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/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*- |
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* |
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* ***** BEGIN LICENSE BLOCK ***** |
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* Version: MPL 1.1/GPL 2.0/LGPL 2.1 |
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* |
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* The contents of this file are subject to the Mozilla Public License Version |
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* 1.1 (the "License"); you may not use this file except in compliance with |
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* the License. You may obtain a copy of the License at |
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* http://www.mozilla.org/MPL/ |
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* |
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* Software distributed under the License is distributed on an "AS IS" basis, |
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* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License |
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* for the specific language governing rights and limitations under the |
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* License. |
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* |
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* The Original Code is Mozilla Communicator client code, released |
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* March 31, 1998. |
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* |
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* The Initial Developer of the Original Code is |
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* Sun Microsystems, Inc. |
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* Portions created by the Initial Developer are Copyright (C) 1998 |
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* the Initial Developer. All Rights Reserved. |
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* |
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* Contributor(s): |
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* |
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* Alternatively, the contents of this file may be used under the terms of |
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* either of the GNU General Public License Version 2 or later (the "GPL"), |
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* or the GNU Lesser General Public License Version 2.1 or later (the "LGPL"), |
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* in which case the provisions of the GPL or the LGPL are applicable instead |
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* of those above. If you wish to allow use of your version of this file only |
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* under the terms of either the GPL or the LGPL, and not to allow others to |
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* use your version of this file under the terms of the MPL, indicate your |
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* decision by deleting the provisions above and replace them with the notice |
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* and other provisions required by the GPL or the LGPL. If you do not delete |
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* the provisions above, a recipient may use your version of this file under |
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* the terms of any one of the MPL, the GPL or the LGPL. |
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* |
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* ***** END LICENSE BLOCK ***** */ |
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|
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/* @(#)k_tan.c 1.3 95/01/18 */ |
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/* |
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* ==================================================== |
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
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* |
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* Developed at SunSoft, a Sun Microsystems, Inc. business. |
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* Permission to use, copy, modify, and distribute this |
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* software is freely granted, provided that this notice |
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* is preserved. |
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* ==================================================== |
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*/ |
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|
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/* __kernel_tan( x, y, k ) |
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* kernel tan function on [-pi/4, pi/4], pi/4 ~ 0.7854 |
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* Input x is assumed to be bounded by ~pi/4 in magnitude. |
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* Input y is the tail of x. |
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* Input k indicates whether tan (if k=1) or |
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* -1/tan (if k= -1) is returned. |
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* |
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* Algorithm |
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* 1. Since tan(-x) = -tan(x), we need only to consider positive x. |
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* 2. if x < 2^-28 (hx<0x3e300000 0), return x with inexact if x!=0. |
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* 3. tan(x) is approximated by a odd polynomial of degree 27 on |
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* [0,0.67434] |
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* 3 27 |
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* tan(x) ~ x + T1*x + ... + T13*x |
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* where |
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* |
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* |tan(x) 2 4 26 | -59.2 |
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* |----- - (1+T1*x +T2*x +.... +T13*x )| <= 2 |
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* | x | |
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* |
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* Note: tan(x+y) = tan(x) + tan'(x)*y |
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* ~ tan(x) + (1+x*x)*y |
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* Therefore, for better accuracy in computing tan(x+y), let |
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* 3 2 2 2 2 |
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* r = x *(T2+x *(T3+x *(...+x *(T12+x *T13)))) |
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* then |
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* 3 2 |
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* tan(x+y) = x + (T1*x + (x *(r+y)+y)) |
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* |
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* 4. For x in [0.67434,pi/4], let y = pi/4 - x, then |
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* tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y)) |
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* = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y))) |
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*/ |
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|
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#include "fdlibm.h" |
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#ifdef __STDC__ |
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static const double |
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#else |
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static double |
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#endif |
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one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ |
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pio4 = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */ |
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pio4lo= 3.06161699786838301793e-17, /* 0x3C81A626, 0x33145C07 */ |
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T[] = { |
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3.33333333333334091986e-01, /* 0x3FD55555, 0x55555563 */ |
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1.33333333333201242699e-01, /* 0x3FC11111, 0x1110FE7A */ |
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5.39682539762260521377e-02, /* 0x3FABA1BA, 0x1BB341FE */ |
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2.18694882948595424599e-02, /* 0x3F9664F4, 0x8406D637 */ |
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8.86323982359930005737e-03, /* 0x3F8226E3, 0xE96E8493 */ |
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3.59207910759131235356e-03, /* 0x3F6D6D22, 0xC9560328 */ |
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1.45620945432529025516e-03, /* 0x3F57DBC8, 0xFEE08315 */ |
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5.88041240820264096874e-04, /* 0x3F4344D8, 0xF2F26501 */ |
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2.46463134818469906812e-04, /* 0x3F3026F7, 0x1A8D1068 */ |
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7.81794442939557092300e-05, /* 0x3F147E88, 0xA03792A6 */ |
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7.14072491382608190305e-05, /* 0x3F12B80F, 0x32F0A7E9 */ |
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-1.85586374855275456654e-05, /* 0xBEF375CB, 0xDB605373 */ |
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2.59073051863633712884e-05, /* 0x3EFB2A70, 0x74BF7AD4 */ |
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}; |
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|
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#ifdef __STDC__ |
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double __kernel_tan(double x, double y, int iy) |
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#else |
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double __kernel_tan(x, y, iy) |
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double x,y; int iy; |
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#endif |
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{ |
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fd_twoints u; |
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double z,r,v,w,s; |
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int ix,hx; |
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u.d = x; |
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hx = __HI(u); /* high word of x */ |
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ix = hx&0x7fffffff; /* high word of |x| */ |
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if(ix<0x3e300000) /* x < 2**-28 */ |
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{if((int)x==0) { /* generate inexact */ |
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u.d =x; |
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if(((ix|__LO(u))|(iy+1))==0) return one/fd_fabs(x); |
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else return (iy==1)? x: -one/x; |
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} |
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} |
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if(ix>=0x3FE59428) { /* |x|>=0.6744 */ |
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if(hx<0) {x = -x; y = -y;} |
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z = pio4-x; |
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w = pio4lo-y; |
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x = z+w; y = 0.0; |
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} |
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z = x*x; |
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w = z*z; |
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/* Break x^5*(T[1]+x^2*T[2]+...) into |
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* x^5(T[1]+x^4*T[3]+...+x^20*T[11]) + |
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* x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12])) |
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*/ |
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r = T[1]+w*(T[3]+w*(T[5]+w*(T[7]+w*(T[9]+w*T[11])))); |
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v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12]))))); |
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s = z*x; |
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r = y + z*(s*(r+v)+y); |
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r += T[0]*s; |
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w = x+r; |
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if(ix>=0x3FE59428) { |
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v = (double)iy; |
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return (double)(1-((hx>>30)&2))*(v-2.0*(x-(w*w/(w+v)-r))); |
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} |
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if(iy==1) return w; |
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else { /* if allow error up to 2 ulp, |
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simply return -1.0/(x+r) here */ |
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/* compute -1.0/(x+r) accurately */ |
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double a,t; |
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z = w; |
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u.d = z; |
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__LO(u) = 0; |
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z = u.d; |
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v = r-(z - x); /* z+v = r+x */ |
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t = a = -1.0/w; /* a = -1.0/w */ |
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u.d = t; |
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__LO(u) = 0; |
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t = u.d; |
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s = 1.0+t*z; |
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return t+a*(s+t*v); |
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} |
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} |
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