/[jscoverage]/trunk/js/src/fdlibm/k_tan.c
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Contents of /trunk/js/src/fdlibm/k_tan.c

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Revision 2 - (show annotations)
Wed Aug 1 13:51:53 2007 UTC (12 years, 1 month ago) by siliconforks
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Initial import.

1 /* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
2 *
3 * ***** BEGIN LICENSE BLOCK *****
4 * Version: MPL 1.1/GPL 2.0/LGPL 2.1
5 *
6 * The contents of this file are subject to the Mozilla Public License Version
7 * 1.1 (the "License"); you may not use this file except in compliance with
8 * the License. You may obtain a copy of the License at
9 * http://www.mozilla.org/MPL/
10 *
11 * Software distributed under the License is distributed on an "AS IS" basis,
12 * WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
13 * for the specific language governing rights and limitations under the
14 * License.
15 *
16 * The Original Code is Mozilla Communicator client code, released
17 * March 31, 1998.
18 *
19 * The Initial Developer of the Original Code is
20 * Sun Microsystems, Inc.
21 * Portions created by the Initial Developer are Copyright (C) 1998
22 * the Initial Developer. All Rights Reserved.
23 *
24 * Contributor(s):
25 *
26 * Alternatively, the contents of this file may be used under the terms of
27 * either of the GNU General Public License Version 2 or later (the "GPL"),
28 * or the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
29 * in which case the provisions of the GPL or the LGPL are applicable instead
30 * of those above. If you wish to allow use of your version of this file only
31 * under the terms of either the GPL or the LGPL, and not to allow others to
32 * use your version of this file under the terms of the MPL, indicate your
33 * decision by deleting the provisions above and replace them with the notice
34 * and other provisions required by the GPL or the LGPL. If you do not delete
35 * the provisions above, a recipient may use your version of this file under
36 * the terms of any one of the MPL, the GPL or the LGPL.
37 *
38 * ***** END LICENSE BLOCK ***** */
39
40 /* @(#)k_tan.c 1.3 95/01/18 */
41 /*
42 * ====================================================
43 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
44 *
45 * Developed at SunSoft, a Sun Microsystems, Inc. business.
46 * Permission to use, copy, modify, and distribute this
47 * software is freely granted, provided that this notice
48 * is preserved.
49 * ====================================================
50 */
51
52 /* __kernel_tan( x, y, k )
53 * kernel tan function on [-pi/4, pi/4], pi/4 ~ 0.7854
54 * Input x is assumed to be bounded by ~pi/4 in magnitude.
55 * Input y is the tail of x.
56 * Input k indicates whether tan (if k=1) or
57 * -1/tan (if k= -1) is returned.
58 *
59 * Algorithm
60 * 1. Since tan(-x) = -tan(x), we need only to consider positive x.
61 * 2. if x < 2^-28 (hx<0x3e300000 0), return x with inexact if x!=0.
62 * 3. tan(x) is approximated by a odd polynomial of degree 27 on
63 * [0,0.67434]
64 * 3 27
65 * tan(x) ~ x + T1*x + ... + T13*x
66 * where
67 *
68 * |tan(x) 2 4 26 | -59.2
69 * |----- - (1+T1*x +T2*x +.... +T13*x )| <= 2
70 * | x |
71 *
72 * Note: tan(x+y) = tan(x) + tan'(x)*y
73 * ~ tan(x) + (1+x*x)*y
74 * Therefore, for better accuracy in computing tan(x+y), let
75 * 3 2 2 2 2
76 * r = x *(T2+x *(T3+x *(...+x *(T12+x *T13))))
77 * then
78 * 3 2
79 * tan(x+y) = x + (T1*x + (x *(r+y)+y))
80 *
81 * 4. For x in [0.67434,pi/4], let y = pi/4 - x, then
82 * tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y))
83 * = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y)))
84 */
85
86 #include "fdlibm.h"
87 #ifdef __STDC__
88 static const double
89 #else
90 static double
91 #endif
92 one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
93 pio4 = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */
94 pio4lo= 3.06161699786838301793e-17, /* 0x3C81A626, 0x33145C07 */
95 T[] = {
96 3.33333333333334091986e-01, /* 0x3FD55555, 0x55555563 */
97 1.33333333333201242699e-01, /* 0x3FC11111, 0x1110FE7A */
98 5.39682539762260521377e-02, /* 0x3FABA1BA, 0x1BB341FE */
99 2.18694882948595424599e-02, /* 0x3F9664F4, 0x8406D637 */
100 8.86323982359930005737e-03, /* 0x3F8226E3, 0xE96E8493 */
101 3.59207910759131235356e-03, /* 0x3F6D6D22, 0xC9560328 */
102 1.45620945432529025516e-03, /* 0x3F57DBC8, 0xFEE08315 */
103 5.88041240820264096874e-04, /* 0x3F4344D8, 0xF2F26501 */
104 2.46463134818469906812e-04, /* 0x3F3026F7, 0x1A8D1068 */
105 7.81794442939557092300e-05, /* 0x3F147E88, 0xA03792A6 */
106 7.14072491382608190305e-05, /* 0x3F12B80F, 0x32F0A7E9 */
107 -1.85586374855275456654e-05, /* 0xBEF375CB, 0xDB605373 */
108 2.59073051863633712884e-05, /* 0x3EFB2A70, 0x74BF7AD4 */
109 };
110
111 #ifdef __STDC__
112 double __kernel_tan(double x, double y, int iy)
113 #else
114 double __kernel_tan(x, y, iy)
115 double x,y; int iy;
116 #endif
117 {
118 fd_twoints u;
119 double z,r,v,w,s;
120 int ix,hx;
121 u.d = x;
122 hx = __HI(u); /* high word of x */
123 ix = hx&0x7fffffff; /* high word of |x| */
124 if(ix<0x3e300000) /* x < 2**-28 */
125 {if((int)x==0) { /* generate inexact */
126 u.d =x;
127 if(((ix|__LO(u))|(iy+1))==0) return one/fd_fabs(x);
128 else return (iy==1)? x: -one/x;
129 }
130 }
131 if(ix>=0x3FE59428) { /* |x|>=0.6744 */
132 if(hx<0) {x = -x; y = -y;}
133 z = pio4-x;
134 w = pio4lo-y;
135 x = z+w; y = 0.0;
136 }
137 z = x*x;
138 w = z*z;
139 /* Break x^5*(T[1]+x^2*T[2]+...) into
140 * x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +
141 * x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))
142 */
143 r = T[1]+w*(T[3]+w*(T[5]+w*(T[7]+w*(T[9]+w*T[11]))));
144 v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12])))));
145 s = z*x;
146 r = y + z*(s*(r+v)+y);
147 r += T[0]*s;
148 w = x+r;
149 if(ix>=0x3FE59428) {
150 v = (double)iy;
151 return (double)(1-((hx>>30)&2))*(v-2.0*(x-(w*w/(w+v)-r)));
152 }
153 if(iy==1) return w;
154 else { /* if allow error up to 2 ulp,
155 simply return -1.0/(x+r) here */
156 /* compute -1.0/(x+r) accurately */
157 double a,t;
158 z = w;
159 u.d = z;
160 __LO(u) = 0;
161 z = u.d;
162 v = r-(z - x); /* z+v = r+x */
163 t = a = -1.0/w; /* a = -1.0/w */
164 u.d = t;
165 __LO(u) = 0;
166 t = u.d;
167 s = 1.0+t*z;
168 return t+a*(s+t*v);
169 }
170 }

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