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))