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

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Wed Aug 1 13:51:53 2007 UTC (14 years, 9 months 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 /* @(#)e_log.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 /* __ieee754_log(x)
53 * Return the logrithm of x
54 *
55 * Method :
56 * 1. Argument Reduction: find k and f such that
57 * x = 2^k * (1+f),
58 * where sqrt(2)/2 < 1+f < sqrt(2) .
59 *
60 * 2. Approximation of log(1+f).
61 * Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
62 * = 2s + 2/3 s**3 + 2/5 s**5 + .....,
63 * = 2s + s*R
64 * We use a special Reme algorithm on [0,0.1716] to generate
65 * a polynomial of degree 14 to approximate R The maximum error
66 * of this polynomial approximation is bounded by 2**-58.45. In
67 * other words,
68 * 2 4 6 8 10 12 14
69 * R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s
70 * (the values of Lg1 to Lg7 are listed in the program)
71 * and
72 * | 2 14 | -58.45
73 * | Lg1*s +...+Lg7*s - R(z) | <= 2
74 * | |
75 * Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2.
76 * In order to guarantee error in log below 1ulp, we compute log
77 * by
78 * log(1+f) = f - s*(f - R) (if f is not too large)
79 * log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy)
80 *
81 * 3. Finally, log(x) = k*ln2 + log(1+f).
82 * = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo)))
83 * Here ln2 is split into two floating point number:
84 * ln2_hi + ln2_lo,
85 * where n*ln2_hi is always exact for |n| < 2000.
86 *
87 * Special cases:
88 * log(x) is NaN with signal if x < 0 (including -INF) ;
89 * log(+INF) is +INF; log(0) is -INF with signal;
90 * log(NaN) is that NaN with no signal.
91 *
92 * Accuracy:
93 * according to an error analysis, the error is always less than
94 * 1 ulp (unit in the last place).
95 *
96 * Constants:
97 * The hexadecimal values are the intended ones for the following
98 * constants. The decimal values may be used, provided that the
99 * compiler will convert from decimal to binary accurately enough
100 * to produce the hexadecimal values shown.
101 */
102
103 #include "fdlibm.h"
104
105 #ifdef __STDC__
106 static const double
107 #else
108 static double
109 #endif
110 ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */
111 ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */
112 two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */
113 Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */
114 Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */
115 Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */
116 Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */
117 Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */
118 Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */
119 Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
120
121 static double zero = 0.0;
122
123 #ifdef __STDC__
124 double __ieee754_log(double x)
125 #else
126 double __ieee754_log(x)
127 double x;
128 #endif
129 {
130 fd_twoints u;
131 double hfsq,f,s,z,R,w,t1,t2,dk;
132 int k,hx,i,j;
133 unsigned lx;
134
135 u.d = x;
136 hx = __HI(u); /* high word of x */
137 lx = __LO(u); /* low word of x */
138
139 k=0;
140 if (hx < 0x00100000) { /* x < 2**-1022 */
141 if (((hx&0x7fffffff)|lx)==0)
142 return -two54/zero; /* log(+-0)=-inf */
143 if (hx<0) return (x-x)/zero; /* log(-#) = NaN */
144 k -= 54; x *= two54; /* subnormal number, scale up x */
145 u.d = x;
146 hx = __HI(u); /* high word of x */
147 }
148 if (hx >= 0x7ff00000) return x+x;
149 k += (hx>>20)-1023;
150 hx &= 0x000fffff;
151 i = (hx+0x95f64)&0x100000;
152 u.d = x;
153 __HI(u) = hx|(i^0x3ff00000); /* normalize x or x/2 */
154 x = u.d;
155 k += (i>>20);
156 f = x-1.0;
157 if((0x000fffff&(2+hx))<3) { /* |f| < 2**-20 */
158 if(f==zero) {
159 if(k==0) return zero; else {dk=(double)k;
160 return dk*ln2_hi+dk*ln2_lo;}
161 }
162 R = f*f*(0.5-0.33333333333333333*f);
163 if(k==0) return f-R; else {dk=(double)k;
164 return dk*ln2_hi-((R-dk*ln2_lo)-f);}
165 }
166 s = f/(2.0+f);
167 dk = (double)k;
168 z = s*s;
169 i = hx-0x6147a;
170 w = z*z;
171 j = 0x6b851-hx;
172 t1= w*(Lg2+w*(Lg4+w*Lg6));
173 t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
174 i |= j;
175 R = t2+t1;
176 if(i>0) {
177 hfsq=0.5*f*f;
178 if(k==0) return f-(hfsq-s*(hfsq+R)); else
179 return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f);
180 } else {
181 if(k==0) return f-s*(f-R); else
182 return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f);
183 }
184 }

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