Question

How to use math functions and constants in Pascal

Answer 1

{ Program Title: Free Pascal Math Functions Demonstration }

program MathExample;

uses
  Math, SysUtils;  { Math = math functions, SysUtils = rounding helpers }

var
  piValue, eValue: Double;
  x, angle, y: Double;
  aFloat, bFloat, value, clamped: Double;  { renamed to avoid conflict }
  AByte, BByte: Byte;                      { renamed to avoid conflict }

begin
  { ============================
    Constants
    ============================ }
  piValue := Pi;      { π constant }
  eValue  := Exp(1);  { Euler's number }

  Writeln('Constants:');
  Writeln('  pi = ', piValue);
  Writeln('  e  = ', eValue);
  Writeln;


  { ============================
    Core Functions
    ============================ }
  x := 2.5;           { sample value }

  Writeln('Core Functions:');
  Writeln('  Sqrt(2.5) = ', Sqrt(x));      { square root }
  Writeln('  Exp(2.5)  = ', Exp(x));       { e^x }
  Writeln('  Ln(2.5)   = ', Ln(x));        { natural log }
  Writeln('  Log10(2.5)= ', Log10(x));     { base-10 log }
  Writeln('  Power(2.5,3)= ', Power(x,3)); { x^3 }
  Writeln;


  { ============================
    Trigonometric Functions
    ============================ }
  angle := Pi / 4;    { 45 degrees in radians }

  Writeln('Trigonometric Functions:');
  Writeln('  Sin(pi/4) = ', Sin(angle));   { sine }
  Writeln('  Cos(pi/4) = ', Cos(angle));   { cosine }
  Writeln('  Tan(pi/4) = ', Tan(angle));   { tangent }
  Writeln('  ArcSin(0.5) = ', ArcSin(0.5)); { arcsine }
  Writeln('  ArcCos(0.5) = ', ArcCos(0.5)); { arccosine }
  Writeln('  ArcTan(1.0) = ', ArcTan(1.0)); { arctangent }
  Writeln;


  { ============================
    Hyperbolic Functions
    ============================ }
  Writeln('Hyperbolic Functions:');
  Writeln('  Sinh(1) = ', Sinh(1));   { hyperbolic sine }
  Writeln('  Cosh(1) = ', Cosh(1));   { hyperbolic cosine }
  Writeln('  Tanh(1) = ', Tanh(1));   { hyperbolic tangent }
  Writeln;


  { ============================
    Rounding Functions
    ============================ }
  y := -2.7;          { negative number for rounding tests }

  Writeln('Rounding Functions:');
  Writeln('  Floor(-2.7) = ', Floor(y));     { round down }
  Writeln('  Ceil(-2.7)  = ', Ceil(y));      { round up }
  Writeln('  Round(-2.7) = ', Round(y));     { nearest integer }
  Writeln('  Trunc(-2.7) = ', Trunc(y));     { remove decimals }
  Writeln;


  { ============================
    Min / Max / Clamp
    ============================ }
  aFloat := 10;
  bFloat := 20;
  value := 15;

  Writeln('Min/Max/Clamp:');
  Writeln('  Min(10,20) = ', Min(aFloat,bFloat));  { smaller of two }
  Writeln('  Max(10,20) = ', Max(aFloat,bFloat));  { larger of two }

  clamped := EnsureRange(value, 0, 10);  { clamp 15 to range 0–10 }
  Writeln('  Clamp(15,0,10) = ', clamped);
  Writeln;


  { ============================
    Bitwise Math (Integers)
    ============================ }
  AByte := $AA;  { 10101010 in hex }
  BByte := $CC;  { 11001100 in hex }

  Writeln('Bitwise Math:');
  Writeln('  A AND B = $', HexStr(AByte and BByte, 2)); { bitwise AND }
  Writeln('  A OR B  = $', HexStr(AByte or BByte, 2));  { bitwise OR }
  Writeln('  A XOR B = $', HexStr(AByte xor BByte, 2)); { bitwise XOR }
  Writeln('  NOT A   = $', HexStr(not AByte, 2));       { bitwise NOT }
  Writeln('  A << 2  = $', HexStr(AByte shl 2, 2));     { left shift }
  Writeln('  B >> 3  = $', HexStr(BByte shr 3, 2));     { right shift }
  Writeln;


  { ============================
    Additional Useful Math
    ============================ }
  Writeln('Additional Math:');
  Writeln('  Abs(-3.14) = ', Abs(-3.14));      { absolute value }
  Writeln('  Frac(3.14) = ', Frac(3.14));      { fractional part }
  Writeln('  Int(3.14)  = ', Int(3.14));       { integer part }
  Writeln('  Hypot(3,4) = ', Hypot(3,4));      { sqrt(x²+y²) }
  Writeln('  DegToRad(180) = ', DegToRad(180)); { convert degrees to radians }
  Writeln('  RadToDeg(pi) = ', RadToDeg(Pi));   { convert radians to degrees }

end.



{
run:

Constants:
  pi =  3.1415926535897931E+000
  e  =  2.7182818284590451E+000

Core Functions:
  Sqrt(2.5) =  1.5811388300841898E+000
  Exp(2.5)  =  1.21824939607034734377E+0001
  Ln(2.5)   =  9.16290731874155065179E-0001
  Log10(2.5)=  3.97940008672037609576E-0001
  Power(2.5,3)=  1.56250000000000000000E+0001

Trigonometric Functions:
  Sin(pi/4) =  7.07106781186547502752E-0001
  Cos(pi/4) =  7.07106781186547546066E-0001
  Tan(pi/4) =  9.99999999999999938743E-0001
  ArcSin(0.5) =  5.23598775598298873067E-0001
  ArcCos(0.5) =  1.04719755119659774613E+0000
  ArcTan(1.0) =  7.85398163397448309628E-0001

Hyperbolic Functions:
  Sinh(1) =  1.17520119364380145688E+0000
  Cosh(1) =  1.54308063481524377855E+0000
  Tanh(1) =  7.61594155955764888109E-0001

Rounding Functions:
  Floor(-2.7) = -3
  Ceil(-2.7)  = -2
  Round(-2.7) = -3
  Trunc(-2.7) = -2

Min/Max/Clamp:
  Min(10,20) =  1.0000000000000000E+001
  Max(10,20) =  2.0000000000000000E+001
  Clamp(15,0,10) =  1.0000000000000000E+001

Bitwise Math:
  A AND B = $88
  A OR B  = $EE
  A XOR B = $66
  NOT A   = $55
  A << 2  = $A8
  B >> 3  = $19

Additional Math:
  Abs(-3.14) =  3.14000000000000000010E+0000
  Frac(3.14) =  1.40000000000000000095E-0001
  Int(3.14)  =  3.00000000000000000000E+0000
  Hypot(3,4) =  5.00000000000000000000E+0000
  DegToRad(180) =  3.14159265358979323851E+0000
  RadToDeg(pi) =  1.80000000000000000000E+0002

}

 

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