179 lines
4.4 KiB
C
179 lines
4.4 KiB
C
#ifndef MAT_H
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#define MAT_H
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#include <gmp.h>
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#include <malloc.h>
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#define LOOP(i,n) for(int i = 0; i < (n); i++)
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// library for matrix computations in variable rings (based on GMP types)
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#ifdef QEXT_SQRT5
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typedef mpq_t NUMBER [2];
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#define INIT(x) do { mpq_init((x)[0]); mpq_init((x)[1]); } while(0)
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#define CLEAR(x) do { mpq_clear((x)[0]); mpq_clear((x)[1]); } while(0)
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#define SET(x,y) do { mpq_set((x)[0],(y)[0]); mpq_set((x)[1],(y)[1]); } while(0)
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#define SET_INT(x,y) do { mpq_set_si((x)[0],(y),1); mpq_set_si((x)[1],0,1); } while(0)
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#define SET_ZERO(x) SET_INT(x,0)
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#define SET_ONE(x) SET_INT(x,1)
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#define ADD(x,y,z) do { mpq_add((x)[0],(y)[0],(z)[0]); mpq_add((x)[1],(y)[1],(z)[1]); } while(0)
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#define SUB(x,y,z) do { mpq_sub((x)[0],(y)[0],(z)[0]); mpq_sub((x)[1],(y)[1],(z)[1]); } while(0)
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#define MUL multiply_sqrt5
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#define DIV divide_sqrt5
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#define CMP compare_sqrt5
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#define PRINT(x) gmp_printf("%Qd + %Qd*sqrt(5)", (x)[0], (x)[1])
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#define SPRINT(buf, x) gmp_sprintf(buf, "%Qd+%Qd*sqrt(5)", (x)[0], (x)[1])
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static void multiply_sqrt5(NUMBER out, NUMBER a, NUMBER b)
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{
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// could be in place!!!
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mpq_t tmp, result[2];
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mpq_inits(tmp, result[0], result[1], 0);
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mpq_mul(result[0], a[1], b[1]);
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mpq_set_si(tmp, 5, 1);
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mpq_mul(result[0], result[0], tmp);
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mpq_mul(tmp, a[0], b[0]);
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mpq_add(result[0], result[0], tmp);
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mpq_mul(result[1], a[1], b[0]);
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mpq_mul(tmp, a[0], b[1]);
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mpq_add(result[1], result[1], tmp);
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mpq_set(out[0], result[0]);
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mpq_set(out[1], result[1]);
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mpq_clears(tmp, result[0], result[1], 0);
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}
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static void divide_sqrt5(NUMBER out, NUMBER a, NUMBER b)
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{
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mpq_t denom, num, tmp, neg5, result[2];
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mpq_inits(denom, num, tmp, neg5, result[0], result[1], 0);
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mpq_set_si(neg5, -5, 1);
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mpq_mul(denom, b[1], b[1]);
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mpq_mul(denom, denom, neg5);
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mpq_mul(tmp, b[0], b[0]);
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mpq_add(denom, denom, tmp);
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mpq_mul(num, a[1], b[1]);
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mpq_mul(num, num, neg5);
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mpq_mul(tmp, a[0], b[0]);
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mpq_add(num, num, tmp);
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mpq_div(result[0], num, denom);
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mpq_mul(num, a[1], b[0]);
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mpq_mul(tmp, a[0], b[1]);
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mpq_sub(num, num, tmp);
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mpq_div(result[1], num, denom);
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mpq_set(out[0], result[0]);
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mpq_set(out[1], result[1]);
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mpq_clears(denom, num, tmp, neg5, result[0], result[1], 0);
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}
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static int compare_sqrt5(NUMBER x, NUMBER y)
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{
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int result;
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mpq_t p, q, p2, q2, c5;
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mpq_inits(p, q, p2, q2, c5, 0);
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mpq_sub(p, x[0], y[0]);
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mpq_sub(q, x[1], y[1]);
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/*
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want to know if p + sqrt(5) q > 0
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if p>0 and q>0: always true
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if p>0 and q<0: equivalent to |p|^2 > 5 |q|^2
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if p<0 and q>0: equivalent to |p|^2 < 5 |q|^2
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if p<0 and q<0: always false
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*/
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if(mpq_sgn(p) > 0 && mpq_sgn(q) > 0) {
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result = 1;
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goto done;
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}
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if(mpq_sgn(p) < 0 && mpq_sgn(q) < 0) {
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result = -1;
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goto done;
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}
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mpq_mul(p2, p, p);
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mpq_mul(q2, q, q);
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mpq_set_si(c5, 5, 1);
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mpq_mul(q2, q2, c5);
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if(mpq_sgn(p) > 0)
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result = mpq_cmp(p2, q2); // this can't be zero, or else |p/q| = sqrt(5), but it's irrational
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else if(mpq_sgn(p) < 0)
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result = -mpq_cmp(p2, q2); // this can be zero if p = 0 and q = 0
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else // p = 0
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return mpq_sgn(q);
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done:
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mpq_clears(p, q, p2, q2, c5, 0);
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return result;
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}
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#endif
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#ifdef QEXT_TRIVIAL
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#define NUMBER mpq_t
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#define INIT mpq_init
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#define CLEAR mpq_clear
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#define SET mpq_set
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#define SET_INT(x,y) mpq_set_si(x,y,1)
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#define SET_ZERO(x) SET_INT(x,0)
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#define SET_ONE(x) SET_INT(x,1)
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#define ADD mpq_add
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#define SUB mpq_sub
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#define MUL mpq_mul
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#define DIV mpq_div
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#define PRINT(x) gmp_printf("%Qd", x)
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#endif
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#define M(m,i,j) ((m)->x[(i)+(m)->n*(j)])
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struct _mat{
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int n;
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NUMBER *x;
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} ;
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typedef struct _mat mat[1];
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typedef struct _mat_workspace {
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mat tmp_mat;
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NUMBER tmp_num;
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NUMBER tmp_num2;
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} mat_workspace;
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mat_workspace *mat_workspace_init(int n);
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void mat_workspace_clear(mat_workspace *ws);
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void mat_init(mat m, int n);
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void mat_get(NUMBER out, mat m, int i, int j);
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void mat_set(mat m, int i, int j, NUMBER x);
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NUMBER *mat_ref(mat m, int i, int j);
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void mat_zero(mat m);
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void mat_identity(mat m);
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void mat_copy(mat to, mat from);
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void mat_clear(mat m);
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int mat_same(mat m1, mat m2);
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static void mat_multiply_outofplace(mat_workspace *ws, mat out, mat in1, mat in2);
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void mat_multiply(mat_workspace *ws, mat out, mat in1, mat in2);
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void mat_det(mat_workspace *ws, NUMBER out, mat in);
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static void mat_pseudoinverse_outofplace(mat_workspace *ws, mat out, mat in);
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void mat_pseudoinverse(mat_workspace *ws, mat out, mat in);
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void mat_trace(NUMBER out, mat in);
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void mat_print(mat in);
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#endif
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