xref: /titanic_51/usr/src/lib/libast/common/uwin/log1p.c (revision 25c28e83beb90e7c80452a7c818c5e6f73a07dc8)
1 #include "FEATURE/uwin"
2 
3 #if !_UWIN || _lib_log1p
4 
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