Added example on Inverses

Author: tomcombriat

examples/Inverses/Inverses.ino

@@ -0,0 +1,71 @@
+/*
+ * FixMath Library - Example demonstrating the different inverse functions and their limitations.
+ *
+ * This example code is in the public domain CONTRARY TO THE LIBRARY itself,
+ * which is licensed the GNU Lesser General Public Licence
+ *
+ */
+
+
+
+#include <FixMath.h>
+
+UFix<8, 8> a = 250.5;
+UFix<8, 8> b = 150.2;
+
+void setup() {
+  Serial.begin(9600);
+}
+
+void loop() {
+
+  /*
+invFast() is able to represent the whole range
+of inverses of a number (ie. minimum and maximum will be approximately correct)
+but not accurately. This is shown here as two very different numbers
+have the same inverse). For a Fix<NI,NF> the invFast is of type Fix<NF,NI>
+*/
+  Serial.print(a.asFloat());
+  Serial.print(".invFast()=");
+  Serial.println(a.invFast().asFloat(), 10);
+
+  Serial.print(b.asFloat());
+  Serial.print(".invFast()=");
+  Serial.println(b.invFast().asFloat(), 10);
+
+
+  /*
+invAccurate provides a better resolution but the output type is
+way bigger: Fix<NI,NF>.invAccurate() is a Fix<2*NF+NI,NI>.
+In most case, this provides different values for every 
+different number.
+Here, the resulting numbers are UFix<8,24>.
+*/
+  Serial.print(a.asFloat());
+  Serial.print(".invAccurate()=");
+  Serial.println(a.invAccurate().asFloat(), 10);
+
+  Serial.print(b.asFloat());
+  Serial.print(".invAccurate()=");
+  Serial.println(b.invAccurate().asFloat(), 10);
+
+  /*
+An intermediate solution is provided by .inv<_NF>(), 
+where the number of fractional bits is specified.
+This allows for optimization over .invAccurate()
+when needed.
+*/
+  Serial.print(a.asFloat());
+  Serial.print(".inv<12>()=");
+  Serial.println(a.inv<12>().asFloat(), 10);
+
+  Serial.print(b.asFloat());
+  Serial.print(".inv<12>()=");
+  Serial.println(b.inv<12>().asFloat(), 10);
+
+  Serial.println();
+  Serial.println();
+
+
+  delay(10000);
+}