1 /* origin: FreeBSD /usr/src/lib/msun/src/e_log10.c */ 2 /* 3 * ==================================================== 4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 5 * 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 9 * is preserved. 10 * ==================================================== 11 */ 12 /* 13 * Return the base 10 logarithm of x. See log.c for most comments. 14 * 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) 18 */ 19 20 #include <math.h> 21 #include <stdint.h> 22 23 static const double 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 */ 35 36 double log10(double x) 37 { 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; 40 uint32_t hx; 41 int k; 42 43 hx = u.i>>32; 44 k = 0; 45 if (hx < 0x00100000 || hx>>31) { 46 if (u.i<<1 == 0) 47 return -1/(x*x); /* log(+-0)=-inf */ 48 if (hx>>31) 49 return (x-x)/0.0; /* log(-#) = NaN */ 50 /* subnormal number, scale x up */ 51 k -= 54; 52 x *= 0x1p54; 53 u.f = x; 54 hx = u.i>>32; 55 } else if (hx >= 0x7ff00000) { 56 return x; 57 } else if (hx == 0x3ff00000 && u.i<<32 == 0) 58 return 0; 59 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); 65 x = u.f; 66 67 f = x - 1.0; 68 hfsq = 0.5*f*f; 69 s = f/(2.0+f); 70 z = s*s; 71 w = z*z; 72 t1 = w*(Lg2+w*(Lg4+w*Lg6)); 73 t2 = z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7))); 74 R = t2 + t1; 75 76 /* See log2.c for details. */ 77 /* hi+lo = f - hfsq + s*(hfsq+R) ~ log(1+f) */ 78 hi = f - hfsq; 79 u.f = hi; 80 u.i &= (uint64_t)-1<<32; 81 hi = u.f; 82 lo = f - hi - hfsq + s*(hfsq+R); 83 84 /* val_hi+val_lo ~ log10(1+f) + k*log10(2) */ 85 val_hi = hi*ivln10hi; 86 dk = k; 87 y = dk*log10_2hi; 88 val_lo = dk*log10_2lo + (lo+hi)*ivln10lo + lo*ivln10hi; 89 90 /* 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. 95 */ 96 w = y + val_hi; 97 val_lo += (y - w) + val_hi; 98 val_hi = w; 99 100 return val_lo + val_hi; 101 } 102