1 | /* origin: FreeBSD /usr/src/lib/msun/ld80/k_tanl.c */
|
---|
2 | /* origin: FreeBSD /usr/src/lib/msun/ld128/k_tanl.c */
|
---|
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 "libm.h"
|
---|
15 |
|
---|
16 | #if (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
|
---|
17 | #if LDBL_MANT_DIG == 64
|
---|
18 | /*
|
---|
19 | * ld80 version of __tan.c. See __tan.c for most comments.
|
---|
20 | */
|
---|
21 | /*
|
---|
22 | * Domain [-0.67434, 0.67434], range ~[-2.25e-22, 1.921e-22]
|
---|
23 | * |tan(x)/x - t(x)| < 2**-71.9
|
---|
24 | *
|
---|
25 | * See __cosl.c for more details about the polynomial.
|
---|
26 | */
|
---|
27 | static const long double
|
---|
28 | T3 = 0.333333333333333333180L, /* 0xaaaaaaaaaaaaaaa5.0p-65 */
|
---|
29 | T5 = 0.133333333333333372290L, /* 0x88888888888893c3.0p-66 */
|
---|
30 | T7 = 0.0539682539682504975744L, /* 0xdd0dd0dd0dc13ba2.0p-68 */
|
---|
31 | pio4 = 0.785398163397448309628L, /* 0xc90fdaa22168c235.0p-64 */
|
---|
32 | pio4lo = -1.25413940316708300586e-20L; /* -0xece675d1fc8f8cbb.0p-130 */
|
---|
33 | static const double
|
---|
34 | T9 = 0.021869488536312216, /* 0x1664f4882cc1c2.0p-58 */
|
---|
35 | T11 = 0.0088632355256619590, /* 0x1226e355c17612.0p-59 */
|
---|
36 | T13 = 0.0035921281113786528, /* 0x1d6d3d185d7ff8.0p-61 */
|
---|
37 | T15 = 0.0014558334756312418, /* 0x17da354aa3f96b.0p-62 */
|
---|
38 | T17 = 0.00059003538700862256, /* 0x13559358685b83.0p-63 */
|
---|
39 | T19 = 0.00023907843576635544, /* 0x1f56242026b5be.0p-65 */
|
---|
40 | T21 = 0.000097154625656538905, /* 0x1977efc26806f4.0p-66 */
|
---|
41 | T23 = 0.000038440165747303162, /* 0x14275a09b3ceac.0p-67 */
|
---|
42 | T25 = 0.000018082171885432524, /* 0x12f5e563e5487e.0p-68 */
|
---|
43 | T27 = 0.0000024196006108814377, /* 0x144c0d80cc6896.0p-71 */
|
---|
44 | T29 = 0.0000078293456938132840, /* 0x106b59141a6cb3.0p-69 */
|
---|
45 | T31 = -0.0000032609076735050182, /* -0x1b5abef3ba4b59.0p-71 */
|
---|
46 | T33 = 0.0000023261313142559411; /* 0x13835436c0c87f.0p-71 */
|
---|
47 | #define RPOLY(w) (T5 + w * (T9 + w * (T13 + w * (T17 + w * (T21 + \
|
---|
48 | w * (T25 + w * (T29 + w * T33)))))))
|
---|
49 | #define VPOLY(w) (T7 + w * (T11 + w * (T15 + w * (T19 + w * (T23 + \
|
---|
50 | w * (T27 + w * T31))))))
|
---|
51 | #elif LDBL_MANT_DIG == 113
|
---|
52 | /*
|
---|
53 | * ld128 version of __tan.c. See __tan.c for most comments.
|
---|
54 | */
|
---|
55 | /*
|
---|
56 | * Domain [-0.67434, 0.67434], range ~[-3.37e-36, 1.982e-37]
|
---|
57 | * |tan(x)/x - t(x)| < 2**-117.8 (XXX should be ~1e-37)
|
---|
58 | *
|
---|
59 | * See __cosl.c for more details about the polynomial.
|
---|
60 | */
|
---|
61 | static const long double
|
---|
62 | T3 = 0x1.5555555555555555555555555553p-2L,
|
---|
63 | T5 = 0x1.1111111111111111111111111eb5p-3L,
|
---|
64 | T7 = 0x1.ba1ba1ba1ba1ba1ba1ba1b694cd6p-5L,
|
---|
65 | T9 = 0x1.664f4882c10f9f32d6bbe09d8bcdp-6L,
|
---|
66 | T11 = 0x1.226e355e6c23c8f5b4f5762322eep-7L,
|
---|
67 | T13 = 0x1.d6d3d0e157ddfb5fed8e84e27b37p-9L,
|
---|
68 | T15 = 0x1.7da36452b75e2b5fce9ee7c2c92ep-10L,
|
---|
69 | T17 = 0x1.355824803674477dfcf726649efep-11L,
|
---|
70 | T19 = 0x1.f57d7734d1656e0aceb716f614c2p-13L,
|
---|
71 | T21 = 0x1.967e18afcb180ed942dfdc518d6cp-14L,
|
---|
72 | T23 = 0x1.497d8eea21e95bc7e2aa79b9f2cdp-15L,
|
---|
73 | T25 = 0x1.0b132d39f055c81be49eff7afd50p-16L,
|
---|
74 | T27 = 0x1.b0f72d33eff7bfa2fbc1059d90b6p-18L,
|
---|
75 | T29 = 0x1.5ef2daf21d1113df38d0fbc00267p-19L,
|
---|
76 | T31 = 0x1.1c77d6eac0234988cdaa04c96626p-20L,
|
---|
77 | T33 = 0x1.cd2a5a292b180e0bdd701057dfe3p-22L,
|
---|
78 | T35 = 0x1.75c7357d0298c01a31d0a6f7d518p-23L,
|
---|
79 | T37 = 0x1.2f3190f4718a9a520f98f50081fcp-24L,
|
---|
80 | pio4 = 0x1.921fb54442d18469898cc51701b8p-1L,
|
---|
81 | pio4lo = 0x1.cd129024e088a67cc74020bbea60p-116L;
|
---|
82 | static const double
|
---|
83 | T39 = 0.000000028443389121318352, /* 0x1e8a7592977938.0p-78 */
|
---|
84 | T41 = 0.000000011981013102001973, /* 0x19baa1b1223219.0p-79 */
|
---|
85 | T43 = 0.0000000038303578044958070, /* 0x107385dfb24529.0p-80 */
|
---|
86 | T45 = 0.0000000034664378216909893, /* 0x1dc6c702a05262.0p-81 */
|
---|
87 | T47 = -0.0000000015090641701997785, /* -0x19ecef3569ebb6.0p-82 */
|
---|
88 | T49 = 0.0000000029449552300483952, /* 0x194c0668da786a.0p-81 */
|
---|
89 | T51 = -0.0000000022006995706097711, /* -0x12e763b8845268.0p-81 */
|
---|
90 | T53 = 0.0000000015468200913196612, /* 0x1a92fc98c29554.0p-82 */
|
---|
91 | T55 = -0.00000000061311613386849674, /* -0x151106cbc779a9.0p-83 */
|
---|
92 | T57 = 1.4912469681508012e-10; /* 0x147edbdba6f43a.0p-85 */
|
---|
93 | #define RPOLY(w) (T5 + w * (T9 + w * (T13 + w * (T17 + w * (T21 + \
|
---|
94 | w * (T25 + w * (T29 + w * (T33 + w * (T37 + w * (T41 + \
|
---|
95 | w * (T45 + w * (T49 + w * (T53 + w * T57)))))))))))))
|
---|
96 | #define VPOLY(w) (T7 + w * (T11 + w * (T15 + w * (T19 + w * (T23 + \
|
---|
97 | w * (T27 + w * (T31 + w * (T35 + w * (T39 + w * (T43 + \
|
---|
98 | w * (T47 + w * (T51 + w * T55))))))))))))
|
---|
99 | #endif
|
---|
100 |
|
---|
101 | long double __tanl(long double x, long double y, int odd) {
|
---|
102 | long double z, r, v, w, s, a, t;
|
---|
103 | int big, sign;
|
---|
104 |
|
---|
105 | big = fabsl(x) >= 0.67434;
|
---|
106 | if (big) {
|
---|
107 | sign = 0;
|
---|
108 | if (x < 0) {
|
---|
109 | sign = 1;
|
---|
110 | x = -x;
|
---|
111 | y = -y;
|
---|
112 | }
|
---|
113 | x = (pio4 - x) + (pio4lo - y);
|
---|
114 | y = 0.0;
|
---|
115 | }
|
---|
116 | z = x * x;
|
---|
117 | w = z * z;
|
---|
118 | r = RPOLY(w);
|
---|
119 | v = z * VPOLY(w);
|
---|
120 | s = z * x;
|
---|
121 | r = y + z * (s * (r + v) + y) + T3 * s;
|
---|
122 | w = x + r;
|
---|
123 | if (big) {
|
---|
124 | s = 1 - 2*odd;
|
---|
125 | v = s - 2.0 * (x + (r - w * w / (w + s)));
|
---|
126 | return sign ? -v : v;
|
---|
127 | }
|
---|
128 | if (!odd)
|
---|
129 | return w;
|
---|
130 | /*
|
---|
131 | * if allow error up to 2 ulp, simply return
|
---|
132 | * -1.0 / (x+r) here
|
---|
133 | */
|
---|
134 | /* compute -1.0 / (x+r) accurately */
|
---|
135 | z = w;
|
---|
136 | z = z + 0x1p32 - 0x1p32;
|
---|
137 | v = r - (z - x); /* z+v = r+x */
|
---|
138 | t = a = -1.0 / w; /* a = -1.0/w */
|
---|
139 | t = t + 0x1p32 - 0x1p32;
|
---|
140 | s = 1.0 + t * z;
|
---|
141 | return t + a * (s + t * v);
|
---|
142 | }
|
---|
143 | #endif
|
---|