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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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48
Task/Numeric-error-propagation/Ada/numeric-error-propagation-1.ada
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@ -1,48 +0,0 @@
generic
type Real is digits <>;
with function Sqrt(X: Real) return Real;
with function "**"(X: Real; Y: Real) return Real;
package Approximation is
type Number is private;
-- create an approximation
function Approx(Value: Real; Sigma: Real) return Number;
-- unary operations and conversion Real to Number
function "+"(X: Real) return Number;
function "-"(X: Real) return Number;
function "+"(X: Number) return Number;
function "-"(X: Number) return Number;
-- addition / subtraction
function "+"(X: Number; Y: Number) return Number;
function "-"(X: Number; Y: Number) return Number;
-- multiplication / division
function "*"(X: Number; Y: Number) return Number;
function "/"(X: Number; Y: Number) return Number;
-- exponentiation
function "**"(X: Number; Y: Positive) return Number;
function "**"(X: Number; Y: Real) return Number;
-- Output to Standard IO (wrapper for Ada.Text_IO and Ada.Text_IO.Float_IO)
procedure Put_Line(Message: String;
Item: Number;
Value_Fore: Natural := 7;
Sigma_Fore: Natural := 4;
Aft: Natural := 2;
Exp: Natural := 0);
procedure Put(Item: Number;
Value_Fore: Natural := 7;
Sigma_Fore: Natural := 3;
Aft: Natural := 2;
Exp: Natural := 0);
private
type Number is record
Value: Real;
Sigma: Real;
end record;
end Approximation;

119
Task/Numeric-error-propagation/Ada/numeric-error-propagation-2.ada
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with Ada.Text_IO;
package body Approximation is
package RIO is new Ada.Text_IO.Float_IO(Real);
-- create an approximation
function Approx(Value: Real; Sigma: Real) return Number is
begin
return (Value, Sigma);
end Approx;
-- unary operations and conversion Real to Number
function "+"(X: Real) return Number is
begin
return Approx(X, 0.0);
end "+";
function "-"(X: Real) return Number is
begin
return Approx(-X, 0.0);
end "-";
function "+"(X: Number) return Number is
begin
return X;
end "+";
function "-"(X: Number) return Number is
begin
return Approx(-X.Value, X.Sigma);
end "-";
-- addition / subtraction
function "+"(X: Number; Y: Number) return Number is
Z: Number;
begin
Z.Value := X.Value + Y.Value;
Z.Sigma := Sqrt(X.Sigma*X.Sigma + Y.Sigma*Y.Sigma);
return Z;
end "+";
function "-"(X: Number; Y: Number) return Number is
begin
return X + (-Y);
end "-";
-- multiplication / division
function "*"(X: Number; Y: Number) return Number is
Z: Number;
begin
Z.Value := X.Value * Y.Value;
Z.Sigma := Z.Value * Sqrt((X.Sigma/X.Value)**2 + (Y.Sigma/Y.Value)**2);
return Z;
end "*";
function "/"(X: Number; Y: Number) return Number is
Z: Number;
begin
Z.Value := X.Value / Y.Value;
Z.Sigma := Z.Value * Sqrt((X.Sigma/X.Value)**2 + (Y.Sigma/Y.Value)**2);
return Z;
end "/";
-- exponentiation
function "**"(X: Number; Y: Positive) return Number is
Z: Number;
begin
Z.Value := X.Value ** Y ;
Z.Sigma := Z.Value * Real(Y) * (X.Sigma/X.Value);
if Z.Sigma < 0.0 then
Z.Sigma := - Z.Sigma;
end if;
return Z;
end "**";
function "**"(X: Number; Y: Real) return Number is
Z: Number;
begin
Z.Value := X.Value ** Y ;
Z.Sigma := Z.Value * Y * (X.Sigma/X.Value);
if Z.Sigma < 0.0 then
Z.Sigma := - Z.Sigma;
end if;
return Z;
end "**";
-- Output to Standard IO (wrapper for Ada.Text_IO.Float_IO)
procedure Put_Line(Message: String;
Item: Number;
Value_Fore: Natural := 7;
Sigma_Fore: Natural := 4;
Aft: Natural := 2;
Exp: Natural := 0) is
begin
Ada.Text_IO.Put(Message);
Put(Item, Value_Fore, Sigma_Fore, Aft, Exp);
Ada.Text_IO.New_Line;
end Put_Line;
procedure Put(Item: Number;
Value_Fore: Natural := 7;
Sigma_Fore: Natural := 3;
Aft: Natural := 2;
Exp: Natural := 0) is
begin
RIO.Put(Item.Value, Value_Fore, Aft, Exp);
Ada.Text_IO.Put(" (+-");
RIO.Put(Item.Sigma, Sigma_Fore, Aft, Exp);
Ada.Text_IO.Put(")");
end Put;
end Approximation;

17
Task/Numeric-error-propagation/Ada/numeric-error-propagation-3.ada
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with Approximation, Ada.Numerics.Elementary_Functions;
procedure Test_Approximations is
package A is new Approximation(Float,
Ada.Numerics.Elementary_Functions.Sqrt,
Ada.Numerics.Elementary_Functions."**");
use type A.Number;
X1: A.Number := A.Approx(100.0, 1.1);
Y1: A.Number := A.Approx( 50.0, 1.2);
X2: A.Number := A.Approx(200.0, 2.2);
Y2: A.Number := A.Approx(100.0, 2.3);
begin
A.Put_Line("Distance:",
((X1-X2)**2 + (Y1 - Y2)**2)**0.5,
Sigma_Fore => 1);
end Test_Approximations;