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, isodd, isscalar, \
43 _signOf, itemsorted, signOf, _xiterable
44from pygeodesy.constants import INF, INT0, MANT_DIG, NEG0, NINF, _0_0, _1_0, \
45 _N_1_0, _isfinite, _pos_self, Float, Int
46from pygeodesy.errors import _AssertionError, _OverflowError, LenError, _TypeError, \
47 _ValueError, _xError, _xError2, _xkwds, _xkwds_get, \
48 _xkwds_get1, _xkwds_not, _xkwds_pop, _xsError
49from pygeodesy.internals import _enquote, _envPYGEODESY, _passarg, typename # _sizeof
50from pygeodesy.interns import NN, _arg_, _COMMASPACE_, _DMAIN_, _DOT_, _from_, \
51 _not_finite_, _SPACE_, _std_, _UNDER_
52# from pygeodesy.lazily import _ALL_LAZY, _ALL_MODS as _MODS # from .named
53from pygeodesy.named import _name__, _name2__, _Named, _NamedTuple, \
54 _NotImplemented, _ALL_LAZY, _MODS
55from pygeodesy.props import _allPropertiesOf_n, deprecated_method, \
56 deprecated_property_RO, Property, \
57 Property_RO, property_RO
58from pygeodesy.streprs import Fmt, fstr, unstr
59# from pygeodesy.units import Float, Int # from .constants
61from math import fabs, isinf, isnan, \
62 ceil as _ceil, floor as _floor # PYCHOK used! .ltp
64__all__ = _ALL_LAZY.fsums
65__version__ = '25.06.03'
67from pygeodesy.interns import (
68 _PLUS_ as _add_op_, # in .auxilats.auxAngle
69 _DSLASH_ as _floordiv_op_,
70 _EQUAL_ as _fset_op_,
71 _RANGLE_ as _gt_op_,
72 _LANGLE_ as _lt_op_,
73 _PERCENT_ as _mod_op_,
74 _STAR_ as _mul_op_,
75 _NOTEQUAL_ as _ne_op_,
76 _DSTAR_ as _pow_op_,
77 _DASH_ as _sub_op_, # in .auxilats.auxAngle
78 _SLASH_ as _truediv_op_
79)
80_divmod_op_ = _floordiv_op_ + _mod_op_
81_F2PRODUCT = _envPYGEODESY('FSUM_F2PRODUCT')
82_iadd_op_ = _add_op_ + _fset_op_ # in .auxilats.auxAngle, .fstats
83_integer_ = 'integer'
84_isub_op_ = _sub_op_ + _fset_op_ # in .auxilats.auxAngle
85_NONFINITEr = _0_0 # NOT INT0!
86_NONFINITES = _envPYGEODESY('FSUM_NONFINITES')
87_non_zero_ = 'non-zero'
88_RESIDUAL_0_0 = _envPYGEODESY('FSUM_RESIDUAL', _0_0)
89_significant_ = 'significant'
90_threshold_ = 'threshold'
93def _2finite(x, _isfine=_isfinite): # in .fstats
94 '''(INTERNAL) return C{float(x)} if finite.
95 '''
96 return (float(x) if _isfine(x) # and isscalar(x)
97 else _nfError(x))
100def _2float(index=None, _isfine=_isfinite, **name_x): # in .fmath, .fstats
101 '''(INTERNAL) Raise C{TypeError} or C{Overflow-/ValueError} if C{x} not finite.
102 '''
103 n, x = name_x.popitem() # _xkwds_item2(name_x)
104 try:
105 f = float(x)
106 return f if _isfine(f) else _nfError(x)
107 except Exception as X:
108 raise _xError(X, Fmt.INDEX(n, index), x)
111try: # MCCABE 26
112 from math import fma as _fma
114 def _2products(x, ys, *zs):
115 # yield(x * y for y in ys) + yield(z in zs)
116 # TwoProductFMA U{Algorithm 3.5
117 # <https://www.TUHH.De/ti3/paper/rump/OgRuOi05.pdf>}
118 for y in ys:
119 f = x * y
120 yield f
121 if _isfinite(f):
122 f = _fma(x, y, -f)
123 if f:
124 yield 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
563 def __ceil__(self): # PYCHOK not special in Python 2-
564 '''Return this instance' C{math.ceil} as C{int} or C{float}.
566 @return: An C{int} in Python 3+, but C{float} in Python 2-.
568 @see: Methods L{Fsum.__floor__} and property L{Fsum.ceil}.
569 '''
570 return self.ceil
572 def __cmp__(self, other): # PYCHOK no cover
573 '''Compare this with an other instance or C{scalar}, Python 2-.
575 @return: -1, 0 or +1 (C{int}).
577 @raise TypeError: Incompatible B{C{other}} C{type}.
578 '''
579 s = self._cmp_0(other, typename(self.cmp))
580 return _signOf(s, 0)
582 def __divmod__(self, other, **raiser_RESIDUAL):
583 '''Return C{divmod(B{self}, B{other})} as a L{DivMod2Tuple}
584 with quotient C{div} an C{int} in Python 3+ or C{float}
585 in Python 2- and remainder C{mod} an L{Fsum} instance.
587 @arg other: Modulus (C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
588 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore
589 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}
590 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.
592 @raise ResidualError: Non-zero, significant residual or invalid
593 B{C{RESIDUAL}}.
595 @see: Method L{Fsum.fdiv}.
596 '''
597 f = self._copyd(self.__divmod__)
598 return f._fdivmod2(other, _divmod_op_, **raiser_RESIDUAL)
600 def __eq__(self, other):
601 '''Return C{(B{self} == B{other})} as C{bool} where B{C{other}}
602 is C{scalar}, an other L{Fsum} or L{Fsum2Tuple}.
603 '''
604 return self._cmp_0(other, _fset_op_ + _fset_op_) == 0
606 def __float__(self):
607 '''Return this instance' current, precision running sum as C{float}.
609 @see: Methods L{Fsum.fsum} and L{Fsum.int_float}.
610 '''
611 return float(self._fprs)
613 def __floor__(self): # PYCHOK not special in Python 2-
614 '''Return this instance' C{math.floor} as C{int} or C{float}.
616 @return: An C{int} in Python 3+, but C{float} in Python 2-.
618 @see: Methods L{Fsum.__ceil__} and property L{Fsum.floor}.
619 '''
620 return self.floor
622 def __floordiv__(self, other):
623 '''Return C{B{self} // B{other}} as an L{Fsum}.
625 @arg other: Divisor (C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
627 @return: The C{floor} quotient (L{Fsum}).
629 @see: Methods L{Fsum.__ifloordiv__}.
630 '''
631 f = self._copyd(self.__floordiv__)
632 return f._floordiv(other, _floordiv_op_)
634# def __format__(self, *other): # PYCHOK no cover
635# '''Not implemented.'''
636# return _NotImplemented(self, *other)
638 def __ge__(self, other):
639 '''Return C{(B{self} >= B{other})}, see C{__eq__}.
640 '''
641 return self._cmp_0(other, _gt_op_ + _fset_op_) >= 0
643 def __gt__(self, other):
644 '''Return C{(B{self} > B{other})}, see C{__eq__}.
645 '''
646 return self._cmp_0(other, _gt_op_) > 0
648 def __hash__(self): # PYCHOK no cover
649 '''Return C{hash(B{self})} as C{float}.
650 '''
651 # @see: U{Notes for type implementors<https://docs.Python.org/
652 # 3/library/numbers.html#numbers.Rational>}
653 return hash(self.partials) # tuple.__hash__()
655 def __iadd__(self, other):
656 '''Apply C{B{self} += B{other}} to this instance.
658 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar} value or
659 an iterable of several of the former.
661 @return: This instance, updated (L{Fsum}).
663 @raise TypeError: Invalid B{C{other}}, not
664 C{scalar} nor L{Fsum}.
666 @see: Methods L{Fsum.fadd_} and L{Fsum.fadd}.
667 '''
668 try:
669 return self._fadd(other, op=_iadd_op_)
670 except TypeError:
671 pass
672 _xiterable(other)
673 return self._facc(other)
675 def __ifloordiv__(self, other):
676 '''Apply C{B{self} //= B{other}} to this instance.
678 @arg other: Divisor (C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
680 @return: This instance, updated (L{Fsum}).
682 @raise ResidualError: Non-zero, significant residual
683 in B{C{other}}.
685 @raise TypeError: Invalid B{C{other}} type.
687 @raise ValueError: Invalid or I{non-finite} B{C{other}}.
689 @raise ZeroDivisionError: Zero B{C{other}}.
691 @see: Methods L{Fsum.__itruediv__}.
692 '''
693 return self._floordiv(other, _floordiv_op_ + _fset_op_)
695 def __imatmul__(self, other): # PYCHOK no cover
696 '''Not implemented.'''
697 return _NotImplemented(self, other)
699 def __imod__(self, other):
700 '''Apply C{B{self} %= B{other}} to this instance.
702 @arg other: Modulus (C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
704 @return: This instance, updated (L{Fsum}).
706 @see: Method L{Fsum.__divmod__}.
707 '''
708 return self._fdivmod2(other, _mod_op_ + _fset_op_).mod
710 def __imul__(self, other):
711 '''Apply C{B{self} *= B{other}} to this instance.
713 @arg other: Factor (C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
715 @return: This instance, updated (L{Fsum}).
717 @raise OverflowError: Partial C{2sum} overflow.
719 @raise TypeError: Invalid B{C{other}} type.
721 @raise ValueError: Invalid or I{non-finite} B{C{other}}.
722 '''
723 return self._fmul(other, _mul_op_ + _fset_op_)
725 def __int__(self):
726 '''Return this instance as an C{int}.
728 @see: Method L{Fsum.int_float} and properties L{Fsum.ceil}
729 and L{Fsum.floor}.
730 '''
731 i, _ = self._fint2
732 return i
734 def __invert__(self): # PYCHOK no cover
735 '''Not implemented.'''
736 # Luciano Ramalho, "Fluent Python", O'Reilly, 2nd Ed, 2022 p. 567
737 return _NotImplemented(self)
739 def __ipow__(self, other, *mod, **raiser_RESIDUAL): # PYCHOK 2 vs 3 args
740 '''Apply C{B{self} **= B{other}} to this instance.
742 @arg other: Exponent (C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
743 @arg mod: Optional modulus (C{int} or C{None}) for the 3-argument
744 C{pow(B{self}, B{other}, B{mod})} version.
745 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore
746 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}
747 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.
749 @return: This instance, updated (L{Fsum}).
751 @note: If B{C{mod}} is given, the result will be an C{integer}
752 L{Fsum} in Python 3+ if this instance C{is_integer} or
753 set to C{as_integer} and B{C{mod}} is given and C{None}.
755 @raise OverflowError: Partial C{2sum} overflow.
757 @raise ResidualError: Invalid B{C{RESIDUAL}} or the residual
758 is non-zero and significant and either
759 B{C{other}} is a fractional or negative
760 C{scalar} or B{C{mod}} is given and not
761 C{None}.
763 @raise TypeError: Invalid B{C{other}} type or 3-argument C{pow}
764 invocation failed.
766 @raise ValueError: If B{C{other}} is a negative C{scalar} and this
767 instance is C{0} or B{C{other}} is a fractional
768 C{scalar} and this instance is negative or has a
769 non-zero and significant residual or B{C{mod}}
770 is given as C{0}.
772 @see: CPython function U{float_pow<https://GitHub.com/
773 python/cpython/blob/main/Objects/floatobject.c>}.
774 '''
775 return self._fpow(other, _pow_op_ + _fset_op_, *mod, **raiser_RESIDUAL)
777 def __isub__(self, other):
778 '''Apply C{B{self} -= B{other}} to this instance.
780 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar} value or
781 an iterable of several of the former.
783 @return: This instance, updated (L{Fsum}).
785 @raise TypeError: Invalid B{C{other}} type.
787 @see: Methods L{Fsum.fsub_} and L{Fsum.fsub}.
788 '''
789 try:
790 return self._fsub(other, _isub_op_)
791 except TypeError:
792 pass
793 _xiterable(other)
794 return self._facc_neg(other)
796 def __iter__(self):
797 '''Return an C{iter}ator over a C{partials} duplicate.
798 '''
799 return iter(self.partials)
801 def __itruediv__(self, other, **raiser_RESIDUAL):
802 '''Apply C{B{self} /= B{other}} to this instance.
804 @arg other: Divisor (C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
805 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore
806 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}
807 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.
809 @return: This instance, updated (L{Fsum}).
811 @raise OverflowError: Partial C{2sum} overflow.
813 @raise ResidualError: Non-zero, significant residual or invalid
814 B{C{RESIDUAL}}.
816 @raise TypeError: Invalid B{C{other}} type.
818 @raise ValueError: Invalid or I{non-finite} B{C{other}}.
820 @raise ZeroDivisionError: Zero B{C{other}}.
822 @see: Method L{Fsum.__ifloordiv__}.
823 '''
824 return self._ftruediv(other, _truediv_op_ + _fset_op_, **raiser_RESIDUAL)
826 def __le__(self, other):
827 '''Return C{(B{self} <= B{other})}, see C{__eq__}.
828 '''
829 return self._cmp_0(other, _lt_op_ + _fset_op_) <= 0
831 def __len__(self):
832 '''Return the number of values accumulated (C{int}).
833 '''
834 return self._n
836 def __lt__(self, other):
837 '''Return C{(B{self} < B{other})}, see C{__eq__}.
838 '''
839 return self._cmp_0(other, _lt_op_) < 0
841 def __matmul__(self, other): # PYCHOK no cover
842 '''Not implemented.'''
843 return _NotImplemented(self, other)
845 def __mod__(self, other):
846 '''Return C{B{self} % B{other}} as an L{Fsum}.
848 @see: Method L{Fsum.__imod__}.
849 '''
850 f = self._copyd(self.__mod__)
851 return f._fdivmod2(other, _mod_op_).mod
853 def __mul__(self, other):
854 '''Return C{B{self} * B{other}} as an L{Fsum}.
856 @see: Method L{Fsum.__imul__}.
857 '''
858 f = self._copyd(self.__mul__)
859 return f._fmul(other, _mul_op_)
861 def __ne__(self, other):
862 '''Return C{(B{self} != B{other})}, see C{__eq__}.
863 '''
864 return self._cmp_0(other, _ne_op_) != 0
866 def __neg__(self):
867 '''Return C{copy(B{self})}, I{negated}.
868 '''
869 f = self._copyd(self.__neg__)
870 return f._fset(self._neg)
872 def __pos__(self):
873 '''Return this instance I{as-is}, like C{float.__pos__()}.
874 '''
875 return self if _pos_self else self._copyd(self.__pos__)
877 def __pow__(self, other, *mod): # PYCHOK 2 vs 3 args
878 '''Return C{B{self}**B{other}} as an L{Fsum}.
880 @see: Method L{Fsum.__ipow__}.
881 '''
882 f = self._copyd(self.__pow__)
883 return f._fpow(other, _pow_op_, *mod)
885 def __radd__(self, other):
886 '''Return C{B{other} + B{self}} as an L{Fsum}.
888 @see: Method L{Fsum.__iadd__}.
889 '''
890 f = self._rcopyd(other, self.__radd__)
891 return f._fadd(self)
893 def __rdivmod__(self, other):
894 '''Return C{divmod(B{other}, B{self})} as 2-tuple
895 C{(quotient, remainder)}.
897 @see: Method L{Fsum.__divmod__}.
898 '''
899 f = self._rcopyd(other, self.__rdivmod__)
900 return f._fdivmod2(self, _divmod_op_)
902# turned off, called by _deepcopy and _copy
903# def __reduce__(self): # Python 3.8+
904# ''' Pickle, like std C{fractions.Fraction}, see U{__reduce__
905# <https://docs.Python.org/3/library/pickle.html#object.__reduce__>}
906# '''
907# dict_ = self._Fsum_as().__dict__ # no __setstate__
908# return (type(self), self.partials, dict_)
910# def __repr__(self):
911# '''Return the default C{repr(this)}.
912# '''
913# return self.toRepr(lenc=True)
915 def __rfloordiv__(self, other):
916 '''Return C{B{other} // B{self}} as an L{Fsum}.
918 @see: Method L{Fsum.__ifloordiv__}.
919 '''
920 f = self._rcopyd(other, self.__rfloordiv__)
921 return f._floordiv(self, _floordiv_op_)
923 def __rmatmul__(self, other): # PYCHOK no cover
924 '''Not implemented.'''
925 return _NotImplemented(self, other)
927 def __rmod__(self, other):
928 '''Return C{B{other} % B{self}} as an L{Fsum}.
930 @see: Method L{Fsum.__imod__}.
931 '''
932 f = self._rcopyd(other, self.__rmod__)
933 return f._fdivmod2(self, _mod_op_).mod
935 def __rmul__(self, other):
936 '''Return C{B{other} * B{self}} as an L{Fsum}.
938 @see: Method L{Fsum.__imul__}.
939 '''
940 f = self._rcopyd(other, self.__rmul__)
941 return f._fmul(self, _mul_op_)
943 def __round__(self, *ndigits): # PYCHOK Python 3+
944 '''Return C{round(B{self}, *B{ndigits}} as an L{Fsum}.
946 @arg ndigits: Optional number of digits (C{int}).
947 '''
948 f = self._copyd(self.__round__)
949 # <https://docs.Python.org/3.12/reference/datamodel.html?#object.__round__>
950 return f._fset(round(float(self), *ndigits)) # can be C{int}
952 def __rpow__(self, other, *mod):
953 '''Return C{B{other}**B{self}} as an L{Fsum}.
955 @see: Method L{Fsum.__ipow__}.
956 '''
957 f = self._rcopyd(other, self.__rpow__)
958 return f._fpow(self, _pow_op_, *mod)
960 def __rsub__(self, other):
961 '''Return C{B{other} - B{self}} as L{Fsum}.
963 @see: Method L{Fsum.__isub__}.
964 '''
965 f = self._rcopyd(other, self.__rsub__)
966 return f._fsub(self, _sub_op_)
968 def __rtruediv__(self, other, **raiser_RESIDUAL):
969 '''Return C{B{other} / B{self}} as an L{Fsum}.
971 @see: Method L{Fsum.__itruediv__}.
972 '''
973 f = self._rcopyd(other, self.__rtruediv__)
974 return f._ftruediv(self, _truediv_op_, **raiser_RESIDUAL)
976# def __sizeof__(self):
977# '''Return the size of this instance (C{int} bytes}).
978# '''
979# return _sizeof(self._ps) + _sizeof(self._n)
981 def __str__(self):
982 '''Return the default C{str(self)}.
983 '''
984 return self.toStr(lenc=True)
986 def __sub__(self, other):
987 '''Return C{B{self} - B{other}} as an L{Fsum}.
989 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar}.
991 @return: The difference (L{Fsum}).
993 @see: Method L{Fsum.__isub__}.
994 '''
995 f = self._copyd(self.__sub__)
996 return f._fsub(other, _sub_op_)
998 def __truediv__(self, other, **raiser_RESIDUAL):
999 '''Return C{B{self} / B{other}} as an L{Fsum}.
1001 @arg other: Divisor (C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
1002 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore
1003 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}
1004 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.
1006 @return: The quotient (L{Fsum}).
1008 @raise ResidualError: Non-zero, significant residual or invalid
1009 B{C{RESIDUAL}}.
1011 @see: Method L{Fsum.__itruediv__}.
1012 '''
1013 return self._truediv(other, _truediv_op_, **raiser_RESIDUAL)
1015 __trunc__ = __int__
1017 if _MODS.sys_version_info2 < (3, 0): # PYCHOK no cover
1018 # <https://docs.Python.org/2/library/operator.html#mapping-operators-to-functions>
1019 __div__ = __truediv__
1020 __idiv__ = __itruediv__
1021 __long__ = __int__
1022 __nonzero__ = __bool__
1023 __rdiv__ = __rtruediv__
1025 def as_integer_ratio(self):
1026 '''Return this instance as the ratio of 2 integers.
1028 @return: 2-Tuple C{(numerator, denominator)} both C{int} with
1029 C{numerator} signed and C{denominator} non-zero and
1030 positive. The C{numerator} is I{non-finite} if this
1031 instance is.
1033 @see: Method L{Fsum.fint2} and C{float.as_integer_ratio} in
1034 Python 2.7+.
1035 '''
1036 n, r = self._fint2
1037 if r:
1038 i, d = float(r).as_integer_ratio()
1039 n, d = _n_d2(n * d + i, d)
1040 else: # PYCHOK no cover
1041 d = 1
1042 return n, d
1044 @property_RO
1045 def as_iscalar(self):
1046 '''Get this instance I{as-is} (L{Fsum} with C{non-zero residual},
1047 C{scalar} or I{non-finite}).
1048 '''
1049 s, r = self._nfprs2
1050 return self if r else s
1052 @property_RO
1053 def ceil(self):
1054 '''Get this instance' C{ceil} value (C{int} in Python 3+, but
1055 C{float} in Python 2-).
1057 @note: This C{ceil} takes the C{residual} into account.
1059 @see: Method L{Fsum.int_float} and properties L{Fsum.floor},
1060 L{Fsum.imag} and L{Fsum.real}.
1061 '''
1062 s, r = self._fprs2
1063 c = _ceil(s) + int(r) - 1
1064 while r > (c - s): # (s + r) > c
1065 c += 1
1066 return c # _ceil(self._n_d)
1068 cmp = __cmp__
1070 def _cmp_0(self, other, op):
1071 '''(INTERNAL) Return C{scalar(self - B{other})} for 0-comparison.
1072 '''
1073 if _isFsum_2Tuple(other):
1074 s = self._ps_1sum(*other._ps)
1075 elif self._scalar(other, op):
1076 s = self._ps_1sum(other)
1077 else:
1078 s = self.signOf() # res=True
1079 return s
1081 def copy(self, deep=False, **name):
1082 '''Copy this instance, C{shallow} or B{C{deep}}.
1084 @kwarg name: Optional, overriding C{B{name}='"copy"} (C{str}).
1086 @return: The copy (L{Fsum}).
1087 '''
1088 n = _name__(name, name__=self.copy)
1089 f = _Named.copy(self, deep=deep, name=n)
1090 if f._ps is self._ps:
1091 f._ps = list(self._ps) # separate list
1092 if not deep:
1093 f._n = 1
1094 # assert f._f2product == self._f2product
1095 # assert f._Fsum is f
1096 # assert f._isfine is self._isfine
1097 # assert f._RESIDUAL is self._RESIDUAL
1098 return f
1100 def _copyd(self, which, name=NN):
1101 '''(INTERNAL) Copy for I{dyadic} operators.
1102 '''
1103 n = name or typename(which)
1104 # NOT .classof due to .Fdot(a, *b) args, etc.
1105 f = _Named.copy(self, deep=False, name=n)
1106 f._ps = list(self._ps) # separate list
1107 # assert f._n == self._n
1108 # assert f._f2product == self._f2product
1109 # assert f._Fsum is f
1110 # assert f._isfine is self._isfine
1111 # assert f._RESIDUAL is self._RESIDUAL
1112 return f
1114 divmod = __divmod__
1116 def _Error(self, op, other, Error, **txt_cause):
1117 '''(INTERNAL) Format an B{C{Error}} for C{{self} B{op} B{other}}.
1118 '''
1119 # self.as_iscalar causes RecursionError for ._fprs2 errors
1120 s = _Psum(self._ps, nonfinites=True, name=self.name)
1121 return Error(_SPACE_(s.as_iscalar, op, other), **txt_cause)
1123 def _ErrorX(self, X, op, other, *mod):
1124 '''(INTERNAL) Format the caught exception C{X}.
1125 '''
1126 E, t = _xError2(X)
1127 if mod:
1128 t = _COMMASPACE_(Fmt.PARENSPACED(mod=mod[0]), t)
1129 return self._Error(op, other, E, txt=t, cause=X)
1131 def _ErrorXs(self, X, xs, **kwds): # in .fmath
1132 '''(INTERNAL) Format the caught exception C{X}.
1133 '''
1134 E, t = _xError2(X)
1135 u = unstr(self.named3, *xs, _ELLIPSIS=4, **kwds)
1136 return E(u, txt=t, cause=X)
1138 def _facc(self, xs, up=True, **_X_x_origin):
1139 '''(INTERNAL) Accumulate more C{scalar}s, L{Fsum}s pr L{Fsum2Tuple}s.
1140 '''
1141 if xs:
1142 kwds = self._isfine
1143 if _X_x_origin:
1144 kwds = _xkwds(_X_x_origin, **kwds)
1145 fs = _xs(xs, **kwds) # PYCHOK yield
1146 ps = self._ps
1147 ps[:] = self._ps_acc(list(ps), fs, up=up)
1148# if len(ps) > 16:
1149# _ = _psum(ps, **self._isfine)
1150 return self
1152 def _facc_args(self, xs, **up):
1153 '''(INTERNAL) Accumulate 0, 1 or more C{xs}, all positional
1154 arguments in the caller of this method.
1155 '''
1156 return self._fadd(xs[0], **up) if len(xs) == 1 else \
1157 self._facc(xs, **up) # origin=1?
1159 def _facc_dot(self, n, xs, ys, **kwds): # in .fmath
1160 '''(INTERNAL) Accumulate C{fdot(B{xs}, *B{ys})}.
1161 '''
1162 if n > 0:
1163 _f = Fsum(**kwds)
1164 self._facc(_f(x).fmul(y) for x, y in zip(xs, ys)) # PYCHOK attr?
1165 return self
1167 def _facc_neg(self, xs, **up_origin):
1168 '''(INTERNAL) Accumulate more C{xs}, negated.
1169 '''
1170 def _N(X):
1171 return X._ps_neg
1173 def _n(x):
1174 return -float(x)
1176 return self._facc(xs, _X=_N, _x=_n, **up_origin)
1178 def _facc_power(self, power, xs, which, **raiser_RESIDUAL): # in .fmath
1179 '''(INTERNAL) Add each C{xs} as C{float(x**power)}.
1180 '''
1181 def _Pow4(p):
1182 r = 0
1183 if _isFsum_2Tuple(p):
1184 s, r = p._fprs2
1185 if r:
1186 m = Fsum._pow
1187 else: # scalar
1188 return _Pow4(s)
1189 elif isint(p, both=True) and int(p) >= 0:
1190 p = s = int(p)
1191 m = Fsum._pow_int
1192 else:
1193 p = s = _2float(power=p, **self._isfine)
1194 m = Fsum._pow_scalar
1195 return m, p, s, r
1197 _Pow, p, s, r = _Pow4(power)
1198 if p: # and xs:
1199 op = typename(which)
1200 _FsT = _Fsum_2Tuple_types
1201 _pow = self._pow_2_3
1203 def _P(X):
1204 f = _Pow(X, p, power, op, **raiser_RESIDUAL)
1205 return f._ps if isinstance(f, _FsT) else (f,)
1207 def _p(x):
1208 x = float(x)
1209 f = _pow(x, s, power, op, **raiser_RESIDUAL)
1210 if f and r:
1211 f *= _pow(x, r, power, op, **raiser_RESIDUAL)
1212 return f
1214 f = self._facc(xs, _X=_P, _x=_p) # origin=1?
1215 else:
1216 f = self._facc_scalar_(float(len(xs))) # x**0 == 1
1217 return f
1219 def _facc_scalar(self, xs, **up):
1220 '''(INTERNAL) Accumulate all C{xs}, each C{scalar}.
1221 '''
1222 if xs:
1223 ps = self._ps
1224 ps[:] = self._ps_acc(list(ps), xs, **up)
1225 return self
1227 def _facc_scalar_(self, *xs, **up):
1228 '''(INTERNAL) Accumulate all positional C{xs}, each C{scalar}.
1229 '''
1230 return self._facc_scalar(xs, **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 _facc_xsum(self, xs, up=True, **origin_which):
1247 '''(INTERNAL) Accumulate all C{xs}, each C{scalar}, an L{Fsum}
1248 or L{Fsum2Tuple}, like function C{_xsum}.
1249 '''
1250 fs = _xs(xs, **_x_isfine(self.nonfinitesOK, _Cdot=type(self),
1251 **origin_which)) # PYCHOK yield
1252 return self._facc_scalar(fs, up=up)
1254 def fadd(self, xs=()):
1255 '''Add an iterable's items to this instance.
1257 @arg xs: Iterable of items to add (each C{scalar},
1258 an L{Fsum} or L{Fsum2Tuple}).
1260 @return: This instance (L{Fsum}).
1262 @raise OverflowError: Partial C{2sum} overflow.
1264 @raise TypeError: An invalid B{C{xs}} item.
1266 @raise ValueError: Invalid or I{non-finite} B{C{xs}} value.
1267 '''
1268 if _isFsum_2Tuple(xs):
1269 self._facc_scalar(xs._ps)
1270 elif isscalar(xs): # for backward compatibility # PYCHOK no cover
1271 x = _2float(x=xs, **self._isfine)
1272 self._facc_scalar_(x)
1273 elif xs: # _xiterable(xs)
1274 self._facc(xs)
1275 return self
1277 def fadd_(self, *xs):
1278 '''Add all positional items to this instance.
1280 @arg xs: Values to add (each C{scalar}, an L{Fsum}
1281 or L{Fsum2Tuple}), all positional.
1283 @see: Method L{Fsum.fadd} for further details.
1284 '''
1285 return self._facc_args(xs)
1287 def _fadd(self, other, op=_add_op_, **up):
1288 '''(INTERNAL) Apply C{B{self} += B{other}}.
1289 '''
1290 if _isFsum_2Tuple(other):
1291 self._facc_scalar(other._ps, **up)
1292 elif self._scalar(other, op):
1293 self._facc_scalar_(other, **up)
1294 return self
1296 fcopy = copy # for backward compatibility
1297 fdiv = __itruediv__
1298 fdivmod = __divmod__
1300 def _fdivmod2(self, other, op, **raiser_RESIDUAL):
1301 '''(INTERNAL) Apply C{B{self} %= B{other}} and return a L{DivMod2Tuple}.
1302 '''
1303 # result mostly follows CPython function U{float_divmod
1304 # <https://GitHub.com/python/cpython/blob/main/Objects/floatobject.c>},
1305 # but at least divmod(-3, 2) equals Cpython's result (-2, 1).
1306 q = self._truediv(other, op, **raiser_RESIDUAL).floor
1307 if q: # == float // other == floor(float / other)
1308 self -= self._Fsum_as(q) * other # NOT other * q!
1310 s = signOf(other) # make signOf(self) == signOf(other)
1311 if s and self.signOf() == -s: # PYCHOK no cover
1312 self += other
1313 q -= 1
1314# t = self.signOf()
1315# if t and t != s:
1316# raise self._Error(op, other, _AssertionError, txt__=signOf)
1317 return DivMod2Tuple(q, self) # q is C{int} in Python 3+, but C{float} in Python 2-
1319 def _fhorner(self, x, cs, where, incx=True): # in .fmath
1320 '''(INTERNAL) Add an L{Fhorner} evaluation of polynomial
1321 C{sum(c * B{x}**i for i, c in _e(cs))} where C{_e =
1322 enumerate if B{incx} else _enumereverse}.
1323 '''
1324 # assert _xiterablen(cs)
1325 try:
1326 n = len(cs)
1327 if n > 1 and _2finite(x, **self._isfine):
1328 H = self._Fsum_as(name__=self._fhorner)
1329 _m = H._mul_Fsum if _isFsum_2Tuple(x) else \
1330 H._mul_scalar
1331 for c in (reversed(cs) if incx else cs):
1332 H._fset(_m(x, _mul_op_), up=False)
1333 H._fadd(c, up=False)
1334 else: # x == 0
1335 H = cs[0] if n else 0
1336 self._fadd(H)
1337 except Exception as X:
1338 t = unstr(where, x, *cs, _ELLIPSIS=4, incx=incx)
1339 raise self._ErrorX(X, _add_op_, t)
1340 return self
1342 def _finite(self, other, op=None):
1343 '''(INTERNAL) Return B{C{other}} if C{finite}.
1344 '''
1345 if _isOK_or_finite(other, **self._isfine):
1346 return other
1347 E = _NonfiniteError(other)
1348 raise self._Error(op, other, E, txt=_not_finite_)
1350 def fint(self, name=NN, **raiser_RESIDUAL):
1351 '''Return this instance' current running sum as C{integer}.
1353 @kwarg name: Optional, overriding C{B{name}="fint"} (C{str}).
1354 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore
1355 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}
1356 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.
1358 @return: The C{integer} sum (L{Fsum}) if this instance C{is_integer}
1359 with a zero or insignificant I{integer} residual.
1361 @raise ResidualError: Non-zero, significant residual or invalid
1362 B{C{RESIDUAL}}.
1364 @see: Methods L{Fsum.fint2}, L{Fsum.int_float} and L{Fsum.is_integer}.
1365 '''
1366 i, r = self._fint2
1367 if r:
1368 R = self._raiser(r, i, **raiser_RESIDUAL)
1369 if R:
1370 t = _stresidual(_integer_, r, **R)
1371 raise ResidualError(_integer_, i, txt=t)
1372 return self._Fsum_as(i, name=_name__(name, name__=self.fint))
1374 def fint2(self, **name):
1375 '''Return this instance' current running sum as C{int} and the
1376 I{integer} residual.
1378 @kwarg name: Optional name (C{str}).
1380 @return: An L{Fsum2Tuple}C{(fsum, residual)} with C{fsum}
1381 an C{int} and I{integer} C{residual} a C{float} or
1382 C{INT0} if the C{fsum} is considered to be I{exact}.
1383 The C{fsum} is I{non-finite} if this instance is.
1384 '''
1385 return Fsum2Tuple(*self._fint2, **name)
1387 @Property
1388 def _fint2(self): # see ._fset
1389 '''(INTERNAL) Get 2-tuple (C{int}, I{integer} residual).
1390 '''
1391 s, r = self._nfprs2
1392 if _isfinite(s):
1393 i = int(s)
1394 r = (self._ps_1sum(i) if len(self._ps) > 1 else
1395 float(s - i)) or INT0
1396 else: # INF, NAN, NINF
1397 i = float(s)
1398# r = _NONFINITEr
1399 return i, r # Fsum2Tuple?
1401 @_fint2.setter_ # PYCHOK setter_UNDERscore!
1402 def _fint2(self, s): # in _fset
1403 '''(INTERNAL) Replace the C{_fint2} value.
1404 '''
1405 if _isfinite(s):
1406 i = int(s)
1407 r = (s - i) or INT0
1408 else: # INF, NAN, NINF
1409 i = float(s)
1410 r = _NONFINITEr
1411 return i, r # like _fint2.getter
1413 @deprecated_property_RO
1414 def float_int(self): # PYCHOK no cover
1415 '''DEPRECATED, use method C{Fsum.int_float}.'''
1416 return self.int_float() # raiser=False
1418 @property_RO
1419 def floor(self):
1420 '''Get this instance' C{floor} (C{int} in Python 3+, but
1421 C{float} in Python 2-).
1423 @note: This C{floor} takes the C{residual} into account.
1425 @see: Method L{Fsum.int_float} and properties L{Fsum.ceil},
1426 L{Fsum.imag} and L{Fsum.real}.
1427 '''
1428 s, r = self._fprs2
1429 f = _floor(s) + _floor(r) + 1
1430 while (f - s) > r: # f > (s + r)
1431 f -= 1
1432 return f # _floor(self._n_d)
1434# ffloordiv = __ifloordiv__ # for naming consistency?
1435# floordiv = __floordiv__ # for naming consistency?
1437 def _floordiv(self, other, op, **raiser_RESIDUAL): # rather _ffloordiv?
1438 '''Apply C{B{self} //= B{other}}.
1439 '''
1440 q = self._ftruediv(other, op, **raiser_RESIDUAL) # == self
1441 return self._fset(q.floor) # floor(q)
1443 def fma(self, other1, other2, **nonfinites): # in .fmath.fma
1444 '''Fused-multiply-add C{self *= B{other1}; self += B{other2}}.
1446 @arg other1: Multiplier (C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
1447 @arg other2: Addend (C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
1448 @kwarg nonfinites: Use C{B{nonfinites}=True} or C{False}, to
1449 override L{nonfinites<Fsum.nonfinites>} and
1450 L{nonfiniterrors} default (C{bool}).
1451 '''
1452 op = typename(self.fma)
1453 _fs = self._ps_other
1454 try:
1455 s, r = self._fprs2
1456 if r:
1457 f = self._f2mul(self.fma, (other1,), **nonfinites)
1458 f += other2
1459 elif _residue(other1) or _residue(other2):
1460 fs = _2split3s(_fs(op, other1))
1461 fs = _2products(s, fs, *_fs(op, other2))
1462 f = _Psum(self._ps_acc([], fs, up=False), name=op)
1463 else:
1464 f = _fma(s, other1, other2)
1465 f = _2finite(f, **self._isfine)
1466 except TypeError as X:
1467 raise self._ErrorX(X, op, (other1, other2))
1468 except (OverflowError, ValueError) as X: # from math.fma
1469 f = self._mul_reduce(s, other1) # INF, NAN, NINF
1470 f += sum(_fs(op, other2))
1471 f = self._nonfiniteX(X, op, f, **nonfinites)
1472 return self._fset(f)
1474 def fma_(self, *xys, **nonfinites):
1475 '''Fused-multiply-accumulate C{for i in range(0, len(xys), B{2}):
1476 self = }L{fma<pygeodesy.fmath.fma>}C{(xys[i], xys[i+1], self)}.
1478 @arg xys: Pairwise multiplicand, multiplier (each C{scalar},
1479 an L{Fsum} or L{Fsum2Tuple}), all positional.
1480 @kwarg nonfinites: Use C{B{nonfinites}=True} or C{False}, to
1481 override L{nonfinites<Fsum.nonfinites>} and
1482 L{nonfiniterrors} default (C{bool}).
1484 @note: Equivalent to L{fdot_<pygeodesy.fmath.fdot_>}C{(*xys,
1485 start=self)}.
1486 '''
1487 if xys:
1488 n = len(xys)
1489 if n < 2 or isodd(n):
1490 raise LenError(self.fma_, xys=n)
1491 f, _fmath_fma = self, _MODS.fmath.fma
1492 for x, y in zip(xys[0::2], xys[1::2]):
1493 f = _fmath_fma(x, y, f, **nonfinites)
1494 self._fset(f)
1495 return self
1497 fmul = __imul__
1499 def _fmul(self, other, op):
1500 '''(INTERNAL) Apply C{B{self} *= B{other}}.
1501 '''
1502 if _isFsum_2Tuple(other):
1503 if len(self._ps) != 1:
1504 f = self._mul_Fsum(other, op)
1505 elif len(other._ps) != 1: # and len(self._ps) == 1
1506 f = self._ps_mul(op, *other._ps) if other._ps else _0_0
1507 elif self._f2product: # len(other._ps) == 1
1508 f = self._mul_scalar(other._ps[0], op)
1509 else: # len(other._ps) == len(self._ps) == 1
1510 f = self._finite(self._ps[0] * other._ps[0], op=op)
1511 else:
1512 s = self._scalar(other, op)
1513 f = self._mul_scalar(s, op)
1514 return self._fset(f) # n=len(self) + 1
1516 @deprecated_method
1517 def f2mul(self, *others, **raiser):
1518 '''DEPRECATED on 2024.09.13, use method L{f2mul_<Fsum.f2mul_>}.'''
1519 return self._fset(self._f2mul(self.f2mul, others, **raiser))
1521 def f2mul_(self, *others, **f2product_nonfinites): # in .fmath.f2mul
1522 '''Return C{B{self} * B{other} * B{other} ...} for all B{C{others}} using cascaded,
1523 accurate multiplication like with L{f2product<Fsum.f2product>}C{(B{True})}.
1525 @arg others: Multipliers (each C{scalar}, an L{Fsum} or L{Fsum2Tuple}), all
1526 positional.
1527 @kwarg f2product_nonfinites: Use C{B{f2product=False}} to override the default
1528 C{True} and C{B{nonfinites}=True} or C{False}, to override
1529 settings L{nonfinites<Fsum.nonfinites>} and L{nonfiniterrors}.
1531 @return: The cascaded I{TwoProduct} (L{Fsum} or C{float}).
1533 @see: U{Equations 2.3<https://www.TUHH.De/ti3/paper/rump/OzOgRuOi06.pdf>}
1534 '''
1535 return self._f2mul(self.f2mul_, others, **f2product_nonfinites)
1537 def _f2mul(self, where, others, f2product=True, **nonfinites_raiser):
1538 '''(INTERNAL) See methods C{fma} and C{f2mul_}.
1539 '''
1540 n = typename(where)
1541 f = _Psum(self._ps, f2product=f2product, name=n)
1542 if others and f:
1543 if f.f2product():
1544 def _pfs(f, ps):
1545 return _2products(f, _2split3s(ps))
1546 else:
1547 def _pfs(f, ps): # PYCHOK redef
1548 return (f * p for p in ps)
1550 op, ps = n, f._ps
1551 try: # as if self.f2product(True)
1552 for other in others: # to pinpoint errors
1553 for p in self._ps_other(op, other):
1554 ps[:] = f._ps_acc([], _pfs(p, ps), update=False)
1555 f._update()
1556 except TypeError as X:
1557 raise self._ErrorX(X, op, other)
1558 except (OverflowError, ValueError) as X:
1559 r = self._mul_reduce(sum(ps), other) # INF, NAN, NINF
1560 r = self._nonfiniteX(X, op, r, **nonfinites_raiser)
1561 f._fset(r)
1562 return f
1564 def fover(self, over, **raiser_RESIDUAL):
1565 '''Apply C{B{self} /= B{over}} and summate.
1567 @arg over: Divisor (C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
1568 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore
1569 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}
1570 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.
1572 @return: Precision running quotient sum (C{float}).
1574 @raise ResidualError: Non-zero, significant residual or invalid
1575 B{C{RESIDUAL}}.
1577 @see: Methods L{Fsum.fdiv}, L{Fsum.__itruediv__} and L{Fsum.fsum}.
1578 '''
1579 return float(self.fdiv(over, **raiser_RESIDUAL)._fprs)
1581 fpow = __ipow__
1583 def _fpow(self, other, op, *mod, **raiser_RESIDUAL):
1584 '''Apply C{B{self} **= B{other}}, optional B{C{mod}} or C{None}.
1585 '''
1586 if mod:
1587 if mod[0] is not None: # == 3-arg C{pow}
1588 f = self._pow_2_3(self, other, other, op, *mod, **raiser_RESIDUAL)
1589 elif self.is_integer():
1590 # return an exact C{int} for C{int}**C{int}
1591 i, _ = self._fint2 # assert _ == 0
1592 x, r = _2tuple2(other) # C{int}, C{float} or other
1593 f = self._Fsum_as(i)._pow_Fsum(other, op, **raiser_RESIDUAL) if r else \
1594 self._pow_2_3(i, x, other, op, **raiser_RESIDUAL)
1595 else: # mod[0] is None, power(self, other)
1596 f = self._pow(other, other, op, **raiser_RESIDUAL)
1597 else: # pow(self, other)
1598 f = self._pow(other, other, op, **raiser_RESIDUAL)
1599 return self._fset(f) # n=max(len(self), 1)
1601 def f2product(self, *two):
1602 '''Get and set accurate I{TwoProduct} multiplication for this
1603 L{Fsum}, overriding the L{f2product} default.
1605 @arg two: If omitted, leave the override unchanged, if C{True},
1606 turn I{TwoProduct} on, if C{False} off, or if C{None}
1607 remove the override (C{bool} or C{None}).
1609 @return: The previous setting (C{bool} or C{None} if not set).
1611 @see: Function L{f2product<fsums.f2product>}.
1613 @note: Use C{f.f2product() or f2product()} to determine whether
1614 multiplication is accurate for L{Fsum} C{f}.
1615 '''
1616 if two: # delattrof(self, _f2product=None)
1617 t = _xkwds_pop(self.__dict__, _f2product=None)
1618 if two[0] is not None:
1619 self._f2product = bool(two[0])
1620 else: # getattrof(self, _f2product=None)
1621 t = _xkwds_get(self.__dict__, _f2product=None)
1622 return t
1624 @Property
1625 def _fprs(self):
1626 '''(INTERNAL) Get and cache this instance' precision
1627 running sum (C{float} or C{int}), ignoring C{residual}.
1629 @note: The precision running C{fsum} after a C{//=} or
1630 C{//} C{floor} division is C{int} in Python 3+.
1631 '''
1632 s, _ = self._fprs2
1633 return s # ._fprs2.fsum
1635 @_fprs.setter_ # PYCHOK setter_UNDERscore!
1636 def _fprs(self, s):
1637 '''(INTERNAL) Replace the C{_fprs} value.
1638 '''
1639 return s
1641 @Property
1642 def _fprs2(self):
1643 '''(INTERNAL) Get and cache this instance' precision
1644 running sum and residual (L{Fsum2Tuple}).
1645 '''
1646 ps = self._ps
1647 n = len(ps)
1648 try:
1649 if n > 2:
1650 s = _psum(ps, **self._isfine)
1651 if not _isfinite(s):
1652 ps[:] = s, # collapse ps
1653 return Fsum2Tuple(s, _NONFINITEr)
1654 n = len(ps)
1655# Fsum._ps_max = max(Fsum._ps_max, n)
1656 if n > 2:
1657 r = self._ps_1sum(s)
1658 return Fsum2Tuple(*_s_r2(s, r))
1659 if n > 1: # len(ps) == 2
1660 s, r = _s_r2(*_2sum(*ps, **self._isfine))
1661 ps[:] = (r, s) if r else (s,)
1662 elif ps: # len(ps) == 1
1663 s = ps[0]
1664 r = INT0 if _isfinite(s) else _NONFINITEr
1665 else: # len(ps) == 0
1666 s = _0_0
1667 r = INT0 if _isfinite(s) else _NONFINITEr
1668 ps[:] = s,
1669 except (OverflowError, ValueError) as X:
1670 op = _fset_op_ # INF, NAN, NINF
1671 ps[:] = sum(ps), # collapse ps
1672 s = self._nonfiniteX(X, op, ps[0])
1673 r = _NONFINITEr
1674 # assert self._ps is ps
1675 return Fsum2Tuple(s, r)
1677 @_fprs2.setter_ # PYCHOK setter_UNDERscore!
1678 def _fprs2(self, s_r):
1679 '''(INTERNAL) Replace the C{_fprs2} value.
1680 '''
1681 return Fsum2Tuple(s_r)
1683 def fset_(self, *xs):
1684 '''Apply C{B{self}.partials = Fsum(*B{xs}).partials}.
1686 @arg xs: Optional, new values (each C{scalar} or an L{Fsum}
1687 or L{Fsum2Tuple} instance), all positional.
1689 @return: This instance, replaced (C{Fsum}).
1691 @see: Method L{Fsum.fadd} for further details.
1692 '''
1693 f = (xs[0] if xs else _0_0) if len(xs) < 2 else \
1694 Fsum(*xs, nonfinites=self.nonfinites()) # self._Fsum_as(*xs)
1695 return self._fset(f, op=_fset_op_)
1697 def _fset(self, other, n=0, up=True, **op):
1698 '''(INTERNAL) Overwrite this instance with an other or a C{scalar}.
1699 '''
1700 if other is self:
1701 pass # from ._fmul, ._ftruediv and ._pow_0_1
1702 elif _isFsum_2Tuple(other):
1703 if op: # and not self.nonfinitesOK:
1704 self._finite(other._fprs, **op)
1705 self._ps[:] = other._ps
1706 self._n = n or other._n
1707 if up: # use or zap the C{Property_RO} values
1708 Fsum._fint2._update_from(self, other)
1709 Fsum._fprs ._update_from(self, other)
1710 Fsum._fprs2._update_from(self, other)
1711 elif isscalar(other):
1712 s = float(self._finite(other, **op)) if op else other
1713 self._ps[:] = s,
1714 self._n = n or 1
1715 if up: # Property _fint2, _fprs and _fprs2 all have
1716 # @.setter_underscore and NOT @.setter because the
1717 # latter's _fset zaps the value set by @.setter
1718 self._fint2 = s
1719 self._fprs = s
1720 self._fprs2 = s, INT0
1721 # assert self._fprs is s
1722 else:
1723 op = _xkwds_get1(op, op=_fset_op_)
1724 raise self._Error(op, other, _TypeError)
1725 return self
1727 def fsub(self, xs=()):
1728 '''Subtract an iterable's items from this instance.
1730 @see: Method L{Fsum.fadd} for further details.
1731 '''
1732 return self._facc_neg(xs)
1734 def fsub_(self, *xs):
1735 '''Subtract all positional items from this instance.
1737 @see: Method L{Fsum.fadd_} for further details.
1738 '''
1739 return self._fsub(xs[0], _sub_op_) if len(xs) == 1 else \
1740 self._facc_neg(xs) # origin=1?
1742 def _fsub(self, other, op):
1743 '''(INTERNAL) Apply C{B{self} -= B{other}}.
1744 '''
1745 if _isFsum_2Tuple(other):
1746 if other is self: # or other._fprs2 == self._fprs2:
1747 self._fset(_0_0, n=len(self) * 2)
1748 elif other._ps:
1749 self._facc_scalar(other._ps_neg)
1750 elif self._scalar(other, op):
1751 self._facc_scalar_(-other)
1752 return self
1754 def fsum(self, xs=()):
1755 '''Add an iterable's items, summate and return the current
1756 precision running sum.
1758 @arg xs: Iterable of items to add (each item C{scalar},
1759 an L{Fsum} or L{Fsum2Tuple}).
1761 @return: Precision running sum (C{float} or C{int}).
1763 @see: Method L{Fsum.fadd}.
1765 @note: Accumulation can continue after summation.
1766 '''
1767 return self._facc(xs)._fprs
1769 def fsum_(self, *xs):
1770 '''Add any positional items, summate and return the current
1771 precision running sum.
1773 @arg xs: Items to add (each C{scalar}, an L{Fsum} or
1774 L{Fsum2Tuple}), all positional.
1776 @return: Precision running sum (C{float} or C{int}).
1778 @see: Methods L{Fsum.fsum}, L{Fsum.Fsum_} and L{Fsum.fsumf_}.
1779 '''
1780 return self._facc_args(xs)._fprs
1782 def Fsum_(self, *xs, **name):
1783 '''Like method L{Fsum.fsum_} but returning a named L{Fsum}.
1785 @kwarg name: Optional name (C{str}).
1787 @return: Copy of this updated instance (L{Fsum}).
1788 '''
1789 return self._facc_args(xs)._copyd(self.Fsum_, **name)
1791 def Fsum2Tuple_(self, *xs, **name):
1792 '''Like method L{Fsum.fsum_} but returning a named L{Fsum2Tuple}.
1794 @kwarg name: Optional name (C{str}).
1796 @return: Precision running sum (L{Fsum2Tuple}).
1797 '''
1798 return Fsum2Tuple(self._facc_args(xs)._nfprs2, **name)
1800 @property_RO
1801 def _Fsum(self): # like L{Fsum2Tuple._Fsum}, in .fstats
1802 return self # NOT @Property_RO, see .copy and ._copyd
1804 def _Fsum_as(self, *xs, **name_f2product_nonfinites_RESIDUAL):
1805 '''(INTERNAL) Return an C{Fsum} with this C{Fsum}'s C{.f2product},
1806 C{.nonfinites} and C{.RESIDUAL} setting, optionally
1807 overridden with C{name_f2product_nonfinites_RESIDUAL} and
1808 with any C{xs} accumulated.
1809 '''
1810 kwds = _xkwds_not(None, Fsum._RESIDUAL, f2product =self.f2product(),
1811 nonfinites=self.nonfinites(),
1812 RESIDUAL =self.RESIDUAL())
1813 if name_f2product_nonfinites_RESIDUAL: # overwrites
1814 kwds.update(name_f2product_nonfinites_RESIDUAL)
1815 f = Fsum(**kwds)
1816 # assert all(v == self.__dict__[n] for n, v in f.__dict__.items())
1817 return (f._facc(xs, up=False) if len(xs) > 1 else
1818 f._fset(xs[0], op=_fset_op_)) if xs else f
1820 def fsum2(self, xs=(), **name):
1821 '''Add an iterable's items, summate and return the
1822 current precision running sum I{and} the C{residual}.
1824 @arg xs: Iterable of items to add (each item C{scalar},
1825 an L{Fsum} or L{Fsum2Tuple}).
1826 @kwarg name: Optional C{B{name}=NN} (C{str}).
1828 @return: L{Fsum2Tuple}C{(fsum, residual)} with C{fsum} the
1829 current precision running sum and C{residual}, the
1830 (precision) sum of the remaining C{partials}. The
1831 C{residual is INT0} if the C{fsum} is considered
1832 to be I{exact}.
1834 @see: Methods L{Fsum.fint2}, L{Fsum.fsum} and L{Fsum.fsum2_}
1835 '''
1836 t = self._facc(xs)._fprs2
1837 return t.dup(name=name) if name else t
1839 def fsum2_(self, *xs):
1840 '''Add any positional items, summate and return the current
1841 precision running sum and the I{differential}.
1843 @arg xs: Values to add (each C{scalar}, an L{Fsum} or
1844 L{Fsum2Tuple}), all positional.
1846 @return: 2Tuple C{(fsum, delta)} with the current, precision
1847 running C{fsum} like method L{Fsum.fsum} and C{delta},
1848 the difference with previous running C{fsum}, C{float}.
1850 @see: Methods L{Fsum.fsum_} and L{Fsum.fsum}.
1851 '''
1852 return self._fsum2(xs, self._facc_args)
1854 def _fsum2(self, xs, _facc, **facc_kwds):
1855 '''(INTERNAL) Helper for L{Fsum.fsum2_} and L{Fsum.fsum2f_}.
1856 '''
1857 p, q = self._fprs2
1858 if xs:
1859 s, r = _facc(xs, **facc_kwds)._fprs2
1860 if _isfinite(s): # _fsum(_1primed((s, -p, r, -q))
1861 d, r = _2sum(s - p, r - q, _isfine=_isOK)
1862 r, _ = _s_r2(d, r)
1863 return s, (r if _isfinite(r) else _NONFINITEr)
1864 else:
1865 return p, _0_0
1867 def fsumf_(self, *xs):
1868 '''Like method L{Fsum.fsum_} iff I{all} C{B{xs}}, each I{known to be}
1869 C{scalar}, an L{Fsum} or L{Fsum2Tuple}.
1870 '''
1871 return self._facc_xsum(xs, which=self.fsumf_)._fprs # origin=1?
1873 def Fsumf_(self, *xs):
1874 '''Like method L{Fsum.Fsum_} iff I{all} C{B{xs}}, each I{known to be}
1875 C{scalar}, an L{Fsum} or L{Fsum2Tuple}.
1876 '''
1877 return self._facc_xsum(xs, which=self.Fsumf_)._copyd(self.Fsumf_) # origin=1?
1879 def fsum2f_(self, *xs):
1880 '''Like method L{Fsum.fsum2_} iff I{all} C{B{xs}}, each I{known to be}
1881 C{scalar}, an L{Fsum} or L{Fsum2Tuple}.
1882 '''
1883 return self._fsum2(xs, self._facc_xsum, which=self.fsum2f_) # origin=1?
1885# ftruediv = __itruediv__ # for naming consistency?
1887 def _ftruediv(self, other, op, **raiser_RESIDUAL):
1888 '''(INTERNAL) Apply C{B{self} /= B{other}}.
1889 '''
1890 n = _1_0
1891 if _isFsum_2Tuple(other):
1892 if other is self or self == other:
1893 return self._fset(n, n=len(self))
1894 d, r = other._fprs2
1895 if r:
1896 R = self._raiser(r, d, **raiser_RESIDUAL)
1897 if R:
1898 raise self._ResidualError(op, other, r, **R)
1899 d, n = other.as_integer_ratio()
1900 else:
1901 d = self._scalar(other, op)
1902 try:
1903 s = n / d
1904 except Exception as X:
1905 raise self._ErrorX(X, op, other)
1906 f = self._mul_scalar(s, _mul_op_) # handles 0, INF, NAN
1907 return self._fset(f)
1909 @property_RO
1910 def imag(self):
1911 '''Get the C{imaginary} part of this instance (C{0.0}, always).
1913 @see: Property L{Fsum.real}.
1914 '''
1915 return _0_0
1917 def int_float(self, **raiser_RESIDUAL):
1918 '''Return this instance' current running sum as C{int} or C{float}.
1920 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore
1921 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}
1922 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.
1924 @return: This C{int} sum if this instance C{is_integer} and
1925 I{finite}, otherwise the C{float} sum if the residual
1926 is zero or not significant.
1928 @raise ResidualError: Non-zero, significant residual or invalid
1929 B{C{RESIDUAL}}.
1931 @see: Methods L{Fsum.fint}, L{Fsum.fint2}, L{Fsum.is_integer},
1932 L{Fsum.RESIDUAL} and property L{Fsum.as_iscalar}.
1933 '''
1934 s, r = self._fint2
1935 if r:
1936 s, r = self._fprs2
1937 if r: # PYCHOK no cover
1938 R = self._raiser(r, s, **raiser_RESIDUAL)
1939 if R:
1940 t = _stresidual(_non_zero_, r, **R)
1941 raise ResidualError(int_float=s, txt=t)
1942 s = float(s)
1943 return s
1945 def is_exact(self):
1946 '''Is this instance' running C{fsum} considered to be exact?
1947 (C{bool}), C{True} only if the C{residual is }L{INT0}.
1948 '''
1949 return self.residual is INT0
1951 def is_finite(self): # in .constants
1952 '''Is this instance C{finite}? (C{bool}).
1954 @see: Function L{isfinite<pygeodesy.isfinite>}.
1955 '''
1956 return _isfinite(sum(self._ps)) # == sum(self)
1958 def is_integer(self):
1959 '''Is this instance' running sum C{integer}? (C{bool}).
1961 @see: Methods L{Fsum.fint}, L{Fsum.fint2} and L{Fsum.is_scalar}.
1962 '''
1963 s, r = self._fint2
1964 return False if r else (_isfinite(s) and isint(s))
1966 def is_math_fma(self):
1967 '''Is accurate L{f2product} multiplication based on Python's C{math.fma}?
1969 @return: C{True} if accurate multiplication uses C{math.fma}, C{False}
1970 an C{fma} implementation as C{math.fma} or C{None}, a previous
1971 C{PyGeodesy} implementation.
1972 '''
1973 return (_2split3s is _passarg) or (False if _integer_ratio2 is None else None)
1975 def is_math_fsum(self):
1976 '''Are the summation functions L{fsum}, L{fsum_}, L{fsumf_}, L{fsum1},
1977 L{fsum1_} and L{fsum1f_} based on Python's C{math.fsum}?
1979 @return: C{True} if summation functions use C{math.fsum}, C{False}
1980 otherwise.
1981 '''
1982 return _sum is _fsum # _fsum.__module__ is fabs.__module__
1984 def is_scalar(self, **raiser_RESIDUAL):
1985 '''Is this instance' running sum C{scalar} with C{0} residual or with
1986 a residual I{ratio} not exceeding the RESIDUAL threshold?
1988 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore
1989 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}
1990 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.
1992 @return: C{True} if this instance' residual is C{0} or C{insignificant},
1993 i.e. its residual C{ratio} doesn't exceed the L{RESIDUAL
1994 <Fsum.RESIDUAL>} threshold (C{bool}).
1996 @raise ResidualError: Non-zero, significant residual or invalid
1997 B{C{RESIDUAL}}.
1999 @see: Methods L{Fsum.RESIDUAL} and L{Fsum.is_integer} and property
2000 L{Fsum.as_iscalar}.
2001 '''
2002 s, r = self._fprs2
2003 return False if r and self._raiser(r, s, **raiser_RESIDUAL) else True
2005 def _mul_Fsum(self, other, op):
2006 '''(INTERNAL) Return C{B{self} * B{other}} as L{Fsum} or C{0}.
2007 '''
2008 # assert _isFsum_2Tuple(other)
2009 if self._ps and other._ps:
2010 try:
2011 f = self._ps_mul(op, *other._ps) # NO .as_iscalar!
2012 except Exception as X:
2013 raise self._ErrorX(X, op, other)
2014 else:
2015 f = _0_0
2016 return f
2018 def _mul_reduce(self, *others):
2019 '''(INTERNAL) Like fmath.fprod for I{non-finite} C{other}s.
2020 '''
2021 r = _1_0
2022 for f in others:
2023 r *= sum(f._ps) if _isFsum_2Tuple(f) else float(f)
2024 return r
2026 def _mul_scalar(self, factor, op):
2027 '''(INTERNAL) Return C{B{self} * scalar B{factor}} as L{Fsum}, C{0.0} or C{self}.
2028 '''
2029 # assert isscalar(factor)
2030 if self._ps and self._finite(factor, op=op):
2031 f = self if factor == _1_0 else (
2032 self._neg if factor == _N_1_0 else
2033 self._ps_mul(op, factor).as_iscalar)
2034 else:
2035 f = _0_0
2036 return f
2038# @property_RO
2039# def _n_d(self):
2040# n, d = self.as_integer_ratio()
2041# return n / d
2043 @property_RO
2044 def _neg(self):
2045 '''(INTERNAL) Return C{Fsum(-self)} or scalar C{NEG0}.
2046 '''
2047 return _Psum(self._ps_neg) if self._ps else NEG0
2049 @property_RO
2050 def _nfprs2(self):
2051 '''(INTERNAL) Handle I{non-finite} C{_fprs2}.
2052 '''
2053 try: # to handle nonfiniterrors, etc.
2054 t = self._fprs2
2055 except (OverflowError, ValueError):
2056 t = Fsum2Tuple(sum(self._ps), _NONFINITEr)
2057 return t
2059 def nonfinites(self, *OK):
2060 '''Handle I{non-finite} C{float}s as C{inf}, C{INF}, C{NINF}, C{nan}
2061 and C{NAN} for this L{Fsum} or throw C{OverflowError} respectively
2062 C{ValueError} exceptions, overriding the L{nonfiniterrors} default.
2064 @arg OK: If omitted, leave the override unchanged, if C{True},
2065 I{non-finites} are C{OK}, if C{False} throw exceptions
2066 or if C{None} remove the override (C{bool} or C{None}).
2068 @return: The previous setting (C{bool} or C{None} if not set).
2070 @see: Function L{nonfiniterrors<fsums.nonfiniterrors>}.
2072 @note: Use property L{nonfinitesOK<Fsum.nonfinitesOK>} to determine
2073 whether I{non-finites} are C{OK} for this L{Fsum} and by the
2074 L{nonfiniterrors} default.
2075 '''
2076 _ks = Fsum._nonfinites_isfine_kwds
2077 if OK: # delattrof(self, _isfine=None)
2078 k = _xkwds_pop(self.__dict__, _isfine=None)
2079 if OK[0] is not None:
2080 self._isfine = _ks[bool(OK[0])]
2081 self._update()
2082 else: # getattrof(self, _isfine=None)
2083 k = _xkwds_get(self.__dict__, _isfine=None)
2084 # dict(map(reversed, _ks.items())).get(k, None)
2085 # raises a TypeError: unhashable type: 'dict'
2086 return True if k is _ks[True] else (
2087 False if k is _ks[False] else None)
2089 _nonfinites_isfine_kwds = {True: dict(_isfine=_isOK),
2090 False: dict(_isfine=_isfinite)}
2092 @property_RO
2093 def nonfinitesOK(self):
2094 '''Are I{non-finites} C{OK} for this L{Fsum} or by default? (C{bool}).
2095 '''
2096# nf = self.nonfinites()
2097# if nf is None:
2098# nf = not nonfiniterrors()
2099 return _isOK_or_finite(INF, **self._isfine)
2101 def _nonfiniteX(self, X, op, f, nonfinites=None, raiser=None):
2102 '''(INTERNAL) Handle a I{non-finite} exception.
2103 '''
2104 if nonfinites is None:
2105 nonfinites = _isOK_or_finite(f, **self._isfine) if raiser is None else (not raiser)
2106 if not nonfinites:
2107 raise self._ErrorX(X, op, f)
2108 return f
2110 def _optionals(self, f2product=None, nonfinites=None, **name_RESIDUAL):
2111 '''(INTERNAL) Re/set options from keyword arguments.
2112 '''
2113 if f2product is not None:
2114 self.f2product(f2product)
2115 if nonfinites is not None:
2116 self.nonfinites(nonfinites)
2117 if name_RESIDUAL: # MUST be last
2118 n, kwds = _name2__(**name_RESIDUAL)
2119 if kwds:
2120 R = Fsum._RESIDUAL
2121 t = _threshold(R, **kwds)
2122 if t != R:
2123 self._RESIDUAL = t
2124 if n:
2125 self.name = n # self.rename(n)
2127 def _1_Over(self, x, op, **raiser_RESIDUAL): # vs _1_over
2128 '''(INTERNAL) Return C{Fsum(1) / B{x}}.
2129 '''
2130 return self._Fsum_as(_1_0)._ftruediv(x, op, **raiser_RESIDUAL)
2132 @property_RO
2133 def partials(self):
2134 '''Get this instance' current, partial sums (C{tuple} of C{float}s).
2135 '''
2136 return tuple(self._ps)
2138 def pow(self, x, *mod, **raiser_RESIDUAL):
2139 '''Return C{B{self}**B{x}} as L{Fsum}.
2141 @arg x: The exponent (C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
2142 @arg mod: Optional modulus (C{int} or C{None}) for the 3-argument
2143 C{pow(B{self}, B{other}, B{mod})} version.
2144 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore
2145 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}
2146 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.
2148 @return: The C{pow(self, B{x})} or C{pow(self, B{x}, *B{mod})}
2149 result (L{Fsum}).
2151 @raise ResidualError: Non-zero, significant residual or invalid
2152 B{C{RESIDUAL}}.
2154 @note: If B{C{mod}} is given and C{None}, the result will be an
2155 C{integer} L{Fsum} provided this instance C{is_integer}
2156 or set to C{integer} by an L{Fsum.fint} call.
2158 @see: Methods L{Fsum.__ipow__}, L{Fsum.fint}, L{Fsum.is_integer}
2159 and L{Fsum.root}.
2160 '''
2161 f = self._copyd(self.pow)
2162 return f._fpow(x, _pow_op_, *mod, **raiser_RESIDUAL) # f = pow(f, x, *mod)
2164 def _pow(self, other, unused, op, **raiser_RESIDUAL):
2165 '''Return C{B{self} ** B{other}}.
2166 '''
2167 if _isFsum_2Tuple(other):
2168 f = self._pow_Fsum(other, op, **raiser_RESIDUAL)
2169 elif self._scalar(other, op):
2170 x = self._finite(other, op=op)
2171 f = self._pow_scalar(x, other, op, **raiser_RESIDUAL)
2172 else:
2173 f = self._pow_0_1(0, other)
2174 return f
2176 def _pow_0_1(self, x, other):
2177 '''(INTERNAL) Return B{C{self}**1} or C{B{self}**0 == 1.0}.
2178 '''
2179 return self if x else (1 if isint(other) and self.is_integer() else _1_0)
2181 def _pow_2_3(self, b, x, other, op, *mod, **raiser_RESIDUAL):
2182 '''(INTERNAL) 2-arg C{pow(B{b}, scalar B{x})} and 3-arg C{pow(B{b},
2183 B{x}, int B{mod} or C{None})}, embellishing errors.
2184 '''
2186 if mod: # b, x, mod all C{int}, unless C{mod} is C{None}
2187 m = mod[0]
2188 # assert _isFsum_2Tuple(b)
2190 def _s(s, r):
2191 R = self._raiser(r, s, **raiser_RESIDUAL)
2192 if R:
2193 raise self._ResidualError(op, other, r, mod=m, **R)
2194 return s
2196 b = _s(*(b._fprs2 if m is None else b._fint2))
2197 x = _s(*_2tuple2(x))
2199 try:
2200 # 0**INF == 0.0, 1**INF == 1.0, -1**2.3 == -(1**2.3)
2201 s = pow(b, x, *mod)
2202 if iscomplex(s):
2203 # neg**frac == complex in Python 3+, but ValueError in 2-
2204 raise ValueError(_strcomplex(s, b, x, *mod))
2205 _ = _2finite(s, **self._isfine) # ignore float
2206 return s
2207 except Exception as X:
2208 raise self._ErrorX(X, op, other, *mod)
2210 def _pow_Fsum(self, other, op, **raiser_RESIDUAL):
2211 '''(INTERNAL) Return C{B{self} **= B{other}} for C{_isFsum_2Tuple(other)}.
2212 '''
2213 # assert _isFsum_2Tuple(other)
2214 x, r = other._fprs2
2215 f = self._pow_scalar(x, other, op, **raiser_RESIDUAL)
2216 if f and r:
2217 f *= self._pow_scalar(r, other, op, **raiser_RESIDUAL)
2218 return f
2220 def _pow_int(self, x, other, op, **raiser_RESIDUAL):
2221 '''(INTERNAL) Return C{B{self} **= B{x}} for C{int B{x} >= 0}.
2222 '''
2223 # assert isint(x) and x >= 0
2224 ps = self._ps
2225 if len(ps) > 1:
2226 _mul_Fsum = Fsum._mul_Fsum
2227 if x > 4:
2228 p = self
2229 f = self if (x & 1) else self._Fsum_as(_1_0)
2230 m = x >> 1 # // 2
2231 while m:
2232 p = _mul_Fsum(p, p, op) # p **= 2
2233 if (m & 1):
2234 f = _mul_Fsum(f, p, op) # f *= p
2235 m >>= 1 # //= 2
2236 elif x > 1: # self**2, 3, or 4
2237 f = _mul_Fsum(self, self, op)
2238 if x > 2: # self**3 or 4
2239 p = self if x < 4 else f
2240 f = _mul_Fsum(f, p, op)
2241 else: # self**1 or self**0 == 1 or _1_0
2242 f = self._pow_0_1(x, other)
2243 elif ps: # self._ps[0]**x
2244 f = self._pow_2_3(ps[0], x, other, op, **raiser_RESIDUAL)
2245 else: # PYCHOK no cover
2246 # 0**pos_int == 0, but 0**0 == 1
2247 f = 0 if x else 1
2248 return f
2250 def _pow_scalar(self, x, other, op, **raiser_RESIDUAL):
2251 '''(INTERNAL) Return C{self**B{x}} for C{scalar B{x}}.
2252 '''
2253 s, r = self._fprs2
2254 if r:
2255 # assert s != 0
2256 if isint(x, both=True): # self**int
2257 x = int(x)
2258 y = abs(x)
2259 if y > 1:
2260 f = self._pow_int(y, other, op, **raiser_RESIDUAL)
2261 if x > 0: # i.e. > 1
2262 return f # Fsum or scalar
2263 # assert x < 0 # i.e. < -1
2264 if _isFsum(f):
2265 s, r = f._fprs2
2266 if r:
2267 return self._1_Over(f, op, **raiser_RESIDUAL)
2268 else: # scalar
2269 s = f
2270 # use s**(-1) to get the CPython
2271 # float_pow error iff s is zero
2272 x = -1
2273 elif x < 0: # self**(-1)
2274 return self._1_Over(self, op, **raiser_RESIDUAL) # 1 / self
2275 else: # self**1 or self**0
2276 return self._pow_0_1(x, other) # self, 1 or 1.0
2277 else: # self**fractional
2278 R = self._raiser(r, s, **raiser_RESIDUAL)
2279 if R:
2280 raise self._ResidualError(op, other, r, **R)
2281 n, d = self.as_integer_ratio()
2282 if abs(n) > abs(d):
2283 n, d, x = d, n, (-x)
2284 s = n / d
2285 # assert isscalar(s) and isscalar(x)
2286 return self._pow_2_3(s, x, other, op, **raiser_RESIDUAL)
2288 def _ps_acc(self, ps, xs, up=True, **unused):
2289 '''(INTERNAL) Accumulate C{xs} known scalars into list C{ps}.
2290 '''
2291 n = 0
2292 _2s = _2sum
2293 _fi = self._isfine
2294 for x in (tuple(xs) if xs is ps else xs):
2295 # assert isscalar(x) and _isOK_or_finite(x, **self._isfine)
2296 if x:
2297 i = 0
2298 for p in ps:
2299 x, p = _2s(x, p, **_fi)
2300 if p:
2301 ps[i] = p
2302 i += 1
2303 ps[i:] = (x,) if x else ()
2304 n += 1
2305 if n:
2306 self._n += n
2307 # Fsum._ps_max = max(Fsum._ps_max, len(ps))
2308 if up:
2309 self._update()
2310# x = sum(ps)
2311# if not _isOK_or_finite(x, **fi):
2312# ps[:] = x, # collapse ps
2313 return ps
2315 def _ps_mul(self, op, *factors):
2316 '''(INTERNAL) Multiply this instance' C{partials} with
2317 each scalar C{factor} and accumulate into an C{Fsum}.
2318 '''
2319 def _psfs(ps, fs, _isfine=_isfinite):
2320 if len(ps) < len(fs):
2321 ps, fs = fs, ps
2322 if self._f2product:
2323 fs, p = _2split3s(fs), fs
2324 if len(ps) > 1 and fs is not p:
2325 fs = tuple(fs) # several ps
2326 _pfs = _2products
2327 else:
2328 def _pfs(p, fs):
2329 return (p * f for f in fs)
2331 for p in ps:
2332 for x in _pfs(p, fs):
2333 yield x if _isfine(x) else _nfError(x)
2335 xs = _psfs(self._ps, factors, **self._isfine)
2336 f = _Psum(self._ps_acc([], xs, up=False), name=op)
2337 return f
2339 @property_RO
2340 def _ps_neg(self):
2341 '''(INTERNAL) Yield the partials, I{negated}.
2342 '''
2343 for p in self._ps:
2344 yield -p
2346 def _ps_other(self, op, other):
2347 '''(INTERNAL) Yield C{other} as C{scalar}s.
2348 '''
2349 if _isFsum_2Tuple(other):
2350 for p in other._ps:
2351 yield p
2352 else:
2353 yield self._scalar(other, op)
2355 def _ps_1sum(self, *less):
2356 '''(INTERNAL) Return the partials sum, 1-primed C{less} some scalars.
2357 '''
2358 def _1psls(ps, ls):
2359 yield _1_0
2360 for p in ps:
2361 yield p
2362 for p in ls:
2363 yield -p
2364 yield _N_1_0
2366 return _fsum(_1psls(self._ps, less))
2368 def _raiser(self, r, s, raiser=True, **RESIDUAL):
2369 '''(INTERNAL) Does ratio C{r / s} exceed the RESIDUAL threshold
2370 I{and} is residual C{r} I{non-zero} or I{significant} (for a
2371 negative respectively positive C{RESIDUAL} threshold)?
2372 '''
2373 if r and raiser:
2374 t = self._RESIDUAL
2375 if RESIDUAL:
2376 t = _threshold(t, **RESIDUAL)
2377 if t < 0 or (s + r) != s:
2378 q = (r / s) if s else s # == 0.
2379 if fabs(q) > fabs(t):
2380 return dict(ratio=q, R=t)
2381 return {}
2383 def _rcopyd(self, other, which):
2384 '''(INTERNAL) Copy for I{reverse-dyadic} operators.
2385 '''
2386 return other._copyd(which) if _isFsum(other) else \
2387 self._copyd(which)._fset(other)
2389 rdiv = __rtruediv__
2391 @property_RO
2392 def real(self):
2393 '''Get the C{real} part of this instance (C{float}).
2395 @see: Methods L{Fsum.__float__} and L{Fsum.fsum}
2396 and properties L{Fsum.ceil}, L{Fsum.floor},
2397 L{Fsum.imag} and L{Fsum.residual}.
2398 '''
2399 return float(self)
2401 @property_RO
2402 def residual(self):
2403 '''Get this instance' residual or residue (C{float} or C{int}):
2404 the C{sum(partials)} less the precision running sum C{fsum}.
2406 @note: The C{residual is INT0} iff the precision running
2407 C{fsum} is considered to be I{exact}.
2409 @see: Methods L{Fsum.fsum}, L{Fsum.fsum2} and L{Fsum.is_exact}.
2410 '''
2411 return self._fprs2.residual
2413 def RESIDUAL(self, *threshold):
2414 '''Get and set this instance' I{ratio} for raising L{ResidualError}s,
2415 overriding the default from env variable C{PYGEODESY_FSUM_RESIDUAL}.
2417 @arg threshold: If C{scalar}, the I{ratio} to exceed for raising
2418 L{ResidualError}s in division and exponention, if
2419 C{None}, restore the default set with env variable
2420 C{PYGEODESY_FSUM_RESIDUAL} or if omitted, keep the
2421 current setting.
2423 @return: The previous C{RESIDUAL} setting (C{float}), default C{0.0}.
2425 @raise ResidualError: Invalid B{C{threshold}}.
2427 @note: L{ResidualError}s may be thrown if (1) the non-zero I{ratio}
2428 C{residual / fsum} exceeds the given B{C{threshold}} and (2)
2429 the C{residual} is non-zero and (3) is I{significant} vs the
2430 C{fsum}, i.e. C{(fsum + residual) != fsum} and (4) optional
2431 keyword argument C{raiser=False} is missing. Specify a
2432 negative B{C{threshold}} for only non-zero C{residual}
2433 testing without the I{significant} case.
2434 '''
2435 r = self._RESIDUAL
2436 if threshold:
2437 t = threshold[0]
2438 self._RESIDUAL = Fsum._RESIDUAL if t is None else ( # for ...
2439 (_0_0 if t else _1_0) if isbool(t) else
2440 _threshold(t)) # ... backward compatibility
2441 return r
2443 def _ResidualError(self, op, other, residual, **mod_R):
2444 '''(INTERNAL) Non-zero B{C{residual}} etc.
2445 '''
2446 def _p(mod=None, R=0, **unused): # ratio=0
2447 return (_non_zero_ if R < 0 else _significant_) \
2448 if mod is None else _integer_
2450 t = _stresidual(_p(**mod_R), residual, **mod_R)
2451 return self._Error(op, other, ResidualError, txt=t)
2453 def root(self, root, **raiser_RESIDUAL):
2454 '''Return C{B{self}**(1 / B{root})} as L{Fsum}.
2456 @arg root: Non-zero order (C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
2457 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore any
2458 L{ResidualError}s (C{bool}) or C{B{RESIDUAL}=scalar}
2459 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.
2461 @return: The C{self ** (1 / B{root})} result (L{Fsum}).
2463 @raise ResidualError: Non-zero, significant residual or invalid
2464 B{C{RESIDUAL}}.
2466 @see: Method L{Fsum.pow}.
2467 '''
2468 x = self._1_Over(root, _truediv_op_, **raiser_RESIDUAL)
2469 f = self._copyd(self.root)
2470 return f._fpow(x, f.name, **raiser_RESIDUAL) # == pow(f, x)
2472 def _scalar(self, other, op, **txt):
2473 '''(INTERNAL) Return scalar C{other} or throw a C{TypeError}.
2474 '''
2475 if isscalar(other):
2476 return other
2477 raise self._Error(op, other, _TypeError, **txt) # _invalid_
2479 def signOf(self, res=True):
2480 '''Determine the sign of this instance.
2482 @kwarg res: If C{True}, consider the residual,
2483 otherwise ignore the latter (C{bool}).
2485 @return: The sign (C{int}, -1, 0 or +1).
2486 '''
2487 s, r = self._nfprs2
2488 r = (-r) if res else 0
2489 return _signOf(s, r)
2491 def toRepr(self, **lenc_prec_sep_fmt): # PYCHOK signature
2492 '''Return this C{Fsum} instance as representation.
2494 @kwarg lenc_prec_sep_fmt: Optional keyword arguments
2495 for method L{Fsum.toStr}.
2497 @return: This instance (C{repr}).
2498 '''
2499 return Fmt.repr_at(self, self.toStr(**lenc_prec_sep_fmt))
2501 def toStr(self, lenc=True, **prec_sep_fmt): # PYCHOK signature
2502 '''Return this C{Fsum} instance as string.
2504 @kwarg lenc: If C{True}, include the current C{[len]} of this
2505 L{Fsum} enclosed in I{[brackets]} (C{bool}).
2506 @kwarg prec_sep_fmt: Optional keyword arguments for method
2507 L{Fsum2Tuple.toStr}.
2509 @return: This instance (C{str}).
2510 '''
2511 p = self.classname
2512 if lenc:
2513 p = Fmt.SQUARE(p, len(self))
2514 n = _enquote(self.name, white=_UNDER_)
2515 t = self._nfprs2.toStr(**prec_sep_fmt)
2516 return NN(p, _SPACE_, n, t)
2518 def _truediv(self, other, op, **raiser_RESIDUAL):
2519 '''(INTERNAL) Return C{B{self} / B{other}} as an L{Fsum}.
2520 '''
2521 f = self._copyd(self.__truediv__)
2522 return f._ftruediv(other, op, **raiser_RESIDUAL)
2524 def _update(self, updated=True): # see ._fset
2525 '''(INTERNAL) Zap all cached C{Property_RO} values.
2526 '''
2527 if updated:
2528 _pop = self.__dict__.pop
2529 for p in _ROs:
2530 _ = _pop(p, None)
2531# Fsum._fint2._update(self)
2532# Fsum._fprs ._update(self)
2533# Fsum._fprs2._update(self)
2534 return self # for .fset_
2536_ROs = _allPropertiesOf_n(3, Fsum, Property_RO) # PYCHOK see Fsum._update
2538if _NONFINITES == _std_: # PYCHOK no cover
2539 _ = nonfiniterrors(False)
2542def _Float_Int(arg, **name_Error):
2543 '''(INTERNAL) L{DivMod2Tuple}, L{Fsum2Tuple} Unit.
2544 '''
2545 U = Int if isint(arg) else Float
2546 return U(arg, **name_Error)
2549class DivMod2Tuple(_NamedTuple):
2550 '''2-Tuple C{(div, mod)} with the quotient C{div} and remainder
2551 C{mod} results of a C{divmod} operation.
2553 @note: Quotient C{div} an C{int} in Python 3+ but a C{float}
2554 in Python 2-. Remainder C{mod} an L{Fsum} instance.
2555 '''
2556 _Names_ = ('div', 'mod')
2557 _Units_ = (_Float_Int, Fsum)
2560class Fsum2Tuple(_NamedTuple): # in .fstats
2561 '''2-Tuple C{(fsum, residual)} with the precision running C{fsum}
2562 and the C{residual}, the sum of the remaining partials. Each
2563 item is C{float} or C{int}.
2565 @note: If the C{residual is INT0}, the C{fsum} is considered
2566 to be I{exact}, see method L{Fsum2Tuple.is_exact}.
2567 '''
2568 _Names_ = ( typename(Fsum.fsum), Fsum.residual.name)
2569 _Units_ = (_Float_Int, _Float_Int)
2571 def __abs__(self): # in .fmath
2572 return self._Fsum.__abs__()
2574 def __bool__(self): # PYCHOK Python 3+
2575 return bool(self._Fsum)
2577 def __eq__(self, other):
2578 return self._other_op(other, self.__eq__)
2580 def __float__(self):
2581 return self._Fsum.__float__()
2583 def __ge__(self, other):
2584 return self._other_op(other, self.__ge__)
2586 def __gt__(self, other):
2587 return self._other_op(other, self.__gt__)
2589 def __le__(self, other):
2590 return self._other_op(other, self.__le__)
2592 def __lt__(self, other):
2593 return self._other_op(other, self.__lt__)
2595 def __int__(self):
2596 return self._Fsum.__int__()
2598 def __ne__(self, other):
2599 return self._other_op(other, self.__ne__)
2601 def __neg__(self):
2602 return self._Fsum.__neg__()
2604 __nonzero__ = __bool__ # Python 2-
2606 def __pos__(self):
2607 return self._Fsum.__pos__()
2609 def as_integer_ratio(self):
2610 '''Return this instance as the ratio of 2 integers.
2612 @see: Method L{Fsum.as_integer_ratio} for further details.
2613 '''
2614 return self._Fsum.as_integer_ratio()
2616 @property_RO
2617 def _fint2(self):
2618 return self._Fsum._fint2
2620 @property_RO
2621 def _fprs2(self):
2622 return self._Fsum._fprs2
2624 @Property_RO
2625 def _Fsum(self): # this C{Fsum2Tuple} as L{Fsum}, in .fstats
2626 s, r = _s_r2(*self)
2627 ps = (r, s) if r else (s,)
2628 return _Psum(ps, name=self.name)
2630 def Fsum_(self, *xs, **name_f2product_nonfinites_RESIDUAL):
2631 '''Return this C{Fsum2Tuple} as an L{Fsum} plus some C{xs}.
2632 '''
2633 return Fsum(self, *xs, **name_f2product_nonfinites_RESIDUAL)
2635 def is_exact(self):
2636 '''Is this L{Fsum2Tuple} considered to be exact? (C{bool}).
2637 '''
2638 return self._Fsum.is_exact()
2640 def is_finite(self): # in .constants
2641 '''Is this L{Fsum2Tuple} C{finite}? (C{bool}).
2643 @see: Function L{isfinite<pygeodesy.isfinite>}.
2644 '''
2645 return self._Fsum.is_finite()
2647 def is_integer(self):
2648 '''Is this L{Fsum2Tuple} C{integer}? (C{bool}).
2649 '''
2650 return self._Fsum.is_integer()
2652 def _mul_scalar(self, other, op): # for Fsum._fmul
2653 return self._Fsum._mul_scalar(other, op)
2655 @property_RO
2656 def _n(self):
2657 return self._Fsum._n
2659 def _other_op(self, other, which):
2660 C, s = (tuple, self) if isinstance(other, tuple) else (Fsum, self._Fsum)
2661 return getattr(C, typename(which))(s, other)
2663 @property_RO
2664 def _ps(self):
2665 return self._Fsum._ps
2667 @property_RO
2668 def _ps_neg(self):
2669 return self._Fsum._ps_neg
2671 def signOf(self, **res):
2672 '''Like method L{Fsum.signOf}.
2673 '''
2674 return self._Fsum.signOf(**res)
2676 def toStr(self, fmt=Fmt.g, **prec_sep): # PYCHOK signature
2677 '''Return this L{Fsum2Tuple} as string (C{str}).
2679 @kwarg fmt: Optional C{float} format (C{letter}).
2680 @kwarg prec_sep: Optional keyword arguments for function
2681 L{fstr<streprs.fstr>}.
2682 '''
2683 return Fmt.PAREN(fstr(self, fmt=fmt, strepr=str, force=False, **prec_sep))
2685_Fsum_2Tuple_types = Fsum, Fsum2Tuple # PYCHOK lines
2688class ResidualError(_ValueError):
2689 '''Error raised for a division, power or root operation of
2690 an L{Fsum} instance with a C{residual} I{ratio} exceeding
2691 the L{RESIDUAL<Fsum.RESIDUAL>} threshold.
2693 @see: Module L{pygeodesy.fsums} and method L{Fsum.RESIDUAL}.
2694 '''
2695 pass
2698try:
2699 from math import fsum as _fsum # precision IEEE-754 sum, Python 2.6+
2701 # make sure _fsum works as expected (XXX check
2702 # float.__getformat__('float')[:4] == 'IEEE'?)
2703 if _fsum((1, 1e101, 1, -1e101)) != 2: # PYCHOK no cover
2704 del _fsum # nope, remove _fsum ...
2705 raise ImportError() # ... use _fsum below
2707 _sum = _fsum
2708except ImportError:
2709 _sum = sum
2711 def _fsum(xs): # in .elliptic
2712 '''(INTERNAL) Precision summation, Python 2.5-.
2713 '''
2714 F = Fsum(name=_fsum.name, f2product=False, nonfinites=True)
2715 return float(F._facc(xs, up=False))
2718def fsum(xs, nonfinites=None, **floats):
2719 '''Precision floating point summation from Python's C{math.fsum}.
2721 @arg xs: Iterable of items to add (each C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
2722 @kwarg nonfinites: Use C{B{nonfinites}=True} if I{non-finites} are C{OK}, if
2723 C{False} I{non-finites} raise an Overflow-/ValueError or if
2724 C{None}, L{nonfiniterrors} applies (C{bool} or C{None}).
2725 @kwarg floats: DEPRECATED keyword argument C{B{floats}=False} (C{bool}), use
2726 keyword argument C{B{nonfinites}=False} instead.
2728 @return: Precision C{fsum} (C{float}).
2730 @raise OverflowError: Infinite B{C{xs}} item or intermediate C{math.fsum} overflow.
2732 @raise TypeError: Invalid B{C{xs}} item.
2734 @raise ValueError: Invalid or C{NAN} B{C{xs}} item.
2736 @see: Function L{nonfiniterrors}, class L{Fsum} and methods L{Fsum.nonfinites},
2737 L{Fsum.fsum}, L{Fsum.fadd} and L{Fsum.fadd_}.
2738 '''
2739 return _xsum(fsum, xs, nonfinites=nonfinites, **floats) if xs else _0_0
2742def fsum_(*xs, **nonfinites):
2743 '''Precision floating point summation of all positional items.
2745 @arg xs: Items to add (each C{scalar}, an L{Fsum} or L{Fsum2Tuple}), all positional.
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(fsum_, xs, **nonfinites) if xs else _0_0 # origin=1?
2753def fsumf_(*xs):
2754 '''Precision floating point summation of all positional items with I{non-finites} C{OK}.
2756 @arg xs: Items to add (each C{scalar}, an L{Fsum} or L{Fsum2Tuple}),
2757 all positional.
2759 @see: Function L{fsum_<fsums.fsum_>} for further details.
2760 '''
2761 return _xsum(fsumf_, xs, nonfinites=True) if xs else _0_0 # origin=1?
2764def fsum1(xs, **nonfinites):
2765 '''Precision floating point summation, 1-primed.
2767 @arg xs: Iterable of items to add (each C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
2768 @kwarg nonfinites: Use C{B{nonfinites}=True} if I{non-finites} are C{OK} (C{bool}).
2770 @see: Function L{fsum<fsums.fsum>} for further details.
2771 '''
2772 return _xsum(fsum1, xs, primed=1, **nonfinites) if xs else _0_0
2775def fsum1_(*xs, **nonfinites):
2776 '''Precision floating point summation of all positional items, 1-primed.
2778 @arg xs: Items to add (each C{scalar}, an L{Fsum} or L{Fsum2Tuple}), all positional.
2779 @kwarg nonfinites: Use C{B{nonfinites}=True} if I{non-finites} are C{OK} (C{bool}).
2781 @see: Function L{fsum_<fsums.fsum_>} for further details.
2782 '''
2783 return _xsum(fsum1_, xs, primed=1, **nonfinites) if xs else _0_0 # origin=1?
2786def fsum1f_(*xs):
2787 '''Precision floating point summation of all positional items, 1-primed and
2788 with I{non-finites} C{OK}.
2790 @see: Function L{fsum_<fsums.fsum_>} for further details.
2791 '''
2792 return _xsum(fsum1f_, xs, nonfinites=True, primed=1) if xs else _0_0
2795def _x_isfine(nfOK, **kwds): # get the C{_x} and C{_isfine} handlers.
2796 _x_kwds = dict(_x= (_passarg if nfOK else _2finite),
2797 _isfine=(_isOK if nfOK else _isfinite)) # PYCHOK kwds
2798 _x_kwds.update(kwds)
2799 return _x_kwds
2802def _X_ps(X): # default C{_X} handler
2803 return X._ps # lambda X: X._ps
2806def _xs(xs, _X=_X_ps, _x=float, _isfine=_isfinite, # defaults for Fsum._facc
2807 origin=0, which=None, **_Cdot):
2808 '''(INTERNAL) Yield each C{xs} item as 1 or more C{float}s.
2809 '''
2810 i, x = 0, xs
2811 try:
2812 for i, x in enumerate(_xiterable(xs)):
2813 if _isFsum_2Tuple(x):
2814 for p in _X(x):
2815 yield p if _isfine(p) else _nfError(p)
2816 else:
2817 f = _x(x)
2818 yield f if _isfine(f) else _nfError(f)
2820 except (OverflowError, TypeError, ValueError) as X:
2821 t = _xsError(X, xs, i + origin, x)
2822 if which: # prefix invokation
2823 w = unstr(which, *xs, _ELLIPSIS=4, **_Cdot)
2824 t = _COMMASPACE_(w, t)
2825 raise _xError(X, t, txt=None)
2828def _xsum(which, xs, nonfinites=None, primed=0, **floats): # origin=0
2829 '''(INTERNAL) Precision summation of C{xs} with conditions.
2830 '''
2831 if floats: # for backward compatibility
2832 nonfinites = _xkwds_get1(floats, floats=nonfinites)
2833 elif nonfinites is None:
2834 nonfinites = not nonfiniterrors()
2835 fs = _xs(xs, **_x_isfine(nonfinites, which=which)) # PYCHOK yield
2836 return _fsum(_1primed(fs) if primed else fs)
2839# delete all decorators, etc.
2840del _allPropertiesOf_n, deprecated_method, deprecated_property_RO, \
2841 Property, Property_RO, property_RO, _ALL_LAZY, _F2PRODUCT, \
2842 MANT_DIG, _NONFINITES, _RESIDUAL_0_0, _envPYGEODESY, _std_
2844if __name__ == _DMAIN_:
2846 # usage: python3 -m pygeodesy.fsums
2848 def _test(n):
2849 # copied from Hettinger, see L{Fsum} reference
2850 from pygeodesy import frandoms, printf
2852 printf(typename(_fsum), end=_COMMASPACE_)
2853 printf(typename(_psum), end=_COMMASPACE_)
2855 F = Fsum()
2856 if F.is_math_fsum():
2857 for t in frandoms(n, seeded=True):
2858 assert float(F.fset_(*t)) == _fsum(t)
2859 printf(_DOT_, end=NN)
2860 printf(NN)
2862 _test(128)
2864# **) MIT License
2865#
2866# Copyright (C) 2016-2025 -- mrJean1 at Gmail -- All Rights Reserved.
2867#
2868# Permission is hereby granted, free of charge, to any person obtaining a
2869# copy of this software and associated documentation files (the "Software"),
2870# to deal in the Software without restriction, including without limitation
2871# the rights to use, copy, modify, merge, publish, distribute, sublicense,
2872# and/or sell copies of the Software, and to permit persons to whom the
2873# Software is furnished to do so, subject to the following conditions:
2874#
2875# The above copyright notice and this permission notice shall be included
2876# in all copies or substantial portions of the Software.
2877#
2878# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
2879# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
2880# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
2881# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
2882# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
2883# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
2884# OTHER DEALINGS IN THE SOFTWARE.