| /* 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> |
| #include <stdint.h> |
| |
| 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; |
| } |