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141 lines
4.1 KiB
Markdown
141 lines
4.1 KiB
Markdown
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[](https://github.com/marketplace/actions/arduino_ci)
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[](https://github.com/RobTillaart/Interval/actions/workflows/arduino-lint.yml)
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[](https://github.com/RobTillaart/Interval/actions/workflows/jsoncheck.yml)
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[](https://github.com/RobTillaart/Interval/blob/master/LICENSE)
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[](https://github.com/RobTillaart/Interval/releases)
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# Interval
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Arduino library for the Interval data type. **Experimental**
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## Description
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This experimental library provides basic math when you do not know a quantity.
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The only thing you do know is the value is in a certain interval.
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After doing some math you want to know the interval of possible outcomes.
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An interval exist of a pair of floats, low and high, the borders of the interval.
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**footnote:**
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The data type Interval was created to do some experiments.
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It was inspired by the **frink** language which has an interval data type.
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Frink itself is not investigated, so semantics are not necessary similar.
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## Interface
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The Interval class implements the public interface of Printable.
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This allows you to print an Interval in human readable form.
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```cpp
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Interval x(3, 4);
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x.setDecimals(2);
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Serial.println(x); // will print [3.00, 4.00]
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```
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### Constructors
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- **Interval()** zero = interval \[0, 0]
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- **Interval(float lo, float hi)** interval \[lo, hi]
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- **Interval(float f)** interval \[f, f]
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### Basic functions
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The basic functions are used to get and set some core attributes.
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- **setDecimals()** set nr of decimals for printing.
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- **value()** is the middle of the interval (as we do not know distribution)
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- **range()** = high() - low()
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- **high()** idem
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- **low()** idem
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- **relAccuracy()** = range() / value()
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- **setRange(float r)** adjust range around value() =- r/2
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### Math Operators
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Math operators
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- **addition + +=**
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- **subtraction - -=**
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- **multiplication \* \*=**
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- **quotient \/ \/=**
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### Functions
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Functions are not implemented yet as these need **to be investigated**.
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For a monotonous function it is relative easy
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```
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Interval v = F( [a, b] ); ==> [ F(a), F(b)]
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e.g.
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Interval f = exp( [a, b]); ==> [exp(a), exp(b)]
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Interval g = log( [a, b]); ==> [log(a), log(b)] a > 0!!
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```
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The math for non monotonous functions is more complex
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as one cannot use the function values as above.
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```
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Interval p = sin( [0, PI] ); ==> [0, 1]
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Interval q = sin( [0, -PI] ); ==> [-1, 0]
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Interval r = sin( [0, 10 * PI] ); ==> [-1, 1]
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Interval s = sqr( [-5, -3] ) ; ==> [9, 25]
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Interval t = sqr( [-5, 3] ) ; ==> [0, 25]
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```
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- change range while keeping value.
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### Comparison operators
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**To be investigated**. The semantics make at least a difference between when
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an interval is Certainly Less Equal or Probably Less or Equal.
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The Certainly group will be boolean math as we know it.
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The Probably group will be more like fuzzy logic so a float between 0..100%.
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- **bool == **
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- **bool != **
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- **bool > **
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- **bool >= **
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- **bool < **
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- **bool <= **
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### Set operators
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**To be investigated** include:
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- If you have two or more intervals, what is the 'super interval' that includes all?
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- How to subtract elements of an interval from another Interval?
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This is different than the subtraction above,
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think of it as " I know the number I look for is in \[1, 4] but it is not in \[3, 5]
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so it is in \[1,3]
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### Other
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- a known problem is difference between border inclusive \[ \] and
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border exclusive \< \>. How to deal with that?
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- 1/\[-1, 1\] ==> ?? singularity for 0?
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- infinity as border? In math we have \[0, \->> for all positive floats.
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## Operation
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See example
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## Future
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- play and extend the library.
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- check all to be investigated above.
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- clean up the documentation.
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