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Analysis

The growing of the school of fishs could be somewhat exponential, but for now we do not know it's growth rate yet.

Design

First - and straight - idea was to simulate the Lanternfish's life and school of (linked) fishs.

type Lanternfish_Ptr is access all Lanternfish;

type Lanternfish is record
    Timer   : Life_Timer      := BabyFish;
    Sibling : Lanternfish_Ptr := null;
end record;

A new baby fish can be created easily throught the use of dynamic allocation when one comes at it's life-timer of 0.

procedure New_Fish (Timer : Life_Timer) is
    (...)
begin
    (...)
    Last_fish := new Lanternfish;
    (...)
    Previous_Last_Fish.Sibling := Last_fish;
    (...)
end New_Fish;

First results

Population

Running the simulation for 18 or 80 days of a school of Lanternfish was cool 😎 ... in the begining

Going further became a nightmare 😫 ... of over-population 🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟!

Day 🐟 Population 🐟 Population
0 5 300
18 26 1_563
20 34 1_959
80 5_934 350_605
120 191_336 11_301_761
150 2_621_894 154_900_658
160 6_311_710 372_489_150
170 14_979_958 883_463_328
180 35_890_123 2_120_130_781
185 55_653_352 3_285_743_983
210 490_587_171 Out of memory
256 Out of memory Out of memory

Some charting shows clearly that growth is a 10 exponential here, with a factor depending on the initial data (5🐟 ou 300🐟) : respectively 24 or 20.

Population growth from 5

Population growth from 300

One can then extrapolate what the population would be after 256 days.

Day 5 Initial Population 300 Initial Population
256 39_300_000_000 3_070_000_000_000
256 39 Giga 3 Tera

Execution time

Execution time (sec) ... on a Ryzen 3900 @ 4.3 GHz equiped with 64 GB of RAM.

Day 5 🐟 at init. 300 🐟 at init.
18 0.005 0.01
20 0.005 0.01
80 0.005 0.01
120 0.015 0.32
150 0.15 4.72
158 0.31 9.24
160 0.195 11.08
170 0.447 26.59
180 2.202 63.76
185 1.80 105.76
199 11.25 Out of memory 162 GB
210 29.25 Out of memory
256 Out of memory Out of memory 284 GB

Clearly, have to find another simulation algorithm 🧞‍♂️

💡 New solution pattern 💡

Lets consider the fish population as counting in the pyramid of age.

Mature : constant := 0;
Young  : constant := 6;
BabyFish : constant := 8;

type Life_Timer is new Natural range Mature .. BabyFish;

type Pyramid_of_Age is array (Life_Timer) of Population;

This is now actually efficient!

Main loop

   -- Time and Life is passing by
    for D in 1 .. Run_Args.Nb_of_Days loop
        Fish_Count := Next_Day;
    end loop;

Applying an aging function

function Next_Day return Population is
(...)
    -- General population aging
    for T in Life_Timer loop
        case T is
            when Mature => -- 0
                New_Young      := Fish_Population (Mature);
                New_Generation := Fish_Population (Mature);
            when others =>
                Fish_Population (T - 1) := Fish_Population (T);
        end case;
    end loop;

    -- New Babies and add youngsters
    Fish_Population (BabyFish) := Next_Generation_Count;
    Fish_Population (Young)    := @ + New_Young;

    Next_Generation_Count := Fish_Population (Mature);
(...)