"""Machine limits for Float32 and Float64 and (long double) if available...
"""
from __future__ import division, absolute_import, print_function
__all__ = ['finfo', 'iinfo']
import warnings
from .machar import MachAr
from . import numeric
from . import numerictypes as ntypes
from .numeric import array, inf
from .umath import log10, exp2
from . import umath
def _fr0(a):
"""fix rank-0 --> rank-1"""
if a.ndim == 0:
a = a.copy()
a.shape = (1,)
return a
def _fr1(a):
"""fix rank > 0 --> rank-0"""
if a.size == 1:
a = a.copy()
a.shape = ()
return a
_convert_to_float = {
ntypes.csingle: ntypes.single,
ntypes.complex_: ntypes.float_,
ntypes.clongfloat: ntypes.longfloat
}
# Parameters for creating MachAr / MachAr-like objects
_title_fmt = 'numpy {} precision floating point number'
_MACHAR_PARAMS = {
ntypes.double: dict(
itype = ntypes.int64,
fmt = '%24.16e',
title = _title_fmt.format('double')),
ntypes.single: dict(
itype = ntypes.int32,
fmt = '%15.7e',
title = _title_fmt.format('single')),
ntypes.longdouble: dict(
itype = ntypes.longlong,
fmt = '%s',
title = _title_fmt.format('long double')),
ntypes.half: dict(
itype = ntypes.int16,
fmt = '%12.5e',
title = _title_fmt.format('half'))}
class MachArLike(object):
""" Object to simulate MachAr instance """
def __init__(self,
ftype,
**kwargs):
params = _MACHAR_PARAMS[ftype]
float_conv = lambda v: array([v], ftype)
float_to_float = lambda v : _fr1(float_conv(v))
self._float_to_str = lambda v: (params['fmt'] %
array(_fr0(v)[0], ftype))
self.title = params['title']
# Parameter types same as for discovered MachAr object.
self.epsilon = self.eps = float_to_float(kwargs.pop('eps'))
self.epsneg = float_to_float(kwargs.pop('epsneg'))
self.xmax = self.huge = float_to_float(kwargs.pop('huge'))
self.xmin = self.tiny = float_to_float(kwargs.pop('tiny'))
self.ibeta = params['itype'](kwargs.pop('ibeta'))
self.__dict__.update(kwargs)
self.precision = int(-log10(self.eps))
self.resolution = float_to_float(float_conv(10) ** (-self.precision))
# Properties below to delay need for float_to_str, and thus avoid circular
# imports during early numpy module loading.
# See: https://github.com/numpy/numpy/pull/8983#discussion_r115838683
@property
def _str_eps(self):
return self._float_to_str(self.eps)
@property
def _str_epsneg(self):
return self._float_to_str(self.epsneg)
@property
def _str_xmin(self):
return self._float_to_str(self.xmin)
@property
def _str_xmax(self):
return self._float_to_str(self.xmax)
@property
def _str_resolution(self):
return self._float_to_str(self.resolution)
# Known parameters for float16
# See docstring of MachAr class for description of parameters.
_f16 = ntypes.float16
_float16_ma = MachArLike(_f16,
machep=-10,
negep=-11,
minexp=-14,
maxexp=16,
it=10,
iexp=5,
ibeta=2,
irnd=5,
ngrd=0,
eps=exp2(_f16(-10)),
epsneg=exp2(_f16(-11)),
huge=_f16(65504),
tiny=_f16(2 ** -14))
# Known parameters for float32
_f32 = ntypes.float32
_float32_ma = MachArLike(_f32,
machep=-23,
negep=-24,
minexp=-126,
maxexp=128,
it=23,
iexp=8,
ibeta=2,
irnd=5,
ngrd=0,
eps=exp2(_f32(-23)),
epsneg=exp2(_f32(-24)),
huge=_f32((1 - 2 ** -24) * 2**128),
tiny=exp2(_f32(-126)))
# Known parameters for float64
_f64 = ntypes.float64
_epsneg_f64 = 2.0 ** -53.0
_tiny_f64 = 2.0 ** -1022.0
_float64_ma = MachArLike(_f64,
machep=-52,
negep=-53,
minexp=-1022,
maxexp=1024,
it=52,
iexp=11,
ibeta=2,
irnd=5,
ngrd=0,
eps=2.0 ** -52.0,
epsneg=_epsneg_f64,
huge=(1.0 - _epsneg_f64) / _tiny_f64 * _f64(4),
tiny=_tiny_f64)
# Known parameters for IEEE 754 128-bit binary float
_ld = ntypes.longdouble
_epsneg_f128 = exp2(_ld(-113))
_tiny_f128 = exp2(_ld(-16382))
# Ignore runtime error when this is not f128
with numeric.errstate(all='ignore'):
_huge_f128 = (_ld(1) - _epsneg_f128) / _tiny_f128 * _ld(4)
_float128_ma = MachArLike(_ld,
machep=-112,
negep=-113,
minexp=-16382,
maxexp=16384,
it=112,
iexp=15,
ibeta=2,
irnd=5,
ngrd=0,
eps=exp2(_ld(-112)),
epsneg=_epsneg_f128,
huge=_huge_f128,
tiny=_tiny_f128)
# Known parameters for float80 (Intel 80-bit extended precision)
_epsneg_f80 = exp2(_ld(-64))
_tiny_f80 = exp2(_ld(-16382))
# Ignore runtime error when this is not f80
with numeric.errstate(all='ignore'):
_huge_f80 = (_ld(1) - _epsneg_f80) / _tiny_f80 * _ld(4)
_float80_ma = MachArLike(_ld,
machep=-63,
negep=-64,
minexp=-16382,
maxexp=16384,
it=63,
iexp=15,
ibeta=2,
irnd=5,
ngrd=0,
eps=exp2(_ld(-63)),
epsneg=_epsneg_f80,
huge=_huge_f80,
tiny=_tiny_f80)
# Guessed / known parameters for double double; see:
# https://en.wikipedia.org/wiki/Quadruple-precision_floating-point_format#Double-double_arithmetic
# These numbers have the same exponent range as float64, but extended number of
# digits in the significand.
_huge_dd = (umath.nextafter(_ld(inf), _ld(0))
if hasattr(umath, 'nextafter') # Missing on some platforms?
else _float64_ma.huge)
_float_dd_ma = MachArLike(_ld,
machep=-105,
negep=-106,
minexp=-1022,
maxexp=1024,
it=105,
iexp=11,
ibeta=2,
irnd=5,
ngrd=0,
eps=exp2(_ld(-105)),
epsneg= exp2(_ld(-106)),
huge=_huge_dd,
tiny=exp2(_ld(-1022)))
# Key to identify the floating point type. Key is result of
# ftype('-0.1').newbyteorder('<').tobytes()
# See:
# https://perl5.git.perl.org/perl.git/blob/3118d7d684b56cbeb702af874f4326683c45f045:/Configure
_KNOWN_TYPES = {
b'\x9a\x99\x99\x99\x99\x99\xb9\xbf' : _float64_ma,
b'\xcd\xcc\xcc\xbd' : _float32_ma,
b'f\xae' : _float16_ma,
# float80, first 10 bytes containing actual storage
b'\xcd\xcc\xcc\xcc\xcc\xcc\xcc\xcc\xfb\xbf' : _float80_ma,
# double double; low, high order (e.g. PPC 64)
b'\x9a\x99\x99\x99\x99\x99Y<\x9a\x99\x99\x99\x99\x99\xb9\xbf' :
_float_dd_ma,
# double double; high, low order (e.g. PPC 64 le)
b'\x9a\x99\x99\x99\x99\x99\xb9\xbf\x9a\x99\x99\x99\x99\x99Y<' :
_float_dd_ma,
# IEEE 754 128-bit binary float
b'\x9a\x99\x99\x99\x99\x99\x99\x99\x99\x99\x99\x99\x99\x99\xfb\xbf' :
_float128_ma,
}
def _get_machar(ftype):
""" Get MachAr instance or MachAr-like instance
Get parameters for floating point type, by first trying signatures of
various known floating point types, then, if none match, attempting to
identify parameters by analysis.
Parameters
----------
ftype : class
Numpy floating point type class (e.g. ``np.float64``)
Returns
-------
ma_like : instance of :class:`MachAr` or :class:`MachArLike`
Object giving floating point parameters for `ftype`.
Warns
-----
UserWarning
If the binary signature of the float type is not in the dictionary of
known float types.
"""
params = _MACHAR_PARAMS.get(ftype)
if params is None:
raise ValueError(repr(ftype))
# Detect known / suspected types
key = ftype('-0.1').newbyteorder('<').tobytes()
ma_like = _KNOWN_TYPES.get(key)
# Could be 80 bit == 10 byte extended precision, where last bytes can be
# random garbage. Try comparing first 10 bytes to pattern.
if ma_like is None and ftype == ntypes.longdouble:
ma_like = _KNOWN_TYPES.get(key[:10])
if ma_like is not None:
return ma_like
# Fall back to parameter discovery
warnings.warn(
'Signature {} for {} does not match any known type: '
'falling back to type probe function'.format(key, ftype),
UserWarning, stacklevel=2)
return _discovered_machar(ftype)
def _discovered_machar(ftype):
""" Create MachAr instance with found information on float types
"""
params = _MACHAR_PARAMS[ftype]
return MachAr(lambda v: array([v], ftype),
lambda v:_fr0(v.astype(params['itype']))[0],
lambda v:array(_fr0(v)[0], ftype),
lambda v: params['fmt'] % array(_fr0(v)[0], ftype),
params['title'])
class finfo(object):
"""
finfo(dtype)
Machine limits for floating point types.
Attributes
----------
bits : int
The number of bits occupied by the type.
eps : float
The smallest representable positive number such that
``1.0 + eps != 1.0``. Type of `eps` is an appropriate floating
point type.
epsneg : floating point number of the appropriate type
The smallest representable positive number such that
``1.0 - epsneg != 1.0``.
iexp : int
The number of bits in the exponent portion of the floating point
representation.
machar : MachAr
The object which calculated these parameters and holds more
detailed information.
machep : int
The exponent that yields `eps`.
max : floating point number of the appropriate type
The largest representable number.
maxexp : int
The smallest positive power of the base (2) that causes overflow.
min : floating point number of the appropriate type
The smallest representable number, typically ``-max``.
minexp : int
The most negative power of the base (2) consistent with there
being no leading 0's in the mantissa.
negep : int
The exponent that yields `epsneg`.
nexp : int
The number of bits in the exponent including its sign and bias.
nmant : int
The number of bits in the mantissa.
precision : int
The approximate number of decimal digits to which this kind of
float is precise.
resolution : floating point number of the appropriate type
The approximate decimal resolution of this type, i.e.,
``10**-precision``.
tiny : float
The smallest positive usable number. Type of `tiny` is an
appropriate floating point type.
Parameters
----------
dtype : float, dtype, or instance
Kind of floating point data-type about which to get information.
See Also
--------
MachAr : The implementation of the tests that produce this information.
iinfo : The equivalent for integer data types.
Notes
-----
For developers of NumPy: do not instantiate this at the module level.
The initial calculation of these parameters is expensive and negatively
impacts import times. These objects are cached, so calling ``finfo()``
repeatedly inside your functions is not a problem.
"""
_finfo_cache = {}
def __new__(cls, dtype):
try:
dtype = numeric.dtype(dtype)
except TypeError:
# In case a float instance was given
dtype = numeric.dtype(type(dtype))
obj = cls._finfo_cache.get(dtype, None)
if obj is not None:
return obj
dtypes = [dtype]
newdtype = numeric.obj2sctype(dtype)
if newdtype is not dtype:
dtypes.append(newdtype)
dtype = newdtype
if not issubclass(dtype, numeric.inexact):
raise ValueError("data type %r not inexact" % (dtype))
obj = cls._finfo_cache.get(dtype, None)
if obj is not None:
return obj
if not issubclass(dtype, numeric.floating):
newdtype = _convert_to_float[dtype]
if newdtype is not dtype:
dtypes.append(newdtype)
dtype = newdtype
obj = cls._finfo_cache.get(dtype, None)
if obj is not None:
return obj
obj = object.__new__(cls)._init(dtype)
for dt in dtypes:
cls._finfo_cache[dt] = obj
return obj
def _init(self, dtype):
self.dtype = numeric.dtype(dtype)
machar = _get_machar(dtype)
for word in ['precision', 'iexp',
'maxexp', 'minexp', 'negep',
'machep']:
setattr(self, word, getattr(machar, word))
for word in ['tiny', 'resolution', 'epsneg']:
setattr(self, word, getattr(machar, word).flat[0])
self.bits = self.dtype.itemsize * 8
self.max = machar.huge.flat[0]
self.min = -self.max
self.eps = machar.eps.flat[0]
self.nexp = machar.iexp
self.nmant = machar.it
self.machar = machar
self._str_tiny = machar._str_xmin.strip()
self._str_max = machar._str_xmax.strip()
self._str_epsneg = machar._str_epsneg.strip()
self._str_eps = machar._str_eps.strip()
self._str_resolution = machar._str_resolution.strip()
return self
def __str__(self):
fmt = (
'Machine parameters for %(dtype)s\n'
'---------------------------------------------------------------\n'
'precision = %(precision)3s resolution = %(_str_resolution)s\n'
'machep = %(machep)6s eps = %(_str_eps)s\n'
'negep = %(negep)6s epsneg = %(_str_epsneg)s\n'
'minexp = %(minexp)6s tiny = %(_str_tiny)s\n'
'maxexp = %(maxexp)6s max = %(_str_max)s\n'
'nexp = %(nexp)6s min = -max\n'
'---------------------------------------------------------------\n'
)
return fmt % self.__dict__
def __repr__(self):
c = self.__class__.__name__
d = self.__dict__.copy()
d['klass'] = c
return (("%(klass)s(resolution=%(resolution)s, min=-%(_str_max)s,"
" max=%(_str_max)s, dtype=%(dtype)s)") % d)
class iinfo(object):
"""
iinfo(type)
Machine limits for integer types.
Attributes
----------
bits : int
The number of bits occupied by the type.
min : int
The smallest integer expressible by the type.
max : int
The largest integer expressible by the type.
Parameters
----------
int_type : integer type, dtype, or instance
The kind of integer data type to get information about.
See Also
--------
finfo : The equivalent for floating point data types.
Examples
--------
With types:
>>> ii16 = np.iinfo(np.int16)
>>> ii16.min
-32768
>>> ii16.max
32767
>>> ii32 = np.iinfo(np.int32)
>>> ii32.min
-2147483648
>>> ii32.max
2147483647
With instances:
>>> ii32 = np.iinfo(np.int32(10))
>>> ii32.min
-2147483648
>>> ii32.max
2147483647
"""
_min_vals = {}
_max_vals = {}
def __init__(self, int_type):
try:
self.dtype = numeric.dtype(int_type)
except TypeError:
self.dtype = numeric.dtype(type(int_type))
self.kind = self.dtype.kind
self.bits = self.dtype.itemsize * 8
self.key = "%s%d" % (self.kind, self.bits)
if self.kind not in 'iu':
raise ValueError("Invalid integer data type.")
def min(self):
"""Minimum value of given dtype."""
if self.kind == 'u':
return 0
else:
try:
val = iinfo._min_vals[self.key]
except KeyError:
val = int(-(1 << (self.bits-1)))
iinfo._min_vals[self.key] = val
return val
min = property(min)
def max(self):
"""Maximum value of given dtype."""
try:
val = iinfo._max_vals[self.key]
except KeyError:
if self.kind == 'u':
val = int((1 << self.bits) - 1)
else:
val = int((1 << (self.bits-1)) - 1)
iinfo._max_vals[self.key] = val
return val
max = property(max)
def __str__(self):
"""String representation."""
fmt = (
'Machine parameters for %(dtype)s\n'
'---------------------------------------------------------------\n'
'min = %(min)s\n'
'max = %(max)s\n'
'---------------------------------------------------------------\n'
)
return fmt % {'dtype': self.dtype, 'min': self.min, 'max': self.max}
def __repr__(self):
return "%s(min=%s, max=%s, dtype=%s)" % (self.__class__.__name__,
self.min, self.max, self.dtype)