1

2# -*- coding: utf-8 -*-

3

4 u'''Class L{Fsum} for precision floating point summation and I{running}

5 summation based on, respectively similar to Python's C{math.fsum}.

6

7 Generally, an L{Fsum} instance is considered a C{float} plus a small or zero

8 C{residual} value, see property L{Fsum.residual}. However, there are several

9 C{integer} L{Fsum} cases, for example the result of C{ceil}, C{floor},

10 C{Fsum.__floordiv__} and methods L{Fsum.fint} and L{Fsum.fint2}.

11

12 Also, L{Fsum} methods L{Fsum.pow}, L{Fsum.__ipow__}, L{Fsum.__pow__} and

13 L{Fsum.__rpow__} return a (very long) C{int} if invoked with optional argument

14 C{mod} set to C{None}. The C{residual} of an C{integer} L{Fsum} may be between

15 C{-1.0} and C{+1.0}, including C{INT0} if considered to be I{exact}.

16

17 Set env variable C{PYGEODESY_FSUM_RESIDUAL} to a C{float} string greater than

18 C{"0.0"} as the threshold to throw a L{ResidualError} for a division, power or

19 root operation of an L{Fsum} instance with a C{residual} I{ratio} exceeding

20 the threshold. See methods L{Fsum.RESIDUAL}, L{Fsum.pow}, L{Fsum.__ipow__}

21 and L{Fsum.__itruediv__}.

22'''

23# make sure int/int division yields float quotient, see .basics

24 from __future__ import division as _; del _ # PYCHOK semicolon

25

26 from pygeodesy.basics import isbool, iscomplex, isint, isscalar, \

27 _signOf, itemsorted, signOf, _xiterable, \

28 _xiterablen, _enquote

29 from pygeodesy.constants import INT0, _isfinite, NEG0, _pos_self, \

30 _0_0, _1_0, _N_1_0, Float, Int

31 from pygeodesy.errors import _OverflowError, _TypeError, _UnexpectedError, \

32 _ValueError, _xError, _xError2, _xkwds_get1, \

33 _xkwds_pop2

34# from pygeodesy.internals import _enquote # from .basics

35 from pygeodesy.interns import NN, _arg_, _COMMASPACE_, _DASH_, _DOT_, \

36 _EQUAL_, _from_, _LANGLE_, _NOTEQUAL_, \

37 _not_finite_, _PERCENT_, _PLUS_, \

38 _RANGLE_, _SLASH_, _SPACE_, _STAR_, _UNDER_

39 from pygeodesy.lazily import _ALL_LAZY, _getenv, _sys_version_info2

40 from pygeodesy.named import _name__, _name2__, _Named, _NamedTuple, \

41 _NotImplemented

42 from pygeodesy.props import _allPropertiesOf_n, deprecated_property_RO, \

43 Property, Property_RO, property_RO

44 from pygeodesy.streprs import Fmt, fstr, unstr

45# from pygeodesy.units import Float, Int # from .constants

46

47 from math import ceil as _ceil, fabs, floor as _floor # PYCHOK used! .ltp

48

49__all__ = _ALL_LAZY.fsums

50__version__ = '24.06.11'

51

52_add_op_ = _PLUS_ # in .auxilats.auxAngle

53_eq_op_ = _EQUAL_ * 2 # _DEQUAL_

54_div_ = 'div'

55_floordiv_op_ = _SLASH_ * 2 # _DSLASH_

56_fset_op_ = _EQUAL_

57_ge_op_ = _RANGLE_ + _EQUAL_

58_gt_op_ = _RANGLE_

59_iadd_op_ = _add_op_ + _EQUAL_ # in .auxilats.auxAngle, .fstats

60_integer_ = 'integer'

61_le_op_ = _LANGLE_ + _EQUAL_

62_lt_op_ = _LANGLE_

63_mod_ = 'mod'

64_mod_op_ = _PERCENT_

65_mul_op_ = _STAR_

66_ne_op_ = _NOTEQUAL_

67_non_zero_ = 'non-zero'

68_pow_op_ = _STAR_ * 2 # _DSTAR_

69_significant_ = 'significant'

70_sub_op_ = _DASH_ # in .auxilats.auxAngle

71_threshold_ = 'threshold'

72_truediv_op_ = _SLASH_

73_divmod_op_ = _floordiv_op_ + _mod_op_

74_isub_op_ = _sub_op_ + _fset_op_ # in .auxilats.auxAngle

75

76

77 def _2delta(*ab):

78 '''(INTERNAL) Helper for C{Fsum._fsum2}.

79 '''

80 try:

81 a, b = _2sum(*ab)

82 except _OverflowError:

83 a, b = ab

84 return float(a if fabs(a) > fabs(b) else b)

85

86

87 def _2error(unused): # in .fstats

88 '''(INTERNAL) Throw a C{not-finite} exception.

89 '''

90 raise ValueError(_not_finite_)

91

92

93 def _2finite(x):

94 '''(INTERNAL) return C{float(x)} if finite.

95 '''

96 x = float(x)

97 return x if _isfinite(x) else _2error(x)

98

99

100 def _2float(index=None, **name_value): # in .fmath, .fstats

101 '''(INTERNAL) Raise C{TypeError} or C{ValueError} if not scalar or infinite.

102 '''

103 n, v = name_value.popitem() # _xkwds_item2(name_value)

104 try:

105 return _2finite(v)

106 except Exception as X:

107 raise _xError(X, Fmt.INDEX(n, index), v)

108

109

110 def _X_ps(X): # for _2floats only

111 return X._ps

112

113

114 def _2floats(xs, origin=0, _X=_X_ps, _x=float):

115 '''(INTERNAL) Yield each B{C{xs}} as a C{float}.

116 '''

117 try:

118 i, x = origin, _X

119 _fin = _isfinite

120 _FsT = _Fsum_Fsum2Tuple_types

121 _isa = isinstance

122 for x in _xiterable(xs):

123 if _isa(x, _FsT):

124 for p in _X(x._Fsum):

125 yield p

126 else:

127 f = _x(x)

128 yield f if _fin(f) else _2error(f)

129 i += 1

130 except Exception as X:

131 raise _xError(X, xs=xs) if x is _X else \

132 _xError(X, Fmt.INDEX(xs=i), x)

133

134

135 def _Fsumf_(*xs): # floats=True, in .auxLat, ...

136 '''(INTERNAL) An C{Fsum} of I{known scalars}.

137 '''

138 return Fsum()._facc_scalar(xs, up=False)

139

140

141 def _Fsum1f_(*xs): # floats=True, in .albers, ...

142 '''(INTERNAL) An C{Fsum} of I{known scalars}, 1-primed.

143 '''

144 return Fsum()._facc_scalar(_1primed(xs), up=False)

145

146

147 def _2halfeven(s, r, p):

148 '''(INTERNAL) Round half-even.

149 '''

150 if (p > 0 and r > 0) or \

151 (p < 0 and r < 0): # signs match

152 r *= 2

153 t = s + r

154 if r == (t - s):

155 s = t

156 return s

157

158

159 def _isFsum(x): # in .fmath

160 '''(INTERNAL) Is C{x} an C{Fsum} instance?

161 '''

162 return isinstance(x, Fsum)

163

164

165 def _isFsumTuple(x): # in .fmath

166 '''(INTERNAL) Is C{x} an C{Fsum} or C{Fsum2Tuple} instance?

167 '''

168 return isinstance(x, _Fsum_Fsum2Tuple_types)

169

170

171 def _1_Over(x, op, **raiser_RESIDUAL): # vs _1_over

172 '''(INTERNAL) Return C{Fsum(1) / B{x}}.

173 '''

174 return _Psum_(_1_0)._ftruediv(x, op, **raiser_RESIDUAL)

175

176

177 def _1primed(xs): # in .fmath

178 '''(INTERNAL) 1-Primed summation of iterable C{xs}

179 items, all I{known} to be C{scalar}.

180 '''

181 yield _1_0

182 for x in xs:

183 yield x

184 yield _N_1_0

185

186

187 def _psum(ps): # PYCHOK used!

188 '''(INTERNAL) Partials summation, updating C{ps}.

189 '''

190 # assert isinstance(ps, list)

191 i = len(ps) - 1

192 s = _0_0 if i < 0 else ps[i]

193 _2s = _2sum

194 while i > 0:

195 i -= 1

196 s, r = _2s(s, ps[i])

197 if r: # sum(ps) became inexact

198 if s:

199 ps[i:] = r, s

200 if i > 0:

201 s = _2halfeven(s, r, ps[i-1])

202 break # return s

203 s = r # PYCHOK no cover

204 ps[i:] = s,

205 return s

206

207

208 def _Psum(ps, **name_RESIDUAL):

209 '''(INTERNAL) Return an C{Fsum} from I{ordered} partials C{ps}.

210 '''

211 f = Fsum(**name_RESIDUAL) if name_RESIDUAL else Fsum()

212 if ps:

213 f._ps[:] = ps

214 f._n = len(f._ps)

215 return f

216

217

218 def _Psum_(*ps, **name_RESIDUAL):

219 '''(INTERNAL) Return an C{Fsum} from 1 or 2 known scalar(s) C{ps}.

220 '''

221 return _Psum(ps, **name_RESIDUAL)

222

223

224 def _2scalar2(other):

225 '''(INTERNAL) Return 2-tuple C{(other, r)} with C{other} as C{int},

226 C{float} or C{as-is} and C{r} the residual of C{as-is}.

227 '''

228 if _isFsumTuple(other):

229 s, r = other._fint2

230 if r:

231 s, r = other._fprs2

232 if r: # PYCHOK no cover

233 s = other # L{Fsum} as-is

234 else:

235 r = 0

236 s = other # C{type} as-is

237 if isint(s, both=True):

238 s = int(s)

239 return s, r

240

241

242 def _s_r(s, r):

243 '''(INTERNAL) Return C{(s, r)}, I{ordered}.

244 '''

245 if r:

246 if fabs(s) < fabs(r):

247 s, r = r, (s or INT0)

248 else:

249 r = INT0

250 return s, r

251

252

253 def _strcomplex(s, *args):

254 '''(INTERNAL) C{Complex} 2- or 3-arg C{pow} error as C{str}.

255 '''

256 c = _strcomplex.__name__[4:]

257 n = _DASH_(len(args), _arg_)

258 t = unstr(pow, *args)

259 return _SPACE_(c, s, _from_, n, t)

260

261

262 def _stresidual(prefix, residual, R=0, **mod_ratio):

263 '''(INTERNAL) Residual error txt C{str}.

264 '''

265 p = _stresidual.__name__[3:]

266 t = Fmt.PARENSPACED(p, Fmt(residual))

267 for n, v in itemsorted(mod_ratio):

268 p = Fmt.PARENSPACED(n, Fmt(v))

269 t = _COMMASPACE_(t, p)

270 return _SPACE_(prefix, t, Fmt.exceeds_R(R), _threshold_)

271

272

273 def _2sum(a, b): # by .testFmath

274 '''(INTERNAL) Return C{a + b} as 2-tuple (sum, residual).

275 '''

276 # Neumaier, A. U{Rundungsfehleranalyse einiger Verfahren zur Summation endlicher

277 # Summen<https://OnlineLibrary.Wiley.com/doi/epdf/10.1002/zamm.19740540106>},

278 # 1974, Zeitschrift für Angewandte Mathmatik und Mechanik, vol 51, nr 1, p 39-51

279 # <https://StackOverflow.com/questions/78633770/can-neumaier-summation-be-sped-up>

280 s = a + b

281 if _isfinite(s):

282 if fabs(a) < fabs(b):

283 r = (b - s) + a

284 else:

285 r = (a - s) + b

286 return s, r

287 u = unstr(_2sum, a, b)

288 t = Fmt.PARENSPACED(_not_finite_, s)

289 raise _OverflowError(u, txt=t)

290

291

292 def _threshold(threshold=_0_0, **kwds):

293 '''(INTERNAL) Get the L{ResidualError}s threshold,

294 optionally from single kwds C{B{RESIDUAL}=scalar}.

295 '''

296 if kwds:

297 threshold, kwds = _xkwds_pop2(kwds, RESIDUAL=threshold)

298# threshold = kwds.pop('RESIDUAL', threshold)

299 if kwds:

300 raise _UnexpectedError(**kwds)

301 try:

302 return _2finite(threshold) # PYCHOK None

303 except Exception as x:

304 raise ResidualError(threshold=threshold, cause=x)

305

306

307 class Fsum(_Named): # sync __methods__ with .vector3dBase.Vector3dBase

308 '''Precision floating point summation and I{running} summation.

309

310 Unlike Python's C{math.fsum}, this class accumulates values and provides intermediate,

311 I{running}, precision floating point summations. Accumulation may continue after any

312 intermediate, I{running} summuation.

313

314 @note: Values may be L{Fsum}, L{Fsum2Tuple}, C{int}, C{float} or C{scalar} instances,

315 any C{type} having method C{__float__} to convert the C{scalar} to a single

316 C{float}, except C{complex}.

317

318 @note: Handling of exceptions and C{inf}, C{INF}, C{nan} and C{NAN} differs from

319 Python's C{math.fsum}.

320

321 @see: U{Hettinger<https://GitHub.com/ActiveState/code/tree/master/recipes/Python/

322 393090_Binary_floating_point_summatiaccurate_full/recipe-393090.py>},

323 U{Kahan<https://WikiPedia.org/wiki/Kahan_summation_algorithm>}, U{Klein

324 <https://Link.Springer.com/article/10.1007/s00607-005-0139-x>}, Python 2.6+

325 file I{Modules/mathmodule.c} and the issue log U{Full precision summation

326 <https://Bugs.Python.org/issue2819>}.

327 '''

328 _math_fsum = None

329 _n = 0

330# _ps = [] # partial sums

331# _ps_max = 0 # max(Fsum._ps_max, len(Fsum._ps))

332 _RESIDUAL = _threshold(_getenv('PYGEODESY_FSUM_RESIDUAL', _0_0))

333

334 def __init__(self, *xs, **name_RESIDUAL):

335 '''New L{Fsum} for I{running} precision floating point summation.

336

337 @arg xs: No, one or more initial items to add (each C{scalar} or

338 an L{Fsum} or L{Fsum2Tuple} instance), all positional.

339 @kwarg name_RESIDUAL: Optional C{B{name}=NN} (C{str}) for this

340 L{Fsum} and the C{B{RESIDUAL}=0.0} threshold for

341 L{ResidualError}s (C{scalar}).

342

343 @see: Methods L{Fsum.fadd} and L{Fsum.RESIDUAL}.

344 '''

345 if name_RESIDUAL:

346 n, kwds = _name2__(**name_RESIDUAL)

347 if kwds:

348 R = Fsum._RESIDUAL

349 t = _threshold(R, **kwds)

350 if t != R:

351 self._RESIDUAL = t

352 if n:

353 self.name = n

354

355 self._ps = [] # [_0_0], see L{Fsum._fprs}

356 if xs:

357 self._facc_1(xs, up=False)

358

359 def __abs__(self):

360 '''Return this instance' absolute value as an L{Fsum}.

361 '''

362 s = self.signOf() # == self._cmp_0(0)

363 return (-self) if s < 0 else self._copy_2(self.__abs__)

364

365 def __add__(self, other):

366 '''Return C{B{self} + B{other}} as an L{Fsum}.

367

368 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar}.

369

370 @return: The sum (L{Fsum}).

371

372 @see: Methods L{Fsum.fadd_} and L{Fsum.fadd}.

373 '''

374 f = self._copy_2(self.__add__)

375 return f._fadd(other, _add_op_)

376

377 def __bool__(self): # PYCHOK Python 3+

378 '''Return C{True} if this instance is I{exactly} non-zero.

379 '''

380 s, r = self._fprs2

381 return bool(s or r) and s != -r # == self != 0

382

383 def __ceil__(self): # PYCHOK not special in Python 2-

384 '''Return this instance' C{math.ceil} as C{int} or C{float}.

385

386 @return: An C{int} in Python 3+, but C{float} in Python 2-.

387

388 @see: Methods L{Fsum.__floor__} and property L{Fsum.ceil}.

389 '''

390 return self.ceil

391

392 def __cmp__(self, other): # PYCHOK no cover

393 '''Compare this with an other instance or C{scalar}, Python 2-.

394

395 @return: -1, 0 or +1 (C{int}).

396

397 @raise TypeError: Incompatible B{C{other}} C{type}.

398 '''

399 s = self._cmp_0(other, self.cmp.__name__)

400 return _signOf(s, 0)

401

402 def __divmod__(self, other, **raiser_RESIDUAL):

403 '''Return C{divmod(B{self}, B{other})} as a L{DivMod2Tuple}

404 with quotient C{div} an C{int} in Python 3+ or C{float}

405 in Python 2- and remainder C{mod} an L{Fsum} instance.

406

407 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar} modulus.

408 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore

409 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}

410 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.

411

412 @raise ResidualError: Non-zero, significant residual or invalid

413 B{C{RESIDUAL}}.

414

415 @see: Method L{Fsum.fdiv}.

416 '''

417 f = self._copy_2(self.__divmod__)

418 return f._fdivmod2(other, _divmod_op_, **raiser_RESIDUAL)

419

420 def __eq__(self, other):

421 '''Compare this with an other instance or C{scalar}.

422 '''

423 return self._cmp_0(other, _eq_op_) == 0

424

425 def __float__(self):

426 '''Return this instance' current, precision running sum as C{float}.

427

428 @see: Methods L{Fsum.fsum} and L{Fsum.int_float}.

429 '''

430 return float(self._fprs)

431

432 def __floor__(self): # PYCHOK not special in Python 2-

433 '''Return this instance' C{math.floor} as C{int} or C{float}.

434

435 @return: An C{int} in Python 3+, but C{float} in Python 2-.

436

437 @see: Methods L{Fsum.__ceil__} and property L{Fsum.floor}.

438 '''

439 return self.floor

440

441 def __floordiv__(self, other):

442 '''Return C{B{self} // B{other}} as an L{Fsum}.

443

444 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar} divisor.

445

446 @return: The C{floor} quotient (L{Fsum}).

447

448 @see: Methods L{Fsum.__ifloordiv__}.

449 '''

450 f = self._copy_2(self.__floordiv__)

451 return f._floordiv(other, _floordiv_op_)

452

453 def __format__(self, *other): # PYCHOK no cover

454 '''Not implemented.'''

455 return _NotImplemented(self, *other)

456

457 def __ge__(self, other):

458 '''Compare this with an other instance or C{scalar}.

459 '''

460 return self._cmp_0(other, _ge_op_) >= 0

461

462 def __gt__(self, other):

463 '''Compare this with an other instance or C{scalar}.

464 '''

465 return self._cmp_0(other, _gt_op_) > 0

466

467 def __hash__(self): # PYCHOK no cover

468 '''Return this instance' C{hash}.

469 '''

470 return hash(self._ps) # XXX id(self)?

471

472 def __iadd__(self, other):

473 '''Apply C{B{self} += B{other}} to this instance.

474

475 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar} value or

476 an iterable of several of the former.

477

478 @return: This instance, updated (L{Fsum}).

479

480 @raise TypeError: Invalid B{C{other}}, not

481 C{scalar} nor L{Fsum}.

482

483 @see: Methods L{Fsum.fadd_} and L{Fsum.fadd}.

484 '''

485 try:

486 return self._fadd(other, _iadd_op_)

487 except TypeError:

488 return self._facc_inplace(other, _iadd_op_, self._facc)

489

490 def __ifloordiv__(self, other):

491 '''Apply C{B{self} //= B{other}} to this instance.

492

493 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar} divisor.

494

495 @return: This instance, updated (L{Fsum}).

496

497 @raise ResidualError: Non-zero, significant residual

498 in B{C{other}}.

499

500 @raise TypeError: Invalid B{C{other}} type.

501

502 @raise ValueError: Invalid or non-finite B{C{other}}.

503

504 @raise ZeroDivisionError: Zero B{C{other}}.

505

506 @see: Methods L{Fsum.__itruediv__}.

507 '''

508 return self._floordiv(other, _floordiv_op_ + _fset_op_)

509

510 def __imatmul__(self, other): # PYCHOK no cover

511 '''Not implemented.'''

512 return _NotImplemented(self, other)

513

514 def __imod__(self, other):

515 '''Apply C{B{self} %= B{other}} to this instance.

516

517 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar} modulus.

518

519 @return: This instance, updated (L{Fsum}).

520

521 @see: Method L{Fsum.__divmod__}.

522 '''

523 return self._fdivmod2(other, _mod_op_ + _fset_op_).mod

524

525 def __imul__(self, other):

526 '''Apply C{B{self} *= B{other}} to this instance.

527

528 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar} factor.

529

530 @return: This instance, updated (L{Fsum}).

531

532 @raise OverflowError: Partial C{2sum} overflow.

533

534 @raise TypeError: Invalid B{C{other}} type.

535

536 @raise ValueError: Invalid or non-finite B{C{other}}.

537 '''

538 return self._fmul(other, _mul_op_ + _fset_op_)

539

540 def __int__(self):

541 '''Return this instance as an C{int}.

542

543 @see: Method L{Fsum.int_float} and properties L{Fsum.ceil}

544 and L{Fsum.floor}.

545 '''

546 i, _ = self._fint2

547 return i

548

549 def __invert__(self): # PYCHOK no cover

550 '''Not implemented.'''

551 # Luciano Ramalho, "Fluent Python", O'Reilly, 2nd Ed, 2022 p. 567

552 return _NotImplemented(self)

553

554 def __ipow__(self, other, *mod, **raiser_RESIDUAL): # PYCHOK 2 vs 3 args

555 '''Apply C{B{self} **= B{other}} to this instance.

556

557 @arg other: The exponent (C{scalar}, L{Fsum} or L{Fsum2Tuple}).

558 @arg mod: Optional modulus (C{int} or C{None}) for the 3-argument

559 C{pow(B{self}, B{other}, B{mod})} version.

560 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore

561 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}

562 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.

563

564 @return: This instance, updated (L{Fsum}).

565

566 @note: If B{C{mod}} is given, the result will be an C{integer}

567 L{Fsum} in Python 3+ if this instance C{is_integer} or

568 set to C{as_integer} and B{C{mod}} is given and C{None}.

569

570 @raise OverflowError: Partial C{2sum} overflow.

571

572 @raise ResidualError: Invalid B{C{RESIDUAL}} or the residual

573 is non-zero and significant and either

574 B{C{other}} is a fractional or negative

575 C{scalar} or B{C{mod}} is given and not

576 C{None}.

577

578 @raise TypeError: Invalid B{C{other}} type or 3-argument C{pow}

579 invocation failed.

580

581 @raise ValueError: If B{C{other}} is a negative C{scalar} and this

582 instance is C{0} or B{C{other}} is a fractional

583 C{scalar} and this instance is negative or has a

584 non-zero and significant residual or B{C{mod}}

585 is given as C{0}.

586

587 @see: CPython function U{float_pow<https://GitHub.com/

588 python/cpython/blob/main/Objects/floatobject.c>}.

589 '''

590 return self._fpow(other, _pow_op_ + _fset_op_, *mod, **raiser_RESIDUAL)

591

592 def __isub__(self, other):

593 '''Apply C{B{self} -= B{other}} to this instance.

594

595 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar} value or

596 an iterable of several of the former.

597

598 @return: This instance, updated (L{Fsum}).

599

600 @raise TypeError: Invalid B{C{other}} type.

601

602 @see: Methods L{Fsum.fsub_} and L{Fsum.fsub}.

603 '''

604 try:

605 return self._fsub(other, _isub_op_)

606 except TypeError:

607 return self._facc_inplace(other, _isub_op_, self._facc_neg)

608

609 def __iter__(self):

610 '''Return an C{iter}ator over a C{partials} duplicate.

611 '''

612 return iter(self.partials)

613

614 def __itruediv__(self, other, **raiser_RESIDUAL):

615 '''Apply C{B{self} /= B{other}} to this instance.

616

617 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar} divisor.

618 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore

619 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}

620 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.

621

622 @return: This instance, updated (L{Fsum}).

623

624 @raise OverflowError: Partial C{2sum} overflow.

625

626 @raise ResidualError: Non-zero, significant residual or invalid

627 B{C{RESIDUAL}}.

628

629 @raise TypeError: Invalid B{C{other}} type.

630

631 @raise ValueError: Invalid or non-finite B{C{other}}.

632

633 @raise ZeroDivisionError: Zero B{C{other}}.

634

635 @see: Method L{Fsum.__ifloordiv__}.

636 '''

637 return self._ftruediv(other, _truediv_op_ + _fset_op_, **raiser_RESIDUAL)

638

639 def __le__(self, other):

640 '''Compare this with an other instance or C{scalar}.

641 '''

642 return self._cmp_0(other, _le_op_) <= 0

643

644 def __len__(self):

645 '''Return the number of values accumulated (C{int}).

646 '''

647 return self._n

648

649 def __lt__(self, other):

650 '''Compare this with an other instance or C{scalar}.

651 '''

652 return self._cmp_0(other, _lt_op_) < 0

653

654 def __matmul__(self, other): # PYCHOK no cover

655 '''Not implemented.'''

656 return _NotImplemented(self, other)

657

658 def __mod__(self, other):

659 '''Return C{B{self} % B{other}} as an L{Fsum}.

660

661 @see: Method L{Fsum.__imod__}.

662 '''

663 f = self._copy_2(self.__mod__)

664 return f._fdivmod2(other, _mod_op_).mod

665

666 def __mul__(self, other):

667 '''Return C{B{self} * B{other}} as an L{Fsum}.

668

669 @see: Method L{Fsum.__imul__}.

670 '''

671 f = self._copy_2(self.__mul__)

672 return f._fmul(other, _mul_op_)

673

674 def __ne__(self, other):

675 '''Compare this with an other instance or C{scalar}.

676 '''

677 return self._cmp_0(other, _ne_op_) != 0

678

679 def __neg__(self):

680 '''Return I{a copy of} this instance, I{negated}.

681 '''

682 f = self._copy_2(self.__neg__)

683 return f._fset(self._neg)

684

685 def __pos__(self):

686 '''Return this instance I{as-is}, like C{float.__pos__()}.

687 '''

688 return self if _pos_self else self._copy_2(self.__pos__)

689

690 def __pow__(self, other, *mod): # PYCHOK 2 vs 3 args

691 '''Return C{B{self}**B{other}} as an L{Fsum}.

692

693 @see: Method L{Fsum.__ipow__}.

694 '''

695 f = self._copy_2(self.__pow__)

696 return f._fpow(other, _pow_op_, *mod)

697

698 def __radd__(self, other):

699 '''Return C{B{other} + B{self}} as an L{Fsum}.

700

701 @see: Method L{Fsum.__iadd__}.

702 '''

703 f = self._copy_2r(other, self.__radd__)

704 return f._fadd(self, _add_op_)

705

706 def __rdivmod__(self, other):

707 '''Return C{divmod(B{other}, B{self})} as 2-tuple

708 C{(quotient, remainder)}.

709

710 @see: Method L{Fsum.__divmod__}.

711 '''

712 f = self._copy_2r(other, self.__rdivmod__)

713 return f._fdivmod2(self, _divmod_op_)

714

715# def __repr__(self):

716# '''Return the default C{repr(this)}.

717# '''

718# return self.toRepr(lenc=True)

719

720 def __rfloordiv__(self, other):

721 '''Return C{B{other} // B{self}} as an L{Fsum}.

722

723 @see: Method L{Fsum.__ifloordiv__}.

724 '''

725 f = self._copy_2r(other, self.__rfloordiv__)

726 return f._floordiv(self, _floordiv_op_)

727

728 def __rmatmul__(self, other): # PYCHOK no cover

729 '''Not implemented.'''

730 return _NotImplemented(self, other)

731

732 def __rmod__(self, other):

733 '''Return C{B{other} % B{self}} as an L{Fsum}.

734

735 @see: Method L{Fsum.__imod__}.

736 '''

737 f = self._copy_2r(other, self.__rmod__)

738 return f._fdivmod2(self, _mod_op_).mod

739

740 def __rmul__(self, other):

741 '''Return C{B{other} * B{self}} as an L{Fsum}.

742

743 @see: Method L{Fsum.__imul__}.

744 '''

745 f = self._copy_2r(other, self.__rmul__)

746 return f._fmul(self, _mul_op_)

747

748 def __round__(self, *ndigits): # PYCHOK Python 3+

749 '''Return C{round(B{self}, *B{ndigits}} as an L{Fsum}.

750

751 @arg ndigits: Optional number of digits (C{int}).

752 '''

753 f = self._copy_2(self.__round__)

754 # <https://docs.Python.org/3.12/reference/datamodel.html?#object.__round__>

755 return f._fset(round(float(self), *ndigits)) # can be C{int}

756

757 def __rpow__(self, other, *mod):

758 '''Return C{B{other}**B{self}} as an L{Fsum}.

759

760 @see: Method L{Fsum.__ipow__}.

761 '''

762 f = self._copy_2r(other, self.__rpow__)

763 return f._fpow(self, _pow_op_, *mod)

764

765 def __rsub__(self, other):

766 '''Return C{B{other} - B{self}} as L{Fsum}.

767

768 @see: Method L{Fsum.__isub__}.

769 '''

770 f = self._copy_2r(other, self.__rsub__)

771 return f._fsub(self, _sub_op_)

772

773 def __rtruediv__(self, other, **raiser_RESIDUAL):

774 '''Return C{B{other} / B{self}} as an L{Fsum}.

775

776 @see: Method L{Fsum.__itruediv__}.

777 '''

778 f = self._copy_2r(other, self.__rtruediv__)

779 return f._ftruediv(self, _truediv_op_, **raiser_RESIDUAL)

780

781 def __str__(self):

782 '''Return the default C{str(self)}.

783 '''

784 return self.toStr(lenc=True)

785

786 def __sub__(self, other):

787 '''Return C{B{self} - B{other}} as an L{Fsum}.

788

789 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar}.

790

791 @return: The difference (L{Fsum}).

792

793 @see: Method L{Fsum.__isub__}.

794 '''

795 f = self._copy_2(self.__sub__)

796 return f._fsub(other, _sub_op_)

797

798 def __truediv__(self, other, **raiser_RESIDUAL):

799 '''Return C{B{self} / B{other}} as an L{Fsum}.

800

801 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar} divisor.

802 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore

803 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}

804 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.

805

806 @return: The quotient (L{Fsum}).

807

808 @raise ResidualError: Non-zero, significant residual or invalid

809 B{C{RESIDUAL}}.

810

811 @see: Method L{Fsum.__itruediv__}.

812 '''

813 return self._truediv(other, _truediv_op_, **raiser_RESIDUAL)

814

815 __trunc__ = __int__

816

817 if _sys_version_info2 < (3, 0): # PYCHOK no cover

818 # <https://docs.Python.org/2/library/operator.html#mapping-operators-to-functions>

819 __div__ = __truediv__

820 __idiv__ = __itruediv__

821 __long__ = __int__

822 __nonzero__ = __bool__

823 __rdiv__ = __rtruediv__

824

825 def as_integer_ratio(self):

826 '''Return this instance as the ratio of 2 integers.

827

828 @return: 2-Tuple C{(numerator, denominator)} both C{int}

829 with C{numerator} signed and C{denominator}

830 non-zero, positive.

831

832 @see: Standard C{float.as_integer_ratio} in Python 2.7+.

833 '''

834 n, r = self._fint2

835 if r:

836 i, d = float(r).as_integer_ratio()

837 n *= d

838 n += i

839 else: # PYCHOK no cover

840 d = 1

841 return n, d

842

843 @property_RO

844 def as_iscalar(self):

845 '''Get this instance I{as-is} (L{Fsum} or C{scalar}), the

846 latter only if the C{residual} equals C{zero}.

847 '''

848 s, r = self._fprs2

849 return self if r else s

850

851 @property_RO

852 def ceil(self):

853 '''Get this instance' C{ceil} value (C{int} in Python 3+, but

854 C{float} in Python 2-).

855

856 @note: This C{ceil} takes the C{residual} into account.

857

858 @see: Method L{Fsum.int_float} and properties L{Fsum.floor},

859 L{Fsum.imag} and L{Fsum.real}.

860 '''

861 s, r = self._fprs2

862 c = _ceil(s) + int(r) - 1

863 while r > (c - s): # (s + r) > c

864 c += 1

865 return c # _ceil(self._n_d)

866

867 cmp = __cmp__

868

869 def _cmp_0(self, other, op):

870 '''(INTERNAL) Return C{scalar(self - B{other})} for 0-comparison.

871 '''

872 if _isFsumTuple(other):

873 s = self._ps_1sum(*other._ps)

874 elif self._scalar(other, op):

875 s = self._ps_1sum(other)

876 else:

877 s = self.signOf() # res=True

878 return s

879

880 def copy(self, deep=False, **name):

881 '''Copy this instance, C{shallow} or B{C{deep}}.

882

883 @kwarg name: Optional, overriding C{B{name}='"copy"} (C{str}).

884

885 @return: The copy (L{Fsum}).

886 '''

887 n = _name__(name, name__=self.copy)

888 f = _Named.copy(self, deep=deep, name=n)

889 if f._ps is self._ps:

890 f._ps = list(self._ps) # separate list

891 if not deep:

892 f._n = 1

893 # assert f._Fsum is f

894 return f

895

896 def _copy_2(self, which, name=NN):

897 '''(INTERNAL) Copy for I{dyadic} operators.

898 '''

899 n = name or which.__name__ # _dunder_nameof

900 # NOT .classof due to .Fdot(a, *b) args, etc.

901 f = _Named.copy(self, deep=False, name=n)

902 f._ps = list(self._ps) # separate list

903 # assert f._n == self._n

904 # assert f._Fsum is f

905 return f

906

907 def _copy_2r(self, other, which):

908 '''(INTERNAL) Copy for I{reverse-dyadic} operators.

909 '''

910 return other._copy_2(which) if _isFsum(other) else \

911 self._copy_2(which)._fset(other)

912

913# def _copy_RESIDUAL(self, other):

914# '''(INTERNAL) Copy C{other._RESIDUAL}.

915# '''

916# R = other._RESIDUAL

917# if R is not Fsum._RESIDUAL:

918# self._RESIDUAL = R

919

920 divmod = __divmod__

921

922 def _Error(self, op, other, Error, **txt_cause):

923 '''(INTERNAL) Format an B{C{Error}} for C{{self} B{op} B{other}}.

924 '''

925 return Error(_SPACE_(self.as_iscalar, op, other), **txt_cause)

926

927 def _ErrorX(self, X, op, other, *mod):

928 '''(INTERNAL) Format the caught exception C{X}.

929 '''

930 E, t = _xError2(X)

931 if mod:

932 t = _COMMASPACE_(Fmt.PARENSPACED(mod=mod[0]), t)

933 return self._Error(op, other, E, txt=t, cause=X)

934

935 def _ErrorXs(self, X, xs, **kwds): # in .fmath

936 '''(INTERNAL) Format the caught exception C{X}.

937 '''

938 E, t = _xError2(X)

939 u = unstr(self.named3, *xs[:3], _ELLIPSIS=len(xs) > 3, **kwds)

940 return E(u, txt=t, cause=X)

941

942 def _facc(self, xs, up=True, **origin_X_x):

943 '''(INTERNAL) Accumulate more C{scalars} or L{Fsum}s.

944 '''

945 if xs:

946 _xs = _2floats(xs, **origin_X_x) # PYCHOK yield

947 ps = self._ps

948 ps[:] = self._ps_acc(list(ps), _xs, up=up)

949 return self

950

951 def _facc_1(self, xs, **up):

952 '''(INTERNAL) Accumulate 0, 1 or more C{scalars} or L{Fsum}s,

953 all positional C{xs} in the caller of this method.

954 '''

955 return self._fadd(xs[0], _add_op_, **up) if len(xs) == 1 else \

956 self._facc(xs, origin=1, **up)

957

958 def _facc_inplace(self, other, op, _facc):

959 '''(INTERNAL) Accumulate from an iterable.

960 '''

961 try:

962 return _facc(other, origin=1) if _xiterable(other) else self

963 except Exception as X:

964 raise self._ErrorX(X, op, other)

965

966 def _facc_neg(self, xs, **up_origin):

967 '''(INTERNAL) Accumulate more C{scalars} or L{Fsum}s, negated.

968 '''

969 def _N(X):

970 return X._ps_neg

971

972 def _n(x):

973 return -float(x)

974

975 return self._facc(xs, _X=_N, _x=_n, **up_origin)

976

977 def _facc_power(self, power, xs, which, **raiser_RESIDUAL): # in .fmath

978 '''(INTERNAL) Add each C{xs} as C{float(x**power)}.

979 '''

980 def _Pow4(p):

981 r = 0

982 if _isFsumTuple(p):

983 s, r = p._fprs2

984 if r:

985 m = Fsum._pow

986 else: # scalar

987 return _Pow4(s)

988 elif isint(p, both=True) and int(p) >= 0:

989 p = s = int(p)

990 m = Fsum._pow_int

991 else:

992 p = s = _2float(power=p)

993 m = Fsum._pow_scalar

994 return m, p, s, r

995

996 _Pow, p, s, r = _Pow4(power)

997 if p: # and xs:

998 op = which.__name__

999 _flt = float

1000 _Fs = Fsum

1001 _isa = isinstance

1002 _pow = self._pow_2_3

1003

1004 def _P(X):

1005 f = _Pow(X, p, power, op, **raiser_RESIDUAL)

1006 return f._ps if _isa(f, _Fs) else (f,)

1007

1008 def _p(x):

1009 x = _flt(x)

1010 f = _pow(x, s, power, op, **raiser_RESIDUAL)

1011 if f and r:

1012 f *= _pow(x, r, power, op, **raiser_RESIDUAL)

1013 return f

1014

1015 f = self._facc(xs, origin=1, _X=_P, _x=_p)

1016 else:

1017 f = self._facc_scalar_(float(len(xs))) # x**0 == 1

1018 return f

1019

1020 def _facc_scalar(self, xs, **up):

1021 '''(INTERNAL) Accumulate all C{xs}, known to be scalar.

1022 '''

1023 if xs:

1024 _ = self._ps_acc(self._ps, xs, **up)

1025 return self

1026

1027 def _facc_scalar_(self, *xs, **up):

1028 '''(INTERNAL) Accumulate all positional C{xs}, known to be scalar.

1029 '''

1030 if xs:

1031 _ = self._ps_acc(self._ps, xs, **up)

1032 return self

1033

1034# def _facc_up(self, up=True):

1035# '''(INTERNAL) Update the C{partials}, by removing

1036# and re-accumulating the final C{partial}.

1037# '''

1038# ps = self._ps

1039# while len(ps) > 1:

1040# p = ps.pop()

1041# if p:

1042# n = self._n

1043# _ = self._ps_acc(ps, (p,), up=False)

1044# self._n = n

1045# break

1046# return self._update() if up else self

1047

1048 def fadd(self, xs=()):

1049 '''Add an iterable's items to this instance.

1050

1051 @arg xs: Iterable of items to add (each C{scalar}

1052 or an L{Fsum} or L{Fsum2Tuple} instance).

1053

1054 @return: This instance (L{Fsum}).

1055

1056 @raise OverflowError: Partial C{2sum} overflow.

1057

1058 @raise TypeError: An invalid B{C{xs}} item.

1059

1060 @raise ValueError: Invalid or non-finite B{C{xs}} value.

1061 '''

1062 if _isFsumTuple(xs):

1063 self._facc_scalar(xs._ps)

1064 elif isscalar(xs): # for backward compatibility

1065 self._facc_scalar_(_2float(x=xs)) # PYCHOK no cover

1066 elif xs: # _xiterable(xs)

1067 self._facc(xs)

1068 return self

1069

1070 def fadd_(self, *xs):

1071 '''Add all positional items to this instance.

1072

1073 @arg xs: Values to add (each C{scalar} or an L{Fsum}

1074 or L{Fsum2Tuple} instance), all positional.

1075

1076 @see: Method L{Fsum.fadd} for further details.

1077 '''

1078 return self._facc_1(xs)

1079

1080 def _fadd(self, other, op, **up): # in .fmath.Fhorner

1081 '''(INTERNAL) Apply C{B{self} += B{other}}.

1082 '''

1083 if not self._ps: # new Fsum(x)

1084 self._fset(other, op=op, **up)

1085 elif _isFsumTuple(other):

1086 self._facc_scalar(other._ps, **up)

1087 elif self._scalar(other, op):

1088 self._facc_scalar_(other, **up)

1089 return self

1090

1091 fcopy = copy # for backward compatibility

1092 fdiv = __itruediv__

1093 fdivmod = __divmod__

1094

1095 def _fdivmod2(self, other, op, **raiser_RESIDUAL):

1096 '''(INTERNAL) Apply C{B{self} %= B{other}} and return a L{DivMod2Tuple}.

1097 '''

1098 # result mostly follows CPython function U{float_divmod

1099 # <https://GitHub.com/python/cpython/blob/main/Objects/floatobject.c>},

1100 # but at least divmod(-3, 2) equals Cpython's result (-2, 1).

1101 q = self._truediv(other, op, **raiser_RESIDUAL).floor

1102 if q: # == float // other == floor(float / other)

1103 self -= Fsum(q) * other # NOT other * q!

1104

1105 s = signOf(other) # make signOf(self) == signOf(other)

1106 if s and self.signOf() == -s: # PYCHOK no cover

1107 self += other

1108 q -= 1

1109# t = self.signOf()

1110# if t and t != s:

1111# raise self._Error(op, other, _AssertionError, txt__=signOf)

1112 return DivMod2Tuple(q, self) # q is C{int} in Python 3+, but C{float} in Python 2-

1113

1114 def _fhorner(self, x, cs, op): # in .fmath

1115 '''(INTERNAL) Add an L{Fhorner} evaluation of polynomial

1116 M{sum(cs[i] * x**i for i=0..len(cs)-1)}.

1117 '''

1118 if _xiterablen(cs):

1119 H = Fsum(name__=self._fhorner)

1120 if _isFsumTuple(x):

1121 _mul = H._mul_Fsum

1122 else:

1123 _mul = H._mul_scalar

1124 x = _2float(x=x)

1125 if len(cs) > 1 and x:

1126 for c in reversed(cs):

1127 H._fset_ps(_mul(x, op))

1128 H._fadd(c, op, up=False)

1129 else: # x == 0

1130 H = cs[0]

1131 self._fadd(H, op)

1132 return self

1133

1134 def _finite(self, other, op=None):

1135 '''(INTERNAL) Return B{C{other}} if C{finite}.

1136 '''

1137 if _isfinite(other):

1138 return other

1139 raise ValueError(_not_finite_) if op is None else \

1140 self._Error(op, other, _ValueError, txt=_not_finite_)

1141

1142 def fint(self, name=NN, **raiser_RESIDUAL):

1143 '''Return this instance' current running sum as C{integer}.

1144

1145 @kwarg name: Optional, overriding C{B{name}="fint"} (C{str}).

1146 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore

1147 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}

1148 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.

1149

1150 @return: The C{integer} sum (L{Fsum}) if this instance C{is_integer}

1151 with a zero or insignificant I{integer} residual.

1152

1153 @raise ResidualError: Non-zero, significant residual or invalid

1154 B{C{RESIDUAL}}.

1155

1156 @see: Methods L{Fsum.fint2}, L{Fsum.int_float} and L{Fsum.is_integer}.

1157 '''

1158 i, r = self._fint2

1159 if r:

1160 R = self._raiser(r, i, **raiser_RESIDUAL)

1161 if R:

1162 t = _stresidual(_integer_, r, **R)

1163 raise ResidualError(_integer_, i, txt=t)

1164 return _Psum_(i, name=_name__(name, name__=self.fint))

1165

1166 def fint2(self, **name):

1167 '''Return this instance' current running sum as C{int} and the

1168 I{integer} residual.

1169

1170 @kwarg name: Optional name (C{str}).

1171

1172 @return: An L{Fsum2Tuple}C{(fsum, residual)} with C{fsum}

1173 an C{int} and I{integer} C{residual} a C{float} or

1174 C{INT0} if the C{fsum} is considered to be I{exact}.

1175 '''

1176 return Fsum2Tuple(*self._fint2, **name)

1177

1178 @Property

1179 def _fint2(self): # see ._fset

1180 '''(INTERNAL) Get 2-tuple (C{int}, I{integer} residual).

1181 '''

1182 s, r = self._fprs2

1183 i = int(s)

1184 n = len(self._ps)

1185 r = self._ps_1sum(i) if r and n > 1 else float(s - i)

1186 return i, (r or INT0) # Fsum2Tuple?

1187

1188 @_fint2.setter_ # PYCHOK setter_underscore!

1189 def _fint2(self, s):

1190 '''(INTERNAL) Replace the C{_fint2} value.

1191 '''

1192 i = int(s)

1193 return i, ((s - i) or INT0)

1194

1195 @deprecated_property_RO

1196 def float_int(self): # PYCHOK no cover

1197 '''DEPRECATED, use method C{Fsum.int_float}.'''

1198 return self.int_float() # raiser=False

1199

1200 @property_RO

1201 def floor(self):

1202 '''Get this instance' C{floor} (C{int} in Python 3+, but

1203 C{float} in Python 2-).

1204

1205 @note: This C{floor} takes the C{residual} into account.

1206

1207 @see: Method L{Fsum.int_float} and properties L{Fsum.ceil},

1208 L{Fsum.imag} and L{Fsum.real}.

1209 '''

1210 s, r = self._fprs2

1211 f = _floor(s) + _floor(r) + 1

1212 while (f - s) > r: # f > (s + r)

1213 f -= 1

1214 return f # _floor(self._n_d)

1215

1216# ffloordiv = __ifloordiv__ # for naming consistency

1217# floordiv = __floordiv__ # for naming consistency

1218

1219 def _floordiv(self, other, op, **raiser_RESIDUAL): # rather _ffloordiv?

1220 '''Apply C{B{self} //= B{other}}.

1221 '''

1222 q = self._ftruediv(other, op, **raiser_RESIDUAL) # == self

1223 return self._fset(q.floor) # floor(q)

1224

1225 fmul = __imul__

1226

1227 def _fmul(self, other, op):

1228 '''(INTERNAL) Apply C{B{self} *= B{other}}.

1229 '''

1230 if _isFsumTuple(other):

1231 if len(self._ps) != 1:

1232 f = self._mul_Fsum(other, op)

1233 elif len(other._ps) != 1: # and len(self._ps) == 1

1234 f = other._mul_scalar(self._ps[0], op)

1235 else: # len(other._ps) == len(self._ps) == 1

1236 f = self._finite(self._ps[0] * other._ps[0])

1237 else:

1238 s = self._scalar(other, op)

1239 f = self._mul_scalar(s, op)

1240 return self._fset(f) # n=len(self) + 1

1241

1242 def fover(self, over, **raiser_RESIDUAL):

1243 '''Apply C{B{self} /= B{over}} and summate.

1244

1245 @arg over: An L{Fsum} or C{scalar} denominator.

1246 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore

1247 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}

1248 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.

1249

1250 @return: Precision running sum (C{float}).

1251

1252 @raise ResidualError: Non-zero, significant residual or invalid

1253 B{C{RESIDUAL}}.

1254

1255 @see: Methods L{Fsum.fsum} and L{Fsum.__itruediv__}.

1256 '''

1257 return float(self.fdiv(over, **raiser_RESIDUAL)._fprs)

1258

1259 fpow = __ipow__

1260

1261 def _fpow(self, other, op, *mod, **raiser_RESIDUAL):

1262 '''Apply C{B{self} **= B{other}}, optional B{C{mod}} or C{None}.

1263 '''

1264 if mod:

1265 if mod[0] is not None: # == 3-arg C{pow}

1266 f = self._pow_2_3(self, other, other, op, *mod, **raiser_RESIDUAL)

1267 elif self.is_integer():

1268 # return an exact C{int} for C{int}**C{int}

1269 i, _ = self._fint2 # assert _ == 0

1270 x, r = _2scalar2(other) # C{int}, C{float} or other

1271 f = _Psum_(i)._pow_Fsum(other, op, **raiser_RESIDUAL) if r else \

1272 self._pow_2_3(i, x, other, op, **raiser_RESIDUAL)

1273 else: # mod[0] is None, power(self, other)

1274 f = self._pow(other, other, op, **raiser_RESIDUAL)

1275 else: # pow(self, other)

1276 f = self._pow(other, other, op, **raiser_RESIDUAL)

1277 return self._fset(f) # n=max(len(self), 1)

1278

1279 @Property

1280 def _fprs(self):

1281 '''(INTERNAL) Get and cache this instance' precision

1282 running sum (C{float} or C{int}), ignoring C{residual}.

1283

1284 @note: The precision running C{fsum} after a C{//=} or

1285 C{//} C{floor} division is C{int} in Python 3+.

1286 '''

1287 s, _ = self._fprs2

1288 return s # ._fprs2.fsum

1289

1290 @_fprs.setter_ # PYCHOK setter_underscore!

1291 def _fprs(self, s):

1292 '''(INTERNAL) Replace the C{_fprs} value.

1293 '''

1294 return s

1295

1296 @Property

1297 def _fprs2(self):

1298 '''(INTERNAL) Get and cache this instance' precision

1299 running sum and residual (L{Fsum2Tuple}).

1300 '''

1301 ps = self._ps

1302 n = len(ps) - 2

1303 if n > 0: # len(ps) > 2

1304 s = _psum(ps)

1305 n = len(ps) - 2

1306 if n > 0:

1307 r = self._ps_1sum(s)

1308 return Fsum2Tuple(*_s_r(s, r))

1309 if n == 0: # len(ps) == 2

1310 s, r = _s_r(*_2sum(*ps))

1311 ps[:] = (r, s) if r else (s,)

1312 elif ps: # len(ps) == 1

1313 s, r = ps[0], INT0

1314 else: # len(ps) == 0

1315 s, r = _0_0, INT0

1316 ps[:] = s,

1317 # assert self._ps is ps

1318 return Fsum2Tuple(s, r)

1319

1320 @_fprs2.setter_ # PYCHOK setter_underscore!

1321 def _fprs2(self, s_r):

1322 '''(INTERNAL) Replace the C{_fprs2} value.

1323 '''

1324 return Fsum2Tuple(s_r)

1325

1326 def fset_(self, *xs):

1327 '''Replace this instance' value with all positional items.

1328

1329 @arg xs: Optional, new values (each C{scalar} or

1330 an L{Fsum} or L{Fsum2Tuple} instance),

1331 all positional.

1332

1333 @return: This instance, replaced (C{Fsum}).

1334

1335 @see: Method L{Fsum.fadd} for further details.

1336 '''

1337 f = xs[0] if len(xs) == 1 else (

1338 Fsum(*xs) if xs else _0_0)

1339 return self._fset(f)

1340

1341 def _fset(self, other, n=0, up=True, **op):

1342 '''(INTERNAL) Overwrite this instance with an other or a C{scalar}.

1343 '''

1344 if other is self:

1345 pass # from ._fmul, ._ftruediv and ._pow_0_1

1346 elif _isFsumTuple(other):

1347 self._ps[:] = other._ps

1348 self._n = n or other._n

1349# self._copy_RESIDUAL(other)

1350 if up: # use or zap the C{Property_RO} values

1351 Fsum._fint2._update_from(self, other)

1352 Fsum._fprs ._update_from(self, other)

1353 Fsum._fprs2._update_from(self, other)

1354 elif isscalar(other):

1355 s = float(self._finite(other, **op)) if op else other

1356 self._ps[:] = s,

1357 self._n = n or 1

1358 if up: # Property _fint2, _fprs and _fprs2 all have

1359 # @.setter_underscore and NOT @.setter because the

1360 # latter's _fset zaps the value set by @.setter

1361 self._fint2 = s

1362 self._fprs = s

1363 self._fprs2 = s, INT0

1364 # assert self._fprs is s

1365 else: # PYCHOK no cover

1366 op = _xkwds_get1(op, op=_fset_op_)

1367 raise self._Error(op, other, _TypeError)

1368 return self

1369

1370 def _fset_ps(self, other): # in .fmath

1371 '''(INTERNAL) Set partials from a known C{scalar}, L{Fsum} or L{Fsum2Tuple}.

1372 '''

1373 return self._fset(other, up=False)

1374

1375 def fsub(self, xs=()):

1376 '''Subtract an iterable's items from this instance.

1377

1378 @see: Method L{Fsum.fadd} for further details.

1379 '''

1380 return self._facc_neg(xs)

1381

1382 def fsub_(self, *xs):

1383 '''Subtract all positional items from this instance.

1384

1385 @see: Method L{Fsum.fadd_} for further details.

1386 '''

1387 return self._fsub(xs[0], _sub_op_) if len(xs) == 1 else \

1388 self._facc_neg(xs, origin=1)

1389

1390 def _fsub(self, other, op):

1391 '''(INTERNAL) Apply C{B{self} -= B{other}}.

1392 '''

1393 if _isFsumTuple(other):

1394 if other is self: # or other._fprs2 == self._fprs2:

1395 self._fset(_0_0, n=len(self) * 2)

1396 elif other._ps:

1397 self._facc_scalar(other._ps_neg)

1398 elif self._scalar(other, op):

1399 self._facc_scalar_(-other)

1400 return self

1401

1402 def fsum(self, xs=()):

1403 '''Add an iterable's items, summate and return the

1404 current precision running sum.

1405

1406 @arg xs: Iterable of items to add (each item C{scalar}

1407 or an L{Fsum} or L{Fsum2Tuple} instance).

1408

1409 @return: Precision running sum (C{float} or C{int}).

1410

1411 @see: Method L{Fsum.fadd}.

1412

1413 @note: Accumulation can continue after summation.

1414 '''

1415 return self._facc(xs)._fprs

1416

1417 def fsum_(self, *xs):

1418 '''Add any positional items, summate and return the

1419 current precision running sum.

1420

1421 @arg xs: Items to add (each C{scalar} or an L{Fsum}

1422 or L{Fsum2Tuple} instance), all positional.

1423

1424 @return: Precision running sum (C{float} or C{int}).

1425

1426 @see: Methods L{Fsum.fsum}, L{Fsum.Fsum_} and L{Fsum.fsumf_}.

1427 '''

1428 return self._facc_1(xs)._fprs

1429

1430 @property_RO

1431 def _Fsum(self): # like L{Fsum2Tuple._Fsum}, for C{_2floats}, .fstats

1432 return self # NOT @Property_RO, see .copy and ._copy_2

1433

1434 def Fsum_(self, *xs, **name):

1435 '''Like method L{Fsum.fsum_} but returning a named L{Fsum}.

1436

1437 @kwarg name: Optional name (C{str}).

1438

1439 @return: Copy of this updated instance (L{Fsum}).

1440 '''

1441 return self._facc_1(xs)._copy_2(self.Fsum_, **name)

1442

1443 def Fsum2Tuple_(self, *xs, **name):

1444 '''Like method L{Fsum.fsum_} but returning a named L{Fsum2Tuple}.

1445

1446 @kwarg name: Optional name (C{str}).

1447

1448 @return: Precision running sum (L{Fsum2Tuple}).

1449 '''

1450 return Fsum2Tuple(self._facc_1(xs)._fprs2, **name)

1451

1452 def fsum2(self, xs=(), **name):

1453 '''Add an iterable's items, summate and return the

1454 current precision running sum I{and} the C{residual}.

1455

1456 @arg xs: Iterable of items to add (each item C{scalar}

1457 or an L{Fsum} or L{Fsum2Tuple} instance).

1458 @kwarg name: Optional C{B{name}=NN} (C{str}).

1459

1460 @return: L{Fsum2Tuple}C{(fsum, residual)} with C{fsum} the

1461 current precision running sum and C{residual}, the

1462 (precision) sum of the remaining C{partials}. The

1463 C{residual is INT0} if the C{fsum} is considered

1464 to be I{exact}.

1465

1466 @see: Methods L{Fsum.fint2}, L{Fsum.fsum} and L{Fsum.fsum2_}

1467 '''

1468 t = self._facc(xs)._fprs2

1469 return t.dup(name=name) if name else t

1470

1471 def fsum2_(self, *xs):

1472 '''Add any positional items, summate and return the current

1473 precision running sum and the I{differential}.

1474

1475 @arg xs: Values to add (each C{scalar} or an L{Fsum} or

1476 L{Fsum2Tuple} instance), all positional.

1477

1478 @return: 2Tuple C{(fsum, delta)} with the current, precision

1479 running C{fsum} like method L{Fsum.fsum} and C{delta},

1480 the difference with previous running C{fsum}, C{float}.

1481

1482 @see: Methods L{Fsum.fsum_} and L{Fsum.fsum}.

1483 '''

1484 return self._fsum2(xs, self._facc_1)

1485

1486 def _fsum2(self, xs, _facc, **origin):

1487 '''(INTERNAL) Helper for L{Fsum.fsum2_} and L{Fsum.fsum2f_}.

1488 '''

1489 p, q = self._fprs2

1490 if xs:

1491 s, r = _facc(xs, **origin)._fprs2

1492 return s, _2delta(s - p, r - q) # _fsum(_1primed((s, -p, r, -q))

1493 else:

1494 return p, _0_0

1495

1496 def fsumf_(self, *xs):

1497 '''Like method L{Fsum.fsum_} iff I{all} C{B{xs}} are I{known to be scalar}.

1498 '''

1499 return self._facc_scalar(xs)._fprs

1500

1501 def Fsumf_(self, *xs):

1502 '''Like method L{Fsum.Fsum_} iff I{all} C{B{xs}} are I{known to be scalar}.

1503 '''

1504 return self._facc_scalar(xs)._copy_2(self.Fsumf_)

1505

1506 def fsum2f_(self, *xs):

1507 '''Like method L{Fsum.fsum2_} iff I{all} C{B{xs}} are I{known to be scalar}.

1508 '''

1509 return self._fsum2(xs, self._facc_scalar, origin=1)

1510

1511# ftruediv = __itruediv__ # for naming consistency?

1512

1513 def _ftruediv(self, other, op, **raiser_RESIDUAL):

1514 '''(INTERNAL) Apply C{B{self} /= B{other}}.

1515 '''

1516 n = _1_0

1517 if _isFsumTuple(other):

1518 if other is self or self == other:

1519 return self._fset(n, n=len(self))

1520 d, r = other._fprs2

1521 if r:

1522 R = self._raiser(r, d, **raiser_RESIDUAL)

1523 if R:

1524 raise self._ResidualError(op, other, r, **R)

1525 d, n = other.as_integer_ratio()

1526 else:

1527 d = self._scalar(other, op)

1528 try:

1529 s = n / d

1530 except Exception as X:

1531 raise self._ErrorX(X, op, other)

1532 f = self._mul_scalar(s, _mul_op_) # handles 0, INF, NAN

1533 return self._fset(f)

1534

1535 @property_RO

1536 def imag(self):

1537 '''Get the C{imaginary} part of this instance (C{0.0}, always).

1538

1539 @see: Property L{Fsum.real}.

1540 '''

1541 return _0_0

1542

1543 def int_float(self, **raiser_RESIDUAL):

1544 '''Return this instance' current running sum as C{int} or C{float}.

1545

1546 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore

1547 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}

1548 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.

1549

1550 @return: This C{integer} sum if this instance C{is_integer},

1551 otherwise return the C{float} sum if the residual is

1552 zero or not significant.

1553

1554 @raise ResidualError: Non-zero, significant residual or invalid

1555 B{C{RESIDUAL}}.

1556

1557 @see: Methods L{Fsum.fint}, L{Fsum.fint2}, L{Fsum.RESIDUAL} and

1558 property L{Fsum.as_iscalar}.

1559 '''

1560 s, r = self._fint2

1561 if r:

1562 s, r = self._fprs2

1563 if r: # PYCHOK no cover

1564 R = self._raiser(r, s, **raiser_RESIDUAL)

1565 if R:

1566 t = _stresidual(_non_zero_, r, **R)

1567 raise ResidualError(int_float=s, txt=t)

1568 s = float(s)

1569 return s

1570

1571 def is_exact(self):

1572 '''Is this instance' running C{fsum} considered to be exact?

1573 (C{bool}), C{True} only if the C{residual is }L{INT0}.

1574 '''

1575 return self.residual is INT0

1576

1577 def is_integer(self):

1578 '''Is this instance' running sum C{integer}? (C{bool}).

1579

1580 @see: Methods L{Fsum.fint}, L{Fsum.fint2} and L{Fsum.is_scalar}.

1581 '''

1582 _, r = self._fint2

1583 return False if r else True

1584

1585 def is_math_fsum(self):

1586 '''Return whether functions L{fsum}, L{fsum_}, L{fsum1} and

1587 L{fsum1_} plus partials summation are based on Python's

1588 C{math.fsum} or not.

1589

1590 @return: C{2} if all functions and partials summation

1591 are based on C{math.fsum}, C{True} if only

1592 the functions are based on C{math.fsum} (and

1593 partials summation is not) or C{False} if

1594 none are.

1595 '''

1596 f = Fsum._math_fsum

1597 return 2 if _psum is f else bool(f)

1598

1599 def is_scalar(self, **raiser_RESIDUAL):

1600 '''Is this instance' running sum C{scalar} without residual or with

1601 a residual I{ratio} not exceeding the RESIDUAL threshold?

1602

1603 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore

1604 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}

1605 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.

1606

1607 @return: C{True} if this instance' non-zero residual C{ratio} exceeds

1608 the L{RESIDUAL<Fsum.RESIDUAL>} threshold (C{bool}).

1609

1610 @raise ResidualError: Non-zero, significant residual or invalid

1611 B{C{RESIDUAL}}.

1612

1613 @see: Method L{Fsum.RESIDUAL}, L{Fsum.is_integer} and property

1614 L{Fsum.as_iscalar}.

1615 '''

1616 s, r = self._fprs2

1617 return False if r and self._raiser(r, s, **raiser_RESIDUAL) else True

1618

1619 def _mul_Fsum(self, other, op=_mul_op_): # in .fmath.Fhorner

1620 '''(INTERNAL) Return C{B{self} * B{other}} as L{Fsum} or C{0}.

1621 '''

1622 # assert _isFsumTuple(other)

1623 if self._ps and other._ps:

1624 f = self._ps_mul(op, *other._ps) # NO .as_iscalar!

1625 else:

1626 f = _0_0

1627 return f

1628

1629 def _mul_scalar(self, factor, op): # in .fmath.Fhorner

1630 '''(INTERNAL) Return C{B{self} * scalar B{factor}} as L{Fsum}, C{0.0} or C{self}.

1631 '''

1632 # assert isscalar(factor)

1633 if self._ps and self._finite(factor, op):

1634 f = self if factor == _1_0 else (

1635 self._neg if factor == _N_1_0 else

1636 self._ps_mul(op, factor).as_iscalar)

1637 else:

1638 f = _0_0

1639 return f

1640

1641# @property_RO

1642# def _n_d(self):

1643# n, d = self.as_integer_ratio()

1644# return n / d

1645

1646 @property_RO

1647 def _neg(self):

1648 '''(INTERNAL) Return C{Fsum(-self)} or scalar C{NEG0}.

1649 '''

1650 return _Psum(self._ps_neg) if self._ps else NEG0

1651

1652 @property_RO

1653 def partials(self):

1654 '''Get this instance' current, partial sums (C{tuple} of C{float}s).

1655 '''

1656 return tuple(self._ps)

1657

1658 def pow(self, x, *mod, **raiser_RESIDUAL):

1659 '''Return C{B{self}**B{x}} as L{Fsum}.

1660

1661 @arg x: The exponent (C{scalar} or L{Fsum}).

1662 @arg mod: Optional modulus (C{int} or C{None}) for the 3-argument

1663 C{pow(B{self}, B{other}, B{mod})} version.

1664 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore

1665 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}

1666 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.

1667

1668 @return: The C{pow(self, B{x})} or C{pow(self, B{x}, *B{mod})}

1669 result (L{Fsum}).

1670

1671 @raise ResidualError: Non-zero, significant residual or invalid

1672 B{C{RESIDUAL}}.

1673

1674 @note: If B{C{mod}} is given and C{None}, the result will be an

1675 C{integer} L{Fsum} provided this instance C{is_integer}

1676 or set to C{integer} by an L{Fsum.fint} call.

1677

1678 @see: Methods L{Fsum.__ipow__}, L{Fsum.fint}, L{Fsum.is_integer}

1679 and L{Fsum.root}.

1680 '''

1681 f = self._copy_2(self.pow)

1682 return f._fpow(x, _pow_op_, *mod, **raiser_RESIDUAL) # f = pow(f, x, *mod)

1683

1684 def _pow(self, other, unused, op, **raiser_RESIDUAL):

1685 '''Return C{B{self} ** B{other}}.

1686 '''

1687 if _isFsumTuple(other):

1688 f = self._pow_Fsum(other, op, **raiser_RESIDUAL)

1689 elif self._scalar(other, op):

1690 x = self._finite(other, op)

1691 f = self._pow_scalar(x, other, op, **raiser_RESIDUAL)

1692 else:

1693 f = self._pow_0_1(0, other)

1694 return f

1695

1696 def _pow_0_1(self, x, other):

1697 '''(INTERNAL) Return B{C{self}**1} or C{B{self}**0 == 1.0}.

1698 '''

1699 return self if x else (1 if isint(other) and self.is_integer() else _1_0)

1700

1701 def _pow_2_3(self, b, x, other, op, *mod, **raiser_RESIDUAL):

1702 '''(INTERNAL) 2-arg C{pow(B{b}, scalar B{x})} and 3-arg C{pow(B{b},

1703 B{x}, int B{mod} or C{None})}, embellishing errors.

1704 '''

1705

1706 if mod: # b, x, mod all C{int}, unless C{mod} is C{None}

1707 m = mod[0]

1708 # assert _isFsumTuple(b)

1709

1710 def _s(s, r):

1711 R = self._raiser(r, s, **raiser_RESIDUAL)

1712 if R:

1713 raise self._ResidualError(op, other, r, mod=m, **R)

1714 return s

1715

1716 b = _s(*(b._fprs2 if m is None else b._fint2))

1717 x = _s(*_2scalar2(x))

1718

1719 try:

1720 # 0**INF == 0.0, 1**INF == 1.0, -1**2.3 == -(1**2.3)

1721 s = pow(b, x, *mod)

1722 if iscomplex(s):

1723 # neg**frac == complex in Python 3+, but ValueError in 2-

1724 raise ValueError(_strcomplex(s, b, x, *mod))

1725 return self._finite(s)

1726 except Exception as X:

1727 raise self._ErrorX(X, op, other, *mod)

1728

1729 def _pow_Fsum(self, other, op, **raiser_RESIDUAL):

1730 '''(INTERNAL) Return C{B{self} **= B{other}} for C{_isFsumTuple(other)}.

1731 '''

1732 # assert _isFsumTuple(other)

1733 x, r = other._fprs2

1734 f = self._pow_scalar(x, other, op, **raiser_RESIDUAL)

1735 if f and r:

1736 f *= self._pow_scalar(r, other, op, **raiser_RESIDUAL)

1737 return f

1738

1739 def _pow_int(self, x, other, op, **raiser_RESIDUAL):

1740 '''(INTERNAL) Return C{B{self} **= B{x}} for C{int B{x} >= 0}.

1741 '''

1742 # assert isint(x) and x >= 0

1743 ps = self._ps

1744 if len(ps) > 1:

1745 _mul_Fsum = Fsum._mul_Fsum

1746 if x > 4:

1747 p = self

1748 f = self if (x & 1) else _Psum_(_1_0)

1749 m = x >> 1 # // 2

1750 while m:

1751 p = _mul_Fsum(p, p, op) # p **= 2

1752 if (m & 1):

1753 f = _mul_Fsum(f, p, op) # f *= p

1754 m >>= 1 # //= 2

1755 elif x > 1: # self**2, 3, or 4

1756 f = _mul_Fsum(self, self, op)

1757 if x > 2: # self**3 or 4

1758 p = self if x < 4 else f

1759 f = _mul_Fsum(f, p, op)

1760 else: # self**1 or self**0 == 1 or _1_0

1761 f = self._pow_0_1(x, other)

1762 elif ps: # self._ps[0]**x

1763 f = self._pow_2_3(ps[0], x, other, op, **raiser_RESIDUAL)

1764 else: # PYCHOK no cover

1765 # 0**pos_int == 0, but 0**0 == 1

1766 f = 0 if x else 1

1767 return f

1768

1769 def _pow_scalar(self, x, other, op, **raiser_RESIDUAL):

1770 '''(INTERNAL) Return C{self**B{x}} for C{scalar B{x}}.

1771 '''

1772 s, r = self._fprs2

1773 if r:

1774 # assert s != 0

1775 if isint(x, both=True): # self**int

1776 x = int(x)

1777 y = abs(x)

1778 if y > 1:

1779 f = self._pow_int(y, other, op, **raiser_RESIDUAL)

1780 if x > 0: # i.e. > 1

1781 return f # Fsum or scalar

1782 # assert x < 0 # i.e. < -1

1783 if _isFsum(f):

1784 s, r = f._fprs2

1785 if r:

1786 return _1_Over(f, op, **raiser_RESIDUAL)

1787 else: # scalar

1788 s = f

1789 # use s**(-1) to get the CPython

1790 # float_pow error iff s is zero

1791 x = -1

1792 elif x < 0: # self**(-1)

1793 return _1_Over(self, op, **raiser_RESIDUAL) # 1 / self

1794 else: # self**1 or self**0

1795 return self._pow_0_1(x, other) # self, 1 or 1.0

1796 else: # self**fractional

1797 R = self._raiser(r, s, **raiser_RESIDUAL)

1798 if R:

1799 raise self._ResidualError(op, other, r, **R)

1800 n, d = self.as_integer_ratio()

1801 if abs(n) > abs(d):

1802 n, d, x = d, n, (-x)

1803 s = n / d

1804 # assert isscalar(s) and isscalar(x)

1805 return self._pow_2_3(s, x, other, op, **raiser_RESIDUAL)

1806

1807 def _ps_acc(self, ps, xs, up=True, **unused):

1808 '''(INTERNAL) Accumulate C{xs} known scalars into list C{ps}.

1809 '''

1810 n = 0

1811 _2s = _2sum

1812 for x in (tuple(xs) if xs is ps else xs):

1813 # assert isscalar(x) and _isfinite(x)

1814 if x:

1815 i = 0

1816 for p in ps:

1817 x, p = _2s(x, p)

1818 if p:

1819 ps[i] = p

1820 i += 1

1821 ps[i:] = (x,) if x else ()

1822 n += 1

1823 if n:

1824 self._n += n

1825 # Fsum._ps_max = max(Fsum._ps_max, len(ps))

1826 if up:

1827 self._update()

1828 return ps

1829

1830 def _ps_mul(self, op, *factors):

1831 '''(INTERNAL) Multiply this instance' C{partials} with

1832 each scalar C{factor} and accumulate into an C{Fsum}.

1833 '''

1834 def _pfs(ps, fs):

1835 if len(ps) < len(fs):

1836 ps, fs = fs, ps

1837 _fin = _isfinite

1838 for f in fs:

1839 for p in ps:

1840 p *= f

1841 yield p if _fin(p) else self._finite(p, op)

1842

1843 return Fsum()._facc_scalar(_pfs(self._ps, factors), up=False)

1844

1845 @property_RO

1846 def _ps_neg(self):

1847 '''(INTERNAL) Yield the partials, I{negated}.

1848 '''

1849 for p in self._ps:

1850 yield -p

1851

1852 def _ps_1sum(self, *less):

1853 '''(INTERNAL) Return the partials sum, 1-primed C{less} some scalars.

1854 '''

1855 def _1pls(ps, ls):

1856 yield _1_0

1857 for p in ps:

1858 yield p

1859 for p in ls:

1860 yield -p

1861 yield _N_1_0

1862

1863 return _fsum(_1pls(self._ps, less))

1864

1865 def _raiser(self, r, s, raiser=True, **RESIDUAL):

1866 '''(INTERNAL) Does ratio C{r / s} exceed the RESIDUAL threshold

1867 I{and} is residual C{r} I{non-zero} or I{significant} (for a

1868 negative respectively positive C{RESIDUAL} threshold)?

1869 '''

1870 if r and raiser:

1871 t = self._RESIDUAL

1872 if RESIDUAL:

1873 t = _threshold(t, **RESIDUAL)

1874 if t < 0 or (s + r) != s:

1875 q = (r / s) if s else s # == 0.

1876 if fabs(q) > fabs(t):

1877 return dict(ratio=q, R=t)

1878 return {}

1879

1880 rdiv = __rtruediv__

1881

1882 @property_RO

1883 def real(self):

1884 '''Get the C{real} part of this instance (C{float}).

1885

1886 @see: Methods L{Fsum.__float__} and L{Fsum.fsum}

1887 and properties L{Fsum.ceil}, L{Fsum.floor},

1888 L{Fsum.imag} and L{Fsum.residual}.

1889 '''

1890 return float(self._fprs)

1891

1892 @property_RO

1893 def residual(self):

1894 '''Get this instance' residual (C{float} or C{int}): the

1895 C{sum(partials)} less the precision running sum C{fsum}.

1896

1897 @note: The C{residual is INT0} iff the precision running

1898 C{fsum} is considered to be I{exact}.

1899

1900 @see: Methods L{Fsum.fsum}, L{Fsum.fsum2} and L{Fsum.is_exact}.

1901 '''

1902 return self._fprs2.residual

1903

1904 def RESIDUAL(self, *threshold):

1905 '''Get and set this instance' I{ratio} for raising L{ResidualError}s,

1906 overriding the default from env variable C{PYGEODESY_FSUM_RESIDUAL}.

1907

1908 @arg threshold: If C{scalar}, the I{ratio} to exceed for raising

1909 L{ResidualError}s in division and exponention, if

1910 C{None} restore the default set with env variable

1911 C{PYGEODESY_FSUM_RESIDUAL} or if omitted, keep the

1912 current setting.

1913

1914 @return: The previous C{RESIDUAL} setting (C{float}), default C{0.0}.

1915

1916 @raise ResidualError: Invalid B{C{threshold}}.

1917

1918 @note: L{ResidualError}s may be thrown if (1) the non-zero I{ratio}

1919 C{residual / fsum} exceeds the given B{C{threshold}} and (2)

1920 the C{residual} is non-zero and (3) I{significant} vs the

1921 C{fsum}, i.e. C{(fsum + residual) != fsum} and (4) optional

1922 keyword argument C{raiser=False} is missing. Specify a

1923 negative B{C{threshold}} for only non-zero C{residual}

1924 testing without I{significant}.

1925 '''

1926 r = self._RESIDUAL

1927 if threshold:

1928 t = threshold[0]

1929 self._RESIDUAL = Fsum._RESIDUAL if t is None else ( # for ...

1930 (_0_0 if t else _1_0) if isbool(t) else

1931 _threshold(t)) # ... backward compatibility

1932 return r

1933

1934 def _ResidualError(self, op, other, residual, **mod_R):

1935 '''(INTERNAL) Non-zero B{C{residual}} etc.

1936 '''

1937 def _p(mod=None, R=0, **unused): # ratio=0

1938 return (_non_zero_ if R < 0 else _significant_) \

1939 if mod is None else _integer_

1940

1941 t = _stresidual(_p(**mod_R), residual, **mod_R)

1942 return self._Error(op, other, ResidualError, txt=t)

1943

1944 def root(self, root, **raiser_RESIDUAL):

1945 '''Return C{B{self}**(1 / B{root})} as L{Fsum}.

1946

1947 @arg root: The order (C{scalar} or L{Fsum}), non-zero.

1948 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore

1949 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}

1950 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.

1951

1952 @return: The C{self ** (1 / B{root})} result (L{Fsum}).

1953

1954 @raise ResidualError: Non-zero, significant residual or invalid

1955 B{C{RESIDUAL}}.

1956

1957 @see: Method L{Fsum.pow}.

1958 '''

1959 x = _1_Over(root, _truediv_op_, **raiser_RESIDUAL)

1960 f = self._copy_2(self.root)

1961 return f._fpow(x, f.name, **raiser_RESIDUAL) # == pow(f, x)

1962

1963 def _scalar(self, other, op, **txt):

1964 '''(INTERNAL) Return scalar C{other}.

1965 '''

1966 if isscalar(other):

1967 return other

1968 raise self._Error(op, other, _TypeError, **txt) # _invalid_

1969

1970 def signOf(self, res=True):

1971 '''Determine the sign of this instance.

1972

1973 @kwarg res: If C{True} consider, otherwise

1974 ignore the residual (C{bool}).

1975

1976 @return: The sign (C{int}, -1, 0 or +1).

1977 '''

1978 s, r = self._fprs2

1979 r = (-r) if res else 0

1980 return _signOf(s, r)

1981

1982 def toRepr(self, **lenc_prec_sep_fmt): # PYCHOK signature

1983 '''Return this C{Fsum} instance as representation.

1984

1985 @kwarg lenc_prec_sep_fmt: Optional keyword arguments

1986 for method L{Fsum.toStr}.

1987

1988 @return: This instance (C{repr}).

1989 '''

1990 return Fmt.repr_at(self, self.toStr(**lenc_prec_sep_fmt))

1991

1992 def toStr(self, lenc=True, **prec_sep_fmt): # PYCHOK signature

1993 '''Return this C{Fsum} instance as string.

1994

1995 @kwarg lenc: If C{True} include the current C{[len]} of this

1996 L{Fsum} enclosed in I{[brackets]} (C{bool}).

1997 @kwarg prec_sep_fmt: Optional keyword arguments for method

1998 L{Fsum2Tuple.toStr}.

1999

2000 @return: This instance (C{str}).

2001 '''

2002 p = self.classname

2003 if lenc:

2004 p = Fmt.SQUARE(p, len(self))

2005 n = _enquote(self.name, white=_UNDER_)

2006 t = self._fprs2.toStr(**prec_sep_fmt)

2007 return NN(p, _SPACE_, n, t)

2008

2009 def _truediv(self, other, op, **raiser_RESIDUAL):

2010 '''(INTERNAL) Return C{B{self} / B{other}} as an L{Fsum}.

2011 '''

2012 f = self._copy_2(self.__truediv__)

2013 return f._ftruediv(other, op, **raiser_RESIDUAL)

2014

2015 def _update(self, updated=True): # see ._fset

2016 '''(INTERNAL) Zap all cached C{Property_RO} values.

2017 '''

2018 if updated:

2019 _pop = self.__dict__.pop

2020 for p in _ROs:

2021 _ = _pop(p, None)

2022# Fsum._fint2._update(self)

2023# Fsum._fprs ._update(self)

2024# Fsum._fprs2._update(self)

2025 return self # for .fset_

2026

2027_ROs = _allPropertiesOf_n(3, Fsum, Property_RO) # PYCHOK see Fsum._update

2028

2029

2030 def _Float_Int(arg, **name_Error):

2031 '''(INTERNAL) Unit of L{Fsum2Tuple} items.

2032 '''

2033 U = Int if isint(arg) else Float

2034 return U(arg, **name_Error)

2035

2036

2037 class DivMod2Tuple(_NamedTuple):

2038 '''2-Tuple C{(div, mod)} with the quotient C{div} and remainder

2039 C{mod} results of a C{divmod} operation.

2040

2041 @note: Quotient C{div} an C{int} in Python 3+ but a C{float}

2042 in Python 2-. Remainder C{mod} an L{Fsum} instance.

2043 '''

2044 _Names_ = (_div_, _mod_)

2045 _Units_ = (_Float_Int, Fsum)

2046

2047

2048 class Fsum2Tuple(_NamedTuple): # in .fstats

2049 '''2-Tuple C{(fsum, residual)} with the precision running C{fsum}

2050 and the C{residual}, the sum of the remaining partials. Each

2051 item is C{float} or C{int}.

2052

2053 @note: If the C{residual is INT0}, the C{fsum} is considered

2054 to be I{exact}, see method L{Fsum2Tuple.is_exact}.

2055 '''

2056 _Names_ = ( Fsum.fsum.__name__, Fsum.residual.name)

2057 _Units_ = (_Float_Int, _Float_Int)

2058

2059 def __abs__(self): # in .fmath

2060 return self._Fsum.__abs__()

2061

2062 def __bool__(self): # PYCHOK Python 3+

2063 return bool(self._Fsum)

2064

2065 def __eq__(self, other):

2066 return self._other_op(other, self.__eq__)

2067

2068 def __float__(self):

2069 return self._Fsum.__float__()

2070

2071 def __ge__(self, other):

2072 return self._other_op(other, self.__ge__)

2073

2074 def __gt__(self, other):

2075 return self._other_op(other, self.__gt__)

2076

2077 def __le__(self, other):

2078 return self._other_op(other, self.__le__)

2079

2080 def __lt__(self, other):

2081 return self._other_op(other, self.__lt__)

2082

2083 def __int__(self):

2084 return self._Fsum.__int__()

2085

2086 def __ne__(self, other):

2087 return self._other_op(other, self.__ne__)

2088

2089 def __neg__(self):

2090 return self._Fsum.__neg__()

2091

2092 __nonzero__ = __bool__ # Python 2-

2093

2094 def __pos__(self):

2095 return self._Fsum.__pos__()

2096

2097 def as_integer_ratio(self):

2098 '''Return this instance as the ratio of 2 integers.

2099

2100 @see: Method L{Fsum.as_integer_ratio} for further details.

2101 '''

2102 return self._Fsum.as_integer_ratio()

2103

2104 @property_RO

2105 def _fint2(self):

2106 return self._Fsum._fint2

2107

2108 @property_RO

2109 def _fprs2(self):

2110 return self._Fsum._fprs2

2111

2112 @Property_RO

2113 def _Fsum(self): # this C{Fsum2Tuple} as L{Fsum}, in .fstats

2114 s, r = _s_r(*self)

2115 ps = (r, s) if r else (s,)

2116 return _Psum(ps, name=self.name)

2117

2118 def Fsum_(self, *xs, **name_RESIDUAL):

2119 '''Return this C{Fsum2Tuple} as an L{Fsum} plus some C{xs}.

2120 '''

2121 f = _Psum(self._Fsum._ps, **name_RESIDUAL)

2122 return f._facc_1(xs, up=False) if xs else f

2123

2124 def is_exact(self):

2125 '''Is this L{Fsum2Tuple} considered to be exact? (C{bool}).

2126 '''

2127 return self._Fsum.is_exact()

2128

2129 def is_integer(self):

2130 '''Is this L{Fsum2Tuple} C{integer}? (C{bool}).

2131 '''

2132 return self._Fsum.is_integer()

2133

2134 def _mul_scalar(self, other, op): # for Fsum._fmul

2135 return self._Fsum._mul_scalar(other, op)

2136

2137 @property_RO

2138 def _n(self):

2139 return self._Fsum._n

2140

2141 def _other_op(self, other, which):

2142 C, s = (tuple, self) if isinstance(other, tuple) else (Fsum, self._Fsum)

2143 return getattr(C, which.__name__)(s, other)

2144

2145 @property_RO

2146 def _ps(self):

2147 return self._Fsum._ps

2148

2149 @property_RO

2150 def _ps_neg(self):

2151 return self._Fsum._ps_neg

2152

2153 def signOf(self, **res):

2154 '''Like method L{Fsum.signOf}.

2155 '''

2156 return self._Fsum.signOf(**res)

2157

2158 def toStr(self, fmt=Fmt.g, **prec_sep): # PYCHOK signature

2159 '''Return this L{Fsum2Tuple} as string (C{str}).

2160

2161 @kwarg fmt: Optional C{float} format (C{letter}).

2162 @kwarg prec_sep: Optional keyword arguments for function

2163 L{fstr<streprs.fstr>}.

2164 '''

2165 return Fmt.PAREN(fstr(self, fmt=fmt, strepr=str, force=False, **prec_sep))

2166

2167_Fsum_Fsum2Tuple_types = Fsum, Fsum2Tuple # PYCHOK lines

2168

2169

2170 class ResidualError(_ValueError):

2171 '''Error raised for a division, power or root operation of

2172 an L{Fsum} instance with a C{residual} I{ratio} exceeding

2173 the L{RESIDUAL<Fsum.RESIDUAL>} threshold.

2174

2175 @see: Module L{pygeodesy.fsums} and method L{Fsum.RESIDUAL}.

2176 '''

2177 pass

2178

2179

2180 try:

2181 from math import fsum as _fsum # precision IEEE-754 sum, Python 2.6+

2182

2183 # make sure _fsum works as expected (XXX check

2184 # float.__getformat__('float')[:4] == 'IEEE'?)

2185 if _fsum((1, 1e101, 1, -1e101)) != 2: # PYCHOK no cover

2186 del _fsum # nope, remove _fsum ...

2187 raise ImportError() # ... use _fsum below

2188

2189 Fsum._math_fsum = _sum = _fsum # PYCHOK exported

2190 except ImportError:

2191 _sum = sum # Fsum(NAN) exception fall-back, in .elliptic

2192

2193 def _fsum(xs):

2194 '''(INTERNAL) Precision summation, Python 2.5-.

2195 '''

2196 F = Fsum()

2197 F.name = _fsum.__name__

2198 return F._facc(xs, up=False)._fprs2.fsum

2199

2200

2201 def fsum(xs, floats=False):

2202 '''Precision floating point summation based on/like Python's C{math.fsum}.

2203

2204 @arg xs: Iterable of items to add (each C{scalar} or an L{Fsum} or L{Fsum2Tuple}

2205 instance).

2206 @kwarg floats: Use C{B{floats}=True} iff I{all} B{C{xs}} items are I{known to

2207 be scalar} (C{bool}).

2208

2209 @return: Precision C{fsum} (C{float}).

2210

2211 @raise OverflowError: Partial C{2sum} overflow.

2212

2213 @raise TypeError: Non-scalar B{C{xs}} item.

2214

2215 @raise ValueError: Invalid or non-finite B{C{xs}} item.

2216

2217 @note: Exception and I{non-finite} handling may differ if not based

2218 on Python's C{math.fsum}.

2219

2220 @see: Class L{Fsum} and methods L{Fsum.fsum} and L{Fsum.fadd}.

2221 '''

2222 return _fsum(xs if floats is True else _2floats(xs)) if xs else _0_0 # PYCHOK yield

2223

2224

2225 def fsum_(*xs, **floats):

2226 '''Precision floating point summation of all positional items.

2227

2228 @arg xs: Items to add (each C{scalar} or an L{Fsum} or L{Fsum2Tuple} instance),

2229 all positional.

2230 @kwarg floats: Use C{B{floats}=True} iff I{all} B{C{xs}} items are I{known to

2231 be scalar} (C{bool}).

2232

2233 @see: Function L{fsum<fsums.fsum>} for further details.

2234 '''

2235 return _fsum(xs if _xkwds_get1(floats, floats=False) is True else

2236 _2floats(xs, origin=1)) if xs else _0_0 # PYCHOK yield

2237

2238

2239 def fsumf_(*xs):

2240 '''Precision floating point summation iff I{all} C{B{xs}} items are I{known to be scalar}.

2241

2242 @see: Function L{fsum_<fsums.fsum_>} for further details.

2243 '''

2244 return _fsum(xs) if xs else _0_0

2245

2246

2247 def fsum1(xs, floats=False):

2248 '''Precision floating point summation, 1-primed.

2249

2250 @arg xs: Iterable of items to add (each C{scalar} or an L{Fsum} or L{Fsum2Tuple}

2251 instance).

2252 @kwarg floats: Use C{B{floats}=True} iff I{all} B{C{xs}} items are I{known to

2253 be scalar} (C{bool}).

2254

2255 @see: Function L{fsum<fsums.fsum>} for further details.

2256 '''

2257 return _fsum(_1primed(xs if floats is True else _2floats(xs))) if xs else _0_0 # PYCHOK yield

2258

2259

2260 def fsum1_(*xs, **floats):

2261 '''Precision floating point summation, 1-primed of all positional items.

2262

2263 @arg xs: Items to add (each C{scalar} or an L{Fsum} or L{Fsum2Tuple} instance),

2264 all positional.

2265 @kwarg floats: Use C{B{floats}=True} iff I{all} B{C{xs}} items are I{known to

2266 be scalar} (C{bool}).

2267

2268 @see: Function L{fsum_<fsums.fsum_>} for further details.

2269 '''

2270 return _fsum(_1primed(xs if _xkwds_get1(floats, floats=False) is True else

2271 _2floats(xs, origin=1))) if xs else _0_0 # PYCHOK yield

2272

2273

2274 def fsum1f_(*xs):

2275 '''Precision floating point summation iff I{all} C{B{xs}} items are I{known to be scalar}.

2276

2277 @see: Function L{fsum_<fsums.fsum_>} for further details.

2278 '''

2279 return _fsum(_1primed(xs)) if xs else _0_0

2280

2281

2282 if __name__ == '__main__':

2283

2284 # usage: [env _psum=fsum] python3 -m pygeodesy.fsums

2285

2286 if _getenv(_psum.__name__, NN) == _fsum.__name__:

2287 _psum = _fsum

2288

2289 def _test(n):

2290 # copied from Hettinger, see L{Fsum} reference

2291 from pygeodesy import frandoms, printf

2292

2293 printf(_fsum.__name__, end=_COMMASPACE_)

2294 printf(_psum.__name__, end=_COMMASPACE_)

2295

2296 F = Fsum()

2297 if F.is_math_fsum():

2298 for t in frandoms(n, seeded=True):

2299 assert float(F.fset_(*t)) == _fsum(t)

2300 printf(_DOT_, end=NN)

2301 printf(NN)

2302

2303 _test(128)

2304

2305# **) MIT License

2306#

2307# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.

2308#

2309# Permission is hereby granted, free of charge, to any person obtaining a

2310# copy of this software and associated documentation files (the "Software"),

2311# to deal in the Software without restriction, including without limitation

2312# the rights to use, copy, modify, merge, publish, distribute, sublicense,

2313# and/or sell copies of the Software, and to permit persons to whom the

2314# Software is furnished to do so, subject to the following conditions:

2315#

2316# The above copyright notice and this permission notice shall be included

2317# in all copies or substantial portions of the Software.

2318#

2319# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS

2320# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

2321# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL

2322# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR

2323# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,

2324# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR

2325# OTHER DEALINGS IN THE SOFTWARE.