1 #include "FEATURE/uwin"
2
3 #if !_UWIN || _lib_log1p
4
_STUB_log1p()5 void _STUB_log1p(){}
6
7 #else
8
9 /*
10 * Copyright (c) 1985, 1993
11 * The Regents of the University of California. All rights reserved.
12 *
13 * Redistribution and use in source and binary forms, with or without
14 * modification, are permitted provided that the following conditions
15 * are met:
16 * 1. Redistributions of source code must retain the above copyright
17 * notice, this list of conditions and the following disclaimer.
18 * 2. Redistributions in binary form must reproduce the above copyright
19 * notice, this list of conditions and the following disclaimer in the
20 * documentation and/or other materials provided with the distribution.
21 * 3. Neither the name of the University nor the names of its contributors
22 * may be used to endorse or promote products derived from this software
23 * without specific prior written permission.
24 *
25 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
26 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
27 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
28 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
29 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
30 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
31 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
32 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
33 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
34 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
35 * SUCH DAMAGE.
36 */
37
38 #ifndef lint
39 static char sccsid[] = "@(#)log1p.c 8.1 (Berkeley) 6/4/93";
40 #endif /* not lint */
41
42 /* LOG1P(x)
43 * RETURN THE LOGARITHM OF 1+x
44 * DOUBLE PRECISION (VAX D FORMAT 56 bits, IEEE DOUBLE 53 BITS)
45 * CODED IN C BY K.C. NG, 1/19/85;
46 * REVISED BY K.C. NG on 2/6/85, 3/7/85, 3/24/85, 4/16/85.
47 *
48 * Required system supported functions:
49 * scalb(x,n)
50 * copysign(x,y)
51 * logb(x)
52 * finite(x)
53 *
54 * Required kernel function:
55 * log__L(z)
56 *
57 * Method :
58 * 1. Argument Reduction: find k and f such that
59 * 1+x = 2^k * (1+f),
60 * where sqrt(2)/2 < 1+f < sqrt(2) .
61 *
62 * 2. Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
63 * = 2s + 2/3 s**3 + 2/5 s**5 + .....,
64 * log(1+f) is computed by
65 *
66 * log(1+f) = 2s + s*log__L(s*s)
67 * where
68 * log__L(z) = z*(L1 + z*(L2 + z*(... (L6 + z*L7)...)))
69 *
70 * See log__L() for the values of the coefficients.
71 *
72 * 3. Finally, log(1+x) = k*ln2 + log(1+f).
73 *
74 * Remarks 1. In step 3 n*ln2 will be stored in two floating point numbers
75 * n*ln2hi + n*ln2lo, where ln2hi is chosen such that the last
76 * 20 bits (for VAX D format), or the last 21 bits ( for IEEE
77 * double) is 0. This ensures n*ln2hi is exactly representable.
78 * 2. In step 1, f may not be representable. A correction term c
79 * for f is computed. It follows that the correction term for
80 * f - t (the leading term of log(1+f) in step 2) is c-c*x. We
81 * add this correction term to n*ln2lo to attenuate the error.
82 *
83 *
84 * Special cases:
85 * log1p(x) is NaN with signal if x < -1; log1p(NaN) is NaN with no signal;
86 * log1p(INF) is +INF; log1p(-1) is -INF with signal;
87 * only log1p(0)=0 is exact for finite argument.
88 *
89 * Accuracy:
90 * log1p(x) returns the exact log(1+x) nearly rounded. In a test run
91 * with 1,536,000 random arguments on a VAX, the maximum observed
92 * error was .846 ulps (units in the last place).
93 *
94 * Constants:
95 * The hexadecimal values are the intended ones for the following constants.
96 * The decimal values may be used, provided that the compiler will convert
97 * from decimal to binary accurately enough to produce the hexadecimal values
98 * shown.
99 */
100
101 #include <errno.h>
102 #include "mathimpl.h"
103
104 vc(ln2hi, 6.9314718055829871446E-1 ,7217,4031,0000,f7d0, 0, .B17217F7D00000)
105 vc(ln2lo, 1.6465949582897081279E-12 ,bcd5,2ce7,d9cc,e4f1, -39, .E7BCD5E4F1D9CC)
106 vc(sqrt2, 1.4142135623730950622E0 ,04f3,40b5,de65,33f9, 1, .B504F333F9DE65)
107
108 ic(ln2hi, 6.9314718036912381649E-1, -1, 1.62E42FEE00000)
109 ic(ln2lo, 1.9082149292705877000E-10, -33, 1.A39EF35793C76)
110 ic(sqrt2, 1.4142135623730951455E0, 0, 1.6A09E667F3BCD)
111
112 #ifdef vccast
113 #define ln2hi vccast(ln2hi)
114 #define ln2lo vccast(ln2lo)
115 #define sqrt2 vccast(sqrt2)
116 #endif
117
118 extern double log1p(x)
119 double x;
120 {
121 const static double zero=0.0, negone= -1.0, one=1.0,
122 half=1.0/2.0, small=1.0E-20; /* 1+small == 1 */
123 double z,s,t,c;
124 int k;
125
126 #if !defined(vax)&&!defined(tahoe)
127 if(x!=x) return(x); /* x is NaN */
128 #endif /* !defined(vax)&&!defined(tahoe) */
129
130 if(finite(x)) {
131 if( x > negone ) {
132
133 /* argument reduction */
134 if(copysign(x,one)<small) return(x);
135 k=(int)logb(one+x); z=scalb(x,-k); t=scalb(one,-k);
136 if(z+t >= sqrt2 )
137 { k += 1 ; z *= half; t *= half; }
138 t += negone; x = z + t;
139 c = (t-x)+z ; /* correction term for x */
140
141 /* compute log(1+x) */
142 s = x/(2+x); t = x*x*half;
143 c += (k*ln2lo-c*x);
144 z = c+s*(t+__log__L(s*s));
145 x += (z - t) ;
146
147 return(k*ln2hi+x);
148 }
149 /* end of if (x > negone) */
150
151 else {
152 #if defined(vax)||defined(tahoe)
153 if ( x == negone )
154 return (infnan(-ERANGE)); /* -INF */
155 else
156 return (infnan(EDOM)); /* NaN */
157 #else /* defined(vax)||defined(tahoe) */
158 /* x = -1, return -INF with signal */
159 if ( x == negone ) return( negone/zero );
160
161 /* negative argument for log, return NaN with signal */
162 else return ( zero / zero );
163 #endif /* defined(vax)||defined(tahoe) */
164 }
165 }
166 /* end of if (finite(x)) */
167
168 /* log(-INF) is NaN */
169 else if(x<0)
170 return(zero/zero);
171
172 /* log(+INF) is INF */
173 else return(x);
174 }
175
176 #endif
177