114 lines
2.4 KiB
C++
114 lines
2.4 KiB
C++
/*
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LA: linear algebra C++ interface library
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Copyright (C) 2024 Jiri Pittner <jiri.pittner@jh-inst.cas.cz> or <jiri@pittnerovi.com>
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This program is free software: you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation, either version 3 of the License, or
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(at your option) any later version.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with this program. If not, see <http://www.gnu.org/licenses/>.
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*/
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#include "miscfunc.h"
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#include "laerror.h"
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#include <stdio.h>
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#include <stdint.h>
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namespace LA {
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#define MAXFACT 20
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unsigned long long factorial(const int n)
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{
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static int ntop=20;
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static unsigned long long a[MAXFACT+1]={1,1,2,6,24,120,720,5040,
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40320,
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362880,
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3628800,
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39916800ULL,
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479001600ULL,
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6227020800ULL,
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87178291200ULL,
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1307674368000ULL,
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20922789888000ULL,
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355687428096000ULL,
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6402373705728000ULL,
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121645100408832000ULL,
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2432902008176640000ULL};
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int j;
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if (n < 0) laerror("negative argument of factorial");
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if (n > MAXFACT) laerror("overflow in factorial");
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while (ntop<n) {
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j=ntop++;
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a[ntop]=a[j]*ntop;
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}
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return a[n];
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}
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#define MAXBINOM 100
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#define ibidxmaxeven(n) ((n-2)*(n-2)/4)
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#define ibidx(n,k) (k-2+(n&1?(n-3)*(n-3)/4:(n/2-1)*(n/2-2)))
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unsigned long long binom(int n, int k)
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{
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unsigned long long p,value;
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int d;
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static unsigned long long ibitab[ibidxmaxeven(MAXBINOM)]= /*only nontrivial are stored,
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zero initialization by compiler assumed*/
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{
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6,
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10,
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15,20,
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21,35,
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28,56,70
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};
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if(k>n||k<0) return(0);
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if(k>n/2) k=n-k;
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if(k==0) return(1);
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if(k==1) return(n);
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int ind=0;
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if(n<=MAXBINOM)
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{
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ind=ibidx(n,k);
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if (ibitab[ind]) return ibitab[ind];
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}
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/* nonrecurent method used anyway */
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d=n-k;
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p=1;
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for(;n>d;n--) p *= n;
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value=p/factorial(k);
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if(n<=MAXBINOM) ibitab[ind]=value;
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return value;
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}
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#undef ibidx
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#undef ibidxmaxeven
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#undef MAXBINOM
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unsigned long long longpow(unsigned long long x, int i)
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{
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if(i<0) return 0;
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unsigned long long y=1;
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do
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{
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if(i&1) y *= x;
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i >>= 1;
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if(i) x *= x;
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}
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while(i);
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return y ;
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}
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}//namespace
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