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 #include <sys/cdefs.h> 16 __FBSDID("$FreeBSD$"); 17 18 #if LDBL_MANT_DIG == 64 /* ld80 version of k_sincosl.c. */ 19 20 #if defined(__amd64__) || defined(__i386__) 21 /* Long double constants are slow on these arches, and broken on i386. */ 22 static const volatile double 23 C1hi = 0.041666666666666664, /* 0x15555555555555.0p-57 */ 24 C1lo = 2.2598839032744733e-18, /* 0x14d80000000000.0p-111 */ 25 S1hi = -0.16666666666666666, /* -0x15555555555555.0p-55 */ 26 S1lo = -9.2563760475949941e-18; /* -0x15580000000000.0p-109 */ 27 #define S1 ((long double)S1hi + S1lo) 28 #define C1 ((long double)C1hi + C1lo) 29 #else 30 static const long double 31 C1 = 0.0416666666666666666136L, /* 0xaaaaaaaaaaaaaa9b.0p-68 */ 32 S1 = -0.166666666666666666671L; /* -0xaaaaaaaaaaaaaaab.0p-66 */ 33 #endif 34 35 static const double 36 C2 = -0.0013888888888888874, /* -0x16c16c16c16c10.0p-62 */ 37 C3 = 0.000024801587301571716, /* 0x1a01a01a018e22.0p-68 */ 38 C4 = -0.00000027557319215507120, /* -0x127e4fb7602f22.0p-74 */ 39 C5 = 0.0000000020876754400407278, /* 0x11eed8caaeccf1.0p-81 */ 40 C6 = -1.1470297442401303e-11, /* -0x19393412bd1529.0p-89 */ 41 C7 = 4.7383039476436467e-14, /* 0x1aac9d9af5c43e.0p-97 */ 42 S2 = 0.0083333333333333332, /* 0x11111111111111.0p-59 */ 43 S3 = -0.00019841269841269427, /* -0x1a01a01a019f81.0p-65 */ 44 S4 = 0.0000027557319223597490, /* 0x171de3a55560f7.0p-71 */ 45 S5 = -0.000000025052108218074604, /* -0x1ae64564f16cad.0p-78 */ 46 S6 = 1.6059006598854211e-10, /* 0x161242b90243b5.0p-85 */ 47 S7 = -7.6429779983024564e-13, /* -0x1ae42ebd1b2e00.0p-93 */ 48 S8 = 2.6174587166648325e-15; /* 0x179372ea0b3f64.0p-101 */ 49 50 static inline void 51 __kernel_sincosl(long double x, long double y, int iy, long double *sn, 52 long double *cs) 53 { 54 long double hz, r, v, w, z; 55 56 z = x * x; 57 v = z * x; 58 /* 59 * XXX Replace Horner scheme with an algorithm suitable for CPUs 60 * with more complex pipelines. 61 */ 62 r = S2 + z * (S3 + z * (S4 + z * (S5 + z * (S6 + z * (S7 + z * S8))))); 63 64 if (iy == 0) 65 *sn = x + v * (S1 + z * r); 66 else 67 *sn = x - ((z * (y / 2 - v * r) - y) - v * S1); 68 69 hz = z / 2; 70 w = 1 - hz; 71 r = z * (C1 + z * (C2 + z * (C3 + z * (C4 + z * (C5 + z * (C6 + 72 z * C7)))))); 73 *cs = w + (((1 - w) - hz) + (z * r - x * y)); 74 } 75 76 #elif LDBL_MANT_DIG == 113 /* ld128 version of k_sincosl.c. */ 77 78 static const long double 79 S1 = -0.16666666666666666666666666666666666606732416116558L, 80 S2 = 0.0083333333333333333333333333333331135404851288270047L, 81 S3 = -0.00019841269841269841269841269839935785325638310428717L, 82 S4 = 0.27557319223985890652557316053039946268333231205686e-5L, 83 S5 = -0.25052108385441718775048214826384312253862930064745e-7L, 84 S6 = 0.16059043836821614596571832194524392581082444805729e-9L, 85 S7 = -0.76471637318198151807063387954939213287488216303768e-12L, 86 S8 = 0.28114572543451292625024967174638477283187397621303e-14L; 87 88 static const double 89 S9 = -0.82206352458348947812512122163446202498005154296863e-17, 90 S10 = 0.19572940011906109418080609928334380560135358385256e-19, 91 S11 = -0.38680813379701966970673724299207480965452616911420e-22, 92 S12 = 0.64038150078671872796678569586315881020659912139412e-25; 93 94 static const long double 95 C1 = 4.16666666666666666666666666666666667e-02L, 96 C2 = -1.38888888888888888888888888888888834e-03L, 97 C3 = 2.48015873015873015873015873015446795e-05L, 98 C4 = -2.75573192239858906525573190949988493e-07L, 99 C5 = 2.08767569878680989792098886701451072e-09L, 100 C6 = -1.14707455977297247136657111139971865e-11L, 101 C7 = 4.77947733238738518870113294139830239e-14L, 102 C8 = -1.56192069685858079920640872925306403e-16L, 103 C9 = 4.11031762320473354032038893429515732e-19L, 104 C10= -8.89679121027589608738005163931958096e-22L, 105 C11= 1.61171797801314301767074036661901531e-24L, 106 C12= -2.46748624357670948912574279501044295e-27L; 107 108 static inline void 109 __kernel_sincosl(long double x, long double y, int iy, long double *sn, 110 long double *cs) 111 { 112 long double hz, r, v, w, z; 113 114 z = x * x; 115 v = z * x; 116 /* 117 * XXX Replace Horner scheme with an algorithm suitable for CPUs 118 * with more complex pipelines. 119 */ 120 r = S2 + z * (S3 + z * (S4 + z * (S5 + z * (S6 + z * (S7 + z * (S8 + 121 z * (S9 + z * (S10 + z * (S11 + z * S12))))))))); 122 123 if (iy == 0) 124 *sn = x + v * (S1 + z * r); 125 else 126 *sn = x - ((z * (y / 2 - v * r) - y) - v * S1); 127 128 hz = z / 2; 129 w = 1 - hz; 130 r = z * (C1 + z * (C2 + z * (C3 + z * (C4 + z * (C5 + z * (C6 + 131 z * (C7 + z * (C8 + z * (C9 + z * (C10 + z * (C11+z*C12))))))))))); 132 133 *cs = w + (((1 - w) - hz) + (z * r - x * y)); 134 } 135 #else 136 #error "Unsupported long double format" 137 #endif 138