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