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
1349393c00Smartynas #include <float.h>
1449393c00Smartynas #include <math.h>
1549393c00Smartynas
167b36286aSmartynas #include "math_private.h"
177b36286aSmartynas
187b36286aSmartynas static const double
197b36286aSmartynas ln2 = 0.6931471805599452862268,
207b36286aSmartynas two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */
217b36286aSmartynas Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */
227b36286aSmartynas Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */
237b36286aSmartynas Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */
247b36286aSmartynas Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */
257b36286aSmartynas Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */
267b36286aSmartynas Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */
277b36286aSmartynas Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
287b36286aSmartynas
297b36286aSmartynas static const double zero = 0.0;
307b36286aSmartynas
317b36286aSmartynas double
log2(double x)327b36286aSmartynas log2(double x)
337b36286aSmartynas {
347b36286aSmartynas double hfsq,f,s,z,R,w,t1,t2,dk;
357b36286aSmartynas int32_t k,hx,i,j;
367b36286aSmartynas u_int32_t lx;
377b36286aSmartynas
387b36286aSmartynas EXTRACT_WORDS(hx,lx,x);
397b36286aSmartynas
407b36286aSmartynas k=0;
417b36286aSmartynas if (hx < 0x00100000) { /* x < 2**-1022 */
427b36286aSmartynas if (((hx&0x7fffffff)|lx)==0)
437b36286aSmartynas return -two54/zero; /* log(+-0)=-inf */
447b36286aSmartynas if (hx<0) return (x-x)/zero; /* log(-#) = NaN */
457b36286aSmartynas k -= 54; x *= two54; /* subnormal number, scale up x */
467b36286aSmartynas GET_HIGH_WORD(hx,x);
477b36286aSmartynas }
487b36286aSmartynas if (hx >= 0x7ff00000) return x+x;
497b36286aSmartynas k += (hx>>20)-1023;
507b36286aSmartynas hx &= 0x000fffff;
517b36286aSmartynas i = (hx+0x95f64)&0x100000;
527b36286aSmartynas SET_HIGH_WORD(x,hx|(i^0x3ff00000)); /* normalize x or x/2 */
537b36286aSmartynas k += (i>>20);
547b36286aSmartynas f = x-1.0;
557b36286aSmartynas dk = (double)k;
567b36286aSmartynas if((0x000fffff&(2+hx))<3) { /* |f| < 2**-20 */
577b36286aSmartynas if (f==zero)
587b36286aSmartynas return (dk);
597b36286aSmartynas R = f*f*(0.5-0.33333333333333333*f);
607b36286aSmartynas return (dk-(R-f)/ln2);
617b36286aSmartynas }
627b36286aSmartynas s = f/(2.0+f);
637b36286aSmartynas z = s*s;
647b36286aSmartynas i = hx-0x6147a;
657b36286aSmartynas w = z*z;
667b36286aSmartynas j = 0x6b851-hx;
677b36286aSmartynas t1= w*(Lg2+w*(Lg4+w*Lg6));
687b36286aSmartynas t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
697b36286aSmartynas i |= j;
707b36286aSmartynas R = t2+t1;
717b36286aSmartynas if(i>0) {
727b36286aSmartynas hfsq=0.5*f*f;
737b36286aSmartynas return (dk-(hfsq-s*(hfsq+R)-f)/ln2);
747b36286aSmartynas } else
757b36286aSmartynas return (dk-((s*(f-R))-f)/ln2);
767b36286aSmartynas }
77*2f2c0062Sguenther DEF_STD(log2);
78*2f2c0062Sguenther LDBL_MAYBE_UNUSED_CLONE(log2);
79