src/fdlibm/e_log10.c

/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
 *
 * ***** BEGIN LICENSE BLOCK *****
 * Version: MPL 1.1/GPL 2.0/LGPL 2.1
 *
 * The contents of this file are subject to the Mozilla Public License Version
 * 1.1 (the "License"); you may not use this file except in compliance with
 * the License. You may obtain a copy of the License at
 * http://www.mozilla.org/MPL/
 *
 * Software distributed under the License is distributed on an "AS IS" basis,
 * WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
 * for the specific language governing rights and limitations under the
 * License.
 *
 * The Original Code is Mozilla Communicator client code, released
 * March 31, 1998.
 *
 * The Initial Developer of the Original Code is
 * Sun Microsystems, Inc.
 * Portions created by the Initial Developer are Copyright (C) 1998
 * the Initial Developer. All Rights Reserved.
 *
 * Contributor(s):
 *
 * Alternatively, the contents of this file may be used under the terms of
 * either of the GNU General Public License Version 2 or later (the "GPL"),
 * or the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
 * in which case the provisions of the GPL or the LGPL are applicable instead
 * of those above. If you wish to allow use of your version of this file only
 * under the terms of either the GPL or the LGPL, and not to allow others to
 * use your version of this file under the terms of the MPL, indicate your
 * decision by deleting the provisions above and replace them with the notice
 * and other provisions required by the GPL or the LGPL. If you do not delete
 * the provisions above, a recipient may use your version of this file under
 * the terms of any one of the MPL, the GPL or the LGPL.
 *
 * ***** END LICENSE BLOCK ***** */

/* @(#)e_log10.c 1.3 95/01/18 */
/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunSoft, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice 
 * is preserved.
 * ====================================================
 */

/* __ieee754_log10(x)
 * Return the base 10 logarithm of x
 * 
 * Method :
 *      Let log10_2hi = leading 40 bits of log10(2) and
 *          log10_2lo = log10(2) - log10_2hi,
 *          ivln10   = 1/log(10) rounded.
 *      Then
 *              n = ilogb(x), 
 *              if(n<0)  n = n+1;
 *              x = scalbn(x,-n);
 *              log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))
 *
 * Note 1:
 *      To guarantee log10(10**n)=n, where 10**n is normal, the rounding 
 *      mode must set to Round-to-Nearest.
 * Note 2:
 *      [1/log(10)] rounded to 53 bits has error  .198   ulps;
 *      log10 is monotonic at all binary break points.
 *
 * Special cases:
 *      log10(x) is NaN with signal if x < 0; 
 *      log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
 *      log10(NaN) is that NaN with no signal;
 *      log10(10**N) = N  for N=0,1,...,22.
 *
 * Constants:
 * The hexadecimal values are the intended ones for the following constants.
 * The decimal values may be used, provided that the compiler will convert
 * from decimal to binary accurately enough to produce the hexadecimal values
 * shown.
 */

#include "fdlibm.h"

#ifdef __STDC__
static const double
#else
static double
#endif
two54      =  1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
ivln10     =  4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */
log10_2hi  =  3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
log10_2lo  =  3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */

static double zero   =  0.0;

#ifdef __STDC__
        double __ieee754_log10(double x)
#else
        double __ieee754_log10(x)
        double x;
#endif
{
        fd_twoints u;
        double y,z;
        int i,k,hx;
        unsigned lx;

        u.d = x;
        hx = __HI(u);   /* high word of x */
        lx = __LO(u);   /* low word of x */

        k=0;
        if (hx < 0x00100000) {                  /* x < 2**-1022  */
            if (((hx&0x7fffffff)|lx)==0)
                return -two54/zero;             /* log(+-0)=-inf */
            if (hx<0) return (x-x)/zero;        /* log(-#) = NaN */
            k -= 54; x *= two54; /* subnormal number, scale up x */
            u.d = x;
            hx = __HI(u);                /* high word of x */
        }
        if (hx >= 0x7ff00000) return x+x;
        k += (hx>>20)-1023;
        i  = ((unsigned)k&0x80000000)>>31;
        hx = (hx&0x000fffff)|((0x3ff-i)<<20);
        y  = (double)(k+i);
        u.d = x;
        __HI(u) = hx;
        x = u.d;
        z  = y*log10_2lo + ivln10*__ieee754_log(x);
        return  z+y*log10_2hi;
}
1	/* -- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 --
2	*
3	* *** BEGIN LICENSE BLOCK ***
4	* Version: MPL 1.1/GPL 2.0/LGPL 2.1
5	*
6	* The contents of this file are subject to the Mozilla Public License Version
7	* 1.1 (the "License"); you may not use this file except in compliance with
8	* the License. You may obtain a copy of the License at
9	* http://www.mozilla.org/MPL/
10	*
11	* Software distributed under the License is distributed on an "AS IS" basis,
12	* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
13	* for the specific language governing rights and limitations under the
14	* License.
15	*
16	* The Original Code is Mozilla Communicator client code, released
17	* March 31, 1998.
18	*
19	* The Initial Developer of the Original Code is
20	* Sun Microsystems, Inc.
21	* Portions created by the Initial Developer are Copyright (C) 1998
22	* the Initial Developer. All Rights Reserved.
23	*
24	* Contributor(s):
25	*
26	* Alternatively, the contents of this file may be used under the terms of
27	* either of the GNU General Public License Version 2 or later (the "GPL"),
28	* or the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
29	* in which case the provisions of the GPL or the LGPL are applicable instead
30	* of those above. If you wish to allow use of your version of this file only
31	* under the terms of either the GPL or the LGPL, and not to allow others to
32	* use your version of this file under the terms of the MPL, indicate your
33	* decision by deleting the provisions above and replace them with the notice
34	* and other provisions required by the GPL or the LGPL. If you do not delete
35	* the provisions above, a recipient may use your version of this file under
36	* the terms of any one of the MPL, the GPL or the LGPL.
37	*
38	* *** END LICENSE BLOCK *** */
39
40	/* @(#)e_log10.c 1.3 95/01/18 */
41	/*
42	* ====================================================
43	* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
44	*
45	* Developed at SunSoft, a Sun Microsystems, Inc. business.
46	* Permission to use, copy, modify, and distribute this
47	* software is freely granted, provided that this notice
48	* is preserved.
49	* ====================================================
50	*/
51
52	/* __ieee754_log10(x)
53	* Return the base 10 logarithm of x
54	*
55	* Method :
56	* Let log10_2hi = leading 40 bits of log10(2) and
57	* log10_2lo = log10(2) - log10_2hi,
58	* ivln10 = 1/log(10) rounded.
59	* Then
60	* n = ilogb(x),
61	* if(n<0) n = n+1;
62	* x = scalbn(x,-n);
63	* log10(x) := nlog10_2hi + (nlog10_2lo + ivln10*log(x))
64	*
65	* Note 1:
66	* To guarantee log10(10n)=n, where 10n is normal, the rounding
67	* mode must set to Round-to-Nearest.
68	* Note 2:
69	* [1/log(10)] rounded to 53 bits has error .198 ulps;
70	* log10 is monotonic at all binary break points.
71	*
72	* Special cases:
73	* log10(x) is NaN with signal if x < 0;
74	* log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
75	* log10(NaN) is that NaN with no signal;
76	* log10(10**N) = N for N=0,1,...,22.
77	*
78	* Constants:
79	* The hexadecimal values are the intended ones for the following constants.
80	* The decimal values may be used, provided that the compiler will convert
81	* from decimal to binary accurately enough to produce the hexadecimal values
82	* shown.
83	*/
84
85	#include "fdlibm.h"
86
87	#ifdef __STDC__
88	static const double
89	#else
90	static double
91	#endif
92	two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
93	ivln10 = 4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */
94	log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
95	log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
96
97	static double zero = 0.0;
98
99	#ifdef __STDC__
100	double __ieee754_log10(double x)
101	#else
102	double __ieee754_log10(x)
103	double x;
104	#endif
105	{
106	fd_twoints u;
107	double y,z;
108	int i,k,hx;
109	unsigned lx;
110
111	u.d = x;
112	hx = __HI(u); /* high word of x */
113	lx = __LO(u); /* low word of x */
114
115	k=0;
116	if (hx < 0x00100000) { /* x < 2*-1022 /
117	if (((hx&0x7fffffff)\|lx)==0)
118	return -two54/zero; /* log(+-0)=-inf */
119	if (hx<0) return (x-x)/zero; /* log(-#) = NaN */
120	k -= 54; x = two54; / subnormal number, scale up x */
121	u.d = x;
122	hx = __HI(u); /* high word of x */
123	}
124	if (hx >= 0x7ff00000) return x+x;
125	k += (hx>>20)-1023;
126	i = ((unsigned)k&0x80000000)>>31;
127	hx = (hx&0x000fffff)\|((0x3ff-i)<<20);
128	y = (double)(k+i);
129	u.d = x;
130	__HI(u) = hx;
131	x = u.d;
132	z = ylog10_2lo + ivln10__ieee754_log(x);
133	return z+y*log10_2hi;
134	}