x194c0668da786a.0p-81 */
59 T51 = -0.0000000022006995706097711, /* -0x12e763b8845268.0p-81 */
60 T53 = 0.0000000015468200913196612, /* 0x1a92fc98c29554.0p-82 */
61 T55 = -0.00000000061311613386849674, /* -0x151106cbc779a9.0p-83 */
62 T57 = 1.4912469681508012e-10; /* 0x147edbdba6f43a.0p-85 */
63
64 long double
__kernel_tanl(long double x,long double y,int iy)65 __kernel_tanl(long double x, long double y, int iy) {
66 long double z, r, v, w, s;
67 long double osign;
68 int i;
69
70 iy = (iy == 1 ? -1 : 1); /* XXX recover original interface */
71 osign = (x >= 0 ? 1.0 : -1.0); /* XXX slow, probably wrong for -0 */
72 if (fabsl(x) >= 0.67434) {
73 if (x < 0) {
74 x = -x;
75 y = -y;
76 }
77 z = pio4 - x;
78 w = pio4lo - y;
79 x = z + w;
80 y = 0.0;
81 i = 1;
82 } else
83 i = 0;
84 z = x * x;
85 w = z * z;
86 r = T5 + w * (T9 + w * (T13 + w * (T17 + w * (T21 +
87 w * (T25 + w * (T29 + w * (T33 +
88 w * (T37 + w * (T41 + w * (T45 + w * (T49 + w * (T53 +
89 w * T57))))))))))));
90 v = z * (T7 + w * (T11 + w * (T15 + w * (T19 + w * (T23 +
91 w * (T27 + w * (T31 + w * (T35 +
92 w * (T39 + w * (T43 + w * (T47 + w * (T51 + w * T55))))))))))));
93 s = z * x;
94 r = y + z * (s * (r + v) + y);
95 r += T3 * s;
96 w = x + r;
97 if (i == 1) {
98 v = (long double) iy;
99 return osign *
100 (v - 2.0 * (x - (w * w / (w + v) - r)));
101 }
102 if (iy == 1)
103 return w;
104 else {
105 /*
106 * if allow error up to 2 ulp, simply return
107 * -1.0 / (x+r) here
108 */
109 /* compute -1.0 / (x+r) accurately */
110 long double a, t;
111 z = w;
112 z = z + 0x1p32 - 0x1p32;
113 v = r - (z - x); /* z+v = r+x */
114 t = a = -1.0 / w; /* a = -1.0/w */
115 t = t + 0x1p32 - 0x1p32;
116 s = 1.0 + t * z;
117 return t + a * (s + t * v);
118 }
119 }
120