| Elliott Hughes | e332f65 | 2018-05-08 15:07:43 -0700 | [diff] [blame^] | 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: head/lib/msun/src/k_sincosl.h 319047 2017-05-28 06:13:38Z mmel $"); |
| 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 | C1 = 0.04166666666666666666666666666666658424671L, |
| 80 | C2 = -0.001388888888888888888888888888863490893732L, |
| 81 | C3 = 0.00002480158730158730158730158600795304914210L, |
| 82 | C4 = -0.2755731922398589065255474947078934284324e-6L, |
| 83 | C5 = 0.2087675698786809897659225313136400793948e-8L, |
| 84 | C6 = -0.1147074559772972315817149986812031204775e-10L, |
| 85 | C7 = 0.4779477332386808976875457937252120293400e-13L, |
| 86 | S1 = -0.16666666666666666666666666666666666606732416116558L, |
| 87 | S2 = 0.0083333333333333333333333333333331135404851288270047L, |
| 88 | S3 = -0.00019841269841269841269841269839935785325638310428717L, |
| 89 | S4 = 0.27557319223985890652557316053039946268333231205686e-5L, |
| 90 | S5 = -0.25052108385441718775048214826384312253862930064745e-7L, |
| 91 | S6 = 0.16059043836821614596571832194524392581082444805729e-9L, |
| 92 | S7 = -0.76471637318198151807063387954939213287488216303768e-12L, |
| 93 | S8 = 0.28114572543451292625024967174638477283187397621303e-14L; |
| 94 | |
| 95 | static const double |
| 96 | C8 = -0.1561920696721507929516718307820958119868e-15, |
| 97 | C9 = 0.4110317413744594971475941557607804508039e-18, |
| 98 | C10 = -0.8896592467191938803288521958313920156409e-21, |
| 99 | C11 = 0.1601061435794535138244346256065192782581e-23, |
| 100 | S9 = -0.82206352458348947812512122163446202498005154296863e-17, |
| 101 | S10 = 0.19572940011906109418080609928334380560135358385256e-19, |
| 102 | S11 = -0.38680813379701966970673724299207480965452616911420e-22, |
| 103 | S12 = 0.64038150078671872796678569586315881020659912139412e-25; |
| 104 | |
| 105 | static inline void |
| 106 | __kernel_sincosl(long double x, long double y, int iy, long double *sn, |
| 107 | long double *cs) |
| 108 | { |
| 109 | long double hz, r, v, w, z; |
| 110 | |
| 111 | z = x * x; |
| 112 | v = z * x; |
| 113 | /* |
| 114 | * XXX Replace Horner scheme with an algorithm suitable for CPUs |
| 115 | * with more complex pipelines. |
| 116 | */ |
| 117 | r = S2 + z * (S3 + z * (S4 + z * (S5 + z * (S6 + z * (S7 + z * (S8 + |
| 118 | z * (S9 + z * (S10 + z * (S11 + z * S12))))))))); |
| 119 | |
| 120 | if (iy == 0) |
| 121 | *sn = x + v * (S1 + z * r); |
| 122 | else |
| 123 | *cs = x - ((z * (y / 2 - v * r) - y) - v * S1); |
| 124 | |
| 125 | hz = z / 2; |
| 126 | w = 1 - hz; |
| 127 | r = z * (C1 + z * (C2 + z * (C3 + z * (C4 + z * (C5 + z * (C6 + |
| 128 | z * (C7 + z * (C8 + z * (C9 + z * (C10 + z * C11)))))))))); |
| 129 | |
| 130 | *cs = w + (((1 - w) - hz) + (z * r - x * y)); |
| 131 | } |
| 132 | #else |
| 133 | #error "Unsupported long double format" |
| 134 | #endif |