def testBasics(self):
self.test('clips', clips('test/testBasics.py', limit=12),
'test/t....ics.py')
self.test('halfs2', halfs2('test/testBasics.py'),
"('test/test', 'Basics.py')")
for f, x, y, s in (
(0, True, False, True),
(0.0, True, False, True),
(1, True, False, True),
(1.0, True, False, True),
(1e300, True, True, True),
(-1e300, True, True, True),
(1e1234, False, False, True), # == INF
(INF, False, False, True),
(NAN, False, False, True),
(NEG0, True, False, True)):
t = str(f)
self.test('isfinite(%s)' % (t, ), isfinite(f), x)
self.test('isint(%s)' % (t, ), isint(f, both=True), x)
self.test('isint(%s+0.5)' % (t, ), isint(f + 0.5, both=True), y)
self.test('isscalar(%s)' % (t, ), isscalar(f), s)
self.test('isneg0(NEG0)', isneg0(NEG0), True)
self.test('isneg0(0.0)', isneg0(0.0), False)
self.test('isneg0(INF)', isneg0(INF), False)
self.test('isneg0(NAN)', isneg0(NAN), False)
self.test('type(%s)' % ('C.r_o', ),
type(C.r_o).__name__, property_RO.__name__)
c = C()
self.test('type(%s)' % ('c.r_o', ), type(c.r_o), bool)
self.test('c.r_o', c.r_o, True)
try:
c.r_o = False
self.test('c.r_o = False', c.r_o, AttributeError.__name__)
except AttributeError as x:
self.test('c.r_o = False', str(x), str(x))
except Exception as x:
self.test('c.r_o = False', repr(x), AttributeError.__name__)
a, b = splice(range(10)) # PYCHOK False
self.test('splice', (a, b),
map1(type(a), (0, 2, 4, 6, 8), (1, 3, 5, 7, 9)))
a, b, c = splice(range(10), n=3) # PYCHOK False
self.test('splice', (a, b, c),
map1(type(a), (0, 3, 6, 9), (1, 4, 7), (2, 5, 8)))
a, b, c = splice(range(10), n=3, fill=-1) # PYCHOK False
self.test('splice', (a, b, c),
map1(type(a), (0, 3, 6, 9), (1, 4, 7, -1), (2, 5, 8, -1)))
t = tuple(splice(range(12), n=5)) # PYCHOK False
self.test(
'splice', t,
map1(type(t[0]), (0, 5, 10), (1, 6, 11), (2, 7), (3, 8), (4, 9)))
def testFmath(self):
# see function _p2 in ellipsoidalVincenty.py
for x in (0.0001, 0.001, 0.01, 0.1, 1, 10, 100, 1000):
p = fpolynomial(x, 16384, 4096, -768, 320, -175) / 16384.0
a = x / 16384.0 * (4096 + x * (-768 + x * (320 - 175 * x))) + 1
self.test('fpolynomialA', p, a)
p = fpolynomial(x, 0, 256, -128, 74, -47) / 1024.0
b = x / 1024.0 * (256 + x * (-128 + x * (74 - 47 * x)))
self.test('fpolynomialB', p, b)
# U{Neumaier<http://wikipedia.org/wiki/Kahan_summation_algorithm>}
t = 1, 1e101, 1, -1e101
for _ in range(10):
s = float(len(t) / 2) # number of ones
self.test('sum', sum(t), s, known=True)
self.test('fsum', fsum(t), s)
f = Fsum()
f.fadd2(t)
self.test('Fsum', f.fsum(), s)
t += t
p = fpowers(2, 10) # PYCHOK false!
self.test('fpowers', len(p), 10)
self.test('fpowers', p[0], 2)
self.test('fpowers', p[9], 2**10)
p = fpowers(2, 10, 4) # PYCHOK false!
self.test('fpowers', len(p), 4)
self.test('fpowers', p[0], 2**4)
self.test('fpowers', p[3], 2**10)
p = fpowers(2, 10, 3) # PYCHOK false!
self.test('fpowers', len(p), 4)
self.test('fpowers', p[0], 2**3)
self.test('fpowers', p[3], 2**9)
self.test('isfinite', isfinite(0), 'True')
self.test('isfinite', isfinite(1e300), 'True')
self.test('isfinite', isfinite(-1e300), 'True')
self.test('isfinite', isfinite(1e1234), 'False')
self.test('isfinite', isfinite(float('inf')), 'False')
self.test('isfinite', isfinite(float('nan')), 'False')
def testFmath(self):
# see function _p2 in ellipsoidalVincenty.py
for i in range(-16, 17):
x = pow(1.0, i)
p = fpolynomial(x, 16384, 4096, -768, 320, -175) / 16384.0
a = x / 16384.0 * (4096 + x * (-768 + x * (320 - 175 * x))) + 1
self.test('fpolynomialA', p, a)
h = fhorner(x, 16384, 4096, -768, 320, -175) / 16384.0
self.test('fhornerA', h, p)
p = fpolynomial(x, 0, 256, -128, 74, -47) / 1024.0
b = x / 1024.0 * (256 + x * (-128 + x * (74 - 47 * x)))
self.test('fpolynomialB', p, b)
h = fhorner(x, 0, 256, -128, 74, -47) / 1024.0
self.test('fhornerB', h, p)
# U{Neumaier<http://WikiPedia.org/wiki/Kahan_summation_algorithm>}
t = 1, 1e101, 1, -1e101
for _ in range(10):
s = float(len(t) / 2) # number of ones
self.test('sum', sum(t), s, known=True)
self.test('fsum', fsum(t), s)
self.test('Fsum', Fsum().fsum(t), s)
t += t
# <http://code.ActiveState.com/recipes/393090>
t = 1.00, 0.00500, 0.00000000000100
s = 1.00500000000100
self.test('sum', sum(t), s, known=True)
self.test('fsum', fsum(t), s)
self.test('Fsum', Fsum().fsum(t), s)
# <http://GitHub.com/python/cpython/blob/master/Modules/mathmodule.c>
t = 1e-16, 1, 1e16
s = '1.0000000000000002e+16' # half-even rounded
self.test('fsum', fsum(t), s, fmt='%.16e')
self.test('Fsum', Fsum().fsum(t), s, fmt='%.16e')
# <http://GitHub.com/ActiveState/code/blob/master/recipes/Python/
# 393090_Binary_floating_point_summatiaccurate_full/recipe-393090.py>
for _ in range(100):
t = [7, 1e100, -7, -1e100, -9e-20, 8e-20] * 10
s = 0
for _ in range(20):
v = gauss(0, random())**7 - s
s += v
t.append(v)
shuffle(t)
s = fsum(t)
self.test('sum', sum(t), s, known=True)
self.test('fsum', s, s)
n = len(t) // 2
f = Fsum()
f.fsum(t[:n]) # test ps
self.test('Fsum', f.fsum(t[n:]), s)
f = Fsum()
f.fsum(t[n:]) # test ps
self.test('Fsum', f.fsum(t[:n]), s)
p = fpowers(2, 10) # PYCHOK false!
self.test('fpowers', len(p), 10)
self.test('fpowers', p[0], 2)
self.test('fpowers', p[9], 2**10)
p = fpowers(2, 10, 4) # PYCHOK false!
self.test('fpowers', len(p), 4)
self.test('fpowers', p[0], 2**4)
self.test('fpowers', p[3], 2**10)
p = fpowers(2, 10, 3) # PYCHOK false!
self.test('fpowers', len(p), 4)
self.test('fpowers', p[0], 2**3)
self.test('fpowers', p[3], 2**9)
self.test('isfinite(0)', isfinite(0), 'True')
self.test('isfinite(1e300)', isfinite(1e300), 'True')
self.test('isfinite(-1e300)', isfinite(-1e300), 'True')
self.test('isfinite(1e1234)', isfinite(1e1234), 'False')
self.test('isfinite(INF)', isfinite(INF), 'False')
self.test('isfinite(NAN)', isfinite(NAN), 'False')
self.test('isfinite(NEG0)', isfinite(NEG0), 'True')
self.test('isneg0(NEG0)', isneg0(NEG0), True)
self.test('isneg0(0.0)', isneg0(0.0), False)
self.test('isneg0(NAN)', isneg0(NAN), False)
for _, E in sorted(Ellipsoids.items()):
Ah = E.a / (1 + E.n) * fhorner(E.n**2, 1., 1. / 4, 1. / 64,
1. / 256, 25. / 16384)
self.test(E.name, Ah, E.A, fmt='%.8f')
Ah = E.a / (1 + E.n) * (fhorner(E.n**2, 16384, 4096, 256, 64, 25) /
16384)
self.test(E.name, Ah, E.A, fmt='%.8f')
Ah = E.a / (1 + E.n) * fhorner(E.n**2, 1., 1. / 4, 1. / 64,
1. / 256, 25. / 16384, 49. / 65536)
self.test(E.name, Ah, E.A, fmt='%.10f')
Ah = E.a / (1 + E.n) * (
fhorner(E.n**2, 65536, 16384, 1024, 256, 100, 49) / 65536)
self.test(E.name, Ah, E.A, fmt='%.10f')
t = 1, 1e101, 1, -1e101
for _ in range(10):
a = Fsum(*t)
b = a.fcopy()
c = a + b
self.test('FSum+', c.fsum(), a.fsum() + b.fsum())
c -= a
self.test('FSum-', c.fsum(), b.fsum())
c -= b
self.test('FSum-', c.fsum(), 0.0)
b = a * 2
a += a
self.test('FSum*', a.fsum(), b.fsum())
t += t
def testFmath(self):
# see function _p2 in ellipsoidalVincenty.py
for x in (0.0001, 0.001, 0.01, 0.1, 1, 10, 100, 1000):
p = fpolynomial(x, 16384, 4096, -768, 320, -175) / 16384.0
a = x / 16384.0 * (4096 + x * (-768 + x * (320 - 175 * x))) + 1
self.test('fpolynomialA', p, a)
p = fpolynomial(x, 0, 256, -128, 74, -47) / 1024.0
b = x / 1024.0 * (256 + x * (-128 + x * (74 - 47 * x)))
self.test('fpolynomialB', p, b)
# U{Neumaier<http://wikipedia.org/wiki/Kahan_summation_algorithm>}
t = 1, 1e101, 1, -1e101
for _ in range(10):
s = float(len(t) / 2) # number of ones
self.test('sum', sum(t), s, known=True)
self.test('fsum', fsum(t), s)
f = Fsum()
f.fadd2(t)
self.test('Fsum', f.fsum(), s)
t += t
# <http://code.activestate.com/recipes/393090>
t = 1.00, 0.00500, 0.00000000000100
s = 1.00500000000100
self.test('sum', sum(t), s, known=True)
self.test('fsum', fsum(t), s)
f = Fsum()
f.fadd2(t)
self.test('Fsum', f.fsum(), s)
# <http://github.com/ActiveState/code/blob/master/recipes/Python/
# 393090_Binary_floating_point_summatiaccurate_full/recipe-393090.py>
for _ in range(100):
t = [7, 1e100, -7, -1e100, -9e-20, 8e-20] * 10
s = 0
for _ in range(20):
v = gauss(0, random())**7 - s
s += v
t.append(v)
shuffle(t)
s = fsum(t)
# self.test('fsum', s, s)
f = Fsum()
f.fadd2(t)
self.test('Fsum', f.fsum(), s)
p = fpowers(2, 10) # PYCHOK false!
self.test('fpowers', len(p), 10)
self.test('fpowers', p[0], 2)
self.test('fpowers', p[9], 2**10)
p = fpowers(2, 10, 4) # PYCHOK false!
self.test('fpowers', len(p), 4)
self.test('fpowers', p[0], 2**4)
self.test('fpowers', p[3], 2**10)
p = fpowers(2, 10, 3) # PYCHOK false!
self.test('fpowers', len(p), 4)
self.test('fpowers', p[0], 2**3)
self.test('fpowers', p[3], 2**9)
self.test('isfinite', isfinite(0), 'True')
self.test('isfinite', isfinite(1e300), 'True')
self.test('isfinite', isfinite(-1e300), 'True')
self.test('isfinite', isfinite(1e1234), 'False')
self.test('isfinite', isfinite(float('inf')), 'False')
self.test('isfinite', isfinite(float('nan')), 'False')