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from mpmath import *
def test_sumem():
mp.dps = 15
assert sumem(lambda k: 1/k**2.5, [50, 100]).ae(0.0012524505324784962)
assert sumem(lambda k: k**4 + 3*k + 1, [10, 100]).ae(2050333103)
def test_nsum():
mp.dps = 15
assert nsum(lambda x: x**2, [1, 3]) == 14
assert nsum(lambda k: 1/factorial(k), [0, inf]).ae(e)
assert nsum(lambda k: (-1)**(k+1) / k, [1, inf]).ae(log(2))
assert nsum(lambda k: (-1)**(k+1) / k**2, [1, inf]).ae(pi**2 / 12)
assert nsum(lambda k: (-1)**k / log(k), [2, inf]).ae(0.9242998972229388)
assert nsum(lambda k: 1/k**2, [1, inf]).ae(pi**2 / 6)
assert nsum(lambda k: 2**k/fac(k), [0, inf]).ae(exp(2))
assert nsum(lambda k: 1/k**2, [4, inf], method='e').ae(0.2838229557371153)
assert abs(fp.nsum(lambda k: 1/k**4, [1, fp.inf]) - 1.082323233711138) < 1e-5
assert abs(fp.nsum(lambda k: 1/k**4, [1, fp.inf], method='e') - 1.082323233711138) < 1e-4
def test_nprod():
mp.dps = 15
assert nprod(lambda k: exp(1/k**2), [1,inf], method='r').ae(exp(pi**2/6))
assert nprod(lambda x: x**2, [1, 3]) == 36
def test_fsum():
mp.dps = 15
assert fsum([]) == 0
assert fsum([-4]) == -4
assert fsum([2,3]) == 5
assert fsum([1e-100,1]) == 1
assert fsum([1,1e-100]) == 1
assert fsum([1e100,1]) == 1e100
assert fsum([1,1e100]) == 1e100
assert fsum([1e-100,0]) == 1e-100
assert fsum([1e-100,1e100,1e-100]) == 1e100
assert fsum([2,1+1j,1]) == 4+1j
assert fsum([2,inf,3]) == inf
assert fsum([2,-1], absolute=1) == 3
assert fsum([2,-1], squared=1) == 5
assert fsum([1,1+j], squared=1) == 1+2j
assert fsum([1,3+4j], absolute=1) == 6
assert fsum([1,2+3j], absolute=1, squared=1) == 14
assert isnan(fsum([inf,-inf]))
assert fsum([inf,-inf], absolute=1) == inf
assert fsum([inf,-inf], squared=1) == inf
assert fsum([inf,-inf], absolute=1, squared=1) == inf
assert iv.fsum([1,mpi(2,3)]) == mpi(3,4)
def test_fprod():
mp.dps = 15
assert fprod([]) == 1
assert fprod([2,3]) == 6
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