math Match numbers place increase

[NumbNutsJunior 61]

What I am trying to do probably makes no sense, and I really have no idea what i'm doing in this place of algebra but here is my problem ...

I am trying to populate a list of values from min (x) to max (y) increasing the values by the step amount (z) easy enough, but I want to have the step value increase in size as the numbers get larger and larger so I don't have  a list the size 'max / step', if max is say 5000000.
So once the current value reaches another place the step value matches in increase by the same amount: min(0); max(5000000); starting step(2500);

                                + 2500                       +25000                                                                                         +250000
Expected output: [0, 2500, 5000, 7500, 10000, 25000, 50000, 75000, 100000, 125000, ... , 975000, 1000000, 1250000, ... ]

Below is probably just a bunch of junk, so maybe cover your eyes from this part, as It likely will lead you no where but I would not really know ...

// Limits
_min_value = 0;
_max_value = 5000000;

// Init
_values = [];
_current_value = _min_value;

// Init loop variables
_value_step = 2500;
_step_power = floor(log _value_step);
_base_step = _value_step / (10 ^ _step_power);

// Populate values
while {_current_value <= _max_value} do {
	
  // Push to value list
  _values pushBack _current_value;
  
  // Figure step amount
  _current_value_power = floor(log _current_value);
  _value_step = _base_step * (10 ^ _current_value_power);
  _powers_difference = _current_value_power - _step_power;

  // ...
	
  // Update current value
  _current_value = _current_value + _value_step;
};

 

I figured this fell into the category of logarithms but I am apparently not very good at learning and using them as I have been stuck on trying to complete this problem all day. Please help 🙂

 

Note: I would like to figure this problem without a bunch of 'if' or 'switch' statements, just good old reliable math

[pierremgi 4738]

Is this just Math for Math or do you have something more consistent to do with?

[Grumpy Old Man 3540]

Had to read the first post at least 5 times and still don't quite get it.

The example also doesn't make sense since 10000+25000 != 25000.

Do you want to increase the step size after a certain value has been reached?

Could be like this:

_output = [];
_max = 500000;
_steps = [2500,25000,250000];
_increaseAt = [0,10000,100000];
_current = 0;
_increase = 0;
while {_current < _max} do {
	if (_increaseAT find _current > -1) then {_increase = _steps#(_increaseAt find _current)};
	_current = _current + _increase;
	_output pushBack _current;
};
hintSilent str _output;
copyToClipboard str _output;
  
//prints:
[2500,5000,7500,10000,35000,60000,85000,110000,135000,160000,185000,210000,235000,260000,285000,310000,335000,360000,385000,410000,435000,460000,485000,510000]

Cheers

[Muzzleflash 111]

So the inputs are Min and Max. Say the "steps" move us along the X-axis, and on the Y-axis we have the value. Using just a linear function where the Y value is the element position in the output: "Y = StepSize * X + Min" where X is the same as Index in this case, it might take a long time (many Index) to reach Y >= Max as you already observed.

 

So rather than that, let us use a polynomial (second-degree) and drop the step size for now and just consider this perhaps: "Y = X^1.8" (this looks like this, https://www.wolframalpha.com/input/?i=y+%3D+x^1.8+where+0+<+x+<%3D+1 ). The thing we are looking for here is whether the "curve" itself looks right. The normal linear is "Y = X^1". This one makes it rise much slower in the start and much faster in the end; notice the midpoint for X=0.5 is only about Y=0.3. So half of the values would be in the first 30%. By increasing, e.g. to ^3, half would be in lower 10% of the value.

To use this we just need to map our index to 0-1 and map the output to the proper value. So how many values? Well you can easily pick that yourself:

NNJ_fnc_Populate = {
    params ["_min", "_max", "_count", ["_pow", 1.8]];
    private _result = [];
    // We iterate from 0 to count-1 and need to divide by count-1 anyway
    private _countMinusOne = _count - 1;
    private _maxMinDiff = _max - _min;
    for "_i" from 0 to _countMinusOne do {
        // Normalize the X value to between 0 and 1 (inclusive)
        private _xVal = _i / _countMinusOne;
        // Compute the normalized Y-value
        private _yVal = _xVal ^ _pow;
        // Map the _yVal back to the desired range
        private _value = _min + _maxMinDiff * _yVal;
        _result pushBack _value;
    };
    _result
};

// So if you want a 1000 values.
private _min = 0;
private _max = 5000000;
private _valuesA = [_min, _max, 1000] call NNJ_fnc_Populate;
// Or you want 3000 values distributed but rounded, and using ^1.2
// Note, if you round with a power too multiple elements in the beginning may be the same, e.g. zeroes and ones.
private _valuesB = ([_min, _max, 1000, 1.2] call NNJ_fnc_Populate) apply {round _x};