1*05a0b428SJohn Marino /* $OpenBSD: k_tanl.c,v 1.1 2008/12/09 20:00:35 martynas Exp $ */
2*05a0b428SJohn Marino /* From: @(#)k_tan.c 1.5 04/04/22 SMI */
3*05a0b428SJohn Marino /*
4*05a0b428SJohn Marino * ====================================================
5*05a0b428SJohn Marino * Copyright 2004 Sun Microsystems, Inc. All Rights Reserved.
6*05a0b428SJohn Marino * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans.
7*05a0b428SJohn Marino *
8*05a0b428SJohn Marino * Permission to use, copy, modify, and distribute this
9*05a0b428SJohn Marino * software is freely granted, provided that this notice
10*05a0b428SJohn Marino * is preserved.
11*05a0b428SJohn Marino * ====================================================
12*05a0b428SJohn Marino */
13*05a0b428SJohn Marino
14*05a0b428SJohn Marino /*
15*05a0b428SJohn Marino * ld80 version of k_tan.c. See ../k_tan.c for most comments.
16*05a0b428SJohn Marino */
17*05a0b428SJohn Marino
18*05a0b428SJohn Marino #include <math.h>
19*05a0b428SJohn Marino
20*05a0b428SJohn Marino #include "math_private.h"
21*05a0b428SJohn Marino
22*05a0b428SJohn Marino /*
23*05a0b428SJohn Marino * Domain [-0.67434, 0.67434], range ~[-2.25e-22, 1.921e-22]
24*05a0b428SJohn Marino * |tan(x)/x - t(x)| < 2**-71.9
25*05a0b428SJohn Marino *
26*05a0b428SJohn Marino * See k_cosl.c for more details about the polynomial.
27*05a0b428SJohn Marino */
28*05a0b428SJohn Marino #if defined(__amd64__) || defined(__i386__)
29*05a0b428SJohn Marino /* Long double constants are slow on these arches, and broken on i386. */
30*05a0b428SJohn Marino static const volatile double
31*05a0b428SJohn Marino T3hi = 0.33333333333333331, /* 0x15555555555555.0p-54 */
32*05a0b428SJohn Marino T3lo = 1.8350121769317163e-17, /* 0x15280000000000.0p-108 */
33*05a0b428SJohn Marino T5hi = 0.13333333333333336, /* 0x11111111111112.0p-55 */
34*05a0b428SJohn Marino T5lo = 1.3051083651294260e-17, /* 0x1e180000000000.0p-109 */
35*05a0b428SJohn Marino T7hi = 0.053968253968250494, /* 0x1ba1ba1ba1b827.0p-57 */
36*05a0b428SJohn Marino T7lo = 3.1509625637859973e-18, /* 0x1d100000000000.0p-111 */
37*05a0b428SJohn Marino pio4_hi = 0.78539816339744828, /* 0x1921fb54442d18.0p-53 */
38*05a0b428SJohn Marino pio4_lo = 3.0628711372715500e-17, /* 0x11a80000000000.0p-107 */
39*05a0b428SJohn Marino pio4lo_hi = -1.2541394031670831e-20, /* -0x1d9cceba3f91f2.0p-119 */
40*05a0b428SJohn Marino pio4lo_lo = 6.1493048227390915e-37; /* 0x1a280000000000.0p-173 */
41*05a0b428SJohn Marino #define T3 ((long double)T3hi + T3lo)
42*05a0b428SJohn Marino #define T5 ((long double)T5hi + T5lo)
43*05a0b428SJohn Marino #define T7 ((long double)T7hi + T7lo)
44*05a0b428SJohn Marino #define pio4 ((long double)pio4_hi + pio4_lo)
45*05a0b428SJohn Marino #define pio4lo ((long double)pio4lo_hi + pio4lo_lo)
46*05a0b428SJohn Marino #else
47*05a0b428SJohn Marino static const long double
48*05a0b428SJohn Marino T3 = 0.333333333333333333180L, /* 0xaaaaaaaaaaaaaaa5.0p-65 */
49*05a0b428SJohn Marino T5 = 0.133333333333333372290L, /* 0x88888888888893c3.0p-66 */
50*05a0b428SJohn Marino T7 = 0.0539682539682504975744L, /* 0xdd0dd0dd0dc13ba2.0p-68 */
51*05a0b428SJohn Marino pio4 = 0.785398163397448309628L, /* 0xc90fdaa22168c235.0p-64 */
52*05a0b428SJohn Marino pio4lo = -1.25413940316708300586e-20L; /* -0xece675d1fc8f8cbb.0p-130 */
53*05a0b428SJohn Marino #endif
54*05a0b428SJohn Marino
55*05a0b428SJohn Marino static const double
56*05a0b428SJohn Marino T9 = 0.021869488536312216, /* 0x1664f4882cc1c2.0p-58 */
57*05a0b428SJohn Marino T11 = 0.0088632355256619590, /* 0x1226e355c17612.0p-59 */
58*05a0b428SJohn Marino T13 = 0.0035921281113786528, /* 0x1d6d3d185d7ff8.0p-61 */
59*05a0b428SJohn Marino T15 = 0.0014558334756312418, /* 0x17da354aa3f96b.0p-62 */
60*05a0b428SJohn Marino T17 = 0.00059003538700862256, /* 0x13559358685b83.0p-63 */
61*05a0b428SJohn Marino T19 = 0.00023907843576635544, /* 0x1f56242026b5be.0p-65 */
62*05a0b428SJohn Marino T21 = 0.000097154625656538905, /* 0x1977efc26806f4.0p-66 */
63*05a0b428SJohn Marino T23 = 0.000038440165747303162, /* 0x14275a09b3ceac.0p-67 */
64*05a0b428SJohn Marino T25 = 0.000018082171885432524, /* 0x12f5e563e5487e.0p-68 */
65*05a0b428SJohn Marino T27 = 0.0000024196006108814377, /* 0x144c0d80cc6896.0p-71 */
66*05a0b428SJohn Marino T29 = 0.0000078293456938132840, /* 0x106b59141a6cb3.0p-69 */
67*05a0b428SJohn Marino T31 = -0.0000032609076735050182, /* -0x1b5abef3ba4b59.0p-71 */
68*05a0b428SJohn Marino T33 = 0.0000023261313142559411; /* 0x13835436c0c87f.0p-71 */
69*05a0b428SJohn Marino
70*05a0b428SJohn Marino long double
__kernel_tanl(long double x,long double y,int iy)71*05a0b428SJohn Marino __kernel_tanl(long double x, long double y, int iy) {
72*05a0b428SJohn Marino long double z, r, v, w, s;
73*05a0b428SJohn Marino long double osign;
74*05a0b428SJohn Marino int i;
75*05a0b428SJohn Marino
76*05a0b428SJohn Marino iy = (iy == 1 ? -1 : 1); /* XXX recover original interface */
77*05a0b428SJohn Marino osign = (x >= 0 ? 1.0 : -1.0); /* XXX slow, probably wrong for -0 */
78*05a0b428SJohn Marino if (fabsl(x) >= 0.67434) {
79*05a0b428SJohn Marino if (x < 0) {
80*05a0b428SJohn Marino x = -x;
81*05a0b428SJohn Marino y = -y;
82*05a0b428SJohn Marino }
83*05a0b428SJohn Marino z = pio4 - x;
84*05a0b428SJohn Marino w = pio4lo - y;
85*05a0b428SJohn Marino x = z + w;
86*05a0b428SJohn Marino y = 0.0;
87*05a0b428SJohn Marino i = 1;
88*05a0b428SJohn Marino } else
89*05a0b428SJohn Marino i = 0;
90*05a0b428SJohn Marino z = x * x;
91*05a0b428SJohn Marino w = z * z;
92*05a0b428SJohn Marino r = T5 + w * (T9 + w * (T13 + w * (T17 + w * (T21 +
93*05a0b428SJohn Marino w * (T25 + w * (T29 + w * T33))))));
94*05a0b428SJohn Marino v = z * (T7 + w * (T11 + w * (T15 + w * (T19 + w * (T23 +
95*05a0b428SJohn Marino w * (T27 + w * T31))))));
96*05a0b428SJohn Marino s = z * x;
97*05a0b428SJohn Marino r = y + z * (s * (r + v) + y);
98*05a0b428SJohn Marino r += T3 * s;
99*05a0b428SJohn Marino w = x + r;
100*05a0b428SJohn Marino if (i == 1) {
101*05a0b428SJohn Marino v = (long double) iy;
102*05a0b428SJohn Marino return osign *
103*05a0b428SJohn Marino (v - 2.0 * (x - (w * w / (w + v) - r)));
104*05a0b428SJohn Marino }
105*05a0b428SJohn Marino if (iy == 1)
106*05a0b428SJohn Marino return w;
107*05a0b428SJohn Marino else {
108*05a0b428SJohn Marino /*
109*05a0b428SJohn Marino * if allow error up to 2 ulp, simply return
110*05a0b428SJohn Marino * -1.0 / (x+r) here
111*05a0b428SJohn Marino */
112*05a0b428SJohn Marino /* compute -1.0 / (x+r) accurately */
113*05a0b428SJohn Marino long double a, t;
114*05a0b428SJohn Marino z = w;
115*05a0b428SJohn Marino z = z + 0x1p32 - 0x1p32;
116*05a0b428SJohn Marino v = r - (z - x); /* z+v = r+x */
117*05a0b428SJohn Marino t = a = -1.0 / w; /* a = -1.0/w */
118*05a0b428SJohn Marino t = t + 0x1p32 - 0x1p32;
119*05a0b428SJohn Marino s = 1.0 + t * z;
120*05a0b428SJohn Marino return t + a * (s + t * v);
121*05a0b428SJohn Marino }
122*05a0b428SJohn Marino }
123