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# FLE

Arduino library for Arduino library for float with error datatype


## Description

This experimental library provides basic math when have a quantity with a certain 
error margin. E.g. when you approximate PI as 22/7 it is not exact. By doing the 
math with FLE's one can see how much error adds up in an calculation.


## Interface

### Printable

The FLE class implements the public interface of Printable.
This allows you to print an FLE in human readable form.

```cpp
    FLE x(3.14, 0.002);
    x.setDecimals(4);
    Serial.println(x);                 // will print 3.1400 ± 0.0020
    Serial.println(x.setDecimals(2));  // will print 3.14 ± 0.00
    Serial.println(x.value());         // will print 3.14
```

When the ± char does not print correctly, one could change the font.


### Functions

- **FLE(val = 0, err = 0)** constructor, with default value and error set to 0.
- **PrintTo(Print& p)** printable interface, define a stream to print to.  
Format is "value ± error" see above (plus-minus ± = char(0177))
- **setDecimals(n)** will print the FLE both value and error with n decimals.
- **setSeparator(char c)** overrules the standard ± char. (0177)
- **value()** returns value part.
- **error()** return error part.
- **relError()** returns relative error, except when value == 0. 
Then the function returns 0. Q: should this be "NaN" ?
- **high()** returns value + error margin (= max real value).
- **low()** returns value - error margin (= min real value).

Furthermore the basic math is implemented, "+, -, \*, /, +=, -=, \*=, /="


#### Set like functions

- **bool in(FLE y)** x.in(y) returns true if x lies completely in y  (range is a subset)
- **FLE shared(FLE y)** returns the overlapping range. 


#### Weak propositions

Experimental.

- **bool peq(FLE &y)** possible equal.
- **bool pne(FLE &y)** possible not equal.
- **bool plt(FLE &y)** possible less than.
- **bool ple(FLE &y)** possible less equal.
- **bool pgt(FLE &y)** possible greater than.
- **bool pge(FLE &y)** possible greater equal.


## Todo

- update documentation
- comparison (investigate, what means equal or less than ..)
- functions log, exp,
- functions sqr, sqrt, pow
- functions sin, cos, tan (+ inverse + hyp)
- test ad infinitum 
- option to set the ± char for platforms that cannot print it.
- test negative numbers
- test large / small numbers.
- test other separator
- more demo sketches...


## Operation

- negative numbers not tested yet

See example