/[jscoverage]/trunk/js/src/fdlibm/e_exp.c
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Annotation of /trunk/js/src/fdlibm/e_exp.c

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Wed Aug 1 13:51:53 2007 UTC (14 years, 11 months ago) by siliconforks
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1 siliconforks 2 /* -*- 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_exp.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_exp(x)
53     * Returns the exponential of x.
54     *
55     * Method
56     * 1. Argument reduction:
57     * Reduce x to an r so that |r| <= 0.5*ln2 ~ 0.34658.
58     * Given x, find r and integer k such that
59     *
60     * x = k*ln2 + r, |r| <= 0.5*ln2.
61     *
62     * Here r will be represented as r = hi-lo for better
63     * accuracy.
64     *
65     * 2. Approximation of exp(r) by a special rational function on
66     * the interval [0,0.34658]:
67     * Write
68     * R(r**2) = r*(exp(r)+1)/(exp(r)-1) = 2 + r*r/6 - r**4/360 + ...
69     * We use a special Reme algorithm on [0,0.34658] to generate
70     * a polynomial of degree 5 to approximate R. The maximum error
71     * of this polynomial approximation is bounded by 2**-59. In
72     * other words,
73     * R(z) ~ 2.0 + P1*z + P2*z**2 + P3*z**3 + P4*z**4 + P5*z**5
74     * (where z=r*r, and the values of P1 to P5 are listed below)
75     * and
76     * | 5 | -59
77     * | 2.0+P1*z+...+P5*z - R(z) | <= 2
78     * | |
79     * The computation of exp(r) thus becomes
80     * 2*r
81     * exp(r) = 1 + -------
82     * R - r
83     * r*R1(r)
84     * = 1 + r + ----------- (for better accuracy)
85     * 2 - R1(r)
86     * where
87     * 2 4 10
88     * R1(r) = r - (P1*r + P2*r + ... + P5*r ).
89     *
90     * 3. Scale back to obtain exp(x):
91     * From step 1, we have
92     * exp(x) = 2^k * exp(r)
93     *
94     * Special cases:
95     * exp(INF) is INF, exp(NaN) is NaN;
96     * exp(-INF) is 0, and
97     * for finite argument, only exp(0)=1 is exact.
98     *
99     * Accuracy:
100     * according to an error analysis, the error is always less than
101     * 1 ulp (unit in the last place).
102     *
103     * Misc. info.
104     * For IEEE double
105     * if x > 7.09782712893383973096e+02 then exp(x) overflow
106     * if x < -7.45133219101941108420e+02 then exp(x) underflow
107     *
108     * Constants:
109     * The hexadecimal values are the intended ones for the following
110     * constants. The decimal values may be used, provided that the
111     * compiler will convert from decimal to binary accurately enough
112     * to produce the hexadecimal values shown.
113     */
114    
115     #include "fdlibm.h"
116    
117     #ifdef __STDC__
118     static const double
119     #else
120     static double
121     #endif
122     one = 1.0,
123     halF[2] = {0.5,-0.5,},
124     really_big = 1.0e+300,
125     twom1000= 9.33263618503218878990e-302, /* 2**-1000=0x01700000,0*/
126     o_threshold= 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */
127     u_threshold= -7.45133219101941108420e+02, /* 0xc0874910, 0xD52D3051 */
128     ln2HI[2] ={ 6.93147180369123816490e-01, /* 0x3fe62e42, 0xfee00000 */
129     -6.93147180369123816490e-01,},/* 0xbfe62e42, 0xfee00000 */
130     ln2LO[2] ={ 1.90821492927058770002e-10, /* 0x3dea39ef, 0x35793c76 */
131     -1.90821492927058770002e-10,},/* 0xbdea39ef, 0x35793c76 */
132     invln2 = 1.44269504088896338700e+00, /* 0x3ff71547, 0x652b82fe */
133     P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */
134     P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */
135     P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */
136     P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
137     P5 = 4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */
138    
139    
140     #ifdef __STDC__
141     double __ieee754_exp(double x) /* default IEEE double exp */
142     #else
143     double __ieee754_exp(x) /* default IEEE double exp */
144     double x;
145     #endif
146     {
147     fd_twoints u;
148     double y,hi,lo,c,t;
149     int k, xsb;
150     unsigned hx;
151    
152     u.d = x;
153     hx = __HI(u); /* high word of x */
154     xsb = (hx>>31)&1; /* sign bit of x */
155     hx &= 0x7fffffff; /* high word of |x| */
156    
157     /* filter out non-finite argument */
158     if(hx >= 0x40862E42) { /* if |x|>=709.78... */
159     if(hx>=0x7ff00000) {
160     u.d = x;
161     if(((hx&0xfffff)|__LO(u))!=0)
162     return x+x; /* NaN */
163     else return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */
164     }
165     if(x > o_threshold) return really_big*really_big; /* overflow */
166     if(x < u_threshold) return twom1000*twom1000; /* underflow */
167     }
168    
169     /* argument reduction */
170     if(hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */
171     if(hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */
172     hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;
173     } else {
174     k = (int)(invln2*x+halF[xsb]);
175     t = k;
176     hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */
177     lo = t*ln2LO[0];
178     }
179     x = hi - lo;
180     }
181     else if(hx < 0x3e300000) { /* when |x|<2**-28 */
182     if(really_big+x>one) return one+x;/* trigger inexact */
183     }
184     else k = 0;
185    
186     /* x is now in primary range */
187     t = x*x;
188     c = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
189     if(k==0) return one-((x*c)/(c-2.0)-x);
190     else y = one-((lo-(x*c)/(2.0-c))-hi);
191     if(k >= -1021) {
192     u.d = y;
193     __HI(u) += (k<<20); /* add k to y's exponent */
194     y = u.d;
195     return y;
196     } else {
197     u.d = y;
198     __HI(u) += ((k+1000)<<20);/* add k to y's exponent */
199     y = u.d;
200     return y*twom1000;
201     }
202     }

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