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