github.com/remobjects/goldbaselibrary@v0.0.0-20230924164425-d458680a936b/Source/Gold/Math.pas

namespace go.math;

uses
  go.builtin;

type
  {$IF ECHOES}PlatformMath = System.Math;{$ENDIF}
  {$IF ISLAND}PlatformMath = RemObjects.Elements.System.Math;{$ENDIF}




const
  MaxInt8   = 1 shl 7 - 1; public;
  MinInt8   = -1  shl  7; public;
  MaxInt16  = 1 shl 15 - 1; public;
  MinInt16  = -1  shl  15; public;
  //MaxInt32  = 1 shl 31 - 1; public;
  MaxInt32 = 2147483647; public;
  MinInt32  = -1  shl  31; public;
  MaxInt64  = 1 shl 63 - 1; public;
  MinInt64  = -1  shl  63; public;
  MaxUint8  = 1 shl 8 - 1; public;
  MaxUint16 = 1 shl 16 - 1; public;
  MaxUint32 = 1 shl  32 - 1; public;
  MaxUint64 = 1 shl 64 - 1; public;


method Trunc(x: Double): Double; public;
begin
  {$IFDEF ECHOES}
  exit System.Math.Truncate(x);
  {$ELSE}
  exit RemObjects.Elements.System.Math.Truncate(x);
  {$ENDIF}
end;

method NaN(): Double; public;
begin
  exit Double.NaN;
end;

method IsInf(v: Double; sign: Integer): Boolean; public;
begin
  if sign < 0 then
    exit Double.IsNegativeInfinity(v);
  if sign > 0 then
    exit Double.IsPositiveInfinity(v);
  exit Double.IsInfinity(v);
end;

method IsNaN(v: Double): Boolean; public;
begin
  exit Double.IsNaN(v);
end;

method Abs(v: Double): Double; public;
begin
  exit PlatformMath.Abs(v);
end;

method Sqrt(v: Double): Double; public; inline;
begin
  exit PlatformMath.Sqrt(v);
end;


method Inf(sign: Integer): Double; public;unsafe;
begin
  if sign < 0 then
    exit Double.NegativeInfinity;
  exit Double.PositiveInfinity
end;

method Float32bits(f: Single): uint32; public;unsafe;
begin
  ^Single(@result)^ := f;
end;

method Float32frombits(b: uint32): Single; public; unsafe;
begin
  ^uint32(@Result)^ := b;
end;

method Float64bits(f: Double): uint64; public;unsafe;
begin
  ^Double(@result)^ := f;
end;

method Float64frombits(b: uint64): Double; public; unsafe;
begin
  ^uint64(@Result)^ := b;
end;

method Log(x: Double): Double; public;
begin
  exit PlatformMath.Log(x);
end;

method Exp(x: Double): Double; public;
begin
  exit PlatformMath.Exp(x);
end;

method Floor(x: Double): Double; public;
begin
  exit PlatformMath.Floor(x);
end;

method Ceil(x: Double): Double; public;
begin
  exit PlatformMath.Ceiling(x);
end;

method Ldexp(frac: Double; aexp: Integer): Double; public;
begin
  exit PlatformMath.Pow(2, aexp) * frac;
end;

method Frexp(value: Double): tuple of (Double, Integer); public;
begin
  {$IF ISLAND}
  var bits: int64 := Convert.ToInt64(value);
  {$ELSEIF ECHOES}
  var bits: int64 := BitConverter.DoubleToInt64Bits(value);
  {$ENDIF}
  var realMant: Double := 1.0;
  var exponent: Integer;
  var resmmantissa: Double;

  if Double.IsNaN(value) or
  (value + value = value) or
  Double.IsInfinity(value) then begin
    exponent := 0;
    resmmantissa := value;
  end   else begin
    var neg := bits < 0;
    exponent := ((bits shr 52) and $7ff);
    var mantissa := bits and $fffffffffffff;

    if(exponent = 0) then begin
      inc(exponent);
    end
    else begin
      mantissa := mantissa or (int64(1) shl 52);
    end;

      // bias the exponent - actually biased by 1023.
      // we are treating the mantissa as m.0 instead of 0.m
      //  so subtract another 52.
    exponent := exponent - 1075;
    realMant := mantissa;

      // normalize
    while(realMant > 1.0)  do begin
      mantissa := mantissa shr 11;
      realMant := realMant / 2.0;
      inc(exponent);
    end;

    if(neg) then begin
      realMant := realMant * -1;
    end;

    resmmantissa := realMant;
  end;
  exit (resmmantissa, exponent);
end;

method Log2(d: Double): Double;
begin
  {$IF ISLAND}
  exit PlatformMath.Log2(d);
  {$ELSEIF ECHOES}
  exit PlatformMath.Log(d, 2);
  {$ENDIF}
end;

method Signbit(d: Double): Boolean;
begin
  exit d < 0;
end;

//
//
//

method Asin(x: float64): float64; public; inline;
begin
  result := PlatformMath.Asin(x);
end;

method Asinh(x: float64): float64; public; inline;
begin
  result := PlatformMath.Log(x + PlatformMath.Sqrt(x * x + 1)) // via https://stackoverflow.com/questions/2840798/c-sharp-math-class-question/2840824
end;

method Atan(x: float64): float64; public; inline;
begin
  result := PlatformMath.Atan(x);
end;

method Atan2(y, x: float64): float64; public; // via https://en.wikipedia.org/wiki/Atan2
begin
  if (x > 0) or (y ≠ 0) then begin
    result := 2 * Atan( y / (Sqrt(x*x + y*y) + x));
  end
  else if (x < 0) and (y = 0) then begin
    result := PlatformMath.PI;
  end
  else begin
    result := Double.NaN;
  end;
end;

method Copysign(x, y: float64): float64; public;
begin
  result := if y > 0 then PlatformMath.Abs(x) else -PlatformMath.Abs(x);
end;

method Cos(x: float64): float64; public; inline;
begin
  result := PlatformMath.Cos(x);
end;

method Cosh(x: float64): float64; public; inline;
begin
  result := PlatformMath.Cosh(x);
end;

method Hypot(p, q: float64): float64; public; inline;
begin
  result := PlatformMath.Sqrt(p * p + q * q);
end;

method Pow(x, y: float64): float64; public; inline;
begin
  result := x ** y;
end;

method Pow10(n: int): float64; public; inline;
begin
  result := 10 ** n;
end;

method Sin(x: float64): float64; public; inline;
begin
  result := PlatformMath.Sin(x);
end;

method Sincos(x: float64): tuple of (sin: float64, cos: float64); public; inline;
begin
  result := (Sin(x), Cos(x));
end;

method Sinh(x: float64): float64; public; inline;
begin
  result := PlatformMath.Sinh(x);
end;

end.