Coverage for pygeodesy/fsums.py: 94%
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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, _getPYGEODESY, _MODS, _passarg
52from pygeodesy.interns import NN, _arg_, _COMMASPACE_, _DOT_, _from_, \
53 _not_finite_, _SPACE_, _std_, _UNDER_
54# from pygeodesy.lazily import _ALL_LAZY # from .named
55from pygeodesy.named import _name__, _name2__, _Named, _NamedTuple, \
56 _NotImplemented, _ALL_LAZY
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__ = '24.10.22'
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 = _getPYGEODESY('FSUM_F2PRODUCT')
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 = _getPYGEODESY('FSUM_NONFINITES')
88_non_zero_ = 'non-zero'
89_pow_op_ = _mul_op_ * 2 # _DSTAR_
90_RESIDUAL_0_0 = _getPYGEODESY('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 = _MODS.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# turned off, called by _deepcopy and _copy
917# def __reduce__(self): # Python 3.8+
918# ''' Pickle, like std C{fractions.Fraction}, see U{__reduce__
919# <https://docs.Python.org/3/library/pickle.html#object.__reduce__>}
920# '''
921# dict_ = self._Fsum_as().__dict__ # no __setstate__
922# return (self.__class__, self.partials, dict_)
924# def __repr__(self):
925# '''Return the default C{repr(this)}.
926# '''
927# return self.toRepr(lenc=True)
929 def __rfloordiv__(self, other):
930 '''Return C{B{other} // B{self}} as an L{Fsum}.
932 @see: Method L{Fsum.__ifloordiv__}.
933 '''
934 f = self._copy_2r(other, self.__rfloordiv__)
935 return f._floordiv(self, _floordiv_op_)
937 def __rmatmul__(self, other): # PYCHOK no coveS
938 '''Not implemented.'''
939 return _NotImplemented(self, other)
941 def __rmod__(self, other):
942 '''Return C{B{other} % B{self}} as an L{Fsum}.
944 @see: Method L{Fsum.__imod__}.
945 '''
946 f = self._copy_2r(other, self.__rmod__)
947 return f._fdivmod2(self, _mod_op_).mod
949 def __rmul__(self, other):
950 '''Return C{B{other} * B{self}} as an L{Fsum}.
952 @see: Method L{Fsum.__imul__}.
953 '''
954 f = self._copy_2r(other, self.__rmul__)
955 return f._fmul(self, _mul_op_)
957 def __round__(self, *ndigits): # PYCHOK Python 3+
958 '''Return C{round(B{self}, *B{ndigits}} as an L{Fsum}.
960 @arg ndigits: Optional number of digits (C{int}).
961 '''
962 f = self._copy_2(self.__round__)
963 # <https://docs.Python.org/3.12/reference/datamodel.html?#object.__round__>
964 return f._fset(round(float(self), *ndigits)) # can be C{int}
966 def __rpow__(self, other, *mod):
967 '''Return C{B{other}**B{self}} as an L{Fsum}.
969 @see: Method L{Fsum.__ipow__}.
970 '''
971 f = self._copy_2r(other, self.__rpow__)
972 return f._fpow(self, _pow_op_, *mod)
974 def __rsub__(self, other):
975 '''Return C{B{other} - B{self}} as L{Fsum}.
977 @see: Method L{Fsum.__isub__}.
978 '''
979 f = self._copy_2r(other, self.__rsub__)
980 return f._fsub(self, _sub_op_)
982 def __rtruediv__(self, other, **raiser_RESIDUAL):
983 '''Return C{B{other} / B{self}} as an L{Fsum}.
985 @see: Method L{Fsum.__itruediv__}.
986 '''
987 f = self._copy_2r(other, self.__rtruediv__)
988 return f._ftruediv(self, _truediv_op_, **raiser_RESIDUAL)
990 def __str__(self):
991 '''Return the default C{str(self)}.
992 '''
993 return self.toStr(lenc=True)
995 def __sub__(self, other):
996 '''Return C{B{self} - B{other}} as an L{Fsum}.
998 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar}.
1000 @return: The difference (L{Fsum}).
1002 @see: Method L{Fsum.__isub__}.
1003 '''
1004 f = self._copy_2(self.__sub__)
1005 return f._fsub(other, _sub_op_)
1007 def __truediv__(self, other, **raiser_RESIDUAL):
1008 '''Return C{B{self} / B{other}} as an L{Fsum}.
1010 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar} divisor.
1011 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore
1012 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}
1013 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.
1015 @return: The quotient (L{Fsum}).
1017 @raise ResidualError: Non-zero, significant residual or invalid
1018 B{C{RESIDUAL}}.
1020 @see: Method L{Fsum.__itruediv__}.
1021 '''
1022 return self._truediv(other, _truediv_op_, **raiser_RESIDUAL)
1024 __trunc__ = __int__
1026 if _MODS.sys_version_info2 < (3, 0): # PYCHOK no cover
1027 # <https://docs.Python.org/2/library/operator.html#mapping-operators-to-functions>
1028 __div__ = __truediv__
1029 __idiv__ = __itruediv__
1030 __long__ = __int__
1031 __nonzero__ = __bool__
1032 __rdiv__ = __rtruediv__
1034 def as_integer_ratio(self):
1035 '''Return this instance as the ratio of 2 integers.
1037 @return: 2-Tuple C{(numerator, denominator)} both C{int} with
1038 C{numerator} signed and C{denominator} non-zero and
1039 positive. The C{numerator} is I{non-finite} if this
1040 instance is.
1042 @see: Method L{Fsum.fint2} and C{float.as_integer_ratio} in
1043 Python 2.7+.
1044 '''
1045 n, r = self._fint2
1046 if r:
1047 i, d = float(r).as_integer_ratio()
1048 n, d = _n_d2(n * d + i, d)
1049 else: # PYCHOK no cover
1050 d = 1
1051 return n, d
1053 @property_RO
1054 def as_iscalar(self):
1055 '''Get this instance I{as-is} (L{Fsum} with C{non-zero residual},
1056 C{scalar} or I{non-finite}).
1057 '''
1058 s, r = self._nfprs2
1059 return self if r else s
1061 @property_RO
1062 def ceil(self):
1063 '''Get this instance' C{ceil} value (C{int} in Python 3+, but
1064 C{float} in Python 2-).
1066 @note: This C{ceil} takes the C{residual} into account.
1068 @see: Method L{Fsum.int_float} and properties L{Fsum.floor},
1069 L{Fsum.imag} and L{Fsum.real}.
1070 '''
1071 s, r = self._fprs2
1072 c = _ceil(s) + int(r) - 1
1073 while r > (c - s): # (s + r) > c
1074 c += 1
1075 return c # _ceil(self._n_d)
1077 cmp = __cmp__
1079 def _cmp_0(self, other, op):
1080 '''(INTERNAL) Return C{scalar(self - B{other})} for 0-comparison.
1081 '''
1082 if _isFsum_2Tuple(other):
1083 s = self._ps_1sum(*other._ps)
1084 elif self._scalar(other, op):
1085 s = self._ps_1sum(other)
1086 else:
1087 s = self.signOf() # res=True
1088 return s
1090 def copy(self, deep=False, **name):
1091 '''Copy this instance, C{shallow} or B{C{deep}}.
1093 @kwarg name: Optional, overriding C{B{name}='"copy"} (C{str}).
1095 @return: The copy (L{Fsum}).
1096 '''
1097 n = _name__(name, name__=self.copy)
1098 f = _Named.copy(self, deep=deep, name=n)
1099 if f._ps is self._ps:
1100 f._ps = list(self._ps) # separate list
1101 if not deep:
1102 f._n = 1
1103 # assert f._f2product == self._f2product
1104 # assert f._Fsum is f
1105 # assert f._isfine is self._isfine
1106 # assert f._RESIDUAL is self._RESIDUAL
1107 return f
1109 def _copy_2(self, which, name=NN):
1110 '''(INTERNAL) Copy for I{dyadic} operators.
1111 '''
1112 n = name or which.__name__ # _DUNDER_nameof
1113 # NOT .classof due to .Fdot(a, *b) args, etc.
1114 f = _Named.copy(self, deep=False, name=n)
1115 f._ps = list(self._ps) # separate list
1116 # assert f._n == self._n
1117 # assert f._f2product == self._f2product
1118 # assert f._Fsum is f
1119 # assert f._isfine is self._isfine
1120 # assert f._RESIDUAL is self._RESIDUAL
1121 return f
1123 def _copy_2r(self, other, which):
1124 '''(INTERNAL) Copy for I{reverse-dyadic} operators.
1125 '''
1126 return other._copy_2(which) if _isFsum(other) else \
1127 self._copy_2(which)._fset(other)
1129 divmod = __divmod__
1131 def _Error(self, op, other, Error, **txt_cause):
1132 '''(INTERNAL) Format an B{C{Error}} for C{{self} B{op} B{other}}.
1133 '''
1134 # self.as_iscalar causes RecursionError for ._fprs2 errors
1135 s = _Psum(self._ps, nonfinites=True, name=self.name)
1136 return Error(_SPACE_(s.as_iscalar, op, other), **txt_cause)
1138 def _ErrorX(self, X, op, other, *mod):
1139 '''(INTERNAL) Format the caught exception C{X}.
1140 '''
1141 E, t = _xError2(X)
1142 if mod:
1143 t = _COMMASPACE_(Fmt.PARENSPACED(mod=mod[0]), t)
1144 return self._Error(op, other, E, txt=t, cause=X)
1146 def _ErrorXs(self, X, xs, **kwds): # in .fmath
1147 '''(INTERNAL) Format the caught exception C{X}.
1148 '''
1149 E, t = _xError2(X)
1150 u = unstr(self.named3, *xs, _ELLIPSIS=4, **kwds)
1151 return E(u, txt=t, cause=X)
1153 def _facc(self, xs, up=True, **_X_x_origin):
1154 '''(INTERNAL) Accumulate more C{scalar}s or L{Fsum}s.
1155 '''
1156 if xs:
1157 kwds = self._isfine
1158 if _X_x_origin:
1159 kwds = _xkwds(_X_x_origin, **kwds)
1160 fs = _xs(xs, **kwds) # PYCHOK yield
1161 ps = self._ps
1162 ps[:] = self._ps_acc(list(ps), fs, up=up)
1163# if len(ps) > 16:
1164# _ = _psum(ps, **self._isfine)
1165 return self
1167 def _facc_args(self, xs, **up):
1168 '''(INTERNAL) Accumulate 0, 1 or more C{xs}, all positional
1169 arguments in the caller of this method.
1170 '''
1171 return self._fadd(xs[0], **up) if len(xs) == 1 else \
1172 self._facc(xs, **up) # origin=1?
1174 def _facc_neg(self, xs, **up_origin):
1175 '''(INTERNAL) Accumulate more C{xs}, negated.
1176 '''
1177 def _N(X):
1178 return X._ps_neg
1180 def _n(x):
1181 return -float(x)
1183 return self._facc(xs, _X=_N, _x=_n, **up_origin)
1185 def _facc_power(self, power, xs, which, **raiser_RESIDUAL): # in .fmath
1186 '''(INTERNAL) Add each C{xs} as C{float(x**power)}.
1187 '''
1188 def _Pow4(p):
1189 r = 0
1190 if _isFsum_2Tuple(p):
1191 s, r = p._fprs2
1192 if r:
1193 m = Fsum._pow
1194 else: # scalar
1195 return _Pow4(s)
1196 elif isint(p, both=True) and int(p) >= 0:
1197 p = s = int(p)
1198 m = Fsum._pow_int
1199 else:
1200 p = s = _2float(power=p, **self._isfine)
1201 m = Fsum._pow_scalar
1202 return m, p, s, r
1204 _Pow, p, s, r = _Pow4(power)
1205 if p: # and xs:
1206 op = which.__name__
1207 _FsT = _Fsum_2Tuple_types
1208 _pow = self._pow_2_3
1210 def _P(X):
1211 f = _Pow(X, p, power, op, **raiser_RESIDUAL)
1212 return f._ps if isinstance(f, _FsT) else (f,)
1214 def _p(x):
1215 x = float(x)
1216 f = _pow(x, s, power, op, **raiser_RESIDUAL)
1217 if f and r:
1218 f *= _pow(x, r, power, op, **raiser_RESIDUAL)
1219 return f
1221 f = self._facc(xs, _X=_P, _x=_p) # origin=1?
1222 else:
1223 f = self._facc_scalar_(float(len(xs))) # x**0 == 1
1224 return f
1226 def _facc_scalar(self, xs, **up):
1227 '''(INTERNAL) Accumulate all C{xs}, each C{scalar}.
1228 '''
1229 if xs:
1230 ps = self._ps
1231 ps[:] = self._ps_acc(list(ps), xs, **up)
1232 return self
1234 def _facc_scalar_(self, *xs, **up):
1235 '''(INTERNAL) Accumulate all positional C{xs}, each C{scalar}.
1236 '''
1237 return self._facc_scalar(xs, **up)
1239 def _facc_scalarf(self, xs, up=True, **origin_which):
1240 '''(INTERNAL) Accumulate all C{xs}, each C{scalar}, an L{Fsum} or
1241 L{Fsum2Tuple}, like function C{_xsum}.
1242 '''
1243 _C = self.__class__
1244 fs = _xs(xs, **_x_isfine(self.nonfinitesOK, _Cdot=_C,
1245 **origin_which)) # PYCHOK yield
1246 return self._facc_scalar(fs, up=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 fadd(self, xs=()):
1263 '''Add an iterable's items to this instance.
1265 @arg xs: Iterable of items to add (each C{scalar},
1266 an L{Fsum} or L{Fsum2Tuple}).
1268 @return: This instance (L{Fsum}).
1270 @raise OverflowError: Partial C{2sum} overflow.
1272 @raise TypeError: An invalid B{C{xs}} item.
1274 @raise ValueError: Invalid or I{non-finite} B{C{xs}} value.
1275 '''
1276 if _isFsum_2Tuple(xs):
1277 self._facc_scalar(xs._ps)
1278 elif isscalar(xs): # for backward compatibility # PYCHOK no cover
1279 x = _2float(x=xs, **self._isfine)
1280 self._facc_scalar_(x)
1281 elif xs: # _xiterable(xs)
1282 self._facc(xs)
1283 return self
1285 def fadd_(self, *xs):
1286 '''Add all positional items to this instance.
1288 @arg xs: Values to add (each C{scalar}, an L{Fsum}
1289 or L{Fsum2Tuple}), all positional.
1291 @see: Method L{Fsum.fadd} for further details.
1292 '''
1293 return self._facc_args(xs)
1295 def _fadd(self, other, op=_add_op_, **up):
1296 '''(INTERNAL) Apply C{B{self} += B{other}}.
1297 '''
1298 if _isFsum_2Tuple(other):
1299 self._facc_scalar(other._ps, **up)
1300 elif self._scalar(other, op):
1301 self._facc_scalar_(other, **up)
1302 return self
1304 fcopy = copy # for backward compatibility
1305 fdiv = __itruediv__
1306 fdivmod = __divmod__
1308 def _fdivmod2(self, other, op, **raiser_RESIDUAL):
1309 '''(INTERNAL) Apply C{B{self} %= B{other}} and return a L{DivMod2Tuple}.
1310 '''
1311 # result mostly follows CPython function U{float_divmod
1312 # <https://GitHub.com/python/cpython/blob/main/Objects/floatobject.c>},
1313 # but at least divmod(-3, 2) equals Cpython's result (-2, 1).
1314 q = self._truediv(other, op, **raiser_RESIDUAL).floor
1315 if q: # == float // other == floor(float / other)
1316 self -= self._Fsum_as(q) * other # NOT other * q!
1318 s = signOf(other) # make signOf(self) == signOf(other)
1319 if s and self.signOf() == -s: # PYCHOK no cover
1320 self += other
1321 q -= 1
1322# t = self.signOf()
1323# if t and t != s:
1324# raise self._Error(op, other, _AssertionError, txt__=signOf)
1325 return DivMod2Tuple(q, self) # q is C{int} in Python 3+, but C{float} in Python 2-
1327 def _fhorner(self, x, cs, where, incx=True): # in .fmath
1328 '''(INTERNAL) Add an L{Fhorner} evaluation of polynomial
1329 C{sum(cs[i] * B{x}**i for i=0..len(cs)-1) if B{incx}
1330 else sum(... i=len(cs)-1..0)}.
1331 '''
1332 # assert _xiterablen(cs)
1333 try:
1334 n = len(cs)
1335 H = self._Fsum_as(name__=self._fhorner)
1336 _m = H._mul_Fsum if _isFsum_2Tuple(x) else \
1337 H._mul_scalar
1338 if _2finite(x, **self._isfine) and n > 1:
1339 for c in (reversed(cs) if incx else cs):
1340 H._fset(_m(x, _mul_op_), up=False)
1341 H._fadd(c, up=False)
1342 else: # x == 0
1343 H = cs[0] if n else 0
1344 self._fadd(H)
1345 except Exception as X:
1346 t = unstr(where, x, *cs, _ELLIPSIS=4, incx=incx)
1347 raise self._ErrorX(X, _add_op_, t)
1348 return self
1350 def _finite(self, other, op=None):
1351 '''(INTERNAL) Return B{C{other}} if C{finite}.
1352 '''
1353 if _isOK_or_finite(other, **self._isfine):
1354 return other
1355 E = _NonfiniteError(other)
1356 raise self._Error(op, other, E, txt=_not_finite_)
1358 def fint(self, name=NN, **raiser_RESIDUAL):
1359 '''Return this instance' current running sum as C{integer}.
1361 @kwarg name: Optional, overriding C{B{name}="fint"} (C{str}).
1362 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore
1363 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}
1364 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.
1366 @return: The C{integer} sum (L{Fsum}) if this instance C{is_integer}
1367 with a zero or insignificant I{integer} residual.
1369 @raise ResidualError: Non-zero, significant residual or invalid
1370 B{C{RESIDUAL}}.
1372 @see: Methods L{Fsum.fint2}, L{Fsum.int_float} and L{Fsum.is_integer}.
1373 '''
1374 i, r = self._fint2
1375 if r:
1376 R = self._raiser(r, i, **raiser_RESIDUAL)
1377 if R:
1378 t = _stresidual(_integer_, r, **R)
1379 raise ResidualError(_integer_, i, txt=t)
1380 return self._Fsum_as(i, name=_name__(name, name__=self.fint))
1382 def fint2(self, **name):
1383 '''Return this instance' current running sum as C{int} and the
1384 I{integer} residual.
1386 @kwarg name: Optional name (C{str}).
1388 @return: An L{Fsum2Tuple}C{(fsum, residual)} with C{fsum}
1389 an C{int} and I{integer} C{residual} a C{float} or
1390 C{INT0} if the C{fsum} is considered to be I{exact}.
1391 The C{fsum} is I{non-finite} if this instance is.
1392 '''
1393 return Fsum2Tuple(*self._fint2, **name)
1395 @Property
1396 def _fint2(self): # see ._fset
1397 '''(INTERNAL) Get 2-tuple (C{int}, I{integer} residual).
1398 '''
1399 s, r = self._nfprs2
1400 if _isfinite(s):
1401 i = int(s)
1402 r = (self._ps_1sum(i) if len(self._ps) > 1 else
1403 float(s - i)) or INT0
1404 else: # INF, NAN, NINF
1405 i = float(s)
1406# r = _NONFINITEr
1407 return i, r # Fsum2Tuple?
1409 @_fint2.setter_ # PYCHOK setter_UNDERscore!
1410 def _fint2(self, s): # in _fset
1411 '''(INTERNAL) Replace the C{_fint2} value.
1412 '''
1413 if _isfinite(s):
1414 i = int(s)
1415 r = (s - i) or INT0
1416 else: # INF, NAN, NINF
1417 i = float(s)
1418 r = _NONFINITEr
1419 return i, r # like _fint2.getter
1421 @deprecated_property_RO
1422 def float_int(self): # PYCHOK no cover
1423 '''DEPRECATED, use method C{Fsum.int_float}.'''
1424 return self.int_float() # raiser=False
1426 @property_RO
1427 def floor(self):
1428 '''Get this instance' C{floor} (C{int} in Python 3+, but
1429 C{float} in Python 2-).
1431 @note: This C{floor} takes the C{residual} into account.
1433 @see: Method L{Fsum.int_float} and properties L{Fsum.ceil},
1434 L{Fsum.imag} and L{Fsum.real}.
1435 '''
1436 s, r = self._fprs2
1437 f = _floor(s) + _floor(r) + 1
1438 while (f - s) > r: # f > (s + r)
1439 f -= 1
1440 return f # _floor(self._n_d)
1442# ffloordiv = __ifloordiv__ # for naming consistency?
1443# floordiv = __floordiv__ # for naming consistency?
1445 def _floordiv(self, other, op, **raiser_RESIDUAL): # rather _ffloordiv?
1446 '''Apply C{B{self} //= B{other}}.
1447 '''
1448 q = self._ftruediv(other, op, **raiser_RESIDUAL) # == self
1449 return self._fset(q.floor) # floor(q)
1451 def fma(self, other1, other2, **nonfinites): # in .fmath.fma
1452 '''Fused-multiply-add C{self *= B{other1}; self += B{other2}}.
1454 @arg other1: Multiplier (C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
1455 @arg other2: Addend (C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
1456 @kwarg nonfinites: Use C{B{nonfinites}=True} or C{False}, to
1457 override L{nonfinites<Fsum.nonfinites>} and
1458 L{nonfiniterrors} default (C{bool}).
1459 '''
1460 op = self.fma.__name__
1461 _fs = self._ps_other
1462 try:
1463 s, r = self._fprs2
1464 if r:
1465 f = self._f2mul(self.fma, other1, **nonfinites)
1466 f += other2
1467 elif _residue(other1) or _residue(other2):
1468 fs = _2split3s(_fs(op, other1))
1469 fs = _2products(s, fs, *_fs(op, other2))
1470 f = _Psum(self._ps_acc([], fs, up=False), name=op)
1471 else:
1472 f = _fma(s, other1, other2)
1473 f = _2finite(f, **self._isfine)
1474 except TypeError as X:
1475 raise self._ErrorX(X, op, (other1, other2))
1476 except (OverflowError, ValueError) as X: # from math.fma
1477 f = self._mul_reduce(s, other1) # INF, NAN, NINF
1478 f += sum(_fs(op, other2))
1479 f = self._nonfiniteX(X, op, f, **nonfinites)
1480 return self._fset(f)
1482 fmul = __imul__
1484 def _fmul(self, other, op):
1485 '''(INTERNAL) Apply C{B{self} *= B{other}}.
1486 '''
1487 if _isFsum_2Tuple(other):
1488 if len(self._ps) != 1:
1489 f = self._mul_Fsum(other, op)
1490 elif len(other._ps) != 1: # and len(self._ps) == 1
1491 f = self._ps_mul(op, *other._ps) if other._ps else _0_0
1492 elif self._f2product: # len(other._ps) == 1
1493 f = self._mul_scalar(other._ps[0], op)
1494 else: # len(other._ps) == len(self._ps) == 1
1495 f = self._finite(self._ps[0] * other._ps[0], op=op)
1496 else:
1497 s = self._scalar(other, op)
1498 f = self._mul_scalar(s, op)
1499 return self._fset(f) # n=len(self) + 1
1501 @deprecated_method
1502 def f2mul(self, *others, **raiser):
1503 '''DEPRECATED on 2024.09.13, use method L{f2mul_<Fsum.f2mul_>}.'''
1504 return self._fset(self.f2mul_(*others, **raiser))
1506 def f2mul_(self, *others, **nonfinites): # in .fmath.f2mul
1507 '''Return C{B{self} * B{other} * B{other} ...} for all B{C{others}} using cascaded,
1508 accurate multiplication like with L{f2product<Fsum.f2product>} set to C{True}.
1510 @arg others: Multipliers (each C{scalar}, an L{Fsum} or L{Fsum2Tuple}), all
1511 positional.
1512 @kwarg nonfinites: Use C{B{nonfinites}=True} or C{False}, to override both
1513 L{nonfinites<Fsum.nonfinites>} and the L{nonfiniterrors}
1514 default (C{bool}).
1516 @return: The cascaded I{TwoProduct} (L{Fsum} or C{float}).
1518 @see: U{Equations 2.3<https://www.TUHH.De/ti3/paper/rump/OzOgRuOi06.pdf>}
1519 '''
1520 return self._f2mul(self.f2mul_, *others, **nonfinites)
1522 def _f2mul(self, where, *others, **nonfinites_raiser):
1523 '''(INTERNAL) See methods C{fma} and C{f2mul_}.
1524 '''
1525 f = self._copy_2(where)
1526 ps = f._ps
1527 if ps and others:
1528 op = where.__name__
1529 try:
1530 for other in others: # to pinpoint errors
1531 for p in self._ps_other(op, other):
1532 pfs = _2products(p, _2split3s(ps))
1533 ps[:] = f._ps_acc([], pfs, up=False)
1534 f._update()
1535 except TypeError as X:
1536 raise self._ErrorX(X, op, other)
1537 except (OverflowError, ValueError) as X:
1538 r = self._mul_reduce(sum(ps), other) # INF, NAN, NINF
1539 r = self._nonfiniteX(X, op, r, **nonfinites_raiser)
1540 f._fset(r)
1541 return f
1543 def fover(self, over, **raiser_RESIDUAL):
1544 '''Apply C{B{self} /= B{over}} and summate.
1546 @arg over: An L{Fsum} or C{scalar} denominator.
1547 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore
1548 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}
1549 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.
1551 @return: Precision running sum (C{float}).
1553 @raise ResidualError: Non-zero, significant residual or invalid
1554 B{C{RESIDUAL}}.
1556 @see: Methods L{Fsum.fsum} and L{Fsum.__itruediv__}.
1557 '''
1558 return float(self.fdiv(over, **raiser_RESIDUAL)._fprs)
1560 fpow = __ipow__
1562 def _fpow(self, other, op, *mod, **raiser_RESIDUAL):
1563 '''Apply C{B{self} **= B{other}}, optional B{C{mod}} or C{None}.
1564 '''
1565 if mod:
1566 if mod[0] is not None: # == 3-arg C{pow}
1567 f = self._pow_2_3(self, other, other, op, *mod, **raiser_RESIDUAL)
1568 elif self.is_integer():
1569 # return an exact C{int} for C{int}**C{int}
1570 i, _ = self._fint2 # assert _ == 0
1571 x, r = _2s_r(other) # C{int}, C{float} or other
1572 f = self._Fsum_as(i)._pow_Fsum(other, op, **raiser_RESIDUAL) if r else \
1573 self._pow_2_3(i, x, other, op, **raiser_RESIDUAL)
1574 else: # mod[0] is None, power(self, other)
1575 f = self._pow(other, other, op, **raiser_RESIDUAL)
1576 else: # pow(self, other)
1577 f = self._pow(other, other, op, **raiser_RESIDUAL)
1578 return self._fset(f) # n=max(len(self), 1)
1580 def f2product(self, *two):
1581 '''Get and set accurate I{TwoProduct} multiplication for this
1582 L{Fsum}, overriding the L{f2product} default.
1584 @arg two: If omitted, leave the override unchanged, if C{True},
1585 turn I{TwoProduct} on, if C{False} off, if C{None}e
1586 remove th override (C{bool} or C{None}).
1588 @return: The previous setting (C{bool} or C{None} if not set).
1590 @see: Function L{f2product<fsums.f2product>}.
1592 @note: Use C{f.f2product() or f2product()} to determine whether
1593 multiplication is accurate for L{Fsum} C{f}.
1594 '''
1595 if two: # delattrof(self, _f2product=None)
1596 t = _xkwds_pop(self.__dict__, _f2product=None)
1597 if two[0] is not None:
1598 self._f2product = bool(two[0])
1599 else: # getattrof(self, _f2product=None)
1600 t = _xkwds_get(self.__dict__, _f2product=None)
1601 return t
1603 @Property
1604 def _fprs(self):
1605 '''(INTERNAL) Get and cache this instance' precision
1606 running sum (C{float} or C{int}), ignoring C{residual}.
1608 @note: The precision running C{fsum} after a C{//=} or
1609 C{//} C{floor} division is C{int} in Python 3+.
1610 '''
1611 s, _ = self._fprs2
1612 return s # ._fprs2.fsum
1614 @_fprs.setter_ # PYCHOK setter_UNDERscore!
1615 def _fprs(self, s):
1616 '''(INTERNAL) Replace the C{_fprs} value.
1617 '''
1618 return s
1620 @Property
1621 def _fprs2(self):
1622 '''(INTERNAL) Get and cache this instance' precision
1623 running sum and residual (L{Fsum2Tuple}).
1624 '''
1625 ps = self._ps
1626 n = len(ps)
1627 try:
1628 if n > 2:
1629 s = _psum(ps, **self._isfine)
1630 if not _isfinite(s):
1631 ps[:] = s, # collapse ps
1632 return Fsum2Tuple(s, _NONFINITEr)
1633 n = len(ps)
1634# Fsum._ps_max = max(Fsum._ps_max, n)
1635 if n > 2:
1636 r = self._ps_1sum(s)
1637 return Fsum2Tuple(*_s_r(s, r))
1638 if n > 1: # len(ps) == 2
1639 s, r = _s_r(*_2sum(*ps, **self._isfine))
1640 ps[:] = (r, s) if r else (s,)
1641 elif ps: # len(ps) == 1
1642 s = ps[0]
1643 r = INT0 if _isfinite(s) else _NONFINITEr
1644 else: # len(ps) == 0
1645 s = _0_0
1646 r = INT0 if _isfinite(s) else _NONFINITEr
1647 ps[:] = s,
1648 except (OverflowError, ValueError) as X:
1649 op = _fset_op_ # INF, NAN, NINF
1650 ps[:] = sum(ps), # collapse ps
1651 s = self._nonfiniteX(X, op, ps[0])
1652 r = _NONFINITEr
1653 # assert self._ps is ps
1654 return Fsum2Tuple(s, r)
1656 @_fprs2.setter_ # PYCHOK setter_UNDERscore!
1657 def _fprs2(self, s_r):
1658 '''(INTERNAL) Replace the C{_fprs2} value.
1659 '''
1660 return Fsum2Tuple(s_r)
1662 def fset_(self, *xs):
1663 '''Apply C{B{self}.partials = Fsum(*B{xs}).partials}.
1665 @arg xs: Optional, new values (each C{scalar} or
1666 an L{Fsum} or L{Fsum2Tuple} instance), all
1667 positional.
1669 @return: This instance, replaced (C{Fsum}).
1671 @see: Method L{Fsum.fadd} for further details.
1672 '''
1673 f = (xs[0] if xs else _0_0) if len(xs) < 2 else \
1674 Fsum(*xs, nonfinites=self.nonfinites()) # self._Fsum_as(*xs)
1675 return self._fset(f, op=_fset_op_)
1677 def _fset(self, other, n=0, up=True, **op):
1678 '''(INTERNAL) Overwrite this instance with an other or a C{scalar}.
1679 '''
1680 if other is self:
1681 pass # from ._fmul, ._ftruediv and ._pow_0_1
1682 elif _isFsum_2Tuple(other):
1683 if op: # and not self.nonfinitesOK:
1684 self._finite(other._fprs, **op)
1685 self._ps[:] = other._ps
1686 self._n = n or other._n
1687 if up: # use or zap the C{Property_RO} values
1688 Fsum._fint2._update_from(self, other)
1689 Fsum._fprs ._update_from(self, other)
1690 Fsum._fprs2._update_from(self, other)
1691 elif isscalar(other):
1692 s = float(self._finite(other, **op)) if op else other
1693 self._ps[:] = s,
1694 self._n = n or 1
1695 if up: # Property _fint2, _fprs and _fprs2 all have
1696 # @.setter_underscore and NOT @.setter because the
1697 # latter's _fset zaps the value set by @.setter
1698 self._fint2 = s
1699 self._fprs = s
1700 self._fprs2 = s, INT0
1701 # assert self._fprs is s
1702 else:
1703 op = _xkwds_get1(op, op=_fset_op_)
1704 raise self._Error(op, other, _TypeError)
1705 return self
1707 def fsub(self, xs=()):
1708 '''Subtract an iterable's items from this instance.
1710 @see: Method L{Fsum.fadd} for further details.
1711 '''
1712 return self._facc_neg(xs)
1714 def fsub_(self, *xs):
1715 '''Subtract all positional items from this instance.
1717 @see: Method L{Fsum.fadd_} for further details.
1718 '''
1719 return self._fsub(xs[0], _sub_op_) if len(xs) == 1 else \
1720 self._facc_neg(xs) # origin=1?
1722 def _fsub(self, other, op):
1723 '''(INTERNAL) Apply C{B{self} -= B{other}}.
1724 '''
1725 if _isFsum_2Tuple(other):
1726 if other is self: # or other._fprs2 == self._fprs2:
1727 self._fset(_0_0, n=len(self) * 2)
1728 elif other._ps:
1729 self._facc_scalar(other._ps_neg)
1730 elif self._scalar(other, op):
1731 self._facc_scalar_(-other)
1732 return self
1734 def fsum(self, xs=()):
1735 '''Add an iterable's items, summate and return the current
1736 precision running sum.
1738 @arg xs: Iterable of items to add (each item C{scalar},
1739 an L{Fsum} or L{Fsum2Tuple}).
1741 @return: Precision running sum (C{float} or C{int}).
1743 @see: Method L{Fsum.fadd}.
1745 @note: Accumulation can continue after summation.
1746 '''
1747 return self._facc(xs)._fprs
1749 def fsum_(self, *xs):
1750 '''Add any positional items, summate and return the current
1751 precision running sum.
1753 @arg xs: Items to add (each C{scalar}, an L{Fsum} or
1754 L{Fsum2Tuple}), all positional.
1756 @return: Precision running sum (C{float} or C{int}).
1758 @see: Methods L{Fsum.fsum}, L{Fsum.Fsum_} and L{Fsum.fsumf_}.
1759 '''
1760 return self._facc_args(xs)._fprs
1762 def Fsum_(self, *xs, **name):
1763 '''Like method L{Fsum.fsum_} but returning a named L{Fsum}.
1765 @kwarg name: Optional name (C{str}).
1767 @return: Copy of this updated instance (L{Fsum}).
1768 '''
1769 return self._facc_args(xs)._copy_2(self.Fsum_, **name)
1771 def Fsum2Tuple_(self, *xs, **name):
1772 '''Like method L{Fsum.fsum_} but returning a named L{Fsum2Tuple}.
1774 @kwarg name: Optional name (C{str}).
1776 @return: Precision running sum (L{Fsum2Tuple}).
1777 '''
1778 return Fsum2Tuple(self._facc_args(xs)._nfprs2, **name)
1780 @property_RO
1781 def _Fsum(self): # like L{Fsum2Tuple._Fsum}, in .fstats
1782 return self # NOT @Property_RO, see .copy and ._copy_2
1784 def _Fsum_as(self, *xs, **name_f2product_nonfinites_RESIDUAL):
1785 '''(INTERNAL) Return an C{Fsum} with this C{Fsum}'s C{.f2product},
1786 C{.nonfinites} and C{.RESIDUAL} setting, optionally
1787 overridden with C{name_f2product_nonfinites_RESIDUAL} and
1788 with any C{xs} accumulated.
1789 '''
1790 kwds = _xkwds_not(None, Fsum._RESIDUAL, f2product =self.f2product(),
1791 nonfinites=self.nonfinites(),
1792 RESIDUAL =self.RESIDUAL())
1793 if name_f2product_nonfinites_RESIDUAL: # overwrites
1794 kwds.update(name_f2product_nonfinites_RESIDUAL)
1795 f = Fsum(**kwds)
1796 # assert all(v == self.__dict__[n] for n, v in f.__dict__.items())
1797 return f._fset(xs[0], op=_fset_op_) if len(xs) == 1 else (
1798 f._facc(xs, up=False) if xs else f)
1800 def fsum2(self, xs=(), **name):
1801 '''Add an iterable's items, summate and return the
1802 current precision running sum I{and} the C{residual}.
1804 @arg xs: Iterable of items to add (each item C{scalar},
1805 an L{Fsum} or L{Fsum2Tuple}).
1806 @kwarg name: Optional C{B{name}=NN} (C{str}).
1808 @return: L{Fsum2Tuple}C{(fsum, residual)} with C{fsum} the
1809 current precision running sum and C{residual}, the
1810 (precision) sum of the remaining C{partials}. The
1811 C{residual is INT0} if the C{fsum} is considered
1812 to be I{exact}.
1814 @see: Methods L{Fsum.fint2}, L{Fsum.fsum} and L{Fsum.fsum2_}
1815 '''
1816 t = self._facc(xs)._fprs2
1817 return t.dup(name=name) if name else t
1819 def fsum2_(self, *xs):
1820 '''Add any positional items, summate and return the current
1821 precision running sum and the I{differential}.
1823 @arg xs: Values to add (each C{scalar}, an L{Fsum} or
1824 L{Fsum2Tuple}), all positional.
1826 @return: 2Tuple C{(fsum, delta)} with the current, precision
1827 running C{fsum} like method L{Fsum.fsum} and C{delta},
1828 the difference with previous running C{fsum}, C{float}.
1830 @see: Methods L{Fsum.fsum_} and L{Fsum.fsum}.
1831 '''
1832 return self._fsum2(xs, self._facc_args)
1834 def _fsum2(self, xs, _facc, **facc_kwds):
1835 '''(INTERNAL) Helper for L{Fsum.fsum2_} and L{Fsum.fsum2f_}.
1836 '''
1837 p, q = self._fprs2
1838 if xs:
1839 s, r = _facc(xs, **facc_kwds)._fprs2
1840 if _isfinite(s): # _fsum(_1primed((s, -p, r, -q))
1841 d, r = _2sum(s - p, r - q, _isfine=_isOK)
1842 r, _ = _s_r(d, r)
1843 return s, (r if _isfinite(r) else _NONFINITEr)
1844 else:
1845 return p, _0_0
1847 def fsumf_(self, *xs):
1848 '''Like method L{Fsum.fsum_} iff I{all} C{B{xs}}, each I{known to be}
1849 C{scalar}, an L{Fsum} or L{Fsum2Tuple}.
1850 '''
1851 return self._facc_scalarf(xs, which=self.fsumf_)._fprs # origin=1?
1853 def Fsumf_(self, *xs):
1854 '''Like method L{Fsum.Fsum_} iff I{all} C{B{xs}}, each I{known to be}
1855 C{scalar}, an L{Fsum} or L{Fsum2Tuple}.
1856 '''
1857 return self._facc_scalarf(xs, which=self.Fsumf_)._copy_2(self.Fsumf_) # origin=1?
1859 def fsum2f_(self, *xs):
1860 '''Like method L{Fsum.fsum2_} iff I{all} C{B{xs}}, each I{known to be}
1861 C{scalar}, an L{Fsum} or L{Fsum2Tuple}.
1862 '''
1863 return self._fsum2(xs, self._facc_scalarf, which=self.fsum2f_) # origin=1?
1865# ftruediv = __itruediv__ # for naming consistency?
1867 def _ftruediv(self, other, op, **raiser_RESIDUAL):
1868 '''(INTERNAL) Apply C{B{self} /= B{other}}.
1869 '''
1870 n = _1_0
1871 if _isFsum_2Tuple(other):
1872 if other is self or self == other:
1873 return self._fset(n, n=len(self))
1874 d, r = other._fprs2
1875 if r:
1876 R = self._raiser(r, d, **raiser_RESIDUAL)
1877 if R:
1878 raise self._ResidualError(op, other, r, **R)
1879 d, n = other.as_integer_ratio()
1880 else:
1881 d = self._scalar(other, op)
1882 try:
1883 s = n / d
1884 except Exception as X:
1885 raise self._ErrorX(X, op, other)
1886 f = self._mul_scalar(s, _mul_op_) # handles 0, INF, NAN
1887 return self._fset(f)
1889 @property_RO
1890 def imag(self):
1891 '''Get the C{imaginary} part of this instance (C{0.0}, always).
1893 @see: Property L{Fsum.real}.
1894 '''
1895 return _0_0
1897 def int_float(self, **raiser_RESIDUAL):
1898 '''Return this instance' current running sum as C{int} or C{float}.
1900 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore
1901 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}
1902 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.
1904 @return: This C{int} sum if this instance C{is_integer} and
1905 I{finite}, otherwise the C{float} sum if the residual
1906 is zero or not significant.
1908 @raise ResidualError: Non-zero, significant residual or invalid
1909 B{C{RESIDUAL}}.
1911 @see: Methods L{Fsum.fint}, L{Fsum.fint2}, L{Fsum.is_integer},
1912 L{Fsum.RESIDUAL} and property L{Fsum.as_iscalar}.
1913 '''
1914 s, r = self._fint2
1915 if r:
1916 s, r = self._fprs2
1917 if r: # PYCHOK no cover
1918 R = self._raiser(r, s, **raiser_RESIDUAL)
1919 if R:
1920 t = _stresidual(_non_zero_, r, **R)
1921 raise ResidualError(int_float=s, txt=t)
1922 s = float(s)
1923 return s
1925 def is_exact(self):
1926 '''Is this instance' running C{fsum} considered to be exact?
1927 (C{bool}), C{True} only if the C{residual is }L{INT0}.
1928 '''
1929 return self.residual is INT0
1931 def is_finite(self): # in .constants
1932 '''Is this instance C{finite}? (C{bool}).
1934 @see: Function L{isfinite<pygeodesy.isfinite>}.
1935 '''
1936 return _isfinite(sum(self._ps)) # == sum(self)
1938 def is_integer(self):
1939 '''Is this instance' running sum C{integer}? (C{bool}).
1941 @see: Methods L{Fsum.fint}, L{Fsum.fint2} and L{Fsum.is_scalar}.
1942 '''
1943 s, r = self._fint2
1944 return False if r else (_isfinite(s) and isint(s))
1946 def is_math_fma(self):
1947 '''Is accurate L{f2product} multiplication based on Python's C{math.fma}?
1949 @return: C{True} if accurate multiplication uses C{math.fma}, C{False}
1950 an C{fma} implementation as C{math.fma} or C{None}, a previous
1951 C{PyGeodesy} implementation.
1952 '''
1953 return (_2split3s is _passarg) or (False if _2n_d is None else None)
1955 def is_math_fsum(self):
1956 '''Are the summation functions L{fsum}, L{fsum_}, L{fsumf_}, L{fsum1},
1957 L{fsum1_} and L{fsum1f_} based on Python's C{math.fsum}?
1959 @return: C{True} if summation functions use C{math.fsum}, C{False}
1960 otherwise.
1961 '''
1962 return _sum is _fsum # _fsum.__module__ is fabs.__module__
1964 def is_scalar(self, **raiser_RESIDUAL):
1965 '''Is this instance' running sum C{scalar} with C{0} residual or with
1966 a residual I{ratio} not exceeding the RESIDUAL threshold?
1968 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore
1969 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}
1970 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.
1972 @return: C{True} if this instance' residual is C{0} or C{insignificant},
1973 i.e. its residual C{ratio} doesn't exceed the L{RESIDUAL
1974 <Fsum.RESIDUAL>} threshold (C{bool}).
1976 @raise ResidualError: Non-zero, significant residual or invalid
1977 B{C{RESIDUAL}}.
1979 @see: Methods L{Fsum.RESIDUAL} and L{Fsum.is_integer} and property
1980 L{Fsum.as_iscalar}.
1981 '''
1982 s, r = self._fprs2
1983 return False if r and self._raiser(r, s, **raiser_RESIDUAL) else True
1985 def _mul_Fsum(self, other, op):
1986 '''(INTERNAL) Return C{B{self} * B{other}} as L{Fsum} or C{0}.
1987 '''
1988 # assert _isFsum_2Tuple(other)
1989 if self._ps and other._ps:
1990 try:
1991 f = self._ps_mul(op, *other._ps) # NO .as_iscalar!
1992 except Exception as X:
1993 raise self._ErrorX(X, op, other)
1994 else:
1995 f = _0_0
1996 return f
1998 def _mul_reduce(self, *others):
1999 '''(INTERNAL) Like fmath.fprod for I{non-finite} C{other}s.
2000 '''
2001 r = _1_0
2002 for f in others:
2003 r *= sum(f._ps) if _isFsum_2Tuple(f) else float(f)
2004 return r
2006 def _mul_scalar(self, factor, op):
2007 '''(INTERNAL) Return C{B{self} * scalar B{factor}} as L{Fsum}, C{0.0} or C{self}.
2008 '''
2009 # assert isscalar(factor)
2010 if self._ps and self._finite(factor, op=op):
2011 f = self if factor == _1_0 else (
2012 self._neg if factor == _N_1_0 else
2013 self._ps_mul(op, factor).as_iscalar)
2014 else:
2015 f = _0_0
2016 return f
2018# @property_RO
2019# def _n_d(self):
2020# n, d = self.as_integer_ratio()
2021# return n / d
2023 @property_RO
2024 def _neg(self):
2025 '''(INTERNAL) Return C{Fsum(-self)} or scalar C{NEG0}.
2026 '''
2027 return _Psum(self._ps_neg) if self._ps else NEG0
2029 @property_RO
2030 def _nfprs2(self):
2031 '''(INTERNAL) Handle I{non-finite} C{_fprs2}.
2032 '''
2033 try: # to handle nonfiniterrors, etc.
2034 t = self._fprs2
2035 except (OverflowError, ValueError):
2036 t = Fsum2Tuple(sum(self._ps), _NONFINITEr)
2037 return t
2039 def nonfinites(self, *OK):
2040 '''Handle I{non-finite} C{float}s as C{inf}, C{INF}, C{NINF}, C{nan}
2041 and C{NAN} for this L{Fsum} or throw C{OverflowError} respectively
2042 C{ValueError} exceptions, overriding the L{nonfiniterrors} default.
2044 @arg OK: If omitted, leave the override unchanged, if C{True},
2045 I{non-finites} are C{OK}, if C{False} throw exceptions
2046 or if C{None} remove the override (C{bool} or C{None}).
2048 @return: The previous setting (C{bool} or C{None} if not set).
2050 @see: Function L{nonfiniterrors<fsums.nonfiniterrors>}.
2052 @note: Use property L{nonfinitesOK<Fsum.nonfinitesOK>} to determine
2053 whether I{non-finites} are C{OK} for this L{Fsum} and by the
2054 L{nonfiniterrors} default.
2055 '''
2056 _ks = Fsum._nonfinites_isfine_kwds
2057 if OK: # delattrof(self, _isfine=None)
2058 k = _xkwds_pop(self.__dict__, _isfine=None)
2059 if OK[0] is not None:
2060 self._isfine = _ks[bool(OK[0])]
2061 self._update()
2062 else: # getattrof(self, _isfine=None)
2063 k = _xkwds_get(self.__dict__, _isfine=None)
2064 # dict(map(reversed, _ks.items())).get(k, None)
2065 # raises a TypeError: unhashable type: 'dict'
2066 return True if k is _ks[True] else (
2067 False if k is _ks[False] else None)
2069 _nonfinites_isfine_kwds = {True: dict(_isfine=_isOK),
2070 False: dict(_isfine=_isfinite)}
2072 @property_RO
2073 def nonfinitesOK(self):
2074 '''Are I{non-finites} C{OK} for this L{Fsum} or by default? (C{bool}).
2075 '''
2076# nf = self.nonfinites()
2077# if nf is None:
2078# nf = not nonfiniterrors()
2079 return _isOK_or_finite(INF, **self._isfine)
2081 def _nonfiniteX(self, X, op, f, nonfinites=None, raiser=None):
2082 '''(INTERNAL) Handle a I{non-finite} exception.
2083 '''
2084 if nonfinites is None:
2085 nonfinites = _isOK_or_finite(f, **self._isfine) if raiser is None else (not raiser)
2086 if not nonfinites:
2087 raise self._ErrorX(X, op, f)
2088 return f
2090 def _optionals(self, f2product=None, nonfinites=None, **name_RESIDUAL):
2091 '''(INTERNAL) Re/set options from keyword arguments.
2092 '''
2093 if f2product is not None:
2094 self.f2product(f2product)
2095 if nonfinites is not None:
2096 self.nonfinites(nonfinites)
2097 if name_RESIDUAL: # MUST be last
2098 n, kwds = _name2__(**name_RESIDUAL)
2099 if kwds:
2100 R = Fsum._RESIDUAL
2101 t = _threshold(R, **kwds)
2102 if t != R:
2103 self._RESIDUAL = t
2104 if n:
2105 self.name = n # self.rename(n)
2107 def _1_Over(self, x, op, **raiser_RESIDUAL): # vs _1_over
2108 '''(INTERNAL) Return C{Fsum(1) / B{x}}.
2109 '''
2110 return self._Fsum_as(_1_0)._ftruediv(x, op, **raiser_RESIDUAL)
2112 @property_RO
2113 def partials(self):
2114 '''Get this instance' current, partial sums (C{tuple} of C{float}s).
2115 '''
2116 return tuple(self._ps)
2118 def pow(self, x, *mod, **raiser_RESIDUAL):
2119 '''Return C{B{self}**B{x}} as L{Fsum}.
2121 @arg x: The exponent (C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
2122 @arg mod: Optional modulus (C{int} or C{None}) for the 3-argument
2123 C{pow(B{self}, B{other}, B{mod})} version.
2124 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore
2125 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}
2126 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.
2128 @return: The C{pow(self, B{x})} or C{pow(self, B{x}, *B{mod})}
2129 result (L{Fsum}).
2131 @raise ResidualError: Non-zero, significant residual or invalid
2132 B{C{RESIDUAL}}.
2134 @note: If B{C{mod}} is given and C{None}, the result will be an
2135 C{integer} L{Fsum} provided this instance C{is_integer}
2136 or set to C{integer} by an L{Fsum.fint} call.
2138 @see: Methods L{Fsum.__ipow__}, L{Fsum.fint}, L{Fsum.is_integer}
2139 and L{Fsum.root}.
2140 '''
2141 f = self._copy_2(self.pow)
2142 return f._fpow(x, _pow_op_, *mod, **raiser_RESIDUAL) # f = pow(f, x, *mod)
2144 def _pow(self, other, unused, op, **raiser_RESIDUAL):
2145 '''Return C{B{self} ** B{other}}.
2146 '''
2147 if _isFsum_2Tuple(other):
2148 f = self._pow_Fsum(other, op, **raiser_RESIDUAL)
2149 elif self._scalar(other, op):
2150 x = self._finite(other, op=op)
2151 f = self._pow_scalar(x, other, op, **raiser_RESIDUAL)
2152 else:
2153 f = self._pow_0_1(0, other)
2154 return f
2156 def _pow_0_1(self, x, other):
2157 '''(INTERNAL) Return B{C{self}**1} or C{B{self}**0 == 1.0}.
2158 '''
2159 return self if x else (1 if isint(other) and self.is_integer() else _1_0)
2161 def _pow_2_3(self, b, x, other, op, *mod, **raiser_RESIDUAL):
2162 '''(INTERNAL) 2-arg C{pow(B{b}, scalar B{x})} and 3-arg C{pow(B{b},
2163 B{x}, int B{mod} or C{None})}, embellishing errors.
2164 '''
2166 if mod: # b, x, mod all C{int}, unless C{mod} is C{None}
2167 m = mod[0]
2168 # assert _isFsum_2Tuple(b)
2170 def _s(s, r):
2171 R = self._raiser(r, s, **raiser_RESIDUAL)
2172 if R:
2173 raise self._ResidualError(op, other, r, mod=m, **R)
2174 return s
2176 b = _s(*(b._fprs2 if m is None else b._fint2))
2177 x = _s(*_2s_r(x))
2179 try:
2180 # 0**INF == 0.0, 1**INF == 1.0, -1**2.3 == -(1**2.3)
2181 s = pow(b, x, *mod)
2182 if iscomplex(s):
2183 # neg**frac == complex in Python 3+, but ValueError in 2-
2184 raise ValueError(_strcomplex(s, b, x, *mod))
2185 _ = _2finite(s, **self._isfine) # ignore float
2186 return s
2187 except Exception as X:
2188 raise self._ErrorX(X, op, other, *mod)
2190 def _pow_Fsum(self, other, op, **raiser_RESIDUAL):
2191 '''(INTERNAL) Return C{B{self} **= B{other}} for C{_isFsum_2Tuple(other)}.
2192 '''
2193 # assert _isFsum_2Tuple(other)
2194 x, r = other._fprs2
2195 f = self._pow_scalar(x, other, op, **raiser_RESIDUAL)
2196 if f and r:
2197 f *= self._pow_scalar(r, other, op, **raiser_RESIDUAL)
2198 return f
2200 def _pow_int(self, x, other, op, **raiser_RESIDUAL):
2201 '''(INTERNAL) Return C{B{self} **= B{x}} for C{int B{x} >= 0}.
2202 '''
2203 # assert isint(x) and x >= 0
2204 ps = self._ps
2205 if len(ps) > 1:
2206 _mul_Fsum = Fsum._mul_Fsum
2207 if x > 4:
2208 p = self
2209 f = self if (x & 1) else self._Fsum_as(_1_0)
2210 m = x >> 1 # // 2
2211 while m:
2212 p = _mul_Fsum(p, p, op) # p **= 2
2213 if (m & 1):
2214 f = _mul_Fsum(f, p, op) # f *= p
2215 m >>= 1 # //= 2
2216 elif x > 1: # self**2, 3, or 4
2217 f = _mul_Fsum(self, self, op)
2218 if x > 2: # self**3 or 4
2219 p = self if x < 4 else f
2220 f = _mul_Fsum(f, p, op)
2221 else: # self**1 or self**0 == 1 or _1_0
2222 f = self._pow_0_1(x, other)
2223 elif ps: # self._ps[0]**x
2224 f = self._pow_2_3(ps[0], x, other, op, **raiser_RESIDUAL)
2225 else: # PYCHOK no cover
2226 # 0**pos_int == 0, but 0**0 == 1
2227 f = 0 if x else 1
2228 return f
2230 def _pow_scalar(self, x, other, op, **raiser_RESIDUAL):
2231 '''(INTERNAL) Return C{self**B{x}} for C{scalar B{x}}.
2232 '''
2233 s, r = self._fprs2
2234 if r:
2235 # assert s != 0
2236 if isint(x, both=True): # self**int
2237 x = int(x)
2238 y = abs(x)
2239 if y > 1:
2240 f = self._pow_int(y, other, op, **raiser_RESIDUAL)
2241 if x > 0: # i.e. > 1
2242 return f # Fsum or scalar
2243 # assert x < 0 # i.e. < -1
2244 if _isFsum(f):
2245 s, r = f._fprs2
2246 if r:
2247 return self._1_Over(f, op, **raiser_RESIDUAL)
2248 else: # scalar
2249 s = f
2250 # use s**(-1) to get the CPython
2251 # float_pow error iff s is zero
2252 x = -1
2253 elif x < 0: # self**(-1)
2254 return self._1_Over(self, op, **raiser_RESIDUAL) # 1 / self
2255 else: # self**1 or self**0
2256 return self._pow_0_1(x, other) # self, 1 or 1.0
2257 else: # self**fractional
2258 R = self._raiser(r, s, **raiser_RESIDUAL)
2259 if R:
2260 raise self._ResidualError(op, other, r, **R)
2261 n, d = self.as_integer_ratio()
2262 if abs(n) > abs(d):
2263 n, d, x = d, n, (-x)
2264 s = n / d
2265 # assert isscalar(s) and isscalar(x)
2266 return self._pow_2_3(s, x, other, op, **raiser_RESIDUAL)
2268 def _ps_acc(self, ps, xs, up=True, **unused):
2269 '''(INTERNAL) Accumulate C{xs} known scalars into list C{ps}.
2270 '''
2271 n = 0
2272 _2s = _2sum
2273 _fi = self._isfine
2274 for x in (tuple(xs) if xs is ps else xs):
2275 # assert isscalar(x) and _isOK_or_finite(x, **self._isfine)
2276 if x:
2277 i = 0
2278 for p in ps:
2279 x, p = _2s(x, p, **_fi)
2280 if p:
2281 ps[i] = p
2282 i += 1
2283 ps[i:] = (x,) if x else ()
2284 n += 1
2285 if n:
2286 self._n += n
2287 # Fsum._ps_max = max(Fsum._ps_max, len(ps))
2288 if up:
2289 self._update()
2290# x = sum(ps)
2291# if not _isOK_or_finite(x, **fi):
2292# ps[:] = x, # collapse ps
2293 return ps
2295 def _ps_mul(self, op, *factors):
2296 '''(INTERNAL) Multiply this instance' C{partials} with
2297 each scalar C{factor} and accumulate into an C{Fsum}.
2298 '''
2299 def _psfs(ps, fs, _isfine=_isfinite):
2300 if len(ps) < len(fs):
2301 ps, fs = fs, ps
2302 if self._f2product:
2303 fs, p = _2split3s(fs), fs
2304 if len(ps) > 1 and fs is not p:
2305 fs = tuple(fs) # several ps
2306 _pfs = _2products
2307 else:
2308 def _pfs(p, fs):
2309 return (p * f for f in fs)
2311 for p in ps:
2312 for f in _pfs(p, fs):
2313 yield f if _isfine(f) else _nfError(f)
2315 fs = _psfs(self._ps, factors, **self._isfine)
2316 f = _Psum(self._ps_acc([], fs, up=False), name=op)
2317 return f
2319 @property_RO
2320 def _ps_neg(self):
2321 '''(INTERNAL) Yield the partials, I{negated}.
2322 '''
2323 for p in self._ps:
2324 yield -p
2326 def _ps_other(self, op, other):
2327 '''(INTERNAL) Yield C{other} as C{scalar}s.
2328 '''
2329 if _isFsum_2Tuple(other):
2330 for p in other._ps:
2331 yield p
2332 else:
2333 yield self._scalar(other, op)
2335 def _ps_1sum(self, *less):
2336 '''(INTERNAL) Return the partials sum, 1-primed C{less} some scalars.
2337 '''
2338 def _1psls(ps, ls):
2339 yield _1_0
2340 for p in ps:
2341 yield p
2342 for p in ls:
2343 yield -p
2344 yield _N_1_0
2346 return _fsum(_1psls(self._ps, less))
2348 def _raiser(self, r, s, raiser=True, **RESIDUAL):
2349 '''(INTERNAL) Does ratio C{r / s} exceed the RESIDUAL threshold
2350 I{and} is residual C{r} I{non-zero} or I{significant} (for a
2351 negative respectively positive C{RESIDUAL} threshold)?
2352 '''
2353 if r and raiser:
2354 t = self._RESIDUAL
2355 if RESIDUAL:
2356 t = _threshold(t, **RESIDUAL)
2357 if t < 0 or (s + r) != s:
2358 q = (r / s) if s else s # == 0.
2359 if fabs(q) > fabs(t):
2360 return dict(ratio=q, R=t)
2361 return {}
2363 rdiv = __rtruediv__
2365 @property_RO
2366 def real(self):
2367 '''Get the C{real} part of this instance (C{float}).
2369 @see: Methods L{Fsum.__float__} and L{Fsum.fsum}
2370 and properties L{Fsum.ceil}, L{Fsum.floor},
2371 L{Fsum.imag} and L{Fsum.residual}.
2372 '''
2373 return float(self)
2375 @property_RO
2376 def residual(self):
2377 '''Get this instance' residual or residue (C{float} or C{int}):
2378 the C{sum(partials)} less the precision running sum C{fsum}.
2380 @note: The C{residual is INT0} iff the precision running
2381 C{fsum} is considered to be I{exact}.
2383 @see: Methods L{Fsum.fsum}, L{Fsum.fsum2} and L{Fsum.is_exact}.
2384 '''
2385 return self._fprs2.residual
2387 def RESIDUAL(self, *threshold):
2388 '''Get and set this instance' I{ratio} for raising L{ResidualError}s,
2389 overriding the default from env variable C{PYGEODESY_FSUM_RESIDUAL}.
2391 @arg threshold: If C{scalar}, the I{ratio} to exceed for raising
2392 L{ResidualError}s in division and exponention, if
2393 C{None}, restore the default set with env variable
2394 C{PYGEODESY_FSUM_RESIDUAL} or if omitted, keep the
2395 current setting.
2397 @return: The previous C{RESIDUAL} setting (C{float}), default C{0.0}.
2399 @raise ResidualError: Invalid B{C{threshold}}.
2401 @note: L{ResidualError}s may be thrown if (1) the non-zero I{ratio}
2402 C{residual / fsum} exceeds the given B{C{threshold}} and (2)
2403 the C{residual} is non-zero and (3) is I{significant} vs the
2404 C{fsum}, i.e. C{(fsum + residual) != fsum} and (4) optional
2405 keyword argument C{raiser=False} is missing. Specify a
2406 negative B{C{threshold}} for only non-zero C{residual}
2407 testing without the I{significant} case.
2408 '''
2409 r = self._RESIDUAL
2410 if threshold:
2411 t = threshold[0]
2412 self._RESIDUAL = Fsum._RESIDUAL if t is None else ( # for ...
2413 (_0_0 if t else _1_0) if isbool(t) else
2414 _threshold(t)) # ... backward compatibility
2415 return r
2417 def _ResidualError(self, op, other, residual, **mod_R):
2418 '''(INTERNAL) Non-zero B{C{residual}} etc.
2419 '''
2420 def _p(mod=None, R=0, **unused): # ratio=0
2421 return (_non_zero_ if R < 0 else _significant_) \
2422 if mod is None else _integer_
2424 t = _stresidual(_p(**mod_R), residual, **mod_R)
2425 return self._Error(op, other, ResidualError, txt=t)
2427 def root(self, root, **raiser_RESIDUAL):
2428 '''Return C{B{self}**(1 / B{root})} as L{Fsum}.
2430 @arg root: Non-zero order (C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
2431 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore any
2432 L{ResidualError}s (C{bool}) or C{B{RESIDUAL}=scalar}
2433 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.
2435 @return: The C{self ** (1 / B{root})} result (L{Fsum}).
2437 @raise ResidualError: Non-zero, significant residual or invalid
2438 B{C{RESIDUAL}}.
2440 @see: Method L{Fsum.pow}.
2441 '''
2442 x = self._1_Over(root, _truediv_op_, **raiser_RESIDUAL)
2443 f = self._copy_2(self.root)
2444 return f._fpow(x, f.name, **raiser_RESIDUAL) # == pow(f, x)
2446 def _scalar(self, other, op, **txt):
2447 '''(INTERNAL) Return scalar C{other} or throw a C{TypeError}.
2448 '''
2449 if isscalar(other):
2450 return other
2451 raise self._Error(op, other, _TypeError, **txt) # _invalid_
2453 def signOf(self, res=True):
2454 '''Determine the sign of this instance.
2456 @kwarg res: If C{True}, consider the residual,
2457 otherwise ignore the latter (C{bool}).
2459 @return: The sign (C{int}, -1, 0 or +1).
2460 '''
2461 s, r = self._nfprs2
2462 r = (-r) if res else 0
2463 return _signOf(s, r)
2465 def toRepr(self, **lenc_prec_sep_fmt): # PYCHOK signature
2466 '''Return this C{Fsum} instance as representation.
2468 @kwarg lenc_prec_sep_fmt: Optional keyword arguments
2469 for method L{Fsum.toStr}.
2471 @return: This instance (C{repr}).
2472 '''
2473 return Fmt.repr_at(self, self.toStr(**lenc_prec_sep_fmt))
2475 def toStr(self, lenc=True, **prec_sep_fmt): # PYCHOK signature
2476 '''Return this C{Fsum} instance as string.
2478 @kwarg lenc: If C{True}, include the current C{[len]} of this
2479 L{Fsum} enclosed in I{[brackets]} (C{bool}).
2480 @kwarg prec_sep_fmt: Optional keyword arguments for method
2481 L{Fsum2Tuple.toStr}.
2483 @return: This instance (C{str}).
2484 '''
2485 p = self.classname
2486 if lenc:
2487 p = Fmt.SQUARE(p, len(self))
2488 n = _enquote(self.name, white=_UNDER_)
2489 t = self._nfprs2.toStr(**prec_sep_fmt)
2490 return NN(p, _SPACE_, n, t)
2492 def _truediv(self, other, op, **raiser_RESIDUAL):
2493 '''(INTERNAL) Return C{B{self} / B{other}} as an L{Fsum}.
2494 '''
2495 f = self._copy_2(self.__truediv__)
2496 return f._ftruediv(other, op, **raiser_RESIDUAL)
2498 def _update(self, updated=True): # see ._fset
2499 '''(INTERNAL) Zap all cached C{Property_RO} values.
2500 '''
2501 if updated:
2502 _pop = self.__dict__.pop
2503 for p in _ROs:
2504 _ = _pop(p, None)
2505# Fsum._fint2._update(self)
2506# Fsum._fprs ._update(self)
2507# Fsum._fprs2._update(self)
2508 return self # for .fset_
2510_ROs = _allPropertiesOf_n(3, Fsum, Property_RO) # PYCHOK see Fsum._update
2512if _NONFINITES == _std_: # PYCHOK no cover
2513 _ = nonfiniterrors(False)
2516def _Float_Int(arg, **name_Error):
2517 '''(INTERNAL) L{DivMod2Tuple}, L{Fsum2Tuple} Unit.
2518 '''
2519 U = Int if isint(arg) else Float
2520 return U(arg, **name_Error)
2523class DivMod2Tuple(_NamedTuple):
2524 '''2-Tuple C{(div, mod)} with the quotient C{div} and remainder
2525 C{mod} results of a C{divmod} operation.
2527 @note: Quotient C{div} an C{int} in Python 3+ but a C{float}
2528 in Python 2-. Remainder C{mod} an L{Fsum} instance.
2529 '''
2530 _Names_ = ('div', 'mod')
2531 _Units_ = (_Float_Int, Fsum)
2534class Fsum2Tuple(_NamedTuple): # in .fstats
2535 '''2-Tuple C{(fsum, residual)} with the precision running C{fsum}
2536 and the C{residual}, the sum of the remaining partials. Each
2537 item is C{float} or C{int}.
2539 @note: If the C{residual is INT0}, the C{fsum} is considered
2540 to be I{exact}, see method L{Fsum2Tuple.is_exact}.
2541 '''
2542 _Names_ = ( Fsum.fsum.__name__, Fsum.residual.name)
2543 _Units_ = (_Float_Int, _Float_Int)
2545 def __abs__(self): # in .fmath
2546 return self._Fsum.__abs__()
2548 def __bool__(self): # PYCHOK Python 3+
2549 return bool(self._Fsum)
2551 def __eq__(self, other):
2552 return self._other_op(other, self.__eq__)
2554 def __float__(self):
2555 return self._Fsum.__float__()
2557 def __ge__(self, other):
2558 return self._other_op(other, self.__ge__)
2560 def __gt__(self, other):
2561 return self._other_op(other, self.__gt__)
2563 def __le__(self, other):
2564 return self._other_op(other, self.__le__)
2566 def __lt__(self, other):
2567 return self._other_op(other, self.__lt__)
2569 def __int__(self):
2570 return self._Fsum.__int__()
2572 def __ne__(self, other):
2573 return self._other_op(other, self.__ne__)
2575 def __neg__(self):
2576 return self._Fsum.__neg__()
2578 __nonzero__ = __bool__ # Python 2-
2580 def __pos__(self):
2581 return self._Fsum.__pos__()
2583 def as_integer_ratio(self):
2584 '''Return this instance as the ratio of 2 integers.
2586 @see: Method L{Fsum.as_integer_ratio} for further details.
2587 '''
2588 return self._Fsum.as_integer_ratio()
2590 @property_RO
2591 def _fint2(self):
2592 return self._Fsum._fint2
2594 @property_RO
2595 def _fprs2(self):
2596 return self._Fsum._fprs2
2598 @Property_RO
2599 def _Fsum(self): # this C{Fsum2Tuple} as L{Fsum}, in .fstats
2600 s, r = _s_r(*self)
2601 ps = (r, s) if r else (s,)
2602 return _Psum(ps, name=self.name)
2604 def Fsum_(self, *xs, **name_f2product_nonfinites_RESIDUAL):
2605 '''Return this C{Fsum2Tuple} as an L{Fsum} plus some C{xs}.
2606 '''
2607 return Fsum(self, *xs, **name_f2product_nonfinites_RESIDUAL)
2609 def is_exact(self):
2610 '''Is this L{Fsum2Tuple} considered to be exact? (C{bool}).
2611 '''
2612 return self._Fsum.is_exact()
2614 def is_finite(self): # in .constants
2615 '''Is this L{Fsum2Tuple} C{finite}? (C{bool}).
2617 @see: Function L{isfinite<pygeodesy.isfinite>}.
2618 '''
2619 return self._Fsum.is_finite()
2621 def is_integer(self):
2622 '''Is this L{Fsum2Tuple} C{integer}? (C{bool}).
2623 '''
2624 return self._Fsum.is_integer()
2626 def _mul_scalar(self, other, op): # for Fsum._fmul
2627 return self._Fsum._mul_scalar(other, op)
2629 @property_RO
2630 def _n(self):
2631 return self._Fsum._n
2633 def _other_op(self, other, which):
2634 C, s = (tuple, self) if isinstance(other, tuple) else (Fsum, self._Fsum)
2635 return getattr(C, which.__name__)(s, other)
2637 @property_RO
2638 def _ps(self):
2639 return self._Fsum._ps
2641 @property_RO
2642 def _ps_neg(self):
2643 return self._Fsum._ps_neg
2645 def signOf(self, **res):
2646 '''Like method L{Fsum.signOf}.
2647 '''
2648 return self._Fsum.signOf(**res)
2650 def toStr(self, fmt=Fmt.g, **prec_sep): # PYCHOK signature
2651 '''Return this L{Fsum2Tuple} as string (C{str}).
2653 @kwarg fmt: Optional C{float} format (C{letter}).
2654 @kwarg prec_sep: Optional keyword arguments for function
2655 L{fstr<streprs.fstr>}.
2656 '''
2657 return Fmt.PAREN(fstr(self, fmt=fmt, strepr=str, force=False, **prec_sep))
2659_Fsum_2Tuple_types = Fsum, Fsum2Tuple # PYCHOK lines
2662class ResidualError(_ValueError):
2663 '''Error raised for a division, power or root operation of
2664 an L{Fsum} instance with a C{residual} I{ratio} exceeding
2665 the L{RESIDUAL<Fsum.RESIDUAL>} threshold.
2667 @see: Module L{pygeodesy.fsums} and method L{Fsum.RESIDUAL}.
2668 '''
2669 pass
2672try:
2673 from math import fsum as _fsum # precision IEEE-754 sum, Python 2.6+
2675 # make sure _fsum works as expected (XXX check
2676 # float.__getformat__('float')[:4] == 'IEEE'?)
2677 if _fsum((1, 1e101, 1, -1e101)) != 2: # PYCHOK no cover
2678 del _fsum # nope, remove _fsum ...
2679 raise ImportError() # ... use _fsum below
2681 _sum = _fsum # in .elliptic
2682except ImportError:
2683 _sum = sum # in .elliptic
2685 def _fsum(xs):
2686 '''(INTERNAL) Precision summation, Python 2.5-.
2687 '''
2688 F = Fsum(name=_fsum.name, f2product=False, nonfinites=True)
2689 return float(F._facc(xs, up=False))
2692def fsum(xs, nonfinites=None, **floats):
2693 '''Precision floating point summation from Python's C{math.fsum}.
2695 @arg xs: Iterable of items to add (each C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
2696 @kwarg nonfinites: Use C{B{nonfinites}=True} if I{non-finites} are C{OK}, if
2697 C{False} I{non-finites} raise an Overflow-/ValueError or if
2698 C{None}, L{nonfiniterrors} applies (C{bool} or C{None}).
2699 @kwarg floats: DEPRECATED keyword argument C{B{floats}=False} (C{bool}), use
2700 keyword argument C{B{nonfinites}=False} instead.
2702 @return: Precision C{fsum} (C{float}).
2704 @raise OverflowError: Infinite B{C{xs}} item or intermediate C{math.fsum} overflow.
2706 @raise TypeError: Invalid B{C{xs}} item.
2708 @raise ValueError: Invalid or C{NAN} B{C{xs}} item.
2710 @see: Function L{nonfiniterrors}, class L{Fsum} and methods L{Fsum.nonfinites},
2711 L{Fsum.fsum}, L{Fsum.fadd} and L{Fsum.fadd_}.
2712 '''
2713 return _xsum(fsum, xs, nonfinites=nonfinites, **floats) if xs else _0_0
2716def fsum_(*xs, **nonfinites):
2717 '''Precision floating point summation of all positional items.
2719 @arg xs: Items to add (each C{scalar}, an L{Fsum} or L{Fsum2Tuple}), all positional.
2720 @kwarg nonfinites: Use C{B{nonfinites}=True} if I{non-finites} are C{OK} (C{bool}).
2722 @see: Function L{fsum<fsums.fsum>} for further details.
2723 '''
2724 return _xsum(fsum_, xs, **nonfinites) if xs else _0_0 # origin=1?
2727def fsumf_(*xs):
2728 '''Precision floating point summation of all positional items with I{non-finites} C{OK}.
2730 @arg xs: Items to add (each C{scalar}, an L{Fsum} or L{Fsum2Tuple}),
2731 all positional.
2733 @see: Function L{fsum_<fsums.fsum_>} for further details.
2734 '''
2735 return _xsum(fsumf_, xs, nonfinites=True) if xs else _0_0 # origin=1?
2738def fsum1(xs, **nonfinites):
2739 '''Precision floating point summation, 1-primed.
2741 @arg xs: Iterable of items to add (each C{scalar}, an L{Fsum} or L{Fsum2Tuple}).
2742 @kwarg nonfinites: Use C{B{nonfinites}=True} if I{non-finites} are C{OK} (C{bool}).
2744 @see: Function L{fsum<fsums.fsum>} for further details.
2745 '''
2746 return _xsum(fsum1, xs, primed=1, **nonfinites) if xs else _0_0
2749def fsum1_(*xs, **nonfinites):
2750 '''Precision floating point summation of all positional items, 1-primed.
2752 @arg xs: Items to add (each C{scalar}, an L{Fsum} or L{Fsum2Tuple}), all positional.
2753 @kwarg nonfinites: Use C{B{nonfinites}=True} if I{non-finites} are C{OK} (C{bool}).
2755 @see: Function L{fsum_<fsums.fsum_>} for further details.
2756 '''
2757 return _xsum(fsum1_, xs, primed=1, **nonfinites) if xs else _0_0 # origin=1?
2760def fsum1f_(*xs):
2761 '''Precision floating point summation of all positional items, 1-primed and
2762 with I{non-finites} C{OK}.
2764 @see: Function L{fsum_<fsums.fsum_>} for further details.
2765 '''
2766 return _xsum(fsum1f_, xs, nonfinites=True, primed=1) if xs else _0_0
2769def _x_isfine(nfOK, **kwds): # get the C{_x} and C{_isfine} handlers.
2770 _x_kwds = dict(_x= (_passarg if nfOK else _2finite),
2771 _isfine=(_isOK if nfOK else _isfinite)) # PYCHOK kwds
2772 _x_kwds.update(kwds)
2773 return _x_kwds
2776def _X_ps(X): # default C{_X} handler
2777 return X._ps # lambda X: X._ps
2780def _xs(xs, _X=_X_ps, _x=float, _isfine=_isfinite, # defaults for Fsum._facc
2781 origin=0, which=None, **_Cdot):
2782 '''(INTERNAL) Yield each C{xs} item as 1 or more C{float}s.
2783 '''
2784 i, x = 0, xs
2785 try:
2786 for i, x in enumerate(_xiterable(xs)):
2787 if isinstance(x, _Fsum_2Tuple_types):
2788 for p in _X(x):
2789 yield p if _isfine(p) else _nfError(p)
2790 else:
2791 f = _x(x)
2792 yield f if _isfine(f) else _nfError(f)
2794 except (OverflowError, TypeError, ValueError) as X:
2795 t = _xsError(X, xs, i + origin, x)
2796 if which: # prefix invokation
2797 w = unstr(which, *xs, _ELLIPSIS=4, **_Cdot)
2798 t = _COMMASPACE_(w, t)
2799 raise _xError(X, t, txt=None)
2802def _xsum(which, xs, nonfinites=None, primed=0, **floats): # origin=0
2803 '''(INTERNAL) Precision summation of C{xs} with conditions.
2804 '''
2805 if floats: # for backward compatibility
2806 nonfinites = _xkwds_get1(floats, floats=nonfinites)
2807 elif nonfinites is None:
2808 nonfinites = not nonfiniterrors()
2809 fs = _xs(xs, **_x_isfine(nonfinites, which=which))
2810 return _fsum(_1primed(fs) if primed else fs)
2813# delete all decorators, etc.
2814del _allPropertiesOf_n, deprecated_method, deprecated_property_RO, \
2815 Property, Property_RO, property_RO, _ALL_LAZY, _F2PRODUCT, \
2816 MANT_DIG, _NONFINITES, _RESIDUAL_0_0, _getPYGEODESY, _std_
2818if __name__ == '__main__':
2820 # usage: python3 -m pygeodesy.fsums
2822 def _test(n):
2823 # copied from Hettinger, see L{Fsum} reference
2824 from pygeodesy import frandoms, printf
2826 printf(_fsum.__name__, end=_COMMASPACE_)
2827 printf(_psum.__name__, end=_COMMASPACE_)
2829 F = Fsum()
2830 if F.is_math_fsum():
2831 for t in frandoms(n, seeded=True):
2832 assert float(F.fset_(*t)) == _fsum(t)
2833 printf(_DOT_, end=NN)
2834 printf(NN)
2836 _test(128)
2838# **) MIT License
2839#
2840# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.
2841#
2842# Permission is hereby granted, free of charge, to any person obtaining a
2843# copy of this software and associated documentation files (the "Software"),
2844# to deal in the Software without restriction, including without limitation
2845# the rights to use, copy, modify, merge, publish, distribute, sublicense,
2846# and/or sell copies of the Software, and to permit persons to whom the
2847# Software is furnished to do so, subject to the following conditions:
2848#
2849# The above copyright notice and this permission notice shall be included
2850# in all copies or substantial portions of the Software.
2851#
2852# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
2853# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
2854# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
2855# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
2856# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
2857# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
2858# OTHER DEALINGS IN THE SOFTWARE.