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 # CLI-pi
-tpi -- C-written, MPFR-based CLI program for calculating pi
+**tpi - C-written, MPFR-based CLI program for calculating pi**
+
+> [!WARNING]
+> For the accuracy of calculations, a large MPFR library is used, there may be delays and high processor loads on weak systems.
+
+The program calculates the pi number with high accuracy. 
+
+In infinite mode, something like AOT compilation is used, first ~10 million decimal places are calculated, and then they are converted to `char[]` through the same MPFR.
+
+$$100,000,000 \text{ ms} = 100,000 \text{ s} = \frac{100,000}{3600} \text{ hours} \approx 27.78 \text{ h}$$
+
+But if you need more, you can change the len variable and recompile the project with `build.sh` for yourself by setting a different limit. Be careful, the CPU load will be higher.
+
+# How does the calculation work?
+Calculations are performed using the Gauss method, which is based on the use of integrals and properties of elliptic integrals. This method, also known as the Gauss-Legandre method, makes it possible to calculate pi with high accuracy using an iterative process.
+
+$$\pi \approx \frac{(a_n + b_n)^2}{4 t_n}$$
+
+In python it looks like: 
+```python
+def gauss_pi(iterations):
+    a = 1.0
+    b = 1.0 / math.sqrt(2)
+    t = 1.0 / 4.0
+    p = 1.0
+
+    for _ in range(iterations):
+        a_next = (a + b) / 2
+        b = math.sqrt(a * b)
+        t -= p * (a - a_next) ** 2
+        a = a_next
+        p *= 2
+
+    return (a + b) ** 2 / (4 * t)
+```
+
+I'm not giving an example from my code because the gnu MPFR syntax is unreadable without an armed eye.