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;