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 /* LINTLIBRARY */ 14 15 #include <sys/cdefs.h> 16 #include <float.h> 17 #include <math.h> 18 19 #include "math_private.h" 20 21 static const double 22 ln2 = 0.6931471805599452862268, 23 two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */ 24 Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */ 25 Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */ 26 Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */ 27 Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */ 28 Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */ 29 Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */ 30 Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */ 31 32 static const double zero = 0.0; 33 34 double 35 log2(double x) 36 { 37 double hfsq,f,s,z,R,w,t1,t2,dk; 38 int32_t k,hx,i,j; 39 u_int32_t lx; 40 41 EXTRACT_WORDS(hx,lx,x); 42 43 k=0; 44 if (hx < 0x00100000) { /* x < 2**-1022 */ 45 if (((hx&0x7fffffff)|lx)==0) 46 return -two54/zero; /* log(+-0)=-inf */ 47 if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ 48 k -= 54; x *= two54; /* subnormal number, scale up x */ 49 GET_HIGH_WORD(hx,x); 50 } 51 if (hx >= 0x7ff00000) return x+x; 52 k += (hx>>20)-1023; 53 hx &= 0x000fffff; 54 i = (hx+0x95f64)&0x100000; 55 SET_HIGH_WORD(x,hx|(i^0x3ff00000)); /* normalize x or x/2 */ 56 k += (i>>20); 57 f = x-1.0; 58 dk = (double)k; 59 if((0x000fffff&(2+hx))<3) { /* |f| < 2**-20 */ 60 if (f==zero) 61 return (dk); 62 R = f*f*(0.5-0.33333333333333333*f); 63 return (dk-(R-f)/ln2); 64 } 65 s = f/(2.0+f); 66 z = s*s; 67 i = hx-0x6147a; 68 w = z*z; 69 j = 0x6b851-hx; 70 t1= w*(Lg2+w*(Lg4+w*Lg6)); 71 t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7))); 72 i |= j; 73 R = t2+t1; 74 if(i>0) { 75 hfsq=0.5*f*f; 76 return (dk-(hfsq-s*(hfsq+R)-f)/ln2); 77 } else 78 return (dk-((s*(f-R))-f)/ln2); 79 } 80 81 #if LDBL_MANT_DIG == 53 82 #ifdef lint 83 /* PROTOLIB1 */ 84 long double log2l(long double); 85 #else /* lint */ 86 __weak_alias(log2l, log2); 87 #endif /* lint */ 88 #endif /* LDBL_MANT_DIG == 53 */ 89