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""" Machine limits for Float32 and Float64 and (long double) if available... """ __all__ = ['finfo','iinfo'] from machar import MachAr import numeric import numerictypes as ntypes from numeric import array def _frz(a): """fix rank-0 --> rank-1""" if a.ndim == 0: a.shape = (1,) return a _convert_to_float = { ntypes.csingle: ntypes.single, ntypes.complex_: ntypes.float_, ntypes.clongfloat: ntypes.longfloat } class finfo(object): """ finfo(dtype) Machine limits for floating point types. Attributes ---------- 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) if dtype is ntypes.double: itype = ntypes.int64 fmt = '%24.16e' precname = 'double' elif dtype is ntypes.single: itype = ntypes.int32 fmt = '%15.7e' precname = 'single' elif dtype is ntypes.longdouble: itype = ntypes.longlong fmt = '%s' precname = 'long double' elif dtype is ntypes.half: itype = ntypes.int16 fmt = '%12.5e' precname = 'half' else: raise ValueError(repr(dtype)) machar = MachAr(lambda v:array([v], dtype), lambda v:_frz(v.astype(itype))[0], lambda v:array(_frz(v)[0], dtype), lambda v: fmt % array(_frz(v)[0], dtype), 'numpy %s precision floating point number' % precname) 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.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): return '''\ Machine parameters for %(dtype)s --------------------------------------------------------------------- precision=%(precision)3s resolution= %(_str_resolution)s machep=%(machep)6s eps= %(_str_eps)s negep =%(negep)6s epsneg= %(_str_epsneg)s minexp=%(minexp)6s tiny= %(_str_tiny)s maxexp=%(maxexp)6s max= %(_str_max)s nexp =%(nexp)6s min= -max --------------------------------------------------------------------- ''' % 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 ---------- min : int The smallest integer expressible by the type. max : int The largest integer expressible by the type. Parameters ---------- 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 not self.kind 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(-(1L << (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((1L << self.bits) - 1) else: val = int((1L << (self.bits-1)) - 1) iinfo._max_vals[self.key] = val return val max = property(max) def __str__(self): """String representation.""" return '''\ Machine parameters for %(dtype)s --------------------------------------------------------------------- min = %(min)s max = %(max)s --------------------------------------------------------------------- ''' % {'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) if __name__ == '__main__': f = finfo(ntypes.single) print 'single epsilon:',f.eps print 'single tiny:',f.tiny f = finfo(ntypes.float) print 'float epsilon:',f.eps print 'float tiny:',f.tiny f = finfo(ntypes.longfloat) print 'longfloat epsilon:',f.eps print 'longfloat tiny:',f.tiny