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<https://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
# <https://code.ActiveState.com/recipes/393090>
t = 1.0, 0.0050, 0.0000000000010
s = 1.0050000000010
self.test('sum', sum(t), s, known=True)
self.test('fsum', fsum(t), s)
self.test('Fsum', Fsum().fsum(t), s)
# <https://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')
# <https://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 = f * (f * 1e10) # coverage Fsum.__imul__
f *= f * 1e10
self.test('fmul', p.fsum(), f.fsum(), fmt='%0.8f')
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
self.testCopy(a, '_fsum2_', '_n', '_ps')
if coverage: # for test coverage
c = a - b
self.test('FSum0', c.fsum(), 0.0)
c -= 0
self.test('FSum0', c.fsum(), 0.0)
c -= c
self.test('FSum0', c.fsum(), 0.0)
c *= Fsum(1.0)
self.test('FSum0', c.fsum(), 0.0)
a.fsub_(*a._ps)
self.test('FSum0', a.fsum(), 0.0)
self.test('Fsum#', len(a), 2049)
self.test('Fsum#', len(a._ps), 1)
self.test('FSum.', a, 'pygeodesy.fmath.Fsum()')
h = hypot_(1.0, 0.0050, 0.0000000000010)
self.test('hypot_', h, '1.0000124999219', fmt='%.13f')
s = hypot3(1.0, 0.0050, 0.0000000000010) # DEPRECATED
self.test('hypot3', s, h, fmt='%.13f')
h = hypot_(3000, 2000, 100) # note, all C{int}
self.test('hypot_', h, '3606.937759', fmt='%.6f')
s = hypot3(3000, 2000, 100) # DEPRECATED
self.test('hypot3', s, h, fmt='%.6f')
h = hypot_(40000, 3000, 200, 10.0)
s = sqrt(40000**2 + 3000**2 + 200**2 + 100)
self.test('hypot_', h, s, fmt='%.3f')
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<https://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
# <https://GitHub.com/ActiveState/code/blob/master/recipes/Python/
# 393090_Binary_floating_point_summatiaccurate_full/recipe-393090.py>
t = 1.0, 0.0050, 0.0000000000010
s = 1.0050000000010
self.test('sum', sum(t), s, known=True)
self.test('fsum', fsum(t), s)
self.test('Fsum', Fsum().fsum(t), s)
# <https://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, prec=-16)
self.test('Fsum', Fsum().fsum(t), s, prec=-16)
# <https://GitHub.com/ActiveState/code/blob/master/recipes/Python/
# 393090_Binary_floating_point_summatiaccurate_full/recipe-393090.py>
for _ in range(100):
t = [7, 1e100, -9e-20, -7, -1e100, 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 = f * (f * 1e10) # coverage Fsum.__imul__
f *= f * 1e10
self.test('fmul', p.fsum(), f.fsum(), prec=8)
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)
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, prec=10, known=abs(Ah - E.A) < 1e-5) # b_None, f_None on iPhone
Ah = E.a / (1 + E.n) * (fhorner(E.n**2, 16384, 4096, 256, 64, 25) / 16384)
self.test(E.name, Ah, E.A, prec=10, known=abs(Ah - E.A) < 1e-5) # b_None, f_None on iPhone
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, prec=10, known=abs(Ah - E.A) < 1e-9)
Ah = E.a / (1 + E.n) * (fhorner(E.n**2, 65536, 16384, 1024, 256, 100, 49) / 65536)
self.test(E.name, Ah, E.A, prec=10, known=abs(Ah - E.A) < 1e-9)
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
self.testCopy(a, '_fsum2_', '_n', '_ps')
if coverage: # for test coverage
c = a - b
self.test('FSum0', c.fsum(), 0.0)
c -= 0
self.test('FSum0', c.fsum(), 0.0)
c -= c
self.test('FSum0', c.fsum(), 0.0)
c *= Fsum(1.0)
self.test('FSum0', c.fsum(), 0.0)
a.fsub_(*a._ps)
self.test('FSum0', a.fsum(), 0.0)
self.test('Fsum#', len(a), 2049)
self.test('Fsum#', len(a._ps), 1)
self.test('FSum.', a, 'fmath.Fsum()')
try:
self.test('_2sum', fmath._2sum(1e308, 1e803), OverflowError.__name__)
except OverflowError as x:
self.test('_2sum', repr(x), repr(x))
h = hypot_(1.0, 0.0050, 0.0000000000010)
self.test('hypot_ ', h, '1.00001250', prec=8)
e = euclid_(1.0, 0.0050, 0.0000000000010)
self.test('euclid_', e, h, prec=8, known=abs(e - h) < h * 0.01)
t = hypot2_(1.0, 0.0050, 0.0000000000010)
self.test('hypot2_', t, '1.00002500', prec=8)
s = hypot3(1.0, 0.0050, 0.0000000000010) # DEPRECATED
self.test('hypot3 ', s, h, prec=8)
h = hypot_(3000, 2000, 100) # note, all C{int}
self.test('hypot_ ', h, '3606.937759', prec=6)
e = euclid_(3000, 2000, 100)
self.test('euclid_', e, h * 1.07, prec=6, known=abs(e - h) < h * 0.07)
t = hypot2_(3000, 2000, 100) # note, all C{int}
s = fsum_(3000**2, 2000**2, 100**2)
self.test('hypot2_', t, s, prec=1)
s = hypot3(3000, 2000, 100) # DEPRECATED
self.test('hypot3 ', s, h, prec=6)
h = hypot_(40000, 3000, 200, 10.0)
s = fsum_(40000**2, 3000**2, 200**2, 100)
self.test('hypot_ ', h, sqrt(s), prec=3)
t = hypot2_(40000, 3000, 200, 10.0)
self.test('hypot2_', t, s, prec=1)
e = euclid_(40000, 3000, 200, 10.0)
self.test('euclid_', e, h * 1.03, prec=3, known=abs(e - h) < h * 0.03)
self.test('cbrt', cbrt(27), '3.00', prec=2)
self.test('cbrt', cbrt(-27), '-3.00', prec=2)
self.test('cbrt2', cbrt2(27), '9.00', prec=2)
self.test('cbrt2', cbrt2(-27), '9.00', prec=2)
self.test('sqrt3', sqrt3(9), '27.00', prec=2)
# Knuth/Kulisch, TAOCP, vol 2, p 245, sec 4.2.2, item 31, see also .testKarney.py
# <https://SeriousComputerist.Atariverse.com/media/pdf/book/
# Art%20of%20Computer%20Programming%20-%20Volume%202%20(Seminumerical%20Algorithms).pdf>
x = 408855776
y = 708158977
self.test('ints', 2*y**2 + 9*x**4 - y**4, 1)
self.test('ints', 2*y**2 + (3*x**2 - y**2) * (3*x**2 + y**2), 1)
t = 2*float(y)**2, 9*float(x)**4, -(float(y)**4)
self.test('fsum ', fsum(t), '1.0', prec=-12, known=True) # -3.589050987400773e+19
self.test('fsum_', fsum_(*t), '1.0', prec=-12, known=True)
self.test('Fsum ', Fsum().fsum_(*t), '1.0', prec=-12, known=True)
self.test('sum ', sum(t), '1.0', prec=-12, known=True)