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//=========================================================================== // // s_cbrt.c // // Part of the standard mathematical function library // //=========================================================================== // ####ECOSGPLCOPYRIGHTBEGIN#### // ------------------------------------------- // This file is part of eCos, the Embedded Configurable Operating System. // Copyright (C) 1998, 1999, 2000, 2001, 2002 Free Software Foundation, Inc. // // eCos is free software; you can redistribute it and/or modify it under // the terms of the GNU General Public License as published by the Free // Software Foundation; either version 2 or (at your option) any later // version. // // eCos is distributed in the hope that it will be useful, but WITHOUT // ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or // FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License // for more details. // // You should have received a copy of the GNU General Public License // along with eCos; if not, write to the Free Software Foundation, Inc., // 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. // // As a special exception, if other files instantiate templates or use // macros or inline functions from this file, or you compile this file // and link it with other works to produce a work based on this file, // this file does not by itself cause the resulting work to be covered by // the GNU General Public License. However the source code for this file // must still be made available in accordance with section (3) of the GNU // General Public License v2. // // This exception does not invalidate any other reasons why a work based // on this file might be covered by the GNU General Public License. // ------------------------------------------- // ####ECOSGPLCOPYRIGHTEND#### //=========================================================================== //#####DESCRIPTIONBEGIN#### // // Author(s): jlarmour // Contributors: jlarmour // Date: 1998-02-13 // Purpose: // Description: // Usage: // //####DESCRIPTIONEND#### // //=========================================================================== // CONFIGURATION #include <pkgconf/libm.h> // Configuration header // Include the Math library? #ifdef CYGPKG_LIBM // Derived from code with the following copyright /* @(#)s_cbrt.c 1.3 95/01/18 */ /* * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. * * Developed at SunSoft, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this * software is freely granted, provided that this notice * is preserved. * ==================================================== * */ #include "mathincl/fdlibm.h" /* cbrt(x) * Return cube root of x */ static const unsigned B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */ B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */ static const double C = 5.42857142857142815906e-01, /* 19/35 = 0x3FE15F15, 0xF15F15F1 */ D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */ E = 1.41428571428571436819e+00, /* 99/70 = 0x3FF6A0EA, 0x0EA0EA0F */ F = 1.60714285714285720630e+00, /* 45/28 = 0x3FF9B6DB, 0x6DB6DB6E */ G = 3.57142857142857150787e-01; /* 5/14 = 0x3FD6DB6D, 0xB6DB6DB7 */ double cbrt(double x) { int hx; double r,s,t=0.0,w; unsigned sign; hx = CYG_LIBM_HI(x); /* high word of x */ sign=hx&0x80000000; /* sign= sign(x) */ hx ^=sign; if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */ if((hx|CYG_LIBM_LO(x))==0) return(x); /* cbrt(0) is itself */ CYG_LIBM_HI(x) = hx; /* x <- |x| */ /* rough cbrt to 5 bits */ if(hx<0x00100000) /* subnormal number */ {CYG_LIBM_HI(t)=0x43500000; /* set t= 2**54 */ t*=x; CYG_LIBM_HI(t)=CYG_LIBM_HI(t)/3+B2; } else CYG_LIBM_HI(t)=hx/3+B1; /* new cbrt to 23 bits, may be implemented in single precision */ r=t*t/x; s=C+r*t; t*=G+F/(s+E+D/s); /* chopped to 20 bits and make it larger than cbrt(x) */ CYG_LIBM_LO(t)=0; CYG_LIBM_HI(t)+=0x00000001; /* one step newton iteration to 53 bits with error less than 0.667 ulps */ s=t*t; /* t*t is exact */ r=x/s; w=t+t; r=(r-t)/(w+r); /* r-s is exact */ t=t+t*r; /* retore the sign bit */ CYG_LIBM_HI(t) |= sign; return(t); } #endif // ifdef CYGPKG_LIBM // EOF s_cbrt.c
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