k_tanl.c revision 176386
1314125Sdelphij/* From: @(#)k_tan.c 1.5 04/04/22 SMI */ 296593Smarkm 396593Smarkm/* 4142429Snectar * ==================================================== 596593Smarkm * Copyright 2004 Sun Microsystems, Inc. All Rights Reserved. 696593Smarkm * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans. 796593Smarkm * 896593Smarkm * Permission to use, copy, modify, and distribute this 996593Smarkm * software is freely granted, provided that this notice 1096593Smarkm * is preserved. 1196593Smarkm * ==================================================== 1296593Smarkm */ 1396593Smarkm 1496593Smarkm#include <sys/cdefs.h> 1596593Smarkm__FBSDID("$FreeBSD: head/lib/msun/ld80/k_tanl.c 176386 2008-02-18 14:09:41Z bde $"); 1696593Smarkm 1796593Smarkm/* 1896593Smarkm * ld80 version of k_tan.c. See ../src/k_tan.c for most comments. 1996593Smarkm */ 20215698Ssimon 21215698Ssimon#include "math.h" 22215698Ssimon#include "math_private.h" 23215698Ssimon 24215698Ssimon/* 2596593Smarkm * Domain [-0.67434, 0.67434], range ~[-2.25e-22, 1.921e-22] 2696593Smarkm * |tan(x)/x - t(x)| < 2**-71.9 2796593Smarkm * 2896593Smarkm * See k_cosl.c for more details about the polynomial. 2996593Smarkm */ 3096593Smarkm#if defined(__amd64__) || defined(__i386__) 3196593Smarkm/* Long double constants are slow on these arches, and broken on i386. */ 3296593Smarkmstatic const volatile double 3396593SmarkmT3hi = 0.33333333333333331, /* 0x15555555555555.0p-54 */ 3496593SmarkmT3lo = 1.8350121769317163e-17, /* 0x15280000000000.0p-108 */ 3596593SmarkmT5hi = 0.13333333333333336, /* 0x11111111111112.0p-55 */ 3696593SmarkmT5lo = 1.3051083651294260e-17, /* 0x1e180000000000.0p-109 */ 3796593SmarkmT7hi = 0.053968253968250494, /* 0x1ba1ba1ba1b827.0p-57 */ 3896593SmarkmT7lo = 3.1509625637859973e-18, /* 0x1d100000000000.0p-111 */ 3996593Smarkmpio4_hi = 0.78539816339744828, /* 0x1921fb54442d18.0p-53 */ 4096593Smarkmpio4_lo = 3.0628711372715500e-17, /* 0x11a80000000000.0p-107 */ 41276861Sjkimpio4lo_hi = -1.2541394031670831e-20, /* -0x1d9cceba3f91f2.0p-119 */ 42276861Sjkimpio4lo_lo = 6.1493048227390915e-37; /* 0x1a280000000000.0p-173 */ 4396593Smarkm#define T3 ((long double)T3hi + T3lo) 4496593Smarkm#define T5 ((long double)T5hi + T5lo) 45215698Ssimon#define T7 ((long double)T7hi + T7lo) 46215698Ssimon#define pio4 ((long double)pio4_hi + pio4_lo) 47215698Ssimon#define pio4lo ((long double)pio4lo_hi + pio4lo_lo) 48215698Ssimon#else 49314125Sdelphijstatic const long double 50215698SsimonT3 = 0.333333333333333333180L, /* 0xaaaaaaaaaaaaaaa5.0p-65 */ 51142429SnectarT5 = 0.133333333333333372290L, /* 0x88888888888893c3.0p-66 */ 52142429SnectarT7 = 0.0539682539682504975744L, /* 0xdd0dd0dd0dc13ba2.0p-68 */ 53276861Sjkimpio4 = 0.785398163397448309628, /* 0xc90fdaa22168c235.0p-64 */ 54276861Sjkimpio4lo = -1.25413940316708300586e-20; /* -0xece675d1fc8f8cbb.0p-130 */ 55276861Sjkim#endif 5696593Smarkm 57314125Sdelphijstatic const double 58314125SdelphijT9 = 0.021869488536312216, /* 0x1664f4882cc1c2.0p-58 */ 59314125SdelphijT11 = 0.0088632355256619590, /* 0x1226e355c17612.0p-59 */ 60314125SdelphijT13 = 0.0035921281113786528, /* 0x1d6d3d185d7ff8.0p-61 */ 61215698SsimonT15 = 0.0014558334756312418, /* 0x17da354aa3f96b.0p-62 */ 62314125SdelphijT17 = 0.00059003538700862256, /* 0x13559358685b83.0p-63 */ 63314125SdelphijT19 = 0.00023907843576635544, /* 0x1f56242026b5be.0p-65 */ 64314125SdelphijT21 = 0.000097154625656538905, /* 0x1977efc26806f4.0p-66 */ 65276861SjkimT23 = 0.000038440165747303162, /* 0x14275a09b3ceac.0p-67 */ 66215698SsimonT25 = 0.000018082171885432524, /* 0x12f5e563e5487e.0p-68 */ 6796593SmarkmT27 = 0.0000024196006108814377, /* 0x144c0d80cc6896.0p-71 */ 6896593SmarkmT29 = 0.0000078293456938132840, /* 0x106b59141a6cb3.0p-69 */ 6996593SmarkmT31 = -0.0000032609076735050182, /* -0x1b5abef3ba4b59.0p-71 */ 7096593SmarkmT33 = 0.0000023261313142559411; /* 0x13835436c0c87f.0p-71 */ 7196593Smarkm 7296593Smarkmlong double 7396593Smarkm__kernel_tanl(long double x, long double y, int iy) { 7496593Smarkm long double z, r, v, w, s; 7596593Smarkm long double osign; 7696593Smarkm int i; 7796593Smarkm 7896593Smarkm iy = (iy == 1 ? -1 : 1); /* XXX recover original interface */ 7996593Smarkm osign = (x >= 0 ? 1.0 : -1.0); /* XXX slow, probably wrong for -0 */ 8096593Smarkm if (fabsl(x) >= 0.67434) { 8196593Smarkm if (x < 0) { 8296593Smarkm x = -x; 8396593Smarkm y = -y; 8496593Smarkm } 8596593Smarkm z = pio4 - x; 8696593Smarkm w = pio4lo - y; 8796593Smarkm x = z + w; 8896593Smarkm y = 0.0; 8996593Smarkm i = 1; 9096593Smarkm } else 9196593Smarkm i = 0; 9296593Smarkm z = x * x; 9396593Smarkm w = z * z; 9496593Smarkm r = T5 + w * (T9 + w * (T13 + w * (T17 + w * (T21 + 9596593Smarkm w * (T25 + w * (T29 + w * T33)))))); 9696593Smarkm v = z * (T7 + w * (T11 + w * (T15 + w * (T19 + w * (T23 + 9796593Smarkm w * (T27 + w * T31)))))); 9896593Smarkm s = z * x; 9996593Smarkm r = y + z * (s * (r + v) + y); 10096593Smarkm r += T3 * s; 10196593Smarkm w = x + r; 10296593Smarkm if (i == 1) { 10396593Smarkm v = (long double) iy; 10496593Smarkm return osign * 10596593Smarkm (v - 2.0 * (x - (w * w / (w + v) - r))); 10696593Smarkm } 10796593Smarkm if (iy == 1) 10896593Smarkm return w; 10996593Smarkm else { 11096593Smarkm /* 11196593Smarkm * if allow error up to 2 ulp, simply return 11296593Smarkm * -1.0 / (x+r) here 11396593Smarkm */ 11496593Smarkm /* compute -1.0 / (x+r) accurately */ 11596593Smarkm long double a, t; 11696593Smarkm z = w; 11796593Smarkm z = z + 0x1p32 - 0x1p32; 11896593Smarkm v = r - (z - x); /* z+v = r+x */ 11996593Smarkm t = a = -1.0 / w; /* a = -1.0/w */ 12096593Smarkm t = t + 0x1p32 - 0x1p32; 12196593Smarkm s = 1.0 + t * z; 12296593Smarkm return t + a * (s + t * v); 12396593Smarkm } 12496593Smarkm} 12596593Smarkm