Data update
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Ingy döt Net
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7735 changed files with 38060 additions and 199180 deletions
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with Ada.Numerics.Generic_Real_Arrays;
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generic
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type Real is digits <>;
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package Thiele is
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package Real_Arrays is new Ada.Numerics.Generic_Real_Arrays (Real);
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subtype Real_Array is Real_Arrays.Real_Vector;
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type Thiele_Interpolation (Length : Natural) is private;
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function Create (X, Y : Real_Array) return Thiele_Interpolation;
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function Inverse (T : Thiele_Interpolation; X : Real) return Real;
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private
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type Thiele_Interpolation (Length : Natural) is record
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X, Y, RhoX : Real_Array (1 .. Length);
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end record;
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end Thiele;
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package body Thiele is
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use type Real_Array;
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function "/" (Left, Right : Real_Array) return Real_Array is
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Result : Real_Array (Left'Range);
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begin
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if Left'Length /= Right'Length then
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raise Constraint_Error with "arrays not same size";
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end if;
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for I in Result'Range loop
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Result (I) := Left (I) / Right (I);
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end loop;
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return Result;
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end "/";
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function Rho (X, Y : Real_Array) return Real_Array is
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N : constant Natural := X'Length;
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P : array (1 .. N) of Real_Array (1 .. N) :=
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(others => (others => 9.9));
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Result : Real_Array (1 .. N);
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begin
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P (1) (1 .. N) := Y (1 .. N);
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P (2) (1 .. N - 1) := (X (1 .. N - 1) - X (2 .. N)) /
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(P (1) (1 .. N - 1) - P (1) (2 .. N));
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for I in 3 .. N loop
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P (I) (1 .. N - I + 1) := P (I - 2) (2 .. N - I + 2) +
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(X (1 .. N - I + 1) - X (I .. N)) /
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(P (I - 1) (1 .. N - I + 1) - P (I - 1) (2 .. N - I + 2));
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end loop;
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for I in X'Range loop
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Result (I) := P (I) (1);
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end loop;
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return Result;
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end Rho;
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function Create (X, Y : Real_Array) return Thiele_Interpolation is
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begin
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if X'Length < 3 then
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raise Constraint_Error with "at least 3 values";
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end if;
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if X'Length /= Y'Length then
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raise Constraint_Error with "input arrays not same size";
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end if;
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return (Length => X'Length, X => X, Y => Y, RhoX => Rho (X, Y));
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end Create;
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function Inverse (T : Thiele_Interpolation; X : Real) return Real is
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A : Real := 0.0;
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begin
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for I in reverse 3 .. T.Length loop
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A := (X - T.X (I - 1)) / (T.RhoX (I) - T.RhoX (I - 2) + A);
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end loop;
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return T.Y (1) + (X - T.X (1)) / (T.RhoX (2) + A);
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end Inverse;
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end Thiele;
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@ -1,43 +0,0 @@
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with Ada.Text_IO;
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with Ada.Numerics.Generic_Elementary_Functions;
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with Thiele;
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procedure Main is
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package Math is new Ada.Numerics.Generic_Elementary_Functions
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(Long_Float);
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package Float_Thiele is new Thiele (Long_Float);
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use Float_Thiele;
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Row_Count : Natural := 32;
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X_Values : Real_Array (1 .. Row_Count);
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Sin_Values : Real_Array (1 .. Row_Count);
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Cos_Values : Real_Array (1 .. Row_Count);
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Tan_Values : Real_Array (1 .. Row_Count);
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begin
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-- build table
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for I in 1 .. Row_Count loop
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X_Values (I) := Long_Float (I) * 0.05 - 0.05;
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Sin_Values (I) := Math.Sin (X_Values (I));
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Cos_Values (I) := Math.Cos (X_Values (I));
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Tan_Values (I) := Math.Tan (X_Values (I));
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end loop;
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declare
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Sin : Thiele_Interpolation := Create (Sin_Values, X_Values);
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Cos : Thiele_Interpolation := Create (Cos_Values, X_Values);
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Tan : Thiele_Interpolation := Create (Tan_Values, X_Values);
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begin
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Ada.Text_IO.Put_Line
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("Internal Math.Pi: " &
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Long_Float'Image (Ada.Numerics.Pi));
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Ada.Text_IO.Put_Line
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("Thiele 6*InvSin(0.5):" &
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Long_Float'Image (6.0 * Inverse (Sin, 0.5)));
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Ada.Text_IO.Put_Line
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("Thiele 3*InvCos(0.5):" &
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Long_Float'Image (3.0 * Inverse (Cos, 0.5)));
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Ada.Text_IO.Put_Line
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("Thiele 4*InvTan(1): " &
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Long_Float'Image (4.0 * Inverse (Tan, 1.0)));
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end;
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end Main;
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@ -1,69 +0,0 @@
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Function Reciprocal-Difference( [Double[][]] $function )
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{
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$rho=@()
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$rho+=0
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$funcl = $function.length
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if( $funcl -gt 0 )
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{
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-2..($funcl-1) | ForEach-Object {
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$i=$_
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#Write-Host "$($i+1) - $($rho[$i+1]) - $($rho[$i+1].GetType())"
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$rho[$i+2] = $( 0..($funcl-$i-1) | Where-Object {$_ -lt $funcl} | ForEach-Object {
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$j=$_
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switch ($i) {
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{$_ -lt 0 } { 0 }
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{$_ -eq 0 } { $function[$j][1] }
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{$_ -gt 0 } { ( $function[$j][0] - $function[$j+$i][0] ) / ( $rho[$i+1][$j] - $rho[$i+1][$j+1] ) + $rho[$i][$j+1] }
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}
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if( $_ -lt $funcl )
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{
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$rho += 0
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}
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})
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}
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}
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$rho
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}
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Function Thiele-Interpolation ( [Double[][]] $function )
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{
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$funcl = $function.length
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$invoke = "{`n`tparam([Double] `$x)`n"
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if($funcl -gt 1)
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{
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$rho = Reciprocal-Difference $function
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($funcl-1)..0 | ForEach-Object {
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$invoke += "`t"
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$invoke += '$x{0} = {1} - {2}' -f $_, @($rho[$_+2])[0], @($rho[$_])[0]
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if($_ -lt ($funcl-1))
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{
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$invoke += ' + ( $x - {0} ) / $x{1} ' -f $function[$_][0], ($_+1)
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}
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$invoke += "`n"
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}
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$invoke+="`t`$x0`n}"
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} else {
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$invoke += "`t`$x`n}"
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}
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invoke-expression $invoke
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}
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$sint=@{}; 0..31 | ForEach-Object { $_ * 0.05 } | ForEach-Object { $sint[$_] = [Math]::sin($_) }
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$cost=@{}; 0..31 | ForEach-Object { $_ * 0.05 } | ForEach-Object { $cost[$_] = [Math]::cos($_) }
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$tant=@{}; 0..31 | ForEach-Object { $_ * 0.05 } | ForEach-Object { $tant[$_] = [Math]::tan($_) }
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$asint=New-Object 'Double[][]' 32,2; $sint.GetEnumerator() | Sort-Object Value | ForEach-Object {$i=0}{ $asint[$i][0] = $_.Value; $asint[$i][1] = $_.Name; $i++ }
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$acost=New-Object 'Double[][]' 32,2; $cost.GetEnumerator() | Sort-Object Value | ForEach-Object { $i=0 }{ $acost[$i][0] = $_.Value; $acost[$i][1] = $_.Name; $i++ }
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$atant=New-Object 'Double[][]' 32,2; $tant.GetEnumerator() | Sort-Object Value | ForEach-Object {$i=0}{ $atant[$i][0] = $_.Value; $atant[$i][1] = $_.Name; $i++ }
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$asin = (Thiele-Interpolation $asint)
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#uncomment to see the function
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#"{$asin}"
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6*$asin.InvokeReturnAsIs(.5)
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$acos = (Thiele-Interpolation $acost)
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#uncomment to see the function
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#"{$acos}"
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3*$acos.InvokeReturnAsIs(.5)
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$atan = (Thiele-Interpolation $atant)
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#uncomment to see the function
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#"{$atan}"
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4*$atan.InvokeReturnAsIs(1)
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