1 /* @(#)e_log.c 1.3 95/01/18 */ 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 #include <float.h> 14 #include <math.h> 15 16 #include "math_private.h" 17 18 static const double 19 ln2 = 0.6931471805599452862268, 20 two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */ 21 Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */ 22 Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */ 23 Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */ 24 Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */ 25 Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */ 26 Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */ 27 Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */ 28 29 static const double zero = 0.0; 30 31 double 32 log2(double x) 33 { 34 double hfsq,f,s,z,R,w,t1,t2,dk; 35 int32_t k,hx,i,j; 36 u_int32_t lx; 37 38 EXTRACT_WORDS(hx,lx,x); 39 40 k=0; 41 if (hx < 0x00100000) { /* x < 2**-1022 */ 42 if (((hx&0x7fffffff)|lx)==0) 43 return -two54/zero; /* log(+-0)=-inf */ 44 if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ 45 k -= 54; x *= two54; /* subnormal number, scale up x */ 46 GET_HIGH_WORD(hx,x); 47 } 48 if (hx >= 0x7ff00000) return x+x; 49 k += (hx>>20)-1023; 50 hx &= 0x000fffff; 51 i = (hx+0x95f64)&0x100000; 52 SET_HIGH_WORD(x,hx|(i^0x3ff00000)); /* normalize x or x/2 */ 53 k += (i>>20); 54 f = x-1.0; 55 dk = (double)k; 56 if((0x000fffff&(2+hx))<3) { /* |f| < 2**-20 */ 57 if (f==zero) 58 return (dk); 59 R = f*f*(0.5-0.33333333333333333*f); 60 return (dk-(R-f)/ln2); 61 } 62 s = f/(2.0+f); 63 z = s*s; 64 i = hx-0x6147a; 65 w = z*z; 66 j = 0x6b851-hx; 67 t1= w*(Lg2+w*(Lg4+w*Lg6)); 68 t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7))); 69 i |= j; 70 R = t2+t1; 71 if(i>0) { 72 hfsq=0.5*f*f; 73 return (dk-(hfsq-s*(hfsq+R)-f)/ln2); 74 } else 75 return (dk-((s*(f-R))-f)/ln2); 76 } 77 78 #if LDBL_MANT_DIG == DBL_MANT_DIG 79 __strong_alias(log2l, log2); 80 #endif /* LDBL_MANT_DIG == DBL_MANT_DIG */ 81