1176357Sdas/* From: @(#)k_tan.c 1.5 04/04/22 SMI */ 2176357Sdas 3176357Sdas/* 4176357Sdas * ==================================================== 5176357Sdas * Copyright 2004 Sun Microsystems, Inc. All Rights Reserved. 6176357Sdas * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans. 7176357Sdas * 8176357Sdas * Permission to use, copy, modify, and distribute this 9176357Sdas * software is freely granted, provided that this notice 10176357Sdas * is preserved. 11176357Sdas * ==================================================== 12176357Sdas */ 13176357Sdas 14176357Sdas#include <sys/cdefs.h> 15176357Sdas__FBSDID("$FreeBSD$"); 16176357Sdas 17176357Sdas/* 18176357Sdas * ld80 version of k_tan.c. See ../src/k_tan.c for most comments. 19176357Sdas */ 20176357Sdas 21176357Sdas#include "math.h" 22176357Sdas#include "math_private.h" 23176357Sdas 24176357Sdas/* 25176357Sdas * Domain [-0.67434, 0.67434], range ~[-2.25e-22, 1.921e-22] 26176357Sdas * |tan(x)/x - t(x)| < 2**-71.9 27176357Sdas * 28176357Sdas * See k_cosl.c for more details about the polynomial. 29176357Sdas */ 30176357Sdas#if defined(__amd64__) || defined(__i386__) 31176357Sdas/* Long double constants are slow on these arches, and broken on i386. */ 32176357Sdasstatic const volatile double 33176357SdasT3hi = 0.33333333333333331, /* 0x15555555555555.0p-54 */ 34176357SdasT3lo = 1.8350121769317163e-17, /* 0x15280000000000.0p-108 */ 35176357SdasT5hi = 0.13333333333333336, /* 0x11111111111112.0p-55 */ 36176357SdasT5lo = 1.3051083651294260e-17, /* 0x1e180000000000.0p-109 */ 37176357SdasT7hi = 0.053968253968250494, /* 0x1ba1ba1ba1b827.0p-57 */ 38176357SdasT7lo = 3.1509625637859973e-18, /* 0x1d100000000000.0p-111 */ 39176357Sdaspio4_hi = 0.78539816339744828, /* 0x1921fb54442d18.0p-53 */ 40176357Sdaspio4_lo = 3.0628711372715500e-17, /* 0x11a80000000000.0p-107 */ 41176357Sdaspio4lo_hi = -1.2541394031670831e-20, /* -0x1d9cceba3f91f2.0p-119 */ 42176357Sdaspio4lo_lo = 6.1493048227390915e-37; /* 0x1a280000000000.0p-173 */ 43176357Sdas#define T3 ((long double)T3hi + T3lo) 44176357Sdas#define T5 ((long double)T5hi + T5lo) 45176357Sdas#define T7 ((long double)T7hi + T7lo) 46176357Sdas#define pio4 ((long double)pio4_hi + pio4_lo) 47176357Sdas#define pio4lo ((long double)pio4lo_hi + pio4lo_lo) 48176357Sdas#else 49176357Sdasstatic const long double 50176357SdasT3 = 0.333333333333333333180L, /* 0xaaaaaaaaaaaaaaa5.0p-65 */ 51176357SdasT5 = 0.133333333333333372290L, /* 0x88888888888893c3.0p-66 */ 52176386SbdeT7 = 0.0539682539682504975744L, /* 0xdd0dd0dd0dc13ba2.0p-68 */ 53176387Sbdepio4 = 0.785398163397448309628L, /* 0xc90fdaa22168c235.0p-64 */ 54176387Sbdepio4lo = -1.25413940316708300586e-20L; /* -0xece675d1fc8f8cbb.0p-130 */ 55176357Sdas#endif 56176357Sdas 57176357Sdasstatic const double 58176357SdasT9 = 0.021869488536312216, /* 0x1664f4882cc1c2.0p-58 */ 59176357SdasT11 = 0.0088632355256619590, /* 0x1226e355c17612.0p-59 */ 60176357SdasT13 = 0.0035921281113786528, /* 0x1d6d3d185d7ff8.0p-61 */ 61176357SdasT15 = 0.0014558334756312418, /* 0x17da354aa3f96b.0p-62 */ 62176357SdasT17 = 0.00059003538700862256, /* 0x13559358685b83.0p-63 */ 63176357SdasT19 = 0.00023907843576635544, /* 0x1f56242026b5be.0p-65 */ 64176357SdasT21 = 0.000097154625656538905, /* 0x1977efc26806f4.0p-66 */ 65176357SdasT23 = 0.000038440165747303162, /* 0x14275a09b3ceac.0p-67 */ 66176357SdasT25 = 0.000018082171885432524, /* 0x12f5e563e5487e.0p-68 */ 67176357SdasT27 = 0.0000024196006108814377, /* 0x144c0d80cc6896.0p-71 */ 68176357SdasT29 = 0.0000078293456938132840, /* 0x106b59141a6cb3.0p-69 */ 69176357SdasT31 = -0.0000032609076735050182, /* -0x1b5abef3ba4b59.0p-71 */ 70176357SdasT33 = 0.0000023261313142559411; /* 0x13835436c0c87f.0p-71 */ 71176357Sdas 72176357Sdaslong double 73176357Sdas__kernel_tanl(long double x, long double y, int iy) { 74176357Sdas long double z, r, v, w, s; 75176357Sdas long double osign; 76176357Sdas int i; 77176357Sdas 78176357Sdas iy = (iy == 1 ? -1 : 1); /* XXX recover original interface */ 79176357Sdas osign = (x >= 0 ? 1.0 : -1.0); /* XXX slow, probably wrong for -0 */ 80176357Sdas if (fabsl(x) >= 0.67434) { 81176357Sdas if (x < 0) { 82176357Sdas x = -x; 83176357Sdas y = -y; 84176357Sdas } 85176357Sdas z = pio4 - x; 86176357Sdas w = pio4lo - y; 87176357Sdas x = z + w; 88176357Sdas y = 0.0; 89176357Sdas i = 1; 90176357Sdas } else 91176357Sdas i = 0; 92176357Sdas z = x * x; 93176357Sdas w = z * z; 94176357Sdas r = T5 + w * (T9 + w * (T13 + w * (T17 + w * (T21 + 95176357Sdas w * (T25 + w * (T29 + w * T33)))))); 96176357Sdas v = z * (T7 + w * (T11 + w * (T15 + w * (T19 + w * (T23 + 97176357Sdas w * (T27 + w * T31)))))); 98176357Sdas s = z * x; 99176357Sdas r = y + z * (s * (r + v) + y); 100176357Sdas r += T3 * s; 101176357Sdas w = x + r; 102176357Sdas if (i == 1) { 103176357Sdas v = (long double) iy; 104176357Sdas return osign * 105176357Sdas (v - 2.0 * (x - (w * w / (w + v) - r))); 106176357Sdas } 107176357Sdas if (iy == 1) 108176357Sdas return w; 109176357Sdas else { 110176357Sdas /* 111176357Sdas * if allow error up to 2 ulp, simply return 112176357Sdas * -1.0 / (x+r) here 113176357Sdas */ 114176357Sdas /* compute -1.0 / (x+r) accurately */ 115176357Sdas long double a, t; 116176357Sdas z = w; 117176357Sdas z = z + 0x1p32 - 0x1p32; 118176357Sdas v = r - (z - x); /* z+v = r+x */ 119176357Sdas t = a = -1.0 / w; /* a = -1.0/w */ 120176357Sdas t = t + 0x1p32 - 0x1p32; 121176357Sdas s = 1.0 + t * z; 122176357Sdas return t + a * (s + t * v); 123176357Sdas } 124176357Sdas} 125