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 e_log.c and k_log.h for most
16 * log10(x) = (f - 0.5*f*f + k_log1p(f)) / ln10 + k * log10(2)
17 * in not-quite-routine extra precision.
24 two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
25 ivln10hi = 4.34294481878168880939e-01, /* 0x3fdbcb7b, 0x15200000 */
26 ivln10lo = 2.50829467116452752298e-11, /* 0x3dbb9438, 0xca9aadd5 */
27 log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
28 log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
30 static const double zero = 0.0;
32 double log10(double x)
34 double f,hfsq,hi,lo,r,val_hi,val_lo,w,y,y2;
38 EXTRACT_WORDS(hx, lx, x);
41 if (hx < 0x00100000) { /* x < 2**-1022 */
42 if (((hx&0x7fffffff)|lx) == 0)
43 return -two54/zero; /* log(+-0)=-inf */
45 return (x-x)/zero; /* log(-#) = NaN */
46 /* subnormal number, scale up x */
53 if (hx == 0x3ff00000 && lx == 0)
54 return zero; /* log(1) = +0 */
57 i = (hx+0x95f64)&0x100000;
58 SET_HIGH_WORD(x, hx|(i^0x3ff00000)); /* normalize x or x/2 */
65 /* See log2.c for details. */
68 lo = (f - hi) - hfsq + r;
71 val_lo = y*log10_2lo + (lo+hi)*ivln10lo + lo*ivln10hi;
74 * Extra precision in for adding y*log10_2hi is not strictly needed
75 * since there is no very large cancellation near x = sqrt(2) or
76 * x = 1/sqrt(2), but we do it anyway since it costs little on CPUs
77 * with some parallelism and it reduces the error for many args.
80 val_lo += (y2 - w) + val_hi;
83 return val_lo + val_hi;