17b36286aSmartynas /* @(#)e_log.c 1.3 95/01/18 */ 27b36286aSmartynas /* 37b36286aSmartynas * ==================================================== 47b36286aSmartynas * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 57b36286aSmartynas * 67b36286aSmartynas * Developed at SunSoft, a Sun Microsystems, Inc. business. 77b36286aSmartynas * Permission to use, copy, modify, and distribute this 87b36286aSmartynas * software is freely granted, provided that this notice 97b36286aSmartynas * is preserved. 107b36286aSmartynas * ==================================================== 117b36286aSmartynas */ 127b36286aSmartynas 13*49393c00Smartynas /* LINTLIBRARY */ 14*49393c00Smartynas 15*49393c00Smartynas #include <sys/cdefs.h> 16*49393c00Smartynas #include <float.h> 17*49393c00Smartynas #include <math.h> 18*49393c00Smartynas 197b36286aSmartynas #include "math_private.h" 207b36286aSmartynas 217b36286aSmartynas static const double 227b36286aSmartynas ln2 = 0.6931471805599452862268, 237b36286aSmartynas two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */ 247b36286aSmartynas Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */ 257b36286aSmartynas Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */ 267b36286aSmartynas Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */ 277b36286aSmartynas Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */ 287b36286aSmartynas Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */ 297b36286aSmartynas Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */ 307b36286aSmartynas Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */ 317b36286aSmartynas 327b36286aSmartynas static const double zero = 0.0; 337b36286aSmartynas 347b36286aSmartynas double 357b36286aSmartynas log2(double x) 367b36286aSmartynas { 377b36286aSmartynas double hfsq,f,s,z,R,w,t1,t2,dk; 387b36286aSmartynas int32_t k,hx,i,j; 397b36286aSmartynas u_int32_t lx; 407b36286aSmartynas 417b36286aSmartynas EXTRACT_WORDS(hx,lx,x); 427b36286aSmartynas 437b36286aSmartynas k=0; 447b36286aSmartynas if (hx < 0x00100000) { /* x < 2**-1022 */ 457b36286aSmartynas if (((hx&0x7fffffff)|lx)==0) 467b36286aSmartynas return -two54/zero; /* log(+-0)=-inf */ 477b36286aSmartynas if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ 487b36286aSmartynas k -= 54; x *= two54; /* subnormal number, scale up x */ 497b36286aSmartynas GET_HIGH_WORD(hx,x); 507b36286aSmartynas } 517b36286aSmartynas if (hx >= 0x7ff00000) return x+x; 527b36286aSmartynas k += (hx>>20)-1023; 537b36286aSmartynas hx &= 0x000fffff; 547b36286aSmartynas i = (hx+0x95f64)&0x100000; 557b36286aSmartynas SET_HIGH_WORD(x,hx|(i^0x3ff00000)); /* normalize x or x/2 */ 567b36286aSmartynas k += (i>>20); 577b36286aSmartynas f = x-1.0; 587b36286aSmartynas dk = (double)k; 597b36286aSmartynas if((0x000fffff&(2+hx))<3) { /* |f| < 2**-20 */ 607b36286aSmartynas if (f==zero) 617b36286aSmartynas return (dk); 627b36286aSmartynas R = f*f*(0.5-0.33333333333333333*f); 637b36286aSmartynas return (dk-(R-f)/ln2); 647b36286aSmartynas } 657b36286aSmartynas s = f/(2.0+f); 667b36286aSmartynas z = s*s; 677b36286aSmartynas i = hx-0x6147a; 687b36286aSmartynas w = z*z; 697b36286aSmartynas j = 0x6b851-hx; 707b36286aSmartynas t1= w*(Lg2+w*(Lg4+w*Lg6)); 717b36286aSmartynas t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7))); 727b36286aSmartynas i |= j; 737b36286aSmartynas R = t2+t1; 747b36286aSmartynas if(i>0) { 757b36286aSmartynas hfsq=0.5*f*f; 767b36286aSmartynas return (dk-(hfsq-s*(hfsq+R)-f)/ln2); 777b36286aSmartynas } else 787b36286aSmartynas return (dk-((s*(f-R))-f)/ln2); 797b36286aSmartynas } 80*49393c00Smartynas 81*49393c00Smartynas #if LDBL_MANT_DIG == 53 82*49393c00Smartynas #ifdef lint 83*49393c00Smartynas /* PROTOLIB1 */ 84*49393c00Smartynas long double log2l(long double); 85*49393c00Smartynas #else /* lint */ 86*49393c00Smartynas __weak_alias(log2l, log2); 87*49393c00Smartynas #endif /* lint */ 88*49393c00Smartynas #endif /* LDBL_MANT_DIG == 53 */ 89