feat: added w1 scripts
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17
w1/matlab/convert2basis.m
Normal file
17
w1/matlab/convert2basis.m
Normal file
@ -0,0 +1,17 @@
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% EX2 a)
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function a = convert2basis(n, b)
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if (b < 2)
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disp('basis needs to be at least 2!')
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return
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end
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v = [];
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while n > 0
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v = [mod(n, b), v];
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n = floor(n / b);
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end
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a = v
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end
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67
w1/matlab/flp.m
Normal file
67
w1/matlab/flp.m
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% EX3 c)
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function [d, v, t] = flp(b, m, n, x)
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% GETS:
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% b: basis
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% m: mantissa length
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% n: exponent length
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% x: number to convert
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% RETURNS:
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% d: mantissa coefficients
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% v: coefficients of the exponent
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% t: sign
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# calculate exponent and mantissa
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exponent = 0
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mantissa = x
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while mantissa > 1
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mantissa /= b
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exponent += 1
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end
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while (mantissa * b) < 1
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mantissa *= b
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exponent -= 1
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end
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inverted = convert2basis(mantissa^-1, b)
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inverted(end)=[]
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val_man = flip(inverted)
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val_exp = convert2basis(abs(exponent), b)
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t = sign(exponent)
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# pad result
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end
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function a = convert2basis(n, b)
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if (b < 2)
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disp('basis needs to be at least 2!')
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return
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end
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v = [];
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while n > 0
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v = [mod(n, b), v];
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n = floor(n / b);
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end
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a = v
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end
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function b = convertDecimal(n, b)
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if (b < 2)
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disp('basis needs to be at least 2!')
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return
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end
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while n < 1
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end
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function res = padArr(arr, len)
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for i = length(arr):len
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arr(i+1) = 0
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end
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res = arr
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end
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21
w1/matlab/interval.practise.m
Executable file
21
w1/matlab/interval.practise.m
Executable file
@ -0,0 +1,21 @@
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function interval(x, a, b)
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if (nargin < 2)
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a = 7;
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b = 12;
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end
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if (a > b)
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bNew = a
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a = b
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b = bNew
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end
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if (a <= x && x <= b)
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disp('x ist im Intervall')
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elseif (x < a)
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disp('x ist unterhalb des Intervals')
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elseif (x > b)
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disp('x ist überhalb des Intervals')
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else
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disp('x ist keine Nummer')
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end
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end
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91
w1/matlab/testConvert2basis.m
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91
w1/matlab/testConvert2basis.m
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@ -0,0 +1,91 @@
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% Angewandte Numerik 1, SoSe 2022
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% Uebungsblatt 01, Aufgabe 02: Darstellung natuerlicher Zahlen
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%
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% Testprogramm fuer die Funktion a = convert2basis(n, b)
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%
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% Letzte Aenderung: 22.04.2022
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%% Initialisierung
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clearvars;
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close all;
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clc;
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fprintf('\n');
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fprintf('Angewandte Numerik 1, Sommersemester 2022\n');
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fprintf('Uebungsblatt 1, Aufgabe 02: Darstellung natuerlicher Zahlen\n');
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fprintf('\n');
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%% Definition und Durchfuehrung der Testfaelle
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testfall = 0;
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while true % alle Testfaelle untersuchen
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testfall = testfall + 1; % naechster Testfall
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%% alle Testfaelle definieren
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switch testfall
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case 1 % Testfall 1: b = 2, n = 30
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b = 2;
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n = 30;
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a = [1 1 1 1 0];
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case 2 % Testfall 2: b = 2, n = 31
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b = 2;
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n = 31;
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a = [1 1 1 1 1];
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case 3 % Testfall 3: b = 2, n = 32
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b = 2;
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n = 32;
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a = [1 0 0 0 0 0];
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case 4 % Testfall 4: b = 2, n = 33
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b = 2;
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n = 33;
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a = [1 0 0 0 0 1];
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case 5 % Testfall 5: b = 2, n = 42
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b = 2;
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n = 42;
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a = [1 0 1 0 1 0];
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case 6 % Testfall 6: b = 2, n = 134110
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b = 2;
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n = 134110;
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a = [1 0 0 0 0 0 1 0 1 1 1 1 0 1 1 1 1 0];
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case 7 % Testfall 7: b = 8, n = 27
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b = 8;
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n = 27;
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a = [3 3];
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case 8 % Testfall 8: b = 8, n = 3652
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b = 8;
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n = 3652;
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a = [7 1 0 4];
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case 9 % Testfall 9: b = 8, n = 46807
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b = 8;
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n = 46807;
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a = [1 3 3 3 2 7];
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case 10 % Testfall 10: b = 10, n = 3121
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b = 10;
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n = 3121;
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a = [3 1 2 1];
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case 11 % Testfall 11: b = 10, n = 192310030133
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b = 10;
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n = 192310030133;
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a = [1 9 2 3 1 0 0 3 0 1 3 3];
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otherwise
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break; % keine Testfaelle mehr vorhanden
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end
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%% Testfall durchfuehren und Ergebnis ausgeben
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spezString = 'Testfall %2d (b = %2d, n = %12d): %s.\n';
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if max(abs(a - convert2basis(n, b))) == 0
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fprintf(spezString, testfall, b, n, 'Bestanden');
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else
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fprintf(2, spezString, testfall, b, n, 'Fehlgeschlagen')
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end
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end
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105
w1/matlab/testFlp.m
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105
w1/matlab/testFlp.m
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@ -0,0 +1,105 @@
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% Angewandte Numerik 1, SoSe 2022
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% Uebungsblatt 01, Aufgabe 03: Wert einer Gleitpunktdarstellung
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%
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% Testprogramm fuer die Funktion [d, v, t] = flp(b, m, n, x)
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%
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% Letzte Aenderung: 22.04.2022
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%% Initialisierung
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clearvars;
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close all;
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clc;
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fprintf('\n');
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fprintf('Angewandte Numerik 1, Sommersemester 2022\n');
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fprintf('Uebungsblatt 1, Aufgabe 3d: Gleitpunkt-Darstellung\n');
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fprintf('\n');
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%% Definition und Durchfuehrung der Testfaelle
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testfall = 0;
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while true % alle Testfaelle untersuchen
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testfall = testfall + 1; % naechster Testfall
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%% alle Testfaelle definieren
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switch testfall
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case 1 % Testfall 1
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b = 2; % Basis
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m = 8; % Laenge der Mantisse
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n = 3; % Laenge des Exponenten
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x = 27.375; % zu konvertierende Zahl
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dSoll = [1 1 0 1 1 0 1 1]; % Mantisse
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vSoll = [1 0 1]; % Exponent
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tSoll = 1; % Vorzeichen Exponent
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case 2 % Testfall 2
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b = 8; % Basis
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m = 8; % Laenge der Mantisse
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n = 3; % Laenge des Exponenten
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x = 27.375; % zu konvertierende Zahl
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dSoll = [3 3 3 0 0 0 0 0]; % Mantisse
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vSoll = [0 0 2]; % Exponent
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tSoll = 1; % Vorzeichen Exponent
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case 3 % Testfall 3
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b = 2; % Basis
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m = 10; % Laenge der Mantisse
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n = 3; % Laenge des Exponenten
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x = 9.140625; % zu konvertierende Zahl
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dSoll = [1 0 0 1 0 0 1 0 0 1]; % Mantisse
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vSoll = [1 0 0]; % Exponent
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tSoll = 1; % Vorzeichen Exponent
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case 4 % Testfall 4
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b = 8; % Basis
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m = 5; % Laenge der Mantisse
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n = 3; % Laenge des Exponenten
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x = 9.140625; % zu konvertierende Zahl
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dSoll = [1 1 1 1 0]; % Mantisse
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vSoll = [0 0 2]; % Exponent
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tSoll = 1; % Vorzeichen Exponent
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case 5 % Testfall 5
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b = 2; % Basis
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m = 3; % Laenge der Mantisse
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n = 2; % Laenge des Exponenten
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x = 0.375; % zu konvertierende Zahl
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dSoll = [1 1 0]; % Mantisse
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vSoll = [0 1]; % Exponent
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tSoll = -1; % Vorzeichen Exponent
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case 6 % Testfall 6
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b = 8; % Basis
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m = 5; % Laenge der Mantisse
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n = 2; % Laenge des Exponenten
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x = 0.0157470703125; % zu konvertierende Zahl
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dSoll = [1 0 0 4 0]; % Mantisse
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vSoll = [0 1]; % Exponent
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tSoll = -1; % Vorzeichen Exponent
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case 7 % Testfall 7
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b = 2; % Basis
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m = 3; % Laenge der Mantisse
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n = 3; % Laenge des Exponenten
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x = 0.0625; % zu konvertierende Zahl
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dSoll = [1 0 0]; % Mantisse
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vSoll = [0 1 1]; % Exponent
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tSoll = -1; % Vorzeichen Exponent
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otherwise
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break; % keine Testfaelle mehr vorhanden
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end
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%% Testfall durchfuehren und Ergebnis ausgeben
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[d, v, t] = flp(b, m, n, x);
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spezString = 'Testfall %d: %s.\n';
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if max(abs([d - dSoll, v - vSoll, t - tSoll])) == 0
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fprintf(spezString, testfall, 'Bestanden');
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else
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fprintf(2, spezString, testfall, 'Fehlgeschlagen');
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end
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end
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67
w1/matlab/testValue.m
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67
w1/matlab/testValue.m
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@ -0,0 +1,67 @@
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% Angewandte Numerik 1, SoSe 2022
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% Uebungsblatt 01, Aufgabe 03: Wert einer Gleitpunktdarstellung
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%
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% Testprogramm fuer die Funktion x = value(b, d, v, t)
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%
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% Letzte Aenderung: 22.04.2022
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%% Initialisierung
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clearvars;
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close all;
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clc;
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tol = 1e-14; % Geforderte Genauigkeit der Berechnungen
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fprintf('\n');
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fprintf('Angewandte Numerik 1, Sommersemester 2022\n');
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fprintf('Uebungsblatt 1, Aufgabe 3b: Gleitpunkt-Darstellung\n');
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fprintf('\n');
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%% Definition und Durchfuehrung der Testfaelle
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testfall = 0;
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while true % alle Testfaelle untersuchen
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testfall = testfall + 1; % naechster Testfall
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%% alle Testfaelle definieren
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switch testfall
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case 1 % Testfall 1
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b = 2; % Basis
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d = [1 0 1 0 0 1 0 0]; % Mantisse
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v = [0 0 1 0 0]; % Exponent
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t = 1; % Vorzeichen Exponent
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x = 10.25; % Wert der Zahl
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case 2 % Testfall 2
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b = 2; % Basis
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d = [1 0 1]; % Mantisse
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v = [0 0 1]; % Exponent
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t = -1; % Vorzeichen Exponent
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x = 0.3125; % Wert der Zahl
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case 3 % Testfall 3
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b = 8; % Basis
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d = [7 5 0]; % Mantisse
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v = [0 0 1]; % Exponent
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t = -1; % Vorzeichen Exponent
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x = 0.119140625; % Wert der Zahl
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otherwise
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break; % keine Testfaelle mehr vorhanden
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end
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%% Testfall durchfuehren und Ergebnis ausgeben
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spezString = 'Testfall %d: %s.\n';
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if abs(x - value(b,d,v,t)) < tol
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fprintf(spezString, testfall, 'Bestanden');
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else
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fprintf(2, spezString, testfall, 'Fehlgeschlagen');
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end
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end
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38
w1/matlab/value.m
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38
w1/matlab/value.m
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@ -0,0 +1,38 @@
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% EX3 a)
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function x = value(b, d, v, t)
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% b: basis
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% d: mantissa coefficients
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% v: coefficients of the exponent
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% t: sign
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if b < 2
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disp('basis needs to be at least 2!')
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return
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elseif !(t == -1 || t == 1)
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disp('t needs to be 1 or -1!')
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return
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end
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exponent = (t * unConvert(v, b))
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prefactor = b ^ exponent
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mantissa = unConvertMantissa(d, b)
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x = prefactor * mantissa
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end
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function val = unConvert(n, b)
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nums = flip(n)
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res = 0
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for i = 1:length(n)
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res += nums(i) * b^(i-1)
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end
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val = res
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end
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function val = unConvertMantissa(m, b)
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res = 0
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for i = 1:length(m)
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res += m(i) * b^(-i)
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end
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val = res
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end
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