1*cfe182f3Schristos /* From: @(#)k_tan.c 1.5 04/04/22 SMI */
2*cfe182f3Schristos
3*cfe182f3Schristos /*
4*cfe182f3Schristos * ====================================================
5*cfe182f3Schristos * Copyright 2004 Sun Microsystems, Inc. All Rights Reserved.
6*cfe182f3Schristos * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans.
7*cfe182f3Schristos *
8*cfe182f3Schristos * Permission to use, copy, modify, and distribute this
9*cfe182f3Schristos * software is freely granted, provided that this notice
10*cfe182f3Schristos * is preserved.
11*cfe182f3Schristos * ====================================================
12*cfe182f3Schristos */
13*cfe182f3Schristos
14*cfe182f3Schristos #include <sys/cdefs.h>
15*cfe182f3Schristos /*
16*cfe182f3Schristos * ld128 version of k_tan.c. See ../src/k_tan.c for most comments.
17*cfe182f3Schristos */
18*cfe182f3Schristos
19*cfe182f3Schristos #include "math.h"
20*cfe182f3Schristos #include "math_private.h"
21*cfe182f3Schristos
22*cfe182f3Schristos /*
23*cfe182f3Schristos * Domain [-0.67434, 0.67434], range ~[-3.37e-36, 1.982e-37]
24*cfe182f3Schristos * |tan(x)/x - t(x)| < 2**-117.8 (XXX should be ~1e-37)
25*cfe182f3Schristos *
26*cfe182f3Schristos * See ../ld80/k_cosl.c for more details about the polynomial.
27*cfe182f3Schristos */
28*cfe182f3Schristos static const long double
29*cfe182f3Schristos T3 = 0x1.5555555555555555555555555553p-2L,
30*cfe182f3Schristos T5 = 0x1.1111111111111111111111111eb5p-3L,
31*cfe182f3Schristos T7 = 0x1.ba1ba1ba1ba1ba1ba1ba1b694cd6p-5L,
32*cfe182f3Schristos T9 = 0x1.664f4882c10f9f32d6bbe09d8bcdp-6L,
33*cfe182f3Schristos T11 = 0x1.226e355e6c23c8f5b4f5762322eep-7L,
34*cfe182f3Schristos T13 = 0x1.d6d3d0e157ddfb5fed8e84e27b37p-9L,
35*cfe182f3Schristos T15 = 0x1.7da36452b75e2b5fce9ee7c2c92ep-10L,
36*cfe182f3Schristos T17 = 0x1.355824803674477dfcf726649efep-11L,
37*cfe182f3Schristos T19 = 0x1.f57d7734d1656e0aceb716f614c2p-13L,
38*cfe182f3Schristos T21 = 0x1.967e18afcb180ed942dfdc518d6cp-14L,
39*cfe182f3Schristos T23 = 0x1.497d8eea21e95bc7e2aa79b9f2cdp-15L,
40*cfe182f3Schristos T25 = 0x1.0b132d39f055c81be49eff7afd50p-16L,
41*cfe182f3Schristos T27 = 0x1.b0f72d33eff7bfa2fbc1059d90b6p-18L,
42*cfe182f3Schristos T29 = 0x1.5ef2daf21d1113df38d0fbc00267p-19L,
43*cfe182f3Schristos T31 = 0x1.1c77d6eac0234988cdaa04c96626p-20L,
44*cfe182f3Schristos T33 = 0x1.cd2a5a292b180e0bdd701057dfe3p-22L,
45*cfe182f3Schristos T35 = 0x1.75c7357d0298c01a31d0a6f7d518p-23L,
46*cfe182f3Schristos T37 = 0x1.2f3190f4718a9a520f98f50081fcp-24L,
47*cfe182f3Schristos pio4 = 0x1.921fb54442d18469898cc51701b8p-1L,
48*cfe182f3Schristos pio4lo = 0x1.cd129024e088a67cc74020bbea60p-116L;
49*cfe182f3Schristos
50*cfe182f3Schristos static const double
51*cfe182f3Schristos T39 = 0.000000028443389121318352, /* 0x1e8a7592977938.0p-78 */
52*cfe182f3Schristos T41 = 0.000000011981013102001973, /* 0x19baa1b1223219.0p-79 */
53*cfe182f3Schristos T43 = 0.0000000038303578044958070, /* 0x107385dfb24529.0p-80 */
54*cfe182f3Schristos T45 = 0.0000000034664378216909893, /* 0x1dc6c702a05262.0p-81 */
55*cfe182f3Schristos T47 = -0.0000000015090641701997785, /* -0x19ecef3569ebb6.0p-82 */
56*cfe182f3Schristos T49 = 0.0000000029449552300483952, /* 0x194c0668da786a.0p-81 */
57*cfe182f3Schristos T51 = -0.0000000022006995706097711, /* -0x12e763b8845268.0p-81 */
58*cfe182f3Schristos T53 = 0.0000000015468200913196612, /* 0x1a92fc98c29554.0p-82 */
59*cfe182f3Schristos T55 = -0.00000000061311613386849674, /* -0x151106cbc779a9.0p-83 */
60*cfe182f3Schristos T57 = 1.4912469681508012e-10; /* 0x147edbdba6f43a.0p-85 */
61*cfe182f3Schristos
62*cfe182f3Schristos long double
__kernel_tanl(long double x,long double y,int iy)63*cfe182f3Schristos __kernel_tanl(long double x, long double y, int iy) {
64*cfe182f3Schristos long double z, r, v, w, s;
65*cfe182f3Schristos long double osign;
66*cfe182f3Schristos int i;
67*cfe182f3Schristos
68*cfe182f3Schristos iy = (iy == 1 ? -1 : 1); /* XXX recover original interface */
69*cfe182f3Schristos osign = (x >= 0 ? 1.0 : -1.0); /* XXX slow, probably wrong for -0 */
70*cfe182f3Schristos if (fabsl(x) >= 0.67434) {
71*cfe182f3Schristos if (x < 0) {
72*cfe182f3Schristos x = -x;
73*cfe182f3Schristos y = -y;
74*cfe182f3Schristos }
75*cfe182f3Schristos z = pio4 - x;
76*cfe182f3Schristos w = pio4lo - y;
77*cfe182f3Schristos x = z + w;
78*cfe182f3Schristos y = 0.0;
79*cfe182f3Schristos i = 1;
80*cfe182f3Schristos } else
81*cfe182f3Schristos i = 0;
82*cfe182f3Schristos z = x * x;
83*cfe182f3Schristos w = z * z;
84*cfe182f3Schristos r = T5 + w * (T9 + w * (T13 + w * (T17 + w * (T21 +
85*cfe182f3Schristos w * (T25 + w * (T29 + w * (T33 +
86*cfe182f3Schristos w * (T37 + w * (T41 + w * (T45 + w * (T49 + w * (T53 +
87*cfe182f3Schristos w * T57))))))))))));
88*cfe182f3Schristos v = z * (T7 + w * (T11 + w * (T15 + w * (T19 + w * (T23 +
89*cfe182f3Schristos w * (T27 + w * (T31 + w * (T35 +
90*cfe182f3Schristos w * (T39 + w * (T43 + w * (T47 + w * (T51 + w * T55))))))))))));
91*cfe182f3Schristos s = z * x;
92*cfe182f3Schristos r = y + z * (s * (r + v) + y);
93*cfe182f3Schristos r += T3 * s;
94*cfe182f3Schristos w = x + r;
95*cfe182f3Schristos if (i == 1) {
96*cfe182f3Schristos v = (long double) iy;
97*cfe182f3Schristos return osign *
98*cfe182f3Schristos (v - 2.0 * (x - (w * w / (w + v) - r)));
99*cfe182f3Schristos }
100*cfe182f3Schristos if (iy == 1)
101*cfe182f3Schristos return w;
102*cfe182f3Schristos else {
103*cfe182f3Schristos /*
104*cfe182f3Schristos * if allow error up to 2 ulp, simply return
105*cfe182f3Schristos * -1.0 / (x+r) here
106*cfe182f3Schristos */
107*cfe182f3Schristos /* compute -1.0 / (x+r) accurately */
108*cfe182f3Schristos long double a, t;
109*cfe182f3Schristos z = w;
110*cfe182f3Schristos z = z + 0x1p32 - 0x1p32;
111*cfe182f3Schristos v = r - (z - x); /* z+v = r+x */
112*cfe182f3Schristos t = a = -1.0 / w; /* a = -1.0/w */
113*cfe182f3Schristos t = t + 0x1p32 - 0x1p32;
114*cfe182f3Schristos s = 1.0 + t * z;
115*cfe182f3Schristos return t + a * (s + t * v);
116*cfe182f3Schristos }
117*cfe182f3Schristos }
118