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PyGeodesy
Package pygeodesy :: Module fsums :: Class Fsum
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Class Fsum

  object --+    
           |    
named._Named --+
               |
              Fsum
Known Subclasses:

Precision floating point summation and running summation.

Unlike Python's math.fsum, this class accumulates values and provides intermediate, running, precision floating point summations. Accumulation may continue after any intermediate, running summuation.

Notes:

See Also: Hettinger, Kahan, Klein, Python 2.6+ file Modules/mathmodule.c and the issue log Full precision summation.

Instance Methods
 
__init__(self, *xs, **name_RESIDUAL)
New Fsum for running precision floating point summation.
 
__abs__(self)
Return this instance' absolute value as an Fsum.
 
__add__(self, other)
Return self + other as an Fsum.
 
__bool__(self)
Return True if this instance is exactly non-zero.
 
__ceil__(self)
Return this instance' math.ceil as int or float.
 
__cmp__(self, other)
Compare this with an other instance or scalar, Python 2-.
 
__divmod__(self, other, **raiser_RESIDUAL)
Return divmod(self, other) as a DivMod2Tuple with quotient div an int in Python 3+ or float in Python 2- and remainder mod an Fsum instance.
 
__eq__(self, other)
Compare this with an other instance or scalar.
 
__float__(self)
Return this instance' current, precision running sum as float.
 
__floor__(self)
Return this instance' math.floor as int or float.
 
__floordiv__(self, other)
Return self // other as an Fsum.
 
__format__(self, *other)
Not implemented.
 
__ge__(self, other)
Compare this with an other instance or scalar.
 
__gt__(self, other)
Compare this with an other instance or scalar.
 
__hash__(self)
Return this instance' hash.
 
__iadd__(self, other)
Apply self += other to this instance.
 
__ifloordiv__(self, other)
Apply self //= other to this instance.
 
__imatmul__(self, other)
Not implemented.
 
__imod__(self, other)
Apply self %= other to this instance.
 
__imul__(self, other)
Apply self *= other to this instance.
 
__int__(self)
Return this instance as an int.
 
__invert__(self)
Not implemented.
 
__ipow__(self, other, *mod, **raiser_RESIDUAL)
Apply self **= other to this instance.
 
__isub__(self, other)
Apply self -= other to this instance.
 
__iter__(self)
Return an iterator over a partials duplicate.
 
__itruediv__(self, other, **raiser_RESIDUAL)
Apply self /= other to this instance.
 
__le__(self, other)
Compare this with an other instance or scalar.
 
__len__(self)
Return the number of values accumulated (int).
 
__lt__(self, other)
Compare this with an other instance or scalar.
 
__matmul__(self, other)
Not implemented.
 
__mod__(self, other)
Return self % other as an Fsum.
 
__mul__(self, other)
Return self * other as an Fsum.
 
__ne__(self, other)
Compare this with an other instance or scalar.
 
__neg__(self)
Return a copy of this instance, negated.
 
__pos__(self)
Return this instance as-is, like float.__pos__().
 
__pow__(self, other, *mod)
Return self**other as an Fsum.
 
__radd__(self, other)
Return other + self as an Fsum.
 
__rdivmod__(self, other)
Return divmod(other, self) as 2-tuple (quotient, remainder).
 
__rfloordiv__(self, other)
Return other // self as an Fsum.
 
__rmatmul__(self, other)
Not implemented.
 
__rmod__(self, other)
Return other % self as an Fsum.
 
__rmul__(self, other)
Return other * self as an Fsum.
 
__round__(self, *ndigits)
Return round(self, *ndigits as an Fsum.
 
__rpow__(self, other, *mod)
Return other**self as an Fsum.
 
__rsub__(self, other)
Return other - self as Fsum.
 
__rtruediv__(self, other, **raiser_RESIDUAL)
Return other / self as an Fsum.
 
__str__(self)
Return the default str(self).
 
__sub__(self, other)
Return self - other as an Fsum.
 
__truediv__(self, other, **raiser_RESIDUAL)
Return self / other as an Fsum.
 
__trunc__(self)
Return this instance as an int.
 
__div__(self, other, **raiser_RESIDUAL)
Return self / other as an Fsum.
 
__idiv__(self, other, **raiser_RESIDUAL)
Apply self /= other to this instance.
 
__long__(self)
Return this instance as an int.
 
__nonzero__(self)
Return True if this instance is exactly non-zero.
 
__rdiv__(self, other, **raiser_RESIDUAL)
Return other / self as an Fsum.
 
as_integer_ratio(self)
Return this instance as the ratio of 2 integers.
 
cmp(self, other)
Compare this with an other instance or scalar, Python 2-.
 
copy(self, deep=False, name='')
Copy this instance, shallow or deep.
 
divmod(self, other, **raiser_RESIDUAL)
Return divmod(self, other) as a DivMod2Tuple with quotient div an int in Python 3+ or float in Python 2- and remainder mod an Fsum instance.
 
fadd(self, xs=())
Add all items from an iterable to this instance.
 
fadd_(self, *xs)
Add all positional arguments to this instance.
 
fcopy(self, deep=False, name='')
Copy this instance, shallow or deep.
 
fdiv(self, other, **raiser_RESIDUAL)
Apply self /= other to this instance.
 
fdivmod(self, other, **raiser_RESIDUAL)
Return divmod(self, other) as a DivMod2Tuple with quotient div an int in Python 3+ or float in Python 2- and remainder mod an Fsum instance.
 
fint(self, name='', **raiser_RESIDUAL)
Return this instance' current running sum as integer.
 
fint2(self, **name)
Return this instance' current running sum as int and the integer residual.
 
fmul(self, other)
Apply self *= other to this instance.
 
fover(self, over, **raiser_RESIDUAL)
Apply self /= over and summate.
 
fpow(self, other, *mod, **raiser_RESIDUAL)
Apply self **= other to this instance.
 
fset_(self, *xs)
Replace this instance' value with xs.
 
fsub(self, xs=())
Subtract all items of an iterable from this instance.
 
fsub_(self, *xs)
Subtract all positional arguments from this instance.
 
fsum(self, xs=())
Add more items from an iterable, summate and return the current precision running sum.
 
fsum_(self, *xs)
Add any positional arguments, summate and return the current precision running sum.
 
Fsum_(self, *xs, **name)
Like method Fsum.fsum_ but returning a named Fsum.
 
Fsum2Tuple_(self, *xs, **name)
Like method Fsum.fsum_ but returning a named Fsum2Tuple.
 
fsum2(self, xs=(), name='')
Add more items from an iterable, summate and return the current precision running sum and the residual.
 
fsum2_(self, *xs)
Add any positional arguments, summate and return the current precision running sum and the differential.
 
fsumf_(self, *xs)
Like method Fsum.fsum_ iff all xs are known to be scalar.
 
Fsumf_(self, *xs)
Like method Fsum.Fsum_ iff all xs are known to be scalar.
 
fsum2f_(self, *xs)
Like method Fsum.fsum2_ iff all xs are known to be scalar.
 
int_float(self, **raiser_RESIDUAL)
Return this instance' current running sum as int or float.
 
is_exact(self)
Is this instance' running fsum considered to be exact? (bool).
 
is_integer(self)
Is this instance' running sum integer? (bool).
 
is_math_fsum(self)
Return whether functions fsum, fsum_, fsum1 and fsum1_ plus partials summation are based on Python's math.fsum or not.
 
is_scalar(self, **raiser_RESIDUAL)
Is this instance' running sum scalar without residual or with a residual ratio not exceeding the RESIDUAL threshold?
 
pow(self, x, *mod, **raiser_RESIDUAL)
Return self**x as Fsum.
 
RESIDUAL(self, *threshold)
Get and set this instance' ratio for raising ResidualErrors, overriding the default from env variable PYGEODESY_FSUM_RESIDUAL.
 
root(self, root, **raiser_RESIDUAL)
Return self**(1 / root) as Fsum.
 
signOf(self, res=True)
Determine the sign of this instance.
 
toRepr(self, **lenc_prec_sep_fmt)
Return this Fsum instance as representation.
 
toStr(self, lenc=True, **prec_sep_fmt)
Return this Fsum instance as string.

Inherited from named._Named: __repr__, attrs, classof, dup, methodname, rename, toStr2

Inherited from object: __delattr__, __getattribute__, __new__, __reduce__, __reduce_ex__, __setattr__, __sizeof__, __subclasshook__

Properties
  as_iscalar
Get this instance as-is (Fsum) or as scalar iff scalar.
  ceil
Get this instance' ceil value (int in Python 3+, but float in Python 2-).
  float_int
DEPRECATED, use method Fsum.int_float.
  floor
Get this instance' floor (int in Python 3+, but float in Python 2-).
  imag
Get the imaginary part of this instance (0.0, always).
  partials
Get this instance' current, partial sums (tuple of floats).
  real
Get the real part of this instance (float).
  residual
Get this instance' residual (float or int): the sum(partials) less the precision running sum fsum.

Inherited from named._Named: classname, classnaming, iteration, name, named, named2, named3, named4, sizeof

Inherited from object: __class__

Method Details

__init__ (self, *xs, **name_RESIDUAL)
(Constructor)

 

New Fsum for running precision floating point summation.

Arguments:
  • xs - No, one or more items to add (each scalar or an Fsum or Fsum2Tuple instance), all positional.
  • name_RESIDUAL - Optional name=NN for this Fsum and the RESIDUAL=0.0 threshold for ResidualErrors.
Overrides: object.__init__

See Also: Methods Fsum.fadd and Fsum.RESIDUAL.

__add__ (self, other)
(Addition operator)

 

Return self + other as an Fsum.

Arguments:
Returns:
The sum (Fsum).

See Also: Method Fsum.__iadd__.

__ceil__ (self)

 

Return this instance' math.ceil as int or float.

Returns:
An int in Python 3+, but float in Python 2-.

See Also: Methods Fsum.__floor__ and property Fsum.ceil.

__cmp__ (self, other)
(Comparison operator)

 

Compare this with an other instance or scalar, Python 2-.

Returns:
-1, 0 or +1 (int).
Raises:
  • TypeError - Incompatible other type.

__divmod__ (self, other, **raiser_RESIDUAL)

 

Return divmod(self, other) as a DivMod2Tuple with quotient div an int in Python 3+ or float in Python 2- and remainder mod an Fsum instance.

Arguments:
Raises:
  • ResidualError - Non-zero, significant residual or invalid RESIDUAL.

See Also: Method Fsum.__itruediv__.

__float__ (self)

 

Return this instance' current, precision running sum as float.

See Also: Methods Fsum.fsum and Fsum.int_float.

__floor__ (self)

 

Return this instance' math.floor as int or float.

Returns:
An int in Python 3+, but float in Python 2-.

See Also: Methods Fsum.__ceil__ and property Fsum.floor.

__floordiv__ (self, other)

 

Return self // other as an Fsum.

Arguments:
Returns:
The floor quotient (Fsum).

See Also: Methods Fsum.__ifloordiv__.

__format__ (self, *other)

 

Not implemented.

Overrides: object.__format__

__hash__ (self)
(Hashing function)

 

Return this instance' hash.

Overrides: object.__hash__

__iadd__ (self, other)

 

Apply self += other to this instance.

Arguments:
Returns:
This instance, updated (Fsum).
Raises:
  • TypeError - Invalid other, not scalar nor Fsum.

See Also: Methods Fsum.fadd and Fsum.fadd_.

__ifloordiv__ (self, other)

 

Apply self //= other to this instance.

Arguments:
Returns:
This instance, updated (Fsum).
Raises:
  • ResidualError - Non-zero, significant residual in other.
  • TypeError - Invalid other type.
  • ValueError - Invalid or non-finite other.
  • ZeroDivisionError - Zero other.

See Also: Methods Fsum.__itruediv__.

__imatmul__ (self, other)

 

Not implemented.

Overrides: named._Named.__imatmul__

__imod__ (self, other)

 

Apply self %= other to this instance.

Arguments:
Returns:
This instance, updated (Fsum).

See Also: Method Fsum.__divmod__.

__imul__ (self, other)

 

Apply self *= other to this instance.

Arguments:
Returns:
This instance, updated (Fsum).
Raises:
  • OverflowError - Partial 2sum overflow.
  • TypeError - Invalid other type.
  • ValueError - Invalid or non-finite other.

__int__ (self)

 

Return this instance as an int.

See Also: Methods Fsum.int_float, Fsum.__ceil__ and Fsum.__floor__ and properties Fsum.ceil and Fsum.floor.

__ipow__ (self, other, *mod, **raiser_RESIDUAL)

 

Apply self **= other to this instance.

Arguments:
  • other - The exponent (scalar, Fsum or Fsum2Tuple).
  • mod - Optional modulus (int or None) for the 3-argument pow(self, other, mod) version.
  • raiser_RESIDUAL - Use raiser=False (bool) to ignore ResidualErrors and RESIDUAL=scalar to override the RESIDUAL.
Returns:
This instance, updated (Fsum).
Raises:
  • OverflowError - Partial 2sum overflow.
  • ResidualError - Invalid RESIDUAL or the residual is non-zero and significant and either other is a fractional or negative scalar or mod is given and not None.
  • TypeError - Invalid other type or 3-argument pow invocation failed.
  • ValueError - If other is a negative scalar and this instance is 0 or other is a fractional scalar and this instance is negative or has a non-zero and significant residual or mod is given as 0.

Note: If mod is given, the result will be an integer Fsum in Python 3+ if this instance is_integer or set to as_integer and mod is given as None.

See Also: CPython function float_pow.

__isub__ (self, other)

 

Apply self -= other to this instance.

Arguments:
Returns:
This instance, updated (Fsum).
Raises:
  • TypeError - Invalid other type.

See Also: Method Fsum.fadd.

__itruediv__ (self, other, **raiser_RESIDUAL)

 

Apply self /= other to this instance.

Arguments:
Returns:
This instance, updated (Fsum).
Raises:
  • OverflowError - Partial 2sum overflow.
  • ResidualError - Non-zero, significant residual or invalid RESIDUAL.
  • TypeError - Invalid other type.
  • ValueError - Invalid or non-finite other.
  • ZeroDivisionError - Zero other.

See Also: Method Fsum.__ifloordiv__.

__matmul__ (self, other)

 

Not implemented.

Overrides: named._Named.__matmul__

__mod__ (self, other)

 

Return self % other as an Fsum.

See Also: Method Fsum.__imod__.

__mul__ (self, other)

 

Return self * other as an Fsum.

See Also: Method Fsum.__imul__.

__pow__ (self, other, *mod)

 

Return self**other as an Fsum.

See Also: Method Fsum.__ipow__.

__radd__ (self, other)
(Right-side addition operator)

 

Return other + self as an Fsum.

See Also: Method Fsum.__iadd__.

__rdivmod__ (self, other)

 

Return divmod(other, self) as 2-tuple (quotient, remainder).

See Also: Method Fsum.__divmod__.

__rfloordiv__ (self, other)

 

Return other // self as an Fsum.

See Also: Method Fsum.__ifloordiv__.

__rmatmul__ (self, other)

 

Not implemented.

Overrides: named._Named.__rmatmul__

__rmod__ (self, other)

 

Return other % self as an Fsum.

See Also: Method Fsum.__imod__.

__rmul__ (self, other)

 

Return other * self as an Fsum.

See Also: Method Fsum.__imul__.

__round__ (self, *ndigits)

 

Return round(self, *ndigits as an Fsum.

Arguments:
  • ndigits - Optional number of digits (int).

__rpow__ (self, other, *mod)

 

Return other**self as an Fsum.

See Also: Method Fsum.__ipow__.

__rsub__ (self, other)

 

Return other - self as Fsum.

See Also: Method Fsum.__isub__.

__rtruediv__ (self, other, **raiser_RESIDUAL)

 

Return other / self as an Fsum.

See Also: Method Fsum.__itruediv__.

__str__ (self)
(Informal representation operator)

 

Return the default str(self).

Overrides: object.__str__

__sub__ (self, other)
(Subtraction operator)

 

Return self - other as an Fsum.

Arguments:
Returns:
The difference (Fsum).

See Also: Method Fsum.__isub__.

__truediv__ (self, other, **raiser_RESIDUAL)

 

Return self / other as an Fsum.

Arguments:
Returns:
The quotient (Fsum).
Raises:
  • ResidualError - Non-zero, significant residual or invalid RESIDUAL.

See Also: Method Fsum.__itruediv__.

__trunc__ (self)

 

Return this instance as an int.

See Also: Methods Fsum.int_float, Fsum.__ceil__ and Fsum.__floor__ and properties Fsum.ceil and Fsum.floor.

__div__ (self, other, **raiser_RESIDUAL)

 

Return self / other as an Fsum.

Arguments:
Returns:
The quotient (Fsum).
Raises:
  • ResidualError - Non-zero, significant residual or invalid RESIDUAL.

See Also: Method Fsum.__itruediv__.

__idiv__ (self, other, **raiser_RESIDUAL)

 

Apply self /= other to this instance.

Arguments:
Returns:
This instance, updated (Fsum).
Raises:
  • OverflowError - Partial 2sum overflow.
  • ResidualError - Non-zero, significant residual or invalid RESIDUAL.
  • TypeError - Invalid other type.
  • ValueError - Invalid or non-finite other.
  • ZeroDivisionError - Zero other.

See Also: Method Fsum.__ifloordiv__.

__long__ (self)

 

Return this instance as an int.

See Also: Methods Fsum.int_float, Fsum.__ceil__ and Fsum.__floor__ and properties Fsum.ceil and Fsum.floor.

__rdiv__ (self, other, **raiser_RESIDUAL)

 

Return other / self as an Fsum.

See Also: Method Fsum.__itruediv__.

as_integer_ratio (self)

 

Return this instance as the ratio of 2 integers.

Returns:
2-Tuple (numerator, denominator) both int and with positive denominator.

See Also: Standard float.as_integer_ratio in Python 3+.

cmp (self, other)

 

Compare this with an other instance or scalar, Python 2-.

Returns:
-1, 0 or +1 (int).
Raises:
  • TypeError - Incompatible other type.

copy (self, deep=False, name='')

 

Copy this instance, shallow or deep.

Arguments:
  • deep - If True make a deep, otherwise a shallow copy (bool).
  • name - Optional, non-empty name (str).
Returns:
The copy (Fsum).
Overrides: named._Named.copy

divmod (self, other, **raiser_RESIDUAL)

 

Return divmod(self, other) as a DivMod2Tuple with quotient div an int in Python 3+ or float in Python 2- and remainder mod an Fsum instance.

Arguments:
Raises:
  • ResidualError - Non-zero, significant residual or invalid RESIDUAL.

See Also: Method Fsum.__itruediv__.

fadd (self, xs=())

 

Add all items from an iterable to this instance.

Arguments:
  • xs - Iterable of items to add (each scalar or an Fsum or Fsum2Tuple instance).
Returns:
This instance (Fsum).
Raises:
  • OverflowError - Partial 2sum overflow.
  • TypeError - An invalid xs item.
  • ValueError - Invalid or non-finite xs value.

fadd_ (self, *xs)

 

Add all positional arguments to this instance.

Arguments:
  • xs - Values to add (each scalar or an Fsum or Fsum2Tuple instance), all positional.

See Also: Method Fsum.fadd for further details.

fcopy (self, deep=False, name='')

 

Copy this instance, shallow or deep.

Arguments:
  • deep - If True make a deep, otherwise a shallow copy (bool).
  • name - Optional, non-empty name (str).
Returns:
The copy (Fsum).

fdiv (self, other, **raiser_RESIDUAL)

 

Apply self /= other to this instance.

Arguments:
Returns:
This instance, updated (Fsum).
Raises:
  • OverflowError - Partial 2sum overflow.
  • ResidualError - Non-zero, significant residual or invalid RESIDUAL.
  • TypeError - Invalid other type.
  • ValueError - Invalid or non-finite other.
  • ZeroDivisionError - Zero other.

See Also: Method Fsum.__ifloordiv__.

fdivmod (self, other, **raiser_RESIDUAL)

 

Return divmod(self, other) as a DivMod2Tuple with quotient div an int in Python 3+ or float in Python 2- and remainder mod an Fsum instance.

Arguments:
Raises:
  • ResidualError - Non-zero, significant residual or invalid RESIDUAL.

See Also: Method Fsum.__itruediv__.

fint (self, name='', **raiser_RESIDUAL)

 

Return this instance' current running sum as integer.

Arguments:
  • name - Optional name (str), overriding "fint".
  • raiser_RESIDUAL - Use raiser=False (bool) to ignore ResidualErrors and RESIDUAL=scalar to override the RESIDUAL.
Returns:
The integer sum (Fsum) if this instance is_integer with a zero or insignificant integer residual.
Raises:
  • ResidualError - Non-zero, significant residual or invalid RESIDUAL.

See Also: Methods Fsum.int_float and Fsum.is_integer.

fint2 (self, **name)

 

Return this instance' current running sum as int and the integer residual.

Arguments:
  • name - Optional name (str).
Returns:
An Fsum2Tuple(fsum, residual) with fsum an int and integer residual a float or INT0 if the fsum is considered to be exact.

fmul (self, other)

 

Apply self *= other to this instance.

Arguments:
Returns:
This instance, updated (Fsum).
Raises:
  • OverflowError - Partial 2sum overflow.
  • TypeError - Invalid other type.
  • ValueError - Invalid or non-finite other.

fover (self, over, **raiser_RESIDUAL)

 

Apply self /= over and summate.

Arguments:
  • over - An Fsum or scalar denominator.
  • raiser_RESIDUAL - Use raiser=False (bool) to ignore ResidualErrors and RESIDUAL=scalar to override the RESIDUAL.
Returns:
Precision running sum (float).
Raises:
  • ResidualError - Non-zero, significant residual or invalid RESIDUAL.

See Also: Methods Fsum.fsum and Fsum.__itruediv__.

fpow (self, other, *mod, **raiser_RESIDUAL)

 

Apply self **= other to this instance.

Arguments:
  • other - The exponent (scalar, Fsum or Fsum2Tuple).
  • mod - Optional modulus (int or None) for the 3-argument pow(self, other, mod) version.
  • raiser_RESIDUAL - Use raiser=False (bool) to ignore ResidualErrors and RESIDUAL=scalar to override the RESIDUAL.
Returns:
This instance, updated (Fsum).
Raises:
  • OverflowError - Partial 2sum overflow.
  • ResidualError - Invalid RESIDUAL or the residual is non-zero and significant and either other is a fractional or negative scalar or mod is given and not None.
  • TypeError - Invalid other type or 3-argument pow invocation failed.
  • ValueError - If other is a negative scalar and this instance is 0 or other is a fractional scalar and this instance is negative or has a non-zero and significant residual or mod is given as 0.

Note: If mod is given, the result will be an integer Fsum in Python 3+ if this instance is_integer or set to as_integer and mod is given as None.

See Also: CPython function float_pow.

fset_ (self, *xs)

 

Replace this instance' value with xs.

Arguments:
  • xs - Optional, new values (each scalar or an Fsum or Fsum2Tuple instance), all positional.
Returns:
This instance (Fsum).

See Also: Method Fsum.fadd for further details.

fsub (self, xs=())

 

Subtract all items of an iterable from this instance.

See Also: Method Fsum.fadd for further details.

fsub_ (self, *xs)

 

Subtract all positional arguments from this instance.

See Also: Method Fsum.fadd_ for further details.

fsum (self, xs=())

 

Add more items from an iterable, summate and return the current precision running sum.

Arguments:
  • xs - Iterable of items to add (each item scalar or an Fsum or Fsum2Tuple instance).
Returns:
Precision running sum (float or int).

See Also: Method Fsum.fadd.

Note: Accumulation can continue after summation.

fsum_ (self, *xs)

 

Add any positional arguments, summate and return the current precision running sum.

Arguments:
  • xs - Values to add (each scalar or an Fsum or Fsum2Tuple instance), all positional.
Returns:
Precision running sum (float or int).

See Also: Methods Fsum.fsum, Fsum.Fsum_ and Fsum.fsumf_.

Fsum_ (self, *xs, **name)

 

Like method Fsum.fsum_ but returning a named Fsum.

Arguments:
  • name - Optional name (str).
Returns:
Current, precision running sum (Fsum).

Fsum2Tuple_ (self, *xs, **name)

 

Like method Fsum.fsum_ but returning a named Fsum2Tuple.

Arguments:
  • name - Optional name (str).
Returns:
Current, precision running sum (Fsum2Tuple).

fsum2 (self, xs=(), name='')

 

Add more items from an iterable, summate and return the current precision running sum and the residual.

Arguments:
  • xs - Iterable of items to add (each item scalar or an Fsum or Fsum2Tuple instance).
  • name - Optional name (str).
Returns:
Fsum2Tuple(fsum, residual) with fsum the current precision running sum and residual, the (precision) sum of the remaining partials. The residual is INT0 if the fsum is considered to be exact.

See Also: Methods Fsum.fint2, Fsum.fsum and Fsum.fsum2_

fsum2_ (self, *xs)

 

Add any positional arguments, summate and return the current precision running sum and the differential.

Arguments:
  • xs - Values to add (each scalar or an Fsum or Fsum2Tuple instance), all positional.
Returns:
2Tuple (fsum, delta) with the current, precision running fsum like method Fsum.fsum and delta, the difference with previous running fsum, float.

See Also: Methods Fsum.fsum_ and Fsum.fsum.

int_float (self, **raiser_RESIDUAL)

 

Return this instance' current running sum as int or float.

Arguments:
  • raiser_RESIDUAL - Use raiser=False (bool) to ignore ResidualErrors and RESIDUAL=scalar to override the RESIDUAL.
Returns:
This integer sum if this instance is_integer, otherwise return the float sum if the residual is zero or not significant.
Raises:
  • ResidualError - Non-zero, significant residual or invalid RESIDUAL.

See Also: Methods Fsum.fint, Fsum.fint2, Fsum.RESIDUAL and property Fsum.as_iscalar.

is_integer (self)

 

Is this instance' running sum integer? (bool).

See Also: Methods Fsum.fint, Fsum.fint2 and Fsum.is_scalar.

is_math_fsum (self)

 

Return whether functions fsum, fsum_, fsum1 and fsum1_ plus partials summation are based on Python's math.fsum or not.

Returns:
2 if all functions and partials summation are based on math.fsum, True if only the functions are based on math.fsum (and partials summation is not) or False if none are.

is_scalar (self, **raiser_RESIDUAL)

 

Is this instance' running sum scalar without residual or with a residual ratio not exceeding the RESIDUAL threshold?

Arguments:
  • raiser_RESIDUAL - Use raiser=False (bool) to ignore ResidualErrors and RESIDUAL=scalar to override the RESIDUAL threshold.
Returns:
True if this instance' non-zero residual ratio exceeds the RESIDUAL threshold (bool).
Raises:
  • ResidualError - Non-zero, significant residual or invalid RESIDUAL.

See Also: Method Fsum.RESIDUAL, Fsum.is_integer and property Fsum.as_iscalar.

pow (self, x, *mod, **raiser_RESIDUAL)

 

Return self**x as Fsum.

Arguments:
  • x - The exponent (scalar or Fsum).
  • mod - Optional modulus (int or None) for the 3-argument pow(self, other, mod) version.
  • raiser_RESIDUAL - Use raiser=False (bool) to ignore ResidualErrors and RESIDUAL=scalar to override the RESIDUAL.
Returns:
The pow(self, x) or pow(self, x, *mod) result (Fsum).
Raises:
  • ResidualError - Non-zero, significant residual or invalid RESIDUAL.

Note: If mod is given as None, the result will be an integer Fsum provided this instance is_integer or set to integer by an Fsum.fint call.

See Also: Methods Fsum.__ipow__, Fsum.fint, Fsum.is_integer and Fsum.root.

RESIDUAL (self, *threshold)

 

Get and set this instance' ratio for raising ResidualErrors, overriding the default from env variable PYGEODESY_FSUM_RESIDUAL.

Arguments:
  • threshold - If scalar, the ratio to exceed for raising ResidualErrors in division and exponention, if None restore the default set with env variable PYGEODESY_FSUM_RESIDUAL or if omitted, keep the current setting.
Returns:
The previous RESIDUAL setting (float), default 0.0.
Raises:

Note: ResidualErrors may be thrown if the non-zero ratio residual / fsum exceeds the given threshold and if the residual is non-zero and significant vs the fsum, i.e. (fsum + residual) != fsum and if optional keyword argument raiser=False is missing. Specify a negative threshold for only non-zero residual testing without significant.

root (self, root, **raiser_RESIDUAL)

 

Return self**(1 / root) as Fsum.

Arguments:
  • root - The order (scalar or Fsum), non-zero.
  • raiser_RESIDUAL - Use raiser=False (bool) to ignore ResidualErrors and RESIDUAL=scalar to override the RESIDUAL.
Returns:
The self ** (1 / root) result (Fsum).
Raises:
  • ResidualError - Non-zero, significant residual or invalid RESIDUAL.

See Also: Method Fsum.pow.

signOf (self, res=True)

 

Determine the sign of this instance.

Arguments:
  • res - If True consider, otherwise ignore the residual (bool).
Returns:
The sign (int, -1, 0 or +1).

toRepr (self, **lenc_prec_sep_fmt)

 

Return this Fsum instance as representation.

Arguments:
  • lenc_prec_sep_fmt - Optional keyword arguments for method Fsum.toStr.
Returns:
This instance (repr).
Overrides: named._Named.toRepr

toStr (self, lenc=True, **prec_sep_fmt)

 

Return this Fsum instance as string.

Arguments:
  • lenc - If True include the current [len] of this Fsum enclosed in [brackets] (bool).
  • prec_sep_fmt - Optional keyword arguments for method Fsum2Tuple.toStr.
Returns:
This instance (str).
Overrides: named._Named.toStr

Property Details

as_iscalar

Get this instance as-is (Fsum) or as scalar iff scalar.

Get method:
as_iscalar(self) - Get this instance as-is (Fsum) or as scalar iff scalar.
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst) - Zap the cached/memoized property value.

ceil

Get this instance' ceil value (int in Python 3+, but float in Python 2-).

Get method:
ceil(self) - Get this instance' ceil value (int in Python 3+, but float in Python 2-).
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst) - Zap the cached/memoized property value.

Note: The ceil takes the residual into account.

See Also: Method Fsum.int_float and properties Fsum.floor, Fsum.imag and Fsum.real.

float_int

DEPRECATED, use method Fsum.int_float.

Get method:
float_int(self) - DEPRECATED, use method Fsum.int_float.
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst) - Zap the cached/memoized property value.

floor

Get this instance' floor (int in Python 3+, but float in Python 2-).

Get method:
floor(self) - Get this instance' floor (int in Python 3+, but float in Python 2-).
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst) - Zap the cached/memoized property value.

Note: The floor takes the residual into account.

See Also: Method Fsum.int_float and properties Fsum.ceil, Fsum.imag and Fsum.real.

imag

Get the imaginary part of this instance (0.0, always).

Get method:
imag(self) - Get the imaginary part of this instance (0.0, always).
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst) - Zap the cached/memoized property value.

See Also: Properties Fsum.ceil, Fsum.floor and Fsum.real.

partials

Get this instance' current, partial sums (tuple of floats).

Get method:
partials(self) - Get this instance' current, partial sums (tuple of floats).
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst) - Zap the cached/memoized property value.

real

Get the real part of this instance (float).

Get method:
real(self) - Get the real part of this instance (float).
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst) - Zap the cached/memoized property value.

See Also: Methods Fsum.__float__ and Fsum.fsum and properties Fsum.ceil, Fsum.floor, Fsum.imag and Fsum.residual.

residual

Get this instance' residual (float or int): the sum(partials) less the precision running sum fsum.

Get method:
residual(self) - Get this instance' residual (float or int): the sum(partials) less the precision running sum fsum.
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst) - Zap the cached/memoized property value.

Note: The residual is INT0 iff the precision running fsum is considered to be exact.

See Also: Methods Fsum.fsum, Fsum.fsum2 and Fsum.is_exact.


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