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exercises.md

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+# Exercises
+
+Here let be listed exercises for the readers of this wiki. You can allow yourself to as many helpers and resources as you find challenging: with each problem you should either find out you know the solution or learn something new while solving it.
+
+1. SOMETHING EASY SHOULD BE HERE SO THAT NUBS ARENT DISCOURAGED BY FIRST QUESTION xD
+2. Write a program in [C](c.md) that computes the value of [pi](pi.md) without using float/double and any libraries except for `stdio.h` and `stdint.h` -- you can only use built-in integer types and those from `stdint.h`. The program must compute pi as accurately as possible (at least 2 decimals) and write the value out as base 10 decimal.
+
+## Solutions
+
+A solution to each problem should be listed here -- keep in mind there may exist other solutions that those listed here.
+
+**solution 1**:
+TODO
+
+**solution 2**:
+
+```
+#include <stdio.h>
+#include <stdint.h>
+
+#define DECIMALS 10000
+
+int main(void)
+{
+  int64_t previousError = 10000000000;
+  uint64_t previousPi = 0;
+
+  for (uint64_t gridSize = 2; gridSize < 200000; gridSize *= 2)
+  {
+    /* We'll sample a grid of points and count those that fall inside the
+       circle with radius of gridSize. Thanks to the 8-symmtery of a circle we
+       only sample the 1/8th of the plane. */
+
+    uint64_t inCircle = 0;
+
+    for (int y = 0; y < gridSize; ++y)
+      for (int x = y; x <= gridSize; ++x)
+        if ((x * x + y * y) / gridSize <= gridSize) // if distance is < radius
+          inCircle++; // count the point
+
+    // compute pi from the formula for circle area (area = 2 * pi * r):
+    uint64_t pi = (inCircle * 8 * DECIMALS) / (gridSize * gridSize);
+
+    int64_t error = pi - previousPi;
+
+    if (error < 0)
+      error *= -1;
+
+    if (error > previousError) // error got bigger due to overflows, stop
+    {
+      puts("that's it");
+      break;
+    }
+
+    previousError = error;
+    previousPi = pi;
+
+    printf("%d.%d\n",pi / DECIMALS,pi % DECIMALS);
+  }
+}
+```