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 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