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 Python
93.13 and newer or an equivalent C{fma} implementation for Python 3.12 and
10older. Set env variable C{PYGEODESY_FSUM_F2PRODUCT} to C{"std"} or any
11non-empty string or invoke function C{pygeodesy.f2product(True)} to enable
12accurate multiplication. With C{"std"} the C{fma} implemention follows
13the C{math.fma} function, otherwise the implementation of the C{PyGeodesy
1424.09.09} release.
16Generally, an L{Fsum} instance is considered a C{float} plus a small or
17zero C{residue} aka C{residual}, 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 L{Fsum} is an I{exact float} or I{exact integer}.
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, Property, \
56 deprecated_property_RO, Property_RO, property_RO
57from pygeodesy.streprs import Fmt, fstr, unstr
58# from pygeodesy.units import Float, Int # from .constants
60from math import fabs, isinf, isnan, \
61 ceil as _ceil, floor as _floor # PYCHOK used! .ltp
63__all__ = _ALL_LAZY.fsums
64__version__ = '26.02.02'
66from pygeodesy.interns import (
67 _PLUS_ as _add_op_, # in .auxilats.auxAngle
68 _DSLASH_ as _floordiv_op_,
69 _EQUAL_ as _fset_op_,
70 _RANGLE_ as _gt_op_,
71 _LANGLE_ as _lt_op_,
72 _PERCENT_ as _mod_op_,
73 _STAR_ as _mul_op_,
74 _NOTEQUAL_ as _ne_op_,
75 _DSTAR_ as _pow_op_,
76 _DASH_ as _sub_op_, # in .auxilats.auxAngle
77 _SLASH_ as _truediv_op_
78)
79_divmod_op_ = _floordiv_op_ + _mod_op_
80_F2PRODUCT = _envPYGEODESY('FSUM_F2PRODUCT')
81_iadd_op_ = _add_op_ + _fset_op_ # in .auxilats.auxAngle, .fstats
82_integer_ = 'integer'
83_isub_op_ = _sub_op_ + _fset_op_ # in .auxilats.auxAngle
84_NONFINITEr = _0_0 # NOT INT0!
85_NONFINITES = _envPYGEODESY('FSUM_NONFINITES')
86_non_zero_ = 'non-zero'
87_RESIDUAL_0_0 = _envPYGEODESY('FSUM_RESIDUAL', _0_0)
88_significant_ = 'significant'
89_threshold_ = 'threshold'
92def _2finite(x, _isfine=_isfinite): # in .fstats
93 '''(INTERNAL) return C{float(x)} if finite.
94 '''
95 return (float(x) if _isfine(x) # and isscalar(x)
96 else _nfError(x))
99def _2float(index=None, _isfine=_isfinite, **name_x): # in .fmath, .fstats
100 '''(INTERNAL) Raise C{TypeError} or C{Overflow-/ValueError} if C{x} not finite.
101 '''
102 n, x = name_x.popitem() # _xkwds_item2(name_x)
103 try:
104 f = float(x)
105 return f if _isfine(f) else _nfError(x)
106 except Exception as X:
107 raise _xError(X, Fmt.INDEX(n, index), x)
110try: # MCCABE 26
111 from math import fma as _fma
113 def _2products(x, ys, *zs):
114 # yield(x * y for y in ys) + yield(z in zs)
115 # TwoProductFMA U{Algorithm 3.5
116 # <https://www.TUHH.De/ti3/paper/rump/OgRuOi05.pdf>}
117 for y in ys:
118 f = x * y
119 yield f
120 if _isfinite(f):
121 f = _fma(x, y, -f)
122 if f:
123 yield f
124 for z in zs:
125 yield z
127# _2split3 = \
128 _2split3s = _passarg # in Fsum.is_math_fma
130except ImportError: # PYCHOK DSPACE! Python 3.12-
132 if _F2PRODUCT and _F2PRODUCT != _std_:
133 # backward to PyGeodesy 24.09.09, with _fmaX
134 from pygeodesy.basics import _integer_ratio2
136 def _fma(*a_b_c): # PYCHOK no cover
137 # mimick C{math.fma} from Python 3.13+,
138 # the same accuracy, but ~14x slower
139 (n, d), (nb, db), (nc, dc) = map(_integer_ratio2, a_b_c)
140 # n, d = (n * nb * dc + d * db * nc), (d * db * dc)
141 d *= db
142 n *= nb * dc
143 n += nc * d
144 d *= dc
145 try:
146 n, d = _n_d2(n, d)
147 r = float(n / d)
148 except OverflowError: # "integer division result too large ..."
149 r = NINF if (_signOf(n, 0) * _signOf(d, 0)) < 0 else INF
150 return r if _isfinite(r) else _fmaX(r, *a_b_c) # "overflow in fma"
151 else:
152 _integer_ratio2 = None # redef, in Fsum.is_math_fma
154 def _fma(a, b, c): # PYCHOK redef
155 # mimick C{math.fma} from Python 3.13+,
156 # the same accuracy, but ~13x slower
157 b3s = _2split3(b), # 1-tuple of 3-tuple
158 r = _fsum(_2products(a, b3s, c))
159 return r if _isfinite(r) else _fmaX(r, a, b, c)
161 def _fmaX(r, *a_b_c): # PYCHOK no cover
162 # handle non-finite fma result as Python 3.13+ C-function U{math_fma_impl
163 # <https://GitHub.com/python/cpython/blob/main/Modules/mathmodule.c#L2305>}:
164 # raise a ValueError for a NAN result from non-NAN C{a_b_c}s, otherwise an
165 # OverflowError for a non-finite, non-NAN result from all finite C{a_b_c}s.
166 if isnan(r):
167 def _x(x):
168 return not isnan(x)
169 else: # non-finite, non-NAN
170 _x = _isfinite
171 if all(map(_x, a_b_c)):
172 raise _nfError(r, unstr(_fma, *a_b_c))
173 return r
175 def _2products(x, y3s, *zs): # PYCHOK in _fma, ...
176 # yield(x * y3 for y3 in y3s) + yield(z in zs)
177 # TwoProduct U{Algorithm 3.3<https://www.TUHH.De/ti3/paper/rump/OgRuOi05.pdf>}, also
178 # in Python 3.13+ C{Modules/mathmodule.c} under #ifndef UNRELIABLE_FMA ... #else ...
179 _, a, b = _2split3(x)
180 for y, c, d in y3s:
181 y *= x
182 yield y
183 if _isfinite(y):
184 # yield b * d - (((y - a * c) - b * c) - a * d)
185 # = b * d + (a * d - ((y - a * c) - b * c))
186 # = b * d + (a * d + (b * c - (y - a * c)))
187 # = b * d + (a * d + (b * c + (a * c - y)))
188 yield a * c - y
189 yield b * c
190 if d:
191 yield a * d
192 yield b * d
193 for z in zs:
194 yield z
196 _2FACTOR = pow(2, (MANT_DIG + 1) // 2) + _1_0 # 134217729 if MANT_DIG == 53
198 def _2split3(x):
199 # Split U{Algorithm 3.2<https://www.TUHH.De/ti3/paper/rump/OgRuOi05.pdf>}
200 a = c = x * _2FACTOR
201 a -= c - x
202 b = x - a
203 return x, a, b
205 def _2split3s(xs): # in Fsum.is_math_fma
206 return map(_2split3, xs)
209def f2product(two=None):
210 '''Turn accurate I{TwoProduct} multiplication on or off.
212 @kwarg two: If C{True}, turn I{TwoProduct} on, if C{False} off or
213 if C{None} or omitted, keep the current setting.
215 @return: The previous setting (C{bool}).
217 @see: I{TwoProduct} multiplication is based on the I{TwoProductFMA}
218 U{Algorithm 3.5 <https://www.TUHH.De/ti3/paper/rump/OgRuOi05.pdf>}
219 using function C{math.fma} from Python 3.13 and later or an
220 equivalent, slower implementation when not available.
221 '''
222 t = Fsum._f2product
223 if two is not None:
224 Fsum._f2product = bool(two)
225 return t
228def _Fsumf_(*xs): # in .auxLat, ...
229 '''(INTERNAL) An C{Fsum(xs)}, all C{scalar}, an L{Fsum} or L{Fsum2Tuple}.
230 '''
231 return Fsum()._facc_xsum(xs, up=False)
234def _Fsum1f_(*xs): # in .albers
235 '''(INTERNAL) An C{Fsum(xs)}, all C{scalar}, an L{Fsum} or L{Fsum2Tuple}, 1-primed.
236 '''
237 return Fsum()._facc_xsum(_1primed(xs), origin=-1, up=False)
240def _halfeven(s, r, p):
241 '''(INTERNAL) Round half-even.
242 '''
243 if (p > 0 and r > 0) or \
244 (p < 0 and r < 0): # signs match
245 r *= 2
246 t = s + r
247 if r == (t - s):
248 s = t
249 return s
252def _isFsum(x): # in .fmath
253 '''(INTERNAL) Is C{x} an C{Fsum} instance?
254 '''
255 return isinstance(x, Fsum)
258def _isFsum_2Tuple(x): # in .basics, .constants, .fmath, .fstats
259 '''(INTERNAL) Is C{x} an C{Fsum} or C{Fsum2Tuple} instance?
260 '''
261 return isinstance(x, _Fsum_2Tuple_types)
264def _isOK(unused):
265 '''(INTERNAL) Helper for C{Fsum._fsum2} and C{Fsum.nonfinites}.
266 '''
267 return True
270def _isOK_or_finite(x, _isfine=_isfinite):
271 '''(INTERNAL) Is C{x} finite or is I{non-finite} OK?
272 '''
273 # assert _isin(_isfine, _isOK, _isfinite)
274 return _isfine(x) # C{bool}
277def _n_d2(n, d):
278 '''(INTERNAL) Reduce C{n} and C{d} by C{gcd}.
279 '''
280 try:
281 c = _gcd(n, d)
282 if c > 1:
283 return (n // c), (d // c)
284 except TypeError: # non-int float
285 pass
286 return n, d
289def _nfError(x, *args):
290 '''(INTERNAL) Throw a C{not-finite} exception.
291 '''
292 E = _NonfiniteError(x)
293 t = Fmt.PARENSPACED(_not_finite_, x)
294 if args: # in _fmaX, _2sum
295 return E(txt=t, *args)
296 raise E(t, txt=None)
299def _NonfiniteError(x):
300 '''(INTERNAL) Return the Error class for C{x}, I{non-finite}.
301 '''
302 return _OverflowError if isinf(x) else (
303 _ValueError if isnan(x) else _AssertionError)
306def nonfiniterrors(raiser=None):
307 '''Throw C{OverflowError} and C{ValueError} exceptions for or
308 handle I{non-finite} C{float}s as C{inf}, C{INF}, C{NINF},
309 C{nan} and C{NAN} in summations and multiplications.
311 @kwarg raiser: If C{True}, throw exceptions, if C{False} handle
312 I{non-finites} or if C{None} or omitted, leave
313 the setting unchanged.
315 @return: Previous setting (C{bool}).
317 @note: C{inf}, C{INF} and C{NINF} throw an C{OverflowError},
318 C{nan} and C{NAN} a C{ValueError}.
319 '''
320 d = Fsum._isfine
321 if raiser is not None:
322 Fsum._isfine = {} if bool(raiser) else _nonfinites_isfine_kwds[True]
323 return (False if d is _nonfinites_isfine_kwds[True] else
324 _xkwds_get1(d, _isfine=_isfinite) is _isfinite) if d else True
327# def _nsum(xs):
328# '''(INTERNAL) U{Neumaier summation
329# <https://StackOverflow.com/questions/78633770/can-neumaier-summation-be-sped-up>},
330# see IV. Verbessertes Kahan-Babuška-Verfahren.
331# '''
332# s = r = _0_0
333# for x in map(float, xs):
334# t = s + x
335# if fabs(x) <= fabs(s):
336# r += (s - t) + x
337# else:
338# r += (x - t) + s
339# s = t
340# return s + r
343def _1primed(xs, *ys): # in .fmath
344 '''(INTERNAL) 1-Primed summation of iterable C{xs} less any C{ys}
345 items, all I{known} to be C{scalar}.
346 '''
347 yield _1_0
348 for x in xs:
349 yield x
350 for y in ys:
351 yield -y
352 yield _N_1_0
355def _psum(ps, **_isfine): # PYCHOK used!
356 '''(INTERNAL) Partials summation, updating C{ps}.
357 '''
358 # assert isinstance(ps, list)
359 i = len(ps) - 1
360 s = _0_0 if i < 0 else ps[i]
361 while i > 0:
362 i -= 1
363 s, r = _2sum(s, ps[i], **_isfine)
364 if r: # sum(ps) became inexact
365 if s:
366 ps[i:] = r, s
367 if i > 0:
368 s = _halfeven(s, r, ps[i-1])
369 break # return s
370 s = r # PYCHOK no cover
371 elif not _isfinite(s): # non-finite OK
372 i = 0 # collapse ps
373 if ps:
374 s += sum(ps)
375 ps[i:] = s,
376 return s
379def _Psum(ps, **name_f2product_nonfinites_RESIDUAL):
380 '''(INTERNAL) Return an C{Fsum} from I{ordered} partials C{ps}.
381 '''
382 F = Fsum(**name_f2product_nonfinites_RESIDUAL)
383 if ps:
384 F._ps[:] = ps
385 F._n = len(F._ps)
386 return F
389def _Psum_(*ps, **name_f2product_nonfinites_RESIDUAL):
390 '''(INTERNAL) Return an C{Fsum} from I{known scalar} C{ps}.
391 '''
392 return _Psum(ps, **name_f2product_nonfinites_RESIDUAL)
395def _residue(other):
396 '''(INTERNAL) Return the C{residual} or C{None} for C{scalar}.
397 '''
398 try:
399 r = other.residual
400 except AttributeError:
401 r = None # float, int, other
402 return r
405def _s_r2(s, r):
406 '''(INTERNAL) Return C{(s, r)}, I{ordered}.
407 '''
408 if _isfinite(s):
409 if r:
410 if fabs(s) < fabs(r):
411 s, r = r, (s or INT0)
412 else:
413 r = INT0
414 else:
415 r = _NONFINITEr
416 return s, r
419def _strcomplex(s, *args):
420 '''(INTERNAL) C{Complex} 2- or 3-arg C{pow} error as C{str}.
421 '''
422 c = typename(_strcomplex)[4:]
423 n = _sub_op_(len(args), _arg_)
424 t = unstr(pow, *args)
425 return _SPACE_(c, s, _from_, n, t)
428def _stresidual(prefix, residual, R=0, **mod_ratio):
429 '''(INTERNAL) Residual error txt C{str}.
430 '''
431 p = typename(_stresidual)[3:]
432 t = Fmt.PARENSPACED(p, Fmt(residual))
433 for n, v in itemsorted(mod_ratio):
434 p = Fmt.PARENSPACED(n, Fmt(v))
435 t = _COMMASPACE_(t, p)
436 return _SPACE_(prefix, t, Fmt.exceeds_R(R), _threshold_)
439def _2sum(a, b, _isfine=_isfinite): # in .testFmath
440 '''(INTERNAL) Return C{a + b} as 2-tuple C{(sum, residual)} with finite C{sum},
441 otherwise as 2-tuple C{(nonfinite, 0)} iff I{non-finites} are OK.
442 '''
443 # FastTwoSum U{Algorithm 1.1<https://www.TUHH.De/ti3/paper/rump/OgRuOi05.pdf>}
445 # Neumaier, A. U{Rundungsfehleranalyse einiger Verfahren zur Summation endlicher
446 # Summen<https://OnlineLibrary.Wiley.com/doi/epdf/10.1002/zamm.19740540106>},
447 # 1974, Zeitschrift für Angewandte Mathmatik und Mechanik, vol 51, nr 1, p 39-51
448 # <https://StackOverflow.com/questions/78633770/can-neumaier-summation-be-sped-up>
449 s = a + b
450 if _isfinite(s):
451 if fabs(a) < fabs(b):
452 r = (b - s) + a
453 else:
454 r = (a - s) + b
455 elif _isfine(s):
456 r = _NONFINITEr
457 else: # non-finite and not OK
458 t = unstr(_2sum, a, b)
459 raise _nfError(s, t)
460 return s, r
463def _threshold(threshold=_0_0, **kwds):
464 '''(INTERNAL) Get the L{ResidualError}s threshold,
465 optionally from single kwds C{B{RESIDUAL}=scalar}.
466 '''
467 if kwds:
468 threshold = _xkwds_get1(kwds, RESIDUAL=threshold)
469 try:
470 return _2finite(threshold) # PYCHOK None
471 except Exception as x:
472 raise ResidualError(threshold=threshold, cause=x)
475def _2tuple2(other):
476 '''(INTERNAL) Return 2-tuple C{(other, r)} with C{other} as C{int},
477 C{float} or C{as-is} and C{r} the residual of C{as-is} or 0.
478 '''
479 if _isFsum_2Tuple(other):
480 s, r = other._fint2
481 if r:
482 s, r = other._nfprs2
483 if r: # PYCHOK no cover
484 s = other # L{Fsum} as-is
485 else:
486 r = 0
487 s = other # C{type} as-is
488 if isint(s, both=True):
489 s = int(s)
490 return s, r
493class Fsum(_Named): # sync __methods__ with .vector3dBase.Vector3dBase, .fstats, ...
494 '''Precision floating point summation, I{running} summation and accurate multiplication.
496 Unlike Python's C{math.fsum}, this class accumulates values and provides intermediate,
497 I{running}, precision floating point summations. Accumulation may continue after any
498 intermediate, I{running} summuation.
500 @note: Values may be L{Fsum}, L{Fsum2Tuple}, C{int}, C{float} or C{scalar} instances,
501 i.e. any C{type} having method C{__float__}.
503 @note: Handling of I{non-finites} as C{inf}, C{INF}, C{NINF}, C{nan} and C{NAN} is
504 determined globally by function L{nonfiniterrors<fsums.nonfiniterrors>} or
505 by method L{nonfinites<Fsum.nonfinites>} for individual C{Fsum} instances,
506 overruling the global setting. For backward compatibility, I{non-finites}
507 raise exceptions by default.
509 @see: U{Hettinger<https://GitHub.com/ActiveState/code/tree/master/recipes/Python/
510 393090_Binary_floating_point_summatiaccurate_full/recipe-393090.py>},
511 U{Kahan<https://WikiPedia.org/wiki/Kahan_summation_algorithm>}, U{Klein
512 <https://Link.Springer.com/article/10.1007/s00607-005-0139-x>}, Python 2.6+
513 file I{Modules/mathmodule.c} and the issue log U{Full precision summation
514 <https://Bugs.Python.org/issue2819>}.
516 @see: Method L{f2product<Fsum.f2product>} for details about accurate I{TwoProduct}
517 multiplication.
519 @see: Module L{fsums<pygeodesy.fsums>} for env variables C{PYGEODESY_FSUM_F2PRODUCT},
520 C{PYGEODESY_FSUM_NONFINITES} and C{PYGEODESY_FSUM_RESIDUAL}.
521 '''
522 _f2product = _MODS.sys_version_info2 > (3, 12) or bool(_F2PRODUCT)
523 _isfine = {} # == _isfinite, see nonfiniterrors()
524 _n = 0
525# _ps = [] # partial sums
526# _ps_max = 0 # max(Fsum._ps_max, len(Fsum._ps)) # 41
527 _RESIDUAL = _threshold(_RESIDUAL_0_0)
529 def __init__(self, *xs, **name_f2product_nonfinites_RESIDUAL):
530 '''New L{Fsum}.
532 @arg xs: No, one or more initial items to accumulate (each C{scalar}, an
533 L{Fsum} or L{Fsum2Tuple}), all positional.
534 @kwarg name_f2product_nonfinites_RESIDUAL: Optional C{B{name}=NN} (C{str})
535 and settings C{B{f2product}=None} (C{bool}), C{B{nonfinites}=None}
536 (C{bool}) and C{B{RESIDUAL}=0.0} threshold (C{scalar}) for this
537 L{Fsum}.
539 @see: Methods L{Fsum.f2product}, L{Fsum.nonfinites}, L{Fsum.RESIDUAL},
540 L{Fsum.fadd} and L{Fsum.fadd_}.
541 '''
542 if name_f2product_nonfinites_RESIDUAL:
543 self._optionals(**name_f2product_nonfinites_RESIDUAL)
544 self._ps = [] # [_0_0], see L{Fsum._fprs}
545 if xs:
546 self._facc_args(xs, up=False)
548 def __abs__(self):
549 '''Return C{abs(self)} as an L{Fsum}.
550 '''
551 s = self.signOf() # == self._cmp_0(0)
552 return (-self) if s < 0 else self._copyd(self.__abs__)
554 def __add__(self, other):
555 '''Return C{B{self} + B{other}} as an L{Fsum}.
557 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar}.
559 @return: The sum (L{Fsum}).
561 @see: Methods L{Fsum.fadd_} and L{Fsum.fadd}.
562 '''
563 f = self._copyd(self.__add__)
564 return f._fadd(other)
566 def __bool__(self): # PYCHOK Python 3+
567 '''Return C{bool(B{self})}, C{True} iff C{residual} is zero.
568 '''
569 s, r = self._nfprs2
570 return bool(s or r) and s != -r # == self != 0
572 def __call__(self, other, **up): # in .fmath
573 '''Reset this C{Fsum} to C{other}, default C{B{up}=True}.
574 '''
575 self._ps[:] = 0, # clear for errors
576 self._fset(other, op=_fset_op_, **up)
577 return self
579 def __ceil__(self): # PYCHOK not special in Python 2-
580 '''Return this instance' C{math.ceil} as C{int} or C{float}.
582 @return: An C{int} in Python 3+, but C{float} in Python 2-.
584 @see: Methods L{Fsum.__floor__} and property L{Fsum.ceil}.
585 '''
586 return self.ceil
588 def __cmp__(self, other): # PYCHOK no cover
589 '''Compare this with an other instance or C{scalar}, Python 2-.
591 @return: -1, 0 or +1 (C{int}).
593 @raise TypeError: Incompatible B{C{other}} C{type}.
594 '''
595 s = self._cmp_0(other, typename(self.cmp))
596 return _signOf(s, 0)
598 def __divmod__(self, other, **raiser_RESIDUAL):
599 '''Return C{divmod(B{self}, B{other})} as a L{DivMod2Tuple}
600 with quotient C{div} an C{int} in Python 3+ or C{float}
601 in Python 2- and remainder C{mod} an L{Fsum} instance.
603 @arg other: Modulus (C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
604 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore
605 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}
606 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.
608 @raise ResidualError: Non-zero, significant residual or invalid
609 B{C{RESIDUAL}}.
611 @see: Method L{Fsum.fdiv}.
612 '''
613 f = self._copyd(self.__divmod__)
614 return f._fdivmod2(other, _divmod_op_, **raiser_RESIDUAL)
616 def __eq__(self, other):
617 '''Return C{(B{self} == B{other})} as C{bool} where B{C{other}}
618 is C{scalar}, an other L{Fsum} or L{Fsum2Tuple}.
619 '''
620 return self._cmp_0(other, _fset_op_ + _fset_op_) == 0
622 def __float__(self):
623 '''Return this instance' current, precision running sum as C{float}.
625 @see: Methods L{Fsum.fsum} and L{Fsum.int_float}.
626 '''
627 return float(self._fprs)
629 def __floor__(self): # PYCHOK not special in Python 2-
630 '''Return this instance' C{math.floor} as C{int} or C{float}.
632 @return: An C{int} in Python 3+, but C{float} in Python 2-.
634 @see: Methods L{Fsum.__ceil__} and property L{Fsum.floor}.
635 '''
636 return self.floor
638 def __floordiv__(self, other):
639 '''Return C{B{self} // B{other}} as an L{Fsum}.
641 @arg other: Divisor (C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
643 @return: The C{floor} quotient (L{Fsum}).
645 @see: Methods L{Fsum.__ifloordiv__}.
646 '''
647 f = self._copyd(self.__floordiv__)
648 return f._floordiv(other, _floordiv_op_)
650# def __format__(self, *other): # PYCHOK no cover
651# '''Not implemented.'''
652# return _NotImplemented(self, *other)
654 def __ge__(self, other):
655 '''Return C{(B{self} >= B{other})}, see C{__eq__}.
656 '''
657 return self._cmp_0(other, _gt_op_ + _fset_op_) >= 0
659 def __gt__(self, other):
660 '''Return C{(B{self} > B{other})}, see C{__eq__}.
661 '''
662 return self._cmp_0(other, _gt_op_) > 0
664 def __hash__(self): # PYCHOK no cover
665 '''Return C{hash(B{self})} as C{float}.
666 '''
667 # @see: U{Notes for type implementors<https://docs.Python.org/
668 # 3/library/numbers.html#numbers.Rational>}
669 return hash(self.partials) # tuple.__hash__()
671 def __iadd__(self, other):
672 '''Apply C{B{self} += B{other}} to this instance.
674 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar} value or
675 an iterable of several of the former.
677 @return: This instance, updated (L{Fsum}).
679 @raise TypeError: Invalid B{C{other}}, not
680 C{scalar} nor L{Fsum}.
682 @see: Methods L{Fsum.fadd_} and L{Fsum.fadd}.
683 '''
684 try:
685 return self._fadd(other, op=_iadd_op_)
686 except TypeError:
687 pass
688 _xiterable(other)
689 return self._facc(other)
691 def __ifloordiv__(self, other):
692 '''Apply C{B{self} //= B{other}} to this instance.
694 @arg other: Divisor (C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
696 @return: This instance, updated (L{Fsum}).
698 @raise ResidualError: Non-zero, significant residual
699 in B{C{other}}.
701 @raise TypeError: Invalid B{C{other}} type.
703 @raise ValueError: Invalid or I{non-finite} B{C{other}}.
705 @raise ZeroDivisionError: Zero B{C{other}}.
707 @see: Methods L{Fsum.__itruediv__}.
708 '''
709 return self._floordiv(other, _floordiv_op_ + _fset_op_)
711 def __imatmul__(self, other): # PYCHOK no cover
712 '''Not implemented.'''
713 return _NotImplemented(self, other)
715 def __imod__(self, other):
716 '''Apply C{B{self} %= B{other}} to this instance.
718 @arg other: Modulus (C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
720 @return: This instance, updated (L{Fsum}).
722 @see: Method L{Fsum.__divmod__}.
723 '''
724 return self._fdivmod2(other, _mod_op_ + _fset_op_).mod
726 def __imul__(self, other):
727 '''Apply C{B{self} *= B{other}} to this instance.
729 @arg other: Factor (C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
731 @return: This instance, updated (L{Fsum}).
733 @raise OverflowError: Partial C{2sum} overflow.
735 @raise TypeError: Invalid B{C{other}} type.
737 @raise ValueError: Invalid or I{non-finite} B{C{other}}.
738 '''
739 return self._fmul(other, _mul_op_ + _fset_op_)
741 def __int__(self):
742 '''Return this instance as an C{int}.
744 @see: Method L{Fsum.int_float} and properties L{Fsum.ceil}
745 and L{Fsum.floor}.
746 '''
747 i, _ = self._fint2
748 return i
750 def __invert__(self): # PYCHOK no cover
751 '''Not implemented.'''
752 # Luciano Ramalho, "Fluent Python", O'Reilly, 2nd Ed, 2022 p. 567
753 return _NotImplemented(self)
755 def __ipow__(self, other, *mod, **raiser_RESIDUAL): # PYCHOK 2 vs 3 args
756 '''Apply C{B{self} **= B{other}} to this instance.
758 @arg other: Exponent (C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
759 @arg mod: Optional modulus (C{int} or C{None}) for the 3-argument
760 C{pow(B{self}, B{other}, B{mod})} version.
761 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore
762 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}
763 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.
765 @return: This instance, updated (L{Fsum}).
767 @note: If B{C{mod}} is given, the result will be an C{integer}
768 L{Fsum} in Python 3+ if this instance C{is_integer} or
769 set to C{as_integer} and B{C{mod}} is given and C{None}.
771 @raise OverflowError: Partial C{2sum} overflow.
773 @raise ResidualError: Invalid B{C{RESIDUAL}} or the residual
774 is non-zero and significant and either
775 B{C{other}} is a fractional or negative
776 C{scalar} or B{C{mod}} is given and not
777 C{None}.
779 @raise TypeError: Invalid B{C{other}} type or 3-argument C{pow}
780 invocation failed.
782 @raise ValueError: If B{C{other}} is a negative C{scalar} and this
783 instance is C{0} or B{C{other}} is a fractional
784 C{scalar} and this instance is negative or has a
785 non-zero and significant residual or B{C{mod}}
786 is given as C{0}.
788 @see: CPython function U{float_pow<https://GitHub.com/
789 python/cpython/blob/main/Objects/floatobject.c>}.
790 '''
791 return self._fpow(other, _pow_op_ + _fset_op_, *mod, **raiser_RESIDUAL)
793 def __isub__(self, other):
794 '''Apply C{B{self} -= B{other}} to this instance.
796 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar} value or
797 an iterable of several of the former.
799 @return: This instance, updated (L{Fsum}).
801 @raise TypeError: Invalid B{C{other}} type.
803 @see: Methods L{Fsum.fsub_} and L{Fsum.fsub}.
804 '''
805 try:
806 return self._fsub(other, _isub_op_)
807 except TypeError:
808 pass
809 _xiterable(other)
810 return self._facc_neg(other)
812 def __iter__(self):
813 '''Return an C{iter}ator over a C{partials} duplicate.
814 '''
815 return iter(self.partials)
817 def __itruediv__(self, other, **raiser_RESIDUAL):
818 '''Apply C{B{self} /= B{other}} to this instance.
820 @arg other: Divisor (C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
821 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore
822 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}
823 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.
825 @return: This instance, updated (L{Fsum}).
827 @raise OverflowError: Partial C{2sum} overflow.
829 @raise ResidualError: Non-zero, significant residual or invalid
830 B{C{RESIDUAL}}.
832 @raise TypeError: Invalid B{C{other}} type.
834 @raise ValueError: Invalid or I{non-finite} B{C{other}}.
836 @raise ZeroDivisionError: Zero B{C{other}}.
838 @see: Method L{Fsum.__ifloordiv__}.
839 '''
840 return self._ftruediv(other, _truediv_op_ + _fset_op_, **raiser_RESIDUAL)
842 def __le__(self, other):
843 '''Return C{(B{self} <= B{other})}, see C{__eq__}.
844 '''
845 return self._cmp_0(other, _lt_op_ + _fset_op_) <= 0
847 def __len__(self):
848 '''Return the number of (non-zero) values accumulated (C{int}).
849 '''
850 return self._n
852 def __lt__(self, other):
853 '''Return C{(B{self} < B{other})}, see C{__eq__}.
854 '''
855 return self._cmp_0(other, _lt_op_) < 0
857 def __matmul__(self, other): # PYCHOK no cover
858 '''Not implemented.'''
859 return _NotImplemented(self, other)
861 def __mod__(self, other):
862 '''Return C{B{self} % B{other}} as an L{Fsum}.
864 @see: Method L{Fsum.__imod__}.
865 '''
866 f = self._copyd(self.__mod__)
867 return f._fdivmod2(other, _mod_op_).mod
869 def __mul__(self, other):
870 '''Return C{B{self} * B{other}} as an L{Fsum}.
872 @see: Method L{Fsum.__imul__}.
873 '''
874 f = self._copyd(self.__mul__)
875 return f._fmul(other, _mul_op_)
877 def __ne__(self, other):
878 '''Return C{(B{self} != B{other})}, see C{__eq__}.
879 '''
880 return self._cmp_0(other, _ne_op_) != 0
882 def __neg__(self):
883 '''Return C{copy(B{self})}, I{negated}.
884 '''
885 f = self._copyd(self.__neg__)
886 return f._fset(self._neg)
888 def __pos__(self):
889 '''Return this instance I{as-is}, like C{float.__pos__()}.
890 '''
891 return self if _pos_self else self._copyd(self.__pos__)
893 def __pow__(self, other, *mod): # PYCHOK 2 vs 3 args
894 '''Return C{B{self}**B{other}} as an L{Fsum}.
896 @see: Method L{Fsum.__ipow__}.
897 '''
898 f = self._copyd(self.__pow__)
899 return f._fpow(other, _pow_op_, *mod)
901 def __radd__(self, other):
902 '''Return C{B{other} + B{self}} as an L{Fsum}.
904 @see: Method L{Fsum.__iadd__}.
905 '''
906 f = self._rcopyd(other, self.__radd__)
907 return f._fadd(self)
909 def __rdivmod__(self, other):
910 '''Return C{divmod(B{other}, B{self})} as 2-tuple
911 C{(quotient, remainder)}.
913 @see: Method L{Fsum.__divmod__}.
914 '''
915 f = self._rcopyd(other, self.__rdivmod__)
916 return f._fdivmod2(self, _divmod_op_)
918# turned off, called by _deepcopy and _copy
919# def __reduce__(self): # Python 3.8+
920# ''' Pickle, like std C{fractions.Fraction}, see U{__reduce__
921# <https://docs.Python.org/3/library/pickle.html#object.__reduce__>}
922# '''
923# dict_ = self._Fsum_as().__dict__ # no __setstate__
924# return (type(self), self.partials, dict_)
926# def __repr__(self):
927# '''Return the default C{repr(this)}.
928# '''
929# return self.toRepr(lenc=True)
931 def __rfloordiv__(self, other):
932 '''Return C{B{other} // B{self}} as an L{Fsum}.
934 @see: Method L{Fsum.__ifloordiv__}.
935 '''
936 f = self._rcopyd(other, self.__rfloordiv__)
937 return f._floordiv(self, _floordiv_op_)
939 def __rmatmul__(self, other): # PYCHOK no cover
940 '''Not implemented.'''
941 return _NotImplemented(self, other)
943 def __rmod__(self, other):
944 '''Return C{B{other} % B{self}} as an L{Fsum}.
946 @see: Method L{Fsum.__imod__}.
947 '''
948 f = self._rcopyd(other, self.__rmod__)
949 return f._fdivmod2(self, _mod_op_).mod
951 def __rmul__(self, other):
952 '''Return C{B{other} * B{self}} as an L{Fsum}.
954 @see: Method L{Fsum.__imul__}.
955 '''
956 f = self._rcopyd(other, self.__rmul__)
957 return f._fmul(self, _mul_op_)
959 def __round__(self, *ndigits): # PYCHOK Python 3+
960 '''Return C{round(B{self}, *B{ndigits}} as an L{Fsum}.
962 @arg ndigits: Optional number of digits (C{int}).
963 '''
964 f = self._copyd(self.__round__)
965 # <https://docs.Python.org/3.12/reference/datamodel.html?#object.__round__>
966 return f._fset(round(float(self), *ndigits)) # can be C{int}
968 def __rpow__(self, other, *mod):
969 '''Return C{B{other}**B{self}} as an L{Fsum}.
971 @see: Method L{Fsum.__ipow__}.
972 '''
973 f = self._rcopyd(other, self.__rpow__)
974 return f._fpow(self, _pow_op_, *mod)
976 def __rsub__(self, other):
977 '''Return C{B{other} - B{self}} as L{Fsum}.
979 @see: Method L{Fsum.__isub__}.
980 '''
981 f = self._rcopyd(other, self.__rsub__)
982 return f._fsub(self, _sub_op_)
984 def __rtruediv__(self, other, **raiser_RESIDUAL):
985 '''Return C{B{other} / B{self}} as an L{Fsum}.
987 @see: Method L{Fsum.__itruediv__}.
988 '''
989 f = self._rcopyd(other, self.__rtruediv__)
990 return f._ftruediv(self, _truediv_op_, **raiser_RESIDUAL)
992# def __sizeof__(self):
993# '''Return the size of this instance (C{int} bytes}).
994# '''
995# return _sizeof(self._ps) + _sizeof(self._n)
997 def __str__(self):
998 '''Return the default C{str(self)}.
999 '''
1000 return self.toStr(lenc=True)
1002 def __sub__(self, other):
1003 '''Return C{B{self} - B{other}} as an L{Fsum}.
1005 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar}.
1007 @return: The difference (L{Fsum}).
1009 @see: Method L{Fsum.__isub__}.
1010 '''
1011 f = self._copyd(self.__sub__)
1012 return f._fsub(other, _sub_op_)
1014 def __truediv__(self, other, **raiser_RESIDUAL):
1015 '''Return C{B{self} / B{other}} as an L{Fsum}.
1017 @arg other: Divisor (C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
1018 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore
1019 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}
1020 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.
1022 @return: The quotient (L{Fsum}).
1024 @raise ResidualError: Non-zero, significant residual or invalid
1025 B{C{RESIDUAL}}.
1027 @see: Method L{Fsum.__itruediv__}.
1028 '''
1029 return self._truediv(other, _truediv_op_, **raiser_RESIDUAL)
1031 __trunc__ = __int__
1033 if _MODS.sys_version_info2 < (3, 0): # PYCHOK no cover
1034 # <https://docs.Python.org/2/library/operator.html#mapping-operators-to-functions>
1035 __div__ = __truediv__
1036 __idiv__ = __itruediv__
1037 __long__ = __int__
1038 __nonzero__ = __bool__
1039 __rdiv__ = __rtruediv__
1041 def as_integer_ratio(self):
1042 '''Return this instance as the ratio of 2 integers.
1044 @return: 2-Tuple C{(numerator, denominator)} both C{int} with
1045 C{numerator} signed and C{denominator} non-zero and
1046 positive. The C{numerator} is I{non-finite} if this
1047 instance is.
1049 @see: Method L{Fsum.fint2} and C{float.as_integer_ratio} in
1050 Python 2.7+.
1051 '''
1052 n, r = self._fint2
1053 if r:
1054 i, d = float(r).as_integer_ratio()
1055 n, d = _n_d2(n * d + i, d)
1056 else: # PYCHOK no cover
1057 d = 1
1058 return n, d
1060 @property_RO
1061 def as_iscalar(self):
1062 '''Get this instance I{as-is} (L{Fsum} with C{non-zero residual},
1063 C{scalar} or I{non-finite}).
1064 '''
1065 s, r = self._nfprs2
1066 return self if r else s
1068 @property_RO
1069 def ceil(self):
1070 '''Get this instance' C{ceil} value (C{int} in Python 3+, but
1071 C{float} in Python 2-).
1073 @note: This C{ceil} takes the C{residual} into account.
1075 @see: Method L{Fsum.int_float} and properties L{Fsum.floor},
1076 L{Fsum.imag} and L{Fsum.real}.
1077 '''
1078 s, r = self._fprs2
1079 c = _ceil(s) + int(r) - 1
1080 while r > (c - s): # (s + r) > c
1081 c += 1
1082 return c # _ceil(self._n_d)
1084 cmp = __cmp__
1086 def _cmp_0(self, other, op):
1087 '''(INTERNAL) Return C{scalar(self - B{other})} for 0-comparison.
1088 '''
1089 if _isFsum_2Tuple(other):
1090 s = self._ps_1sum(*other._ps)
1091 elif self._scalar(other, op):
1092 s = self._ps_1sum(other)
1093 else:
1094 s = self.signOf() # res=True
1095 return s
1097 def copy(self, deep=False, **name):
1098 '''Copy this instance, C{shallow} or B{C{deep}}.
1100 @kwarg name: Optional, overriding C{B{name}='"copy"} (C{str}).
1102 @return: The copy (L{Fsum}).
1103 '''
1104 n = _name__(name, name__=self.copy)
1105 f = _Named.copy(self, deep=deep, name=n)
1106 if f._ps is self._ps:
1107 f._ps = list(self._ps) # separate list
1108 if not deep:
1109 f._n = 1
1110 # assert f._f2product == self._f2product
1111 # assert f._Fsum is f
1112 # assert f._isfine is self._isfine
1113 # assert f._RESIDUAL is self._RESIDUAL
1114 return f
1116 def _copyd(self, which, name=NN):
1117 '''(INTERNAL) Copy for I{dyadic} operators.
1118 '''
1119 n = name or typename(which)
1120 # NOT .classof due to .Fdot(a, *b) args, etc.
1121 f = _Named.copy(self, deep=False, name=n)
1122 f._ps = list(self._ps) # separate list
1123 # assert f._n == self._n
1124 # assert f._f2product == self._f2product
1125 # assert f._Fsum is f
1126 # assert f._isfine is self._isfine
1127 # assert f._RESIDUAL is self._RESIDUAL
1128 return f
1130 divmod = __divmod__
1132 def _Error(self, op, other, Error, **txt_cause):
1133 '''(INTERNAL) Format an B{C{Error}} for C{{self} B{op} B{other}}.
1134 '''
1135 # self.as_iscalar causes RecursionError for ._fprs2 errors
1136 s = _Psum(self._ps, nonfinites=True, name=self.name)
1137 return Error(_SPACE_(s.as_iscalar, op, other), **txt_cause)
1139 def _ErrorX(self, X, op, other, *mod):
1140 '''(INTERNAL) Format the caught exception C{X}.
1141 '''
1142 E, t = _xError2(X)
1143 if mod:
1144 t = _COMMASPACE_(Fmt.PARENSPACED(mod=mod[0]), t)
1145 return self._Error(op, other, E, txt=t, cause=X)
1147 def _ErrorXs(self, X, xs, **kwds): # in .fmath
1148 '''(INTERNAL) Format the caught exception C{X}.
1149 '''
1150 E, t = _xError2(X)
1151 u = unstr(self.named3, *xs, _ELLIPSIS=4, **kwds)
1152 return E(u, txt=t, cause=X)
1154 def _facc(self, xs, up=True, **_X_x_origin):
1155 '''(INTERNAL) Accumulate more C{scalar}s, L{Fsum}s pr L{Fsum2Tuple}s.
1156 '''
1157 if xs:
1158 kwds = self._isfine
1159 if _X_x_origin:
1160 kwds = _xkwds(_X_x_origin, **kwds)
1161 fs = _xs(xs, **kwds) # PYCHOK yield
1162 ps = self._ps
1163 ps[:] = self._ps_acc(list(ps), fs, up=up)
1164# if len(ps) > 16:
1165# _ = _psum(ps, **self._isfine)
1166 return self
1168 def _facc_args(self, xs, **up):
1169 '''(INTERNAL) Accumulate 0, 1 or more C{xs}, all positional
1170 arguments in the caller of this method.
1171 '''
1172 return self._fadd(xs[0], **up) if len(xs) == 1 else \
1173 self._facc(xs, **up) # origin=1?
1175 def _facc_dot(self, n, xs, ys, **kwds): # in .fmath
1176 '''(INTERNAL) Accumulate C{fdot(B{xs}, *B{ys})}.
1177 '''
1178 if n > 0:
1179 _f = Fsum(**kwds)
1180 self._facc(_f(x).fmul(y) for x, y in zip(xs, ys)) # PYCHOK attr?
1181 return self
1183 def _facc_neg(self, xs, **up_origin):
1184 '''(INTERNAL) Accumulate more C{xs}, negated.
1185 '''
1186 def _N(X):
1187 return X._ps_neg
1189 def _n(x):
1190 return -float(x)
1192 return self._facc(xs, _X=_N, _x=_n, **up_origin)
1194 def _facc_power(self, power, xs, which, **raiser_RESIDUAL): # in .fmath
1195 '''(INTERNAL) Add each C{xs} as C{float(x**power)}.
1196 '''
1197 def _Pow4(p):
1198 r = 0
1199 if _isFsum_2Tuple(p):
1200 s, r = p._fprs2
1201 if r:
1202 m = Fsum._pow
1203 else: # scalar
1204 return _Pow4(s)
1205 elif isint(p, both=True) and int(p) >= 0:
1206 p = s = int(p)
1207 m = Fsum._pow_int
1208 else:
1209 p = s = _2float(power=p, **self._isfine)
1210 m = Fsum._pow_scalar
1211 return m, p, s, r
1213 _Pow, p, s, r = _Pow4(power)
1214 if p: # and xs:
1215 op = typename(which)
1216 _FsT = _Fsum_2Tuple_types
1217 _pow = self._pow_2_3
1219 def _P(X):
1220 f = _Pow(X, p, power, op, **raiser_RESIDUAL)
1221 return f._ps if isinstance(f, _FsT) else (f,)
1223 def _p(x):
1224 x = float(x)
1225 f = _pow(x, s, power, op, **raiser_RESIDUAL)
1226 if f and r:
1227 f *= _pow(x, r, power, op, **raiser_RESIDUAL)
1228 return f
1230 f = self._facc(xs, _X=_P, _x=_p) # origin=1?
1231 else:
1232 f = self._facc_scalar_(float(len(xs))) # x**0 == 1
1233 return f
1235 def _facc_scalar(self, xs, **up):
1236 '''(INTERNAL) Accumulate all C{xs}, each C{scalar}.
1237 '''
1238 if xs:
1239 ps = self._ps
1240 ps[:] = self._ps_acc(list(ps), xs, **up)
1241 return self
1243 def _facc_scalar_(self, *xs, **up):
1244 '''(INTERNAL) Accumulate all positional C{xs}, each C{scalar}.
1245 '''
1246 return self._facc_scalar(xs, **up)
1248# def _facc_up(self, up=True):
1249# '''(INTERNAL) Update the C{partials}, by removing
1250# and re-accumulating the final C{partial}.
1251# '''
1252# ps = self._ps
1253# while len(ps) > 1:
1254# p = ps.pop()
1255# if p:
1256# n = self._n
1257# _ = self._ps_acc(ps, (p,), up=False)
1258# self._n = n
1259# break
1260# return self._update() if up else self
1262 def _facc_xsum(self, xs, up=True, **origin_which):
1263 '''(INTERNAL) Accumulate all C{xs}, each C{scalar}, an L{Fsum}
1264 or L{Fsum2Tuple}, like function C{_xsum}.
1265 '''
1266 fs = _xs(xs, **_x_isfine(self.nonfinitesOK, _Cdot=type(self),
1267 **origin_which)) # PYCHOK yield
1268 return self._facc_scalar(fs, up=up)
1270 def fadd(self, xs=()):
1271 '''Add an iterable's items to this instance.
1273 @arg xs: Iterable of items to add (each C{scalar},
1274 an L{Fsum} or L{Fsum2Tuple}).
1276 @return: This instance (L{Fsum}).
1278 @raise OverflowError: Partial C{2sum} overflow.
1280 @raise TypeError: An invalid B{C{xs}} item.
1282 @raise ValueError: Invalid or I{non-finite} B{C{xs}} value.
1283 '''
1284 if _isFsum_2Tuple(xs):
1285 self._facc_scalar(xs._ps)
1286 elif isscalar(xs): # for backward compatibility # PYCHOK no cover
1287 x = _2float(x=xs, **self._isfine)
1288 self._facc_scalar_(x)
1289 elif xs: # _xiterable(xs)
1290 self._facc(xs)
1291 return self
1293 def fadd_(self, *xs):
1294 '''Add all positional items to this instance.
1296 @arg xs: Values to add (each C{scalar}, an L{Fsum}
1297 or L{Fsum2Tuple}), all positional.
1299 @see: Method L{Fsum.fadd} for further details.
1300 '''
1301 return self._facc_args(xs)
1303 def _fadd(self, other, op=_add_op_, **up):
1304 '''(INTERNAL) Apply C{B{self} += B{other}}.
1305 '''
1306 if _isFsum_2Tuple(other):
1307 self._facc_scalar(other._ps, **up)
1308 elif self._scalar(other, op):
1309 self._facc_scalar_(other, **up)
1310 return self
1312 fcopy = copy # for backward compatibility
1313 fdiv = __itruediv__
1314 fdivmod = __divmod__
1316 def _fdivmod2(self, other, op, **raiser_RESIDUAL):
1317 '''(INTERNAL) Apply C{B{self} %= B{other}} and return a L{DivMod2Tuple}.
1318 '''
1319 # result mostly follows CPython function U{float_divmod
1320 # <https://GitHub.com/python/cpython/blob/main/Objects/floatobject.c>},
1321 # but at least divmod(-3, 2) equals Cpython's result (-2, 1).
1322 q = self._truediv(other, op, **raiser_RESIDUAL).floor
1323 if q: # == float // other == floor(float / other)
1324 self -= self._Fsum_as(q) * other # NOT other * q!
1326 s = signOf(other) # make signOf(self) == signOf(other)
1327 if s and self.signOf() == -s: # PYCHOK no cover
1328 self += other
1329 q -= 1
1330# t = self.signOf()
1331# if t and t != s:
1332# raise self._Error(op, other, _AssertionError, txt__=signOf)
1333 return DivMod2Tuple(q, self) # q is C{int} in Python 3+, but C{float} in Python 2-
1335 def _fhorner(self, x, cs, where, incx=True): # in .fmath
1336 '''(INTERNAL) Add an L{Fhorner} evaluation of polynomial
1337 C{sum(c * B{x}**i for i, c in _e(cs))} where C{_e =
1338 enumerate if B{incx} else _enumereverse}.
1339 '''
1340 # assert _xiterablen(cs)
1341 try:
1342 n = len(cs)
1343 if n > 1 and _2finite(x, **self._isfine):
1344 H = self._Fsum_as(name__=self._fhorner)
1345 _m = H._mul_Fsum if _isFsum_2Tuple(x) else \
1346 H._mul_scalar
1347 for c in (reversed(cs) if incx else cs):
1348 H._fset(_m(x, _mul_op_), up=False)
1349 H._fadd(c, up=False)
1350 else: # x == 0
1351 H = cs[0] if n else 0
1352 return self._fadd(H)
1353 except Exception as X:
1354 t = unstr(where, x, *cs, _ELLIPSIS=4, incx=incx)
1355 raise self._ErrorX(X, _add_op_, t)
1357 def _finite(self, other, op=None):
1358 '''(INTERNAL) Return B{C{other}} if C{finite}.
1359 '''
1360 if _isOK_or_finite(other, **self._isfine):
1361 return other
1362 E = _NonfiniteError(other)
1363 raise self._Error(op, other, E, txt=_not_finite_)
1365 def fint(self, name=NN, **raiser_RESIDUAL):
1366 '''Return this instance' current running sum as C{integer}.
1368 @kwarg name: Optional, overriding C{B{name}="fint"} (C{str}).
1369 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore
1370 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}
1371 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.
1373 @return: The C{integer} sum (L{Fsum}) if this instance C{is_integer}
1374 with a zero or insignificant I{integer} residual.
1376 @raise ResidualError: Non-zero, significant residual or invalid
1377 B{C{RESIDUAL}}.
1379 @see: Methods L{Fsum.fint2}, L{Fsum.int_float} and L{Fsum.is_integer}.
1380 '''
1381 i, r = self._fint2
1382 if r:
1383 R = self._raiser(r, i, **raiser_RESIDUAL)
1384 if R:
1385 t = _stresidual(_integer_, r, **R)
1386 raise ResidualError(_integer_, i, txt=t)
1387 return self._Fsum_as(i, name=_name__(name, name__=self.fint))
1389 def fint2(self, **name):
1390 '''Return this instance' current running sum as C{int} and the
1391 I{integer} residual.
1393 @kwarg name: Optional name (C{str}).
1395 @return: An L{Fsum2Tuple}C{(fsum, residual)} with C{fsum}
1396 an C{int} and I{integer} C{residual} a C{float} or
1397 C{INT0} if the C{fsum} is considered to be I{exact}.
1398 The C{fsum} is I{non-finite} if this instance is.
1399 '''
1400 return Fsum2Tuple(*self._fint2, **name)
1402 @Property
1403 def _fint2(self): # see ._fset
1404 '''(INTERNAL) Get 2-tuple (C{int}, I{integer} residual).
1405 '''
1406 s, r = self._nfprs2
1407 if _isfinite(s):
1408 i = int(s)
1409 r = (self._ps_1sum(i) if len(self._ps) > 1 else
1410 float(s - i)) or INT0
1411 else: # INF, NAN, NINF
1412 i = float(s)
1413# r = _NONFINITEr
1414 return i, r # Fsum2Tuple?
1416 @_fint2.setter_ # PYCHOK setter_UNDERscore!
1417 def _fint2(self, s): # in _fset
1418 '''(INTERNAL) Replace the C{_fint2} value.
1419 '''
1420 if _isfinite(s):
1421 i = int(s)
1422 r = (s - i) or INT0
1423 else: # INF, NAN, NINF
1424 i = float(s)
1425 r = _NONFINITEr
1426 return i, r # like _fint2.getter
1428 @deprecated_property_RO
1429 def float_int(self): # PYCHOK no cover
1430 '''DEPRECATED, use method C{Fsum.int_float}.'''
1431 return self.int_float() # raiser=False
1433 @property_RO
1434 def floor(self):
1435 '''Get this instance' C{floor} (C{int} in Python 3+, but
1436 C{float} in Python 2-).
1438 @note: This C{floor} takes the C{residual} into account.
1440 @see: Method L{Fsum.int_float} and properties L{Fsum.ceil},
1441 L{Fsum.imag} and L{Fsum.real}.
1442 '''
1443 s, r = self._fprs2
1444 f = _floor(s) + _floor(r) + 1
1445 while (f - s) > r: # f > (s + r)
1446 f -= 1
1447 return f # _floor(self._n_d)
1449# ffloordiv = __ifloordiv__ # for naming consistency?
1450# floordiv = __floordiv__ # for naming consistency?
1452 def _floordiv(self, other, op, **raiser_RESIDUAL): # rather _ffloordiv?
1453 '''Apply C{B{self} //= B{other}}.
1454 '''
1455 q = self._ftruediv(other, op, **raiser_RESIDUAL) # == self
1456 return self._fset(q.floor) # floor(q)
1458 def fma(self, other1, other2, **nonfinites): # in .fmath.fma
1459 '''Fused-multiply-add C{self *= B{other1}; self += B{other2}}.
1461 @arg other1: Multiplier (C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
1462 @arg other2: Addend (C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
1463 @kwarg nonfinites: Use C{B{nonfinites}=True} or C{False}, to
1464 override L{nonfinites<Fsum.nonfinites>} and
1465 the L{nonfiniterrors} default (C{bool}).
1466 '''
1467 f = self._fma(other1, other2, **nonfinites)
1468 return self._fset(f)
1470 def _fma(self, other1, other2, **nonfinites): # in .elliptic
1471 '''(INTERNAL) Return C{self * B{other1} + B{other2}}.
1472 '''
1473 op = typename(self.fma)
1474 _fs = self._ps_other
1475 try:
1476 s, r = self._fprs2
1477 if r:
1478 f = self._f2mul(self.fma, (other1,), **nonfinites)
1479 f += other2
1480 elif _residue(other1) or _residue(other2):
1481 fs = _2split3s(_fs(op, other1))
1482 fs = _2products(s, fs, *_fs(op, other2))
1483 f = Fsum(fs, name=op, **nonfinites)
1484 else:
1485 f = _fma(s, other1, other2)
1486 f = _2finite(f, **self._isfine)
1487 except TypeError as X:
1488 raise self._ErrorX(X, op, (other1, other2))
1489 except (OverflowError, ValueError) as X: # from math.fma
1490 f = self._mul_reduce(s, other1) # INF, NAN, NINF
1491 f += sum(_fs(op, other2))
1492 f = self._nonfiniteX(X, op, f, **nonfinites)
1493 return f
1495 def fma_(self, *xys, **nonfinites):
1496 '''Fused-multiply-accumulate C{for i in range(0, len(xys), B{2}):
1497 self = }L{fma<pygeodesy.fmath.fma>}C{(xys[i], xys[i+1], self)}.
1499 @arg xys: Pairwise multiplicand, multiplier (each C{scalar},
1500 an L{Fsum} or L{Fsum2Tuple}), all positional.
1501 @kwarg nonfinites: Use C{B{nonfinites}=True} or C{False}, to
1502 override L{nonfinites<Fsum.nonfinites>} and
1503 the L{nonfiniterrors} default (C{bool}).
1505 @note: Equivalent to L{fdot_<pygeodesy.fmath.fdot_>}C{(*xys,
1506 start=self)}.
1507 '''
1508 if xys:
1509 n = len(xys)
1510 if n < 2 or isodd(n):
1511 raise LenError(self.fma_, xys=n)
1512 f, _fmath_fma = self, _MODS.fmath.fma
1513 for x, y in zip(xys[0::2], xys[1::2]):
1514 f = _fmath_fma(x, y, f, **nonfinites)
1515 self._fset(f)
1516 return self
1518 fmul = __imul__
1520 def _fmul(self, other, op):
1521 '''(INTERNAL) Apply C{B{self} *= B{other}}.
1522 '''
1523 if _isFsum_2Tuple(other):
1524 if len(self._ps) != 1:
1525 f = self._mul_Fsum(other, op)
1526 elif len(other._ps) != 1: # and len(self._ps) == 1
1527 f = self._ps_mul(op, *other._ps) if other._ps else _0_0
1528 elif self._f2product: # len(other._ps) == 1
1529 f = self._mul_scalar(other._ps[0], op)
1530 else: # len(other._ps) == len(self._ps) == 1
1531 f = self._finite(self._ps[0] * other._ps[0], op=op)
1532 else:
1533 s = self._scalar(other, op)
1534 f = self._mul_scalar(s, op)
1535 return self._fset(f) # n=len(self) + 1
1537 @deprecated_method
1538 def f2mul(self, *others, **raiser):
1539 '''DEPRECATED on 2024.09.13, use method L{f2mul_<Fsum.f2mul_>}.'''
1540 return self._fset(self._f2mul(self.f2mul, others, **raiser))
1542 def f2mul_(self, *others, **f2product_nonfinites): # in .fmath.f2mul
1543 '''Return C{B{self} * B{other} * B{other} ...} for all B{C{others}} using cascaded,
1544 accurate multiplication like with L{f2product<Fsum.f2product>}C{(B{True})}.
1546 @arg others: Multipliers (each C{scalar}, an L{Fsum} or L{Fsum2Tuple}), all
1547 positional.
1548 @kwarg f2product_nonfinites: Use C{B{f2product=False}} to override the default
1549 C{True} and C{B{nonfinites}=True} or C{False}, to override
1550 settings L{nonfinites<Fsum.nonfinites>} and L{nonfiniterrors}.
1552 @return: The cascaded I{TwoProduct} (L{Fsum} or C{float}).
1554 @see: U{Equations 2.3<https://www.TUHH.De/ti3/paper/rump/OzOgRuOi06.pdf>}
1555 '''
1556 return self._f2mul(self.f2mul_, others, **f2product_nonfinites)
1558 def _f2mul(self, where, others, f2product=True, **nonfinites_raiser):
1559 '''(INTERNAL) See methods C{fma} and C{f2mul_}.
1560 '''
1561 n = typename(where)
1562 f = _Psum(self._ps, f2product=f2product, name=n)
1563 if others and f:
1564 if f.f2product():
1565 def _pfs(f, ps):
1566 return _2products(f, _2split3s(ps))
1567 else:
1568 def _pfs(f, ps): # PYCHOK redef
1569 return (f * p for p in ps)
1571 op, ps = n, f._ps
1572 try: # as if self.f2product(True)
1573 for other in others: # to pinpoint errors
1574 for p in self._ps_other(op, other):
1575 ps[:] = f._ps_acc([], _pfs(p, ps), update=False)
1576 f._update()
1577 except TypeError as X:
1578 raise self._ErrorX(X, op, other)
1579 except (OverflowError, ValueError) as X:
1580 r = self._mul_reduce(sum(ps), other) # INF, NAN, NINF
1581 r = self._nonfiniteX(X, op, r, **nonfinites_raiser)
1582 f._fset(r)
1583 return f
1585 def fover(self, over, **raiser_RESIDUAL):
1586 '''Apply C{B{self} /= B{over}} and summate.
1588 @arg over: Divisor (C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
1589 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore
1590 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}
1591 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.
1593 @return: Precision running quotient sum (C{float}).
1595 @raise ResidualError: Non-zero, significant residual or invalid
1596 B{C{RESIDUAL}}.
1598 @see: Methods L{Fsum.fdiv}, L{Fsum.__itruediv__} and L{Fsum.fsum}.
1599 '''
1600 return float(self.fdiv(over, **raiser_RESIDUAL)._fprs)
1602 fpow = __ipow__
1604 def _fpow(self, other, op, *mod, **raiser_RESIDUAL):
1605 '''Apply C{B{self} **= B{other}}, optional B{C{mod}} or C{None}.
1606 '''
1607 if mod:
1608 if mod[0] is not None: # == 3-arg C{pow}
1609 f = self._pow_2_3(self, other, other, op, *mod, **raiser_RESIDUAL)
1610 elif self.is_integer():
1611 # return an exact C{int} for C{int}**C{int}
1612 i, _ = self._fint2 # assert _ == 0
1613 x, r = _2tuple2(other) # C{int}, C{float} or other
1614 f = self._Fsum_as(i)._pow_Fsum(other, op, **raiser_RESIDUAL) if r else \
1615 self._pow_2_3(i, x, other, op, **raiser_RESIDUAL)
1616 else: # mod[0] is None, power(self, other)
1617 f = self._pow(other, other, op, **raiser_RESIDUAL)
1618 else: # pow(self, other)
1619 f = self._pow(other, other, op, **raiser_RESIDUAL)
1620 return self._fset(f) # n=max(len(self), 1)
1622 def f2product(self, *two):
1623 '''Get and set accurate I{TwoProduct} multiplication for this
1624 L{Fsum}, overriding the L{f2product} default.
1626 @arg two: If omitted, leave the override unchanged, if C{True},
1627 turn I{TwoProduct} on, if C{False} off, or if C{None}
1628 remove the override (C{bool} or C{None}).
1630 @return: The previous setting (C{bool} or C{None} if not set).
1632 @see: Function L{f2product<fsums.f2product>}.
1634 @note: Use C{f.f2product() or f2product()} to determine whether
1635 multiplication is accurate for L{Fsum} C{f}.
1636 '''
1637 if two: # delattrof(self, _f2product=None)
1638 t = _xkwds_pop(self.__dict__, _f2product=None)
1639 self._optionals(f2product=two[0])
1640 else: # getattrof(self, _f2product=None)
1641 t = _xkwds_get(self.__dict__, _f2product=None)
1642 return t
1644 @Property
1645 def _fprs(self):
1646 '''(INTERNAL) Get and cache this instance' precision
1647 running sum (C{float} or C{int}), ignoring C{residual}.
1649 @note: The precision running C{fsum} after a C{//=} or
1650 C{//} C{floor} division is C{int} in Python 3+.
1651 '''
1652 s, _ = self._fprs2
1653 return s # ._fprs2.fsum
1655 @_fprs.setter_ # PYCHOK setter_UNDERscore!
1656 def _fprs(self, s):
1657 '''(INTERNAL) Replace the C{_fprs} value.
1658 '''
1659 return s
1661 @Property
1662 def _fprs2(self):
1663 '''(INTERNAL) Get and cache this instance' precision
1664 running sum and residual (L{Fsum2Tuple}).
1665 '''
1666 ps = self._ps
1667 n = len(ps)
1668 try:
1669 if n > 2:
1670 s = _psum(ps, **self._isfine)
1671 if not _isfinite(s):
1672 ps[:] = s, # collapse ps
1673 return Fsum2Tuple(s, _NONFINITEr)
1674 n = len(ps)
1675# Fsum._ps_max = max(Fsum._ps_max, n)
1676 if n > 2:
1677 r = self._ps_1sum(s)
1678 return Fsum2Tuple(*_s_r2(s, r))
1679 if n > 1: # len(ps) == 2
1680 s, r = _s_r2(*_2sum(*ps, **self._isfine))
1681 ps[:] = (r, s) if r else (s,)
1682 elif ps: # len(ps) == 1
1683 s = ps[0]
1684 r = INT0 if _isfinite(s) else _NONFINITEr
1685 else: # len(ps) == 0
1686 s = _0_0
1687 r = INT0 if _isfinite(s) else _NONFINITEr
1688 ps[:] = s,
1689 except (OverflowError, ValueError) as X:
1690 op = _fset_op_ # INF, NAN, NINF
1691 ps[:] = sum(ps), # collapse ps
1692 s = self._nonfiniteX(X, op, ps[0])
1693 r = _NONFINITEr
1694 # assert self._ps is ps
1695 return Fsum2Tuple(s, r)
1697 @_fprs2.setter_ # PYCHOK setter_UNDERscore!
1698 def _fprs2(self, s_r):
1699 '''(INTERNAL) Replace the C{_fprs2} value.
1700 '''
1701 return Fsum2Tuple(s_r)
1703 def fset_(self, *xs):
1704 '''Apply C{B{self}.partials = Fsum(*B{xs}).partials}.
1706 @arg xs: Optional, new values (each C{scalar} or an L{Fsum}
1707 or L{Fsum2Tuple} instance), all positional.
1709 @return: This instance, replaced (C{Fsum}).
1711 @see: Method L{Fsum.fadd} for further details.
1712 '''
1713 f = (xs[0] if xs else _0_0) if len(xs) < 2 else \
1714 Fsum(*xs, nonfinites=self.nonfinites()) # self._Fsum_as(*xs)
1715 return self._fset(f, op=_fset_op_)
1717 def _fset(self, other, n=0, up=True, **op):
1718 '''(INTERNAL) Overwrite this instance with an other or a C{scalar}.
1719 '''
1720 if other is self:
1721 pass # from ._fmul, ._ftruediv and ._pow_0_1
1722 elif _isFsum_2Tuple(other):
1723 if op: # and not self.nonfinitesOK:
1724 self._finite(other._fprs, **op)
1725 self._ps[:] = other._ps
1726 self._n = n or other._n
1727 if up: # use or zap the C{Property_RO} values
1728 Fsum._fint2._update_from(self, other)
1729 Fsum._fprs ._update_from(self, other)
1730 Fsum._fprs2._update_from(self, other)
1731 elif isscalar(other):
1732 s = float(self._finite(other, **op)) if op else other
1733 self._ps[:] = s,
1734 self._n = n or 1
1735 if up: # Property _fint2, _fprs and _fprs2 all have
1736 # @.setter_underscore and NOT @.setter because the
1737 # latter's _fset zaps the value set by @.setter
1738 self._fint2 = s
1739 self._fprs = s
1740 self._fprs2 = s, INT0
1741 # assert self._fprs is s
1742 else:
1743 op = _xkwds_get1(op, op=_fset_op_)
1744 raise self._Error(op, other, _TypeError)
1745 return self
1747 def fsub(self, xs=()):
1748 '''Subtract an iterable's items from this instance.
1750 @see: Method L{Fsum.fadd} for further details.
1751 '''
1752 return self._facc_neg(xs)
1754 def fsub_(self, *xs):
1755 '''Subtract all positional items from this instance.
1757 @see: Method L{Fsum.fadd_} for further details.
1758 '''
1759 return self._fsub(xs[0], _sub_op_) if len(xs) == 1 else \
1760 self._facc_neg(xs) # origin=1?
1762 def _fsub(self, other, op):
1763 '''(INTERNAL) Apply C{B{self} -= B{other}}.
1764 '''
1765 if _isFsum_2Tuple(other):
1766 if other is self: # or other._fprs2 == self._fprs2:
1767 self._fset(_0_0, n=len(self) * 2)
1768 elif other._ps:
1769 self._facc_scalar(other._ps_neg)
1770 elif self._scalar(other, op):
1771 self._facc_scalar_(-other)
1772 return self
1774 def fsum(self, xs=()):
1775 '''Add an iterable's items, summate and return the current
1776 precision running sum.
1778 @arg xs: Iterable of items to add (each item C{scalar},
1779 an L{Fsum} or L{Fsum2Tuple}).
1781 @return: Precision running sum (C{float} or C{int}).
1783 @see: Method L{Fsum.fadd}.
1785 @note: Accumulation can continue after summation.
1786 '''
1787 return self._facc(xs)._fprs
1789 def fsum_(self, *xs):
1790 '''Add any positional items, summate and return the current
1791 precision running sum.
1793 @arg xs: Items to add (each C{scalar}, an L{Fsum} or
1794 L{Fsum2Tuple}), all positional.
1796 @return: Precision running sum (C{float} or C{int}).
1798 @see: Methods L{Fsum.fsum}, L{Fsum.Fsum_} and L{Fsum.fsumf_}.
1799 '''
1800 return self._facc_args(xs)._fprs
1802 def Fsum_(self, *xs, **name):
1803 '''Like method L{Fsum.fsum_} but returning a named L{Fsum}.
1805 @kwarg name: Optional name (C{str}).
1807 @return: Copy of this updated instance (L{Fsum}).
1808 '''
1809 return self._facc_args(xs)._copyd(self.Fsum_, **name)
1811 def Fsum2Tuple_(self, *xs, **name):
1812 '''Like method L{Fsum.fsum_} but returning a named L{Fsum2Tuple}.
1814 @kwarg name: Optional name (C{str}).
1816 @return: Precision running sum (L{Fsum2Tuple}).
1817 '''
1818 return Fsum2Tuple(self._facc_args(xs)._nfprs2, **name)
1820 @property_RO
1821 def _Fsum(self): # like L{Fsum2Tuple._Fsum}, in .fstats
1822 return self # NOT @Property_RO, see .copy and ._copyd
1824 def _Fsum_as(self, *xs, **name_f2product_nonfinites_RESIDUAL):
1825 '''(INTERNAL) Return an C{Fsum} with this C{Fsum}'s C{.f2product},
1826 C{.nonfinites} and C{.RESIDUAL} setting, optionally
1827 overridden with C{name_f2product_nonfinites_RESIDUAL} and
1828 with any C{xs} accumulated.
1829 '''
1830 kwds = _xkwds_not(None, Fsum._RESIDUAL, f2product =self.f2product(),
1831 nonfinites=self.nonfinites(),
1832 RESIDUAL =self.RESIDUAL())
1833 if name_f2product_nonfinites_RESIDUAL: # overwrites
1834 kwds.update(name_f2product_nonfinites_RESIDUAL)
1835 f = Fsum(**kwds)
1836 # assert all(v == self.__dict__[n] for n, v in f.__dict__.items())
1837 return (f._facc(xs, up=False) if len(xs) > 1 else
1838 f._fset(xs[0], op=_fset_op_)) if xs else f
1840 def fsum2(self, xs=(), **name):
1841 '''Add an iterable's items, summate and return the
1842 current precision running sum I{and} the C{residual}.
1844 @arg xs: Iterable of items to add (each item C{scalar},
1845 an L{Fsum} or L{Fsum2Tuple}).
1846 @kwarg name: Optional C{B{name}=NN} (C{str}).
1848 @return: L{Fsum2Tuple}C{(fsum, residual)} with C{fsum} the
1849 current precision running sum and C{residual}, the
1850 (precision) sum of the remaining C{partials}. The
1851 C{residual is INT0} if the C{fsum} is considered
1852 to be I{exact}.
1854 @see: Methods L{Fsum.fint2}, L{Fsum.fsum} and L{Fsum.fsum2_}
1855 '''
1856 t = self._facc(xs)._fprs2
1857 return t.dup(name=name) if name else t
1859 def fsum2_(self, *xs):
1860 '''Add any positional items, summate and return the current
1861 precision running sum and the I{differential}.
1863 @arg xs: Values to add (each C{scalar}, an L{Fsum} or
1864 L{Fsum2Tuple}), all positional.
1866 @return: 2Tuple C{(fsum, delta)} with the current, precision
1867 running C{fsum} like method L{Fsum.fsum} and C{delta},
1868 the difference with previous running C{fsum}, C{float}.
1870 @see: Methods L{Fsum.fsum_} and L{Fsum.fsum}.
1871 '''
1872 return self._fsum2(xs, self._facc_args)
1874 def _fsum2(self, xs, _facc, **facc_kwds):
1875 '''(INTERNAL) Helper for L{Fsum.fsum2_} and L{Fsum.fsum2f_}.
1876 '''
1877 p, q = self._fprs2
1878 if xs:
1879 s, r = _facc(xs, **facc_kwds)._fprs2
1880 if _isfinite(s): # _fsum(_1primed((s, -p, r, -q))
1881 d, r = _2sum(s - p, r - q, _isfine=_isOK)
1882 r, _ = _s_r2(d, r)
1883 return s, (r if _isfinite(r) else _NONFINITEr)
1884 else:
1885 return p, _0_0
1887 def fsumf_(self, *xs):
1888 '''Like method L{Fsum.fsum_} iff I{all} C{B{xs}}, each I{known to be}
1889 C{scalar}, an L{Fsum} or L{Fsum2Tuple}.
1890 '''
1891 return self._facc_xsum(xs, which=self.fsumf_)._fprs # origin=1?
1893 def Fsumf_(self, *xs):
1894 '''Like method L{Fsum.Fsum_} iff I{all} C{B{xs}}, each I{known to be}
1895 C{scalar}, an L{Fsum} or L{Fsum2Tuple}.
1896 '''
1897 return self._facc_xsum(xs, which=self.Fsumf_)._copyd(self.Fsumf_) # origin=1?
1899 def fsum2f_(self, *xs):
1900 '''Like method L{Fsum.fsum2_} iff I{all} C{B{xs}}, each I{known to be}
1901 C{scalar}, an L{Fsum} or L{Fsum2Tuple}.
1902 '''
1903 return self._fsum2(xs, self._facc_xsum, which=self.fsum2f_) # origin=1?
1905# ftruediv = __itruediv__ # for naming consistency?
1907 def _ftruediv(self, other, op, **raiser_RESIDUAL):
1908 '''(INTERNAL) Apply C{B{self} /= B{other}}.
1909 '''
1910 n = _1_0
1911 if _isFsum_2Tuple(other):
1912 if other is self or self == other:
1913 return self._fset(n, n=len(self))
1914 d, r = other._fprs2
1915 if r:
1916 R = self._raiser(r, d, **raiser_RESIDUAL)
1917 if R:
1918 raise self._ResidualError(op, other, r, **R)
1919 d, n = other.as_integer_ratio()
1920 else:
1921 d = self._scalar(other, op)
1922 try:
1923 s = n / d
1924 except Exception as X:
1925 raise self._ErrorX(X, op, other)
1926 f = self._mul_scalar(s, _mul_op_) # handles 0, INF, NAN
1927 return self._fset(f)
1929 @property_RO
1930 def imag(self):
1931 '''Get the C{imaginary} part of this instance (C{0.0}, always).
1933 @see: Property L{Fsum.real}.
1934 '''
1935 return _0_0
1937 def int_float(self, **raiser_RESIDUAL):
1938 '''Return this instance' current running sum as C{int} or C{float}.
1940 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore
1941 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}
1942 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.
1944 @return: This C{int} sum if this instance C{is_integer} and
1945 I{finite}, otherwise the C{float} sum if the residual
1946 is zero or not significant.
1948 @raise ResidualError: Non-zero, significant residual or invalid
1949 B{C{RESIDUAL}}.
1951 @see: Methods L{Fsum.fint}, L{Fsum.fint2}, L{Fsum.is_integer},
1952 L{Fsum.RESIDUAL} and property L{Fsum.as_iscalar}.
1953 '''
1954 s, r = self._fint2
1955 if r:
1956 s, r = self._fprs2
1957 if r: # PYCHOK no cover
1958 R = self._raiser(r, s, **raiser_RESIDUAL)
1959 if R:
1960 t = _stresidual(_non_zero_, r, **R)
1961 raise ResidualError(int_float=s, txt=t)
1962 s = float(s)
1963 return s
1965 def is_exact(self):
1966 '''Is this instance' running C{fsum} considered to be exact?
1967 (C{bool}), C{True} only if the C{residual is }L{INT0}.
1968 '''
1969 return self.residual is INT0
1971 def is_finite(self): # in .constants
1972 '''Is this instance C{finite}? (C{bool}).
1974 @see: Function L{isfinite<pygeodesy.isfinite>}.
1975 '''
1976 return _isfinite(sum(self._ps)) # == sum(self)
1978 def is_integer(self):
1979 '''Is this instance' running sum C{integer}? (C{bool}).
1981 @see: Methods L{Fsum.fint}, L{Fsum.fint2} and L{Fsum.is_scalar}.
1982 '''
1983 s, r = self._fint2
1984 return False if r else (_isfinite(s) and isint(s))
1986 def is_math_fma(self):
1987 '''Is accurate L{f2product} multiplication based on Python's C{math.fma}?
1989 @return: C{True} if accurate multiplication uses C{math.fma}, C{False}
1990 an C{fma} implementation as C{math.fma} or C{None}, a previous
1991 C{PyGeodesy} implementation.
1992 '''
1993 return (_2split3s is _passarg) or (False if _integer_ratio2 is None else None)
1995 def is_math_fsum(self):
1996 '''Are the summation functions L{fsum}, L{fsum_}, L{fsumf_}, L{fsum1},
1997 L{fsum1_} and L{fsum1f_} based on Python's C{math.fsum}?
1999 @return: C{True} if summation functions use C{math.fsum}, C{False}
2000 otherwise.
2001 '''
2002 return _sum is _fsum # _fsum.__module__ is fabs.__module__
2004 def is_scalar(self, **raiser_RESIDUAL):
2005 '''Is this instance' running sum C{scalar} with C{0} residual or with
2006 a residual I{ratio} not exceeding the RESIDUAL threshold?
2008 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore
2009 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}
2010 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.
2012 @return: C{True} if this instance' residual is C{0} or C{insignificant},
2013 i.e. its residual C{ratio} doesn't exceed the L{RESIDUAL
2014 <Fsum.RESIDUAL>} threshold (C{bool}).
2016 @raise ResidualError: Non-zero, significant residual or invalid
2017 B{C{RESIDUAL}}.
2019 @see: Methods L{Fsum.RESIDUAL} and L{Fsum.is_integer} and property
2020 L{Fsum.as_iscalar}.
2021 '''
2022 s, r = self._fprs2
2023 return False if r and self._raiser(r, s, **raiser_RESIDUAL) else True
2025 def _mul_Fsum(self, other, op):
2026 '''(INTERNAL) Return C{B{self} * B{other}} as L{Fsum} or C{0}.
2027 '''
2028 # assert _isFsum_2Tuple(other)
2029 if self._ps and other._ps:
2030 try:
2031 f = self._ps_mul(op, *other._ps) # NO .as_iscalar!
2032 except Exception as X:
2033 raise self._ErrorX(X, op, other)
2034 else:
2035 f = _0_0
2036 return f
2038 def _mul_reduce(self, *others):
2039 '''(INTERNAL) Like fmath.fprod for I{non-finite} C{other}s.
2040 '''
2041 r = _1_0
2042 for f in others:
2043 r *= sum(f._ps) if _isFsum_2Tuple(f) else float(f)
2044 return r
2046 def _mul_scalar(self, factor, op):
2047 '''(INTERNAL) Return C{B{self} * scalar B{factor}} as L{Fsum}, C{0.0} or C{self}.
2048 '''
2049 # assert isscalar(factor)
2050 if self._ps and self._finite(factor, op=op):
2051 f = self if factor == _1_0 else (
2052 self._neg if factor == _N_1_0 else
2053 self._ps_mul(op, factor).as_iscalar)
2054 else:
2055 f = _0_0
2056 return f
2058# @property_RO
2059# def _n_d(self):
2060# n, d = self.as_integer_ratio()
2061# return n / d
2063 @property_RO
2064 def _neg(self):
2065 '''(INTERNAL) Return C{Fsum(-self)} or scalar C{NEG0}.
2066 '''
2067 return _Psum(self._ps_neg) if self._ps else NEG0
2069 @property_RO
2070 def _nfprs2(self):
2071 '''(INTERNAL) Handle I{non-finite} C{_fprs2}.
2072 '''
2073 try: # to handle nonfiniterrors, etc.
2074 t = self._fprs2
2075 except (OverflowError, ValueError):
2076 t = Fsum2Tuple(sum(self._ps), _NONFINITEr)
2077 return t
2079 def nonfinites(self, *OK):
2080 '''Handle I{non-finite} C{float}s as C{inf}, C{INF}, C{NINF}, C{nan}
2081 and C{NAN} for this L{Fsum} or throw C{OverflowError} respectively
2082 C{ValueError} exceptions, overriding the L{nonfiniterrors} default.
2084 @arg OK: If omitted, leave the override unchanged, if C{True},
2085 I{non-finites} are C{OK}, if C{False} throw exceptions
2086 or if C{None} remove the override (C{bool} or C{None}).
2088 @return: The previous setting (C{bool} or C{None} if not set).
2090 @see: Function L{nonfiniterrors<fsums.nonfiniterrors>}.
2092 @note: Use property L{nonfinitesOK<Fsum.nonfinitesOK>} to determine
2093 whether I{non-finites} are C{OK} for this L{Fsum} or by the
2094 L{nonfiniterrors} default.
2095 '''
2096 if OK: # delattrof(self, _isfine=None)
2097 k = _xkwds_pop(self.__dict__, _isfine=None)
2098 self._optionals(nonfinites=OK[0])
2099 self._update()
2100 else: # getattrof(self, _isfine=None)
2101 k = _xkwds_get(self.__dict__, _isfine=None)
2102 _ks = _nonfinites_isfine_kwds
2103 # dict(map(reversed, _ks.items())).get(k, None)
2104 # raises a TypeError: unhashable type: 'dict'
2105 return True if k is _ks[True] else (
2106 False if k is _ks[False] else None)
2108 @property_RO
2109 def nonfinitesOK(self):
2110 '''Are I{non-finites} C{OK} for this L{Fsum} or by default? (C{bool}).
2111 '''
2112# nf = self.nonfinites()
2113# if nf is None:
2114# nf = not nonfiniterrors()
2115 return _isOK_or_finite(INF, **self._isfine)
2117 def _nonfiniteX(self, X, op, f, nonfinites=None, raiser=None):
2118 '''(INTERNAL) Handle a I{non-finite} exception.
2119 '''
2120 if nonfinites is None:
2121 nonfinites = _isOK_or_finite(f, **self._isfine) if raiser is None else (not raiser)
2122 if not nonfinites:
2123 raise self._ErrorX(X, op, f)
2124 return f
2126 def _optionals(self, f2product=None, nonfinites=None, **name_RESIDUAL):
2127 '''(INTERNAL) Re/set options from keyword arguments.
2128 '''
2129 if f2product is not None:
2130 self._f2product = bool(f2product)
2131 if nonfinites is not None:
2132 self._isfine = _nonfinites_isfine_kwds[bool(nonfinites)]
2133 if name_RESIDUAL: # MUST be last
2134 n, kwds = _name2__(**name_RESIDUAL)
2135 if kwds:
2136 R = Fsum._RESIDUAL
2137 t = _threshold(R, **kwds)
2138 if t != R:
2139 self._RESIDUAL = t
2140 if n:
2141 self.name = n # self.rename(n)
2143 def _1_Over(self, x, op, **raiser_RESIDUAL): # vs _1_over
2144 '''(INTERNAL) Return C{Fsum(1) / B{x}}.
2145 '''
2146 return self._Fsum_as(_1_0)._ftruediv(x, op, **raiser_RESIDUAL)
2148 @property_RO
2149 def partials(self):
2150 '''Get this instance' current, partial sums (C{tuple} of C{float}s).
2151 '''
2152 return tuple(self._ps)
2154 def pow(self, x, *mod, **raiser_RESIDUAL):
2155 '''Return C{B{self}**B{x}} as L{Fsum}.
2157 @arg x: The exponent (C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
2158 @arg mod: Optional modulus (C{int} or C{None}) for the 3-argument
2159 C{pow(B{self}, B{other}, B{mod})} version.
2160 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore
2161 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}
2162 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.
2164 @return: The C{pow(self, B{x})} or C{pow(self, B{x}, *B{mod})}
2165 result (L{Fsum}).
2167 @raise ResidualError: Non-zero, significant residual or invalid
2168 B{C{RESIDUAL}}.
2170 @note: If B{C{mod}} is given and C{None}, the result will be an
2171 C{integer} L{Fsum} provided this instance C{is_integer}
2172 or set to C{integer} by an L{Fsum.fint} call.
2174 @see: Methods L{Fsum.__ipow__}, L{Fsum.fint}, L{Fsum.is_integer}
2175 and L{Fsum.root}.
2176 '''
2177 f = self._copyd(self.pow)
2178 return f._fpow(x, _pow_op_, *mod, **raiser_RESIDUAL) # f = pow(f, x, *mod)
2180 def _pow(self, other, unused, op, **raiser_RESIDUAL):
2181 '''Return C{B{self} ** B{other}}.
2182 '''
2183 if _isFsum_2Tuple(other):
2184 f = self._pow_Fsum(other, op, **raiser_RESIDUAL)
2185 elif self._scalar(other, op):
2186 x = self._finite(other, op=op)
2187 f = self._pow_scalar(x, other, op, **raiser_RESIDUAL)
2188 else:
2189 f = self._pow_0_1(0, other)
2190 return f
2192 def _pow_0_1(self, x, other):
2193 '''(INTERNAL) Return B{C{self}**1} or C{B{self}**0 == 1.0}.
2194 '''
2195 return self if x else (1 if isint(other) and self.is_integer() else _1_0)
2197 def _pow_2_3(self, b, x, other, op, *mod, **raiser_RESIDUAL):
2198 '''(INTERNAL) 2-arg C{pow(B{b}, scalar B{x})} and 3-arg C{pow(B{b},
2199 B{x}, int B{mod} or C{None})}, embellishing errors.
2200 '''
2202 if mod: # b, x, mod all C{int}, unless C{mod} is C{None}
2203 m = mod[0]
2204 # assert _isFsum_2Tuple(b)
2206 def _s(s, r):
2207 R = self._raiser(r, s, **raiser_RESIDUAL)
2208 if R:
2209 raise self._ResidualError(op, other, r, mod=m, **R)
2210 return s
2212 b = _s(*(b._fprs2 if m is None else b._fint2))
2213 x = _s(*_2tuple2(x))
2215 try:
2216 # 0**INF == 0.0, 1**INF == 1.0, -1**2.3 == -(1**2.3)
2217 s = pow(b, x, *mod)
2218 if iscomplex(s):
2219 # neg**frac == complex in Python 3+, but ValueError in 2-
2220 raise ValueError(_strcomplex(s, b, x, *mod))
2221 _ = _2finite(s, **self._isfine) # ignore float
2222 return s
2223 except Exception as X:
2224 raise self._ErrorX(X, op, other, *mod)
2226 def _pow_Fsum(self, other, op, **raiser_RESIDUAL):
2227 '''(INTERNAL) Return C{B{self} **= B{other}} for C{_isFsum_2Tuple(other)}.
2228 '''
2229 # assert _isFsum_2Tuple(other)
2230 x, r = other._fprs2
2231 f = self._pow_scalar(x, other, op, **raiser_RESIDUAL)
2232 if f and r:
2233 f *= self._pow_scalar(r, other, op, **raiser_RESIDUAL)
2234 return f
2236 def _pow_int(self, x, other, op, **raiser_RESIDUAL):
2237 '''(INTERNAL) Return C{B{self} **= B{x}} for C{int B{x} >= 0}.
2238 '''
2239 # assert isint(x) and x >= 0
2240 ps = self._ps
2241 if len(ps) > 1:
2242 _mul_Fsum = Fsum._mul_Fsum
2243 if x > 4:
2244 p = self
2245 f = self if (x & 1) else self._Fsum_as(_1_0)
2246 m = x >> 1 # // 2
2247 while m:
2248 p = _mul_Fsum(p, p, op) # p **= 2
2249 if (m & 1):
2250 f = _mul_Fsum(f, p, op) # f *= p
2251 m >>= 1 # //= 2
2252 elif x > 1: # self**2, 3, or 4
2253 f = _mul_Fsum(self, self, op)
2254 if x > 2: # self**3 or 4
2255 p = self if x < 4 else f
2256 f = _mul_Fsum(f, p, op)
2257 else: # self**1 or self**0 == 1 or _1_0
2258 f = self._pow_0_1(x, other)
2259 elif ps: # self._ps[0]**x
2260 f = self._pow_2_3(ps[0], x, other, op, **raiser_RESIDUAL)
2261 else: # PYCHOK no cover
2262 # 0**pos_int == 0, but 0**0 == 1
2263 f = 0 if x else 1
2264 return f
2266 def _pow_scalar(self, x, other, op, **raiser_RESIDUAL):
2267 '''(INTERNAL) Return C{self**B{x}} for C{scalar B{x}}.
2268 '''
2269 s, r = self._fprs2
2270 if r:
2271 # assert s != 0
2272 if isint(x, both=True): # self**int
2273 x = int(x)
2274 y = abs(x)
2275 if y > 1:
2276 f = self._pow_int(y, other, op, **raiser_RESIDUAL)
2277 if x > 0: # i.e. > 1
2278 return f # Fsum or scalar
2279 # assert x < 0 # i.e. < -1
2280 if _isFsum(f):
2281 s, r = f._fprs2
2282 if r:
2283 return self._1_Over(f, op, **raiser_RESIDUAL)
2284 else: # scalar
2285 s = f
2286 # use s**(-1) to get the CPython
2287 # float_pow error iff s is zero
2288 x = -1
2289 elif x < 0: # self**(-1)
2290 return self._1_Over(self, op, **raiser_RESIDUAL) # 1 / self
2291 else: # self**1 or self**0
2292 return self._pow_0_1(x, other) # self, 1 or 1.0
2293 else: # self**fractional
2294 R = self._raiser(r, s, **raiser_RESIDUAL)
2295 if R:
2296 raise self._ResidualError(op, other, r, **R)
2297 n, d = self.as_integer_ratio()
2298 if abs(n) > abs(d):
2299 n, d, x = d, n, (-x)
2300 s = n / d
2301 # assert isscalar(s) and isscalar(x)
2302 return self._pow_2_3(s, x, other, op, **raiser_RESIDUAL)
2304 def _ps_acc(self, ps, xs, up=True, **unused): # in .geoids._Dotf and ._Hornerf
2305 '''(INTERNAL) Accumulate C{xs} known scalars into list C{ps}.
2306 '''
2307 n = 0
2308 _2s = _2sum
2309 _fi = self._isfine
2310 for x in (tuple(xs) if xs is ps else xs):
2311 # assert isscalar(x) and _isOK_or_finite(x, **self._isfine)
2312 if x:
2313 i = 0
2314 for p in ps:
2315 x, p = _2s(x, p, **_fi)
2316 if p:
2317 ps[i] = p
2318 i += 1
2319 ps[i:] = (x,) if x else ()
2320 n += 1
2321 if n:
2322 self._n += n
2323 # Fsum._ps_max = max(Fsum._ps_max, len(ps))
2324 if up:
2325 self._update()
2326# x = sum(ps)
2327# if not _isOK_or_finite(x, **fi):
2328# ps[:] = x, # collapse ps
2329 return ps
2331 def _ps_mul(self, op, *factors):
2332 '''(INTERNAL) Multiply this instance' C{partials} with
2333 each scalar C{factor} and accumulate into an C{Fsum}.
2334 '''
2335 def _psfs(ps, fs, _isfine=_isfinite):
2336 if len(ps) < len(fs):
2337 ps, fs = fs, ps
2338 if self._f2product:
2339 fs, p = _2split3s(fs), fs
2340 if len(ps) > 1 and fs is not p:
2341 fs = tuple(fs) # several ps
2342 _pfs = _2products
2343 else:
2344 def _pfs(p, fs):
2345 return (p * f for f in fs)
2347 for p in ps:
2348 for x in _pfs(p, fs):
2349 yield x if _isfine(x) else _nfError(x)
2351 xs = _psfs(self._ps, factors, **self._isfine)
2352 f = _Psum(self._ps_acc([], xs, up=False), name=op)
2353 return f
2355 @property_RO
2356 def _ps_neg(self):
2357 '''(INTERNAL) Yield the partials, I{negated}.
2358 '''
2359 for p in self._ps:
2360 yield -p
2362 def _ps_other(self, op, other):
2363 '''(INTERNAL) Yield C{other} as C{scalar}s.
2364 '''
2365 if _isFsum_2Tuple(other):
2366 for p in other._ps:
2367 yield p
2368 else:
2369 yield self._scalar(other, op)
2371 def _ps_1sum(self, *less):
2372 '''(INTERNAL) Return the partials sum, 1-primed C{less} some scalars.
2373 '''
2374 return _fsum(_1primed(self._ps, *less))
2376 def _raiser(self, r, s, raiser=True, **RESIDUAL):
2377 '''(INTERNAL) Does ratio C{r / s} exceed the RESIDUAL threshold
2378 I{and} is residual C{r} I{non-zero} or I{significant} (for a
2379 negative respectively positive C{RESIDUAL} threshold)?
2380 '''
2381 if r and raiser:
2382 t = self._RESIDUAL
2383 if RESIDUAL:
2384 t = _threshold(t, **RESIDUAL)
2385 if t < 0 or (s + r) != s:
2386 q = (r / s) if s else s # == 0.
2387 if fabs(q) > fabs(t):
2388 return dict(ratio=q, R=t)
2389 return {}
2391 def _rcopyd(self, other, which):
2392 '''(INTERNAL) Copy for I{reverse-dyadic} operators.
2393 '''
2394 return other._copyd(which) if _isFsum(other) else \
2395 self._copyd(which)._fset(other)
2397 rdiv = __rtruediv__
2399 @property_RO
2400 def real(self):
2401 '''Get the C{real} part of this instance (C{float}).
2403 @see: Methods L{Fsum.__float__} and L{Fsum.fsum}
2404 and properties L{Fsum.ceil}, L{Fsum.floor},
2405 L{Fsum.imag} and L{Fsum.residual}.
2406 '''
2407 return float(self)
2409 @property_RO
2410 def residual(self):
2411 '''Get this instance' residual or residue (C{float} or C{int}):
2412 the C{sum(partials)} less the precision running sum C{fsum}.
2414 @note: The C{residual is INT0} iff the precision running
2415 C{fsum} is considered to be I{exact}.
2417 @see: Methods L{Fsum.fsum}, L{Fsum.fsum2} and L{Fsum.is_exact}.
2418 '''
2419 return self._fprs2.residual
2421 def RESIDUAL(self, *threshold):
2422 '''Get and set this instance' I{ratio} for raising L{ResidualError}s,
2423 overriding the default from env variable C{PYGEODESY_FSUM_RESIDUAL}.
2425 @arg threshold: If C{scalar}, the I{ratio} to exceed for raising
2426 L{ResidualError}s in division and exponention, if
2427 C{None}, restore the default set with env variable
2428 C{PYGEODESY_FSUM_RESIDUAL} or if omitted, keep the
2429 current setting.
2431 @return: The previous C{RESIDUAL} setting (C{float}), default C{0.0}.
2433 @raise ResidualError: Invalid B{C{threshold}}.
2435 @note: L{ResidualError}s may be thrown if (1) the non-zero I{ratio}
2436 C{residual / fsum} exceeds the given B{C{threshold}} and (2)
2437 the C{residual} is non-zero and (3) is I{significant} vs the
2438 C{fsum}, i.e. C{(fsum + residual) != fsum} and (4) optional
2439 keyword argument C{raiser=False} is missing. Specify a
2440 negative B{C{threshold}} for only non-zero C{residual}
2441 testing without the I{significant} case.
2442 '''
2443 r = self._RESIDUAL
2444 if threshold:
2445 t = threshold[0]
2446 self._RESIDUAL = Fsum._RESIDUAL if t is None else ( # for ...
2447 (_0_0 if t else _1_0) if isbool(t) else
2448 _threshold(t)) # ... backward compatibility
2449 return r
2451 def _ResidualError(self, op, other, residual, **mod_R):
2452 '''(INTERNAL) Non-zero B{C{residual}} etc.
2453 '''
2454 def _p(mod=None, R=0, **unused): # ratio=0
2455 return (_non_zero_ if R < 0 else _significant_) \
2456 if mod is None else _integer_
2458 t = _stresidual(_p(**mod_R), residual, **mod_R)
2459 return self._Error(op, other, ResidualError, txt=t)
2461 def root(self, root, **raiser_RESIDUAL):
2462 '''Return C{B{self}**(1 / B{root})} as L{Fsum}.
2464 @arg root: Non-zero order (C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
2465 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore any
2466 L{ResidualError}s (C{bool}) or C{B{RESIDUAL}=scalar}
2467 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.
2469 @return: The C{self ** (1 / B{root})} result (L{Fsum}).
2471 @raise ResidualError: Non-zero, significant residual or invalid
2472 B{C{RESIDUAL}}.
2474 @see: Method L{Fsum.pow}.
2475 '''
2476 x = self._1_Over(root, _truediv_op_, **raiser_RESIDUAL)
2477 f = self._copyd(self.root)
2478 return f._fpow(x, f.name, **raiser_RESIDUAL) # == pow(f, x)
2480 def _scalar(self, other, op, **txt):
2481 '''(INTERNAL) Return scalar C{other} or throw a C{TypeError}.
2482 '''
2483 if isscalar(other):
2484 return other
2485 raise self._Error(op, other, _TypeError, **txt) # _invalid_
2487 def signOf(self, res=True):
2488 '''Determine the sign of this instance.
2490 @kwarg res: If C{True}, consider the residual,
2491 otherwise ignore the latter (C{bool}).
2493 @return: The sign (C{int}, -1, 0 or +1).
2494 '''
2495 s, r = self._nfprs2
2496 r = (-r) if res else 0
2497 return _signOf(s, r)
2499 def toRepr(self, **lenc_prec_sep_fmt): # PYCHOK signature
2500 '''Return this C{Fsum} instance as representation.
2502 @kwarg lenc_prec_sep_fmt: Optional keyword arguments
2503 for method L{Fsum.toStr}.
2505 @return: This instance (C{repr}).
2506 '''
2507 return Fmt.repr_at(self, self.toStr(**lenc_prec_sep_fmt))
2509 def toStr(self, lenc=True, **prec_sep_fmt): # PYCHOK signature
2510 '''Return this C{Fsum} instance as string.
2512 @kwarg lenc: If C{True}, include the current C{[len]} of this
2513 L{Fsum} enclosed in I{[brackets]} (C{bool}).
2514 @kwarg prec_sep_fmt: Optional keyword arguments for method
2515 L{Fsum2Tuple.toStr}.
2517 @return: This instance (C{str}).
2518 '''
2519 p = self.classname
2520 if lenc:
2521 p = Fmt.SQUARE(p, len(self))
2522 n = _enquote(self.name, white=_UNDER_)
2523 t = self._nfprs2.toStr(**prec_sep_fmt)
2524 return NN(p, _SPACE_, n, t)
2526 def _truediv(self, other, op, **raiser_RESIDUAL):
2527 '''(INTERNAL) Return C{B{self} / B{other}} as an L{Fsum}.
2528 '''
2529 f = self._copyd(self.__truediv__)
2530 return f._ftruediv(other, op, **raiser_RESIDUAL)
2532 def _update(self, updated=True): # see ._fset
2533 '''(INTERNAL) Zap all cached C{Property_RO} values.
2534 '''
2535 if updated:
2536 _pop = self.__dict__.pop
2537 for p in _ROs:
2538 _ = _pop(p, None)
2539# Fsum._fint2._update(self)
2540# Fsum._fprs ._update(self)
2541# Fsum._fprs2._update(self)
2542 return self # for .fset_
2544_ROs = _allPropertiesOf_n(3, Fsum, Property_RO) # PYCHOK see Fsum._update
2546_nonfinites_isfine_kwds = {True: dict(_isfine=_isOK),
2547 False: dict(_isfine=_isfinite)}
2548if _NONFINITES == _std_: # PYCHOK no cover
2549 _ = nonfiniterrors(False)
2552def _Float_Int(arg, **name_Error):
2553 '''(INTERNAL) L{DivMod2Tuple}, L{Fsum2Tuple} Unit.
2554 '''
2555 U = Int if isint(arg) else Float
2556 return U(arg, **name_Error)
2559class DivMod2Tuple(_NamedTuple):
2560 '''2-Tuple C{(div, mod)} with the quotient C{div} and remainder
2561 C{mod} results of a C{divmod} operation.
2563 @note: Quotient C{div} an C{int} in Python 3+ but a C{float}
2564 in Python 2-. Remainder C{mod} an L{Fsum} instance.
2565 '''
2566 _Names_ = ('div', 'mod')
2567 _Units_ = (_Float_Int, Fsum)
2570class Fsum2Tuple(_NamedTuple): # in .fstats
2571 '''2-Tuple C{(fsum, residual)} with the precision running C{fsum}
2572 and the C{residual}, the sum of the remaining partials. Each
2573 item is C{float} or C{int}.
2575 @note: If the C{residual is INT0}, the C{fsum} is considered
2576 to be I{exact}, see method L{Fsum2Tuple.is_exact}.
2577 '''
2578 _Names_ = ( typename(Fsum.fsum), Fsum.residual.name)
2579 _Units_ = (_Float_Int, _Float_Int)
2581 def __abs__(self): # in .fmath
2582 return self._Fsum.__abs__()
2584 def __bool__(self): # PYCHOK Python 3+
2585 return bool(self._Fsum)
2587 def __eq__(self, other):
2588 return self._other_op(other, self.__eq__)
2590 def __float__(self):
2591 return self._Fsum.__float__()
2593 def __ge__(self, other):
2594 return self._other_op(other, self.__ge__)
2596 def __gt__(self, other):
2597 return self._other_op(other, self.__gt__)
2599 def __le__(self, other):
2600 return self._other_op(other, self.__le__)
2602 def __lt__(self, other):
2603 return self._other_op(other, self.__lt__)
2605 def __int__(self):
2606 return self._Fsum.__int__()
2608 def __ne__(self, other):
2609 return self._other_op(other, self.__ne__)
2611 def __neg__(self):
2612 return self._Fsum.__neg__()
2614 __nonzero__ = __bool__ # Python 2-
2616 def __pos__(self):
2617 return self._Fsum.__pos__()
2619 def as_integer_ratio(self):
2620 '''Return this instance as the ratio of 2 integers.
2622 @see: Method L{Fsum.as_integer_ratio} for further details.
2623 '''
2624 return self._Fsum.as_integer_ratio()
2626 @property_RO
2627 def _fint2(self):
2628 return self._Fsum._fint2
2630 @property_RO
2631 def _fprs2(self):
2632 return self._Fsum._fprs2
2634 @Property_RO
2635 def _Fsum(self): # this C{Fsum2Tuple} as L{Fsum}, in .fstats
2636 s, r = _s_r2(*self)
2637 ps = (r, s) if r else (s,)
2638 return _Psum(ps, name=self.name)
2640 def Fsum_(self, *xs, **name_f2product_nonfinites_RESIDUAL):
2641 '''Return this C{Fsum2Tuple} as an L{Fsum} plus some C{xs}.
2642 '''
2643 return Fsum(self, *xs, **name_f2product_nonfinites_RESIDUAL)
2645 def is_exact(self):
2646 '''Is this L{Fsum2Tuple} considered to be exact? (C{bool}).
2647 '''
2648 return self._Fsum.is_exact()
2650 def is_finite(self): # in .constants
2651 '''Is this L{Fsum2Tuple} C{finite}? (C{bool}).
2653 @see: Function L{isfinite<pygeodesy.isfinite>}.
2654 '''
2655 return self._Fsum.is_finite()
2657 def is_integer(self):
2658 '''Is this L{Fsum2Tuple} C{integer}? (C{bool}).
2659 '''
2660 return self._Fsum.is_integer()
2662 def _mul_scalar(self, other, op): # for Fsum._fmul
2663 return self._Fsum._mul_scalar(other, op)
2665 @property_RO
2666 def _n(self):
2667 return self._Fsum._n
2669 def _other_op(self, other, which):
2670 C, s = (tuple, self) if isinstance(other, tuple) else (Fsum, self._Fsum)
2671 return getattr(C, typename(which))(s, other)
2673 @property_RO
2674 def _ps(self):
2675 return self._Fsum._ps
2677 @property_RO
2678 def _ps_neg(self):
2679 return self._Fsum._ps_neg
2681 def signOf(self, **res):
2682 '''Like method L{Fsum.signOf}.
2683 '''
2684 return self._Fsum.signOf(**res)
2686 def toStr(self, fmt=Fmt.g, **prec_sep): # PYCHOK signature
2687 '''Return this L{Fsum2Tuple} as string (C{str}).
2689 @kwarg fmt: Optional C{float} format (C{letter}).
2690 @kwarg prec_sep: Optional keyword arguments for function
2691 L{fstr<streprs.fstr>}.
2692 '''
2693 return Fmt.PAREN(fstr(self, fmt=fmt, strepr=str, force=False, **prec_sep))
2695_Fsum_2Tuple_types = Fsum, Fsum2Tuple # PYCHOK lines
2698class _Ksum(Fsum):
2699 '''(INTERNAL) For C{.karney._sum3}, specifically and only.
2700 '''
2701 _isfine = _nonfinites_isfine_kwds[True]
2703 def __init__(self, s, t, *xs):
2704 ps = [t, s] if t else [s]
2705 self._ps = self._ps_acc(ps, xs, up=False)
2707 @property_RO
2708 def _s_t_n3(self):
2709 s, t = self._fprs2
2710 return s, t, self._n
2713class ResidualError(_ValueError):
2714 '''Error raised for a division, power or root operation of
2715 an L{Fsum} instance with a C{residual} I{ratio} exceeding
2716 the L{RESIDUAL<Fsum.RESIDUAL>} threshold.
2718 @see: Module L{pygeodesy.fsums} and method L{Fsum.RESIDUAL}.
2719 '''
2720 pass
2723try:
2724 from math import fsum as _fsum # precision IEEE-754 sum, Python 2.6+
2726 # make sure _fsum works as expected (XXX check
2727 # float.__getformat__('float')[:4] == 'IEEE'?)
2728 if _fsum((1, 1e101, 1, -1e101)) != 2: # PYCHOK no cover
2729 del _fsum # nope, remove _fsum ...
2730 raise ImportError() # ... use _fsum below
2732 _sum = _fsum
2733except ImportError:
2734 _sum = sum
2736 def _fsum(xs): # in .elliptic, .geoids
2737 '''(INTERNAL) Precision summation, Python 2.5-.
2738 '''
2739 F = Fsum(name=_fsum.name, f2product=False, nonfinites=True)
2740 return float(F._facc(xs, up=False))
2743def fsum(xs, nonfinites=None, **floats):
2744 '''Precision floating point summation from Python's C{math.fsum}.
2746 @arg xs: Iterable of items to add (each C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
2747 @kwarg nonfinites: Use C{B{nonfinites}=True} if I{non-finites} are C{OK}, if
2748 C{False} I{non-finites} raise an Overflow-/ValueError or if
2749 C{None}, L{nonfiniterrors} applies (C{bool} or C{None}).
2750 @kwarg floats: DEPRECATED keyword argument C{B{floats}=False} (C{bool}), use
2751 keyword argument C{B{nonfinites}=False} instead.
2753 @return: Precision C{fsum} (C{float}).
2755 @raise OverflowError: Infinite B{C{xs}} item or intermediate C{math.fsum} overflow.
2757 @raise TypeError: Invalid B{C{xs}} item.
2759 @raise ValueError: Invalid or C{NAN} B{C{xs}} item.
2761 @see: Function L{nonfiniterrors}, class L{Fsum} and methods L{Fsum.nonfinites},
2762 L{Fsum.fsum}, L{Fsum.fadd} and L{Fsum.fadd_}.
2763 '''
2764 return _xsum(fsum, xs, nonfinites=nonfinites, **floats) if xs else _0_0
2767def fsum_(*xs, **nonfinites):
2768 '''Precision floating point summation of all positional items.
2770 @arg xs: Items to add (each C{scalar}, an L{Fsum} or L{Fsum2Tuple}), all positional.
2771 @kwarg nonfinites: Use C{B{nonfinites}=True} if I{non-finites} are C{OK} (C{bool}).
2773 @see: Function L{fsum<fsums.fsum>} for further details.
2774 '''
2775 return _xsum(fsum_, xs, **nonfinites) if xs else _0_0 # origin=1?
2778def fsumf_(*xs):
2779 '''Precision floating point summation of all positional items with I{non-finites} C{OK}.
2781 @arg xs: Items to add (each C{scalar}, an L{Fsum} or L{Fsum2Tuple}),
2782 all positional.
2784 @see: Function L{fsum_<fsums.fsum_>} for further details.
2785 '''
2786 return _xsum(fsumf_, xs, nonfinites=True) if xs else _0_0 # origin=1?
2789def fsum1(xs, **nonfinites):
2790 '''Precision floating point summation, 1-primed.
2792 @arg xs: Iterable of items to add (each C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
2793 @kwarg nonfinites: Use C{B{nonfinites}=True} if I{non-finites} are C{OK} (C{bool}).
2795 @see: Function L{fsum<fsums.fsum>} for further details.
2796 '''
2797 return _xsum(fsum1, xs, primed=1, **nonfinites) if xs else _0_0
2800def fsum1_(*xs, **nonfinites):
2801 '''Precision floating point summation of all positional items, 1-primed.
2803 @arg xs: Items to add (each C{scalar}, an L{Fsum} or L{Fsum2Tuple}), all positional.
2804 @kwarg nonfinites: Use C{B{nonfinites}=True} if I{non-finites} are C{OK} (C{bool}).
2806 @see: Function L{fsum_<fsums.fsum_>} for further details.
2807 '''
2808 return _xsum(fsum1_, xs, primed=1, **nonfinites) if xs else _0_0 # origin=1?
2811def fsum1f_(*xs):
2812 '''Precision floating point summation of all positional items, 1-primed and
2813 with I{non-finites} C{OK}.
2815 @see: Function L{fsum_<fsums.fsum_>} for further details.
2816 '''
2817 return _xsum(fsum1f_, xs, nonfinites=True, primed=1) if xs else _0_0
2820def _x_isfine(nfOK, **kwds): # get the C{_x} and C{_isfine} handlers.
2821 _x_kwds = dict(_x= (_passarg if nfOK else _2finite),
2822 _isfine=(_isOK if nfOK else _isfinite)) # PYCHOK kwds
2823 _x_kwds.update(kwds)
2824 return _x_kwds
2827def _X_ps(X): # default C{_X} handler
2828 return X._ps # lambda X: X._ps
2831def _xs(xs, _X=_X_ps, _x=float, _isfine=_isfinite, # defaults for Fsum._facc
2832 origin=0, which=None, **_Cdot):
2833 '''(INTERNAL) Yield each C{xs} item as 1 or more C{float}s.
2834 '''
2835 i, x = 0, xs
2836 try:
2837 for i, x in enumerate(_xiterable(xs)):
2838 if _isFsum_2Tuple(x):
2839 for p in _X(x):
2840 yield p if _isfine(p) else _nfError(p)
2841 else:
2842 f = _x(x)
2843 yield f if _isfine(f) else _nfError(f)
2845 except (OverflowError, TypeError, ValueError) as X:
2846 t = _xsError(X, xs, i + origin, x)
2847 if which: # prefix invokation
2848 w = unstr(which, *xs, _ELLIPSIS=4, **_Cdot)
2849 t = _COMMASPACE_(w, t)
2850 raise _xError(X, t, txt=None)
2853def _xsum(which, xs, nonfinites=None, primed=0, **floats): # origin=0
2854 '''(INTERNAL) Precision summation of C{xs} with conditions.
2855 '''
2856 if floats: # for backward compatibility
2857 nonfinites = _xkwds_get1(floats, floats=nonfinites)
2858 elif nonfinites is None:
2859 nonfinites = not nonfiniterrors()
2860 fs = _xs(xs, **_x_isfine(nonfinites, which=which)) # PYCHOK yield
2861 return _fsum(_1primed(fs) if primed else fs)
2864# delete all decorators, etc.
2865del _allPropertiesOf_n, deprecated_method, deprecated_property_RO, \
2866 Property, Property_RO, property_RO, _ALL_LAZY, _F2PRODUCT, \
2867 MANT_DIG, _NONFINITES, _RESIDUAL_0_0, _envPYGEODESY, _std_
2869if __name__ == _DMAIN_:
2871 # usage: python3 -m pygeodesy.fsums
2873 def _test(n):
2874 # copied from Hettinger, see L{Fsum} reference
2875 from pygeodesy import frandoms, printf
2877# printf(typename(_sum), end=_COMMASPACE_)
2878 printf(typename(_fsum), end=_COMMASPACE_)
2879 printf(typename(_psum), end=_COMMASPACE_)
2880 printf(len(Fsum.__dict__), end=_COMMASPACE_)
2881# printf(len(globals()), end=_COMMASPACE_)
2883 F = Fsum()
2884 if F.is_math_fsum():
2885 for t in frandoms(n, seeded=True):
2886 assert float(F.fset_(*t)) == _fsum(t)
2887 printf(_DOT_, end=NN)
2888 printf(NN)
2890 _test(128)
2892# **) MIT License
2893#
2894# Copyright (C) 2016-2026 -- mrJean1 at Gmail -- All Rights Reserved.
2895#
2896# Permission is hereby granted, free of charge, to any person obtaining a
2897# copy of this software and associated documentation files (the "Software"),
2898# to deal in the Software without restriction, including without limitation
2899# the rights to use, copy, modify, merge, publish, distribute, sublicense,
2900# and/or sell copies of the Software, and to permit persons to whom the
2901# Software is furnished to do so, subject to the following conditions:
2902#
2903# The above copyright notice and this permission notice shall be included
2904# in all copies or substantial portions of the Software.
2905#
2906# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
2907# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
2908# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
2909# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
2910# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
2911# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
2912# OTHER DEALINGS IN THE SOFTWARE.