452 lines
15 KiB
Python
452 lines
15 KiB
Python
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import mpmath
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from mpmath import *
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from mpmath.libmp import *
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import random
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import sys
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try:
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long = long
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except NameError:
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long = int
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def test_type_compare():
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assert mpf(2) == mpc(2,0)
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assert mpf(0) == mpc(0)
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assert mpf(2) != mpc(2, 0.00001)
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assert mpf(2) == 2.0
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assert mpf(2) != 3.0
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assert mpf(2) == 2
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assert mpf(2) != '2.0'
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assert mpc(2) != '2.0'
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def test_add():
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assert mpf(2.5) + mpf(3) == 5.5
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assert mpf(2.5) + 3 == 5.5
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assert mpf(2.5) + 3.0 == 5.5
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assert 3 + mpf(2.5) == 5.5
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assert 3.0 + mpf(2.5) == 5.5
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assert (3+0j) + mpf(2.5) == 5.5
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assert mpc(2.5) + mpf(3) == 5.5
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assert mpc(2.5) + 3 == 5.5
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assert mpc(2.5) + 3.0 == 5.5
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assert mpc(2.5) + (3+0j) == 5.5
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assert 3 + mpc(2.5) == 5.5
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assert 3.0 + mpc(2.5) == 5.5
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assert (3+0j) + mpc(2.5) == 5.5
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def test_sub():
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assert mpf(2.5) - mpf(3) == -0.5
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assert mpf(2.5) - 3 == -0.5
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assert mpf(2.5) - 3.0 == -0.5
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assert 3 - mpf(2.5) == 0.5
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assert 3.0 - mpf(2.5) == 0.5
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assert (3+0j) - mpf(2.5) == 0.5
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assert mpc(2.5) - mpf(3) == -0.5
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assert mpc(2.5) - 3 == -0.5
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assert mpc(2.5) - 3.0 == -0.5
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assert mpc(2.5) - (3+0j) == -0.5
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assert 3 - mpc(2.5) == 0.5
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assert 3.0 - mpc(2.5) == 0.5
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assert (3+0j) - mpc(2.5) == 0.5
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def test_mul():
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assert mpf(2.5) * mpf(3) == 7.5
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assert mpf(2.5) * 3 == 7.5
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assert mpf(2.5) * 3.0 == 7.5
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assert 3 * mpf(2.5) == 7.5
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assert 3.0 * mpf(2.5) == 7.5
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assert (3+0j) * mpf(2.5) == 7.5
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assert mpc(2.5) * mpf(3) == 7.5
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assert mpc(2.5) * 3 == 7.5
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assert mpc(2.5) * 3.0 == 7.5
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assert mpc(2.5) * (3+0j) == 7.5
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assert 3 * mpc(2.5) == 7.5
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assert 3.0 * mpc(2.5) == 7.5
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assert (3+0j) * mpc(2.5) == 7.5
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def test_div():
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assert mpf(6) / mpf(3) == 2.0
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assert mpf(6) / 3 == 2.0
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assert mpf(6) / 3.0 == 2.0
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assert 6 / mpf(3) == 2.0
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assert 6.0 / mpf(3) == 2.0
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assert (6+0j) / mpf(3.0) == 2.0
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assert mpc(6) / mpf(3) == 2.0
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assert mpc(6) / 3 == 2.0
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assert mpc(6) / 3.0 == 2.0
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assert mpc(6) / (3+0j) == 2.0
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assert 6 / mpc(3) == 2.0
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assert 6.0 / mpc(3) == 2.0
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assert (6+0j) / mpc(3) == 2.0
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def test_pow():
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assert mpf(6) ** mpf(3) == 216.0
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assert mpf(6) ** 3 == 216.0
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assert mpf(6) ** 3.0 == 216.0
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assert 6 ** mpf(3) == 216.0
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assert 6.0 ** mpf(3) == 216.0
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assert (6+0j) ** mpf(3.0) == 216.0
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assert mpc(6) ** mpf(3) == 216.0
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assert mpc(6) ** 3 == 216.0
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assert mpc(6) ** 3.0 == 216.0
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assert mpc(6) ** (3+0j) == 216.0
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assert 6 ** mpc(3) == 216.0
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assert 6.0 ** mpc(3) == 216.0
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assert (6+0j) ** mpc(3) == 216.0
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def test_mixed_misc():
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assert 1 + mpf(3) == mpf(3) + 1 == 4
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assert 1 - mpf(3) == -(mpf(3) - 1) == -2
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assert 3 * mpf(2) == mpf(2) * 3 == 6
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assert 6 / mpf(2) == mpf(6) / 2 == 3
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assert 1.0 + mpf(3) == mpf(3) + 1.0 == 4
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assert 1.0 - mpf(3) == -(mpf(3) - 1.0) == -2
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assert 3.0 * mpf(2) == mpf(2) * 3.0 == 6
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assert 6.0 / mpf(2) == mpf(6) / 2.0 == 3
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def test_add_misc():
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mp.dps = 15
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assert mpf(4) + mpf(-70) == -66
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assert mpf(1) + mpf(1.1)/80 == 1 + 1.1/80
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assert mpf((1, 10000000000)) + mpf(3) == mpf((1, 10000000000))
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assert mpf(3) + mpf((1, 10000000000)) == mpf((1, 10000000000))
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assert mpf((1, -10000000000)) + mpf(3) == mpf(3)
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assert mpf(3) + mpf((1, -10000000000)) == mpf(3)
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assert mpf(1) + 1e-15 != 1
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assert mpf(1) + 1e-20 == 1
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assert mpf(1.07e-22) + 0 == mpf(1.07e-22)
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assert mpf(0) + mpf(1.07e-22) == mpf(1.07e-22)
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def test_complex_misc():
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# many more tests needed
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assert 1 + mpc(2) == 3
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assert not mpc(2).ae(2 + 1e-13)
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assert mpc(2+1e-15j).ae(2)
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def test_complex_zeros():
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for a in [0,2]:
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for b in [0,3]:
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for c in [0,4]:
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for d in [0,5]:
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assert mpc(a,b)*mpc(c,d) == complex(a,b)*complex(c,d)
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def test_hash():
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for i in range(-256, 256):
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assert hash(mpf(i)) == hash(i)
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assert hash(mpf(0.5)) == hash(0.5)
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assert hash(mpc(2,3)) == hash(2+3j)
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# Check that this doesn't fail
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assert hash(inf)
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# Check that overflow doesn't assign equal hashes to large numbers
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assert hash(mpf('1e1000')) != hash('1e10000')
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assert hash(mpc(100,'1e1000')) != hash(mpc(200,'1e1000'))
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from mpmath.rational import mpq
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assert hash(mp.mpq(1,3))
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assert hash(mp.mpq(0,1)) == 0
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assert hash(mp.mpq(-1,1)) == hash(-1)
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assert hash(mp.mpq(1,1)) == hash(1)
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assert hash(mp.mpq(5,1)) == hash(5)
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assert hash(mp.mpq(1,2)) == hash(0.5)
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if sys.version_info >= (3, 2):
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assert hash(mpf(1)*2**2000) == hash(2**2000)
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assert hash(mpf(1)/2**2000) == hash(mpq(1,2**2000))
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# Advanced rounding test
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def test_add_rounding():
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mp.dps = 15
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a = from_float(1e-50)
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assert mpf_sub(mpf_add(fone, a, 53, round_up), fone, 53, round_up) == from_float(2.2204460492503131e-16)
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assert mpf_sub(fone, a, 53, round_up) == fone
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assert mpf_sub(fone, mpf_sub(fone, a, 53, round_down), 53, round_down) == from_float(1.1102230246251565e-16)
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assert mpf_add(fone, a, 53, round_down) == fone
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def test_almost_equal():
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assert mpf(1.2).ae(mpf(1.20000001), 1e-7)
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assert not mpf(1.2).ae(mpf(1.20000001), 1e-9)
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assert not mpf(-0.7818314824680298).ae(mpf(-0.774695868667929))
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def test_arithmetic_functions():
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import operator
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ops = [(operator.add, fadd), (operator.sub, fsub), (operator.mul, fmul),
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(operator.truediv, fdiv)]
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a = mpf(0.27)
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b = mpf(1.13)
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c = mpc(0.51+2.16j)
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d = mpc(1.08-0.99j)
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for x in [a,b,c,d]:
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for y in [a,b,c,d]:
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for op, fop in ops:
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if fop is not fdiv:
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mp.prec = 200
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z0 = op(x,y)
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mp.prec = 60
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z1 = op(x,y)
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mp.prec = 53
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z2 = op(x,y)
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assert fop(x, y, prec=60) == z1
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assert fop(x, y) == z2
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if fop is not fdiv:
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assert fop(x, y, prec=inf) == z0
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assert fop(x, y, dps=inf) == z0
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assert fop(x, y, exact=True) == z0
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assert fneg(fneg(z1, exact=True), prec=inf) == z1
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assert fneg(z1) == -(+z1)
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mp.dps = 15
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def test_exact_integer_arithmetic():
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# XXX: re-fix this so that all operations are tested with all rounding modes
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random.seed(0)
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for prec in [6, 10, 25, 40, 100, 250, 725]:
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for rounding in ['d', 'u', 'f', 'c', 'n']:
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mp.dps = prec
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M = 10**(prec-2)
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M2 = 10**(prec//2-2)
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for i in range(10):
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a = random.randint(-M, M)
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b = random.randint(-M, M)
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assert mpf(a, rounding=rounding) == a
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assert int(mpf(a, rounding=rounding)) == a
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assert int(mpf(str(a), rounding=rounding)) == a
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assert mpf(a) + mpf(b) == a + b
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assert mpf(a) - mpf(b) == a - b
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assert -mpf(a) == -a
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a = random.randint(-M2, M2)
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b = random.randint(-M2, M2)
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assert mpf(a) * mpf(b) == a*b
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assert mpf_mul(from_int(a), from_int(b), mp.prec, rounding) == from_int(a*b)
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mp.dps = 15
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def test_odd_int_bug():
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assert to_int(from_int(3), round_nearest) == 3
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def test_str_1000_digits():
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mp.dps = 1001
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# last digit may be wrong
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assert str(mpf(2)**0.5)[-10:-1] == '9518488472'[:9]
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assert str(pi)[-10:-1] == '2164201989'[:9]
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mp.dps = 15
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def test_str_10000_digits():
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mp.dps = 10001
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# last digit may be wrong
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assert str(mpf(2)**0.5)[-10:-1] == '5873258351'[:9]
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assert str(pi)[-10:-1] == '5256375678'[:9]
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mp.dps = 15
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def test_monitor():
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f = lambda x: x**2
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a = []
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b = []
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g = monitor(f, a.append, b.append)
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assert g(3) == 9
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assert g(4) == 16
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assert a[0] == ((3,), {})
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assert b[0] == 9
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def test_nint_distance():
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assert nint_distance(mpf(-3)) == (-3, -inf)
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assert nint_distance(mpc(-3)) == (-3, -inf)
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assert nint_distance(mpf(-3.1)) == (-3, -3)
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assert nint_distance(mpf(-3.01)) == (-3, -6)
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assert nint_distance(mpf(-3.001)) == (-3, -9)
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assert nint_distance(mpf(-3.0001)) == (-3, -13)
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assert nint_distance(mpf(-2.9)) == (-3, -3)
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assert nint_distance(mpf(-2.99)) == (-3, -6)
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assert nint_distance(mpf(-2.999)) == (-3, -9)
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assert nint_distance(mpf(-2.9999)) == (-3, -13)
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assert nint_distance(mpc(-3+0.1j)) == (-3, -3)
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assert nint_distance(mpc(-3+0.01j)) == (-3, -6)
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assert nint_distance(mpc(-3.1+0.1j)) == (-3, -3)
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assert nint_distance(mpc(-3.01+0.01j)) == (-3, -6)
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assert nint_distance(mpc(-3.001+0.001j)) == (-3, -9)
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assert nint_distance(mpf(0)) == (0, -inf)
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assert nint_distance(mpf(0.01)) == (0, -6)
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assert nint_distance(mpf('1e-100')) == (0, -332)
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def test_floor_ceil_nint_frac():
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mp.dps = 15
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for n in range(-10,10):
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assert floor(n) == n
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assert floor(n+0.5) == n
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assert ceil(n) == n
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assert ceil(n+0.5) == n+1
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assert nint(n) == n
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# nint rounds to even
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if n % 2 == 1:
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assert nint(n+0.5) == n+1
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else:
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assert nint(n+0.5) == n
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assert floor(inf) == inf
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assert floor(ninf) == ninf
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assert isnan(floor(nan))
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assert ceil(inf) == inf
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assert ceil(ninf) == ninf
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assert isnan(ceil(nan))
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assert nint(inf) == inf
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assert nint(ninf) == ninf
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assert isnan(nint(nan))
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assert floor(0.1) == 0
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assert floor(0.9) == 0
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assert floor(-0.1) == -1
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assert floor(-0.9) == -1
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assert floor(10000000000.1) == 10000000000
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assert floor(10000000000.9) == 10000000000
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assert floor(-10000000000.1) == -10000000000-1
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assert floor(-10000000000.9) == -10000000000-1
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assert floor(1e-100) == 0
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assert floor(-1e-100) == -1
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assert floor(1e100) == 1e100
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assert floor(-1e100) == -1e100
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assert ceil(0.1) == 1
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assert ceil(0.9) == 1
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assert ceil(-0.1) == 0
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assert ceil(-0.9) == 0
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assert ceil(10000000000.1) == 10000000000+1
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assert ceil(10000000000.9) == 10000000000+1
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assert ceil(-10000000000.1) == -10000000000
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assert ceil(-10000000000.9) == -10000000000
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assert ceil(1e-100) == 1
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assert ceil(-1e-100) == 0
|
||
|
|
assert ceil(1e100) == 1e100
|
||
|
|
assert ceil(-1e100) == -1e100
|
||
|
|
assert nint(0.1) == 0
|
||
|
|
assert nint(0.9) == 1
|
||
|
|
assert nint(-0.1) == 0
|
||
|
|
assert nint(-0.9) == -1
|
||
|
|
assert nint(10000000000.1) == 10000000000
|
||
|
|
assert nint(10000000000.9) == 10000000000+1
|
||
|
|
assert nint(-10000000000.1) == -10000000000
|
||
|
|
assert nint(-10000000000.9) == -10000000000-1
|
||
|
|
assert nint(1e-100) == 0
|
||
|
|
assert nint(-1e-100) == 0
|
||
|
|
assert nint(1e100) == 1e100
|
||
|
|
assert nint(-1e100) == -1e100
|
||
|
|
assert floor(3.2+4.6j) == 3+4j
|
||
|
|
assert ceil(3.2+4.6j) == 4+5j
|
||
|
|
assert nint(3.2+4.6j) == 3+5j
|
||
|
|
for n in range(-10,10):
|
||
|
|
assert frac(n) == 0
|
||
|
|
assert frac(0.25) == 0.25
|
||
|
|
assert frac(1.25) == 0.25
|
||
|
|
assert frac(2.25) == 0.25
|
||
|
|
assert frac(-0.25) == 0.75
|
||
|
|
assert frac(-1.25) == 0.75
|
||
|
|
assert frac(-2.25) == 0.75
|
||
|
|
assert frac('1e100000000000000') == 0
|
||
|
|
u = mpf('1e-100000000000000')
|
||
|
|
assert frac(u) == u
|
||
|
|
assert frac(-u) == 1 # rounding!
|
||
|
|
u = mpf('1e-400')
|
||
|
|
assert frac(-u, prec=0) == fsub(1, u, exact=True)
|
||
|
|
assert frac(3.25+4.75j) == 0.25+0.75j
|
||
|
|
|
||
|
|
def test_isnan_etc():
|
||
|
|
from mpmath.rational import mpq
|
||
|
|
assert isnan(nan) == True
|
||
|
|
assert isnan(3) == False
|
||
|
|
assert isnan(mpf(3)) == False
|
||
|
|
assert isnan(inf) == False
|
||
|
|
assert isnan(mpc(2,nan)) == True
|
||
|
|
assert isnan(mpc(2,nan)) == True
|
||
|
|
assert isnan(mpc(nan,nan)) == True
|
||
|
|
assert isnan(mpc(2,2)) == False
|
||
|
|
assert isnan(mpc(nan,inf)) == True
|
||
|
|
assert isnan(mpc(inf,inf)) == False
|
||
|
|
assert isnan(mpq((3,2))) == False
|
||
|
|
assert isnan(mpq((0,1))) == False
|
||
|
|
assert isinf(inf) == True
|
||
|
|
assert isinf(-inf) == True
|
||
|
|
assert isinf(3) == False
|
||
|
|
assert isinf(nan) == False
|
||
|
|
assert isinf(3+4j) == False
|
||
|
|
assert isinf(mpc(inf)) == True
|
||
|
|
assert isinf(mpc(3,inf)) == True
|
||
|
|
assert isinf(mpc(inf,3)) == True
|
||
|
|
assert isinf(mpc(inf,inf)) == True
|
||
|
|
assert isinf(mpc(nan,inf)) == True
|
||
|
|
assert isinf(mpc(inf,nan)) == True
|
||
|
|
assert isinf(mpc(nan,nan)) == False
|
||
|
|
assert isinf(mpq((3,2))) == False
|
||
|
|
assert isinf(mpq((0,1))) == False
|
||
|
|
assert isnormal(3) == True
|
||
|
|
assert isnormal(3.5) == True
|
||
|
|
assert isnormal(mpf(3.5)) == True
|
||
|
|
assert isnormal(0) == False
|
||
|
|
assert isnormal(mpf(0)) == False
|
||
|
|
assert isnormal(0.0) == False
|
||
|
|
assert isnormal(inf) == False
|
||
|
|
assert isnormal(-inf) == False
|
||
|
|
assert isnormal(nan) == False
|
||
|
|
assert isnormal(float(inf)) == False
|
||
|
|
assert isnormal(mpc(0,0)) == False
|
||
|
|
assert isnormal(mpc(3,0)) == True
|
||
|
|
assert isnormal(mpc(0,3)) == True
|
||
|
|
assert isnormal(mpc(3,3)) == True
|
||
|
|
assert isnormal(mpc(0,nan)) == False
|
||
|
|
assert isnormal(mpc(0,inf)) == False
|
||
|
|
assert isnormal(mpc(3,nan)) == False
|
||
|
|
assert isnormal(mpc(3,inf)) == False
|
||
|
|
assert isnormal(mpc(3,-inf)) == False
|
||
|
|
assert isnormal(mpc(nan,0)) == False
|
||
|
|
assert isnormal(mpc(inf,0)) == False
|
||
|
|
assert isnormal(mpc(nan,3)) == False
|
||
|
|
assert isnormal(mpc(inf,3)) == False
|
||
|
|
assert isnormal(mpc(inf,nan)) == False
|
||
|
|
assert isnormal(mpc(nan,inf)) == False
|
||
|
|
assert isnormal(mpc(nan,nan)) == False
|
||
|
|
assert isnormal(mpc(inf,inf)) == False
|
||
|
|
assert isnormal(mpq((3,2))) == True
|
||
|
|
assert isnormal(mpq((0,1))) == False
|
||
|
|
assert isint(3) == True
|
||
|
|
assert isint(0) == True
|
||
|
|
assert isint(long(3)) == True
|
||
|
|
assert isint(long(0)) == True
|
||
|
|
assert isint(mpf(3)) == True
|
||
|
|
assert isint(mpf(0)) == True
|
||
|
|
assert isint(mpf(-3)) == True
|
||
|
|
assert isint(mpf(3.2)) == False
|
||
|
|
assert isint(3.2) == False
|
||
|
|
assert isint(nan) == False
|
||
|
|
assert isint(inf) == False
|
||
|
|
assert isint(-inf) == False
|
||
|
|
assert isint(mpc(0)) == True
|
||
|
|
assert isint(mpc(3)) == True
|
||
|
|
assert isint(mpc(3.2)) == False
|
||
|
|
assert isint(mpc(3,inf)) == False
|
||
|
|
assert isint(mpc(inf)) == False
|
||
|
|
assert isint(mpc(3,2)) == False
|
||
|
|
assert isint(mpc(0,2)) == False
|
||
|
|
assert isint(mpc(3,2),gaussian=True) == True
|
||
|
|
assert isint(mpc(3,0),gaussian=True) == True
|
||
|
|
assert isint(mpc(0,3),gaussian=True) == True
|
||
|
|
assert isint(3+4j) == False
|
||
|
|
assert isint(3+4j, gaussian=True) == True
|
||
|
|
assert isint(3+0j) == True
|
||
|
|
assert isint(mpq((3,2))) == False
|
||
|
|
assert isint(mpq((3,9))) == False
|
||
|
|
assert isint(mpq((9,3))) == True
|
||
|
|
assert isint(mpq((0,4))) == True
|
||
|
|
assert isint(mpq((1,1))) == True
|
||
|
|
assert isint(mpq((-1,1))) == True
|
||
|
|
assert mp.isnpint(0) == True
|
||
|
|
assert mp.isnpint(1) == False
|
||
|
|
assert mp.isnpint(-1) == True
|
||
|
|
assert mp.isnpint(-1.1) == False
|
||
|
|
assert mp.isnpint(-1.0) == True
|
||
|
|
assert mp.isnpint(mp.mpq(1,2)) == False
|
||
|
|
assert mp.isnpint(mp.mpq(-1,2)) == False
|
||
|
|
assert mp.isnpint(mp.mpq(-3,1)) == True
|
||
|
|
assert mp.isnpint(mp.mpq(0,1)) == True
|
||
|
|
assert mp.isnpint(mp.mpq(1,1)) == False
|
||
|
|
assert mp.isnpint(0+0j) == True
|
||
|
|
assert mp.isnpint(-1+0j) == True
|
||
|
|
assert mp.isnpint(-1.1+0j) == False
|
||
|
|
assert mp.isnpint(-1+0.1j) == False
|
||
|
|
assert mp.isnpint(0+0.1j) == False
|
||
|
|
|
||
|
|
|
||
|
|
def test_issue_438():
|
||
|
|
assert mpf(finf) == mpf('inf')
|
||
|
|
assert mpf(fninf) == mpf('-inf')
|
||
|
|
assert mpf(fnan)._mpf_ == mpf('nan')._mpf_
|