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Ingy döt Net 2026-02-01 16:33:20 -08:00
parent 5150844a7d
commit 4bb20c9b71
7735 changed files with 38060 additions and 199180 deletions
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7
Task/Fast-Fourier-transform/Ada/fast-fourier-transform-1.ada
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with Ada.Numerics.Generic_Complex_Arrays;
generic
with package Complex_Arrays is
new Ada.Numerics.Generic_Complex_Arrays (<>);
use Complex_Arrays;
function Generic_FFT (X : Complex_Vector) return Complex_Vector;

39
Task/Fast-Fourier-transform/Ada/fast-fourier-transform-2.ada
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with Ada.Numerics;
with Ada.Numerics.Generic_Complex_Elementary_Functions;
function Generic_FFT (X : Complex_Vector) return Complex_Vector is
package Complex_Elementary_Functions is
new Ada.Numerics.Generic_Complex_Elementary_Functions
(Complex_Arrays.Complex_Types);
use Ada.Numerics;
use Complex_Elementary_Functions;
use Complex_Arrays.Complex_Types;
function FFT (X : Complex_Vector; N, S : Positive)
return Complex_Vector is
begin
if N = 1 then
return (1..1 => X (X'First));
else
declare
F : constant Complex := exp (Pi * j / Real_Arrays.Real (N/2));
Even : Complex_Vector := FFT (X, N/2, 2*S);
Odd : Complex_Vector := FFT (X (X'First + S..X'Last), N/2, 2*S);
begin
for K in 0..N/2 - 1 loop
declare
T : constant Complex := Odd (Odd'First + K) / F ** K;
begin
Odd (Odd'First + K) := Even (Even'First + K) - T;
Even (Even'First + K) := Even (Even'First + K) + T;
end;
end loop;
return Even & Odd;
end;
end if;
end FFT;
begin
return FFT (X, X'Length, 1);
end Generic_FFT;

20
Task/Fast-Fourier-transform/Ada/fast-fourier-transform-3.ada
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with Ada.Numerics.Complex_Arrays; use Ada.Numerics.Complex_Arrays;
with Ada.Complex_Text_IO; use Ada.Complex_Text_IO;
with Ada.Text_IO; use Ada.Text_IO;
with Ada.Numerics.Complex_Elementary_Functions;
with Generic_FFT;
procedure Example is
function FFT is new Generic_FFT (Ada.Numerics.Complex_Arrays);
X : Complex_Vector := (1..4 => (1.0, 0.0), 5..8 => (0.0, 0.0));
Y : Complex_Vector := FFT (X);
begin
Put_Line (" X FFT X ");
for I in Y'Range loop
Put (X (I - Y'First + X'First), Aft => 3, Exp => 0);
Put (" ");
Put (Y (I), Aft => 3, Exp => 0);
New_Line;
end loop;
end;

32
Task/Fast-Fourier-transform/PowerShell/fast-fourier-transform.psh
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Function FFT($Arr){
$Len = $Arr.Count
If($Len -le 1){Return $Arr}
$Len_Over_2 = [Math]::Floor(($Len/2))
$Output = New-Object System.Numerics.Complex[] $Len
$EvenArr = @()
$OddArr = @()
For($i = 0; $i -lt $Len; $i++){
If($i % 2){
$OddArr+=$Arr[$i]
}Else{
$EvenArr+=$Arr[$i]
}
}
$Even = FFT($EvenArr)
$Odd = FFT($OddArr)
For($i = 0; $i -lt $Len_Over_2; $i++){
$Twiddle = [System.Numerics.Complex]::Exp([System.Numerics.Complex]::ImaginaryOne*[Math]::Pi*($i*-2/$Len))*$Odd[$i]
$Output[$i] = $Even[$i] + $Twiddle
$Output[$i+$Len_Over_2] = $Even[$i] - $Twiddle
}
Return $Output
}