def check_int_a2f(in_type, out_type):
    # Check that array to / from file returns roughly the same as input
    big_floater = np.maximum_sctype(np.float)
    info = type_info(in_type)
    this_min, this_max = info['min'], info['max']
    if not in_type in np.sctypes['complex']:
        data = np.array([this_min, this_max], in_type)
    else: # Funny behavior with complex256
        data = np.zeros((2,), in_type)
        data[0] = this_min + 0j
        data[1] = this_max + 0j
    str_io = BytesIO()
    try:
        scale, inter, mn, mx = calculate_scale(data, out_type, True)
    except ValueError:
        if DEBUG:
            print in_type, out_type, sys.exc_info()[1]
        return
    array_to_file(data, str_io, out_type, 0, inter, scale, mn, mx)
    data_back = array_from_file(data.shape, out_type, str_io)
    data_back = apply_read_scaling(data_back, scale, inter)
    assert_true(np.allclose(big_floater(data), big_floater(data_back)))
    # Try with analyze-size scale and inter
    scale32 = np.float32(scale)
    inter32 = np.float32(inter)
    if scale32 == np.inf or inter32 == np.inf:
        return
    data_back = array_from_file(data.shape, out_type, str_io)
    data_back = apply_read_scaling(data_back, scale32, inter32)
    # Clip at extremes to remove inf
    info = type_info(in_type)
    out_min, out_max = info['min'], info['max']
    assert_true(np.allclose(big_floater(data),
                            big_floater(np.clip(data_back, out_min, out_max))))

def test_scale_min_max():
    mx_dt = np.maximum_sctype(np.float)
    for tp in np.sctypes['uint'] + np.sctypes['int']:
        info = np.iinfo(tp)
        # Need to pump up to max fp type to contain python longs
        imin = np.array(info.min, dtype=mx_dt)
        imax = np.array(info.max, dtype=mx_dt)
        value_pairs = (
            (0, imax),
            (imin, 0),
            (imin, imax),
            (1, 10),
            (-1, -1),
            (1, 1),
            (-10, -1),
            (-100, 10))
        for mn, mx in value_pairs:
            # with intercept
            scale, inter = scale_min_max(mn, mx, tp, True)
            if mx - mn:
                assert_array_almost_equal, (mx - inter) / scale, imax
                assert_array_almost_equal, (mn - inter) / scale, imin
            else:
                assert_equal, (scale, inter), (1.0, mn)
            # without intercept
            if imin == 0 and mn < 0 and mx > 0:
                (assert_raises, ValueError,
                 scale_min_max, mn, mx, tp, False)
                continue
            scale, inter = scale_min_max(mn, mx, tp, False)
            assert_equal, inter, 0.0
            if mn == 0 and mx == 0:
                assert_equal, scale, 1.0
                continue
            sc_mn = mn / scale
            sc_mx = mx / scale
            assert_true, sc_mn >= imin
            assert_true, sc_mx <= imax
            if imin == 0:
                if mx > 0:  # numbers all +ve
                    assert_array_almost_equal, mx / scale, imax
                else:  # numbers all -ve
                    assert_array_almost_equal, mn / scale, imax
                continue
            if abs(mx) >= abs(mn):
                assert_array_almost_equal, mx / scale, imax
            else:
                assert_array_almost_equal, mn / scale, imin

real (scalar) part, and ``x, y, z`` are the complex (vector) part.

Note - rotation matrices here apply to column vectors, that is,
they are applied on the left of the vector.  For example:

>>> import numpy as np
>>> q = [0, 1, 0, 0] # 180 degree rotation around axis 0
>>> M = quat2mat(q) # from this module
>>> vec = np.array([1, 2, 3]).reshape((3,1)) # column vector
>>> tvec = np.dot(M, vec)
'''

import math
import numpy as np

MAX_FLOAT = np.maximum_sctype(np.float)
FLOAT_EPS = np.finfo(np.float).eps


def fillpositive(xyz, w2_thresh=None):
    ''' Compute unit quaternion from last 3 values

    Parameters
    ----------
    xyz : iterable
       iterable containing 3 values, corresponding to quaternion x, y, z
    w2_thresh : None or float, optional
       threshold to determine if w squared is really negative.
       If None (default) then w2_thresh set equal to
       ``-np.finfo(xyz.dtype).eps``, if possible, otherwise
       ``-np.finfo(np.float).eps``

 def test_other(self, t):
     assert_equal(np.maximum_sctype(t), t)

 def test_complex(self, t):
     assert_equal(np.maximum_sctype(t), np.sctypes['complex'][-1])

 def test_float(self, t):
     assert_equal(np.maximum_sctype(t), np.sctypes['float'][-1])

 def test_uint(self, t):
     assert_equal(np.maximum_sctype(t), np.sctypes['uint'][-1])

def scale_min_max(mn, mx, out_type, allow_intercept):
    ''' Return scaling and intercept min, max of data, given output type

    Returns ``scalefactor`` and ``intercept`` to best fit data with
    given ``mn`` and ``mx`` min and max values into range of data type
    with ``type_min`` and ``type_max`` min and max values for type.

    The calculated scaling is therefore::

        scaled_data = (data-intercept) / scalefactor

    Parameters
    ----------
    mn : scalar
       data minimum value
    mx : scalar
       data maximum value
    out_type : numpy type
       numpy type of output
    allow_intercept : bool
       If true, allow calculation of non-zero intercept.  Otherwise,
       returned intercept is always 0.0

    Returns
    -------
    scalefactor : numpy scalar, dtype=np.maximum_sctype(np.float)
       scalefactor by which to divide data after subtracting intercept
    intercept : numpy scalar, dtype=np.maximum_sctype(np.float)
       value to subtract from data before dividing by scalefactor

    Examples
    --------
    >>> scale_min_max(0, 255, np.uint8, False)
    (1.0, 0.0)
    >>> scale_min_max(-128, 127, np.int8, False)
    (1.0, 0.0)
    >>> scale_min_max(0, 127, np.int8, False)
    (1.0, 0.0)
    >>> scaling, intercept = scale_min_max(0, 127, np.int8,  True)
    >>> np.allclose((0 - intercept) / scaling, -128)
    True
    >>> np.allclose((127 - intercept) / scaling, 127)
    True
    >>> scaling, intercept = scale_min_max(-10, -1, np.int8, True)
    >>> np.allclose((-10 - intercept) / scaling, -128)
    True
    >>> np.allclose((-1 - intercept) / scaling, 127)
    True
    >>> scaling, intercept = scale_min_max(1, 10, np.int8, True)
    >>> np.allclose((1 - intercept) / scaling, -128)
    True
    >>> np.allclose((10 - intercept) / scaling, 127)
    True

    Notes
    -----
    We don't use this function anywhere in nibabel now, it's here for API
    compatibility only.

    The large integers lead to python long types as max / min for type.
    To contain the rounding error, we need to use the maximum numpy
    float types when casting to float.
    '''
    if mn > mx:
        raise ValueError('min value > max value')
    info = type_info(out_type)
    mn, mx, type_min, type_max = np.array(
        [mn, mx, info['min'], info['max']], np.maximum_sctype(np.float))
    # with intercept
    if allow_intercept:
        data_range = mx-mn
        if data_range == 0:
            return 1.0, mn
        type_range = type_max - type_min
        scaling = data_range / type_range
        intercept = mn - type_min * scaling
        return scaling, intercept
    # without intercept
    if mx == 0 and mn == 0:
        return 1.0, 0.0
    if type_min == 0: # uint
        if mn < 0 and mx > 0:
            raise ValueError('Cannot scale negative and positive '
                             'numbers to uint without intercept')
        if mx < 0:
            scaling = mn / type_max
        else:
            scaling = mx / type_max
    else: # int
        if abs(mx) >= abs(mn):
            scaling = mx / type_max
        else:
            scaling = mn / type_min
    return scaling, 0.0

#          and string comma- (or '+') separated lists of bit flags).
#       5. Added 'is_bit_flag()' function to check if an integer number has
#          only one bit set (i.e., that it is a power of 2).
# 1.1.0 (29-January-2018) - Multiple enhancements:
#       1. Added support for long type in Python 2.7 in
#          `interpret_bit_flags()` and `bitfield_to_boolean_mask()`.
#       2. `interpret_bit_flags()` now always returns `int` (or `int` or `long`
#           in Python 2.7). Previously when input was of integer-like type
#           (i.e., `numpy.uint64`), it was not converted to Python `int`.
#       3. `bitfield_to_boolean_mask()` will no longer crash when
#          `ignore_flags` argument contains bit flags beyond what the type of
#          the argument `bitfield` can hold.
# 1.1.1 (30-January-2018) - Improved filtering of high bits in flags.
#
INT_TYPE = (int, long,) if sys.version_info < (3,) else (int,)
MAX_UINT_TYPE = np.maximum_sctype(np.uint)
SUPPORTED_FLAGS = int(np.bitwise_not(
    0, dtype=MAX_UINT_TYPE, casting='unsafe'
))


def is_bit_flag(n):
    """
    Verifies if the input number is a bit flag (i.e., an integer number that is
    an integer power of 2).

    Parameters
    ----------
    n : int
        A positive integer number. Non-positive integers are considered not to
        be "flags".