update examples

CHANGELOG.md

@@ -20,7 +20,9 @@ and this project adheres to [Semantic Versioning](http://semver.org/).
   - add **fraction_sqrts.ino** test sketch
   - add **fraction_fast.ino**, fast determination of fraction with 9900 as denominator.
     - this is very fast, with an accuracy ~1e-4
+  - add **fraction_full_scan.ino** for a full scan search.
   - optimized **FractionMediant.ino** determine fraction with mediant.
+  - add **fraction_setDenominator.ino** demo
   - add **FactionPowers2.ino**, fast determination of fraction with powers of 2.- add examples including tests.
 - update readme.md
 

README.md

@@ -136,7 +136,7 @@ The format is "(n/d)", where n has optionally the sign.
 
 - **Fraction mediant(const Fraction&, const Fraction&)**
 - **Fraction middle(const Fraction&, const Fraction&)**
-- **Fraction setDenominator(const Fraction&, uint16_t)**
+- **Fraction setDenominator(const Fraction&, uint16_t)** (might be simplified still)
 
 
 ## Use with care

examples/Fraction_full_scan/Fraction_full_scan.ino

@@ -0,0 +1,106 @@
+//
+//    FILE: Fraction_full_scan.ino
+//  AUTHOR: Rob Tillaart
+// PURPOSE: Find fraction by full scan possible values.
+//     URL: https://github.com/RobTillaart/Fraction
+//
+//  This method is very slow but it scans the whole range (in fact only half)
+//  for all possible fractions, resulting in very good approximations.
+//  Works for positive values only (for now).
+//
+//  Takes up to 3 seconds per search on a 16 MHz UNO.
+//  Takes up to 12 milliseconds per search on a 240 MHz ESP32.
+
+#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.toString());
+  Serial.println(x.toDouble(), 10);
+  Serial.println();
+
+  f = EULER;
+  start = micros();
+  Fraction y = fractionize(f);
+  stop = micros();
+  Serial.println(stop - start);
+  Serial.println(y.toString());
+  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.toString());
+  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.toString());
+  Serial.print("\t");
+  Serial.print(f, 10);
+  Serial.print("\t");
+  Serial.print(y.toDouble(), 10);
+  Serial.print("\t");
+  Serial.println(f - y.toDouble(), 10);
+}
+
+// very very slow but very good.
+Fraction fractionize(float f)
+{
+  int best = 1;
+  float smallest = 1.0;
+  //  smaller denominators will all be detected as 5000..10000 are multiples.
+  for (int d = 5000; d < 10000; d++)
+  {
+    Fraction frac(f * d + 0.5, d);
+    float tmp = abs(f - frac.toFloat());
+    if ( tmp < smallest)
+    {
+      smallest = tmp;
+      best = d;
+    }
+  }
+  Fraction frac(round(f * best), best);
+  return frac;
+}
+
+
+//  -- END OF FILE --

examples/Fraction_setDenominator/Fraction_setDenominator.ino

@@ -0,0 +1,51 @@
+//
+//    FILE: Fraction_setDenominator.ino
+//  AUTHOR: Rob Tillaart
+// PURPOSE: Calculate fraction with well chosen number.
+//     URL: https://github.com/RobTillaart/Fraction
+
+
+#include "fraction.h"
+
+
+void setup()
+{
+  Serial.begin(115200);
+  Serial.print(__FILE__);
+  Serial.println();
+  Serial.println();
+
+  Fraction pi(PI);
+  Fraction appr = Fraction::setDenominator(pi, 32);
+  Serial.println(pi.toString());
+  Serial.println(pi.toDouble(), 10);
+  Serial.println(appr.toString());
+  Serial.println(appr.toDouble(), 10);
+  Serial.println();
+
+  Fraction ee(EULER);
+  appr = Fraction::setDenominator(ee, 32);
+  Serial.println(ee.toString());
+  Serial.println(ee.toDouble(), 10);
+  Serial.println(appr.toString());
+  Serial.println(appr.toDouble(), 10);
+  Serial.println();
+
+  Fraction tt(0.125);
+  appr = Fraction::setDenominator(tt, 32);
+  Serial.println(tt.toString());
+  Serial.println(tt.toDouble(), 10);
+  Serial.println(appr.toString());
+  Serial.println(appr.toDouble(), 10);
+  Serial.println();
+
+  Serial.println("done...\n");
+}
+
+
+void loop()
+{
+}
+
+
+//  -- END OF FILE --