1 /*      $NetBSD: n_log1p.c,v 1.9 2024/07/16 14:52:50 riastradh Exp $ */
2 /*
3  * Copyright (c) 1985, 1993
4  *        The Regents of the University of California.  All rights reserved.
5  *
6  * Redistribution and use in source and binary forms, with or without
7  * modification, are permitted provided that the following conditions
8  * are met:
9  * 1. Redistributions of source code must retain the above copyright
10  *    notice, this list of conditions and the following disclaimer.
11  * 2. Redistributions in binary form must reproduce the above copyright
12  *    notice, this list of conditions and the following disclaimer in the
13  *    documentation and/or other materials provided with the distribution.
14  * 3. Neither the name of the University nor the names of its contributors
15  *    may be used to endorse or promote products derived from this software
16  *    without specific prior written permission.
17  *
18  * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
19  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
20  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
21  * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
22  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
23  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
24  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
25  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
26  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
27  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
28  * SUCH DAMAGE.
29  */
30 
31 #include <sys/cdefs.h>
32 __RCSID("$NetBSD: n_log1p.c,v 1.9 2024/07/16 14:52:50 riastradh Exp $");
33 
34 #ifndef lint
35 #if 0
36 static char sccsid[] = "@(#)log1p.c     8.1 (Berkeley) 6/4/93";
37 #endif
38 #endif /* not lint */
39 
40 /* LOG1P(x)
41  * RETURN THE LOGARITHM OF 1+x
42  * DOUBLE PRECISION (VAX D FORMAT 56 bits, IEEE DOUBLE 53 BITS)
43  * CODED IN C BY K.C. NG, 1/19/85;
44  * REVISED BY K.C. NG on 2/6/85, 3/7/85, 3/24/85, 4/16/85.
45  *
46  * Required system supported functions:
47  *        scalb(x,n)
48  *        copysign(x,y)
49  *        logb(x)
50  *        finite(x)
51  *
52  * Required kernel function:
53  *        log__L(z)
54  *
55  * Method :
56  *        1. Argument Reduction: find k and f such that
57  *                            1+x  = 2^k * (1+f),
58  *           where  sqrt(2)/2 < 1+f < sqrt(2) .
59  *
60  *        2. Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
61  *                   = 2s + 2/3 s**3 + 2/5 s**5 + .....,
62  *           log(1+f) is computed by
63  *
64  *                            log(1+f) = 2s + s*log__L(s*s)
65  *           where
66  *                  log__L(z) = z*(L1 + z*(L2 + z*(... (L6 + z*L7)...)))
67  *
68  *           See log__L() for the values of the coefficients.
69  *
70  *        3. Finally,  log(1+x) = k*ln2 + log(1+f).
71  *
72  *        Remarks 1. In step 3 n*ln2 will be stored in two floating point numbers
73  *                     n*ln2hi + n*ln2lo, where ln2hi is chosen such that the last
74  *                     20 bits (for VAX D format), or the last 21 bits ( for IEEE
75  *                     double) is 0. This ensures n*ln2hi is exactly representable.
76  *                  2. In step 1, f may not be representable. A correction term c
77  *                     for f is computed. It follows that the correction term for
78  *                     f - t (the leading term of log(1+f) in step 2) is c-c*x. We
79  *                     add this correction term to n*ln2lo to attenuate the error.
80  *
81  *
82  * Special cases:
83  *        log1p(x) is NaN with signal if x < -1; log1p(NaN) is NaN with no signal;
84  *        log1p(INF) is +INF; log1p(-1) is -INF with signal;
85  *        only log1p(0)=0 is exact for finite argument.
86  *
87  * Accuracy:
88  *        log1p(x) returns the exact log(1+x) nearly rounded. In a test run
89  *        with 1,536,000 random arguments on a VAX, the maximum observed
90  *        error was .846 ulps (units in the last place).
91  *
92  * Constants:
93  * The hexadecimal values are the intended ones for the following constants.
94  * The decimal values may be used, provided that the compiler will convert
95  * from decimal to binary accurately enough to produce the hexadecimal values
96  * shown.
97  */
98 
99 #include "namespace.h"
100 
101 #include <errno.h>
102 #define _LIBM_STATIC
103 #include "mathimpl.h"
104 
__weak_alias(log1pl,_log1pl)105 __weak_alias(log1pl, _log1pl)
106 __strong_alias(_log1pl, _log1p)
107 
108 vc(ln2hi, 6.9314718055829871446E-1  ,7217,4031,0000,f7d0,   0, .B17217F7D00000)
109 vc(ln2lo, 1.6465949582897081279E-12 ,bcd5,2ce7,d9cc,e4f1, -39, .E7BCD5E4F1D9CC)
110 vc(sqrt2, 1.4142135623730950622E0   ,04f3,40b5,de65,33f9,   1, .B504F333F9DE65)
111 
112 ic(ln2hi, 6.9314718036912381649E-1,   -1, 1.62E42FEE00000)
113 ic(ln2lo, 1.9082149292705877000E-10, -33, 1.A39EF35793C76)
114 ic(sqrt2, 1.4142135623730951455E0,     0, 1.6A09E667F3BCD)
115 
116 #ifdef vccast
117 #define   ln2hi     vccast(ln2hi)
118 #define   ln2lo     vccast(ln2lo)
119 #define   sqrt2     vccast(sqrt2)
120 #endif
121 
122 __weak_alias(log1p, _log1p)
123 double
124 log1p(double x)
125 {
126           static const double zero=0.0, negone= -1.0, one=1.0,
127                           half=1.0/2.0, small=1.0E-20;   /* 1+small == 1 */
128           double z,s,t,c;
129           int k;
130 
131 #if !defined(__vax__)&&!defined(tahoe)
132           if(x!=x) return(x); /* x is NaN */
133 #endif    /* !defined(__vax__)&&!defined(tahoe) */
134 
135           if(finite(x)) {
136              if( x > negone ) {
137 
138              /* argument reduction */
139                 if(copysign(x,one)<small) return(x);
140                 k=logb(one+x); z=scalb(x,-k); t=scalb(one,-k);
141                 if(z+t >= sqrt2 )
142                       { k += 1 ; z *= half; t *= half; }
143                 t += negone; x = z + t;
144                 c = (t-x)+z ;           /* correction term for x */
145 
146              /* compute log(1+x)  */
147               s = x/(2+x); t = x*x*half;
148                 c += (k*ln2lo-c*x);
149                 z = c+s*(t+__log__L(s*s));
150                 x += (z - t) ;
151 
152                 return(k*ln2hi+x);
153              }
154           /* end of if (x > negone) */
155 
156               else {
157 #if defined(__vax__)||defined(tahoe)
158                     if ( x == negone )
159                         return (infnan(-ERANGE)); /* -INF */
160                     else
161                         return (infnan(EDOM));    /* NaN */
162 #else     /* defined(__vax__)||defined(tahoe) */
163                     /* x = -1, return -INF with signal */
164                     if ( x == negone ) return( negone/zero );
165 
166                     /* negative argument for log, return NaN with signal */
167                   else return ( zero / zero );
168 #endif    /* defined(__vax__)||defined(tahoe) */
169               }
170           }
171     /* end of if (finite(x)) */
172 
173     /* log(-INF) is NaN */
174           else if(x<0)
175                return(zero/zero);
176 
177     /* log(+INF) is INF */
178           else return(x);
179 }
180 
__weak_alias(log1pf,_log1pf)181 __weak_alias(log1pf, _log1pf)
182 float
183 log1pf(float x)
184 {
185           return log1p(x);
186 }
187