Started task 6
This commit is contained in:
AZEN-SGG
parent
47a464aa9e
commit
af90d91e29
9 changed files with 225 additions and 102 deletions
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@ -21,7 +21,7 @@ else
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endif
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TARGET = a06.$(EXE)
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OBJ = main.o solve.o init_f.o
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OBJ = main.o solve.o init_f.o array_io.o polynom.o
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%.o: %.c
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gcc $(WFLAGS) $(LDFLAGS) -c $< -o $@
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41
2025.05.02/06Ex/array_io.c
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41
2025.05.02/06Ex/array_io.c
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@ -0,0 +1,41 @@
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#include "array_io.h"
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#include "comp.h"
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int init_array (
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double (*f) (double),
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double *d, int m,
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double a, double b,
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double eps, double *ret
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) {
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const double h = (b - a) / m;
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const int len = m+1;
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double *y_lst = d;
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double *x_lst = d + len;
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double *t_lst = d + (len < 1);
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double x = a;
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for (int i = 0; i < len; ++i)
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{
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double y = f(x);
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if (is_eps(y, eps))
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{
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*ret = x;
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return 1;
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}
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for (int j = 0; j < i; ++j)
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if (is_equal(y, y_lst[j]))
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return -1;
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y_lst[i] = y;
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x_lst[i] = x;
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t_lst[i] = x;
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x += h;
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}
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return 0;
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}
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11
2025.05.02/06Ex/array_io.h
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11
2025.05.02/06Ex/array_io.h
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@ -0,0 +1,11 @@
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#ifndef ARRAY_IO_H
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#define ARRAY_IO_H
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int init_array (
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double (*f) (double),
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double *d, int m,
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double a, double b,
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double eps, double *ret
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);
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#endif
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50
2025.05.02/06Ex/comp.h
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50
2025.05.02/06Ex/comp.h
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@ -0,0 +1,50 @@
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#ifndef COMP_H
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#define COMP_H
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#include <float.h>
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#include <math.h>
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static inline double * fpmax (double *pa, double *pb, double fa, double fb, double *max_f_p)
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{
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if ((fa - fb) > DBL_EPSILON)
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{
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*max_f_p = fa;
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return pa;
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} else
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{
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*max_f_p = fb;
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return pb;
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}
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}
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static inline double * fp_abs_max (double *pa, double *pb, double *fa, double *fb, double **max_f_p)
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{
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if ((fabs(*fa) - fabs(*fb)) > DBL_EPSILON)
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{
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*max_f_p = fa;
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return pa;
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} else
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{
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*max_f_p = fb;
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return pb;
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}
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}
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static inline int is_equal (const double a, const double b)
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{
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double diff = a - b;
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double max_val = (a > b) ? a : b;
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return ((diff < 0) ? -diff : diff) < (DBL_EPSILON * max_val);
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}
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static inline int is_null (const double a)
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{
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return ((a < 0) ? -a : a) < DBL_EPSILON;
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}
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static inline int is_eps (const double a, const double eps)
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{
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return (((a < 0) ? -a : a) - eps) < DBL_EPSILON;
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}
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#endif
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@ -1,48 +1,65 @@
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#include <stdio.h>
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#include <stdlib.h>
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#include <time.h>
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#include <math.h>
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#include "init_f.h"
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#include "array_io.h"
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#include "solve.h"
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/* ./a.out a b eps M k */
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/* ./a.out m a b eps M k */
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int main(int argc, char *argv[])
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{
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double t, a, b, eps, x = 0;
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int m, k, cl, it, task = 1;
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double t = 0, *d, a, b, eps, x = 0;
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int deg_poly, num_iter, k, cl, it, task = 6;
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double (*f) (double);
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double (*f_lst[]) (double) = {f0, f1, f2, f3, f4, f5, f6};
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int len_f = sizeof(f_lst) / sizeof(f_lst[0]);
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if (
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!((argc == 6) &&
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sscanf(argv[1], "%lf", &a) == 1 &&
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sscanf(argv[2], "%lf", &b) == 1 &&
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!((argc == 7) &&
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sscanf(argv[1], "%d", °_poly) == 1 &&
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sscanf(argv[2], "%lf", &a) == 1 &&
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sscanf(argv[3], "%lf", &b) == 1 &&
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(a <= b) &&
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(sscanf(argv[3], "%lf", &eps) == 1 && (eps >= 0)) &&
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((sscanf(argv[4], "%d", &m) == 1) && m > 0) &&
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((sscanf(argv[5], "%d", &k) == 1) && ((0 <= k) && (k <= len_f))))
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(sscanf(argv[4], "%lf", &eps) == 1 && (eps >= 0)) &&
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((sscanf(argv[5], "%d", &num_iter) == 1) && num_iter > 0) &&
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((sscanf(argv[6], "%d", &k) == 1) && ((0 <= k) && (k <= len_f))))
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) {
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fprintf(stderr, "Usage: %s a b eps M k\n", argv[0]);
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fprintf(stderr, "Usage: %s m a b eps M k\n", argv[0]);
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return -1;
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}
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d = (double *)malloc(3 * (deg_poly + 1) * sizeof(double));
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if (!d)
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{
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fprintf(stderr, "Error: Not enough memory!\n");
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return -2;
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}
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f = f_lst[k];
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it = init_array(f, d, deg_poly, a, b, eps, &x);
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if (!it)
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{
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t = clock();
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it = t6_solve(f, deg_poly, d, a, b, eps, num_iter, &x);
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t = (clock() - t) / CLOCKS_PER_SEC;
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}
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t = clock();
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it = t1_solve(f, a, b, eps, m, &x);
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t = (clock() - t) / CLOCKS_PER_SEC;
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cl = get_call_count();
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free(d);
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if (it < 0)
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{
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fprintf(stdout, "%s : Task = %d NOT FOUND Count = %d T = %.2f\n", argv[0], task, cl, t);
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return -2;
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} else
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{
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printf("%s : Task = %d X = %e Res = %e Its = %d Count = %d T = %.2f\n", argv[0], task, x, f(x), it, cl, t);
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fprintf(stdout, "%s : Task = %d X = %e Res = %e Its = %d Count = %d T = %.2f\n", argv[0], task, x, f(x), it, cl, t);
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return 0;
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}
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}
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43
2025.05.02/06Ex/polynom.c
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43
2025.05.02/06Ex/polynom.c
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@ -0,0 +1,43 @@
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#include "polynom.h"
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#include <float.h>
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#include <math.h>
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#include <stdio.h>
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// the Newton interpolation polynomial
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double construct_poly (const double x_0, const int n, const double * restrict X, double * restrict Y)
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{
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double value, start_value;
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for (int k = 0; k < n-1; ++k)
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{
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double last_x;
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double last_y = Y[n-1];
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for (int i = n-2; i >= k; --i)
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{
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const double x_i = X[i-k];
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const double y_i = Y[i];
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last_x = X[i+1];
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if (fabs(last_x - x_i) < DBL_EPSILON)
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return DBL_MAX;
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Y[i+1] = (last_y - y_i) / (last_x - x_i);
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last_y = y_i;
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}
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}
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start_value = 1;
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value = 0;
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for (int i = 0; i < n; ++i)
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{
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value += Y[i] * start_value;
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start_value *= (x_0 - X[i]);
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}
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return value;
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}
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6
2025.05.02/06Ex/polynom.h
Normal file
6
2025.05.02/06Ex/polynom.h
Normal file
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#ifndef POLYNOM_H
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#define POLYNOM_H
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double construct_poly (const double x_0, const int n, const double * restrict X, double * restrict Y);
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#endif
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#include "solve.h"
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#include "comp.h"
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#include "polynom.h"
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#include <math.h>
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#include <float.h>
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#include <stdbool.h>
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#include <stdint.h>
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#include <string.h>
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int t1_solve (
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double (*f) (double),
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double a, double b,
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double eps, int m, double *x
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) {
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int it = 0;
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uint64_t bits;
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double c = DBL_MAX, y, y_a = f(a), y_b = f(b);
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bool sgn_a, sgn_b, sgn_c;
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memcpy(&bits, &y_a, sizeof(bits));
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sgn_a = (bits >> 63) & 1;
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memcpy(&bits, &y_b, sizeof(bits));
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sgn_b = (bits >> 63) & 1;
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if (fabs(y_a) - eps < DBL_EPSILON)
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{
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*x = a;
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return 1;
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} if (fabs(y_b) - eps < DBL_EPSILON)
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{
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*x = b;
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return 1;
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}
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if (sgn_a == sgn_b)
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{
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*x = DBL_MAX;
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return -1;
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}
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for (it = 1; it <= m; ++it)
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{
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c = (a + b) * 0.5;
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y = f(c);
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memcpy(&bits, &y, sizeof(bits));
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sgn_c = (bits >> 63) & 1;
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if (fabs(y) - eps < DBL_EPSILON)
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break;
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else if ((fabs(c - a) < DBL_EPSILON) || (fabs(c - b) < DBL_EPSILON))
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it = m+1;
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else if (sgn_c == sgn_a)
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{
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a = c;
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y_a = y;
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} else if (sgn_c == sgn_b)
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{
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b = c;
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y_b = y;
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}
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}
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if (it > m)
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it = -1;
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*x = c;
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return it;
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}
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int t6_solve (
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double (*f) (double),
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const int m, double *d
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const int m, double *d,
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double a, double b,
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const double eps, const int M, double *x
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const double eps, const int M, double *res
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) {
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const int len = m + 1;
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double *maximum = d;
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const int len = m + 1;
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double *y_lst = d;
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double *x_lst = d + len;
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double *t_lst = d + (len << 1);
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double last_x = a;
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double last_y = f(a);
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const int h = (b - a) / m;
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y_lst[0] = last_y;
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x_lst[0] = last_x;
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t_lst[0] = last_x;
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for (int i = 1, double t_x = a ; i < len ; i++, t_x += h)
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int it;
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for (it = 1; it <= M; ++it)
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{
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double t_y = f(t_x);
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double x = construct_poly(0, len, y_lst, x_lst);
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double y = f(x);
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y_lst[i] = t_y;
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x_lst[i] = t_x;
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if (is_eps(y, eps))
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{
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*res = x;
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return it;
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}
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// Можно возвращение значений функции в y_lst можно было встроить в суммирование полинома, но мало толку
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for (int i = 0; i < len; ++i)
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{
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double yi = t_lst[i];
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y_lst[i] = yi;
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if (is_equal(y, yi))
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return -1;
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if ((fabs(yi) - fabs(*maximum)) > DBL_EPSILON)
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maximum = &yi;
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}
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*maximum = y;
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*(maximum + len) = x;
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*(maximum + (len << 1)) = y;
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}
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(void)a;
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(void)b;
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return -1;
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}
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@ -1,10 +1,11 @@
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#ifndef SOLVE_H
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#define SOLVE_H
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int t1_solve (
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int t6_solve (
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double (*f) (double),
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const int m, double *d,
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double a, double b,
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double eps, int m, double *x
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);
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const double eps, const int M, double *res
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);
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#endif
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