| /* From: @(#)k_tan.c 1.5 04/04/22 SMI */ |
| |
| /* |
| * ==================================================== |
| * Copyright 2004 Sun Microsystems, Inc. All Rights Reserved. |
| * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans. |
| * |
| * Permission to use, copy, modify, and distribute this |
| * software is freely granted, provided that this notice |
| * is preserved. |
| * ==================================================== |
| */ |
| |
| #include <sys/cdefs.h> |
| __FBSDID("$FreeBSD$"); |
| |
| /* |
| * ld128 version of k_tan.c. See ../src/k_tan.c for most comments. |
| */ |
| |
| #include "math.h" |
| #include "math_private.h" |
| |
| /* |
| * Domain [-0.67434, 0.67434], range ~[-3.37e-36, 1.982e-37] |
| * |tan(x)/x - t(x)| < 2**-117.8 (XXX should be ~1e-37) |
| * |
| * See ../ld80/k_cosl.c for more details about the polynomial. |
| */ |
| static const long double |
| T3 = 0x1.5555555555555555555555555553p-2L, |
| T5 = 0x1.1111111111111111111111111eb5p-3L, |
| T7 = 0x1.ba1ba1ba1ba1ba1ba1ba1b694cd6p-5L, |
| T9 = 0x1.664f4882c10f9f32d6bbe09d8bcdp-6L, |
| T11 = 0x1.226e355e6c23c8f5b4f5762322eep-7L, |
| T13 = 0x1.d6d3d0e157ddfb5fed8e84e27b37p-9L, |
| T15 = 0x1.7da36452b75e2b5fce9ee7c2c92ep-10L, |
| T17 = 0x1.355824803674477dfcf726649efep-11L, |
| T19 = 0x1.f57d7734d1656e0aceb716f614c2p-13L, |
| T21 = 0x1.967e18afcb180ed942dfdc518d6cp-14L, |
| T23 = 0x1.497d8eea21e95bc7e2aa79b9f2cdp-15L, |
| T25 = 0x1.0b132d39f055c81be49eff7afd50p-16L, |
| T27 = 0x1.b0f72d33eff7bfa2fbc1059d90b6p-18L, |
| T29 = 0x1.5ef2daf21d1113df38d0fbc00267p-19L, |
| T31 = 0x1.1c77d6eac0234988cdaa04c96626p-20L, |
| T33 = 0x1.cd2a5a292b180e0bdd701057dfe3p-22L, |
| T35 = 0x1.75c7357d0298c01a31d0a6f7d518p-23L, |
| T37 = 0x1.2f3190f4718a9a520f98f50081fcp-24L, |
| pio4 = 0x1.921fb54442d18469898cc51701b8p-1L, |
| pio4lo = 0x1.cd129024e088a67cc74020bbea60p-116L; |
| |
| static const double |
| T39 = 0.000000028443389121318352, /* 0x1e8a7592977938.0p-78 */ |
| T41 = 0.000000011981013102001973, /* 0x19baa1b1223219.0p-79 */ |
| T43 = 0.0000000038303578044958070, /* 0x107385dfb24529.0p-80 */ |
| T45 = 0.0000000034664378216909893, /* 0x1dc6c702a05262.0p-81 */ |
| T47 = -0.0000000015090641701997785, /* -0x19ecef3569ebb6.0p-82 */ |
| T49 = 0.0000000029449552300483952, /* 0x194c0668da786a.0p-81 */ |
| T51 = -0.0000000022006995706097711, /* -0x12e763b8845268.0p-81 */ |
| T53 = 0.0000000015468200913196612, /* 0x1a92fc98c29554.0p-82 */ |
| T55 = -0.00000000061311613386849674, /* -0x151106cbc779a9.0p-83 */ |
| T57 = 1.4912469681508012e-10; /* 0x147edbdba6f43a.0p-85 */ |
| |
| long double |
| __kernel_tanl(long double x, long double y, int iy) { |
| long double z, r, v, w, s; |
| long double osign; |
| int i; |
| |
| iy = (iy == 1 ? -1 : 1); /* XXX recover original interface */ |
| osign = (x >= 0 ? 1.0 : -1.0); /* XXX slow, probably wrong for -0 */ |
| if (fabsl(x) >= 0.67434) { |
| if (x < 0) { |
| x = -x; |
| y = -y; |
| } |
| z = pio4 - x; |
| w = pio4lo - y; |
| x = z + w; |
| y = 0.0; |
| i = 1; |
| } else |
| i = 0; |
| z = x * x; |
| w = z * z; |
| r = T5 + w * (T9 + w * (T13 + w * (T17 + w * (T21 + |
| w * (T25 + w * (T29 + w * (T33 + |
| w * (T37 + w * (T41 + w * (T45 + w * (T49 + w * (T53 + |
| w * T57)))))))))))); |
| v = z * (T7 + w * (T11 + w * (T15 + w * (T19 + w * (T23 + |
| w * (T27 + w * (T31 + w * (T35 + |
| w * (T39 + w * (T43 + w * (T47 + w * (T51 + w * T55)))))))))))); |
| s = z * x; |
| r = y + z * (s * (r + v) + y); |
| r += T3 * s; |
| w = x + r; |
| if (i == 1) { |
| v = (long double) iy; |
| return osign * |
| (v - 2.0 * (x - (w * w / (w + v) - r))); |
| } |
| if (iy == 1) |
| return w; |
| else { |
| /* |
| * if allow error up to 2 ulp, simply return |
| * -1.0 / (x+r) here |
| */ |
| /* compute -1.0 / (x+r) accurately */ |
| long double a, t; |
| z = w; |
| z = z + 0x1p32 - 0x1p32; |
| v = r - (z - x); /* z+v = r+x */ |
| t = a = -1.0 / w; /* a = -1.0/w */ |
| t = t + 0x1p32 - 0x1p32; |
| s = 1.0 + t * z; |
| return t + a * (s + t * v); |
| } |
| } |