| |
| /* |
| * Copyright (c) 1998, 2004, Oracle and/or its affiliates. All rights reserved. |
| * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. |
| * |
| * This code is free software; you can redistribute it and/or modify it |
| * under the terms of the GNU General Public License version 2 only, as |
| * published by the Free Software Foundation. Oracle designates this |
| * particular file as subject to the "Classpath" exception as provided |
| * by Oracle in the LICENSE file that accompanied this code. |
| * |
| * This code is distributed in the hope that it will be useful, but WITHOUT |
| * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
| * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
| * version 2 for more details (a copy is included in the LICENSE file that |
| * accompanied this code). |
| * |
| * You should have received a copy of the GNU General Public License version |
| * 2 along with this work; if not, write to the Free Software Foundation, |
| * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. |
| * |
| * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA |
| * or visit www.oracle.com if you need additional information or have any |
| * questions. |
| */ |
| |
| /* __kernel_tan( x, y, k ) |
| * kernel tan function on [-pi/4, pi/4], pi/4 ~ 0.7854 |
| * Input x is assumed to be bounded by ~pi/4 in magnitude. |
| * Input y is the tail of x. |
| * Input k indicates whether tan (if k=1) or |
| * -1/tan (if k= -1) is returned. |
| * |
| * Algorithm |
| * 1. Since tan(-x) = -tan(x), we need only to consider positive x. |
| * 2. if x < 2^-28 (hx<0x3e300000 0), return x with inexact if x!=0. |
| * 3. tan(x) is approximated by a odd polynomial of degree 27 on |
| * [0,0.67434] |
| * 3 27 |
| * tan(x) ~ x + T1*x + ... + T13*x |
| * where |
| * |
| * |tan(x) 2 4 26 | -59.2 |
| * |----- - (1+T1*x +T2*x +.... +T13*x )| <= 2 |
| * | x | |
| * |
| * Note: tan(x+y) = tan(x) + tan'(x)*y |
| * ~ tan(x) + (1+x*x)*y |
| * Therefore, for better accuracy in computing tan(x+y), let |
| * 3 2 2 2 2 |
| * r = x *(T2+x *(T3+x *(...+x *(T12+x *T13)))) |
| * then |
| * 3 2 |
| * tan(x+y) = x + (T1*x + (x *(r+y)+y)) |
| * |
| * 4. For x in [0.67434,pi/4], let y = pi/4 - x, then |
| * tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y)) |
| * = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y))) |
| */ |
| |
| #include "fdlibm.h" |
| #ifdef __STDC__ |
| static const double |
| #else |
| static double |
| #endif |
| one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ |
| pio4 = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */ |
| pio4lo= 3.06161699786838301793e-17, /* 0x3C81A626, 0x33145C07 */ |
| T[] = { |
| 3.33333333333334091986e-01, /* 0x3FD55555, 0x55555563 */ |
| 1.33333333333201242699e-01, /* 0x3FC11111, 0x1110FE7A */ |
| 5.39682539762260521377e-02, /* 0x3FABA1BA, 0x1BB341FE */ |
| 2.18694882948595424599e-02, /* 0x3F9664F4, 0x8406D637 */ |
| 8.86323982359930005737e-03, /* 0x3F8226E3, 0xE96E8493 */ |
| 3.59207910759131235356e-03, /* 0x3F6D6D22, 0xC9560328 */ |
| 1.45620945432529025516e-03, /* 0x3F57DBC8, 0xFEE08315 */ |
| 5.88041240820264096874e-04, /* 0x3F4344D8, 0xF2F26501 */ |
| 2.46463134818469906812e-04, /* 0x3F3026F7, 0x1A8D1068 */ |
| 7.81794442939557092300e-05, /* 0x3F147E88, 0xA03792A6 */ |
| 7.14072491382608190305e-05, /* 0x3F12B80F, 0x32F0A7E9 */ |
| -1.85586374855275456654e-05, /* 0xBEF375CB, 0xDB605373 */ |
| 2.59073051863633712884e-05, /* 0x3EFB2A70, 0x74BF7AD4 */ |
| }; |
| |
| #ifdef __STDC__ |
| double __kernel_tan(double x, double y, int iy) |
| #else |
| double __kernel_tan(x, y, iy) |
| double x,y; int iy; |
| #endif |
| { |
| double z,r,v,w,s; |
| int ix,hx; |
| hx = __HI(x); /* high word of x */ |
| ix = hx&0x7fffffff; /* high word of |x| */ |
| if(ix<0x3e300000) { /* x < 2**-28 */ |
| if((int)x==0) { /* generate inexact */ |
| if (((ix | __LO(x)) | (iy + 1)) == 0) |
| return one / fabs(x); |
| else { |
| if (iy == 1) |
| return x; |
| else { /* compute -1 / (x+y) carefully */ |
| double a, t; |
| |
| z = w = x + y; |
| __LO(z) = 0; |
| v = y - (z - x); |
| t = a = -one / w; |
| __LO(t) = 0; |
| s = one + t * z; |
| return t + a * (s + t * v); |
| } |
| } |
| } |
| } |
| if(ix>=0x3FE59428) { /* |x|>=0.6744 */ |
| if(hx<0) {x = -x; y = -y;} |
| z = pio4-x; |
| w = pio4lo-y; |
| x = z+w; y = 0.0; |
| } |
| z = x*x; |
| w = z*z; |
| /* Break x^5*(T[1]+x^2*T[2]+...) into |
| * x^5(T[1]+x^4*T[3]+...+x^20*T[11]) + |
| * x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12])) |
| */ |
| r = T[1]+w*(T[3]+w*(T[5]+w*(T[7]+w*(T[9]+w*T[11])))); |
| v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12]))))); |
| s = z*x; |
| r = y + z*(s*(r+v)+y); |
| r += T[0]*s; |
| w = x+r; |
| if(ix>=0x3FE59428) { |
| v = (double)iy; |
| return (double)(1-((hx>>30)&2))*(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 */ |
| double a,t; |
| z = w; |
| __LO(z) = 0; |
| v = r-(z - x); /* z+v = r+x */ |
| t = a = -1.0/w; /* a = -1.0/w */ |
| __LO(t) = 0; |
| s = 1.0+t*z; |
| return t+a*(s+t*v); |
| } |
| } |
