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 <math_private.h>
48 #include <fix-int-fp-convert-zero.h>
50 static const double two54
= 1.80143985094819840000e+16; /* 0x43500000, 0x00000000 */
51 static const double ivln10
= 4.34294481903251816668e-01; /* 0x3FDBCB7B, 0x1526E50E */
52 static const double log10_2hi
= 3.01029995663611771306e-01; /* 0x3FD34413, 0x509F6000 */
53 static const double log10_2lo
= 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
56 __ieee754_log10 (double x
)
62 EXTRACT_WORDS (hx
, lx
, x
);
67 if (__glibc_unlikely (((hx
& 0x7fffffff) | lx
) == 0))
68 return -two54
/ __fabs (x
); /* log(+-0)=-inf */
69 if (__glibc_unlikely (hx
< 0))
70 return (x
- x
) / (x
- x
); /* log(-#) = NaN */
72 x
*= two54
; /* subnormal number, scale up x */
73 GET_HIGH_WORD (hx
, x
);
75 if (__glibc_unlikely (hx
>= 0x7ff00000))
77 k
+= (hx
>> 20) - 1023;
78 i
= ((u_int32_t
) k
& 0x80000000) >> 31;
79 hx
= (hx
& 0x000fffff) | ((0x3ff - i
) << 20);
81 if (FIX_INT_FP_CONVERT_ZERO
&& y
== 0.0)
83 SET_HIGH_WORD (x
, hx
);
84 z
= y
* log10_2lo
+ ivln10
* __ieee754_log (x
);
85 return z
+ y
* log10_2hi
;
88 strong_alias (__ieee754_log10
, __log10_finite
)