Merge pull request #70 from matthew-brett/floating-stash

Floating point casting machinery

Routines for robust casting of floating point to integer, checking for overflow.

Author: matthew-brett

nibabel/casting.py

@@ -0,0 +1,352 @@
+""" Utilties for casting floats to integers
+"""
+
+import numpy as np
+
+
+class CastingError(Exception):
+    pass
+
+
+def float_to_int(arr, int_type, nan2zero=True, infmax=False):
+    """ Convert floating point array `arr` to type `int_type`
+
+    * Rounds numbers to nearest integer
+    * Clips values to prevent overflows when casting
+    * Converts NaN to 0 (for `nan2zero`==True
+
+    Casting floats to integers is delicate because the result is undefined
+    and platform specific for float values outside the range of `int_type`.
+    Define ``shared_min`` to be the minimum value that can be exactly
+    represented in both the float type of `arr` and `int_type`. Define
+    `shared_max` to be the equivalent maximum value.  To avoid undefined results
+    we threshold `arr` at ``shared_min`` and ``shared_max``.
+
+    Parameters
+    ----------
+    arr : array-like
+        Array of floating point type
+    int_type : object
+        Numpy integer type
+    nan2zero : {True, False}
+        Whether to convert NaN value to zero.  Default is True.  If False, and
+        NaNs are present, raise CastingError
+    infmax : {False, True}
+        If True, set np.inf values in `arr` to be `int_type` integer maximum
+        value, -np.inf as `int_type` integer minimum.  If False, set +/- infs to
+        be ``shared_min``, ``shared_max`` as defined above.  Therefore False
+        gives faster conversion at the expense of infs that are further from
+        infinity.
+
+    Returns
+    -------
+    iarr : ndarray
+        of type `int_type`
+
+    Examples
+    --------
+    >>> float_to_int([np.nan, np.inf, -np.inf, 1.1, 6.6], np.int16)
+    array([     0,  32767, -32768,      1,      7], dtype=int16)
+
+    Notes
+    -----
+    Numpy relies on the C library to cast from float to int using the standard
+    ``astype`` method of the array.
+
+    Quoting from section F4 of the C99 standard:
+
+        If the floating value is infinite or NaN or if the integral part of the
+        floating value exceeds the range of the integer type, then the
+        "invalid" floating-point exception is raised and the resulting value
+        is unspecified.
+
+    Hence we threshold at ``shared_min`` and ``shared_max`` to avoid casting to
+    values that are undefined.
+
+    See: http://en.wikipedia.org/wiki/C99 . There are links to the C99 standard
+    from that page.
+    """
+    arr = np.asarray(arr)
+    flt_type = arr.dtype.type
+    int_type = np.dtype(int_type).type
+    # Deal with scalar as input; fancy indexing needs 1D
+    shape = arr.shape
+    arr = np.atleast_1d(arr)
+    mn, mx = _cached_int_clippers(flt_type, int_type)
+    nans = np.isnan(arr)
+    have_nans = np.any(nans)
+    if not nan2zero and have_nans:
+        raise CastingError('NaNs in array, nan2zero not True')
+    iarr = np.clip(np.rint(arr), mn, mx).astype(int_type)
+    if have_nans:
+        iarr[nans] = 0
+    if not infmax:
+        return iarr.reshape(shape)
+    ii = np.iinfo(int_type)
+    iarr[arr == np.inf] = ii.max
+    if ii.min != int(mn):
+        iarr[arr == -np.inf] = ii.min
+    return iarr.reshape(shape)
+
+
+def int_clippers(flt_type, int_type):
+    """ Min and max in float type that are >=min, <=max in integer type
+
+    This is not as easy as it sounds, because the float type may not be able to
+    exactly represent the max or min integer values, so we have to find the next
+    exactly representable floating point value to do the thresholding.
+
+    Parameters
+    ----------
+    flt_type : object
+        numpy floating point type
+    int_type : object
+        numpy integer type
+
+    Returns
+    -------
+    mn : object
+        Number of type `flt_type` that is the minumum value in the range of
+        `int_type`, such that ``mn.astype(int_type)`` >= min of `int_type`
+    mx : object
+        Number of type `flt_type` that is the maximum value in the range of
+        `int_type`, such that ``mx.astype(int_type)`` <= max of `int_type`
+    """
+    ii = np.iinfo(int_type)
+    return floor_exact(ii.min, flt_type), floor_exact(ii.max, flt_type)
+
+
+# Cache clip values
+FLT_INT_CLIPS = {}
+
+def _cached_int_clippers(flt_type, int_type):
+    if not (flt_type, int_type) in FLT_INT_CLIPS:
+        FLT_INT_CLIPS[flt_type, int_type] = int_clippers(flt_type, int_type)
+    return FLT_INT_CLIPS[(flt_type, int_type)]
+
+# ---------------------------------------------------------------------------
+# Routines to work out the next lowest representable intger in floating point
+# types.
+# ---------------------------------------------------------------------------
+
+try:
+    _float16 = np.float16
+except AttributeError: # float16 not present in np < 1.6
+    _float16 = None
+
+# The number of significand digits in IEEE floating point formats, not including
+# the implicit leading 0.  See http://en.wikipedia.org/wiki/IEEE_754-2008
+_flt_nmant = {
+    _float16: 10,
+    np.float32: 23,
+    np.float64: 52,
+    }
+
+
+class FloatingError(Exception):
+    pass
+
+
+def flt2nmant(flt_type):
+    """ Number of significand bits in float type `flt_type`
+
+    Parameters
+    ----------
+    flt_type : object
+        Numpy floating point type, such as np.float32
+
+    Returns
+    -------
+    nmant : int
+        Number of digits in the signficand
+    """
+    try:
+        return _flt_nmant[flt_type]
+    except KeyError:
+        pass
+    nmant = np.finfo(flt_type).nmant
+    # Assuming the np.float type is always IEEE 64 bit
+    if flt_type is np.float and nmant == 52:
+        return 52
+    # Now we should be testing long doubles
+    assert flt_type is np.longdouble
+    if nmant == 63: # 80-bit intel type
+        return 63 # Not including explicit first digit
+    raise FloatingError('Cannot be confident of nmant value for %s' % flt_type)
+
+
+def as_int(x, check=True):
+    """ Return python integer representation of number
+
+    This is useful because the numpy int(val) mechanism is broken for large
+    values in np.longdouble.
+
+    This routine will still break for values that are outside the range of
+    float64.
+
+    Parameters
+    ----------
+    x : object
+        Floating point value
+    check : {True, False}
+        If True, raise error for values that are not integers
+
+    Returns
+    -------
+    i : int
+        Python integer
+
+    Examples
+    --------
+    >>> as_int(2.0)
+    2
+    >>> as_int(-2.0)
+    -2
+    >>> as_int(2.1)
+    Traceback (most recent call last):
+        ...
+    FloatingError: Not an integer: 2.1
+    >>> as_int(2.1, check=False)
+    2
+    """
+    ix = int(x)
+    if ix == x:
+        return ix
+    fx = np.floor(x)
+    if check and fx != x:
+        raise FloatingError('Not an integer: %s' % x)
+    f64 = np.float64(fx)
+    i64 = int(f64)
+    assert f64 == i64
+    res = fx - f64
+    return ix + int(res)
+
+
+def int_to_float(val, flt_type):
+    """ Convert integer `val` to floating point type `flt_type`
+
+    Useful because casting to ``np.longdouble`` loses precision as it appears to
+    go through casting to np.float64.
+
+    Parameters
+    ----------
+    val : int
+        Integer value
+    flt_type : object
+        numpy floating point type
+
+    Returns
+    -------
+    f : numpy scalar
+        of type `flt_type`
+    """
+    if not flt_type is np.longdouble:
+        return flt_type(val)
+    f64 = np.float64(val)
+    res = val - int(f64)
+    return np.longdouble(f64) + np.longdouble(res)
+
+
+def floor_exact(val, flt_type):
+    """ Get nearest exact integer to `val`, towards 0, in float type `flt_type`
+
+    Parameters
+    ----------
+    val : int
+        We have to pass val as an int rather than the floating point type
+        because large integers cast as floating point may be rounded by the
+        casting process.
+    flt_type : numpy type
+        numpy float type.  Only IEEE types supported (np.float16, np.float32,
+        np.float64)
+
+    Returns
+    -------
+    floor_val : object
+        value of same floating point type as `val`, that is the next excat
+        integer in this type, towards zero, or == `val` if val is exactly
+        representable.
+
+    Examples
+    --------
+    Obviously 2 is within the range of representable integers for float32
+
+    >>> floor_exact(2, np.float32)
+    2.0
+
+    As is 2**24-1 (the number of significand digits is 23 + 1 implicit)
+
+    >>> floor_exact(2**24-1, np.float32) == 2**24-1
+    True
+
+    But 2**24+1 gives a number that float32 can't represent exactly
+
+    >>> floor_exact(2**24+1, np.float32) == 2**24
+    True
+    """
+    val = int(val)
+    flt_type = np.dtype(flt_type).type
+    sign = val > 0 and 1 or -1
+    aval = abs(val)
+    if flt_type is np.longdouble:
+        # longdouble seems to go through casting to float64, so getting the
+        # value into float128 with the given precision needs to go through two
+        # steps, first float64, then adding the remainder.
+        f64 = floor_exact(aval, np.float64)
+        i64 = int(f64)
+        assert f64 == i64
+        res = aval - i64
+        try:
+            faval = flt_type(i64) + flt_type(res)
+        except OverflowError:
+            faval = np.inf
+        if faval == np.inf:
+            return sign * np.finfo(flt_type).max
+        if (faval - f64) <= res:
+            # Float casting has made the value go down or stay the same
+            return sign * faval
+    else: # Normal case
+        try:
+            faval = flt_type(aval)
+        except OverflowError:
+            faval = np.inf
+        if faval == np.inf:
+            return sign * np.finfo(flt_type).max
+        if int(faval) <= aval:
+            # Float casting has made the value go down or stay the same
+            return sign * faval
+    # Float casting made the value go up
+    nmant = flt2nmant(flt_type)
+    biggest_gap = 2**(floor_log2(aval) - nmant)
+    assert biggest_gap > 1
+    faval -= flt_type(biggest_gap)
+    return sign * faval
+
+
+def floor_log2(x):
+    """ floor of log2 of abs(`x`)
+
+    Embarrassingly, from http://en.wikipedia.org/wiki/Binary_logarithm
+
+    Parameters
+    ----------
+    x : int
+
+    Returns
+    -------
+    L : int
+        floor of base 2 log of `x`
+
+    Examples
+    --------
+    >>> floor_log2(2**9+1)
+    9
+    >>> floor_log2(-2**9+1)
+    8
+    """
+    ip = 0
+    rem = abs(x)
+    while rem>=2:
+        ip += 1
+        rem /= 2
+    return ip