feat: libraries lab complete

OSs/lab-libs/lib.c

@@ -0,0 +1,45 @@
+#include "lib.h"
+
+#include <math.h>
+
+#define ZEROIN_MAX_ITERATIONS 1000
+
+size_t fibo(size_t n)
+{
+    size_t prev = 0, cur = 1, tmp = 0;
+    for (size_t i = 0; i < n; i++) {
+        tmp = cur;
+        cur = cur + prev;
+        prev = tmp;
+    }
+    return cur;
+}
+
+double zeroin(double (*f)(double), double err, double a, double b)
+{
+    double left = f(a);
+    if (fabs(left) < err) return left;
+    double right = f(b);
+    if (fabs(right) < err) return right;
+    if (left * right > 0) {
+        return NAN;
+    }
+
+    double x = NAN;
+    double cur = NAN;
+    size_t n = 0;
+    do {
+        x = (a + b) / 2;
+        cur = f(x);
+        if (cur * left > 0) {
+            left = cur;
+            a = x;
+        }
+        else {
+            right = cur;
+            b = x;
+        }
+        n++;
+    } while (fabs(cur) > err || n < ZEROIN_MAX_ITERATIONS);
+    return x;
+}