0.2.0 statHelpers

libraries/statHelpers/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

libraries/statHelpers/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

libraries/statHelpers/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.
-- **uint32_t semiFactorial(n)** exact up to 20!!
-- **uint64_t semiFactorial64(n)** exact up to 33!!  (Print 64 bit integers with my printHelpers)
-- **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
+- **odd** values:  n!! == n x (n-2) x (n-4) ... x 1
-- **even** values: n x (n-2) x (n-4) ... x 2
+- **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 printHelpers library)
+- **double dSemiFactorial(n)** not exact up to 56!! (4 byte) or 300!! (8 byte)
 
 
 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)
+- fill table for skipFactorial for **double**
-  - e.g. skipFactorial(12, 4) = 12 x 8 x 4.
+
-  - skipFactorial(n, 2) == semiFactorial(n);
 
 #### Wont
 

libraries/statHelpers/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 --
 

libraries/statHelpers/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 --
 

libraries/statHelpers/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 --
 

libraries/statHelpers/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 --
 

libraries/statHelpers/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 --
 

libraries/statHelpers/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 --
 

libraries/statHelpers/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 --
 

libraries/statHelpers/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
+//  WARNING TAKES LONG
-// ========================================================================
+//  ========================================================================
-// ESP32 @ 240 MHz string length 8  ==> ~8100 milliseconds  => printing!!
+//  ESP32 @ 240 MHz string length 8  ==> ~8100 milliseconds  => printing!!
-// UNO no printing string length 8  ==> ~431 milliseconds
+//  UNO no printing string length 8  ==> ~431 milliseconds
-// UNO no printing string length 10 ==> ~38763 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;
   }
 
@@ -46,6 +49,11 @@ 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: ");
@@ -65,5 +73,4 @@ void loop()
 }
 
 
-// -- END OF FILE --
+//  -- END OF FILE --
-

libraries/statHelpers/examples/permutations/permutations.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("permutations(n, k)");
   delay(10);
@@ -40,6 +44,7 @@ void setup()
   Serial.println(duration1);
   Serial.println();
 
+
   ///////////////////////////////////////////
 
   Serial.println("permutations64(n, k)");
@@ -62,6 +67,7 @@ void setup()
   Serial.println(duration1);
   Serial.println();
 
+
   ///////////////////////////////////////////
 
   Serial.println("dpermutations(n, k) - double can be 4 or 8 bit.");
@@ -95,5 +101,5 @@ void loop()
 }
 
 
-// -- END OF FILE --
+//  -- END OF FILE --
 

libraries/statHelpers/examples/semiFactorial/semiFactorial.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();
 
   int m = 60;
   if (sizeof(double) == 8) m = 301;
@@ -39,7 +42,7 @@ void setup()
   delay(100);
   uint8_t n = 25;
   start = micros();
-  double d1 = semiFactorial(n);  // will fail but indicative
+  double d1 = semiFactorial(n);  //  will fail but indicative
   duration1 = micros() - start;
   start = micros();
   double d2 = semiFactorial64(n);
@@ -74,5 +77,5 @@ void loop()
 }
 
 
-// -- END OF FILE --
+//  -- END OF FILE --
 

libraries/statHelpers/examples/skipFactorial/skipFactorial.ino

@@ -0,0 +1,82 @@
+//
+//    FILE: skipFactorial.ino
+//  AUTHOR: Rob Tillaart
+// PURPOSE: demo
+//    DATE: 2024-01-06
+//     URL: https://github.com/RobTillaart/statHelpers
+
+
+#include "statHelpers.h"
+#include "printHelpers.h"  //  to print large numbers....
+
+
+uint32_t start, duration1, duration2, duration3;
+
+
+void setup()
+{
+  Serial.begin(115200);
+  Serial.println(__FILE__);
+  Serial.print("STATHELPERS_LIB_VERSION: ");
+  Serial.println(STATHELPERS_LIB_VERSION);
+  Serial.println();
+
+  int m = 300;
+  int skip = 10;
+  if (sizeof(double) == 8) m = 301;
+
+  Serial.println("Skip factorial (n, 3)  -  max reached at n = 27, n = 45, n = 60");
+  for (int i = 27; i < m; i++)
+  {
+    Serial.print(i);
+    Serial.print('\t');
+    Serial.print(skipFactorial(i, skip));
+    Serial.print('\t');
+    Serial.print(print64(skipFactorial64(i, skip)));
+    Serial.print('\t');
+    Serial.print(sci(dSkipFactorial(i, skip), 15));
+    Serial.println();
+  }
+  Serial.println();
+  
+  Serial.println("PERFORMANCE");
+  Serial.println("n\tskipFactorial, skipFactorial64, dSkipFactorial usec\t values");
+  delay(100);
+  uint8_t n = 25;
+  start = micros();
+  double d1 = skipFactorial(n, 3);  //  will fail but indicative
+  duration1 = micros() - start;
+  start = micros();
+  double d2 = skipFactorial64(n, 3);
+  duration2 = micros() - start;
+  start = micros();
+  double d3 = dSkipFactorial(n, 3);
+  duration3 = micros() - start;
+  Serial.print(n);
+  Serial.print('\t');
+  Serial.print(duration1);
+  Serial.print('\t');
+  Serial.print('\t');
+  Serial.print(duration2);
+  Serial.print('\t');
+  Serial.print('\t');
+  Serial.print(duration3);
+  Serial.println();
+  Serial.print('\t');
+  Serial.print(sci(d1, 10));
+  Serial.print('\t');
+  Serial.print(sci(d2, 10));
+  Serial.print('\t');
+  Serial.print(sci(d3, 10));
+  Serial.println();
+
+  Serial.println("\n Done...");
+}
+
+
+void loop()
+{
+}
+
+
+//  -- END OF FILE --

libraries/statHelpers/library.json

@@ -15,7 +15,7 @@
     "type": "git",
     "url": "https://github.com/RobTillaart/statHelpers.git"
   },
-  "version": "0.1.8",
+  "version": "0.2.0",
   "license": "MIT",
   "frameworks": "*",
   "platforms": "*",

libraries/statHelpers/library.properties

@@ -1,5 +1,5 @@
 name=statHelpers
-version=0.1.8
+version=0.2.0
 author=Rob Tillaart <rob.tillaart@gmail.com>
 maintainer=Rob Tillaart <rob.tillaart@gmail.com>
 sentence=Arduino library with a number of statistic helper functions.

libraries/statHelpers/statHelpers.cpp

@@ -1,7 +1,7 @@
 //
 //    FILE: statHelpers.cpp
 //  AUTHOR: Rob Tillaart
-// VERSION: 0.1.8
+// VERSION: 0.2.0
 // PURPOSE: Arduino library with a number of statistic helper functions.
 //    DATE: 2020-07-01
 //     URL: https://github.com/RobTillaart/statHelpers
@@ -190,7 +190,7 @@ double stirling(uint8_t n)
 
 ///////////////////////////////////////////////////////////////////////////
 //
-//  SEMIFACTORIAL
+//  SEMI_FACTORIAL
 //
 
 //  exact ==> 20!!
@@ -239,6 +239,53 @@ double dSemiFactorial(uint16_t n)
 }
 
 
+
+///////////////////////////////////////////////////////////////////////////
+//
+//  SKIP_FACTORIAL
+//
+
+uint32_t skipFactorial(uint32_t n, uint32_t skip)
+{
+  if (skip == 0) return 0;
+  uint32_t f = 1;
+  while(n > skip)
+  {
+    f *= n;
+    n -= skip;
+  }
+  return f;
+}
+
+
+uint64_t skipFactorial64(uint32_t n, uint32_t skip)
+{
+  if (skip == 0) return 0;
+  uint64_t f = 1;
+  while(n > skip)
+  {
+    f *= n;
+    n -= skip;
+  }
+  return f;
+}
+
+
+//  float  (4 byte)
+//  double (8 byte)
+double dSkipFactorial(uint32_t n, uint32_t skip)
+{
+  if (skip == 0) return 0;
+  double f = 1;
+  while(n > skip)   //  optimize like sSemiFactorial?
+  {
+    f *= n;
+    n -= skip;
+  }
+  return f;
+}
+
+
 ///////////////////////////////////////////////////////////////////////////
 //
 //  COMBINATIONS

libraries/statHelpers/statHelpers.h

@@ -2,7 +2,7 @@
 //
 //    FILE: statHelpers.h
 //  AUTHOR: Rob Tillaart
-// VERSION: 0.1.8
+// VERSION: 0.2.0
 // PURPOSE: Arduino library with a number of statistic helper functions.
 //    DATE: 2020-07-01
 //     URL: https://github.com/RobTillaart/statHelpers
@@ -11,7 +11,7 @@
 #include "Arduino.h"
 
 
-#define STATHELPERS_LIB_VERSION               (F("0.1.8"))
+#define STATHELPERS_LIB_VERSION               (F("0.2.0"))
 
 
 ///////////////////////////////////////////////////////////////////////////
@@ -127,7 +127,7 @@ double dfactorial(uint8_t n);
 double stirling(uint8_t n);
 
 
-//  SEMIFACTORIAL
+//  SEMI_FACTORIAL
 
 //  exact ==> 20!!
 uint32_t semiFactorial(uint8_t n);
@@ -140,6 +140,15 @@ uint64_t semiFactorial64(uint8_t n);
 double dSemiFactorial(uint16_t n);
 
 
+//  SKIP_FACTORIAL  (experimental)
+
+//  note step must be larger than 0
+//  note when step == 1  ==> factorial
+//  note when step == 2  ==> semiFactorial
+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);
+
 
 ///////////////////////////////////////////////////////////////////////////
 //