1

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

3

4 u'''Class L{Fsum} for precision floating point summation similar to

5 Python's C{math.fsum} enhanced with I{running} summation and as an

6 option, accurate I{TwoProduct} multiplication.

7

8 Accurate multiplication is based on the C{math.fma} function for

9 Python 3.13 and newer or one of two equivalent C{fma} implementations

10 for Python 3.12 and older. To enable accurate multiplication, set

11 env variable C{PYGEODESY_FSUM_F2PRODUCT} to C{"std"} or any non-empty

12 string or invoke function C{pygeodesy.f2product(True)} or set. With

13 C{"std"} the C{fma} implemention follows the C{math.fma} function,

14 otherwise the C{PyGeodesy 24.09.09} release.

15

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

17 zero C{residue} aka C{residual} value, see property L{Fsum.residual}.

18

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

20 than C{"0.0"} as the threshold to throw a L{ResidualError} for a division,

21 power or root operation of an L{Fsum} with a C{residual} I{ratio} exceeding

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

23 and L{Fsum.__itruediv__}.

24

25 There are several C{integer} L{Fsum} cases, for example the result from

26 functions C{ceil}, C{floor}, C{Fsum.__floordiv__} and methods L{Fsum.fint},

27 L{Fsum.fint2} and L{Fsum.is_integer}. Also, L{Fsum} methods L{Fsum.pow},

28 L{Fsum.__ipow__}, L{Fsum.__pow__} and L{Fsum.__rpow__} return a (very long)

29 C{int} if invoked with optional argument C{mod} set to C{None}. The

30 C{residual} of an C{integer} L{Fsum} is between C{-1.0} and C{+1.0} and

31 will be C{INT0} if that is considered to be I{exact}.

32

33 Set env variable C{PYGEODESY_FSUM_NONFINITES} to C{"std"} or use function

34 C{pygeodesy.nonfiniterrors(False)} to allow I{non-finite} C{float}s like

35 C{inf}, C{INF}, C{NINF}, C{nan} and C{NAN} and to ignore C{OverflowError}

36 respectively C{ValueError} exceptions. However, in that case I{non-finite}

37 results may differ from Python's C{math.fsum} results.

38'''

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

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

41

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

43 _signOf, itemsorted, signOf, _xiterable, \

44 _xiterablen

45 from pygeodesy.constants import INF, INT0, MANT_DIG, NEG0, NINF, _0_0, \

46 _1_0, _N_1_0, _isfinite, _pos_self, \

47 Float, Int

48 from pygeodesy.errors import _AssertionError, _OverflowError, _TypeError, \

49 _ValueError, _xError, _xError2, _xkwds_get, \

50 _xkwds, _xkwds_get1, _xkwds_not, _xkwds_pop, \

51 _xsError

52 from pygeodesy.internals import _enquote, _passarg

53 from pygeodesy.interns import NN, _arg_, _COMMASPACE_, _DOT_, _from_, \

54 _not_finite_, _SPACE_, _std_, _UNDER_

55 from pygeodesy.lazily import _ALL_LAZY, _getenv, _sys_version_info2

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

57 _NotImplemented

58 from pygeodesy.props import _allPropertiesOf_n, deprecated_method, \

59 deprecated_property_RO, Property, \

60 Property_RO, property_RO

61 from pygeodesy.streprs import Fmt, fstr, unstr

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

63

64 from math import fabs, isinf, isnan, \

65 ceil as _ceil, floor as _floor # PYCHOK used! .ltp

66

67__all__ = _ALL_LAZY.fsums

68__version__ = '24.09.29'

69

70 from pygeodesy.interns import (

71 _PLUS_ as _add_op_, # in .auxilats.auxAngle

72 _EQUAL_ as _fset_op_,

73 _RANGLE_ as _gt_op_,

74 _LANGLE_ as _lt_op_,

75 _PERCENT_ as _mod_op_,

76 _STAR_ as _mul_op_,

77 _NOTEQUAL_ as _ne_op_,

78 _DASH_ as _sub_op_, # in .auxilats.auxAngle

79 _SLASH_ as _truediv_op_

80)

81_eq_op_ = _fset_op_ * 2 # _DEQUAL_

82_floordiv_op_ = _truediv_op_ * 2 # _DSLASH_

83_divmod_op_ = _floordiv_op_ + _mod_op_

84_F2PRODUCT = _getenv('PYGEODESY_FSUM_F2PRODUCT', NN)

85_ge_op_ = _gt_op_ + _fset_op_

86_iadd_op_ = _add_op_ + _fset_op_ # in .auxilats.auxAngle, .fstats

87_integer_ = 'integer'

88_isub_op_ = _sub_op_ + _fset_op_ # in .auxilats.auxAngle

89_le_op_ = _lt_op_ + _fset_op_

90_NONFINITEr = _0_0

91_NONFINITES = _getenv('PYGEODESY_FSUM_NONFINITES', NN)

92_non_zero_ = 'non-zero'

93_pow_op_ = _mul_op_ * 2 # _DSTAR_

94_RESIDUAL_0_0 = _getenv('PYGEODESY_FSUM_RESIDUAL', _0_0)

95_significant_ = 'significant'

96_threshold_ = 'threshold'

97

98

99 def _2finite(x): # in .fstats

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

101 '''

102 return (float(x) if _isfinite(x) # and isscalar(x)

103 else _nfError(x))

104

105

106 def _2float(index=None, _isfine=_isfinite, **name_x): # in .fmath, .fstats

107 '''(INTERNAL) Raise C{TypeError} or C{Overflow-/ValueError} if not finite.

108 '''

109 n, x = name_x.popitem() # _xkwds_item2(name_x)

110 try:

111 f = float(x)

112 return f if _isfine(f) else _nfError(x)

113 except Exception as X:

114 raise _xError(X, Fmt.INDEX(n, index), x)

115

116

117 def _X_ps(X): # for _2floats only

118 return X._ps

119

120

121 def _2floats(xs, origin=0, _X=_X_ps, _x=float, _isfine=_isfinite):

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

123 '''

124 try:

125 i, x = origin, xs

126 _FsT = _Fsum_2Tuple_types

127 for x in _xiterable(xs):

128 if isinstance(x, _FsT):

129 for p in _X(x._Fsum):

130 yield p

131 else:

132 f = _x(x)

133 yield f if _isfine(f) else _nfError(f)

134 i += 1

135 except Exception as X:

136 raise _xsError(X, xs, i, x)

137

138

139 try: # MCCABE 26

140 from math import fma as _fma

141

142 def _2products(x, ys, *zs):

143 # yield(x * y for y in ys) + yield(z in zs)

144 # TwoProductFMA U{Algorithm 3.5

145 # <https://www.TUHH.De/ti3/paper/rump/OgRuOi05.pdf>}

146 for y in ys:

147 f = x * y

148 yield f

149 yield _fma(x, y, -f)

150 for z in zs:

151 yield z

152

153# _2split3 = \

154 _2split3s = _passarg # in Fsum.is_math_fma

155

156 except ImportError: # PYCHOK DSPACE! Python 3.12-

157

158 if _F2PRODUCT and _F2PRODUCT != _std_:

159 # back to PyGeodesy 24.09.09, with _fmaX

160

161 def _fma(*a_b_c): # PYCHOK no cover

162 # mimick C{math.fma} from Python 3.13+,

163 # the same accuracy, but ~14x slower

164 (na, da), (nb, db), (nc, dc) = map(_2n_d, a_b_c)

165 n = na * nb * dc

166 n += da * db * nc

167 d = da * db * dc

168 try:

169 r = float(n / d)

170 except OverflowError: # "integer division result too large ..."

171 r = NINF if (_signOf(n, 0) * _signOf(d, 0)) < 0 else INF

172 return r if _isfinite(r) else _fmaX(r, *a_b_c) # "overflow in fma"

173

174 def _2n_d(x):

175 try: # int.as_integer_ratio in 3.8+

176 return x.as_integer_ratio()

177 except (AttributeError, OverflowError, TypeError, ValueError):

178 return (x if isint(x) else float(x)), 1

179 else:

180

181 def _fma(a, b, c): # PYCHOK redef

182 # mimick C{math.fma} from Python 3.13+,

183 # the same accuracy, but ~13x slower

184 b3s = _2split3(b), # 1-tuple of 3-tuple

185 r = _fsum(_2products(a, b3s, c))

186 return r if _isfinite(r) else _fmaX(r, a, b, c)

187

188 _2n_d = None # redef

189

190 def _fmaX(r, *a_b_c): # like Python 3.13+ I{Modules/mathmodule.c}:

191 # raise a ValueError for a NAN result from non-NAN C{a_b_c}s or

192 # OverflowError for a non-NAN result from all finite C{a_b_c}s.

193 if isnan(r):

194 def _x(x):

195 return not isnan(x)

196 else:

197 _x = _isfinite

198 if all(map(_x, a_b_c)):

199 raise _nfError(r, unstr(_fma, *a_b_c))

200 return r

201

202 def _2products(x, y3s, *zs): # PYCHOK in Fsum._f2mul

203 # yield(x * y3 for y3 in y3s) + yield(z in zs)

204 # TwoProduct U{Algorithm 3.3

205 # <https://www.TUHH.De/ti3/paper/rump/OgRuOi05.pdf>}

206 # also in Python 3.13+ C{Modules/mathmodule.c} under

207 # #ifndef UNRELIABLE_FMA ... #else ... #endif

208 _, a, b = _2split3(x)

209 for y, c, d in y3s:

210 y *= x

211 yield y

212 if False: # no cover

213 yield b * d - (((y - a * c) - b * c) - a * d)

214 # = b * d + (a * d - ((y - a * c) - b * c))

215 # = b * d + (a * d + (b * c - (y - a * c)))

216 # = b * d + (a * d + (b * c + (a * c - y)))

217 elif a:

218 yield a * c - y

219 yield b * c

220 if d:

221 yield a * d

222 yield b * d

223 else:

224 yield b * c - y

225 yield b * d

226 for z in zs:

227 yield z

228

229 _2FACTOR = pow(2, (MANT_DIG + 1) // 2) + _1_0 # 134217729 if MANT_DIG == 53

230

231 def _2split3(x):

232 # Split U{Algorithm 3.2

233 # <https://www.TUHH.De/ti3/paper/rump/OgRuOi05.pdf>}

234 a = c = x * _2FACTOR

235 a -= c - x

236 b = x - a

237 return x, a, b

238

239 def _2split3s(xs): # in Fsum.is_math_fma

240 return map(_2split3, xs)

241

242

243 def f2product(*two):

244 '''Turn accurate I{TwoProduct} multiplication on or off.

245

246 @arg two: If C{True}, turn I{TwoProduct} on, if C{False} off or

247 if C{None} or omitted, keep the current setting.

248

249 @return: The previous setting (C{bool}).

250

251 @see: I{TwoProduct} multiplication is based on the I{TwoProductFMA}

252 U{Algorithm 3.5 <https://www.TUHH.De/ti3/paper/rump/OgRuOi05.pdf>}

253 using function C{math.fma} from Python 3.13 and later or an

254 equivalent, slower implementation when not available.

255 '''

256 t = Fsum._f2product

257 if two and two[0] is not None:

258 Fsum._f2product = bool(two[0])

259 return t

260

261

262 def _Fsumf_(*xs): # in .auxLat, .ltp, ...

263 '''(INTERNAL) An C{Fsum(xs)}, all C{scalar}, an L{Fsum} or L{Fsum2Tuple}.

264 '''

265 return Fsum()._facc_scalarf(xs, up=False)

266

267

268 def _Fsum1f_(*xs): # in .albers

269 '''(INTERNAL) An C{Fsum(xs)}, all C{scalar}, an L{Fsum} or L{Fsum2Tuple}, 1-primed.

270 '''

271 return Fsum()._facc_scalarf(_1primed(xs), up=False)

272

273

274 def _2halfeven(s, r, p):

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

276 '''

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

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

279 r *= 2

280 t = s + r

281 if r == (t - s):

282 s = t

283 return s

284

285

286 def _isFsum(x): # in .fmath

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

288 '''

289 return isinstance(x, Fsum)

290

291

292 def _isFsum_2Tuple(x): # in .basics, .constants, .fmath, .fstats

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

294 '''

295 return isinstance(x, _Fsum_2Tuple_types)

296

297

298 def _isOK(unused):

299 '''(INTERNAL) Helper for C{Fsum._fsum2} and C{Fsum.nonfinites}.

300 '''

301 return True

302

303

304 def _isOK_or_finite(x, _isfine=_isfinite):

305 '''(INTERNAL) Is C{x} finite or is I{non-finite} OK?.

306 '''

307 # assert _isfine in (_isOK, _isfinite)

308 return _isfine(x)

309

310

311 def _ixError(X, xs, i, x, origin=0, which=None):

312 '''(INTERNAL) Error for C{xs} or C{x}, item C{xs[i]}.

313 '''

314 t = _xsError(X, xs, i + origin, x)

315 if which:

316 t = _COMMASPACE_(unstr(which, _Cdot=Fsum), t)

317 return _xError(X, t, txt=None)

318

319

320 def _nfError(x, *args):

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

322 '''

323 E = _NonfiniteError(x)

324 t = Fmt.PARENSPACED(_not_finite_, x)

325 if args: # in _fmaX, _2sum

326 return E(txt=t, *args)

327 raise E(t, txt=None)

328

329

330 def nonfiniterrors(*raiser):

331 '''Throw C{OverflowError} and C{ValueError} exceptions for or

332 handle I{non-finite} C{float}s as C{inf}, C{INF}, C{NINF},

333 C{nan} and C{NAN} in summations and multiplications.

334

335 @arg raiser: If C{True}, throw exceptions, if C{False} handle

336 I{non-finites} or if C{None} or omitted, leave

337 the setting unchanged.

338

339 @return: Previous setting (C{bool}).

340

341 @note: C{inf}, C{INF} and C{NINF} throw an C{OverflowError},

342 C{nan} and C{NAN} a C{ValueError}.

343 '''

344 d = Fsum._isfine

345 if raiser and raiser[0] is not None:

346 Fsum._isfine = {} if bool(raiser[0]) else Fsum._nonfinites_isfine_kwds[True]

347 return _xkwds_get1(d, _isfine=_isfinite) is _isfinite

348

349

350 def _NonfiniteError(x):

351 '''(INTERNAL) Return the Error class for C{x}, I{non-finite}.

352 '''

353 return _OverflowError if isinf(x) else (

354 _ValueError if isnan(x) else _AssertionError)

355

356

357 def _1primed(xs): # in .fmath

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

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

360 '''

361 yield _1_0

362 for x in xs:

363 yield x

364 yield _N_1_0

365

366

367 def _psum(ps, **_isfine): # PYCHOK used!

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

369 '''

370 # assert isinstance(ps, list)

371 i = len(ps) - 1

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

373 while i > 0:

374 i -= 1

375 s, r = _2sum(s, ps[i], **_isfine)

376 if r: # sum(ps) became inexact

377 if s:

378 ps[i:] = r, s

379 if i > 0:

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

381 break # return s

382 s = r # PYCHOK no cover

383 elif not _isfinite(s): # non-finite OK

384 i = 0 # collapse ps

385 if ps:

386 s += sum(ps)

387 ps[i:] = s,

388 return s

389

390

391 def _Psum(ps, **name_f2product_nonfinites_RESIDUAL):

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

393 '''

394 F = Fsum(**name_f2product_nonfinites_RESIDUAL)

395 if ps:

396 F._ps[:] = ps

397 F._n = len(F._ps)

398 return F

399

400

401 def _Psum_(*ps, **name_f2product_nonfinites_RESIDUAL): # in .fmath

402 '''(INTERNAL) Return an C{Fsum} from I{known scalar} C{ps}.

403 '''

404 return _Psum(ps, **name_f2product_nonfinites_RESIDUAL)

405

406

407 def _2scalar2(other):

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

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

410 '''

411 if _isFsum_2Tuple(other):

412 s, r = other._fint2

413 if r:

414 s, r = other._fprs2

415 if r: # PYCHOK no cover

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

417 else:

418 r = 0

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

420 if isint(s, both=True):

421 s = int(s)

422 return s, r

423

424

425 def _s_r(s, r):

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

427 '''

428 if r and _isfinite(s):

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

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

431 else:

432 r = INT0

433 return s, r

434

435

436 def _strcomplex(s, *args):

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

438 '''

439 c = _strcomplex.__name__[4:]

440 n = _sub_op_(len(args), _arg_)

441 t = unstr(pow, *args)

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

443

444

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

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

447 '''

448 p = _stresidual.__name__[3:]

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

450 for n, v in itemsorted(mod_ratio):

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

452 t = _COMMASPACE_(t, p)

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

454

455

456 def _2sum(a, b, _isfine=_isfinite): # in .testFmath

457 '''(INTERNAL) Return C{a + b} as 2-tuple C{(sum, residual)} with finite C{sum},

458 otherwise as 2-tuple C{(nonfinite, 0)} iff I{non-finites} are OK.

459 '''

460 # FastTwoSum U{Algorithm 1.1<https://www.TUHH.De/ti3/paper/rump/OgRuOi05.pdf>}

461

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

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

464 # 1974, Zeitschrift für Angewandte Mathmatik und Mechanik, vol 51, nr 1, p 39-51

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

466 s = a + b

467 if _isfinite(s):

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

469 r = (b - s) + a

470 else:

471 r = (a - s) + b

472 elif _isfine(s):

473 r = _NONFINITEr

474 else: # non-finite and not OK

475 t = unstr(_2sum, a, b)

476 raise _nfError(s, t)

477 return s, r

478

479

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

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

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

483 '''

484 if kwds:

485 threshold = _xkwds_get1(kwds, RESIDUAL=threshold)

486 try:

487 return _2finite(threshold) # PYCHOK None

488 except Exception as x:

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

490

491

492 class Fsum(_Named): # sync __methods__ with .vector3dBase.Vector3dBase, .fstats, ...

493 '''Precision floating point summation, I{running} summation and accurate multiplication.

494

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

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

497 intermediate, I{running} summuation.

498

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

500 i.e. any C{type} having method C{__float__}.

501

502 @note: Handling of I{non-finites} as C{inf}, C{INF}, C{NINF}, C{nan} and C{NAN} is

503 determined by function L{nonfiniterrors<fsums.nonfiniterrors>} for the default

504 and by method L{nonfinites<Fsum.nonfinites>} for individual C{Fsum} instances,

505 overruling the default. For backward compatibility, I{non-finites} raise

506 exceptions by default.

507

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

509 393090_Binary_floating_point_summatiaccurate_full/recipe-393090.py>},

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

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

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

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

514

515 @see: Method L{f2product<Fsum.f2product>} for details about accurate I{TwoProduct}

516 multiplication.

517

518 @see: Module L{fsums<pygeodesy.fsums>} for env variables C{PYGEODESY_FSUM_F2PRODUCT},

519 C{PYGEODESY_FSUM_NONFINITES} and C{PYGEODESY_FSUM_RESIDUAL}.

520 '''

521 _f2product = _sys_version_info2 > (3, 12) or bool(_F2PRODUCT)

522 _isfine = {} # == _isfinite

523 _n = 0

524# _ps = [] # partial sums

525# _ps_max = 0 # max(Fsum._ps_max, len(Fsum._ps)) # 41

526 _RESIDUAL = _threshold(_RESIDUAL_0_0)

527

528 def __init__(self, *xs, **name_f2product_nonfinites_RESIDUAL):

529 '''New L{Fsum}.

530

531 @arg xs: No, one or more initial items to accumulate (each C{scalar}, an

532 L{Fsum} or L{Fsum2Tuple}), all positional.

533 @kwarg name_f2product_nonfinites_RESIDUAL: Optional C{B{name}=NN} (C{str})

534 and settings C{B{f2product}=None} (C{bool}), C{B{nonfinites}=None}

535 (C{bool}) and C{B{RESIDUAL}=0.0} threshold (C{scalar}) for this

536 L{Fsum}.

537

538 @see: Methods L{Fsum.f2product}, L{Fsum.nonfinites}, L{Fsum.RESIDUAL},

539 L{Fsum.fadd} and L{Fsum.fadd_}.

540 '''

541 if name_f2product_nonfinites_RESIDUAL:

542 self._optionals(**name_f2product_nonfinites_RESIDUAL)

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

544 if xs:

545 self._facc_args(xs, up=False)

546

547 def __abs__(self):

548 '''Return C{abs(self)} as an L{Fsum}.

549 '''

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

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

552

553 def __add__(self, other):

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

555

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

557

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

559

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

561 '''

562 f = self._copy_2(self.__add__)

563 return f._fadd(other, _add_op_)

564

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

566 '''Return C{bool(B{self})}, C{True} iff C{residual} is zero.

567 '''

568 s, r = self._fprs2

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

570

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

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

573

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

575

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

577 '''

578 return self.ceil

579

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

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

582

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

584

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

586 '''

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

588 return _signOf(s, 0)

589

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

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

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

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

594

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

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

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

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

599

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

601 B{C{RESIDUAL}}.

602

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

604 '''

605 f = self._copy_2(self.__divmod__)

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

607

608 def __eq__(self, other):

609 '''Return C{(B{self} == B{other})} as C{bool} where B{C{other}}

610 is C{scalar}, an other L{Fsum} or L{Fsum2Tuple}.

611 '''

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

613

614 def __float__(self):

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

616

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

618 '''

619 return float(self._fprs)

620

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

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

623

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

625

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

627 '''

628 return self.floor

629

630 def __floordiv__(self, other):

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

632

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

634

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

636

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

638 '''

639 f = self._copy_2(self.__floordiv__)

640 return f._floordiv(other, _floordiv_op_)

641

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

643 '''Not implemented.'''

644 return _NotImplemented(self, *other)

645

646 def __ge__(self, other):

647 '''Return C{(B{self} >= B{other})}, see C{__eq__}.

648 '''

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

650

651 def __gt__(self, other):

652 '''Return C{(B{self} > B{other})}, see C{__eq__}.

653 '''

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

655

656 def __hash__(self): # PYCHOK no cover

657 '''Return C{hash(B{self})} as C{float}.

658 '''

659 # @see: U{Notes for type implementors<https://docs.Python.org/

660 # 3/library/numbers.html#numbers.Rational>}

661 return hash(self.partials) # tuple.__hash__()

662

663 def __iadd__(self, other):

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

665

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

667 an iterable of several of the former.

668

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

670

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

672 C{scalar} nor L{Fsum}.

673

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

675 '''

676 try:

677 return self._fadd(other, _iadd_op_)

678 except TypeError:

679 pass

680 _xiterable(other)

681 return self._facc(other)

682

683 def __ifloordiv__(self, other):

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

685

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

687

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

689

690 @raise ResidualError: Non-zero, significant residual

691 in B{C{other}}.

692

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

694

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

696

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

698

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

700 '''

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

702

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

704 '''Not implemented.'''

705 return _NotImplemented(self, other)

706

707 def __imod__(self, other):

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

709

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

711

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

713

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

715 '''

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

717

718 def __imul__(self, other):

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

720

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

722

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

724

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

726

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

728

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

730 '''

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

732

733 def __int__(self):

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

735

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

737 and L{Fsum.floor}.

738 '''

739 i, _ = self._fint2

740 return i

741

742 def __invert__(self): # PYCHOK no cover

743 '''Not implemented.'''

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

745 return _NotImplemented(self)

746

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

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

749

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

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

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

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

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

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

756

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

758

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

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

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

762

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

764

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

766 is non-zero and significant and either

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

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

769 C{None}.

770

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

772 invocation failed.

773

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

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

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

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

778 is given as C{0}.

779

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

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

782 '''

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

784

785 def __isub__(self, other):

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

787

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

789 an iterable of several of the former.

790

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

792

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

794

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

796 '''

797 try:

798 return self._fsub(other, _isub_op_)

799 except TypeError:

800 pass

801 _xiterable(other)

802 return self._facc_neg(other)

803

804 def __iter__(self):

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

806 '''

807 return iter(self.partials)

808

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

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

811

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

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

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

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

816

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

818

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

820

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

822 B{C{RESIDUAL}}.

823

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

825

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

827

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

829

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

831 '''

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

833

834 def __le__(self, other):

835 '''Return C{(B{self} <= B{other})}, see C{__eq__}.

836 '''

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

838

839 def __len__(self):

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

841 '''

842 return self._n

843

844 def __lt__(self, other):

845 '''Return C{(B{self} < B{other})}, see C{__eq__}.

846 '''

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

848

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

850 '''Not implemented.'''

851 return _NotImplemented(self, other)

852

853 def __mod__(self, other):

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

855

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

857 '''

858 f = self._copy_2(self.__mod__)

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

860

861 def __mul__(self, other):

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

863

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

865 '''

866 f = self._copy_2(self.__mul__)

867 return f._fmul(other, _mul_op_)

868

869 def __ne__(self, other):

870 '''Return C{(B{self} != B{other})}, see C{__eq__}.

871 '''

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

873

874 def __neg__(self):

875 '''Return C{copy(B{self})}, I{negated}.

876 '''

877 f = self._copy_2(self.__neg__)

878 return f._fset(self._neg)

879

880 def __pos__(self):

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

882 '''

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

884

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

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

887

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

889 '''

890 f = self._copy_2(self.__pow__)

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

892

893 def __radd__(self, other):

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

895

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

897 '''

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

899 return f._fadd(self, _add_op_)

900

901 def __rdivmod__(self, other):

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

903 C{(quotient, remainder)}.

904

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

906 '''

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

908 return f._fdivmod2(self, _divmod_op_)

909

910# def __repr__(self):

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

912# '''

913# return self.toRepr(lenc=True)

914

915 def __rfloordiv__(self, other):

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

917

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

919 '''

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

921 return f._floordiv(self, _floordiv_op_)

922

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

924 '''Not implemented.'''

925 return _NotImplemented(self, other)

926

927 def __rmod__(self, other):

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

929

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

931 '''

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

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

934

935 def __rmul__(self, other):

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

937

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

939 '''

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

941 return f._fmul(self, _mul_op_)

942

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

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

945

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

947 '''

948 f = self._copy_2(self.__round__)

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

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

951

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

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

954

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

956 '''

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

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

959

960 def __rsub__(self, other):

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

962

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

964 '''

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

966 return f._fsub(self, _sub_op_)

967

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

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

970

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

972 '''

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

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

975

976 def __str__(self):

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

978 '''

979 return self.toStr(lenc=True)

980

981 def __sub__(self, other):

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

983

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

985

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

987

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

989 '''

990 f = self._copy_2(self.__sub__)

991 return f._fsub(other, _sub_op_)

992

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

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

995

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

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

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

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

1000

1001 @return: The quotient (L{Fsum}).

1002

1003 @raise ResidualError: Non-zero, significant residual or invalid

1004 B{C{RESIDUAL}}.

1005

1006 @see: Method L{Fsum.__itruediv__}.

1007 '''

1008 return self._truediv(other, _truediv_op_, **raiser_RESIDUAL)

1009

1010 __trunc__ = __int__

1011

1012 if _sys_version_info2 < (3, 0): # PYCHOK no cover

1013 # <https://docs.Python.org/2/library/operator.html#mapping-operators-to-functions>

1014 __div__ = __truediv__

1015 __idiv__ = __itruediv__

1016 __long__ = __int__

1017 __nonzero__ = __bool__

1018 __rdiv__ = __rtruediv__

1019

1020 def as_integer_ratio(self):

1021 '''Return this instance as the ratio of 2 integers.

1022

1023 @return: 2-Tuple C{(numerator, denominator)} both C{int} with

1024 C{numerator} signed and C{denominator} non-zero and

1025 positive. The C{numerator} is I{non-finite} if this

1026 instance is.

1027

1028 @see: Method L{Fsum.fint2} and C{float.as_integer_ratio} in

1029 Python 2.7+.

1030 '''

1031 n, r = self._fint2

1032 if r:

1033 i, d = float(r).as_integer_ratio()

1034 n *= d

1035 n += i

1036 else: # PYCHOK no cover

1037 d = 1

1038 return n, d

1039

1040 @property_RO

1041 def as_iscalar(self):

1042 '''Get this instance I{as-is} (L{Fsum} with C{non-zero residual},

1043 C{scalar} or I{non-finite}).

1044 '''

1045 s, r = self._fprs2

1046 return self if r else s

1047

1048 @property_RO

1049 def ceil(self):

1050 '''Get this instance' C{ceil} value (C{int} in Python 3+, but

1051 C{float} in Python 2-).

1052

1053 @note: This C{ceil} takes the C{residual} into account.

1054

1055 @see: Method L{Fsum.int_float} and properties L{Fsum.floor},

1056 L{Fsum.imag} and L{Fsum.real}.

1057 '''

1058 s, r = self._fprs2

1059 c = _ceil(s) + int(r) - 1

1060 while r > (c - s): # (s + r) > c

1061 c += 1

1062 return c # _ceil(self._n_d)

1063

1064 cmp = __cmp__

1065

1066 def _cmp_0(self, other, op):

1067 '''(INTERNAL) Return C{scalar(self - B{other})} for 0-comparison.

1068 '''

1069 if _isFsum_2Tuple(other):

1070 s = self._ps_1sum(*other._ps)

1071 elif self._scalar(other, op):

1072 s = self._ps_1sum(other)

1073 else:

1074 s = self.signOf() # res=True

1075 return s

1076

1077 def copy(self, deep=False, **name):

1078 '''Copy this instance, C{shallow} or B{C{deep}}.

1079

1080 @kwarg name: Optional, overriding C{B{name}='"copy"} (C{str}).

1081

1082 @return: The copy (L{Fsum}).

1083 '''

1084 n = _name__(name, name__=self.copy)

1085 f = _Named.copy(self, deep=deep, name=n)

1086 if f._ps is self._ps:

1087 f._ps = list(self._ps) # separate list

1088 if not deep:

1089 f._n = 1

1090 # assert f._f2product == self._f2product

1091 # assert f._Fsum is f

1092 return f

1093

1094 def _copy_2(self, which, name=NN):

1095 '''(INTERNAL) Copy for I{dyadic} operators.

1096 '''

1097 n = name or which.__name__ # _dunder_nameof

1098 # NOT .classof due to .Fdot(a, *b) args, etc.

1099 f = _Named.copy(self, deep=False, name=n)

1100 f._ps = list(self._ps) # separate list

1101 # assert f._n == self._n

1102 # assert f._f2product == self._f2product

1103 # assert f._Fsum is f

1104 return f

1105

1106 def _copy_2r(self, other, which):

1107 '''(INTERNAL) Copy for I{reverse-dyadic} operators.

1108 '''

1109 return other._copy_2(which) if _isFsum(other) else \

1110 self._copy_2(which)._fset(other)

1111

1112 divmod = __divmod__

1113

1114 def _Error(self, op, other, Error, **txt_cause):

1115 '''(INTERNAL) Format an B{C{Error}} for C{{self} B{op} B{other}}.

1116 '''

1117 # self.as_iscalar causes RecursionError for ._fprs2 errors

1118 s = _Psum(self._ps, nonfinites=True, name=self.name)

1119 return Error(_SPACE_(s.as_iscalar, op, other), **txt_cause)

1120

1121 def _ErrorX(self, X, op, other, *mod):

1122 '''(INTERNAL) Format the caught exception C{X}.

1123 '''

1124 E, t = _xError2(X)

1125 if mod:

1126 t = _COMMASPACE_(Fmt.PARENSPACED(mod=mod[0]), t)

1127 return self._Error(op, other, E, txt=t, cause=X)

1128

1129 def _ErrorXs(self, X, xs, **kwds): # in .fmath

1130 '''(INTERNAL) Format the caught exception C{X}.

1131 '''

1132 E, t = _xError2(X)

1133 u = unstr(self.named3, *xs[:3], _ELLIPSIS=len(xs) > 3, **kwds)

1134 return E(u, txt=t, cause=X)

1135

1136 def _facc(self, xs, up=True, **origin_X_x):

1137 '''(INTERNAL) Accumulate more C{scalars} or L{Fsum}s.

1138 '''

1139 if xs:

1140 kwds = _xkwds(self._isfine, **origin_X_x)

1141 fs = _2floats(xs, **kwds) # PYCHOK yield

1142 ps = self._ps

1143 ps[:] = self._ps_acc(list(ps), fs, up=up)

1144 return self

1145

1146 def _facc_args(self, xs, **up):

1147 '''(INTERNAL) Accumulate 0, 1 or more C{xs}, all positional

1148 arguments in the caller of this method.

1149 '''

1150 return self._facc(xs, origin=1, **up) if len(xs) != 1 else \

1151 self._fadd(xs[0], _add_op_, **up)

1152

1153 def _facc_neg(self, xs, **up_origin):

1154 '''(INTERNAL) Accumulate more C{xs}, negated.

1155 '''

1156 def _N(X):

1157 return X._ps_neg

1158

1159 def _n(x):

1160 return -float(x)

1161

1162 return self._facc(xs, _X=_N, _x=_n, **up_origin)

1163

1164 def _facc_power(self, power, xs, which, **raiser_RESIDUAL): # in .fmath

1165 '''(INTERNAL) Add each C{xs} as C{float(x**power)}.

1166 '''

1167 def _Pow4(p):

1168 r = 0

1169 if _isFsum_2Tuple(p):

1170 s, r = p._fprs2

1171 if r:

1172 m = Fsum._pow

1173 else: # scalar

1174 return _Pow4(s)

1175 elif isint(p, both=True) and int(p) >= 0:

1176 p = s = int(p)

1177 m = Fsum._pow_int

1178 else:

1179 p = s = _2float(power=p, **self._isfine)

1180 m = Fsum._pow_scalar

1181 return m, p, s, r

1182

1183 _Pow, p, s, r = _Pow4(power)

1184 if p: # and xs:

1185 op = which.__name__

1186 _FsT = _Fsum_2Tuple_types

1187 _pow = self._pow_2_3

1188

1189 def _P(X):

1190 f = _Pow(X, p, power, op, **raiser_RESIDUAL)

1191 return f._ps if isinstance(f, _FsT) else (f,)

1192

1193 def _p(x):

1194 x = float(x)

1195 f = _pow(x, s, power, op, **raiser_RESIDUAL)

1196 if f and r:

1197 f *= _pow(x, r, power, op, **raiser_RESIDUAL)

1198 return f

1199

1200 f = self._facc(xs, origin=1, _X=_P, _x=_p)

1201 else:

1202 f = self._facc_scalar_(float(len(xs))) # x**0 == 1

1203 return f

1204

1205 def _facc_scalar(self, xs, **up):

1206 '''(INTERNAL) Accumulate all C{xs}, each C{scalar}.

1207 '''

1208 if xs:

1209 _ = self._ps_acc(self._ps, xs, **up)

1210 return self

1211

1212 def _facc_scalar_(self, *xs, **up):

1213 '''(INTERNAL) Accumulate all positional C{xs}, each C{scalar}.

1214 '''

1215 return self._facc_scalar(xs, **up)

1216

1217 def _facc_scalarf(self, xs, **origin_which):

1218 '''(INTERNAL) Accumulate all C{xs}, each C{scalar}, an L{Fsum} or

1219 L{Fsum2Tuple}, like function C{_xsum}.

1220 '''

1221 i_x = [0, xs]

1222 try:

1223 nf = self.nonfinitesOK

1224 return self._facc_scalar(_xs(xs, i_x, nf))

1225 except (OverflowError, TypeError, ValueError) as X:

1226 raise _ixError(X, xs, *i_x, **origin_which)

1227

1228# def _facc_up(self, up=True):

1229# '''(INTERNAL) Update the C{partials}, by removing

1230# and re-accumulating the final C{partial}.

1231# '''

1232# ps = self._ps

1233# while len(ps) > 1:

1234# p = ps.pop()

1235# if p:

1236# n = self._n

1237# _ = self._ps_acc(ps, (p,), up=False)

1238# self._n = n

1239# break

1240# return self._update() if up else self

1241

1242 def fadd(self, xs=()):

1243 '''Add an iterable's items to this instance.

1244

1245 @arg xs: Iterable of items to add (each C{scalar}

1246 or an L{Fsum} or L{Fsum2Tuple} instance).

1247

1248 @return: This instance (L{Fsum}).

1249

1250 @raise OverflowError: Partial C{2sum} overflow.

1251

1252 @raise TypeError: An invalid B{C{xs}} item.

1253

1254 @raise ValueError: Invalid or I{non-finite} B{C{xs}} value.

1255 '''

1256 if _isFsum_2Tuple(xs):

1257 self._facc_scalar(xs._ps)

1258 elif isscalar(xs): # for backward compatibility # PYCHOK no cover

1259 x = _2float(x=xs, **self._isfine)

1260 self._facc_scalar_(x)

1261 elif xs: # _xiterable(xs)

1262 self._facc(xs)

1263 return self

1264

1265 def fadd_(self, *xs):

1266 '''Add all positional items to this instance.

1267

1268 @arg xs: Values to add (each C{scalar} or an L{Fsum}

1269 or L{Fsum2Tuple} instance), all positional.

1270

1271 @see: Method L{Fsum.fadd} for further details.

1272 '''

1273 return self._facc_args(xs)

1274

1275 def _fadd(self, other, op, **up): # in .fmath.Fhorner

1276 '''(INTERNAL) Apply C{B{self} += B{other}}.

1277 '''

1278 if _isFsum_2Tuple(other):

1279 if self._ps:

1280 self._facc_scalar(other._ps, **up)

1281 else:

1282 self._fset(other, op=op, **up)

1283 elif self._scalar(other, op):

1284 if self._ps:

1285 self._facc_scalar_(other, **up)

1286 else:

1287 self._fset(other, op=op, **up)

1288 return self

1289

1290 fcopy = copy # for backward compatibility

1291 fdiv = __itruediv__

1292 fdivmod = __divmod__

1293

1294 def _fdivmod2(self, other, op, **raiser_RESIDUAL):

1295 '''(INTERNAL) Apply C{B{self} %= B{other}} and return a L{DivMod2Tuple}.

1296 '''

1297 # result mostly follows CPython function U{float_divmod

1298 # <https://GitHub.com/python/cpython/blob/main/Objects/floatobject.c>},

1299 # but at least divmod(-3, 2) equals Cpython's result (-2, 1).

1300 q = self._truediv(other, op, **raiser_RESIDUAL).floor

1301 if q: # == float // other == floor(float / other)

1302 self -= self._Fsum_as(q) * other # NOT other * q!

1303

1304 s = signOf(other) # make signOf(self) == signOf(other)

1305 if s and self.signOf() == -s: # PYCHOK no cover

1306 self += other

1307 q -= 1

1308# t = self.signOf()

1309# if t and t != s:

1310# raise self._Error(op, other, _AssertionError, txt__=signOf)

1311 return DivMod2Tuple(q, self) # q is C{int} in Python 3+, but C{float} in Python 2-

1312

1313 def _fhorner(self, x, cs, op, incx=True): # in .fmath

1314 '''(INTERNAL) Add an L{Fhorner} evaluation of polynomial

1315 C{sum(cs[i] * B{x}**i for i=0..len(cs)-1) if B{incx}

1316 else sum(... i=len(cs)-1..0)}.

1317 '''

1318 if _xiterablen(cs):

1319 H = self._Fsum_as(name__=self._fhorner)

1320 if _isFsum_2Tuple(x):

1321 _mul = H._mul_Fsum

1322 else:

1323 _mul = H._mul_scalar

1324 x = _2float(x=x, **self._isfine)

1325 if len(cs) > 1 and x:

1326 for c in (reversed(cs) if incx else cs):

1327 H._fset_ps(_mul(x, op))

1328 H._fadd(c, op, up=False)

1329 else: # x == 0

1330 H = cs[0] if cs else _0_0

1331 self._fadd(H, op)

1332 return self

1333

1334 def _finite(self, other, op=None):

1335 '''(INTERNAL) Return B{C{other}} if C{finite}.

1336 '''

1337 if _isOK_or_finite(other, **self._isfine):

1338 return other

1339 E = _NonfiniteError(other)

1340 raise self._Error(op, other, E, txt=_not_finite_)

1341

1342 def fint(self, name=NN, **raiser_RESIDUAL):

1343 '''Return this instance' current running sum as C{integer}.

1344

1345 @kwarg name: Optional, overriding C{B{name}="fint"} (C{str}).

1346 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore

1347 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}

1348 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.

1349

1350 @return: The C{integer} sum (L{Fsum}) if this instance C{is_integer}

1351 with a zero or insignificant I{integer} residual.

1352

1353 @raise ResidualError: Non-zero, significant residual or invalid

1354 B{C{RESIDUAL}}.

1355

1356 @see: Methods L{Fsum.fint2}, L{Fsum.int_float} and L{Fsum.is_integer}.

1357 '''

1358 i, r = self._fint2

1359 if r:

1360 R = self._raiser(r, i, **raiser_RESIDUAL)

1361 if R:

1362 t = _stresidual(_integer_, r, **R)

1363 raise ResidualError(_integer_, i, txt=t)

1364 return self._Fsum_as(i, name=_name__(name, name__=self.fint))

1365

1366 def fint2(self, **name):

1367 '''Return this instance' current running sum as C{int} and the

1368 I{integer} residual.

1369

1370 @kwarg name: Optional name (C{str}).

1371

1372 @return: An L{Fsum2Tuple}C{(fsum, residual)} with C{fsum}

1373 an C{int} and I{integer} C{residual} a C{float} or

1374 C{INT0} if the C{fsum} is considered to be I{exact}.

1375 The C{fsum} is I{non-finite} if this instance is.

1376 '''

1377 return Fsum2Tuple(*self._fint2, **name)

1378

1379 @Property

1380 def _fint2(self): # see ._fset

1381 '''(INTERNAL) Get 2-tuple (C{int}, I{integer} residual).

1382 '''

1383 s, _ = self._fprs2

1384 try:

1385 i = int(s)

1386 r = (self._ps_1sum(i) if len(self._ps) > 1 else

1387 float(s - i)) or INT0

1388 except (OverflowError, ValueError) as X:

1389 r = _NONFINITEr # INF, NAN, NINF

1390 i = self._fintX(X, sum(self._ps))

1391 return i, r # Fsum2Tuple?

1392

1393 @_fint2.setter_ # PYCHOK setter_UNDERscore!

1394 def _fint2(self, s): # in _fset

1395 '''(INTERNAL) Replace the C{_fint2} value.

1396 '''

1397 try:

1398 i = int(s)

1399 r = (s - i) or INT0

1400 except (OverflowError, ValueError) as X:

1401 r = _NONFINITEr # INF, NAN, NINF

1402 i = self._fintX(X, float(s))

1403 return i, r # like _fint2.getter

1404

1405 def _fintX(self, X, i): # PYCHOK X

1406 '''(INTERNAL) Handle I{non-finite} C{int}.

1407 '''

1408 # "cannot convert float infinity to integer"

1409 return i # ignore such Overflow-/ValueErrors

1410 # op = int.__name__

1411 # return self._nonfiniteX(X, op, i)

1412

1413 @deprecated_property_RO

1414 def float_int(self): # PYCHOK no cover

1415 '''DEPRECATED, use method C{Fsum.int_float}.'''

1416 return self.int_float() # raiser=False

1417

1418 @property_RO

1419 def floor(self):

1420 '''Get this instance' C{floor} (C{int} in Python 3+, but

1421 C{float} in Python 2-).

1422

1423 @note: This C{floor} takes the C{residual} into account.

1424

1425 @see: Method L{Fsum.int_float} and properties L{Fsum.ceil},

1426 L{Fsum.imag} and L{Fsum.real}.

1427 '''

1428 s, r = self._fprs2

1429 f = _floor(s) + _floor(r) + 1

1430 while (f - s) > r: # f > (s + r)

1431 f -= 1

1432 return f # _floor(self._n_d)

1433

1434# ffloordiv = __ifloordiv__ # for naming consistency?

1435# floordiv = __floordiv__ # for naming consistency?

1436

1437 def _floordiv(self, other, op, **raiser_RESIDUAL): # rather _ffloordiv?

1438 '''Apply C{B{self} //= B{other}}.

1439 '''

1440 q = self._ftruediv(other, op, **raiser_RESIDUAL) # == self

1441 return self._fset(q.floor) # floor(q)

1442

1443 def fma(self, other1, other2, **nonfinites): # in .fmath.fma

1444 '''Fused-multiply-add C{self *= B{other1}; self += B{other2}}.

1445

1446 @arg other1: Multiplier (C{scalar}, an L{Fsum} or L{Fsum2Tuple}).

1447 @arg other2: Addend (C{scalar}, an L{Fsum} or L{Fsum2Tuple}).

1448 @kwarg nonfinites: Use C{B{nonfinites}=True} or C{False}, to

1449 override L{nonfinites<Fsum.nonfinites>} and

1450 L{nonfiniterrors} default (C{bool}).

1451 '''

1452 op = self.fma.__name__

1453 _fs = self._ps_other

1454 try:

1455 s, r = self._fprs2

1456 if r:

1457 f = self._f2mul(self.fma, other1, **nonfinites)

1458 f += other2

1459 else:

1460 fs = _2split3s(_fs(op, other1))

1461 fs = _2products(s, fs, *_fs(op, other2))

1462 f = _Psum(self._ps_acc([], fs, up=False), name=op)

1463 except TypeError as X:

1464 raise self._ErrorX(X, op, (other1, other2))

1465 except (OverflowError, ValueError) as X: # from math.fma

1466 f = self._mul_reduce(op, s, other1) # INF, NAN, NINF

1467 f = sum(_fs(op, f, other2))

1468 f = self._nonfiniteX(X, op, f, **nonfinites)

1469 return self._fset(f)

1470

1471 fmul = __imul__

1472

1473 def _fmul(self, other, op):

1474 '''(INTERNAL) Apply C{B{self} *= B{other}}.

1475 '''

1476 if _isFsum_2Tuple(other):

1477 if len(self._ps) != 1:

1478 f = self._mul_Fsum(other, op)

1479 elif len(other._ps) != 1: # and len(self._ps) == 1

1480 f = self._ps_mul(op, *other._ps) if other._ps else _0_0

1481 elif self._f2product: # len(other._ps) == 1

1482 f = self._mul_scalar(other._ps[0], op)

1483 else: # len(other._ps) == len(self._ps) == 1

1484 f = self._finite(self._ps[0] * other._ps[0], op=op)

1485 else:

1486 s = self._scalar(other, op)

1487 f = self._mul_scalar(s, op)

1488 return self._fset(f) # n=len(self) + 1

1489

1490 @deprecated_method

1491 def f2mul(self, *others, **raiser):

1492 '''DEPRECATED on 2024.09.13, use method L{f2mul_<Fsum.f2mul_>}.'''

1493 return self._fset(self.f2mul_(*others, **raiser))

1494

1495 def f2mul_(self, *others, **nonfinites): # in .fmath.f2mul

1496 '''Return C{B{self} * B{other} * B{other} ...} for all B{C{others}} using cascaded,

1497 accurate multiplication like with L{f2product<Fsum.f2product>} set to C{True}.

1498

1499 @arg others: Multipliers (each C{scalar}, an L{Fsum} or L{Fsum2Tuple}), all

1500 positional.

1501 @kwarg nonfinites: Use C{B{nonfinites}=True} or C{False}, to override both

1502 L{nonfinites<Fsum.nonfinites>} and the L{nonfiniterrors}

1503 default (C{bool}).

1504

1505 @return: The cascaded I{TwoProduct} (L{Fsum} or C{float}).

1506

1507 @see: U{Equations 2.3<https://www.TUHH.De/ti3/paper/rump/OzOgRuOi06.pdf>}

1508 '''

1509 return self._f2mul(self.f2mul_, *others, **nonfinites)

1510

1511 def _f2mul(self, where, *others, **nonfinites_raiser):

1512 '''(INTERNAL) See methods C{fma} and C{f2mul_}.

1513 '''

1514 f = self._copy_2(where)

1515 ps = f._ps

1516 if ps and others:

1517 op = where.__name__

1518 try:

1519 for other in others: # to pinpoint errors

1520 for p in self._ps_other(op, other):

1521 pfs = _2products(p, _2split3s(ps))

1522 ps[:] = f._ps_acc([], pfs, up=False)

1523 f._update()

1524 except TypeError as X:

1525 raise self._ErrorX(X, op, other)

1526 except (OverflowError, ValueError) as X:

1527 r = self._mul_reduce(op, sum(ps), other) # INF, NAN, NINF

1528 r = self._nonfiniteX(X, op, r, **nonfinites_raiser)

1529 f._fset(r)

1530 return f

1531

1532 def fover(self, over, **raiser_RESIDUAL):

1533 '''Apply C{B{self} /= B{over}} and summate.

1534

1535 @arg over: An L{Fsum} or C{scalar} denominator.

1536 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore

1537 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}

1538 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.

1539

1540 @return: Precision running sum (C{float}).

1541

1542 @raise ResidualError: Non-zero, significant residual or invalid

1543 B{C{RESIDUAL}}.

1544

1545 @see: Methods L{Fsum.fsum} and L{Fsum.__itruediv__}.

1546 '''

1547 return float(self.fdiv(over, **raiser_RESIDUAL)._fprs)

1548

1549 fpow = __ipow__

1550

1551 def _fpow(self, other, op, *mod, **raiser_RESIDUAL):

1552 '''Apply C{B{self} **= B{other}}, optional B{C{mod}} or C{None}.

1553 '''

1554 if mod:

1555 if mod[0] is not None: # == 3-arg C{pow}

1556 f = self._pow_2_3(self, other, other, op, *mod, **raiser_RESIDUAL)

1557 elif self.is_integer():

1558 # return an exact C{int} for C{int}**C{int}

1559 i, _ = self._fint2 # assert _ == 0

1560 x, r = _2scalar2(other) # C{int}, C{float} or other

1561 f = self._Fsum_as(i)._pow_Fsum(other, op, **raiser_RESIDUAL) if r else \

1562 self._pow_2_3(i, x, other, op, **raiser_RESIDUAL)

1563 else: # mod[0] is None, power(self, other)

1564 f = self._pow(other, other, op, **raiser_RESIDUAL)

1565 else: # pow(self, other)

1566 f = self._pow(other, other, op, **raiser_RESIDUAL)

1567 return self._fset(f) # n=max(len(self), 1)

1568

1569 def f2product(self, *two):

1570 '''Get and set accurate I{TwoProduct} multiplication for this

1571 L{Fsum}, overriding the L{f2product} default.

1572

1573 @arg two: If omitted, leave the override unchanged, if C{True},

1574 turn I{TwoProduct} on, if C{False} off, if C{None}e

1575 remove th override (C{bool} or C{None}).

1576

1577 @return: The previous setting (C{bool} or C{None} if not set).

1578

1579 @see: Function L{f2product<fsums.f2product>}.

1580

1581 @note: Use C{f.f2product() or f2product()} to determine whether

1582 multiplication is accurate for L{Fsum} C{f}.

1583 '''

1584 if two: # delattrof(self, _f2product=None)

1585 t = _xkwds_pop(self.__dict__, _f2product=None)

1586 if two[0] is not None:

1587 self._f2product = bool(two[0])

1588 else: # getattrof(self, _f2product=None)

1589 t = _xkwds_get(self.__dict__, _f2product=None)

1590 return t

1591

1592 @Property

1593 def _fprs(self):

1594 '''(INTERNAL) Get and cache this instance' precision

1595 running sum (C{float} or C{int}), ignoring C{residual}.

1596

1597 @note: The precision running C{fsum} after a C{//=} or

1598 C{//} C{floor} division is C{int} in Python 3+.

1599 '''

1600 s, _ = self._fprs2

1601 return s # ._fprs2.fsum

1602

1603 @_fprs.setter_ # PYCHOK setter_UNDERscore!

1604 def _fprs(self, s):

1605 '''(INTERNAL) Replace the C{_fprs} value.

1606 '''

1607 return s

1608

1609 @Property

1610 def _fprs2(self):

1611 '''(INTERNAL) Get and cache this instance' precision

1612 running sum and residual (L{Fsum2Tuple}).

1613 '''

1614 ps = self._ps

1615 n = len(ps)

1616 try:

1617 if n > 2:

1618 s = _psum(ps, **self._isfine)

1619 if not _isfinite(s):

1620 ps[:] = s, # collapse ps

1621 return Fsum2Tuple(s, _NONFINITEr)

1622 n = len(ps)

1623# Fsum._ps_max = max(Fsum._ps_max, n)

1624 if n > 2:

1625 r = self._ps_1sum(s)

1626 return Fsum2Tuple(*_s_r(s, r))

1627 if n > 1: # len(ps) == 2

1628 s, r = _s_r(*_2sum(*ps, **self._isfine))

1629 ps[:] = (r, s) if r else (s,)

1630 elif ps: # len(ps) == 1

1631 s = ps[0]

1632 r = INT0 if _isfinite(s) else _NONFINITEr

1633 else: # len(ps) == 0

1634 s, r = _0_0, INT0

1635 ps[:] = s,

1636 except (OverflowError, ValueError) as X:

1637 op = sum.__name__ # INF, NAN, NINF

1638 ps[:] = sum(ps), # collapse ps

1639 s = self._nonfiniteX(X, op, ps[0])

1640 r = _NONFINITEr

1641 # assert self._ps is ps

1642 return Fsum2Tuple(s, r)

1643

1644 @_fprs2.setter_ # PYCHOK setter_UNDERscore!

1645 def _fprs2(self, s_r):

1646 '''(INTERNAL) Replace the C{_fprs2} value.

1647 '''

1648 return Fsum2Tuple(s_r)

1649

1650 def fset_(self, *xs):

1651 '''Apply C{B{self}.partials = Fsum(*B{xs}).partials}.

1652

1653 @arg xs: Optional, new values (each C{scalar} or

1654 an L{Fsum} or L{Fsum2Tuple} instance), all

1655 positional.

1656

1657 @return: This instance, replaced (C{Fsum}).

1658

1659 @see: Method L{Fsum.fadd} for further details.

1660 '''

1661 f = self._Fsum_as(*xs)

1662 return self._fset(f, up=False, op=_fset_op_)

1663

1664 def _fset(self, other, n=0, up=True, **op):

1665 '''(INTERNAL) Overwrite this instance with an other or a C{scalar}.

1666 '''

1667 if other is self:

1668 pass # from ._fmul, ._ftruediv and ._pow_0_1

1669 elif _isFsum_2Tuple(other):

1670 self._ps[:] = other._ps

1671 self._n = n or other._n

1672 if up: # use or zap the C{Property_RO} values

1673 Fsum._fint2._update_from(self, other)

1674 Fsum._fprs ._update_from(self, other)

1675 Fsum._fprs2._update_from(self, other)

1676 elif isscalar(other):

1677 s = float(self._finite(other, **op)) if op else other

1678 self._ps[:] = s,

1679 self._n = n or 1

1680 if up: # Property _fint2, _fprs and _fprs2 all have

1681 # @.setter_underscore and NOT @.setter because the

1682 # latter's _fset zaps the value set by @.setter

1683 self._fint2 = s

1684 self._fprs = s

1685 self._fprs2 = s, INT0

1686 # assert self._fprs is s

1687 else:

1688 op = _xkwds_get1(op, op=_fset_op_)

1689 raise self._Error(op, other, _TypeError)

1690 return self

1691

1692 def _fset_ps(self, other): # in .fmath._Fsum__init__

1693 '''(INTERNAL) Set partials from a known C{other}.

1694 '''

1695 return self._fset(other, up=False)

1696

1697 def fsub(self, xs=()):

1698 '''Subtract an iterable's items from this instance.

1699

1700 @see: Method L{Fsum.fadd} for further details.

1701 '''

1702 return self._facc_neg(xs)

1703

1704 def fsub_(self, *xs):

1705 '''Subtract all positional items from this instance.

1706

1707 @see: Method L{Fsum.fadd_} for further details.

1708 '''

1709 return self._facc_neg(xs, origin=1) if len(xs) != 1 else \

1710 self._fsub(xs[0], _sub_op_)

1711

1712 def _fsub(self, other, op):

1713 '''(INTERNAL) Apply C{B{self} -= B{other}}.

1714 '''

1715 if _isFsum_2Tuple(other):

1716 if other is self: # or other._fprs2 == self._fprs2:

1717 self._fset(_0_0, n=len(self) * 2)

1718 elif other._ps:

1719 self._facc_scalar(other._ps_neg)

1720 elif self._scalar(other, op):

1721 self._facc_scalar_(-other)

1722 return self

1723

1724 def fsum(self, xs=()):

1725 '''Add an iterable's items, summate and return the current

1726 precision running sum.

1727

1728 @arg xs: Iterable of items to add (each item C{scalar}

1729 or an L{Fsum} or L{Fsum2Tuple} instance).

1730

1731 @return: Precision running sum (C{float} or C{int}).

1732

1733 @see: Method L{Fsum.fadd}.

1734

1735 @note: Accumulation can continue after summation.

1736 '''

1737 return self._facc(xs)._fprs

1738

1739 def fsum_(self, *xs):

1740 '''Add any positional items, summate and return the current

1741 precision running sum.

1742

1743 @arg xs: Items to add (each C{scalar} or an L{Fsum}

1744 or L{Fsum2Tuple} instance), all positional.

1745

1746 @return: Precision running sum (C{float} or C{int}).

1747

1748 @see: Methods L{Fsum.fsum}, L{Fsum.Fsum_} and L{Fsum.fsumf_}.

1749 '''

1750 return self._facc_args(xs)._fprs

1751

1752 def Fsum_(self, *xs, **name):

1753 '''Like method L{Fsum.fsum_} but returning a named L{Fsum}.

1754

1755 @kwarg name: Optional name (C{str}).

1756

1757 @return: Copy of this updated instance (L{Fsum}).

1758 '''

1759 return self._facc_args(xs)._copy_2(self.Fsum_, **name)

1760

1761 def Fsum2Tuple_(self, *xs, **name):

1762 '''Like method L{Fsum.fsum_} but returning a named L{Fsum2Tuple}.

1763

1764 @kwarg name: Optional name (C{str}).

1765

1766 @return: Precision running sum (L{Fsum2Tuple}).

1767 '''

1768 return Fsum2Tuple(self._facc_args(xs)._fprs2, **name)

1769

1770 @property_RO

1771 def _Fsum(self): # like L{Fsum2Tuple._Fsum}, for C{_2floats}, .fstats

1772 return self # NOT @Property_RO, see .copy and ._copy_2

1773

1774 def _Fsum_as(self, *xs, **name_f2product_nonfinites_RESIDUAL):

1775 '''(INTERNAL) Return an C{Fsum} with this C{Fsum}'s C{.f2product},

1776 C{.nonfinites} and C{.RESIDUAL} setting, optionally

1777 overridden with C{name_f2product_nonfinites_RESIDUAL} and

1778 with any C{xs} accumulated.

1779 '''

1780 kwds = _xkwds_not(None, Fsum._RESIDUAL, f2product =self.f2product(),

1781 nonfinites=self.nonfinites(),

1782 RESIDUAL =self.RESIDUAL())

1783 if name_f2product_nonfinites_RESIDUAL: # overwrites

1784 kwds.update(name_f2product_nonfinites_RESIDUAL)

1785 F = Fsum(**kwds)

1786 # assert all(v == self.__dict__[n] for n, v in F.__dict__.items())

1787 return F._fset(xs[0], op=_fset_op_) if len(xs) == 1 else (

1788 F._facc(xs, up=False) if xs else F)

1789

1790 def fsum2(self, xs=(), **name):

1791 '''Add an iterable's items, summate and return the

1792 current precision running sum I{and} the C{residual}.

1793

1794 @arg xs: Iterable of items to add (each item C{scalar}

1795 or an L{Fsum} or L{Fsum2Tuple} instance).

1796 @kwarg name: Optional C{B{name}=NN} (C{str}).

1797

1798 @return: L{Fsum2Tuple}C{(fsum, residual)} with C{fsum} the

1799 current precision running sum and C{residual}, the

1800 (precision) sum of the remaining C{partials}. The

1801 C{residual is INT0} if the C{fsum} is considered

1802 to be I{exact}.

1803

1804 @see: Methods L{Fsum.fint2}, L{Fsum.fsum} and L{Fsum.fsum2_}

1805 '''

1806 t = self._facc(xs)._fprs2

1807 return t.dup(name=name) if name else t

1808

1809 def fsum2_(self, *xs):

1810 '''Add any positional items, summate and return the current

1811 precision running sum and the I{differential}.

1812

1813 @arg xs: Values to add (each C{scalar} or an L{Fsum} or

1814 L{Fsum2Tuple} instance), all positional.

1815

1816 @return: 2Tuple C{(fsum, delta)} with the current, precision

1817 running C{fsum} like method L{Fsum.fsum} and C{delta},

1818 the difference with previous running C{fsum}, C{float}.

1819

1820 @see: Methods L{Fsum.fsum_} and L{Fsum.fsum}.

1821 '''

1822 return self._fsum2(xs, self._facc_args)

1823

1824 def _fsum2(self, xs, _facc, **facc_kwds):

1825 '''(INTERNAL) Helper for L{Fsum.fsum2_} and L{Fsum.fsum2f_}.

1826 '''

1827 p, q = self._fprs2

1828 if xs:

1829 s, r = _facc(xs, **facc_kwds)._fprs2

1830 if _isfinite(s): # _fsum(_1primed((s, -p, r, -q))

1831 d, r = _2sum(s - p, r - q, _isfine=_isOK)

1832 r, _ = _s_r(d, r)

1833 return s, (r if _isfinite(r) else _NONFINITEr)

1834 else:

1835 return p, _0_0

1836

1837 def fsumf_(self, *xs):

1838 '''Like method L{Fsum.fsum_} iff I{all} C{B{xs}}, each I{known to be}

1839 C{scalar}, an L{Fsum} or L{Fsum2Tuple}.

1840 '''

1841 return self._facc_scalarf(xs, origin=1, which=self.fsumf_)._fprs

1842

1843 def Fsumf_(self, *xs):

1844 '''Like method L{Fsum.Fsum_} iff I{all} C{B{xs}}, each I{known to be}

1845 C{scalar}, an L{Fsum} or L{Fsum2Tuple}.

1846 '''

1847 return self._facc_scalarf(xs, origin=1, which=self.Fsumf_)._copy_2(self.Fsumf_)

1848

1849 def fsum2f_(self, *xs):

1850 '''Like method L{Fsum.fsum2_} iff I{all} C{B{xs}}, each I{known to be}

1851 C{scalar}, an L{Fsum} or L{Fsum2Tuple}.

1852 '''

1853 return self._fsum2(xs, self._facc_scalarf, origin=1, which=self.fsum2f_)

1854

1855# ftruediv = __itruediv__ # for naming consistency?

1856

1857 def _ftruediv(self, other, op, **raiser_RESIDUAL):

1858 '''(INTERNAL) Apply C{B{self} /= B{other}}.

1859 '''

1860 n = _1_0

1861 if _isFsum_2Tuple(other):

1862 if other is self or self == other:

1863 return self._fset(n, n=len(self))

1864 d, r = other._fprs2

1865 if r:

1866 R = self._raiser(r, d, **raiser_RESIDUAL)

1867 if R:

1868 raise self._ResidualError(op, other, r, **R)

1869 d, n = other.as_integer_ratio()

1870 else:

1871 d = self._scalar(other, op)

1872 try:

1873 s = n / d

1874 except Exception as X:

1875 raise self._ErrorX(X, op, other)

1876 f = self._mul_scalar(s, _mul_op_) # handles 0, INF, NAN

1877 return self._fset(f)

1878

1879 @property_RO

1880 def imag(self):

1881 '''Get the C{imaginary} part of this instance (C{0.0}, always).

1882

1883 @see: Property L{Fsum.real}.

1884 '''

1885 return _0_0

1886

1887 def int_float(self, **raiser_RESIDUAL):

1888 '''Return this instance' current running sum as C{int} or C{float}.

1889

1890 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore

1891 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}

1892 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.

1893

1894 @return: This C{int} sum if this instance C{is_integer}, otherwise

1895 the C{float} sum if the residual is zero or not significant.

1896

1897 @raise ResidualError: Non-zero, significant residual or invalid

1898 B{C{RESIDUAL}}.

1899

1900 @see: Methods L{Fsum.fint}, L{Fsum.fint2}, L{Fsum.is_integer},

1901 L{Fsum.RESIDUAL} and property L{Fsum.as_iscalar}.

1902 '''

1903 s, r = self._fint2

1904 if r:

1905 s, r = self._fprs2

1906 if r: # PYCHOK no cover

1907 R = self._raiser(r, s, **raiser_RESIDUAL)

1908 if R:

1909 t = _stresidual(_non_zero_, r, **R)

1910 raise ResidualError(int_float=s, txt=t)

1911 s = float(s)

1912 return s

1913

1914 def is_exact(self):

1915 '''Is this instance' running C{fsum} considered to be exact?

1916 (C{bool}), C{True} only if the C{residual is }L{INT0}.

1917 '''

1918 return self.residual is INT0

1919

1920 def is_finite(self): # in .constants

1921 '''Is this instance C{finite}? (C{bool}).

1922

1923 @see: Function L{isfinite<pygeodesy.isfinite>}.

1924 '''

1925 return _isfinite(sum(self._ps)) # == sum(self)

1926

1927 def is_integer(self):

1928 '''Is this instance' running sum C{integer}? (C{bool}).

1929

1930 @see: Methods L{Fsum.fint}, L{Fsum.fint2} and L{Fsum.is_scalar}.

1931 '''

1932 s, r = self._fint2

1933 return False if r else (_isfinite(s) and isint(s))

1934

1935 def is_math_fma(self):

1936 '''Is accurate L{f2product} multiplication based on Python's C{math.fma}?

1937

1938 @return: C{True} if accurate multiplication uses C{math.fma}, C{False}

1939 an C{fma} implementation as C{math.fma} or C{None}, a previous

1940 C{PyGeodesy} implementation.

1941 '''

1942 return (_2split3s is _passarg) or (False if _2n_d is None else None)

1943

1944 def is_math_fsum(self):

1945 '''Are the summation functions L{fsum}, L{fsum_}, L{fsumf_}, L{fsum1},

1946 L{fsum1_} and L{fsum1f_} based on Python's C{math.fsum}?

1947

1948 @return: C{True} if summation functions use C{math.fsum}, C{False}

1949 otherwise.

1950 '''

1951 return _sum is _fsum # _fsum.__module__ is fabs.__module__

1952

1953 def is_scalar(self, **raiser_RESIDUAL):

1954 '''Is this instance' running sum C{scalar} without residual or with

1955 a residual I{ratio} not exceeding the RESIDUAL threshold?

1956

1957 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore

1958 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}

1959 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.

1960

1961 @return: C{True} if this instance' non-zero residual C{ratio} exceeds

1962 the L{RESIDUAL<Fsum.RESIDUAL>} threshold (C{bool}).

1963

1964 @raise ResidualError: Non-zero, significant residual or invalid

1965 B{C{RESIDUAL}}.

1966

1967 @see: Method L{Fsum.RESIDUAL}, L{Fsum.is_integer} and property

1968 L{Fsum.as_iscalar}.

1969 '''

1970 s, r = self._fprs2

1971 return False if r and self._raiser(r, s, **raiser_RESIDUAL) else True

1972

1973 def _mul_Fsum(self, other, op=_mul_op_): # in .fmath.Fhorner

1974 '''(INTERNAL) Return C{B{self} * B{other}} as L{Fsum} or C{0}.

1975 '''

1976 # assert _isFsum_2Tuple(other)

1977 if self._ps and other._ps:

1978 f = self._ps_mul(op, *other._ps) # NO .as_iscalar!

1979 else:

1980 f = _0_0

1981 return f

1982

1983 def _mul_reduce(self, op, start, *others):

1984 '''(INTERNAL) Like fmath.freduce(_operator.mul, ...)

1985 for I{non-finite} C{start} and/or C{others}.

1986 '''

1987 for p in self._ps_other(op, *others):

1988 start *= p

1989 return start

1990

1991 def _mul_scalar(self, factor, op): # in .fmath.Fhorner

1992 '''(INTERNAL) Return C{B{self} * scalar B{factor}} as L{Fsum}, C{0.0} or C{self}.

1993 '''

1994 # assert isscalar(factor)

1995 if self._ps and self._finite(factor, op):

1996 f = self if factor == _1_0 else (

1997 self._neg if factor == _N_1_0 else

1998 self._ps_mul(op, factor).as_iscalar)

1999 else:

2000 f = _0_0

2001 return f

2002

2003# @property_RO

2004# def _n_d(self):

2005# n, d = self.as_integer_ratio()

2006# return n / d

2007

2008 @property_RO

2009 def _neg(self):

2010 '''(INTERNAL) Return C{Fsum(-self)} or scalar C{NEG0}.

2011 '''

2012 return _Psum(self._ps_neg) if self._ps else NEG0

2013

2014 def nonfinites(self, *OK):

2015 '''Handle I{non-finite} C{float}s as C{inf}, C{INF}, C{NINF}, C{nan}

2016 and C{NAN} for this L{Fsum} or throw C{OverflowError} respectively

2017 C{ValueError} exceptions, overriding the L{nonfiniterrors} default.

2018

2019 @arg OK: If omitted, leave the override unchanged, if C{True},

2020 I{non-finites} are C{OK}, if C{False} throw exceptions

2021 or if C{None} remove the override (C{bool} or C{None}).

2022

2023 @return: The previous setting (C{bool} or C{None} if not set).

2024

2025 @see: Function L{nonfiniterrors<fsums.nonfiniterrors>}.

2026

2027 @note: Use property L{nonfinitesOK<Fsum.nonfinitesOK>} to determine

2028 whether I{non-finites} are C{OK} for this L{Fsum} and by the

2029 L{nonfiniterrors} default.

2030 '''

2031 _ks = Fsum._nonfinites_isfine_kwds

2032 if OK: # delattrof(self, _isfine=None)

2033 k = _xkwds_pop(self.__dict__, _isfine=None)

2034 if OK[0] is not None:

2035 self._isfine = _ks[bool(OK[0])]

2036 self._update()

2037 else: # getattrof(self, _isfine=None)

2038 k = _xkwds_get(self.__dict__, _isfine=None)

2039 # dict(map(reversed, _ks.items())).get(k, None)

2040 # raises a TypeError: unhashable type: 'dict'

2041 return True if k is _ks[True] else (

2042 False if k is _ks[False] else None)

2043

2044 _nonfinites_isfine_kwds = {True: dict(_isfine=_isOK),

2045 False: dict(_isfine=_isfinite)}

2046

2047 @property_RO

2048 def nonfinitesOK(self):

2049 '''Are I{non-finites} C{OK} for this L{Fsum} or by default? (C{bool}).

2050 '''

2051 nf = self.nonfinites()

2052 if nf is None:

2053 nf = not nonfiniterrors()

2054 return nf

2055

2056 def _nonfiniteX(self, X, op, f, nonfinites=None, raiser=None):

2057 '''(INTERNAL) Handle a I{non-finite} exception.

2058 '''

2059 if nonfinites is None:

2060 nonfinites = _isOK_or_finite(f, **self._isfine) if raiser is None else (not raiser)

2061 if not nonfinites:

2062 raise self._ErrorX(X, op, f)

2063 return f

2064

2065 def _optionals(self, f2product=None, nonfinites=None, **name_RESIDUAL):

2066 '''(INTERNAL) Re/set options from keyword arguments.

2067 '''

2068 if f2product is not None:

2069 self.f2product(f2product)

2070 if nonfinites is not None:

2071 self.nonfinites(nonfinites)

2072 if name_RESIDUAL: # MUST be last

2073 n, kwds = _name2__(**name_RESIDUAL)

2074 if kwds:

2075 R = Fsum._RESIDUAL

2076 t = _threshold(R, **kwds)

2077 if t != R:

2078 self._RESIDUAL = t

2079 if n:

2080 self.name = n # self.rename(n)

2081

2082 def _1_Over(self, x, op, **raiser_RESIDUAL): # vs _1_over

2083 '''(INTERNAL) Return C{Fsum(1) / B{x}}.

2084 '''

2085 return self._Fsum_as(_1_0)._ftruediv(x, op, **raiser_RESIDUAL)

2086

2087 @property_RO

2088 def partials(self):

2089 '''Get this instance' current, partial sums (C{tuple} of C{float}s).

2090 '''

2091 return tuple(self._ps)

2092

2093 def pow(self, x, *mod, **raiser_RESIDUAL):

2094 '''Return C{B{self}**B{x}} as L{Fsum}.

2095

2096 @arg x: The exponent (C{scalar}, an L{Fsum} or L{Fsum2Tuple}).

2097 @arg mod: Optional modulus (C{int} or C{None}) for the 3-argument

2098 C{pow(B{self}, B{other}, B{mod})} version.

2099 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore

2100 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar}

2101 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.

2102

2103 @return: The C{pow(self, B{x})} or C{pow(self, B{x}, *B{mod})}

2104 result (L{Fsum}).

2105

2106 @raise ResidualError: Non-zero, significant residual or invalid

2107 B{C{RESIDUAL}}.

2108

2109 @note: If B{C{mod}} is given and C{None}, the result will be an

2110 C{integer} L{Fsum} provided this instance C{is_integer}

2111 or set to C{integer} by an L{Fsum.fint} call.

2112

2113 @see: Methods L{Fsum.__ipow__}, L{Fsum.fint}, L{Fsum.is_integer}

2114 and L{Fsum.root}.

2115 '''

2116 f = self._copy_2(self.pow)

2117 return f._fpow(x, _pow_op_, *mod, **raiser_RESIDUAL) # f = pow(f, x, *mod)

2118

2119 def _pow(self, other, unused, op, **raiser_RESIDUAL):

2120 '''Return C{B{self} ** B{other}}.

2121 '''

2122 if _isFsum_2Tuple(other):

2123 f = self._pow_Fsum(other, op, **raiser_RESIDUAL)

2124 elif self._scalar(other, op):

2125 x = self._finite(other, op)

2126 f = self._pow_scalar(x, other, op, **raiser_RESIDUAL)

2127 else:

2128 f = self._pow_0_1(0, other)

2129 return f

2130

2131 def _pow_0_1(self, x, other):

2132 '''(INTERNAL) Return B{C{self}**1} or C{B{self}**0 == 1.0}.

2133 '''

2134 return self if x else (1 if isint(other) and self.is_integer() else _1_0)

2135

2136 def _pow_2_3(self, b, x, other, op, *mod, **raiser_RESIDUAL):

2137 '''(INTERNAL) 2-arg C{pow(B{b}, scalar B{x})} and 3-arg C{pow(B{b},

2138 B{x}, int B{mod} or C{None})}, embellishing errors.

2139 '''

2140

2141 if mod: # b, x, mod all C{int}, unless C{mod} is C{None}

2142 m = mod[0]

2143 # assert _isFsum_2Tuple(b)

2144

2145 def _s(s, r):

2146 R = self._raiser(r, s, **raiser_RESIDUAL)

2147 if R:

2148 raise self._ResidualError(op, other, r, mod=m, **R)

2149 return s

2150

2151 b = _s(*(b._fprs2 if m is None else b._fint2))

2152 x = _s(*_2scalar2(x))

2153

2154 try:

2155 # 0**INF == 0.0, 1**INF == 1.0, -1**2.3 == -(1**2.3)

2156 s = pow(b, x, *mod)

2157 if iscomplex(s):

2158 # neg**frac == complex in Python 3+, but ValueError in 2-

2159 raise ValueError(_strcomplex(s, b, x, *mod))

2160 return self._finite(s)

2161 except Exception as X:

2162 raise self._ErrorX(X, op, other, *mod)

2163

2164 def _pow_Fsum(self, other, op, **raiser_RESIDUAL):

2165 '''(INTERNAL) Return C{B{self} **= B{other}} for C{_isFsum_2Tuple(other)}.

2166 '''

2167 # assert _isFsum_2Tuple(other)

2168 x, r = other._fprs2

2169 f = self._pow_scalar(x, other, op, **raiser_RESIDUAL)

2170 if f and r:

2171 f *= self._pow_scalar(r, other, op, **raiser_RESIDUAL)

2172 return f

2173

2174 def _pow_int(self, x, other, op, **raiser_RESIDUAL):

2175 '''(INTERNAL) Return C{B{self} **= B{x}} for C{int B{x} >= 0}.

2176 '''

2177 # assert isint(x) and x >= 0

2178 ps = self._ps

2179 if len(ps) > 1:

2180 _mul_Fsum = Fsum._mul_Fsum

2181 if x > 4:

2182 p = self

2183 f = self if (x & 1) else self._Fsum_as(_1_0)

2184 m = x >> 1 # // 2

2185 while m:

2186 p = _mul_Fsum(p, p, op) # p **= 2

2187 if (m & 1):

2188 f = _mul_Fsum(f, p, op) # f *= p

2189 m >>= 1 # //= 2

2190 elif x > 1: # self**2, 3, or 4

2191 f = _mul_Fsum(self, self, op)

2192 if x > 2: # self**3 or 4

2193 p = self if x < 4 else f

2194 f = _mul_Fsum(f, p, op)

2195 else: # self**1 or self**0 == 1 or _1_0

2196 f = self._pow_0_1(x, other)

2197 elif ps: # self._ps[0]**x

2198 f = self._pow_2_3(ps[0], x, other, op, **raiser_RESIDUAL)

2199 else: # PYCHOK no cover

2200 # 0**pos_int == 0, but 0**0 == 1

2201 f = 0 if x else 1

2202 return f

2203

2204 def _pow_scalar(self, x, other, op, **raiser_RESIDUAL):

2205 '''(INTERNAL) Return C{self**B{x}} for C{scalar B{x}}.

2206 '''

2207 s, r = self._fprs2

2208 if r:

2209 # assert s != 0

2210 if isint(x, both=True): # self**int

2211 x = int(x)

2212 y = abs(x)

2213 if y > 1:

2214 f = self._pow_int(y, other, op, **raiser_RESIDUAL)

2215 if x > 0: # i.e. > 1

2216 return f # Fsum or scalar

2217 # assert x < 0 # i.e. < -1

2218 if _isFsum(f):

2219 s, r = f._fprs2

2220 if r:

2221 return self._1_Over(f, op, **raiser_RESIDUAL)

2222 else: # scalar

2223 s = f

2224 # use s**(-1) to get the CPython

2225 # float_pow error iff s is zero

2226 x = -1

2227 elif x < 0: # self**(-1)

2228 return self._1_Over(self, op, **raiser_RESIDUAL) # 1 / self

2229 else: # self**1 or self**0

2230 return self._pow_0_1(x, other) # self, 1 or 1.0

2231 else: # self**fractional

2232 R = self._raiser(r, s, **raiser_RESIDUAL)

2233 if R:

2234 raise self._ResidualError(op, other, r, **R)

2235 n, d = self.as_integer_ratio()

2236 if abs(n) > abs(d):

2237 n, d, x = d, n, (-x)

2238 s = n / d

2239 # assert isscalar(s) and isscalar(x)

2240 return self._pow_2_3(s, x, other, op, **raiser_RESIDUAL)

2241

2242 def _ps_acc(self, ps, xs, up=True, **unused):

2243 '''(INTERNAL) Accumulate C{xs} known scalars into list C{ps}.

2244 '''

2245 n = 0

2246 _2s = _2sum

2247 _fi = self._isfine

2248 for x in (tuple(xs) if xs is ps else xs):

2249 # assert isscalar(x) and _isOK_or_finite(x, **self._isfine)

2250 if x:

2251 i = 0

2252 for p in ps:

2253 x, p = _2s(x, p, **_fi)

2254 if p:

2255 ps[i] = p

2256 i += 1

2257 ps[i:] = (x,) if x else ()

2258 n += 1

2259 if n:

2260 self._n += n

2261# if _fi: # collapse ps if non-finite

2262# x = sum(ps)

2263# if not _isfinite(x):

2264# ps[:] = x,

2265 # Fsum._ps_max = max(Fsum._ps_max, len(ps))

2266 if up:

2267 self._update()

2268 return ps

2269

2270 def _ps_mul(self, op, *factors):

2271 '''(INTERNAL) Multiply this instance' C{partials} with

2272 each scalar C{factor} and accumulate into an C{Fsum}.

2273 '''

2274 def _psfs(ps, fs, _isfine=_isfinite):

2275 if len(ps) < len(fs):

2276 ps, fs = fs, ps

2277 if self._f2product:

2278 fs, p = _2split3s(fs), fs

2279 if len(ps) > 1 and fs is not p:

2280 fs = tuple(fs) # several ps

2281 _pfs = _2products

2282 else:

2283 def _pfs(p, fs):

2284 return (p * f for f in fs)

2285

2286 for p in ps:

2287 for f in _pfs(p, fs):

2288 yield f if _isfine(f) else self._finite(f, op)

2289

2290 fs = _psfs(self._ps, factors, **self._isfine)

2291 f = _Psum(self._ps_acc([], fs, up=False), name=op)

2292 return f

2293

2294 @property_RO

2295 def _ps_neg(self):

2296 '''(INTERNAL) Yield the partials, I{negated}.

2297 '''

2298 for p in self._ps:

2299 yield -p

2300

2301 def _ps_other(self, op, *others):

2302 '''(INTERNAL) Yield all C{other}s as C{scalar}.

2303 '''

2304 for other in others:

2305 if _isFsum_2Tuple(other):

2306 for p in other._ps:

2307 yield p

2308 else:

2309 yield self._scalar(other, op)

2310

2311 def _ps_1sum(self, *less):

2312 '''(INTERNAL) Return the partials sum, 1-primed C{less} some scalars.

2313 '''

2314 def _1psls(ps, ls):

2315 yield _1_0

2316 for p in ps:

2317 yield p

2318 for p in ls:

2319 yield -p

2320 yield _N_1_0

2321

2322 return _fsum(_1psls(self._ps, less))

2323

2324 def _raiser(self, r, s, raiser=True, **RESIDUAL):

2325 '''(INTERNAL) Does ratio C{r / s} exceed the RESIDUAL threshold

2326 I{and} is residual C{r} I{non-zero} or I{significant} (for a

2327 negative respectively positive C{RESIDUAL} threshold)?

2328 '''

2329 if r and raiser:

2330 t = self._RESIDUAL

2331 if RESIDUAL:

2332 t = _threshold(t, **RESIDUAL)

2333 if t < 0 or (s + r) != s:

2334 q = (r / s) if s else s # == 0.

2335 if fabs(q) > fabs(t):

2336 return dict(ratio=q, R=t)

2337 return {}

2338

2339 rdiv = __rtruediv__

2340

2341 @property_RO

2342 def real(self):

2343 '''Get the C{real} part of this instance (C{float}).

2344

2345 @see: Methods L{Fsum.__float__} and L{Fsum.fsum}

2346 and properties L{Fsum.ceil}, L{Fsum.floor},

2347 L{Fsum.imag} and L{Fsum.residual}.

2348 '''

2349 return float(self)

2350

2351 @property_RO

2352 def residual(self):

2353 '''Get this instance' residual or residue (C{float} or C{int}):

2354 the C{sum(partials)} less the precision running sum C{fsum}.

2355

2356 @note: The C{residual is INT0} iff the precision running

2357 C{fsum} is considered to be I{exact}.

2358

2359 @see: Methods L{Fsum.fsum}, L{Fsum.fsum2} and L{Fsum.is_exact}.

2360 '''

2361 return self._fprs2.residual

2362

2363 def RESIDUAL(self, *threshold):

2364 '''Get and set this instance' I{ratio} for raising L{ResidualError}s,

2365 overriding the default from env variable C{PYGEODESY_FSUM_RESIDUAL}.

2366

2367 @arg threshold: If C{scalar}, the I{ratio} to exceed for raising

2368 L{ResidualError}s in division and exponention, if

2369 C{None}, restore the default set with env variable

2370 C{PYGEODESY_FSUM_RESIDUAL} or if omitted, keep the

2371 current setting.

2372

2373 @return: The previous C{RESIDUAL} setting (C{float}), default C{0.0}.

2374

2375 @raise ResidualError: Invalid B{C{threshold}}.

2376

2377 @note: L{ResidualError}s may be thrown if (1) the non-zero I{ratio}

2378 C{residual / fsum} exceeds the given B{C{threshold}} and (2)

2379 the C{residual} is non-zero and (3) is I{significant} vs the

2380 C{fsum}, i.e. C{(fsum + residual) != fsum} and (4) optional

2381 keyword argument C{raiser=False} is missing. Specify a

2382 negative B{C{threshold}} for only non-zero C{residual}

2383 testing without the I{significant} case.

2384 '''

2385 r = self._RESIDUAL

2386 if threshold:

2387 t = threshold[0]

2388 self._RESIDUAL = Fsum._RESIDUAL if t is None else ( # for ...

2389 (_0_0 if t else _1_0) if isbool(t) else

2390 _threshold(t)) # ... backward compatibility

2391 return r

2392

2393 def _ResidualError(self, op, other, residual, **mod_R):

2394 '''(INTERNAL) Non-zero B{C{residual}} etc.

2395 '''

2396 def _p(mod=None, R=0, **unused): # ratio=0

2397 return (_non_zero_ if R < 0 else _significant_) \

2398 if mod is None else _integer_

2399

2400 t = _stresidual(_p(**mod_R), residual, **mod_R)

2401 return self._Error(op, other, ResidualError, txt=t)

2402

2403 def root(self, root, **raiser_RESIDUAL):

2404 '''Return C{B{self}**(1 / B{root})} as L{Fsum}.

2405

2406 @arg root: Non-zero order (C{scalar}, an L{Fsum} or L{Fsum2Tuple}).

2407 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore any

2408 L{ResidualError}s (C{bool}) or C{B{RESIDUAL}=scalar}

2409 to override the current L{RESIDUAL<Fsum.RESIDUAL>}.

2410

2411 @return: The C{self ** (1 / B{root})} result (L{Fsum}).

2412

2413 @raise ResidualError: Non-zero, significant residual or invalid

2414 B{C{RESIDUAL}}.

2415

2416 @see: Method L{Fsum.pow}.

2417 '''

2418 x = self._1_Over(root, _truediv_op_, **raiser_RESIDUAL)

2419 f = self._copy_2(self.root)

2420 return f._fpow(x, f.name, **raiser_RESIDUAL) # == pow(f, x)

2421

2422 def _scalar(self, other, op, **txt):

2423 '''(INTERNAL) Return scalar C{other} or throw a C{TypeError}.

2424 '''

2425 if isscalar(other):

2426 return other

2427 raise self._Error(op, other, _TypeError, **txt) # _invalid_

2428

2429 def signOf(self, res=True):

2430 '''Determine the sign of this instance.

2431

2432 @kwarg res: If C{True}, consider the residual,

2433 otherwise ignore the latter (C{bool}).

2434

2435 @return: The sign (C{int}, -1, 0 or +1).

2436 '''

2437 s, r = self._fprs2

2438 r = (-r) if res else 0

2439 return _signOf(s, r)

2440

2441 def toRepr(self, **lenc_prec_sep_fmt): # PYCHOK signature

2442 '''Return this C{Fsum} instance as representation.

2443

2444 @kwarg lenc_prec_sep_fmt: Optional keyword arguments

2445 for method L{Fsum.toStr}.

2446

2447 @return: This instance (C{repr}).

2448 '''

2449 return Fmt.repr_at(self, self.toStr(**lenc_prec_sep_fmt))

2450

2451 def toStr(self, lenc=True, **prec_sep_fmt): # PYCHOK signature

2452 '''Return this C{Fsum} instance as string.

2453

2454 @kwarg lenc: If C{True}, include the current C{[len]} of this

2455 L{Fsum} enclosed in I{[brackets]} (C{bool}).

2456 @kwarg prec_sep_fmt: Optional keyword arguments for method

2457 L{Fsum2Tuple.toStr}.

2458

2459 @return: This instance (C{str}).

2460 '''

2461 p = self.classname

2462 if lenc:

2463 p = Fmt.SQUARE(p, len(self))

2464 n = _enquote(self.name, white=_UNDER_)

2465 t = self._fprs2.toStr(**prec_sep_fmt)

2466 return NN(p, _SPACE_, n, t)

2467

2468 def _truediv(self, other, op, **raiser_RESIDUAL):

2469 '''(INTERNAL) Return C{B{self} / B{other}} as an L{Fsum}.

2470 '''

2471 f = self._copy_2(self.__truediv__)

2472 return f._ftruediv(other, op, **raiser_RESIDUAL)

2473

2474 def _update(self, updated=True): # see ._fset

2475 '''(INTERNAL) Zap all cached C{Property_RO} values.

2476 '''

2477 if updated:

2478 _pop = self.__dict__.pop

2479 for p in _ROs:

2480 _ = _pop(p, None)

2481# Fsum._fint2._update(self)

2482# Fsum._fprs ._update(self)

2483# Fsum._fprs2._update(self)

2484 return self # for .fset_

2485

2486_ROs = _allPropertiesOf_n(3, Fsum, Property_RO) # PYCHOK see Fsum._update

2487

2488 if _NONFINITES == _std_: # PYCHOK no cover

2489 _ = nonfiniterrors(False)

2490

2491

2492 def _Float_Int(arg, **name_Error):

2493 '''(INTERNAL) L{DivMod2Tuple}, L{Fsum2Tuple} Unit.

2494 '''

2495 U = Int if isint(arg) else Float

2496 return U(arg, **name_Error)

2497

2498

2499 class DivMod2Tuple(_NamedTuple):

2500 '''2-Tuple C{(div, mod)} with the quotient C{div} and remainder

2501 C{mod} results of a C{divmod} operation.

2502

2503 @note: Quotient C{div} an C{int} in Python 3+ but a C{float}

2504 in Python 2-. Remainder C{mod} an L{Fsum} instance.

2505 '''

2506 _Names_ = ('div', 'mod')

2507 _Units_ = (_Float_Int, Fsum)

2508

2509

2510 class Fsum2Tuple(_NamedTuple): # in .fstats

2511 '''2-Tuple C{(fsum, residual)} with the precision running C{fsum}

2512 and the C{residual}, the sum of the remaining partials. Each

2513 item is C{float} or C{int}.

2514

2515 @note: If the C{residual is INT0}, the C{fsum} is considered

2516 to be I{exact}, see method L{Fsum2Tuple.is_exact}.

2517 '''

2518 _Names_ = ( Fsum.fsum.__name__, Fsum.residual.name)

2519 _Units_ = (_Float_Int, _Float_Int)

2520

2521 def __abs__(self): # in .fmath

2522 return self._Fsum.__abs__()

2523

2524 def __bool__(self): # PYCHOK Python 3+

2525 return bool(self._Fsum)

2526

2527 def __eq__(self, other):

2528 return self._other_op(other, self.__eq__)

2529

2530 def __float__(self):

2531 return self._Fsum.__float__()

2532

2533 def __ge__(self, other):

2534 return self._other_op(other, self.__ge__)

2535

2536 def __gt__(self, other):

2537 return self._other_op(other, self.__gt__)

2538

2539 def __le__(self, other):

2540 return self._other_op(other, self.__le__)

2541

2542 def __lt__(self, other):

2543 return self._other_op(other, self.__lt__)

2544

2545 def __int__(self):

2546 return self._Fsum.__int__()

2547

2548 def __ne__(self, other):

2549 return self._other_op(other, self.__ne__)

2550

2551 def __neg__(self):

2552 return self._Fsum.__neg__()

2553

2554 __nonzero__ = __bool__ # Python 2-

2555

2556 def __pos__(self):

2557 return self._Fsum.__pos__()

2558

2559 def as_integer_ratio(self):

2560 '''Return this instance as the ratio of 2 integers.

2561

2562 @see: Method L{Fsum.as_integer_ratio} for further details.

2563 '''

2564 return self._Fsum.as_integer_ratio()

2565

2566 @property_RO

2567 def _fint2(self):

2568 return self._Fsum._fint2

2569

2570 @property_RO

2571 def _fprs2(self):

2572 return self._Fsum._fprs2

2573

2574 @Property_RO

2575 def _Fsum(self): # this C{Fsum2Tuple} as L{Fsum}, in .fstats

2576 s, r = _s_r(*self)

2577 ps = (r, s) if r else (s,)

2578 return _Psum(ps, name=self.name)

2579

2580 def Fsum_(self, *xs, **name_f2product_nonfinites_RESIDUAL):

2581 '''Return this C{Fsum2Tuple} as an L{Fsum} plus some C{xs}.

2582 '''

2583 return Fsum(self, *xs, **name_f2product_nonfinites_RESIDUAL)

2584

2585 def is_exact(self):

2586 '''Is this L{Fsum2Tuple} considered to be exact? (C{bool}).

2587 '''

2588 return self._Fsum.is_exact()

2589

2590 def is_finite(self): # in .constants

2591 '''Is this L{Fsum2Tuple} C{finite}? (C{bool}).

2592

2593 @see: Function L{isfinite<pygeodesy.isfinite>}.

2594 '''

2595 return self._Fsum.is_finite()

2596

2597 def is_integer(self):

2598 '''Is this L{Fsum2Tuple} C{integer}? (C{bool}).

2599 '''

2600 return self._Fsum.is_integer()

2601

2602 def _mul_scalar(self, other, op): # for Fsum._fmul

2603 return self._Fsum._mul_scalar(other, op)

2604

2605 @property_RO

2606 def _n(self):

2607 return self._Fsum._n

2608

2609 def _other_op(self, other, which):

2610 C, s = (tuple, self) if isinstance(other, tuple) else (Fsum, self._Fsum)

2611 return getattr(C, which.__name__)(s, other)

2612

2613 @property_RO

2614 def _ps(self):

2615 return self._Fsum._ps

2616

2617 @property_RO

2618 def _ps_neg(self):

2619 return self._Fsum._ps_neg

2620

2621 def signOf(self, **res):

2622 '''Like method L{Fsum.signOf}.

2623 '''

2624 return self._Fsum.signOf(**res)

2625

2626 def toStr(self, fmt=Fmt.g, **prec_sep): # PYCHOK signature

2627 '''Return this L{Fsum2Tuple} as string (C{str}).

2628

2629 @kwarg fmt: Optional C{float} format (C{letter}).

2630 @kwarg prec_sep: Optional keyword arguments for function

2631 L{fstr<streprs.fstr>}.

2632 '''

2633 return Fmt.PAREN(fstr(self, fmt=fmt, strepr=str, force=False, **prec_sep))

2634

2635_Fsum_2Tuple_types = Fsum, Fsum2Tuple # PYCHOK lines

2636

2637

2638 class ResidualError(_ValueError):

2639 '''Error raised for a division, power or root operation of

2640 an L{Fsum} instance with a C{residual} I{ratio} exceeding

2641 the L{RESIDUAL<Fsum.RESIDUAL>} threshold.

2642

2643 @see: Module L{pygeodesy.fsums} and method L{Fsum.RESIDUAL}.

2644 '''

2645 pass

2646

2647

2648 try:

2649 from math import fsum as _fsum # precision IEEE-754 sum, Python 2.6+

2650

2651 # make sure _fsum works as expected (XXX check

2652 # float.__getformat__('float')[:4] == 'IEEE'?)

2653 if _fsum((1, 1e101, 1, -1e101)) != 2: # PYCHOK no cover

2654 del _fsum # nope, remove _fsum ...

2655 raise ImportError() # ... use _fsum below

2656

2657 _sum = _fsum # in .elliptic

2658 except ImportError:

2659 _sum = sum # in .elliptic

2660

2661 def _fsum(xs):

2662 '''(INTERNAL) Precision summation, Python 2.5-.

2663 '''

2664 F = Fsum(name=_fsum.name, f2product=False, nonfinites=True)

2665 return float(F._facc(xs, up=False))

2666

2667

2668 def fsum(xs, nonfinites=None, **floats):

2669 '''Precision floating point summation from Python's C{math.fsum}.

2670

2671 @arg xs: Iterable of items to add (each C{scalar}, an L{Fsum} or L{Fsum2Tuple}).

2672 @kwarg nonfinites: Use C{B{nonfinites}=True} if I{non-finites} are C{OK}, if

2673 C{False} I{non-finites} raise an Overflow-/ValueError or if

2674 C{None}, L{nonfiniterrors} applies (C{bool} or C{None}).

2675 @kwarg floats: DEPRECATED keyword argument C{B{floats}=False} (C{bool}), use

2676 keyword argument C{B{nonfinites}=False} instead.

2677

2678 @return: Precision C{fsum} (C{float}).

2679

2680 @raise OverflowError: Infinite B{C{xs}} item or intermediate C{math.fsum} overflow.

2681

2682 @raise TypeError: Invalid B{C{xs}} item.

2683

2684 @raise ValueError: Invalid or C{NAN} B{C{xs}} item.

2685

2686 @see: Function L{nonfiniterrors}, class L{Fsum} and methods L{Fsum.nonfinites},

2687 L{Fsum.fsum}, L{Fsum.fadd} and L{Fsum.fadd_}.

2688 '''

2689 return _xsum(fsum, xs, nonfinites=nonfinites, **floats) if xs else _0_0

2690

2691

2692 def fsum_(*xs, **nonfinites):

2693 '''Precision floating point summation of all positional items.

2694

2695 @arg xs: Items to add (each C{scalar}, an L{Fsum} or L{Fsum2Tuple}), all positional.

2696 @kwarg nonfinites: Use C{B{nonfinites}=True} if I{non-finites} are C{OK} (C{bool}).

2697

2698 @see: Function L{fsum<fsums.fsum>} for further details.

2699 '''

2700 return _xsum(fsum_, xs, origin=1, **nonfinites) if xs else _0_0

2701

2702

2703 def fsumf_(*xs):

2704 '''Precision floating point summation of all positional items with I{non-finites} C{OK}.

2705

2706 @arg xs: Items to add (each C{scalar}, an L{Fsum} or L{Fsum2Tuple}),

2707 all positional.

2708

2709 @see: Function L{fsum_<fsums.fsum_>} for further details.

2710 '''

2711 return _xsum(fsumf_, xs, nonfinites=True, origin=1) if xs else _0_0

2712

2713

2714 def fsum1(xs, **nonfinites):

2715 '''Precision floating point summation, 1-primed.

2716

2717 @arg xs: Iterable of items to add (each C{scalar}, an L{Fsum} or L{Fsum2Tuple}).

2718 @kwarg nonfinites: Use C{B{nonfinites}=True} if I{non-finites} are C{OK} (C{bool}).

2719

2720 @see: Function L{fsum<fsums.fsum>} for further details.

2721 '''

2722 return _xsum(fsum1, xs, primed=1, **nonfinites) if xs else _0_0

2723

2724

2725 def fsum1_(*xs, **nonfinites):

2726 '''Precision floating point summation of all positional items, 1-primed.

2727

2728 @arg xs: Items to add (each C{scalar}, an L{Fsum} or L{Fsum2Tuple}), all positional.

2729 @kwarg nonfinites: Use C{B{nonfinites}=True} if I{non-finites} are C{OK} (C{bool}).

2730

2731 @see: Function L{fsum_<fsums.fsum_>} for further details.

2732 '''

2733 return _xsum(fsum1_, xs, origin=1, primed=1, **nonfinites) if xs else _0_0

2734

2735

2736 def fsum1f_(*xs):

2737 '''Precision floating point summation of all positional items, 1-primed and

2738 with I{non-finites} C{OK}.

2739

2740 @see: Function L{fsum_<fsums.fsum_>} for further details.

2741 '''

2742 return _xsum(fsum1f_, xs, nonfinites=True, primed=1) if xs else _0_0

2743

2744

2745 def _xs(xs, i_x, nfOK): # in Fsum._facc_scalarf

2746 '''(INTERNAL) Yield all C{xs} as C{scalar}.

2747 '''

2748 _x = _passarg if nfOK else _2finite

2749 for i, x in enumerate(xs):

2750 i_x[:] = i, x

2751 if _isFsum_2Tuple(x):

2752 for p in map(_x, x._ps):

2753 yield p

2754 else:

2755 yield _x(x)

2756

2757

2758 def _xsum(which, xs, nonfinites=None, origin=0, primed=0, **floats):

2759 '''(INTERNAL) Precision summation of C{xs} with conditions.

2760 '''

2761 i_x = [0, xs]

2762 try:

2763 if floats: # for backward compatibility

2764 nonfinites = _xkwds_get1(floats, floats=nonfinites)

2765 elif nonfinites is None:

2766 nonfinites = not nonfiniterrors()

2767 fs = _xs(xs, i_x, nonfinites)

2768 return _fsum(_1primed(fs) if primed else fs)

2769 except (OverflowError, TypeError, ValueError) as X:

2770 origin -= 1 if primed else 0

2771 i_x += [origin, which]

2772 raise _ixError(X, xs, *i_x)

2773

2774

2775# delete all decorators, etc.

2776 del _allPropertiesOf_n, deprecated_method, deprecated_property_RO, \

2777 Property, Property_RO, property_RO, _ALL_LAZY, _F2PRODUCT, \

2778 MANT_DIG, _NONFINITES, _RESIDUAL_0_0, _getenv, _std_

2779

2780 if __name__ == '__main__':

2781

2782 # usage: python3 -m pygeodesy.fsums

2783

2784 def _test(n):

2785 # copied from Hettinger, see L{Fsum} reference

2786 from pygeodesy import frandoms, printf

2787

2788 printf(_fsum.__name__, end=_COMMASPACE_)

2789 printf(_psum.__name__, end=_COMMASPACE_)

2790

2791 F = Fsum()

2792 if F.is_math_fsum():

2793 for t in frandoms(n, seeded=True):

2794 assert float(F.fset_(*t)) == _fsum(t)

2795 printf(_DOT_, end=NN)

2796 printf(NN)

2797

2798 _test(128)

2799

2800# **) MIT License

2801#

2802# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.

2803#

2804# Permission is hereby granted, free of charge, to any person obtaining a

2805# copy of this software and associated documentation files (the "Software"),

2806# to deal in the Software without restriction, including without limitation

2807# the rights to use, copy, modify, merge, publish, distribute, sublicense,

2808# and/or sell copies of the Software, and to permit persons to whom the

2809# Software is furnished to do so, subject to the following conditions:

2810#

2811# The above copyright notice and this permission notice shall be included

2812# in all copies or substantial portions of the Software.

2813#

2814# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS

2815# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

2816# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL

2817# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR

2818# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,

2819# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR

2820# OTHER DEALINGS IN THE SOFTWARE.