1 /* From: @(#)k_tan.c 1.5 04/04/22 SMI */
4 * ====================================================
5 * Copyright 2004 Sun Microsystems, Inc. All Rights Reserved.
6 * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans.
8 * Permission to use, copy, modify, and distribute this
9 * software is freely granted, provided that this notice
11 * ====================================================
14 //__FBSDID("$FreeBSD: src/lib/msun/ld80/k_tanl.c,v 1.3 2008/02/18 15:39:52 bde Exp $");
17 * ld80 version of k_tan.c. See ../src/k_tan.c for most comments.
22 #include "math_private.h"
25 * Domain [-0.67434, 0.67434], range ~[-2.25e-22, 1.921e-22]
26 * |tan(x)/x - t(x)| < 2**-71.9
28 * See k_cosl.c for more details about the polynomial.
30 #if defined(__amd64__) || defined(__i386__)
31 /* Long double constants are slow on these arches, and broken on i386. */
32 static const volatile double
33 T3hi
__attribute__ ((__section__(".rodata"))) = 0.33333333333333331, /* 0x15555555555555.0p-54 */
34 T3lo
__attribute__ ((__section__(".rodata"))) = 1.8350121769317163e-17, /* 0x15280000000000.0p-108 */
35 T5hi
__attribute__ ((__section__(".rodata"))) = 0.13333333333333336, /* 0x11111111111112.0p-55 */
36 T5lo
__attribute__ ((__section__(".rodata"))) = 1.3051083651294260e-17, /* 0x1e180000000000.0p-109 */
37 T7hi
__attribute__ ((__section__(".rodata"))) = 0.053968253968250494, /* 0x1ba1ba1ba1b827.0p-57 */
38 T7lo
__attribute__ ((__section__(".rodata"))) = 3.1509625637859973e-18, /* 0x1d100000000000.0p-111 */
39 pio4_hi
__attribute__ ((__section__(".rodata"))) = 0.78539816339744828, /* 0x1921fb54442d18.0p-53 */
40 pio4_lo
__attribute__ ((__section__(".rodata"))) = 3.0628711372715500e-17, /* 0x11a80000000000.0p-107 */
41 pio4lo_hi
__attribute__ ((__section__(".rodata"))) = -1.2541394031670831e-20, /* -0x1d9cceba3f91f2.0p-119 */
42 pio4lo_lo
__attribute__ ((__section__(".rodata"))) = 6.1493048227390915e-37; /* 0x1a280000000000.0p-173 */
43 #define T3 ((long double)T3hi + T3lo)
44 #define T5 ((long double)T5hi + T5lo)
45 #define T7 ((long double)T7hi + T7lo)
46 #define pio4 ((long double)pio4_hi + pio4_lo)
47 #define pio4lo ((long double)pio4lo_hi + pio4lo_lo)
49 static const long double
50 T3
= 0.333333333333333333180L, /* 0xaaaaaaaaaaaaaaa5.0p-65 */
51 T5
= 0.133333333333333372290L, /* 0x88888888888893c3.0p-66 */
52 T7
= 0.0539682539682504975744L, /* 0xdd0dd0dd0dc13ba2.0p-68 */
53 pio4
= 0.785398163397448309628L, /* 0xc90fdaa22168c235.0p-64 */
54 pio4lo
= -1.25413940316708300586e-20L; /* -0xece675d1fc8f8cbb.0p-130 */
58 T9
= 0.021869488536312216, /* 0x1664f4882cc1c2.0p-58 */
59 T11
= 0.0088632355256619590, /* 0x1226e355c17612.0p-59 */
60 T13
= 0.0035921281113786528, /* 0x1d6d3d185d7ff8.0p-61 */
61 T15
= 0.0014558334756312418, /* 0x17da354aa3f96b.0p-62 */
62 T17
= 0.00059003538700862256, /* 0x13559358685b83.0p-63 */
63 T19
= 0.00023907843576635544, /* 0x1f56242026b5be.0p-65 */
64 T21
= 0.000097154625656538905, /* 0x1977efc26806f4.0p-66 */
65 T23
= 0.000038440165747303162, /* 0x14275a09b3ceac.0p-67 */
66 T25
= 0.000018082171885432524, /* 0x12f5e563e5487e.0p-68 */
67 T27
= 0.0000024196006108814377, /* 0x144c0d80cc6896.0p-71 */
68 T29
= 0.0000078293456938132840, /* 0x106b59141a6cb3.0p-69 */
69 T31
= -0.0000032609076735050182, /* -0x1b5abef3ba4b59.0p-71 */
70 T33
= 0.0000023261313142559411; /* 0x13835436c0c87f.0p-71 */
73 __kernel_tanl(long double x
, long double y
, int iy
) {
74 long double z
, r
, v
, w
, s
;
78 iy
= (iy
== 1 ? -1 : 1); /* XXX recover original interface */
79 osign
= (x
>= 0 ? 1.0 : -1.0); /* XXX slow, probably wrong for -0 */
80 if (fabsl(x
) >= 0.67434) {
94 r
= T5
+ w
* (T9
+ w
* (T13
+ w
* (T17
+ w
* (T21
+
95 w
* (T25
+ w
* (T29
+ w
* T33
))))));
96 v
= z
* (T7
+ w
* (T11
+ w
* (T15
+ w
* (T19
+ w
* (T23
+
97 w
* (T27
+ w
* T31
))))));
99 r
= y
+ z
* (s
* (r
+ v
) + y
);
103 v
= (long double) iy
;
105 (v
- 2.0 * (x
- (w
* w
/ (w
+ v
) - r
)));
111 * if allow error up to 2 ulp, simply return
114 /* compute -1.0 / (x+r) accurately */
117 z
= z
+ 0x1p
32 - 0x1p
32;
118 v
= r
- (z
- x
); /* z+v = r+x */
119 t
= a
= -1.0 / w
; /* a = -1.0/w */
120 t
= t
+ 0x1p
32 - 0x1p
32;
122 return t
+ a
* (s
+ t
* v
);