mathslib.pas

Delphi for fun library v12, latest. This is the library for manuplating list, combination-permutati

unit MathsLib;

{Copyright 2005,2008 Gary Darby, www.DelphiForFun.org

 This program may be used or modified for any non-commercial purpose
 so long as this original notice remains in place.
 All other rights are reserved
 }

 {Assortment of math related functions and procedure in various states}


 {Revision Copyright 2006, Charles Doumar,  January 2006
 Added:
   Tprimes.BSPrime ... Binary search function to find index of prime in prime table.
   Tprimes.MaxPrimeInTable ... Returns Max Prime in prime table.
   Tprimes.GetNthPrime ... Returns Nth prime in table (returns -1 if not in table).
 Optimized:
    Tprimes.IsPrime ... Optimized for values greater than MaxPrimeInTable squared.
    Tprimes.NextPrime ... Speed up lookup of values within table range, added large value support
    Tprime.PrevPrime ... Speed up lookup of values within table range, added large value support
    Tprime.GetFactors ... Now returns factors for numbers greater than MaxPrimeInTable Squared
  }

interface

uses Classes, SysUtils, Windows, Dialogs,  UBigIntsV2;

type
  intset = set of byte;

  TPoint64=record
    x,y:int64;
  end;

function GetNextPandigital(size: integer; var Digits: array of integer): boolean;
function IsPolygonal(T: int64; var rank: array of integer): boolean;
function GeneratePentagon(n: integer): integer;
function IsPentagon(p: integer): boolean;
function isSquare(const N: int64): boolean;
function isCube(const N: int64): boolean;


function isPalindrome(n: int64): boolean;
function GetEulerPhi(n: int64): int64;


function IntPower(a, b: int64): int64; overload;
function IntPower(a:extended; b: int64): extended; overload;

function gcd2(a, b: int64): int64;
function GCDMany(A: array of integer): integer;
function LCMMany(A: array of integer): integer;
procedure ContinuedFraction(A: array of int64; const wholepart: integer;
  var numerator, denominator: int64);
function Factorial(n: int64): int64;


function digitcount(n:int64):integer;


function convertfloattofractionstring( N:extended; maxdenom:integer;multipleof:boolean):string;
function convertStringToDecimal(s:string; var n:extended):Boolean;  {string may include fractions}
function InttoBinaryStr(nn: integer): string;


{Latitude Longitude Routines}
  function StrtoAngle(const s:string; var angle:extended):boolean;
  function AngleToStr(angle:extended):string;
  function deg2rad(deg:extended):extended;
  function rad2deg(rad:extended):extended;
  function GetLongToMercProjection(const long:extended):extended;
  function GetLatToMercProjection(const Lat:Extended):Extended;
  function GetMercProjectionToLong(const ProjLong:extended):extended;
  function GetMercProjectionToLat(const ProjLat:extended):extended;




type
  {*********** TPrimes Class *******}
  TPrimes = class(TObject)
  protected
    function BSPrime(const n: int64; var index: integer): boolean;
  public
    Prime:    array of int64;  {Array of primes - 0th entry is not used}
    nbrprimes, nbrfactors, nbrcanonicalfactors, nbrdivisors: integer;
    Factors:  array of int64; {array of factors - 0th entry is not used}
    CanonicalFactors: array of TPoint64;
    Divisors: array of int64;
    function GetNextPrime(n: int64): int64;
    function GetPrevPrime(n: int64): int64;
    function IsPrime(n: int64): boolean;
    procedure GetFactors(const n: int64);  {get all prime factors}
    function MaxPrimeInTable: int64;
    function GetNthPrime(const n: integer): int64;
    procedure GetCanonicalFactors(const n: int64);  {get ccanonical prime factors}
    procedure GetDivisors(const n: int64);          {get all divisors}
    function Getnbrdivisors(n: int64): integer;
    function radical(n:int64):int64;   {product of unique prime factors}
    constructor Create;
    destructor Destroy; override;
  end;


const deg=chr(176); {'