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/* origin: FreeBSD /usr/src/lib/msun/src/e_log10.c */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/*
* Return the base 10 logarithm of x. See log.c for most comments.
*
* Reduce x to 2^k (1+f) and calculate r = log(1+f) - f + f*f/2
* as in log.c, then combine and scale in extra precision:
* log10(x) = (f - f*f/2 + r)/log(10) + k*log10(2)
*/
#include <math.h> // for double_t, log10
#include <stdint.h> // for uint64_t, uint32_t
static const double ivln10hi = 4.34294481878168880939e-01, /* 0x3fdbcb7b,
0x15200000 */
ivln10lo = 2.50829467116452752298e-11, /* 0x3dbb9438, 0xca9aadd5 */
log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
log10_2lo = 3.69423907715893078616e-13, /* 0x3D59FEF3, 0x11F12B36 */
Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */
Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */
Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */
Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */
Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */
Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */
Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
double log10(double x)
{
union {
double f;
uint64_t i;
} u = { x };
double_t hfsq, f, s, z, R, w, t1, t2, dk, y, hi, lo, val_hi, val_lo;
uint32_t hx;
int k;
hx = u.i >> 32;
k = 0;
if (hx < 0x00100000 || hx >> 31) {
if (u.i << 1 == 0)
return -1 / (x * x); /* log(+-0)=-inf */
if (hx >> 31)
return (x - x) / 0.0; /* log(-#) = NaN */
/* subnormal number, scale x up */
k -= 54;
x *= 0x1p54;
u.f = x;
hx = u.i >> 32;
} else if (hx >= 0x7ff00000) {
return x;
} else if (hx == 0x3ff00000 && u.i << 32 == 0)
return 0;
/* reduce x into [sqrt(2)/2, sqrt(2)] */
hx += 0x3ff00000 - 0x3fe6a09e;
k += (int)(hx >> 20) - 0x3ff;
hx = (hx & 0x000fffff) + 0x3fe6a09e;
u.i = (uint64_t)hx << 32 | (u.i & 0xffffffff);
x = u.f;
f = x - 1.0;
hfsq = 0.5 * f * f;
s = f / (2.0 + f);
z = s * s;
w = z * z;
t1 = w * (Lg2 + w * (Lg4 + w * Lg6));
t2 = z * (Lg1 + w * (Lg3 + w * (Lg5 + w * Lg7)));
R = t2 + t1;
/* See log2.c for details. */
/* hi+lo = f - hfsq + s*(hfsq+R) ~ log(1+f) */
hi = f - hfsq;
u.f = hi;
u.i &= (uint64_t)-1 << 32;
hi = u.f;
lo = f - hi - hfsq + s * (hfsq + R);
/* val_hi+val_lo ~ log10(1+f) + k*log10(2) */
val_hi = hi * ivln10hi;
dk = k;
y = dk * log10_2hi;
val_lo = dk * log10_2lo + (lo + hi) * ivln10lo + lo * ivln10hi;
/*
* Extra precision in for adding y is not strictly needed
* since there is no very large cancellation near x = sqrt(2) or
* x = 1/sqrt(2), but we do it anyway since it costs little on CPUs
* with some parallelism and it reduces the error for many args.
*/
w = y + val_hi;
val_lo += (y - w) + val_hi;
val_hi = w;
return val_lo + val_hi;
}
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