1 /* origin: FreeBSD /usr/src/lib/msun/src/e_log10.c */
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6 * Developed at SunSoft, a Sun Microsystems, Inc. business.
7 * Permission to use, copy, modify, and distribute this
8 * software is freely granted, provided that this notice
10 * ====================================================
13 * Return the base 10 logarithm of x. See log.c for most comments.
15 * Reduce x to 2^k (1+f) and calculate r = log(1+f) - f + f*f/2
16 * as in log.c, then combine and scale in extra precision:
17 * log10(x) = (f - f*f/2 + r)/log(10) + k*log10(2)
24 ivln10hi
= 4.34294481878168880939e-01, /* 0x3fdbcb7b, 0x15200000 */
25 ivln10lo
= 2.50829467116452752298e-11, /* 0x3dbb9438, 0xca9aadd5 */
26 log10_2hi
= 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
27 log10_2lo
= 3.69423907715893078616e-13, /* 0x3D59FEF3, 0x11F12B36 */
28 Lg1
= 6.666666666666735130e-01, /* 3FE55555 55555593 */
29 Lg2
= 3.999999999940941908e-01, /* 3FD99999 9997FA04 */
30 Lg3
= 2.857142874366239149e-01, /* 3FD24924 94229359 */
31 Lg4
= 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */
32 Lg5
= 1.818357216161805012e-01, /* 3FC74664 96CB03DE */
33 Lg6
= 1.531383769920937332e-01, /* 3FC39A09 D078C69F */
34 Lg7
= 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
36 double log10(double x
)
38 union {double f
; uint64_t i
;} u
= {x
};
39 double_t hfsq
,f
,s
,z
,R
,w
,t1
,t2
,dk
,y
,hi
,lo
,val_hi
,val_lo
;
45 if (hx
< 0x00100000 || hx
>>31) {
47 return -1/(x
*x
); /* log(+-0)=-inf */
49 return (x
-x
)/0.0; /* log(-#) = NaN */
50 /* subnormal number, scale x up */
55 } else if (hx
>= 0x7ff00000) {
57 } else if (hx
== 0x3ff00000 && u
.i
<<32 == 0)
60 /* reduce x into [sqrt(2)/2, sqrt(2)] */
61 hx
+= 0x3ff00000 - 0x3fe6a09e;
62 k
+= (int)(hx
>>20) - 0x3ff;
63 hx
= (hx
&0x000fffff) + 0x3fe6a09e;
64 u
.i
= (uint64_t)hx
<<32 | (u
.i
&0xffffffff);
72 t1
= w
*(Lg2
+w
*(Lg4
+w
*Lg6
));
73 t2
= z
*(Lg1
+w
*(Lg3
+w
*(Lg5
+w
*Lg7
)));
76 /* See log2.c for details. */
77 /* hi+lo = f - hfsq + s*(hfsq+R) ~ log(1+f) */
80 u
.i
&= (uint64_t)-1<<32;
82 lo
= f
- hi
- hfsq
+ s
*(hfsq
+R
);
84 /* val_hi+val_lo ~ log10(1+f) + k*log10(2) */
88 val_lo
= dk
*log10_2lo
+ (lo
+hi
)*ivln10lo
+ lo
*ivln10hi
;
91 * Extra precision in for adding y is not strictly needed
92 * since there is no very large cancellation near x = sqrt(2) or
93 * x = 1/sqrt(2), but we do it anyway since it costs little on CPUs
94 * with some parallelism and it reduces the error for many args.
97 val_lo
+= (y
- w
) + val_hi
;
100 return val_lo
+ val_hi
;