# Coverage for pygeodesy/fsums.py : 98%

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1622 1623 1624 1625 1626 1627 1628 1629 1630 1631 1632 1633 1634 1635 1636 1637 1638 1639 1640 1641 1642 1643 1644 1645 1646 1647 1648 1649 1650 1651 1652 1653 1654 1655 1656 1657 1658 1659 1660 1661 1662 1663 1664 1665 1666 1667 1668 1669 1670 1671 1672 1673 1674 1675 1676 1677 1678 1679 1680 1681 1682 1683 1684 1685 1686 1687 1688 1689 1690 1691 1692 1693 1694 1695 1696 1697 1698 1699 1700 1701 1702 1703 1704 1705 1706 1707 1708 1709 1710 1711 1712 | # -*- coding: utf-8 -*- u'''Class L{Fsum} for precision floating point I{running} summation. 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, 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 anywhere between C{-1.0} and C{+1.0}, including C{INT0} if considered to be I{exact}. Set env variable C{PYGEODESY_FSUM_RESIDUAL} to any non-empty string to throw a L{ResidualError} for division or exponention by an L{Fsum} instance with a non-zero C{residual}, see methods L{Fsum.RESIDUAL}, L{Fsum.pow}, L{Fsum.__itruediv__} and L{Fsum.__ipow__}. ''' # make sure int/int division yields float quotient, see .basics from __future__ import division as _; del _ # PYCHOK semicolon from pygeodesy.basics import iscomplex, _isfinite, isinf, isint, isnan, \ isscalar, map1, neg, signOf, _signOf from pygeodesy.errors import _OverflowError, _TypeError, _ValueError, \ _xError2, _xkwds_get, _ZeroDivisionError from pygeodesy.interns import INT0, NN, _COMMASPACE_, _DASH_, _EQUAL_, _from_, \ _iadd_, _not_finite_, _not_scalar_, _PERCENT_, \ _PLUS_, _SLASH_, _SPACE_, _STAR_, _0_0, _1_0, _N_1_0 from pygeodesy.lazily import _ALL_LAZY, _getenv, _sys_version_info2 from pygeodesy.named import _Named, _NamedTuple, _NotImplemented from pygeodesy.props import deprecated_property_RO, Property_RO, property_RO from pygeodesy.streprs import Fmt, pairs, unstr from pygeodesy.units import Float, Int from math import ceil as _ceil, floor as _floor # PYCHOK used! __all__ = _ALL_LAZY.fsums __version__ = '22.03.01' _eq_ = _EQUAL_ * 2 _ge_ = '>=' _gt_ = '>' # _RANGLE_ _le_ = '<=' _lt_ = '<' # _LANGLE_ _ne_ = '!=' _add_ = _PLUS_ _arg_ = 'arg' _floordiv_ = _SLASH_ * 2 _fset_ = _EQUAL_ _integer_ = 'integer' _mod_ = _PERCENT_ _divmod_ = _floordiv_ + _mod_ _mul_ = _STAR_ _non_zero_ = 'non-zero' _pow_ = _STAR_ * 2 _residual_ = 'residual' _sub_ = _DASH_ _truediv_ = _SLASH_ _pos_self = _1_0.__pos__() is _1_0 def _2even(s, r, p): '''(INTERNAL) Half-even rounding. ''' if (r > 0 and p > 0) or \ (r < 0 and p < 0): # signs match r, p = _2sum(s, p * 2) if not p: s = r return s 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): '''(INTERNAL) Yield all B{C{xs}} as C{float}s. ''' _2f = _2float if primed: yield _1_0 i = origin for x in xs: if 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 _2Fsum(other, name=NN): '''(INTERNAL) Return B{C{other}} as an L{Fsum} instance. ''' return other.copy(name=name) if isinstance(other, Fsum) else \ Fsum(name=name)._fset(_2float(other=other), asis=True) def _2scalar(other, raiser=False): '''(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: if raiser: raise ValueError(_2stresidual(_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 _2strcomplex(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 _2stresidual(prefix, residual, **name_values): '''(INTERNAL) Residual error C{str}. ''' def _fmt(s): return str(s) if isint(s) and abs(s) < 1e9 else ( Fmt.g(s, prec=9) if isscalar(s) else repr(s)) p = _SPACE_(prefix, _residual_) t = Fmt.PARENSPACED(p, _fmt(residual)) for n, v in name_values.items(): n = Fmt.PARENSPACED(n, _fmt(v)) t = _COMMASPACE_(t, n) return t def _2sum(a, b): # by .testFmath '''(INTERNAL) Precision C{2sum} of M{a + b} as 2-tuple (sum, residual). ''' s = a + b if not _isfinite(s): raise _OverflowError(unstr(_2sum.__name__, a, b), txt=str(s)) if abs(a) < abs(b): a, b = b, a return s, (b - (s - a)) # abs(b) <= abs(a) 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 C{scalar} or other L{Fsum} instances with C{scalar} meaning type C{float}, C{int} or any C{type} convertible into a single-instance 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 _RESIDUAL = bool(_getenv('PYGEODESY_FSUM_RESIDUAL', NN)) def __init__(self, *xs, **name_NN): '''New L{Fsum} for precision floating point I{running} summation. @arg xs: No, one or more initial values (C{scalar} or L{Fsum} instances). @kwarg name_NN: Optional name (C{str}). @see: Method L{Fsum.fadd}. ''' # self._n = 0 self._ps = [] # [_0_0], see L{Fsum._fprs} if name_NN: self.name = _xkwds_get(name_NN, name=NN) if xs: self._facc(_2floats(xs, origin=1)) def __abs__(self): '''Return this instance' absolute value as an L{Fsum}. ''' f = self.copy(name=self.__abs__.__name__) return f._fneg() if f < 0 else f def __add__(self, other): '''Return the sum C{B{self} + B{other}} as an L{Fsum}. @arg other: An L{Fsum} or C{scalar}. @return: The sum (L{Fsum}). @see: Method L{Fsum.__iadd__}. ''' f = self.copy(name=self.__add__.__name__) return f._fadd(other, _add_) def __bool__(self): # PYCHOK not special in Python 2- '''Return C{True} if this instance is non-zero. ''' s, r = self._fprs2 return bool(s or r) 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(name=self.__divmod__.__name__) return f._fdivmod(other, _divmod_) def __eq__(self, other): '''Compare this with an other instance or scalar. ''' s, r = self._cmp2(other, _eq_) return not bool(s or r) 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(name=self.__floordiv__.__name__) return f._floordiv(other, _floordiv_) 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. ''' s, r = self._cmp2(other, _ge_) return r >= -s def __gt__(self, other): '''Compare this with an other instance or scalar. ''' s, r = self._cmp2(other, _gt_) return r > -s 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_ + _fset_) 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._fdivmod(other, _mod_ + _fset_) 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_ + _fset_) 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}. ''' return int(self._fprs) 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_ + _fset_, *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_ + _fset_) 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_ + _fset_) def __le__(self, other): '''Compare this with an other instance or scalar. ''' s, r = self._cmp2(other, _le_) return r <= -s def __len__(self): '''Return the I{total} number of values accumulated (C{int}). ''' return self._n def __lt__(self, other): '''Compare this with an other instance or scalar. ''' s, r = self._cmp2(other, _lt_) return r < -s 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(name=self.__mod__.__name__) return f._fdivmod(other, _mod_)[1] def __mul__(self, other): '''Return C{B{self} * B{other}} as an L{Fsum}. @see: Method L{Fsum.__imul__}. ''' f = self.copy(name=self.__mul__.__name__) return f._fmul(other, _mul_) def __ne__(self, other): '''Compare this with an other instance or scalar. ''' s, r = self._cmp2(other, _ne_) return bool(s or r) def __neg__(self): '''Return I{a copy of} this instance, negated. ''' f = self.copy(name=self.__neg__.__name__) return f._fneg() def __pos__(self): '''Return this instance I{as-is}, like C{float.__pos__()}. ''' return self if _pos_self else self.copy(name=self.__pos__.__name__) 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(name=self.__pow__.__name__) return f._fpow(other, _pow_, *mod) def __radd__(self, other): '''Return C{B{other} + B{self}} as an L{Fsum}. @see: Method L{Fsum.__iadd__}. ''' f = _2Fsum(other, name=self.__radd__.__name__) return f._fadd(self, _add_) def __rdivmod__(self, other): '''Return C{divmod(B{other}, B{self})} as 2-tuple C{(quotient, remainder)}. @see: Method L{Fsum.__divmod__}. ''' f = _2Fsum(other, name=self.__rdivmod__.__name__) return f._fdivmod(self, _divmod_) # def __repr__(self): # '''Return the default C{repr(this)}. # ''' # return self.toRepr() def __rfloordiv__(self, other): '''Return C{B{other} // B{self}} as an L{Fsum}. @see: Method L{Fsum.__ifloordiv__}. ''' f = _2Fsum(other, name=self.__rfloordiv__.__name__) return f._floordiv(self, _floordiv_) 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 = _2Fsum(other, name=self.__rmod__.__name__) return f._fdivmod(self, _mod_)[1] def __rmul__(self, other): '''Return C{B{other} * B{self}} as an L{Fsum}. @see: Method L{Fsum.__imul__}. ''' f = _2Fsum(other, name=self.__rmul__.__name__) return f._fmul(self, _mul_) 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 = _2Fsum(other, name=self.__rpow__.__name__) return f._fpow(self, _pow_, *mod) def __rsub__(self, other): '''Return C{B{other} - B{self}} as L{Fsum}. @see: Method L{Fsum.__isub__}. ''' f = _2Fsum(other, name=self.__rsub__.__name__) return f._fsub(self, _sub_) def __rtruediv__(self, other): '''Return C{B{other} / B{self}} as an L{Fsum}. @see: Method L{Fsum.__itruediv__}. ''' f = _2Fsum(other, name=self.__rtruediv__.__name__) return f._ftruediv(self, _truediv_) def __sizeof__(self): # PYCHOK not special in Python 2- '''Return the size of this instance in C{bytes}. ''' from sys import getsizeof return sum(map1(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() 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(name=self.__sub__.__name__) return f._fsub(other, _sub_) 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(name=self.__truediv__.__name__) return f._ftruediv(other, _truediv_) __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 integer ratio. @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 = (n * d) + 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 _cmp2(self, other, op): '''(INTERNAL) Subtract an B{C{other}} instance or scalar and return an L{Fsum2Tuple}C{(fsum, residual)} for comparison operator B{C{op}}. ''' if isinstance(other, Fsum): f = self._copy()._facc(map(neg, other._ps)) elif not isscalar(other): raise self._TypeError(op, other, txt=_not_scalar_) elif self._finite(other, op): f = self._copy()._facc_(-other) else: f = self return f._fprs2 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._update(other=self) f._n = self._n if deep else 1 f._ps = list(self._ps) # separate list return f def _copy(self, _fprs2=False): '''(INTERNAL) Fast, un-named copy. ''' f = Fsum() # NN f._n = self._n f._ps[:] = self._ps if _fprs2: 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__}. ''' return self.copy(name=self.divmod.__name__)._fdivmod(other, _divmod_) 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 _facc(self, xs): '''(INTERNAL) Accumulate more C{scalar}s. ''' ps, n, _2s = self._ps, 0, _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 self._update() return self def _facc_(self, *xs): '''(INTERNAL) Accumulate any positional C{scalar}s. ''' return self._facc(xs) def _facc_up(self): '''(INTERNAL) Update the C{partials}, by removing and re-adding the final C{partial}. ''' while len(self._ps) > 1: p = self._ps.pop() if p: self._facc_(p) self._n -= 1 break else: # force zap self._update() return self._fpsqz() def fadd(self, xs=()): '''Add more C{scalar} or L{Fsum} instances from an iterable. @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 any positional C{scalar} or L{Fsum} instances. @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: # or other._fprs2 == self._fprs2: self._fmul(2, op) # == self += self self._n *= 2 elif other._ps: self._facc(other._ps) elif not isscalar(other): raise self._TypeError(op, other, txt=_not_scalar_) elif other: self._facc_(other) return self fcopy = copy # for backward compatibility fdiv = __itruediv__ # for backward compatibility fdivmod = __divmod__ # for backward compatibility def _fdivmod(self, other, op): '''(INTERNAL) C{divmod(B{self}, B{other})} as 2-tuple (C{int} or C{float}, C{self}). ''' # mostly like like 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(_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: 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 = _2stresidual(_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): '''Return this instance' current running sum as C{int} and the I{integer} residual. @return: 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 I{exact}. ''' return Fsum2Tuple(*self._fint2) @Property_RO def _fint2(self): '''(INTERNAL) Get 2-tuple (C{int}, I{integer} residual). ''' i = int(self._fprs) # int(self) # assert len(self._ps) > 0 r = _fsum(self._ps1(i)) if len(self._ps) > 1 else ( (self._ps[0] - i) or INT0) return i, r @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}}. ''' a = False if isinstance(other, Fsum): if len(self._ps) != 1: f = self._mul_Fsum(other, op) elif len(other._ps) != 1: f = other._mul_scalar(self._ps[0], op) f._n = self._n else: f = self._finite(other._ps[0] * self._ps[0], op) a = isint(f) elif not isscalar(other): raise self._TypeError(op, other, txt=_not_scalar_) else: f = self._mul_scalar(other, op) return self._fset(f, asis=a) def _fneg(self): '''(INTERNAL) Negate this instance. ''' if self._ps: self._ps[:] = map(neg, self._ps) self._facc_up() return self 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._fint2 # assert _ == 0 x = _2scalar(other) # C{int}, C{float} or other if isscalar(x): s = self._Fsum(i)._pow_2(x, other, op) else: s = self._Fsum(i)._fpow(other, op) else: # pow(self, other) == pow(self, other, None) p = None if isinstance(other, Fsum): x, r = other._fprs2 if r: if self._RESIDUAL: raise self._ResidualError(op, other, r) p = self._pow_scalar(r, other, op) p = _2scalar(p) # raiser=False elif not isscalar(other): raise self._TypeError(op, other, txt=_not_scalar_) else: x = self._finite(other, op) s = self._pow_scalar(x, other, op) if p not in (None, _1_0, 1): s *= p # each C{scalar} or L{Fsum} return self._fset(s, asis=isint(s)) @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 i = len(ps) - 1 if i < 0: s = _0_0 ps[:] = [s] else: s, _2s = ps[i], _2sum while i > 0: i -= 1 s, p = _2s(s, ps[i]) ps[i:] = [s] if p: # sum(ps) became inexact if s: ps.append(p) if i > 0: # half-even round if signs match s = _2even(s, ps[i-1], p) break else: # PYCHOK no cover ps[i] = s = p # replace and continue # 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._ps1(s)) if len(self._ps) > 1 else INT0 return Fsum2Tuple(s, r) 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 ._pow_scalar elif isinstance(other, Fsum): self._n = other._n self._ps[:] = other._ps self._update(other=other) elif isscalar(other): s = other if asis else float(other) self._n = n self._ps[:] = [s] self._update(_fprs=s, _fprs2=Fsum2Tuple(s, INT0)) else: # PYCHOK no cover raise self._TypeError(_fset_, other) # txt=_invalid_ return self def fsub(self, xs=()): '''Subtract C{scalar} or L{Fsum} instances from an iterable. @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 any positional C{scalar} or L{Fsum} instances. @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(map(neg, other._ps)) elif not isscalar(other): raise self._TypeError(op, other, txt=_not_scalar_) elif other: self._facc_(-other) return self def _Fsum(self, x): '''(INTERNAL) Fast, single-scalar C{_Fsum}, named the same. ''' f = _Fsum(x) # C{int} or C{scalar} f._name = self.name # .rename calls _update_all return f def fsum(self, xs=()): '''Add more C{scalar} or L{Fsum} instances and sum all. @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 any positional C{scalar} or L{Fsum} instances and sum all. @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=()): '''Add more C{scalar} or L{Fsum} instances and return the current precision running sum and residual. @kwarg xs: Iterable, list, tuple, etc. (C{scalar} or L{Fsum} instances). @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}. @see: Methods L{Fsum.fint2}, L{Fsum.fsum} and L{Fsum.fsum2_} ''' f = self._facc(_2floats(xs)) if xs else self return f._fprs2 def fsum2_(self, *xs): '''Add any positional C{scalar} or L{Fsum} instances and return the precision running sum and the increase. @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). @note: If the C{residual is INT0}, the C{fsum} is considered to be I{exact}. @see: Methods L{Fsum.fsum_} and L{Fsum.fsum}. ''' p, r = self._fprs2 s, t = self._facc(_2floats(xs, origin=1))._fprs2 if xs else (p, r) return s, ((s - p) + (t - r)) # == _fsum((s, -p, t, -r)) # ftruediv = __itruediv__ # for naming consistency def _ftruediv(self, other, op): '''(INTERNAL) Apply C{B{self} /= B{other}}. ''' if isinstance(other, Fsum): if other is self or other._fprs2 == self._fprs2: return self._fset(_1_0, asis=True) d, r = other._fprs2 if r: if self._RESIDUAL: raise self._ResidualError(op, other, r) if d: # self / (d + r) == self * n / d # n = d / (d + r) = 1 / (1 + r / d) # d' = d / n = d * (1 + r / d), but # may be moot if (1 + r / d) == 1 d *= r / d + _1_0 else: # PYCHOK no cover d = r 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(_1_0 / d)) except Exception as x: E, t = _xError2(x) raise self._Error(op, d, E, txt=t) f = self._mul_scalar(s, _mul_) # 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} or this C{float} sum if the residual is zero or ignored. @raise ResidualError: Non-zero residual. @see: Methods L{Fsum.fint} and L{Fsum.fint2}. ''' s, r = self._fint2 if r: s, r = self._fprs2 if r and raiser: t = _2stresidual(_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 not r def is_math_fsum(self): '''Return C{True} if functions L{fsum}, L{fsum_}, L{fsum1} and L{fsum1_} are all based on Python's C{math.fsum}, C{False} otherwise. ''' return bool(Fsum._math_fsum) def _mul_Fsum(self, other, op): '''(INTERNAL) Return C{B{self} * Fsum B{other}} as L{Fsum}. ''' # assert isinstance(other, Fsum) return self._Fsum(_0_0)._facc(self._ps_x(op, *other._ps))._fpsqz() 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: f = self._Fsum(0) f._n = self._n f._ps[:] = self._ps_x(op, factor) f._facc_up() else: f = self else: # to allow setting f._n f = _Fsum(_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(name=self.pow.__name__) if f and isint(x) and x >= 0 and not mod: f._pow_int(x, x, _pow_) # f **= x else: f._fpow(x, _pow_, *mod) # f = pow(f, x, *mod) return f def _pow_0_1(self, x): '''(INTERNAL) Return B{C{self}**1} or C{B{self}**0 == 1.0}. ''' return self if x 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**2.2) 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, _2strcomplex(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._RESIDUAL: t = _non_zero_ if mod is None else _integer_ E, t = ResidualError, _2stresidual(t, r, mod=mod) else: try: # b, other, mod all C{int}, unless C{mod} is C{None} x = _2scalar(other, raiser=self._RESIDUAL) 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, _2strcomplex(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() m = 1 # single-bit mask if x & m: x -= m # x ^= m f = p._copy() else: f = _Fsum(_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) 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)) 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: s = self._copy()._pow_int(y, other, op) if x < 0: _, r = s._fprs2 if r: s, x = self._Fsum(_1_0)._ftruediv(s, op), None else: # use **= -1 for the CPython float_pow # error if s is zero, and not s = 1 / s s, x = s._fprs, -1 else: x = None elif x < 0: # self**-1 == 1 / self if r: s, x = self._Fsum(_1_0)._ftruediv(self, op), None else: # self**1 or self**0 s, x = self._pow_0_1(x), None elif not isscalar(x): # assert ... raise self._TypeError(op, other, txt=_not_scalar_) elif r: # non-zero residual**fractional raise self._ResidualError(op, other, r, fractional=x) if x is not None: # assert isscalar(s) and isscalar(x) s = self._Fsum(s)._pow_2(x, other, op) return s # C{int}, C{scalar}, C{self} or an L{Fsum} def _ps1(self, less): '''(INTERNAL) Yield partials, pseudo-sorted, 1-primed minus C{less} if non-zero. ''' yield _1_0 if less: yield -less for p in self._ps: if p > 0: yield p for p in self._ps: if p < 0: yield p yield _N_1_0 def _ps_x(self, op, *factors): # see .fmath.Fhorner '''(INTERNAL) Yield all C{partials} times each B{C{factor}}. ''' _f = self._finite ps = self._ps if len(ps) < len(factors): ps, factors = factors, ps for f in factors: for p in ps: yield _f(p * f, op) @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 sum of the C{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 RESIDUAL(self, *raiser): '''Do or don't raise L{ResidualError}s for this instance, overriding the default setting from env var C{PYGEODESY_FSUM_RESIDUAL}. @arg raiser: If C{True} throw L{ResidualError}s for division and exponention, if C{False} don't, if C{None} restore the default setting (C{bool}) and if omitted, maintain the current setting. @return: The previous C{RESIDUAL} setting (C{bool}). ''' r = self._RESIDUAL if raiser: s = raiser[0] self._RESIDUAL = Fsum._RESIDUAL if s is None else bool(s) return r def _ResidualError(self, op, other, residual, **name_values): '''(INTERNAL) Non-zero B{C{residual}} and C{name=value, ...} error. ''' t = _2stresidual(_non_zero_, residual, **name_values) 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=6, sep=_COMMASPACE_, fmt=Fmt.g, **unused): # PYCHOK signature '''Return this C{Fsum} instance as representation. @kwarg prec: The C{float} precision, number of decimal digits (0..9). Trailing zero decimals are stripped for B{C{prec}} values of 1 and above, but kept for negative B{C{prec}} values. @kwarg sep: Optional separator to join (C{str}). @kwarg fmt: Optional, C{float} format (C{str}). @return: This instance (C{str}). ''' t = sep.join(pairs(self._fprs2.items(), prec=prec, fmt=fmt)) return _SPACE_(Fmt.SQUARE(self.named3, len(self)), Fmt.PAREN(t)) def toStr(self, prec=6, sep=_COMMASPACE_, fmt=Fmt.g, **unused): # PYCHOK signature '''Return this C{Fsum} instance as string. @kwarg prec: The C{float} precision, number of decimal digits (0..9). Trailing zero decimals are stripped for B{C{prec}} values of 1 and above, but kept for negative B{C{prec}} values. @kwarg sep: Optional separator to join (C{str}). @kwarg fmt: Optional, C{float} format (C{str}). @return: This instance (C{repr}). ''' t = self._fprs2.toStr(prec=prec, sep=sep, fmt=fmt) return _SPACE_(Fmt.SQUARE(self.named3, len(self)), t) def _TypeError(self, op, other, **txt): # PYCHOK no cover '''(INTERNAL) Return a C{TypeError}. ''' return self._Error(op, other, _TypeError, **txt) def _update(self, other=None, **setters): '''(INTERNAL) Copy, set or zap all cached C{Property_RO} values. ''' if other is None: # zap if present Fsum._fint2._update(self) Fsum._fprs ._update(self) Fsum._fprs2._update(self) else: # dup if present, otherwise zap Fsum._fint2._update_from(self, other) Fsum._fprs ._update_from(self, other) Fsum._fprs2._update_from(self, other) if setters: # 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(setters) 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): '''(INTERNAL) Return a C{ZeroDivisionError}. ''' return self._Error(op, other, _ZeroDivisionError, **txt) class _Fsum(Fsum): '''(INTERNAL) Fast, single-scalar L{Fsum}. ''' _n = 1 def __init__(self, x): self._ps = [x] # assert isscalar(x) and isfinite(x) _Fsum._name = _Fsum.__name__ # PYCHOK set once 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}. ''' _Names_ = ( Fsum.fsum.__name__, _residual_) _Units_ = (_Float_Int, _Float_Int) 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 except ImportError: def _fsum(xs): '''(INTERNAL) Precision summation, Python 2.5-. ''' return Fsum(name=_fsum.__name__)._facc(xs)._fprs def fsum(xs): '''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). @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)) if xs else _0_0 def fsum_(*xs): '''Precision floating point summation of all positional arguments. @arg xs: Values to be added (C{scalar} or L{Fsum} instances), all positional. @return: Precision C{fsum} (C{float}). @see: Function C{fsum}. ''' return _fsum(_2floats(xs, origin=1)) if xs else _0_0 def fsum1(xs): '''Precision floating point summation of a few values, 1-primed. @arg xs: Iterable, list, tuple, etc. of values (C{scalar} or L{Fsum} instances). @return: Precision C{fsum} (C{float}). @see: Function C{fsum}. ''' return _fsum(_2floats(xs, primed=True)) if xs else _0_0 def fsum1_(*xs): '''Precision floating point summation of a few arguments, 1-primed. @arg xs: Values to be added (C{scalar} or L{Fsum} instances), all positional. @return: Precision C{fsum} (C{float}). @see: Function C{fsum} ''' return _fsum(_2floats(xs, origin=1, primed=True)) if xs else _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.