# Coverage for pygeodesy/fsums.py : 98%

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1422 1423 1424 1425 1426 1427 1428 1429 1430 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440 1441 1442 1443 1444 1445 1446 1447 1448 1449 1450 1451 1452 1453 1454 1455 1456 1457 1458 1459 1460 1461 1462 1463 1464 1465 1466 1467 1468 1469 1470 1471 1472 1473 1474 1475 1476 1477 1478 | # -*- coding: utf-8 -*- u'''Class L{Fsum} for precision I{running} floating point summation. Set env variable C{PYGEODESY_FSUM_RESIDUAL} to nay non-empty string to throw a L{ResidualError} for division or exponention by an L{Fsum} instance with a non-zero C{residual}, see methoda L{Fsum.fdiv} and L{Fsum.fpow}. ''' # make sure int/int division yields float quotient, see .basics from __future__ import division as _; del _ # PYCHOK semicolon from pygeodesy.basics import _isfinite, isint, isscalar, map1, \ neg, signOf from pygeodesy.errors import _NotImplementedError, _OverflowError, \ _TypeError, _ValueError, _xkwds_get, \ _ZeroDivisionError from pygeodesy.interns import NN, _COMMASPACE_, _DASH_, _EQUAL_, \ _finite_, _iadd_, _negative_, _not_, \ _PERCENT_, _scalar_, _SLASH_, _SPACE_, \ _STAR_, _supported_, _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 Property_RO, property_RO from pygeodesy.streprs import Fmt, fstr, pairs, unstr from pygeodesy.units import Float, Int, Property_RO, property_RO from math import ceil as _ceil, floor as _floor # PYCHOK used! __all__ = _ALL_LAZY.fsums __version__ = '22.02.09' _eq_ = _EQUAL_ * 2 _ge_ = '>=' _gt_ = '>' # _RANGLE_ _le_ = '<=' _lt_ = '<' # _LANGLE_ _ne_ = '!=' _floordiv_ = _SLASH_ * 2 _fset_ = _EQUAL_ _mod_ = _PERCENT_ _divmod_ = _floordiv_ + _mod_ _mul_ = _STAR_ _non_zero_ = 'non-zero' _pow_ = _STAR_ * 2 _residual_ = 'residual' _sub_ = _DASH_ _truediv_ = _SLASH_ _int0 = 0 _1p0iself = _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() try: if _isfinite(v): return v if isinstance(v, float) else float(v) X, t = _ValueError, _not_(_finite_) except TypeError as x: X, t = _TypeError, str(x) except ValueError as x: X, t = _ValueError, str(x) except Exception as x: X, t = _NotImplementedError, repr(x) if index is not None: n = Fmt.SQUARE(n, index) raise X(n, v, txt=t) def _2floats(xs, origin=0, prime=False, sub=False): '''(INTERNAL) Yield all items as C{float}s. ''' _2f = _2float if prime: 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 prime: yield _N_1_0 def _2Fsum(other, name=NN): '''(INTERNAL) Return B{C{other}} as an L{Fsum}. ''' if not isinstance(other, Fsum): other = _2float(other=other) return Fsum(name=name)._fset(other) 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 ResidualError(_ValueError): '''Error raised for an operation involving an L{Fsum} with a non-zero residual. ''' pass class Fsum(_Named): '''Precision I{running} floating point summation similar to standard Python's C{math.fsum}. Unlike C{math.fsum}, this class accumulates values and provides intermediate, I{running} precision floating point summation. Accumulation may continue after intermediate, I{running} summations. @note: Handling of exceptions, C{inf}, C{INF}, C{nan} and C{NAN} values differs from standard Python's C{math.fsum}. @note: Values to be accumulated are C{scalar} or L{fsum} instances with C{scalar} meaning type C{float}, C{int} or any type convertible to C{float}. @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 = [] # partials _Rx = bool(_getenv('PYGEODESY_FSUM_RESIDUAL', NN)) def __init__(self, *xs, **name_NN): '''New L{Fsum} for I{running} precision floating point 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 = [] if name_NN: self.name = _xkwds_get(name_NN, name=NN) if xs: self._fadd(_2floats(xs, origin=1)) def __abs__(self): '''Return this instance' absolute value as an L{Fsum}. ''' f = self.fcopy(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.fcopy(name=self.__add__.__name__) f += other return f def as_integer_ratio(self): '''Return this instance as the integer ratio. @return: 2-Tuple C{(numerator, denominator)} both C{int} and with C{denominator} positive. @see: Standard C{float.as_integer_ratio} in Python 3+. ''' s, r = self._fsum2 n, d = (int(s), 1) if isint(s) else s.as_integer_ratio() if r: if isint(r): # PYCHOK no cover n += int(r) * d else: rn, rd = r.as_integer_ratio() n = (n * rd) + (rn * d) d *= rd return n, d def __bool__(self): # PYCHOK not special in Python 2- '''Return C{True} if this instance is non-zero. ''' s, r = self._fsum2 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+, 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.fcopy(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} or C{int}. @see: Method L{Fsum.fsum}. ''' return self._fsum0 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+, 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.fcopy(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}. @return: This instance, updated (L{Fsum}). @raise TypeError: Invalid B{C{other}} type. @see: Method L{Fsum.fadd}. ''' if isinstance(other, Fsum): if other is self: # or other._fsum2 == self._fsum2: self._fmul(2) elif other._ps: self._fadd(other._ps) elif not isscalar(other): raise self._TypeError(_iadd_, other) elif other: self._fadd_(other) return self 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. @see: Method L{Fsum.fmul}. ''' if isinstance(other, Fsum): a = False if len(self._ps) != 1: f = self._mul_Fsum(other) elif len(other._ps) != 1: f = other._copy()._fmul(self._ps[0]) f._n = self._n else: f = other._ps[0] * self._ps[0] a = isint(f) self._fset(f, asis=a) elif isscalar(other): self._fmul(other) else: raise self._TypeError(_mul_ + _fset_, other) return self def __int__(self): '''Return this instance as an C{int}. @see: Methods L{Fsum.__ceil__} and L{Fsum.__floor__}. ''' return int(self._fsum0) def __ipow__(self, other, *mod): # PYCHOK 2 vs 3 args '''Apply C{B{self} **= B{other}} to this instance. @arg other: An L{Fsum} or C{scalar} exponent. @arg mod: Optional modulus (C{int}) for the 3-argument version C{pow(B{self}, B{other}, *B{mod})}. @return: This instance, updated (L{Fsum}). @raise OverflowError: Partial C{2sum} overflow. @raise ResidualError: Non-zero residual in B{C{other}} a negative or fractional C{scalar} B{C{other}} and this instance has a non-zero residual. @raise TypeError: Invalid B{C{other}} type or the 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{other}} is an L{Fsum} with a non-zero residual. @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}. ''' if isinstance(other, Fsum): if other is self: # or other._fsum2 == self._fsum2: self._fset(_0_0) elif other._ps: self._fadd(map(neg, other._ps)) elif not isscalar(other): raise self._TypeError(_sub_ + _fset_, other) elif other: self._fadd_(neg(other)) return self 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}}. @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.fcopy(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.fcopy(name=self.__mul__.__name__) f *= other return f 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.fcopy(name=self.__neg__.__name__) return f._fneg() def __pos__(self): '''Return this instance I{as-is}, like C{float.__pos__()}. ''' return self if _1p0iself else self.fcopy(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.fcopy(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._ps) 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__) f *= self return f 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__) f -= self return f 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._fsum0, self._fsum2, self._fsum2.fsum, self._fsum2.residual, self._n, self._ps, *self._ps)) def __str__(self): '''Return the default C{str(this)}. ''' 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.fcopy(name=self.__sub__.__name__) f -= other return f 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.fcopy(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__ @property_RO def ceil(self): '''Get this instance' C{ceil} value (C{int} in Python 3+, C{float} in Python 2-). @note: The C{ceil} accounts for the C{residual}. @see: Properties L{Fsum.floor}, L{Fsum.imag} and L{Fsum.real}. ''' s, r = self._fsum2 c = _ceil(s) + int(r) - 1 while r > (c - s): # (s + r) > c c += 1 return c def _cmp2(self, other, cop): '''(INTERNAL) Subtract an B{C{other}} instance or scalar and return an L{Fsum2Tuple}C{(fsum, residual)} for comparison operator B{C{cop}}. ''' if other: f = self._copy() # fast fcopy, no caches if isinstance(other, Fsum): f._fadd(map(neg, other._ps)) # fast f -= other elif isscalar(other): f._fadd_(-other) # fast f -= other else: raise self._TypeError(cop, other) else: f = self return f._fsum2 def _copy(self, _fsum2=False): '''(INTERNAL) Make a fast, un-named copy. ''' f = Fsum() # NN f._n = self._n f._ps[:] = self._ps if _fsum2: Fsum._fsum2._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.fcopy(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 fadd(self, xs): '''Accumulate more scalar values 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: Non-scalar B{C{xs}} value. @raise ValueError: Invalid or non-finite B{C{xs}} value. ''' if isinstance(xs, Fsum): self._fadd(xs._ps) elif not isscalar(xs): # for ... self._fadd(_2floats(xs)) else: # ... backward compatibility self._fadd_(_2float(xs=xs)) # PYCHOK no cover return self def fadd_(self, *xs): '''Accumulate more I{scalar} values from positional arguments. @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: Non-scalar B{C{xs}} value. @raise ValueError: Invalid or non-finite B{C{xs}} value. ''' return self._fadd(_2floats(xs, origin=1)) def _fadd(self, xs): '''(INTERNAL) Accumulate more I{known} C{scalar}s. ''' ps, n, _2s = self._ps, 0, _2sum for x in xs: # _iter() 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 _fadd_(self, *xs): '''(INTERNAL) Add all positional, I{known} C{scalar}s. ''' return self._fadd(xs) def _fadd_1(self): '''(INTERNAL) Adjust the C{partials}, by removing and re-adding the final C{partial}. ''' while len(self._ps) > 1: p = self._ps.pop() if p: self._fadd_(p) self._n -= 1 break else: # must zap self._update() return self def fcopy(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 copy = fcopy 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(_fsum2=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 = f.signOf() # if t and t != s: # from pygeodesy.errors import _AssertionError # raise f._Error(_dimo_, other, _AssertionError, txt=signOf.__name__) return q, self # q is C{int} in Python 3+, but C{float} in Python 2- @property_RO def floor(self): '''Get this instance' C{floor} (C{int} in Python 3+, C{float} in Python 2-). @note: The C{floor} accounts for the C{residual}. @see: Properties L{Fsum.ceil}, L{Fsum.imag} and L{Fsum.real}. ''' s, r = self._fsum2 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): '''(INTERNAL) Apply C{B{self} *= B{other}}. ''' if isinstance(other, Fsum): # PYCHOK no cover self._fset(self._mul_Fsum(other)) elif other and self._ps: if other != _1_0: # multiply and adjust partials self._ps[:] = self._ps_x(other) self._fadd_1() else: self._fset(_0_0) # assert self._ps is ps return self def _fneg(self): '''(INTERNAL) Negate this instance. ''' if self._ps: self._ps[:] = map(neg, self._ps) self._fadd_1() return self fpow = __ipow__ # for backward compatibility def _fpow(self, other, op, *mod): '''Apply C{B{self} **= B{other}}. ''' if mod: try: f = int(self) if self.is_integer() else self._fsum0 # throw the same TypeError as C{pow} if not all # self._fsum0, other and mod are C{int} and map # the ValueError for mod==0 into TypeError s = pow(f, other, *mod) a = isint(s) except (TypeError, ValueError) as x: t = str(x) t = _COMMASPACE_(Fmt.PARENSPACED(mod=mod[0]), t) raise self._TypeError(op, other, txt=t) else: x, p = other, _1_0 if isinstance(x, Fsum): x, r = x._fsum2 if r: if Fsum._Rx: raise self._ResidualError(op, other, r) p = self._pow_scalar(r, other, op) s = self._pow_scalar(x, other, op) if p != _1_0: s *= p # C{scalar}s or L{Fsum}s a = False return self._fset(s, asis=a) def _fset(self, other, asis=False): '''(INTERNAL) Overwrite this instance with an other or a C{scalar}. ''' if other is self: pass # from ._fpow_scalar elif isinstance(other, Fsum): self._n = other._n self._ps[:] = other._ps self._update(other=other) elif isscalar(other): f = other if asis else float(other) self._n = 1 self._ps[:] = [f] self._update(_fsum0=f, _fsum2=Fsum2Tuple(f, _int0)) else: # PYCHOK no cover raise self._TypeError(_fset_, other) return self def fsub(self, xs): '''Subtract several values. @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._fadd(_2floats(xs, sub=True)) if xs else self def fsub_(self, *xs): '''Subtract any positional value. @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._fadd(_2floats(xs, sub=True)) if xs else self def fsum(self, xs=None): '''Add C{None} or several values and sum all. @kwarg xs: Iterable, list, tuple, etc. (C{scalar} or L{Fsum} instances). @return: Precision running sum (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: Accumulation can continue after summation. ''' f = self._fadd(_2floats(xs)) if xs else self return f._fsum0 def fsum_(self, *xs): '''Add any positional value and sum all. @arg xs: Values to add (C{scalar} or L{Fsum} instances), all positional. @return: Precision running sum (C{float}). @see: Method L{Fsum.fsum}. ''' f = self._fadd(_2floats(xs, origin=1)) if xs else self return f._fsum0 @Property_RO def _fsum0(self): '''(INTERNAL) Get this instance', memoized precision running sum (C{float} or C{int}), without C{residual}. @note: The precision running C{fsum} after a C{//=} or C{//} C{floor} division is C{int} in Python 3+. @see: Method L{Fsum.fsum2} and property L{Fsum.residual}. ''' ps = self._ps i = len(ps) - 1 if i < 0: s = _0_0 # XXX 0? 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 # swap s and p and continue # else: # s = float(s) # assert self._ps is ps # assert self.__dict__.get(Fsum._fsum2.name, None) is None # Fsum._fsum2._update(self) return s def fsum2(self, xs=None): '''Add C{None} or several values 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 and C{residual}, the sum of the remaining C{partials}. @see: Methods L{Fsum.fsum} and L{Fsum.fsum2_} ''' f = self._fadd(_2floats(xs)) if xs else self return f._fsum2 @Property_RO def _fsum2(self): '''(INTERNAL) Get this instance', memoized current precision running sum and residual (L{Fsum2Tuple}). @note: If the C{residual} is C{int(0)}, the precision running C{fsum} is considered to be I{exact}. @see: Method L{Fsum.fsum} and property L{Fsum.residual}. ''' s = self._fsum0 r = _fsum(self._ps1(s)) if len(self._ps) > 1 else _int0 t = Fsum2Tuple(s, r) if s else Fsum2Tuple((r or _0_0), _int0) return t def fsum2_(self, *xs): '''Add any positional value and return the current precision running sum and C{delta}, the increment. @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 prior running C{fsum} (C{float}s). @see: Method L{Fsum.fsum_}. ''' p, r = self._fsum2 s, t = self._fadd(_2floats(xs, origin=1))._fsum2 if xs else (p, r) return s, ((s - p) + (r - t)) # == _fsum((s, -p, r, -t)) # 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._fsum2 == self._fsum2: return self._fset(_1_0) d, r = other._fsum2 if r: if Fsum._Rx: 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 # is pointless if (1 + r / d) == 1 d *= r / d + _1_0 else: # PYCHOK no cover d = r elif isscalar(other): d = other else: raise self._TypeError(op, other) try: self._fmul(_1_0 / d) except ZeroDivisionError as x: raise self._ZeroDivisionError(op, d, txt=str(x)) except (TypeError, ValueError) as x: raise self._ValueError(op, d, txt=str(x)) return self @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 is_exact(self): '''Is this instance' precision running C{fsum} considered to be exact? (C{bool}). ''' return self.residual is _int0 def is_integer(self): '''Return C{True} if this instance is an integer, C{False} otherwise. ''' s, r = self._fsum2 if len(self._ps) != 1 else (self._ps[0], 0) return (not r) and isint(s, both=True) def is_math_fsum(self): '''Return C{True} if functions C{fsum}, C{fsum}_, C{fsum1} and C{fsum1_} are all based on Python's C{math.fsum}, C{False} otherwise. ''' return bool(Fsum._math_fsum) def _mul_Fsum(self, other): '''(INTERNAL) Return C{B{self} * B{other}} L{Fsum} as L{Fsum}. ''' return Fsum(_0_0)._fadd(self._ps_x(*other._ps)) @property_RO def partials(self): '''Get this instance' current partial sums (C{tuple} of C{float}s). ''' return tuple(self._ps) def pow(self, x): '''Return C{B{self}**B{x}} as L{Fsum}. @arg x: The exponent (C{scalar} or L{Fsum} instance). @return: The C{pow(self, B{x})} (L{Fsum}). @raise ResidualError: This residual non-zero and negative or fractional B{C{x}}. @raise TypeError: Non-scalar B{C{x}}. @raise ValueError: Invalid or non-finite B{C{factor}}. @see: Method L{Fsum.__ipow__}. ''' if isint(x, both=True) and int(x) >= 0: f = self._pow_int(int(x), _pow_) else: # negative or not int B{C{x}} f = self.fcopy(name=self.pow.__name__)._fpow(x, _pow_) # f **= x return f def _pow_int(self, x, op): '''(INTERNAL) Return C{B{self}**B{x}} for C{int B{x} >= 0} only. ''' if x < 0: # assert x >= 0 raise self._ValueError(op, x, txt=_SPACE_(_negative_, int.__name__)) a = False if len(self._ps) > 1: if x > 2: m = 1 # single-bit mask p = self._copy() if x & m: x -= m # x ^= m f = p._copy() else: f = Fsum(_1_0) while x: p = p._mul_Fsum(p) # p **= 2 m += m # m <<= 1 if x & m: f = f._mul_Fsum(p) # f *= p x -= m # x ^= m elif x > 1: # self**2 f = self._mul_Fsum(self) else: # self**1 or self**0 f = self if x else _1_0 elif self._ps: f = self._ps[0]**x a = True # preserve C{type(ps[0])} else: # 0**non0 == 0, but 0**0 == 1 f = _0_0 if x else _1_0 return Fsum(name=self.pow.__name__)._fset(f, asis=a) def _pow_scalar(self, x, other, op): # MCCABE 14 '''(INTERNAL) Return C{self**B{x}} for C{scalar B{x}} only. ''' s, r = self._fsum2 if isint(x, both=True): x = int(x) # Fsum**int y = abs(x) if y > 1: if r: s = self._pow_int(y, op) if x < 0: s, r = s._fsum2 if r: raise self._ResidualError(op, other, r) # use **= -1 for the CPython float_pow # error if s is zero, and not s = 1 / s x = -1 else: x = None elif x < 0: if r: # self**-1 == 1 / self s = Fsum(_1_0)._ftruediv(self, op) x = None else: # self**1 or self**0 s = self if x else _1_0 x = None elif not isscalar(x): # assert ... raise self._TypeError(op, other, txt=_not_(_scalar_)) elif r: # non0_residual**fractional raise self._ResidualError(op, other, r) elif s < 0: # neg**fractional yields complex raise self._ValueError(op, other, txt=_not_(_supported_)) if x not in (None, _1_0): try: s **= x except Exception as e: raise self._ValueError(op, other, txt=str(e)) return s # C{scalar} 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, *factors): '''(INTERNAL) Yield C{partials}, multiplied by each of the B{C{factors}}. ''' ps = self._ps if len(ps) < len(factors): ps, factors = factors, ps for f in factors: for p in ps: p *= f if p: yield p @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._fsum0) @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 C{int(0)}, 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._fsum2.residual def _ResidualError(self, op, other, residual): '''(INTERNAL) Non-zero residual C{ValueError}. ''' t = _SPACE_(_non_zero_, _residual_) t = Fmt.PARENSPACED(t, fstr(residual, fmt=Fmt.e, prec=8)) 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._fsum2 if res else (self._fsum0, 0) return signOf(r, off=-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._fsum2.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._fsum2.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) Operand 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 all Fsum._fsum0._update(self) Fsum._fsum2._update(self) else: # dup if present, otherwise zap Fsum._fsum0._update_from(self, other) Fsum._fsum2._update_from(self, other) if setters: # Property_RO ._fsum0 and ._fsum2 can't be a Property since # 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) 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 if any. Each item is either C{float} or C{int}. ''' _Names_ = ( Fsum.fsum.__name__, _residual_) _Units_ = (_Float_Int, _Float_Int) 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__)._fadd(xs)._fsum0 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, prime=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, prime=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.