Coverage for pygeodesy/fsums.py: 94%

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1 

2# -*- coding: utf-8 -*- 

3 

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

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

6option, accurate I{TwoProduct} multiplication. 

7 

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

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

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

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

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

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

14otherwise the C{PyGeodesy 24.09.09} release. 

15 

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

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

18 

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

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

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

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

23and L{Fsum.__itruediv__}. 

24 

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

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

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

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

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

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

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

32 

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

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

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

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

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

38''' 

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

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

41 

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

43 _signOf, itemsorted, signOf, _xiterable, \ 

44 _xiterablen 

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

46 _1_0, _N_1_0, _isfinite, _pos_self, \ 

47 Float, Int 

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

49 _ValueError, _xError, _xError2, _xkwds_get, \ 

50 _xkwds, _xkwds_get1, _xkwds_not, _xkwds_pop, \ 

51 _xsError 

52from pygeodesy.internals import _enquote, _passarg 

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

54 _not_finite_, _SPACE_, _std_, _UNDER_ 

55from pygeodesy.lazily import _ALL_LAZY, _getenv, _sys_version_info2 

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

57 _NotImplemented 

58from pygeodesy.props import _allPropertiesOf_n, deprecated_method, \ 

59 deprecated_property_RO, Property, \ 

60 Property_RO, property_RO 

61from pygeodesy.streprs import Fmt, fstr, unstr 

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

63 

64from 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 

70from 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 

99def _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 

106def _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 

117def _X_ps(X): # for _2floats only 

118 return X._ps 

119 

120 

121def _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 

139try: # 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 

156except 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 

243def 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 

262def _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 

268def _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 

274def _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 

286def _isFsum(x): # in .fmath 

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

288 ''' 

289 return isinstance(x, Fsum) 

290 

291 

292def _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 

298def _isOK(unused): 

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

300 ''' 

301 return True 

302 

303 

304def _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 

311def _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 

320def _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 

330def 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 

350def _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 

357def _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 

367def _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 

391def _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 

401def _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 

407def _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 

425def _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 

436def _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 

445def _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 

456def _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 

480def _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 

492class 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 

2488if _NONFINITES == _std_: # PYCHOK no cover 

2489 _ = nonfiniterrors(False) 

2490 

2491 

2492def _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 

2499class 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 

2510class 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 

2638class 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 

2648try: 

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 

2658except 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 

2668def 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 

2692def 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 

2703def 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 

2714def 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 

2725def 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 

2736def 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 

2745def _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 

2758def _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. 

2776del _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 

2780if __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.