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git.proxmox.com Git - mirror_edk2.git/blob - StdLib/LibC/Math/e_log10.c
2 Compute the base 10 logrithm of x.
4 Copyright (c) 2010 - 2011, Intel Corporation. All rights reserved.<BR>
5 This program and the accompanying materials are licensed and made available under
6 the terms and conditions of the BSD License that accompanies this distribution.
7 The full text of the license may be found at
8 http://opensource.org/licenses/bsd-license.
10 THE PROGRAM IS DISTRIBUTED UNDER THE BSD LICENSE ON AN "AS IS" BASIS,
11 WITHOUT WARRANTIES OR REPRESENTATIONS OF ANY KIND, EITHER EXPRESS OR IMPLIED.
13 * ====================================================
14 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
16 * Developed at SunPro, a Sun Microsystems, Inc. business.
17 * Permission to use, copy, modify, and distribute this
18 * software is freely granted, provided that this notice
20 * ====================================================
22 e_log10.c 5.1 93/09/24
23 NetBSD: e_log10.c,v 1.12 2002/05/26 22:01:51 wiz Exp
25 #include <LibConfig.h>
26 #include <sys/EfiCdefs.h>
29 * Return the base 10 logarithm of x
32 * Let log10_2hi = leading 40 bits of log10(2) and
33 * log10_2lo = log10(2) - log10_2hi,
34 * ivln10 = 1/log(10) rounded.
39 * log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))
42 * To guarantee log10(10**n)=n, where 10**n is normal, the rounding
43 * mode must set to Round-to-Nearest.
45 * [1/log(10)] rounded to 53 bits has error .198 ulps;
46 * log10 is monotonic at all binary break points.
49 * log10(x) is NaN with signal if x < 0;
50 * log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
51 * log10(NaN) is that NaN with no signal;
52 * log10(10**N) = N for N=0,1,...,22.
55 * The hexadecimal values are the intended ones for the following constants.
56 * The decimal values may be used, provided that the compiler will convert
57 * from decimal to binary accurately enough to produce the hexadecimal values
62 #include "math_private.h"
65 #if defined(_MSC_VER) /* Handle Microsoft VC++ compiler specifics. */
66 // potential divide by 0 -- near line 80, (x-x)/zero is on purpose
67 #pragma warning ( disable : 4723 )
71 two54
= 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
72 ivln10
= 4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */
73 log10_2hi
= 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
74 log10_2lo
= 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
76 static const double zero
= 0.0;
79 __ieee754_log10(double x
)
85 EXTRACT_WORDS(hx
,lx
,x
);
88 if (hx
< 0x00100000) { /* x < 2**-1022 */
89 if (((hx
&0x7fffffff)|lx
)==0)
90 return -two54
/zero
; /* log(+-0)=-inf */
93 return (x
-x
)/zero
; /* log(-#) = NaN */
95 k
-= 54; x
*= two54
; /* subnormal number, scale up x */
98 if (hx
>= 0x7ff00000) return x
+x
;
100 i
= ((u_int32_t
)k
&0x80000000)>>31;
101 hx
= (hx
&0x000fffff)|((0x3ff-i
)<<20);
104 z
= y
*log10_2lo
+ ivln10
*__ieee754_log(x
);
105 return z
+y
*log10_2hi
;