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 >= "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
