2025-02-Numerical/hws/hw1/main.c

#include "nr.h"
#include <stdio.h>
#include <math.h>

void get_eps(float *eps) {
    *eps = 1.0f;

    while ((1.0f + *eps / 2.0f) > 1.0f) {
        *eps /= 2.0f;
    }
}

void get_eps_double(double *eps) {
    *eps = 1.0;

    while ((1.0 + *eps / 2.0) > 1.0) {
        *eps /= 2.0;
    }
}

#define CONV(i) ((double) (i))

void machar_double(int *ibeta, int *it, int *irnd, int *ngrd, int *machep, int *negep, int *iexp, int *minexp, int *maxexp,
                   double *eps, double *epsneg, double *xmin, double *xmax) {
    int i, itemp, iz, j, k, mx, nxres;
    double a, b, beta, betah, betain, one, t, temp, temp1, tempa, two, y, z, zero;

    one = CONV(1);
    two = one + one;
    zero = one - one;
    a = one;
    do {
        a += a;
        temp = a + one;
        temp1 = temp - a;
    } while (temp1 - one == zero);
    b = one;
    do {
        b += b;
        temp = a + b;
        itemp = (int) (temp - a);
    } while (itemp == 0);
    *ibeta = itemp;
    beta = CONV(*ibeta);
    *it = 0;
    b = one;
    do {
        ++(*it);
        b *= beta;
        temp = b + one;
        temp1 = temp - b;
    } while (temp1 - one == zero);
    *irnd = 0;
    betah = beta / two;
    temp = a + betah;
    if (temp - a != zero) *irnd = 1;
    tempa = a + beta;
    temp = tempa + betah;
    if (*irnd == 0 && temp - tempa != zero) *irnd = 2;
    *negep = (*it) + 3;
    betain = one / beta;
    a = one;
    for (i = 1; i <= (*negep); i++) a *= betain;
    b = a;
    for (;;) {
        temp = one - a;
        if (temp - one != zero) break;
        a *= beta;
        --(*negep);
    }
    *negep = -(*negep);
    *epsneg = a;
    *machep = -(*it) - 3;
    a = b;
    for (;;) {
        temp = one + a;
        if (temp - one != zero) break;
        a *= beta;
        ++(*machep);
    }
    *eps = a;
    *ngrd = 0;
    temp = one + (*eps);
    if (*irnd == 0 && temp * one - one != zero) *ngrd = 1;
    i = 0;
    k = 1;
    z = betain;
    t = one + (*eps);
    nxres = 0;
    for (;;) {
        y = z;
        z = y * y;
        a = z * one;
        temp = z * t;
        if (a + a == zero || fabs(z) >= y) break;
        temp1 = temp * betain;
        if (temp1 * beta == z) break;
        ++i;
        k += k;
    }
    if (*ibeta != 10) {
        *iexp = i + 1;
        mx = k + k;
    } else {
        *iexp = 2;
        iz = (*ibeta);
        while (k >= iz) {
            iz *= *ibeta;
            ++(*iexp);
        }
        mx = iz + iz - 1;
    }
    for (;;) {
        *xmin = y;
        y *= betain;
        a = y * one;
        temp = y * t;
        if (a + a != zero && fabs(y) < *xmin) {
            ++k;
            temp1 = temp * betain;
            if (temp1 * beta == y && temp != y) {
                nxres = 3;
                *xmin = y;
                break;
            }
        } else
            break;
    }
    *minexp = -k;
    if (mx <= k + k - 3 && *ibeta != 10) {
        mx += mx;
        ++(*iexp);
    }
    *maxexp = mx + (*minexp);
    *irnd += nxres;
    if (*irnd >= 2) *maxexp -= 2;
    i = (*maxexp) + (*minexp);
    if (*ibeta == 2 && !i) --(*maxexp);
    if (i > 20) --(*maxexp);
    if (a != y) *maxexp -= 2;
    *xmax = one - (*epsneg);
    if ((*xmax) * one != *xmax) *xmax = one - beta * (*epsneg);
    *xmax /= (*xmin * beta * beta * beta);
    i = (*maxexp) + (*minexp) + 3;
    for (j = 1; j <= i; j++) {
        if (*ibeta == 2) *xmax += *xmax;
        else
            *xmax *= beta;
    }
}
#undef CONV

int main() {
    int ibeta, it, irnd, ngrd, machep, negep, iexp, minexp, maxexp;
    float eps, epsneg, xmin, xmax;

    machar(&ibeta, &it, &irnd, &ngrd, &machep, &negep, &iexp, &minexp, &maxexp,
           &eps, &epsneg, &xmin, &xmax);

    printf("Machine Accuracy for float (machar): \t\t%0.20f\n", eps);

    get_eps(&eps);

    printf("Machine Accuracy for float (get_eps): \t\t%0.20f\n", eps);
    double eps_double, epsneg_double, xmin_double, xmax_double;

    machar_double(&ibeta, &it, &irnd, &ngrd, &machep, &negep, &iexp, &minexp, &maxexp,
                  &eps_double, &epsneg_double, &xmin_double, &xmax_double);
    printf("Machine Accuracy for double (machar_double): \t%0.20f\n", eps_double);

    get_eps_double(&eps_double);
    printf("Machine Accuracy for double (get_eps_double): \t%0.20f\n", eps_double);

    return 0;
}