Add skipFactorial() function (#11)

- add **skipFactorial(n, skip);** experimental - Fix URL in examples - minor edits
RobTillaart · Jan 6, 2024 · e45f754 · e45f754
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diff --git a/CHANGELOG.md b/CHANGELOG.md
@@ -6,10 +6,16 @@ The format is based on [Keep a Changelog](http://keepachangelog.com/)
 and this project adheres to [Semantic Versioning](http://semver.org/).
 
 
+## [0.2.0] - 2024-01-06
+- add **skipFactorial(n, skip);** experimental
+- Fix URL in examples
+- minor edits
+
+----
+
 ## [0.1.8] - 2023-11-22
 - update readme.md
 
-
 ## [0.1.7] - 2023-03-15
 - update readme.md
 - update GitHub actions

diff --git a/LICENSE b/LICENSE
@@ -1,6 +1,6 @@
 MIT License
 
-Copyright (c) 2010-2023 Rob Tillaart
+Copyright (c) 2010-2024 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

diff --git a/README.md b/README.md
@@ -81,18 +81,52 @@ but accuracy is less than the **dfactorial()**, see example.
 ### SemiFactorial
 
 SemiFactorials are like factorials but skipping every other.
+SemiFactorials are written as a number with two exclamation marks.
+
+SemiFactorial are defined for
+- **odd** values:  n!! == n x (n-2) x (n-4) ... x 1
+- **even** values: n!! == n x (n-2) x (n-4) ... x 2
+
+Example 12!! = 12 x 10 x 8 x 6 x 4 x 2 = 46080
 
 - **uint32_t semiFactorial(n)** exact up to 20!!
-- **uint64_t semiFactorial64(n)** exact up to 33!!  (Print 64 bit integers with my printHelpers)
+- **uint64_t semiFactorial64(n)** exact up to 33!!  (Print 64 bit integers with printHelpers library)
 - **double dSemiFactorial(n)** not exact up to 56!! (4 byte) or 300!! (8 byte)
 
-SemiFactorial are defined for
-- **odd** values:  n x (n-2) x (n-4) ... x 1
-- **even** values: n x (n-2) x (n-4) ... x 2
-
 
 Notes:  
-```n! = n!! x (n-1)!!``` this formula allows to calculate the value of n! indirectly
+```
+n! = n!! x (n-1)!!
+``` 
+This formula allows to calculate the value of n! indirectly.
+
+
+### SkipFactorial (experimental)
+
+- **uint32_t skipFactorial(uint32_t n, uint32_t skip)** 
+- **uint64_t skipFactorial64(uint32_t n, uint32_t skip)** 
+- **double dSkipFactorial(uint32_t n, uint32_t skip)** 
+
+SkipFactorials are like factorials and semiFactorials but they skip **skip** numbers.
+- **skipFactorial(12, 4)** = 12 x 8 x 4 = 384
+- **skipFactorial(17, 5)** = 17 x 12 x 7 x 2 = 2856
+- **skipFactorial(n, 1)** == **factorial(n)**
+- **skipFactorial(n, 2)** == **semiFactorial(n)**
+
+As the maximum depends on both n and step sizze there is no single maximum for n.
+This is similar to combinations and permutations.
+
+An indicative table of maxima per function call, the larger the skip, the larger the maximum n.
+Note that for skip <= 10 n still is an 8 bit number.
+
+|   function        |  n, 2   |  n, 3   |  n, 4   |  n, 5   |  n, 10  |  notes  |
+|:------------------|:-------:|:-------:|:-------:|:-------:|:-------:|:--------|
+|  skipFactorial    |   20    |   27    |   32    |    40   |    69   |  max expected smaller than 7 x skip when skip > 10.
+|  skipFactorial64  |   33    |   45    |   55    |    66   |   115   |  max expected smaller than 12 x skip when skip > 10.
+|  dSkipFactorial   |   56    |   77    |   95    |   115   |   200   |  float  (4 bytes)  max expected smaller than 20 x skip when skip > 10.
+|  dSkipFactorial   |  300    |         |         |         |         |  double (8 bytes) 
+
+Note that for the function the **max / skip** is decreasing when **skip grows**.
 
 
 ### Combinations
@@ -184,9 +218,8 @@ See examples
 
 - investigate a bigFloat class to do math for permutations and combinations to substantially larger values.
 - Look for ways to extend the scope
-- **skipFactorial(uint32_t n, uint32_t skip)** == n x (n-skip) x (n -skip -skip) ... x S (depends on size of skip)
-  - e.g. skipFactorial(12, 4) = 12 x 8 x 4.
-  - skipFactorial(n, 2) == semiFactorial(n);
+- fill table for skipFactorial for **double**
+
 
 #### Wont
 

diff --git a/examples/bigCombinations/bigCombinations.ino b/examples/bigCombinations/bigCombinations.ino
@@ -18,6 +18,9 @@ void setup()
 {
   Serial.begin(115200);
   Serial.println(__FILE__);
+  Serial.print("STATHELPERS_LIB_VERSION: ");
+  Serial.println(STATHELPERS_LIB_VERSION);
+  Serial.println();
 
   Serial.println("dcombinations(n, k); ");
   delay(10);
@@ -63,7 +66,7 @@ void setup()
       Serial.print(expo);
       Serial.println();
     }
-    //Serial.println();
+    // Serial.println();
   }
   duration1 = micros() - start;
   Serial.println(duration1);
@@ -78,5 +81,5 @@ void loop()
 }
 
 
-// -- END OF FILE --
+//  -- END OF FILE --
 
diff --git a/examples/bigFactorial/bigFactorial.ino b/examples/bigFactorial/bigFactorial.ino
@@ -7,7 +7,7 @@
 
 
 #include "statHelpers.h"
-#include "printHelpers.h"  // to print large numbers....
+#include "printHelpers.h"  //  to print large numbers ...
 
 
 uint32_t start, duration1, duration2, duration3;
@@ -17,6 +17,9 @@ void setup()
 {
   Serial.begin(115200);
   Serial.println(__FILE__);
+  Serial.print("STATHELPERS_LIB_VERSION: ");
+  Serial.println(STATHELPERS_LIB_VERSION);
+  Serial.println();
 
   uint32_t m    = 10000001;
   double   mant = 0;
@@ -77,5 +80,5 @@ void loop()
 }
 
 
-// -- END OF FILE --
+//  -- END OF FILE --
 
diff --git a/examples/bigPermutations/bigPermutations.ino b/examples/bigPermutations/bigPermutations.ino
@@ -18,6 +18,10 @@ void setup()
 {
   Serial.begin(115200);
   Serial.println(__FILE__);
+  Serial.print("STATHELPERS_LIB_VERSION: ");
+  Serial.println(STATHELPERS_LIB_VERSION);
+  Serial.println();
+
 
   ///////////////////////////////////////////
 
@@ -123,7 +127,8 @@ void setup()
   Serial.println();
   */
 
-  // pick 1000 persons from 4294967295  (maxLong)
+
+  //  pick 1000 persons from 4294967295  (maxLong)
   double   mant = 0;
   uint32_t expo = 0;
   bigPermutations(4294967295, 1000, mant, expo);
@@ -141,5 +146,5 @@ void loop()
 }
 
 
-// -- END OF FILE --
+//  -- END OF FILE --
 
diff --git a/examples/combinations/combinations.ino b/examples/combinations/combinations.ino
@@ -18,6 +18,10 @@ void setup()
 {
   Serial.begin(115200);
   Serial.println(__FILE__);
+  Serial.print("STATHELPERS_LIB_VERSION: ");
+  Serial.println(STATHELPERS_LIB_VERSION);
+  Serial.println();
+
 
   Serial.println("combinations(n, k)");
   delay(10);
@@ -35,7 +39,7 @@ void setup()
       //      Serial.print(combinations(n, k));
       //      Serial.println();
     }
-    //Serial.println();
+    // Serial.println();
   }
   duration1 = micros() - start;
   Serial.println(duration1);
@@ -57,7 +61,7 @@ void setup()
       //      Serial.print(combinations(n, k));
       //      Serial.println();
     }
-    //Serial.println();
+    // Serial.println();
   }
   duration1 = micros() - start;
   Serial.println(duration1);
@@ -80,7 +84,7 @@ void setup()
       //      Serial.print(print64(combinations64(n, k)));
       //      Serial.println();
     }
-    //Serial.println();
+    // Serial.println();
   }
   duration1 = micros() - start;
   Serial.println(duration1);
@@ -101,7 +105,7 @@ void setup()
       //      Serial.print(print64(combinations64(n, k)));
       //      Serial.println();
     }
-    //Serial.println();
+    // Serial.println();
   }
   duration1 = micros() - start;
   Serial.println(duration1);
@@ -126,7 +130,7 @@ void setup()
       //      Serial.print(comb(n, k));
       //      Serial.println();
     }
-    //Serial.println();
+    // Serial.println();
   }
   duration1 = micros() - start;
   Serial.println(duration1);
@@ -141,5 +145,5 @@ void loop()
 }
 
 
-// -- END OF FILE --
+//  -- END OF FILE --
 
diff --git a/examples/factorial/factorial.ino b/examples/factorial/factorial.ino
@@ -7,7 +7,7 @@
 
 
 #include "statHelpers.h"
-#include "printHelpers.h"  // to print large numbers....
+#include "printHelpers.h"  //  to print large numbers....
 
 
 uint32_t start, duration1, duration2;
@@ -17,6 +17,10 @@ void setup()
 {
   Serial.begin(115200);
   Serial.println(__FILE__);
+  Serial.print("STATHELPERS_LIB_VERSION: ");
+  Serial.println(STATHELPERS_LIB_VERSION);
+  Serial.println();
+
 
   int m = 35;
   if (sizeof(double) == 8) m = 175;
@@ -94,5 +98,5 @@ void loop()
 }
 
 
-// -- END OF FILE --
+//  -- END OF FILE --
 
diff --git a/examples/factorial_performance/factorial_performance.ino b/examples/factorial_performance/factorial_performance.ino
@@ -7,7 +7,7 @@
 
 
 #include "statHelpers.h"
-#include "printHelpers.h"  // to print large numbers....
+#include "printHelpers.h"  //  to print large numbers....
 
 
 uint32_t start, duration1, duration2, duration3;
@@ -17,6 +17,10 @@ void setup()
 {
   Serial.begin(115200);
   Serial.println(__FILE__);
+  Serial.print("STATHELPERS_LIB_VERSION: ");
+  Serial.println(STATHELPERS_LIB_VERSION);
+  Serial.println();
+
 
   int m = 35;
   int decimals = 7;
@@ -67,5 +71,5 @@ void loop()
 }
 
 
-// -- END OF FILE --
+//  -- END OF FILE --
 
diff --git a/examples/nextPermutation/nextPermutation.ino b/examples/nextPermutation/nextPermutation.ino
@@ -21,7 +21,9 @@ void setup()
 {
   Serial.begin(115200);
   Serial.println(__FILE__);
-
+  Serial.print("STATHELPERS_LIB_VERSION: ");
+  Serial.println(STATHELPERS_LIB_VERSION);
+  Serial.println();
 
   Serial.println("120 permutations + print");
   do
@@ -32,6 +34,7 @@ void setup()
   }
   while (nextPermutation<char>(hello, 5));
 
+
   ////////////////////////////////////////////////////////////////
 
   Serial.println("timing 720 permutations + print");
@@ -52,6 +55,7 @@ void setup()
   Serial.println(duration1);
   delay(10);
 
+
   ////////////////////////////////////////////////////////////////
 
   start = micros();
@@ -70,5 +74,5 @@ void loop()
 }
 
 
-// -- END OF FILE --
+//  -- END OF FILE --
 
diff --git a/examples/perm1/perm1.ino b/examples/perm1/perm1.ino
@@ -2,26 +2,29 @@
 //    FILE: perm1.ino
 //  AUTHOR: Rob Tillaart
 //    DATE: 2010-11-23
-// PUPROSE: demo permutations
+// PURPOSE: demo permutations
+//     URL: https://github.com/RobTillaart/statHelpers
 //
 //
-// WARNING TAKES LONG
-// ========================================================================
-// ESP32 @ 240 MHz string length 8  ==> ~8100 milliseconds  => printing!!
-// UNO no printing string length 8  ==> ~431 milliseconds
-// UNO no printing string length 10 ==> ~38763 milliseconds
+//  WARNING TAKES LONG
+//  ========================================================================
+//  ESP32 @ 240 MHz string length 8  ==> ~8100 milliseconds  => printing!!
+//  UNO no printing string length 8  ==> ~431 milliseconds
+//  UNO no printing string length 10 ==> ~38763 milliseconds
 
 
-char permstring[12] = "0123456789";    // can be made slightly longer
+#include "statHelpers.h"
+
+char permstring[12] = "0123456789";    //  can be made slightly longer
 
 uint32_t start, stop;
 
 
 void permutate(char * array, uint8_t n)
 {
-  if (n == 0) // end reached print the string
+  if (n == 0)  //  end reached print the string
   {
-    // Serial.println(array);      // process permutation
+    // Serial.println(array);      //  process permutation
     return;
   }
 
@@ -46,7 +49,12 @@ void permutate(char * array, uint8_t n)
 void setup()
 {
   Serial.begin(500000);
-
+  Serial.println(__FILE__);
+  Serial.print("STATHELPERS_LIB_VERSION: ");
+  Serial.println(STATHELPERS_LIB_VERSION);
+  Serial.println();
+
+
   Serial.println("Will take some time..");
   Serial.print("perm1 strlen: ");
   Serial.println(strlen(permstring));
@@ -65,5 +73,4 @@ void loop()
 }
 
 
-// -- END OF FILE --
-
+//  -- END OF FILE --