1 /* @(#)e_log10.c 5.1 93/09/24 */
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6 * Developed at SunPro, a Sun Microsystems, Inc. business.
7 * Permission to use, copy, modify, and distribute this
8 * software is freely granted, provided that this notice
10 * ====================================================
14 * Return the base 10 logarithm of x
17 * Let log10_2hi = leading 40 bits of log10(2) and
18 * log10_2lo = log10(2) - log10_2hi,
19 * ivln10 = 1/log(10) rounded.
24 * log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))
27 * To guarantee log10(10**n)=n, where 10**n is normal, the rounding
28 * mode must set to Round-to-Nearest.
30 * [1/log(10)] rounded to 53 bits has error .198 ulps;
31 * log10 is monotonic at all binary break points.
34 * log10(x) is NaN with signal if x < 0;
35 * log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
36 * log10(NaN) is that NaN with no signal;
37 * log10(10**N) = N for N=0,1,...,22.
40 * The hexadecimal values are the intended ones for the following constants.
41 * The decimal values may be used, provided that the compiler will convert
42 * from decimal to binary accurately enough to produce the hexadecimal values
47 #include <fix-int-fp-convert-zero.h>
48 #include <math_private.h>
50 #include <libm-alias-finite.h>
52 static const double two54
= 1.80143985094819840000e+16; /* 0x4350000000000000 */
53 static const double ivln10
= 4.34294481903251816668e-01; /* 0x3FDBCB7B1526E50E */
54 static const double log10_2hi
= 3.01029995663611771306e-01; /* 0x3FD34413509F6000 */
55 static const double log10_2lo
= 3.69423907715893078616e-13; /* 0x3D59FEF311F12B36 */
58 __ieee754_log10 (double x
)
64 EXTRACT_WORDS64 (hx
, x
);
67 if (hx
< INT64_C(0x0010000000000000))
69 if (__glibc_unlikely ((hx
& UINT64_C(0x7fffffffffffffff)) == 0))
70 return -two54
/ fabs (x
); /* log(+-0)=-inf */
71 if (__glibc_unlikely (hx
< 0))
72 return (x
- x
) / (x
- x
); /* log(-#) = NaN */
74 x
*= two54
; /* subnormal number, scale up x */
75 EXTRACT_WORDS64 (hx
, x
);
77 /* scale up resulted in a NaN number */
78 if (__glibc_unlikely (hx
>= UINT64_C(0x7ff0000000000000)))
80 k
+= (hx
>> 52) - 1023;
81 i
= ((uint64_t) k
& UINT64_C(0x8000000000000000)) >> 63;
82 hx
= (hx
& UINT64_C(0x000fffffffffffff)) | ((0x3ff - i
) << 52);
84 if (FIX_INT_FP_CONVERT_ZERO
&& y
== 0.0)
86 INSERT_WORDS64 (x
, hx
);
87 z
= y
* log10_2lo
+ ivln10
* __ieee754_log (x
);
88 return z
+ y
* log10_2hi
;
90 libm_alias_finite (__ieee754_log10
, __log10
)