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path: root/src/math/log10.c
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 ```1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 ``` ``````/* 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 #include 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; } ``````