create Makefile and hw1/main.c

hws/hw1/main.c

@@ -0,0 +1,175 @@
+#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;
+}