]>
git.proxmox.com Git - mirror_edk2.git/blob - StdLib/LibC/Math/e_log.c
2 Compute the 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 * ====================================================
23 NetBSD: e_log.c,v 1.12 2002/05/26 22:01:51 wiz Exp
25 #include <LibConfig.h>
26 #include <sys/EfiCdefs.h>
28 #if defined(_MSC_VER) /* Handle Microsoft VC++ compiler specifics. */
29 // potential divide by 0 -- near line 118, (x-x)/zero is on purpose
30 #pragma warning ( disable : 4723 )
34 * Return the logrithm of x
37 * 1. Argument Reduction: find k and f such that
39 * where sqrt(2)/2 < 1+f < sqrt(2) .
41 * 2. Approximation of log(1+f).
42 * Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
43 * = 2s + 2/3 s**3 + 2/5 s**5 + .....,
45 * We use a special Reme algorithm on [0,0.1716] to generate
46 * a polynomial of degree 14 to approximate R The maximum error
47 * of this polynomial approximation is bounded by 2**-58.45. In
50 * R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s
51 * (the values of Lg1 to Lg7 are listed in the program)
54 * | Lg1*s +...+Lg7*s - R(z) | <= 2
56 * Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2.
57 * In order to guarantee error in log below 1ulp, we compute log
59 * log(1+f) = f - s*(f - R) (if f is not too large)
60 * log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy)
62 * 3. Finally, log(x) = k*ln2 + log(1+f).
63 * = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo)))
64 * Here ln2 is split into two floating point number:
66 * where n*ln2_hi is always exact for |n| < 2000.
69 * log(x) is NaN with signal if x < 0 (including -INF) ;
70 * log(+INF) is +INF; log(0) is -INF with signal;
71 * log(NaN) is that NaN with no signal.
74 * according to an error analysis, the error is always less than
75 * 1 ulp (unit in the last place).
78 * The hexadecimal values are the intended ones for the following
79 * constants. The decimal values may be used, provided that the
80 * compiler will convert from decimal to binary accurately enough
81 * to produce the hexadecimal values shown.
85 #include "math_private.h"
89 ln2_hi
= 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */
90 ln2_lo
= 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */
91 two54
= 1.80143985094819840000e+16, /* 43500000 00000000 */
92 Lg1
= 6.666666666666735130e-01, /* 3FE55555 55555593 */
93 Lg2
= 3.999999999940941908e-01, /* 3FD99999 9997FA04 */
94 Lg3
= 2.857142874366239149e-01, /* 3FD24924 94229359 */
95 Lg4
= 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */
96 Lg5
= 1.818357216161805012e-01, /* 3FC74664 96CB03DE */
97 Lg6
= 1.531383769920937332e-01, /* 3FC39A09 D078C69F */
98 Lg7
= 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
100 static const double zero
= 0.0;
103 __ieee754_log(double x
)
105 double hfsq
,f
,s
,z
,R
,w
,t1
,t2
,dk
;
109 EXTRACT_WORDS(hx
,lx
,x
);
112 if (hx
< 0x00100000) { /* x < 2**-1022 */
113 if (((hx
&0x7fffffff)|lx
)==0)
114 return -two54
/zero
; /* log(+-0)=-inf */
117 return (x
-x
)/zero
; /* log(-#) = NaN */
119 k
-= 54; x
*= two54
; /* subnormal number, scale up x */
122 if (hx
>= 0x7ff00000) return x
+x
;
125 i
= (hx
+0x95f64)&0x100000;
126 SET_HIGH_WORD(x
,hx
|(i
^0x3ff00000)); /* normalize x or x/2 */
129 if((0x000fffff&(2+hx
))<3) { /* |f| < 2**-20 */
130 if(f
==zero
) { if(k
==0) return zero
; else {dk
=(double)k
;
131 return dk
*ln2_hi
+dk
*ln2_lo
;}
133 R
= f
*f
*(0.5-0.33333333333333333*f
);
134 if(k
==0) return f
-R
; else {dk
=(double)k
;
135 return dk
*ln2_hi
-((R
-dk
*ln2_lo
)-f
);}
143 t1
= w
*(Lg2
+w
*(Lg4
+w
*Lg6
));
144 t2
= z
*(Lg1
+w
*(Lg3
+w
*(Lg5
+w
*Lg7
)));
149 if(k
==0) return f
-(hfsq
-s
*(hfsq
+R
)); else
150 return dk
*ln2_hi
-((hfsq
-(s
*(hfsq
+R
)+dk
*ln2_lo
))-f
);
152 if(k
==0) return f
-s
*(f
-R
); else
153 return dk
*ln2_hi
-((s
*(f
-R
)-dk
*ln2_lo
)-f
);