"""Includes test functions for fftpack.helper module

Copied from fftpack.helper by Pearu Peterson, October 2005
Modified for Array API, 2023

"""
from scipy.fft._helper import next_fast_len, prev_fast_len, _init_nd_shape_and_axes
from numpy.testing import assert_equal
from pytest import raises as assert_raises
import pytest
import numpy as np
import sys
from scipy.conftest import array_api_compatible
from scipy._lib._array_api import (
    xp_assert_close, get_xp_devices, xp_device, array_namespace
)
from scipy import fft

pytestmark = [array_api_compatible, pytest.mark.usefixtures("skip_xp_backends")]
skip_xp_backends = pytest.mark.skip_xp_backends

_5_smooth_numbers = [
    2, 3, 4, 5, 6, 8, 9, 10,
    2 * 3 * 5,
    2**3 * 3**5,
    2**3 * 3**3 * 5**2,
]

def test_next_fast_len():
    for n in _5_smooth_numbers:
        assert_equal(next_fast_len(n), n)


def _assert_n_smooth(x, n):
    x_orig = x
    if n < 2:
        assert False

    while True:
        q, r = divmod(x, 2)
        if r != 0:
            break
        x = q

    for d in range(3, n+1, 2):
        while True:
            q, r = divmod(x, d)
            if r != 0:
                break
            x = q

    assert x == 1, \
           f'x={x_orig} is not {n}-smooth, remainder={x}'


@skip_xp_backends(np_only=True)
class TestNextFastLen:

    def test_next_fast_len(self):
        np.random.seed(1234)

        def nums():
            yield from range(1, 1000)
            yield 2**5 * 3**5 * 4**5 + 1

        for n in nums():
            m = next_fast_len(n)
            _assert_n_smooth(m, 11)
            assert m == next_fast_len(n, False)

            m = next_fast_len(n, True)
            _assert_n_smooth(m, 5)

    def test_np_integers(self):
        ITYPES = [np.int16, np.int32, np.int64, np.uint16, np.uint32, np.uint64]
        for ityp in ITYPES:
            x = ityp(12345)
            testN = next_fast_len(x)
            assert_equal(testN, next_fast_len(int(x)))

    def testnext_fast_len_small(self):
        hams = {
            1: 1, 2: 2, 3: 3, 4: 4, 5: 5, 6: 6, 7: 8, 8: 8, 14: 15, 15: 15,
            16: 16, 17: 18, 1021: 1024, 1536: 1536, 51200000: 51200000
        }
        for x, y in hams.items():
            assert_equal(next_fast_len(x, True), y)

    @pytest.mark.xfail(sys.maxsize < 2**32,
                       reason="Hamming Numbers too large for 32-bit",
                       raises=ValueError, strict=True)
    def testnext_fast_len_big(self):
        hams = {
            510183360: 510183360, 510183360 + 1: 512000000,
            511000000: 512000000,
            854296875: 854296875, 854296875 + 1: 859963392,
            196608000000: 196608000000, 196608000000 + 1: 196830000000,
            8789062500000: 8789062500000, 8789062500000 + 1: 8796093022208,
            206391214080000: 206391214080000,
            206391214080000 + 1: 206624260800000,
            470184984576000: 470184984576000,
            470184984576000 + 1: 470715894135000,
            7222041363087360: 7222041363087360,
            7222041363087360 + 1: 7230196133913600,
            # power of 5    5**23
            11920928955078125: 11920928955078125,
            11920928955078125 - 1: 11920928955078125,
            # power of 3    3**34
            16677181699666569: 16677181699666569,
            16677181699666569 - 1: 16677181699666569,
            # power of 2   2**54
            18014398509481984: 18014398509481984,
            18014398509481984 - 1: 18014398509481984,
            # above this, int(ceil(n)) == int(ceil(n+1))
            19200000000000000: 19200000000000000,
            19200000000000000 + 1: 19221679687500000,
            288230376151711744: 288230376151711744,
            288230376151711744 + 1: 288325195312500000,
            288325195312500000 - 1: 288325195312500000,
            288325195312500000: 288325195312500000,
            288325195312500000 + 1: 288555831593533440,
        }
        for x, y in hams.items():
            assert_equal(next_fast_len(x, True), y)

    def test_keyword_args(self):
        assert next_fast_len(11, real=True) == 12
        assert next_fast_len(target=7, real=False) == 7

@skip_xp_backends(np_only=True)
class TestPrevFastLen:

    def test_prev_fast_len(self):
        np.random.seed(1234)

        def nums():
            yield from range(1, 1000)
            yield 2**5 * 3**5 * 4**5 + 1

        for n in nums():
            m = prev_fast_len(n)
            _assert_n_smooth(m, 11)
            assert m == prev_fast_len(n, False)

            m = prev_fast_len(n, True)
            _assert_n_smooth(m, 5)

    def test_np_integers(self):
        ITYPES = [np.int16, np.int32, np.int64, np.uint16, np.uint32, 
                    np.uint64]
        for ityp in ITYPES:
            x = ityp(12345)
            testN = prev_fast_len(x)
            assert_equal(testN, prev_fast_len(int(x)))

            testN = prev_fast_len(x, real=True)
            assert_equal(testN, prev_fast_len(int(x), real=True))

    def testprev_fast_len_small(self):
        hams = {
            1: 1, 2: 2, 3: 3, 4: 4, 5: 5, 6: 6, 7: 6, 8: 8, 14: 12, 15: 15,
            16: 16, 17: 16, 1021: 1000, 1536: 1536, 51200000: 51200000
        }
        for x, y in hams.items():
            assert_equal(prev_fast_len(x, True), y)

        hams = {
            1: 1, 2: 2, 3: 3, 4: 4, 5: 5, 6: 6, 7: 7, 8: 8, 9: 9, 10: 10,
            11: 11, 12: 12, 13: 12, 14: 14, 15: 15, 16: 16, 17: 16, 18: 18,
            19: 18, 20: 20, 21: 21, 22: 22, 120: 120, 121: 121, 122: 121,
            1021: 1008, 1536: 1536, 51200000: 51200000
        }
        for x, y in hams.items():
            assert_equal(prev_fast_len(x, False), y)

    @pytest.mark.xfail(sys.maxsize < 2**32,
                       reason="Hamming Numbers too large for 32-bit",
                       raises=ValueError, strict=True)
    def testprev_fast_len_big(self):
        hams = {
            # 2**6 * 3**13 * 5**1
            510183360: 510183360,
            510183360 + 1: 510183360,
            510183360 - 1: 509607936,  # 2**21 * 3**5
            # 2**6 * 5**6 * 7**1 * 73**1
            511000000: 510183360,
            511000000 + 1: 510183360,
            511000000 - 1: 510183360,  # 2**6 * 3**13 * 5**1
            # 3**7 * 5**8
            854296875: 854296875,
            854296875 + 1: 854296875,
            854296875 - 1: 850305600,  # 2**6 * 3**12 * 5**2
            # 2**22 * 3**1 * 5**6
            196608000000: 196608000000,
            196608000000 + 1: 196608000000,
            196608000000 - 1: 195910410240,  # 2**13 * 3**14 * 5**1
            # 2**5 * 3**2 * 5**15
            8789062500000: 8789062500000,
            8789062500000 + 1: 8789062500000,
            8789062500000 - 1: 8748000000000,  # 2**11 * 3**7 * 5**9
            # 2**24 * 3**9 * 5**4
            206391214080000: 206391214080000,
            206391214080000 + 1: 206391214080000,
            206391214080000 - 1: 206158430208000,  # 2**39 * 3**1 * 5**3
            # 2**18 * 3**15 * 5**3
            470184984576000: 470184984576000,
            470184984576000 + 1: 470184984576000,
            470184984576000 - 1: 469654673817600,  # 2**33 * 3**7 **5**2
            # 2**25 * 3**16 * 5**1
            7222041363087360: 7222041363087360,
            7222041363087360 + 1: 7222041363087360,
            7222041363087360 - 1: 7213895789838336,  # 2**40 * 3**8
            # power of 5    5**23
            11920928955078125: 11920928955078125,
            11920928955078125 + 1: 11920928955078125,
            11920928955078125 - 1: 11901557422080000,  # 2**14 * 3**19 * 5**4
            # power of 3    3**34
            16677181699666569: 16677181699666569,
            16677181699666569 + 1: 16677181699666569,
            16677181699666569 - 1: 16607531250000000,  # 2**7 * 3**12 * 5**12
            # power of 2   2**54
            18014398509481984: 18014398509481984,
            18014398509481984 + 1: 18014398509481984,
            18014398509481984 - 1: 18000000000000000,  # 2**16 * 3**2 * 5**15
            # 2**20 * 3**1 * 5**14
            19200000000000000: 19200000000000000,
            19200000000000000 + 1: 19200000000000000,
            19200000000000000 - 1: 19131876000000000,  # 2**11 * 3**14 * 5**9
            # 2**58
            288230376151711744: 288230376151711744,
            288230376151711744 + 1: 288230376151711744,
            288230376151711744 - 1: 288000000000000000,  # 2**20 * 3**2 * 5**15
            # 2**5 * 3**10 * 5**16
            288325195312500000: 288325195312500000,
            288325195312500000 + 1: 288325195312500000,
            288325195312500000 - 1: 288230376151711744,  # 2**58
        }
        for x, y in hams.items():
            assert_equal(prev_fast_len(x, True), y)

    def test_keyword_args(self):
        assert prev_fast_len(11, real=True) == 10
        assert prev_fast_len(target=7, real=False) == 7


@skip_xp_backends(cpu_only=True)
class Test_init_nd_shape_and_axes:

    def test_py_0d_defaults(self, xp):
        x = xp.asarray(4)
        shape = None
        axes = None

        shape_expected = ()
        axes_expected = []

        shape_res, axes_res = _init_nd_shape_and_axes(x, shape, axes)

        assert shape_res == shape_expected
        assert axes_res == axes_expected

    def test_xp_0d_defaults(self, xp):
        x = xp.asarray(7.)
        shape = None
        axes = None

        shape_expected = ()
        axes_expected = []

        shape_res, axes_res = _init_nd_shape_and_axes(x, shape, axes)

        assert shape_res == shape_expected
        assert axes_res == axes_expected

    def test_py_1d_defaults(self, xp):
        x = xp.asarray([1, 2, 3])
        shape = None
        axes = None

        shape_expected = (3,)
        axes_expected = [0]

        shape_res, axes_res = _init_nd_shape_and_axes(x, shape, axes)

        assert shape_res == shape_expected
        assert axes_res == axes_expected

    def test_xp_1d_defaults(self, xp):
        x = xp.arange(0, 1, .1)
        shape = None
        axes = None

        shape_expected = (10,)
        axes_expected = [0]

        shape_res, axes_res = _init_nd_shape_and_axes(x, shape, axes)

        assert shape_res == shape_expected
        assert axes_res == axes_expected

    def test_py_2d_defaults(self, xp):
        x = xp.asarray([[1, 2, 3, 4],
                        [5, 6, 7, 8]])
        shape = None
        axes = None

        shape_expected = (2, 4)
        axes_expected = [0, 1]

        shape_res, axes_res = _init_nd_shape_and_axes(x, shape, axes)

        assert shape_res == shape_expected
        assert axes_res == axes_expected

    def test_xp_2d_defaults(self, xp):
        x = xp.arange(0, 1, .1)
        x = xp.reshape(x, (5, 2))
        shape = None
        axes = None

        shape_expected = (5, 2)
        axes_expected = [0, 1]

        shape_res, axes_res = _init_nd_shape_and_axes(x, shape, axes)

        assert shape_res == shape_expected
        assert axes_res == axes_expected

    def test_xp_5d_defaults(self, xp):
        x = xp.zeros([6, 2, 5, 3, 4])
        shape = None
        axes = None

        shape_expected = (6, 2, 5, 3, 4)
        axes_expected = [0, 1, 2, 3, 4]

        shape_res, axes_res = _init_nd_shape_and_axes(x, shape, axes)

        assert shape_res == shape_expected
        assert axes_res == axes_expected

    def test_xp_5d_set_shape(self, xp):
        x = xp.zeros([6, 2, 5, 3, 4])
        shape = [10, -1, -1, 1, 4]
        axes = None

        shape_expected = (10, 2, 5, 1, 4)
        axes_expected = [0, 1, 2, 3, 4]

        shape_res, axes_res = _init_nd_shape_and_axes(x, shape, axes)

        assert shape_res == shape_expected
        assert axes_res == axes_expected

    def test_xp_5d_set_axes(self, xp):
        x = xp.zeros([6, 2, 5, 3, 4])
        shape = None
        axes = [4, 1, 2]

        shape_expected = (4, 2, 5)
        axes_expected = [4, 1, 2]

        shape_res, axes_res = _init_nd_shape_and_axes(x, shape, axes)

        assert shape_res == shape_expected
        assert axes_res == axes_expected

    def test_xp_5d_set_shape_axes(self, xp):
        x = xp.zeros([6, 2, 5, 3, 4])
        shape = [10, -1, 2]
        axes = [1, 0, 3]

        shape_expected = (10, 6, 2)
        axes_expected = [1, 0, 3]

        shape_res, axes_res = _init_nd_shape_and_axes(x, shape, axes)

        assert shape_res == shape_expected
        assert axes_res == axes_expected

    def test_shape_axes_subset(self, xp):
        x = xp.zeros((2, 3, 4, 5))
        shape, axes = _init_nd_shape_and_axes(x, shape=(5, 5, 5), axes=None)

        assert shape == (5, 5, 5)
        assert axes == [1, 2, 3]

    def test_errors(self, xp):
        x = xp.zeros(1)
        with assert_raises(ValueError, match="axes must be a scalar or "
                           "iterable of integers"):
            _init_nd_shape_and_axes(x, shape=None, axes=[[1, 2], [3, 4]])

        with assert_raises(ValueError, match="axes must be a scalar or "
                           "iterable of integers"):
            _init_nd_shape_and_axes(x, shape=None, axes=[1., 2., 3., 4.])

        with assert_raises(ValueError,
                           match="axes exceeds dimensionality of input"):
            _init_nd_shape_and_axes(x, shape=None, axes=[1])

        with assert_raises(ValueError,
                           match="axes exceeds dimensionality of input"):
            _init_nd_shape_and_axes(x, shape=None, axes=[-2])

        with assert_raises(ValueError,
                           match="all axes must be unique"):
            _init_nd_shape_and_axes(x, shape=None, axes=[0, 0])

        with assert_raises(ValueError, match="shape must be a scalar or "
                           "iterable of integers"):
            _init_nd_shape_and_axes(x, shape=[[1, 2], [3, 4]], axes=None)

        with assert_raises(ValueError, match="shape must be a scalar or "
                           "iterable of integers"):
            _init_nd_shape_and_axes(x, shape=[1., 2., 3., 4.], axes=None)

        with assert_raises(ValueError,
                           match="when given, axes and shape arguments"
                           " have to be of the same length"):
            _init_nd_shape_and_axes(xp.zeros([1, 1, 1, 1]),
                                    shape=[1, 2, 3], axes=[1])

        with assert_raises(ValueError,
                           match="invalid number of data points"
                           r" \(\[0\]\) specified"):
            _init_nd_shape_and_axes(x, shape=[0], axes=None)

        with assert_raises(ValueError,
                           match="invalid number of data points"
                           r" \(\[-2\]\) specified"):
            _init_nd_shape_and_axes(x, shape=-2, axes=None)


class TestFFTShift:

    def test_definition(self, xp):
        x = xp.asarray([0., 1, 2, 3, 4, -4, -3, -2, -1])
        y = xp.asarray([-4., -3, -2, -1, 0, 1, 2, 3, 4])
        xp_assert_close(fft.fftshift(x), y)
        xp_assert_close(fft.ifftshift(y), x)
        x = xp.asarray([0., 1, 2, 3, 4, -5, -4, -3, -2, -1])
        y = xp.asarray([-5., -4, -3, -2, -1, 0, 1, 2, 3, 4])
        xp_assert_close(fft.fftshift(x), y)
        xp_assert_close(fft.ifftshift(y), x)

    def test_inverse(self, xp):
        for n in [1, 4, 9, 100, 211]:
            x = xp.asarray(np.random.random((n,)))
            xp_assert_close(fft.ifftshift(fft.fftshift(x)), x)

    @skip_xp_backends('cupy', reason='cupy/cupy#8393')
    def test_axes_keyword(self, xp):
        freqs = xp.asarray([[0., 1, 2], [3, 4, -4], [-3, -2, -1]])
        shifted = xp.asarray([[-1., -3, -2], [2, 0, 1], [-4, 3, 4]])
        xp_assert_close(fft.fftshift(freqs, axes=(0, 1)), shifted)
        xp_assert_close(fft.fftshift(freqs, axes=0), fft.fftshift(freqs, axes=(0,)))
        xp_assert_close(fft.ifftshift(shifted, axes=(0, 1)), freqs)
        xp_assert_close(fft.ifftshift(shifted, axes=0),
                        fft.ifftshift(shifted, axes=(0,)))
        xp_assert_close(fft.fftshift(freqs), shifted)
        xp_assert_close(fft.ifftshift(shifted), freqs)
    
    @skip_xp_backends('cupy', reason='cupy/cupy#8393')
    def test_uneven_dims(self, xp):
        """ Test 2D input, which has uneven dimension sizes """
        freqs = xp.asarray([
            [0, 1],
            [2, 3],
            [4, 5]
        ], dtype=xp.float64)

        # shift in dimension 0
        shift_dim0 = xp.asarray([
            [4, 5],
            [0, 1],
            [2, 3]
        ], dtype=xp.float64)
        xp_assert_close(fft.fftshift(freqs, axes=0), shift_dim0)
        xp_assert_close(fft.ifftshift(shift_dim0, axes=0), freqs)
        xp_assert_close(fft.fftshift(freqs, axes=(0,)), shift_dim0)
        xp_assert_close(fft.ifftshift(shift_dim0, axes=[0]), freqs)

        # shift in dimension 1
        shift_dim1 = xp.asarray([
            [1, 0],
            [3, 2],
            [5, 4]
        ], dtype=xp.float64)
        xp_assert_close(fft.fftshift(freqs, axes=1), shift_dim1)
        xp_assert_close(fft.ifftshift(shift_dim1, axes=1), freqs)

        # shift in both dimensions
        shift_dim_both = xp.asarray([
            [5, 4],
            [1, 0],
            [3, 2]
        ], dtype=xp.float64)
        xp_assert_close(fft.fftshift(freqs, axes=(0, 1)), shift_dim_both)
        xp_assert_close(fft.ifftshift(shift_dim_both, axes=(0, 1)), freqs)
        xp_assert_close(fft.fftshift(freqs, axes=[0, 1]), shift_dim_both)
        xp_assert_close(fft.ifftshift(shift_dim_both, axes=[0, 1]), freqs)

        # axes=None (default) shift in all dimensions
        xp_assert_close(fft.fftshift(freqs, axes=None), shift_dim_both)
        xp_assert_close(fft.ifftshift(shift_dim_both, axes=None), freqs)
        xp_assert_close(fft.fftshift(freqs), shift_dim_both)
        xp_assert_close(fft.ifftshift(shift_dim_both), freqs)


@skip_xp_backends("cupy",
                  reason="CuPy has not implemented the `device` param")
@skip_xp_backends("jax.numpy",
                  reason="JAX has not implemented the `device` param")
class TestFFTFreq:

    def test_definition(self, xp):
        x = xp.asarray([0, 1, 2, 3, 4, -4, -3, -2, -1], dtype=xp.float64)
        x2 = xp.asarray([0, 1, 2, 3, 4, -5, -4, -3, -2, -1], dtype=xp.float64)

        # default dtype varies across backends

        y = 9 * fft.fftfreq(9, xp=xp)
        xp_assert_close(y, x, check_dtype=False, check_namespace=True)

        y = 9 * xp.pi * fft.fftfreq(9, xp.pi, xp=xp)
        xp_assert_close(y, x, check_dtype=False)

        y = 10 * fft.fftfreq(10, xp=xp)
        xp_assert_close(y, x2, check_dtype=False)

        y = 10 * xp.pi * fft.fftfreq(10, xp.pi, xp=xp)
        xp_assert_close(y, x2, check_dtype=False)

    def test_device(self, xp):
        xp_test = array_namespace(xp.empty(0))
        devices = get_xp_devices(xp)
        for d in devices:
            y = fft.fftfreq(9, xp=xp, device=d)
            x = xp_test.empty(0, device=d)
            assert xp_device(y) == xp_device(x)


@skip_xp_backends("cupy",
                  reason="CuPy has not implemented the `device` param")
@skip_xp_backends("jax.numpy",
                  reason="JAX has not implemented the `device` param")
class TestRFFTFreq:

    def test_definition(self, xp):
        x = xp.asarray([0, 1, 2, 3, 4], dtype=xp.float64)
        x2 = xp.asarray([0, 1, 2, 3, 4, 5], dtype=xp.float64)

        # default dtype varies across backends
        
        y = 9 * fft.rfftfreq(9, xp=xp)
        xp_assert_close(y, x, check_dtype=False, check_namespace=True)

        y = 9 * xp.pi * fft.rfftfreq(9, xp.pi, xp=xp)
        xp_assert_close(y, x, check_dtype=False)

        y = 10 * fft.rfftfreq(10, xp=xp)
        xp_assert_close(y, x2, check_dtype=False)

        y = 10 * xp.pi * fft.rfftfreq(10, xp.pi, xp=xp)
        xp_assert_close(y, x2, check_dtype=False)

    def test_device(self, xp):
        xp_test = array_namespace(xp.empty(0))
        devices = get_xp_devices(xp)
        for d in devices:
            y = fft.rfftfreq(9, xp=xp, device=d)
            x = xp_test.empty(0, device=d)
            assert xp_device(y) == xp_device(x)
