## Estimation of Pi by the Monte Carlo method

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ratwolf
Posts: 31
Joined: Fri Feb 12, 2021 1:00 am

### Estimation of Pi by the Monte Carlo method

PiMC.png (1.45 KiB) Viewed 644 times

Simulation of random (x, y) points in a unit square as a domain and a unit circle within the same domain inscribed in the unit square. The ratio of the number of points within the circle and the total number of points generated is then calculated, multiplied by 4

Please use in 4STK mode. Enter the number of loops. Press R/S. The estimate of Pi is then displayed in X.

Not bad: with Mathematica on my MacBook Pro, this takes about 50 seconds:

approxPi[n_] := 4. Count[Map[Norm, RandomReal[{-1, 1}, {n, 2}]], _?(# <= 1 &)]/n
approxPi[10^8]

With Free42 for Mac (v. 3.0.3, binary version) with 10^8 loops and the code shown below, it takes about 90 seconds.

Code: Select all

00 { 98-Byte Prgm }
01▸LBL "PiMC"
02 0
03 SEED
04 STO "Circle"
05 STO "Square"
06 INPUT "Loop"
07▸LBL 01
08 RAN
09 X↑2
10 RAN
11 X↑2
12 +
13 1
14 X<Y?
15 GTO 02
16 STO+ "Circle"
17▸LBL 02
18 STO+ "Square"
19 STO- "Loop"
20 0<? "Loop"
21 GTO 01
22 RCL "Circle"
23 RCL÷ "Square"
24 4
25 ×
26 END
Attachments
PiMC.raw