1 /*-
2 * ====================================================
3 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
4 * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans.
5 *
6 * Developed at SunSoft, a Sun Microsystems, Inc. business.
7 * Permission to use, copy, modify, and distribute this
8 * software is freely granted, provided that this notice
9 * is preserved.
10 * ====================================================
11 *
12 * k_sinl.c and k_cosl.c merged by Steven G. Kargl
13 */
14
15 #if defined(__amd64__) || defined(__i386__)
16 /* Long double constants are slow on these arches, and broken on i386. */
17 static const volatile double
18 C1hi = 0.041666666666666664, /* 0x15555555555555.0p-57 */
19 C1lo = 2.2598839032744733e-18, /* 0x14d80000000000.0p-111 */
20 S1hi = -0.16666666666666666, /* -0x15555555555555.0p-55 */
21 S1lo = -9.2563760475949941e-18; /* -0x15580000000000.0p-109 */
22 #define S1 ((long double)S1hi + S1lo)
23 #define C1 ((long double)C1hi + C1lo)
24 #else
25 static const long double
26 C1 = 0.0416666666666666666136L; /* 0xaaaaaaaaaaaaaa9b.0p-68 */
27 S1 = -0.166666666666666666671L, /* -0xaaaaaaaaaaaaaaab.0p-66 */
28 #endif
29
30 static const double
31 C2 = -0.0013888888888888874, /* -0x16c16c16c16c10.0p-62 */
32 C3 = 0.000024801587301571716, /* 0x1a01a01a018e22.0p-68 */
33 C4 = -0.00000027557319215507120, /* -0x127e4fb7602f22.0p-74 */
34 C5 = 0.0000000020876754400407278, /* 0x11eed8caaeccf1.0p-81 */
35 C6 = -1.1470297442401303e-11, /* -0x19393412bd1529.0p-89 */
36 C7 = 4.7383039476436467e-14, /* 0x1aac9d9af5c43e.0p-97 */
37 S2 = 0.0083333333333333332, /* 0x11111111111111.0p-59 */
38 S3 = -0.00019841269841269427, /* -0x1a01a01a019f81.0p-65 */
39 S4 = 0.0000027557319223597490, /* 0x171de3a55560f7.0p-71 */
40 S5 = -0.000000025052108218074604, /* -0x1ae64564f16cad.0p-78 */
41 S6 = 1.6059006598854211e-10, /* 0x161242b90243b5.0p-85 */
42 S7 = -7.6429779983024564e-13, /* -0x1ae42ebd1b2e00.0p-93 */
43 S8 = 2.6174587166648325e-15; /* 0x179372ea0b3f64.0p-101 */
44
45 static inline void
__kernel_sincosl(long double x,long double y,int iy,long double * sn,long double * cs)46 __kernel_sincosl(long double x, long double y, int iy, long double *sn,
47 long double *cs)
48 {
49 long double hz, r, v, w, z;
50
51 z = x * x;
52 v = z * x;
53 /*
54 * XXX Replace Horner scheme with an algorithm suitable for CPUs
55 * with more complex pipelines.
56 */
57 r = S2 + z * (S3 + z * (S4 + z * (S5 + z * (S6 + z * (S7 + z * S8)))));
58
59 if (iy == 0)
60 *sn = x + v * (S1 + z * r);
61 else
62 *sn = x - ((z * (y / 2 - v * r) - y) - v * S1);
63
64 hz = z / 2;
65 w = 1 - hz;
66 r = z * (C1 + z * (C2 + z * (C3 + z * (C4 + z * (C5 + z * (C6 +
67 z * C7))))));
68 *cs = w + (((1 - w) - hz) + (z * r - x * y));
69 }
70