/* * 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)))
*/
#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);
}
}
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