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