def fadd(self, iterable):
'''Accumulate more values from an iterable.
@arg iterable: Sequence, list, tuple, etc. (C{scalar}s).
@raise OverflowError: Partial C{2sum} overflow.
@raise TypeError: Non-scalar B{C{iterable}} value.
@raise ValueError: Invalid or non-finite B{C{iterable}} value.
'''
if isscalar(iterable): # for backward compatibility
iterable = tuple(iterable)
ps = self._ps
for a in map(float, iterable): # _iter()
if not isfinite(a):
raise _ValueError(iterable=a, txt=_not_(_finite_))
i = 0
for p in ps:
a, p = _2sum(a, p)
if p:
ps[i] = p
i += 1
ps[i:] = [a]
self._n += 1
# assert self._ps is ps
self._fsum2_ = None
def fpowers(x, n, alts=0):
'''Return a series of powers M{[x**i for i=1..n]}.
@arg x: Value (C{scalar}).
@arg n: Highest exponent (C{int}).
@kwarg alts: Only alternating powers, starting with
this exponent (C{int}).
@return: Powers of B{C{x}} (C{float}[]).
@raise TypeError: Non-scalar B{C{x}} or B{C{n}} not C{int}.
@raise ValueError: Non-finite B{C{x}} or non-positive B{C{n}}.
'''
if not isfinite(x):
raise _ValueError(x=x, txt=_not_(_finite_))
if not isint(n):
raise _IsnotError(int.__name__, n=n)
elif n < 1:
raise _ValueError(n=n)
xs = [x]
for _ in range(1, n):
xs.append(xs[-1] * x)
if alts > 0: # x**2, x**4, ...
# XXX PyChecker chokes on xs[alts-1::2]
xs = xs[slice(alts - 1, None, 2)]
# XXX PyChecker claims result is None
return xs
def __init__(self, x, *cs):
'''New L{Fpolynomial} evaluation of the polynomial
M{sum(cs[i] * x**i for i=0..len(cs))}.
@arg x: Polynomial argument (C{scalar}).
@arg cs: Polynomial coeffients (C{scalar}[]).
@raise OverflowError: Partial C{2sum} overflow.
@raise TypeError: Non-scalar B{C{x}}.
@raise ValueError: No B{C{cs}} coefficients or B{C{x}} is not finite.
@see: Function L{fpolynomial} and method L{Fsum.fadd}.
'''
if not isfinite(x):
raise _ValueError(x=x, txt=_not_(_finite_))
if not cs:
raise _ValueError(cs=cs, txt=MISSING)
x, cs, xp = float(x), list(cs), _1_0
Fsum.__init__(self, cs.pop(0))
while cs:
xp *= x
self.fadd_(xp * cs.pop(0))
def __init__(self, x, *cs):
'''New L{Fhorner} evaluation of the polynomial
M{sum(cs[i] * x**i for i=0..len(cs))}.
@arg x: Polynomial argument (C{scalar}).
@arg cs: Polynomial coeffients (C{scalar}[]).
@raise OverflowError: Partial C{2sum} overflow.
@raise TypeError: Non-scalar B{C{x}}.
@raise ValueError: No B{C{cs}} coefficients or B{C{x}} is not finite.
@see: Function L{fhorner} and methods L{Fsum.fadd} and L{Fsum.fmul}.
'''
if not isfinite(x):
raise _ValueError(x=x, txt=_not_finite_)
if not cs:
raise _ValueError(cs=cs, txt=_Missing)
x, cs = float(x), list(cs)
Fsum.__init__(self, cs.pop())
while cs:
self.fmul(x)
self.fadd_(cs.pop())
def _2sum(a, b): # by .testFmath
'''(INTERNAL) Precision C{2sum} of M{a + b}.
'''
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)
def _2sum(a, b):
'''(INTERNAL) Precision C{2sum} of M{a + b}.
'''
s = a + b
if not isfinite(s):
raise OverflowError('%s: %r' % (_2sum.__name__, s))
if abs(a) < abs(b):
a, b = b, a
return s, b - (s - a)
def fmul(self, factor):
'''Multiple the current, partial sum by a factor.
@arg factor: The multiplier (C{scalar}).
@raise TypeError: Non-scalar B{C{factor}}.
@raise ValueError: Invalid or non-finite B{C{factor}}.
@see: Method L{Fsum.fadd}.
'''
if not isfinite(factor):
raise _ValueError(factor=factor, txt=_not_(_finite_))
f, ps = float(factor), self._ps
if ps: # multiply and adjust partial sums
ps[:] = [p * f for p in ps]
self.fadd_(ps.pop())
self._n -= 1
def fmul(self, factor):
'''Multiple the current, partial sum by a factor.
@arg factor: The multiplier (C{scalar}).
@raise TypeError: Non-scalar B{C{factor}}.
@raise ValueError: Invalid or non-finite B{C{factor}}.
@see: Method L{Fsum.fadd}.
'''
if not isfinite(factor):
raise ValueError('%s, not %s: %r' % (self, 'finite', factor))
ps = self._ps
if ps: # multiply and adjust partial sums
ps[:] = [p * factor for p in ps]
self.fadd_(ps.pop())
self._n -= 1
def fadd(self, iterable):
'''Accumulate more values from an iterable.
@arg iterable: Sequence, list, tuple, etc. (C{scalar}s).
@raise OverflowError: Partial C{2sum} overflow.
@raise TypeError: Non-scalar B{C{iterable}} value.
@raise ValueError: Invalid or non-finite B{C{iterable}} value.
'''
if isscalar(iterable): # for backward compatibility
iterable = tuple(iterable)
# def _iter():
# for a in iterable:
# if isinstance(a, Fsum):
# if a is self:
# self.fmul(2)
# else:
# for a in a._ps:
# yield a
# else:
# yield a
ps = self._ps
for a in iterable: # _iter()
if not isfinite(a):
raise ValueError('%s, not %s: %r' % (self, 'finite', a))
i = 0
for p in ps:
a, p = _2sum(a, p)
if p:
ps[i] = p
i += 1
ps[i:] = [a]
self._n += 1
# assert self._ps is ps
self._fsum2_ = None
