# Coverage for pygeodesy/fsums.py : 98%

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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_, _BANG_, _COMMASPACE_, _DASH_, \ _EQUAL_, _exceeds_, _from_, _iadd_, _LANGLE_, \ _negative_, _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__ = '22.09.24' _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_ = _BANG_ + _EQUAL_ _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 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): '''Precision floating point I{running} summation similar to standard Python's C{math.fsum}. Unlike C{math.fsum}, this class accumulates values and provides I{intermediate} precision floating point summation. Accumulation may continue after I{intermediate} summuation, aka I{running} summation. @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 of values C{inf}, C{INF}, C{nan} and C{NAN} differs from standard 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 __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): '''(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.