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- 2.5%3 -2.5%3 2%(-3) 2%3
- python 2.5 0.5 -1 2
- ruby 2.5 0.5 -1 2
- octave 2.5 0.5 -1 2
- graph 2.5 0.5 -1 2
- geogebra 2.5 0.5 2 2
- calc 2.5 -2.5 -1 2
- php 2.5 -2.5 2 2
- nodejs 2.5 -2.5 2 2
- GROUPE Amod
- x-floor(x/y)*y decript bien les lignes [2.5|0.5|-1|2]
- f(2.5,3.0) = 2.5
- f(-2.5,3.0) = 0.5
- f(2.0,-3.0) = -1.0
- f(2.0,3.0) = 2.0
- GROUPE Bmod
- x-floor(x/y)*y+(y*(sign(x)-1))/2 decript bien les lignes [2.5|-2.5|-1|2] **
- f(2.5,3.0) = 2.5
- f(-2.5,3.0) = -2.5
- f(2.0,-3.0) = -1.0
- f(2.0,3.0) = 2.0
- GROUPE Cmod
- x-floor(x/abs(y))*abs(y)+(abs(y)*(sign(x)-1))/2 decript bien les lignes [2.5,-2.5,2,2]
- f(2.5,3.0) = 2.5
- f(-2.5,3.0) = -2.5
- f(2.0,-3.0) = 2.0
- f(2.0,3.0) = 2.0
- GROUPE Dmod
- x-floor(x/abs(y))*abs(y) decript bien les lignes [2.5|0.5|2|2]
- f(2.5,3.0) = 2.5
- f(-2.5,3.0) = 0.5
- f(2.0,-3.0) = 2.0
- f(2.0,3.0) = 2.0
- ** un peu plus d'elements semblant montrer que calc implemente le modulo comme decript :
- >>> f = lambda x,y: x-floor(x/y)*y+(y*(copysign(1,x)-1))/2
- predictions python verification calc
- >>> f(-8,-4.5) # ; -8 % -4.5
- 1.0 # 1
- >>> f(-2,-2.5) # ; -2 % -2.5
- 0.5 # 0.5
- >>> f(2,-2.5) # ; 2 % -2.5
- -0.5 # -0.5
- >>> f(2,-4) # ; 2 % -4
- -2.0 # -2
- >>> f(-68.84,-4338.4) # -68.84 % -4338.4
- 4269.56 # 4269.56
- Amod = lambda x,y: x-floor(x/y)*y
- Bmod = lambda x,y: x-floor(x/y)*y+(y*(copysign(1,x)-1))/2
- Cmod = lambda x,y: x-floor(x/abs(y))*abs(y)+(abs(y)*(copysign(1,x)-1))/2
- Dmod = lambda x,y: x-floor(x/abs(y))*abs(y)
- testcase = [(0.0,1.0),(0.0,-1.0),(1.0,-1.0),
- (-1.0,-1.0),(9.0,91.5),(-3.8,7.0),
- (-66.0,53.75),(-66.0,-53.75),(-1.5,0.5),
- (900,-9000),(-900,-9000),(-900,9000)]
- expectations = map(lambda x: map(lambda u: x(*u),testcase),[Amod,Bmod,Cmod,Dmod])
- labels = ['Amod','Bmod','Cmod','Dmod']
- lines = map(lambda x: str(x)+' ',testcase)
- lines.insert(0,max(map(len,lines))*'-')
- for group in expectations:
- label = labels.pop(0)
- lines[0] += ' { %s } ' % label
- for i,result in enumerate(group):
- lines[i+1] += ('%s ' % result)
- for line in lines:
- print(line)
- ------------------ { Amod } { Bmod } { Cmod } { Dmod }
- (0.0, 1.0) 0.0 0.0 0.0 0.0
- (0.0, -1.0) 0.0 0.0 0.0 0.0
- (1.0, -1.0) 0.0 0.0 0.0 0.0
- (-1.0, -1.0) 0.0 1.0 -1.0 0.0
- (9.0, 91.5) 9.0 9.0 9.0 9.0
- (-3.8, 7.0) 3.2 -3.8 -3.8 3.2
- (-66.0, 53.75) 41.5 -12.25 -12.25 41.5
- (-66.0, -53.75) -12.25 41.5 -12.25 41.5
- (-1.5, 0.5) 0.0 -0.5 -0.5 0.0
- (900, -9000) -8100.0 -8100.0 900.0 900.0
- (-900, -9000) -900.0 8100.0 -900.0 8100.0
- (-900, 9000) 8100.0 -900.0 -900.0 8100.0
- python
- [0.0, 0.0, 0.0, 0.0, 9.0, 3.2, 41.5, -12.25, 0.0, -8100, -900, 8100]
- v v v v v v v v v v v v Amod
- php > $testcase = [[0,1],[0,-1],[1,-1],[-1,-1],[9,91.5],[-3.8,7],[-66,53.75],[-66,-53.75],[-1.5,0.5],[900,-9000],[-900,-9000],[-900,9000]];
- php > foreach ($testcase as $elem) {
- php { echo $elem[0].' '.$elem[1].' = '.fmod($elem[0],$elem[1])."\n";
- php { }
- 0 1 = 0 ok
- 0 -1 = 0 ok
- 1 -1 = 0 ok
- -1 -1 = -0 nok (-1)
- 9 91.5 = 9 ok
- -3.8 7 = -3.8 ok
- -66 53.75 = -12.25 ok
- -66 -53.75 = -15.25 ok
- -1.5 0.5 = -0 nok (-0.5)
- 900 -9000 = 900 ok
- -900 -9000 = -900 ok
- -900 9000 = -900 ok
- -> Cmod mal defini ou nouveau groupe
- irb(main):001:0> 0.0 % 1.0
- => 0.0 ok
- irb(main):002:0> 0.0 % -1.0
- => 0.0 ok
- irb(main):003:0> 1.0 % -1.0
- => 0.0 ok
- irb(main):004:0> -1.0 % -1.0
- => -0.0 ok (-0.0 ?)
- irb(main):005:0> 9.0 % 91.5
- => 9.0 ok
- irb(main):006:0> -3.8 % 7.0
- => 3.2 ok
- irb(main):007:0> -66.0 % 53.75
- => 41.5 ok
- irb(main):001:0> -66.0 % -53.75
- => -12.25 ok
- irb(main):008:0> -1.5 % 0.5
- => -0.0 ok (-0.0 ?)
- irb(main):009:0> 900.0 % -9000.0
- => -8100.0 ok
- irb(main):010:0> -900.0 % -9000.0
- => -900.0 ok
- irb(main):011:0> -900.0 % 9000.0
- => 8100.0 ok
- => conforme avec Amod
- geogebra :
- 0.00000000000000 1.00000000000000 0.00000000000000 ok
- 0.00000000000000 -1.00000000000000 0.00000000000000 ok
- 1.00000000000000 -1.00000000000000 0.00000000000000 ok
- -1.00000000000000 -1.00000000000000 0.00000000000000 ok
- 9.00000000000000 91.5000000000001 9.00000000000000 ok
- -3.80000000000000 7.00000000000000 3.20000000000000 ok
- -66.0000000000000 53.7500000000001 41.5000000000000 ok
- -66.0000000000000 -53.7500000000001 41.5000000000000 ok
- -1.50000000000000 0.500000000000001 0.00000000000000 ok
- 900.000000000000 -9000.00000000000 900.000000000000 ok
- -900.000000000000 -9000.00000000000 8100.00000000000 ok
- -900.000000000000 9000.00000000000 8100.00000000000 ok
- => conforme avec Dmod
- Calc
- ; 0 % 1
- 0 ok
- ; 0.0 % -1.0
- 0 ok
- ; 1.0 % -1.0
- 0 ok
- ; -1.0 % -1.0
- 0 nok (1)
- ; 9.0 % 91.5
- 9 ok
- ; -3.8 % 7.0
- -3.8 ok
- ; -66.0 % 53.75
- -12.25 ok
- ; -66.0 % -53.75
- 41.5 ok
- ; -1.5 % 0.5
- 0 nok (-0.5)
- ; 900.0 % -9000.0
- -8100 ok
- ; -900.0 % -9000.0
- 8100 ok
- ; -900.0 % 9000.0
- -900 ok
- => irregularités avec Bmod ... mon modele est probablement faux
- nodejs
- > 0.0 % 1.0
- 0 ok
- > 0.0 % -1.0
- 0 ok
- > 1.0 % -1.0
- 0 ok
- > -1.0 % -1.0
- -0 nok (-1)
- > 9.0 % 91.5
- 9 ok
- > -3.8 % 7.0
- -3.8 ok
- > -66.0 % 53.75
- -12.25 ok
- > -66.0 % -53.75
- -12.25 ok
- > -1.5 % 0.5
- -0 nok (-0.5)
- > 900.0 % -9000.0
- 900 ok
- > -900.0 % -9000.0
- -900 ok
- > -900.0 % 9000.0
- -900 ok
- => toujours les memes irregularites avec Cmod, mon modele EST proche mais faux
- graph
- 0 1 0 ok
- 0 -1 0 ok
- 1 -1 0 ok
- -1 -1 0 ok
- 9 91.5 9 ok
- -3.8 7 3.2 ok
- -66 53.75 41.5 ok
- -66 53.75 -12.25 ok
- -1.5 0.5 0 ok
- 900 -9000 -8100 ok
- -900 -9000 -900 ok
- -900 9000 8100 ok
- => conforme a Amod
- octave:1> mod(0,1)
- ans = 0 ok
- octave:2> mod(0,-1)
- ans = 0 ok
- octave:3> mod(1,-1)
- ans = 0 ok
- octave:4> mod(-1,-1)
- ans = 0 ok
- octave:5> mod(9,91.5)
- ans = 9 ok
- octave:6> mod(-3.8,7)
- ans = 3.2000 ok
- octave:7> mod(-66,53.75)
- ans = 41.500 ok
- octave:8> mod(-66,-53.75)
- ans = -12.250 ok
- octave:9> mod(-1.5,-0.5)
- ans = 0 ok
- octave:10> mod(900,-9000)
- ans = -8100 ok
- octave:11> mod(-900,-9000)
- ans = -900 ok
- octave:12> mod(-900,9000)
- ans = 8100 ok
- => conforme a Amod
- Attendu Obtenu
- python Amod 12 predictions obtenus sur 12
- ruby Amod 12 / 12
- octave Amod 12 / 12
- graph Amod 12 / 12
- geogebra Dmod 12 / 12
- calc Bmod 10 / 12 (-1.0 % -1.0 = 0 [predit 1], -1.5 % 0.5 = 0 [predit -0.5])
- php Cmod 10 / 12 (-1.0 % -1.0 = 0 [predit -1], -1.5 % 0.5 = 0 [predit -0.5])
- nodejs Cmod 10 / 12 (-1.0 % -1.0 = 0 [predit -1], -1.5 % 0.5 = 0 [predit -0.5])
- conclusion:
- Amod probablement juste.
- Dmod probablement juste (mais a tester mieux).
- Bmod et Cmod probablement proches, mais comportent une erreur nettement definis definis, les cas d'echec etant les memes pour chaque implementations testes.
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