def test_fourth(self): " 1/4 is exact." from operator import truediv assert 1 / 4.0 == fpu.down(lambda: truediv(1.0, 4.0)) assert 1 / 4.0 == fpu.up (lambda: truediv(1.0, 4.0)) assert -1 / 4.0 == fpu.up (lambda: truediv(1.0, -4.0)) assert -1 / 4.0 == fpu.down(lambda: truediv(1.0, -4.0))
def test_third(self): "Nearest rounding of 1/3 is downwards." from operator import truediv assert 1 / 3.0 == fpu.down(lambda: truediv(1.0, 3.0)) assert 1 / 3.0 < fpu.up (lambda: truediv(1.0, 3.0)) assert -1 / 3.0 == fpu.up (lambda: truediv(1.0, -3.0)) assert -1 / 3.0 > fpu.down(lambda: truediv(1.0, -3.0))
def test_fifth(self): "Nearest rounding of 1/5 is upwards." from operator import truediv assert 1 / 5.0 == fpu.up (lambda: truediv(1.0, 5.0)) assert 1 / 5.0 > fpu.down(lambda: truediv(1.0, 5.0)) assert -1 / 5.0 == fpu.down(lambda: truediv(1.0, -5.0)) assert -1 / 5.0 < fpu.up (lambda: truediv(1.0, -5.0))
def test_fifth(self): "Nearest rounding of 1/5 is upwards." from operator import truediv assert 1 / 5.0 == fpu.up (lambda: truediv(1.0, 5.0)) assert 1 / 5.0 > fpu.down(lambda: truediv(1.0, 5.0)) assert -1 / 5.0 == fpu.down(lambda: truediv(1.0, -5.0)) assert -1 / 5.0 < fpu.up (lambda: truediv(1.0, -5.0))
def test_fourth(self): " 1/4 is exact." from operator import truediv assert 1 / 4.0 == fpu.down(lambda: truediv(1.0, 4.0)) assert 1 / 4.0 == fpu.up (lambda: truediv(1.0, 4.0)) assert -1 / 4.0 == fpu.up (lambda: truediv(1.0, -4.0)) assert -1 / 4.0 == fpu.down(lambda: truediv(1.0, -4.0))
def ATANPIItv( self, a): aa=str(a) if (aa=="nan;nan"): return "nan;nan" elif aa.count(";")==0: b1=down(lambda: float(a)) b2=up(lambda: float(a)) res1=atanpi(interval([b1,b2])) res2=str(interval.hull([res1])) aa=res2.split("[")[1] bb=aa.split(",")[0] cc=aa.split(" ")[1] dd=cc.split("]")[0] return bb +";"+dd else: a1=down(lambda: float(a.split(";")[0])) a2=up(lambda: float(a.split(";")[1])) c=interval([a1,a2]) res=atanpi(c) res1=str(interval.hull([res])) aa=res1.split("[")[1] bb=aa.split(",")[0] cc=aa.split(" ")[1] dd=cc.split("]")[0] return bb +";"+dd
def test_third(self): "Nearest rounding of 1/3 is downwards." from operator import truediv assert 1 / 3.0 == fpu.down(lambda: truediv(1.0, 3.0)) assert 1 / 3.0 < fpu.up (lambda: truediv(1.0, 3.0)) assert -1 / 3.0 == fpu.up (lambda: truediv(1.0, -3.0)) assert -1 / 3.0 > fpu.down(lambda: truediv(1.0, -3.0))
def INItv( self, a, b ): a1=down(lambda: float(a.split(";")[0])) b1=down(lambda: float(b.split(";")[0])) a2=up(lambda: float(a.split(";")[1])) b2=up(lambda: float(b.split(";")[1])) from interval import interval x=interval([a1,a2]) y=interval([b1,b2]) if (x.__rand__(y)==x): return True else: return False
def test_power(self): x = 1 / 3.0 # The cube of one third should depend on the rounding mode assert fpu.down(lambda: x * x * x) < fpu.up(lambda: x * x * x) # But using the built-in power operator, it doesn't necessarily do it # fpu.down(lambda: x ** 3) < fpu.up(lambda: x ** 3)) # So we define an integer power methods that does assert fpu.power_rd( x, 3) < fpu.power_ru( x, 3) assert fpu.power_rd(-x, 3) < fpu.power_ru(-x, 3) assert fpu.power_rd( x, 4) < fpu.power_ru( x, 4) assert fpu.power_rd(-x, 4) < fpu.power_ru(-x, 4) assert (fpu.down(lambda: x * x * x), fpu.up(lambda: x * x * x)) == (fpu.power_rd(x, 3), fpu.power_ru(x, 3))
def test_power(self): x = 1 / 3.0 # The cube of one third should depend on the rounding mode assert fpu.down(lambda: x * x * x) < fpu.up(lambda: x * x * x) # But using the built-in power operator, it doesn't necessarily do it # fpu.down(lambda: x ** 3) < fpu.up(lambda: x ** 3)) # So we define an integer power methods that does assert fpu.power_rd( x, 3) < fpu.power_ru( x, 3) assert fpu.power_rd(-x, 3) < fpu.power_ru(-x, 3) assert fpu.power_rd( x, 4) < fpu.power_ru( x, 4) assert fpu.power_rd(-x, 4) < fpu.power_ru(-x, 4) assert (fpu.down(lambda: x * x * x), fpu.up(lambda: x * x * x)) == (fpu.power_rd(x, 3), fpu.power_ru(x, 3))
def INTERItv( self, a, b ): if a.count(";")==0 and b.count(";")==0: a1=down(lambda: float(a)) b1=down(lambda: float(b)) a2=up(lambda: float(a)) b2=up(lambda: float(b)) elif a.count(";")==0: a1=down(lambda: float(a)) a2=up(lambda: float(a)) b1=down(lambda: float(b.split(";")[0])) b2=up(lambda: float(b.split(";")[1])) elif b.count(";")==0: a1=down(lambda: float(a.split(";")[0])) b1=down(lambda: float(b)) a2=up(lambda: float(a.split(";")[1])) b2=up(lambda: float(b)) else: a1=down(lambda: float(a.split(";")[0])) b1=down(lambda: float(b.split(";")[0])) a2=up(lambda: float(a.split(";")[1])) b2=up(lambda: float(b.split(";")[1])) from interval import interval p=str(interval([a1,a2]) & interval([b1,b2])) if (p=="interval()"): return "nan;nan" if p.count(",")==0: aa=p.split("[")[1] dd=aa.split("]")[0] return dd aa=p.split("[")[1] bb=aa.split(",")[0] cc=aa.split(" ")[1] dd=cc.split("]")[0] return bb +";"+dd
def test_power(self): self.assertRaises(TypeError, lambda: interval[1, 2] ** (1.3)) self.assertEqual((-interval[1, 2]).inverse(), (-interval[1, 2]) ** -1) self.assertEqual(interval[0, 4], interval[-1, 2] ** 2) self.assertEqual(interval[-27, 8], interval[-3, 2] ** 3) self.assertEqual(interval[-1, 2], (interval[-1,2]**-1)**-1) self.assertEqual(interval([-0.38712442133802405]) ** 3, interval([-0.058016524353106828, -0.058016524353106808])) self.assertEqual( interval[fpu.down(lambda: (1/3.0)*(1/3.0)), fpu.up(lambda: (1/3.0)*(1/3.0))], (interval[1]/3.0) ** 2) self.assertEqual( interval[fpu.down(lambda: (1/3.0)*(1/3.0)*(1/3.0)), fpu.up(lambda: (1/3.0)*(1/3.0)*(1/3.0))], (interval[1]/3.0) ** 3)
def UNIONItv( self, *args ): from interval import interval somme=interval() c=str(args) c=c.replace(",,",",") c=c.replace(")","") c=c.replace("(","") c=c.replace(",,",",") c=c.replace("'","") c=c.replace(" ","") c=c.replace("''","") c=c.replace(",,",",") mm=c.split(",") i=0 while (i<len(mm)): #< len(mm) cour=str(mm[i]) if cour != "None" and cour !="": cour=cour.replace("'","") cour=cour.replace(" ","") cour=cour.replace(",","") if cour=="nan;nan": somme=somme elif cour.count(";")==0: b1=down(lambda: float(cour)) b2=up(lambda: float(cour)) from interval import interval, inf, imath somme=somme|interval([b1,b2]) else: a1=down(lambda:float(cour.split(";")[0])) a2=up(lambda:float(cour.split(";")[1])) #from interval import interval somme=somme|interval([a1,a2]) somme=interval.hull([somme]) i+=1 res=str(somme) if res.count(",")==0: res1=res.split("[")[1] res2=res1.split("]")[0] return str(res2 ) else: aa=res.split("[")[1] bb=aa.split(",")[0] cc=aa.split(" ")[1] dd=cc.split("]")[0] return bb +";"+dd
def test_power(self): self.assertRaises(TypeError, lambda: interval[1, 2]**(1.3)) self.assertEqual((-interval[1, 2]).inverse(), (-interval[1, 2])**-1) self.assertEqual(interval[0, 4], interval[-1, 2]**2) self.assertEqual(interval[-27, 8], interval[-3, 2]**3) self.assertEqual(interval[-1, 2], (interval[-1, 2]**-1)**-1) self.assertEqual( interval([-0.38712442133802405])**3, interval([-0.058016524353106828, -0.058016524353106808])) self.assertEqual( interval[fpu.down(lambda: (1 / 3.0) * (1 / 3.0)), fpu.up(lambda: (1 / 3.0) * (1 / 3.0))], (interval[1] / 3.0)**2) self.assertEqual( interval[fpu.down(lambda: (1 / 3.0) * (1 / 3.0) * (1 / 3.0)), fpu.up(lambda: (1 / 3.0) * (1 / 3.0) * (1 / 3.0))], (interval[1] / 3.0)**3)
def test_power(self): self.assertRaises(TypeError, lambda: interval[1, 2] ** (1.3)) assert (-interval[1, 2]).inverse() == (-interval[1, 2]) ** -1 assert interval[0, 4] == interval[-1, 2] ** 2 assert interval[-27, 8] == interval[-3, 2] ** 3 assert interval[-1, 2] == (interval[-1, 2] ** -1) ** -1 assert interval([-0.38712442133802405]) ** 3 == interval([-0.058016524353106828, -0.058016524353106808]) from operator import truediv assert ( interval[ fpu.down(lambda: truediv(1, 3.0) * truediv(1, 3.0)), fpu.up (lambda: truediv(1, 3.0) * truediv(1, 3.0))] == (interval[1] / 3.0) ** 2) assert ( interval[ fpu.down(lambda: truediv(1, 3.0) * truediv(1, 3.0) * truediv(1, 3.0)), fpu.up(lambda: truediv(1, 3.0) * truediv(1, 3.0) * truediv(1, 3.0))] == (interval[1] / 3.0) ** 3)
def test_power(self): self.assertRaises(TypeError, lambda: interval[1, 2] ** (1.3)) assert (-interval[1, 2]).inverse() == (-interval[1, 2]) ** -1 assert interval[0, 4] == interval[-1, 2] ** 2 assert interval[-27, 8] == interval[-3, 2] ** 3 assert interval[-1, 2] == (interval[-1, 2] ** -1) ** -1 assert interval([-0.38712442133802405]) ** 3 == interval([-0.058016524353106828, -0.058016524353106808]) from operator import truediv assert ( interval[ fpu.down(lambda: truediv(1, 3.0) * truediv(1, 3.0)), fpu.up (lambda: truediv(1, 3.0) * truediv(1, 3.0))] == (interval[1] / 3.0) ** 2) assert ( interval[ fpu.down(lambda: truediv(1, 3.0) * truediv(1, 3.0) * truediv(1, 3.0)), fpu.up(lambda: truediv(1, 3.0) * truediv(1, 3.0) * truediv(1, 3.0))] == (interval[1] / 3.0) ** 3)
def ABSItv( self, a): aa=str(a) if (aa=="nan;nan"): return "nan;nan" elif aa.count(";")==0: a1=down(lambda: float(aa)) a2=up(lambda: float(aa)) else: a1=down(lambda: float(a.split(";")[0])) a2=up(lambda: float(a.split(";")[1])) c=interval([a1,a2]) res=c.__abs__() res1=str(interval.hull([res])) if res1.count(" ")==0: aa=res1.split("[")[1] dd=aa.split("]")[0] return dd +";"+dd else: aa=res1.split("[")[1] bb=aa.split(",")[0] cc=aa.split(" ")[1] dd=cc.split("]")[0] return bb +";"+dd
def COMPItv( self, a, b ): if a==b: return "3" elif a.count(";")==0 and b.count(";")==0: a1=down(lambda: float(a)) b1=down(lambda: float(b)) a2=up(lambda: float(a)) b2=up(lambda: float(b)) elif a.count(";")==0: a1=down(lambda: float(a)) a2=up(lambda: float(a)) b1=down(lambda: float(b.split(";")[0])) b2=up(lambda: float(b.split(";")[1])) elif b.count(";")==0: a1=down(lambda: float(a.split(";")[0])) b1=down(lambda: float(b)) a2=up(lambda: float(a.split(";")[1])) b2=up(lambda: float(b)) else: a1=down(lambda: float(a.split(";")[0])) b1=down(lambda: float(b.split(";")[0])) a2=up(lambda: float(a.split(";")[1])) b2=up(lambda: float(b.split(";")[1])) from interval import interval if a1>b2: return "1" elif a1>=b1 and a1<=b2 and a2>b2: return "2" elif a1>=b1 and a1<=b2 and a2<=b2: return "5" elif a==b: return "3" elif b1>a2: return "4" elif b1>=a1 and b1<=a2 and b2>a2: return "5" elif b1>=a1 and b1<=a2 and b2<=a2: return "2"
def DIVItv( self, a, b ): if a=="nan;nan" or b=="nan;nan": return "nan;nan" else: if a.count(";")==0 and b.count(";")==0: a1=down(lambda: float(a)) b1=down(lambda: float(b)) a2=up(lambda: float(a)) b2=up(lambda: float(b)) elif a.count(";")==0: a1=down(lambda: float(a)) a2=up(lambda: float(a)) b1=down(lambda: float(b.split(";")[0])) b2=up(lambda: float(b.split(";")[1])) elif b.count(";")==0: a1=down(lambda: float(a.split(";")[0])) b1=down(lambda: float(b)) a2=up(lambda: float(a.split(";")[1])) b2=up(lambda: float(b)) else: a1=down(lambda: float(a.split(";")[0])) b1=down(lambda: float(b.split(";")[0])) a2=up(lambda: float(a.split(";")[1])) b2=up(lambda: float(b.split(";")[1])) from interval import interval inv=interval([b1,b2]) invcomplet=inv.inverse() res=interval([a1,a2])*invcomplet res1=str(interval.hull([res])) if res1.count(" ")==0: aa=res1.split("[")[1] dd=aa.split("]")[0] return dd +";"+dd else: aa=res1.split("[")[1] bb=aa.split(",")[0] cc=aa.split(" ")[1] dd=cc.split("]")[0] return bb +";"+dd
def DIFFItv( self, a, b ): if a=="nan;nan" or b=="nan;nan": return "nan;nan" else: if a.count(";")==0 and b.count(";")==0: a1=down(lambda: float(a)) b1=down(lambda: float(b)) a2=up(lambda: float(a)) b2=up(lambda: float(b)) elif a.count(";")==0: a1=down(lambda: float(a)) a2=up(lambda: float(a)) b1=down(lambda: float(b.split(";")[0])) b2=up(lambda: float(b.split(";")[1])) elif b.count(";")==0: a1=down(lambda: float(a.split(";")[0])) b1=down(lambda: float(b)) a2=up(lambda: float(a.split(";")[1])) b2=up(lambda: float(b)) else: a1=down(lambda: float(a.split(";")[0])) b1=down(lambda: float(b.split(";")[0])) a2=up(lambda: float(a.split(";")[1])) b2=up(lambda: float(b.split(";")[1])) from interval import interval res=str(interval([a1,a2])-interval([b1,b2])) if res.count(" ")==0: aa=res.split("[")[1] dd=aa.split("]")[0] return dd +";"+dd else: aa=res.split("[")[1] bb=aa.split(",")[0] cc=aa.split(" ")[1] dd=cc.split("]")[0] return bb +";"+dd
def test_third(self): "Nearest rounding of 1/3 is downwards." self.assertEqual(1/3.0, fpu.down(lambda: 1.0 / 3.0)) self.assertTrue(1/3.0 < fpu.up(lambda: 1.0 / 3.0)) self.assertEqual(-1/3.0, fpu.up(lambda: 1.0 / -3.0)) self.assertTrue(-1/3.0 > fpu.down(lambda: 1.0 / -3.0))
def test_fourth(self): " 1/4 is exact." self.assertEqual(1/4.0, fpu.down(lambda: 1.0 / 4.0)) self.assertEqual(1/4.0, fpu.up(lambda: 1.0 / 4.0)) self.assertEqual(-1/4.0, fpu.up(lambda: 1.0 / -4.0)) self.assertEqual(-1/4.0, fpu.down(lambda: 1.0 / -4.0))
def test_third(self): "Nearest rounding of 1/3 is downwards." self.assertEqual(1 / 3.0, fpu.down(lambda: 1.0 / 3.0)) self.assertTrue(1 / 3.0 < fpu.up(lambda: 1.0 / 3.0)) self.assertEqual(-1 / 3.0, fpu.up(lambda: 1.0 / -3.0)) self.assertTrue(-1 / 3.0 > fpu.down(lambda: 1.0 / -3.0))
def test_fifth(self): "Nearest rounding of 1/5 is upwards." self.assertEqual(1 / 5.0, fpu.up(lambda: 1.0 / 5.0)) self.assertTrue(1 / 5.0 > fpu.down(lambda: 1.0 / 5.0)) self.assertEqual(-1 / 5.0, fpu.down(lambda: 1.0 / -5.0)) self.assertTrue(-1 / 5.0 < fpu.up(lambda: 1.0 / -5.0))
def test_fourth(self): " 1/4 is exact." self.assertEqual(1 / 4.0, fpu.down(lambda: 1.0 / 4.0)) self.assertEqual(1 / 4.0, fpu.up(lambda: 1.0 / 4.0)) self.assertEqual(-1 / 4.0, fpu.up(lambda: 1.0 / -4.0)) self.assertEqual(-1 / 4.0, fpu.down(lambda: 1.0 / -4.0))
def test_fifth(self): "Nearest rounding of 1/5 is upwards." self.assertEqual(1/5.0, fpu.up(lambda: 1.0 / 5.0)) self.assertTrue(1/5.0 > fpu.down(lambda: 1.0 / 5.0)) self.assertEqual(-1/5.0, fpu.down(lambda: 1.0 / -5.0)) self.assertTrue(-1/5.0 < fpu.up(lambda: 1.0 / -5.0))