Coverage for pygeodesy/fsums.py: 95%
1094 statements
« prev ^ index » next coverage.py v7.6.1, created at 2025-04-25 13:15 -0400
« prev ^ index » next coverage.py v7.6.1, created at 2025-04-25 13:15 -0400
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 _ # PYCHOK semicolon
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
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__ = '25.04.14'
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_scalarf(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_scalarf(_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: An L{Fsum}, L{Fsum2Tuple} or C{scalar} modulus.
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: An L{Fsum}, L{Fsum2Tuple} or C{scalar} divisor.
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 __ge__(self, other):
636 '''Return C{(B{self} >= B{other})}, see C{__eq__}.
637 '''
638 return self._cmp_0(other, _gt_op_ + _fset_op_) >= 0
640 def __gt__(self, other):
641 '''Return C{(B{self} > B{other})}, see C{__eq__}.
642 '''
643 return self._cmp_0(other, _gt_op_) > 0
645 def __hash__(self): # PYCHOK no cover
646 '''Return C{hash(B{self})} as C{float}.
647 '''
648 # @see: U{Notes for type implementors<https://docs.Python.org/
649 # 3/library/numbers.html#numbers.Rational>}
650 return hash(self.partials) # tuple.__hash__()
652 def __iadd__(self, other):
653 '''Apply C{B{self} += B{other}} to this instance.
655 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar} value or
656 an iterable of several of the former.
658 @return: This instance, updated (L{Fsum}).
660 @raise TypeError: Invalid B{C{other}}, not
661 C{scalar} nor L{Fsum}.
663 @see: Methods L{Fsum.fadd_} and L{Fsum.fadd}.
664 '''
665 try:
666 return self._fadd(other, op=_iadd_op_)
667 except TypeError:
668 pass
669 _xiterable(other)
670 return self._facc(other)
672 def __ifloordiv__(self, other):
673 '''Apply C{B{self} //= B{other}} to this instance.
675 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar} divisor.
677 @return: This instance, updated (L{Fsum}).
679 @raise ResidualError: Non-zero, significant residual
680 in B{C{other}}.
682 @raise TypeError: Invalid B{C{other}} type.
684 @raise ValueError: Invalid or I{non-finite} B{C{other}}.
686 @raise ZeroDivisionError: Zero B{C{other}}.
688 @see: Methods L{Fsum.__itruediv__}.
689 '''
690 return self._floordiv(other, _floordiv_op_ + _fset_op_)
692 def __imatmul__(self, other): # PYCHOK no cover
693 '''Not implemented.'''
694 return _NotImplemented(self, other)
696 def __imod__(self, other):
697 '''Apply C{B{self} %= B{other}} to this instance.
699 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar} modulus.
701 @return: This instance, updated (L{Fsum}).
703 @see: Method L{Fsum.__divmod__}.
704 '''
705 return self._fdivmod2(other, _mod_op_ + _fset_op_).mod
707 def __imul__(self, other):
708 '''Apply C{B{self} *= B{other}} to this instance.
710 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar} factor.
712 @return: This instance, updated (L{Fsum}).
714 @raise OverflowError: Partial C{2sum} overflow.
716 @raise TypeError: Invalid B{C{other}} type.
718 @raise ValueError: Invalid or I{non-finite} B{C{other}}.
719 '''
720 return self._fmul(other, _mul_op_ + _fset_op_)
722 def __int__(self):
723 '''Return this instance as an C{int}.
725 @see: Method L{Fsum.int_float} and properties L{Fsum.ceil}
726 and L{Fsum.floor}.
727 '''
728 i, _ = self._fint2
729 return i
731 def __invert__(self): # PYCHOK no cover
732 '''Not implemented.'''
733 # Luciano Ramalho, "Fluent Python", O'Reilly, 2nd Ed, 2022 p. 567
734 return _NotImplemented(self)
736 def __ipow__(self, other, *mod, **raiser_RESIDUAL): # PYCHOK 2 vs 3 args
737 '''Apply C{B{self} **= B{other}} to this instance.
739 @arg other: The exponent (C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
740 @arg mod: Optional modulus (C{int} or C{None}) for the 3-argument
741 C{pow(B{self}, B{other}, B{mod})} version.
742 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore
743 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}
744 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.
746 @return: This instance, updated (L{Fsum}).
748 @note: If B{C{mod}} is given, the result will be an C{integer}
749 L{Fsum} in Python 3+ if this instance C{is_integer} or
750 set to C{as_integer} and B{C{mod}} is given and C{None}.
752 @raise OverflowError: Partial C{2sum} overflow.
754 @raise ResidualError: Invalid B{C{RESIDUAL}} or the residual
755 is non-zero and significant and either
756 B{C{other}} is a fractional or negative
757 C{scalar} or B{C{mod}} is given and not
758 C{None}.
760 @raise TypeError: Invalid B{C{other}} type or 3-argument C{pow}
761 invocation failed.
763 @raise ValueError: If B{C{other}} is a negative C{scalar} and this
764 instance is C{0} or B{C{other}} is a fractional
765 C{scalar} and this instance is negative or has a
766 non-zero and significant residual or B{C{mod}}
767 is given as C{0}.
769 @see: CPython function U{float_pow<https://GitHub.com/
770 python/cpython/blob/main/Objects/floatobject.c>}.
771 '''
772 return self._fpow(other, _pow_op_ + _fset_op_, *mod, **raiser_RESIDUAL)
774 def __isub__(self, other):
775 '''Apply C{B{self} -= B{other}} to this instance.
777 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar} value or
778 an iterable of several of the former.
780 @return: This instance, updated (L{Fsum}).
782 @raise TypeError: Invalid B{C{other}} type.
784 @see: Methods L{Fsum.fsub_} and L{Fsum.fsub}.
785 '''
786 try:
787 return self._fsub(other, _isub_op_)
788 except TypeError:
789 pass
790 _xiterable(other)
791 return self._facc_neg(other)
793 def __iter__(self):
794 '''Return an C{iter}ator over a C{partials} duplicate.
795 '''
796 return iter(self.partials)
798 def __itruediv__(self, other, **raiser_RESIDUAL):
799 '''Apply C{B{self} /= B{other}} to this instance.
801 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar} divisor.
802 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore
803 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}
804 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.
806 @return: This instance, updated (L{Fsum}).
808 @raise OverflowError: Partial C{2sum} overflow.
810 @raise ResidualError: Non-zero, significant residual or invalid
811 B{C{RESIDUAL}}.
813 @raise TypeError: Invalid B{C{other}} type.
815 @raise ValueError: Invalid or I{non-finite} B{C{other}}.
817 @raise ZeroDivisionError: Zero B{C{other}}.
819 @see: Method L{Fsum.__ifloordiv__}.
820 '''
821 return self._ftruediv(other, _truediv_op_ + _fset_op_, **raiser_RESIDUAL)
823 def __le__(self, other):
824 '''Return C{(B{self} <= B{other})}, see C{__eq__}.
825 '''
826 return self._cmp_0(other, _lt_op_ + _fset_op_) <= 0
828 def __len__(self):
829 '''Return the number of values accumulated (C{int}).
830 '''
831 return self._n
833 def __lt__(self, other):
834 '''Return C{(B{self} < B{other})}, see C{__eq__}.
835 '''
836 return self._cmp_0(other, _lt_op_) < 0
838 def __matmul__(self, other): # PYCHOK no cover
839 '''Not implemented.'''
840 return _NotImplemented(self, other)
842 def __mod__(self, other):
843 '''Return C{B{self} % B{other}} as an L{Fsum}.
845 @see: Method L{Fsum.__imod__}.
846 '''
847 f = self._copyd(self.__mod__)
848 return f._fdivmod2(other, _mod_op_).mod
850 def __mul__(self, other):
851 '''Return C{B{self} * B{other}} as an L{Fsum}.
853 @see: Method L{Fsum.__imul__}.
854 '''
855 f = self._copyd(self.__mul__)
856 return f._fmul(other, _mul_op_)
858 def __ne__(self, other):
859 '''Return C{(B{self} != B{other})}, see C{__eq__}.
860 '''
861 return self._cmp_0(other, _ne_op_) != 0
863 def __neg__(self):
864 '''Return C{copy(B{self})}, I{negated}.
865 '''
866 f = self._copyd(self.__neg__)
867 return f._fset(self._neg)
869 def __pos__(self):
870 '''Return this instance I{as-is}, like C{float.__pos__()}.
871 '''
872 return self if _pos_self else self._copyd(self.__pos__)
874 def __pow__(self, other, *mod): # PYCHOK 2 vs 3 args
875 '''Return C{B{self}**B{other}} as an L{Fsum}.
877 @see: Method L{Fsum.__ipow__}.
878 '''
879 f = self._copyd(self.__pow__)
880 return f._fpow(other, _pow_op_, *mod)
882 def __radd__(self, other):
883 '''Return C{B{other} + B{self}} as an L{Fsum}.
885 @see: Method L{Fsum.__iadd__}.
886 '''
887 f = self._rcopyd(other, self.__radd__)
888 return f._fadd(self)
890 def __rdivmod__(self, other):
891 '''Return C{divmod(B{other}, B{self})} as 2-tuple
892 C{(quotient, remainder)}.
894 @see: Method L{Fsum.__divmod__}.
895 '''
896 f = self._rcopyd(other, self.__rdivmod__)
897 return f._fdivmod2(self, _divmod_op_)
899# turned off, called by _deepcopy and _copy
900# def __reduce__(self): # Python 3.8+
901# ''' Pickle, like std C{fractions.Fraction}, see U{__reduce__
902# <https://docs.Python.org/3/library/pickle.html#object.__reduce__>}
903# '''
904# dict_ = self._Fsum_as().__dict__ # no __setstate__
905# return (type(self), self.partials, dict_)
907# def __repr__(self):
908# '''Return the default C{repr(this)}.
909# '''
910# return self.toRepr(lenc=True)
912 def __rfloordiv__(self, other):
913 '''Return C{B{other} // B{self}} as an L{Fsum}.
915 @see: Method L{Fsum.__ifloordiv__}.
916 '''
917 f = self._rcopyd(other, self.__rfloordiv__)
918 return f._floordiv(self, _floordiv_op_)
920 def __rmatmul__(self, other): # PYCHOK no coveS
921 '''Not implemented.'''
922 return _NotImplemented(self, other)
924 def __rmod__(self, other):
925 '''Return C{B{other} % B{self}} as an L{Fsum}.
927 @see: Method L{Fsum.__imod__}.
928 '''
929 f = self._rcopyd(other, self.__rmod__)
930 return f._fdivmod2(self, _mod_op_).mod
932 def __rmul__(self, other):
933 '''Return C{B{other} * B{self}} as an L{Fsum}.
935 @see: Method L{Fsum.__imul__}.
936 '''
937 f = self._rcopyd(other, self.__rmul__)
938 return f._fmul(self, _mul_op_)
940 def __round__(self, *ndigits): # PYCHOK Python 3+
941 '''Return C{round(B{self}, *B{ndigits}} as an L{Fsum}.
943 @arg ndigits: Optional number of digits (C{int}).
944 '''
945 f = self._copyd(self.__round__)
946 # <https://docs.Python.org/3.12/reference/datamodel.html?#object.__round__>
947 return f._fset(round(float(self), *ndigits)) # can be C{int}
949 def __rpow__(self, other, *mod):
950 '''Return C{B{other}**B{self}} as an L{Fsum}.
952 @see: Method L{Fsum.__ipow__}.
953 '''
954 f = self._rcopyd(other, self.__rpow__)
955 return f._fpow(self, _pow_op_, *mod)
957 def __rsub__(self, other):
958 '''Return C{B{other} - B{self}} as L{Fsum}.
960 @see: Method L{Fsum.__isub__}.
961 '''
962 f = self._rcopyd(other, self.__rsub__)
963 return f._fsub(self, _sub_op_)
965 def __rtruediv__(self, other, **raiser_RESIDUAL):
966 '''Return C{B{other} / B{self}} as an L{Fsum}.
968 @see: Method L{Fsum.__itruediv__}.
969 '''
970 f = self._rcopyd(other, self.__rtruediv__)
971 return f._ftruediv(self, _truediv_op_, **raiser_RESIDUAL)
973 def __str__(self):
974 '''Return the default C{str(self)}.
975 '''
976 return self.toStr(lenc=True)
978 def __sub__(self, other):
979 '''Return C{B{self} - B{other}} as an L{Fsum}.
981 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar}.
983 @return: The difference (L{Fsum}).
985 @see: Method L{Fsum.__isub__}.
986 '''
987 f = self._copyd(self.__sub__)
988 return f._fsub(other, _sub_op_)
990 def __truediv__(self, other, **raiser_RESIDUAL):
991 '''Return C{B{self} / B{other}} as an L{Fsum}.
993 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar} divisor.
994 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore
995 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}
996 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.
998 @return: The quotient (L{Fsum}).
1000 @raise ResidualError: Non-zero, significant residual or invalid
1001 B{C{RESIDUAL}}.
1003 @see: Method L{Fsum.__itruediv__}.
1004 '''
1005 return self._truediv(other, _truediv_op_, **raiser_RESIDUAL)
1007 __trunc__ = __int__
1009 if _MODS.sys_version_info2 < (3, 0): # PYCHOK no cover
1010 # <https://docs.Python.org/2/library/operator.html#mapping-operators-to-functions>
1011 __div__ = __truediv__
1012 __idiv__ = __itruediv__
1013 __long__ = __int__
1014 __nonzero__ = __bool__
1015 __rdiv__ = __rtruediv__
1017 def as_integer_ratio(self):
1018 '''Return this instance as the ratio of 2 integers.
1020 @return: 2-Tuple C{(numerator, denominator)} both C{int} with
1021 C{numerator} signed and C{denominator} non-zero and
1022 positive. The C{numerator} is I{non-finite} if this
1023 instance is.
1025 @see: Method L{Fsum.fint2} and C{float.as_integer_ratio} in
1026 Python 2.7+.
1027 '''
1028 n, r = self._fint2
1029 if r:
1030 i, d = float(r).as_integer_ratio()
1031 n, d = _n_d2(n * d + i, d)
1032 else: # PYCHOK no cover
1033 d = 1
1034 return n, d
1036 @property_RO
1037 def as_iscalar(self):
1038 '''Get this instance I{as-is} (L{Fsum} with C{non-zero residual},
1039 C{scalar} or I{non-finite}).
1040 '''
1041 s, r = self._nfprs2
1042 return self if r else s
1044 @property_RO
1045 def ceil(self):
1046 '''Get this instance' C{ceil} value (C{int} in Python 3+, but
1047 C{float} in Python 2-).
1049 @note: This C{ceil} takes the C{residual} into account.
1051 @see: Method L{Fsum.int_float} and properties L{Fsum.floor},
1052 L{Fsum.imag} and L{Fsum.real}.
1053 '''
1054 s, r = self._fprs2
1055 c = _ceil(s) + int(r) - 1
1056 while r > (c - s): # (s + r) > c
1057 c += 1
1058 return c # _ceil(self._n_d)
1060 cmp = __cmp__
1062 def _cmp_0(self, other, op):
1063 '''(INTERNAL) Return C{scalar(self - B{other})} for 0-comparison.
1064 '''
1065 if _isFsum_2Tuple(other):
1066 s = self._ps_1sum(*other._ps)
1067 elif self._scalar(other, op):
1068 s = self._ps_1sum(other)
1069 else:
1070 s = self.signOf() # res=True
1071 return s
1073 def copy(self, deep=False, **name):
1074 '''Copy this instance, C{shallow} or B{C{deep}}.
1076 @kwarg name: Optional, overriding C{B{name}='"copy"} (C{str}).
1078 @return: The copy (L{Fsum}).
1079 '''
1080 n = _name__(name, name__=self.copy)
1081 f = _Named.copy(self, deep=deep, name=n)
1082 if f._ps is self._ps:
1083 f._ps = list(self._ps) # separate list
1084 if not deep:
1085 f._n = 1
1086 # assert f._f2product == self._f2product
1087 # assert f._Fsum is f
1088 # assert f._isfine is self._isfine
1089 # assert f._RESIDUAL is self._RESIDUAL
1090 return f
1092 def _copyd(self, which, name=NN):
1093 '''(INTERNAL) Copy for I{dyadic} operators.
1094 '''
1095 n = name or typename(which)
1096 # NOT .classof due to .Fdot(a, *b) args, etc.
1097 f = _Named.copy(self, deep=False, name=n)
1098 f._ps = list(self._ps) # separate list
1099 # assert f._n == self._n
1100 # assert f._f2product == self._f2product
1101 # assert f._Fsum is f
1102 # assert f._isfine is self._isfine
1103 # assert f._RESIDUAL is self._RESIDUAL
1104 return f
1106 divmod = __divmod__
1108 def _Error(self, op, other, Error, **txt_cause):
1109 '''(INTERNAL) Format an B{C{Error}} for C{{self} B{op} B{other}}.
1110 '''
1111 # self.as_iscalar causes RecursionError for ._fprs2 errors
1112 s = _Psum(self._ps, nonfinites=True, name=self.name)
1113 return Error(_SPACE_(s.as_iscalar, op, other), **txt_cause)
1115 def _ErrorX(self, X, op, other, *mod):
1116 '''(INTERNAL) Format the caught exception C{X}.
1117 '''
1118 E, t = _xError2(X)
1119 if mod:
1120 t = _COMMASPACE_(Fmt.PARENSPACED(mod=mod[0]), t)
1121 return self._Error(op, other, E, txt=t, cause=X)
1123 def _ErrorXs(self, X, xs, **kwds): # in .fmath
1124 '''(INTERNAL) Format the caught exception C{X}.
1125 '''
1126 E, t = _xError2(X)
1127 u = unstr(self.named3, *xs, _ELLIPSIS=4, **kwds)
1128 return E(u, txt=t, cause=X)
1130 def _facc(self, xs, up=True, **_X_x_origin):
1131 '''(INTERNAL) Accumulate more C{scalar}s or L{Fsum}s.
1132 '''
1133 if xs:
1134 kwds = self._isfine
1135 if _X_x_origin:
1136 kwds = _xkwds(_X_x_origin, **kwds)
1137 fs = _xs(xs, **kwds) # PYCHOK yield
1138 ps = self._ps
1139 ps[:] = self._ps_acc(list(ps), fs, up=up)
1140# if len(ps) > 16:
1141# _ = _psum(ps, **self._isfine)
1142 return self
1144 def _facc_args(self, xs, **up):
1145 '''(INTERNAL) Accumulate 0, 1 or more C{xs}, all positional
1146 arguments in the caller of this method.
1147 '''
1148 return self._fadd(xs[0], **up) if len(xs) == 1 else \
1149 self._facc(xs, **up) # origin=1?
1151 def _facc_dot(self, n, xs, ys, **kwds): # in .fmath
1152 '''(INTERNAL) Accumulate C{fdot(B{xs}, *B{ys})}.
1153 '''
1154 if n > 0:
1155 _f = Fsum(**kwds)
1156 self._facc(_f(x).fmul(y) for x, y in zip(xs, ys)) # PYCHOK attr?
1157 return self
1159 def _facc_neg(self, xs, **up_origin):
1160 '''(INTERNAL) Accumulate more C{xs}, negated.
1161 '''
1162 def _N(X):
1163 return X._ps_neg
1165 def _n(x):
1166 return -float(x)
1168 return self._facc(xs, _X=_N, _x=_n, **up_origin)
1170 def _facc_power(self, power, xs, which, **raiser_RESIDUAL): # in .fmath
1171 '''(INTERNAL) Add each C{xs} as C{float(x**power)}.
1172 '''
1173 def _Pow4(p):
1174 r = 0
1175 if _isFsum_2Tuple(p):
1176 s, r = p._fprs2
1177 if r:
1178 m = Fsum._pow
1179 else: # scalar
1180 return _Pow4(s)
1181 elif isint(p, both=True) and int(p) >= 0:
1182 p = s = int(p)
1183 m = Fsum._pow_int
1184 else:
1185 p = s = _2float(power=p, **self._isfine)
1186 m = Fsum._pow_scalar
1187 return m, p, s, r
1189 _Pow, p, s, r = _Pow4(power)
1190 if p: # and xs:
1191 op = typename(which)
1192 _FsT = _Fsum_2Tuple_types
1193 _pow = self._pow_2_3
1195 def _P(X):
1196 f = _Pow(X, p, power, op, **raiser_RESIDUAL)
1197 return f._ps if isinstance(f, _FsT) else (f,)
1199 def _p(x):
1200 x = float(x)
1201 f = _pow(x, s, power, op, **raiser_RESIDUAL)
1202 if f and r:
1203 f *= _pow(x, r, power, op, **raiser_RESIDUAL)
1204 return f
1206 f = self._facc(xs, _X=_P, _x=_p) # origin=1?
1207 else:
1208 f = self._facc_scalar_(float(len(xs))) # x**0 == 1
1209 return f
1211 def _facc_scalar(self, xs, **up):
1212 '''(INTERNAL) Accumulate all C{xs}, each C{scalar}.
1213 '''
1214 if xs:
1215 ps = self._ps
1216 ps[:] = self._ps_acc(list(ps), xs, **up)
1217 return self
1219 def _facc_scalar_(self, *xs, **up):
1220 '''(INTERNAL) Accumulate all positional C{xs}, each C{scalar}.
1221 '''
1222 return self._facc_scalar(xs, **up)
1224 def _facc_scalarf(self, xs, up=True, **origin_which):
1225 '''(INTERNAL) Accumulate all C{xs}, each C{scalar}, an L{Fsum} or
1226 L{Fsum2Tuple}, like function C{_xsum}.
1227 '''
1228 fs = _xs(xs, **_x_isfine(self.nonfinitesOK, _Cdot=type(self),
1229 **origin_which)) # PYCHOK yield
1230 return self._facc_scalar(fs, up=up)
1232# def _facc_up(self, up=True):
1233# '''(INTERNAL) Update the C{partials}, by removing
1234# and re-accumulating the final C{partial}.
1235# '''
1236# ps = self._ps
1237# while len(ps) > 1:
1238# p = ps.pop()
1239# if p:
1240# n = self._n
1241# _ = self._ps_acc(ps, (p,), up=False)
1242# self._n = n
1243# break
1244# return self._update() if up else self
1246 def fadd(self, xs=()):
1247 '''Add an iterable's items to this instance.
1249 @arg xs: Iterable of items to add (each C{scalar},
1250 an L{Fsum} or L{Fsum2Tuple}).
1252 @return: This instance (L{Fsum}).
1254 @raise OverflowError: Partial C{2sum} overflow.
1256 @raise TypeError: An invalid B{C{xs}} item.
1258 @raise ValueError: Invalid or I{non-finite} B{C{xs}} value.
1259 '''
1260 if _isFsum_2Tuple(xs):
1261 self._facc_scalar(xs._ps)
1262 elif isscalar(xs): # for backward compatibility # PYCHOK no cover
1263 x = _2float(x=xs, **self._isfine)
1264 self._facc_scalar_(x)
1265 elif xs: # _xiterable(xs)
1266 self._facc(xs)
1267 return self
1269 def fadd_(self, *xs):
1270 '''Add all positional items to this instance.
1272 @arg xs: Values to add (each C{scalar}, an L{Fsum}
1273 or L{Fsum2Tuple}), all positional.
1275 @see: Method L{Fsum.fadd} for further details.
1276 '''
1277 return self._facc_args(xs)
1279 def _fadd(self, other, op=_add_op_, **up):
1280 '''(INTERNAL) Apply C{B{self} += B{other}}.
1281 '''
1282 if _isFsum_2Tuple(other):
1283 self._facc_scalar(other._ps, **up)
1284 elif self._scalar(other, op):
1285 self._facc_scalar_(other, **up)
1286 return self
1288 fcopy = copy # for backward compatibility
1289 fdiv = __itruediv__
1290 fdivmod = __divmod__
1292 def _fdivmod2(self, other, op, **raiser_RESIDUAL):
1293 '''(INTERNAL) Apply C{B{self} %= B{other}} and return a L{DivMod2Tuple}.
1294 '''
1295 # result mostly follows CPython function U{float_divmod
1296 # <https://GitHub.com/python/cpython/blob/main/Objects/floatobject.c>},
1297 # but at least divmod(-3, 2) equals Cpython's result (-2, 1).
1298 q = self._truediv(other, op, **raiser_RESIDUAL).floor
1299 if q: # == float // other == floor(float / other)
1300 self -= self._Fsum_as(q) * other # NOT other * q!
1302 s = signOf(other) # make signOf(self) == signOf(other)
1303 if s and self.signOf() == -s: # PYCHOK no cover
1304 self += other
1305 q -= 1
1306# t = self.signOf()
1307# if t and t != s:
1308# raise self._Error(op, other, _AssertionError, txt__=signOf)
1309 return DivMod2Tuple(q, self) # q is C{int} in Python 3+, but C{float} in Python 2-
1311 def _fhorner(self, x, cs, where, incx=True): # in .fmath
1312 '''(INTERNAL) Add an L{Fhorner} evaluation of polynomial
1313 C{sum(c * B{x}**i for i, c in _e(cs))} where C{_e =
1314 enumerate if B{incx} else _enumereverse}.
1315 '''
1316 # assert _xiterablen(cs)
1317 try:
1318 n = len(cs)
1319 if n > 1 and _2finite(x, **self._isfine):
1320 H = self._Fsum_as(name__=self._fhorner)
1321 _m = H._mul_Fsum if _isFsum_2Tuple(x) else \
1322 H._mul_scalar
1323 for c in (reversed(cs) if incx else cs):
1324 H._fset(_m(x, _mul_op_), up=False)
1325 H._fadd(c, up=False)
1326 else: # x == 0
1327 H = cs[0] if n else 0
1328 self._fadd(H)
1329 except Exception as X:
1330 t = unstr(where, x, *cs, _ELLIPSIS=4, incx=incx)
1331 raise self._ErrorX(X, _add_op_, t)
1332 return self
1334 def _finite(self, other, op=None):
1335 '''(INTERNAL) Return B{C{other}} if C{finite}.
1336 '''
1337 if _isOK_or_finite(other, **self._isfine):
1338 return other
1339 E = _NonfiniteError(other)
1340 raise self._Error(op, other, E, txt=_not_finite_)
1342 def fint(self, name=NN, **raiser_RESIDUAL):
1343 '''Return this instance' current running sum as C{integer}.
1345 @kwarg name: Optional, overriding C{B{name}="fint"} (C{str}).
1346 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore
1347 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}
1348 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.
1350 @return: The C{integer} sum (L{Fsum}) if this instance C{is_integer}
1351 with a zero or insignificant I{integer} residual.
1353 @raise ResidualError: Non-zero, significant residual or invalid
1354 B{C{RESIDUAL}}.
1356 @see: Methods L{Fsum.fint2}, L{Fsum.int_float} and L{Fsum.is_integer}.
1357 '''
1358 i, r = self._fint2
1359 if r:
1360 R = self._raiser(r, i, **raiser_RESIDUAL)
1361 if R:
1362 t = _stresidual(_integer_, r, **R)
1363 raise ResidualError(_integer_, i, txt=t)
1364 return self._Fsum_as(i, name=_name__(name, name__=self.fint))
1366 def fint2(self, **name):
1367 '''Return this instance' current running sum as C{int} and the
1368 I{integer} residual.
1370 @kwarg name: Optional name (C{str}).
1372 @return: An L{Fsum2Tuple}C{(fsum, residual)} with C{fsum}
1373 an C{int} and I{integer} C{residual} a C{float} or
1374 C{INT0} if the C{fsum} is considered to be I{exact}.
1375 The C{fsum} is I{non-finite} if this instance is.
1376 '''
1377 return Fsum2Tuple(*self._fint2, **name)
1379 @Property
1380 def _fint2(self): # see ._fset
1381 '''(INTERNAL) Get 2-tuple (C{int}, I{integer} residual).
1382 '''
1383 s, r = self._nfprs2
1384 if _isfinite(s):
1385 i = int(s)
1386 r = (self._ps_1sum(i) if len(self._ps) > 1 else
1387 float(s - i)) or INT0
1388 else: # INF, NAN, NINF
1389 i = float(s)
1390# r = _NONFINITEr
1391 return i, r # Fsum2Tuple?
1393 @_fint2.setter_ # PYCHOK setter_UNDERscore!
1394 def _fint2(self, s): # in _fset
1395 '''(INTERNAL) Replace the C{_fint2} value.
1396 '''
1397 if _isfinite(s):
1398 i = int(s)
1399 r = (s - i) or INT0
1400 else: # INF, NAN, NINF
1401 i = float(s)
1402 r = _NONFINITEr
1403 return i, r # like _fint2.getter
1405 @deprecated_property_RO
1406 def float_int(self): # PYCHOK no cover
1407 '''DEPRECATED, use method C{Fsum.int_float}.'''
1408 return self.int_float() # raiser=False
1410 @property_RO
1411 def floor(self):
1412 '''Get this instance' C{floor} (C{int} in Python 3+, but
1413 C{float} in Python 2-).
1415 @note: This C{floor} takes the C{residual} into account.
1417 @see: Method L{Fsum.int_float} and properties L{Fsum.ceil},
1418 L{Fsum.imag} and L{Fsum.real}.
1419 '''
1420 s, r = self._fprs2
1421 f = _floor(s) + _floor(r) + 1
1422 while (f - s) > r: # f > (s + r)
1423 f -= 1
1424 return f # _floor(self._n_d)
1426# ffloordiv = __ifloordiv__ # for naming consistency?
1427# floordiv = __floordiv__ # for naming consistency?
1429 def _floordiv(self, other, op, **raiser_RESIDUAL): # rather _ffloordiv?
1430 '''Apply C{B{self} //= B{other}}.
1431 '''
1432 q = self._ftruediv(other, op, **raiser_RESIDUAL) # == self
1433 return self._fset(q.floor) # floor(q)
1435 def fma(self, other1, other2, **nonfinites): # in .fmath.fma
1436 '''Fused-multiply-add C{self *= B{other1}; self += B{other2}}.
1438 @arg other1: Multiplier (C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
1439 @arg other2: Addend (C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
1440 @kwarg nonfinites: Use C{B{nonfinites}=True} or C{False}, to
1441 override L{nonfinites<Fsum.nonfinites>} and
1442 L{nonfiniterrors} default (C{bool}).
1443 '''
1444 op = typename(self.fma)
1445 _fs = self._ps_other
1446 try:
1447 s, r = self._fprs2
1448 if r:
1449 f = self._f2mul(self.fma, (other1,), **nonfinites)
1450 f += other2
1451 elif _residue(other1) or _residue(other2):
1452 fs = _2split3s(_fs(op, other1))
1453 fs = _2products(s, fs, *_fs(op, other2))
1454 f = _Psum(self._ps_acc([], fs, up=False), name=op)
1455 else:
1456 f = _fma(s, other1, other2)
1457 f = _2finite(f, **self._isfine)
1458 except TypeError as X:
1459 raise self._ErrorX(X, op, (other1, other2))
1460 except (OverflowError, ValueError) as X: # from math.fma
1461 f = self._mul_reduce(s, other1) # INF, NAN, NINF
1462 f += sum(_fs(op, other2))
1463 f = self._nonfiniteX(X, op, f, **nonfinites)
1464 return self._fset(f)
1466 fmul = __imul__
1468 def _fmul(self, other, op):
1469 '''(INTERNAL) Apply C{B{self} *= B{other}}.
1470 '''
1471 if _isFsum_2Tuple(other):
1472 if len(self._ps) != 1:
1473 f = self._mul_Fsum(other, op)
1474 elif len(other._ps) != 1: # and len(self._ps) == 1
1475 f = self._ps_mul(op, *other._ps) if other._ps else _0_0
1476 elif self._f2product: # len(other._ps) == 1
1477 f = self._mul_scalar(other._ps[0], op)
1478 else: # len(other._ps) == len(self._ps) == 1
1479 f = self._finite(self._ps[0] * other._ps[0], op=op)
1480 else:
1481 s = self._scalar(other, op)
1482 f = self._mul_scalar(s, op)
1483 return self._fset(f) # n=len(self) + 1
1485 @deprecated_method
1486 def f2mul(self, *others, **raiser):
1487 '''DEPRECATED on 2024.09.13, use method L{f2mul_<Fsum.f2mul_>}.'''
1488 return self._fset(self.f2mul_(others, **raiser))
1490 def f2mul_(self, *others, **f2product_nonfinites): # in .fmath.f2mul
1491 '''Return C{B{self} * B{other} * B{other} ...} for all B{C{others}} using cascaded,
1492 accurate multiplication like with L{f2product<Fsum.f2product>}C{(B{True})}.
1494 @arg others: Multipliers (each C{scalar}, an L{Fsum} or L{Fsum2Tuple}), all
1495 positional.
1496 @kwarg f2product_nonfinites: Use C{B{f2product=False}} to override the default
1497 C{True} and C{B{nonfinites}=True} or C{False}, to override
1498 settings L{nonfinites<Fsum.nonfinites>} and L{nonfiniterrors}.
1500 @return: The cascaded I{TwoProduct} (L{Fsum} or C{float}).
1502 @see: U{Equations 2.3<https://www.TUHH.De/ti3/paper/rump/OzOgRuOi06.pdf>}
1503 '''
1504 return self._f2mul(self.f2mul_, others, **f2product_nonfinites)
1506 def _f2mul(self, where, others, f2product=True, **nonfinites_raiser):
1507 '''(INTERNAL) See methods C{fma} and C{f2mul_}.
1508 '''
1509 n = typename(where)
1510 f = _Psum(self._ps, f2product=f2product, name=n)
1511 if others and f:
1512 if f.f2product():
1513 def _pfs(f, ps):
1514 return _2products(f, _2split3s(ps))
1515 else:
1516 def _pfs(f, ps): # PYCHOK redef
1517 return (f * p for p in ps)
1519 op, ps = n, f._ps
1520 try: # as if self.f2product(True)
1521 for other in others: # to pinpoint errors
1522 for p in self._ps_other(op, other):
1523 ps[:] = f._ps_acc([], _pfs(p, ps), update=False)
1524 f._update()
1525 except TypeError as X:
1526 raise self._ErrorX(X, op, other)
1527 except (OverflowError, ValueError) as X:
1528 r = self._mul_reduce(sum(ps), other) # INF, NAN, NINF
1529 r = self._nonfiniteX(X, op, r, **nonfinites_raiser)
1530 f._fset(r)
1531 return f
1533 def fover(self, over, **raiser_RESIDUAL):
1534 '''Apply C{B{self} /= B{over}} and summate.
1536 @arg over: An L{Fsum} or C{scalar} denominator.
1537 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore
1538 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}
1539 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.
1541 @return: Precision running sum (C{float}).
1543 @raise ResidualError: Non-zero, significant residual or invalid
1544 B{C{RESIDUAL}}.
1546 @see: Methods L{Fsum.fsum} and L{Fsum.__itruediv__}.
1547 '''
1548 return float(self.fdiv(over, **raiser_RESIDUAL)._fprs)
1550 fpow = __ipow__
1552 def _fpow(self, other, op, *mod, **raiser_RESIDUAL):
1553 '''Apply C{B{self} **= B{other}}, optional B{C{mod}} or C{None}.
1554 '''
1555 if mod:
1556 if mod[0] is not None: # == 3-arg C{pow}
1557 f = self._pow_2_3(self, other, other, op, *mod, **raiser_RESIDUAL)
1558 elif self.is_integer():
1559 # return an exact C{int} for C{int}**C{int}
1560 i, _ = self._fint2 # assert _ == 0
1561 x, r = _2tuple2(other) # C{int}, C{float} or other
1562 f = self._Fsum_as(i)._pow_Fsum(other, op, **raiser_RESIDUAL) if r else \
1563 self._pow_2_3(i, x, other, op, **raiser_RESIDUAL)
1564 else: # mod[0] is None, power(self, other)
1565 f = self._pow(other, other, op, **raiser_RESIDUAL)
1566 else: # pow(self, other)
1567 f = self._pow(other, other, op, **raiser_RESIDUAL)
1568 return self._fset(f) # n=max(len(self), 1)
1570 def f2product(self, *two):
1571 '''Get and set accurate I{TwoProduct} multiplication for this
1572 L{Fsum}, overriding the L{f2product} default.
1574 @arg two: If omitted, leave the override unchanged, if C{True},
1575 turn I{TwoProduct} on, if C{False} off, if C{None}e
1576 remove th override (C{bool} or C{None}).
1578 @return: The previous setting (C{bool} or C{None} if not set).
1580 @see: Function L{f2product<fsums.f2product>}.
1582 @note: Use C{f.f2product() or f2product()} to determine whether
1583 multiplication is accurate for L{Fsum} C{f}.
1584 '''
1585 if two: # delattrof(self, _f2product=None)
1586 t = _xkwds_pop(self.__dict__, _f2product=None)
1587 if two[0] is not None:
1588 self._f2product = bool(two[0])
1589 else: # getattrof(self, _f2product=None)
1590 t = _xkwds_get(self.__dict__, _f2product=None)
1591 return t
1593 @Property
1594 def _fprs(self):
1595 '''(INTERNAL) Get and cache this instance' precision
1596 running sum (C{float} or C{int}), ignoring C{residual}.
1598 @note: The precision running C{fsum} after a C{//=} or
1599 C{//} C{floor} division is C{int} in Python 3+.
1600 '''
1601 s, _ = self._fprs2
1602 return s # ._fprs2.fsum
1604 @_fprs.setter_ # PYCHOK setter_UNDERscore!
1605 def _fprs(self, s):
1606 '''(INTERNAL) Replace the C{_fprs} value.
1607 '''
1608 return s
1610 @Property
1611 def _fprs2(self):
1612 '''(INTERNAL) Get and cache this instance' precision
1613 running sum and residual (L{Fsum2Tuple}).
1614 '''
1615 ps = self._ps
1616 n = len(ps)
1617 try:
1618 if n > 2:
1619 s = _psum(ps, **self._isfine)
1620 if not _isfinite(s):
1621 ps[:] = s, # collapse ps
1622 return Fsum2Tuple(s, _NONFINITEr)
1623 n = len(ps)
1624# Fsum._ps_max = max(Fsum._ps_max, n)
1625 if n > 2:
1626 r = self._ps_1sum(s)
1627 return Fsum2Tuple(*_s_r2(s, r))
1628 if n > 1: # len(ps) == 2
1629 s, r = _s_r2(*_2sum(*ps, **self._isfine))
1630 ps[:] = (r, s) if r else (s,)
1631 elif ps: # len(ps) == 1
1632 s = ps[0]
1633 r = INT0 if _isfinite(s) else _NONFINITEr
1634 else: # len(ps) == 0
1635 s = _0_0
1636 r = INT0 if _isfinite(s) else _NONFINITEr
1637 ps[:] = s,
1638 except (OverflowError, ValueError) as X:
1639 op = _fset_op_ # INF, NAN, NINF
1640 ps[:] = sum(ps), # collapse ps
1641 s = self._nonfiniteX(X, op, ps[0])
1642 r = _NONFINITEr
1643 # assert self._ps is ps
1644 return Fsum2Tuple(s, r)
1646 @_fprs2.setter_ # PYCHOK setter_UNDERscore!
1647 def _fprs2(self, s_r):
1648 '''(INTERNAL) Replace the C{_fprs2} value.
1649 '''
1650 return Fsum2Tuple(s_r)
1652 def fset_(self, *xs):
1653 '''Apply C{B{self}.partials = Fsum(*B{xs}).partials}.
1655 @arg xs: Optional, new values (each C{scalar} or an L{Fsum}
1656 or L{Fsum2Tuple} instance), all positional.
1658 @return: This instance, replaced (C{Fsum}).
1660 @see: Method L{Fsum.fadd} for further details.
1661 '''
1662 f = (xs[0] if xs else _0_0) if len(xs) < 2 else \
1663 Fsum(*xs, nonfinites=self.nonfinites()) # self._Fsum_as(*xs)
1664 return self._fset(f, op=_fset_op_)
1666 def _fset(self, other, n=0, up=True, **op):
1667 '''(INTERNAL) Overwrite this instance with an other or a C{scalar}.
1668 '''
1669 if other is self:
1670 pass # from ._fmul, ._ftruediv and ._pow_0_1
1671 elif _isFsum_2Tuple(other):
1672 if op: # and not self.nonfinitesOK:
1673 self._finite(other._fprs, **op)
1674 self._ps[:] = other._ps
1675 self._n = n or other._n
1676 if up: # use or zap the C{Property_RO} values
1677 Fsum._fint2._update_from(self, other)
1678 Fsum._fprs ._update_from(self, other)
1679 Fsum._fprs2._update_from(self, other)
1680 elif isscalar(other):
1681 s = float(self._finite(other, **op)) if op else other
1682 self._ps[:] = s,
1683 self._n = n or 1
1684 if up: # Property _fint2, _fprs and _fprs2 all have
1685 # @.setter_underscore and NOT @.setter because the
1686 # latter's _fset zaps the value set by @.setter
1687 self._fint2 = s
1688 self._fprs = s
1689 self._fprs2 = s, INT0
1690 # assert self._fprs is s
1691 else:
1692 op = _xkwds_get1(op, op=_fset_op_)
1693 raise self._Error(op, other, _TypeError)
1694 return self
1696 def fsub(self, xs=()):
1697 '''Subtract an iterable's items from this instance.
1699 @see: Method L{Fsum.fadd} for further details.
1700 '''
1701 return self._facc_neg(xs)
1703 def fsub_(self, *xs):
1704 '''Subtract all positional items from this instance.
1706 @see: Method L{Fsum.fadd_} for further details.
1707 '''
1708 return self._fsub(xs[0], _sub_op_) if len(xs) == 1 else \
1709 self._facc_neg(xs) # origin=1?
1711 def _fsub(self, other, op):
1712 '''(INTERNAL) Apply C{B{self} -= B{other}}.
1713 '''
1714 if _isFsum_2Tuple(other):
1715 if other is self: # or other._fprs2 == self._fprs2:
1716 self._fset(_0_0, n=len(self) * 2)
1717 elif other._ps:
1718 self._facc_scalar(other._ps_neg)
1719 elif self._scalar(other, op):
1720 self._facc_scalar_(-other)
1721 return self
1723 def fsum(self, xs=()):
1724 '''Add an iterable's items, summate and return the current
1725 precision running sum.
1727 @arg xs: Iterable of items to add (each item C{scalar},
1728 an L{Fsum} or L{Fsum2Tuple}).
1730 @return: Precision running sum (C{float} or C{int}).
1732 @see: Method L{Fsum.fadd}.
1734 @note: Accumulation can continue after summation.
1735 '''
1736 return self._facc(xs)._fprs
1738 def fsum_(self, *xs):
1739 '''Add any positional items, summate and return the current
1740 precision running sum.
1742 @arg xs: Items to add (each C{scalar}, an L{Fsum} or
1743 L{Fsum2Tuple}), all positional.
1745 @return: Precision running sum (C{float} or C{int}).
1747 @see: Methods L{Fsum.fsum}, L{Fsum.Fsum_} and L{Fsum.fsumf_}.
1748 '''
1749 return self._facc_args(xs)._fprs
1751 def Fsum_(self, *xs, **name):
1752 '''Like method L{Fsum.fsum_} but returning a named L{Fsum}.
1754 @kwarg name: Optional name (C{str}).
1756 @return: Copy of this updated instance (L{Fsum}).
1757 '''
1758 return self._facc_args(xs)._copyd(self.Fsum_, **name)
1760 def Fsum2Tuple_(self, *xs, **name):
1761 '''Like method L{Fsum.fsum_} but returning a named L{Fsum2Tuple}.
1763 @kwarg name: Optional name (C{str}).
1765 @return: Precision running sum (L{Fsum2Tuple}).
1766 '''
1767 return Fsum2Tuple(self._facc_args(xs)._nfprs2, **name)
1769 @property_RO
1770 def _Fsum(self): # like L{Fsum2Tuple._Fsum}, in .fstats
1771 return self # NOT @Property_RO, see .copy and ._copyd
1773 def _Fsum_as(self, *xs, **name_f2product_nonfinites_RESIDUAL):
1774 '''(INTERNAL) Return an C{Fsum} with this C{Fsum}'s C{.f2product},
1775 C{.nonfinites} and C{.RESIDUAL} setting, optionally
1776 overridden with C{name_f2product_nonfinites_RESIDUAL} and
1777 with any C{xs} accumulated.
1778 '''
1779 kwds = _xkwds_not(None, Fsum._RESIDUAL, f2product =self.f2product(),
1780 nonfinites=self.nonfinites(),
1781 RESIDUAL =self.RESIDUAL())
1782 if name_f2product_nonfinites_RESIDUAL: # overwrites
1783 kwds.update(name_f2product_nonfinites_RESIDUAL)
1784 f = Fsum(**kwds)
1785 # assert all(v == self.__dict__[n] for n, v in f.__dict__.items())
1786 return (f._facc(xs, up=False) if len(xs) > 1 else
1787 f._fset(xs[0], op=_fset_op_)) if xs else f
1789 def fsum2(self, xs=(), **name):
1790 '''Add an iterable's items, summate and return the
1791 current precision running sum I{and} the C{residual}.
1793 @arg xs: Iterable of items to add (each item C{scalar},
1794 an L{Fsum} or L{Fsum2Tuple}).
1795 @kwarg name: Optional C{B{name}=NN} (C{str}).
1797 @return: L{Fsum2Tuple}C{(fsum, residual)} with C{fsum} the
1798 current precision running sum and C{residual}, the
1799 (precision) sum of the remaining C{partials}. The
1800 C{residual is INT0} if the C{fsum} is considered
1801 to be I{exact}.
1803 @see: Methods L{Fsum.fint2}, L{Fsum.fsum} and L{Fsum.fsum2_}
1804 '''
1805 t = self._facc(xs)._fprs2
1806 return t.dup(name=name) if name else t
1808 def fsum2_(self, *xs):
1809 '''Add any positional items, summate and return the current
1810 precision running sum and the I{differential}.
1812 @arg xs: Values to add (each C{scalar}, an L{Fsum} or
1813 L{Fsum2Tuple}), all positional.
1815 @return: 2Tuple C{(fsum, delta)} with the current, precision
1816 running C{fsum} like method L{Fsum.fsum} and C{delta},
1817 the difference with previous running C{fsum}, C{float}.
1819 @see: Methods L{Fsum.fsum_} and L{Fsum.fsum}.
1820 '''
1821 return self._fsum2(xs, self._facc_args)
1823 def _fsum2(self, xs, _facc, **facc_kwds):
1824 '''(INTERNAL) Helper for L{Fsum.fsum2_} and L{Fsum.fsum2f_}.
1825 '''
1826 p, q = self._fprs2
1827 if xs:
1828 s, r = _facc(xs, **facc_kwds)._fprs2
1829 if _isfinite(s): # _fsum(_1primed((s, -p, r, -q))
1830 d, r = _2sum(s - p, r - q, _isfine=_isOK)
1831 r, _ = _s_r2(d, r)
1832 return s, (r if _isfinite(r) else _NONFINITEr)
1833 else:
1834 return p, _0_0
1836 def fsumf_(self, *xs):
1837 '''Like method L{Fsum.fsum_} iff I{all} C{B{xs}}, each I{known to be}
1838 C{scalar}, an L{Fsum} or L{Fsum2Tuple}.
1839 '''
1840 return self._facc_scalarf(xs, which=self.fsumf_)._fprs # origin=1?
1842 def Fsumf_(self, *xs):
1843 '''Like method L{Fsum.Fsum_} iff I{all} C{B{xs}}, each I{known to be}
1844 C{scalar}, an L{Fsum} or L{Fsum2Tuple}.
1845 '''
1846 return self._facc_scalarf(xs, which=self.Fsumf_)._copyd(self.Fsumf_) # origin=1?
1848 def fsum2f_(self, *xs):
1849 '''Like method L{Fsum.fsum2_} iff I{all} C{B{xs}}, each I{known to be}
1850 C{scalar}, an L{Fsum} or L{Fsum2Tuple}.
1851 '''
1852 return self._fsum2(xs, self._facc_scalarf, which=self.fsum2f_) # origin=1?
1854# ftruediv = __itruediv__ # for naming consistency?
1856 def _ftruediv(self, other, op, **raiser_RESIDUAL):
1857 '''(INTERNAL) Apply C{B{self} /= B{other}}.
1858 '''
1859 n = _1_0
1860 if _isFsum_2Tuple(other):
1861 if other is self or self == other:
1862 return self._fset(n, n=len(self))
1863 d, r = other._fprs2
1864 if r:
1865 R = self._raiser(r, d, **raiser_RESIDUAL)
1866 if R:
1867 raise self._ResidualError(op, other, r, **R)
1868 d, n = other.as_integer_ratio()
1869 else:
1870 d = self._scalar(other, op)
1871 try:
1872 s = n / d
1873 except Exception as X:
1874 raise self._ErrorX(X, op, other)
1875 f = self._mul_scalar(s, _mul_op_) # handles 0, INF, NAN
1876 return self._fset(f)
1878 @property_RO
1879 def imag(self):
1880 '''Get the C{imaginary} part of this instance (C{0.0}, always).
1882 @see: Property L{Fsum.real}.
1883 '''
1884 return _0_0
1886 def int_float(self, **raiser_RESIDUAL):
1887 '''Return this instance' current running sum as C{int} or C{float}.
1889 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore
1890 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}
1891 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.
1893 @return: This C{int} sum if this instance C{is_integer} and
1894 I{finite}, otherwise the C{float} sum if the residual
1895 is zero or not significant.
1897 @raise ResidualError: Non-zero, significant residual or invalid
1898 B{C{RESIDUAL}}.
1900 @see: Methods L{Fsum.fint}, L{Fsum.fint2}, L{Fsum.is_integer},
1901 L{Fsum.RESIDUAL} and property L{Fsum.as_iscalar}.
1902 '''
1903 s, r = self._fint2
1904 if r:
1905 s, r = self._fprs2
1906 if r: # PYCHOK no cover
1907 R = self._raiser(r, s, **raiser_RESIDUAL)
1908 if R:
1909 t = _stresidual(_non_zero_, r, **R)
1910 raise ResidualError(int_float=s, txt=t)
1911 s = float(s)
1912 return s
1914 def is_exact(self):
1915 '''Is this instance' running C{fsum} considered to be exact?
1916 (C{bool}), C{True} only if the C{residual is }L{INT0}.
1917 '''
1918 return self.residual is INT0
1920 def is_finite(self): # in .constants
1921 '''Is this instance C{finite}? (C{bool}).
1923 @see: Function L{isfinite<pygeodesy.isfinite>}.
1924 '''
1925 return _isfinite(sum(self._ps)) # == sum(self)
1927 def is_integer(self):
1928 '''Is this instance' running sum C{integer}? (C{bool}).
1930 @see: Methods L{Fsum.fint}, L{Fsum.fint2} and L{Fsum.is_scalar}.
1931 '''
1932 s, r = self._fint2
1933 return False if r else (_isfinite(s) and isint(s))
1935 def is_math_fma(self):
1936 '''Is accurate L{f2product} multiplication based on Python's C{math.fma}?
1938 @return: C{True} if accurate multiplication uses C{math.fma}, C{False}
1939 an C{fma} implementation as C{math.fma} or C{None}, a previous
1940 C{PyGeodesy} implementation.
1941 '''
1942 return (_2split3s is _passarg) or (False if _integer_ratio2 is None else None)
1944 def is_math_fsum(self):
1945 '''Are the summation functions L{fsum}, L{fsum_}, L{fsumf_}, L{fsum1},
1946 L{fsum1_} and L{fsum1f_} based on Python's C{math.fsum}?
1948 @return: C{True} if summation functions use C{math.fsum}, C{False}
1949 otherwise.
1950 '''
1951 return _sum is _fsum # _fsum.__module__ is fabs.__module__
1953 def is_scalar(self, **raiser_RESIDUAL):
1954 '''Is this instance' running sum C{scalar} with C{0} residual or with
1955 a residual I{ratio} not exceeding the RESIDUAL threshold?
1957 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore
1958 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}
1959 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.
1961 @return: C{True} if this instance' residual is C{0} or C{insignificant},
1962 i.e. its residual C{ratio} doesn't exceed the L{RESIDUAL
1963 <Fsum.RESIDUAL>} threshold (C{bool}).
1965 @raise ResidualError: Non-zero, significant residual or invalid
1966 B{C{RESIDUAL}}.
1968 @see: Methods L{Fsum.RESIDUAL} and L{Fsum.is_integer} and property
1969 L{Fsum.as_iscalar}.
1970 '''
1971 s, r = self._fprs2
1972 return False if r and self._raiser(r, s, **raiser_RESIDUAL) else True
1974 def _mul_Fsum(self, other, op):
1975 '''(INTERNAL) Return C{B{self} * B{other}} as L{Fsum} or C{0}.
1976 '''
1977 # assert _isFsum_2Tuple(other)
1978 if self._ps and other._ps:
1979 try:
1980 f = self._ps_mul(op, *other._ps) # NO .as_iscalar!
1981 except Exception as X:
1982 raise self._ErrorX(X, op, other)
1983 else:
1984 f = _0_0
1985 return f
1987 def _mul_reduce(self, *others):
1988 '''(INTERNAL) Like fmath.fprod for I{non-finite} C{other}s.
1989 '''
1990 r = _1_0
1991 for f in others:
1992 r *= sum(f._ps) if _isFsum_2Tuple(f) else float(f)
1993 return r
1995 def _mul_scalar(self, factor, op):
1996 '''(INTERNAL) Return C{B{self} * scalar B{factor}} as L{Fsum}, C{0.0} or C{self}.
1997 '''
1998 # assert isscalar(factor)
1999 if self._ps and self._finite(factor, op=op):
2000 f = self if factor == _1_0 else (
2001 self._neg if factor == _N_1_0 else
2002 self._ps_mul(op, factor).as_iscalar)
2003 else:
2004 f = _0_0
2005 return f
2007# @property_RO
2008# def _n_d(self):
2009# n, d = self.as_integer_ratio()
2010# return n / d
2012 @property_RO
2013 def _neg(self):
2014 '''(INTERNAL) Return C{Fsum(-self)} or scalar C{NEG0}.
2015 '''
2016 return _Psum(self._ps_neg) if self._ps else NEG0
2018 @property_RO
2019 def _nfprs2(self):
2020 '''(INTERNAL) Handle I{non-finite} C{_fprs2}.
2021 '''
2022 try: # to handle nonfiniterrors, etc.
2023 t = self._fprs2
2024 except (OverflowError, ValueError):
2025 t = Fsum2Tuple(sum(self._ps), _NONFINITEr)
2026 return t
2028 def nonfinites(self, *OK):
2029 '''Handle I{non-finite} C{float}s as C{inf}, C{INF}, C{NINF}, C{nan}
2030 and C{NAN} for this L{Fsum} or throw C{OverflowError} respectively
2031 C{ValueError} exceptions, overriding the L{nonfiniterrors} default.
2033 @arg OK: If omitted, leave the override unchanged, if C{True},
2034 I{non-finites} are C{OK}, if C{False} throw exceptions
2035 or if C{None} remove the override (C{bool} or C{None}).
2037 @return: The previous setting (C{bool} or C{None} if not set).
2039 @see: Function L{nonfiniterrors<fsums.nonfiniterrors>}.
2041 @note: Use property L{nonfinitesOK<Fsum.nonfinitesOK>} to determine
2042 whether I{non-finites} are C{OK} for this L{Fsum} and by the
2043 L{nonfiniterrors} default.
2044 '''
2045 _ks = Fsum._nonfinites_isfine_kwds
2046 if OK: # delattrof(self, _isfine=None)
2047 k = _xkwds_pop(self.__dict__, _isfine=None)
2048 if OK[0] is not None:
2049 self._isfine = _ks[bool(OK[0])]
2050 self._update()
2051 else: # getattrof(self, _isfine=None)
2052 k = _xkwds_get(self.__dict__, _isfine=None)
2053 # dict(map(reversed, _ks.items())).get(k, None)
2054 # raises a TypeError: unhashable type: 'dict'
2055 return True if k is _ks[True] else (
2056 False if k is _ks[False] else None)
2058 _nonfinites_isfine_kwds = {True: dict(_isfine=_isOK),
2059 False: dict(_isfine=_isfinite)}
2061 @property_RO
2062 def nonfinitesOK(self):
2063 '''Are I{non-finites} C{OK} for this L{Fsum} or by default? (C{bool}).
2064 '''
2065# nf = self.nonfinites()
2066# if nf is None:
2067# nf = not nonfiniterrors()
2068 return _isOK_or_finite(INF, **self._isfine)
2070 def _nonfiniteX(self, X, op, f, nonfinites=None, raiser=None):
2071 '''(INTERNAL) Handle a I{non-finite} exception.
2072 '''
2073 if nonfinites is None:
2074 nonfinites = _isOK_or_finite(f, **self._isfine) if raiser is None else (not raiser)
2075 if not nonfinites:
2076 raise self._ErrorX(X, op, f)
2077 return f
2079 def _optionals(self, f2product=None, nonfinites=None, **name_RESIDUAL):
2080 '''(INTERNAL) Re/set options from keyword arguments.
2081 '''
2082 if f2product is not None:
2083 self.f2product(f2product)
2084 if nonfinites is not None:
2085 self.nonfinites(nonfinites)
2086 if name_RESIDUAL: # MUST be last
2087 n, kwds = _name2__(**name_RESIDUAL)
2088 if kwds:
2089 R = Fsum._RESIDUAL
2090 t = _threshold(R, **kwds)
2091 if t != R:
2092 self._RESIDUAL = t
2093 if n:
2094 self.name = n # self.rename(n)
2096 def _1_Over(self, x, op, **raiser_RESIDUAL): # vs _1_over
2097 '''(INTERNAL) Return C{Fsum(1) / B{x}}.
2098 '''
2099 return self._Fsum_as(_1_0)._ftruediv(x, op, **raiser_RESIDUAL)
2101 @property_RO
2102 def partials(self):
2103 '''Get this instance' current, partial sums (C{tuple} of C{float}s).
2104 '''
2105 return tuple(self._ps)
2107 def pow(self, x, *mod, **raiser_RESIDUAL):
2108 '''Return C{B{self}**B{x}} as L{Fsum}.
2110 @arg x: The exponent (C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
2111 @arg mod: Optional modulus (C{int} or C{None}) for the 3-argument
2112 C{pow(B{self}, B{other}, B{mod})} version.
2113 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore
2114 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}
2115 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.
2117 @return: The C{pow(self, B{x})} or C{pow(self, B{x}, *B{mod})}
2118 result (L{Fsum}).
2120 @raise ResidualError: Non-zero, significant residual or invalid
2121 B{C{RESIDUAL}}.
2123 @note: If B{C{mod}} is given and C{None}, the result will be an
2124 C{integer} L{Fsum} provided this instance C{is_integer}
2125 or set to C{integer} by an L{Fsum.fint} call.
2127 @see: Methods L{Fsum.__ipow__}, L{Fsum.fint}, L{Fsum.is_integer}
2128 and L{Fsum.root}.
2129 '''
2130 f = self._copyd(self.pow)
2131 return f._fpow(x, _pow_op_, *mod, **raiser_RESIDUAL) # f = pow(f, x, *mod)
2133 def _pow(self, other, unused, op, **raiser_RESIDUAL):
2134 '''Return C{B{self} ** B{other}}.
2135 '''
2136 if _isFsum_2Tuple(other):
2137 f = self._pow_Fsum(other, op, **raiser_RESIDUAL)
2138 elif self._scalar(other, op):
2139 x = self._finite(other, op=op)
2140 f = self._pow_scalar(x, other, op, **raiser_RESIDUAL)
2141 else:
2142 f = self._pow_0_1(0, other)
2143 return f
2145 def _pow_0_1(self, x, other):
2146 '''(INTERNAL) Return B{C{self}**1} or C{B{self}**0 == 1.0}.
2147 '''
2148 return self if x else (1 if isint(other) and self.is_integer() else _1_0)
2150 def _pow_2_3(self, b, x, other, op, *mod, **raiser_RESIDUAL):
2151 '''(INTERNAL) 2-arg C{pow(B{b}, scalar B{x})} and 3-arg C{pow(B{b},
2152 B{x}, int B{mod} or C{None})}, embellishing errors.
2153 '''
2155 if mod: # b, x, mod all C{int}, unless C{mod} is C{None}
2156 m = mod[0]
2157 # assert _isFsum_2Tuple(b)
2159 def _s(s, r):
2160 R = self._raiser(r, s, **raiser_RESIDUAL)
2161 if R:
2162 raise self._ResidualError(op, other, r, mod=m, **R)
2163 return s
2165 b = _s(*(b._fprs2 if m is None else b._fint2))
2166 x = _s(*_2tuple2(x))
2168 try:
2169 # 0**INF == 0.0, 1**INF == 1.0, -1**2.3 == -(1**2.3)
2170 s = pow(b, x, *mod)
2171 if iscomplex(s):
2172 # neg**frac == complex in Python 3+, but ValueError in 2-
2173 raise ValueError(_strcomplex(s, b, x, *mod))
2174 _ = _2finite(s, **self._isfine) # ignore float
2175 return s
2176 except Exception as X:
2177 raise self._ErrorX(X, op, other, *mod)
2179 def _pow_Fsum(self, other, op, **raiser_RESIDUAL):
2180 '''(INTERNAL) Return C{B{self} **= B{other}} for C{_isFsum_2Tuple(other)}.
2181 '''
2182 # assert _isFsum_2Tuple(other)
2183 x, r = other._fprs2
2184 f = self._pow_scalar(x, other, op, **raiser_RESIDUAL)
2185 if f and r:
2186 f *= self._pow_scalar(r, other, op, **raiser_RESIDUAL)
2187 return f
2189 def _pow_int(self, x, other, op, **raiser_RESIDUAL):
2190 '''(INTERNAL) Return C{B{self} **= B{x}} for C{int B{x} >= 0}.
2191 '''
2192 # assert isint(x) and x >= 0
2193 ps = self._ps
2194 if len(ps) > 1:
2195 _mul_Fsum = Fsum._mul_Fsum
2196 if x > 4:
2197 p = self
2198 f = self if (x & 1) else self._Fsum_as(_1_0)
2199 m = x >> 1 # // 2
2200 while m:
2201 p = _mul_Fsum(p, p, op) # p **= 2
2202 if (m & 1):
2203 f = _mul_Fsum(f, p, op) # f *= p
2204 m >>= 1 # //= 2
2205 elif x > 1: # self**2, 3, or 4
2206 f = _mul_Fsum(self, self, op)
2207 if x > 2: # self**3 or 4
2208 p = self if x < 4 else f
2209 f = _mul_Fsum(f, p, op)
2210 else: # self**1 or self**0 == 1 or _1_0
2211 f = self._pow_0_1(x, other)
2212 elif ps: # self._ps[0]**x
2213 f = self._pow_2_3(ps[0], x, other, op, **raiser_RESIDUAL)
2214 else: # PYCHOK no cover
2215 # 0**pos_int == 0, but 0**0 == 1
2216 f = 0 if x else 1
2217 return f
2219 def _pow_scalar(self, x, other, op, **raiser_RESIDUAL):
2220 '''(INTERNAL) Return C{self**B{x}} for C{scalar B{x}}.
2221 '''
2222 s, r = self._fprs2
2223 if r:
2224 # assert s != 0
2225 if isint(x, both=True): # self**int
2226 x = int(x)
2227 y = abs(x)
2228 if y > 1:
2229 f = self._pow_int(y, other, op, **raiser_RESIDUAL)
2230 if x > 0: # i.e. > 1
2231 return f # Fsum or scalar
2232 # assert x < 0 # i.e. < -1
2233 if _isFsum(f):
2234 s, r = f._fprs2
2235 if r:
2236 return self._1_Over(f, op, **raiser_RESIDUAL)
2237 else: # scalar
2238 s = f
2239 # use s**(-1) to get the CPython
2240 # float_pow error iff s is zero
2241 x = -1
2242 elif x < 0: # self**(-1)
2243 return self._1_Over(self, op, **raiser_RESIDUAL) # 1 / self
2244 else: # self**1 or self**0
2245 return self._pow_0_1(x, other) # self, 1 or 1.0
2246 else: # self**fractional
2247 R = self._raiser(r, s, **raiser_RESIDUAL)
2248 if R:
2249 raise self._ResidualError(op, other, r, **R)
2250 n, d = self.as_integer_ratio()
2251 if abs(n) > abs(d):
2252 n, d, x = d, n, (-x)
2253 s = n / d
2254 # assert isscalar(s) and isscalar(x)
2255 return self._pow_2_3(s, x, other, op, **raiser_RESIDUAL)
2257 def _ps_acc(self, ps, xs, up=True, **unused):
2258 '''(INTERNAL) Accumulate C{xs} known scalars into list C{ps}.
2259 '''
2260 n = 0
2261 _2s = _2sum
2262 _fi = self._isfine
2263 for x in (tuple(xs) if xs is ps else xs):
2264 # assert isscalar(x) and _isOK_or_finite(x, **self._isfine)
2265 if x:
2266 i = 0
2267 for p in ps:
2268 x, p = _2s(x, p, **_fi)
2269 if p:
2270 ps[i] = p
2271 i += 1
2272 ps[i:] = (x,) if x else ()
2273 n += 1
2274 if n:
2275 self._n += n
2276 # Fsum._ps_max = max(Fsum._ps_max, len(ps))
2277 if up:
2278 self._update()
2279# x = sum(ps)
2280# if not _isOK_or_finite(x, **fi):
2281# ps[:] = x, # collapse ps
2282 return ps
2284 def _ps_mul(self, op, *factors):
2285 '''(INTERNAL) Multiply this instance' C{partials} with
2286 each scalar C{factor} and accumulate into an C{Fsum}.
2287 '''
2288 def _psfs(ps, fs, _isfine=_isfinite):
2289 if len(ps) < len(fs):
2290 ps, fs = fs, ps
2291 if self._f2product:
2292 fs, p = _2split3s(fs), fs
2293 if len(ps) > 1 and fs is not p:
2294 fs = tuple(fs) # several ps
2295 _pfs = _2products
2296 else:
2297 def _pfs(p, fs):
2298 return (p * f for f in fs)
2300 for p in ps:
2301 for x in _pfs(p, fs):
2302 yield x if _isfine(x) else _nfError(x)
2304 xs = _psfs(self._ps, factors, **self._isfine)
2305 f = _Psum(self._ps_acc([], xs, up=False), name=op)
2306 return f
2308 @property_RO
2309 def _ps_neg(self):
2310 '''(INTERNAL) Yield the partials, I{negated}.
2311 '''
2312 for p in self._ps:
2313 yield -p
2315 def _ps_other(self, op, other):
2316 '''(INTERNAL) Yield C{other} as C{scalar}s.
2317 '''
2318 if _isFsum_2Tuple(other):
2319 for p in other._ps:
2320 yield p
2321 else:
2322 yield self._scalar(other, op)
2324 def _ps_1sum(self, *less):
2325 '''(INTERNAL) Return the partials sum, 1-primed C{less} some scalars.
2326 '''
2327 def _1psls(ps, ls):
2328 yield _1_0
2329 for p in ps:
2330 yield p
2331 for p in ls:
2332 yield -p
2333 yield _N_1_0
2335 return _fsum(_1psls(self._ps, less))
2337 def _raiser(self, r, s, raiser=True, **RESIDUAL):
2338 '''(INTERNAL) Does ratio C{r / s} exceed the RESIDUAL threshold
2339 I{and} is residual C{r} I{non-zero} or I{significant} (for a
2340 negative respectively positive C{RESIDUAL} threshold)?
2341 '''
2342 if r and raiser:
2343 t = self._RESIDUAL
2344 if RESIDUAL:
2345 t = _threshold(t, **RESIDUAL)
2346 if t < 0 or (s + r) != s:
2347 q = (r / s) if s else s # == 0.
2348 if fabs(q) > fabs(t):
2349 return dict(ratio=q, R=t)
2350 return {}
2352 def _rcopyd(self, other, which):
2353 '''(INTERNAL) Copy for I{reverse-dyadic} operators.
2354 '''
2355 return other._copyd(which) if _isFsum(other) else \
2356 self._copyd(which)._fset(other)
2358 rdiv = __rtruediv__
2360 @property_RO
2361 def real(self):
2362 '''Get the C{real} part of this instance (C{float}).
2364 @see: Methods L{Fsum.__float__} and L{Fsum.fsum}
2365 and properties L{Fsum.ceil}, L{Fsum.floor},
2366 L{Fsum.imag} and L{Fsum.residual}.
2367 '''
2368 return float(self)
2370 @property_RO
2371 def residual(self):
2372 '''Get this instance' residual or residue (C{float} or C{int}):
2373 the C{sum(partials)} less the precision running sum C{fsum}.
2375 @note: The C{residual is INT0} iff the precision running
2376 C{fsum} is considered to be I{exact}.
2378 @see: Methods L{Fsum.fsum}, L{Fsum.fsum2} and L{Fsum.is_exact}.
2379 '''
2380 return self._fprs2.residual
2382 def RESIDUAL(self, *threshold):
2383 '''Get and set this instance' I{ratio} for raising L{ResidualError}s,
2384 overriding the default from env variable C{PYGEODESY_FSUM_RESIDUAL}.
2386 @arg threshold: If C{scalar}, the I{ratio} to exceed for raising
2387 L{ResidualError}s in division and exponention, if
2388 C{None}, restore the default set with env variable
2389 C{PYGEODESY_FSUM_RESIDUAL} or if omitted, keep the
2390 current setting.
2392 @return: The previous C{RESIDUAL} setting (C{float}), default C{0.0}.
2394 @raise ResidualError: Invalid B{C{threshold}}.
2396 @note: L{ResidualError}s may be thrown if (1) the non-zero I{ratio}
2397 C{residual / fsum} exceeds the given B{C{threshold}} and (2)
2398 the C{residual} is non-zero and (3) is I{significant} vs the
2399 C{fsum}, i.e. C{(fsum + residual) != fsum} and (4) optional
2400 keyword argument C{raiser=False} is missing. Specify a
2401 negative B{C{threshold}} for only non-zero C{residual}
2402 testing without the I{significant} case.
2403 '''
2404 r = self._RESIDUAL
2405 if threshold:
2406 t = threshold[0]
2407 self._RESIDUAL = Fsum._RESIDUAL if t is None else ( # for ...
2408 (_0_0 if t else _1_0) if isbool(t) else
2409 _threshold(t)) # ... backward compatibility
2410 return r
2412 def _ResidualError(self, op, other, residual, **mod_R):
2413 '''(INTERNAL) Non-zero B{C{residual}} etc.
2414 '''
2415 def _p(mod=None, R=0, **unused): # ratio=0
2416 return (_non_zero_ if R < 0 else _significant_) \
2417 if mod is None else _integer_
2419 t = _stresidual(_p(**mod_R), residual, **mod_R)
2420 return self._Error(op, other, ResidualError, txt=t)
2422 def root(self, root, **raiser_RESIDUAL):
2423 '''Return C{B{self}**(1 / B{root})} as L{Fsum}.
2425 @arg root: Non-zero order (C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
2426 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore any
2427 L{ResidualError}s (C{bool}) or C{B{RESIDUAL}=scalar}
2428 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.
2430 @return: The C{self ** (1 / B{root})} result (L{Fsum}).
2432 @raise ResidualError: Non-zero, significant residual or invalid
2433 B{C{RESIDUAL}}.
2435 @see: Method L{Fsum.pow}.
2436 '''
2437 x = self._1_Over(root, _truediv_op_, **raiser_RESIDUAL)
2438 f = self._copyd(self.root)
2439 return f._fpow(x, f.name, **raiser_RESIDUAL) # == pow(f, x)
2441 def _scalar(self, other, op, **txt):
2442 '''(INTERNAL) Return scalar C{other} or throw a C{TypeError}.
2443 '''
2444 if isscalar(other):
2445 return other
2446 raise self._Error(op, other, _TypeError, **txt) # _invalid_
2448 def signOf(self, res=True):
2449 '''Determine the sign of this instance.
2451 @kwarg res: If C{True}, consider the residual,
2452 otherwise ignore the latter (C{bool}).
2454 @return: The sign (C{int}, -1, 0 or +1).
2455 '''
2456 s, r = self._nfprs2
2457 r = (-r) if res else 0
2458 return _signOf(s, r)
2460 def toRepr(self, **lenc_prec_sep_fmt): # PYCHOK signature
2461 '''Return this C{Fsum} instance as representation.
2463 @kwarg lenc_prec_sep_fmt: Optional keyword arguments
2464 for method L{Fsum.toStr}.
2466 @return: This instance (C{repr}).
2467 '''
2468 return Fmt.repr_at(self, self.toStr(**lenc_prec_sep_fmt))
2470 def toStr(self, lenc=True, **prec_sep_fmt): # PYCHOK signature
2471 '''Return this C{Fsum} instance as string.
2473 @kwarg lenc: If C{True}, include the current C{[len]} of this
2474 L{Fsum} enclosed in I{[brackets]} (C{bool}).
2475 @kwarg prec_sep_fmt: Optional keyword arguments for method
2476 L{Fsum2Tuple.toStr}.
2478 @return: This instance (C{str}).
2479 '''
2480 p = self.classname
2481 if lenc:
2482 p = Fmt.SQUARE(p, len(self))
2483 n = _enquote(self.name, white=_UNDER_)
2484 t = self._nfprs2.toStr(**prec_sep_fmt)
2485 return NN(p, _SPACE_, n, t)
2487 def _truediv(self, other, op, **raiser_RESIDUAL):
2488 '''(INTERNAL) Return C{B{self} / B{other}} as an L{Fsum}.
2489 '''
2490 f = self._copyd(self.__truediv__)
2491 return f._ftruediv(other, op, **raiser_RESIDUAL)
2493 def _update(self, updated=True): # see ._fset
2494 '''(INTERNAL) Zap all cached C{Property_RO} values.
2495 '''
2496 if updated:
2497 _pop = self.__dict__.pop
2498 for p in _ROs:
2499 _ = _pop(p, None)
2500# Fsum._fint2._update(self)
2501# Fsum._fprs ._update(self)
2502# Fsum._fprs2._update(self)
2503 return self # for .fset_
2505_ROs = _allPropertiesOf_n(3, Fsum, Property_RO) # PYCHOK see Fsum._update
2507if _NONFINITES == _std_: # PYCHOK no cover
2508 _ = nonfiniterrors(False)
2511def _Float_Int(arg, **name_Error):
2512 '''(INTERNAL) L{DivMod2Tuple}, L{Fsum2Tuple} Unit.
2513 '''
2514 U = Int if isint(arg) else Float
2515 return U(arg, **name_Error)
2518class DivMod2Tuple(_NamedTuple):
2519 '''2-Tuple C{(div, mod)} with the quotient C{div} and remainder
2520 C{mod} results of a C{divmod} operation.
2522 @note: Quotient C{div} an C{int} in Python 3+ but a C{float}
2523 in Python 2-. Remainder C{mod} an L{Fsum} instance.
2524 '''
2525 _Names_ = ('div', 'mod')
2526 _Units_ = (_Float_Int, Fsum)
2529class Fsum2Tuple(_NamedTuple): # in .fstats
2530 '''2-Tuple C{(fsum, residual)} with the precision running C{fsum}
2531 and the C{residual}, the sum of the remaining partials. Each
2532 item is C{float} or C{int}.
2534 @note: If the C{residual is INT0}, the C{fsum} is considered
2535 to be I{exact}, see method L{Fsum2Tuple.is_exact}.
2536 '''
2537 _Names_ = ( typename(Fsum.fsum), Fsum.residual.name)
2538 _Units_ = (_Float_Int, _Float_Int)
2540 def __abs__(self): # in .fmath
2541 return self._Fsum.__abs__()
2543 def __bool__(self): # PYCHOK Python 3+
2544 return bool(self._Fsum)
2546 def __eq__(self, other):
2547 return self._other_op(other, self.__eq__)
2549 def __float__(self):
2550 return self._Fsum.__float__()
2552 def __ge__(self, other):
2553 return self._other_op(other, self.__ge__)
2555 def __gt__(self, other):
2556 return self._other_op(other, self.__gt__)
2558 def __le__(self, other):
2559 return self._other_op(other, self.__le__)
2561 def __lt__(self, other):
2562 return self._other_op(other, self.__lt__)
2564 def __int__(self):
2565 return self._Fsum.__int__()
2567 def __ne__(self, other):
2568 return self._other_op(other, self.__ne__)
2570 def __neg__(self):
2571 return self._Fsum.__neg__()
2573 __nonzero__ = __bool__ # Python 2-
2575 def __pos__(self):
2576 return self._Fsum.__pos__()
2578 def as_integer_ratio(self):
2579 '''Return this instance as the ratio of 2 integers.
2581 @see: Method L{Fsum.as_integer_ratio} for further details.
2582 '''
2583 return self._Fsum.as_integer_ratio()
2585 @property_RO
2586 def _fint2(self):
2587 return self._Fsum._fint2
2589 @property_RO
2590 def _fprs2(self):
2591 return self._Fsum._fprs2
2593 @Property_RO
2594 def _Fsum(self): # this C{Fsum2Tuple} as L{Fsum}, in .fstats
2595 s, r = _s_r2(*self)
2596 ps = (r, s) if r else (s,)
2597 return _Psum(ps, name=self.name)
2599 def Fsum_(self, *xs, **name_f2product_nonfinites_RESIDUAL):
2600 '''Return this C{Fsum2Tuple} as an L{Fsum} plus some C{xs}.
2601 '''
2602 return Fsum(self, *xs, **name_f2product_nonfinites_RESIDUAL)
2604 def is_exact(self):
2605 '''Is this L{Fsum2Tuple} considered to be exact? (C{bool}).
2606 '''
2607 return self._Fsum.is_exact()
2609 def is_finite(self): # in .constants
2610 '''Is this L{Fsum2Tuple} C{finite}? (C{bool}).
2612 @see: Function L{isfinite<pygeodesy.isfinite>}.
2613 '''
2614 return self._Fsum.is_finite()
2616 def is_integer(self):
2617 '''Is this L{Fsum2Tuple} C{integer}? (C{bool}).
2618 '''
2619 return self._Fsum.is_integer()
2621 def _mul_scalar(self, other, op): # for Fsum._fmul
2622 return self._Fsum._mul_scalar(other, op)
2624 @property_RO
2625 def _n(self):
2626 return self._Fsum._n
2628 def _other_op(self, other, which):
2629 C, s = (tuple, self) if isinstance(other, tuple) else (Fsum, self._Fsum)
2630 return getattr(C, typename(which))(s, other)
2632 @property_RO
2633 def _ps(self):
2634 return self._Fsum._ps
2636 @property_RO
2637 def _ps_neg(self):
2638 return self._Fsum._ps_neg
2640 def signOf(self, **res):
2641 '''Like method L{Fsum.signOf}.
2642 '''
2643 return self._Fsum.signOf(**res)
2645 def toStr(self, fmt=Fmt.g, **prec_sep): # PYCHOK signature
2646 '''Return this L{Fsum2Tuple} as string (C{str}).
2648 @kwarg fmt: Optional C{float} format (C{letter}).
2649 @kwarg prec_sep: Optional keyword arguments for function
2650 L{fstr<streprs.fstr>}.
2651 '''
2652 return Fmt.PAREN(fstr(self, fmt=fmt, strepr=str, force=False, **prec_sep))
2654_Fsum_2Tuple_types = Fsum, Fsum2Tuple # PYCHOK lines
2657class ResidualError(_ValueError):
2658 '''Error raised for a division, power or root operation of
2659 an L{Fsum} instance with a C{residual} I{ratio} exceeding
2660 the L{RESIDUAL<Fsum.RESIDUAL>} threshold.
2662 @see: Module L{pygeodesy.fsums} and method L{Fsum.RESIDUAL}.
2663 '''
2664 pass
2667try:
2668 from math import fsum as _fsum # precision IEEE-754 sum, Python 2.6+
2670 # make sure _fsum works as expected (XXX check
2671 # float.__getformat__('float')[:4] == 'IEEE'?)
2672 if _fsum((1, 1e101, 1, -1e101)) != 2: # PYCHOK no cover
2673 del _fsum # nope, remove _fsum ...
2674 raise ImportError() # ... use _fsum below
2676 _sum = _fsum # in .elliptic
2677except ImportError:
2678 _sum = sum # in .elliptic
2680 def _fsum(xs):
2681 '''(INTERNAL) Precision summation, Python 2.5-.
2682 '''
2683 F = Fsum(name=_fsum.name, f2product=False, nonfinites=True)
2684 return float(F._facc(xs, up=False))
2687def fsum(xs, nonfinites=None, **floats):
2688 '''Precision floating point summation from Python's C{math.fsum}.
2690 @arg xs: Iterable of items to add (each C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
2691 @kwarg nonfinites: Use C{B{nonfinites}=True} if I{non-finites} are C{OK}, if
2692 C{False} I{non-finites} raise an Overflow-/ValueError or if
2693 C{None}, L{nonfiniterrors} applies (C{bool} or C{None}).
2694 @kwarg floats: DEPRECATED keyword argument C{B{floats}=False} (C{bool}), use
2695 keyword argument C{B{nonfinites}=False} instead.
2697 @return: Precision C{fsum} (C{float}).
2699 @raise OverflowError: Infinite B{C{xs}} item or intermediate C{math.fsum} overflow.
2701 @raise TypeError: Invalid B{C{xs}} item.
2703 @raise ValueError: Invalid or C{NAN} B{C{xs}} item.
2705 @see: Function L{nonfiniterrors}, class L{Fsum} and methods L{Fsum.nonfinites},
2706 L{Fsum.fsum}, L{Fsum.fadd} and L{Fsum.fadd_}.
2707 '''
2708 return _xsum(fsum, xs, nonfinites=nonfinites, **floats) if xs else _0_0
2711def fsum_(*xs, **nonfinites):
2712 '''Precision floating point summation of all positional items.
2714 @arg xs: Items to add (each C{scalar}, an L{Fsum} or L{Fsum2Tuple}), all positional.
2715 @kwarg nonfinites: Use C{B{nonfinites}=True} if I{non-finites} are C{OK} (C{bool}).
2717 @see: Function L{fsum<fsums.fsum>} for further details.
2718 '''
2719 return _xsum(fsum_, xs, **nonfinites) if xs else _0_0 # origin=1?
2722def fsumf_(*xs):
2723 '''Precision floating point summation of all positional items with I{non-finites} C{OK}.
2725 @arg xs: Items to add (each C{scalar}, an L{Fsum} or L{Fsum2Tuple}),
2726 all positional.
2728 @see: Function L{fsum_<fsums.fsum_>} for further details.
2729 '''
2730 return _xsum(fsumf_, xs, nonfinites=True) if xs else _0_0 # origin=1?
2733def fsum1(xs, **nonfinites):
2734 '''Precision floating point summation, 1-primed.
2736 @arg xs: Iterable of items to add (each C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
2737 @kwarg nonfinites: Use C{B{nonfinites}=True} if I{non-finites} are C{OK} (C{bool}).
2739 @see: Function L{fsum<fsums.fsum>} for further details.
2740 '''
2741 return _xsum(fsum1, xs, primed=1, **nonfinites) if xs else _0_0
2744def fsum1_(*xs, **nonfinites):
2745 '''Precision floating point summation of all positional items, 1-primed.
2747 @arg xs: Items to add (each C{scalar}, an L{Fsum} or L{Fsum2Tuple}), all positional.
2748 @kwarg nonfinites: Use C{B{nonfinites}=True} if I{non-finites} are C{OK} (C{bool}).
2750 @see: Function L{fsum_<fsums.fsum_>} for further details.
2751 '''
2752 return _xsum(fsum1_, xs, primed=1, **nonfinites) if xs else _0_0 # origin=1?
2755def fsum1f_(*xs):
2756 '''Precision floating point summation of all positional items, 1-primed and
2757 with I{non-finites} C{OK}.
2759 @see: Function L{fsum_<fsums.fsum_>} for further details.
2760 '''
2761 return _xsum(fsum1f_, xs, nonfinites=True, primed=1) if xs else _0_0
2764def _x_isfine(nfOK, **kwds): # get the C{_x} and C{_isfine} handlers.
2765 _x_kwds = dict(_x= (_passarg if nfOK else _2finite),
2766 _isfine=(_isOK if nfOK else _isfinite)) # PYCHOK kwds
2767 _x_kwds.update(kwds)
2768 return _x_kwds
2771def _X_ps(X): # default C{_X} handler
2772 return X._ps # lambda X: X._ps
2775def _xs(xs, _X=_X_ps, _x=float, _isfine=_isfinite, # defaults for Fsum._facc
2776 origin=0, which=None, **_Cdot):
2777 '''(INTERNAL) Yield each C{xs} item as 1 or more C{float}s.
2778 '''
2779 i, x = 0, xs
2780 try:
2781 for i, x in enumerate(_xiterable(xs)):
2782 if _isFsum_2Tuple(x):
2783 for p in _X(x):
2784 yield p if _isfine(p) else _nfError(p)
2785 else:
2786 f = _x(x)
2787 yield f if _isfine(f) else _nfError(f)
2789 except (OverflowError, TypeError, ValueError) as X:
2790 t = _xsError(X, xs, i + origin, x)
2791 if which: # prefix invokation
2792 w = unstr(which, *xs, _ELLIPSIS=4, **_Cdot)
2793 t = _COMMASPACE_(w, t)
2794 raise _xError(X, t, txt=None)
2797def _xsum(which, xs, nonfinites=None, primed=0, **floats): # origin=0
2798 '''(INTERNAL) Precision summation of C{xs} with conditions.
2799 '''
2800 if floats: # for backward compatibility
2801 nonfinites = _xkwds_get1(floats, floats=nonfinites)
2802 elif nonfinites is None:
2803 nonfinites = not nonfiniterrors()
2804 fs = _xs(xs, **_x_isfine(nonfinites, which=which)) # PYCHOK yield
2805 return _fsum(_1primed(fs) if primed else fs)
2808# delete all decorators, etc.
2809del _allPropertiesOf_n, deprecated_method, deprecated_property_RO, \
2810 Property, Property_RO, property_RO, _ALL_LAZY, _F2PRODUCT, \
2811 MANT_DIG, _NONFINITES, _RESIDUAL_0_0, _envPYGEODESY, _std_
2813if __name__ == _DMAIN_:
2815 # usage: python3 -m pygeodesy.fsums
2817 def _test(n):
2818 # copied from Hettinger, see L{Fsum} reference
2819 from pygeodesy import frandoms, printf
2821 printf(typename(_fsum), end=_COMMASPACE_)
2822 printf(typename(_psum), end=_COMMASPACE_)
2824 F = Fsum()
2825 if F.is_math_fsum():
2826 for t in frandoms(n, seeded=True):
2827 assert float(F.fset_(*t)) == _fsum(t)
2828 printf(_DOT_, end=NN)
2829 printf(NN)
2831 _test(128)
2833# **) MIT License
2834#
2835# Copyright (C) 2016-2025 -- mrJean1 at Gmail -- All Rights Reserved.
2836#
2837# Permission is hereby granted, free of charge, to any person obtaining a
2838# copy of this software and associated documentation files (the "Software"),
2839# to deal in the Software without restriction, including without limitation
2840# the rights to use, copy, modify, merge, publish, distribute, sublicense,
2841# and/or sell copies of the Software, and to permit persons to whom the
2842# Software is furnished to do so, subject to the following conditions:
2843#
2844# The above copyright notice and this permission notice shall be included
2845# in all copies or substantial portions of the Software.
2846#
2847# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
2848# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
2849# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
2850# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
2851# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
2852# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
2853# OTHER DEALINGS IN THE SOFTWARE.