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} enhanced with I{running} summation and as an
6option, accurate I{TwoProduct} multiplication.
8Accurate multiplication is based on the C{math.fma} function for
9Python 3.13 and newer or one of two equivalent C{fma} implementations
10for Python 3.12 and older. To enable accurate multiplication, set
11env variable C{PYGEODESY_FSUM_F2PRODUCT} to C{"std"} or any non-empty
12string or invoke function C{pygeodesy.f2product(True)} or set. With
13C{"std"} the C{fma} implemention follows the C{math.fma} function,
14otherwise the C{PyGeodesy 24.09.09} release.
16Generally, an L{Fsum} instance is considered a C{float} plus a small or
17zero C{residue} aka C{residual} value, see property L{Fsum.residual}.
19Set env variable C{PYGEODESY_FSUM_RESIDUAL} to a C{float} string greater
20than C{"0.0"} as the threshold to throw a L{ResidualError} for a division,
21power or root operation of an L{Fsum} with a C{residual} I{ratio} exceeding
22the threshold. See methods L{Fsum.RESIDUAL}, L{Fsum.pow}, L{Fsum.__ipow__}
23and L{Fsum.__itruediv__}.
25There are several C{integer} L{Fsum} cases, for example the result from
26functions C{ceil}, C{floor}, C{Fsum.__floordiv__} and methods L{Fsum.fint},
27L{Fsum.fint2} and L{Fsum.is_integer}. Also, L{Fsum} methods L{Fsum.pow},
28L{Fsum.__ipow__}, L{Fsum.__pow__} and L{Fsum.__rpow__} return a (very long)
29C{int} if invoked with optional argument C{mod} set to C{None}. The
30C{residual} of an C{integer} L{Fsum} is between C{-1.0} and C{+1.0} and
31will be C{INT0} if that is considered to be I{exact}.
33Set env variable C{PYGEODESY_FSUM_NONFINITES} to C{"std"} or use function
34C{pygeodesy.nonfiniterrors(False)} to allow I{non-finite} C{float}s like
35C{inf}, C{INF}, C{NINF}, C{nan} and C{NAN} and to ignore C{OverflowError}
36respectively C{ValueError} exceptions. However, in that case I{non-finite}
37results may differ from Python's C{math.fsum} results.
38'''
39# make sure int/int division yields float quotient, see .basics
40from __future__ import division as _; del _ # PYCHOK semicolon
42from pygeodesy.basics import isbool, iscomplex, isint, isscalar, \
43 _signOf, itemsorted, signOf, _xiterable
44from pygeodesy.constants import INF, INT0, MANT_DIG, NEG0, NINF, _0_0, \
45 _1_0, _N_1_0, _isfinite, _pos_self, \
46 Float, Int
47from pygeodesy.errors import _AssertionError, _OverflowError, _TypeError, \
48 _ValueError, _xError, _xError2, _xkwds, \
49 _xkwds_get, _xkwds_get1, _xkwds_not, \
50 _xkwds_pop, _xsError
51from pygeodesy.internals import _enquote, _passarg
52from pygeodesy.interns import NN, _arg_, _COMMASPACE_, _DOT_, _from_, \
53 _not_finite_, _SPACE_, _std_, _UNDER_
54from pygeodesy.lazily import _ALL_LAZY, _getenv, _sys_version_info2
55from pygeodesy.named import _name__, _name2__, _Named, _NamedTuple, \
56 _NotImplemented
57from pygeodesy.props import _allPropertiesOf_n, deprecated_method, \
58 deprecated_property_RO, Property, \
59 Property_RO, property_RO
60from pygeodesy.streprs import Fmt, fstr, unstr
61# from pygeodesy.units import Float, Int # from .constants
63from math import fabs, isinf, isnan, \
64 ceil as _ceil, floor as _floor # PYCHOK used! .ltp
66__all__ = _ALL_LAZY.fsums
67__version__ = '24.10.09'
69from pygeodesy.interns import (
70 _PLUS_ as _add_op_, # in .auxilats.auxAngle
71 _EQUAL_ as _fset_op_,
72 _RANGLE_ as _gt_op_,
73 _LANGLE_ as _lt_op_,
74 _PERCENT_ as _mod_op_,
75 _STAR_ as _mul_op_,
76 _NOTEQUAL_ as _ne_op_,
77 _DASH_ as _sub_op_, # in .auxilats.auxAngle
78 _SLASH_ as _truediv_op_
79)
80_floordiv_op_ = _truediv_op_ * 2 # _DSLASH_
81_divmod_op_ = _floordiv_op_ + _mod_op_
82_F2PRODUCT = _getenv('PYGEODESY_FSUM_F2PRODUCT', NN)
83_iadd_op_ = _add_op_ + _fset_op_ # in .auxilats.auxAngle, .fstats
84_integer_ = 'integer'
85_isub_op_ = _sub_op_ + _fset_op_ # in .auxilats.auxAngle
86_NONFINITEr = _0_0 # NOT INT0!
87_NONFINITES = _getenv('PYGEODESY_FSUM_NONFINITES', NN)
88_non_zero_ = 'non-zero'
89_pow_op_ = _mul_op_ * 2 # _DSTAR_
90_RESIDUAL_0_0 = _getenv('PYGEODESY_FSUM_RESIDUAL', _0_0)
91_significant_ = 'significant'
92_threshold_ = 'threshold'
95def _2finite(x, _isfine=_isfinite): # in .fstats
96 '''(INTERNAL) return C{float(x)} if finite.
97 '''
98 return (float(x) if _isfine(x) # and isscalar(x)
99 else _nfError(x))
102def _2float(index=None, _isfine=_isfinite, **name_x): # in .fmath, .fstats
103 '''(INTERNAL) Raise C{TypeError} or C{Overflow-/ValueError} if not finite.
104 '''
105 n, x = name_x.popitem() # _xkwds_item2(name_x)
106 try:
107 f = float(x)
108 return f if _isfine(f) else _nfError(x)
109 except Exception as X:
110 raise _xError(X, Fmt.INDEX(n, index), x)
113try: # MCCABE 26
114 from math import fma as _fma
116 def _2products(x, ys, *zs):
117 # yield(x * y for y in ys) + yield(z in zs)
118 # TwoProductFMA U{Algorithm 3.5
119 # <https://www.TUHH.De/ti3/paper/rump/OgRuOi05.pdf>}
120 for y in ys:
121 f = x * y
122 yield f
123 if _isfinite(f):
124 yield _fma(x, y, -f)
125 for z in zs:
126 yield z
128# _2split3 = \
129 _2split3s = _passarg # in Fsum.is_math_fma
131except ImportError: # PYCHOK DSPACE! Python 3.12-
133 if _F2PRODUCT and _F2PRODUCT != _std_:
134 # backward to PyGeodesy 24.09.09, with _fmaX
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 (na, da), (nb, db), (nc, dc) = map(_2n_d, a_b_c)
140 n = na * nb * dc
141 n += da * db * nc
142 d = da * db * dc
143 try:
144 n, d = _n_d2(n, d)
145 r = float(n / d)
146 except OverflowError: # "integer division result too large ..."
147 r = NINF if (_signOf(n, 0) * _signOf(d, 0)) < 0 else INF
148 return r if _isfinite(r) else _fmaX(r, *a_b_c) # "overflow in fma"
150 def _2n_d(x): # PYCHOK no cover
151 try: # int.as_integer_ratio in 3.8+
152 return x.as_integer_ratio()
153 except (AttributeError, OverflowError, TypeError, ValueError):
154 return (x if isint(x) else float(x)), 1
155 else:
157 def _fma(a, b, c): # PYCHOK redef
158 # mimick C{math.fma} from Python 3.13+,
159 # the same accuracy, but ~13x slower
160 b3s = _2split3(b), # 1-tuple of 3-tuple
161 r = _fsum(_2products(a, b3s, c))
162 return r if _isfinite(r) else _fmaX(r, a, b, c)
164 _2n_d = None # redef
166 def _fmaX(r, *a_b_c): # like Python 3.13+ I{Modules/mathmodule.c}:
167 # raise a ValueError for a NAN result from non-NAN C{a_b_c}s or an
168 # OverflowError for a non-NAN non-finite from all finite C{a_b_c}s.
169 if isnan(r):
170 def _x(x):
171 return not isnan(x)
172 else: # non-NAN non-finite
173 _x = _isfinite
174 if all(map(_x, a_b_c)):
175 raise _nfError(r, unstr(_fma, *a_b_c))
176 return r
178 def _2products(x, y3s, *zs): # PYCHOK in _fma, ...
179 # yield(x * y3 for y3 in y3s) + yield(z in zs)
180 # TwoProduct U{Algorithm 3.3
181 # <https://www.TUHH.De/ti3/paper/rump/OgRuOi05.pdf>}
182 # also in Python 3.13+ C{Modules/mathmodule.c} under
183 # #ifndef UNRELIABLE_FMA ... #else ... #endif
184 _, a, b = _2split3(x)
185 for y, c, d in y3s:
186 y *= x
187 yield y
188 if _isfinite(y):
189 # yield b * d - (((y - a * c) - b * c) - a * d)
190 # = b * d + (a * d - ((y - a * c) - b * c))
191 # = b * d + (a * d + (b * c - (y - a * c)))
192 # = b * d + (a * d + (b * c + (a * c - y)))
193 yield a * c - y
194 yield b * c
195 if d:
196 yield a * d
197 yield b * d
198 for z in zs:
199 yield z
201 _2FACTOR = pow(2, (MANT_DIG + 1) // 2) + _1_0 # 134217729 if MANT_DIG == 53
203 def _2split3(x):
204 # Split U{Algorithm 3.2
205 # <https://www.TUHH.De/ti3/paper/rump/OgRuOi05.pdf>}
206 a = c = x * _2FACTOR
207 a -= c - x
208 b = x - a
209 return x, a, b
211 def _2split3s(xs): # in Fsum.is_math_fma
212 return map(_2split3, xs)
215def f2product(*two):
216 '''Turn accurate I{TwoProduct} multiplication on or off.
218 @arg two: If C{True}, turn I{TwoProduct} on, if C{False} off or
219 if C{None} or omitted, keep the current setting.
221 @return: The previous setting (C{bool}).
223 @see: I{TwoProduct} multiplication is based on the I{TwoProductFMA}
224 U{Algorithm 3.5 <https://www.TUHH.De/ti3/paper/rump/OgRuOi05.pdf>}
225 using function C{math.fma} from Python 3.13 and later or an
226 equivalent, slower implementation when not available.
227 '''
228 t = Fsum._f2product
229 if two and two[0] is not None:
230 Fsum._f2product = bool(two[0])
231 return t
234def _Fsumf_(*xs): # in .auxLat, .ltp, ...
235 '''(INTERNAL) An C{Fsum(xs)}, all C{scalar}, an L{Fsum} or L{Fsum2Tuple}.
236 '''
237 return Fsum()._facc_scalarf(xs, up=False)
240def _Fsum1f_(*xs): # in .albers
241 '''(INTERNAL) An C{Fsum(xs)}, all C{scalar}, an L{Fsum} or L{Fsum2Tuple}, 1-primed.
242 '''
243 return Fsum()._facc_scalarf(_1primed(xs), origin=-1, up=False)
246def _halfeven(s, r, p):
247 '''(INTERNAL) Round half-even.
248 '''
249 if (p > 0 and r > 0) or \
250 (p < 0 and r < 0): # signs match
251 r *= 2
252 t = s + r
253 if r == (t - s):
254 s = t
255 return s
258def _isFsum(x): # in .fmath
259 '''(INTERNAL) Is C{x} an C{Fsum} instance?
260 '''
261 return isinstance(x, Fsum)
264def _isFsum_2Tuple(x): # in .basics, .constants, .fmath, .fstats
265 '''(INTERNAL) Is C{x} an C{Fsum} or C{Fsum2Tuple} instance?
266 '''
267 return isinstance(x, _Fsum_2Tuple_types)
270def _isOK(unused):
271 '''(INTERNAL) Helper for C{Fsum._fsum2} and C{Fsum.nonfinites}.
272 '''
273 return True
276def _isOK_or_finite(x, _isfine=_isfinite):
277 '''(INTERNAL) Is C{x} finite or is I{non-finite} OK?
278 '''
279 # assert _isfine in (_isOK, _isfinite)
280 return _isfine(x) # C{bool}
283try:
284 from math import gcd as _gcd
286 def _n_d2(n, d):
287 '''(INTERNAL) Reduce C{n} and C{d} by C{gcd}.
288 '''
289 if n and d:
290 try:
291 c = _gcd(n, d)
292 if c > 1:
293 n, d = (n // c), (d // c)
294 except TypeError: # non-int float
295 pass
296 return n, d
298except ImportError: # 3.4-
300 def _n_d2(*n_d): # PYCHOK redef
301 return n_d
304def _nfError(x, *args):
305 '''(INTERNAL) Throw a C{not-finite} exception.
306 '''
307 E = _NonfiniteError(x)
308 t = Fmt.PARENSPACED(_not_finite_, x)
309 if args: # in _fmaX, _2sum
310 return E(txt=t, *args)
311 raise E(t, txt=None)
314def _NonfiniteError(x):
315 '''(INTERNAL) Return the Error class for C{x}, I{non-finite}.
316 '''
317 return _OverflowError if isinf(x) else (
318 _ValueError if isnan(x) else _AssertionError)
321def nonfiniterrors(*raiser):
322 '''Throw C{OverflowError} and C{ValueError} exceptions for or
323 handle I{non-finite} C{float}s as C{inf}, C{INF}, C{NINF},
324 C{nan} and C{NAN} in summations and multiplications.
326 @arg raiser: If C{True}, throw exceptions, if C{False} handle
327 I{non-finites} or if C{None} or omitted, leave
328 the setting unchanged.
330 @return: Previous setting (C{bool}).
332 @note: C{inf}, C{INF} and C{NINF} throw an C{OverflowError},
333 C{nan} and C{NAN} a C{ValueError}.
334 '''
335 d = Fsum._isfine
336 if raiser and raiser[0] is not None:
337 Fsum._isfine = {} if bool(raiser[0]) else Fsum._nonfinites_isfine_kwds[True]
338 return (False if d is Fsum._nonfinites_isfine_kwds[True] else
339 _xkwds_get1(d, _isfine=_isfinite) is _isfinite) if d else True
342def _1primed(xs): # in .fmath
343 '''(INTERNAL) 1-Primed summation of iterable C{xs}
344 items, all I{known} to be C{scalar}.
345 '''
346 yield _1_0
347 for x in xs:
348 yield x
349 yield _N_1_0
352def _psum(ps, **_isfine): # PYCHOK used!
353 '''(INTERNAL) Partials summation, updating C{ps}.
354 '''
355 # assert isinstance(ps, list)
356 i = len(ps) - 1
357 s = _0_0 if i < 0 else ps[i]
358 while i > 0:
359 i -= 1
360 s, r = _2sum(s, ps[i], **_isfine)
361 if r: # sum(ps) became inexact
362 if s:
363 ps[i:] = r, s
364 if i > 0:
365 s = _halfeven(s, r, ps[i-1])
366 break # return s
367 s = r # PYCHOK no cover
368 elif not _isfinite(s): # non-finite OK
369 i = 0 # collapse ps
370 if ps:
371 s += sum(ps)
372 ps[i:] = s,
373 return s
376def _Psum(ps, **name_f2product_nonfinites_RESIDUAL):
377 '''(INTERNAL) Return an C{Fsum} from I{ordered} partials C{ps}.
378 '''
379 F = Fsum(**name_f2product_nonfinites_RESIDUAL)
380 if ps:
381 F._ps[:] = ps
382 F._n = len(F._ps)
383 return F
386def _Psum_(*ps, **name_f2product_nonfinites_RESIDUAL): # in .fmath
387 '''(INTERNAL) Return an C{Fsum} from I{known scalar} C{ps}.
388 '''
389 return _Psum(ps, **name_f2product_nonfinites_RESIDUAL)
392def _residue(other):
393 '''(INTERNAL) Return the C{residual} or C{None} for C{scalar}.
394 '''
395 try:
396 r = other.residual
397 except AttributeError:
398 r = None # float, int, other
399 return r
402def _s_r(s, r):
403 '''(INTERNAL) Return C{(s, r)}, I{ordered}.
404 '''
405 if _isfinite(s):
406 if r:
407 if fabs(s) < fabs(r):
408 s, r = r, (s or INT0)
409 else:
410 r = INT0
411 else:
412 r = _NONFINITEr
413 return s, r
416def _2s_r(other):
417 '''(INTERNAL) Return 2-tuple C{(other, r)} with C{other} as C{int},
418 C{float} or C{as-is} and C{r} the residual of C{as-is} or 0.
419 '''
420 if _isFsum_2Tuple(other):
421 s, r = other._fint2
422 if r:
423 s, r = other._nfprs2
424 if r: # PYCHOK no cover
425 s = other # L{Fsum} as-is
426 else:
427 r = 0
428 s = other # C{type} as-is
429 if isint(s, both=True):
430 s = int(s)
431 return s, r
434def _strcomplex(s, *args):
435 '''(INTERNAL) C{Complex} 2- or 3-arg C{pow} error as C{str}.
436 '''
437 c = _strcomplex.__name__[4:]
438 n = _sub_op_(len(args), _arg_)
439 t = unstr(pow, *args)
440 return _SPACE_(c, s, _from_, n, t)
443def _stresidual(prefix, residual, R=0, **mod_ratio):
444 '''(INTERNAL) Residual error txt C{str}.
445 '''
446 p = _stresidual.__name__[3:]
447 t = Fmt.PARENSPACED(p, Fmt(residual))
448 for n, v in itemsorted(mod_ratio):
449 p = Fmt.PARENSPACED(n, Fmt(v))
450 t = _COMMASPACE_(t, p)
451 return _SPACE_(prefix, t, Fmt.exceeds_R(R), _threshold_)
454def _2sum(a, b, _isfine=_isfinite): # in .testFmath
455 '''(INTERNAL) Return C{a + b} as 2-tuple C{(sum, residual)} with finite C{sum},
456 otherwise as 2-tuple C{(nonfinite, 0)} iff I{non-finites} are OK.
457 '''
458 # FastTwoSum U{Algorithm 1.1<https://www.TUHH.De/ti3/paper/rump/OgRuOi05.pdf>}
460 # Neumaier, A. U{Rundungsfehleranalyse einiger Verfahren zur Summation endlicher
461 # Summen<https://OnlineLibrary.Wiley.com/doi/epdf/10.1002/zamm.19740540106>},
462 # 1974, Zeitschrift für Angewandte Mathmatik und Mechanik, vol 51, nr 1, p 39-51
463 # <https://StackOverflow.com/questions/78633770/can-neumaier-summation-be-sped-up>
464 s = a + b
465 if _isfinite(s):
466 if fabs(a) < fabs(b):
467 r = (b - s) + a
468 else:
469 r = (a - s) + b
470 elif _isfine(s):
471 r = _NONFINITEr
472 else: # non-finite and not OK
473 t = unstr(_2sum, a, b)
474 raise _nfError(s, t)
475 return s, r
478def _threshold(threshold=_0_0, **kwds):
479 '''(INTERNAL) Get the L{ResidualError}s threshold,
480 optionally from single kwds C{B{RESIDUAL}=scalar}.
481 '''
482 if kwds:
483 threshold = _xkwds_get1(kwds, RESIDUAL=threshold)
484 try:
485 return _2finite(threshold) # PYCHOK None
486 except Exception as x:
487 raise ResidualError(threshold=threshold, cause=x)
490class Fsum(_Named): # sync __methods__ with .vector3dBase.Vector3dBase, .fstats, ...
491 '''Precision floating point summation, I{running} summation and accurate multiplication.
493 Unlike Python's C{math.fsum}, this class accumulates values and provides intermediate,
494 I{running}, precision floating point summations. Accumulation may continue after any
495 intermediate, I{running} summuation.
497 @note: Values may be L{Fsum}, L{Fsum2Tuple}, C{int}, C{float} or C{scalar} instances,
498 i.e. any C{type} having method C{__float__}.
500 @note: Handling of I{non-finites} as C{inf}, C{INF}, C{NINF}, C{nan} and C{NAN} is
501 determined by function L{nonfiniterrors<fsums.nonfiniterrors>} for the default
502 and by method L{nonfinites<Fsum.nonfinites>} for individual C{Fsum} instances,
503 overruling the default. For backward compatibility, I{non-finites} raise
504 exceptions by default.
506 @see: U{Hettinger<https://GitHub.com/ActiveState/code/tree/master/recipes/Python/
507 393090_Binary_floating_point_summatiaccurate_full/recipe-393090.py>},
508 U{Kahan<https://WikiPedia.org/wiki/Kahan_summation_algorithm>}, U{Klein
509 <https://Link.Springer.com/article/10.1007/s00607-005-0139-x>}, Python 2.6+
510 file I{Modules/mathmodule.c} and the issue log U{Full precision summation
511 <https://Bugs.Python.org/issue2819>}.
513 @see: Method L{f2product<Fsum.f2product>} for details about accurate I{TwoProduct}
514 multiplication.
516 @see: Module L{fsums<pygeodesy.fsums>} for env variables C{PYGEODESY_FSUM_F2PRODUCT},
517 C{PYGEODESY_FSUM_NONFINITES} and C{PYGEODESY_FSUM_RESIDUAL}.
518 '''
519 _f2product = _sys_version_info2 > (3, 12) or bool(_F2PRODUCT)
520 _isfine = {} # == _isfinite, see nonfiniterrors()
521 _n = 0
522# _ps = [] # partial sums
523# _ps_max = 0 # max(Fsum._ps_max, len(Fsum._ps)) # 41
524 _RESIDUAL = _threshold(_RESIDUAL_0_0)
526 def __init__(self, *xs, **name_f2product_nonfinites_RESIDUAL):
527 '''New L{Fsum}.
529 @arg xs: No, one or more initial items to accumulate (each C{scalar}, an
530 L{Fsum} or L{Fsum2Tuple}), all positional.
531 @kwarg name_f2product_nonfinites_RESIDUAL: Optional C{B{name}=NN} (C{str})
532 and settings C{B{f2product}=None} (C{bool}), C{B{nonfinites}=None}
533 (C{bool}) and C{B{RESIDUAL}=0.0} threshold (C{scalar}) for this
534 L{Fsum}.
536 @see: Methods L{Fsum.f2product}, L{Fsum.nonfinites}, L{Fsum.RESIDUAL},
537 L{Fsum.fadd} and L{Fsum.fadd_}.
538 '''
539 if name_f2product_nonfinites_RESIDUAL:
540 self._optionals(**name_f2product_nonfinites_RESIDUAL)
541 self._ps = [] # [_0_0], see L{Fsum._fprs}
542 if xs:
543 self._facc_args(xs, up=False)
545 def __abs__(self):
546 '''Return C{abs(self)} as an L{Fsum}.
547 '''
548 s = self.signOf() # == self._cmp_0(0)
549 return (-self) if s < 0 else self._copy_2(self.__abs__)
551 def __add__(self, other):
552 '''Return C{B{self} + B{other}} as an L{Fsum}.
554 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar}.
556 @return: The sum (L{Fsum}).
558 @see: Methods L{Fsum.fadd_} and L{Fsum.fadd}.
559 '''
560 f = self._copy_2(self.__add__)
561 return f._fadd(other)
563 def __bool__(self): # PYCHOK Python 3+
564 '''Return C{bool(B{self})}, C{True} iff C{residual} is zero.
565 '''
566 s, r = self._nfprs2
567 return bool(s or r) and s != -r # == self != 0
569 def __call__(self, other, **up): # in .fmath
570 '''Reset this C{Fsum} to C{other}, default C{B{up}=True}.
571 '''
572 self._ps[:] = 0, # clear for errors
573 self._fset(other, op=_fset_op_, **up)
574 return self
577 def __ceil__(self): # PYCHOK not special in Python 2-
578 '''Return this instance' C{math.ceil} as C{int} or C{float}.
580 @return: An C{int} in Python 3+, but C{float} in Python 2-.
582 @see: Methods L{Fsum.__floor__} and property L{Fsum.ceil}.
583 '''
584 return self.ceil
586 def __cmp__(self, other): # PYCHOK no cover
587 '''Compare this with an other instance or C{scalar}, Python 2-.
589 @return: -1, 0 or +1 (C{int}).
591 @raise TypeError: Incompatible B{C{other}} C{type}.
592 '''
593 s = self._cmp_0(other, self.cmp.__name__)
594 return _signOf(s, 0)
596 def __divmod__(self, other, **raiser_RESIDUAL):
597 '''Return C{divmod(B{self}, B{other})} as a L{DivMod2Tuple}
598 with quotient C{div} an C{int} in Python 3+ or C{float}
599 in Python 2- and remainder C{mod} an L{Fsum} instance.
601 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar} modulus.
602 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore
603 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}
604 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.
606 @raise ResidualError: Non-zero, significant residual or invalid
607 B{C{RESIDUAL}}.
609 @see: Method L{Fsum.fdiv}.
610 '''
611 f = self._copy_2(self.__divmod__)
612 return f._fdivmod2(other, _divmod_op_, **raiser_RESIDUAL)
614 def __eq__(self, other):
615 '''Return C{(B{self} == B{other})} as C{bool} where B{C{other}}
616 is C{scalar}, an other L{Fsum} or L{Fsum2Tuple}.
617 '''
618 return self._cmp_0(other, _fset_op_ + _fset_op_) == 0
620 def __float__(self):
621 '''Return this instance' current, precision running sum as C{float}.
623 @see: Methods L{Fsum.fsum} and L{Fsum.int_float}.
624 '''
625 return float(self._fprs)
627 def __floor__(self): # PYCHOK not special in Python 2-
628 '''Return this instance' C{math.floor} as C{int} or C{float}.
630 @return: An C{int} in Python 3+, but C{float} in Python 2-.
632 @see: Methods L{Fsum.__ceil__} and property L{Fsum.floor}.
633 '''
634 return self.floor
636 def __floordiv__(self, other):
637 '''Return C{B{self} // B{other}} as an L{Fsum}.
639 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar} divisor.
641 @return: The C{floor} quotient (L{Fsum}).
643 @see: Methods L{Fsum.__ifloordiv__}.
644 '''
645 f = self._copy_2(self.__floordiv__)
646 return f._floordiv(other, _floordiv_op_)
648 def __format__(self, *other): # PYCHOK no cover
649 '''Not implemented.'''
650 return _NotImplemented(self, *other)
652 def __ge__(self, other):
653 '''Return C{(B{self} >= B{other})}, see C{__eq__}.
654 '''
655 return self._cmp_0(other, _gt_op_ + _fset_op_) >= 0
657 def __gt__(self, other):
658 '''Return C{(B{self} > B{other})}, see C{__eq__}.
659 '''
660 return self._cmp_0(other, _gt_op_) > 0
662 def __hash__(self): # PYCHOK no cover
663 '''Return C{hash(B{self})} as C{float}.
664 '''
665 # @see: U{Notes for type implementors<https://docs.Python.org/
666 # 3/library/numbers.html#numbers.Rational>}
667 return hash(self.partials) # tuple.__hash__()
669 def __iadd__(self, other):
670 '''Apply C{B{self} += B{other}} to this instance.
672 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar} value or
673 an iterable of several of the former.
675 @return: This instance, updated (L{Fsum}).
677 @raise TypeError: Invalid B{C{other}}, not
678 C{scalar} nor L{Fsum}.
680 @see: Methods L{Fsum.fadd_} and L{Fsum.fadd}.
681 '''
682 try:
683 return self._fadd(other, op=_iadd_op_)
684 except TypeError:
685 pass
686 _xiterable(other)
687 return self._facc(other)
689 def __ifloordiv__(self, other):
690 '''Apply C{B{self} //= B{other}} to this instance.
692 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar} divisor.
694 @return: This instance, updated (L{Fsum}).
696 @raise ResidualError: Non-zero, significant residual
697 in B{C{other}}.
699 @raise TypeError: Invalid B{C{other}} type.
701 @raise ValueError: Invalid or I{non-finite} B{C{other}}.
703 @raise ZeroDivisionError: Zero B{C{other}}.
705 @see: Methods L{Fsum.__itruediv__}.
706 '''
707 return self._floordiv(other, _floordiv_op_ + _fset_op_)
709 def __imatmul__(self, other): # PYCHOK no cover
710 '''Not implemented.'''
711 return _NotImplemented(self, other)
713 def __imod__(self, other):
714 '''Apply C{B{self} %= B{other}} to this instance.
716 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar} modulus.
718 @return: This instance, updated (L{Fsum}).
720 @see: Method L{Fsum.__divmod__}.
721 '''
722 return self._fdivmod2(other, _mod_op_ + _fset_op_).mod
724 def __imul__(self, other):
725 '''Apply C{B{self} *= B{other}} to this instance.
727 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar} factor.
729 @return: This instance, updated (L{Fsum}).
731 @raise OverflowError: Partial C{2sum} overflow.
733 @raise TypeError: Invalid B{C{other}} type.
735 @raise ValueError: Invalid or I{non-finite} B{C{other}}.
736 '''
737 return self._fmul(other, _mul_op_ + _fset_op_)
739 def __int__(self):
740 '''Return this instance as an C{int}.
742 @see: Method L{Fsum.int_float} and properties L{Fsum.ceil}
743 and L{Fsum.floor}.
744 '''
745 i, _ = self._fint2
746 return i
748 def __invert__(self): # PYCHOK no cover
749 '''Not implemented.'''
750 # Luciano Ramalho, "Fluent Python", O'Reilly, 2nd Ed, 2022 p. 567
751 return _NotImplemented(self)
753 def __ipow__(self, other, *mod, **raiser_RESIDUAL): # PYCHOK 2 vs 3 args
754 '''Apply C{B{self} **= B{other}} to this instance.
756 @arg other: The exponent (C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
757 @arg mod: Optional modulus (C{int} or C{None}) for the 3-argument
758 C{pow(B{self}, B{other}, B{mod})} version.
759 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore
760 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}
761 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.
763 @return: This instance, updated (L{Fsum}).
765 @note: If B{C{mod}} is given, the result will be an C{integer}
766 L{Fsum} in Python 3+ if this instance C{is_integer} or
767 set to C{as_integer} and B{C{mod}} is given and C{None}.
769 @raise OverflowError: Partial C{2sum} overflow.
771 @raise ResidualError: Invalid B{C{RESIDUAL}} or the residual
772 is non-zero and significant and either
773 B{C{other}} is a fractional or negative
774 C{scalar} or B{C{mod}} is given and not
775 C{None}.
777 @raise TypeError: Invalid B{C{other}} type or 3-argument C{pow}
778 invocation failed.
780 @raise ValueError: If B{C{other}} is a negative C{scalar} and this
781 instance is C{0} or B{C{other}} is a fractional
782 C{scalar} and this instance is negative or has a
783 non-zero and significant residual or B{C{mod}}
784 is given as C{0}.
786 @see: CPython function U{float_pow<https://GitHub.com/
787 python/cpython/blob/main/Objects/floatobject.c>}.
788 '''
789 return self._fpow(other, _pow_op_ + _fset_op_, *mod, **raiser_RESIDUAL)
791 def __isub__(self, other):
792 '''Apply C{B{self} -= B{other}} to this instance.
794 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar} value or
795 an iterable of several of the former.
797 @return: This instance, updated (L{Fsum}).
799 @raise TypeError: Invalid B{C{other}} type.
801 @see: Methods L{Fsum.fsub_} and L{Fsum.fsub}.
802 '''
803 try:
804 return self._fsub(other, _isub_op_)
805 except TypeError:
806 pass
807 _xiterable(other)
808 return self._facc_neg(other)
810 def __iter__(self):
811 '''Return an C{iter}ator over a C{partials} duplicate.
812 '''
813 return iter(self.partials)
815 def __itruediv__(self, other, **raiser_RESIDUAL):
816 '''Apply C{B{self} /= B{other}} to this instance.
818 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar} divisor.
819 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore
820 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}
821 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.
823 @return: This instance, updated (L{Fsum}).
825 @raise OverflowError: Partial C{2sum} overflow.
827 @raise ResidualError: Non-zero, significant residual or invalid
828 B{C{RESIDUAL}}.
830 @raise TypeError: Invalid B{C{other}} type.
832 @raise ValueError: Invalid or I{non-finite} B{C{other}}.
834 @raise ZeroDivisionError: Zero B{C{other}}.
836 @see: Method L{Fsum.__ifloordiv__}.
837 '''
838 return self._ftruediv(other, _truediv_op_ + _fset_op_, **raiser_RESIDUAL)
840 def __le__(self, other):
841 '''Return C{(B{self} <= B{other})}, see C{__eq__}.
842 '''
843 return self._cmp_0(other, _lt_op_ + _fset_op_) <= 0
845 def __len__(self):
846 '''Return the number of values accumulated (C{int}).
847 '''
848 return self._n
850 def __lt__(self, other):
851 '''Return C{(B{self} < B{other})}, see C{__eq__}.
852 '''
853 return self._cmp_0(other, _lt_op_) < 0
855 def __matmul__(self, other): # PYCHOK no cover
856 '''Not implemented.'''
857 return _NotImplemented(self, other)
859 def __mod__(self, other):
860 '''Return C{B{self} % B{other}} as an L{Fsum}.
862 @see: Method L{Fsum.__imod__}.
863 '''
864 f = self._copy_2(self.__mod__)
865 return f._fdivmod2(other, _mod_op_).mod
867 def __mul__(self, other):
868 '''Return C{B{self} * B{other}} as an L{Fsum}.
870 @see: Method L{Fsum.__imul__}.
871 '''
872 f = self._copy_2(self.__mul__)
873 return f._fmul(other, _mul_op_)
875 def __ne__(self, other):
876 '''Return C{(B{self} != B{other})}, see C{__eq__}.
877 '''
878 return self._cmp_0(other, _ne_op_) != 0
880 def __neg__(self):
881 '''Return C{copy(B{self})}, I{negated}.
882 '''
883 f = self._copy_2(self.__neg__)
884 return f._fset(self._neg)
886 def __pos__(self):
887 '''Return this instance I{as-is}, like C{float.__pos__()}.
888 '''
889 return self if _pos_self else self._copy_2(self.__pos__)
891 def __pow__(self, other, *mod): # PYCHOK 2 vs 3 args
892 '''Return C{B{self}**B{other}} as an L{Fsum}.
894 @see: Method L{Fsum.__ipow__}.
895 '''
896 f = self._copy_2(self.__pow__)
897 return f._fpow(other, _pow_op_, *mod)
899 def __radd__(self, other):
900 '''Return C{B{other} + B{self}} as an L{Fsum}.
902 @see: Method L{Fsum.__iadd__}.
903 '''
904 f = self._copy_2r(other, self.__radd__)
905 return f._fadd(self)
907 def __rdivmod__(self, other):
908 '''Return C{divmod(B{other}, B{self})} as 2-tuple
909 C{(quotient, remainder)}.
911 @see: Method L{Fsum.__divmod__}.
912 '''
913 f = self._copy_2r(other, self.__rdivmod__)
914 return f._fdivmod2(self, _divmod_op_)
916# def __repr__(self):
917# '''Return the default C{repr(this)}.
918# '''
919# return self.toRepr(lenc=True)
921 def __rfloordiv__(self, other):
922 '''Return C{B{other} // B{self}} as an L{Fsum}.
924 @see: Method L{Fsum.__ifloordiv__}.
925 '''
926 f = self._copy_2r(other, self.__rfloordiv__)
927 return f._floordiv(self, _floordiv_op_)
929 def __rmatmul__(self, other): # PYCHOK no cover
930 '''Not implemented.'''
931 return _NotImplemented(self, other)
933 def __rmod__(self, other):
934 '''Return C{B{other} % B{self}} as an L{Fsum}.
936 @see: Method L{Fsum.__imod__}.
937 '''
938 f = self._copy_2r(other, self.__rmod__)
939 return f._fdivmod2(self, _mod_op_).mod
941 def __rmul__(self, other):
942 '''Return C{B{other} * B{self}} as an L{Fsum}.
944 @see: Method L{Fsum.__imul__}.
945 '''
946 f = self._copy_2r(other, self.__rmul__)
947 return f._fmul(self, _mul_op_)
949 def __round__(self, *ndigits): # PYCHOK Python 3+
950 '''Return C{round(B{self}, *B{ndigits}} as an L{Fsum}.
952 @arg ndigits: Optional number of digits (C{int}).
953 '''
954 f = self._copy_2(self.__round__)
955 # <https://docs.Python.org/3.12/reference/datamodel.html?#object.__round__>
956 return f._fset(round(float(self), *ndigits)) # can be C{int}
958 def __rpow__(self, other, *mod):
959 '''Return C{B{other}**B{self}} as an L{Fsum}.
961 @see: Method L{Fsum.__ipow__}.
962 '''
963 f = self._copy_2r(other, self.__rpow__)
964 return f._fpow(self, _pow_op_, *mod)
966 def __rsub__(self, other):
967 '''Return C{B{other} - B{self}} as L{Fsum}.
969 @see: Method L{Fsum.__isub__}.
970 '''
971 f = self._copy_2r(other, self.__rsub__)
972 return f._fsub(self, _sub_op_)
974 def __rtruediv__(self, other, **raiser_RESIDUAL):
975 '''Return C{B{other} / B{self}} as an L{Fsum}.
977 @see: Method L{Fsum.__itruediv__}.
978 '''
979 f = self._copy_2r(other, self.__rtruediv__)
980 return f._ftruediv(self, _truediv_op_, **raiser_RESIDUAL)
982 def __str__(self):
983 '''Return the default C{str(self)}.
984 '''
985 return self.toStr(lenc=True)
987 def __sub__(self, other):
988 '''Return C{B{self} - B{other}} as an L{Fsum}.
990 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar}.
992 @return: The difference (L{Fsum}).
994 @see: Method L{Fsum.__isub__}.
995 '''
996 f = self._copy_2(self.__sub__)
997 return f._fsub(other, _sub_op_)
999 def __truediv__(self, other, **raiser_RESIDUAL):
1000 '''Return C{B{self} / B{other}} as an L{Fsum}.
1002 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar} divisor.
1003 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore
1004 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}
1005 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.
1007 @return: The quotient (L{Fsum}).
1009 @raise ResidualError: Non-zero, significant residual or invalid
1010 B{C{RESIDUAL}}.
1012 @see: Method L{Fsum.__itruediv__}.
1013 '''
1014 return self._truediv(other, _truediv_op_, **raiser_RESIDUAL)
1016 __trunc__ = __int__
1018 if _sys_version_info2 < (3, 0): # PYCHOK no cover
1019 # <https://docs.Python.org/2/library/operator.html#mapping-operators-to-functions>
1020 __div__ = __truediv__
1021 __idiv__ = __itruediv__
1022 __long__ = __int__
1023 __nonzero__ = __bool__
1024 __rdiv__ = __rtruediv__
1026 def as_integer_ratio(self):
1027 '''Return this instance as the ratio of 2 integers.
1029 @return: 2-Tuple C{(numerator, denominator)} both C{int} with
1030 C{numerator} signed and C{denominator} non-zero and
1031 positive. The C{numerator} is I{non-finite} if this
1032 instance is.
1034 @see: Method L{Fsum.fint2} and C{float.as_integer_ratio} in
1035 Python 2.7+.
1036 '''
1037 n, r = self._fint2
1038 if r:
1039 i, d = float(r).as_integer_ratio()
1040 n, d = _n_d2(n * d + i, d)
1041 else: # PYCHOK no cover
1042 d = 1
1043 return n, d
1045 @property_RO
1046 def as_iscalar(self):
1047 '''Get this instance I{as-is} (L{Fsum} with C{non-zero residual},
1048 C{scalar} or I{non-finite}).
1049 '''
1050 s, r = self._nfprs2
1051 return self if r else s
1053 @property_RO
1054 def ceil(self):
1055 '''Get this instance' C{ceil} value (C{int} in Python 3+, but
1056 C{float} in Python 2-).
1058 @note: This C{ceil} takes the C{residual} into account.
1060 @see: Method L{Fsum.int_float} and properties L{Fsum.floor},
1061 L{Fsum.imag} and L{Fsum.real}.
1062 '''
1063 s, r = self._fprs2
1064 c = _ceil(s) + int(r) - 1
1065 while r > (c - s): # (s + r) > c
1066 c += 1
1067 return c # _ceil(self._n_d)
1069 cmp = __cmp__
1071 def _cmp_0(self, other, op):
1072 '''(INTERNAL) Return C{scalar(self - B{other})} for 0-comparison.
1073 '''
1074 if _isFsum_2Tuple(other):
1075 s = self._ps_1sum(*other._ps)
1076 elif self._scalar(other, op):
1077 s = self._ps_1sum(other)
1078 else:
1079 s = self.signOf() # res=True
1080 return s
1082 def copy(self, deep=False, **name):
1083 '''Copy this instance, C{shallow} or B{C{deep}}.
1085 @kwarg name: Optional, overriding C{B{name}='"copy"} (C{str}).
1087 @return: The copy (L{Fsum}).
1088 '''
1089 n = _name__(name, name__=self.copy)
1090 f = _Named.copy(self, deep=deep, name=n)
1091 if f._ps is self._ps:
1092 f._ps = list(self._ps) # separate list
1093 if not deep:
1094 f._n = 1
1095 # assert f._f2product == self._f2product
1096 # assert f._Fsum is f
1097 # assert f._isfine is self._isfine
1098 # assert f._RESIDUAL is self._RESIDUAL
1099 return f
1101 def _copy_2(self, which, name=NN):
1102 '''(INTERNAL) Copy for I{dyadic} operators.
1103 '''
1104 n = name or which.__name__ # _dunder_nameof
1105 # NOT .classof due to .Fdot(a, *b) args, etc.
1106 f = _Named.copy(self, deep=False, name=n)
1107 f._ps = list(self._ps) # separate list
1108 # assert f._n == self._n
1109 # assert f._f2product == self._f2product
1110 # assert f._Fsum is f
1111 # assert f._isfine is self._isfine
1112 # assert f._RESIDUAL is self._RESIDUAL
1113 return f
1115 def _copy_2r(self, other, which):
1116 '''(INTERNAL) Copy for I{reverse-dyadic} operators.
1117 '''
1118 return other._copy_2(which) if _isFsum(other) else \
1119 self._copy_2(which)._fset(other)
1121 divmod = __divmod__
1123 def _Error(self, op, other, Error, **txt_cause):
1124 '''(INTERNAL) Format an B{C{Error}} for C{{self} B{op} B{other}}.
1125 '''
1126 # self.as_iscalar causes RecursionError for ._fprs2 errors
1127 s = _Psum(self._ps, nonfinites=True, name=self.name)
1128 return Error(_SPACE_(s.as_iscalar, op, other), **txt_cause)
1130 def _ErrorX(self, X, op, other, *mod):
1131 '''(INTERNAL) Format the caught exception C{X}.
1132 '''
1133 E, t = _xError2(X)
1134 if mod:
1135 t = _COMMASPACE_(Fmt.PARENSPACED(mod=mod[0]), t)
1136 return self._Error(op, other, E, txt=t, cause=X)
1138 def _ErrorXs(self, X, xs, **kwds): # in .fmath
1139 '''(INTERNAL) Format the caught exception C{X}.
1140 '''
1141 E, t = _xError2(X)
1142 u = unstr(self.named3, *xs, _ELLIPSIS=4, **kwds)
1143 return E(u, txt=t, cause=X)
1145 def _facc(self, xs, up=True, **_X_x_origin):
1146 '''(INTERNAL) Accumulate more C{scalar}s or L{Fsum}s.
1147 '''
1148 if xs:
1149 kwds = self._isfine
1150 if _X_x_origin:
1151 kwds = _xkwds(_X_x_origin, **kwds)
1152 fs = _xs(xs, **kwds) # PYCHOK yield
1153 ps = self._ps
1154 ps[:] = self._ps_acc(list(ps), fs, up=up)
1155 return self
1157 def _facc_args(self, xs, **up):
1158 '''(INTERNAL) Accumulate 0, 1 or more C{xs}, all positional
1159 arguments in the caller of this method.
1160 '''
1161 return self._fadd(xs[0], **up) if len(xs) == 1 else \
1162 self._facc(xs, **up) # origin=1?
1164 def _facc_neg(self, xs, **up_origin):
1165 '''(INTERNAL) Accumulate more C{xs}, negated.
1166 '''
1167 def _N(X):
1168 return X._ps_neg
1170 def _n(x):
1171 return -float(x)
1173 return self._facc(xs, _X=_N, _x=_n, **up_origin)
1175 def _facc_power(self, power, xs, which, **raiser_RESIDUAL): # in .fmath
1176 '''(INTERNAL) Add each C{xs} as C{float(x**power)}.
1177 '''
1178 def _Pow4(p):
1179 r = 0
1180 if _isFsum_2Tuple(p):
1181 s, r = p._fprs2
1182 if r:
1183 m = Fsum._pow
1184 else: # scalar
1185 return _Pow4(s)
1186 elif isint(p, both=True) and int(p) >= 0:
1187 p = s = int(p)
1188 m = Fsum._pow_int
1189 else:
1190 p = s = _2float(power=p, **self._isfine)
1191 m = Fsum._pow_scalar
1192 return m, p, s, r
1194 _Pow, p, s, r = _Pow4(power)
1195 if p: # and xs:
1196 op = which.__name__
1197 _FsT = _Fsum_2Tuple_types
1198 _pow = self._pow_2_3
1200 def _P(X):
1201 f = _Pow(X, p, power, op, **raiser_RESIDUAL)
1202 return f._ps if isinstance(f, _FsT) else (f,)
1204 def _p(x):
1205 x = float(x)
1206 f = _pow(x, s, power, op, **raiser_RESIDUAL)
1207 if f and r:
1208 f *= _pow(x, r, power, op, **raiser_RESIDUAL)
1209 return f
1211 f = self._facc(xs, _X=_P, _x=_p) # origin=1?
1212 else:
1213 f = self._facc_scalar_(float(len(xs))) # x**0 == 1
1214 return f
1216 def _facc_scalar(self, xs, **up):
1217 '''(INTERNAL) Accumulate all C{xs}, each C{scalar}.
1218 '''
1219 if xs:
1220 ps = self._ps
1221 ps[:] = self._ps_acc(list(ps), xs, **up)
1222 return self
1224 def _facc_scalar_(self, *xs, **up):
1225 '''(INTERNAL) Accumulate all positional C{xs}, each C{scalar}.
1226 '''
1227 return self._facc_scalar(xs, **up)
1229 def _facc_scalarf(self, xs, up=True, **origin_which):
1230 '''(INTERNAL) Accumulate all C{xs}, each C{scalar}, an L{Fsum} or
1231 L{Fsum2Tuple}, like function C{_xsum}.
1232 '''
1233 _C = self.__class__
1234 fs = _xs(xs, **_x_isfine(self.nonfinitesOK, _Cdot=_C,
1235 **origin_which)) # PYCHOK yield
1236 return self._facc_scalar(fs, up=up)
1238# def _facc_up(self, up=True):
1239# '''(INTERNAL) Update the C{partials}, by removing
1240# and re-accumulating the final C{partial}.
1241# '''
1242# ps = self._ps
1243# while len(ps) > 1:
1244# p = ps.pop()
1245# if p:
1246# n = self._n
1247# _ = self._ps_acc(ps, (p,), up=False)
1248# self._n = n
1249# break
1250# return self._update() if up else self
1252 def fadd(self, xs=()):
1253 '''Add an iterable's items to this instance.
1255 @arg xs: Iterable of items to add (each C{scalar},
1256 an L{Fsum} or L{Fsum2Tuple}).
1258 @return: This instance (L{Fsum}).
1260 @raise OverflowError: Partial C{2sum} overflow.
1262 @raise TypeError: An invalid B{C{xs}} item.
1264 @raise ValueError: Invalid or I{non-finite} B{C{xs}} value.
1265 '''
1266 if _isFsum_2Tuple(xs):
1267 self._facc_scalar(xs._ps)
1268 elif isscalar(xs): # for backward compatibility # PYCHOK no cover
1269 x = _2float(x=xs, **self._isfine)
1270 self._facc_scalar_(x)
1271 elif xs: # _xiterable(xs)
1272 self._facc(xs)
1273 return self
1275 def fadd_(self, *xs):
1276 '''Add all positional items to this instance.
1278 @arg xs: Values to add (each C{scalar}, an L{Fsum}
1279 or L{Fsum2Tuple}), all positional.
1281 @see: Method L{Fsum.fadd} for further details.
1282 '''
1283 return self._facc_args(xs)
1285 def _fadd(self, other, op=_add_op_, **up):
1286 '''(INTERNAL) Apply C{B{self} += B{other}}.
1287 '''
1288 if _isFsum_2Tuple(other):
1289 self._facc_scalar(other._ps, **up)
1290 elif self._scalar(other, op):
1291 self._facc_scalar_(other, **up)
1292 return self
1294 fcopy = copy # for backward compatibility
1295 fdiv = __itruediv__
1296 fdivmod = __divmod__
1298 def _fdivmod2(self, other, op, **raiser_RESIDUAL):
1299 '''(INTERNAL) Apply C{B{self} %= B{other}} and return a L{DivMod2Tuple}.
1300 '''
1301 # result mostly follows CPython function U{float_divmod
1302 # <https://GitHub.com/python/cpython/blob/main/Objects/floatobject.c>},
1303 # but at least divmod(-3, 2) equals Cpython's result (-2, 1).
1304 q = self._truediv(other, op, **raiser_RESIDUAL).floor
1305 if q: # == float // other == floor(float / other)
1306 self -= self._Fsum_as(q) * other # NOT other * q!
1308 s = signOf(other) # make signOf(self) == signOf(other)
1309 if s and self.signOf() == -s: # PYCHOK no cover
1310 self += other
1311 q -= 1
1312# t = self.signOf()
1313# if t and t != s:
1314# raise self._Error(op, other, _AssertionError, txt__=signOf)
1315 return DivMod2Tuple(q, self) # q is C{int} in Python 3+, but C{float} in Python 2-
1317 def _fhorner(self, x, cs, where, incx=True): # in .fmath
1318 '''(INTERNAL) Add an L{Fhorner} evaluation of polynomial
1319 C{sum(cs[i] * B{x}**i for i=0..len(cs)-1) if B{incx}
1320 else sum(... i=len(cs)-1..0)}.
1321 '''
1322 # assert _xiterablen(cs)
1323 try:
1324 n = len(cs)
1325 H = self._Fsum_as(name__=self._fhorner)
1326 _m = H._mul_Fsum if _isFsum_2Tuple(x) else \
1327 H._mul_scalar
1328 if _2finite(x, **self._isfine) and n > 1:
1329 for c in (reversed(cs) if incx else cs):
1330 H._fset(_m(x, _mul_op_), up=False)
1331 H._fadd(c, up=False)
1332 else: # x == 0
1333 H = cs[0] if n else 0
1334 self._fadd(H)
1335 except Exception as X:
1336 t = unstr(where, x, *cs, _ELLIPSIS=4, incx=incx)
1337 raise self._ErrorX(X, _add_op_, t)
1338 return self
1340 def _finite(self, other, op=None):
1341 '''(INTERNAL) Return B{C{other}} if C{finite}.
1342 '''
1343 if _isOK_or_finite(other, **self._isfine):
1344 return other
1345 E = _NonfiniteError(other)
1346 raise self._Error(op, other, E, txt=_not_finite_)
1348 def fint(self, name=NN, **raiser_RESIDUAL):
1349 '''Return this instance' current running sum as C{integer}.
1351 @kwarg name: Optional, overriding C{B{name}="fint"} (C{str}).
1352 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore
1353 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}
1354 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.
1356 @return: The C{integer} sum (L{Fsum}) if this instance C{is_integer}
1357 with a zero or insignificant I{integer} residual.
1359 @raise ResidualError: Non-zero, significant residual or invalid
1360 B{C{RESIDUAL}}.
1362 @see: Methods L{Fsum.fint2}, L{Fsum.int_float} and L{Fsum.is_integer}.
1363 '''
1364 i, r = self._fint2
1365 if r:
1366 R = self._raiser(r, i, **raiser_RESIDUAL)
1367 if R:
1368 t = _stresidual(_integer_, r, **R)
1369 raise ResidualError(_integer_, i, txt=t)
1370 return self._Fsum_as(i, name=_name__(name, name__=self.fint))
1372 def fint2(self, **name):
1373 '''Return this instance' current running sum as C{int} and the
1374 I{integer} residual.
1376 @kwarg name: Optional name (C{str}).
1378 @return: An L{Fsum2Tuple}C{(fsum, residual)} with C{fsum}
1379 an C{int} and I{integer} C{residual} a C{float} or
1380 C{INT0} if the C{fsum} is considered to be I{exact}.
1381 The C{fsum} is I{non-finite} if this instance is.
1382 '''
1383 return Fsum2Tuple(*self._fint2, **name)
1385 @Property
1386 def _fint2(self): # see ._fset
1387 '''(INTERNAL) Get 2-tuple (C{int}, I{integer} residual).
1388 '''
1389 s, r = self._nfprs2
1390 if _isfinite(s):
1391 i = int(s)
1392 r = (self._ps_1sum(i) if len(self._ps) > 1 else
1393 float(s - i)) or INT0
1394 else: # INF, NAN, NINF
1395 i = float(s)
1396# r = _NONFINITEr
1397 return i, r # Fsum2Tuple?
1399 @_fint2.setter_ # PYCHOK setter_UNDERscore!
1400 def _fint2(self, s): # in _fset
1401 '''(INTERNAL) Replace the C{_fint2} value.
1402 '''
1403 if _isfinite(s):
1404 i = int(s)
1405 r = (s - i) or INT0
1406 else: # INF, NAN, NINF
1407 i = float(s)
1408 r = _NONFINITEr
1409 return i, r # like _fint2.getter
1411 @deprecated_property_RO
1412 def float_int(self): # PYCHOK no cover
1413 '''DEPRECATED, use method C{Fsum.int_float}.'''
1414 return self.int_float() # raiser=False
1416 @property_RO
1417 def floor(self):
1418 '''Get this instance' C{floor} (C{int} in Python 3+, but
1419 C{float} in Python 2-).
1421 @note: This C{floor} takes the C{residual} into account.
1423 @see: Method L{Fsum.int_float} and properties L{Fsum.ceil},
1424 L{Fsum.imag} and L{Fsum.real}.
1425 '''
1426 s, r = self._fprs2
1427 f = _floor(s) + _floor(r) + 1
1428 while (f - s) > r: # f > (s + r)
1429 f -= 1
1430 return f # _floor(self._n_d)
1432# ffloordiv = __ifloordiv__ # for naming consistency?
1433# floordiv = __floordiv__ # for naming consistency?
1435 def _floordiv(self, other, op, **raiser_RESIDUAL): # rather _ffloordiv?
1436 '''Apply C{B{self} //= B{other}}.
1437 '''
1438 q = self._ftruediv(other, op, **raiser_RESIDUAL) # == self
1439 return self._fset(q.floor) # floor(q)
1441 def fma(self, other1, other2, **nonfinites): # in .fmath.fma
1442 '''Fused-multiply-add C{self *= B{other1}; self += B{other2}}.
1444 @arg other1: Multiplier (C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
1445 @arg other2: Addend (C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
1446 @kwarg nonfinites: Use C{B{nonfinites}=True} or C{False}, to
1447 override L{nonfinites<Fsum.nonfinites>} and
1448 L{nonfiniterrors} default (C{bool}).
1449 '''
1450 op = self.fma.__name__
1451 _fs = self._ps_other
1452 try:
1453 s, r = self._fprs2
1454 if r:
1455 f = self._f2mul(self.fma, other1, **nonfinites)
1456 f += other2
1457 elif _residue(other1) or _residue(other2):
1458 fs = _2split3s(_fs(op, other1))
1459 fs = _2products(s, fs, *_fs(op, other2))
1460 f = _Psum(self._ps_acc([], fs, up=False), name=op)
1461 else:
1462 f = _fma(s, other1, other2)
1463 f = _2finite(f, **self._isfine)
1464 except TypeError as X:
1465 raise self._ErrorX(X, op, (other1, other2))
1466 except (OverflowError, ValueError) as X: # from math.fma
1467 f = self._mul_reduce(s, other1) # INF, NAN, NINF
1468 f += sum(_fs(op, other2))
1469 f = self._nonfiniteX(X, op, f, **nonfinites)
1470 return self._fset(f)
1472 fmul = __imul__
1474 def _fmul(self, other, op):
1475 '''(INTERNAL) Apply C{B{self} *= B{other}}.
1476 '''
1477 if _isFsum_2Tuple(other):
1478 if len(self._ps) != 1:
1479 f = self._mul_Fsum(other, op)
1480 elif len(other._ps) != 1: # and len(self._ps) == 1
1481 f = self._ps_mul(op, *other._ps) if other._ps else _0_0
1482 elif self._f2product: # len(other._ps) == 1
1483 f = self._mul_scalar(other._ps[0], op)
1484 else: # len(other._ps) == len(self._ps) == 1
1485 f = self._finite(self._ps[0] * other._ps[0], op=op)
1486 else:
1487 s = self._scalar(other, op)
1488 f = self._mul_scalar(s, op)
1489 return self._fset(f) # n=len(self) + 1
1491 @deprecated_method
1492 def f2mul(self, *others, **raiser):
1493 '''DEPRECATED on 2024.09.13, use method L{f2mul_<Fsum.f2mul_>}.'''
1494 return self._fset(self.f2mul_(*others, **raiser))
1496 def f2mul_(self, *others, **nonfinites): # in .fmath.f2mul
1497 '''Return C{B{self} * B{other} * B{other} ...} for all B{C{others}} using cascaded,
1498 accurate multiplication like with L{f2product<Fsum.f2product>} set to C{True}.
1500 @arg others: Multipliers (each C{scalar}, an L{Fsum} or L{Fsum2Tuple}), all
1501 positional.
1502 @kwarg nonfinites: Use C{B{nonfinites}=True} or C{False}, to override both
1503 L{nonfinites<Fsum.nonfinites>} and the L{nonfiniterrors}
1504 default (C{bool}).
1506 @return: The cascaded I{TwoProduct} (L{Fsum} or C{float}).
1508 @see: U{Equations 2.3<https://www.TUHH.De/ti3/paper/rump/OzOgRuOi06.pdf>}
1509 '''
1510 return self._f2mul(self.f2mul_, *others, **nonfinites)
1512 def _f2mul(self, where, *others, **nonfinites_raiser):
1513 '''(INTERNAL) See methods C{fma} and C{f2mul_}.
1514 '''
1515 f = self._copy_2(where)
1516 ps = f._ps
1517 if ps and others:
1518 op = where.__name__
1519 try:
1520 for other in others: # to pinpoint errors
1521 for p in self._ps_other(op, other):
1522 pfs = _2products(p, _2split3s(ps))
1523 ps[:] = f._ps_acc([], pfs, up=False)
1524 f._update()
1525 except TypeError as X:
1526 raise self._ErrorX(X, op, other)
1527 except (OverflowError, ValueError) as X:
1528 r = self._mul_reduce(sum(ps), other) # INF, NAN, NINF
1529 r = self._nonfiniteX(X, op, r, **nonfinites_raiser)
1530 f._fset(r)
1531 return f
1533 def fover(self, over, **raiser_RESIDUAL):
1534 '''Apply C{B{self} /= B{over}} and summate.
1536 @arg over: An L{Fsum} or C{scalar} denominator.
1537 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore
1538 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}
1539 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.
1541 @return: Precision running sum (C{float}).
1543 @raise ResidualError: Non-zero, significant residual or invalid
1544 B{C{RESIDUAL}}.
1546 @see: Methods L{Fsum.fsum} and L{Fsum.__itruediv__}.
1547 '''
1548 return float(self.fdiv(over, **raiser_RESIDUAL)._fprs)
1550 fpow = __ipow__
1552 def _fpow(self, other, op, *mod, **raiser_RESIDUAL):
1553 '''Apply C{B{self} **= B{other}}, optional B{C{mod}} or C{None}.
1554 '''
1555 if mod:
1556 if mod[0] is not None: # == 3-arg C{pow}
1557 f = self._pow_2_3(self, other, other, op, *mod, **raiser_RESIDUAL)
1558 elif self.is_integer():
1559 # return an exact C{int} for C{int}**C{int}
1560 i, _ = self._fint2 # assert _ == 0
1561 x, r = _2s_r(other) # C{int}, C{float} or other
1562 f = self._Fsum_as(i)._pow_Fsum(other, op, **raiser_RESIDUAL) if r else \
1563 self._pow_2_3(i, x, other, op, **raiser_RESIDUAL)
1564 else: # mod[0] is None, power(self, other)
1565 f = self._pow(other, other, op, **raiser_RESIDUAL)
1566 else: # pow(self, other)
1567 f = self._pow(other, other, op, **raiser_RESIDUAL)
1568 return self._fset(f) # n=max(len(self), 1)
1570 def f2product(self, *two):
1571 '''Get and set accurate I{TwoProduct} multiplication for this
1572 L{Fsum}, overriding the L{f2product} default.
1574 @arg two: If omitted, leave the override unchanged, if C{True},
1575 turn I{TwoProduct} on, if C{False} off, if C{None}e
1576 remove th override (C{bool} or C{None}).
1578 @return: The previous setting (C{bool} or C{None} if not set).
1580 @see: Function L{f2product<fsums.f2product>}.
1582 @note: Use C{f.f2product() or f2product()} to determine whether
1583 multiplication is accurate for L{Fsum} C{f}.
1584 '''
1585 if two: # delattrof(self, _f2product=None)
1586 t = _xkwds_pop(self.__dict__, _f2product=None)
1587 if two[0] is not None:
1588 self._f2product = bool(two[0])
1589 else: # getattrof(self, _f2product=None)
1590 t = _xkwds_get(self.__dict__, _f2product=None)
1591 return t
1593 @Property
1594 def _fprs(self):
1595 '''(INTERNAL) Get and cache this instance' precision
1596 running sum (C{float} or C{int}), ignoring C{residual}.
1598 @note: The precision running C{fsum} after a C{//=} or
1599 C{//} C{floor} division is C{int} in Python 3+.
1600 '''
1601 s, _ = self._fprs2
1602 return s # ._fprs2.fsum
1604 @_fprs.setter_ # PYCHOK setter_UNDERscore!
1605 def _fprs(self, s):
1606 '''(INTERNAL) Replace the C{_fprs} value.
1607 '''
1608 return s
1610 @Property
1611 def _fprs2(self):
1612 '''(INTERNAL) Get and cache this instance' precision
1613 running sum and residual (L{Fsum2Tuple}).
1614 '''
1615 ps = self._ps
1616 n = len(ps)
1617 try:
1618 if n > 2:
1619 s = _psum(ps, **self._isfine)
1620 if not _isfinite(s):
1621 ps[:] = s, # collapse ps
1622 return Fsum2Tuple(s, _NONFINITEr)
1623 n = len(ps)
1624# Fsum._ps_max = max(Fsum._ps_max, n)
1625 if n > 2:
1626 r = self._ps_1sum(s)
1627 return Fsum2Tuple(*_s_r(s, r))
1628 if n > 1: # len(ps) == 2
1629 s, r = _s_r(*_2sum(*ps, **self._isfine))
1630 ps[:] = (r, s) if r else (s,)
1631 elif ps: # len(ps) == 1
1632 s = ps[0]
1633 r = INT0 if _isfinite(s) else _NONFINITEr
1634 else: # len(ps) == 0
1635 s = _0_0
1636 r = INT0 if _isfinite(s) else _NONFINITEr
1637 ps[:] = s,
1638 except (OverflowError, ValueError) as X:
1639 op = _fset_op_ # INF, NAN, NINF
1640 ps[:] = sum(ps), # collapse ps
1641 s = self._nonfiniteX(X, op, ps[0])
1642 r = _NONFINITEr
1643 # assert self._ps is ps
1644 return Fsum2Tuple(s, r)
1646 @_fprs2.setter_ # PYCHOK setter_UNDERscore!
1647 def _fprs2(self, s_r):
1648 '''(INTERNAL) Replace the C{_fprs2} value.
1649 '''
1650 return Fsum2Tuple(s_r)
1652 def fset_(self, *xs):
1653 '''Apply C{B{self}.partials = Fsum(*B{xs}).partials}.
1655 @arg xs: Optional, new values (each C{scalar} or
1656 an L{Fsum} or L{Fsum2Tuple} instance), all
1657 positional.
1659 @return: This instance, replaced (C{Fsum}).
1661 @see: Method L{Fsum.fadd} for further details.
1662 '''
1663 f = (xs[0] if xs else _0_0) if len(xs) < 2 else \
1664 Fsum(*xs, nonfinites=self.nonfinites()) # self._Fsum_as(*xs)
1665 return self._fset(f, op=_fset_op_)
1667 def _fset(self, other, n=0, up=True, **op):
1668 '''(INTERNAL) Overwrite this instance with an other or a C{scalar}.
1669 '''
1670 if other is self:
1671 pass # from ._fmul, ._ftruediv and ._pow_0_1
1672 elif _isFsum_2Tuple(other):
1673 if op: # and not self.nonfinitesOK:
1674 self._finite(other._fprs, **op)
1675 self._ps[:] = other._ps
1676 self._n = n or other._n
1677 if up: # use or zap the C{Property_RO} values
1678 Fsum._fint2._update_from(self, other)
1679 Fsum._fprs ._update_from(self, other)
1680 Fsum._fprs2._update_from(self, other)
1681 elif isscalar(other):
1682 s = float(self._finite(other, **op)) if op else other
1683 self._ps[:] = s,
1684 self._n = n or 1
1685 if up: # Property _fint2, _fprs and _fprs2 all have
1686 # @.setter_underscore and NOT @.setter because the
1687 # latter's _fset zaps the value set by @.setter
1688 self._fint2 = s
1689 self._fprs = s
1690 self._fprs2 = s, INT0
1691 # assert self._fprs is s
1692 else:
1693 op = _xkwds_get1(op, op=_fset_op_)
1694 raise self._Error(op, other, _TypeError)
1695 return self
1697 def fsub(self, xs=()):
1698 '''Subtract an iterable's items from this instance.
1700 @see: Method L{Fsum.fadd} for further details.
1701 '''
1702 return self._facc_neg(xs)
1704 def fsub_(self, *xs):
1705 '''Subtract all positional items from this instance.
1707 @see: Method L{Fsum.fadd_} for further details.
1708 '''
1709 return self._fsub(xs[0], _sub_op_) if len(xs) == 1 else \
1710 self._facc_neg(xs) # origin=1?
1712 def _fsub(self, other, op):
1713 '''(INTERNAL) Apply C{B{self} -= B{other}}.
1714 '''
1715 if _isFsum_2Tuple(other):
1716 if other is self: # or other._fprs2 == self._fprs2:
1717 self._fset(_0_0, n=len(self) * 2)
1718 elif other._ps:
1719 self._facc_scalar(other._ps_neg)
1720 elif self._scalar(other, op):
1721 self._facc_scalar_(-other)
1722 return self
1724 def fsum(self, xs=()):
1725 '''Add an iterable's items, summate and return the current
1726 precision running sum.
1728 @arg xs: Iterable of items to add (each item C{scalar},
1729 an L{Fsum} or L{Fsum2Tuple}).
1731 @return: Precision running sum (C{float} or C{int}).
1733 @see: Method L{Fsum.fadd}.
1735 @note: Accumulation can continue after summation.
1736 '''
1737 return self._facc(xs)._fprs
1739 def fsum_(self, *xs):
1740 '''Add any positional items, summate and return the current
1741 precision running sum.
1743 @arg xs: Items to add (each C{scalar}, an L{Fsum} or
1744 L{Fsum2Tuple}), all positional.
1746 @return: Precision running sum (C{float} or C{int}).
1748 @see: Methods L{Fsum.fsum}, L{Fsum.Fsum_} and L{Fsum.fsumf_}.
1749 '''
1750 return self._facc_args(xs)._fprs
1752 def Fsum_(self, *xs, **name):
1753 '''Like method L{Fsum.fsum_} but returning a named L{Fsum}.
1755 @kwarg name: Optional name (C{str}).
1757 @return: Copy of this updated instance (L{Fsum}).
1758 '''
1759 return self._facc_args(xs)._copy_2(self.Fsum_, **name)
1761 def Fsum2Tuple_(self, *xs, **name):
1762 '''Like method L{Fsum.fsum_} but returning a named L{Fsum2Tuple}.
1764 @kwarg name: Optional name (C{str}).
1766 @return: Precision running sum (L{Fsum2Tuple}).
1767 '''
1768 return Fsum2Tuple(self._facc_args(xs)._nfprs2, **name)
1770 @property_RO
1771 def _Fsum(self): # like L{Fsum2Tuple._Fsum}, in .fstats
1772 return self # NOT @Property_RO, see .copy and ._copy_2
1774 def _Fsum_as(self, *xs, **name_f2product_nonfinites_RESIDUAL):
1775 '''(INTERNAL) Return an C{Fsum} with this C{Fsum}'s C{.f2product},
1776 C{.nonfinites} and C{.RESIDUAL} setting, optionally
1777 overridden with C{name_f2product_nonfinites_RESIDUAL} and
1778 with any C{xs} accumulated.
1779 '''
1780 kwds = _xkwds_not(None, Fsum._RESIDUAL, f2product =self.f2product(),
1781 nonfinites=self.nonfinites(),
1782 RESIDUAL =self.RESIDUAL())
1783 if name_f2product_nonfinites_RESIDUAL: # overwrites
1784 kwds.update(name_f2product_nonfinites_RESIDUAL)
1785 f = Fsum(**kwds)
1786 # assert all(v == self.__dict__[n] for n, v in f.__dict__.items())
1787 return f._fset(xs[0], op=_fset_op_) if len(xs) == 1 else (
1788 f._facc(xs, up=False) if xs else f)
1790 def fsum2(self, xs=(), **name):
1791 '''Add an iterable's items, summate and return the
1792 current precision running sum I{and} the C{residual}.
1794 @arg xs: Iterable of items to add (each item C{scalar},
1795 an L{Fsum} or L{Fsum2Tuple}).
1796 @kwarg name: Optional C{B{name}=NN} (C{str}).
1798 @return: L{Fsum2Tuple}C{(fsum, residual)} with C{fsum} the
1799 current precision running sum and C{residual}, the
1800 (precision) sum of the remaining C{partials}. The
1801 C{residual is INT0} if the C{fsum} is considered
1802 to be I{exact}.
1804 @see: Methods L{Fsum.fint2}, L{Fsum.fsum} and L{Fsum.fsum2_}
1805 '''
1806 t = self._facc(xs)._fprs2
1807 return t.dup(name=name) if name else t
1809 def fsum2_(self, *xs):
1810 '''Add any positional items, summate and return the current
1811 precision running sum and the I{differential}.
1813 @arg xs: Values to add (each C{scalar}, an L{Fsum} or
1814 L{Fsum2Tuple}), all positional.
1816 @return: 2Tuple C{(fsum, delta)} with the current, precision
1817 running C{fsum} like method L{Fsum.fsum} and C{delta},
1818 the difference with previous running C{fsum}, C{float}.
1820 @see: Methods L{Fsum.fsum_} and L{Fsum.fsum}.
1821 '''
1822 return self._fsum2(xs, self._facc_args)
1824 def _fsum2(self, xs, _facc, **facc_kwds):
1825 '''(INTERNAL) Helper for L{Fsum.fsum2_} and L{Fsum.fsum2f_}.
1826 '''
1827 p, q = self._fprs2
1828 if xs:
1829 s, r = _facc(xs, **facc_kwds)._fprs2
1830 if _isfinite(s): # _fsum(_1primed((s, -p, r, -q))
1831 d, r = _2sum(s - p, r - q, _isfine=_isOK)
1832 r, _ = _s_r(d, r)
1833 return s, (r if _isfinite(r) else _NONFINITEr)
1834 else:
1835 return p, _0_0
1837 def fsumf_(self, *xs):
1838 '''Like method L{Fsum.fsum_} iff I{all} C{B{xs}}, each I{known to be}
1839 C{scalar}, an L{Fsum} or L{Fsum2Tuple}.
1840 '''
1841 return self._facc_scalarf(xs, which=self.fsumf_)._fprs # origin=1?
1843 def Fsumf_(self, *xs):
1844 '''Like method L{Fsum.Fsum_} iff I{all} C{B{xs}}, each I{known to be}
1845 C{scalar}, an L{Fsum} or L{Fsum2Tuple}.
1846 '''
1847 return self._facc_scalarf(xs, which=self.Fsumf_)._copy_2(self.Fsumf_) # origin=1?
1849 def fsum2f_(self, *xs):
1850 '''Like method L{Fsum.fsum2_} iff I{all} C{B{xs}}, each I{known to be}
1851 C{scalar}, an L{Fsum} or L{Fsum2Tuple}.
1852 '''
1853 return self._fsum2(xs, self._facc_scalarf, which=self.fsum2f_) # origin=1?
1855# ftruediv = __itruediv__ # for naming consistency?
1857 def _ftruediv(self, other, op, **raiser_RESIDUAL):
1858 '''(INTERNAL) Apply C{B{self} /= B{other}}.
1859 '''
1860 n = _1_0
1861 if _isFsum_2Tuple(other):
1862 if other is self or self == other:
1863 return self._fset(n, n=len(self))
1864 d, r = other._fprs2
1865 if r:
1866 R = self._raiser(r, d, **raiser_RESIDUAL)
1867 if R:
1868 raise self._ResidualError(op, other, r, **R)
1869 d, n = other.as_integer_ratio()
1870 else:
1871 d = self._scalar(other, op)
1872 try:
1873 s = n / d
1874 except Exception as X:
1875 raise self._ErrorX(X, op, other)
1876 f = self._mul_scalar(s, _mul_op_) # handles 0, INF, NAN
1877 return self._fset(f)
1879 @property_RO
1880 def imag(self):
1881 '''Get the C{imaginary} part of this instance (C{0.0}, always).
1883 @see: Property L{Fsum.real}.
1884 '''
1885 return _0_0
1887 def int_float(self, **raiser_RESIDUAL):
1888 '''Return this instance' current running sum as C{int} or C{float}.
1890 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore
1891 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}
1892 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.
1894 @return: This C{int} sum if this instance C{is_integer} and
1895 I{finite}, otherwise the C{float} sum if the residual
1896 is zero or not significant.
1898 @raise ResidualError: Non-zero, significant residual or invalid
1899 B{C{RESIDUAL}}.
1901 @see: Methods L{Fsum.fint}, L{Fsum.fint2}, L{Fsum.is_integer},
1902 L{Fsum.RESIDUAL} and property L{Fsum.as_iscalar}.
1903 '''
1904 s, r = self._fint2
1905 if r:
1906 s, r = self._fprs2
1907 if r: # PYCHOK no cover
1908 R = self._raiser(r, s, **raiser_RESIDUAL)
1909 if R:
1910 t = _stresidual(_non_zero_, r, **R)
1911 raise ResidualError(int_float=s, txt=t)
1912 s = float(s)
1913 return s
1915 def is_exact(self):
1916 '''Is this instance' running C{fsum} considered to be exact?
1917 (C{bool}), C{True} only if the C{residual is }L{INT0}.
1918 '''
1919 return self.residual is INT0
1921 def is_finite(self): # in .constants
1922 '''Is this instance C{finite}? (C{bool}).
1924 @see: Function L{isfinite<pygeodesy.isfinite>}.
1925 '''
1926 return _isfinite(sum(self._ps)) # == sum(self)
1928 def is_integer(self):
1929 '''Is this instance' running sum C{integer}? (C{bool}).
1931 @see: Methods L{Fsum.fint}, L{Fsum.fint2} and L{Fsum.is_scalar}.
1932 '''
1933 s, r = self._fint2
1934 return False if r else (_isfinite(s) and isint(s))
1936 def is_math_fma(self):
1937 '''Is accurate L{f2product} multiplication based on Python's C{math.fma}?
1939 @return: C{True} if accurate multiplication uses C{math.fma}, C{False}
1940 an C{fma} implementation as C{math.fma} or C{None}, a previous
1941 C{PyGeodesy} implementation.
1942 '''
1943 return (_2split3s is _passarg) or (False if _2n_d is None else None)
1945 def is_math_fsum(self):
1946 '''Are the summation functions L{fsum}, L{fsum_}, L{fsumf_}, L{fsum1},
1947 L{fsum1_} and L{fsum1f_} based on Python's C{math.fsum}?
1949 @return: C{True} if summation functions use C{math.fsum}, C{False}
1950 otherwise.
1951 '''
1952 return _sum is _fsum # _fsum.__module__ is fabs.__module__
1954 def is_scalar(self, **raiser_RESIDUAL):
1955 '''Is this instance' running sum C{scalar} with C{0} residual or with
1956 a residual I{ratio} not exceeding the RESIDUAL threshold?
1958 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore
1959 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}
1960 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.
1962 @return: C{True} if this instance' residual is C{0} or C{insignificant},
1963 i.e. its residual C{ratio} doesn't exceed the L{RESIDUAL
1964 <Fsum.RESIDUAL>} threshold (C{bool}).
1966 @raise ResidualError: Non-zero, significant residual or invalid
1967 B{C{RESIDUAL}}.
1969 @see: Methods L{Fsum.RESIDUAL} and L{Fsum.is_integer} and property
1970 L{Fsum.as_iscalar}.
1971 '''
1972 s, r = self._fprs2
1973 return False if r and self._raiser(r, s, **raiser_RESIDUAL) else True
1975 def _mul_Fsum(self, other, op):
1976 '''(INTERNAL) Return C{B{self} * B{other}} as L{Fsum} or C{0}.
1977 '''
1978 # assert _isFsum_2Tuple(other)
1979 if self._ps and other._ps:
1980 try:
1981 f = self._ps_mul(op, *other._ps) # NO .as_iscalar!
1982 except Exception as X:
1983 raise self._ErrorX(X, op, other)
1984 else:
1985 f = _0_0
1986 return f
1988 def _mul_reduce(self, *others):
1989 '''(INTERNAL) Like fmath.fprod for I{non-finite} C{other}s.
1990 '''
1991 r = _1_0
1992 for f in others:
1993 r *= sum(f._ps) if _isFsum_2Tuple(f) else float(f)
1994 return r
1996 def _mul_scalar(self, factor, op):
1997 '''(INTERNAL) Return C{B{self} * scalar B{factor}} as L{Fsum}, C{0.0} or C{self}.
1998 '''
1999 # assert isscalar(factor)
2000 if self._ps and self._finite(factor, op=op):
2001 f = self if factor == _1_0 else (
2002 self._neg if factor == _N_1_0 else
2003 self._ps_mul(op, factor).as_iscalar)
2004 else:
2005 f = _0_0
2006 return f
2008# @property_RO
2009# def _n_d(self):
2010# n, d = self.as_integer_ratio()
2011# return n / d
2013 @property_RO
2014 def _neg(self):
2015 '''(INTERNAL) Return C{Fsum(-self)} or scalar C{NEG0}.
2016 '''
2017 return _Psum(self._ps_neg) if self._ps else NEG0
2019 @property_RO
2020 def _nfprs2(self):
2021 '''(INTERNAL) Handle I{non-finite} C{_fprs2}.
2022 '''
2023 try: # to handle nonfiniterrors, etc.
2024 t = self._fprs2
2025 except (OverflowError, ValueError):
2026 t = Fsum2Tuple(sum(self._ps), _NONFINITEr)
2027 return t
2029 def nonfinites(self, *OK):
2030 '''Handle I{non-finite} C{float}s as C{inf}, C{INF}, C{NINF}, C{nan}
2031 and C{NAN} for this L{Fsum} or throw C{OverflowError} respectively
2032 C{ValueError} exceptions, overriding the L{nonfiniterrors} default.
2034 @arg OK: If omitted, leave the override unchanged, if C{True},
2035 I{non-finites} are C{OK}, if C{False} throw exceptions
2036 or if C{None} remove the override (C{bool} or C{None}).
2038 @return: The previous setting (C{bool} or C{None} if not set).
2040 @see: Function L{nonfiniterrors<fsums.nonfiniterrors>}.
2042 @note: Use property L{nonfinitesOK<Fsum.nonfinitesOK>} to determine
2043 whether I{non-finites} are C{OK} for this L{Fsum} and by the
2044 L{nonfiniterrors} default.
2045 '''
2046 _ks = Fsum._nonfinites_isfine_kwds
2047 if OK: # delattrof(self, _isfine=None)
2048 k = _xkwds_pop(self.__dict__, _isfine=None)
2049 if OK[0] is not None:
2050 self._isfine = _ks[bool(OK[0])]
2051 self._update()
2052 else: # getattrof(self, _isfine=None)
2053 k = _xkwds_get(self.__dict__, _isfine=None)
2054 # dict(map(reversed, _ks.items())).get(k, None)
2055 # raises a TypeError: unhashable type: 'dict'
2056 return True if k is _ks[True] else (
2057 False if k is _ks[False] else None)
2059 _nonfinites_isfine_kwds = {True: dict(_isfine=_isOK),
2060 False: dict(_isfine=_isfinite)}
2062 @property_RO
2063 def nonfinitesOK(self):
2064 '''Are I{non-finites} C{OK} for this L{Fsum} or by default? (C{bool}).
2065 '''
2066# nf = self.nonfinites()
2067# if nf is None:
2068# nf = not nonfiniterrors()
2069 return _isOK_or_finite(INF, **self._isfine)
2071 def _nonfiniteX(self, X, op, f, nonfinites=None, raiser=None):
2072 '''(INTERNAL) Handle a I{non-finite} exception.
2073 '''
2074 if nonfinites is None:
2075 nonfinites = _isOK_or_finite(f, **self._isfine) if raiser is None else (not raiser)
2076 if not nonfinites:
2077 raise self._ErrorX(X, op, f)
2078 return f
2080 def _optionals(self, f2product=None, nonfinites=None, **name_RESIDUAL):
2081 '''(INTERNAL) Re/set options from keyword arguments.
2082 '''
2083 if f2product is not None:
2084 self.f2product(f2product)
2085 if nonfinites is not None:
2086 self.nonfinites(nonfinites)
2087 if name_RESIDUAL: # MUST be last
2088 n, kwds = _name2__(**name_RESIDUAL)
2089 if kwds:
2090 R = Fsum._RESIDUAL
2091 t = _threshold(R, **kwds)
2092 if t != R:
2093 self._RESIDUAL = t
2094 if n:
2095 self.name = n # self.rename(n)
2097 def _1_Over(self, x, op, **raiser_RESIDUAL): # vs _1_over
2098 '''(INTERNAL) Return C{Fsum(1) / B{x}}.
2099 '''
2100 return self._Fsum_as(_1_0)._ftruediv(x, op, **raiser_RESIDUAL)
2102 @property_RO
2103 def partials(self):
2104 '''Get this instance' current, partial sums (C{tuple} of C{float}s).
2105 '''
2106 return tuple(self._ps)
2108 def pow(self, x, *mod, **raiser_RESIDUAL):
2109 '''Return C{B{self}**B{x}} as L{Fsum}.
2111 @arg x: The exponent (C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
2112 @arg mod: Optional modulus (C{int} or C{None}) for the 3-argument
2113 C{pow(B{self}, B{other}, B{mod})} version.
2114 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore
2115 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}
2116 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.
2118 @return: The C{pow(self, B{x})} or C{pow(self, B{x}, *B{mod})}
2119 result (L{Fsum}).
2121 @raise ResidualError: Non-zero, significant residual or invalid
2122 B{C{RESIDUAL}}.
2124 @note: If B{C{mod}} is given and C{None}, the result will be an
2125 C{integer} L{Fsum} provided this instance C{is_integer}
2126 or set to C{integer} by an L{Fsum.fint} call.
2128 @see: Methods L{Fsum.__ipow__}, L{Fsum.fint}, L{Fsum.is_integer}
2129 and L{Fsum.root}.
2130 '''
2131 f = self._copy_2(self.pow)
2132 return f._fpow(x, _pow_op_, *mod, **raiser_RESIDUAL) # f = pow(f, x, *mod)
2134 def _pow(self, other, unused, op, **raiser_RESIDUAL):
2135 '''Return C{B{self} ** B{other}}.
2136 '''
2137 if _isFsum_2Tuple(other):
2138 f = self._pow_Fsum(other, op, **raiser_RESIDUAL)
2139 elif self._scalar(other, op):
2140 x = self._finite(other, op=op)
2141 f = self._pow_scalar(x, other, op, **raiser_RESIDUAL)
2142 else:
2143 f = self._pow_0_1(0, other)
2144 return f
2146 def _pow_0_1(self, x, other):
2147 '''(INTERNAL) Return B{C{self}**1} or C{B{self}**0 == 1.0}.
2148 '''
2149 return self if x else (1 if isint(other) and self.is_integer() else _1_0)
2151 def _pow_2_3(self, b, x, other, op, *mod, **raiser_RESIDUAL):
2152 '''(INTERNAL) 2-arg C{pow(B{b}, scalar B{x})} and 3-arg C{pow(B{b},
2153 B{x}, int B{mod} or C{None})}, embellishing errors.
2154 '''
2156 if mod: # b, x, mod all C{int}, unless C{mod} is C{None}
2157 m = mod[0]
2158 # assert _isFsum_2Tuple(b)
2160 def _s(s, r):
2161 R = self._raiser(r, s, **raiser_RESIDUAL)
2162 if R:
2163 raise self._ResidualError(op, other, r, mod=m, **R)
2164 return s
2166 b = _s(*(b._fprs2 if m is None else b._fint2))
2167 x = _s(*_2s_r(x))
2169 try:
2170 # 0**INF == 0.0, 1**INF == 1.0, -1**2.3 == -(1**2.3)
2171 s = pow(b, x, *mod)
2172 if iscomplex(s):
2173 # neg**frac == complex in Python 3+, but ValueError in 2-
2174 raise ValueError(_strcomplex(s, b, x, *mod))
2175 _ = _2finite(s, **self._isfine) # ignore float
2176 return s
2177 except Exception as X:
2178 raise self._ErrorX(X, op, other, *mod)
2180 def _pow_Fsum(self, other, op, **raiser_RESIDUAL):
2181 '''(INTERNAL) Return C{B{self} **= B{other}} for C{_isFsum_2Tuple(other)}.
2182 '''
2183 # assert _isFsum_2Tuple(other)
2184 x, r = other._fprs2
2185 f = self._pow_scalar(x, other, op, **raiser_RESIDUAL)
2186 if f and r:
2187 f *= self._pow_scalar(r, other, op, **raiser_RESIDUAL)
2188 return f
2190 def _pow_int(self, x, other, op, **raiser_RESIDUAL):
2191 '''(INTERNAL) Return C{B{self} **= B{x}} for C{int B{x} >= 0}.
2192 '''
2193 # assert isint(x) and x >= 0
2194 ps = self._ps
2195 if len(ps) > 1:
2196 _mul_Fsum = Fsum._mul_Fsum
2197 if x > 4:
2198 p = self
2199 f = self if (x & 1) else self._Fsum_as(_1_0)
2200 m = x >> 1 # // 2
2201 while m:
2202 p = _mul_Fsum(p, p, op) # p **= 2
2203 if (m & 1):
2204 f = _mul_Fsum(f, p, op) # f *= p
2205 m >>= 1 # //= 2
2206 elif x > 1: # self**2, 3, or 4
2207 f = _mul_Fsum(self, self, op)
2208 if x > 2: # self**3 or 4
2209 p = self if x < 4 else f
2210 f = _mul_Fsum(f, p, op)
2211 else: # self**1 or self**0 == 1 or _1_0
2212 f = self._pow_0_1(x, other)
2213 elif ps: # self._ps[0]**x
2214 f = self._pow_2_3(ps[0], x, other, op, **raiser_RESIDUAL)
2215 else: # PYCHOK no cover
2216 # 0**pos_int == 0, but 0**0 == 1
2217 f = 0 if x else 1
2218 return f
2220 def _pow_scalar(self, x, other, op, **raiser_RESIDUAL):
2221 '''(INTERNAL) Return C{self**B{x}} for C{scalar B{x}}.
2222 '''
2223 s, r = self._fprs2
2224 if r:
2225 # assert s != 0
2226 if isint(x, both=True): # self**int
2227 x = int(x)
2228 y = abs(x)
2229 if y > 1:
2230 f = self._pow_int(y, other, op, **raiser_RESIDUAL)
2231 if x > 0: # i.e. > 1
2232 return f # Fsum or scalar
2233 # assert x < 0 # i.e. < -1
2234 if _isFsum(f):
2235 s, r = f._fprs2
2236 if r:
2237 return self._1_Over(f, op, **raiser_RESIDUAL)
2238 else: # scalar
2239 s = f
2240 # use s**(-1) to get the CPython
2241 # float_pow error iff s is zero
2242 x = -1
2243 elif x < 0: # self**(-1)
2244 return self._1_Over(self, op, **raiser_RESIDUAL) # 1 / self
2245 else: # self**1 or self**0
2246 return self._pow_0_1(x, other) # self, 1 or 1.0
2247 else: # self**fractional
2248 R = self._raiser(r, s, **raiser_RESIDUAL)
2249 if R:
2250 raise self._ResidualError(op, other, r, **R)
2251 n, d = self.as_integer_ratio()
2252 if abs(n) > abs(d):
2253 n, d, x = d, n, (-x)
2254 s = n / d
2255 # assert isscalar(s) and isscalar(x)
2256 return self._pow_2_3(s, x, other, op, **raiser_RESIDUAL)
2258 def _ps_acc(self, ps, xs, up=True, **unused):
2259 '''(INTERNAL) Accumulate C{xs} known scalars into list C{ps}.
2260 '''
2261 n = 0
2262 _2s = _2sum
2263 _fi = self._isfine
2264 for x in (tuple(xs) if xs is ps else xs):
2265 # assert isscalar(x) and _isOK_or_finite(x, **self._isfine)
2266 if x:
2267 i = 0
2268 for p in ps:
2269 x, p = _2s(x, p, **_fi)
2270 if p:
2271 ps[i] = p
2272 i += 1
2273 ps[i:] = (x,) if x else ()
2274 n += 1
2275 if n:
2276 self._n += n
2277 # Fsum._ps_max = max(Fsum._ps_max, len(ps))
2278 if up:
2279 self._update()
2280# x = sum(ps)
2281# if not _isOK_or_finite(x, **fi):
2282# ps[:] = x, # collapse ps
2283 return ps
2285 def _ps_mul(self, op, *factors):
2286 '''(INTERNAL) Multiply this instance' C{partials} with
2287 each scalar C{factor} and accumulate into an C{Fsum}.
2288 '''
2289 def _psfs(ps, fs, _isfine=_isfinite):
2290 if len(ps) < len(fs):
2291 ps, fs = fs, ps
2292 if self._f2product:
2293 fs, p = _2split3s(fs), fs
2294 if len(ps) > 1 and fs is not p:
2295 fs = tuple(fs) # several ps
2296 _pfs = _2products
2297 else:
2298 def _pfs(p, fs):
2299 return (p * f for f in fs)
2301 for p in ps:
2302 for f in _pfs(p, fs):
2303 yield f if _isfine(f) else _nfError(f)
2305 fs = _psfs(self._ps, factors, **self._isfine)
2306 f = _Psum(self._ps_acc([], fs, up=False), name=op)
2307 return f
2309 @property_RO
2310 def _ps_neg(self):
2311 '''(INTERNAL) Yield the partials, I{negated}.
2312 '''
2313 for p in self._ps:
2314 yield -p
2316 def _ps_other(self, op, other):
2317 '''(INTERNAL) Yield C{other} as C{scalar}s.
2318 '''
2319 if _isFsum_2Tuple(other):
2320 for p in other._ps:
2321 yield p
2322 else:
2323 yield self._scalar(other, op)
2325 def _ps_1sum(self, *less):
2326 '''(INTERNAL) Return the partials sum, 1-primed C{less} some scalars.
2327 '''
2328 def _1psls(ps, ls):
2329 yield _1_0
2330 for p in ps:
2331 yield p
2332 for p in ls:
2333 yield -p
2334 yield _N_1_0
2336 return _fsum(_1psls(self._ps, less))
2338 def _raiser(self, r, s, raiser=True, **RESIDUAL):
2339 '''(INTERNAL) Does ratio C{r / s} exceed the RESIDUAL threshold
2340 I{and} is residual C{r} I{non-zero} or I{significant} (for a
2341 negative respectively positive C{RESIDUAL} threshold)?
2342 '''
2343 if r and raiser:
2344 t = self._RESIDUAL
2345 if RESIDUAL:
2346 t = _threshold(t, **RESIDUAL)
2347 if t < 0 or (s + r) != s:
2348 q = (r / s) if s else s # == 0.
2349 if fabs(q) > fabs(t):
2350 return dict(ratio=q, R=t)
2351 return {}
2353 rdiv = __rtruediv__
2355 @property_RO
2356 def real(self):
2357 '''Get the C{real} part of this instance (C{float}).
2359 @see: Methods L{Fsum.__float__} and L{Fsum.fsum}
2360 and properties L{Fsum.ceil}, L{Fsum.floor},
2361 L{Fsum.imag} and L{Fsum.residual}.
2362 '''
2363 return float(self)
2365 @property_RO
2366 def residual(self):
2367 '''Get this instance' residual or residue (C{float} or C{int}):
2368 the C{sum(partials)} less the precision running sum C{fsum}.
2370 @note: The C{residual is INT0} iff the precision running
2371 C{fsum} is considered to be I{exact}.
2373 @see: Methods L{Fsum.fsum}, L{Fsum.fsum2} and L{Fsum.is_exact}.
2374 '''
2375 return self._fprs2.residual
2377 def RESIDUAL(self, *threshold):
2378 '''Get and set this instance' I{ratio} for raising L{ResidualError}s,
2379 overriding the default from env variable C{PYGEODESY_FSUM_RESIDUAL}.
2381 @arg threshold: If C{scalar}, the I{ratio} to exceed for raising
2382 L{ResidualError}s in division and exponention, if
2383 C{None}, restore the default set with env variable
2384 C{PYGEODESY_FSUM_RESIDUAL} or if omitted, keep the
2385 current setting.
2387 @return: The previous C{RESIDUAL} setting (C{float}), default C{0.0}.
2389 @raise ResidualError: Invalid B{C{threshold}}.
2391 @note: L{ResidualError}s may be thrown if (1) the non-zero I{ratio}
2392 C{residual / fsum} exceeds the given B{C{threshold}} and (2)
2393 the C{residual} is non-zero and (3) is I{significant} vs the
2394 C{fsum}, i.e. C{(fsum + residual) != fsum} and (4) optional
2395 keyword argument C{raiser=False} is missing. Specify a
2396 negative B{C{threshold}} for only non-zero C{residual}
2397 testing without the I{significant} case.
2398 '''
2399 r = self._RESIDUAL
2400 if threshold:
2401 t = threshold[0]
2402 self._RESIDUAL = Fsum._RESIDUAL if t is None else ( # for ...
2403 (_0_0 if t else _1_0) if isbool(t) else
2404 _threshold(t)) # ... backward compatibility
2405 return r
2407 def _ResidualError(self, op, other, residual, **mod_R):
2408 '''(INTERNAL) Non-zero B{C{residual}} etc.
2409 '''
2410 def _p(mod=None, R=0, **unused): # ratio=0
2411 return (_non_zero_ if R < 0 else _significant_) \
2412 if mod is None else _integer_
2414 t = _stresidual(_p(**mod_R), residual, **mod_R)
2415 return self._Error(op, other, ResidualError, txt=t)
2417 def root(self, root, **raiser_RESIDUAL):
2418 '''Return C{B{self}**(1 / B{root})} as L{Fsum}.
2420 @arg root: Non-zero order (C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
2421 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore any
2422 L{ResidualError}s (C{bool}) or C{B{RESIDUAL}=scalar}
2423 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.
2425 @return: The C{self ** (1 / B{root})} result (L{Fsum}).
2427 @raise ResidualError: Non-zero, significant residual or invalid
2428 B{C{RESIDUAL}}.
2430 @see: Method L{Fsum.pow}.
2431 '''
2432 x = self._1_Over(root, _truediv_op_, **raiser_RESIDUAL)
2433 f = self._copy_2(self.root)
2434 return f._fpow(x, f.name, **raiser_RESIDUAL) # == pow(f, x)
2436 def _scalar(self, other, op, **txt):
2437 '''(INTERNAL) Return scalar C{other} or throw a C{TypeError}.
2438 '''
2439 if isscalar(other):
2440 return other
2441 raise self._Error(op, other, _TypeError, **txt) # _invalid_
2443 def signOf(self, res=True):
2444 '''Determine the sign of this instance.
2446 @kwarg res: If C{True}, consider the residual,
2447 otherwise ignore the latter (C{bool}).
2449 @return: The sign (C{int}, -1, 0 or +1).
2450 '''
2451 s, r = self._nfprs2
2452 r = (-r) if res else 0
2453 return _signOf(s, r)
2455 def toRepr(self, **lenc_prec_sep_fmt): # PYCHOK signature
2456 '''Return this C{Fsum} instance as representation.
2458 @kwarg lenc_prec_sep_fmt: Optional keyword arguments
2459 for method L{Fsum.toStr}.
2461 @return: This instance (C{repr}).
2462 '''
2463 return Fmt.repr_at(self, self.toStr(**lenc_prec_sep_fmt))
2465 def toStr(self, lenc=True, **prec_sep_fmt): # PYCHOK signature
2466 '''Return this C{Fsum} instance as string.
2468 @kwarg lenc: If C{True}, include the current C{[len]} of this
2469 L{Fsum} enclosed in I{[brackets]} (C{bool}).
2470 @kwarg prec_sep_fmt: Optional keyword arguments for method
2471 L{Fsum2Tuple.toStr}.
2473 @return: This instance (C{str}).
2474 '''
2475 p = self.classname
2476 if lenc:
2477 p = Fmt.SQUARE(p, len(self))
2478 n = _enquote(self.name, white=_UNDER_)
2479 t = self._nfprs2.toStr(**prec_sep_fmt)
2480 return NN(p, _SPACE_, n, t)
2482 def _truediv(self, other, op, **raiser_RESIDUAL):
2483 '''(INTERNAL) Return C{B{self} / B{other}} as an L{Fsum}.
2484 '''
2485 f = self._copy_2(self.__truediv__)
2486 return f._ftruediv(other, op, **raiser_RESIDUAL)
2488 def _update(self, updated=True): # see ._fset
2489 '''(INTERNAL) Zap all cached C{Property_RO} values.
2490 '''
2491 if updated:
2492 _pop = self.__dict__.pop
2493 for p in _ROs:
2494 _ = _pop(p, None)
2495# Fsum._fint2._update(self)
2496# Fsum._fprs ._update(self)
2497# Fsum._fprs2._update(self)
2498 return self # for .fset_
2500_ROs = _allPropertiesOf_n(3, Fsum, Property_RO) # PYCHOK see Fsum._update
2502if _NONFINITES == _std_: # PYCHOK no cover
2503 _ = nonfiniterrors(False)
2506def _Float_Int(arg, **name_Error):
2507 '''(INTERNAL) L{DivMod2Tuple}, L{Fsum2Tuple} Unit.
2508 '''
2509 U = Int if isint(arg) else Float
2510 return U(arg, **name_Error)
2513class DivMod2Tuple(_NamedTuple):
2514 '''2-Tuple C{(div, mod)} with the quotient C{div} and remainder
2515 C{mod} results of a C{divmod} operation.
2517 @note: Quotient C{div} an C{int} in Python 3+ but a C{float}
2518 in Python 2-. Remainder C{mod} an L{Fsum} instance.
2519 '''
2520 _Names_ = ('div', 'mod')
2521 _Units_ = (_Float_Int, Fsum)
2524class Fsum2Tuple(_NamedTuple): # in .fstats
2525 '''2-Tuple C{(fsum, residual)} with the precision running C{fsum}
2526 and the C{residual}, the sum of the remaining partials. Each
2527 item is C{float} or C{int}.
2529 @note: If the C{residual is INT0}, the C{fsum} is considered
2530 to be I{exact}, see method L{Fsum2Tuple.is_exact}.
2531 '''
2532 _Names_ = ( Fsum.fsum.__name__, Fsum.residual.name)
2533 _Units_ = (_Float_Int, _Float_Int)
2535 def __abs__(self): # in .fmath
2536 return self._Fsum.__abs__()
2538 def __bool__(self): # PYCHOK Python 3+
2539 return bool(self._Fsum)
2541 def __eq__(self, other):
2542 return self._other_op(other, self.__eq__)
2544 def __float__(self):
2545 return self._Fsum.__float__()
2547 def __ge__(self, other):
2548 return self._other_op(other, self.__ge__)
2550 def __gt__(self, other):
2551 return self._other_op(other, self.__gt__)
2553 def __le__(self, other):
2554 return self._other_op(other, self.__le__)
2556 def __lt__(self, other):
2557 return self._other_op(other, self.__lt__)
2559 def __int__(self):
2560 return self._Fsum.__int__()
2562 def __ne__(self, other):
2563 return self._other_op(other, self.__ne__)
2565 def __neg__(self):
2566 return self._Fsum.__neg__()
2568 __nonzero__ = __bool__ # Python 2-
2570 def __pos__(self):
2571 return self._Fsum.__pos__()
2573 def as_integer_ratio(self):
2574 '''Return this instance as the ratio of 2 integers.
2576 @see: Method L{Fsum.as_integer_ratio} for further details.
2577 '''
2578 return self._Fsum.as_integer_ratio()
2580 @property_RO
2581 def _fint2(self):
2582 return self._Fsum._fint2
2584 @property_RO
2585 def _fprs2(self):
2586 return self._Fsum._fprs2
2588 @Property_RO
2589 def _Fsum(self): # this C{Fsum2Tuple} as L{Fsum}, in .fstats
2590 s, r = _s_r(*self)
2591 ps = (r, s) if r else (s,)
2592 return _Psum(ps, name=self.name)
2594 def Fsum_(self, *xs, **name_f2product_nonfinites_RESIDUAL):
2595 '''Return this C{Fsum2Tuple} as an L{Fsum} plus some C{xs}.
2596 '''
2597 return Fsum(self, *xs, **name_f2product_nonfinites_RESIDUAL)
2599 def is_exact(self):
2600 '''Is this L{Fsum2Tuple} considered to be exact? (C{bool}).
2601 '''
2602 return self._Fsum.is_exact()
2604 def is_finite(self): # in .constants
2605 '''Is this L{Fsum2Tuple} C{finite}? (C{bool}).
2607 @see: Function L{isfinite<pygeodesy.isfinite>}.
2608 '''
2609 return self._Fsum.is_finite()
2611 def is_integer(self):
2612 '''Is this L{Fsum2Tuple} C{integer}? (C{bool}).
2613 '''
2614 return self._Fsum.is_integer()
2616 def _mul_scalar(self, other, op): # for Fsum._fmul
2617 return self._Fsum._mul_scalar(other, op)
2619 @property_RO
2620 def _n(self):
2621 return self._Fsum._n
2623 def _other_op(self, other, which):
2624 C, s = (tuple, self) if isinstance(other, tuple) else (Fsum, self._Fsum)
2625 return getattr(C, which.__name__)(s, other)
2627 @property_RO
2628 def _ps(self):
2629 return self._Fsum._ps
2631 @property_RO
2632 def _ps_neg(self):
2633 return self._Fsum._ps_neg
2635 def signOf(self, **res):
2636 '''Like method L{Fsum.signOf}.
2637 '''
2638 return self._Fsum.signOf(**res)
2640 def toStr(self, fmt=Fmt.g, **prec_sep): # PYCHOK signature
2641 '''Return this L{Fsum2Tuple} as string (C{str}).
2643 @kwarg fmt: Optional C{float} format (C{letter}).
2644 @kwarg prec_sep: Optional keyword arguments for function
2645 L{fstr<streprs.fstr>}.
2646 '''
2647 return Fmt.PAREN(fstr(self, fmt=fmt, strepr=str, force=False, **prec_sep))
2649_Fsum_2Tuple_types = Fsum, Fsum2Tuple # PYCHOK lines
2652class ResidualError(_ValueError):
2653 '''Error raised for a division, power or root operation of
2654 an L{Fsum} instance with a C{residual} I{ratio} exceeding
2655 the L{RESIDUAL<Fsum.RESIDUAL>} threshold.
2657 @see: Module L{pygeodesy.fsums} and method L{Fsum.RESIDUAL}.
2658 '''
2659 pass
2662try:
2663 from math import fsum as _fsum # precision IEEE-754 sum, Python 2.6+
2665 # make sure _fsum works as expected (XXX check
2666 # float.__getformat__('float')[:4] == 'IEEE'?)
2667 if _fsum((1, 1e101, 1, -1e101)) != 2: # PYCHOK no cover
2668 del _fsum # nope, remove _fsum ...
2669 raise ImportError() # ... use _fsum below
2671 _sum = _fsum # in .elliptic
2672except ImportError:
2673 _sum = sum # in .elliptic
2675 def _fsum(xs):
2676 '''(INTERNAL) Precision summation, Python 2.5-.
2677 '''
2678 F = Fsum(name=_fsum.name, f2product=False, nonfinites=True)
2679 return float(F._facc(xs, up=False))
2682def fsum(xs, nonfinites=None, **floats):
2683 '''Precision floating point summation from Python's C{math.fsum}.
2685 @arg xs: Iterable of items to add (each C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
2686 @kwarg nonfinites: Use C{B{nonfinites}=True} if I{non-finites} are C{OK}, if
2687 C{False} I{non-finites} raise an Overflow-/ValueError or if
2688 C{None}, L{nonfiniterrors} applies (C{bool} or C{None}).
2689 @kwarg floats: DEPRECATED keyword argument C{B{floats}=False} (C{bool}), use
2690 keyword argument C{B{nonfinites}=False} instead.
2692 @return: Precision C{fsum} (C{float}).
2694 @raise OverflowError: Infinite B{C{xs}} item or intermediate C{math.fsum} overflow.
2696 @raise TypeError: Invalid B{C{xs}} item.
2698 @raise ValueError: Invalid or C{NAN} B{C{xs}} item.
2700 @see: Function L{nonfiniterrors}, class L{Fsum} and methods L{Fsum.nonfinites},
2701 L{Fsum.fsum}, L{Fsum.fadd} and L{Fsum.fadd_}.
2702 '''
2703 return _xsum(fsum, xs, nonfinites=nonfinites, **floats) if xs else _0_0
2706def fsum_(*xs, **nonfinites):
2707 '''Precision floating point summation of all positional items.
2709 @arg xs: Items to add (each C{scalar}, an L{Fsum} or L{Fsum2Tuple}), all positional.
2710 @kwarg nonfinites: Use C{B{nonfinites}=True} if I{non-finites} are C{OK} (C{bool}).
2712 @see: Function L{fsum<fsums.fsum>} for further details.
2713 '''
2714 return _xsum(fsum_, xs, **nonfinites) if xs else _0_0 # origin=1?
2717def fsumf_(*xs):
2718 '''Precision floating point summation of all positional items with I{non-finites} C{OK}.
2720 @arg xs: Items to add (each C{scalar}, an L{Fsum} or L{Fsum2Tuple}),
2721 all positional.
2723 @see: Function L{fsum_<fsums.fsum_>} for further details.
2724 '''
2725 return _xsum(fsumf_, xs, nonfinites=True) if xs else _0_0 # origin=1?
2728def fsum1(xs, **nonfinites):
2729 '''Precision floating point summation, 1-primed.
2731 @arg xs: Iterable of items to add (each C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
2732 @kwarg nonfinites: Use C{B{nonfinites}=True} if I{non-finites} are C{OK} (C{bool}).
2734 @see: Function L{fsum<fsums.fsum>} for further details.
2735 '''
2736 return _xsum(fsum1, xs, primed=1, **nonfinites) if xs else _0_0
2739def fsum1_(*xs, **nonfinites):
2740 '''Precision floating point summation of all positional items, 1-primed.
2742 @arg xs: Items to add (each C{scalar}, an L{Fsum} or L{Fsum2Tuple}), all positional.
2743 @kwarg nonfinites: Use C{B{nonfinites}=True} if I{non-finites} are C{OK} (C{bool}).
2745 @see: Function L{fsum_<fsums.fsum_>} for further details.
2746 '''
2747 return _xsum(fsum1_, xs, primed=1, **nonfinites) if xs else _0_0 # origin=1?
2750def fsum1f_(*xs):
2751 '''Precision floating point summation of all positional items, 1-primed and
2752 with I{non-finites} C{OK}.
2754 @see: Function L{fsum_<fsums.fsum_>} for further details.
2755 '''
2756 return _xsum(fsum1f_, xs, nonfinites=True, primed=1) if xs else _0_0
2759def _x_isfine(nfOK, **kwds): # get the C{_x} and C{_isfine} handlers.
2760 _x_kwds = dict(_x= (_passarg if nfOK else _2finite),
2761 _isfine=(_isOK if nfOK else _isfinite)) # PYCHOK kwds
2762 _x_kwds.update(kwds)
2763 return _x_kwds
2766def _X_ps(X): # default C{_X} handler
2767 return X._ps # lambda X: X._ps
2770def _xs(xs, _X=_X_ps, _x=float, _isfine=_isfinite, # defaults for Fsum._facc
2771 origin=0, which=None, **_Cdot):
2772 '''(INTERNAL) Yield each C{xs} item as 1 or more C{float}s.
2773 '''
2774 i, x = 0, xs
2775 try:
2776 for i, x in enumerate(_xiterable(xs)):
2777 if isinstance(x, _Fsum_2Tuple_types):
2778 for p in _X(x):
2779 yield p if _isfine(p) else _nfError(p)
2780 else:
2781 f = _x(x)
2782 yield f if _isfine(f) else _nfError(f)
2784 except (OverflowError, TypeError, ValueError) as X:
2785 t = _xsError(X, xs, i + origin, x)
2786 if which: # prefix invokation
2787 w = unstr(which, *xs, _ELLIPSIS=4, **_Cdot)
2788 t = _COMMASPACE_(w, t)
2789 raise _xError(X, t, txt=None)
2792def _xsum(which, xs, nonfinites=None, primed=0, **floats): # origin=0
2793 '''(INTERNAL) Precision summation of C{xs} with conditions.
2794 '''
2795 if floats: # for backward compatibility
2796 nonfinites = _xkwds_get1(floats, floats=nonfinites)
2797 elif nonfinites is None:
2798 nonfinites = not nonfiniterrors()
2799 fs = _xs(xs, **_x_isfine(nonfinites, which=which))
2800 return _fsum(_1primed(fs) if primed else fs)
2803# delete all decorators, etc.
2804del _allPropertiesOf_n, deprecated_method, deprecated_property_RO, \
2805 Property, Property_RO, property_RO, _ALL_LAZY, _F2PRODUCT, \
2806 MANT_DIG, _NONFINITES, _RESIDUAL_0_0, _getenv, _std_
2808if __name__ == '__main__':
2810 # usage: python3 -m pygeodesy.fsums
2812 def _test(n):
2813 # copied from Hettinger, see L{Fsum} reference
2814 from pygeodesy import frandoms, printf
2816 printf(_fsum.__name__, end=_COMMASPACE_)
2817 printf(_psum.__name__, end=_COMMASPACE_)
2819 F = Fsum()
2820 if F.is_math_fsum():
2821 for t in frandoms(n, seeded=True):
2822 assert float(F.fset_(*t)) == _fsum(t)
2823 printf(_DOT_, end=NN)
2824 printf(NN)
2826 _test(128)
2828# **) MIT License
2829#
2830# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.
2831#
2832# Permission is hereby granted, free of charge, to any person obtaining a
2833# copy of this software and associated documentation files (the "Software"),
2834# to deal in the Software without restriction, including without limitation
2835# the rights to use, copy, modify, merge, publish, distribute, sublicense,
2836# and/or sell copies of the Software, and to permit persons to whom the
2837# Software is furnished to do so, subject to the following conditions:
2838#
2839# The above copyright notice and this permission notice shall be included
2840# in all copies or substantial portions of the Software.
2841#
2842# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
2843# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
2844# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
2845# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
2846# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
2847# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
2848# OTHER DEALINGS IN THE SOFTWARE.