Data update
This commit is contained in:
Ingy döt Net
parent
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commit
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7735 changed files with 38060 additions and 199180 deletions
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generic
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type Real is digits <>;
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with function Sqrt(X: Real) return Real;
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with function "**"(X: Real; Y: Real) return Real;
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package Approximation is
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type Number is private;
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-- create an approximation
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function Approx(Value: Real; Sigma: Real) return Number;
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-- unary operations and conversion Real to Number
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function "+"(X: Real) return Number;
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function "-"(X: Real) return Number;
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function "+"(X: Number) return Number;
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function "-"(X: Number) return Number;
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-- addition / subtraction
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function "+"(X: Number; Y: Number) return Number;
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function "-"(X: Number; Y: Number) return Number;
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-- multiplication / division
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function "*"(X: Number; Y: Number) return Number;
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function "/"(X: Number; Y: Number) return Number;
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-- exponentiation
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function "**"(X: Number; Y: Positive) return Number;
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function "**"(X: Number; Y: Real) return Number;
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-- Output to Standard IO (wrapper for Ada.Text_IO and Ada.Text_IO.Float_IO)
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procedure Put_Line(Message: String;
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Item: Number;
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Value_Fore: Natural := 7;
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Sigma_Fore: Natural := 4;
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Aft: Natural := 2;
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Exp: Natural := 0);
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procedure Put(Item: Number;
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Value_Fore: Natural := 7;
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Sigma_Fore: Natural := 3;
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Aft: Natural := 2;
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Exp: Natural := 0);
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private
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type Number is record
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Value: Real;
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Sigma: Real;
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end record;
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end Approximation;
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@ -1,119 +0,0 @@
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with Ada.Text_IO;
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package body Approximation is
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package RIO is new Ada.Text_IO.Float_IO(Real);
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-- create an approximation
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function Approx(Value: Real; Sigma: Real) return Number is
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begin
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return (Value, Sigma);
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end Approx;
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-- unary operations and conversion Real to Number
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function "+"(X: Real) return Number is
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begin
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return Approx(X, 0.0);
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end "+";
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function "-"(X: Real) return Number is
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begin
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return Approx(-X, 0.0);
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end "-";
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function "+"(X: Number) return Number is
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begin
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return X;
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end "+";
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function "-"(X: Number) return Number is
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begin
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return Approx(-X.Value, X.Sigma);
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end "-";
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-- addition / subtraction
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function "+"(X: Number; Y: Number) return Number is
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Z: Number;
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begin
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Z.Value := X.Value + Y.Value;
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Z.Sigma := Sqrt(X.Sigma*X.Sigma + Y.Sigma*Y.Sigma);
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return Z;
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end "+";
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function "-"(X: Number; Y: Number) return Number is
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begin
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return X + (-Y);
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end "-";
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-- multiplication / division
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function "*"(X: Number; Y: Number) return Number is
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Z: Number;
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begin
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Z.Value := X.Value * Y.Value;
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Z.Sigma := Z.Value * Sqrt((X.Sigma/X.Value)**2 + (Y.Sigma/Y.Value)**2);
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return Z;
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end "*";
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function "/"(X: Number; Y: Number) return Number is
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Z: Number;
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begin
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Z.Value := X.Value / Y.Value;
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Z.Sigma := Z.Value * Sqrt((X.Sigma/X.Value)**2 + (Y.Sigma/Y.Value)**2);
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return Z;
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end "/";
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-- exponentiation
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function "**"(X: Number; Y: Positive) return Number is
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Z: Number;
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begin
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Z.Value := X.Value ** Y ;
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Z.Sigma := Z.Value * Real(Y) * (X.Sigma/X.Value);
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if Z.Sigma < 0.0 then
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Z.Sigma := - Z.Sigma;
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end if;
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return Z;
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end "**";
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function "**"(X: Number; Y: Real) return Number is
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Z: Number;
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begin
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Z.Value := X.Value ** Y ;
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Z.Sigma := Z.Value * Y * (X.Sigma/X.Value);
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if Z.Sigma < 0.0 then
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Z.Sigma := - Z.Sigma;
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end if;
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return Z;
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end "**";
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-- Output to Standard IO (wrapper for Ada.Text_IO.Float_IO)
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procedure Put_Line(Message: String;
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Item: Number;
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Value_Fore: Natural := 7;
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Sigma_Fore: Natural := 4;
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Aft: Natural := 2;
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Exp: Natural := 0) is
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begin
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Ada.Text_IO.Put(Message);
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Put(Item, Value_Fore, Sigma_Fore, Aft, Exp);
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Ada.Text_IO.New_Line;
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end Put_Line;
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procedure Put(Item: Number;
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Value_Fore: Natural := 7;
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Sigma_Fore: Natural := 3;
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Aft: Natural := 2;
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Exp: Natural := 0) is
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begin
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RIO.Put(Item.Value, Value_Fore, Aft, Exp);
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Ada.Text_IO.Put(" (+-");
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RIO.Put(Item.Sigma, Sigma_Fore, Aft, Exp);
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Ada.Text_IO.Put(")");
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end Put;
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end Approximation;
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@ -1,17 +0,0 @@
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with Approximation, Ada.Numerics.Elementary_Functions;
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procedure Test_Approximations is
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package A is new Approximation(Float,
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Ada.Numerics.Elementary_Functions.Sqrt,
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Ada.Numerics.Elementary_Functions."**");
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use type A.Number;
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X1: A.Number := A.Approx(100.0, 1.1);
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Y1: A.Number := A.Approx( 50.0, 1.2);
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X2: A.Number := A.Approx(200.0, 2.2);
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Y2: A.Number := A.Approx(100.0, 2.3);
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begin
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A.Put_Line("Distance:",
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((X1-X2)**2 + (Y1 - Y2)**2)**0.5,
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Sigma_Fore => 1);
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end Test_Approximations;
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@ -1,59 +1,51 @@
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(phixonline)-->
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<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
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<span style="color: #008080;">enum</span> <span style="color: #000000;">VALUE</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">DELTA</span>
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with javascript_semantics
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enum VALUE, DELTA
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<span style="color: #008080;">type</span> <span style="color: #000000;">imprecise</span><span style="color: #0000FF;">(</span><span style="color: #004080;">object</span> <span style="color: #000000;">imp</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">return</span> <span style="color: #004080;">sequence</span><span style="color: #0000FF;">(</span><span style="color: #000000;">imp</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">and</span> <span style="color: #004080;">atom</span><span style="color: #0000FF;">(</span><span style="color: #000000;">imp</span><span style="color: #0000FF;">[</span><span style="color: #000000;">VALUE</span><span style="color: #0000FF;">])</span> <span style="color: #008080;">and</span> <span style="color: #004080;">atom</span><span style="color: #0000FF;">(</span><span style="color: #000000;">imp</span><span style="color: #0000FF;">[</span><span style="color: #000000;">DELTA</span><span style="color: #0000FF;">])</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">type</span>
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type imprecise(object imp)
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return sequence(imp) and atom(imp[VALUE]) and atom(imp[DELTA])
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end type
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<span style="color: #008080;">function</span> <span style="color: #000000;">sqr</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">return</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">*</span><span style="color: #000000;">a</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
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function sqr(atom a)
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return a*a
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end function
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<span style="color: #008080;">function</span> <span style="color: #000000;">imprecise_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">imprecise</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">atom</span> <span style="color: #000000;">delta</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sqr</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">DELTA</span><span style="color: #0000FF;">])</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">sqr</span><span style="color: #0000FF;">(</span><span style="color: #000000;">b</span><span style="color: #0000FF;">[</span><span style="color: #000000;">DELTA</span><span style="color: #0000FF;">]))</span>
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<span style="color: #000000;">imprecise</span> <span style="color: #000000;">ret</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">VALUE</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">[</span><span style="color: #000000;">VALUE</span><span style="color: #0000FF;">],</span> <span style="color: #000000;">delta</span><span style="color: #0000FF;">}</span>
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<span style="color: #008080;">return</span> <span style="color: #000000;">ret</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
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function imprecise_add(imprecise a, b)
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atom delta = sqrt(sqr(a[DELTA]) + sqr(b[DELTA]))
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imprecise ret = {a[VALUE] + b[VALUE], delta}
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return ret
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end function
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<span style="color: #008080;">function</span> <span style="color: #000000;">imprecise_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">imprecise</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">atom</span> <span style="color: #000000;">delta</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sqr</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">VALUE</span><span style="color: #0000FF;">]*</span><span style="color: #000000;">b</span><span style="color: #0000FF;">[</span><span style="color: #000000;">DELTA</span><span style="color: #0000FF;">])</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">sqr</span><span style="color: #0000FF;">(</span><span style="color: #000000;">b</span><span style="color: #0000FF;">[</span><span style="color: #000000;">VALUE</span><span style="color: #0000FF;">]*</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">DELTA</span><span style="color: #0000FF;">]))</span>
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<span style="color: #000000;">imprecise</span> <span style="color: #000000;">ret</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">VALUE</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">[</span><span style="color: #000000;">VALUE</span><span style="color: #0000FF;">],</span><span style="color: #000000;">delta</span><span style="color: #0000FF;">}</span>
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<span style="color: #008080;">return</span> <span style="color: #000000;">ret</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
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function imprecise_mul(imprecise a, b)
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atom delta = sqrt(sqr(a[VALUE]*b[DELTA]) + sqr(b[VALUE]*a[DELTA]))
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imprecise ret = {a[VALUE] * b[VALUE],delta}
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return ret
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end function
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<span style="color: #008080;">function</span> <span style="color: #000000;">imprecise_div</span><span style="color: #0000FF;">(</span><span style="color: #000000;">imprecise</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">atom</span> <span style="color: #000000;">delta</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sqr</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">VALUE</span><span style="color: #0000FF;">]*</span><span style="color: #000000;">b</span><span style="color: #0000FF;">[</span><span style="color: #000000;">DELTA</span><span style="color: #0000FF;">])</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">sqr</span><span style="color: #0000FF;">(</span><span style="color: #000000;">b</span><span style="color: #0000FF;">[</span><span style="color: #000000;">VALUE</span><span style="color: #0000FF;">]*</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">DELTA</span><span style="color: #0000FF;">]))/</span><span style="color: #000000;">sqr</span><span style="color: #0000FF;">(</span><span style="color: #000000;">b</span><span style="color: #0000FF;">[</span><span style="color: #000000;">VALUE</span><span style="color: #0000FF;">])</span>
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<span style="color: #000000;">imprecise</span> <span style="color: #000000;">ret</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">VALUE</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">/</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">[</span><span style="color: #000000;">VALUE</span><span style="color: #0000FF;">],</span> <span style="color: #000000;">delta</span><span style="color: #0000FF;">}</span>
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<span style="color: #008080;">return</span> <span style="color: #000000;">ret</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
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function imprecise_div(imprecise a, b)
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atom delta = sqrt(sqr(a[VALUE]*b[DELTA]) + sqr(b[VALUE]*a[DELTA]))/sqr(b[VALUE])
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imprecise ret = {a[VALUE] / b[VALUE], delta}
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return ret
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end function
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<span style="color: #008080;">function</span> <span style="color: #000000;">imprecise_pow</span><span style="color: #0000FF;">(</span><span style="color: #000000;">imprecise</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">atom</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">atom</span> <span style="color: #000000;">v</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">VALUE</span><span style="color: #0000FF;">],</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">),</span>
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<span style="color: #000000;">delta</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">abs</span><span style="color: #0000FF;">(</span><span style="color: #000000;">v</span><span style="color: #0000FF;">*</span><span style="color: #000000;">c</span><span style="color: #0000FF;">*</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">DELTA</span><span style="color: #0000FF;">]/</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">VALUE</span><span style="color: #0000FF;">])</span>
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<span style="color: #000000;">imprecise</span> <span style="color: #000000;">ret</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">v</span><span style="color: #0000FF;">,</span><span style="color: #000000;">delta</span><span style="color: #0000FF;">}</span>
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<span style="color: #008080;">return</span> <span style="color: #000000;">ret</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
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function imprecise_pow(imprecise a, atom c)
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atom v = power(a[VALUE], c),
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delta = abs(v*c*a[DELTA]/a[VALUE])
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imprecise ret = {v,delta}
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return ret
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end function
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<span style="color: #008080;">function</span> <span style="color: #000000;">printImprecise</span><span style="color: #0000FF;">(</span><span style="color: #000000;">imprecise</span> <span style="color: #000000;">imp</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">return</span> <span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"%g+/-%g"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">imp</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
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function imprecise_str(imprecise imp)
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return sprintf("%g+/-%g",imp)
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end function
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<span style="color: #000000;">imprecise</span> <span style="color: #000000;">x1</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">100</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.1</span><span style="color: #0000FF;">},</span>
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<span style="color: #000000;">y1</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">50</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.2</span><span style="color: #0000FF;">},</span>
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<span style="color: #000000;">x2</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{-</span><span style="color: #000000;">200</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2.2</span><span style="color: #0000FF;">},</span>
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<span style="color: #000000;">y2</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{-</span><span style="color: #000000;">100</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2.3</span><span style="color: #0000FF;">},</span>
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<span style="color: #000000;">tmp1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">tmp2</span><span style="color: #0000FF;">,</span>
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<span style="color: #000000;">d</span>
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<span style="color: #000000;">tmp1</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">imprecise_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">x2</span><span style="color: #0000FF;">)</span>
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<span style="color: #000000;">tmp1</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">imprecise_pow</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tmp1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">tmp2</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">imprecise_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">y1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">y2</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">tmp2</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">imprecise_pow</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tmp2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">d</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">imprecise_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tmp1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">tmp2</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">d</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">imprecise_pow</span><span style="color: #0000FF;">(</span><span style="color: #000000;">d</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.5</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Distance, d, between the following points :"</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\n( x1, y1) = ( %s, %s)"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">printImprecise</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x1</span><span style="color: #0000FF;">),</span><span style="color: #000000;">printImprecise</span><span style="color: #0000FF;">(</span><span style="color: #000000;">y1</span><span style="color: #0000FF;">)})</span>
|
||||
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\n( x2, y2) = ( %s, %s)"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">printImprecise</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x2</span><span style="color: #0000FF;">),</span><span style="color: #000000;">printImprecise</span><span style="color: #0000FF;">(</span><span style="color: #000000;">y2</span><span style="color: #0000FF;">)})</span>
|
||||
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\nis d = %s\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">printImprecise</span><span style="color: #0000FF;">(</span><span style="color: #000000;">d</span><span style="color: #0000FF;">)})</span>
|
||||
<!--
|
||||
imprecise x1 = {100, 1.1},
|
||||
y1 = {50, 1.2},
|
||||
x2 = {-200, 2.2},
|
||||
y2 = {-100, 2.3},
|
||||
tmp1 = imprecise_pow(imprecise_add(x1, x2), 2),
|
||||
tmp2 = imprecise_pow(imprecise_add(y1, y2), 2),
|
||||
d = imprecise_pow(imprecise_add(tmp1,tmp2), 0.5)
|
||||
printf(1,"Distance, d, between the following points :\n")
|
||||
printf(1," (x1, y1) = (%s, %s)\n",{imprecise_str(x1),imprecise_str(y1)})
|
||||
printf(1," (x2, y2) = (%s, %s)\n",{imprecise_str(x2),imprecise_str(y2)})
|
||||
printf(1," is d = %s\n", {imprecise_str(d)})
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue