2 * ====================================================
3 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 * Developed at SunPro, a Sun Microsystems, Inc. business.
6 * Permission to use, copy, modify, and distribute this
7 * software is freely granted, provided that this notice
9 * ====================================================
13 * Return the base 10 logarithm of x
16 * Let log10_2hi = leading 40 bits of log10(2) and
17 * log10_2lo = log10(2) - log10_2hi,
18 * ivln10 = 1/log(10) rounded.
23 * log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))
26 * To guarantee log10(10**n)=n, where 10**n is normal, the rounding
27 * mode must set to Round-to-Nearest.
29 * [1/log(10)] rounded to 53 bits has error .198 ulps;
30 * log10 is monotonic at all binary break points.
33 * log10(x) is NaN with signal if x < 0;
34 * log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
35 * log10(NaN) is that NaN with no signal;
36 * log10(10**N) = N for N=0,1,...,22.
39 * The hexadecimal values are the intended ones for the following constants.
40 * The decimal values may be used, provided that the compiler will convert
41 * from decimal to binary accurately enough to produce the hexadecimal values
46 #include "math_private.h"
49 two54
= 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
50 ivln10
= 4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */
51 log10_2hi
= 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
52 log10_2lo
= 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
54 static const double zero
= 0.0;
56 double attribute_hidden
__ieee754_log10(double x
)
62 EXTRACT_WORDS(hx
,lx
,x
);
65 if (hx
< 0x00100000) { /* x < 2**-1022 */
66 if (((hx
&0x7fffffff)|lx
)==0)
67 return -two54
/zero
; /* log(+-0)=-inf */
68 if (hx
<0) return (x
-x
)/zero
; /* log(-#) = NaN */
69 k
-= 54; x
*= two54
; /* subnormal number, scale up x */
72 if (hx
>= 0x7ff00000) return x
+x
;
74 i
= ((u_int32_t
)k
&0x80000000)>>31;
75 hx
= (hx
&0x000fffff)|((0x3ff-i
)<<20);
78 z
= y
*log10_2lo
+ ivln10
*__ieee754_log(x
);
86 double log10(double x
)
88 double z
= __ieee754_log10(x
);
89 if (_LIB_VERSION
== _IEEE_
|| isnan(x
))
93 return __kernel_standard(x
, x
, 18); /* log10(0) */
94 return __kernel_standard(x
, x
, 19); /* log10(x<0) */
99 strong_alias(__ieee754_log10
, log10
)
101 libm_hidden_def(log10
)