# Coverage for pygeodesy/fsums.py : 97%

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1822 1823 1824 1825 1826 1827 1828 1829 1830 1831 1832 1833 1834 1835 1836 1837 1838 1839 1840 1841 1842 1843 1844 1845 1846 1847 1848 1849 1850 1851 1852 1853 1854 1855 1856 1857 1858 1859 1860 1861 1862 1863 1864 1865 1866 1867 1868 1869 1870 1871 1872 1873 1874 | # -*- coding: utf-8 -*- u'''Class L{Fsum} for precision floating point summation and I{running} summation, based on respectively similar to Python's C{math.fsum}. Generally, an L{Fsum} instance is considered a C{float} plus a small or zero C{residual} value, see property L{Fsum.residual}. However, there are several C{integer} L{Fsum} cases, for example the result of C{ceil}, C{floor}, C{Fsum.__floordiv__} and methods L{Fsum.fint} and L{Fsum.fint2}. Also, L{Fsum} methods L{Fsum.pow}, L{Fsum.__ipow__}, L{Fsum.__pow__} and L{Fsum.__rpow__} return a (very long) C{int} if invoked with optional argument C{mod} set to C{None}. The C{residual} of an C{integer} L{Fsum} may be between C{-1.0} and C{+1.0}, including C{INT0} if considered to be I{exact}. Set env variable C{PYGEODESY_FSUM_PARTIALS} to an empty string (or anything other than C{"fsum"}) for backward compatible summation of L{Fsum} partials. Set env variable C{PYGEODESY_FSUM_RESIDUAL} to a C{float} string for the threshold to throw a L{ResidualError} in division or exponention of an L{Fsum} instance with a I{relative} C{residual} exceeding the threshold, see methods L{Fsum.RESIDUAL}, L{Fsum.pow}, L{Fsum.__ipow__} and L{Fsum.__itruediv__}. ''' # make sure int/int division yields float quotient, see .basics from __future__ import division as _; del _ # PYCHOK semicolon from pygeodesy.basics import iscomplex, isint, isscalar, map1, neg, \ signOf, _signOf from pygeodesy.constants import INT0, _isfinite, isinf, isnan, \ _0_0, _1_0, _N_1_0 from pygeodesy.errors import itemsorted, _OverflowError, _TypeError, \ _ValueError, _xError2, _xkwds_get, _xkwds_get_, \ _ZeroDivisionError from pygeodesy.interns import NN, _arg_, _COMMASPACE_, _DASH_, _EQUAL_, \ _exceeds_, _from_, _iadd_, _LANGLE_, _negative_, \ _NOTEQUAL_, _not_finite_, _not_scalar_, \ _PERCENT_, _PLUS_, _R_, _RANGLE_, _SLASH_, \ _SPACE_, _STAR_, _UNDER_ from pygeodesy.lazily import _ALL_LAZY, _getenv, _sys, _sys_version_info2 from pygeodesy.named import _Named, _NamedTuple, _NotImplemented, Fmt, unstr from pygeodesy.props import _allPropertiesOf_n, deprecated_property_RO, \ Property_RO, property_RO # from pygeodesy.streprs import Fmt, unstr # from .named from pygeodesy.units import Float, Int from math import ceil as _ceil, fabs, floor as _floor # PYCHOK used! .ltp __all__ = _ALL_LAZY.fsums __version__ = '22.10.09' _add_op_ = _PLUS_ _eq_op_ = _EQUAL_ * 2 # _DEQUAL_ _COMMASPACE_R_ = _COMMASPACE_ + _R_ _exceeds_R_ = _SPACE_ + _exceeds_(_R_) _floordiv_op_ = _SLASH_ * 2 # _DSLASH_ _fset_op_ = _EQUAL_ _ge_op_ = _RANGLE_ + _EQUAL_ _gt_op_ = _RANGLE_ _integer_ = 'integer' _le_op_ = _LANGLE_ + _EQUAL_ _lt_op_ = _LANGLE_ _mod_op_ = _PERCENT_ _mul_op_ = _STAR_ _ne_op_ = _NOTEQUAL_ _non_zero_ = 'non-zero' _pow_op_ = _STAR_ * 2 # _DSTAR_, in .fmath _sub_op_ = _DASH_ _truediv_op_ = _SLASH_ _divmod_op_ = _floordiv_op_ + _mod_op_ _pos_self = _1_0.__pos__() is _1_0 # in .vector3dBase def _2float(index=None, **name_value): '''(INTERNAL) Raise C{TypeError} or C{ValueError} if not scalar or infinite. ''' n, v = name_value.popitem() # _xkwds_popitem(name_value) try: v = float(v) if _isfinite(v): return v E, t = _ValueError, _not_finite_ except Exception as X: E, t = _xError2(X) if index is not None: n = Fmt.SQUARE(n, index) raise E(n, v, txt=t) def _2floats(xs, origin=0, primed=False, sub=False, floats=False): '''(INTERNAL) Yield all B{C{xs}} as C{float}s. ''' _2f = _2float if primed: yield _1_0 i = origin for x in xs: if floats: yield x elif isinstance(x, Fsum): ps = x._ps if ps: if sub: ps = map(neg, ps) for x in ps: yield x else: x = _2f(index=i, xs=x) if x: yield (-x) if sub else x i += 1 if primed: yield _N_1_0 def _Powers(power, xs, origin=1): # in .fmath '''(INTERNAL) Yield each C{xs} as C{float(x**power)}. ''' i = None s = 2 == power _2f = _2float try: for i, x in enumerate(xs): if isinstance(x, Fsum): T = x._mul_Fsum(x) if s else x.pow(power) for t in T._ps: yield t else: t = _2f(_=x) if t: yield _2f(__=t**power) except Exception as X: E, t = _xError2(X) if i is None: i = Fmt.PARENSPACED(xs=xs) else: i = Fmt.SQUARE(xs=i + origin) i = Fmt.PARENSPACED(i, x) raise E(i, txt=t) def _psum(ps): # PYCHOK used! '''(INTERNAL) Partials summation updating C{ps}, I{overridden below}. ''' i = len(ps) - 1 # len(ps) > 2 s = ps[i] _2s = _2sum while i > 0: i -= 1 s, r = _2s(s, ps[i]) if r: # sum(ps) became inexact ps[i:] = [s, r] if s else [r] if i > 0: p = ps[i-1] # round half-even if (p > 0 and r > 0) or \ (p < 0 and r < 0): # signs match r *= 2 t = s + r if r == (t - s): s = t break ps[i:] = [s] return s def _2scalar(other, _raiser=None): '''(INTERNAL) Return B{C{other}} as C{int}, C{float} or C{as-is}. ''' if isinstance(other, Fsum): s, r = other._fint2 if r: s, r = other._fprs2 if r: # PYCHOK no cover if _raiser and _raiser(r, s): raise ValueError(_stresidual(_non_zero_, r)) s = other # L{Fsum} as-is else: s = other # C{type} as-is if isint(s, both=True): s = int(s) return s def _strcomplex(s, *args): '''(INTERNAL) C{Complex} 2- or 3-arg C{pow} error C{str}. ''' c = iscomplex.__name__[2:] n = _DASH_(len(args), _arg_) t = _SPACE_(c, s, _from_, n, pow.__name__) return unstr(t, *args) def _stresidual(prefix, residual, **name_values): '''(INTERNAL) Residual error C{str}. ''' p = _SPACE_(prefix, Fsum.residual.name) t = Fmt.PARENSPACED(p, Fmt(residual)) for n, v in itemsorted(name_values): n = n.replace(_UNDER_, _SPACE_) p = Fmt.PARENSPACED(n, Fmt(v)) t = _COMMASPACE_(t, p) return t def _2sum(a, b): # by .testFmath '''(INTERNAL) Return C{a + b} as 2-tuple (sum, residual). ''' s = a + b if not _isfinite(s): u = unstr(_2sum.__name__, a, b) t = Fmt.PARENSPACED(_not_finite_, s) raise _OverflowError(u, txt=t) r = (a - (s - b)) if abs(a) < abs(b) else \ (b - (s - a)) # abs(a) >= abs(b) return s, r class Fsum(_Named): # sync __methods__ with .vector3dBase.Vector3dBase '''Precision floating point I{running} summation. Unlike Python's C{math.fsum}, this class accumulates values and provides intermediate, I{running} precision floating point summation. Accumulation may continue after intermediate, I{running} summuation. @note: Accumulated values may be L{Fsum} or C{scalar} instances with C{scalar} meaning type C{float}, C{int} or any C{type} convertible to a single C{float}, having method C{__float__}. @note: Handling of exceptions and C{inf}, C{INF}, C{nan} and C{NAN} differs from Python's C{math.fsum}. @see: U{Hettinger<https://GitHub.com/ActiveState/code/blob/master/recipes/Python/ 393090_Binary_floating_point_summatiaccurate_full/recipe-393090.py>}, U{Kahan <https://WikiPedia.org/wiki/Kahan_summation_algorithm>}, U{Klein <https://Link.Springer.com/article/10.1007/s00607-005-0139-x>}, Python 2.6+ file I{Modules/mathmodule.c} and the issue log U{Full precision summation <https://Bugs.Python.org/issue2819>}. ''' _math_fsum = None _n = 0 # _ps = [] # partial sums # _px = 0 _ratio = None _RESIDUAL = max(float(_getenv('PYGEODESY_FSUM_RESIDUAL', _0_0)), _0_0) def __init__(self, *xs, **name_RESIDUAL): '''New L{Fsum} for precision floating point I{running} summation. @arg xs: No, one or more initial values (each C{scalar} or an L{Fsum} instance). @kwarg name_RESIDUAL: Optional C{B{name}=NN} for this L{Fsum} (C{str}) and C{B{RESIDUAL}=None} for the L{ResidualError} threshold. @see: Methods L{Fsum.fadd} and L{Fsum.RESIDUAL}. ''' if name_RESIDUAL: n, r = _xkwds_get_(name_RESIDUAL, name=NN, RESIDUAL=None) if n: # set name ... self.name = n if r is not None: self.RESIDUAL(r) # ... for ResidualError # self._n = 0 self._ps = [] # [_0_0], see L{Fsum._fprs} if len(xs) > 1: self._facc(_2floats(xs, origin=1), up=False) elif xs: # len(xs) == 1 self._ps = [_2float(x=xs[0])] self._n = 1 def __abs__(self): '''Return this instance' absolute value as an L{Fsum}. ''' s = _fsum(self._ps_1()) # == self._cmp_0(0, ...) return self._copy_n(self.__abs__) if s < 0 else \ self._copy_2(self.__abs__) def __add__(self, other): '''Return the C{Fsum(B{self}, B{other})}. @arg other: An L{Fsum} or C{scalar}. @return: The sum (L{Fsum}). @see: Method L{Fsum.__iadd__}. ''' f = self._copy_2(self.__add__) return f._fadd(other, _add_op_) def __bool__(self): # PYCHOK not special in Python 2- '''Return C{True} if this instance is non-zero. ''' return self != 0 def __ceil__(self): # PYCHOK not special in Python 2- '''Return this instance' C{math.ceil} as C{int} or C{float}. @return: An C{int} in Python 3+, but C{float} in Python 2-. @see: Methods L{Fsum.__floor__} and property L{Fsum.ceil}. ''' return self.ceil def __cmp__(self, other): # Python 2- '''Compare this with an other instance or scalar. @return: -1, 0 or +1 (C{int}). @raise TypeError: Incompatible B{C{other}} C{type}. ''' s = self._cmp_0(other, self.cmp.__name__) return -1 if s < 0 else (+1 if s > 0 else 0) cmp = __cmp__ def __divmod__(self, other): '''Return C{divmod(B{self}, B{other})} as 2-tuple C{(quotient, remainder)}, an C{int} in Python 3+ or C{float} in Python 2- and an L{Fsum}. @arg other: An L{Fsum} or C{scalar} modulus. @see: Method L{Fsum.__itruediv__}. ''' f = self._copy_2(self.__divmod__) return f._fdivmod2(other, _divmod_op_) def __eq__(self, other): '''Compare this with an other instance or scalar. ''' return self._cmp_0(other, _eq_op_) == 0 def __float__(self): '''Return this instance' current precision running sum as C{float}. @see: Methods L{Fsum.fsum} and L{Fsum.int_float}. ''' return float(self._fprs) def __floor__(self): # PYCHOK not special in Python 2- '''Return this instance' C{math.floor} as C{int} or C{float}. @return: An C{int} in Python 3+, but C{float} in Python 2-. @see: Methods L{Fsum.__ceil__} and property L{Fsum.floor}. ''' return self.floor def __floordiv__(self, other): '''Return C{B{self} // B{other}} as an L{Fsum}. @arg other: An L{Fsum} or C{scalar} divisor. @return: The C{floor} quotient (L{Fsum}). @see: Methods L{Fsum.__ifloordiv__}. ''' f = self._copy_2(self.__floordiv__) return f._floordiv(other, _floordiv_op_) def __format__(self, *other): # PYCHOK no cover '''Not implemented.''' return _NotImplemented(self, *other) def __ge__(self, other): '''Compare this with an other instance or scalar. ''' return self._cmp_0(other, _ge_op_) >= 0 def __gt__(self, other): '''Compare this with an other instance or scalar. ''' return self._cmp_0(other, _gt_op_) > 0 def __hash__(self): # PYCHOK no cover '''Return this instance' C{hash}. ''' return hash(self._ps) # XXX id(self)? def __iadd__(self, other): '''Apply C{B{self} += B{other}} to this instance. @arg other: An L{Fsum} or C{scalar} instance. @return: This instance, updated (L{Fsum}). @raise TypeError: Invalid B{C{other}}, not C{scalar} nor L{Fsum}. @see: Methods L{Fsum.fadd} and L{Fsum.fadd_}. ''' return self._fadd(other, _iadd_) def __ifloordiv__(self, other): '''Apply C{B{self} //= B{other}} to this instance. @arg other: An L{Fsum} or C{scalar} divisor. @return: This instance, updated (L{Fsum}). @raise ResidualError: Non-zero residual in B{C{other}}. @raise TypeError: Invalid B{C{other}} type. @raise ValueError: Invalid or non-finite B{C{other}}. @raise ZeroDivisionError: Zero B{C{other}}. @see: Methods L{Fsum.__itruediv__}. ''' return self._floordiv(other, _floordiv_op_ + _fset_op_) def __imatmul__(self, other): # PYCHOK no cover '''Not implemented.''' return _NotImplemented(self, other) def __imod__(self, other): '''Apply C{B{self} %= B{other}} to this instance. @arg other: An L{Fsum} or C{scalar} modulus. @return: This instance, updated (L{Fsum}). @see: Method L{Fsum.__divmod__}. ''' self._fdivmod2(other, _mod_op_ + _fset_op_) return self def __imul__(self, other): '''Apply C{B{self} *= B{other}} to this instance. @arg other: An L{Fsum} or C{scalar} factor. @return: This instance, updated (L{Fsum}). @raise OverflowError: Partial C{2sum} overflow. @raise TypeError: Invalid B{C{other}} type. @raise ValueError: Invalid or non-finite B{C{other}}. ''' return self._fmul(other, _mul_op_ + _fset_op_) def __int__(self): '''Return this instance as an C{int}. @see: Methods L{Fsum.int_float}, L{Fsum.__ceil__} and L{Fsum.__floor__} and properties L{Fsum.ceil} and L{Fsum.floor}. ''' i, _ = self._fint2 return i def __ipow__(self, other, *mod): # PYCHOK 2 vs 3 args '''Apply C{B{self} **= B{other}} to this instance. @arg other: The exponent (L{Fsum} or C{scalar}). @arg mod: Optional modulus (C{int} or C{None}) for the 3-argument C{pow(B{self}, B{other}, B{mod})} version. @return: This instance, updated (L{Fsum}). @note: If B{C{mod}} is given, the result will be an C{integer} L{Fsum} in Python 3+ if this instance C{is_integer} or set to C{as_integer} if B{C{mod}} given as C{None}. @raise OverflowError: Partial C{2sum} overflow. @raise ResidualError: Non-zero residual in B{C{other}} and env var C{PYGEODESY_FSUM_RESIDUAL} set or this instance has a non-zero residual and either B{C{mod}} is given and non-C{None} or B{C{other}} is a negative or fractional C{scalar}. @raise TypeError: Invalid B{C{other}} type or 3-argument C{pow} invocation failed. @raise ValueError: If B{C{other}} is a negative C{scalar} and this instance is C{0} or B{C{other}} is a fractional C{scalar} and this instance is negative or has a non-zero residual or B{C{mod}} is given and C{0}. @see: CPython function U{float_pow<https://GitHub.com/ python/cpython/blob/main/Objects/floatobject.c>}. ''' return self._fpow(other, _pow_op_ + _fset_op_, *mod) def __isub__(self, other): '''Apply C{B{self} -= B{other}} to this instance. @arg other: An L{Fsum} or C{scalar}. @return: This instance, updated (L{Fsum}). @raise TypeError: Invalid B{C{other}} type. @see: Method L{Fsum.fadd}. ''' return self._fsub(other, _sub_op_ + _fset_op_) def __iter__(self): '''Return an C{iter}ator over a C{partials} duplicate. ''' return iter(self.partials) def __itruediv__(self, other): '''Apply C{B{self} /= B{other}} to this instance. @arg other: An L{Fsum} or C{scalar} divisor. @return: This instance, updated (L{Fsum}). @raise OverflowError: Partial C{2sum} overflow. @raise ResidualError: Non-zero residual in B{C{other}} and env var C{PYGEODESY_FSUM_RESIDUAL} set. @raise TypeError: Invalid B{C{other}} type. @raise ValueError: Invalid or non-finite B{C{other}}. @raise ZeroDivisionError: Zero B{C{other}}. @see: Method L{Fsum.__ifloordiv__}. ''' return self._ftruediv(other, _truediv_op_ + _fset_op_) def __le__(self, other): '''Compare this with an other instance or scalar. ''' return self._cmp_0(other, _le_op_) <= 0 def __len__(self): '''Return the I{total} number accumulations (C{int}). ''' return self._n def __lt__(self, other): '''Compare this with an other instance or scalar. ''' return self._cmp_0(other, _lt_op_) < 0 def __matmul__(self, other): # PYCHOK no cover '''Not implemented.''' return _NotImplemented(self, other) def __mod__(self, other): '''Return C{B{self} % B{other}} as an L{Fsum}. @see: Method L{Fsum.__imod__}. ''' f = self._copy_2(self.__mod__) return f._fdivmod2(other, _mod_op_)[1] def __mul__(self, other): '''Return C{B{self} * B{other}} as an L{Fsum}. @see: Method L{Fsum.__imul__}. ''' f = self._copy_2(self.__mul__) return f._fmul(other, _mul_op_) def __ne__(self, other): '''Compare this with an other instance or scalar. ''' return self._cmp_0(other, _ne_op_) != 0 def __neg__(self): '''Return I{a copy of} this instance, negated. ''' return self._copy_n(self.__neg__) def __pos__(self): '''Return this instance I{as-is}, like C{float.__pos__()}. ''' return self if _pos_self else self._copy_2(self.__pos__) def __pow__(self, other, *mod): # PYCHOK 2 vs 3 args '''Return C{B{self}**B{other}} as an L{Fsum}. @see: Method L{Fsum.__ipow__}. ''' f = self._copy_2(self.__pow__) return f._fpow(other, _pow_op_, *mod) def __radd__(self, other): '''Return C{B{other} + B{self}} as an L{Fsum}. @see: Method L{Fsum.__iadd__}. ''' f = self._copy_r2(other, self.__radd__) return f._fadd(self, _add_op_) def __rdivmod__(self, other): '''Return C{divmod(B{other}, B{self})} as 2-tuple C{(quotient, remainder)}. @see: Method L{Fsum.__divmod__}. ''' f = self._copy_r2(other, self.__rdivmod__) return f._fdivmod2(self, _divmod_op_) # def __repr__(self): # '''Return the default C{repr(this)}. # ''' # return self.toRepr(lenc=True) def __rfloordiv__(self, other): '''Return C{B{other} // B{self}} as an L{Fsum}. @see: Method L{Fsum.__ifloordiv__}. ''' f = self._copy_r2(other, self.__rfloordiv__) return f._floordiv(self, _floordiv_op_) def __rmatmul__(self, other): # PYCHOK no cover '''Not implemented.''' return _NotImplemented(self, other) def __rmod__(self, other): '''Return C{B{other} % B{self}} as an L{Fsum}. @see: Method L{Fsum.__imod__}. ''' f = self._copy_r2(other, self.__rmod__) return f._fdivmod2(self, _mod_op_)[1] def __rmul__(self, other): '''Return C{B{other} * B{self}} as an L{Fsum}. @see: Method L{Fsum.__imul__}. ''' f = self._copy_r2(other, self.__rmul__) return f._fmul(self, _mul_op_) def __round__(self, ndigits=None): # PYCHOK no cover '''Not implemented.''' return _NotImplemented(self, ndigits=ndigits) def __rpow__(self, other, *mod): '''Return C{B{other}**B{self}} as an L{Fsum}. @see: Method L{Fsum.__ipow__}. ''' f = self._copy_r2(other, self.__rpow__) return f._fpow(self, _pow_op_, *mod) def __rsub__(self, other): '''Return C{B{other} - B{self}} as L{Fsum}. @see: Method L{Fsum.__isub__}. ''' f = self._copy_r2(other, self.__rsub__) return f._fsub(self, _sub_op_) def __rtruediv__(self, other): '''Return C{B{other} / B{self}} as an L{Fsum}. @see: Method L{Fsum.__itruediv__}. ''' f = self._copy_r2(other, self.__rtruediv__) return f._ftruediv(self, _truediv_op_) def __sizeof__(self): # PYCHOK not special in Python 2- '''Return the current size of this instance in C{bytes}. ''' return sum(map1(_sys.getsizeof, self._fint2, self._fint2[0], self._fint2[1], self._fprs, self._fprs2, self._fprs2.fsum, self._fprs2.residual, self._n, self._ps, *self._ps)) def __str__(self): '''Return the default C{str(self)}. ''' return self.toStr(lenc=True) def __sub__(self, other): '''Return C{B{self} - B{other}} as an L{Fsum}. @arg other: An L{Fsum} or C{scalar}. @return: The difference (L{Fsum}). @see: Method L{Fsum.__isub__}. ''' f = self._copy_2(self.__sub__) return f._fsub(other, _sub_op_) def __truediv__(self, other): '''Return C{B{self} / B{other}} as an L{Fsum}. @arg other: An L{Fsum} or C{scalar} divisor. @return: The quotient (L{Fsum}). @see: Method L{Fsum.__itruediv__}. ''' f = self._copy_2(self.__truediv__) return f._ftruediv(other, _truediv_op_) __trunc__ = __int__ if _sys_version_info2 < (3, 0): # PYCHOK no cover # <https://docs.Python.org/2/library/operator.html#mapping-operators-to-functions> __div__ = __truediv__ __idiv__ = __itruediv__ __long__ = __int__ __nonzero__ = __bool__ __rdiv__ = __rtruediv__ def as_integer_ratio(self): '''Return this instance as the ratio of 2 integers. @return: 2-Tuple C{(numerator, denominator)} both C{int} and with positive C{denominator}. @see: Standard C{float.as_integer_ratio} in Python 3+. ''' n, r = self._fint2 if r: i, d = r.as_integer_ratio() n *= d n += i else: # PYCHOK no cover d = 1 return n, d @property_RO def ceil(self): '''Get this instance' C{ceil} value (C{int} in Python 3+, but C{float} in Python 2-). @note: The C{ceil} takes the C{residual} into account. @see: Method L{Fsum.int_float} and properties L{Fsum.floor}, L{Fsum.imag} and L{Fsum.real}. ''' s, r = self._fprs2 c = _ceil(s) + int(r) - 1 while r > (c - s): # (s + r) > c c += 1 return c def _cmp_0(self, other, op): '''(INTERNAL) Return C{scalar(self - B{other})} for 0-comparison. ''' if isscalar(other): s = _fsum(self._ps_1(other)) elif isinstance(other, Fsum): s = _fsum(self._ps_1(*other._ps)) else: raise self._TypeError(op, other) # txt=_invalid_ return s def copy(self, deep=False, name=NN): '''Copy this instance, C{shallow} or B{C{deep}}. @return: The copy (L{Fsum}). ''' f = _Named.copy(self, deep=deep, name=name) f._n = self._n if deep else 1 f._ps = list(self._ps) # separate list return f def _copy_0(self, *xs): '''(INTERNAL) Copy with/-out overriding C{partials}. ''' # for x in xs: # assert isscalar(x) f = self._Fsum(self._n + len(xs), *xs) if self.name: f._name = self.name # .rename calls _update_attrs return f def _copy_2(self, which): '''(INTERNAL) Copy for I{dyadic} operators. ''' # NOT .classof due to .Fdot(a, *b) args, etc. f = _Named.copy(self, deep=False, name=which.__name__) # assert f._n == self._n f._ps = list(self._ps) # separate list return f def _copy_n(self, which): '''(INTERNAL) Negated copy for I{monadic} C{__abs__} and C{__neg__}. ''' if self._ps: f = self._Fsum(self._n) f._ps[:] = self._ps_n() # f._facc_up(up=False) else: f = self._Fsum(self._n, _0_0) f._name = which.__name__ # .rename calls _update_attrs return f def _copy_r2(self, other, which): '''(INTERNAL) Copy for I{reverse-dyadic} operators. ''' return other._copy_2(which) if isinstance(other, Fsum) else \ Fsum(other, name=which.__name__) # see ._copy_2 def _copy_RESIDUAL(self, other): '''(INTERNAL) Copy C{other._RESIDUAL}. ''' R = other._RESIDUAL if R is not Fsum._RESIDUAL: self._RESIDUAL = R def _copy_up(self, _fprs2=False): '''(INTERNAL) Minimal, anonymous copy. ''' f = self._Fsum(self._n, *self._ps) if _fprs2: # only the ._fprs2 2-tuple Fsum._fprs2._update_from(f, self) return f def divmod(self, other): '''Return C{divmod(B{self}, B{other})} as 2-tuple C{(quotient, remainder)}. @arg other: An L{Fsum} or C{scalar} divisor. @return: 2-Tuple C{(quotient, remainder)}, with the C{quotient} an C{int} in Python 3+ or a C{float} in Python 2- and the C{remainder} an L{Fsum} instance. @see: Method L{Fsum.__itruediv__}. ''' f = self._copy_2(self.divmod) return f._fdivmod2(other, _divmod_op_) def _Error(self, op, other, Error, **txt): '''(INTERNAL) Format an B{C{Error}} for C{{self} B{op} B{other}}. ''' return Error(_SPACE_(self.toRepr(), op, repr(other)), **txt) def _ErrorX(self, X, xs, **kwds): # in .fmath '''(INTERNAL) Format a caught exception. ''' E, t = _xError2(X) n = unstr(self.named3, *xs[:3], _ELLIPSIS=len(xs) > 3, **kwds) return E(n, txt=t, cause=X) def _facc(self, xs, up=True): # from .elliptic._Defer.Fsum '''(INTERNAL) Accumulate more known C{scalar}s. ''' n, ps, _2s = 0, self._ps, _2sum for x in xs: # _iter() # assert isscalar(x) and isfinite(x) i = 0 for p in ps: x, p = _2s(x, p) if p: ps[i] = p i += 1 ps[i:] = [x] n += 1 # assert self._ps is ps if n: self._n += n # Fsum._px = max(Fsum._px, len(ps)) if up: self._update() return self def _facc_(self, *xs, **up): '''(INTERNAL) Accumulate all positional C{scalar}s. ''' return self._facc(xs, **up) if xs else self # def _facc_up(self, up=True): # '''(INTERNAL) Update the C{partials}, by removing # and re-accumulating the final C{partial}. # ''' # while len(self._ps) > 1: # p = self._ps.pop() # if p: # n = self._n # self._facc_(p, up=False) # self._n = n # break # return self._update() if up else self # ._fpsqz() def fadd(self, xs=()): '''Add an iterable of C{scalar} or L{Fsum} instances to this instance. @arg xs: Iterable, list, tuple, etc. (C{scalar} or L{Fsum} instances). @return: This instance (L{Fsum}). @raise OverflowError: Partial C{2sum} overflow. @raise TypeError: An invalid B{C{xs}} type, not C{scalar} nor L{Fsum}. @raise ValueError: Invalid or non-finite B{C{xs}} value. ''' if isinstance(xs, Fsum): self._facc(xs._ps) elif isscalar(xs): # for backward compatibility self._facc_(_2float(x=xs)) # PYCHOK no cover elif xs: self._facc(_2floats(xs)) return self def fadd_(self, *xs): '''Add all positional C{scalar} or L{Fsum} instances to this instance. @arg xs: Values to add (C{scalar} or L{Fsum} instances), all positional. @return: This instance (L{Fsum}). @raise OverflowError: Partial C{2sum} overflow. @raise TypeError: An invalid B{C{xs}} type, not C{scalar} nor L{Fsum}. @raise ValueError: Invalid or non-finite B{C{xs}} value. ''' return self._facc(_2floats(xs, origin=1)) def _fadd(self, other, op): # in .fmath.Fhorner '''(INTERNAL) Apply C{B{self} += B{other}}. ''' if isinstance(other, Fsum): if other is self: self._facc_(*other._ps) # == ._facc(tuple(other._ps)) elif other._ps: self._facc(other._ps) elif not isscalar(other): raise self._TypeError(op, other) # txt=_invalid_ elif other: self._facc_(other) return self fcopy = copy # for backward compatibility fdiv = __itruediv__ # for backward compatibility fdivmod = __divmod__ # for backward compatibility def _fdivmod2(self, other, op): '''(INTERNAL) C{divmod(B{self}, B{other})} as 2-tuple (C{int} or C{float}, remainder C{self}). ''' # result mostly follows CPython function U{float_divmod # <https://GitHub.com/python/cpython/blob/main/Objects/floatobject.c>}, # but at least divmod(-3, 2) equals Cpython's result (-2, 1). q = self._copy_up(_fprs2=True)._ftruediv(other, op).floor if q: # == float // other == floor(float / other) self -= other * q s = signOf(other) # make signOf(self) == signOf(other) if s and self.signOf() == -s: # PYCHOK no cover self += other q -= 1 # t = self.signOf() # if t and t != s: # from pygeodesy.errors import _AssertionError # raise self._Error(op, other, _AssertionError, txt=signOf.__name__) return q, self # q is C{int} in Python 3+, but C{float} in Python 2- def _finite(self, other, op=None): '''(INTERNAL) Return B{C{other}} if C{finite}. ''' if _isfinite(other): return other raise ValueError(_not_finite_) if not op else \ self._ValueError(op, other, txt=_not_finite_) def fint(self, raiser=True, name=NN): '''Return this instance' current running sum as C{integer}. @kwarg raiser: If C{True} throw a L{ResidualError} if the I{integer} residual is non-zero. @kwarg name: Optional name (C{str}), overriding C{"fint"}. @return: The C{integer} (L{Fsum}). @raise ResidualError: Non-zero I{integer} residual. @see: Methods L{Fsum.int_float} and L{Fsum.is_integer}. ''' i, r = self._fint2 if r and raiser: t = _stresidual(_integer_, r) raise ResidualError(_integer_, i, txt=t) n = name or self.fint.__name__ return Fsum(name=n)._fset(i, asis=True) def fint2(self, **name): '''Return this instance' current running sum as C{int} and the I{integer} residual. @kwarg name: Optional name (C{str}). @return: An L{Fsum2Tuple}C{(fsum, residual)} with C{fsum} an C{int} and I{integer} C{residual} a C{float} or C{INT0} if the C{fsum} is considered to be I{exact}. ''' return Fsum2Tuple(*self._fint2, **name) @Property_RO def _fint2(self): # see ._fset '''(INTERNAL) Get 2-tuple (C{int}, I{integer} residual). ''' i = int(self._fprs) # int(self) r = _fsum(self._ps_1(i)) if len(self._ps) > 1 else ( (self._ps[0] - i) if self._ps else -i) return i, (r or INT0) @deprecated_property_RO def float_int(self): # PYCHOK no cover '''DEPRECATED, use method C{Fsum.int_float}.''' return self.int_float() # raiser=False @property_RO def floor(self): '''Get this instance' C{floor} (C{int} in Python 3+, but C{float} in Python 2-). @note: The C{floor} takes the C{residual} into account. @see: Method L{Fsum.int_float} and properties L{Fsum.ceil}, L{Fsum.imag} and L{Fsum.real}. ''' s, r = self._fprs2 f = _floor(s) + _floor(r) + 1 while r < (f - s): # (s + r) < f f -= 1 return f # floordiv = __floordiv__ # for naming consistency def _floordiv(self, other, op): # rather _ffloordiv? '''Apply C{B{self} //= B{other}}. ''' q = self._ftruediv(other, op) # == self return self._fset(q.floor, asis=True) # floor(q) fmul = __imul__ # for backward compatibility def _fmul(self, other, op): '''(INTERNAL) Apply C{B{self} *= B{other}}. ''' if isscalar(other): f = self._mul_scalar(other, op) elif not isinstance(other, Fsum): raise self._TypeError(op, other) # txt=_invalid_ elif len(self._ps) != 1: f = self._mul_Fsum(other, op) elif len(other._ps) != 1: # len(self._ps) == 1 f = other._copy_up()._mul_scalar(self._ps[0], op) else: # len(other._ps) == len(self._ps) == 1 s = self._finite(self._ps[0] * other._ps[0]) return self._fset(s, asis=True, n=len(self) + 1) return self._fset(f) def fover(self, over): '''Apply C{B{self} /= B{over}} and summate. @arg over: An L{Fsum} or C{scalar} denominator. @return: Precision running sum (C{float}). @see: Methods L{Fsum.fsum} and L{Fsum.__itruediv__}. ''' return float(self.fdiv(over)._fprs) fpow = __ipow__ # for backward compatibility def _fpow(self, other, op, *mod): '''Apply C{B{self} **= B{other}}, optional B{C{mod}} or C{None}. ''' if mod and mod[0] is not None: # == 3-arg C{pow} s = self._pow_3(other, mod[0], op) elif mod and mod[0] is None and self.is_integer(): # return an exact C{int} for C{int}**C{int} i = self._copy_0(self._fint2[0]) # assert _fint2[1] == 0 x = _2scalar(other) # C{int}, C{float} or other s = i._pow_2(x, other, op) if isscalar(x) else i._fpow(x, op) else: # pow(self, other) == pow(self, other, None) p = None if isinstance(other, Fsum): x, r = other._fprs2 if r: if self._raiser(r, x): raise self._ResidualError(op, other, r) p = self._pow_scalar(r, other, op) # p = _2scalar(p) # _raiser = None elif not isscalar(other): raise self._TypeError(op, other) # txt=_invalid_ else: x = self._finite(other, op) s = self._pow_scalar(x, other, op) if p is not None: s *= p return self._fset(s, asis=isint(s), n=max(len(self), 1)) @Property_RO def _fprs(self): '''(INTERNAL) Get and cache this instance' precision running sum (C{float} or C{int}), ignoring C{residual}. @note: The precision running C{fsum} after a C{//=} or C{//} C{floor} division is C{int} in Python 3+. ''' ps = self._ps n = len(ps) - 1 if n > 1: s = _psum(ps) elif n > 0: # len(ps) == 2 s, p = _2sum(*ps) if ps[1] else ps ps[:] = ([p, s] if s else [p]) if p else [s] elif n < 0: # see L{Fsum.__init__} s = _0_0 ps[:] = [s] else: # len(ps) == 1 s = ps[0] # assert self._ps is ps # assert Fsum._fprs2.name not in self.__dict__ return s @Property_RO def _fprs2(self): '''(INTERNAL) Get and cache this instance' precision running sum and residual (L{Fsum2Tuple}). ''' s = self._fprs r = _fsum(self._ps_1(s)) if len(self._ps) > 1 else INT0 return Fsum2Tuple(s, r) # name=Fsum.fsum2.__name__ # def _fpsqz(self): # '''(INTERNAL) Compress, squeeze the C{partials}. # ''' # if len(self._ps) > 2: # _ = self._fprs # return self def _fset(self, other, asis=False, n=1): '''(INTERNAL) Overwrite this instance with an other or a C{scalar}. ''' if other is self: pass # from ._fmul, ._ftruediv and ._pow_scalar elif isinstance(other, Fsum): self._n = other._n self._ps[:] = other._ps self._copy_RESIDUAL(other) # use or zap the C{Property_RO} values Fsum._fint2._update_from(self, other) Fsum._fprs ._update_from(self, other) Fsum._fprs2._update_from(self, other) elif isscalar(other): s = other if asis else float(other) i = int(s) # see ._fint2 t = i, ((s - i) or INT0) self._n = n self._ps[:] = [s] # Property_RO _fint2, _fprs and _fprs2 can't be a Property: # Property's _fset zaps the value just set by the @setter self.__dict__.update(_fint2=t, _fprs=s, _fprs2=Fsum2Tuple(s, INT0)) else: # PYCHOK no cover raise self._TypeError(_fset_op_, other) # txt=_invalid_ return self def fsub(self, xs=()): '''Subtract an iterable of C{scalar} or L{Fsum} instances from this instance. @arg xs: Iterable, list, tuple. etc. (C{scalar} or L{Fsum} instances). @return: This instance, updated (L{Fsum}). @see: Method L{Fsum.fadd}. ''' return self._facc(_2floats(xs, sub=True)) if xs else self def fsub_(self, *xs): '''Subtract all positional C{scalar} or L{Fsum} instances from this instance. @arg xs: Values to subtract (C{scalar} or L{Fsum} instances), all positional. @return: This instance, updated (L{Fsum}). @see: Method L{Fsum.fadd}. ''' return self._facc(_2floats(xs, origin=1, sub=True)) if xs else self def _fsub(self, other, op): '''(INTERNAL) Apply C{B{self} -= B{other}}. ''' if isinstance(other, Fsum): if other is self: # or other._fprs2 == self._fprs2: self._fset(_0_0, asis=True, n=len(self) * 2) # self -= self elif other._ps: self._facc(other._ps_n()) elif not isscalar(other): raise self._TypeError(op, other) # txt=_invalid_ elif self._finite(other, op): self._facc_(-other) return self def _Fsum(self, n, *ps): '''(INTERNAL) New L{Fsum} instance. ''' f = Fsum() f._n = n if ps: f._ps[:] = ps f._copy_RESIDUAL(self) return f def fsum(self, xs=()): '''Add more C{scalar} or L{Fsum} instances and summate. @kwarg xs: Iterable, list, tuple, etc. (C{scalar} or L{Fsum} instances). @return: Precision running sum (C{float} or C{int}). @see: Method L{Fsum.fadd}. @note: Accumulation can continue after summation. ''' f = self._facc(_2floats(xs)) if xs else self return f._fprs def fsum_(self, *xs): '''Add all positional C{scalar} or L{Fsum} instances and summate. @arg xs: Values to add (C{scalar} or L{Fsum} instances), all positional. @return: Precision running sum (C{float} or C{int}). @see: Method L{Fsum.fsum}. ''' f = self._facc(_2floats(xs, origin=1)) if xs else self return f._fprs def fsum2(self, xs=(), **name): '''Add more C{scalar} or L{Fsum} instances and return the current precision running sum and the C{residual}. @kwarg xs: Iterable, list, tuple, etc. (C{scalar} or L{Fsum} instances). @kwarg name: Optional name (C{str}). @return: L{Fsum2Tuple}C{(fsum, residual)} with C{fsum} the current precision running sum and C{residual}, the (precision) sum of the remaining C{partials}. The C{residual is INT0} if the C{fsum} is considered to be I{exact}. @see: Methods L{Fsum.fint2}, L{Fsum.fsum} and L{Fsum.fsum2_} ''' f = self._facc(_2floats(xs)) if xs else self t = f._fprs2 if name: t = t.dup(name=_xkwds_get(name, name=NN)) return t def fsum2_(self, *xs): '''Add any positional C{scalar} or L{Fsum} instances and return the precision running sum and the C{differential}. @arg xs: Values to add (C{scalar} or L{Fsum} instances), all positional. @return: 2-Tuple C{(fsum, delta)} with the current precision running C{fsum} and C{delta}, the difference with the previous running C{fsum} (C{float}s). @see: Methods L{Fsum.fsum_} and L{Fsum.fsum}. ''' p, r = self._fprs2 if xs: s, t = self._facc(_2floats(xs, origin=1))._fprs2 return s, _fsum((s, -p, r, -t)) # ((s - p) + (r - t)) else: # PYCHOK no cover return p, _0_0 # ftruediv = __itruediv__ # for naming consistency def _ftruediv(self, other, op): '''(INTERNAL) Apply C{B{self} /= B{other}}. ''' n = _1_0 if isinstance(other, Fsum): if other is self or other._fprs2 == self._fprs2: return self._fset(_1_0, asis=True, n=len(self)) d, r = other._fprs2 if r: if not d: # PYCHOK no cover d = r elif self._raiser(r, d): raise self._ResidualError(op, other, r) else: d, n = other.as_integer_ratio() elif isscalar(other): d = other else: # PYCHOK no cover raise self._TypeError(op, other) # txt=_invalid_ try: s = 0 if isinf(d) else ( d if isnan(d) else self._finite(n / d)) except Exception as x: E, t = _xError2(x) raise self._Error(op, other, E, txt=t) f = self._mul_scalar(s, _mul_op_) # handles 0, NAN, etc. return self._fset(f) @property_RO def imag(self): '''Get the C{imaginary} part of this instance (C{0.0}, always). @see: Properties L{Fsum.ceil}, L{Fsum.floor} and L{Fsum.real}. ''' return _0_0 def int_float(self, raiser=False): '''Return this instance' current running sum as C{int} or C{float}. @kwarg raiser: If C{True} throw a L{ResidualError} if the residual is non-zero. @return: This C{integer} sum if this instance C{is_integer}, otherwise return the C{float} sum if the residual is zero or if C{B{raiser}=False}. @raise ResidualError: Non-zero residual and C{B{raiser}=True}. @see: Methods L{Fsum.fint} and L{Fsum.fint2}. ''' s, r = self._fint2 if r: s, r = self._fprs2 if r and raiser: # PYCHOK no cover t = _stresidual(_non_zero_, r) raise ResidualError(int_float=s, txt=t) s = float(s) # redundant return s def is_exact(self): '''Is this instance' current running C{fsum} considered to be exact? (C{bool}). ''' return self.residual is INT0 def is_integer(self): '''Is this instance' current running sum C{integer}? (C{bool}). @see: Methods L{Fsum.fint} and L{Fsum.fint2}. ''' _, r = self._fint2 return False if r else True def is_math_fsum(self): '''Return whether functions L{fsum}, L{fsum_}, L{fsum1} and L{fsum1_} plus partials summation are based on Python's C{math.fsum} or not. @return: C{2} if all functions and partials summation are based on C{math.fsum}, C{True} if only the functions are based on C{math.fsum} (and partials summation is not) or C{False} if none are. ''' f = Fsum._math_fsum return 2 if _psum is f else bool(f) def _mul_Fsum(self, other, op=_mul_op_): '''(INTERNAL) Return C{B{self} * Fsum B{other}} as L{Fsum}. ''' # assert isinstance(other, Fsum) return self._copy_0()._facc(self._ps_x(op, *other._ps), up=False) def _mul_scalar(self, factor, op): '''(INTERNAL) Return C{B{self} * scalar B{factor}} as L{Fsum} or C{0}. ''' # assert isscalar(factor) if self._finite(factor, op) and self._ps: if factor == _1_0: return self f = self._copy_0()._facc(self._ps_x(op, factor), up=False) else: f = self._copy_0(_0_0) return f @property_RO def partials(self): '''Get this instance' current partial sums (C{tuple} of C{float}s and/or C{int}s). ''' return tuple(self._ps) def pow(self, x, *mod): '''Return C{B{self}**B{x}} as L{Fsum}. @arg x: The exponent (L{Fsum} or C{scalar}). @arg mod: Optional modulus (C{int} or C{None}) for the 3-argument C{pow(B{self}, B{other}, B{mod})} version. @return: The C{pow(self, B{x})} or C{pow(self, B{x}, *B{mod})} result (L{Fsum}). @note: If B{C{mod}} is given as C{None}, the result will be an C{integer} L{Fsum} provided this instance C{is_integer} or set C{integer} with L{Fsum.fint}. @see: Methods L{Fsum.__ipow__}, L{Fsum.fint} and L{Fsum.is_integer}. ''' f = self._copy_2(self.pow) if f and isint(x) and x >= 0 and not mod: f._pow_int(x, x, _pow_op_) # f **= x else: f._fpow(x, _pow_op_, *mod) # f = pow(f, x, *mod) return f def _pow_0_1(self, x, other): '''(INTERNAL) Return B{C{self}**1} or C{B{self}**0 == 1.0}. ''' return self if x else (1 if self.is_integer() and isint(other) else _1_0) def _pow_2(self, x, other, op): '''(INTERNAL) 2-arg C{pow(B{self}, scalar B{x})} embellishing errors. ''' # assert len(self._ps) == 1 and isscalar(x) b = self._ps[0] # assert isscalar(b) try: # type(s) == type(x) if x in (_1_0, 1) s = pow(b, x) # -1**2.3 == -(1**2.3) if not iscomplex(s): return self._finite(s) # 0**INF == 0.0, 1**INF==1.0 # neg**frac == complex in Python 3+, but ValueError in 2- E, t = _ValueError, _strcomplex(s, b, x) # PYCHOK no cover except Exception as x: E, t = _xError2(x) raise self._Error(op, other, E, txt=t) def _pow_3(self, other, mod, op): '''(INTERNAL) 3-arg C{pow(B{self}, B{other}, int B{mod} or C{None})}. ''' b, r = self._fprs2 if mod is None else self._fint2 if r and self._raiser(r, b): t = _non_zero_ if mod is None else _integer_ E, t = ResidualError, _stresidual(t, r, mod=mod) else: try: # b, other, mod all C{int}, unless C{mod} is C{None} x = _2scalar(other, _raiser=self._raiser) s = pow(b, x, mod) if not iscomplex(s): return self._finite(s) # neg**frac == complex in Python 3+, but ValueError in 2- E, t = _ValueError, _strcomplex(s, b, x, mod) # PYCHOK no cover except Exception as x: E, t = _xError2(x) t = _COMMASPACE_(Fmt.PARENSPACED(mod=mod), t) raise self._Error(op, other, E, txt=t) def _pow_int(self, x, other, op): '''(INTERNAL) Return C{B{self} **= B{x}} for C{int B{x} >= 0}. ''' # assert isint(x) and x >= 0 if len(self._ps) > 1: if x > 2: p = self._copy_up() m = 1 # single-bit mask if x & m: x -= m # x ^= m f = p._copy_up() else: f = self._copy_0(_1_0) while x: p = p._mul_Fsum(p, op) # p **= 2 m += m # m <<= 1 if x & m: x -= m # x ^= m f = f._mul_Fsum(p, op) # f *= p elif x > 1: # self**2 f = self._mul_Fsum(self, op) else: # self**1 or self**0 f = self._pow_0_1(x, other) elif self._ps: # self._ps[0]**x f = self._pow_2(x, other, op) else: # PYCHOK no cover # 0**pos_int == 0, but 0**0 == 1 f = 0 if x else 1 # like ._fprs return self._fset(f, asis=isint(f), n=len(self)) def _pow_scalar(self, x, other, op): '''(INTERNAL) Return C{self**B{x}} for C{scalar B{x}}. ''' s, r = self._fprs2 if isint(x, both=True): x = int(x) # Fsum**int y = abs(x) if y > 1: if r: f = self._copy_up()._pow_int(y, other, op) if x > 0: # > 1 return f # assert x < 0 # < -1 s, r = f._fprs2 if r: return self._copy_0(_1_0)._ftruediv(f, op) # use **= -1 for the CPython float_pow # error if s is zero, and not s = 1 / s x = -1 # elif y > 1: # self**2 or self**-2 # f = self._mul_Fsum(self, op) # if x < 0: # f = f._copy_0(_1_0)._ftruediv(f, op) # return f elif x < 0: # self**-1 == 1 / self if r: return self._copy_0(_1_0)._ftruediv(self, op) else: # self**1 or self**0 return self._pow_0_1(x, other) # self or 0.0 elif not isscalar(x): # assert ... raise self._TypeError(op, other, txt=_not_scalar_) elif r and self._raiser(r, s): # non-zero residual**fractional # raise self._ResidualError(op, other, r, fractional_power=x) t = _stresidual(_non_zero_, r, fractional_power=x) raise self._Error(op, other, ResidualError, txt=t) # assert isscalar(s) and isscalar(x) return self._copy_0(s)._pow_2(x, other, op) def _ps_1(self, *less): '''(INTERNAL) Yield partials, 1-primed and subtract any C{less}. ''' yield _1_0 for p in self._ps: if p: yield p for p in less: if p: yield -p yield _N_1_0 def _ps_n(self): '''(INTERNAL) Yield partials, negated. ''' for p in self._ps: if p: yield -p def _ps_x(self, op, *factors): # see .fmath.Fhorner '''(INTERNAL) Yield all C{partials} times each B{C{factor}}, in total, up to C{len(partials) * len(factors)} items. ''' ps = self._ps if len(ps) < len(factors): ps, factors = factors, ps _f = _isfinite for f in factors: for p in ps: p *= f if _f(p): yield p else: # PYCHOK no cover self._finite(p, op) # throw ValueError @property_RO def real(self): '''Get the C{real} part of this instance (C{float}). @see: Methods L{Fsum.__float__} and L{Fsum.fsum} and properties L{Fsum.ceil}, L{Fsum.floor}, L{Fsum.imag} and L{Fsum.residual}. ''' return float(self._fprs) @property_RO def residual(self): '''Get this instance' residual (C{float} or C{int}), the C{sum(partials)} less the precision running sum C{fsum}. @note: If the C{residual is INT0}, the precision running C{fsum} is considered to be I{exact}. @see: Methods L{Fsum.fsum}, L{Fsum.fsum2} and L{Fsum.is_exact}. ''' return self._fprs2.residual def _raiser(self, r, s): '''(INTERNAL) Does the ratio C{r / s} exceed threshold? ''' self._ratio = t = fabs((r / s) if s else r) return t > self._RESIDUAL def RESIDUAL(self, *threshold): '''Get and set this instance' I{ratio} for raising L{ResidualError}s, overriding the default from env variable C{PYGEODESY_FSUM_RESIDUAL}. @arg threshold: If C{scalar}, the I{ratio} to exceed for raising L{ResidualError}s in division and exponention, if C{None} restore the default set with env variable C{PYGEODESY_FSUM_RESIDUAL} or if omitted, keep the current setting. @return: The previous C{RESIDUAL} setting (C{float}). @raise ValueError: Negative B{C{threshold}}. @note: A L{ResidualError} is thrown if the non-zero I{ratio} C{residual} / C{fsum} exceeds the B{C{threshold}}. ''' r = self._RESIDUAL if threshold: t = threshold[0] t = Fsum._RESIDUAL if t is None else ( float(t) if isscalar(t) else ( # for backward ... _0_0 if bool(t) else _1_0)) # ... compatibility if t < 0: u = self._unstr(self.RESIDUAL, *threshold) raise _ValueError(u, RESIDUAL=t, txt=_negative_) self._RESIDUAL = t return r def _ResidualError(self, op, other, residual): '''(INTERNAL) Non-zero B{C{residual}} etc. ''' t = _stresidual(_non_zero_, residual, ratio=self._ratio, RESIDUAL=self._RESIDUAL) t = t.replace(_COMMASPACE_R_, _exceeds_R_) return self._Error(op, other, ResidualError, txt=t) def signOf(self, res=True): '''Determine the sign of this instance. @kwarg res: If C{True} consider, otherwise ignore the residual (C{bool}). @return: The sign (C{int}, -1, 0 or +1). ''' s, r = self._fprs2 if res else (self._fprs, 0) return _signOf(r, -s) def toRepr(self, **prec_sep_fmt_lenc): # PYCHOK signature '''Return this C{Fsum} instance as representation. @kwarg prec_sep_fmt_lenc: Optional keyword arguments for method L{Fsum2Tuple.toRepr} plus C{B{lenc}=True} (C{bool}) to in-/exclude the current C{[len]} of this L{Fsum} enclosed in I{[brackets]}. @return: This instance (C{repr}). ''' return self._toT(self._fprs2.toRepr, **prec_sep_fmt_lenc) def toStr(self, **prec_sep_fmt_lenc): # PYCHOK signature '''Return this C{Fsum} instance as string. @kwarg prec_sep_fmt_lenc: Optional keyword arguments for method L{Fsum2Tuple.toStr} plus C{B{lenc}=True} (C{bool}) to in-/exclude the current C{[len]} of this L{Fsum} enclosed in I{[brackets]}. @return: This instance (C{str}). ''' return self._toT(self._fprs2.toStr, **prec_sep_fmt_lenc) def _toT(self, toT, fmt=Fmt.g, lenc=True, **kwds): '''(INTERNAL) Helper for C{toRepr} and C{toStr}. ''' n = self.named3 if lenc: n = Fmt.SQUARE(n, len(self)) return _SPACE_(n, toT(fmt=fmt, **kwds)) def _TypeError(self, op, other, **txt): # PYCHOK no cover '''(INTERNAL) Return a C{TypeError}. ''' return self._Error(op, other, _TypeError, **txt) def _update(self): # see ._fset '''(INTERNAL) Zap all cached C{Property_RO} values. ''' Fsum._fint2._update(self) Fsum._fprs ._update(self) Fsum._fprs2._update(self) return self def _ValueError(self, op, other, **txt): # PYCHOK no cover '''(INTERNAL) Return a C{ValueError}. ''' return self._Error(op, other, _ValueError, **txt) def _ZeroDivisionError(self, op, other, **txt): # PYCHOK no cover '''(INTERNAL) Return a C{ZeroDivisionError}. ''' return self._Error(op, other, _ZeroDivisionError, **txt) _allPropertiesOf_n(3, Fsum, Property_RO) # PYCHOK assert, see Fsum._fset, -._update def _Float_Int(arg, **name_Error): '''(INTERNAL) Unit of L{Fsum2Tuple} items. ''' U = Int if isint(arg) else Float return U(arg, **name_Error) class Fsum2Tuple(_NamedTuple): '''2-Tuple C{(fsum, residual)} with the precision running C{fsum} and the C{residual}, the sum of the remaining partials. Each item is either C{float} or C{int}. @note: If the C{residual is INT0}, the C{fsum} is considered to be I{exact}, see method L{Fsum2Tuple.is_exact}. ''' _Names_ = ( Fsum.fsum.__name__, Fsum.residual.name) _Units_ = (_Float_Int, _Float_Int) @Property_RO def Fsum(self): '''Get this L{Fsum2Tuple} as an L{Fsum}. ''' f = Fsum(name=self.name) return f._copy_0(*(s for s in reversed(self) if s)) def is_exact(self): '''Is this L{Fsum2Tuple} considered to be exact? (C{bool}). ''' return self.Fsum.is_exact() def is_integer(self): '''Is this L{Fsum2Tuple} C{integer}? (C{bool}). ''' return self.Fsum.is_integer() class ResidualError(_ValueError): '''Error raised for an operation involving a L{pygeodesy.sums.Fsum} instance with a non-zero C{residual}, I{integer} or otherwise. @see: Module L{pygeodesy.fsums} and method L{Fsum.RESIDUAL}. ''' pass try: from math import fsum as _fsum # precision IEEE-754 sum, Python 2.6+ # make sure _fsum works as expected (XXX check # float.__getformat__('float')[:4] == 'IEEE'?) if _fsum((1, 1e101, 1, -1e101)) != 2: # PYCHOK no cover del _fsum # nope, remove _fsum ... raise ImportError # ... use _fsum below Fsum._math_fsum = _fsum if _getenv('PYGEODESY_FSUM_PARTIALS', _fsum.__name__) == _fsum.__name__: _psum = _fsum # PYCHOK redef except ImportError: def _fsum(xs): '''(INTERNAL) Precision summation, Python 2.5-. ''' return Fsum(name=_fsum.__name__)._facc(xs, up=False)._fprs def fsum(xs, floats=False): '''Precision floating point summation based on or like Python's C{math.fsum}. @arg xs: Iterable, list, tuple, etc. of values (C{scalar} or L{Fsum} instances). @kwarg floats: Optionally, set C{B{floats}=True} iff I{all} B{C{xs}} are known to be C{float}. @return: Precision C{fsum} (C{float}). @raise OverflowError: Partial C{2sum} overflow. @raise TypeError: Non-scalar B{C{xs}} value. @raise ValueError: Invalid or non-finite B{C{xs}} value. @note: Exceptions and I{non-finite} handling may differ if not based on Python's C{math.fsum}. @see: Class L{Fsum} and methods L{Fsum.fsum} and L{Fsum.fadd}. ''' return _fsum(_2floats(xs, floats=floats)) if xs else _0_0 def fsum_(*xs, **floats): '''Precision floating point summation of all positional arguments. @arg xs: Values to be added (C{scalar} or L{Fsum} instances), all positional. @kwarg floats: Optionally, set C{B{floats}=True} iff I{all} B{C{xs}} are known to be C{float}. @return: Precision C{fsum} (C{float}). @see: Function C{fsum}. ''' if xs: f = _xkwds_get(floats, floats=False) return _fsum(_2floats(xs, origin=1, floats=f)) else: # PYCHOK no cover return _0_0 def fsum1(xs, floats=False): '''Precision floating point summation of a few values, 1-primed. @arg xs: Iterable, list, tuple, etc. of values (C{scalar} or L{Fsum} instances). @kwarg floats: Optionally, set C{B{floats}=True} iff I{all} B{C{xs}} are known to be C{float}. @return: Precision C{fsum} (C{float}). @see: Function C{fsum}. ''' return _fsum(_2floats(xs, primed=True, floats=floats)) if xs else _0_0 def fsum1_(*xs, **floats): '''Precision floating point summation of a few arguments, 1-primed. @arg xs: Values to be added (C{scalar} or L{Fsum} instances), all positional. @kwarg floats: Optionally, set C{B{floats}=True} iff I{all} B{C{xs}} are known to be C{float}. @return: Precision C{fsum} (C{float}). @see: Function C{fsum} ''' if xs: f = _xkwds_get(floats, floats=False) return _fsum(_2floats(xs, origin=1, primed=True, floats=f)) else: # PYCHOK no cover return _0_0 # **) MIT License # # Copyright (C) 2016-2022 -- mrJean1 at Gmail -- All Rights Reserved. # # Permission is hereby granted, free of charge, to any person obtaining a # copy of this software and associated documentation files (the "Software"), # to deal in the Software without restriction, including without limitation # the rights to use, copy, modify, merge, publish, distribute, sublicense, # and/or sell copies of the Software, and to permit persons to whom the # Software is furnished to do so, subject to the following conditions: # # The above copyright notice and this permission notice shall be included # in all copies or substantial portions of the Software. # # THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS # OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, # FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL # THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR # OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, # ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR # OTHER DEALINGS IN THE SOFTWARE.