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

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Wed Aug 1 13:51:53 2007 UTC (12 years 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_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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