0.1.9 refactor - experimental

LICENSE

@@ -1,6 +1,6 @@
 MIT License
 
-Copyright (c) 2020 Rob Tillaart
+Copyright (c) 2015-2020 Rob Tillaart
 
 Permission is hereby granted, free of charge, to any person obtaining a copy
 of this software and associated documentation files (the "Software"), to deal

README.md

@@ -1,2 +1,30 @@
 # Fraction
-Arduino library to implement a Fraction datatype
+
+Arduino library to implement a Fraction datatype (experimental)
+
+## Description
+
+The fraction library implements fractional numbers a.k.a. Q, 
+(integers are Z and floats/doubles are R),
+and the conversion to floats.
+
+The code is working with a number of limitations among others:
+- denominator is max 4 digits to keep code for multiply and divide simple
+- Fractions are not exact (even floats are not exact)
+- the range of numbers supported is limited.
+- code is experimental still.
+
+That said, the library is useful e.g. to display float numbers as a fraction.
+From programming point of view the fractionize function, converting a double
+into a fraction is a nice programming problem, fast with a minimal error.
+
+In short, use fractions with care otherwise your sketch might get broken ;)
+
+## Operations
+
+See examples
+
+## Use with care
+
+The library is reasonably tested, and if problems arise please let me know.
+

examples/FractionFindSum/FractionFindSum.ino

@@ -0,0 +1,66 @@
+//
+//    FILE: FractionFindSum.ino
+//  AUTHOR: Rob Tillaart
+// VERSION: 0.1.1
+// PURPOSE: demo
+//    DATE: 13-feb-2015
+//     URL: https://github.com/RobTillaart/Fraction
+//
+
+#include "fraction.h"
+
+uint32_t start;
+uint32_t stop;
+
+void setup()
+{
+  pinMode(13, OUTPUT);
+  Serial.begin(115200);
+  Serial.print("\n\nStart F: ");
+  Serial.println(FRACTIONLIBVERSION);
+  Serial.println();
+  randomSeed(analogRead(A0) * 256 + analogRead(A1));
+
+  start = micros();
+  stop = micros();
+  // Serial.println(stop - start);
+
+  for (int i = 1; i < 93; i++)
+  {
+    Fraction f(i, 93);
+    findSum(f);
+  }
+}
+
+void findSum(Fraction f)
+{
+  Fraction z(0);
+
+  Serial.print(f);
+  Serial.print(" =\t ");
+  for (long i = 1; i < 10000; i++)
+  {
+    Fraction g(1, i);
+    if (g <= f)
+    {
+      f -= g;
+      z += g;
+      Serial.print(g);
+      Serial.print(" + ");
+    }
+    if (f == Fraction(0))
+    {
+      break;
+    }
+  }
+  Serial.print("\t => ");
+  Serial.println(z);
+  Serial.println();
+}
+
+
+void loop()
+{
+}
+
+// -- END OF FILE --

examples/FractionMediant/FractionMediant.ino

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+//
+//    FILE: FractionMediant.ino
+//  AUTHOR: Rob Tillaart
+// VERSION: 0.1.0
+// PURPOSE: Find fraction by binary search with mediant.
+//    DATE: 2020-04-21
+//
+
+// this method is not that fast but it shows a nice application for 
+// the mediant.
+
+#include "fraction.h"
+
+uint32_t start, stop;
+
+void setup()
+{
+  Serial.begin(115200);
+  Serial.print(__FILE__);
+  Serial.println();
+  Serial.println();
+
+  float f = PI;
+  start = micros();
+  Fraction x = fractionize(f);
+  stop = micros();
+  Serial.println(stop - start);
+  Serial.println(x);
+  Serial.println(x.toDouble(), 10);
+  Serial.println();
+
+  f = EULER;
+  start = micros();
+  Fraction y = fractionize(f);
+  stop = micros();
+  Serial.println(stop - start);
+  Serial.println(y);
+  Serial.println(y.toDouble(), 10);
+  Serial.println();
+
+  Serial.println("done...\n");
+
+}
+
+
+void loop()
+{
+  float f = random(1000000) * 0.000001;
+
+  // reference
+  start = micros();
+  Fraction y(f);
+  stop = micros();
+
+  Serial.println();
+  Serial.print(stop - start);
+  Serial.print("\t");
+  Serial.print(y);
+  Serial.print("\t");
+  Serial.print(f, 10);
+  Serial.print("\t");
+  Serial.print(y.toDouble(), 10);
+  Serial.print("\t");
+  Serial.println(f - y.toDouble(), 10);
+
+  // mediant method.
+  start = micros();
+  y = fractionize(f);
+  stop = micros();
+
+  Serial.print(stop - start);
+  Serial.print("\t");
+  Serial.print(y);
+  Serial.print("\t");
+  Serial.print(f, 10);
+  Serial.print("\t");
+  Serial.print(y.toDouble(), 10);
+  Serial.print("\t");
+  Serial.println(f - y.toDouble(), 10);
+}
+
+
+Fraction fractionize(float f)
+{
+  float acc = 1e-6;
+  float d1 = 0;
+  float d2 = 0;
+  Fraction a(0, 1);
+  Fraction b(9999, 1);
+  Fraction q(f);
+
+  for (int i = 0; i < 500; i++)
+  {
+    Fraction c = Fraction::mediant(a, b);   // NOTE middle(a,b) is slower and worse!
+    if ( c.toDouble() < f) a = c;
+    else b = c;
+
+    d1 = abs(f - a.toDouble());
+    d2 = abs(f - b.toDouble());
+    if (d1 < acc && d2 < acc) break;
+  }
+  if (d1 < d2) return a;
+  return b;
+}
+
+
+
+// -- END OF FILE --