Coverage for pygeodesy/fsums.py: 95%
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2# -*- coding: utf-8 -*-
4u'''Class L{Fsum} for precision floating point summation similar to
5Python's C{math.fsum}, but enhanced with I{precision running} summation
6plus optionally, accurate I{TwoProduct} multiplication.
8Accurate multiplication is based on the C{math.fma} function from
9Python 3.13 and newer or an equivalent C{fma} implementation for
10Python 3.12 and older. To enable accurate multiplication, set env
11variable C{PYGEODESY_FSUM_F2PRODUCT} to C{"std"} or any non-empty
12string or invoke function C{pygeodesy.f2product(True)} or set. With
13C{"std"} the C{fma} implemention follows the C{math.fma} function,
14otherwise the C{PyGeodesy 24.09.09} release.
16Generally, an L{Fsum} instance is considered a C{float} plus a small or
17zero C{residue} aka C{residual} value, see property L{Fsum.residual}.
19Set env variable C{PYGEODESY_FSUM_RESIDUAL} to a C{float} string greater
20than C{"0.0"} as the threshold to throw a L{ResidualError} for a division,
21power or root operation of an L{Fsum} with a C{residual} I{ratio} exceeding
22the threshold. See methods L{Fsum.RESIDUAL}, L{Fsum.pow}, L{Fsum.__ipow__}
23and L{Fsum.__itruediv__}.
25There are several C{integer} L{Fsum} cases, for example the result from
26functions C{ceil}, C{floor}, C{Fsum.__floordiv__} and methods L{Fsum.fint},
27L{Fsum.fint2} and L{Fsum.is_integer}. Also, L{Fsum} methods L{Fsum.pow},
28L{Fsum.__ipow__}, L{Fsum.__pow__} and L{Fsum.__rpow__} return a (very long)
29C{int} if invoked with optional argument C{mod} set to C{None}. The
30C{residual} of an C{integer} L{Fsum} is between C{-1.0} and C{+1.0} and
31will be C{INT0} if that is considered to be I{exact}.
33Set env variable C{PYGEODESY_FSUM_NONFINITES} to C{"std"} or use function
34C{pygeodesy.nonfiniterrors(False)} to allow I{non-finite} C{float}s like
35C{inf}, C{INF}, C{NINF}, C{nan} and C{NAN} and to ignore C{OverflowError}
36respectively C{ValueError} exceptions. However, in that case I{non-finite}
37results may differ from Python's C{math.fsum} results.
38'''
39# make sure int/int division yields float quotient, see .basics
40from __future__ import division as _; del _ # noqa: E702 ;
42from pygeodesy.basics import _gcd, isbool, iscomplex, isint, isscalar, \
43 _signOf, itemsorted, signOf, _xiterable
44from pygeodesy.constants import INF, INT0, MANT_DIG, NEG0, NINF, _0_0, \
45 _1_0, _N_1_0, _isfinite, _pos_self, \
46 Float, Int
47from pygeodesy.errors import _AssertionError, _OverflowError, _TypeError, \
48 _ValueError, _xError, _xError2, _xkwds, \
49 _xkwds_get, _xkwds_get1, _xkwds_not, \
50 _xkwds_pop, _xsError
51from pygeodesy.internals import _enquote, _envPYGEODESY, _passarg, typename # _sizeof
52from pygeodesy.interns import NN, _arg_, _COMMASPACE_, _DMAIN_, _DOT_, _from_, \
53 _not_finite_, _SPACE_, _std_, _UNDER_
54# from pygeodesy.lazily import _ALL_LAZY, _ALL_MODS as _MODS # from .named
55from pygeodesy.named import _name__, _name2__, _Named, _NamedTuple, \
56 _NotImplemented, _ALL_LAZY, _MODS
57from pygeodesy.props import _allPropertiesOf_n, deprecated_method, \
58 deprecated_property_RO, Property, \
59 Property_RO, property_RO
60from pygeodesy.streprs import Fmt, fstr, unstr
61# from pygeodesy.units import Float, Int # from .constants
63from math import fabs, isinf, isnan, \
64 ceil as _ceil, floor as _floor # PYCHOK used! .ltp
66__all__ = _ALL_LAZY.fsums
67__version__ = '25.05.12'
69from pygeodesy.interns import (
70 _PLUS_ as _add_op_, # in .auxilats.auxAngle
71 _DSLASH_ as _floordiv_op_,
72 _EQUAL_ as _fset_op_,
73 _RANGLE_ as _gt_op_,
74 _LANGLE_ as _lt_op_,
75 _PERCENT_ as _mod_op_,
76 _STAR_ as _mul_op_,
77 _NOTEQUAL_ as _ne_op_,
78 _DSTAR_ as _pow_op_,
79 _DASH_ as _sub_op_, # in .auxilats.auxAngle
80 _SLASH_ as _truediv_op_
81)
82_divmod_op_ = _floordiv_op_ + _mod_op_
83_F2PRODUCT = _envPYGEODESY('FSUM_F2PRODUCT')
84_iadd_op_ = _add_op_ + _fset_op_ # in .auxilats.auxAngle, .fstats
85_integer_ = 'integer'
86_isub_op_ = _sub_op_ + _fset_op_ # in .auxilats.auxAngle
87_NONFINITEr = _0_0 # NOT INT0!
88_NONFINITES = _envPYGEODESY('FSUM_NONFINITES')
89_non_zero_ = 'non-zero'
90_RESIDUAL_0_0 = _envPYGEODESY('FSUM_RESIDUAL', _0_0)
91_significant_ = 'significant'
92_threshold_ = 'threshold'
95def _2finite(x, _isfine=_isfinite): # in .fstats
96 '''(INTERNAL) return C{float(x)} if finite.
97 '''
98 return (float(x) if _isfine(x) # and isscalar(x)
99 else _nfError(x))
102def _2float(index=None, _isfine=_isfinite, **name_x): # in .fmath, .fstats
103 '''(INTERNAL) Raise C{TypeError} or C{Overflow-/ValueError} if C{x} not finite.
104 '''
105 n, x = name_x.popitem() # _xkwds_item2(name_x)
106 try:
107 f = float(x)
108 return f if _isfine(f) else _nfError(x)
109 except Exception as X:
110 raise _xError(X, Fmt.INDEX(n, index), x)
113try: # MCCABE 26
114 from math import fma as _fma
116 def _2products(x, ys, *zs):
117 # yield(x * y for y in ys) + yield(z in zs)
118 # TwoProductFMA U{Algorithm 3.5
119 # <https://www.TUHH.De/ti3/paper/rump/OgRuOi05.pdf>}
120 for y in ys:
121 f = x * y
122 yield f
123 if _isfinite(f):
124 yield _fma(x, y, -f)
125 for z in zs:
126 yield z
128# _2split3 = \
129 _2split3s = _passarg # in Fsum.is_math_fma
131except ImportError: # PYCHOK DSPACE! Python 3.12-
133 if _F2PRODUCT and _F2PRODUCT != _std_:
134 # backward to PyGeodesy 24.09.09, with _fmaX
135 from pygeodesy.basics import _integer_ratio2
137 def _fma(*a_b_c): # PYCHOK no cover
138 # mimick C{math.fma} from Python 3.13+,
139 # the same accuracy, but ~14x slower
140 (n, d), (nb, db), (nc, dc) = map(_integer_ratio2, a_b_c)
141 # n, d = (n * nb * dc + d * db * nc), (d * db * dc)
142 d *= db
143 n *= nb * dc
144 n += nc * d
145 d *= dc
146 try:
147 n, d = _n_d2(n, d)
148 r = float(n / d)
149 except OverflowError: # "integer division result too large ..."
150 r = NINF if (_signOf(n, 0) * _signOf(d, 0)) < 0 else INF
151 return r if _isfinite(r) else _fmaX(r, *a_b_c) # "overflow in fma"
152 else:
153 _integer_ratio2 = None # redef, in Fsum.is_math_fma
155 def _fma(a, b, c): # PYCHOK redef
156 # mimick C{math.fma} from Python 3.13+,
157 # the same accuracy, but ~13x slower
158 b3s = _2split3(b), # 1-tuple of 3-tuple
159 r = _fsum(_2products(a, b3s, c))
160 return r if _isfinite(r) else _fmaX(r, a, b, c)
162 def _fmaX(r, *a_b_c): # PYCHOK no cover
163 # handle non-finite fma result as Python 3.13+ C-function U{math_fma_impl
164 # <https://GitHub.com/python/cpython/blob/main/Modules/mathmodule.c#L2305>}:
165 # raise a ValueError for a NAN result from non-NAN C{a_b_c}s otherwise an
166 # OverflowError for a non-finite, non-NAN result from all finite C{a_b_c}s.
167 if isnan(r):
168 def _x(x):
169 return not isnan(x)
170 else: # non-finite, non-NAN
171 _x = _isfinite
172 if all(map(_x, a_b_c)):
173 raise _nfError(r, unstr(_fma, *a_b_c))
174 return r
176 def _2products(x, y3s, *zs): # PYCHOK in _fma, ...
177 # yield(x * y3 for y3 in y3s) + yield(z in zs)
178 # TwoProduct U{Algorithm 3.3<https://www.TUHH.De/ti3/paper/rump/OgRuOi05.pdf>}, also
179 # in Python 3.13+ C{Modules/mathmodule.c} under #ifndef UNRELIABLE_FMA ... #else ...
180 _, a, b = _2split3(x)
181 for y, c, d in y3s:
182 y *= x
183 yield y
184 if _isfinite(y):
185 # yield b * d - (((y - a * c) - b * c) - a * d)
186 # = b * d + (a * d - ((y - a * c) - b * c))
187 # = b * d + (a * d + (b * c - (y - a * c)))
188 # = b * d + (a * d + (b * c + (a * c - y)))
189 yield a * c - y
190 yield b * c
191 if d:
192 yield a * d
193 yield b * d
194 for z in zs:
195 yield z
197 _2FACTOR = pow(2, (MANT_DIG + 1) // 2) + _1_0 # 134217729 if MANT_DIG == 53
199 def _2split3(x):
200 # Split U{Algorithm 3.2
201 # <https://www.TUHH.De/ti3/paper/rump/OgRuOi05.pdf>}
202 a = c = x * _2FACTOR
203 a -= c - x
204 b = x - a
205 return x, a, b
207 def _2split3s(xs): # in Fsum.is_math_fma
208 return map(_2split3, xs)
211def f2product(two=None):
212 '''Turn accurate I{TwoProduct} multiplication on or off.
214 @kwarg two: If C{True}, turn I{TwoProduct} on, if C{False} off or
215 if C{None} or omitted, keep the current setting.
217 @return: The previous setting (C{bool}).
219 @see: I{TwoProduct} multiplication is based on the I{TwoProductFMA}
220 U{Algorithm 3.5 <https://www.TUHH.De/ti3/paper/rump/OgRuOi05.pdf>}
221 using function C{math.fma} from Python 3.13 and later or an
222 equivalent, slower implementation when not available.
223 '''
224 t = Fsum._f2product
225 if two is not None:
226 Fsum._f2product = bool(two)
227 return t
230def _Fsumf_(*xs): # in .auxLat, ...
231 '''(INTERNAL) An C{Fsum(xs)}, all C{scalar}, an L{Fsum} or L{Fsum2Tuple}.
232 '''
233 return Fsum()._facc_xsum(xs, up=False)
236def _Fsum1f_(*xs): # in .albers
237 '''(INTERNAL) An C{Fsum(xs)}, all C{scalar}, an L{Fsum} or L{Fsum2Tuple}, 1-primed.
238 '''
239 return Fsum()._facc_xsum(_1primed(xs), origin=-1, up=False)
242def _halfeven(s, r, p):
243 '''(INTERNAL) Round half-even.
244 '''
245 if (p > 0 and r > 0) or \
246 (p < 0 and r < 0): # signs match
247 r *= 2
248 t = s + r
249 if r == (t - s):
250 s = t
251 return s
254def _isFsum(x): # in .fmath
255 '''(INTERNAL) Is C{x} an C{Fsum} instance?
256 '''
257 return isinstance(x, Fsum)
260def _isFsum_2Tuple(x): # in .basics, .constants, .fmath, .fstats
261 '''(INTERNAL) Is C{x} an C{Fsum} or C{Fsum2Tuple} instance?
262 '''
263 return isinstance(x, _Fsum_2Tuple_types)
266def _isOK(unused):
267 '''(INTERNAL) Helper for C{Fsum._fsum2} and C{Fsum.nonfinites}.
268 '''
269 return True
272def _isOK_or_finite(x, _isfine=_isfinite):
273 '''(INTERNAL) Is C{x} finite or is I{non-finite} OK?
274 '''
275 # assert _isin(_isfine, _isOK, _isfinite)
276 return _isfine(x) # C{bool}
279def _n_d2(n, d):
280 '''(INTERNAL) Reduce C{n} and C{d} by C{gcd}.
281 '''
282 try:
283 c = _gcd(n, d)
284 if c > 1:
285 return (n // c), (d // c)
286 except TypeError: # non-int float
287 pass
288 return n, d
291def _nfError(x, *args):
292 '''(INTERNAL) Throw a C{not-finite} exception.
293 '''
294 E = _NonfiniteError(x)
295 t = Fmt.PARENSPACED(_not_finite_, x)
296 if args: # in _fmaX, _2sum
297 return E(txt=t, *args)
298 raise E(t, txt=None)
301def _NonfiniteError(x):
302 '''(INTERNAL) Return the Error class for C{x}, I{non-finite}.
303 '''
304 return _OverflowError if isinf(x) else (
305 _ValueError if isnan(x) else _AssertionError)
308def nonfiniterrors(raiser=None):
309 '''Throw C{OverflowError} and C{ValueError} exceptions for or
310 handle I{non-finite} C{float}s as C{inf}, C{INF}, C{NINF},
311 C{nan} and C{NAN} in summations and multiplications.
313 @kwarg raiser: If C{True}, throw exceptions, if C{False} handle
314 I{non-finites} or if C{None} or omitted, leave
315 the setting unchanged.
317 @return: Previous setting (C{bool}).
319 @note: C{inf}, C{INF} and C{NINF} throw an C{OverflowError},
320 C{nan} and C{NAN} a C{ValueError}.
321 '''
322 d = Fsum._isfine
323 if raiser is not None:
324 Fsum._isfine = {} if bool(raiser) else Fsum._nonfinites_isfine_kwds[True]
325 return (False if d is Fsum._nonfinites_isfine_kwds[True] else
326 _xkwds_get1(d, _isfine=_isfinite) is _isfinite) if d else True
329def _1primed(xs): # in .fmath
330 '''(INTERNAL) 1-Primed summation of iterable C{xs}
331 items, all I{known} to be C{scalar}.
332 '''
333 yield _1_0
334 for x in xs:
335 yield x
336 yield _N_1_0
339def _psum(ps, **_isfine): # PYCHOK used!
340 '''(INTERNAL) Partials summation, updating C{ps}.
341 '''
342 # assert isinstance(ps, list)
343 i = len(ps) - 1
344 s = _0_0 if i < 0 else ps[i]
345 while i > 0:
346 i -= 1
347 s, r = _2sum(s, ps[i], **_isfine)
348 if r: # sum(ps) became inexact
349 if s:
350 ps[i:] = r, s
351 if i > 0:
352 s = _halfeven(s, r, ps[i-1])
353 break # return s
354 s = r # PYCHOK no cover
355 elif not _isfinite(s): # non-finite OK
356 i = 0 # collapse ps
357 if ps:
358 s += sum(ps)
359 ps[i:] = s,
360 return s
363def _Psum(ps, **name_f2product_nonfinites_RESIDUAL):
364 '''(INTERNAL) Return an C{Fsum} from I{ordered} partials C{ps}.
365 '''
366 F = Fsum(**name_f2product_nonfinites_RESIDUAL)
367 if ps:
368 F._ps[:] = ps
369 F._n = len(F._ps)
370 return F
373def _Psum_(*ps, **name_f2product_nonfinites_RESIDUAL): # in .fmath
374 '''(INTERNAL) Return an C{Fsum} from I{known scalar} C{ps}.
375 '''
376 return _Psum(ps, **name_f2product_nonfinites_RESIDUAL)
379def _residue(other):
380 '''(INTERNAL) Return the C{residual} or C{None} for C{scalar}.
381 '''
382 try:
383 r = other.residual
384 except AttributeError:
385 r = None # float, int, other
386 return r
389def _s_r2(s, r):
390 '''(INTERNAL) Return C{(s, r)}, I{ordered}.
391 '''
392 if _isfinite(s):
393 if r:
394 if fabs(s) < fabs(r):
395 s, r = r, (s or INT0)
396 else:
397 r = INT0
398 else:
399 r = _NONFINITEr
400 return s, r
403def _strcomplex(s, *args):
404 '''(INTERNAL) C{Complex} 2- or 3-arg C{pow} error as C{str}.
405 '''
406 c = typename(_strcomplex)[4:]
407 n = _sub_op_(len(args), _arg_)
408 t = unstr(pow, *args)
409 return _SPACE_(c, s, _from_, n, t)
412def _stresidual(prefix, residual, R=0, **mod_ratio):
413 '''(INTERNAL) Residual error txt C{str}.
414 '''
415 p = typename(_stresidual)[3:]
416 t = Fmt.PARENSPACED(p, Fmt(residual))
417 for n, v in itemsorted(mod_ratio):
418 p = Fmt.PARENSPACED(n, Fmt(v))
419 t = _COMMASPACE_(t, p)
420 return _SPACE_(prefix, t, Fmt.exceeds_R(R), _threshold_)
423def _2sum(a, b, _isfine=_isfinite): # in .testFmath
424 '''(INTERNAL) Return C{a + b} as 2-tuple C{(sum, residual)} with finite C{sum},
425 otherwise as 2-tuple C{(nonfinite, 0)} iff I{non-finites} are OK.
426 '''
427 # FastTwoSum U{Algorithm 1.1<https://www.TUHH.De/ti3/paper/rump/OgRuOi05.pdf>}
429 # Neumaier, A. U{Rundungsfehleranalyse einiger Verfahren zur Summation endlicher
430 # Summen<https://OnlineLibrary.Wiley.com/doi/epdf/10.1002/zamm.19740540106>},
431 # 1974, Zeitschrift für Angewandte Mathmatik und Mechanik, vol 51, nr 1, p 39-51
432 # <https://StackOverflow.com/questions/78633770/can-neumaier-summation-be-sped-up>
433 s = a + b
434 if _isfinite(s):
435 if fabs(a) < fabs(b):
436 r = (b - s) + a
437 else:
438 r = (a - s) + b
439 elif _isfine(s):
440 r = _NONFINITEr
441 else: # non-finite and not OK
442 t = unstr(_2sum, a, b)
443 raise _nfError(s, t)
444 return s, r
447def _threshold(threshold=_0_0, **kwds):
448 '''(INTERNAL) Get the L{ResidualError}s threshold,
449 optionally from single kwds C{B{RESIDUAL}=scalar}.
450 '''
451 if kwds:
452 threshold = _xkwds_get1(kwds, RESIDUAL=threshold)
453 try:
454 return _2finite(threshold) # PYCHOK None
455 except Exception as x:
456 raise ResidualError(threshold=threshold, cause=x)
459def _2tuple2(other):
460 '''(INTERNAL) Return 2-tuple C{(other, r)} with C{other} as C{int},
461 C{float} or C{as-is} and C{r} the residual of C{as-is} or 0.
462 '''
463 if _isFsum_2Tuple(other):
464 s, r = other._fint2
465 if r:
466 s, r = other._nfprs2
467 if r: # PYCHOK no cover
468 s = other # L{Fsum} as-is
469 else:
470 r = 0
471 s = other # C{type} as-is
472 if isint(s, both=True):
473 s = int(s)
474 return s, r
477class Fsum(_Named): # sync __methods__ with .vector3dBase.Vector3dBase, .fstats, ...
478 '''Precision floating point summation, I{running} summation and accurate multiplication.
480 Unlike Python's C{math.fsum}, this class accumulates values and provides intermediate,
481 I{running}, precision floating point summations. Accumulation may continue after any
482 intermediate, I{running} summuation.
484 @note: Values may be L{Fsum}, L{Fsum2Tuple}, C{int}, C{float} or C{scalar} instances,
485 i.e. any C{type} having method C{__float__}.
487 @note: Handling of I{non-finites} as C{inf}, C{INF}, C{NINF}, C{nan} and C{NAN} is
488 determined by function L{nonfiniterrors<fsums.nonfiniterrors>} for the default
489 and by method L{nonfinites<Fsum.nonfinites>} for individual C{Fsum} instances,
490 overruling the default. For backward compatibility, I{non-finites} raise
491 exceptions by default.
493 @see: U{Hettinger<https://GitHub.com/ActiveState/code/tree/master/recipes/Python/
494 393090_Binary_floating_point_summatiaccurate_full/recipe-393090.py>},
495 U{Kahan<https://WikiPedia.org/wiki/Kahan_summation_algorithm>}, U{Klein
496 <https://Link.Springer.com/article/10.1007/s00607-005-0139-x>}, Python 2.6+
497 file I{Modules/mathmodule.c} and the issue log U{Full precision summation
498 <https://Bugs.Python.org/issue2819>}.
500 @see: Method L{f2product<Fsum.f2product>} for details about accurate I{TwoProduct}
501 multiplication.
503 @see: Module L{fsums<pygeodesy.fsums>} for env variables C{PYGEODESY_FSUM_F2PRODUCT},
504 C{PYGEODESY_FSUM_NONFINITES} and C{PYGEODESY_FSUM_RESIDUAL}.
505 '''
506 _f2product = _MODS.sys_version_info2 > (3, 12) or bool(_F2PRODUCT)
507 _isfine = {} # == _isfinite, see nonfiniterrors()
508 _n = 0
509# _ps = [] # partial sums
510# _ps_max = 0 # max(Fsum._ps_max, len(Fsum._ps)) # 41
511 _RESIDUAL = _threshold(_RESIDUAL_0_0)
513 def __init__(self, *xs, **name_f2product_nonfinites_RESIDUAL):
514 '''New L{Fsum}.
516 @arg xs: No, one or more initial items to accumulate (each C{scalar}, an
517 L{Fsum} or L{Fsum2Tuple}), all positional.
518 @kwarg name_f2product_nonfinites_RESIDUAL: Optional C{B{name}=NN} (C{str})
519 and settings C{B{f2product}=None} (C{bool}), C{B{nonfinites}=None}
520 (C{bool}) and C{B{RESIDUAL}=0.0} threshold (C{scalar}) for this
521 L{Fsum}.
523 @see: Methods L{Fsum.f2product}, L{Fsum.nonfinites}, L{Fsum.RESIDUAL},
524 L{Fsum.fadd} and L{Fsum.fadd_}.
525 '''
526 if name_f2product_nonfinites_RESIDUAL:
527 self._optionals(**name_f2product_nonfinites_RESIDUAL)
528 self._ps = [] # [_0_0], see L{Fsum._fprs}
529 if xs:
530 self._facc_args(xs, up=False)
532 def __abs__(self):
533 '''Return C{abs(self)} as an L{Fsum}.
534 '''
535 s = self.signOf() # == self._cmp_0(0)
536 return (-self) if s < 0 else self._copyd(self.__abs__)
538 def __add__(self, other):
539 '''Return C{B{self} + B{other}} as an L{Fsum}.
541 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar}.
543 @return: The sum (L{Fsum}).
545 @see: Methods L{Fsum.fadd_} and L{Fsum.fadd}.
546 '''
547 f = self._copyd(self.__add__)
548 return f._fadd(other)
550 def __bool__(self): # PYCHOK Python 3+
551 '''Return C{bool(B{self})}, C{True} iff C{residual} is zero.
552 '''
553 s, r = self._nfprs2
554 return bool(s or r) and s != -r # == self != 0
556 def __call__(self, other, **up): # in .fmath
557 '''Reset this C{Fsum} to C{other}, default C{B{up}=True}.
558 '''
559 self._ps[:] = 0, # clear for errors
560 self._fset(other, op=_fset_op_, **up)
561 return self
564 def __ceil__(self): # PYCHOK not special in Python 2-
565 '''Return this instance' C{math.ceil} as C{int} or C{float}.
567 @return: An C{int} in Python 3+, but C{float} in Python 2-.
569 @see: Methods L{Fsum.__floor__} and property L{Fsum.ceil}.
570 '''
571 return self.ceil
573 def __cmp__(self, other): # PYCHOK no cover
574 '''Compare this with an other instance or C{scalar}, Python 2-.
576 @return: -1, 0 or +1 (C{int}).
578 @raise TypeError: Incompatible B{C{other}} C{type}.
579 '''
580 s = self._cmp_0(other, typename(self.cmp))
581 return _signOf(s, 0)
583 def __divmod__(self, other, **raiser_RESIDUAL):
584 '''Return C{divmod(B{self}, B{other})} as a L{DivMod2Tuple}
585 with quotient C{div} an C{int} in Python 3+ or C{float}
586 in Python 2- and remainder C{mod} an L{Fsum} instance.
588 @arg other: Modulus (C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
589 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore
590 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}
591 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.
593 @raise ResidualError: Non-zero, significant residual or invalid
594 B{C{RESIDUAL}}.
596 @see: Method L{Fsum.fdiv}.
597 '''
598 f = self._copyd(self.__divmod__)
599 return f._fdivmod2(other, _divmod_op_, **raiser_RESIDUAL)
601 def __eq__(self, other):
602 '''Return C{(B{self} == B{other})} as C{bool} where B{C{other}}
603 is C{scalar}, an other L{Fsum} or L{Fsum2Tuple}.
604 '''
605 return self._cmp_0(other, _fset_op_ + _fset_op_) == 0
607 def __float__(self):
608 '''Return this instance' current, precision running sum as C{float}.
610 @see: Methods L{Fsum.fsum} and L{Fsum.int_float}.
611 '''
612 return float(self._fprs)
614 def __floor__(self): # PYCHOK not special in Python 2-
615 '''Return this instance' C{math.floor} as C{int} or C{float}.
617 @return: An C{int} in Python 3+, but C{float} in Python 2-.
619 @see: Methods L{Fsum.__ceil__} and property L{Fsum.floor}.
620 '''
621 return self.floor
623 def __floordiv__(self, other):
624 '''Return C{B{self} // B{other}} as an L{Fsum}.
626 @arg other: Divisor (C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
628 @return: The C{floor} quotient (L{Fsum}).
630 @see: Methods L{Fsum.__ifloordiv__}.
631 '''
632 f = self._copyd(self.__floordiv__)
633 return f._floordiv(other, _floordiv_op_)
635# def __format__(self, *other): # PYCHOK no cover
636# '''Not implemented.'''
637# return _NotImplemented(self, *other)
639 def __ge__(self, other):
640 '''Return C{(B{self} >= B{other})}, see C{__eq__}.
641 '''
642 return self._cmp_0(other, _gt_op_ + _fset_op_) >= 0
644 def __gt__(self, other):
645 '''Return C{(B{self} > B{other})}, see C{__eq__}.
646 '''
647 return self._cmp_0(other, _gt_op_) > 0
649 def __hash__(self): # PYCHOK no cover
650 '''Return C{hash(B{self})} as C{float}.
651 '''
652 # @see: U{Notes for type implementors<https://docs.Python.org/
653 # 3/library/numbers.html#numbers.Rational>}
654 return hash(self.partials) # tuple.__hash__()
656 def __iadd__(self, other):
657 '''Apply C{B{self} += B{other}} to this instance.
659 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar} value or
660 an iterable of several of the former.
662 @return: This instance, updated (L{Fsum}).
664 @raise TypeError: Invalid B{C{other}}, not
665 C{scalar} nor L{Fsum}.
667 @see: Methods L{Fsum.fadd_} and L{Fsum.fadd}.
668 '''
669 try:
670 return self._fadd(other, op=_iadd_op_)
671 except TypeError:
672 pass
673 _xiterable(other)
674 return self._facc(other)
676 def __ifloordiv__(self, other):
677 '''Apply C{B{self} //= B{other}} to this instance.
679 @arg other: Divisor (C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
681 @return: This instance, updated (L{Fsum}).
683 @raise ResidualError: Non-zero, significant residual
684 in B{C{other}}.
686 @raise TypeError: Invalid B{C{other}} type.
688 @raise ValueError: Invalid or I{non-finite} B{C{other}}.
690 @raise ZeroDivisionError: Zero B{C{other}}.
692 @see: Methods L{Fsum.__itruediv__}.
693 '''
694 return self._floordiv(other, _floordiv_op_ + _fset_op_)
696 def __imatmul__(self, other): # PYCHOK no cover
697 '''Not implemented.'''
698 return _NotImplemented(self, other)
700 def __imod__(self, other):
701 '''Apply C{B{self} %= B{other}} to this instance.
703 @arg other: Modulus (C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
705 @return: This instance, updated (L{Fsum}).
707 @see: Method L{Fsum.__divmod__}.
708 '''
709 return self._fdivmod2(other, _mod_op_ + _fset_op_).mod
711 def __imul__(self, other):
712 '''Apply C{B{self} *= B{other}} to this instance.
714 @arg other: Factor (C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
716 @return: This instance, updated (L{Fsum}).
718 @raise OverflowError: Partial C{2sum} overflow.
720 @raise TypeError: Invalid B{C{other}} type.
722 @raise ValueError: Invalid or I{non-finite} B{C{other}}.
723 '''
724 return self._fmul(other, _mul_op_ + _fset_op_)
726 def __int__(self):
727 '''Return this instance as an C{int}.
729 @see: Method L{Fsum.int_float} and properties L{Fsum.ceil}
730 and L{Fsum.floor}.
731 '''
732 i, _ = self._fint2
733 return i
735 def __invert__(self): # PYCHOK no cover
736 '''Not implemented.'''
737 # Luciano Ramalho, "Fluent Python", O'Reilly, 2nd Ed, 2022 p. 567
738 return _NotImplemented(self)
740 def __ipow__(self, other, *mod, **raiser_RESIDUAL): # PYCHOK 2 vs 3 args
741 '''Apply C{B{self} **= B{other}} to this instance.
743 @arg other: Exponent (C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
744 @arg mod: Optional modulus (C{int} or C{None}) for the 3-argument
745 C{pow(B{self}, B{other}, B{mod})} version.
746 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore
747 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}
748 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.
750 @return: This instance, updated (L{Fsum}).
752 @note: If B{C{mod}} is given, the result will be an C{integer}
753 L{Fsum} in Python 3+ if this instance C{is_integer} or
754 set to C{as_integer} and B{C{mod}} is given and C{None}.
756 @raise OverflowError: Partial C{2sum} overflow.
758 @raise ResidualError: Invalid B{C{RESIDUAL}} or the residual
759 is non-zero and significant and either
760 B{C{other}} is a fractional or negative
761 C{scalar} or B{C{mod}} is given and not
762 C{None}.
764 @raise TypeError: Invalid B{C{other}} type or 3-argument C{pow}
765 invocation failed.
767 @raise ValueError: If B{C{other}} is a negative C{scalar} and this
768 instance is C{0} or B{C{other}} is a fractional
769 C{scalar} and this instance is negative or has a
770 non-zero and significant residual or B{C{mod}}
771 is given as C{0}.
773 @see: CPython function U{float_pow<https://GitHub.com/
774 python/cpython/blob/main/Objects/floatobject.c>}.
775 '''
776 return self._fpow(other, _pow_op_ + _fset_op_, *mod, **raiser_RESIDUAL)
778 def __isub__(self, other):
779 '''Apply C{B{self} -= B{other}} to this instance.
781 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar} value or
782 an iterable of several of the former.
784 @return: This instance, updated (L{Fsum}).
786 @raise TypeError: Invalid B{C{other}} type.
788 @see: Methods L{Fsum.fsub_} and L{Fsum.fsub}.
789 '''
790 try:
791 return self._fsub(other, _isub_op_)
792 except TypeError:
793 pass
794 _xiterable(other)
795 return self._facc_neg(other)
797 def __iter__(self):
798 '''Return an C{iter}ator over a C{partials} duplicate.
799 '''
800 return iter(self.partials)
802 def __itruediv__(self, other, **raiser_RESIDUAL):
803 '''Apply C{B{self} /= B{other}} to this instance.
805 @arg other: Divisor (C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
806 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore
807 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}
808 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.
810 @return: This instance, updated (L{Fsum}).
812 @raise OverflowError: Partial C{2sum} overflow.
814 @raise ResidualError: Non-zero, significant residual or invalid
815 B{C{RESIDUAL}}.
817 @raise TypeError: Invalid B{C{other}} type.
819 @raise ValueError: Invalid or I{non-finite} B{C{other}}.
821 @raise ZeroDivisionError: Zero B{C{other}}.
823 @see: Method L{Fsum.__ifloordiv__}.
824 '''
825 return self._ftruediv(other, _truediv_op_ + _fset_op_, **raiser_RESIDUAL)
827 def __le__(self, other):
828 '''Return C{(B{self} <= B{other})}, see C{__eq__}.
829 '''
830 return self._cmp_0(other, _lt_op_ + _fset_op_) <= 0
832 def __len__(self):
833 '''Return the number of values accumulated (C{int}).
834 '''
835 return self._n
837 def __lt__(self, other):
838 '''Return C{(B{self} < B{other})}, see C{__eq__}.
839 '''
840 return self._cmp_0(other, _lt_op_) < 0
842 def __matmul__(self, other): # PYCHOK no cover
843 '''Not implemented.'''
844 return _NotImplemented(self, other)
846 def __mod__(self, other):
847 '''Return C{B{self} % B{other}} as an L{Fsum}.
849 @see: Method L{Fsum.__imod__}.
850 '''
851 f = self._copyd(self.__mod__)
852 return f._fdivmod2(other, _mod_op_).mod
854 def __mul__(self, other):
855 '''Return C{B{self} * B{other}} as an L{Fsum}.
857 @see: Method L{Fsum.__imul__}.
858 '''
859 f = self._copyd(self.__mul__)
860 return f._fmul(other, _mul_op_)
862 def __ne__(self, other):
863 '''Return C{(B{self} != B{other})}, see C{__eq__}.
864 '''
865 return self._cmp_0(other, _ne_op_) != 0
867 def __neg__(self):
868 '''Return C{copy(B{self})}, I{negated}.
869 '''
870 f = self._copyd(self.__neg__)
871 return f._fset(self._neg)
873 def __pos__(self):
874 '''Return this instance I{as-is}, like C{float.__pos__()}.
875 '''
876 return self if _pos_self else self._copyd(self.__pos__)
878 def __pow__(self, other, *mod): # PYCHOK 2 vs 3 args
879 '''Return C{B{self}**B{other}} as an L{Fsum}.
881 @see: Method L{Fsum.__ipow__}.
882 '''
883 f = self._copyd(self.__pow__)
884 return f._fpow(other, _pow_op_, *mod)
886 def __radd__(self, other):
887 '''Return C{B{other} + B{self}} as an L{Fsum}.
889 @see: Method L{Fsum.__iadd__}.
890 '''
891 f = self._rcopyd(other, self.__radd__)
892 return f._fadd(self)
894 def __rdivmod__(self, other):
895 '''Return C{divmod(B{other}, B{self})} as 2-tuple
896 C{(quotient, remainder)}.
898 @see: Method L{Fsum.__divmod__}.
899 '''
900 f = self._rcopyd(other, self.__rdivmod__)
901 return f._fdivmod2(self, _divmod_op_)
903# turned off, called by _deepcopy and _copy
904# def __reduce__(self): # Python 3.8+
905# ''' Pickle, like std C{fractions.Fraction}, see U{__reduce__
906# <https://docs.Python.org/3/library/pickle.html#object.__reduce__>}
907# '''
908# dict_ = self._Fsum_as().__dict__ # no __setstate__
909# return (type(self), self.partials, dict_)
911# def __repr__(self):
912# '''Return the default C{repr(this)}.
913# '''
914# return self.toRepr(lenc=True)
916 def __rfloordiv__(self, other):
917 '''Return C{B{other} // B{self}} as an L{Fsum}.
919 @see: Method L{Fsum.__ifloordiv__}.
920 '''
921 f = self._rcopyd(other, self.__rfloordiv__)
922 return f._floordiv(self, _floordiv_op_)
924 def __rmatmul__(self, other): # PYCHOK no cover
925 '''Not implemented.'''
926 return _NotImplemented(self, other)
928 def __rmod__(self, other):
929 '''Return C{B{other} % B{self}} as an L{Fsum}.
931 @see: Method L{Fsum.__imod__}.
932 '''
933 f = self._rcopyd(other, self.__rmod__)
934 return f._fdivmod2(self, _mod_op_).mod
936 def __rmul__(self, other):
937 '''Return C{B{other} * B{self}} as an L{Fsum}.
939 @see: Method L{Fsum.__imul__}.
940 '''
941 f = self._rcopyd(other, self.__rmul__)
942 return f._fmul(self, _mul_op_)
944 def __round__(self, *ndigits): # PYCHOK Python 3+
945 '''Return C{round(B{self}, *B{ndigits}} as an L{Fsum}.
947 @arg ndigits: Optional number of digits (C{int}).
948 '''
949 f = self._copyd(self.__round__)
950 # <https://docs.Python.org/3.12/reference/datamodel.html?#object.__round__>
951 return f._fset(round(float(self), *ndigits)) # can be C{int}
953 def __rpow__(self, other, *mod):
954 '''Return C{B{other}**B{self}} as an L{Fsum}.
956 @see: Method L{Fsum.__ipow__}.
957 '''
958 f = self._rcopyd(other, self.__rpow__)
959 return f._fpow(self, _pow_op_, *mod)
961 def __rsub__(self, other):
962 '''Return C{B{other} - B{self}} as L{Fsum}.
964 @see: Method L{Fsum.__isub__}.
965 '''
966 f = self._rcopyd(other, self.__rsub__)
967 return f._fsub(self, _sub_op_)
969 def __rtruediv__(self, other, **raiser_RESIDUAL):
970 '''Return C{B{other} / B{self}} as an L{Fsum}.
972 @see: Method L{Fsum.__itruediv__}.
973 '''
974 f = self._rcopyd(other, self.__rtruediv__)
975 return f._ftruediv(self, _truediv_op_, **raiser_RESIDUAL)
977# def __sizeof__(self):
978# '''Return the size of this instance (C{int} bytes}).
979# '''
980# return _sizeof(self._ps) + _sizeof(self._n)
982 def __str__(self):
983 '''Return the default C{str(self)}.
984 '''
985 return self.toStr(lenc=True)
987 def __sub__(self, other):
988 '''Return C{B{self} - B{other}} as an L{Fsum}.
990 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar}.
992 @return: The difference (L{Fsum}).
994 @see: Method L{Fsum.__isub__}.
995 '''
996 f = self._copyd(self.__sub__)
997 return f._fsub(other, _sub_op_)
999 def __truediv__(self, other, **raiser_RESIDUAL):
1000 '''Return C{B{self} / B{other}} as an L{Fsum}.
1002 @arg other: Divisor (C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
1003 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore
1004 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}
1005 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.
1007 @return: The quotient (L{Fsum}).
1009 @raise ResidualError: Non-zero, significant residual or invalid
1010 B{C{RESIDUAL}}.
1012 @see: Method L{Fsum.__itruediv__}.
1013 '''
1014 return self._truediv(other, _truediv_op_, **raiser_RESIDUAL)
1016 __trunc__ = __int__
1018 if _MODS.sys_version_info2 < (3, 0): # PYCHOK no cover
1019 # <https://docs.Python.org/2/library/operator.html#mapping-operators-to-functions>
1020 __div__ = __truediv__
1021 __idiv__ = __itruediv__
1022 __long__ = __int__
1023 __nonzero__ = __bool__
1024 __rdiv__ = __rtruediv__
1026 def as_integer_ratio(self):
1027 '''Return this instance as the ratio of 2 integers.
1029 @return: 2-Tuple C{(numerator, denominator)} both C{int} with
1030 C{numerator} signed and C{denominator} non-zero and
1031 positive. The C{numerator} is I{non-finite} if this
1032 instance is.
1034 @see: Method L{Fsum.fint2} and C{float.as_integer_ratio} in
1035 Python 2.7+.
1036 '''
1037 n, r = self._fint2
1038 if r:
1039 i, d = float(r).as_integer_ratio()
1040 n, d = _n_d2(n * d + i, d)
1041 else: # PYCHOK no cover
1042 d = 1
1043 return n, d
1045 @property_RO
1046 def as_iscalar(self):
1047 '''Get this instance I{as-is} (L{Fsum} with C{non-zero residual},
1048 C{scalar} or I{non-finite}).
1049 '''
1050 s, r = self._nfprs2
1051 return self if r else s
1053 @property_RO
1054 def ceil(self):
1055 '''Get this instance' C{ceil} value (C{int} in Python 3+, but
1056 C{float} in Python 2-).
1058 @note: This C{ceil} takes the C{residual} into account.
1060 @see: Method L{Fsum.int_float} and properties L{Fsum.floor},
1061 L{Fsum.imag} and L{Fsum.real}.
1062 '''
1063 s, r = self._fprs2
1064 c = _ceil(s) + int(r) - 1
1065 while r > (c - s): # (s + r) > c
1066 c += 1
1067 return c # _ceil(self._n_d)
1069 cmp = __cmp__
1071 def _cmp_0(self, other, op):
1072 '''(INTERNAL) Return C{scalar(self - B{other})} for 0-comparison.
1073 '''
1074 if _isFsum_2Tuple(other):
1075 s = self._ps_1sum(*other._ps)
1076 elif self._scalar(other, op):
1077 s = self._ps_1sum(other)
1078 else:
1079 s = self.signOf() # res=True
1080 return s
1082 def copy(self, deep=False, **name):
1083 '''Copy this instance, C{shallow} or B{C{deep}}.
1085 @kwarg name: Optional, overriding C{B{name}='"copy"} (C{str}).
1087 @return: The copy (L{Fsum}).
1088 '''
1089 n = _name__(name, name__=self.copy)
1090 f = _Named.copy(self, deep=deep, name=n)
1091 if f._ps is self._ps:
1092 f._ps = list(self._ps) # separate list
1093 if not deep:
1094 f._n = 1
1095 # assert f._f2product == self._f2product
1096 # assert f._Fsum is f
1097 # assert f._isfine is self._isfine
1098 # assert f._RESIDUAL is self._RESIDUAL
1099 return f
1101 def _copyd(self, which, name=NN):
1102 '''(INTERNAL) Copy for I{dyadic} operators.
1103 '''
1104 n = name or typename(which)
1105 # NOT .classof due to .Fdot(a, *b) args, etc.
1106 f = _Named.copy(self, deep=False, name=n)
1107 f._ps = list(self._ps) # separate list
1108 # assert f._n == self._n
1109 # assert f._f2product == self._f2product
1110 # assert f._Fsum is f
1111 # assert f._isfine is self._isfine
1112 # assert f._RESIDUAL is self._RESIDUAL
1113 return f
1115 divmod = __divmod__
1117 def _Error(self, op, other, Error, **txt_cause):
1118 '''(INTERNAL) Format an B{C{Error}} for C{{self} B{op} B{other}}.
1119 '''
1120 # self.as_iscalar causes RecursionError for ._fprs2 errors
1121 s = _Psum(self._ps, nonfinites=True, name=self.name)
1122 return Error(_SPACE_(s.as_iscalar, op, other), **txt_cause)
1124 def _ErrorX(self, X, op, other, *mod):
1125 '''(INTERNAL) Format the caught exception C{X}.
1126 '''
1127 E, t = _xError2(X)
1128 if mod:
1129 t = _COMMASPACE_(Fmt.PARENSPACED(mod=mod[0]), t)
1130 return self._Error(op, other, E, txt=t, cause=X)
1132 def _ErrorXs(self, X, xs, **kwds): # in .fmath
1133 '''(INTERNAL) Format the caught exception C{X}.
1134 '''
1135 E, t = _xError2(X)
1136 u = unstr(self.named3, *xs, _ELLIPSIS=4, **kwds)
1137 return E(u, txt=t, cause=X)
1139 def _facc(self, xs, up=True, **_X_x_origin):
1140 '''(INTERNAL) Accumulate more C{scalar}s or L{Fsum}s.
1141 '''
1142 if xs:
1143 kwds = self._isfine
1144 if _X_x_origin:
1145 kwds = _xkwds(_X_x_origin, **kwds)
1146 fs = _xs(xs, **kwds) # PYCHOK yield
1147 ps = self._ps
1148 ps[:] = self._ps_acc(list(ps), fs, up=up)
1149# if len(ps) > 16:
1150# _ = _psum(ps, **self._isfine)
1151 return self
1153 def _facc_args(self, xs, **up):
1154 '''(INTERNAL) Accumulate 0, 1 or more C{xs}, all positional
1155 arguments in the caller of this method.
1156 '''
1157 return self._fadd(xs[0], **up) if len(xs) == 1 else \
1158 self._facc(xs, **up) # origin=1?
1160 def _facc_dot(self, n, xs, ys, **kwds): # in .fmath
1161 '''(INTERNAL) Accumulate C{fdot(B{xs}, *B{ys})}.
1162 '''
1163 if n > 0:
1164 _f = Fsum(**kwds)
1165 self._facc(_f(x).fmul(y) for x, y in zip(xs, ys)) # PYCHOK attr?
1166 return self
1168 def _facc_neg(self, xs, **up_origin):
1169 '''(INTERNAL) Accumulate more C{xs}, negated.
1170 '''
1171 def _N(X):
1172 return X._ps_neg
1174 def _n(x):
1175 return -float(x)
1177 return self._facc(xs, _X=_N, _x=_n, **up_origin)
1179 def _facc_power(self, power, xs, which, **raiser_RESIDUAL): # in .fmath
1180 '''(INTERNAL) Add each C{xs} as C{float(x**power)}.
1181 '''
1182 def _Pow4(p):
1183 r = 0
1184 if _isFsum_2Tuple(p):
1185 s, r = p._fprs2
1186 if r:
1187 m = Fsum._pow
1188 else: # scalar
1189 return _Pow4(s)
1190 elif isint(p, both=True) and int(p) >= 0:
1191 p = s = int(p)
1192 m = Fsum._pow_int
1193 else:
1194 p = s = _2float(power=p, **self._isfine)
1195 m = Fsum._pow_scalar
1196 return m, p, s, r
1198 _Pow, p, s, r = _Pow4(power)
1199 if p: # and xs:
1200 op = typename(which)
1201 _FsT = _Fsum_2Tuple_types
1202 _pow = self._pow_2_3
1204 def _P(X):
1205 f = _Pow(X, p, power, op, **raiser_RESIDUAL)
1206 return f._ps if isinstance(f, _FsT) else (f,)
1208 def _p(x):
1209 x = float(x)
1210 f = _pow(x, s, power, op, **raiser_RESIDUAL)
1211 if f and r:
1212 f *= _pow(x, r, power, op, **raiser_RESIDUAL)
1213 return f
1215 f = self._facc(xs, _X=_P, _x=_p) # origin=1?
1216 else:
1217 f = self._facc_scalar_(float(len(xs))) # x**0 == 1
1218 return f
1220 def _facc_scalar(self, xs, **up):
1221 '''(INTERNAL) Accumulate all C{xs}, each C{scalar}.
1222 '''
1223 if xs:
1224 ps = self._ps
1225 ps[:] = self._ps_acc(list(ps), xs, **up)
1226 return self
1228 def _facc_scalar_(self, *xs, **up):
1229 '''(INTERNAL) Accumulate all positional C{xs}, each C{scalar}.
1230 '''
1231 return self._facc_scalar(xs, **up)
1233# def _facc_up(self, up=True):
1234# '''(INTERNAL) Update the C{partials}, by removing
1235# and re-accumulating the final C{partial}.
1236# '''
1237# ps = self._ps
1238# while len(ps) > 1:
1239# p = ps.pop()
1240# if p:
1241# n = self._n
1242# _ = self._ps_acc(ps, (p,), up=False)
1243# self._n = n
1244# break
1245# return self._update() if up else self
1247 def _facc_xsum(self, xs, up=True, **origin_which):
1248 '''(INTERNAL) Accumulate all C{xs}, each C{scalar}, an L{Fsum}
1249 or L{Fsum2Tuple}, like function C{_xsum}.
1250 '''
1251 fs = _xs(xs, **_x_isfine(self.nonfinitesOK, _Cdot=type(self),
1252 **origin_which)) # PYCHOK yield
1253 return self._facc_scalar(fs, up=up)
1255 def fadd(self, xs=()):
1256 '''Add an iterable's items to this instance.
1258 @arg xs: Iterable of items to add (each C{scalar},
1259 an L{Fsum} or L{Fsum2Tuple}).
1261 @return: This instance (L{Fsum}).
1263 @raise OverflowError: Partial C{2sum} overflow.
1265 @raise TypeError: An invalid B{C{xs}} item.
1267 @raise ValueError: Invalid or I{non-finite} B{C{xs}} value.
1268 '''
1269 if _isFsum_2Tuple(xs):
1270 self._facc_scalar(xs._ps)
1271 elif isscalar(xs): # for backward compatibility # PYCHOK no cover
1272 x = _2float(x=xs, **self._isfine)
1273 self._facc_scalar_(x)
1274 elif xs: # _xiterable(xs)
1275 self._facc(xs)
1276 return self
1278 def fadd_(self, *xs):
1279 '''Add all positional items to this instance.
1281 @arg xs: Values to add (each C{scalar}, an L{Fsum}
1282 or L{Fsum2Tuple}), all positional.
1284 @see: Method L{Fsum.fadd} for further details.
1285 '''
1286 return self._facc_args(xs)
1288 def _fadd(self, other, op=_add_op_, **up):
1289 '''(INTERNAL) Apply C{B{self} += B{other}}.
1290 '''
1291 if _isFsum_2Tuple(other):
1292 self._facc_scalar(other._ps, **up)
1293 elif self._scalar(other, op):
1294 self._facc_scalar_(other, **up)
1295 return self
1297 fcopy = copy # for backward compatibility
1298 fdiv = __itruediv__
1299 fdivmod = __divmod__
1301 def _fdivmod2(self, other, op, **raiser_RESIDUAL):
1302 '''(INTERNAL) Apply C{B{self} %= B{other}} and return a L{DivMod2Tuple}.
1303 '''
1304 # result mostly follows CPython function U{float_divmod
1305 # <https://GitHub.com/python/cpython/blob/main/Objects/floatobject.c>},
1306 # but at least divmod(-3, 2) equals Cpython's result (-2, 1).
1307 q = self._truediv(other, op, **raiser_RESIDUAL).floor
1308 if q: # == float // other == floor(float / other)
1309 self -= self._Fsum_as(q) * other # NOT other * q!
1311 s = signOf(other) # make signOf(self) == signOf(other)
1312 if s and self.signOf() == -s: # PYCHOK no cover
1313 self += other
1314 q -= 1
1315# t = self.signOf()
1316# if t and t != s:
1317# raise self._Error(op, other, _AssertionError, txt__=signOf)
1318 return DivMod2Tuple(q, self) # q is C{int} in Python 3+, but C{float} in Python 2-
1320 def _fhorner(self, x, cs, where, incx=True): # in .fmath
1321 '''(INTERNAL) Add an L{Fhorner} evaluation of polynomial
1322 C{sum(c * B{x}**i for i, c in _e(cs))} where C{_e =
1323 enumerate if B{incx} else _enumereverse}.
1324 '''
1325 # assert _xiterablen(cs)
1326 try:
1327 n = len(cs)
1328 if n > 1 and _2finite(x, **self._isfine):
1329 H = self._Fsum_as(name__=self._fhorner)
1330 _m = H._mul_Fsum if _isFsum_2Tuple(x) else \
1331 H._mul_scalar
1332 for c in (reversed(cs) if incx else cs):
1333 H._fset(_m(x, _mul_op_), up=False)
1334 H._fadd(c, up=False)
1335 else: # x == 0
1336 H = cs[0] if n else 0
1337 self._fadd(H)
1338 except Exception as X:
1339 t = unstr(where, x, *cs, _ELLIPSIS=4, incx=incx)
1340 raise self._ErrorX(X, _add_op_, t)
1341 return self
1343 def _finite(self, other, op=None):
1344 '''(INTERNAL) Return B{C{other}} if C{finite}.
1345 '''
1346 if _isOK_or_finite(other, **self._isfine):
1347 return other
1348 E = _NonfiniteError(other)
1349 raise self._Error(op, other, E, txt=_not_finite_)
1351 def fint(self, name=NN, **raiser_RESIDUAL):
1352 '''Return this instance' current running sum as C{integer}.
1354 @kwarg name: Optional, overriding C{B{name}="fint"} (C{str}).
1355 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore
1356 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}
1357 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.
1359 @return: The C{integer} sum (L{Fsum}) if this instance C{is_integer}
1360 with a zero or insignificant I{integer} residual.
1362 @raise ResidualError: Non-zero, significant residual or invalid
1363 B{C{RESIDUAL}}.
1365 @see: Methods L{Fsum.fint2}, L{Fsum.int_float} and L{Fsum.is_integer}.
1366 '''
1367 i, r = self._fint2
1368 if r:
1369 R = self._raiser(r, i, **raiser_RESIDUAL)
1370 if R:
1371 t = _stresidual(_integer_, r, **R)
1372 raise ResidualError(_integer_, i, txt=t)
1373 return self._Fsum_as(i, name=_name__(name, name__=self.fint))
1375 def fint2(self, **name):
1376 '''Return this instance' current running sum as C{int} and the
1377 I{integer} residual.
1379 @kwarg name: Optional name (C{str}).
1381 @return: An L{Fsum2Tuple}C{(fsum, residual)} with C{fsum}
1382 an C{int} and I{integer} C{residual} a C{float} or
1383 C{INT0} if the C{fsum} is considered to be I{exact}.
1384 The C{fsum} is I{non-finite} if this instance is.
1385 '''
1386 return Fsum2Tuple(*self._fint2, **name)
1388 @Property
1389 def _fint2(self): # see ._fset
1390 '''(INTERNAL) Get 2-tuple (C{int}, I{integer} residual).
1391 '''
1392 s, r = self._nfprs2
1393 if _isfinite(s):
1394 i = int(s)
1395 r = (self._ps_1sum(i) if len(self._ps) > 1 else
1396 float(s - i)) or INT0
1397 else: # INF, NAN, NINF
1398 i = float(s)
1399# r = _NONFINITEr
1400 return i, r # Fsum2Tuple?
1402 @_fint2.setter_ # PYCHOK setter_UNDERscore!
1403 def _fint2(self, s): # in _fset
1404 '''(INTERNAL) Replace the C{_fint2} value.
1405 '''
1406 if _isfinite(s):
1407 i = int(s)
1408 r = (s - i) or INT0
1409 else: # INF, NAN, NINF
1410 i = float(s)
1411 r = _NONFINITEr
1412 return i, r # like _fint2.getter
1414 @deprecated_property_RO
1415 def float_int(self): # PYCHOK no cover
1416 '''DEPRECATED, use method C{Fsum.int_float}.'''
1417 return self.int_float() # raiser=False
1419 @property_RO
1420 def floor(self):
1421 '''Get this instance' C{floor} (C{int} in Python 3+, but
1422 C{float} in Python 2-).
1424 @note: This C{floor} takes the C{residual} into account.
1426 @see: Method L{Fsum.int_float} and properties L{Fsum.ceil},
1427 L{Fsum.imag} and L{Fsum.real}.
1428 '''
1429 s, r = self._fprs2
1430 f = _floor(s) + _floor(r) + 1
1431 while (f - s) > r: # f > (s + r)
1432 f -= 1
1433 return f # _floor(self._n_d)
1435# ffloordiv = __ifloordiv__ # for naming consistency?
1436# floordiv = __floordiv__ # for naming consistency?
1438 def _floordiv(self, other, op, **raiser_RESIDUAL): # rather _ffloordiv?
1439 '''Apply C{B{self} //= B{other}}.
1440 '''
1441 q = self._ftruediv(other, op, **raiser_RESIDUAL) # == self
1442 return self._fset(q.floor) # floor(q)
1444 def fma(self, other1, other2, **nonfinites): # in .fmath.fma
1445 '''Fused-multiply-add C{self *= B{other1}; self += B{other2}}.
1447 @arg other1: Multiplier (C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
1448 @arg other2: Addend (C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
1449 @kwarg nonfinites: Use C{B{nonfinites}=True} or C{False}, to
1450 override L{nonfinites<Fsum.nonfinites>} and
1451 L{nonfiniterrors} default (C{bool}).
1452 '''
1453 op = typename(self.fma)
1454 _fs = self._ps_other
1455 try:
1456 s, r = self._fprs2
1457 if r:
1458 f = self._f2mul(self.fma, (other1,), **nonfinites)
1459 f += other2
1460 elif _residue(other1) or _residue(other2):
1461 fs = _2split3s(_fs(op, other1))
1462 fs = _2products(s, fs, *_fs(op, other2))
1463 f = _Psum(self._ps_acc([], fs, up=False), name=op)
1464 else:
1465 f = _fma(s, other1, other2)
1466 f = _2finite(f, **self._isfine)
1467 except TypeError as X:
1468 raise self._ErrorX(X, op, (other1, other2))
1469 except (OverflowError, ValueError) as X: # from math.fma
1470 f = self._mul_reduce(s, other1) # INF, NAN, NINF
1471 f += sum(_fs(op, other2))
1472 f = self._nonfiniteX(X, op, f, **nonfinites)
1473 return self._fset(f)
1475 fmul = __imul__
1477 def _fmul(self, other, op):
1478 '''(INTERNAL) Apply C{B{self} *= B{other}}.
1479 '''
1480 if _isFsum_2Tuple(other):
1481 if len(self._ps) != 1:
1482 f = self._mul_Fsum(other, op)
1483 elif len(other._ps) != 1: # and len(self._ps) == 1
1484 f = self._ps_mul(op, *other._ps) if other._ps else _0_0
1485 elif self._f2product: # len(other._ps) == 1
1486 f = self._mul_scalar(other._ps[0], op)
1487 else: # len(other._ps) == len(self._ps) == 1
1488 f = self._finite(self._ps[0] * other._ps[0], op=op)
1489 else:
1490 s = self._scalar(other, op)
1491 f = self._mul_scalar(s, op)
1492 return self._fset(f) # n=len(self) + 1
1494 @deprecated_method
1495 def f2mul(self, *others, **raiser):
1496 '''DEPRECATED on 2024.09.13, use method L{f2mul_<Fsum.f2mul_>}.'''
1497 return self._fset(self._f2mul(self.f2mul, others, **raiser))
1499 def f2mul_(self, *others, **f2product_nonfinites): # in .fmath.f2mul
1500 '''Return C{B{self} * B{other} * B{other} ...} for all B{C{others}} using cascaded,
1501 accurate multiplication like with L{f2product<Fsum.f2product>}C{(B{True})}.
1503 @arg others: Multipliers (each C{scalar}, an L{Fsum} or L{Fsum2Tuple}), all
1504 positional.
1505 @kwarg f2product_nonfinites: Use C{B{f2product=False}} to override the default
1506 C{True} and C{B{nonfinites}=True} or C{False}, to override
1507 settings L{nonfinites<Fsum.nonfinites>} and L{nonfiniterrors}.
1509 @return: The cascaded I{TwoProduct} (L{Fsum} or C{float}).
1511 @see: U{Equations 2.3<https://www.TUHH.De/ti3/paper/rump/OzOgRuOi06.pdf>}
1512 '''
1513 return self._f2mul(self.f2mul_, others, **f2product_nonfinites)
1515 def _f2mul(self, where, others, f2product=True, **nonfinites_raiser):
1516 '''(INTERNAL) See methods C{fma} and C{f2mul_}.
1517 '''
1518 n = typename(where)
1519 f = _Psum(self._ps, f2product=f2product, name=n)
1520 if others and f:
1521 if f.f2product():
1522 def _pfs(f, ps):
1523 return _2products(f, _2split3s(ps))
1524 else:
1525 def _pfs(f, ps): # PYCHOK redef
1526 return (f * p for p in ps)
1528 op, ps = n, f._ps
1529 try: # as if self.f2product(True)
1530 for other in others: # to pinpoint errors
1531 for p in self._ps_other(op, other):
1532 ps[:] = f._ps_acc([], _pfs(p, ps), update=False)
1533 f._update()
1534 except TypeError as X:
1535 raise self._ErrorX(X, op, other)
1536 except (OverflowError, ValueError) as X:
1537 r = self._mul_reduce(sum(ps), other) # INF, NAN, NINF
1538 r = self._nonfiniteX(X, op, r, **nonfinites_raiser)
1539 f._fset(r)
1540 return f
1542 def fover(self, over, **raiser_RESIDUAL):
1543 '''Apply C{B{self} /= B{over}} and summate.
1545 @arg over: Divisor (C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
1546 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore
1547 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}
1548 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.
1550 @return: Precision running quotient sum (C{float}).
1552 @raise ResidualError: Non-zero, significant residual or invalid
1553 B{C{RESIDUAL}}.
1555 @see: Methods L{Fsum.fdiv}, L{Fsum.__itruediv__} and L{Fsum.fsum}.
1556 '''
1557 return float(self.fdiv(over, **raiser_RESIDUAL)._fprs)
1559 fpow = __ipow__
1561 def _fpow(self, other, op, *mod, **raiser_RESIDUAL):
1562 '''Apply C{B{self} **= B{other}}, optional B{C{mod}} or C{None}.
1563 '''
1564 if mod:
1565 if mod[0] is not None: # == 3-arg C{pow}
1566 f = self._pow_2_3(self, other, other, op, *mod, **raiser_RESIDUAL)
1567 elif self.is_integer():
1568 # return an exact C{int} for C{int}**C{int}
1569 i, _ = self._fint2 # assert _ == 0
1570 x, r = _2tuple2(other) # C{int}, C{float} or other
1571 f = self._Fsum_as(i)._pow_Fsum(other, op, **raiser_RESIDUAL) if r else \
1572 self._pow_2_3(i, x, other, op, **raiser_RESIDUAL)
1573 else: # mod[0] is None, power(self, other)
1574 f = self._pow(other, other, op, **raiser_RESIDUAL)
1575 else: # pow(self, other)
1576 f = self._pow(other, other, op, **raiser_RESIDUAL)
1577 return self._fset(f) # n=max(len(self), 1)
1579 def f2product(self, *two):
1580 '''Get and set accurate I{TwoProduct} multiplication for this
1581 L{Fsum}, overriding the L{f2product} default.
1583 @arg two: If omitted, leave the override unchanged, if C{True},
1584 turn I{TwoProduct} on, if C{False} off, if C{None}e
1585 remove th override (C{bool} or C{None}).
1587 @return: The previous setting (C{bool} or C{None} if not set).
1589 @see: Function L{f2product<fsums.f2product>}.
1591 @note: Use C{f.f2product() or f2product()} to determine whether
1592 multiplication is accurate for L{Fsum} C{f}.
1593 '''
1594 if two: # delattrof(self, _f2product=None)
1595 t = _xkwds_pop(self.__dict__, _f2product=None)
1596 if two[0] is not None:
1597 self._f2product = bool(two[0])
1598 else: # getattrof(self, _f2product=None)
1599 t = _xkwds_get(self.__dict__, _f2product=None)
1600 return t
1602 @Property
1603 def _fprs(self):
1604 '''(INTERNAL) Get and cache this instance' precision
1605 running sum (C{float} or C{int}), ignoring C{residual}.
1607 @note: The precision running C{fsum} after a C{//=} or
1608 C{//} C{floor} division is C{int} in Python 3+.
1609 '''
1610 s, _ = self._fprs2
1611 return s # ._fprs2.fsum
1613 @_fprs.setter_ # PYCHOK setter_UNDERscore!
1614 def _fprs(self, s):
1615 '''(INTERNAL) Replace the C{_fprs} value.
1616 '''
1617 return s
1619 @Property
1620 def _fprs2(self):
1621 '''(INTERNAL) Get and cache this instance' precision
1622 running sum and residual (L{Fsum2Tuple}).
1623 '''
1624 ps = self._ps
1625 n = len(ps)
1626 try:
1627 if n > 2:
1628 s = _psum(ps, **self._isfine)
1629 if not _isfinite(s):
1630 ps[:] = s, # collapse ps
1631 return Fsum2Tuple(s, _NONFINITEr)
1632 n = len(ps)
1633# Fsum._ps_max = max(Fsum._ps_max, n)
1634 if n > 2:
1635 r = self._ps_1sum(s)
1636 return Fsum2Tuple(*_s_r2(s, r))
1637 if n > 1: # len(ps) == 2
1638 s, r = _s_r2(*_2sum(*ps, **self._isfine))
1639 ps[:] = (r, s) if r else (s,)
1640 elif ps: # len(ps) == 1
1641 s = ps[0]
1642 r = INT0 if _isfinite(s) else _NONFINITEr
1643 else: # len(ps) == 0
1644 s = _0_0
1645 r = INT0 if _isfinite(s) else _NONFINITEr
1646 ps[:] = s,
1647 except (OverflowError, ValueError) as X:
1648 op = _fset_op_ # INF, NAN, NINF
1649 ps[:] = sum(ps), # collapse ps
1650 s = self._nonfiniteX(X, op, ps[0])
1651 r = _NONFINITEr
1652 # assert self._ps is ps
1653 return Fsum2Tuple(s, r)
1655 @_fprs2.setter_ # PYCHOK setter_UNDERscore!
1656 def _fprs2(self, s_r):
1657 '''(INTERNAL) Replace the C{_fprs2} value.
1658 '''
1659 return Fsum2Tuple(s_r)
1661 def fset_(self, *xs):
1662 '''Apply C{B{self}.partials = Fsum(*B{xs}).partials}.
1664 @arg xs: Optional, new values (each C{scalar} or an L{Fsum}
1665 or L{Fsum2Tuple} instance), all positional.
1667 @return: This instance, replaced (C{Fsum}).
1669 @see: Method L{Fsum.fadd} for further details.
1670 '''
1671 f = (xs[0] if xs else _0_0) if len(xs) < 2 else \
1672 Fsum(*xs, nonfinites=self.nonfinites()) # self._Fsum_as(*xs)
1673 return self._fset(f, op=_fset_op_)
1675 def _fset(self, other, n=0, up=True, **op):
1676 '''(INTERNAL) Overwrite this instance with an other or a C{scalar}.
1677 '''
1678 if other is self:
1679 pass # from ._fmul, ._ftruediv and ._pow_0_1
1680 elif _isFsum_2Tuple(other):
1681 if op: # and not self.nonfinitesOK:
1682 self._finite(other._fprs, **op)
1683 self._ps[:] = other._ps
1684 self._n = n or other._n
1685 if up: # use or zap the C{Property_RO} values
1686 Fsum._fint2._update_from(self, other)
1687 Fsum._fprs ._update_from(self, other)
1688 Fsum._fprs2._update_from(self, other)
1689 elif isscalar(other):
1690 s = float(self._finite(other, **op)) if op else other
1691 self._ps[:] = s,
1692 self._n = n or 1
1693 if up: # Property _fint2, _fprs and _fprs2 all have
1694 # @.setter_underscore and NOT @.setter because the
1695 # latter's _fset zaps the value set by @.setter
1696 self._fint2 = s
1697 self._fprs = s
1698 self._fprs2 = s, INT0
1699 # assert self._fprs is s
1700 else:
1701 op = _xkwds_get1(op, op=_fset_op_)
1702 raise self._Error(op, other, _TypeError)
1703 return self
1705 def fsub(self, xs=()):
1706 '''Subtract an iterable's items from this instance.
1708 @see: Method L{Fsum.fadd} for further details.
1709 '''
1710 return self._facc_neg(xs)
1712 def fsub_(self, *xs):
1713 '''Subtract all positional items from this instance.
1715 @see: Method L{Fsum.fadd_} for further details.
1716 '''
1717 return self._fsub(xs[0], _sub_op_) if len(xs) == 1 else \
1718 self._facc_neg(xs) # origin=1?
1720 def _fsub(self, other, op):
1721 '''(INTERNAL) Apply C{B{self} -= B{other}}.
1722 '''
1723 if _isFsum_2Tuple(other):
1724 if other is self: # or other._fprs2 == self._fprs2:
1725 self._fset(_0_0, n=len(self) * 2)
1726 elif other._ps:
1727 self._facc_scalar(other._ps_neg)
1728 elif self._scalar(other, op):
1729 self._facc_scalar_(-other)
1730 return self
1732 def fsum(self, xs=()):
1733 '''Add an iterable's items, summate and return the current
1734 precision running sum.
1736 @arg xs: Iterable of items to add (each item C{scalar},
1737 an L{Fsum} or L{Fsum2Tuple}).
1739 @return: Precision running sum (C{float} or C{int}).
1741 @see: Method L{Fsum.fadd}.
1743 @note: Accumulation can continue after summation.
1744 '''
1745 return self._facc(xs)._fprs
1747 def fsum_(self, *xs):
1748 '''Add any positional items, summate and return the current
1749 precision running sum.
1751 @arg xs: Items to add (each C{scalar}, an L{Fsum} or
1752 L{Fsum2Tuple}), all positional.
1754 @return: Precision running sum (C{float} or C{int}).
1756 @see: Methods L{Fsum.fsum}, L{Fsum.Fsum_} and L{Fsum.fsumf_}.
1757 '''
1758 return self._facc_args(xs)._fprs
1760 def Fsum_(self, *xs, **name):
1761 '''Like method L{Fsum.fsum_} but returning a named L{Fsum}.
1763 @kwarg name: Optional name (C{str}).
1765 @return: Copy of this updated instance (L{Fsum}).
1766 '''
1767 return self._facc_args(xs)._copyd(self.Fsum_, **name)
1769 def Fsum2Tuple_(self, *xs, **name):
1770 '''Like method L{Fsum.fsum_} but returning a named L{Fsum2Tuple}.
1772 @kwarg name: Optional name (C{str}).
1774 @return: Precision running sum (L{Fsum2Tuple}).
1775 '''
1776 return Fsum2Tuple(self._facc_args(xs)._nfprs2, **name)
1778 @property_RO
1779 def _Fsum(self): # like L{Fsum2Tuple._Fsum}, in .fstats
1780 return self # NOT @Property_RO, see .copy and ._copyd
1782 def _Fsum_as(self, *xs, **name_f2product_nonfinites_RESIDUAL):
1783 '''(INTERNAL) Return an C{Fsum} with this C{Fsum}'s C{.f2product},
1784 C{.nonfinites} and C{.RESIDUAL} setting, optionally
1785 overridden with C{name_f2product_nonfinites_RESIDUAL} and
1786 with any C{xs} accumulated.
1787 '''
1788 kwds = _xkwds_not(None, Fsum._RESIDUAL, f2product =self.f2product(),
1789 nonfinites=self.nonfinites(),
1790 RESIDUAL =self.RESIDUAL())
1791 if name_f2product_nonfinites_RESIDUAL: # overwrites
1792 kwds.update(name_f2product_nonfinites_RESIDUAL)
1793 f = Fsum(**kwds)
1794 # assert all(v == self.__dict__[n] for n, v in f.__dict__.items())
1795 return (f._facc(xs, up=False) if len(xs) > 1 else
1796 f._fset(xs[0], op=_fset_op_)) if xs else f
1798 def fsum2(self, xs=(), **name):
1799 '''Add an iterable's items, summate and return the
1800 current precision running sum I{and} the C{residual}.
1802 @arg xs: Iterable of items to add (each item C{scalar},
1803 an L{Fsum} or L{Fsum2Tuple}).
1804 @kwarg name: Optional C{B{name}=NN} (C{str}).
1806 @return: L{Fsum2Tuple}C{(fsum, residual)} with C{fsum} the
1807 current precision running sum and C{residual}, the
1808 (precision) sum of the remaining C{partials}. The
1809 C{residual is INT0} if the C{fsum} is considered
1810 to be I{exact}.
1812 @see: Methods L{Fsum.fint2}, L{Fsum.fsum} and L{Fsum.fsum2_}
1813 '''
1814 t = self._facc(xs)._fprs2
1815 return t.dup(name=name) if name else t
1817 def fsum2_(self, *xs):
1818 '''Add any positional items, summate and return the current
1819 precision running sum and the I{differential}.
1821 @arg xs: Values to add (each C{scalar}, an L{Fsum} or
1822 L{Fsum2Tuple}), all positional.
1824 @return: 2Tuple C{(fsum, delta)} with the current, precision
1825 running C{fsum} like method L{Fsum.fsum} and C{delta},
1826 the difference with previous running C{fsum}, C{float}.
1828 @see: Methods L{Fsum.fsum_} and L{Fsum.fsum}.
1829 '''
1830 return self._fsum2(xs, self._facc_args)
1832 def _fsum2(self, xs, _facc, **facc_kwds):
1833 '''(INTERNAL) Helper for L{Fsum.fsum2_} and L{Fsum.fsum2f_}.
1834 '''
1835 p, q = self._fprs2
1836 if xs:
1837 s, r = _facc(xs, **facc_kwds)._fprs2
1838 if _isfinite(s): # _fsum(_1primed((s, -p, r, -q))
1839 d, r = _2sum(s - p, r - q, _isfine=_isOK)
1840 r, _ = _s_r2(d, r)
1841 return s, (r if _isfinite(r) else _NONFINITEr)
1842 else:
1843 return p, _0_0
1845 def fsumf_(self, *xs):
1846 '''Like method L{Fsum.fsum_} iff I{all} C{B{xs}}, each I{known to be}
1847 C{scalar}, an L{Fsum} or L{Fsum2Tuple}.
1848 '''
1849 return self._facc_xsum(xs, which=self.fsumf_)._fprs # origin=1?
1851 def Fsumf_(self, *xs):
1852 '''Like method L{Fsum.Fsum_} iff I{all} C{B{xs}}, each I{known to be}
1853 C{scalar}, an L{Fsum} or L{Fsum2Tuple}.
1854 '''
1855 return self._facc_xsum(xs, which=self.Fsumf_)._copyd(self.Fsumf_) # origin=1?
1857 def fsum2f_(self, *xs):
1858 '''Like method L{Fsum.fsum2_} iff I{all} C{B{xs}}, each I{known to be}
1859 C{scalar}, an L{Fsum} or L{Fsum2Tuple}.
1860 '''
1861 return self._fsum2(xs, self._facc_xsum, which=self.fsum2f_) # origin=1?
1863# ftruediv = __itruediv__ # for naming consistency?
1865 def _ftruediv(self, other, op, **raiser_RESIDUAL):
1866 '''(INTERNAL) Apply C{B{self} /= B{other}}.
1867 '''
1868 n = _1_0
1869 if _isFsum_2Tuple(other):
1870 if other is self or self == other:
1871 return self._fset(n, n=len(self))
1872 d, r = other._fprs2
1873 if r:
1874 R = self._raiser(r, d, **raiser_RESIDUAL)
1875 if R:
1876 raise self._ResidualError(op, other, r, **R)
1877 d, n = other.as_integer_ratio()
1878 else:
1879 d = self._scalar(other, op)
1880 try:
1881 s = n / d
1882 except Exception as X:
1883 raise self._ErrorX(X, op, other)
1884 f = self._mul_scalar(s, _mul_op_) # handles 0, INF, NAN
1885 return self._fset(f)
1887 @property_RO
1888 def imag(self):
1889 '''Get the C{imaginary} part of this instance (C{0.0}, always).
1891 @see: Property L{Fsum.real}.
1892 '''
1893 return _0_0
1895 def int_float(self, **raiser_RESIDUAL):
1896 '''Return this instance' current running sum as C{int} or C{float}.
1898 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore
1899 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}
1900 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.
1902 @return: This C{int} sum if this instance C{is_integer} and
1903 I{finite}, otherwise the C{float} sum if the residual
1904 is zero or not significant.
1906 @raise ResidualError: Non-zero, significant residual or invalid
1907 B{C{RESIDUAL}}.
1909 @see: Methods L{Fsum.fint}, L{Fsum.fint2}, L{Fsum.is_integer},
1910 L{Fsum.RESIDUAL} and property L{Fsum.as_iscalar}.
1911 '''
1912 s, r = self._fint2
1913 if r:
1914 s, r = self._fprs2
1915 if r: # PYCHOK no cover
1916 R = self._raiser(r, s, **raiser_RESIDUAL)
1917 if R:
1918 t = _stresidual(_non_zero_, r, **R)
1919 raise ResidualError(int_float=s, txt=t)
1920 s = float(s)
1921 return s
1923 def is_exact(self):
1924 '''Is this instance' running C{fsum} considered to be exact?
1925 (C{bool}), C{True} only if the C{residual is }L{INT0}.
1926 '''
1927 return self.residual is INT0
1929 def is_finite(self): # in .constants
1930 '''Is this instance C{finite}? (C{bool}).
1932 @see: Function L{isfinite<pygeodesy.isfinite>}.
1933 '''
1934 return _isfinite(sum(self._ps)) # == sum(self)
1936 def is_integer(self):
1937 '''Is this instance' running sum C{integer}? (C{bool}).
1939 @see: Methods L{Fsum.fint}, L{Fsum.fint2} and L{Fsum.is_scalar}.
1940 '''
1941 s, r = self._fint2
1942 return False if r else (_isfinite(s) and isint(s))
1944 def is_math_fma(self):
1945 '''Is accurate L{f2product} multiplication based on Python's C{math.fma}?
1947 @return: C{True} if accurate multiplication uses C{math.fma}, C{False}
1948 an C{fma} implementation as C{math.fma} or C{None}, a previous
1949 C{PyGeodesy} implementation.
1950 '''
1951 return (_2split3s is _passarg) or (False if _integer_ratio2 is None else None)
1953 def is_math_fsum(self):
1954 '''Are the summation functions L{fsum}, L{fsum_}, L{fsumf_}, L{fsum1},
1955 L{fsum1_} and L{fsum1f_} based on Python's C{math.fsum}?
1957 @return: C{True} if summation functions use C{math.fsum}, C{False}
1958 otherwise.
1959 '''
1960 return _sum is _fsum # _fsum.__module__ is fabs.__module__
1962 def is_scalar(self, **raiser_RESIDUAL):
1963 '''Is this instance' running sum C{scalar} with C{0} residual or with
1964 a residual I{ratio} not exceeding the RESIDUAL threshold?
1966 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore
1967 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}
1968 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.
1970 @return: C{True} if this instance' residual is C{0} or C{insignificant},
1971 i.e. its residual C{ratio} doesn't exceed the L{RESIDUAL
1972 <Fsum.RESIDUAL>} threshold (C{bool}).
1974 @raise ResidualError: Non-zero, significant residual or invalid
1975 B{C{RESIDUAL}}.
1977 @see: Methods L{Fsum.RESIDUAL} and L{Fsum.is_integer} and property
1978 L{Fsum.as_iscalar}.
1979 '''
1980 s, r = self._fprs2
1981 return False if r and self._raiser(r, s, **raiser_RESIDUAL) else True
1983 def _mul_Fsum(self, other, op):
1984 '''(INTERNAL) Return C{B{self} * B{other}} as L{Fsum} or C{0}.
1985 '''
1986 # assert _isFsum_2Tuple(other)
1987 if self._ps and other._ps:
1988 try:
1989 f = self._ps_mul(op, *other._ps) # NO .as_iscalar!
1990 except Exception as X:
1991 raise self._ErrorX(X, op, other)
1992 else:
1993 f = _0_0
1994 return f
1996 def _mul_reduce(self, *others):
1997 '''(INTERNAL) Like fmath.fprod for I{non-finite} C{other}s.
1998 '''
1999 r = _1_0
2000 for f in others:
2001 r *= sum(f._ps) if _isFsum_2Tuple(f) else float(f)
2002 return r
2004 def _mul_scalar(self, factor, op):
2005 '''(INTERNAL) Return C{B{self} * scalar B{factor}} as L{Fsum}, C{0.0} or C{self}.
2006 '''
2007 # assert isscalar(factor)
2008 if self._ps and self._finite(factor, op=op):
2009 f = self if factor == _1_0 else (
2010 self._neg if factor == _N_1_0 else
2011 self._ps_mul(op, factor).as_iscalar)
2012 else:
2013 f = _0_0
2014 return f
2016# @property_RO
2017# def _n_d(self):
2018# n, d = self.as_integer_ratio()
2019# return n / d
2021 @property_RO
2022 def _neg(self):
2023 '''(INTERNAL) Return C{Fsum(-self)} or scalar C{NEG0}.
2024 '''
2025 return _Psum(self._ps_neg) if self._ps else NEG0
2027 @property_RO
2028 def _nfprs2(self):
2029 '''(INTERNAL) Handle I{non-finite} C{_fprs2}.
2030 '''
2031 try: # to handle nonfiniterrors, etc.
2032 t = self._fprs2
2033 except (OverflowError, ValueError):
2034 t = Fsum2Tuple(sum(self._ps), _NONFINITEr)
2035 return t
2037 def nonfinites(self, *OK):
2038 '''Handle I{non-finite} C{float}s as C{inf}, C{INF}, C{NINF}, C{nan}
2039 and C{NAN} for this L{Fsum} or throw C{OverflowError} respectively
2040 C{ValueError} exceptions, overriding the L{nonfiniterrors} default.
2042 @arg OK: If omitted, leave the override unchanged, if C{True},
2043 I{non-finites} are C{OK}, if C{False} throw exceptions
2044 or if C{None} remove the override (C{bool} or C{None}).
2046 @return: The previous setting (C{bool} or C{None} if not set).
2048 @see: Function L{nonfiniterrors<fsums.nonfiniterrors>}.
2050 @note: Use property L{nonfinitesOK<Fsum.nonfinitesOK>} to determine
2051 whether I{non-finites} are C{OK} for this L{Fsum} and by the
2052 L{nonfiniterrors} default.
2053 '''
2054 _ks = Fsum._nonfinites_isfine_kwds
2055 if OK: # delattrof(self, _isfine=None)
2056 k = _xkwds_pop(self.__dict__, _isfine=None)
2057 if OK[0] is not None:
2058 self._isfine = _ks[bool(OK[0])]
2059 self._update()
2060 else: # getattrof(self, _isfine=None)
2061 k = _xkwds_get(self.__dict__, _isfine=None)
2062 # dict(map(reversed, _ks.items())).get(k, None)
2063 # raises a TypeError: unhashable type: 'dict'
2064 return True if k is _ks[True] else (
2065 False if k is _ks[False] else None)
2067 _nonfinites_isfine_kwds = {True: dict(_isfine=_isOK),
2068 False: dict(_isfine=_isfinite)}
2070 @property_RO
2071 def nonfinitesOK(self):
2072 '''Are I{non-finites} C{OK} for this L{Fsum} or by default? (C{bool}).
2073 '''
2074# nf = self.nonfinites()
2075# if nf is None:
2076# nf = not nonfiniterrors()
2077 return _isOK_or_finite(INF, **self._isfine)
2079 def _nonfiniteX(self, X, op, f, nonfinites=None, raiser=None):
2080 '''(INTERNAL) Handle a I{non-finite} exception.
2081 '''
2082 if nonfinites is None:
2083 nonfinites = _isOK_or_finite(f, **self._isfine) if raiser is None else (not raiser)
2084 if not nonfinites:
2085 raise self._ErrorX(X, op, f)
2086 return f
2088 def _optionals(self, f2product=None, nonfinites=None, **name_RESIDUAL):
2089 '''(INTERNAL) Re/set options from keyword arguments.
2090 '''
2091 if f2product is not None:
2092 self.f2product(f2product)
2093 if nonfinites is not None:
2094 self.nonfinites(nonfinites)
2095 if name_RESIDUAL: # MUST be last
2096 n, kwds = _name2__(**name_RESIDUAL)
2097 if kwds:
2098 R = Fsum._RESIDUAL
2099 t = _threshold(R, **kwds)
2100 if t != R:
2101 self._RESIDUAL = t
2102 if n:
2103 self.name = n # self.rename(n)
2105 def _1_Over(self, x, op, **raiser_RESIDUAL): # vs _1_over
2106 '''(INTERNAL) Return C{Fsum(1) / B{x}}.
2107 '''
2108 return self._Fsum_as(_1_0)._ftruediv(x, op, **raiser_RESIDUAL)
2110 @property_RO
2111 def partials(self):
2112 '''Get this instance' current, partial sums (C{tuple} of C{float}s).
2113 '''
2114 return tuple(self._ps)
2116 def pow(self, x, *mod, **raiser_RESIDUAL):
2117 '''Return C{B{self}**B{x}} as L{Fsum}.
2119 @arg x: The exponent (C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
2120 @arg mod: Optional modulus (C{int} or C{None}) for the 3-argument
2121 C{pow(B{self}, B{other}, B{mod})} version.
2122 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore
2123 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}
2124 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.
2126 @return: The C{pow(self, B{x})} or C{pow(self, B{x}, *B{mod})}
2127 result (L{Fsum}).
2129 @raise ResidualError: Non-zero, significant residual or invalid
2130 B{C{RESIDUAL}}.
2132 @note: If B{C{mod}} is given and C{None}, the result will be an
2133 C{integer} L{Fsum} provided this instance C{is_integer}
2134 or set to C{integer} by an L{Fsum.fint} call.
2136 @see: Methods L{Fsum.__ipow__}, L{Fsum.fint}, L{Fsum.is_integer}
2137 and L{Fsum.root}.
2138 '''
2139 f = self._copyd(self.pow)
2140 return f._fpow(x, _pow_op_, *mod, **raiser_RESIDUAL) # f = pow(f, x, *mod)
2142 def _pow(self, other, unused, op, **raiser_RESIDUAL):
2143 '''Return C{B{self} ** B{other}}.
2144 '''
2145 if _isFsum_2Tuple(other):
2146 f = self._pow_Fsum(other, op, **raiser_RESIDUAL)
2147 elif self._scalar(other, op):
2148 x = self._finite(other, op=op)
2149 f = self._pow_scalar(x, other, op, **raiser_RESIDUAL)
2150 else:
2151 f = self._pow_0_1(0, other)
2152 return f
2154 def _pow_0_1(self, x, other):
2155 '''(INTERNAL) Return B{C{self}**1} or C{B{self}**0 == 1.0}.
2156 '''
2157 return self if x else (1 if isint(other) and self.is_integer() else _1_0)
2159 def _pow_2_3(self, b, x, other, op, *mod, **raiser_RESIDUAL):
2160 '''(INTERNAL) 2-arg C{pow(B{b}, scalar B{x})} and 3-arg C{pow(B{b},
2161 B{x}, int B{mod} or C{None})}, embellishing errors.
2162 '''
2164 if mod: # b, x, mod all C{int}, unless C{mod} is C{None}
2165 m = mod[0]
2166 # assert _isFsum_2Tuple(b)
2168 def _s(s, r):
2169 R = self._raiser(r, s, **raiser_RESIDUAL)
2170 if R:
2171 raise self._ResidualError(op, other, r, mod=m, **R)
2172 return s
2174 b = _s(*(b._fprs2 if m is None else b._fint2))
2175 x = _s(*_2tuple2(x))
2177 try:
2178 # 0**INF == 0.0, 1**INF == 1.0, -1**2.3 == -(1**2.3)
2179 s = pow(b, x, *mod)
2180 if iscomplex(s):
2181 # neg**frac == complex in Python 3+, but ValueError in 2-
2182 raise ValueError(_strcomplex(s, b, x, *mod))
2183 _ = _2finite(s, **self._isfine) # ignore float
2184 return s
2185 except Exception as X:
2186 raise self._ErrorX(X, op, other, *mod)
2188 def _pow_Fsum(self, other, op, **raiser_RESIDUAL):
2189 '''(INTERNAL) Return C{B{self} **= B{other}} for C{_isFsum_2Tuple(other)}.
2190 '''
2191 # assert _isFsum_2Tuple(other)
2192 x, r = other._fprs2
2193 f = self._pow_scalar(x, other, op, **raiser_RESIDUAL)
2194 if f and r:
2195 f *= self._pow_scalar(r, other, op, **raiser_RESIDUAL)
2196 return f
2198 def _pow_int(self, x, other, op, **raiser_RESIDUAL):
2199 '''(INTERNAL) Return C{B{self} **= B{x}} for C{int B{x} >= 0}.
2200 '''
2201 # assert isint(x) and x >= 0
2202 ps = self._ps
2203 if len(ps) > 1:
2204 _mul_Fsum = Fsum._mul_Fsum
2205 if x > 4:
2206 p = self
2207 f = self if (x & 1) else self._Fsum_as(_1_0)
2208 m = x >> 1 # // 2
2209 while m:
2210 p = _mul_Fsum(p, p, op) # p **= 2
2211 if (m & 1):
2212 f = _mul_Fsum(f, p, op) # f *= p
2213 m >>= 1 # //= 2
2214 elif x > 1: # self**2, 3, or 4
2215 f = _mul_Fsum(self, self, op)
2216 if x > 2: # self**3 or 4
2217 p = self if x < 4 else f
2218 f = _mul_Fsum(f, p, op)
2219 else: # self**1 or self**0 == 1 or _1_0
2220 f = self._pow_0_1(x, other)
2221 elif ps: # self._ps[0]**x
2222 f = self._pow_2_3(ps[0], x, other, op, **raiser_RESIDUAL)
2223 else: # PYCHOK no cover
2224 # 0**pos_int == 0, but 0**0 == 1
2225 f = 0 if x else 1
2226 return f
2228 def _pow_scalar(self, x, other, op, **raiser_RESIDUAL):
2229 '''(INTERNAL) Return C{self**B{x}} for C{scalar B{x}}.
2230 '''
2231 s, r = self._fprs2
2232 if r:
2233 # assert s != 0
2234 if isint(x, both=True): # self**int
2235 x = int(x)
2236 y = abs(x)
2237 if y > 1:
2238 f = self._pow_int(y, other, op, **raiser_RESIDUAL)
2239 if x > 0: # i.e. > 1
2240 return f # Fsum or scalar
2241 # assert x < 0 # i.e. < -1
2242 if _isFsum(f):
2243 s, r = f._fprs2
2244 if r:
2245 return self._1_Over(f, op, **raiser_RESIDUAL)
2246 else: # scalar
2247 s = f
2248 # use s**(-1) to get the CPython
2249 # float_pow error iff s is zero
2250 x = -1
2251 elif x < 0: # self**(-1)
2252 return self._1_Over(self, op, **raiser_RESIDUAL) # 1 / self
2253 else: # self**1 or self**0
2254 return self._pow_0_1(x, other) # self, 1 or 1.0
2255 else: # self**fractional
2256 R = self._raiser(r, s, **raiser_RESIDUAL)
2257 if R:
2258 raise self._ResidualError(op, other, r, **R)
2259 n, d = self.as_integer_ratio()
2260 if abs(n) > abs(d):
2261 n, d, x = d, n, (-x)
2262 s = n / d
2263 # assert isscalar(s) and isscalar(x)
2264 return self._pow_2_3(s, x, other, op, **raiser_RESIDUAL)
2266 def _ps_acc(self, ps, xs, up=True, **unused):
2267 '''(INTERNAL) Accumulate C{xs} known scalars into list C{ps}.
2268 '''
2269 n = 0
2270 _2s = _2sum
2271 _fi = self._isfine
2272 for x in (tuple(xs) if xs is ps else xs):
2273 # assert isscalar(x) and _isOK_or_finite(x, **self._isfine)
2274 if x:
2275 i = 0
2276 for p in ps:
2277 x, p = _2s(x, p, **_fi)
2278 if p:
2279 ps[i] = p
2280 i += 1
2281 ps[i:] = (x,) if x else ()
2282 n += 1
2283 if n:
2284 self._n += n
2285 # Fsum._ps_max = max(Fsum._ps_max, len(ps))
2286 if up:
2287 self._update()
2288# x = sum(ps)
2289# if not _isOK_or_finite(x, **fi):
2290# ps[:] = x, # collapse ps
2291 return ps
2293 def _ps_mul(self, op, *factors):
2294 '''(INTERNAL) Multiply this instance' C{partials} with
2295 each scalar C{factor} and accumulate into an C{Fsum}.
2296 '''
2297 def _psfs(ps, fs, _isfine=_isfinite):
2298 if len(ps) < len(fs):
2299 ps, fs = fs, ps
2300 if self._f2product:
2301 fs, p = _2split3s(fs), fs
2302 if len(ps) > 1 and fs is not p:
2303 fs = tuple(fs) # several ps
2304 _pfs = _2products
2305 else:
2306 def _pfs(p, fs):
2307 return (p * f for f in fs)
2309 for p in ps:
2310 for x in _pfs(p, fs):
2311 yield x if _isfine(x) else _nfError(x)
2313 xs = _psfs(self._ps, factors, **self._isfine)
2314 f = _Psum(self._ps_acc([], xs, up=False), name=op)
2315 return f
2317 @property_RO
2318 def _ps_neg(self):
2319 '''(INTERNAL) Yield the partials, I{negated}.
2320 '''
2321 for p in self._ps:
2322 yield -p
2324 def _ps_other(self, op, other):
2325 '''(INTERNAL) Yield C{other} as C{scalar}s.
2326 '''
2327 if _isFsum_2Tuple(other):
2328 for p in other._ps:
2329 yield p
2330 else:
2331 yield self._scalar(other, op)
2333 def _ps_1sum(self, *less):
2334 '''(INTERNAL) Return the partials sum, 1-primed C{less} some scalars.
2335 '''
2336 def _1psls(ps, ls):
2337 yield _1_0
2338 for p in ps:
2339 yield p
2340 for p in ls:
2341 yield -p
2342 yield _N_1_0
2344 return _fsum(_1psls(self._ps, less))
2346 def _raiser(self, r, s, raiser=True, **RESIDUAL):
2347 '''(INTERNAL) Does ratio C{r / s} exceed the RESIDUAL threshold
2348 I{and} is residual C{r} I{non-zero} or I{significant} (for a
2349 negative respectively positive C{RESIDUAL} threshold)?
2350 '''
2351 if r and raiser:
2352 t = self._RESIDUAL
2353 if RESIDUAL:
2354 t = _threshold(t, **RESIDUAL)
2355 if t < 0 or (s + r) != s:
2356 q = (r / s) if s else s # == 0.
2357 if fabs(q) > fabs(t):
2358 return dict(ratio=q, R=t)
2359 return {}
2361 def _rcopyd(self, other, which):
2362 '''(INTERNAL) Copy for I{reverse-dyadic} operators.
2363 '''
2364 return other._copyd(which) if _isFsum(other) else \
2365 self._copyd(which)._fset(other)
2367 rdiv = __rtruediv__
2369 @property_RO
2370 def real(self):
2371 '''Get the C{real} part of this instance (C{float}).
2373 @see: Methods L{Fsum.__float__} and L{Fsum.fsum}
2374 and properties L{Fsum.ceil}, L{Fsum.floor},
2375 L{Fsum.imag} and L{Fsum.residual}.
2376 '''
2377 return float(self)
2379 @property_RO
2380 def residual(self):
2381 '''Get this instance' residual or residue (C{float} or C{int}):
2382 the C{sum(partials)} less the precision running sum C{fsum}.
2384 @note: The C{residual is INT0} iff the precision running
2385 C{fsum} is considered to be I{exact}.
2387 @see: Methods L{Fsum.fsum}, L{Fsum.fsum2} and L{Fsum.is_exact}.
2388 '''
2389 return self._fprs2.residual
2391 def RESIDUAL(self, *threshold):
2392 '''Get and set this instance' I{ratio} for raising L{ResidualError}s,
2393 overriding the default from env variable C{PYGEODESY_FSUM_RESIDUAL}.
2395 @arg threshold: If C{scalar}, the I{ratio} to exceed for raising
2396 L{ResidualError}s in division and exponention, if
2397 C{None}, restore the default set with env variable
2398 C{PYGEODESY_FSUM_RESIDUAL} or if omitted, keep the
2399 current setting.
2401 @return: The previous C{RESIDUAL} setting (C{float}), default C{0.0}.
2403 @raise ResidualError: Invalid B{C{threshold}}.
2405 @note: L{ResidualError}s may be thrown if (1) the non-zero I{ratio}
2406 C{residual / fsum} exceeds the given B{C{threshold}} and (2)
2407 the C{residual} is non-zero and (3) is I{significant} vs the
2408 C{fsum}, i.e. C{(fsum + residual) != fsum} and (4) optional
2409 keyword argument C{raiser=False} is missing. Specify a
2410 negative B{C{threshold}} for only non-zero C{residual}
2411 testing without the I{significant} case.
2412 '''
2413 r = self._RESIDUAL
2414 if threshold:
2415 t = threshold[0]
2416 self._RESIDUAL = Fsum._RESIDUAL if t is None else ( # for ...
2417 (_0_0 if t else _1_0) if isbool(t) else
2418 _threshold(t)) # ... backward compatibility
2419 return r
2421 def _ResidualError(self, op, other, residual, **mod_R):
2422 '''(INTERNAL) Non-zero B{C{residual}} etc.
2423 '''
2424 def _p(mod=None, R=0, **unused): # ratio=0
2425 return (_non_zero_ if R < 0 else _significant_) \
2426 if mod is None else _integer_
2428 t = _stresidual(_p(**mod_R), residual, **mod_R)
2429 return self._Error(op, other, ResidualError, txt=t)
2431 def root(self, root, **raiser_RESIDUAL):
2432 '''Return C{B{self}**(1 / B{root})} as L{Fsum}.
2434 @arg root: Non-zero order (C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
2435 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore any
2436 L{ResidualError}s (C{bool}) or C{B{RESIDUAL}=scalar}
2437 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.
2439 @return: The C{self ** (1 / B{root})} result (L{Fsum}).
2441 @raise ResidualError: Non-zero, significant residual or invalid
2442 B{C{RESIDUAL}}.
2444 @see: Method L{Fsum.pow}.
2445 '''
2446 x = self._1_Over(root, _truediv_op_, **raiser_RESIDUAL)
2447 f = self._copyd(self.root)
2448 return f._fpow(x, f.name, **raiser_RESIDUAL) # == pow(f, x)
2450 def _scalar(self, other, op, **txt):
2451 '''(INTERNAL) Return scalar C{other} or throw a C{TypeError}.
2452 '''
2453 if isscalar(other):
2454 return other
2455 raise self._Error(op, other, _TypeError, **txt) # _invalid_
2457 def signOf(self, res=True):
2458 '''Determine the sign of this instance.
2460 @kwarg res: If C{True}, consider the residual,
2461 otherwise ignore the latter (C{bool}).
2463 @return: The sign (C{int}, -1, 0 or +1).
2464 '''
2465 s, r = self._nfprs2
2466 r = (-r) if res else 0
2467 return _signOf(s, r)
2469 def toRepr(self, **lenc_prec_sep_fmt): # PYCHOK signature
2470 '''Return this C{Fsum} instance as representation.
2472 @kwarg lenc_prec_sep_fmt: Optional keyword arguments
2473 for method L{Fsum.toStr}.
2475 @return: This instance (C{repr}).
2476 '''
2477 return Fmt.repr_at(self, self.toStr(**lenc_prec_sep_fmt))
2479 def toStr(self, lenc=True, **prec_sep_fmt): # PYCHOK signature
2480 '''Return this C{Fsum} instance as string.
2482 @kwarg lenc: If C{True}, include the current C{[len]} of this
2483 L{Fsum} enclosed in I{[brackets]} (C{bool}).
2484 @kwarg prec_sep_fmt: Optional keyword arguments for method
2485 L{Fsum2Tuple.toStr}.
2487 @return: This instance (C{str}).
2488 '''
2489 p = self.classname
2490 if lenc:
2491 p = Fmt.SQUARE(p, len(self))
2492 n = _enquote(self.name, white=_UNDER_)
2493 t = self._nfprs2.toStr(**prec_sep_fmt)
2494 return NN(p, _SPACE_, n, t)
2496 def _truediv(self, other, op, **raiser_RESIDUAL):
2497 '''(INTERNAL) Return C{B{self} / B{other}} as an L{Fsum}.
2498 '''
2499 f = self._copyd(self.__truediv__)
2500 return f._ftruediv(other, op, **raiser_RESIDUAL)
2502 def _update(self, updated=True): # see ._fset
2503 '''(INTERNAL) Zap all cached C{Property_RO} values.
2504 '''
2505 if updated:
2506 _pop = self.__dict__.pop
2507 for p in _ROs:
2508 _ = _pop(p, None)
2509# Fsum._fint2._update(self)
2510# Fsum._fprs ._update(self)
2511# Fsum._fprs2._update(self)
2512 return self # for .fset_
2514_ROs = _allPropertiesOf_n(3, Fsum, Property_RO) # PYCHOK see Fsum._update
2516if _NONFINITES == _std_: # PYCHOK no cover
2517 _ = nonfiniterrors(False)
2520def _Float_Int(arg, **name_Error):
2521 '''(INTERNAL) L{DivMod2Tuple}, L{Fsum2Tuple} Unit.
2522 '''
2523 U = Int if isint(arg) else Float
2524 return U(arg, **name_Error)
2527class DivMod2Tuple(_NamedTuple):
2528 '''2-Tuple C{(div, mod)} with the quotient C{div} and remainder
2529 C{mod} results of a C{divmod} operation.
2531 @note: Quotient C{div} an C{int} in Python 3+ but a C{float}
2532 in Python 2-. Remainder C{mod} an L{Fsum} instance.
2533 '''
2534 _Names_ = ('div', 'mod')
2535 _Units_ = (_Float_Int, Fsum)
2538class Fsum2Tuple(_NamedTuple): # in .fstats
2539 '''2-Tuple C{(fsum, residual)} with the precision running C{fsum}
2540 and the C{residual}, the sum of the remaining partials. Each
2541 item is C{float} or C{int}.
2543 @note: If the C{residual is INT0}, the C{fsum} is considered
2544 to be I{exact}, see method L{Fsum2Tuple.is_exact}.
2545 '''
2546 _Names_ = ( typename(Fsum.fsum), Fsum.residual.name)
2547 _Units_ = (_Float_Int, _Float_Int)
2549 def __abs__(self): # in .fmath
2550 return self._Fsum.__abs__()
2552 def __bool__(self): # PYCHOK Python 3+
2553 return bool(self._Fsum)
2555 def __eq__(self, other):
2556 return self._other_op(other, self.__eq__)
2558 def __float__(self):
2559 return self._Fsum.__float__()
2561 def __ge__(self, other):
2562 return self._other_op(other, self.__ge__)
2564 def __gt__(self, other):
2565 return self._other_op(other, self.__gt__)
2567 def __le__(self, other):
2568 return self._other_op(other, self.__le__)
2570 def __lt__(self, other):
2571 return self._other_op(other, self.__lt__)
2573 def __int__(self):
2574 return self._Fsum.__int__()
2576 def __ne__(self, other):
2577 return self._other_op(other, self.__ne__)
2579 def __neg__(self):
2580 return self._Fsum.__neg__()
2582 __nonzero__ = __bool__ # Python 2-
2584 def __pos__(self):
2585 return self._Fsum.__pos__()
2587 def as_integer_ratio(self):
2588 '''Return this instance as the ratio of 2 integers.
2590 @see: Method L{Fsum.as_integer_ratio} for further details.
2591 '''
2592 return self._Fsum.as_integer_ratio()
2594 @property_RO
2595 def _fint2(self):
2596 return self._Fsum._fint2
2598 @property_RO
2599 def _fprs2(self):
2600 return self._Fsum._fprs2
2602 @Property_RO
2603 def _Fsum(self): # this C{Fsum2Tuple} as L{Fsum}, in .fstats
2604 s, r = _s_r2(*self)
2605 ps = (r, s) if r else (s,)
2606 return _Psum(ps, name=self.name)
2608 def Fsum_(self, *xs, **name_f2product_nonfinites_RESIDUAL):
2609 '''Return this C{Fsum2Tuple} as an L{Fsum} plus some C{xs}.
2610 '''
2611 return Fsum(self, *xs, **name_f2product_nonfinites_RESIDUAL)
2613 def is_exact(self):
2614 '''Is this L{Fsum2Tuple} considered to be exact? (C{bool}).
2615 '''
2616 return self._Fsum.is_exact()
2618 def is_finite(self): # in .constants
2619 '''Is this L{Fsum2Tuple} C{finite}? (C{bool}).
2621 @see: Function L{isfinite<pygeodesy.isfinite>}.
2622 '''
2623 return self._Fsum.is_finite()
2625 def is_integer(self):
2626 '''Is this L{Fsum2Tuple} C{integer}? (C{bool}).
2627 '''
2628 return self._Fsum.is_integer()
2630 def _mul_scalar(self, other, op): # for Fsum._fmul
2631 return self._Fsum._mul_scalar(other, op)
2633 @property_RO
2634 def _n(self):
2635 return self._Fsum._n
2637 def _other_op(self, other, which):
2638 C, s = (tuple, self) if isinstance(other, tuple) else (Fsum, self._Fsum)
2639 return getattr(C, typename(which))(s, other)
2641 @property_RO
2642 def _ps(self):
2643 return self._Fsum._ps
2645 @property_RO
2646 def _ps_neg(self):
2647 return self._Fsum._ps_neg
2649 def signOf(self, **res):
2650 '''Like method L{Fsum.signOf}.
2651 '''
2652 return self._Fsum.signOf(**res)
2654 def toStr(self, fmt=Fmt.g, **prec_sep): # PYCHOK signature
2655 '''Return this L{Fsum2Tuple} as string (C{str}).
2657 @kwarg fmt: Optional C{float} format (C{letter}).
2658 @kwarg prec_sep: Optional keyword arguments for function
2659 L{fstr<streprs.fstr>}.
2660 '''
2661 return Fmt.PAREN(fstr(self, fmt=fmt, strepr=str, force=False, **prec_sep))
2663_Fsum_2Tuple_types = Fsum, Fsum2Tuple # PYCHOK lines
2666class ResidualError(_ValueError):
2667 '''Error raised for a division, power or root operation of
2668 an L{Fsum} instance with a C{residual} I{ratio} exceeding
2669 the L{RESIDUAL<Fsum.RESIDUAL>} threshold.
2671 @see: Module L{pygeodesy.fsums} and method L{Fsum.RESIDUAL}.
2672 '''
2673 pass
2676try:
2677 from math import fsum as _fsum # precision IEEE-754 sum, Python 2.6+
2679 # make sure _fsum works as expected (XXX check
2680 # float.__getformat__('float')[:4] == 'IEEE'?)
2681 if _fsum((1, 1e101, 1, -1e101)) != 2: # PYCHOK no cover
2682 del _fsum # nope, remove _fsum ...
2683 raise ImportError() # ... use _fsum below
2685 _sum = _fsum # in .elliptic
2686except ImportError:
2687 _sum = sum # in .elliptic
2689 def _fsum(xs):
2690 '''(INTERNAL) Precision summation, Python 2.5-.
2691 '''
2692 F = Fsum(name=_fsum.name, f2product=False, nonfinites=True)
2693 return float(F._facc(xs, up=False))
2696def fsum(xs, nonfinites=None, **floats):
2697 '''Precision floating point summation from Python's C{math.fsum}.
2699 @arg xs: Iterable of items to add (each C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
2700 @kwarg nonfinites: Use C{B{nonfinites}=True} if I{non-finites} are C{OK}, if
2701 C{False} I{non-finites} raise an Overflow-/ValueError or if
2702 C{None}, L{nonfiniterrors} applies (C{bool} or C{None}).
2703 @kwarg floats: DEPRECATED keyword argument C{B{floats}=False} (C{bool}), use
2704 keyword argument C{B{nonfinites}=False} instead.
2706 @return: Precision C{fsum} (C{float}).
2708 @raise OverflowError: Infinite B{C{xs}} item or intermediate C{math.fsum} overflow.
2710 @raise TypeError: Invalid B{C{xs}} item.
2712 @raise ValueError: Invalid or C{NAN} B{C{xs}} item.
2714 @see: Function L{nonfiniterrors}, class L{Fsum} and methods L{Fsum.nonfinites},
2715 L{Fsum.fsum}, L{Fsum.fadd} and L{Fsum.fadd_}.
2716 '''
2717 return _xsum(fsum, xs, nonfinites=nonfinites, **floats) if xs else _0_0
2720def fsum_(*xs, **nonfinites):
2721 '''Precision floating point summation of all positional items.
2723 @arg xs: Items to add (each C{scalar}, an L{Fsum} or L{Fsum2Tuple}), all positional.
2724 @kwarg nonfinites: Use C{B{nonfinites}=True} if I{non-finites} are C{OK} (C{bool}).
2726 @see: Function L{fsum<fsums.fsum>} for further details.
2727 '''
2728 return _xsum(fsum_, xs, **nonfinites) if xs else _0_0 # origin=1?
2731def fsumf_(*xs):
2732 '''Precision floating point summation of all positional items with I{non-finites} C{OK}.
2734 @arg xs: Items to add (each C{scalar}, an L{Fsum} or L{Fsum2Tuple}),
2735 all positional.
2737 @see: Function L{fsum_<fsums.fsum_>} for further details.
2738 '''
2739 return _xsum(fsumf_, xs, nonfinites=True) if xs else _0_0 # origin=1?
2742def fsum1(xs, **nonfinites):
2743 '''Precision floating point summation, 1-primed.
2745 @arg xs: Iterable of items to add (each C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
2746 @kwarg nonfinites: Use C{B{nonfinites}=True} if I{non-finites} are C{OK} (C{bool}).
2748 @see: Function L{fsum<fsums.fsum>} for further details.
2749 '''
2750 return _xsum(fsum1, xs, primed=1, **nonfinites) if xs else _0_0
2753def fsum1_(*xs, **nonfinites):
2754 '''Precision floating point summation of all positional items, 1-primed.
2756 @arg xs: Items to add (each C{scalar}, an L{Fsum} or L{Fsum2Tuple}), all positional.
2757 @kwarg nonfinites: Use C{B{nonfinites}=True} if I{non-finites} are C{OK} (C{bool}).
2759 @see: Function L{fsum_<fsums.fsum_>} for further details.
2760 '''
2761 return _xsum(fsum1_, xs, primed=1, **nonfinites) if xs else _0_0 # origin=1?
2764def fsum1f_(*xs):
2765 '''Precision floating point summation of all positional items, 1-primed and
2766 with I{non-finites} C{OK}.
2768 @see: Function L{fsum_<fsums.fsum_>} for further details.
2769 '''
2770 return _xsum(fsum1f_, xs, nonfinites=True, primed=1) if xs else _0_0
2773def _x_isfine(nfOK, **kwds): # get the C{_x} and C{_isfine} handlers.
2774 _x_kwds = dict(_x= (_passarg if nfOK else _2finite),
2775 _isfine=(_isOK if nfOK else _isfinite)) # PYCHOK kwds
2776 _x_kwds.update(kwds)
2777 return _x_kwds
2780def _X_ps(X): # default C{_X} handler
2781 return X._ps # lambda X: X._ps
2784def _xs(xs, _X=_X_ps, _x=float, _isfine=_isfinite, # defaults for Fsum._facc
2785 origin=0, which=None, **_Cdot):
2786 '''(INTERNAL) Yield each C{xs} item as 1 or more C{float}s.
2787 '''
2788 i, x = 0, xs
2789 try:
2790 for i, x in enumerate(_xiterable(xs)):
2791 if _isFsum_2Tuple(x):
2792 for p in _X(x):
2793 yield p if _isfine(p) else _nfError(p)
2794 else:
2795 f = _x(x)
2796 yield f if _isfine(f) else _nfError(f)
2798 except (OverflowError, TypeError, ValueError) as X:
2799 t = _xsError(X, xs, i + origin, x)
2800 if which: # prefix invokation
2801 w = unstr(which, *xs, _ELLIPSIS=4, **_Cdot)
2802 t = _COMMASPACE_(w, t)
2803 raise _xError(X, t, txt=None)
2806def _xsum(which, xs, nonfinites=None, primed=0, **floats): # origin=0
2807 '''(INTERNAL) Precision summation of C{xs} with conditions.
2808 '''
2809 if floats: # for backward compatibility
2810 nonfinites = _xkwds_get1(floats, floats=nonfinites)
2811 elif nonfinites is None:
2812 nonfinites = not nonfiniterrors()
2813 fs = _xs(xs, **_x_isfine(nonfinites, which=which)) # PYCHOK yield
2814 return _fsum(_1primed(fs) if primed else fs)
2817# delete all decorators, etc.
2818del _allPropertiesOf_n, deprecated_method, deprecated_property_RO, \
2819 Property, Property_RO, property_RO, _ALL_LAZY, _F2PRODUCT, \
2820 MANT_DIG, _NONFINITES, _RESIDUAL_0_0, _envPYGEODESY, _std_
2822if __name__ == _DMAIN_:
2824 # usage: python3 -m pygeodesy.fsums
2826 def _test(n):
2827 # copied from Hettinger, see L{Fsum} reference
2828 from pygeodesy import frandoms, printf
2830 printf(typename(_fsum), end=_COMMASPACE_)
2831 printf(typename(_psum), end=_COMMASPACE_)
2833 F = Fsum()
2834 if F.is_math_fsum():
2835 for t in frandoms(n, seeded=True):
2836 assert float(F.fset_(*t)) == _fsum(t)
2837 printf(_DOT_, end=NN)
2838 printf(NN)
2840 _test(128)
2842# **) MIT License
2843#
2844# Copyright (C) 2016-2025 -- mrJean1 at Gmail -- All Rights Reserved.
2845#
2846# Permission is hereby granted, free of charge, to any person obtaining a
2847# copy of this software and associated documentation files (the "Software"),
2848# to deal in the Software without restriction, including without limitation
2849# the rights to use, copy, modify, merge, publish, distribute, sublicense,
2850# and/or sell copies of the Software, and to permit persons to whom the
2851# Software is furnished to do so, subject to the following conditions:
2852#
2853# The above copyright notice and this permission notice shall be included
2854# in all copies or substantial portions of the Software.
2855#
2856# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
2857# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
2858# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
2859# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
2860# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
2861# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
2862# OTHER DEALINGS IN THE SOFTWARE.