casting

Utilties for casting numpy values in various ways

Most routines work round some numpy oddities in floating point precision and casting. Others work round numpy casting to and from python ints

CastingError

FloatingError

able_int_type(values)

Find the smallest integer numpy type to contain sequence values

as_int(x[, check])

Return python integer representation of number

best_float()

Floating point type with best precision

ceil_exact(val, flt_type)

Return nearest exact integer >= val in float type flt_type

float_to_int(arr, int_type[, nan2zero, infmax])

Convert floating point array arr to type int_type

floor_exact(val, flt_type)

Return nearest exact integer <= val in float type flt_type

floor_log2(x)

floor of log2 of abs(x)

have_binary128()

True if we have a binary128 IEEE longdouble

int_abs(arr)

Absolute values of array taking care of max negative int values

int_to_float(val, flt_type)

Convert integer val to floating point type flt_type

longdouble_lte_float64()

Return True if longdouble appears to have the same precision as float64

longdouble_precision_improved()

True if longdouble precision increased since initial import

ok_floats()

Return floating point types sorted by precision

on_powerpc()

True if we are running on a Power PC platform

shared_range(flt_type, int_type)

Min and max in float type that are >=min, <=max in integer type

type_info(np_type)

Return dict with min, max, nexp, nmant, width for numpy type np_type

ulp([val])

Return gap between val and nearest representable number of same type

CastingError

class nibabel.casting.CastingError

Bases: Exception

__init__($self, /, *args, **kwargs)

Initialize self. See help(type(self)) for accurate signature.

FloatingError

class nibabel.casting.FloatingError

Bases: Exception

__init__($self, /, *args, **kwargs)

Initialize self. See help(type(self)) for accurate signature.

able_int_type

nibabel.casting.able_int_type(values)

Find the smallest integer numpy type to contain sequence values

Prefers uint to int if minimum is >= 0

Parameters
valuessequence

sequence of integer values

Returns
itypeNone or numpy type

numpy integer type or None if no integer type holds all values

Examples

>>> able_int_type([0, 1]) == np.uint8
True
>>> able_int_type([-1, 1]) == np.int8
True

as_int

nibabel.casting.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.

It is also useful to work around a numpy 1.4.1 bug in conversion of uints to python ints.

This routine will still raise an OverflowError for values that are outside the range of float64.

Parameters
xobject

integer, unsigned integer or floating point value

check{True, False}

If True, raise error for values that are not integers

Returns
iint

Python integer

Examples

>>> as_int(2.0)
2
>>> as_int(-2.0)
-2
>>> as_int(2.1) #doctest: +IGNORE_EXCEPTION_DETAIL
Traceback (most recent call last):
    ...
FloatingError: Not an integer: 2.1
>>> as_int(2.1, check=False)
2

best_float

nibabel.casting.best_float()

Floating point type with best precision

This is nearly always np.longdouble, except on Windows, where np.longdouble is Intel80 storage, but with float64 precision for calculations. In that case we return float64 on the basis it’s the fastest and smallest at the highest precision.

SPARC float128 also proved so slow that we prefer float64.

Returns
best_typenumpy type

floating point type with highest precision

Notes

Needs to run without error for module import, because it is called in ok_floats below, and therefore in setting module global OK_FLOATS.

ceil_exact

nibabel.casting.ceil_exact(val, flt_type)

Return nearest exact integer >= val in float type flt_type

Parameters
valint

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_typenumpy type

numpy float type.

Returns
ceil_valobject

value of same floating point type as val, that is the nearest exact integer in this type such that floor_val >= val. Thus if val is exact in flt_type, ceil_val == val.

Examples

Obviously 2 is within the range of representable integers for float32

>>> ceil_exact(2, np.float32)
2.0

As is 2**24-1 (the number of significand digits is 23 + 1 implicit)

>>> ceil_exact(2**24-1, np.float32) == 2**24-1
True

But 2**24+1 gives a number that float32 can’t represent exactly

>>> ceil_exact(2**24+1, np.float32) == 2**24+2
True

As for the numpy ceil function, negatives ceil towards inf

>>> ceil_exact(-2**24-1, np.float32) == -2**24
True

float_to_int

nibabel.casting.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
arrarray-like

Array of floating point type

int_typeobject

Numpy integer type

nan2zero{True, False, None}

Whether to convert NaN value to zero. Default is True. If False, and NaNs are present, raise CastingError. If None, do not check for NaN values and pass through directly to the astype casting mechanism. In this last case, the resulting value is undefined.

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
iarrndarray

of type int_type

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: https://en.wikipedia.org/wiki/C99 . There are links to the C99 standard from that page.

Examples

>>> float_to_int([np.nan, np.inf, -np.inf, 1.1, 6.6], np.int16)
array([     0,  32767, -32768,      1,      7], dtype=int16)

floor_exact

nibabel.casting.floor_exact(val, flt_type)

Return nearest exact integer <= val in float type flt_type

Parameters
valint

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_typenumpy type

numpy float type.

Returns
floor_valobject

value of same floating point type as val, that is the nearest exact integer in this type such that floor_val <= val. Thus if val is exact in flt_type, floor_val == val.

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

As for the numpy floor function, negatives floor towards -inf

>>> floor_exact(-2**24-1, np.float32) == -2**24-2
True

floor_log2

nibabel.casting.floor_log2(x)

floor of log2 of abs(x)

Embarrassingly, from https://en.wikipedia.org/wiki/Binary_logarithm

Parameters
xint
Returns
LNone or int

floor of base 2 log of x. None if x == 0.

Examples

>>> floor_log2(2**9+1)
9
>>> floor_log2(-2**9+1)
8
>>> floor_log2(0.5)
-1
>>> floor_log2(0) is None
True

have_binary128

nibabel.casting.have_binary128()

True if we have a binary128 IEEE longdouble

int_abs

nibabel.casting.int_abs(arr)

Absolute values of array taking care of max negative int values

Parameters
arrarray-like
Returns
abs_arrarray

array the same shape as arr in which all negative numbers have been changed to positive numbers with the magnitude.

Examples

This kind of thing is confusing in base numpy:

>>> import numpy as np
>>> np.abs(np.int8(-128))
-128

int_abs fixes that:

>>> int_abs(np.int8(-128))
128
>>> int_abs(np.array([-128, 127], dtype=np.int8))
array([128, 127], dtype=uint8)
>>> int_abs(np.array([-128, 127], dtype=np.float32))
array([ 128.,  127.], dtype=float32)

int_to_float

nibabel.casting.int_to_float(val, flt_type)

Convert integer val to floating point type flt_type

Why is this so complicated?

At least in numpy <= 1.6.1, numpy longdoubles do not correctly convert to ints, and ints do not correctly convert to longdoubles. Specifically, in both cases, the values seem to go through float64 conversion on the way, so to convert better, we need to split into float64s and sum up the result.

Parameters
valint

Integer value

flt_typeobject

numpy floating point type

Returns
fnumpy scalar

of type flt_type

longdouble_lte_float64

nibabel.casting.longdouble_lte_float64()

Return True if longdouble appears to have the same precision as float64

longdouble_precision_improved

nibabel.casting.longdouble_precision_improved()

True if longdouble precision increased since initial import

This can happen on Windows compiled with MSVC. It may be because libraries compiled with mingw (longdouble is Intel80) get linked to numpy compiled with MSVC (longdouble is Float64)

ok_floats

nibabel.casting.ok_floats()

Return floating point types sorted by precision

Remove longdouble if it has no higher precision than float64

on_powerpc

nibabel.casting.on_powerpc()

True if we are running on a Power PC platform

Has to deal with older Macs and IBM POWER7 series among others

shared_range

nibabel.casting.shared_range(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_typedtype specifier

A dtype specifier referring to a numpy floating point type. For example, f4, np.dtype('f4'), np.float32 are equivalent.

int_typedtype specifier

A dtype specifier referring to a numpy integer type. For example, i4, np.dtype('i4'), np.int32 are equivalent

Returns
mnobject

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

mxobject

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

Examples

>>> shared_range(np.float32, np.int32) == (-2147483648.0, 2147483520.0)
True
>>> shared_range('f4', 'i4') == (-2147483648.0, 2147483520.0)
True

type_info

nibabel.casting.type_info(np_type)

Return dict with min, max, nexp, nmant, width for numpy type np_type

Type can be integer in which case nexp and nmant are None.

Parameters
np_typenumpy type specifier

Any specifier for a numpy dtype

Returns
infodict

with fields min (minimum value), max (maximum value), nexp (exponent width), nmant (significand precision not including implicit first digit), minexp (minimum exponent), maxexp (maximum exponent), width (width in bytes). (nexp, nmant, minexp, maxexp) are None for integer types. Both min and max are of type np_type.

Raises
FloatingError

for floating point types we don’t recognize

Notes

You might be thinking that np.finfo does this job, and it does, except for PPC long doubles (https://github.com/numpy/numpy/issues/2669) and float96 on Windows compiled with Mingw. This routine protects against such errors in np.finfo by only accepting values that we know are likely to be correct.

ulp

nibabel.casting.ulp(val=1.0)

Return gap between val and nearest representable number of same type

This is the value of a unit in the last place (ULP), and is similar in meaning to the MATLAB eps function.

Parameters
valscalar, optional

scalar value of any numpy type. Default is 1.0 (float64)

Returns
ulp_valscalar

gap between val and nearest representable number of same type

Notes

The wikipedia article on machine epsilon points out that the term epsilon can be used in the sense of a unit in the last place (ULP), or as the maximum relative rounding error. The MATLAB eps function uses the ULP meaning, but this function is ulp rather than eps to avoid confusion between different meanings of eps.