This file contains other people's software and their documentation for it. Contents: Keith Briggs: doubledouble.cc, math.cc, doubledouble.h, inline.h Brendan McKay: nauty.c, nautil.c, nauty.h, nug.alw U.C. Berkeley: random.c (From http://www.ajk.tele.fi/libc/stdlib/random.c.html#random.) Notes: 1. atan2 and asin have been commented out in doubledouble.h and math.cc. 2. In doubledouble.h, the line which includes nan.h has been modified so that math.h is included if the operating system is Openstep or Linux. Ditto for math.cc. 3. Definition of doubledoubleRand48 commented out of doubledouble.h. 4. Include lines for random.c have been adjusted. 5. nauty.h, nauty.c, nautil.c: set changed to SET, bit changed to BIT ------------------------------------------------------------------------------ ifelse(UNAME,OPENSTEP,DEFINE(UNAME,Openstep)) |-> inc/doubledouble.h // doubledouble.h // Keith Briggs. Last revised 98 Feb 09 /* Copyright (C) 1997 Keith Martin Briggs Except where otherwise indicated, this program 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 of the License, or (at your option) any later version. This program 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 this program; if not, write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. */ // Change log: (See doubledouble.cc also) // 97 Dec 22 KMB added x86_FIX // Eliminates -ffloat-store requirement // 97 Aug 04 KMB added ldexp // 97Jul25 (WH) - fixed Qrand48 to return drand48 + (2^-47)*drand48 // 97Jul11 (WH) added qtoa declaration. // - made all constants (Pi etc) member constants, moved to quad.cc // - added doubledoubleRand48(). // - cleaned up constructors (fewer, with default arguments). // - added some code for integer exponent, but commented it out. It // looks hard. eg, adding numbers with different exponents. Almost // always the smaller would be essentially zero, but near boundaries... // 96Nov20 added normalizing constructor doubledouble(double,double) (needed by floor) #ifndef __QUAD_H__ #define __QUAD_H__ #define DEBUG_QUAD 0 #ifdef SGI_CC #define bool int #undefine _G_HAVE_BOOL #endif #ifdef __GNUC__ #if (__GNUC_MAJOR__<=2 && __GNUC_MINOR__<=6) #define bool int #define explicit #ifndef __isinf #define __isinf(x) ((x)!=(x)) // gcc 2.7.2 defines __isinf as a function #endif #endif #endif ifelse(UNAME,Openstep,`#include', `ifelse(UNAME,Linux,`#include',`#include')') // #include // defines NAN, at least in gcc #include // DOMAIN_ERROR=action to take on function domain errors #ifdef NAN #define DOMAIN_ERROR return(doubledouble(NAN,NAN)) #else #define DOMAIN_ERROR assert(0) #endif #ifdef x86 #define x86_FIX \ unsigned short __old_cw, __new_cw; \ asm volatile ("fnstcw %0":"=m" (__old_cw)); \ __new_cw = (__old_cw & ~0x300) | 0x200; \ asm volatile ("fldcw %0": :"m" (__new_cw)); #define END_x86_FIX asm volatile ("fldcw %0": :"m" (__old_cw)); #else #define x86_FIX #define END_x86_FIX #endif /* C++ functions for doubledouble (i.e. double+double) precision. These functions use techniques due to Dekker, Linnainmaa, Kahan, Knuth and Priest. I credit Kahan with the addition algorithm (the simplification which permits the elimination of the tests and branches is due to Knuth); Dekker and Linnainmaa with the multiply, divide, and square root routines, and Priest for the initial transcription into C++. A doubledouble x is represented as a pair of doubles, x.hi and x.lo, such that the number represented by x is x.hi + x.lo, where |x.lo| <= 0.5*ulp(x.hi), (*) and ulp(y) means `unit in the last place of y'. For the software to work correctly, IEEE Standard Arithmetic is sufficient. That includes just about every modern workstation. Also sufficient is any platform that implements arithmetic with correct rounding, i.e., given double floating point numbers a and b, a op b is computed exactly and then rounded to the nearest double. The tie-breaking rule is not important. See: T. J. Dekker Point Technique for Extending the Available Precision, Numer. Math. 18 (1971), pp. 224-242. S. Linnainmaa Software for doubled-precision floating point computations ACM TOMS 7, 172-283 (1081). D. Priest On properties of floating point arithmetics: numerical stability and the cost of accurate computations. Ph.D. Diss, Berkeley 1992. and more references in http://www.cs.wisc.edu/~shoup/ntl/quad_float.txt. */ #include #include #include #include #include class doubledouble { protected: double hi, lo; public: // Public data members, initialized in doubledouble.cc static const double Split; // cannot be initialized here; see ARM 9.4 static const doubledouble Log2, Log10, Pi, TwoPi, Pion2, Pion4, _Pi; // Public access to hi and lo inline double h() const { return hi; } inline double l() const { return lo; } // Constructors inline doubledouble():hi(0.0),lo(0.0) {} inline doubledouble(const int n) { hi=double(n); lo=0.0; } inline doubledouble(const double x, const double y); inline doubledouble(const doubledouble&); doubledouble(const char*); // Operators doubledouble& operator +=(const doubledouble&); doubledouble& operator +=(const double&); doubledouble& operator +=(const int); doubledouble& operator -=(const doubledouble&); doubledouble& operator -=(const double&); doubledouble& operator -=(const int); doubledouble& operator *=(const doubledouble&); doubledouble& operator *=(const double&); doubledouble& operator *=(const int); doubledouble& operator /=(const doubledouble&); doubledouble& operator /=(const double&); doubledouble& operator /=(const int); doubledouble& operator=(const doubledouble&); doubledouble& operator=(const double&); doubledouble& operator=(const int); // Get funny errors without this doubledouble& operator=(const char*); // Type conversion operator. Not really necessary... operator double() const { return hi+lo; } operator int() const { return (int)(hi+lo); } inline doubledouble normalize(void) { double h=hi+lo; lo=lo+(hi-h); hi=h; return *this; } void dump(char*) const; // debugging use only // Friends inline friend doubledouble operator -(const doubledouble& x); // Unary - friend doubledouble operator +(const doubledouble&, const doubledouble& ); friend doubledouble operator +(const double&, const doubledouble& ); friend doubledouble operator +(const int, const doubledouble& ); friend doubledouble operator +(const doubledouble&, const double& ); friend doubledouble operator +(const doubledouble&, const int ); friend doubledouble operator -(const doubledouble&, const doubledouble& ); friend doubledouble operator -(const double&, const doubledouble& ); friend doubledouble operator -(const int, const doubledouble& ); friend doubledouble operator -(const doubledouble&, const double& ); friend doubledouble operator -(const doubledouble&, const int ); friend doubledouble operator *(const doubledouble&, const doubledouble& ); friend doubledouble operator *(const double&, const doubledouble& ); friend doubledouble operator *(const int, const doubledouble& ); friend doubledouble operator *(const doubledouble&, const double& ); friend doubledouble operator *(const doubledouble&, const int ); friend doubledouble operator /(const doubledouble&, const doubledouble& ); friend doubledouble operator /(const doubledouble&, const double& ); friend doubledouble operator /(const doubledouble&, const int ); friend doubledouble operator /(const double&, const doubledouble& ); friend doubledouble operator /(const int, const doubledouble& ); friend doubledouble recip(const doubledouble &); friend doubledouble operator |(const doubledouble&, const doubledouble& ); friend double dnorm(const doubledouble&); friend int intq(const doubledouble&); friend doubledouble ldexp(const doubledouble x, const int exp); // member functions bool operator!=(const doubledouble& y) { return hi!=y.h() || lo!=y.l(); }; }; // end class doubledouble void base_and_prec(void); doubledouble atodd(const char *); // string to doubledouble conversion // doubledouble to string conversion. W must be long enough. Returns W. char *qtoa(char *Word, int prec, int fmtch, doubledouble q); bool operator> (const doubledouble&, const doubledouble&); bool operator>=(const doubledouble&, const doubledouble&); bool operator< (const doubledouble&, const doubledouble&); bool operator<=(const doubledouble&, const doubledouble&); bool operator==(const doubledouble&, const doubledouble&); //bool operator!=(const doubledouble&, const doubledouble&); // inline members inline doubledouble::doubledouble(const double x, const double y = 0.0) { x86_FIX hi=x+y; lo=y+(x-hi); // normalize END_x86_FIX } inline doubledouble::doubledouble(const doubledouble& x):hi(x.hi),lo(x.lo) {} inline doubledouble& doubledouble::operator=(const doubledouble& x){ hi=x.hi; lo=x.lo; return *this;} inline doubledouble& doubledouble::operator=(const double& x){ hi=x; lo=0.0; return *this;} inline doubledouble& doubledouble::operator=(const int x){ hi=x; lo=0.0; return *this;} // inline functions inline doubledouble operator-(const doubledouble& x) { return doubledouble(-x.hi, -x.lo); } inline doubledouble normalize(const doubledouble& x) { return doubledouble(x.h(), x.l()); } inline double dnorm(const doubledouble& x) { return fabs(x.h());} inline int intq(const doubledouble& x) { // explicit type conversion doubledouble -> int return int(x.h()); } // inline doubledouble doubledoubleRand48(void) { // return doubledouble(drand48(), ldexp(drand48(), -47)); // } // inline functions (defined in doubledouble.cc) doubledouble Qcopysign(const doubledouble&, const double); // non inline functions (defined in doubledouble.cc and math.cc) istream& operator >> (istream&, doubledouble&); ostream& operator << (ostream&, const doubledouble&); int sign(const doubledouble&); doubledouble hypot(const doubledouble, const doubledouble); doubledouble recip(const doubledouble&); doubledouble sqrt(const doubledouble&); doubledouble sqr(const doubledouble&); doubledouble cub(const doubledouble&); doubledouble sqr_double(const double&); doubledouble rint(const doubledouble&); doubledouble floor(const doubledouble&); doubledouble trunc(const doubledouble&); doubledouble fmod(const doubledouble&, const int); doubledouble modf(const doubledouble&, doubledouble *ip); doubledouble fabs(const doubledouble&); doubledouble exp(const doubledouble&); doubledouble log(const doubledouble&); doubledouble log10(const doubledouble&); doubledouble powint(const doubledouble&, const int); doubledouble pow(const doubledouble&, const doubledouble&); doubledouble sin(const doubledouble&); void sincos(const doubledouble x, doubledouble& sinx, doubledouble& cosx); doubledouble cos(const doubledouble&); doubledouble atan(const doubledouble&); // doubledouble atan2(const doubledouble&, const doubledouble&); // doubledouble asin(const doubledouble&); doubledouble sinh(const doubledouble&); doubledouble cosh(const doubledouble&); doubledouble tanh(const doubledouble&); doubledouble erf(const doubledouble); doubledouble erfc(const doubledouble); doubledouble gamma(const doubledouble); int digits(const doubledouble&,const doubledouble&); doubledouble modr(const doubledouble a, const doubledouble b, int& n, doubledouble& rem); #ifdef DD_INLINE #include "inline.h" #endif // DD_INLINE #endif // __QUAD_H__ |-> inc/inline.h // inline.h // KMB 97 Dec 29 /* Copyright (C) 1997 Keith Martin Briggs Except where otherwise indicated, this program 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 of the License, or (at your option) any later version. This program 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 this program; if not, write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. */ // 97 Aug 04 KMB added ldexp // 97 Jul 11 Moved this stuff out of quad.h, created inline.h so it can // be #included even if we're not inlining, by just "#define inline" // 97 Jul 12 Added all combos of doubledouble/double/int +-*/. Only a couple actually // written; most just call the others by swapping arguments. Generates // equivalent code with a good inlining compiler (tested with g++ 2.7.2). // - e.g., all subtraction is now done by addition of unary minus. // - removed if's from doubledouble*int. Zero-branch code is 2.5 faster (tested) // - generally cleaned up and re-organized the order of the functions, // now they're grouped nicely by function. // - tested Newton's division. Works but is terribly slow, because // it needs to do several doubledouble + and * operations, and doubledouble / // without it is about the same speed at doubledouble * anyway, so no win. // - moved recip here as an inline. // - checked and tested doubledouble/double (BUG?), seems fine. // Absolute value inline doubledouble fabs(const doubledouble& x) { if (x.h()>=0.0) return x; else return -x; } // Addition /* (C) W. Kahan 1989 * NOTICE: * Copyrighted programs may not be translated, used, nor * reproduced without the author's permission. Normally that * permission is granted freely for academic and scientific * purposes subject to the following three requirements: * 1. This NOTICE and the copyright notices must remain attached * to the programs and their translations. * 2. Users of such a program should regard themselves as voluntary * participants in the author's researches and so are obliged * to report their experience with the program back to the author. * 3. Neither the author nor the institution that employs him will * be held responsible for the consequences of using a program * for which neither has received payment. * Would-be commercial users of these programs must correspond * with the author to arrange terms of payment and warranty. */ /////////////////////////////////////////////////////////////// /////////////////// Addition and Subtraction ///////////////// /////////////////////////////////////////////////////////////// // Binary addition inline doubledouble operator +(const doubledouble& x, const doubledouble& y) { x86_FIX double H, h, T, t, S, s, e, f; S = x.hi+y.hi; T = x.lo+y.lo; e = S-x.hi; f = T-x.lo; s = S-e; t = T-f; s = (y.hi-e)+(x.hi-s); t = (y.lo-f)+(x.lo-t); e = s+T; H = S+e; h = e+(S-H); e = t+h; doubledouble z; z.hi = H+e; z.lo = e+double(H-z.hi); END_x86_FIX return z; } inline doubledouble operator +(const double& x, const doubledouble& y) { x86_FIX double H, h, S, s, e; S = x+y.hi; e = S-x; s = S-e; s = (y.hi-e)+(x-s); H = S+(s+y.lo); h = (s+y.lo)+(S-H); doubledouble z; z.hi = H+h; z.lo = h+double(H-z.hi); END_x86_FIX return z; } inline doubledouble operator +(const doubledouble& x,const double& y ) { return y+x; } inline doubledouble operator +(const int x, const doubledouble& y) { return double(x)+y; } inline doubledouble operator +(const doubledouble& x, const int y) { return y+x; } // Subtraction inline doubledouble operator -(const doubledouble& x, const doubledouble& y) { return x+(-y); } inline doubledouble operator -(const double& x, const doubledouble& y) { return x+(-y); } inline doubledouble operator -(const int x, const doubledouble& y) { return x+(-y); } inline doubledouble operator -(const doubledouble& x, const double& y) { return x+(-y); } inline doubledouble operator -(const doubledouble& x, const int y) { return x+(-y); } ////////////////////////// Self-Addition /////////////////////// inline doubledouble& doubledouble::operator +=(const doubledouble& y) { x86_FIX double H, h, T, t, S, s, e, f; S = hi+y.hi; T = lo+y.lo; e = S-hi; f = T-lo; s = S-e; t = T-f; s = (y.hi-e)+(hi-s); t = (y.lo-f)+(lo-t); f = s+T; H = S+f; h = f+(S-H); hi = H+(t+h); lo = (t+h)+double(H-hi); END_x86_FIX return *this; } inline doubledouble& doubledouble::operator +=(const double& y) { x86_FIX double H, h, S, s, e, f; S = hi+y; e = S-hi; s = S-e; s = (y-e)+(hi-s); f = s+lo; H = S+f; h = f+(S-H); hi = H+h; lo = h+double(H-hi); END_x86_FIX return *this; } inline doubledouble& doubledouble::operator +=(const int y) { return *this += double(y); } // Self-Subtraction inline doubledouble& doubledouble::operator -=(const doubledouble& y) { return *this += -y; } inline doubledouble& doubledouble::operator -=(const double& y) { return *this += -y; } inline doubledouble& doubledouble::operator -=(const int y) { return *this += -y; } ///////////////////////////////////////////////////////////// //////////////////// Multiplication /////////////////////// ///////////////////////////////////////////////////////////// // Binary Multiplication inline doubledouble operator *(const doubledouble& x, const doubledouble& y) { x86_FIX double hx, tx, hy, ty, C, c; C = doubledouble::Split*x.hi; hx = C-x.hi; c = doubledouble::Split*y.hi; hx = C-hx; tx = x.hi-hx; hy = c-y.hi; C = x.hi*y.hi; hy = c-hy; ty = y.hi-hy; c = ((((hx*hy-C)+hx*ty)+tx*hy)+tx*ty)+(x.hi*y.lo+x.lo*y.hi); doubledouble z; z.hi = C+c; hx=C-z.hi; z.lo = c+hx; END_x86_FIX return z; } // double*doubledouble inline doubledouble operator *(const double& x, const doubledouble& y) { x86_FIX double hx, tx, hy, ty, C, c; C = doubledouble::Split*x; hx = C-x; c = doubledouble::Split*y.hi; hx = C-hx ; tx = x-hx; hy = c-y.hi; C = x*y.hi; hy = c-hy; ty = y.hi - hy; c = ((((hx*hy-C)+hx*ty)+tx*hy)+tx*ty)+x*y.lo; doubledouble z; z.hi = C+c; z.lo = c+double(C-z.hi); END_x86_FIX return z; } inline doubledouble operator *(const int x, const doubledouble& y ) { return double(x)*y; } inline doubledouble operator *(const doubledouble& x, const double& y ) { return y*x; } inline doubledouble operator *(const doubledouble& x, const int y ) { return y*x; } // Self-multiplication inline doubledouble& doubledouble::operator *=(const doubledouble& y ) { x86_FIX double hx, tx, hy, ty, C, c; C = Split*hi; hx = C-hi; c = Split*y.hi; hx = C-hx; tx = hi-hx; hy = c-y.hi; C = hi*y.hi; hy = c-hy; ty = y.hi-hy; c = ((((hx*hy-C)+hx*ty)+tx*hy)+tx*ty)+(hi*y.lo+lo*y.hi); hx = C+c; hi = hx; lo = c+double(C-hx); END_x86_FIX return *this; } inline doubledouble& doubledouble::operator *=(const double& y ) { x86_FIX double hx, tx, hy, ty, C, c; C = Split*hi; hx = C-hi; c = Split*y; hx = C-hx; tx = hi-hx; hy = c-y; C = hi*y; hy = c-hy; ty = y-hy; c = ((((hx*hy-C)+hx*ty)+tx*hy)+tx*ty)+(lo*y); hx = C+c; hi = hx; lo = c+double(C-hx); END_x86_FIX return *this; } inline doubledouble& doubledouble::operator *=(const int y ) { return *this *= double(y); } //////////////////////////////////////////////////////////////// ////////////////////////// Division ////////////////////////// //////////////////////////////////////////////////////////////// // Reciprocal inline doubledouble recip(const doubledouble& y) { x86_FIX double hc, tc, hy, ty, C, c, U, u; C = 1.0/y.h(); c = doubledouble::Split*C; hc =c-C; u = doubledouble::Split*y.h(); hc = c-hc; tc = C-hc; hy = u-y.h(); U = C*y.h(); hy = u-hy; ty = y.h()-hy; u = (((hc*hy-U)+hc*ty)+tc*hy)+tc*ty; c = ((((1.0-U)-u))-C*y.l())/y.h(); doubledouble z; z.hi = C+c; z.lo = double(C-z.hi)+c; END_x86_FIX return z; } inline doubledouble operator /(const doubledouble& x,const doubledouble& y ) { x86_FIX double hc, tc, hy, ty, C, c, U, u; C = x.hi/y.hi; c = doubledouble::Split*C; hc =c-C; u = doubledouble::Split*y.hi; hc = c-hc; tc = C-hc; hy = u-y.hi; U = C * y.hi; hy = u-hy; ty = y.hi-hy; u = (((hc*hy-U)+hc*ty)+tc*hy)+tc*ty; c = ((((x.hi-U)-u)+x.lo)-C*y.lo)/y.hi; doubledouble z; z.hi = C+c; z.lo = double(C-z.hi)+c; END_x86_FIX return z; } // double/doubledouble: inline doubledouble operator /(const double& x,const doubledouble& y ) { x86_FIX double hc, tc, hy, ty, C, c, U, u; C = x/y.hi; c = doubledouble::Split*C; hc =c-C; u = doubledouble::Split*y.hi; hc = c-hc; tc = C-hc; hy = u-y.hi; U = C*y.hi; hy = u-hy; ty = y.hi-hy; u = (((hc*hy-U)+hc*ty)+tc*hy)+tc*ty; c = ((((x-U)-u))-C*y.lo)/y.hi; doubledouble z; z.hi = C+c; z.lo = double(C-z.hi)+c; END_x86_FIX return z; } inline doubledouble operator /(const doubledouble& x,const double& y ) { x86_FIX double hc, tc, hy, ty, C, c, U, u; C = x.hi/y; c = doubledouble::Split*C; hc = c-C; u = doubledouble::Split*y; hc = c-hc; tc = C-hc; hy = u-y; U = C*y; hy = u-hy; ty = y-hy; u = (((hc*hy-U)+hc*ty)+tc*hy)+tc*ty; c = (((x.hi-U)-u)+x.lo)/y; doubledouble z; z.hi = C+c; z.lo = double(C-z.hi)+c; END_x86_FIX return z; } // doubledouble/int inline doubledouble operator /(const doubledouble& x, const int y) { return x/double(y); } inline doubledouble operator /(const int x, const doubledouble& y) { return double(x)/y; } // Self-division. inline doubledouble& doubledouble::operator /=(const doubledouble& y) { x86_FIX double hc, tc, hy, ty, C, c, U, u; C = hi/y.hi; c = Split*C; hc =c-C; u = Split*y.hi; hc = c-hc; tc = C-hc; hy = u-y.hi; U = C * y.hi; hy = u-hy; ty = y.hi-hy; u = (((hc*hy-U)+hc*ty)+tc*hy)+tc*ty; c = ((((hi-U)-u)+lo)-C*y.lo)/y.hi; u = C+c; hi = u; lo = double(C-u)+c; END_x86_FIX return *this; } inline doubledouble& doubledouble::operator /=(const double& y) { x86_FIX double hc, tc, hy, ty, C, c, U, u; C = hi/y; c = Split*C; hc =c-C; u = Split*y; hc = c-hc; tc = C-hc; hy = u-y; U = C * y; hy = u-hy; ty = y-hy; u = (((hc*hy-U)+hc*ty)+tc*hy)+tc*ty; c = (((hi-U)-u)+lo)/y; u = C+c; hi = u; lo = double(C-u)+c; END_x86_FIX return *this; } inline doubledouble& doubledouble::operator /=(const int y) { return *this/=double(y); } |-> cc/doubledouble.cc // doubledouble.cc // KMB 98 Jan 19 /* Copyright (C) 1997 Keith Martin Briggs Except where otherwise indicated, this program 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 of the License, or (at your option) any later version. This program 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 this program; if not, write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. */ #include "doubledouble.h" #include #include // member constants const double doubledouble::Split = 134217729.0L; // 2^27+1, for IEEE double const doubledouble doubledouble::Log2 ="0.6931471805599453094172321214581765680755"; const doubledouble doubledouble::Log10="2.302585092994045684017991454684364207601"; const doubledouble doubledouble::Pi ="3.1415926535897932384626433832795028841972"; const doubledouble doubledouble::TwoPi="6.2831853071795864769252867665590057683943"; const doubledouble doubledouble::Pion2="1.5707963267948966192313216916397514420985"; const doubledouble doubledouble::Pion4="0.7853981633974483096156608458198757210493"; const doubledouble doubledouble::_Pi ="0.3183098861837906715377675267450287240689"; void base_and_prec(void) { // Linnainmaa ACM TOMS 7, 272 Thm 3 int p; x86_FIX cerr<<"Base and precision determination by Linnainmaa's method:"<=0.0) return fabs(x); else return -fabs(x); } doubledouble atodd(const char *s) { doubledouble result = 0; int n, sign, ex = 0; /* eat whitespace */ while (*s == ' ' || *s == '\t' || *s == '\n') s++; switch (*s) { // get sign of mantissa case '-': { sign = -1; s++; break; } case '+': s++; // no break default: sign = 1; } /* get digits before decimal point */ while (n=(*s++)-'0', n>=0 && n<10) result = 10.0*result+n; s--; if (*s == '.') /* get digits after decimal point */ { s++; while (n=(*s++)-'0', n>=0 && n<10) { result = 10.0*result+n; --ex; } s--; } if (*s == 'e' || *s == 'E') /* get exponent */ ex+=atoi(++s); /* exponent adjustment */ // cerr<<"atodd: result="<> (istream& s, doubledouble& x){ doubledouble result=0.0; int n, sign=1, ex=0; char ch; s>>ws; // eat whitespace s>>ch; if (ch=='-') { sign = -1; s>>ch; } else if (ch=='+') { s>>ch; } // get digits before decimal point n=ch-'0'; while (n>=0 && n<10) { result = 10*result+n; s.get(ch); // cannot use s>>ch; as that will eat whitespace if (ch == ' ' || ch == '\t' || ch == '\n') goto fixup; n=ch-'0'; } if (ch=='.') { // get digits after decimal point s>>ch; n=ch-'0'; while (n>=0 && n<10) { result = 10*result+n; s.get(ch); n=ch-'0'; --ex; if (ch == ' ' || ch == '\t' || ch == '\n') goto fixup; } } n=0; if (ch == 'e' || ch == 'E') { s>>n; ex+=n; } // get exponent else s.putback(ch); fixup: if (sign<0) result = -result; // exponent adjustment while (ex-- > 0) result *= 10; while (++ex < 0) result /= 10; x = result; return s; } // output ostream& operator << (ostream& s, const doubledouble& x){ if (x.h()==0.0) { s << "0.0 "; return s; } if (x.h()!=x.h()) { s << "NaN "; return s; } int Digits=s.precision(); doubledouble ten=10.0,y=fabs(x); double q=log10(y.h()); int m,n=int(floor(q)); if (n<0) n++; doubledouble l = powint(ten,n); y = y/l; if (sign(x)<0) s<<"-"; //else s<<" "; int d = Digits>34 ? 34 : Digits; d = d<3 ? 3 : d; for (int i=1; i<=d; i++) { if (2==i) s<<"."; m = int(floor(y)); if (m<0 || m>9) { cerr<<"Internal error in doubledouble.cc: digit="<=0.0) return floor(x); else return -floor(-x); } doubledouble fmod(const doubledouble& x, const int n) { return x-n*floor(x/n); } /* Same as the ANSI modf for doubles. ** BEWARE: contains ugly, magical code */ doubledouble modf(const doubledouble &D, doubledouble *id) { int sign=1; doubledouble qFrac, d = D; double lowFrac, highFrac, lowInt, highInt; if (d < doubledouble(0)) { sign = -1; d = -d; } if (d < doubledouble(1)) { /* it's all fraction, no integer */ *id = 0; return sign*d; } if (d + 1 == d) { /* It's all integer, no fraction */ *id = sign*d; return 0.0; } highFrac = modf(d.h(), &highInt); lowFrac = modf(d.l(), &lowInt); /* special case: if d.l is opposite in sign to d.h, then adding them ** together changes the integer part. */ if (highInt == d.h() && d.l() < 0) { #if 1 if (lowFrac != 0) { *id = doubledouble(highInt) + doubledouble(lowInt) - 1; qFrac = 1 + doubledouble(lowFrac); } else { qFrac = lowFrac; *id = doubledouble(highInt) + doubledouble(lowInt); } #else /* loop method, slow but should work */ *id = 0; top = QUAD_BITS; while (1) { /* Invariant: *id <= d */ if (!(*id <= d)) printf("Oops, !(*id <= d): %f %f\n\n", *id, d); if (d < *id + 1) break; for(i = top-1; i >= 0 && (*id + ldexp(1.,i) > d); i--) ; *id += ldexp(1.,i); top = i; } *id *= sign; qFrac = d - sign*(*id); printf("loop Int = %.16g %.16g, frac = %.16g %.16g\n", id->h, id->l, qFrac.h, qFrac.l); #endif } else { *id = doubledouble(highInt) + doubledouble(lowInt); qFrac = doubledouble(highFrac) + doubledouble(lowFrac); } if (sign == -1) { *id = -*id; return -qFrac; } else return qFrac; } // Signum int sign(const doubledouble& x){ if (x.h()>0.0) return 1; else if (x.h()<0.0) return -1; else return 0; } // Comparison bool operator> (const doubledouble& x, const doubledouble& y) { return (x.h()> y.h()) || (x.h()==y.h() && x.l()> y.l()); } bool operator>=(const doubledouble& x, const doubledouble& y) { return (x.h()>y.h()) || (x.h()==y.h() && x.l()>=y.l()); } bool operator< (const doubledouble& x, const doubledouble& y) { return (x.h()< y.h()) || (x.h()==y.h() && x.l()< y.l()); } bool operator<=(const doubledouble& x, const doubledouble& y) { return (x.h() #include #include #define MAX_STRING 512 /* reasonable size for string to hold a doubledouble */ /* * Define FLOATING_POINT to get floating point. */ #define FLOATING_POINT /* end of configuration stuff */ #ifdef FLOATING_POINT #define BUF (MAXEXP+MAXFRACT+1) /* + decimal point */ #define DEFPREC 6 #else /* no FLOATING_POINT */ #define BUF 40 #endif /* FLOATING_POINT */ /* 11-bit exponent (VAX G floating point) is 308 decimal digits */ #define MAXEXP 308 /* 128 bit fraction takes up 39 decimal digits; max reasonable precision */ #define MAXFRACT 39 /* * Copyright (c) 1990 Regents of the University of California. * All rights reserved. * * Redistribution and use in source and binary forms are permitted * provided that the above copyright notice and this paragraph are * duplicated in all such forms and that any documentation, * advertising materials, and other materials related to such * distribution and use acknowledge that the software was developed * by the University of California, Berkeley. The name of the * University may not be used to endorse or promote products derived * from this software without specific prior written permission. * THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR * IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. */ /* * Actual printf innards. * * This code is large and complicated... */ /* * Macros for converting digits to letters and vice versa */ #define to_digit(c) ((c) - '0') #define is_digit(c) ((unsigned)to_digit(c) <= 9) #define to_char(n) ((n) + '0') inline int dd_to_char(doubledouble n) { return '0' + (int)n;} /* * Flags used during conversion. */ #define LONGINT 0x01 /* long integer */ #define LONGDBL 0x02 /* long doubledouble; unimplemented */ #define SHORTINT 0x04 /* short integer */ #define ALT 0x08 /* alternate form */ #define LADJUST 0x10 /* left adjustment */ #define ZEROPAD 0x20 /* zero (as opposed to blank) pad */ #define HEXPREFIX 0x40 /* add 0x or 0X prefix */ static char *exponent(register char *p, register int exp, int fmtch) { register char *t; char expbuf[MAXEXP]; *p++ = fmtch; if (exp < 0) { exp = -exp; *p++ = '-'; } else *p++ = '+'; t = expbuf + MAXEXP; if (exp > 9) { do { *--t = to_char(exp % 10); } while ((exp /= 10) > 9); *--t = to_char(exp); for (; t < expbuf + MAXEXP; *p++ = *t++); } else { *p++ = '0'; *p++ = to_char(exp); } return (p); } static char * round(doubledouble fract, int *exp, register char *start, register char *end, char ch, int *signp) { doubledouble tmp; if (fract != doubledouble(0)) (void)modf(fract * 10, &tmp); else tmp = to_digit(ch); if (tmp > doubledouble(4)) for (;; --end) { if (*end == '.') --end; if (++*end <= '9') break; *end = '0'; if (end == start) { if (exp) { /* e/E; increment exponent */ *end = '1'; ++*exp; } else { /* f; add extra digit */ *--end = '1'; --start; } break; } } /* ``"%.3f", (doubledouble)-0.0004'' gives you a negative 0. */ else if (*signp == '-') for (;; --end) { if (*end == '.') --end; if (*end != '0') break; if (end == start) *signp = 0; } return (start); } int __cvt_doubledouble(doubledouble number, register int prec, int flags, int *signp, int fmtch, char *startp, char *endp) { register char *p, *t; doubledouble fract; int dotrim = 0, expcnt, gformat = 0; doubledouble integer, tmp; expcnt = 0; if (number < doubledouble(0)) { number = -number; *signp = '-'; } else *signp = 0; fract = modf(number, &integer); /* get an extra slot for rounding. */ t = ++startp; /* * get integer portion of number; put into the end of the buffer; the * .01 is added for modf(356.0 / 10, &integer) returning .59999999... */ for (p = endp - 1; integer != doubledouble(0); ++expcnt) { tmp = modf(integer / 10, &integer); *p-- = to_char((int)((tmp + .01) * 10)); } switch (fmtch) { case 'f': case 'F': /* reverse integer into beginning of buffer */ if (expcnt) for (; ++p < endp; *t++ = *p); else *t++ = '0'; /* * if precision required or alternate flag set, add in a * decimal point. */ if (prec || flags&ALT) *t++ = '.'; /* if requires more precision and some fraction left */ if (fract != doubledouble(0)) { if (prec) do { fract = modf(fract * 10, &tmp); *t++ = dd_to_char(tmp); } while (--prec && fract != doubledouble(0)); if (fract != doubledouble(0)) startp = round(fract, (int *)NULL, startp, t - 1, (char)0, signp); } for (; prec--; *t++ = '0'); break; case 'e': case 'E': eformat: if (expcnt) { *t++ = *++p; if (prec || flags&ALT) *t++ = '.'; /* if requires more precision and some integer left */ for (; prec && ++p < endp; --prec) *t++ = *p; /* * if done precision and more of the integer component, * round using it; adjust fract so we don't re-round * later. */ if (!prec && ++p < endp) { fract = 0; startp = round((doubledouble)0, &expcnt, startp, t - 1, *p, signp); } /* adjust expcnt for digit in front of decimal */ --expcnt; } /* until first fractional digit, decrement exponent */ else if (fract != doubledouble(0)) { /* adjust expcnt for digit in front of decimal */ for (expcnt = -1;; --expcnt) { fract = modf(fract * 10, &tmp); if (tmp != doubledouble(0)) break; } *t++ = dd_to_char(tmp); if (prec || flags&ALT) *t++ = '.'; } else { *t++ = '0'; if (prec || flags&ALT) *t++ = '.'; } /* if requires more precision and some fraction left */ if (fract != doubledouble(0)) { if (prec) do { fract = modf(fract * 10, &tmp); *t++ = dd_to_char(tmp); } while (--prec && fract != doubledouble(0)); if (fract != doubledouble(0)) startp = round(fract, &expcnt, startp, t - 1, (char)0, signp); } /* if requires more precision */ for (; prec--; *t++ = '0'); /* unless alternate flag, trim any g/G format trailing 0's */ if (gformat && !(flags&ALT)) { while (t > startp && *--t == '0'); if (*t == '.') --t; ++t; } t = exponent(t, expcnt, fmtch); break; case 'g': case 'G': /* a precision of 0 is treated as a precision of 1. */ if (!prec) ++prec; /* * ``The style used depends on the value converted; style e * will be used only if the exponent resulting from the * conversion is less than -4 or greater than the precision.'' * -- ANSI X3J11 */ if (expcnt > prec || (!expcnt && fract != doubledouble(0) && fract < doubledouble(0.0001))) { /* * g/G format counts "significant digits, not digits of * precision; for the e/E format, this just causes an * off-by-one problem, i.e. g/G considers the digit * before the decimal point significant and e/E doesn't * count it as precision. */ --prec; fmtch -= 2; /* G->E, g->e */ gformat = 1; goto eformat; } /* * reverse integer into beginning of buffer, * note, decrement precision */ if (expcnt) for (; ++p < endp; *t++ = *p, --prec); else *t++ = '0'; /* * if precision required or alternate flag set, add in a * decimal point. If no digits yet, add in leading 0. */ if (prec || flags&ALT) { dotrim = 1; *t++ = '.'; } else dotrim = 0; /* if requires more precision and some fraction left */ if (fract != doubledouble(0)) { if (prec) { /* If no integer part, don't count initial * zeros as significant digits. */ do { fract = modf(fract * 10, &tmp); *t++ = dd_to_char(tmp); } while(tmp == doubledouble(0) && !expcnt); while (--prec && fract != doubledouble(0)) { fract = modf(fract * 10, &tmp); *t++ = dd_to_char(tmp); } } if (fract != doubledouble(0)) startp = round(fract, (int *)NULL, startp, t - 1, (char)0, signp); } /* alternate format, adds 0's for precision, else trim 0's */ if (flags&ALT) for (; prec--; *t++ = '0'); else if (dotrim) { while (t > startp && *--t == '0'); if (*t != '.') ++t; } } return (t - startp); } /* ** From here down is not UCB code, it's Wayne Hayes code. ** ** Convert doubledouble to ASCII. 'word' should be no less than prec+8 long. */ char *qtoa(char *Word, int prec, int fmtch, doubledouble q) { int flags = 0, sign_char; static char buf[MAX_STRING], *word; word = buf; *word = '\0'; prec = __cvt_doubledouble(q, prec, flags, &sign_char, fmtch, buf, buf+sizeof(buf)); if (sign_char) word[0] = sign_char, prec++; if (word[0] == '\0') word++; word[prec] = '\0'; if (Word) return strcpy(Word, word); else return word; } |-> cc/math.cc // math.cc // KMB 98 Feb 03 /* Copyright (C) 1997 Keith Martin Briggs Except where otherwise indicated, this program 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 of the License, or (at your option) any later version. This program 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 this program; if not, write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. */ #include "doubledouble.h" #include #include ifelse(UNAME,Openstep,`#include', `ifelse(UNAME,Linux,`#include',`#include')') #include doubledouble exp(const doubledouble& x) { /* Uses some ideas by Alan Miller Method: x x.log2(e) nint[x.log2(e)] + frac[x.log2(e)] e = 2 = 2 iy fy = 2 . 2 Then fy y.loge(2) 2 = e Now y.loge(2) will be less than 0.3466 in absolute value. This is halved and a Pade' approximant is used to approximate e^x over the region (-0.1733, +0.1733). This approximation is then squared. */ if (x.h()<-744.4400719213812) return 0.0; // exp(x)<1e-300 int iy; doubledouble y,temp,ysq,sum1,sum2; y=x/doubledouble::Log2; temp=iy=rint(y); y=(y-temp)*doubledouble::Log2; y=ldexp(y,-1); ysq=sqr(y); sum1=y*((((ysq+3960.)*ysq+2162160.)*ysq+302702400.)*ysq+8821612800.); sum2=(((90.*ysq+110880.)*ysq+30270240.)*ysq+2075673600.)*ysq+17643225600.; /* sum2 + sum1 2.sum1 Now approximation = ----------- = 1 + ----------- = 1 + 2.temp sum2 - sum1 sum2 - sum1 Then (1 + 2.temp)^2 = 4.temp.(1 + temp) + 1 */ temp=sum1/(sum2-sum1); y=temp*(temp+1); y=ldexp(y,2); return ldexp(y+1,iy); } // See Higham "Accuracy and Stability of Numerical Algorithms", p 511 doubledouble hypot(const doubledouble a, const doubledouble b) { doubledouble p,q,r,s,aa,ab,four=4.0; aa=fabs(a); ab=fabs(b); if (aa>ab) { p=aa; q=ab; } else { q=aa; p=ab; } // now p>=q if (0.0==p.h()) return q; while (1) { r=sqr(q/p); if (four==(aa=r+four)) return p; s=r/aa; p+=2*s*p; q*=s; } // Never get here } // square root doubledouble sqrt(const doubledouble& y) { x86_FIX double c,p,q,hx,tx,u,uu,cc,hi=y.h(); if (hi<0.0) { cerr << "\ndoubledouble: attempt to take sqrt of " << hi << endl; DOMAIN_ERROR; } if (0.0==hi) return y; c=sqrt(hi); p=doubledouble::Split*c; hx=c-p; hx+=p; tx=c-hx; p=hx*hx; q=2.0*hx*tx; u=p+q; uu=(p-u)+q+tx*tx; cc=(((y.h()-u)-uu)+y.l())/(c+c); u=c+cc; doubledouble r=doubledouble(u,cc+(c-u)); END_x86_FIX return r; } // Natural logarithm doubledouble log(const doubledouble& x) { // Newton method if (x.h()<0.0) { cerr<<"\ndoubledouble: attempt to take log of negative argument!\n"; DOMAIN_ERROR; } if (x.h()==0.0) { cerr<<"\ndoubledouble: attempt to take log(0)!\n"; DOMAIN_ERROR; } doubledouble s=log(x.h()), e=exp(s); // s=double approximation to result return s+(x-e)/e; // Newton correction, good enough //doubledouble d=(x-e)/e; return s+d-0.5*sqr(d); // or 2nd order correction } // logarithm base 10 doubledouble log10(const doubledouble& t) { static const doubledouble one_on_log10="0.4342944819032518276511289189166050822944"; return one_on_log10*log(t); } // doubledouble^doubledouble doubledouble pow(const doubledouble& a, const doubledouble& b) { return exp(b*log(a)); } // doubledouble^int doubledouble powint(const doubledouble& u, const int c) { if (c<0) return recip(powint(u,-c)); switch (c) { case 0: return u.h()==0.0?doubledouble(pow(0.0,0.0)):doubledouble(1.0); // let math.h handle 0^0. case 1: return u; case 2: return sqr(u); case 3: return sqr(u)*u; default: { // binary method int n=c, m; doubledouble y=1.0, z=u; if (n<0) n=-n; while (1) { m=n; n/=2; if (n+n!=m) { // if m odd y*=z; if (0==n) return y; } z=sqr(z); } } } } // Like Miller's modr // a=n*b+rem, |rem|<=b/2, exact result. doubledouble modr(const doubledouble a, const doubledouble b, int& n, doubledouble& rem) { if (0.0==b.h()) { cerr<<"\ndoubledouble: divisor is zero in modr!\n"; DOMAIN_ERROR; } doubledouble temp; temp=a/b; n=int(rint(temp.h())); temp=n*doubledouble(b.h()); rem=doubledouble(a.h()); temp=rem-temp; rem=doubledouble(a.l()); temp=rem+temp; rem=n*doubledouble(b.l()); rem=temp-rem; return rem; } doubledouble sin(const doubledouble& x) { static const doubledouble tab[9]={ // tab[b] := sin(b*Pi/16)... 0.0, "0.1950903220161282678482848684770222409277", "0.3826834323650897717284599840303988667613", "0.5555702330196022247428308139485328743749", "0.7071067811865475244008443621048490392850", "0.8314696123025452370787883776179057567386", "0.9238795325112867561281831893967882868225", "0.9807852804032304491261822361342390369739", 1.0 }; static const doubledouble sinsTab[7] = { // Chebyshev coefficients "0.9999999999999999999999999999993767021096", "-0.1666666666666666666666666602899977158461", "8333333333333333333322459353395394180616.0e-42", "-1984126984126984056685882073709830240680.0e-43", "2755731922396443936999523827282063607870.0e-45", "-2505210805220830174499424295197047025509.0e-47", "1605649194713006247696761143618673476113.0e-49" }; if (fabs(x.h())<1.0e-7) return x*(1.0-sqr(x)/3); int a,b; doubledouble sins, coss, k1, k3, t2, s, s2, sinb, cosb; // reduce x: -Pi < x <= Pi k1=x/doubledouble::TwoPi; k3=k1-rint(k1); // determine integers a and b to minimize |s|, where s=x-a*Pi/2-b*Pi/16 t2=4*k3; a=int(rint(t2)); b=int(rint((8*(t2-a)))); // must have |a|<=2 and |b|<=7 now s=doubledouble::Pi*(k3+k3-(8*a+b)/16.0); // s is now reduced argument. -Pi/32 < s < Pi/32 s2=sqr(s); // Chebyshev series on -Pi/32..Pi/32, max abs error 2^-98=3.16e-30, whereas // power series has error 6e-28 at Pi/32 with terms up to x^13 included. sins=s*(sinsTab[0]+(sinsTab[1]+(sinsTab[2]+(sinsTab[3]+(sinsTab[4]+ (sinsTab[5]+sinsTab[6]*s2)*s2)*s2)*s2)*s2)*s2); coss=sqrt(1.0-sqr(sins)); // ok as -Pi/32 < s < Pi/32 // here sinb=sin(b*Pi/16) etc. sinb= (b>=0) ? tab[b] : -tab[-b]; cosb=tab[8-abs(b)]; if (0==a) { return sins*cosb+coss*sinb; } else if (1==a) { return -sins*sinb+coss*cosb; } else if (-1==a) { return sins*sinb-coss*cosb; } else { // |a|=2 return -sins*cosb-coss*sinb; } // i.e. return sins*(cosa*cosb-sina*sinb)+coss*(sina*cosb+cosa*sinb); } // sin and cos. Faster than separate calls of sin and cos. void sincos(const doubledouble x, doubledouble& sinx, doubledouble& cosx) { static const doubledouble tab[9]={ // tab[b] := sin(b*Pi/16)... 0.0, "0.1950903220161282678482848684770222409277", "0.3826834323650897717284599840303988667613", "0.5555702330196022247428308139485328743749", "0.7071067811865475244008443621048490392850", "0.8314696123025452370787883776179057567386", "0.9238795325112867561281831893967882868225", "0.9807852804032304491261822361342390369739", 1.0 }; static const doubledouble sinsTab[7] = { // Chebyshev coefficients "0.9999999999999999999999999999993767021096", "-0.1666666666666666666666666602899977158461", "8333333333333333333322459353395394180616.0e-42", "-1984126984126984056685882073709830240680.0e-43", "2755731922396443936999523827282063607870.0e-45", "-2505210805220830174499424295197047025509.0e-47", "1605649194713006247696761143618673476113.0e-49" }; if (fabs(x.h())<1.0e-11) { sinx=x; cosx=1.0-0.5*sqr(x); return; } int a,b; doubledouble sins, coss, k1, k3, t2, s, s2, sinb, cosb; k1=x/doubledouble::TwoPi; k3=k1-rint(k1); t2=4*k3; a=int(rint(t2)); b=int(rint((8*(t2-a)))); s=doubledouble::Pi*(k3+k3-(8*a+b)/16.0); s2=sqr(s); sins=s*(sinsTab[0]+(sinsTab[1]+(sinsTab[2]+(sinsTab[3]+(sinsTab[4]+ (sinsTab[5]+sinsTab[6]*s2)*s2)*s2)*s2)*s2)*s2); coss=sqrt(1.0-sqr(sins)); // ok, sins is small sinb= (b>=0) ? tab[b] : -tab[-b]; cosb=tab[8-abs(b)]; // sin(x)= // sin(s)(cos(1/2 a Pi) cos(1/16 b Pi) - sin(1/2 a Pi) sin(1/16 b Pi)) // cos(s)(sin(1/2 a Pi) cos(1/16 b Pi) + cos(1/2 a Pi) sin(1/16 b Pi)) // cos(x)= // cos(s)(cos(1/2 a Pi) cos(1/16 b Pi) - sin(1/2 a Pi) sin(1/16 b Pi)) //-sin(s)(sin(1/2 a Pi) cos(1/16 b Pi) + cos(1/2 a Pi) sin(1/16 b Pi)) if (0==a) { sinx= sins*cosb+coss*sinb; cosx= coss*cosb-sins*sinb; } else if (1==a) { sinx=-sins*sinb+coss*cosb; cosx=-coss*sinb-sins*cosb; } else if (-1==a) { sinx= sins*sinb-coss*cosb; cosx= coss*sinb+sins*cosb; } else { // |a|=2 sinx=-sins*cosb-coss*sinb; cosx=-coss*cosb+sins*sinb; } return; } // cos doubledouble cos(const doubledouble& x) { return sin(doubledouble::Pion2-x); } // hyperbolic doubledouble sinh(const doubledouble& x) { if (fabs(x.h())<1.0e-5) { // avoid cancellation in e^x-e^(-x), use Taylor series... doubledouble q=sqr(x); return x*(1+q/6*(1+q/20*(1+q/42))); } doubledouble t=exp(x); return 0.5*(t-recip(t)); } doubledouble cosh(const doubledouble& x) { doubledouble t=exp(x); return 0.5*(t+recip(t)); } doubledouble tanh(const doubledouble& z) { doubledouble e; if (z.h()>0.0) { e=exp(-2.0*z); return (1.0-e)/(1.0+e); } else { e=exp( 2.0*z); return (e-1.0)/(1.0+e); } } doubledouble atan(const doubledouble& x) { double xh=x.h(); if (0.0==xh) return doubledouble(0.0); // Asymptotic formula for large |x|... if (fabs(xh)>1.0e6) { doubledouble r=recip(x), r2=sqr(r); return doubledouble::Pion2-r+r2*r*(1.0-"0.6"*r2)/3; } doubledouble s,c,a=atan(xh); // a=double approx to result sincos(a,s,c); return a+c*(c*x-s); // Newton step } /* doubledouble atan2(const doubledouble& qy, const doubledouble& qx) { // Based on GNU libc atan2.c static const double one=1.0, zero=0.0; double x, y; x=qx.h(); y=qy.h(); double signx, signy; if (x!=x) return qx; // x=NaN if (y!=y) return qy; signy=copysign(one,y); signx=copysign(one,x); if (y==zero) return signx==one ? qy : Qcopysign(doubledouble::Pi,signy); if (x==zero) return Qcopysign(doubledouble::Pion2,signy); if (__isinf(x)) { if (__isinf(y)) return Qcopysign(signx==one ? doubledouble::Pion4 : 3.0*doubledouble::Pion4,signy); else return Qcopysign(signx==one ? doubledouble(0.0) : doubledouble::Pi,signy); } if (__isinf(y)) return Qcopysign(doubledouble::Pion2,signy); doubledouble aqy=fabs(qy); if (x<0.0) // X is negative. return Qcopysign(doubledouble::Pi-atan(aqy/(-qx)),signy); return Qcopysign(atan(aqy/qx),signy); } */ // arcsin /* doubledouble asin(const doubledouble& x) { if (fabs(x)>doubledouble(1.0)) { cerr<<"\ndoubledouble |Argument|>1 in asin!\n"; DOMAIN_ERROR; } return atan2(x,sqrt(1.0-sqr(x))); } */ // KMB 96 Oct 28 version 0.3 97 Dec 22 OK now. // erfc written 97 Dec 22, NOT CHECKED!!!!!!! // Based on series and continued fraction for incomplete gamma function. doubledouble erf(const doubledouble x) { if (0.0==x.h()) return 0.0; int i; doubledouble y,r; // const below is evalf(1/sqrt(Pi),40) static const doubledouble oneonrootpi="0.564189583547756286948079451560772585844"; const double cut=1.5; // switch to continued fraction here y=fabs(x); if (y.h()>26.0) { // erf is +or- 1 to 300 dp. r=1; } else if (y.h()199) { cerr<<"\ndoubledouble: no convergence in erf power series, x="<=cut, use continued fraction, Lentz method double an,small=1e-300; doubledouble b,c,d,h,del,x2; x2=sqr(x); b=x2+0.5; c=1.0e300; d=recip(b); h=d; for (i=1; i<300; i++) { an=i*(0.5-i); b+=2.0; d=an*d+b; if (fabs(d.h())199) { cerr<<"\ndoubledouble: no convergence in erfc power series, x="<=cut, use continued fraction double an,small=1e-300; doubledouble b,c,d,h,del,x2; x2=sqr(x); b=x2+0.5; c=1e300; h=d=recip(b); for (i=1; i<300; i++) { an=i*(0.5-i); b+=2.0; d=an*d+b; if (fabs(d.h())one) { ss-=1; f*=ss; } while (ss=0; i--) sum=c[i]+ss*sum; return f/(ss*sum+1); } // end of math.cc |-> inc/nauty.h /***************************************************************************** /* This is the header file for Version 1.9+ of nauty(). * *****************************************************************************/ #ifndef NAUTYH_READ /* only process this file once */ #include /* Exactly one of the symbols with names starting with "SYS_" should have the value 1. All the others should have the value 0. */ #define SYS_VAXBSD 0 /* older BSD unix 4.2 on a VAX */ #define SYS_CRAY 0 /* Cray UNIX, portable or standard C */ #define SYS_APOLLO 0 /* DOMAIN C on Apollo */ #define SYS_BSDUNIX 0 /* other BSD unix (cc or gcc compilers) */ #define SYS_UNIX 1 /* miscellaneous non-BSD unix, including A/UX */ #define SYS_ALPHA 0 /* Alpha UNIX */ #define SYS_VAXVMS 0 /* VAX11C or GCC on a VAX under VMS */ #define SYS_MACLSC 0 /* Lightspeed C on an Apple Macintosh (Version 1) */ #define SYS_MACTHINK 0 /* THINK C on an Apple Macintosh (Version 4) */ #define SYS_MACAZT 0 /* Aztec C on an Apple Macintosh */ #define SYS_MACMPW 0 /* Apple Macintosh Workshop C */ #define SYS_AMIGALC 0 /* Lattice C on a Commodore Amiga */ #define SYS_AMIGAAZT 0 /* Aztec C on a Commodore Amiga */ #define SYS_PCMS4 0 /* Microsoft C 4.0 on IBM PC */ #define SYS_PCMS5 0 /* Microsoft C 5.1 or Quick C 2.5 on IBM PC */ #define SYS_PCTURBO 0 /* Turbo C on IBM PC */ #define SYS_IBMC 0 /* IBM C Set/2 under OS/2 */ #define SYS_MISC 0 /* anything else */ /***************************************************************************** * * * AUTHOR: Brendan D. McKay * * Computer Science Department, Australian National University, * * GPO Box 4, Canberra, Australia 0200 * * phone: +61 6 249 3845 fax: +61 6 249 0010 * * email: bdm@cs.anu.edu.au * * * * Copyright (1984-1993) Brendan McKay. All rights reserved. Permission * * is hereby given for use and/or distribution with the exception of * * sale for profit or application with nontrivial military significance. * * You must not remove this copyright notice, and you must document any * * changes that you make to this program. * * This software is subject to this copyright only, irrespective of * * any copyright attached to any package of which this is a part. * * * * This program is only provided "as is". No responsibility will be taken * * by the author, his employer or his pet rabbit* for any misfortune which * * befalls you because of its use. I don't think it will delete all your * * files, burn down your computer room or turn your children against you, * * but if it does: stiff cheddar. On the other hand, I very much welcome * * bug reports, or at least I would if there were any bugs. * * * RIP, 1989 * * * * If you wish to acknowledge use of this program in published articles, * * please do so by citing the User's Guide: * * * * B. D. McKay, nauty User's Guide (Version 1.5), Technical Report * * TR-CS-90-02, Australian National University, Department of * * Computer Science, 1990. * * * * CHANGE HISTORY * * 10-Nov-87 : final changes for version 1.2 * * 5-Dec-87 : renamed to version 1.3 (no changes to this file) * * 28-Sep-88 : added PC Turbo C support, making version 1.4 * * 23-Mar-89 : changes for version 1.5 : * * - reworked M==1 code * * - defined NAUTYVERSION string * * - made NAUTYH_READ to allow this file to be read twice * * - added optional ANSI function prototypes * * - added validity check for WORDSIZE * * - added new fields to optionblk structure * * - updated DEFAULTOPTIONS to add invariants fields * * - added (set*) cast to definition of GRAPHROW * * - added definition of ALLOCS and FREES * * 25-Mar-89 : - added declaration of new function doref() * * - added UNION macro * * 29-Mar-89 : - reduced the default MAXN for small machines * * - removed OUTOFSPACE (no longer used) * * - added SETDIFF and XOR macros * * 2-Apr-89 : - extended statsblk structure * * 4-Apr-89 : - added IS_* macros * * - added ERRFILE definition * * - replaced statsblk.outofspace by statsblk.errstatus * * 5-Apr-89 : - deleted definition of np2vector (no longer used) * * - introduced EMPTYSET macro * * 12-Apr-89 : - eliminated MARK, UNMARK and ISMARKED (no longer used) * * 18-Apr-89 : - added MTOOBIG and CANONGNIL * * 12-May-89 : - made ISELEM1 and ISELEMENT return 0 or 1 * * 2-Mar-90 : - added EXTPROC macro and used it * * 12-Mar-90 : - added SYS_CRAY, with help from N. Sloane and A. Grosky * * - added dummy groupopts field to optionblk * * - select some ANSI things if __STDC__ exists * * 20-Mar-90 : - changed default MAXN for Macintosh versions * * - created SYS_MACTHINK for Macintosh THINK compiler * * 27-Mar-90 : - split SYS_MSDOS into SYS_PCMS4 and SYS_PCMS5 * * 13-Oct-90 : changes for version 1.6: * * - fix definition of setword for WORDSIZE==64 * * 14-Oct-90 : - added SYS_APOLLO version to avoid compiler bug * * 15-Oct-90 : - improve detection of ANSI conformance * * 17-Oct-90 : - changed temp name in EMPTYSET to avoid A/UX bug * * 16-Apr-91 : changes for version 1.7: * * - made version SYS_PCTURBO use free(), not cfree() * * 2-Sep-91 : - noted that SYS_PCMS5 also works for Quick C * * - moved MULTIPLY to here from nauty.c * * 12-Jun-92 : - changed the top part of this comment * * 27-Aug-92 : - added version SYS_IBMC, thanks to Ivo Duentsch * * 5-Jun-93 : - renamed to version 1.7+, only change in naututil.h * * 29-Jul-93 : changes for version 1.8: * * - fixed error in default 64-bit version of FIRSTBIT * * (not used in any version before ALPHA) * * - installed ALPHA version (thanks to Gordon Royle) * * - defined ALLOCS,FREES for SYS_IBMC * * 3-Sep-93 : - make calloc void* in ALPHA version * * 17-Sep-93 : - renamed to version 1.9, * * changed only dreadnaut.c and nautinv.c * * 24-Feb-94 : changes for version 1.10: * * - added version SYS_AMIGAAZT, thanks to Carsten Saager * * (making 1.9+) * * 19-Apr-95 : - added prototype wrapper for C++, * * thanks to Daniel Huson * * * *****************************************************************************/ #define IS_UNIX (SYS_VAXBSD | SYS_BSDUNIX | SYS_CRAY | \ SYS_UNIX | SYS_APOLLO | SYS_ALPHA) #define IS_MAC (SYS_MACMPW | SYS_MACAZT | SYS_MACLSC | SYS_MACTHINK) #define IS_PC (SYS_PCTURBO | SYS_PCMS4 | SYS_PCMS5) #define IS_AMIGA (SYS_AMIGALC | SYS_AMIGAAZT) /***************************************************************************** * * * 16-bit, 32-bit and 64-bit versions can be selected by defining WORDSIZE. * * The largest graph that can be handled has MAXN vertices. * * Both WORDSIZE and MAXN can be defined on the command line. * * WORDSIZE must be 16, 32 or 64; MAXN must be <= INFINITY - 2; * * If only very small graphs need to be processed, use MAXN<=WORDSIZE * * since this causes substantial code optimizations. * * The symbol EXTDEFS should be defined (with arbitrary value) before this * * file is included, except for one of each group of files linked together. * * The file containing the main program is suggested. This ensures that * * arrays bit, bytecount and leftbit, and parameter labelorg, are only * * initialised once, which some linkers think is necessary. * * * * Conventions and Assumptions: * * * * A 'setword' is the chunk of memory that is occupied by one part of * * a set. This is assumed to be >= WORDSIZE bits in size. * * * * The rightmost (loworder) WORDSIZE bits of setwords are numbered * * 0..WORDSIZE-1, left to right. It is necessary that the 2^WORDSIZE * * setwords with the other bits zero are totally ordered under <,=,>. * * This needs care on a 1's-complement machine. * * * * The int variables m and n have consistent meanings throughout. * * Graphs have n vertices always, and sets have m setwords always. * * * * A 'set' consists of m contiguous setwords, whose bits are numbered * * 0,1,2,... from left (high-order) to right (low-order), using only * * the rightmost WORDSIZE bits of each setword. It is used to * * represent a subset of {0,1,...,n-1} in the usual way - bit number x * * is 1 iff x is in the subset. Bits numbered n or greater, and * * unnumbered bits, are assumed permanently zero. * * * * A 'graph' consists of n contiguous sets. The i-th set represents * * the vertices adjacent to vertex i, for i = 0,1,...,n-1. * * * * A 'permutation' is an array of n short ints, repesenting a * * permutation of the set {0,1,...,n-1}. The value of the i-th entry * * is the number to which i is mapped. * * * * If g is a graph and p is a permutation, then g^p is the graph in * * which vertex i is adjacent to vertex j iff vertex p[i] is adjacent * * to vertex p[j] in g. * * * * An 'nvector' is any array of n ints. Actually, nvector==int. * * * * A partition nest is represented by a pair (lab,ptn), where lab and ptn * * are nvectors. The "partition at level x" is the partition whose cells * * are {lab[i],lab[i+1],...,lab[j]}, where [i,j] is a maximal subinterval * * of [0,n-1] such that ptn[k] > x for i <= k < j and ptn[j] <= x. * * The partition at level 0 is given to nauty by the user. This is * * refined for the root of the tree, which has level 1. * * * *****************************************************************************/ #if SYS_VAXBSD #define NAUTYVERSION "1.9+ (VAXBSD)" #endif #if SYS_BSDUNIX #define NAUTYVERSION "1.9+ (BSDUNIX)" #endif #if SYS_UNIX #define NAUTYVERSION "1.9+ (UNIX)" #endif #if SYS_APOLLO #define NAUTYVERSION "1.9+ (APOLLO)" #endif #if SYS_VAXVMS #define NAUTYVERSION "1.9+ (VAXVMS)" #endif #if SYS_MACLSC #define NAUTYVERSION "1.9+ (MACLSC)" #endif #if SYS_MACTHINK #define NAUTYVERSION "1.9+ (MACTHINK)" #endif #if SYS_MACAZT #define NAUTYVERSION "1.9+ (MACAZT)" #endif #if SYS_MACMPW #define NAUTYVERSION "1.9+ (MACMPW)" #endif #if SYS_AMIGALC #define NAUTYVERSION "1.9+ (AMIGALC)" #endif #if SYS_AMIGAAZT #define NAUTYVERSION "1.9+ (AMIGAAZT)" #endif #if SYS_PCMS4 #define NAUTYVERSION "1.9+ (PCMS4)" #endif #if SYS_PCMS5 #define NAUTYVERSION "1.9+ (PCMS5)" #endif #if SYS_PCTURBO #define NAUTYVERSION "1.9+ (PCTURBO)" #endif #if SYS_CRAY #define NAUTYVERSION "1.9+ (CRAY)" #endif #if SYS_IBMC #define NAUTYVERSION "1.9+ (IBM C Set/2 for OS/2)" #endif #if SYS_ALPHA #define NAUTYVERSION "1.9+ (Alpha)" #endif #if SYS_MISC #define NAUTYVERSION "1.9+ (MISC)" #endif #ifdef WORDSIZE #if ((WORDSIZE != 16) & (WORDSIZE != 32) & (WORDSIZE != 64)) ERROR: WORDSIZE must be 16, 32 or 64 #endif #else /* WORDSIZE undefined */ #if IS_PC #define WORDSIZE 16 /* number of set elements per setword (16 or 32) */ #else #if (SYS_CRAY | SYS_ALPHA) #define WORDSIZE 64 #else #define WORDSIZE 32 #endif #endif #endif /* WORDSIZE */ #ifndef MAXN /* maximum allowed n value */ /* can be defined outside */ #if (IS_AMIGA | SYS_MISC | SYS_PCMS4 | SYS_PCMS5 | SYS_PCTURBO) #define MAXN 448 #endif #if (SYS_MACLSC | SYS_MACAZT | SYS_MACMPW) #define MAXN 480 #endif #if SYS_MACTHINK #define MAXN 640 #endif #if (SYS_UNIX | SYS_BSDUNIX | SYS_VAXBSD | SYS_APOLLO | SYS_IBMC) #define MAXN 1024 #endif #if (SYS_VAXVMS | SYS_CRAY | SYS_ALPHA) #define MAXN 2048 #endif #endif /* MAXN */ #define MAXM ((MAXN+WORDSIZE-1)/WORDSIZE) /* max setwords in a set */ /* set operations (setadd is its address, pos is the bit number): */ #if MAXM==1 #define SETWD(pos) 0 #define SETBT(pos) (pos) #else /* MAXM > 1 */ #if WORDSIZE==64 #define SETWD(pos) ((pos)>>6) /* number of setword containing bit pos */ #define SETBT(pos) ((pos)&077) /* position within setword of bit pos */ #else #if WORDSIZE==32 #define SETWD(pos) ((pos)>>5) #define SETBT(pos) ((pos)&037) #else /* WORDSIZE==16 */ #define SETWD(pos) ((pos)>>4) #define SETBT(pos) ((pos)&017) #endif #endif #endif /* MAXM */ #if WORDSIZE==64 #define TIMESWORDSIZE(w) ((w)<<6) /* w*WORDSIZE */ #else #if WORDSIZE==32 #define TIMESWORDSIZE(w) ((w)<<5) #else /* WORDSIZE==16 */ #define TIMESWORDSIZE(w) ((w)<<4) #endif #endif #define ADDELEM1(setadd,pos) (*(setadd) |= BIT[pos]) #define DELELEM1(setadd,pos) (*(setadd) &= ~BIT[pos]) #define ISELEM1(setadd,pos) ((*(setadd) & BIT[pos]) != 0) #define ADDELEMENT(setadd,pos) ((setadd)[SETWD(pos)] |= BIT[SETBT(pos)]) #define DELELEMENT(setadd,pos) ((setadd)[SETWD(pos)] &= ~BIT[SETBT(pos)]) #define ISELEMENT(setadd,pos) (((setadd)[SETWD(pos)] & BIT[SETBT(pos)]) != 0) #if MAXM==1 /* initialise set to empty */ #define EMPTYSET(setadd,m) *(setadd) = 0; #else #define EMPTYSET(setadd,m) \ {register setword *es; \ for (es = (setword*)(setadd)+(m); --es >= (setword*)(setadd);) *es=0;} #endif #if MAXM==1 /* obsolete version of EMPTYSET */ #define MAKEEMPTY(setadd,m,i) *(setadd) = 0 #else #define MAKEEMPTY(setadd,m,i) for(i=m;--i>=0;)setadd[i]=0 #endif #define NOTSUBSET(word1,word2) ((word1) & ~(word2)) /* test if the 1-bits in setword word1 do not form a subset of those in word2 */ #define INTERSECT(word1,word2) ((word1) &= (word2)) /* AND word2 into word1 */ #define UNION(word1,word2) ((word1) |= (word2)) /* OR word2 into word1 */ #define SETDIFF(word1,word2) ((word1) &= ~(word2)) /* - word2 into word1 */ #define XOR(word1,word2) ((word1) ^= (word2)) /* XOR word2 into word1 */ #define ZAPBIT(word,x) ((word) &= ~BIT[x]) /* delete bit x in setword */ #if WORDSIZE==64 #if SYS_CRAY #define POPCOUNT(x) _popcnt(x) #define FIRSTBIT(x) _leadz(x) #define BITMASK(x) _mask(65+(x)) #else #define POPCOUNT(x) (bytecount[(x)>>56 & 0377] + bytecount[(x)>>48 & 0377] \ + bytecount[(x)>>40 & 0377] + bytecount[(x)>>32 & 0377] \ + bytecount[(x)>>24 & 0377] + bytecount[(x)>>16 & 0377] \ + bytecount[(x)>>8 & 0377] + bytecount[(x) & 0377]) /* number of 1-bits in a setword */ #define FIRSTBIT(x) ((x) & 01777777777740000000000 ? \ (x) & 01777770000000000000000 ? \ (x) & 01774000000000000000000 ? \ 0+leftbit[((x)>>56) & 0377] : \ 8+leftbit[(x)>>48] \ : (x) & 07760000000000000 ? \ 16+leftbit[(x)>>40] : \ 24+leftbit[(x)>>32] \ : (x) & 037777600000 ? \ (x) & 037700000000 ? \ 32+leftbit[(x)>>24] : \ 40+leftbit[(x)>>16] \ : (x) & 0177400 ? \ 48+leftbit[(x)>>8] : \ 56+leftbit[x]) /* get number of first 1-bit in non-zero setword (0..WORDSIZE-1) */ #define BITMASK(x) (0777777777777777777777 >> (x)) /* setword whose rightmost WORDSIZE-x-1 (numbered) bits are 1 and the rest 0 (0 <= x < WORDSIZE) */ #endif /* CRAY */ #else #if WORDSIZE==32 #define POPCOUNT(x) (bytecount[(x)>>24 & 0377] + bytecount[(x)>>16 & 0377] \ + bytecount[(x)>>8 & 0377] + bytecount[(x) & 0377]) #define FIRSTBIT(x) ((x) & 037777600000 ? ((x) & 037700000000 ? \ leftbit[((x)>>24) & 0377] : 8+leftbit[(x)>>16]) \ : ((x) & 0177400 ? 16+leftbit[(x)>>8] : 24+leftbit[x])) #define BITMASK(x) (017777777777 >> (x)) /* setword whose rightmost WORDSIZE-x-1 (numbered) bits are 1 and the rest 0 (0 <= x < WORDSIZE) */ #else /* WORDSIZE==16 */ #define POPCOUNT(x) (bytecount[(x)>>8 & 0377] + bytecount[(x) & 0377]) #define FIRSTBIT(x) ((x) & 0177400 ? leftbit[((x)>>8) & 0377] : 8+leftbit[x]) #define BITMASK(x) (077777 >> (x)) #endif #endif #if MAXM==1 #define GRAPHROW(g,v,m) ((SET*)(g) + (v)) #else #define GRAPHROW(g,v,m) ((SET*)(g) + (long)(v) * (long)(m)) /* address of row v of graph g. v and m are ints. Beware of v*m being too large for an int. */ #endif /* various constants: */ #define FALSE 0 #define TRUE 1 #define INFINITY 077777 /* positive short int greater than MAXN+2 */ /* typedefs for sets, graphs, permutations, etc.: */ typedef int Boolean; /* Boolean MUST be the same as int */ #if WORDSIZE>16 typedef unsigned long setword; #else typedef unsigned short setword; #endif #if SYS_VAXBSD #define UPROC int /* avoids compiler bug in BSD 4.2 on VAX */ #else #define UPROC void /* type of user-defined procedures */ #endif typedef setword SET,graph; typedef int nvector,np2vector; typedef short permutation; typedef struct { int group_xyz; /* dummy field to make it non-empty */ } groupblk; typedef struct { Boolean getcanon; /* make canong and canonlab? */ Boolean digraph; /* multiple edges or loops? */ Boolean writeautoms; /* write automorphisms? */ Boolean writemarkers; /* write stats on pts fixed, etc.? */ Boolean defaultptn; /* set lab,ptn,active for single cell? */ Boolean cartesian; /* use cartesian rep for writing automs? */ int linelength; /* max chars/line (excl. '\n') for output */ FILE *outfile; /* file for output, if any */ UPROC (*userrefproc)(); /* replacement for usual refine procedure */ UPROC (*userautomproc)(); /* procedure called for each automorphism */ UPROC (*userlevelproc)(); /* procedure called for each level */ UPROC (*usernodeproc)(); /* procedure called for each node */ UPROC (*usertcellproc)(); /* replacement for targetcell procedure */ UPROC (*invarproc)(); /* procedure to compute vertex-invariant */ int tc_level; /* max level for smart target cell choosing */ int mininvarlevel; /* min level for invariant computation */ int maxinvarlevel; /* max level for invariant computation */ int invararg; /* value passed to (*invarproc)() */ groupblk *groupopts; /* placeholder for future group options */ } optionblk; #if (SYS_MACAZT | SYS_MACMPW) #define CONSOLWIDTH 72 #else #if IS_AMIGA #define CONSOLWIDTH 75 #else #define CONSOLWIDTH 78 #endif #endif #define NILFUNCTION ((UPROC(*)())NULL) /* nil pointer to user-function */ #define NILSET ((SET*)NULL) /* nil pointer to set */ #define NILGRAPH ((graph*)NULL) /* nil pointer to graph */ #define DEFAULTOPTIONS(options) optionblk options = {FALSE,FALSE,TRUE,TRUE,\ TRUE,FALSE,CONSOLWIDTH,(FILE*)NULL,NILFUNCTION,NILFUNCTION,NILFUNCTION,\ NILFUNCTION,NILFUNCTION,NILFUNCTION,0,0,0,0,(groupblk*)NULL} #if IS_AMIGA #define PUTC(c,f) fputc(c,f) /* best way to write character c to file f */ #else #define PUTC(c,f) putc(c,f) #endif typedef struct { double grpsize1; /* size of group is */ int grpsize2; /* grpsize1 * 10^grpsize2 */ #if !SYS_MACAZT #define groupsize1 grpsize1 /* for backwards compatibility */ #define groupsize2 grpsize2 #endif int numorbits; /* number of orbits in group */ int numgenerators; /* number of generators found */ int errstatus; /* if non-zero : an error code */ #define outofspace errstatus; /* for backwards compatibility */ long numnodes; /* total number of nodes */ long numbadleaves; /* number of leaves of no use */ int maxlevel; /* maximum depth of search */ long tctotal; /* total size of all target cells */ long canupdates; /* number of updates of best label */ long invapplics; /* number of applications of invarproc */ long invsuccesses; /* number of successful applics of invarproc() */ int invarsuclevel; /* least level where invarproc worked */ } statsblk; /* codes for errstatus field: */ #define NTOOBIG 1 /* n > MAXN or n > WORDSIZE*m */ #define MTOOBIG 2 /* m > MAXM */ #define CANONGNIL 3 /* canong = NILGRAPH, but getcanon = TRUE */ /* manipulation of real approximation to group size */ #define MULTIPLY(s1,s2,i) if ((s1 *= i) >= 1e10) {s1 /= 1e10; s2 += 10;} #define ANSI_STDC 0 #ifdef __STDC__ #if __STDC__ == 1 #undef ANSI_STDC #define ANSI_STDC 1 #endif #endif /* The dynamic memory macros below are currently (version 1.9+) not used by nauty, only by dreadnaut. They are defined in this file, though, because their use by a future version of nauty is highly likely. ALLOCS(x,y) should return a pointer (any pointer type) to x*y units of new storage, not necessarily initialised. A "unit" of storage is defined by the sizeof operator. x and y are int values, but x*y may well be too large for an int. On failure, ALLOCS(x,y) should return a NULL pointer. FREES(p) should free (or pretend to free) storage previously allocated by ALLOCS, where p is the value that ALLOCS returned. */ #if SYS_MACAZT extern char *NewPtr(); extern void DisposPtr(); #define ALLOCS(x,y) NewPtr((long)(x) * (long)(y)) #define FREES(p) DisposPtr(p) #endif #if (IS_UNIX | SYS_PCTURBO | SYS_PCMS4 | SYS_VAXVMS \ | SYS_MACLSC | SYS_MISC | SYS_IBMC) #if ANSI_STDC #if SYS_APOLLO #include /* Domain C has no stddef.h */ #else #include #endif /* SYS_APOLLO */ extern void *calloc(size_t,size_t); extern void free(void*); #define ALLOCS(x,y) calloc(x,y) #define FREES(p) free(p) #else /* not ANSI_STDC */ #if SYS_ALPHA extern void *calloc(); #else extern char *calloc(); #endif /* SYS_ALPHA */ extern void cfree(); #define ALLOCS(x,y) calloc(x,y) #if (SYS_PCTURBO | SYS_IBMC) #define FREES(p) free(p) #else #define FREES(p) cfree(p) #endif /* SYS_PCTURBO | SYS_IBMC */ #endif /* ANSI_STDC */ #endif /* IS_UNIX ... */ #if SYS_PCMS5 #include #define ALLOCS(x,y) calloc(x,y) #define FREES(p) free(p) #endif #if SYS_MACTHINK #include extern void *calloc(size_t,size_t); extern void free(void*); #define ALLOCS(x,y) calloc(x,y) #define FREES(p) free(p) #endif #if (SYS_MACMPW | IS_AMIGA) extern char *calloc(); extern void free(); #define ALLOCS(x,y) calloc(x,y) #define FREES(p) free(p) #endif /* File to write error messages to (used as first argument to fprintf()). Leave it undefined to get no error messages. dreadnaut uses this too. */ #define ERRFILE stderr #ifdef EXTDEFS extern setword BIT[]; extern int bytecount[]; extern int leftbit[]; extern int labelorg; #else /* array giving setwords with single 1-bit */ #if WORDSIZE==64 setword BIT[] = {01000000000000000000000,0400000000000000000000, 0200000000000000000000,0100000000000000000000, 040000000000000000000,020000000000000000000, 010000000000000000000,04000000000000000000, 02000000000000000000,01000000000000000000, 0400000000000000000,0200000000000000000, 0100000000000000000,040000000000000000,020000000000000000, 010000000000000000,04000000000000000,02000000000000000, 01000000000000000,0400000000000000,0200000000000000, 0100000000000000,040000000000000,020000000000000, 010000000000000,04000000000000,02000000000000, 01000000000000,0400000000000,0200000000000,0100000000000, 040000000000,020000000000,010000000000,04000000000, 02000000000,01000000000,0400000000,0200000000,0100000000, 040000000,020000000,010000000,04000000,02000000,01000000, 0400000,0200000,0100000,040000,020000,010000,04000, 02000,01000,0400,0200,0100,040,020,010,04,02,01}; #else #if WORDSIZE==32 setword BIT[] = {020000000000,010000000000,04000000000,02000000000, 01000000000,0400000000,0200000000,0100000000,040000000, 020000000,010000000,04000000,02000000,01000000,0400000, 0200000,0100000,040000,020000,010000,04000,02000,01000, 0400,0200,0100,040,020,010,04,02,01}; #else /* WORDSIZE==16 */ setword BIT[] = {0100000,040000,020000,010000,04000,02000,01000,0400,0200, 0100,040,020,010,04,02,01}; #endif #endif /* array giving number of 1-bits in bytes valued 0..255: */ int bytecount[] = {0,1,1,2,1,2,2,3,1,2,2,3,2,3,3,4, 1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5, 1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5, 2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6, 1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5, 2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6, 2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6, 3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7, 1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5, 2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6, 2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6, 3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7, 2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6, 3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7, 3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7, 4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8}; /* array giving position (1..7) of high-order 1-bit in byte: */ int leftbit[] = {8,7,6,6,5,5,5,5,4,4,4,4,4,4,4,4, 3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3, 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}; int labelorg = 0; /* number of least-numbered vertex */ #endif /* EXTDEFS */ #if ANSI_STDC #ifndef ANSIPROT #define ANSIPROT 1 #endif #endif #ifdef ANSIPROT #define EXTPROC(func,args) extern func args; #else #define EXTPROC(func,args) extern func(); #endif /* The following is for C++ programs that read nauty.h. Compile nauty itself using C, not C++. */ #ifdef __cplusplus extern "C" { #endif EXTPROC(int bestcell,(graph*,nvector*,nvector*,int,int,int,int)) EXTPROC(void breakout,(nvector*,nvector*,int,int,int,SET*,int)) EXTPROC(Boolean cheapautom,(nvector*,int,Boolean,int)) EXTPROC(void doref,(graph*,nvector*,nvector*,int,int*,int*,permutation*,SET*, int*,UPROC(*)(),UPROC(*)(),int,int,int,Boolean,int,int)) EXTPROC(Boolean isautom,(graph*,permutation*,Boolean,int,int)) EXTPROC(int itos,(int,char*)) EXTPROC(void fmperm,(permutation*,SET*,SET*,int,int)) EXTPROC(void fmptn,(nvector*,nvector*,int,SET*,SET*,int,int)) EXTPROC(void longprune,(SET*,SET*,SET*,SET*,int)) EXTPROC(void nauty,(graph*,nvector*,nvector*,SET*,nvector*,optionblk*, statsblk*,SET*,int,int,int,graph*)) EXTPROC(int nextelement,(SET*,int,int)) EXTPROC(int orbjoin,(nvector*,permutation*,int)) EXTPROC(void permset,(SET*,SET*,int,permutation*)) EXTPROC(void putstring,(FILE*,char*)) EXTPROC(UPROC refine,(graph*,nvector*,nvector*,int,int*, permutation*,SET*,int*,int,int)) EXTPROC(UPROC refine1,(graph*,nvector*,nvector*,int,int*, permutation*,SET*,int*,int,int)) EXTPROC(void shortprune,(SET*,SET*,int)) EXTPROC(UPROC targetcell,(graph*,nvector*,nvector*,int,int,SET*,int*, int*,int,int,int,int)) EXTPROC(int testcanlab,(graph*,graph*,nvector*,int*,int,int)) EXTPROC(void updatecan,(graph*,graph*,permutation*,int,int,int)) EXTPROC(void writeperm,(FILE*,permutation*,Boolean,int,int)) #ifdef __cplusplus } #endif #define NAUTYH_READ 1 #endif /* NAUTYH_READ */ |-> cc/nauty.c /***************************************************************************** * * * Main source file for version 1.9 of nauty. * * * * Copyright (1984-1993) Brendan McKay. All rights reserved. Permission * * Subject to the waivers and disclaimers in nauty.h. * * * * CHANGE HISTORY * * 10-Nov-87 : final changes for version 1.2 * * 5-Dec-87 : renamed to version 1.3 (no changes to this file) * * 28-Sep-88 : renamed to version 1.4 (no changes to this file) * * 23-Mar-89 : changes for version 1.5 : * * - add use of refine1 instead of refine for m==1 * * - changes for new optionblk syntax * * - disable tc_level use for digraphs * * - interposed doref() interface to refine() so that * * options.invarproc can be supported * * - declared local routines static * * 28-Mar-89 : - implemented mininvarlevel/maxinvarlevel < 0 options * * 2-Apr-89 : - added invarproc fields in stats * * 5-Apr-89 : - modified error returns from nauty() * * - added error message to ERRFILE * * - changed MAKEEMPTY uses to EMPTYSET * * 18-Apr-89 : - added MTOOBIG and CANONGNIL * * 8-May-89 : - changed firstcode[] and canoncode[] to short * * 10-Nov-90 : changes for version 1.6 : * * - added dummy routine nauty_null (see dreadnaut.c) * * 2-Sep-91 : changes for version 1.7 : * * - moved MULTIPLY into nauty.h * * 27-Mar-92 : - changed 'n' into 'm' in error message in nauty() * * 5-Jun-93 : renamed to version 1.7+ (no changes to this file) * * 18-Aug-93 : renamed to version 1.8 (no changes to this file) * * 17-Sep-93 : renamed to version 1.9 (no changes to this file) * * * *****************************************************************************/ #define EXTDEFS 1 #include "nauty.h" static int firstpathnode(); static void firstterminal(); static int othernode(); static int processnode(); static void recover(); static void writemarker(); #if MAXM==1 #define M 1 #else #define M m #endif #define OPTCALL(proc) if (proc != NILFUNCTION) (*proc) /* copies of some of the options: */ static Boolean getcanon,digraph,writeautoms,domarkers,cartesian; static int linelength,tc_level,mininvarlevel,maxinvarlevel,invararg; static UPROC (*usernodeproc)(),(*userautomproc)(),(*userlevelproc)(), (*refproc)(),(*tcellproc)(),(*invarproc)(); static FILE *outfile; /* local versions of some of the arguments: */ static int m,n; static graph *g,*canong; static nvector *orbits; static statsblk *stats; /* temporary versions of some stats: */ static long invapplics,invsuccesses; static int invarsuclevel; /* working variables: */ static int gca_first, /* level of greatest common ancestor of current node and first leaf */ gca_canon, /* ditto for current node and bsf leaf */ noncheaplevel, /* level of greatest ancestor for which cheapautom == FALSE */ allsamelevel, /* level of least ancestor of first leaf for which all descendant leaves are known to be equivalent */ eqlev_first, /* level to which codes for this node match those for first leaf */ eqlev_canon, /* level to which codes for this node match those for the bsf leaf. */ comp_canon, /* -1,0,1 according as code at eqlev_canon+1 is <,==,> that for bsf leaf. Also used for similar purpose during leaf processing */ samerows, /* number of rows of canong which are correct for the bsf leaf BDM:correct? */ canonlevel, /* level of bsf leaf */ stabvertex, /* point fixed in ancestor of first leaf at level gca_canon */ cosetindex; /* the point being fixed at level gca_first */ static Boolean needshortprune; /* used to flag calls to shortprune */ static SET defltwork[2*MAXM]; /* workspace in case none provided */ static permutation workperm[MAXN]; /* various scratch uses */ static SET fixedpts[MAXM]; /* points which were explicitly fixed to get current node */ static permutation firstlab[MAXN], /* label from first leaf */ canonlab[MAXN]; /* label from bsf leaf */ static short firstcode[MAXN+2], /* codes for first leaf */ canoncode[MAXN+2]; /* codes for bsf leaf */ static short firsttc[MAXN+2]; /* index of target cell for left path */ static SET active[MAXM]; /* used to contain index to cells now active for refinement purposes */ static SET *workspace,*worktop; /* first and just-after-last addresses of work area to hold automorphism data */ static SET *fmptr; /* pointer into workspace */ /***************************************************************************** * * * This procedure finds generators for the automorphism group of a * * vertex-coloured graph and optionally finds a canonically labelled * * isomorph. A description of the data structures can be found in * * nauty.h and in the "nauty User's Guide". The Guide also gives * * many more details about its use, and implementation notes. * * * * Parameters - means read-only, means write-only, means both: * * g - the graph * * lab,ptn - used for the partition nest which defines the colouring * * of g. The initial colouring will be set by the program, * * using the same colour for every vertex, if * * options->defaultptn!=FALSE. Otherwise, you must set it * * yourself (see the Guide). If options->getcanon!=FALSE, * * the contents of lab on return give the labelling of g * * corresponding to canong. This does not change the * * initial colouring of g as defined by (lab,ptn), since * * the labelling is consistent with the colouring. * * active - If this is not NILSET and options->defaultptn==FALSE, * * it is a set indicating the initial set of active colours. * * See the Guide for details. * * orbits - On return, orbits[i] contains the number of the * * least-numbered vertex in the same orbit as i, for * * i=0,1,...,n-1. * * options - A list of options. See nauty.h and/or the Guide * * for details. * * stats - A list of statistics produced by the procedure. See * * nauty.h and/or the Guide for details. * * workspace - A chunk of memory for working storage. * * worksize - The number of setwords in workspace. See the Guide * * for guidance. * * m - The number of setwords in sets. This must be at * * least ceil(n / WORDSIZE) and at most MAXM. * * n - The number of vertices. This must be at least 1 and * * at most MAXN. * * canong - The canononically labelled isomorph of g. This is * * only produced if options->getcanon!=FALSE, and can be * * given as NILGRAPH otherwise. * * * * FUNCTIONS CALLED: firstpathnode(),updatecan() * * * *****************************************************************************/ void nauty(g_arg,lab,ptn,active_arg,orbits_arg,options,stats_arg, ws_arg,worksize,m_arg,n_arg,canong_arg) graph *g_arg,*canong_arg; SET *active_arg,*ws_arg; nvector *lab,*ptn,*orbits_arg; int worksize,m_arg,n_arg; optionblk *options; statsblk *stats_arg; { register int i; int numcells; /* check for excessive sizes: */ if (m_arg > MAXM) { stats_arg->errstatus = MTOOBIG; #ifdef ERRFILE fprintf(ERRFILE,"nauty: need m <= %d\n\n",MAXM); #endif return; } if (n_arg > MAXN || n_arg > WORDSIZE * m_arg) { stats_arg->errstatus = NTOOBIG; #ifdef ERRFILE fprintf(ERRFILE, "nauty: need n <= min(%d,%d*m)\n\n",MAXM,WORDSIZE); #endif return; } /* take copies of some args, and options: */ m = m_arg; n = n_arg; g = g_arg; orbits = orbits_arg; stats = stats_arg; getcanon = options->getcanon; digraph = options->digraph; writeautoms = options->writeautoms; domarkers = options->writemarkers; cartesian = options->cartesian; linelength = options->linelength; if (digraph) tc_level = 0; else tc_level = options->tc_level; outfile = (options->outfile == (FILE*)NULL ? stdout : options->outfile); usernodeproc = options->usernodeproc; userautomproc = options->userautomproc; userlevelproc = options->userlevelproc; if (options->userrefproc == NILFUNCTION) if (m == 1) refproc = refine1; else refproc = refine; else refproc = options->userrefproc; if (options->usertcellproc == NILFUNCTION) tcellproc = targetcell; else tcellproc = options->usertcellproc; invarproc = options->invarproc; if (options->mininvarlevel < 0 && options->getcanon) mininvarlevel = -options->mininvarlevel; else mininvarlevel = options->mininvarlevel; if (options->maxinvarlevel < 0 && options->getcanon) maxinvarlevel = -options->maxinvarlevel; else maxinvarlevel = options->maxinvarlevel; invararg = options->invararg; if (getcanon) if (canong_arg == NILGRAPH) { stats_arg->errstatus = CANONGNIL; #ifdef ERRFILE fprintf(ERRFILE, "nauty: canong=NILGRAPH but options.getcanon=TRUE\n\n"); #endif return; } else canong = canong_arg; /* initialize everything: */ if (options->defaultptn) { for (i = 0; i < n; ++i) /* give all verts same colour */ { lab[i] = i; ptn[i] = INFINITY; } ptn[n-1] = 0; EMPTYSET(active,m); ADDELEMENT(active,0); numcells = 1; } else { ptn[n-1] = 0; numcells = 0; for (i = 0; i < n; ++i) if (ptn[i] != 0) ptn[i] = INFINITY; else ++numcells; if (active_arg == NILSET) { EMPTYSET(active,m); for (i = 0; i < n; ++i) { ADDELEMENT(active,i); while (ptn[i]) ++i; } } else for (i = 0; i < M; ++i) active[i] = active_arg[i]; } for (i = 0; i < n; ++i) orbits[i] = i; stats->grpsize1 = 1.0; stats->grpsize2 = 0; stats->numgenerators = 0; stats->numnodes = 0; stats->numbadleaves = 0; stats->tctotal = 0; stats->canupdates = 0; stats->numorbits = n; EMPTYSET(fixedpts,m); noncheaplevel = 1; eqlev_canon = -1; /* needed even if !getcanon */ if (worksize >= 2 * m) workspace = ws_arg; else { workspace = defltwork; worksize = 2 * MAXM; } worktop = workspace + (worksize - worksize % (2 * m)); fmptr = workspace; /* here goes: */ stats->errstatus = 0; needshortprune = FALSE; invarsuclevel = INFINITY; invapplics = invsuccesses = 0; firstpathnode(lab,ptn,1,numcells); if (getcanon) { updatecan(g,canong,canonlab,samerows,M,n); for (i = 0; i < n; ++i) lab[i] = canonlab[i]; } stats->invarsuclevel = (invarsuclevel == INFINITY ? 0 : invarsuclevel); stats->invapplics = invapplics; stats->invsuccesses = invsuccesses; } /***************************************************************************** * * * firstpathnode(lab,ptn,level,numcells) produces a node on the leftmost * * path down the tree. The parameters describe the level and the current * * colour partition. The set of active cells is taken from the global set * * 'active'. If the refined partition is not discrete, the leftmost child * * is produced by calling firstpathnode, and the other children by calling * * othernode. * * The value returned is the level to return to. * * * * FUNCTIONS CALLED: (*usernodeproc)(),doref(),cheapautom(), * * firstterminal(),nextelement(),breakout(), * * firstpathnode(),othernode(),recover(),writestats(), * * (*userlevelproc)(),(*tcellproc)(),shortprune() * * * *****************************************************************************/ static int firstpathnode(lab,ptn,level,numcells) nvector *lab,*ptn; int level,numcells; { register int tv; int tv1,index,rtnlevel,tcellsize,tc,childcount,qinvar,refcode; SET tcell[MAXM]; ++stats->numnodes; /* refine partition : */ doref(g,lab,ptn,level,&numcells,&qinvar,workperm, active,&refcode,refproc,invarproc, mininvarlevel,maxinvarlevel,invararg,digraph,M,n); firstcode[level] = (short)refcode; if (qinvar > 0) { ++invapplics; if (qinvar == 2) { ++invsuccesses; if (mininvarlevel < 0) mininvarlevel = level; if (maxinvarlevel < 0) maxinvarlevel = level; if (level < invarsuclevel) invarsuclevel = level; } } tc = -1; if (numcells != n) { /* locate new target cell, setting tc to its position in lab, tcell to its contents, and tcellsize to its size: */ (*tcellproc)(g,lab,ptn,level,numcells,tcell,&tcellsize, &tc,tc_level,-1,M,n); stats->tctotal += tcellsize; } firsttc[level] = tc; /* optionally call user-defined node examination procedure: */ OPTCALL(usernodeproc) (g,lab,ptn,level,numcells,tc,(int)firstcode[level],M,n); if (numcells == n) /* found first leaf? */ { firstterminal(lab,level); OPTCALL(userlevelproc)(lab,ptn,level,orbits,stats,0,1,1,n,0,n); return(level - 1); } if (noncheaplevel >= level && !cheapautom(ptn,level,digraph,n)) noncheaplevel = level + 1; /* use the elements of the target cell to produce the children: */ index = 0; for (tv1 = tv = nextelement(tcell,M,-1); tv >= 0; tv = nextelement(tcell,M,tv)) { if (orbits[tv] == tv) /* ie, not equiv to previous child */ { breakout(lab,ptn,level + 1,tc,tv,active,M); ADDELEMENT(fixedpts,tv); cosetindex = tv; if (tv == tv1) { rtnlevel = firstpathnode(lab,ptn,level + 1,numcells + 1); childcount = 1; gca_first = level; stabvertex = tv1; } else { rtnlevel = othernode(lab,ptn,level + 1,numcells + 1); ++childcount; } DELELEMENT(fixedpts,tv); if (rtnlevel < level) return(rtnlevel); if (needshortprune) { needshortprune = FALSE; shortprune(tcell,fmptr - M,M); } recover(ptn,level); } if (orbits[tv] == tv1) /* ie, in same orbit as tv1 */ ++index; } MULTIPLY(stats->grpsize1,stats->grpsize2,index); if (tcellsize == index && allsamelevel == level + 1) --allsamelevel; if (domarkers) writemarker(level,tv1,index,tcellsize,stats->numorbits,numcells); OPTCALL(userlevelproc)(lab,ptn,level,orbits,stats,tv1,index,tcellsize, numcells,childcount,n); return(level - 1); } /***************************************************************************** * * * othernode(lab,ptn,level,numcells) produces a node other than an ancestor * * of the first leaf. The parameters describe the level and the colour * * partition. The list of active cells is found in the global set 'active'. * * The value returned is the level to return to. * * * * FUNCTIONS CALLED: (*usernodeproc)(),doref(),refine(),recover(), * * processnode(),cheapautom(),(*tcellproc)(),shortprune(), * * nextelement(),breakout(),othernode(),longprune() * * * *****************************************************************************/ static int othernode(lab,ptn,level,numcells) nvector *lab,*ptn; int level,numcells; { register int tv; SET tcell[MAXM]; int tv1,refcode,rtnlevel,tcellsize,tc,qinvar; short code; ++stats->numnodes; /* refine partition : */ doref(g,lab,ptn,level,&numcells,&qinvar,workperm,active, &refcode,refproc,invarproc,mininvarlevel,maxinvarlevel, invararg,digraph,M,n); code = (short)refcode; if (qinvar > 0) { ++invapplics; if (qinvar == 2) { ++invsuccesses; if (level < invarsuclevel) invarsuclevel = level; } } if (eqlev_first == level - 1 && code == firstcode[level]) eqlev_first = level; if (getcanon) { if (eqlev_canon == level - 1) { if (code < canoncode[level]) comp_canon = -1; else if (code > canoncode[level]) comp_canon = 1; else { comp_canon = 0; eqlev_canon = level; } } if (comp_canon > 0) canoncode[level] = code; } tc = -1; /* If children will be required, find new target cell and set tc to its position in lab, tcell to its contents, and tcellsize to its size: */ if (numcells < n && (eqlev_first == level || getcanon && comp_canon >= 0)) { if (!getcanon || comp_canon < 0) { (*tcellproc)(g,lab,ptn,level,numcells,tcell,&tcellsize, &tc,tc_level,firsttc[level],M,n); if (tc != firsttc[level]) eqlev_first = level - 1; } else (*tcellproc)(g,lab,ptn,level,numcells,tcell,&tcellsize, &tc,tc_level,-1,M,n); stats->tctotal += tcellsize; } /* optionally call user-defined node examination procedure: */ OPTCALL(usernodeproc)(g,lab,ptn,level,numcells,tc,(int)code,M,n); /* call processnode to classify the type of this node: */ rtnlevel = processnode(lab,ptn,level,numcells); if (rtnlevel < level) /* keep returning if necessary */ return(rtnlevel); if (needshortprune) { needshortprune = FALSE; shortprune(tcell,fmptr - M,M); } if (!cheapautom(ptn,level,digraph,n)) noncheaplevel = level + 1; /* use the elements of the target cell to produce the children: */ for (tv1 = tv = nextelement(tcell,M,-1); tv >= 0; tv = nextelement(tcell,M,tv)) { breakout(lab,ptn,level + 1,tc,tv,active,M); ADDELEMENT(fixedpts,tv); rtnlevel = othernode(lab,ptn,level + 1,numcells + 1); DELELEMENT(fixedpts,tv); if (rtnlevel < level) return(rtnlevel); /* use stored automorphism data to prune target cell: */ if (needshortprune) { needshortprune = FALSE; shortprune(tcell,fmptr - M,M); } if (tv == tv1) longprune(tcell,fixedpts,workspace,fmptr,M); recover(ptn,level); } return(level - 1); } /***************************************************************************** * * * Process the first leaf of the tree. * * * * FUNCTIONS CALLED: NONE * * * *****************************************************************************/ static void firstterminal(lab,level) nvector *lab; register int level; { register int i; stats->maxlevel = level; gca_first = allsamelevel = eqlev_first = level; firstcode[level + 1] = INFINITY; firsttc[level + 1] = -1; for (i = 0; i < n; ++i) firstlab[i] = lab[i]; if (getcanon) { canonlevel = eqlev_canon = gca_canon = level; comp_canon = 0; samerows = 0; for (i = 0; i < n; ++i) canonlab[i] = lab[i]; for (i = 0; i <= level; ++i) canoncode[i] = firstcode[i]; canoncode[level + 1] = INFINITY; stats->canupdates = 1; } } /***************************************************************************** * * * Process a node other than the first leaf or its ancestors. It is first * * classified into one of five types and then action is taken appropriate * * to that type. The types are * * * * 0: Nothing unusual. This is just a node internal to the tree whose * * children need to be generated sometime. * * 1: This is a leaf equivalent to the first leaf. The mapping from * * firstlab to lab is thus an automorphism. After processing the * * automorphism, we can return all the way to the closest invocation * * of firstpathnode. * * 2: This is a leaf equivalent to the bsf leaf. Again, we have found an * * automorphism, but it may or may not be as useful as one from a * * type-1 node. Return as far up the tree as possible. * * 3: This is a new bsf node, provably better than the previous bsf node. * * After updating canonlab etc., treat it the same as type 4. * * 4: This is a leaf for which we can prove that no descendant is * * equivalent to the first or bsf leaf or better than the bsf leaf. * * Return up the tree as far as possible, but this may only be by * * one level. * * * * Types 2 and 3 can't occur if getcanon==FALSE. * * The value returned is the level in the tree to return to, which can be * * anywhere up to the closest invocation of firstpathnode. * * * * FUNCTIONS CALLED: isautom(),updatecan(),testcanlab(),fmperm(), * * writeperm(),(*userautomproc)(),orbjoin(), * * shortprune(),fmptn() * * * *****************************************************************************/ static int processnode(lab,ptn,level,numcells) nvector *lab,*ptn; int level,numcells; { register int i,code,save,newlevel; Boolean ispruneok; int sr; code = 0; if (eqlev_first != level && (!getcanon || comp_canon < 0)) code = 4; else if (numcells == n) { if (eqlev_first == level) { for (i = 0; i < n; ++i) workperm[firstlab[i]] = lab[i]; if (gca_first >= noncheaplevel || isautom(g,workperm,digraph,M,n)) code = 1; } if (code == 0) if (getcanon) { sr = 0; if (comp_canon == 0) { if (level < canonlevel) comp_canon = 1; else { updatecan(g,canong,canonlab, samerows,M,n); samerows = n; comp_canon = testcanlab(g,canong,lab,&sr,M,n); } } if (comp_canon == 0) { for (i = 0; i < n; ++i) workperm[canonlab[i]] = lab[i]; code = 2; } else if (comp_canon > 0) code = 3; else code = 4; } else code = 4; } if (code != 0 && level > stats->maxlevel) stats->maxlevel = level; switch (code) { case 0: /* nothing unusual noticed */ return(level); case 1: /* lab is equivalent to firstlab */ if (fmptr == worktop) fmptr -= 2 * M; fmperm(workperm,fmptr,fmptr + M,M,n); fmptr += 2 * M; if (writeautoms) writeperm(outfile,workperm,cartesian,linelength,n); stats->numorbits = orbjoin(orbits,workperm,n); ++stats->numgenerators; OPTCALL(userautomproc)(stats->numgenerators,workperm,orbits, stats->numorbits,stabvertex,n); return(gca_first); case 2: /* lab is equivalent to canonlab */ if (fmptr == worktop) fmptr -= 2 * M; fmperm(workperm,fmptr,fmptr + M,M,n); fmptr += 2 * M; save = stats->numorbits; stats->numorbits = orbjoin(orbits,workperm,n); if (stats->numorbits == save) { if (gca_canon != gca_first) needshortprune = TRUE; return(gca_canon); } if (writeautoms) writeperm(outfile,workperm,cartesian,linelength,n); ++stats->numgenerators; OPTCALL(userautomproc)(stats->numgenerators,workperm,orbits, stats->numorbits,stabvertex,n); if (orbits[cosetindex] < cosetindex) return(gca_first); if (gca_canon != gca_first) needshortprune = TRUE; return(gca_canon); case 3: /* lab is better than canonlab */ ++stats->canupdates; for (i = 0; i < n; ++i) canonlab[i] = lab[i]; canonlevel = eqlev_canon = gca_canon = level; comp_canon = 0; canoncode[level + 1] = INFINITY; samerows = sr; break; case 4: /* non-automorphism terminal node */ ++stats->numbadleaves; break; } /* end of switch statement */ /* only cases 3 and 4 get this far: */ if (level != noncheaplevel) { ispruneok = TRUE; if (fmptr == worktop) fmptr -= 2 * M; fmptn(lab,ptn,noncheaplevel,fmptr,fmptr + M,M,n); fmptr += 2 * M; } else ispruneok = FALSE; save = (allsamelevel > eqlev_canon ? allsamelevel - 1 : eqlev_canon); newlevel = (noncheaplevel <= save ? noncheaplevel - 1 : save); if (ispruneok && newlevel != gca_first) needshortprune = TRUE; return(newlevel); } /***************************************************************************** * * * Recover the partition nest at level 'level' and update various other * * parameters. * * * * FUNCTIONS CALLED: NONE * * * *****************************************************************************/ static void recover(ptn,level) register nvector *ptn; register int level; { register int i; for (i = 0; i < n; ++i) if (ptn[i] > level) ptn[i] = INFINITY; if (level < noncheaplevel) noncheaplevel = level + 1; if (level < eqlev_first) eqlev_first = level; if (getcanon) { if (level < gca_canon) gca_canon = level; if (level <= eqlev_canon) { eqlev_canon = level; comp_canon = 0; } } } /***************************************************************************** * * * Write statistics concerning an ancestor of the first leaf. * * * * level = its level * * tv = the vertex fixed to get the first child = the smallest-numbered * * vertex in the target cell * * cellsize = the size of the target cell * * index = the number of vertices in the target cell which were equivalent * * to tv = the index of the stabiliser of tv in the group * * fixing the colour partition at this level * * * * numorbits = the number of orbits of the group generated by all the * * automorphisms so far discovered * * * * numcells = the total number of cells in the equitable partition at this * * level * * * * FUNCTIONS CALLED: itos(),putstring() * * * *****************************************************************************/ static void writemarker(level,tv,index,tcellsize,numorbits,numcells) int level,tv,index,tcellsize,numorbits,numcells; { char s[30]; #define PUTINT(i) itos(i,s); putstring(outfile,s) #define PUTSTR(x) putstring(outfile,x) PUTSTR("level "); PUTINT(level); PUTSTR(": "); if (numcells != numorbits) { PUTINT(numcells); PUTSTR(" cell"); if (numcells == 1) PUTSTR("; "); else PUTSTR("s; "); } PUTINT(numorbits); PUTSTR(" orbit"); if (numorbits == 1) PUTSTR("; "); else PUTSTR("s; "); PUTINT(tv + labelorg); PUTSTR(" fixed; index "); PUTINT(index); if (tcellsize != index) { PUTSTR("/"); PUTINT(tcellsize); } PUTSTR("\n"); } /***************************************************************************** * * * nauty_null() does nothing. See dreadnaut.c for its purpose. * * * *****************************************************************************/ void nauty_null() { } |-> cc/nautil.c /***************************************************************************** * * * Auxiliary source file for version 1.9 of nauty. * * * * Copyright (1984-1993) Brendan McKay. All rights reserved. * * Subject to waivers and disclaimers in nauty.h. * * * * CHANGE HISTORY * * 10-Nov-87 : final changes for version 1.2 * * 5-Dec-87 : renamed to version 1.3 (no changes to this file) * * 28-Sep-88 : renamed to version 1.4 (no changes to this file) * * 23-Mar-89 : changes for version 1.5 : * * - added procedure refine1() * * - changed type of ptn from int* to nvector* in fmptn() * * - declared level in breakout() * * - changed char[] to char* in a few places * * - minor rearrangement in bestcell() * * 31-Mar-89 : - added procedure doref() * * 5-Apr-89 : - changed MAKEEMPTY uses to EMPTYSET * * 12-Apr-89 : - changed writeperm() and fmperm() to not use MARKing * * 5-May-89 : - redefined MASH to gain about 8% efficiency * * 18-Oct-90 : changes for version 1.6 : * * - improved line breaking in writeperm() * * 10-Nov-90 : - added dummy routine nautil_null() * * 27-Aug-92 : changes for version 1.7 : * * - made linelength <= 0 mean no line breaks * * 5-Jun-93 : renamed to version 1.7+ (no changes to this file) * * 18-Aug-93 : renamed to version 1.8 (no changes to this file) * * 17-Sep-93 : renamed to version 1.9 (no changes to this file) * * 29-Jun-95 : changes for version 1.10 : * * - replaced loop in nextelement() to save reference past * * end of array (thanks to Kevin Maylsiak) * * * *****************************************************************************/ #define EXTDEFS 1 #include "nauty.h" /* macros for hash-codes: */ #define MASH(l,i) ((((l) ^ 065435) + (i)) & 077777) /* : expression whose long value depends only on long l and int/long i. Anything goes, preferably non-commutative. */ #define CLEANUP(l) ((int)((l) % INFINITY)) /* : expression whose value depends on long l and is less than INFINITY when converted to int then short. Anything goes. */ #if MAXM==1 #define M 1 #else #define M m #endif static SET workset[MAXM]; /* used for scratch work */ static permutation workperm[MAXN]; static short bucket[MAXN+2]; /***************************************************************************** * * * nextelement(set1,m,pos) = the position of the first element in set set1 * * which occupies a position greater than pos. If no such element exists, * * the value is -1. pos can have any value less than n, including negative * * values. * * * * GLOBALS ACCESSED: none * * * *****************************************************************************/ int nextelement(set1,m,pos) register SET *set1; int m,pos; { register setword setwd; register int w; #if MAXM==1 if (pos < 0) setwd = set1[0]; else setwd = set1[0] & BITMASK(pos); if (setwd == 0) return(-1); else return(FIRSTBIT(setwd)); #else if (pos < 0) { w = 0; setwd = set1[0]; } else { w = SETWD(pos); setwd = set1[w] & BITMASK(SETBT(pos)); } /* do { if (setwd != 0) return(TIMESWORDSIZE(w) + FIRSTBIT(setwd)); setwd = set1[++w]; } while (w < m); return(-1); */ for (;;) { if (setwd != 0) return(TIMESWORDSIZE(w) + FIRSTBIT(setwd)); if (++w == m) return -1; setwd = set1[w]; } #endif } /***************************************************************************** * * * permset(set1,set2,m,perm) defines set2 to be the set * * {perm[i] | i in set1}. * * * * GLOBALS ACCESSED: bit,leftbit * * * *****************************************************************************/ void permset(set1,set2,m,perm) SET *set1,*set2; permutation *perm; int m; { register setword setw; register int pos,w,b; EMPTYSET(set2,m); setw = set1[0]; #if MAXM==1 while (setw != 0) { b = FIRSTBIT(setw); ZAPBIT(setw,b); pos = perm[b]; ADDELEMENT(set2,pos); } #else w = 0; do { while (setw != 0) { b = FIRSTBIT(setw); ZAPBIT(setw,b); pos = perm[TIMESWORDSIZE(w) + b]; ADDELEMENT(set2,pos); } setw = set1[++w]; } while (w < m); #endif } /***************************************************************************** * * * isautom(g,perm,digraph,m,n) = TRUE iff perm is an automorphism of g * * (i.e., g^perm = g). Symmetry is assumed unless digraph = TRUE. * * * * GLOBALS ACCESSED: bit,nextelement() * * * *****************************************************************************/ Boolean isautom(g,perm,digraph,m,n) graph *g; register permutation *perm; Boolean digraph; int m,n; { register SET *pg; register int pos; SET *pgp; int posp,i; for (pg = g, i = 0; i < n; pg += M, ++i) { pgp = GRAPHROW(g,perm[i],M); pos = (digraph ? -1 : i); while ((pos = nextelement(pg,M,pos)) >= 0) { posp = perm[pos]; if (!ISELEMENT(pgp,posp)) return(FALSE); } } return(TRUE); } /***************************************************************************** * * * putstring(f,s) writes the nul-terminated string s to file f. * * * *****************************************************************************/ void putstring(f,s) FILE *f; register char *s; { while (*s != '\0') { PUTC(*s,f); ++s; } } /***************************************************************************** * * * itos(i,s) converts the int i to a nul-terminated decimal character * * string s. The value returned is the number of characters excluding * * the nul. * * * * GLOBALS ACCESSED: NONE * * * *****************************************************************************/ int itos(i,s) register int i; register char *s; { register int digit,j,k; register char c; int ans; if (i < 0) { k = 0; i = -i; j = 1; s[0] = '-'; } else { k = -1; j = 0; } do { digit = i % 10; i = i / 10; s[++k] = digit + '0'; } while (i); s[k+1] = '\0'; ans = k + 1; for (;j < k; ++j, --k) { c = s[j]; s[j] = s[k]; s[k] = c; } return(ans); } /***************************************************************************** * * * orbits represents a partition of {0,1,...,n-1}, by orbits[i] = the * * smallest element in the same cell as i. orbjoin(orbits,autom,n) updates * * the partition orbits to the join of its current value and the cycle * * partition of perm. The function value returned is the new number of * * cells. * * * * GLOBALS ACCESSED: NONE * * * *****************************************************************************/ int orbjoin(orbits,perm,n) register nvector *orbits; permutation *perm; int n; { register int i,j1,j2; for (i = 0; i < n; ++i) { j1 = orbits[i]; while (orbits[j1] != j1) j1 = orbits[j1]; j2 = orbits[perm[i]]; while (orbits[j2] != j2) j2 = orbits[j2]; if (j1 < j2) orbits[j2] = j1; else if (j1 > j2) orbits[j1] = j2; } j1 = 0; for (i = 0; i < n; ++i) if ((orbits[i] = orbits[orbits[i]]) == i) ++j1; return(j1); } /***************************************************************************** * * * writeperm(f,perm,cartesian,linelength,n) writes the permutation perm to * * the file f. The cartesian representation (i.e. perm itself) is used if * * cartesian != FALSE; otherwise the cyclic representation is used. No * * more than linelength characters (not counting '\n') are written on each * * line, unless linelength is ridiculously small. linelength<=0 causes no * * line breaks at all to be made. The global int labelorg is added to each * * vertex number. * * * * GLOBALS ACCESSED: itos(),putstring() * * * *****************************************************************************/ void writeperm(f,perm,cartesian,linelength,n) FILE *f; permutation *perm; Boolean cartesian; int linelength,n; { register int i,k,l,curlen,intlen; char s[30]; /* CONDNL(x) writes end-of-line and 3 spaces if x characters won't fit on the current line. */ #define CONDNL(x) if (linelength>0 && curlen+(x)>linelength)\ {putstring(f,"\n ");curlen=3;} curlen = 0; if (cartesian) { for (i = 0; i < n; ++i) { intlen = itos(perm[i] + labelorg,s); CONDNL(intlen+1); PUTC(' ',f); putstring(f,s); curlen += intlen + 1; } PUTC('\n',f); } else { for (i = n; --i >= 0;) workperm[i] = 0; for (i = 0; i < n; ++i) { if (workperm[i] == 0 && perm[i] != i) { l = i; intlen = itos(l + labelorg,s); if (curlen > 3) CONDNL(2*intlen+4); PUTC('(',f); do { putstring(f,s); curlen += intlen + 1; k = l; l = perm[l]; workperm[k] = 1; if (l != i) { intlen = itos(l + labelorg,s); CONDNL(intlen+2); PUTC(' ',f); } } while (l != i); PUTC(')',f); ++curlen; } } if (curlen == 0) putstring(f,"(1)\n"); else PUTC('\n',f); } } /***************************************************************************** * * * testcanlab(g,canong,lab,samerows,m,n) compares g^lab to canong, * * using an ordering which is immaterial since it's only used here. The * * value returned is -1,0,1 if g^lab <,=,> canong. *samerows is set to * * the number of rows (0..n) of canong which are the same as those of g^lab. * * * * GLOBALS ACCESSED: workset,permset(),workperm * * * *****************************************************************************/ int testcanlab(g,canong,lab,samerows,m,n) graph *g,*canong; nvector *lab; int m,n,*samerows; { register int i,j; register SET *ph; for (i = 0; i < n; ++i) workperm[lab[i]] = i; for (i = 0, ph = canong; i < n; ++i, ph += M) { permset(GRAPHROW(g,lab[i],M),workset,M,workperm); for (j = 0; j < M; ++j) if (workset[j] < ph[j]) { *samerows = i; return(-1); } else if (workset[j] > ph[j]) { *samerows = i; return(1); } } *samerows = n; return(0); } /***************************************************************************** * * * updatecan(g,canong,lab,samerows,m,n) sets canong = g^lab, assuming * * the first samerows of canong are ok already. * * * * GLOBALS ACCESSED: permset(),workperm * * * *****************************************************************************/ void updatecan(g,canong,lab,samerows,m,n) graph *g,*canong; permutation *lab; int m,n,samerows; { register int i; register SET *ph; for (i = 0; i < n; ++i) workperm[lab[i]] = i; for (i = samerows, ph = GRAPHROW(canong,samerows,M); i < n; ++i, ph += M) permset(GRAPHROW(g,lab[i],M),ph,M,workperm); } /***************************************************************************** * * * fmperm(perm,fix,mcr,m,n) uses perm to construct fix and mcr. fix * * contains those points are fixed by perm, while mcr contains the set of * * those points which are least in their orbits. * * * * GLOBALS ACCESSED: bit * * * *****************************************************************************/ void fmperm(perm,fix,mcr,m,n) register permutation *perm; SET *fix,*mcr; int m,n; { register int i,k,l; EMPTYSET(fix,m); EMPTYSET(mcr,m); for (i = n; --i >= 0;) workperm[i] = 0; for (i = 0; i < n; ++i) if (perm[i] == i) { ADDELEMENT(fix,i); ADDELEMENT(mcr,i); } else if (workperm[i] == 0) { l = i; do { k = l; l = perm[l]; workperm[k] = 1; } while (l != i); ADDELEMENT(mcr,i); } } /***************************************************************************** * * * fmptn(lab,ptn,level,fix,mcr,m,n) uses the partition at the specified * * level in the partition nest (lab,ptn) to make sets fix and mcr. fix * * represents the points in trivial cells of the partition, while mcr * * represents those points which are least in their cells. * * * * GLOBALS ACCESSED: bit * * * *****************************************************************************/ void fmptn(lab,ptn,level,fix,mcr,m,n) nvector *lab,*ptn; register int level; SET *fix,*mcr; int m,n; { register int i,lmin; EMPTYSET(fix,m); EMPTYSET(mcr,m); for (i = 0; i < n; ++i) if (ptn[i] <= level) { ADDELEMENT(fix,lab[i]); ADDELEMENT(mcr,lab[i]); } else { lmin = lab[i]; do if (lab[++i] < lmin) lmin = lab[i]; while (ptn[i] > level); ADDELEMENT(mcr,lmin); } } /***************************************************************************** * * * refine(g,lab,ptn,level,numcells,count,active,code,m,n) performs a * * refinement operation on the partition at the specified level of the * * partition nest (lab,ptn). *numcells is assumed to contain the number of * * cells on input, and is updated. The initial set of active cells (alpha * * in the paper) is specified in the set active. Precisely, x is in active * * iff the cell starting at index x in lab is active. * * The resulting partition is equitable if active is correct (see the paper * * and the Guide). * * *code is set to a value which depends on the fine detail of the * * algorithm, but which is independent of the labelling of the graph. * * count is used for work space. * * * * GLOBALS ACCESSED: workset,bit,nextelement(),bucket,workperm * * * *****************************************************************************/ UPROC refine(g,lab,ptn,level,numcells,count,active,code,m,n) graph *g; register nvector *lab,*ptn; permutation *count; int *numcells,level,m,n,*code; SET *active; { register int i,c1,c2,labc1; register setword x; register SET *set1,*set2; int split1,split2,cell1,cell2; int cnt,bmin,bmax; long longcode; SET *gptr; longcode = *numcells; split1 = -1; while (*numcells < n && ((split1 = nextelement(active,M,split1)) >= 0 || (split1 = nextelement(active,M,-1)) >= 0)) { DELELEMENT(active,split1); for (split2 = split1; ptn[split2] > level; ++split2) {} longcode = MASH(longcode,split1 + split2); if (split1 == split2) /* trivial splitting cell */ { gptr = GRAPHROW(g,lab[split1],M); for (cell1 = 0; cell1 < n; cell1 = cell2 + 1) { for (cell2 = cell1; ptn[cell2] > level; ++cell2) {} if (cell1 == cell2) continue; c1 = cell1; c2 = cell2; while (c1 <= c2) { labc1 = lab[c1]; if (ISELEMENT(gptr,labc1)) ++c1; else { lab[c1] = lab[c2]; lab[c2] = labc1; --c2; } } if (c2 >= cell1 && c1 <= cell2) { ptn[c2] = level; longcode = MASH(longcode,c2); ++*numcells; ADDELEMENT(active,c1); } } } else /* nontrivial splitting cell */ { EMPTYSET(workset,m); for (i = split1; i <= split2; ++i) ADDELEMENT(workset,lab[i]); longcode = MASH(longcode,split2 - split1 + 1); for (cell1 = 0; cell1 < n; cell1 = cell2 + 1) { for (cell2 = cell1; ptn[cell2] > level; ++cell2) {} if (cell1 == cell2) continue; i = cell1; #if MAXM==1 if (x = workset[0] & g[lab[i]]) /* not == */ cnt = POPCOUNT(x); else cnt = 0; #else set1 = workset; set2 = GRAPHROW(g,lab[i],m); cnt = 0; for (c1 = m; --c1 >= 0;) if (x = (*set1++) & (*set2++)) /* not == */ cnt += POPCOUNT(x); #endif count[i] = bmin = bmax = cnt; bucket[cnt] = 1; while (++i <= cell2) { #if MAXM==1 if (x = workset[0] & g[lab[i]]) /* not == */ cnt = POPCOUNT(x); else cnt = 0; #else set1 = workset; set2 = GRAPHROW(g,lab[i],m); cnt = 0; for (c1 = m; --c1 >= 0;) if (x = (*set1++) & (*set2++)) /* not == */ cnt += POPCOUNT(x); #endif while (bmin > cnt) bucket[--bmin] = 0; while (bmax < cnt) bucket[++bmax] = 0; ++bucket[cnt]; count[i] = cnt; } if (bmin == bmax) { longcode = MASH(longcode,bmin + cell1); continue; } c1 = cell1; for (i = bmin; i <= bmax; ++i) if (bucket[i]) { c2 = c1 + bucket[i]; bucket[i] = c1; longcode = MASH(longcode,i + c1); if (c1 != cell1) { ADDELEMENT(active,c1); ++*numcells; } if (c2 <= cell2) ptn[c2-1] = level; c1 = c2; } for (i = cell1; i <= cell2; ++i) workperm[bucket[count[i]]++] = lab[i]; for (i = cell1; i <= cell2; ++i) lab[i] = workperm[i]; } } } longcode = MASH(longcode,*numcells); *code = CLEANUP(longcode); } /***************************************************************************** * * * refine1(g,lab,ptn,level,numcells,count,active,code,m,n) is the same as * * refine(g,lab,ptn,level,numcells,count,active,code,m,n), except that * * m==1 is assumed for greater efficiency. The results are identical in all * * respects. See refine (above) for the specs. * * * *****************************************************************************/ UPROC refine1(g,lab,ptn,level,numcells,count,active,code,m,n) graph *g; register nvector *lab,*ptn; permutation *count; int *numcells,level,m,n,*code; SET *active; { register int i,c1,c2,labc1; register setword x; int split1,split2,cell1,cell2; int cnt,bmin,bmax; long longcode; SET *gptr; longcode = *numcells; split1 = -1; while (*numcells < n && ((split1 = nextelement(active,1,split1)) >= 0 || (split1 = nextelement(active,1,-1)) >= 0)) { DELELEM1(active,split1); for (split2 = split1; ptn[split2] > level; ++split2) {} longcode = MASH(longcode,split1 + split2); if (split1 == split2) /* trivial splitting cell */ { gptr = GRAPHROW(g,lab[split1],1); for (cell1 = 0; cell1 < n; cell1 = cell2 + 1) { for (cell2 = cell1; ptn[cell2] > level; ++cell2) {} if (cell1 == cell2) continue; c1 = cell1; c2 = cell2; while (c1 <= c2) { labc1 = lab[c1]; if (ISELEM1(gptr,labc1)) ++c1; else { lab[c1] = lab[c2]; lab[c2] = labc1; --c2; } } if (c2 >= cell1 && c1 <= cell2) { ptn[c2] = level; longcode = MASH(longcode,c2); ++*numcells; ADDELEM1(active,c1); } } } else /* nontrivial splitting cell */ { *workset = 0; for (i = split1; i <= split2; ++i) ADDELEM1(workset,lab[i]); longcode = MASH(longcode,split2 - split1 + 1); for (cell1 = 0; cell1 < n; cell1 = cell2 + 1) { for (cell2 = cell1; ptn[cell2] > level; ++cell2) {} if (cell1 == cell2) continue; i = cell1; if (x = workset[0] & g[lab[i]]) /* not == */ cnt = POPCOUNT(x); else cnt = 0; count[i] = bmin = bmax = cnt; bucket[cnt] = 1; while (++i <= cell2) { if (x = workset[0] & g[lab[i]]) /* not == */ cnt = POPCOUNT(x); else cnt = 0; while (bmin > cnt) bucket[--bmin] = 0; while (bmax < cnt) bucket[++bmax] = 0; ++bucket[cnt]; count[i] = cnt; } if (bmin == bmax) { longcode = MASH(longcode,bmin + cell1); continue; } c1 = cell1; for (i = bmin; i <= bmax; ++i) if (bucket[i]) { c2 = c1 + bucket[i]; bucket[i] = c1; longcode = MASH(longcode,i + c1); if (c1 != cell1) { ADDELEM1(active,c1); ++*numcells; } if (c2 <= cell2) ptn[c2-1] = level; c1 = c2; } for (i = cell1; i <= cell2; ++i) workperm[bucket[count[i]]++] = lab[i]; for (i = cell1; i <= cell2; ++i) lab[i] = workperm[i]; } } } longcode = MASH(longcode,*numcells); *code = CLEANUP(longcode); } /***************************************************************************** * * * doref(g,lab,ptn,level,numcells,qinvar,invar,active,code,refproc, * * invarproc,mininvarlev,maxinvarlev,invararg,digraph,m,n) * * is used to perform a refinement on the partition at the given level in * * (lab,ptn). The number of cells is *numcells both for input and output. * * The input active is the active set for input to the refinement procedure * * (*refproc)(), which must have the argument list of refine(). * * active may be arbitrarily changed. invar is used for working storage. * * First, (*refproc)() is called. Then, if invarproc!=NILFUNCTION and * * |mininvarlev| <= level <= |maxinvarlev|, the routine (*invarproc)() is * * used to compute a vertex-invariant which may refine the partition * * further. If it does, (*refproc)() is called again, using an active set * * containing all but the first fragment of each old cell. Unless g is a * * digraph, this guarantees that the final partition is equitable. The * * arguments invararg and digraph are passed to (*invarproc)() * * uninterpretted. The output argument code is a composite of the codes * * from all the calls to (*refproc)(). The output argument qinvar is set * * to 0 if (*invarproc)() is not applied, 1 if it is applied but fails to * * refine the partition, and 2 if it succeeds. * * See the file nautinv.c for a further discussion of vertex-invariants. * * Note that the dreadnaut I command generates a call to this procedure * * with level = mininvarlevel = maxinvarlevel = 0. * * * *****************************************************************************/ void doref(g,lab,ptn,level,numcells,qinvar,invar,active,code,refproc,invarproc, mininvarlev,maxinvarlev,invararg,digraph,m,n) graph *g; nvector *lab,*ptn; int level,*numcells,*qinvar,*code,mininvarlev,maxinvarlev,invararg,m,n; Boolean digraph; permutation *invar; SET *active; UPROC (*refproc)(),(*invarproc)(); { register int j,h; register permutation pw; nvector iw; int i,cell1,cell2,nc,tvpos,minlev,maxlev; long longcode; Boolean same; if ((tvpos = nextelement(active,M,-1)) < 0) tvpos = 0; (*refproc)(g,lab,ptn,level,numcells,invar,active,code,M,n); minlev = (mininvarlev < 0 ? -mininvarlev : mininvarlev); maxlev = (maxinvarlev < 0 ? -maxinvarlev : maxinvarlev); if (invarproc != NILFUNCTION && *numcells < n && level >= minlev && level <= maxlev) { (*invarproc)(g,lab,ptn,level,*numcells,tvpos,invar,invararg, digraph,M,n); EMPTYSET(active,m); for (i = n; --i >= 0;) workperm[i] = invar[lab[i]]; nc = *numcells; for (cell1 = 0; cell1 < n; cell1 = cell2 + 1) { pw = workperm[cell1]; same = TRUE; for (cell2 = cell1; ptn[cell2] > level; ++cell2) if (workperm[cell2+1] != pw) same = FALSE; if (same) continue; j = (cell2 - cell1 + 1) / 3; h = 1; do h = 3 * h + 1; while (h < j); do /* shell sort */ { for (i = cell1 + h; i <= cell2; ++i) { iw = lab[i]; pw = workperm[i]; for (j = i; workperm[j-h] > pw; ) { workperm[j] = workperm[j-h]; lab[j] = lab[j-h]; if ((j -= h) < cell1 + h) break; } workperm[j] = pw; lab[j] = iw; } h /= 3; } while (h > 0); for (i = cell1 + 1; i <= cell2; ++i) if (workperm[i] != workperm[i-1]) { ptn[i-1] = level; ++*numcells; ADDELEMENT(active,i); } } if (*numcells > nc) { *qinvar = 2; longcode = *code; (*refproc)(g,lab,ptn,level,numcells,invar,active,code,M,n); longcode = MASH(longcode,*code); *code = CLEANUP(longcode); } else *qinvar = 1; } else *qinvar = 0; } /***************************************************************************** * * * cheapautom(ptn,level,digraph,n) returns TRUE if the partition at the * * specified level in the partition nest (lab,ptn) {lab is not needed here} * * satisfies a simple sufficient condition for its cells to be the orbits of * * some subgroup of the automorphism group. Otherwise it returns FALSE. * * It always returns FALSE if digraph!=FALSE. * * * * nauty assumes that this function will always return TRUE for any * * partition finer than one for which it returns TRUE. * * * *****************************************************************************/ Boolean cheapautom(ptn,level,digraph,n) register nvector *ptn; register int level; Boolean digraph; int n; { register int i,k,nnt; if (digraph) return(FALSE); k = n; nnt = 0; for (i = 0; i < n; ++i) { --k; if (ptn[i] > level) { ++nnt; while (ptn[++i] > level) {} } } return(k <= nnt + 1 || k <= 4); } /***************************************************************************** * * * targetcell(g,lab,ptn,level,numcells,tcell,tcellsize,&cellpos,tc_level, * * hint,m,n) * * examines the partition at the specified level in the partition nest * * (lab,ptn) and finds a non-trival cell (if none, the first cell). * * If hint >= 0 and there is a non-trivial cell starting at position hint * * in lab, that cell is chosen. * * Else, If level <= tc_level, bestcell is called to choose a cell. * * Else, the first non-trivial cell is chosen. * * When a cell is chosen, tcell is set to its contents, *tcellsize to its * * size, and cellpos to its starting position in lab. * * * * GLOBALS ACCESSED: bit,bestcell() * * * *****************************************************************************/ UPROC targetcell(g,lab,ptn,level,numcells,tcell,tcellsize,cellpos,tc_level,hint,m,n) graph *g; register nvector *lab,*ptn; SET *tcell; register int level; int numcells,*tcellsize,*cellpos,tc_level,hint,m,n; { register int i,j,k; if (hint >= 0 && ptn[hint] > level && (hint == 0 || ptn[hint-1] <= level)) i = hint; else if (level <= tc_level) i = bestcell(g,lab,ptn,level,tc_level,m,n); else for (i = 0; i < n && ptn[i] <= level; ++i) {} if (i == n) i = j = 0; else for (j = i + 1; ptn[j] > level; ++j) {} *tcellsize = j - i + 1; EMPTYSET(tcell,m); for (k = i; k <= j; ++k) ADDELEMENT(tcell,lab[k]); *cellpos = i; } /***************************************************************************** * * * bestcell(g,lab,ptn,level,tc_level,m,n) returns the index in lab of the * * start of the "best non-singleton cell" for fixing. If there is no * * non-singleton cell it returns n. * * This implementation finds the first cell which is non-trivially joined * * to the greatest number of other cells. * * * * GLOBALS ACCESSED: bit,workperm,workset,bucket * * * *****************************************************************************/ int bestcell(g,lab,ptn,level,tc_level,m,n) graph *g; nvector *lab,*ptn; int level,tc_level,m,n; { register int i; SET *gp; register setword setword1,setword2; int v1,v2,nnt; /* find non-singleton cells: put starts in workperm[0..nnt-1] */ i = nnt = 0; while (i < n) { if (ptn[i] > level) { workperm[nnt++] = i; while (ptn[i] > level) ++i; } ++i; } if (nnt == 0) return(n); /* set bucket[i] to # non-trivial neighbours of n.s. cell i */ for (i = nnt; --i >= 0;) bucket[i] = 0; for (v2 = 1; v2 < nnt; ++v2) { EMPTYSET(workset,m); i = workperm[v2] - 1; do { ++i; ADDELEMENT(workset,lab[i]); } while (ptn[i] > level); for (v1 = 0; v1 < v2; ++v1) { gp = GRAPHROW(g,lab[workperm[v1]],m); #if MAXM==1 setword1 = *workset & *gp; setword2 = *workset & ~*gp; #else setword1 = setword2 = 0; for (i = m; --i >= 0;) { setword1 |= workset[i] & gp[i]; setword2 |= workset[i] & ~gp[i]; } #endif if (setword1 != 0 && setword2 != 0) { ++bucket[v1]; ++bucket[v2]; } } } /* find first greatest bucket value */ v1 = 0; v2 = bucket[0]; for (i = 1; i < nnt; ++i) if (bucket[i] > v2) { v1 = i; v2 = bucket[i]; } return((int)workperm[v1]); } /***************************************************************************** * * * shortprune(set1,set2,m) ANDs the contents of set set2 into set set1. * * * * GLOBALS ACCESSED: NONE * * * *****************************************************************************/ void shortprune(set1,set2,m) register SET *set1,*set2; register int m; { register int i; for (i = 0; i < M; ++i) INTERSECT(set1[i],set2[i]); } /***************************************************************************** * * * breakout(lab,ptn,level,tc,tv,active,m) operates on the partition at * * the specified level in the partition nest (lab,ptn). It finds the * * element tv, which is in the cell C starting at index tc in lab (it had * * better be) and splits C in the two cells {tv} and C\{tv}, in that order. * * It also sets the set active to contain just the element tc. * * * * GLOBALS ACCESSED: bit * * * *****************************************************************************/ void breakout(lab,ptn,level,tc,tv,active,m) nvector *lab,*ptn; SET *active; int level,tc,tv,m; { register int i,prev,next; EMPTYSET(active,m); ADDELEMENT(active,tc); i = tc; prev = tv; do { next = lab[i]; lab[i++] = prev; prev = next; } while (prev != tv); ptn[tc] = level; } /***************************************************************************** * * * longprune(tcell,fix,bottom,top,m) removes zero or elements of the set * * tcell. It is assumed that addresses bottom through top-1 contain * * contiguous pairs of sets (f1,m1),(f2,m2), ... . tcell is intersected * * with each mi such that fi is a subset of fix. * * * * GLOBALS ACCESSED: NONE * * * *****************************************************************************/ void longprune(tcell,fix,bottom,top,m) register SET *tcell,*fix,*bottom; SET *top; int m; { register int i; while (bottom < top) { for (i = 0; i < M; ++i) if (NOTSUBSET(fix[i],bottom[i])) break; bottom += M; if (i == M) for (i = 0; i < M; ++i) INTERSECT(tcell[i],bottom[i]); bottom += M; } } /***************************************************************************** * * * nautil_null() does nothing. See dreadnaut.c for its purpose. * * * *****************************************************************************/ void nautil_null() { } |-> doc/nug.alw %! %%Dimensions: 0 0 595 842 %%Title: dvialw nug %%CreationDate: Sun Mar 29 10:39:22 1992 %%Creator: bdm and [DVIALW Version 2.06b/ANU1.5 for PostScript [Apple LaserWriter]] %%Pages: (atend) %%BugHistory: Incorporates X-on/X-off bug fix %%EndComments %%EndProlog ([Starting TeX job sent by bdm]\n) print flush /TeXdict 200 dict def TeXdict begin /bdf {bind def} def /B { /h exch def /w exch def gsave currentpoint newpath moveto w 1 sub 0 rlineto 0 h 1 sub rlineto w 1 sub neg 0 rlineto closepath fill grestore } bdf /BOJ { 72 Resolution div 72 Resolution div scale NOTE } bdf /BOP { clear Mtrx setmatrix 25 0 translate } bdf /ch-image {ch-data 0 get} bdf /ch-xoff {ch-data 1 get} bdf /ch-yoff {ch-data 2 get} bdf /ch-width {ch-data 3 get} bdf /ch-height {ch-data 4 get} bdf /ch-tfmw {ch-data 5 get} bdf /CharBuilder { /ch-code exch def /font-dict exch def /ch-data font-dict /BitMaps get ch-code get def ch-data null eq not { ch-tfmw 0 ch-xoff neg ch-yoff ch-height sub ch-width ch-xoff sub ch-yoff setcachedevice 0 0 transform floor 0.5 add exch floor 0.5 add exch itransform translate ch-width ch-height true [ 1 0 0 -1 ch-xoff ch-yoff 1 add ] {ch-image} imagemask } if } bdf /D { /ch-code exch def /ch-data exch def currentfont /BitMaps get ch-code ch-data put currentfont /Encoding get ch-code dup 3 string cvs cvn put } bdf /EOJ { end } bdf /EOP { /#copies exch def showpage } bdf /LANDSCAPE { a4 initmatrix 72 Resolution div dup scale -1420 3508 translate -90 rotate Mtrx currentmatrix pop } bdf /LEGAL { legal initmatrix 72 Resolution div dup scale 69 267 translate Mtrx currentmatrix pop } bdf /LETTER { letter initmatrix 72 Resolution div dup scale 77 -620 translate Mtrx currentmatrix pop } bdf /A4 { a4 initmatrix 72 Resolution div dup scale -16 -420 translate Mtrx currentmatrix pop } bdf /M { moveto } bdf /Mtrx 6 array def /NF { /newname exch def newname 7 dict def newname load begin /BitMaps 128 array def /BuildChar { CharBuilder } def /Encoding 128 array def 0 1 127 { Encoding exch /.notdef put } for /FontBBox [ 0 0 1 1 ] def /FontMatrix [ 1 0 0 1 0 0 ] def /FontType 3 def end newname newname load definefont def } bdf() pop /NOTE { userdict /note known {note} {letter} ifelse initmatrix 72 Resolution div dup scale -23 -420 translate Mtrx currentmatrix pop } bdf /P {show} bdf() pop /Q {moveto w h B} bdf() pop /R {0 rmoveto show} bdf() pop /Resolution 300 def /S {moveto show} bdf() pop /SF { setfont } bdf() pop /T {currentpoint exch pop moveto show} bdf() pop /L {lineto} bdf /RM {2 copy neg exch neg exch 5 2 roll translate rotate translate} bdf /SC {/currY exch def /currX exch def /currT exch def} bdf /CP {currX currY moveto} bdf /AP {arcto pop pop pop pop} bdf /PSFONT {Resolution mul 72 div exch findfont exch scalefont setfont} bdf /MANFEED {statusdict begin /manualfeedtimeout 300 def /manualfeed true def end} bdf /SHOWPAT {/Mag exch def /Rot exch def /Bitpat exch def save currentpoint 1 add L Rot rotate /Cellsize Mag 8 mul def pathbbox Cellsize add /ury exch def Cellsize add /urx exch def Cellsize sub /lly exch def Cellsize sub /llx exch def SPCLIP /FFIL /filpatfont NF FFIL Mag scalefont SF [Bitpat 0 0 8 8 8] 1 D lly Cellsize ury {llx exch moveto llx Cellsize urx {pop <01> show} for} for restore} def /showpattern {/SPCLIP {clip} def SHOWPAT} def /eoshowpattern {/SPCLIP {eoclip} def SHOWPAT} def /GF { /basefontname exch def /newscalefactor exch def /newfontname exch def /TeXstr 40 string def basefontname length 4 add string /savedfontname exch def savedfontname 4 basefontname putinterval savedfontname 0 (TeX-) putinterval savedfontname cvn /savedfontname exch def FontDirectory savedfontname known not { /basefontdict basefontname findfont def /newfont basefontdict maxlength dict def basefontdict { exch dup /FID ne { dup /Encoding eq { exch dup length array copy newfont 3 1 roll put } { exch newfont 3 1 roll put } ifelse } { pop pop } ifelse } forall basefontname TeXstr cvs (Dingbat) search { pop pop pop } {(Symbol) search {pop pop pop} {pop /TeXvec basefontname TeXstr cvs (Courier) search { pop pop pop TeXcourvec } { pop TeXnormalvec } ifelse def TeXvec aload pop TeXvec length 2 idiv { newfont /Encoding get 3 1 roll put } repeat } ifelse } ifelse savedfontname savedfontname newfont definefont def } if newfontname savedfontname findfont newscalefactor scalefont def } def /TeXnormalvec [ 8#014 /fi 8#015 /fl 8#020 /dotlessi 8#022 /grave 8#023 /acute 8#024 /caron 8#025 /breve 8#026 /macron 8#027 /ring 8#030 /cedilla 8#031 /germandbls 8#032 /ae 8#033 /oe 8#034 /oslash 8#035 /AE 8#036 /OE 8#037 /Oslash 8#042 /quotedblright 8#074 /exclamdown 8#076 /questiondown 8#134 /quotedblleft 8#136 /circumflex 8#137 /dotaccent 8#173 /endash 8#174 /emdash 8#175 /hungarumlaut 8#176 /tilde 8#177 /dieresis 8#200 /quotedbl 8#201 /less 8#202 /greater 8#203 /backslash 8#204 /asciicircum 8#205 /underscore 8#206 /braceleft 8#207 /bar 8#210 /braceright 8#211 /asciitilde ] def /TeXcourvec [ 8#016 /exclamdown 8#017 /questiondown 8#020 /dotlessi 8#022 /grave 8#023 /acute 8#024 /caron 8#025 /breve 8#026 /macron 8#027 /ring 8#030 /cedilla 8#031 /germandbls 8#034 /oslash 8#037 /Oslash 8#042 /quotedblright 8#074 /less 8#076 /greater 8#136 /circumflex 8#137 /dotaccent 8#175 /hungarumlaut 8#176 /tilde 8#177 /dieresis 8#200 /quotedbl 8#205 /underscore 8#206 /braceleft 8#207 /bar 8#210 /braceright 8#211 /asciitilde ] def end /Times-Roman findfont setfont TeXdict begin BOJ NOTE /F41 /cmmib10_1643 NF % /usr/lib/tex/fonts/cmmib10.329pk /F37 /cmti9_1643 NF % /usr/lib/tex/fonts/cmti9.329pk /F36 /cmti10_1643 NF % /usr/lib/tex/fonts/cmti10.329pk /F33 /cmsl10_1643 NF % /usr/lib/tex/fonts/cmsl10.329pk /F30 /cmtt9_1643 NF % /usr/lib/tex/fonts/cmtt9.329pk /F29 /cmtt10_1643 NF % /usr/lib/tex/fonts/cmtt10.329pk /F23 /cmbx10_1643 NF % /usr/lib/tex/fonts/cmbx10.329pk /F18 /cmex10_1643 NF % /usr/lib/tex/fonts/cmex10.329pk /F17 /cmsy5_1643 NF % /usr/lib/tex/fonts/cmsy5.329pk /F15 /cmsy7_1643 NF % /usr/lib/tex/fonts/cmsy7.329pk /F14 /cmsy8_1643 NF % /usr/lib/tex/fonts/cmsy8.329pk /F12 /cmsy10_1643 NF % /usr/lib/tex/fonts/cmsy10.329pk /F11 /cmmi5_1643 NF % /usr/lib/tex/fonts/cmmi5.329pk /F9 /cmmi7_1643 NF % /usr/lib/tex/fonts/cmmi7.329pk /F6 /cmmi10_1643 NF % /usr/lib/tex/fonts/cmmi10.329pk /F5 /cmr5_1643 NF % /usr/lib/tex/fonts/cmr5.329pk /F3 /cmr7_1643 NF % /usr/lib/tex/fonts/cmr7.329pk /F2 /cmr8_1643 NF % /usr/lib/tex/fonts/cmr8.329pk /F1 /cmr9_1643 NF % /usr/lib/tex/fonts/cmr9.329pk /F0 /cmr10_1643 NF % /usr/lib/tex/fonts/cmr10.329pk %%Page: 26 1 BOP F23 SF [< 0000E00000 0000E00000 0001F00000 0001F00000 0001F00000 0003F80000 0003F80000 0006FC0000 0006FC0000 000EFE0000 000C7E0000 000C7E0000 00183F0000 00183F0000 00303F8000 00301F8000 00701FC000 00600FC000 00600FC000 00C007E000 00FFFFE000 01FFFFF000 018003F000 018003F000 030001F800 030001F800 060001FC00 060000FC00 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FC00 F000 6000 >-2 24 16 22 21.4857533]62 D ()493 T (#define)300 3055 S [< FC0FC0 FE1FC0 FE1FC0 3A1700 3B3700 3B3700 3B3700 3B3700 3B3700 3B3700 3B3700 3B3700 392700 392700 39E700 39E700 38C700 380700 380700 380700 380700 380700 FE1FC0 FE1FC0 FE1FC0 >-1 25 18 25 21.4857533]77 D [< 01E000 01E000 01E000 033000 033000 033000 033000 033000 073800 073800 073800 073800 061800 0E1C00 0E1C00 0E1C00 0FFC00 0FFC00 1FFE00 1C0E00 1C0E00 1C0E00 7F3F80 FF3FC0 7F3F80 >-1 25 18 25 21.4857533]65 D [< 7E3F00 7F3F80 7E3F00 0E1C00 0E3800 0F3800 077000 07F000 03F000 03E000 01E000 01C000 01E000 03E000 03F000 03F000 077800 073800 0E3C00 0E1C00 1E1C00 1C0E00 7E1F80 FF3FC0 7E1F80 >-1 25 18 25 21.4857533]88 D [< 7E0FE0 FF1FF0 7F0FE0 1D8380 1D8380 1D8380 1DC380 1CC380 1CC380 1CC380 1CE380 1CE380 1C6380 1C7380 1C7380 1C3380 1C3380 1C3380 1C3B80 1C1B80 1C1B80 1C1B80 7F0F80 FF8F80 7F0780 >0 25 20 25 21.4857533]78 D (MAXN)472 T [< 0180 0380 0380 0780 0F80 7F80 FF80 7380 0380 0380 0380 0380 0380 0380 0380 0380 0380 0380 0380 0380 0380 0380 7FFC 7FFC 7FFC >-3 25 14 25 21.4857533]49 D [< 03C0 0FF0 1FF8 3C3C 381C 781E 700E 700E E007 E007 E007 E007 E007 E007 E007 E007 F00F 700E 700E 781E 381C 3C3C 1FF8 0FF0 03C0 >-2 25 16 25 21.4857533]48 D (100)579 T (#include)300 3007 S [< 2010 7038 F03C F03C 7038 7038 7038 7038 7038 7038 7038 7038 >-3 26 14 12 21.4857533]34 D ("nauty.h")493 T [< 00E0 01E0 03E0 0780 0F00 1E00 3C00 3800 7000 7000 7000 E000 E000 E000 E000 E000 E000 E000 E000 7000 7000 7000 3800 3C00 1E00 0F00 0780 03E0 01E0 00E0 >-5 28 11 30 21.4857533]40 D [< 6000 F000 7800 3C00 1E00 0F00 0780 0380 01C0 01C0 01C0 00E0 00E0 00E0 00E0 00E0 00E0 00E0 00E0 01C0 01C0 01C0 0380 0780 0F00 1E00 3C00 7800 F000 6000 >-4 28 11 30 21.4857533]41 D (main\(\))300 2913 S [< 001F 007F 00FF 01E0 01C0 01C0 01C0 01C0 01C0 01C0 01C0 01C0 01C0 03C0 FF80 FF00 FF80 03C0 01C0 01C0 01C0 01C0 01C0 01C0 01C0 01C0 01C0 01E0 00FF 007F 001F >-2 28 16 31 21.4857533]123 D ({)300 2866 S (graph)472 2818 S [< FFE0 FFE0 FFE0 E000 E000 E000 E000 E000 E000 E000 E000 E000 E000 E000 E000 E000 E000 E000 E000 E000 E000 E000 E000 E000 E000 E000 E000 E000 FFE0 FFE0 FFE0 >-8 28 11 31 21.4857533]91 D [< FFE0 FFE0 FFE0 00E0 00E0 00E0 00E0 00E0 00E0 00E0 00E0 00E0 00E0 00E0 00E0 00E0 00E0 00E0 00E0 00E0 00E0 00E0 00E0 00E0 00E0 00E0 00E0 00E0 FFE0 FFE0 FFE0 >-1 28 11 31 21.4857533]93 D [< 38 7C 7C 7C 38 00 00 00 00 00 00 00 00 38 78 7C 7C 3C 1C 1C 38 F8 F0 C0 >-7 18 6 24 21.4857533]59 D (g[MAXN*MAXM];)601 T (nvector)472 2771 S (lab[MAXN],ptn[MAXN],orbits[MAXN];)644 T (static)472 2724 S [< 7FF800 FFFC00 7FFE00 1C1F00 1C0700 1C0780 1C0380 1C0380 1C03C0 1C01C0 1C01C0 1C01C0 1C01C0 1C01C0 1C01C0 1C01C0 1C01C0 1C0380 1C0380 1C0780 1C0700 1C1F00 7FFE00 FFFC00 7FF800 >0 25 18 25 21.4857533]68 D [< 7FFF80 FFFF80 7FFF80 1C0380 1C0380 1C0380 1C0380 1C0000 1C0000 1C3800 1C3800 1FF800 1FF800 1FF800 1C3800 1C3800 1C0000 1C01C0 1C01C0 1C01C0 1C01C0 1C01C0 7FFFC0 FFFFC0 7FFFC0 >-1 25 18 25 21.4857533]69 D [< FFFFC0 FFFFC0 FFFFC0 1C01C0 1C01C0 1C01C0 1C01C0 1C0000 1C0000 1C3800 1C3800 1FF800 1FF800 1FF800 1C3800 1C3800 1C0000 1C0000 1C0000 1C0000 1C0000 1C0000 FF8000 FFC000 FF8000 >-1 25 18 25 21.4857533]70 D [< 7F0FE0 FF9FF0 7F0FE0 1C0380 1C0380 1C0380 1C0380 1C0380 1C0380 1C0380 1C0380 1C0380 1C0380 1C0380 1C0380 1C0380 1C0380 1C0380 1C0380 1C0380 0E0700 0F0F00 07FE00 03FC00 00F000 >0 25 20 25 21.4857533]85 D [< FFC000 FFC000 FFC000 1C0000 1C0000 1C0000 1C0000 1C0000 1C0000 1C0000 1C0000 1C0000 1C0000 1C0000 1C0000 1C0000 1C0000 1C0080 1C01C0 1C01C0 1C01C0 1C01C0 FFFFC0 FFFFC0 FFFFC0 >-1 25 18 25 21.4857533]76 D [< 1FF8 3FFC 7FFE 781E F00F E007 E007 E007 E007 E007 E007 E007 E007 E007 E007 E007 E007 E007 E007 E007 F00F 781E 7FFE 3FFC 1FF8 >-2 25 16 25 21.4857533]79 D [< 7FF800 FFFC00 7FFE00 1C0F00 1C0700 1C0380 1C0380 1C0380 1C0380 1C0380 1C0700 1C0F00 1FFE00 1FFC00 1FF800 1C0000 1C0000 1C0000 1C0000 1C0000 1C0000 1C0000 7F0000 FF8000 7F0000 >-1 25 17 25 21.4857533]80 D [< 07EE 1FFE 3FFE 783E F00E E00E E00E E000 F000 7800 3F00 1FF0 0FF8 00FC 001E 000E 0007 0007 6007 E007 E00E F01E FFFC FFF8 EFE0 >-2 25 16 25 21.4857533]83 D (DEFAULTOPTIONS\(options\);)622 T (statsblk\(stats\);)472 2677 S (setword)472 2629 S [< 3FFC 3FFC 3FFC 3800 3800 3800 3800 3800 3800 3800 3FE0 3FF8 3FFC 381E 300E 0007 0007 6007 F007 F007 E00E 783E 7FFC 1FF0 07C0 >-2 25 16 25 21.4857533]53 D (workspace[50*MAXM];)644 T (int)472 2535 S (n,m,v;)558 T (set)472 2487 S (*gv;)558 T (options.writemarkers)472 2393 S [< 7FFE FFFF FFFF FFFF 0000 0000 0000 0000 FFFF FFFF FFFF 7FFE >-2 19 16 12 21.4857533]61 D (=)923 T (FALSE;)966 T (printf\("enter)472 2298 S (n)773 T [< 70 F8 F8 F8 70 00 00 00 00 00 00 00 00 70 F8 F8 F8 70 >-8 18 5 18 21.4857533]58 D (:)816 T ("\);)859 T (if)472 2251 S [< 380600 7C0F00 7C0F00 EE1F00 EE1E00 EE1E00 EE3E00 EE3C00 7C7C00 7C7800 387800 00F800 00F000 00F000 01F000 01E000 03E000 03C000 03C000 07C000 078700 078F80 0F8F80 0F1DC0 1F1DC0 1E1DC0 1E1DC0 3E1DC0 3C0F80 3C0F80 180700 >-1 28 18 31 21.4857533]37 D [< 038000 0FC000 0FC000 1CE000 1CE000 1CE000 1CE000 1CEFC0 1DCFC0 1FCFC0 1F8E00 0F0E00 1E1C00 3E1C00 3F1C00 773800 F7B800 E3F000 E1F000 E1E100 E0E380 71F380 7FFF80 3FBF00 1E0E00 >-1 25 18 25 21.4857533]38 D (\(scanf\("%d",&n\))536 T [< 60 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 60 00 00 00 00 00 60 F0 F0 60 >-8 25 4 25 21.4857533]33 D (!=)880 T (1)945 T [< 60 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 60 >-8 28 4 31 21.4857533]124 D (||)988 T (n)1052 T (<)1095 T (1)1138 T (||)1181 T (n)1245 T (>)1288 T (MAXN\))1331 T ({)472 2204 S (printf\("The)558 2157 S (input)816 T (must)945 T (be)1052 T (an)1116 T (integer)1181 T (in)1353 T (the)1417 T (range)1503 T [< 6000 F000 F000 F800 7800 7C00 3C00 3E00 1E00 1F00 0F00 0F00 0F80 0780 07C0 03C0 03E0 01E0 01F0 00F0 00F0 00F8 0078 007C 003C 003E 001E 001F 000F 000F 0006 >-2 28 16 31 21.4857533]92 D (1..%d.\\n",MAXN\);)1632 T (exit\(1\);)558 2109 S [< 7C00 FF00 FF80 03C0 01C0 01C0 01C0 01C0 01C0 01C0 01C0 01C0 01C0 01E0 00FF 007F 00FF 01E0 01C0 01C0 01C0 01C0 01C0 01C0 01C0 01C0 01C0 03C0 FF80 FF00 7C00 >-2 28 16 31 21.4857533]125 D (})472 2062 S (m)472 1968 S (=)515 T (\(n)558 T [< 0180 03C0 03C0 03C0 03C0 03C0 03C0 7FFE FFFF FFFF 7FFE 03C0 03C0 03C0 03C0 03C0 03C0 0180 >-2 22 16 18 21.4857533]43 D (+)622 T [< 7E07E0 FF0FF0 7E07E0 3801C0 3801C0 3801C0 3801C0 3801C0 180180 1C0380 1CF380 1DFB80 1DFB80 1D9B80 1D9B80 1D9B80 1D9B80 0D9B00 0D9B00 0D9B00 0D9B00 0D9B00 0F0F00 0F0F00 070E00 >0 25 20 25 21.4857533]87 D [< 7FF000 FFF800 7FFC00 1C1E00 1C0F00 1C0700 1C0700 1C0700 1C0700 1C0F00 1C1E00 1FFC00 1FF800 1FFC00 1C1C00 1C0E00 1C0E00 1C0E00 1C0E00 1C0E20 1C0E70 1C0E70 7F07E0 FF87E0 7F03C0 >0 25 20 25 21.4857533]82 D [< 7FFF FFFF FFFF E00E E01E E01C E038 0078 0070 00E0 00E0 01C0 03C0 0380 0700 0700 0E00 1E07 1C07 3807 7807 7007 FFFF FFFF FFFF >-2 25 16 25 21.4857533]90 D (WORDSIZE)665 T (-)859 T (1\))902 T (/)966 T (WORDSIZE;)1009 T (for)472 1873 S (\(v)558 T (=)622 T (0;)665 T (v)730 T (<)773 T (n;)816 T (++v\))880 T ({)472 1826 S (gv)558 1779 S (=)622 T [< 03CE00 0FFE00 1FFE00 1C3E00 381E00 380E00 700E00 700E00 E00000 E00000 E00000 E00000 E00000 E07F00 E07F80 E07F00 E00E00 700E00 700E00 381E00 381E00 1C3E00 1FFE00 0FFE00 03CE00 >-2 25 17 25 21.4857533]71 D [< 7F0FE0 FF9FF0 7F0FE0 1C0380 1C0380 1C0380 1C0380 1C0380 1C0380 1C0380 1FFF80 1FFF80 1FFF80 1C0380 1C0380 1C0380 1C0380 1C0380 1C0380 1C0380 1C0380 1C0380 7F0FE0 FF9FF0 7F0FE0 >0 25 20 25 21.4857533]72 D (GRAPHROW\(g,v,m\);)665 T [< FE1FC0 FF3FC0 FE1FC0 1C0F00 1C0E00 0E1E00 0E1C00 071C00 073C00 073800 03B800 03B000 01F000 01F000 00E000 00E000 00E000 00E000 00E000 00E000 00E000 00E000 03F800 07FC00 03F800 >-1 25 18 25 21.4857533]89 D (EMPTYSET\(gv,m\);)558 1684 S (ADDELEMENT\(gv,\(v+n-1\)%n\);)558 1637 S (ADDELEMENT\(gv,\(v+1\)%n\);)558 1589 S (})472 1542 S (printf\("Generators)472 1448 S (for)880 T [< 01E7 07FF 0FFF 1E1F 3C0F 3807 7007 7007 E000 E000 E000 E000 E000 E000 E000 E000 E000 7007 7007 3807 3C0F 1E1E 0FFC 07F8 01E0 >-2 25 16 25 21.4857533]67 D (Aut\(C[%d]\):\\n",n\);)966 T (nauty\(g,lab,ptn,NILSET,orbits,&options,&stats,)472 1400 S (workspace,50*MAXM,m,n,NILGRAPH\);)816 1353 S (})300 1306 S F0 SF [< 03F000 0C1C00 100E00 200700 400780 800780 F007C0 F803C0 F803C0 F803C0 2007C0 0007C0 000780 000780 000F00 000E00 001C00 003800 007000 006000 00C000 018000 030000 060040 0C0040 180040 100080 3FFF80 7FFF80 FFFF80 >-2 30 18 30 22.7365806]50 D [< 007C00 018200 070100 0E0380 0C0780 1C0780 380300 380000 780000 700000 700000 F1F000 F21C00 F40600 F80700 F80380 F80380 F003C0 F003C0 F003C0 F003C0 F003C0 7003C0 7003C0 700380 380380 380700 180700 0C0E00 061C00 01F000 >-2 30 18 31 22.7365806]54 D (26)1201 610 S 1 EOP %%Page: 25 2 BOP F23 SF [< 00E000 01E000 0FE000 FFE000 F3E000 03E000 03E000 03E000 03E000 03E000 03E000 03E000 03E000 03E000 03E000 03E000 03E000 03E000 03E000 03E000 03E000 03E000 03E000 03E000 03E000 03E000 03E000 FFFF80 FFFF80 >-4 29 17 29 26.1468491]49 D [< 003F00 01FFC0 07E0E0 0F81E0 1F03F0 1E03F0 3E03F0 7C03F0 7C01E0 7C0000 FC1000 FCFF00 FDFFC0 FD03E0 FE01F0 FE01F0 FC01F8 FC01F8 FC01F8 FC01F8 7C01F8 7C01F8 7C01F8 3C01F0 3E01F0 1E03E0 0F07C0 07FF80 01FE00 >-2 29 21 29 26.1468491]54 D (16.)300 3555 S [< FFFFF80000 FFFFFF0000 07E01FC000 07E007E000 07E003F000 07E003F000 07E003F800 07E003F800 07E003F800 07E003F800 07E003F000 07E003F000 07E007E000 07E01FC000 07FFFF0000 07FFFC0000 07E03E0000 07E01F0000 07E00F8000 07E00F8000 07E00FC000 07E00FC000 07E00FC000 07E00FE000 07E00FE000 07E00FE000 07E00FE030 07E007F030 07E003F860 FFFF01FFC0 FFFF007F80 >-2 31 36 31 39.2202737]82 D [< 001F80 00FFC0 01F3E0 03E7E0 03C7E0 07C7E0 07C3C0 07C000 07C000 07C000 07C000 07C000 FFFC00 FFFC00 07C000 07C000 07C000 07C000 07C000 07C000 07C000 07C000 07C000 07C000 07C000 07C000 07C000 07C000 07C000 07C000 3FFC00 3FFC00 >-1 32 19 32 15.9786300]102 D [< FE3E00 FE7F80 1ECFC0 1E8FC0 1E8FC0 1F8FC0 1F0300 1F0000 1F0000 1F0000 1F0000 1F0000 1F0000 1F0000 1F0000 1F0000 1F0000 1F0000 FFF000 FFF000 >-2 20 18 20 21.5364747]114 D [< 01FE00 07FF80 1F0FC0 3E0FC0 3E0FC0 7C0FC0 7C0300 FC0000 FC0000 FC0000 FC0000 FC0000 FC0000 7C0000 7E0000 3E0060 3F00C0 1F81C0 07FF00 01FC00 >-2 20 19 20 23.2416437]99 D [< 0FE6 3FFE 701E 600E E006 E006 F800 FFC0 7FF8 3FFC 1FFE 03FE 001F C007 C007 E007 F006 F81E FFFC C7F0 >-2 20 16 20 20.6268894]115 D (References.)390 T F0 SF [< FE FE C0 C0 C0 C0 C0 C0 C0 C0 C0 C0 C0 C0 C0 C0 C0 C0 C0 C0 C0 C0 C0 C0 C0 C0 C0 C0 C0 C0 C0 C0 C0 C0 C0 C0 C0 C0 C0 C0 C0 C0 C0 FE FE >-4 34 7 45 12.6314337]91 D [< 0180 0380 0F80 F380 0380 0380 0380 0380 0380 0380 0380 0380 0380 0380 0380 0380 0380 0380 0380 0380 0380 0380 0380 0380 0380 0380 0380 0380 07C0 FFFE >-4 30 15 30 22.7365806]49 D [< FE FE 06 06 06 06 06 06 06 06 06 06 06 06 06 06 06 06 06 06 06 06 06 06 06 06 06 06 06 06 06 06 06 06 06 06 06 06 06 06 06 06 06 FE FE >-1 34 7 45 12.6314337]93 D ([1])300 3486 S [< FFFFE000 0F803800 07801E00 07801F00 07800F00 07800F80 07800F80 07800F80 07800F80 07800F80 07800F00 07801F00 07801E00 07803C00 07FFF000 07803C00 07801E00 07800F00 07800F80 07800780 078007C0 078007C0 078007C0 078007C0 078007C0 07800780 07800F80 07800F00 07801F00 0F803C00 FFFFF000 >-2 31 26 31 32.2101732]66 D (B.)391 T [< FFF07FF81FF0 1F800FC007C0 0F0007800380 0F0007800100 0F0007C00100 078007C00200 078007C00200 078007C00200 03C009E00400 03C009E00400 03C009E00400 03E010F00C00 01E010F00800 01E010F00800 01F020780800 00F020781000 00F020781000 00F0403C1000 0078403C2000 0078403C2000 0078C03E2000 003C801E4000 003C801E4000 003C801E4000 001F000F8000 001F000F8000 001F000F8000 001E00078000 000E00070000 000E00070000 000C00030000 000400020000 >-1 31 44 32 46.7362699]87 D (W.)461 T [< FFFC0FFC 0FC003E0 07800180 07800100 07800200 07800400 07800800 07801000 07802000 07804000 07808000 07810000 07830000 07878000 078F8000 0793C000 0791E000 07A1E000 07C0F000 0780F000 07807800 07803C00 07803C00 07801E00 07801E00 07800F00 07800780 07800780 078007C0 0FC007E0 FFFC3FFC >-2 31 30 31 35.3680143]75 D [< 0E3E00 FE4300 0E8180 0F01C0 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41 25.5658081]12 D [< 0002 0002 0006 000E 003C 00DC 031C 001C 0038 0038 0038 0038 0070 0070 0070 0070 00E0 00E0 00E0 00E0 01C0 01C0 01C0 01C0 0380 0380 0380 0380 0780 FFF8 >-5 30 15 30 23.2416437]49 D (e\014ne1)956 T F0 SF (whic)1088 T (h)1178 T (is)1215 T (automatically)1257 T (used)1540 T (in)1640 T (place)1689 T (of)1801 T F36 SF (r)1849 T (e\014ne)1867 T F0 SF (if)1974 T F6 SF [< 1E07C07C00 2318618600 23A0320300 43C0340300 4380380380 4380380380 8700700700 0700700700 0700700700 0700700700 0E00E00E00 0E00E00E00 0E00E00E00 0E00E01C10 1C01C01C20 1C01C03820 1C01C03840 1C01C01840 3803801880 1801800F00 >-2 20 36 20 39.9259326]109 D (m)2012 T F0 SF [< 7FFFFFE0 FFFFFFF0 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 FFFFFFF0 7FFFFFE0 >-3 17 28 12 35.3680143]61 D (=)2065 T (1.)2113 T (This)436 1053 S (gains)540 T (some)657 T (e\016ciency)771 T (without)966 T (c)1136 T (hanging)1156 T (the)1326 T (output)1405 T (at)1554 T (all.)1609 T (\(m\))300 978 S (A)436 T (c)490 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0FFE00 1FFE00 3C3E00 781E00 701E00 E00E00 E00E00 E00E00 E00E00 E00E00 E00E00 701E00 701E00 387E00 3FFE00 1FEE00 07CE00 000E00 000E00 000E00 000E00 000E00 000E00 007FC0 00FFE0 007FC0 >-2 18 19 27 21.4857533]113 D (q)343 T 343 1102 Q F1 SF [< 03E080 0E1980 1C0580 380780 780380 780380 F00380 F00380 F00380 F00380 F00380 F00380 700380 780380 380780 1C0780 0E1B80 03E380 000380 000380 000380 000380 000380 000380 000380 001FF0 >-1 18 20 26 22.1995305]113 D (quit)916 1109 S F0 SF (F)391 1046 S (or)418 T (man)474 T (y)560 T (families)599 T (of)765 T (blo)818 T (c)879 T (k)899 T (designs,)940 T (it)1111 T (can)1157 T (b)1242 T (e)1268 T (pro)1305 T (v)1371 T (ed)1394 T (that)1454 T (the)1554 T (isomorphism)1633 T (class)1900 T (of)2008 T (eac)2061 T (h)2124 T (design)300 992 S (is)438 T (uniquely)483 T (determined)667 T (b)903 T (y)928 T (the)966 T (isomorphism)1043 T (class)1308 T (of)1414 T (its)1465 T (blo)1527 T (c)1588 T (k-in)1608 T (tersection)1684 T (graph,)1891 T (where)2032 T (that)300 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1C0F0200 0C0F0400 0E130800 03E1F000 >-4 20 27 20 30.2141368]119 D (write)1374 T (automs)1472 T F0 SF (and)1629 T F36 SF [< 01E000 0FE000 01C000 01C000 01C000 01C000 038000 038000 038000 038000 070000 070000 0703C0 070420 0E08E0 0E11E0 0E21E0 0E40C0 1C8000 1D0000 1E0000 1FC000 38E000 387000 387000 383840 707080 707080 707080 703100 E03100 601E00 >-3 32 19 32 20.9174099]107 D (writemarkers)1716 T F0 SF (options,)1991 T (the)436 3059 S (automorphism)513 T (group)813 T (will)940 T (b)1025 T (e)1051 T (displa)1085 T (y)1200 T (ed)1224 T (while)1282 T F36 SF (nauty)1399 T F0 SF (is)1528 T (running.)1572 T (See)1758 T (Section)1838 T (5)1995 T (for)2032 T (an)2100 T (explanation)436 3004 S (of)682 T (the)733 T (output.)811 T (When)978 T F36 SF (nauty)1110 T F0 SF (returns,)1239 T F36 SF (dr)1408 T (e)1449 T (adnaut)1469 T F0 SF (will)1620 T (displa)1706 T (y)1821 T (some)1860 T (statistics)1973 T (ab)436 2950 S (out)485 T (it.)572 T (See)652 T (Section)738 T (4)903 T (for)947 T (the)1022 T 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(h)1636 T F0 SF (.)1662 T (This)1695 T (allo)1798 T (ws)1868 T (quic)1933 T (k)2014 T (com-)2052 T (parison)436 2467 S (b)598 T (et)624 T (w)662 T (een)694 T (graphs.)775 T (Isomorphic)944 T (graphs)1180 T (giv)1329 T (e)1388 T (the)1424 T (same)1504 T (v)1619 T (alues,)1641 T (but)1769 T (not)1854 T (con)1937 T (v)2005 T (ersely)2028 T (.)2137 T (Only)436 2413 S (p)549 T (ossible)575 T (after)720 T F29 SF (x)827 T F0 SF (with)866 T (option)970 T F36 SF (getc)1111 T (anon)1188 T F0 SF (selected.)1303 T F29 SF (#)300 2343 S F0 SF (Compare)436 T (the)631 T (lab)710 T (elled)771 T (graphs)879 T F6 SF (h)1026 T F0 SF (and)1068 T F6 SF (h)1156 T F15 SF (0)1182 2359 S F0 SF (.)1195 2343 S (Both)1230 T (m)1343 T (ust)1381 T (ha)1456 T (v)1504 T (e)1528 T (b)1561 T (een)1587 T (already)1669 T (de\014ned)1830 T (\(using)1987 T F29 SF (x)2124 T F0 SF (and)436 2288 S F29 SF (@)524 T F0 SF (\).)548 T (The)598 T (complete)690 T (pro)881 T (cess)948 T (for)1038 T (testing)1106 T (t)1255 T (w)1273 T 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F0 SF (is)1260 T (iden)1311 T (tical)1393 T (to)1499 T F6 SF (h)1559 T F15 SF (0)1585 2016 S F0 SF (,)1598 2000 S (y)1632 T (ou)1656 T (will)1723 T (also)1814 T (b)1910 T (e)1936 T (giv)1976 T (en)2035 T (an)2100 T (isomorphism)436 1946 S (from)703 T F6 SF (g)811 T F3 SF (1)833 1939 S F0 SF (to)869 1946 S F6 SF (g)926 T F3 SF (2)948 1939 S F0 SF (.)968 1946 S (This)1003 T (is)1108 T (in)1154 T (the)1208 T (form)1287 T (of)1396 T (a)1448 T (sequence)1487 T (of)1676 T (pairs)1729 T F6 SF (v)1841 T F9 SF (i)1863 1939 S F29 SF (-)1878 1946 S F6 SF [< 0F006060 118070F0 2180E0F8 21C0E078 41C0E038 4380E018 8381C010 0701C010 0701C010 0701C010 0E038020 0E038020 0E038020 0E038040 0E038040 0E038080 0E078080 06078100 07098600 01F07800 >-2 20 29 20 32.5548845]119 D (w)1902 T F9 SF (i)1935 1939 S F0 SF (,)1950 1946 S (where)1979 T F6 SF (v)2111 T F9 SF (i)2133 1939 S F0 SF (is)436 1891 S (a)484 T (v)523 T (ertex)547 T (of)662 T F6 SF (g)716 T F3 SF (1)738 1884 S F0 SF (and)774 1891 S F6 SF (w)864 T 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S F0 SF (Restore)436 T (the)604 T (v)685 T (ertex)709 T (n)826 T (um)851 T (b)914 T (ering)940 T (origin)1055 T (to)1187 T (what)1245 T (it)1361 T (w)1410 T (as)1443 T (just)1500 T (b)1592 T (efore)1618 T (the)1732 T (last)1813 T F29 SF ($)1902 T F0 SF (command.)1943 T (Only)436 2143 S (one)549 T (previous)632 T (v)813 T (alue)835 T (is)931 T (remem)976 T (b)1110 T (ered.)1136 T F29 SF (l)300 2075 S (=)327 2070 S (#)353 2075 S F0 SF (Set)436 T (v)513 T (alue)535 T (of)628 T (option)678 T F36 SF (linelength)817 T F0 SF (:)1020 T (the)1052 T (length)1128 T (of)1265 T (the)1315 T (longest)1391 T (line)1543 T (p)1627 T (ermitted)1653 T (for)1836 T (output.)1904 T (The)2070 T (default)436 2021 S (v)589 T (alue)611 T (is)707 T (installation-dep)752 T (enden)1060 T (t)1176 T (\(t)1210 T (ypically)1246 T (78\).)1413 T F29 SF [< FF8FF8 FF8FF8 FF8FF8 3800E0 3800E0 3800E0 1C01C0 1C01C0 1C71C0 1CF9C0 1CF9C0 1CD9C0 1CD9C0 0DDD80 0DDD80 0DDD80 0D8D80 0F8F80 0F8F80 070700 >-1 20 21 20 23.8731286]119 D (w)300 1953 S (=)327 1948 S (#)353 1953 S F0 SF (Set)436 T (v)514 T (alue)536 T (of)631 T F36 SF (worksize)683 T F0 SF (:)863 T (the)896 T (amoun)974 T (t)1108 T (of)1139 T (space)1190 T (pro)1311 T (vided)1377 T (for)1498 T F36 SF (nauty)1567 T F0 SF (to)1696 T (store)1751 T (automorphism)1862 T (data.)436 1899 S (The)565 T (maxim)661 T (um)796 T (v)876 T (alue)898 T (is)996 T (installation-de\014ned,)1044 T (and)1454 T (the)1545 T (default)1626 T (is)1781 T (the)1829 T (same)1910 T (as)2027 T (the)2085 T (maxim)436 1844 S (um.)571 T (There's)666 T (little)828 T (reason)937 T (to)1079 T (ev)1134 T (er)1178 T (use)1231 T (this)1309 T (command.)1398 T F29 SF [< 006000 00F000 00F000 00F000 00F000 00F000 00F000 00F000 7FFFC0 FFFFE0 FFFFE0 7FFFC0 00F000 00F000 00F000 00F000 00F000 00F000 00F000 006000 >-2 24 19 20 23.8731286]43 D (+)300 1777 S F0 SF (Ignored.)436 T (Pro)620 T (vided)692 T (for)812 T (con)882 T (trast)950 T (with)1058 T (\\)1162 T F36 SF (-)1185 T F0 SF (".)1201 T F29 SF (d,-d)300 1710 S F0 SF (Set)443 T (option)527 T F36 SF (digr)673 T (aph)749 T F0 SF (to)842 T (TR)902 T (UE)968 T (or)1053 T (F)1114 T (ALSE,)1140 T (resp)1290 T (ectiv)1372 T (ely)1466 T (.)1519 T (Y)1567 T (ou)1598 T (m)1666 T (ust)1704 T (set)1784 T (it)1860 T (to)1910 T (TR)1971 T (UE)2037 T (if)2121 T (y)436 1655 S (ou)460 T (wish)526 T (to)633 T (de\014ne)692 T F6 SF (g)827 T F0 SF (to)869 T (b)928 T (e)954 T (a)993 T (digraph)1034 T (or)1204 T (a)1264 T (graph)1305 T (with)1437 T (lo)1544 T (ops.)1580 T (The)1690 T (default)1787 T (is)1943 T (F)1992 T (ALSE.)2018 T (Changing)436 1601 S (it)641 T (from)687 T (TR)794 T (UE)860 T (to)940 T (F)995 T (ALSE)1021 T (also)1154 T (causes)1245 T (the)1385 T (graph)1463 T F6 SF (g)1592 T F0 SF (to)1631 T (b)1686 T (ecome)1712 T (unde\014ned,)1849 T (as)2069 T (a)2125 T (safet)436 1546 S (y)529 T (measure.)567 T F29 SF (c,-c)300 1479 S F0 SF (Set)443 T (option)519 T F36 SF (getc)658 T (anon)735 T F0 SF (to)847 T (TR)900 T (UE)966 T (or)1043 T (F)1096 T (ALSE,)1122 T (resp)1264 T (ectiv)1346 T (ely)1440 T (.)1493 T (This)1525 T (tells)1627 T F36 SF (nauty)1720 T F0 SF (whether)1847 T (to)2019 T (\014nd)2072 T (a)436 1424 S (canonical)474 T (lab)674 T (elling)735 T (or)857 T (just)913 T (the)1003 T (automorphism)1081 T (group.)1382 T (The)1529 T (default)1622 T (is)1775 T (F)1821 T (ALSE.)1847 T F29 SF (a,-a)300 1357 S F0 SF (Set)443 T (option)521 T F36 SF (write)662 T (automs)760 T F0 SF (to)919 T (TR)974 T (UE)1040 T (or)1119 T (F)1174 T (ALSE,)1200 T (resp)1344 T (ectiv)1426 T (ely)1520 T (.)1573 T (This)1606 T (tells)1709 T F36 SF (nauty)1805 T F0 SF (whether)1934 T (to)2108 T (displa)436 1303 S (y)551 T (the)591 T (automorphisms)669 T (it)988 T (\014nds.)1034 T (The)1160 T (default)1254 T (is)1406 T (TR)1452 T (UE.)1518 T F29 SF [< 7CE0E000 FFFBF800 7FFFF800 1F1F1C00 1E1E1C00 1E1E1C00 1C1C1C00 1C1C1C00 1C1C1C00 1C1C1C00 1C1C1C00 1C1C1C00 1C1C1C00 1C1C1C00 1C1C1C00 1C1C1C00 1C1C1C00 7F1F1F00 FFBFBF80 7F1F1F00 >1 20 25 20 23.8731286]109 D (m,-m)300 1235 S F0 SF (Set)443 T (option)524 T F36 SF (writemarkers)667 T F0 SF (to)947 T (TR)1005 T (UE)1071 T (or)1152 T (F)1210 T (ALSE,)1236 T (resp)1384 T (ectiv)1466 T (ely)1560 T (.)1613 T (This)1652 T (tells)1758 T F36 SF (nauty)1857 T F0 SF (whether)1989 T (to)436 1181 S (displa)490 T (y)605 T (the)643 T (lev)719 T (el)775 T (mark)821 T (ers)924 T (\\)991 T F29 SF [< 7F8FF0 FF8FF8 7F8FF0 1E03C0 0E0380 0E0380 0E0380 070700 070700 070700 038E00 038E00 038E00 038E00 01DC00 01DC00 01DC00 00F800 00F800 007000 >-1 20 21 20 23.8731286]118 D (level)1014 T F6 SF (:)1157 T (:)1178 T (:)1199 T F0 SF (".)1218 T (See)1273 T (Section)1352 T (5)1509 T (for)1545 T (their)1613 T (meaning.)1720 T (The)1919 T (default)2010 T (is)436 1126 S (TR)482 T (UE.)548 T F29 SF [< 7E3E00 FEFF80 7FFFC0 0FC1E0 0F80E0 0F0070 0E0070 0E0038 0E0038 0E0038 0E0038 0E0038 0E0038 0F0070 0F0070 0F80E0 0FC1E0 0FFFC0 0EFF80 0E3E00 0E0000 0E0000 0E0000 0E0000 0E0000 0E0000 0E0000 7FC000 FFE000 7FC000 >0 20 21 30 23.8731286]112 D (p,-p)300 1059 S F0 SF (Set)443 T (option)526 T F36 SF (c)673 T (artesian)693 T F0 SF (to)874 T (TR)935 T (UE)1001 T (or)1085 T (F)1145 T (ALSE,)1171 T (resp)1321 T (ectiv)1403 T (ely)1497 T (.)1550 T (This)1597 T (tells)1706 T F36 SF (nauty)1807 T F0 SF (to)1941 T (use)2002 T (the)2085 T (\\cartesian")436 1004 S (form)676 T (when)784 T (writing)904 T (automorphisms.)1063 T (Precisely)1403 T (,)1575 T (the)1605 T (automorphism)1685 T F6 SF [< 03E004 0FF008 1FF808 3FF810 301C10 400C10 C00420 800420 000240 000240 000280 000280 000280 000300 000300 000300 000200 000200 000200 000600 000600 000600 000C00 000C00 000C00 000C00 001800 001800 001800 001000 >-1 20 22 30 23.5427803]13 D (\015)1987 T F0 SF (is)2030 T (dis-)2077 T (pla)436 950 S (y)496 T (ed)520 T (as)581 T (a)638 T (list)678 T F6 SF (v)755 T F9 SF [< 078040 1FC040 38E080 603080 C01080 801100 000900 000A00 000A00 000A00 000C00 000C00 000C00 000800 000800 000800 001000 001000 001000 001000 >-1 14 18 20 19.1010147]13 D (\015)779 971 S F3 SF (1)777 938 S F6 SF (v)819 950 S F9 SF (\015)843 971 S F3 SF (2)841 938 S F6 SF (:)890 950 S (:)911 T (:)932 T (v)951 T F9 SF (\015)975 966 S [< 383C00 44C600 470200 460200 8E0600 0C0600 0C0600 0C0C00 180C00 180C40 181840 181880 300880 300F00 >-2 14 18 14 22.4788104]110 D (n)973 939 S F0 SF (,)998 950 S (where)1028 T F6 SF (v)1161 T F3 SF (1)1183 943 S F6 SF (;)1203 950 S (v)1224 T F3 SF (2)1246 943 S F6 SF (;)1266 950 S (:)1287 T (:)1308 T (:)1328 T (;)1347 T (v)1368 T F9 SF (n)1390 943 S F0 SF (are)1430 950 S (the)1508 T (v)1588 T (ertices)1612 T (of)1754 T F6 SF (g)1807 T F0 SF (.)1831 T (The)1868 T (default)1963 T (is)2117 T (F)436 895 S (ALSE.)462 T F29 SF (y)300 828 S (=)327 823 S (#)353 828 S F0 SF (Set)436 T (the)521 T (v)605 T (alue)627 T (of)729 T (option)787 T F36 SF (tc)934 T 973 828 M 14 2 B (level)987 828 S F0 SF (.)1074 T (A)1124 T (v)1180 T (alue)1202 T (of)1303 T F6 SF (k)1361 T F0 SF (tells)1408 T F36 SF (nauty)1510 T F0 SF (to)1646 T (use)1707 T (an)1792 T (adv)1861 T (anced,)1931 T (but)2080 T (exp)436 773 S (ensiv)506 T (e,)605 T (algorithm)653 T (for)859 T (c)927 T (ho)947 T (osing)996 T (target)1111 T (cells)1244 T (in)1341 T (the)1393 T (top)1470 T F6 SF (k)1550 T F0 SF (lev)1589 T (els)1645 T (of)1709 T (the)1760 T (searc)1837 T (h)1936 T (tree.)1974 T (See)2082 T (Section)436 719 S (4)598 T (for)638 T (a)710 T (more)750 T (detailed)866 T (description.)1040 T (A)1297 T (v)1348 T (alue)1370 T (suc)1468 T (h)1531 T (as)1573 T (3)1631 T (or)1671 T (4)1729 T (sometimes)1769 T (leads)1991 T (to)2108 T (19)1201 610 S 1 EOP %%Page: 18 9 BOP F0 SF (A)391 3555 S (t)425 T (an)457 T (y)505 T (p)543 T (oin)569 T (t)629 T (of)661 T (time,)713 T F36 SF (dr)829 T (e)870 T (adnaut)890 T F0 SF (kno)1042 T (ws)1114 T (the)1179 T (follo)1257 T (wing)1341 T (information:)1449 T (\(a\))306 3500 S (The)406 T (n)500 T (um)525 T (b)587 T (er)613 T (of)665 T (v)717 T (ertices,)741 T F6 SF (n)894 T F0 SF (.)921 T (\(b\))303 3445 S (The)406 T (\\curren)500 T (t)649 T (graph")680 T F6 SF (g)832 T F0 SF (,)856 T (if)883 T (de\014ned.)925 T (\(c\))308 3391 S (The)406 T (\\curren)500 T (t)649 T (partition")680 T F6 SF (\031)893 T F0 SF (,)921 T (if)948 T (de\014ned.)990 T (\(d\))303 3336 S (The)406 T (orbits)500 T (of)629 T (the)681 T (\(coloured\))759 T (graph)976 T (\()1105 T F6 SF (g)1123 T (;)1147 T (\031)1168 T F0 SF (\),)1196 T (if)1239 T (de\014ned.)1281 T (\(e\))308 3282 S (The)406 T (canonically)500 T (lab)736 T (elled)797 T (isomorph)904 T (of)1101 T F6 SF (g)1153 T F0 SF (,)1177 T (called)1204 T F6 SF (h)1333 T F0 SF (,)1359 T (if)1387 T (de\014ned.)1429 T (\(Also)1603 T (called)1723 T F36 SF (c)1852 T (anong)1872 T F0 SF (.\))1991 T (\(f)311 3227 S (\))347 T (An)406 T (extra)481 T (graph)598 T (called)727 T F6 SF (h)856 T F15 SF (0)882 3243 S F0 SF (,)895 3227 S (if)923 T (de\014ned.)964 T (\(Also)1139 T (called)1259 T F36 SF (save)1388 T (dg)1471 T F0 SF (.\))1515 T (\(g\))306 3173 S (V)406 T 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T F0 SF (,)971 T (edges)998 T (only)1120 T (need)1219 T (to)1326 T (b)1381 T (e)1407 T (en)1443 T (tered)1488 T (in)1604 T (one)1657 T (direction.\))1740 T F29 SF (-)436 2486 S (#)460 T F0 SF (:)518 T (delete)546 T (the)677 T (edge,)756 T (if)872 T (an)914 T (y)962 T (,)983 T (from)1008 T (the)1116 T (curren)1194 T (t)1320 T (v)1352 T (ertex)1376 T (to)1490 T (the)1546 T (sp)1624 T (eci\014ed)1668 T (v)1807 T (ertex.)1831 T F29 SF [< 18 3C 7E 7E 3C 18 00 00 00 00 00 00 00 00 18 3C 7E 7E 3E 1E 0E 1C 3C 78 F0 60 >-8 20 7 26 23.8731286]59 D (;)436 2432 S F0 SF (:)518 T (incremen)546 T (t)724 T (the)757 T (curren)835 T (t)961 T (v)994 T (ertex.)1018 T (If)1149 T (it)1195 T (b)1240 T (ecomes)1266 T (to)1421 T (o)1463 T (high)1501 T (for)1602 T (a)1671 T (v)1709 T (ertex)1733 T (lab)1847 T (el,)1908 T (stop.)1969 T F29 SF (#)436 2377 S (:)460 T F0 SF (:)518 T (mak)546 T (e)631 T (the)665 T (sp)743 T (eci\014ed)787 T (v)927 T (ertex)951 T (the)1064 T (curren)1143 T (t)1269 T (v)1301 T 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(1\);)1749 T F6 SF (A)300 2158 S F3 SF [< 0FC0 3060 6030 7038 7038 0038 0030 0070 00E0 07C0 0070 0038 0018 001C 001C E01C E01C C018 4038 3070 0FC0 >-1 21 14 21 18.1261368]51 D (35)334 2151 S F0 SF ({)373 2158 S F6 SF (D)396 T F3 SF (35)434 2151 S F0 SF (:)472 2158 S (1.1)503 T (seconds)573 T (\(0.02)734 T (seconds)844 T (using)1006 T (v)1121 T (ertex-in)1145 T (v)1297 T (arian)1319 T (t)1419 T F36 SF (cliques)1447 T F0 SF (with)1594 T (parameter)1694 T (4)1908 T (at)1942 T (lev)1995 T (el)2051 T (1\);)2095 T F6 SF (A)300 2103 S F3 SF (52)334 2096 S F0 SF (:)373 2103 S (3.9)405 T (seconds)479 T (\(0.18)643 T (seconds)757 T (using)922 T (v)1041 T (ertex-in)1065 T (v)1217 T (arian)1239 T (t)1339 T F36 SF (cliques)1370 T F0 SF (with)1520 T (parameter)1623 T (5)1841 T (at)1879 T (lev)1934 T (el)1990 T (1\);)2038 T F6 SF (B)300 2049 S F3 SF (52)334 2042 S F0 SF (:)373 2049 S (8.7)406 T (seconds)479 T (\(0.16)644 T (seconds)758 T (using)922 T (v)1041 T (ertex-in)1065 T (v)1217 T (arian)1239 T 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