1#include "FEATURE/uwin"
2
3#if !_UWIN || _lib_log1p
4
5void _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
39static 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
104vc(ln2hi, 6.9314718055829871446E-1  ,7217,4031,0000,f7d0,   0, .B17217F7D00000)
105vc(ln2lo, 1.6465949582897081279E-12 ,bcd5,2ce7,d9cc,e4f1, -39, .E7BCD5E4F1D9CC)
106vc(sqrt2, 1.4142135623730950622E0   ,04f3,40b5,de65,33f9,   1, .B504F333F9DE65)
107
108ic(ln2hi, 6.9314718036912381649E-1,   -1, 1.62E42FEE00000)
109ic(ln2lo, 1.9082149292705877000E-10, -33, 1.A39EF35793C76)
110ic(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
118extern double log1p(x)
119double 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