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getlimits.py
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"""Machine limits for Float32 and Float64 and (long double) if available... """ __all__ = ['finfo', 'iinfo'] import warnings from .._utils import set_module from ._machar import MachAr from . import numeric from . import numerictypes as ntypes from .numeric import array, inf, NaN from .umath import log10, exp2, nextafter, isnan 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 class MachArLike: """ Object to simulate MachAr instance """ def __init__(self, ftype, *, eps, epsneg, huge, tiny, ibeta, smallest_subnormal=None, **kwargs): self.params = _MACHAR_PARAMS[ftype] self.ftype = ftype self.title = self.params['title'] # Parameter types same as for discovered MachAr object. if not smallest_subnormal: self._smallest_subnormal = nextafter( self.ftype(0), self.ftype(1), dtype=self.ftype) else: self._smallest_subnormal = smallest_subnormal self.epsilon = self.eps = self._float_to_float(eps) self.epsneg = self._float_to_float(epsneg) self.xmax = self.huge = self._float_to_float(huge) self.xmin = self._float_to_float(tiny) self.smallest_normal = self.tiny = self._float_to_float(tiny) self.ibeta = self.params['itype'](ibeta) self.__dict__.update(kwargs) self.precision = int(-log10(self.eps)) self.resolution = self._float_to_float( self._float_conv(10) ** (-self.precision)) self._str_eps = self._float_to_str(self.eps) self._str_epsneg = self._float_to_str(self.epsneg) self._str_xmin = self._float_to_str(self.xmin) self._str_xmax = self._float_to_str(self.xmax) self._str_resolution = self._float_to_str(self.resolution) self._str_smallest_normal = self._float_to_str(self.xmin) @property def smallest_subnormal(self): """Return the value for the smallest subnormal. Returns ------- smallest_subnormal : float value for the smallest subnormal. Warns ----- UserWarning If the calculated value for the smallest subnormal is zero. """ # Check that the calculated value is not zero, in case it raises a # warning. value = self._smallest_subnormal if self.ftype(0) == value: warnings.warn( 'The value of the smallest subnormal for {} type ' 'is zero.'.format(self.ftype), UserWarning, stacklevel=2) return self._float_to_float(value) @property def _str_smallest_subnormal(self): """Return the string representation of the smallest subnormal.""" return self._float_to_str(self.smallest_subnormal) def _float_to_float(self, value): """Converts float to float. Parameters ---------- value : float value to be converted. """ return _fr1(self._float_conv(value)) def _float_conv(self, value): """Converts float to conv. Parameters ---------- value : float value to be converted. """ return array([value], self.ftype) def _float_to_str(self, value): """Converts float to str. Parameters ---------- value : float value to be converted. """ return self.params['fmt'] % array(_fr0(value)[0], self.ftype) _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'))} # Key to identify the floating point type. Key is result of # ftype('-0.1').newbyteorder('<').tobytes() # # 20230201 - use (ftype(-1.0) / ftype(10.0)).newbyteorder('<').tobytes() # instead because stold may have deficiencies on some platforms. # See: # https://perl5.git.perl.org/perl.git/blob/3118d7d684b56cbeb702af874f4326683c45f045:/Configure _KNOWN_TYPES = {} def _register_type(machar, bytepat): _KNOWN_TYPES[bytepat] = machar _float_ma = {} def _register_known_types(): # 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)) _register_type(float16_ma, b'f\xae') _float_ma[16] = float16_ma # 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))) _register_type(float32_ma, b'\xcd\xcc\xcc\xbd') _float_ma[32] = float32_ma # 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) _register_type(float64_ma, b'\x9a\x99\x99\x99\x99\x99\xb9\xbf') _float_ma[64] = float64_ma # 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) # IEEE 754 128-bit binary float _register_type(float128_ma, b'\x9a\x99\x99\x99\x99\x99\x99\x99\x99\x99\x99\x99\x99\x99\xfb\xbf') _float_ma[128] = float128_ma # 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) # float80, first 10 bytes containing actual storage _register_type(float80_ma, b'\xcd\xcc\xcc\xcc\xcc\xcc\xcc\xcc\xfb\xbf') _float_ma[80] = float80_ma # 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 = nextafter(ld(inf), ld(0), dtype=ld) # As the smallest_normal in double double is so hard to calculate we set # it to NaN. smallest_normal_dd = NaN # Leave the same value for the smallest subnormal as double smallest_subnormal_dd = ld(nextafter(0., 1.)) 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=smallest_normal_dd, smallest_subnormal=smallest_subnormal_dd) # double double; low, high order (e.g. PPC 64) _register_type(float_dd_ma, b'\x9a\x99\x99\x99\x99\x99Y<\x9a\x99\x99\x99\x99\x99\xb9\xbf') # double double; high, low order (e.g. PPC 64 le) _register_type(float_dd_ma, b'\x9a\x99\x99\x99\x99\x99\xb9\xbf\x9a\x99\x99\x99\x99\x99Y<') _float_ma['dd'] = float_dd_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 # ftype(-1.0) / ftype(10.0) is better than ftype('-0.1') because stold # may be deficient key = (ftype(-1.0) / ftype(10.)).newbyteorder('<').tobytes() ma_like = None if ftype == ntypes.longdouble: # Could be 80 bit == 10 byte extended precision, where last bytes can # be random garbage. # Comparing first 10 bytes to pattern first to avoid branching on the # random garbage. ma_like = _KNOWN_TYPES.get(key[:10]) if ma_like is None: # see if the full key is known. ma_like = _KNOWN_TYPES.get(key) if ma_like is None and len(key) == 16: # machine limits could be f80 masquerading as np.float128, # find all keys with length 16 and make new dict, but make the keys # only 10 bytes long, the last bytes can be random garbage _kt = {k[:10]: v for k, v in _KNOWN_TYPES.items() if len(k) == 16} ma_like = _kt.get(key[:10]) if ma_like is not None: return ma_like # Fall back to parameter discovery warnings.warn( f'Signature {key} for {ftype} does not match any known type: ' 'falling back to type probe function.\n' 'This warnings indicates broken support for the dtype!', UserWarning, stacklevel=2) return _discovered_machar(ftype) def _discovered_machar(ftype): """ Create MachAr instance with found information on float types TODO: MachAr should be retired completely ideally. We currently only ever use it system with broken longdouble (valgrind, WSL). """ 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']) @set_module('numpy') class finfo: """ finfo(dtype) Machine limits for floating point types. Attributes ---------- bits : int The number of bits occupied by the type. dtype : dtype Returns the dtype for which `finfo` returns information. For complex input, the returned dtype is the associated ``float*`` dtype for its real and complex components. eps : float The difference between 1.0 and the next smallest representable float larger than 1.0. For example, for 64-bit binary floats in the IEEE-754 standard, ``eps = 2**-52``, approximately 2.22e-16. epsneg : float The difference between 1.0 and the next smallest representable float less than 1.0. For example, for 64-bit binary floats in the IEEE-754 standard, ``epsneg = 2**-53``, approximately 1.11e-16. iexp : int The number of bits in the exponent portion of the floating point representation. 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 An alias for `smallest_normal`, kept for backwards compatibility. smallest_normal : float The smallest positive floating point number with 1 as leading bit in the mantissa following IEEE-754 (see Notes). smallest_subnormal : float The smallest positive floating point number with 0 as leading bit in the mantissa following IEEE-754. Parameters ---------- dtype : float, dtype, or instance Kind of floating point or complex floating point data-type about which to get information. See Also -------- iinfo : The equivalent for integer data types. spacing : The distance between a value and the nearest adjacent number nextafter : The next floating point value after x1 towards x2 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. Note that ``smallest_normal`` is not actually the smallest positive representable value in a NumPy floating point type. As in the IEEE-754 standard [1]_, NumPy floating point types make use of subnormal numbers to fill the gap between 0 and ``smallest_normal``. However, subnormal numbers may have significantly reduced precision [2]_. This function can also be used for complex data types as well. If used, the output will be the same as the corresponding real float type (e.g. numpy.finfo(numpy.csingle) is the same as numpy.finfo(numpy.single)). However, the output is true for the real and imaginary components. References ---------- .. [1] IEEE Standard for Floating-Point Arithmetic, IEEE Std 754-2008, pp.1-70, 2008, http://www.doi.org/10.1109/IEEESTD.2008.4610935 .. [2] Wikipedia, "Denormal Numbers", https://en.wikipedia.org/wiki/Denormal_number Examples -------- >>> np.finfo(np.float64).dtype dtype('float64') >>> np.finfo(np.complex64).dtype dtype('float32') """ _finfo_cache = {} def __new__(cls, dtype): try: obj = cls._finfo_cache.get(dtype) # most common path if obj is not None: return obj except TypeError: pass if dtype is None: # Deprecated in NumPy 1.25, 2023-01-16 warnings.warn( "finfo() dtype cannot be None. This behavior will " "raise an error in the future. (Deprecated in NumPy 1.25)", DeprecationWarning, stacklevel=2 ) 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) 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) if obj is not None: return obj if not issubclass(dtype, numeric.floating): newdtype = _convert_to_float[dtype] if newdtype is not dtype: # dtype changed, for example from complex128 to float64 dtypes.append(newdtype) dtype = newdtype obj = cls._finfo_cache.get(dtype, None) if obj is not None: # the original dtype was not in the cache, but the new # dtype is in the cache. we add the original dtypes to # the cache and return the result for dt in dtypes: cls._finfo_cache[dt] = obj 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 ['resolution', 'epsneg', 'smallest_subnormal']: 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() self._str_smallest_normal = machar._str_smallest_normal.strip() self._str_smallest_subnormal = machar._str_smallest_subnormal.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' 'smallest_normal = %(_str_smallest_normal)s ' 'smallest_subnormal = %(_str_smallest_subnormal)s\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) @property def smallest_normal(self): """Return the value for the smallest normal. Returns ------- smallest_normal : float Value for the smallest normal. Warns ----- UserWarning If the calculated value for the smallest normal is requested for double-double. """ # This check is necessary because the value for smallest_normal is # platform dependent for longdouble types. if isnan(self._machar.smallest_normal.flat[0]): warnings.warn( 'The value of smallest normal is undefined for double double', UserWarning, stacklevel=2) return self._machar.smallest_normal.flat[0] @property def tiny(self): """Return the value for tiny, alias of smallest_normal. Returns ------- tiny : float Value for the smallest normal, alias of smallest_normal. Warns ----- UserWarning If the calculated value for the smallest normal is requested for double-double. """ return self.smallest_normal @set_module('numpy') class iinfo: """ iinfo(type) Machine limits for integer types. Attributes ---------- bits : int The number of bits occupied by the type. dtype : dtype Returns the dtype for which `iinfo` returns information. 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 %r." % (self.kind,)) @property 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 @property 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 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)