10Sduke/* $OpenBSD: k_tanl.c,v 1.1 2008/12/09 20:00:35 martynas Exp $ */ 211884Sykantser/* From: @(#)k_tan.c 1.5 04/04/22 SMI */ 30Sduke/* 40Sduke * ==================================================== 50Sduke * Copyright 2004 Sun Microsystems, Inc. All Rights Reserved. 60Sduke * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans. 70Sduke * 80Sduke * Permission to use, copy, modify, and distribute this 90Sduke * software is freely granted, provided that this notice 100Sduke * is preserved. 110Sduke * ==================================================== 120Sduke */ 130Sduke 140Sduke/* 150Sduke * ld128 version of k_tan.c. See ../k_tan.c for most comments. 160Sduke */ 170Sduke 180Sduke#include <math.h> 192362Sohair 202362Sohair#include "math_private.h" 212362Sohair 220Sduke/* 230Sduke * Domain [-0.67434, 0.67434], range ~[-3.37e-36, 1.982e-37] 240Sduke * |tan(x)/x - t(x)| < 2**-117.8 (XXX should be ~1e-37) 250Sduke * 260Sduke * See ../ld80/k_cosl.c for more details about the polynomial. 270Sduke */ 280Sdukestatic const long double 2916958SiignatyevT3 = 0x1.5555555555555555555555555553p-2L, 3013200SakulyakhT5 = 0x1.1111111111111111111111111eb5p-3L, 3116958SiignatyevT7 = 0x1.ba1ba1ba1ba1ba1ba1ba1b694cd6p-5L, 320SdukeT9 = 0x1.664f4882c10f9f32d6bbe09d8bcdp-6L, 330SdukeT11 = 0x1.226e355e6c23c8f5b4f5762322eep-7L, 340SdukeT13 = 0x1.d6d3d0e157ddfb5fed8e84e27b37p-9L, 350SdukeT15 = 0x1.7da36452b75e2b5fce9ee7c2c92ep-10L, 360SdukeT17 = 0x1.355824803674477dfcf726649efep-11L, 370SdukeT19 = 0x1.f57d7734d1656e0aceb716f614c2p-13L, 3811884SykantserT21 = 0x1.967e18afcb180ed942dfdc518d6cp-14L, 390SdukeT23 = 0x1.497d8eea21e95bc7e2aa79b9f2cdp-15L, 400SdukeT25 = 0x1.0b132d39f055c81be49eff7afd50p-16L, 410SdukeT27 = 0x1.b0f72d33eff7bfa2fbc1059d90b6p-18L, 420SdukeT29 = 0x1.5ef2daf21d1113df38d0fbc00267p-19L, 4313200SakulyakhT31 = 0x1.1c77d6eac0234988cdaa04c96626p-20L, 440SdukeT33 = 0x1.cd2a5a292b180e0bdd701057dfe3p-22L, 450SdukeT35 = 0x1.75c7357d0298c01a31d0a6f7d518p-23L, 460SdukeT37 = 0x1.2f3190f4718a9a520f98f50081fcp-24L, 470Sdukepio4 = 0x1.921fb54442d18469898cc51701b8p-1L, 480Sdukepio4lo = 0x1.cd129024e088a67cc74020bbea60p-116L; 490Sduke 500Sdukestatic const double 510SdukeT39 = 0.000000028443389121318352, /* 0x1e8a7592977938.0p-78 */ 520SdukeT41 = 0.000000011981013102001973, /* 0x19baa1b1223219.0p-79 */ 530SdukeT43 = 0.0000000038303578044958070, /* 0x107385dfb24529.0p-80 */ 540SdukeT45 = 0.0000000034664378216909893, /* 0x1dc6c702a05262.0p-81 */ 550SdukeT47 = -0.0000000015090641701997785, /* -0x19ecef3569ebb6.0p-82 */ 560SdukeT49 = 0.0000000029449552300483952, /* 0x194c0668da786a.0p-81 */ 570SdukeT51 = -0.0000000022006995706097711, /* -0x12e763b8845268.0p-81 */ 580SdukeT53 = 0.0000000015468200913196612, /* 0x1a92fc98c29554.0p-82 */ 590SdukeT55 = -0.00000000061311613386849674, /* -0x151106cbc779a9.0p-83 */ 600SdukeT57 = 1.4912469681508012e-10; /* 0x147edbdba6f43a.0p-85 */ 610Sduke 620Sdukelong double 630Sduke__kernel_tanl(long double x, long double y, int iy) { 6411884Sykantser long double z, r, v, w, s; 6511884Sykantser long double osign; 660Sduke int i; 6711884Sykantser 6811884Sykantser iy = (iy == 1 ? -1 : 1); /* XXX recover original interface */ 6911884Sykantser osign = (x >= 0 ? 1.0 : -1.0); /* XXX slow, probably wrong for -0 */ 7011884Sykantser if (fabsl(x) >= 0.67434) { 7111884Sykantser if (x < 0) { 7211884Sykantser x = -x; 730Sduke y = -y; 740Sduke } 750Sduke z = pio4 - x; 7611884Sykantser w = pio4lo - y; 770Sduke x = z + w; 780Sduke y = 0.0; 790Sduke i = 1; 8011884Sykantser } else 810Sduke i = 0; 820Sduke z = x * x; 830Sduke w = z * z; 840Sduke r = T5 + w * (T9 + w * (T13 + w * (T17 + w * (T21 + 850Sduke w * (T25 + w * (T29 + w * (T33 + 860Sduke w * (T37 + w * (T41 + w * (T45 + w * (T49 + w * (T53 + 870Sduke w * T57)))))))))))); 880Sduke v = z * (T7 + w * (T11 + w * (T15 + w * (T19 + w * (T23 + 890Sduke w * (T27 + w * (T31 + w * (T35 + 900Sduke w * (T39 + w * (T43 + w * (T47 + w * (T51 + w * T55)))))))))))); 910Sduke s = z * x; 920Sduke r = y + z * (s * (r + v) + y); 930Sduke r += T3 * s; 940Sduke w = x + r; 950Sduke if (i == 1) { 960Sduke v = (long double) iy; 970Sduke return osign * 980Sduke (v - 2.0 * (x - (w * w / (w + v) - r))); 990Sduke } 1000Sduke if (iy == 1) 1010Sduke return w; 1020Sduke else { 1030Sduke /* 1040Sduke * if allow error up to 2 ulp, simply return 1050Sduke * -1.0 / (x+r) here 1060Sduke */ 1070Sduke /* compute -1.0 / (x+r) accurately */ 1080Sduke long double a, t; 1090Sduke z = w; 1100Sduke z = z + 0x1p32 - 0x1p32; 1110Sduke v = r - (z - x); /* z+v = r+x */ 1120Sduke t = a = -1.0 / w; /* a = -1.0/w */ 1130Sduke t = t + 0x1p32 - 0x1p32; 1140Sduke s = 1.0 + t * z; 1150Sduke return t + a * (s + t * v); 1160Sduke } 1170Sduke} 1180Sduke