Coverage for pygeodesy/fsums.py: 95%

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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 _gcd, isbool, iscomplex, isint, isscalar, \ 

43 _signOf, itemsorted, signOf, _xiterable 

44from pygeodesy.constants import INF, INT0, MANT_DIG, NEG0, NINF, _0_0, \ 

45 _1_0, _N_1_0, _isfinite, _pos_self, \ 

46 Float, Int 

47from pygeodesy.errors import _AssertionError, _OverflowError, _TypeError, \ 

48 _ValueError, _xError, _xError2, _xkwds, \ 

49 _xkwds_get, _xkwds_get1, _xkwds_not, \ 

50 _xkwds_pop, _xsError 

51from pygeodesy.internals import _enquote, _getPYGEODESY, _MODS, _passarg 

52from pygeodesy.interns import NN, _arg_, _COMMASPACE_, _DOT_, _from_, \ 

53 _not_finite_, _SPACE_, _std_, _UNDER_ 

54# from pygeodesy.lazily import _ALL_LAZY # from .named 

55from pygeodesy.named import _name__, _name2__, _Named, _NamedTuple, \ 

56 _NotImplemented, _ALL_LAZY 

57from pygeodesy.props import _allPropertiesOf_n, deprecated_method, \ 

58 deprecated_property_RO, Property, \ 

59 Property_RO, property_RO 

60from pygeodesy.streprs import Fmt, fstr, unstr 

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

62 

63from math import fabs, isinf, isnan, \ 

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

65 

66__all__ = _ALL_LAZY.fsums 

67__version__ = '25.01.12' 

68 

69from pygeodesy.interns import ( 

70 _PLUS_ as _add_op_, # in .auxilats.auxAngle 

71 _DSLASH_ as _floordiv_op_, 

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 _DSTAR_ as _pow_op_, 

79 _DASH_ as _sub_op_, # in .auxilats.auxAngle 

80 _SLASH_ as _truediv_op_ 

81) 

82_divmod_op_ = _floordiv_op_ + _mod_op_ 

83_F2PRODUCT = _getPYGEODESY('FSUM_F2PRODUCT') 

84_iadd_op_ = _add_op_ + _fset_op_ # in .auxilats.auxAngle, .fstats 

85_integer_ = 'integer' 

86_isub_op_ = _sub_op_ + _fset_op_ # in .auxilats.auxAngle 

87_NONFINITEr = _0_0 # NOT INT0! 

88_NONFINITES = _getPYGEODESY('FSUM_NONFINITES') 

89_non_zero_ = 'non-zero' 

90_RESIDUAL_0_0 = _getPYGEODESY('FSUM_RESIDUAL', _0_0) 

91_significant_ = 'significant' 

92_threshold_ = 'threshold' 

93 

94 

95def _2finite(x, _isfine=_isfinite): # in .fstats 

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

97 ''' 

98 return (float(x) if _isfine(x) # and isscalar(x) 

99 else _nfError(x)) 

100 

101 

102def _2float(index=None, _isfine=_isfinite, **name_x): # in .fmath, .fstats 

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

104 ''' 

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

106 try: 

107 f = float(x) 

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

109 except Exception as X: 

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

111 

112 

113try: # MCCABE 26 

114 from math import fma as _fma 

115 

116 def _2products(x, ys, *zs): 

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

118 # TwoProductFMA U{Algorithm 3.5 

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

120 for y in ys: 

121 f = x * y 

122 yield f 

123 if _isfinite(f): 

124 yield _fma(x, y, -f) 

125 for z in zs: 

126 yield z 

127 

128# _2split3 = \ 

129 _2split3s = _passarg # in Fsum.is_math_fma 

130 

131except ImportError: # PYCHOK DSPACE! Python 3.12- 

132 

133 if _F2PRODUCT and _F2PRODUCT != _std_: 

134 # backward to PyGeodesy 24.09.09, with _fmaX 

135 from pygeodesy.basics import _integer_ratio2 

136 

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

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

139 # the same accuracy, but ~14x slower 

140 (na, da), (nb, db), (nc, dc) = map(_integer_ratio2, a_b_c) 

141 n = na * nb * dc 

142 n += da * db * nc 

143 d = da * db * dc 

144 try: 

145 n, d = _n_d2(n, d) 

146 r = float(n / d) 

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

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

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

150 else: 

151 _integer_ratio2 = None # redef, in Fsum.is_math_fma 

152 

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

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

155 # the same accuracy, but ~13x slower 

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

157 r = _fsum(_2products(a, b3s, c)) 

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

159 

160 def _fmaX(r, *a_b_c): # PYCHOK no cover 

161 # handle non-finite fma result as Python 3.13+ C-function U{math_fma_impl 

162 # <https://GitHub.com/python/cpython/blob/main/Modules/mathmodule.c#L2305>}: 

163 # raise a ValueError for a NAN result from non-NAN C{a_b_c}s otherwise an 

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

165 if isnan(r): 

166 def _x(x): 

167 return not isnan(x) 

168 else: # non-finite, non-NAN 

169 _x = _isfinite 

170 if all(map(_x, a_b_c)): 

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

172 return r 

173 

174 def _2products(x, y3s, *zs): # PYCHOK in _fma, ... 

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

176 # TwoProduct U{Algorithm 3.3<https://www.TUHH.De/ti3/paper/rump/OgRuOi05.pdf>}, also 

177 # in Python 3.13+ C{Modules/mathmodule.c} under #ifndef UNRELIABLE_FMA ... #else ... 

178 _, a, b = _2split3(x) 

179 for y, c, d in y3s: 

180 y *= x 

181 yield y 

182 if _isfinite(y): 

183 # yield b * d - (((y - a * c) - b * c) - a * d) 

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

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

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

187 yield a * c - y 

188 yield b * c 

189 if d: 

190 yield a * d 

191 yield b * d 

192 for z in zs: 

193 yield z 

194 

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

196 

197 def _2split3(x): 

198 # Split U{Algorithm 3.2 

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

200 a = c = x * _2FACTOR 

201 a -= c - x 

202 b = x - a 

203 return x, a, b 

204 

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

206 return map(_2split3, xs) 

207 

208 

209def f2product(two=None): 

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

211 

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

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

214 

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

216 

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

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

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

220 equivalent, slower implementation when not available. 

221 ''' 

222 t = Fsum._f2product 

223 if two is not None: 

224 Fsum._f2product = bool(two) 

225 return t 

226 

227 

228def _Fsumf_(*xs): # in .auxLat, ... 

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

230 ''' 

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

232 

233 

234def _Fsum1f_(*xs): # in .albers 

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

236 ''' 

237 return Fsum()._facc_scalarf(_1primed(xs), origin=-1, up=False) 

238 

239 

240def _halfeven(s, r, p): 

241 '''(INTERNAL) Round half-even. 

242 ''' 

243 if (p > 0 and r > 0) or \ 

244 (p < 0 and r < 0): # signs match 

245 r *= 2 

246 t = s + r 

247 if r == (t - s): 

248 s = t 

249 return s 

250 

251 

252def _isFsum(x): # in .fmath 

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

254 ''' 

255 return isinstance(x, Fsum) 

256 

257 

258def _isFsum_2Tuple(x): # in .basics, .constants, .fmath, .fstats 

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

260 ''' 

261 return isinstance(x, _Fsum_2Tuple_types) 

262 

263 

264def _isOK(unused): 

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

266 ''' 

267 return True 

268 

269 

270def _isOK_or_finite(x, _isfine=_isfinite): 

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

272 ''' 

273 # assert _isfine in (_isOK, _isfinite) 

274 return _isfine(x) # C{bool} 

275 

276 

277def _n_d2(n, d): 

278 '''(INTERNAL) Reduce C{n} and C{d} by C{gcd}. 

279 ''' 

280 if n and d: 

281 try: 

282 c = _gcd(n, d) 

283 if c > 1: 

284 return (n // c), (d // c) 

285 except TypeError: # non-int float 

286 pass 

287 return n, d 

288 

289 

290def _nfError(x, *args): 

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

292 ''' 

293 E = _NonfiniteError(x) 

294 t = Fmt.PARENSPACED(_not_finite_, x) 

295 if args: # in _fmaX, _2sum 

296 return E(txt=t, *args) 

297 raise E(t, txt=None) 

298 

299 

300def _NonfiniteError(x): 

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

302 ''' 

303 return _OverflowError if isinf(x) else ( 

304 _ValueError if isnan(x) else _AssertionError) 

305 

306 

307def nonfiniterrors(raiser=None): 

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

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

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

311 

312 @kwarg raiser: If C{True}, throw exceptions, if C{False} handle 

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

314 the setting unchanged. 

315 

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

317 

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

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

320 ''' 

321 d = Fsum._isfine 

322 if raiser is not None: 

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

324 return (False if d is Fsum._nonfinites_isfine_kwds[True] else 

325 _xkwds_get1(d, _isfine=_isfinite) is _isfinite) if d else True 

326 

327 

328def _1primed(xs): # in .fmath 

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

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

331 ''' 

332 yield _1_0 

333 for x in xs: 

334 yield x 

335 yield _N_1_0 

336 

337 

338def _psum(ps, **_isfine): # PYCHOK used! 

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

340 ''' 

341 # assert isinstance(ps, list) 

342 i = len(ps) - 1 

343 s = _0_0 if i < 0 else ps[i] 

344 while i > 0: 

345 i -= 1 

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

347 if r: # sum(ps) became inexact 

348 if s: 

349 ps[i:] = r, s 

350 if i > 0: 

351 s = _halfeven(s, r, ps[i-1]) 

352 break # return s 

353 s = r # PYCHOK no cover 

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

355 i = 0 # collapse ps 

356 if ps: 

357 s += sum(ps) 

358 ps[i:] = s, 

359 return s 

360 

361 

362def _Psum(ps, **name_f2product_nonfinites_RESIDUAL): 

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

364 ''' 

365 F = Fsum(**name_f2product_nonfinites_RESIDUAL) 

366 if ps: 

367 F._ps[:] = ps 

368 F._n = len(F._ps) 

369 return F 

370 

371 

372def _Psum_(*ps, **name_f2product_nonfinites_RESIDUAL): # in .fmath 

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

374 ''' 

375 return _Psum(ps, **name_f2product_nonfinites_RESIDUAL) 

376 

377 

378def _residue(other): 

379 '''(INTERNAL) Return the C{residual} or C{None} for C{scalar}. 

380 ''' 

381 try: 

382 r = other.residual 

383 except AttributeError: 

384 r = None # float, int, other 

385 return r 

386 

387 

388def _s_r2(s, r): 

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

390 ''' 

391 if _isfinite(s): 

392 if r: 

393 if fabs(s) < fabs(r): 

394 s, r = r, (s or INT0) 

395 else: 

396 r = INT0 

397 else: 

398 r = _NONFINITEr 

399 return s, r 

400 

401 

402def _strcomplex(s, *args): 

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

404 ''' 

405 c = _strcomplex.__name__[4:] 

406 n = _sub_op_(len(args), _arg_) 

407 t = unstr(pow, *args) 

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

409 

410 

411def _stresidual(prefix, residual, R=0, **mod_ratio): 

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

413 ''' 

414 p = _stresidual.__name__[3:] 

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

416 for n, v in itemsorted(mod_ratio): 

417 p = Fmt.PARENSPACED(n, Fmt(v)) 

418 t = _COMMASPACE_(t, p) 

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

420 

421 

422def _2sum(a, b, _isfine=_isfinite): # in .testFmath 

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

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

425 ''' 

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

427 

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

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

430 # 1974, Zeitschrift für Angewandte Mathmatik und Mechanik, vol 51, nr 1, p 39-51 

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

432 s = a + b 

433 if _isfinite(s): 

434 if fabs(a) < fabs(b): 

435 r = (b - s) + a 

436 else: 

437 r = (a - s) + b 

438 elif _isfine(s): 

439 r = _NONFINITEr 

440 else: # non-finite and not OK 

441 t = unstr(_2sum, a, b) 

442 raise _nfError(s, t) 

443 return s, r 

444 

445 

446def _threshold(threshold=_0_0, **kwds): 

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

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

449 ''' 

450 if kwds: 

451 threshold = _xkwds_get1(kwds, RESIDUAL=threshold) 

452 try: 

453 return _2finite(threshold) # PYCHOK None 

454 except Exception as x: 

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

456 

457 

458def _2tuple2(other): 

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

460 C{float} or C{as-is} and C{r} the residual of C{as-is} or 0. 

461 ''' 

462 if _isFsum_2Tuple(other): 

463 s, r = other._fint2 

464 if r: 

465 s, r = other._nfprs2 

466 if r: # PYCHOK no cover 

467 s = other # L{Fsum} as-is 

468 else: 

469 r = 0 

470 s = other # C{type} as-is 

471 if isint(s, both=True): 

472 s = int(s) 

473 return s, r 

474 

475 

476class Fsum(_Named): # sync __methods__ with .vector3dBase.Vector3dBase, .fstats, ... 

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

478 

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

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

481 intermediate, I{running} summuation. 

482 

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

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

485 

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

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

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

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

490 exceptions by default. 

491 

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

493 393090_Binary_floating_point_summatiaccurate_full/recipe-393090.py>}, 

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

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

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

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

498 

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

500 multiplication. 

501 

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

503 C{PYGEODESY_FSUM_NONFINITES} and C{PYGEODESY_FSUM_RESIDUAL}. 

504 ''' 

505 _f2product = _MODS.sys_version_info2 > (3, 12) or bool(_F2PRODUCT) 

506 _isfine = {} # == _isfinite, see nonfiniterrors() 

507 _n = 0 

508# _ps = [] # partial sums 

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

510 _RESIDUAL = _threshold(_RESIDUAL_0_0) 

511 

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

513 '''New L{Fsum}. 

514 

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

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

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

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

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

520 L{Fsum}. 

521 

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

523 L{Fsum.fadd} and L{Fsum.fadd_}. 

524 ''' 

525 if name_f2product_nonfinites_RESIDUAL: 

526 self._optionals(**name_f2product_nonfinites_RESIDUAL) 

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

528 if xs: 

529 self._facc_args(xs, up=False) 

530 

531 def __abs__(self): 

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

533 ''' 

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

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

536 

537 def __add__(self, other): 

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

539 

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

541 

542 @return: The sum (L{Fsum}). 

543 

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

545 ''' 

546 f = self._copy_2(self.__add__) 

547 return f._fadd(other) 

548 

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

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

551 ''' 

552 s, r = self._nfprs2 

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

554 

555 def __call__(self, other, **up): # in .fmath 

556 '''Reset this C{Fsum} to C{other}, default C{B{up}=True}. 

557 ''' 

558 self._ps[:] = 0, # clear for errors 

559 self._fset(other, op=_fset_op_, **up) 

560 return self 

561 

562 

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

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

565 

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

567 

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

569 ''' 

570 return self.ceil 

571 

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

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

574 

575 @return: -1, 0 or +1 (C{int}). 

576 

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

578 ''' 

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

580 return _signOf(s, 0) 

581 

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

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

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

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

586 

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

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

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

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

591 

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

593 B{C{RESIDUAL}}. 

594 

595 @see: Method L{Fsum.fdiv}. 

596 ''' 

597 f = self._copy_2(self.__divmod__) 

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

599 

600 def __eq__(self, other): 

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

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

603 ''' 

604 return self._cmp_0(other, _fset_op_ + _fset_op_) == 0 

605 

606 def __float__(self): 

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

608 

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

610 ''' 

611 return float(self._fprs) 

612 

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

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

615 

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

617 

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

619 ''' 

620 return self.floor 

621 

622 def __floordiv__(self, other): 

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

624 

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

626 

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

628 

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

630 ''' 

631 f = self._copy_2(self.__floordiv__) 

632 return f._floordiv(other, _floordiv_op_) 

633 

634 def __ge__(self, other): 

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

636 ''' 

637 return self._cmp_0(other, _gt_op_ + _fset_op_) >= 0 

638 

639 def __gt__(self, other): 

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

641 ''' 

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

643 

644 def __hash__(self): # PYCHOK no cover 

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

646 ''' 

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

648 # 3/library/numbers.html#numbers.Rational>} 

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

650 

651 def __iadd__(self, other): 

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

653 

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

655 an iterable of several of the former. 

656 

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

658 

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

660 C{scalar} nor L{Fsum}. 

661 

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

663 ''' 

664 try: 

665 return self._fadd(other, op=_iadd_op_) 

666 except TypeError: 

667 pass 

668 _xiterable(other) 

669 return self._facc(other) 

670 

671 def __ifloordiv__(self, other): 

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

673 

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

675 

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

677 

678 @raise ResidualError: Non-zero, significant residual 

679 in B{C{other}}. 

680 

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

682 

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

684 

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

686 

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

688 ''' 

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

690 

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

692 '''Not implemented.''' 

693 return _NotImplemented(self, other) 

694 

695 def __imod__(self, other): 

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

697 

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

699 

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

701 

702 @see: Method L{Fsum.__divmod__}. 

703 ''' 

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

705 

706 def __imul__(self, other): 

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

708 

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

710 

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

712 

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

714 

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

716 

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

718 ''' 

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

720 

721 def __int__(self): 

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

723 

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

725 and L{Fsum.floor}. 

726 ''' 

727 i, _ = self._fint2 

728 return i 

729 

730 def __invert__(self): # PYCHOK no cover 

731 '''Not implemented.''' 

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

733 return _NotImplemented(self) 

734 

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

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

737 

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

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

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

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

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

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

744 

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

746 

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

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

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

750 

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

752 

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

754 is non-zero and significant and either 

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

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

757 C{None}. 

758 

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

760 invocation failed. 

761 

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

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

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

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

766 is given as C{0}. 

767 

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

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

770 ''' 

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

772 

773 def __isub__(self, other): 

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

775 

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

777 an iterable of several of the former. 

778 

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

780 

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

782 

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

784 ''' 

785 try: 

786 return self._fsub(other, _isub_op_) 

787 except TypeError: 

788 pass 

789 _xiterable(other) 

790 return self._facc_neg(other) 

791 

792 def __iter__(self): 

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

794 ''' 

795 return iter(self.partials) 

796 

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

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

799 

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

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

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

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

804 

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

806 

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

808 

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

810 B{C{RESIDUAL}}. 

811 

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

813 

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

815 

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

817 

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

819 ''' 

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

821 

822 def __le__(self, other): 

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

824 ''' 

825 return self._cmp_0(other, _lt_op_ + _fset_op_) <= 0 

826 

827 def __len__(self): 

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

829 ''' 

830 return self._n 

831 

832 def __lt__(self, other): 

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

834 ''' 

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

836 

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

838 '''Not implemented.''' 

839 return _NotImplemented(self, other) 

840 

841 def __mod__(self, other): 

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

843 

844 @see: Method L{Fsum.__imod__}. 

845 ''' 

846 f = self._copy_2(self.__mod__) 

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

848 

849 def __mul__(self, other): 

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

851 

852 @see: Method L{Fsum.__imul__}. 

853 ''' 

854 f = self._copy_2(self.__mul__) 

855 return f._fmul(other, _mul_op_) 

856 

857 def __ne__(self, other): 

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

859 ''' 

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

861 

862 def __neg__(self): 

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

864 ''' 

865 f = self._copy_2(self.__neg__) 

866 return f._fset(self._neg) 

867 

868 def __pos__(self): 

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

870 ''' 

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

872 

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

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

875 

876 @see: Method L{Fsum.__ipow__}. 

877 ''' 

878 f = self._copy_2(self.__pow__) 

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

880 

881 def __radd__(self, other): 

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

883 

884 @see: Method L{Fsum.__iadd__}. 

885 ''' 

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

887 return f._fadd(self) 

888 

889 def __rdivmod__(self, other): 

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

891 C{(quotient, remainder)}. 

892 

893 @see: Method L{Fsum.__divmod__}. 

894 ''' 

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

896 return f._fdivmod2(self, _divmod_op_) 

897 

898# turned off, called by _deepcopy and _copy 

899# def __reduce__(self): # Python 3.8+ 

900# ''' Pickle, like std C{fractions.Fraction}, see U{__reduce__ 

901# <https://docs.Python.org/3/library/pickle.html#object.__reduce__>} 

902# ''' 

903# dict_ = self._Fsum_as().__dict__ # no __setstate__ 

904# return (self.__class__, self.partials, dict_) 

905 

906# def __repr__(self): 

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

908# ''' 

909# return self.toRepr(lenc=True) 

910 

911 def __rfloordiv__(self, other): 

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

913 

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

915 ''' 

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

917 return f._floordiv(self, _floordiv_op_) 

918 

919 def __rmatmul__(self, other): # PYCHOK no coveS 

920 '''Not implemented.''' 

921 return _NotImplemented(self, other) 

922 

923 def __rmod__(self, other): 

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

925 

926 @see: Method L{Fsum.__imod__}. 

927 ''' 

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

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

930 

931 def __rmul__(self, other): 

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

933 

934 @see: Method L{Fsum.__imul__}. 

935 ''' 

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

937 return f._fmul(self, _mul_op_) 

938 

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

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

941 

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

943 ''' 

944 f = self._copy_2(self.__round__) 

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

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

947 

948 def __rpow__(self, other, *mod): 

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

950 

951 @see: Method L{Fsum.__ipow__}. 

952 ''' 

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

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

955 

956 def __rsub__(self, other): 

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

958 

959 @see: Method L{Fsum.__isub__}. 

960 ''' 

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

962 return f._fsub(self, _sub_op_) 

963 

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

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

966 

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

968 ''' 

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

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

971 

972 def __str__(self): 

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

974 ''' 

975 return self.toStr(lenc=True) 

976 

977 def __sub__(self, other): 

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

979 

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

981 

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

983 

984 @see: Method L{Fsum.__isub__}. 

985 ''' 

986 f = self._copy_2(self.__sub__) 

987 return f._fsub(other, _sub_op_) 

988 

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

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

991 

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

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

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

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

996 

997 @return: The quotient (L{Fsum}). 

998 

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

1000 B{C{RESIDUAL}}. 

1001 

1002 @see: Method L{Fsum.__itruediv__}. 

1003 ''' 

1004 return self._truediv(other, _truediv_op_, **raiser_RESIDUAL) 

1005 

1006 __trunc__ = __int__ 

1007 

1008 if _MODS.sys_version_info2 < (3, 0): # PYCHOK no cover 

1009 # <https://docs.Python.org/2/library/operator.html#mapping-operators-to-functions> 

1010 __div__ = __truediv__ 

1011 __idiv__ = __itruediv__ 

1012 __long__ = __int__ 

1013 __nonzero__ = __bool__ 

1014 __rdiv__ = __rtruediv__ 

1015 

1016 def as_integer_ratio(self): 

1017 '''Return this instance as the ratio of 2 integers. 

1018 

1019 @return: 2-Tuple C{(numerator, denominator)} both C{int} with 

1020 C{numerator} signed and C{denominator} non-zero and 

1021 positive. The C{numerator} is I{non-finite} if this 

1022 instance is. 

1023 

1024 @see: Method L{Fsum.fint2} and C{float.as_integer_ratio} in 

1025 Python 2.7+. 

1026 ''' 

1027 n, r = self._fint2 

1028 if r: 

1029 i, d = float(r).as_integer_ratio() 

1030 n, d = _n_d2(n * d + i, d) 

1031 else: # PYCHOK no cover 

1032 d = 1 

1033 return n, d 

1034 

1035 @property_RO 

1036 def as_iscalar(self): 

1037 '''Get this instance I{as-is} (L{Fsum} with C{non-zero residual}, 

1038 C{scalar} or I{non-finite}). 

1039 ''' 

1040 s, r = self._nfprs2 

1041 return self if r else s 

1042 

1043 @property_RO 

1044 def ceil(self): 

1045 '''Get this instance' C{ceil} value (C{int} in Python 3+, but 

1046 C{float} in Python 2-). 

1047 

1048 @note: This C{ceil} takes the C{residual} into account. 

1049 

1050 @see: Method L{Fsum.int_float} and properties L{Fsum.floor}, 

1051 L{Fsum.imag} and L{Fsum.real}. 

1052 ''' 

1053 s, r = self._fprs2 

1054 c = _ceil(s) + int(r) - 1 

1055 while r > (c - s): # (s + r) > c 

1056 c += 1 

1057 return c # _ceil(self._n_d) 

1058 

1059 cmp = __cmp__ 

1060 

1061 def _cmp_0(self, other, op): 

1062 '''(INTERNAL) Return C{scalar(self - B{other})} for 0-comparison. 

1063 ''' 

1064 if _isFsum_2Tuple(other): 

1065 s = self._ps_1sum(*other._ps) 

1066 elif self._scalar(other, op): 

1067 s = self._ps_1sum(other) 

1068 else: 

1069 s = self.signOf() # res=True 

1070 return s 

1071 

1072 def copy(self, deep=False, **name): 

1073 '''Copy this instance, C{shallow} or B{C{deep}}. 

1074 

1075 @kwarg name: Optional, overriding C{B{name}='"copy"} (C{str}). 

1076 

1077 @return: The copy (L{Fsum}). 

1078 ''' 

1079 n = _name__(name, name__=self.copy) 

1080 f = _Named.copy(self, deep=deep, name=n) 

1081 if f._ps is self._ps: 

1082 f._ps = list(self._ps) # separate list 

1083 if not deep: 

1084 f._n = 1 

1085 # assert f._f2product == self._f2product 

1086 # assert f._Fsum is f 

1087 # assert f._isfine is self._isfine 

1088 # assert f._RESIDUAL is self._RESIDUAL 

1089 return f 

1090 

1091 def _copy_2(self, which, name=NN): 

1092 '''(INTERNAL) Copy for I{dyadic} operators. 

1093 ''' 

1094 n = name or which.__name__ # _DUNDER_nameof 

1095 # NOT .classof due to .Fdot(a, *b) args, etc. 

1096 f = _Named.copy(self, deep=False, name=n) 

1097 f._ps = list(self._ps) # separate list 

1098 # assert f._n == self._n 

1099 # assert f._f2product == self._f2product 

1100 # assert f._Fsum is f 

1101 # assert f._isfine is self._isfine 

1102 # assert f._RESIDUAL is self._RESIDUAL 

1103 return f 

1104 

1105 def _copy_2r(self, other, which): 

1106 '''(INTERNAL) Copy for I{reverse-dyadic} operators. 

1107 ''' 

1108 return other._copy_2(which) if _isFsum(other) else \ 

1109 self._copy_2(which)._fset(other) 

1110 

1111 divmod = __divmod__ 

1112 

1113 def _Error(self, op, other, Error, **txt_cause): 

1114 '''(INTERNAL) Format an B{C{Error}} for C{{self} B{op} B{other}}. 

1115 ''' 

1116 # self.as_iscalar causes RecursionError for ._fprs2 errors 

1117 s = _Psum(self._ps, nonfinites=True, name=self.name) 

1118 return Error(_SPACE_(s.as_iscalar, op, other), **txt_cause) 

1119 

1120 def _ErrorX(self, X, op, other, *mod): 

1121 '''(INTERNAL) Format the caught exception C{X}. 

1122 ''' 

1123 E, t = _xError2(X) 

1124 if mod: 

1125 t = _COMMASPACE_(Fmt.PARENSPACED(mod=mod[0]), t) 

1126 return self._Error(op, other, E, txt=t, cause=X) 

1127 

1128 def _ErrorXs(self, X, xs, **kwds): # in .fmath 

1129 '''(INTERNAL) Format the caught exception C{X}. 

1130 ''' 

1131 E, t = _xError2(X) 

1132 u = unstr(self.named3, *xs, _ELLIPSIS=4, **kwds) 

1133 return E(u, txt=t, cause=X) 

1134 

1135 def _facc(self, xs, up=True, **_X_x_origin): 

1136 '''(INTERNAL) Accumulate more C{scalar}s or L{Fsum}s. 

1137 ''' 

1138 if xs: 

1139 kwds = self._isfine 

1140 if _X_x_origin: 

1141 kwds = _xkwds(_X_x_origin, **kwds) 

1142 fs = _xs(xs, **kwds) # PYCHOK yield 

1143 ps = self._ps 

1144 ps[:] = self._ps_acc(list(ps), fs, up=up) 

1145# if len(ps) > 16: 

1146# _ = _psum(ps, **self._isfine) 

1147 return self 

1148 

1149 def _facc_args(self, xs, **up): 

1150 '''(INTERNAL) Accumulate 0, 1 or more C{xs}, all positional 

1151 arguments in the caller of this method. 

1152 ''' 

1153 return self._fadd(xs[0], **up) if len(xs) == 1 else \ 

1154 self._facc(xs, **up) # origin=1? 

1155 

1156 def _facc_dot(self, n, xs, ys, **kwds): # in .fmath 

1157 '''(INTERNAL) Accumulate C{fdot(B{xs}, *B{ys})}. 

1158 ''' 

1159 if n > 0: 

1160 _f = Fsum(**kwds) 

1161 self._facc(_f(x).fmul(y) for x, y in zip(xs, ys)) # PYCHOK attr? 

1162 return self 

1163 

1164 def _facc_neg(self, xs, **up_origin): 

1165 '''(INTERNAL) Accumulate more C{xs}, negated. 

1166 ''' 

1167 def _N(X): 

1168 return X._ps_neg 

1169 

1170 def _n(x): 

1171 return -float(x) 

1172 

1173 return self._facc(xs, _X=_N, _x=_n, **up_origin) 

1174 

1175 def _facc_power(self, power, xs, which, **raiser_RESIDUAL): # in .fmath 

1176 '''(INTERNAL) Add each C{xs} as C{float(x**power)}. 

1177 ''' 

1178 def _Pow4(p): 

1179 r = 0 

1180 if _isFsum_2Tuple(p): 

1181 s, r = p._fprs2 

1182 if r: 

1183 m = Fsum._pow 

1184 else: # scalar 

1185 return _Pow4(s) 

1186 elif isint(p, both=True) and int(p) >= 0: 

1187 p = s = int(p) 

1188 m = Fsum._pow_int 

1189 else: 

1190 p = s = _2float(power=p, **self._isfine) 

1191 m = Fsum._pow_scalar 

1192 return m, p, s, r 

1193 

1194 _Pow, p, s, r = _Pow4(power) 

1195 if p: # and xs: 

1196 op = which.__name__ 

1197 _FsT = _Fsum_2Tuple_types 

1198 _pow = self._pow_2_3 

1199 

1200 def _P(X): 

1201 f = _Pow(X, p, power, op, **raiser_RESIDUAL) 

1202 return f._ps if isinstance(f, _FsT) else (f,) 

1203 

1204 def _p(x): 

1205 x = float(x) 

1206 f = _pow(x, s, power, op, **raiser_RESIDUAL) 

1207 if f and r: 

1208 f *= _pow(x, r, power, op, **raiser_RESIDUAL) 

1209 return f 

1210 

1211 f = self._facc(xs, _X=_P, _x=_p) # origin=1? 

1212 else: 

1213 f = self._facc_scalar_(float(len(xs))) # x**0 == 1 

1214 return f 

1215 

1216 def _facc_scalar(self, xs, **up): 

1217 '''(INTERNAL) Accumulate all C{xs}, each C{scalar}. 

1218 ''' 

1219 if xs: 

1220 ps = self._ps 

1221 ps[:] = self._ps_acc(list(ps), xs, **up) 

1222 return self 

1223 

1224 def _facc_scalar_(self, *xs, **up): 

1225 '''(INTERNAL) Accumulate all positional C{xs}, each C{scalar}. 

1226 ''' 

1227 return self._facc_scalar(xs, **up) 

1228 

1229 def _facc_scalarf(self, xs, up=True, **origin_which): 

1230 '''(INTERNAL) Accumulate all C{xs}, each C{scalar}, an L{Fsum} or 

1231 L{Fsum2Tuple}, like function C{_xsum}. 

1232 ''' 

1233 _C = self.__class__ 

1234 fs = _xs(xs, **_x_isfine(self.nonfinitesOK, _Cdot=_C, 

1235 **origin_which)) # PYCHOK yield 

1236 return self._facc_scalar(fs, up=up) 

1237 

1238# def _facc_up(self, up=True): 

1239# '''(INTERNAL) Update the C{partials}, by removing 

1240# and re-accumulating the final C{partial}. 

1241# ''' 

1242# ps = self._ps 

1243# while len(ps) > 1: 

1244# p = ps.pop() 

1245# if p: 

1246# n = self._n 

1247# _ = self._ps_acc(ps, (p,), up=False) 

1248# self._n = n 

1249# break 

1250# return self._update() if up else self 

1251 

1252 def fadd(self, xs=()): 

1253 '''Add an iterable's items to this instance. 

1254 

1255 @arg xs: Iterable of items to add (each C{scalar}, 

1256 an L{Fsum} or L{Fsum2Tuple}). 

1257 

1258 @return: This instance (L{Fsum}). 

1259 

1260 @raise OverflowError: Partial C{2sum} overflow. 

1261 

1262 @raise TypeError: An invalid B{C{xs}} item. 

1263 

1264 @raise ValueError: Invalid or I{non-finite} B{C{xs}} value. 

1265 ''' 

1266 if _isFsum_2Tuple(xs): 

1267 self._facc_scalar(xs._ps) 

1268 elif isscalar(xs): # for backward compatibility # PYCHOK no cover 

1269 x = _2float(x=xs, **self._isfine) 

1270 self._facc_scalar_(x) 

1271 elif xs: # _xiterable(xs) 

1272 self._facc(xs) 

1273 return self 

1274 

1275 def fadd_(self, *xs): 

1276 '''Add all positional items to this instance. 

1277 

1278 @arg xs: Values to add (each C{scalar}, an L{Fsum} 

1279 or L{Fsum2Tuple}), all positional. 

1280 

1281 @see: Method L{Fsum.fadd} for further details. 

1282 ''' 

1283 return self._facc_args(xs) 

1284 

1285 def _fadd(self, other, op=_add_op_, **up): 

1286 '''(INTERNAL) Apply C{B{self} += B{other}}. 

1287 ''' 

1288 if _isFsum_2Tuple(other): 

1289 self._facc_scalar(other._ps, **up) 

1290 elif self._scalar(other, op): 

1291 self._facc_scalar_(other, **up) 

1292 return self 

1293 

1294 fcopy = copy # for backward compatibility 

1295 fdiv = __itruediv__ 

1296 fdivmod = __divmod__ 

1297 

1298 def _fdivmod2(self, other, op, **raiser_RESIDUAL): 

1299 '''(INTERNAL) Apply C{B{self} %= B{other}} and return a L{DivMod2Tuple}. 

1300 ''' 

1301 # result mostly follows CPython function U{float_divmod 

1302 # <https://GitHub.com/python/cpython/blob/main/Objects/floatobject.c>}, 

1303 # but at least divmod(-3, 2) equals Cpython's result (-2, 1). 

1304 q = self._truediv(other, op, **raiser_RESIDUAL).floor 

1305 if q: # == float // other == floor(float / other) 

1306 self -= self._Fsum_as(q) * other # NOT other * q! 

1307 

1308 s = signOf(other) # make signOf(self) == signOf(other) 

1309 if s and self.signOf() == -s: # PYCHOK no cover 

1310 self += other 

1311 q -= 1 

1312# t = self.signOf() 

1313# if t and t != s: 

1314# raise self._Error(op, other, _AssertionError, txt__=signOf) 

1315 return DivMod2Tuple(q, self) # q is C{int} in Python 3+, but C{float} in Python 2- 

1316 

1317 def _fhorner(self, x, cs, where, incx=True): # in .fmath 

1318 '''(INTERNAL) Add an L{Fhorner} evaluation of polynomial 

1319 C{sum(c * B{x}**i for i, c in _e(cs))} where C{_e = 

1320 enumerate if B{incx} else _enumereverse}. 

1321 ''' 

1322 # assert _xiterablen(cs) 

1323 try: 

1324 n = len(cs) 

1325 if n > 1 and _2finite(x, **self._isfine): 

1326 H = self._Fsum_as(name__=self._fhorner) 

1327 _m = H._mul_Fsum if _isFsum_2Tuple(x) else \ 

1328 H._mul_scalar 

1329 for c in (reversed(cs) if incx else cs): 

1330 H._fset(_m(x, _mul_op_), up=False) 

1331 H._fadd(c, up=False) 

1332 else: # x == 0 

1333 H = cs[0] if n else 0 

1334 self._fadd(H) 

1335 except Exception as X: 

1336 t = unstr(where, x, *cs, _ELLIPSIS=4, incx=incx) 

1337 raise self._ErrorX(X, _add_op_, t) 

1338 return self 

1339 

1340 def _finite(self, other, op=None): 

1341 '''(INTERNAL) Return B{C{other}} if C{finite}. 

1342 ''' 

1343 if _isOK_or_finite(other, **self._isfine): 

1344 return other 

1345 E = _NonfiniteError(other) 

1346 raise self._Error(op, other, E, txt=_not_finite_) 

1347 

1348 def fint(self, name=NN, **raiser_RESIDUAL): 

1349 '''Return this instance' current running sum as C{integer}. 

1350 

1351 @kwarg name: Optional, overriding C{B{name}="fint"} (C{str}). 

1352 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore 

1353 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar} 

1354 to override the current L{RESIDUAL<Fsum.RESIDUAL>}. 

1355 

1356 @return: The C{integer} sum (L{Fsum}) if this instance C{is_integer} 

1357 with a zero or insignificant I{integer} residual. 

1358 

1359 @raise ResidualError: Non-zero, significant residual or invalid 

1360 B{C{RESIDUAL}}. 

1361 

1362 @see: Methods L{Fsum.fint2}, L{Fsum.int_float} and L{Fsum.is_integer}. 

1363 ''' 

1364 i, r = self._fint2 

1365 if r: 

1366 R = self._raiser(r, i, **raiser_RESIDUAL) 

1367 if R: 

1368 t = _stresidual(_integer_, r, **R) 

1369 raise ResidualError(_integer_, i, txt=t) 

1370 return self._Fsum_as(i, name=_name__(name, name__=self.fint)) 

1371 

1372 def fint2(self, **name): 

1373 '''Return this instance' current running sum as C{int} and the 

1374 I{integer} residual. 

1375 

1376 @kwarg name: Optional name (C{str}). 

1377 

1378 @return: An L{Fsum2Tuple}C{(fsum, residual)} with C{fsum} 

1379 an C{int} and I{integer} C{residual} a C{float} or 

1380 C{INT0} if the C{fsum} is considered to be I{exact}. 

1381 The C{fsum} is I{non-finite} if this instance is. 

1382 ''' 

1383 return Fsum2Tuple(*self._fint2, **name) 

1384 

1385 @Property 

1386 def _fint2(self): # see ._fset 

1387 '''(INTERNAL) Get 2-tuple (C{int}, I{integer} residual). 

1388 ''' 

1389 s, r = self._nfprs2 

1390 if _isfinite(s): 

1391 i = int(s) 

1392 r = (self._ps_1sum(i) if len(self._ps) > 1 else 

1393 float(s - i)) or INT0 

1394 else: # INF, NAN, NINF 

1395 i = float(s) 

1396# r = _NONFINITEr 

1397 return i, r # Fsum2Tuple? 

1398 

1399 @_fint2.setter_ # PYCHOK setter_UNDERscore! 

1400 def _fint2(self, s): # in _fset 

1401 '''(INTERNAL) Replace the C{_fint2} value. 

1402 ''' 

1403 if _isfinite(s): 

1404 i = int(s) 

1405 r = (s - i) or INT0 

1406 else: # INF, NAN, NINF 

1407 i = float(s) 

1408 r = _NONFINITEr 

1409 return i, r # like _fint2.getter 

1410 

1411 @deprecated_property_RO 

1412 def float_int(self): # PYCHOK no cover 

1413 '''DEPRECATED, use method C{Fsum.int_float}.''' 

1414 return self.int_float() # raiser=False 

1415 

1416 @property_RO 

1417 def floor(self): 

1418 '''Get this instance' C{floor} (C{int} in Python 3+, but 

1419 C{float} in Python 2-). 

1420 

1421 @note: This C{floor} takes the C{residual} into account. 

1422 

1423 @see: Method L{Fsum.int_float} and properties L{Fsum.ceil}, 

1424 L{Fsum.imag} and L{Fsum.real}. 

1425 ''' 

1426 s, r = self._fprs2 

1427 f = _floor(s) + _floor(r) + 1 

1428 while (f - s) > r: # f > (s + r) 

1429 f -= 1 

1430 return f # _floor(self._n_d) 

1431 

1432# ffloordiv = __ifloordiv__ # for naming consistency? 

1433# floordiv = __floordiv__ # for naming consistency? 

1434 

1435 def _floordiv(self, other, op, **raiser_RESIDUAL): # rather _ffloordiv? 

1436 '''Apply C{B{self} //= B{other}}. 

1437 ''' 

1438 q = self._ftruediv(other, op, **raiser_RESIDUAL) # == self 

1439 return self._fset(q.floor) # floor(q) 

1440 

1441 def fma(self, other1, other2, **nonfinites): # in .fmath.fma 

1442 '''Fused-multiply-add C{self *= B{other1}; self += B{other2}}. 

1443 

1444 @arg other1: Multiplier (C{scalar}, an L{Fsum} or L{Fsum2Tuple}). 

1445 @arg other2: Addend (C{scalar}, an L{Fsum} or L{Fsum2Tuple}). 

1446 @kwarg nonfinites: Use C{B{nonfinites}=True} or C{False}, to 

1447 override L{nonfinites<Fsum.nonfinites>} and 

1448 L{nonfiniterrors} default (C{bool}). 

1449 ''' 

1450 op = self.fma.__name__ 

1451 _fs = self._ps_other 

1452 try: 

1453 s, r = self._fprs2 

1454 if r: 

1455 f = self._f2mul(self.fma, (other1,), **nonfinites) 

1456 f += other2 

1457 elif _residue(other1) or _residue(other2): 

1458 fs = _2split3s(_fs(op, other1)) 

1459 fs = _2products(s, fs, *_fs(op, other2)) 

1460 f = _Psum(self._ps_acc([], fs, up=False), name=op) 

1461 else: 

1462 f = _fma(s, other1, other2) 

1463 f = _2finite(f, **self._isfine) 

1464 except TypeError as X: 

1465 raise self._ErrorX(X, op, (other1, other2)) 

1466 except (OverflowError, ValueError) as X: # from math.fma 

1467 f = self._mul_reduce(s, other1) # INF, NAN, NINF 

1468 f += sum(_fs(op, other2)) 

1469 f = self._nonfiniteX(X, op, f, **nonfinites) 

1470 return self._fset(f) 

1471 

1472 fmul = __imul__ 

1473 

1474 def _fmul(self, other, op): 

1475 '''(INTERNAL) Apply C{B{self} *= B{other}}. 

1476 ''' 

1477 if _isFsum_2Tuple(other): 

1478 if len(self._ps) != 1: 

1479 f = self._mul_Fsum(other, op) 

1480 elif len(other._ps) != 1: # and len(self._ps) == 1 

1481 f = self._ps_mul(op, *other._ps) if other._ps else _0_0 

1482 elif self._f2product: # len(other._ps) == 1 

1483 f = self._mul_scalar(other._ps[0], op) 

1484 else: # len(other._ps) == len(self._ps) == 1 

1485 f = self._finite(self._ps[0] * other._ps[0], op=op) 

1486 else: 

1487 s = self._scalar(other, op) 

1488 f = self._mul_scalar(s, op) 

1489 return self._fset(f) # n=len(self) + 1 

1490 

1491 @deprecated_method 

1492 def f2mul(self, *others, **raiser): 

1493 '''DEPRECATED on 2024.09.13, use method L{f2mul_<Fsum.f2mul_>}.''' 

1494 return self._fset(self.f2mul_(others, **raiser)) 

1495 

1496 def f2mul_(self, *others, **f2product_nonfinites): # in .fmath.f2mul 

1497 '''Return C{B{self} * B{other} * B{other} ...} for all B{C{others}} using cascaded, 

1498 accurate multiplication like with L{f2product<Fsum.f2product>}C{(B{True})}. 

1499 

1500 @arg others: Multipliers (each C{scalar}, an L{Fsum} or L{Fsum2Tuple}), all 

1501 positional. 

1502 @kwarg f2product_nonfinites: Use C{B{f2product=False}} to override the default 

1503 C{True} and C{B{nonfinites}=True} or C{False}, to override 

1504 settings L{nonfinites<Fsum.nonfinites>} and L{nonfiniterrors}. 

1505 

1506 @return: The cascaded I{TwoProduct} (L{Fsum} or C{float}). 

1507 

1508 @see: U{Equations 2.3<https://www.TUHH.De/ti3/paper/rump/OzOgRuOi06.pdf>} 

1509 ''' 

1510 return self._f2mul(self.f2mul_, others, **f2product_nonfinites) 

1511 

1512 def _f2mul(self, where, others, f2product=True, **nonfinites_raiser): 

1513 '''(INTERNAL) See methods C{fma} and C{f2mul_}. 

1514 ''' 

1515 f = _Psum(self._ps, f2product=f2product, name=where.__name__) 

1516 if others and f: 

1517 if f.f2product(): 

1518 def _pfs(f, ps): 

1519 return _2products(f, _2split3s(ps)) 

1520 else: 

1521 def _pfs(f, ps): # PYCHOK redef 

1522 return (f * p for p in ps) 

1523 

1524 op, ps = where.__name__, f._ps 

1525 try: # as if self.f2product(True) 

1526 for other in others: # to pinpoint errors 

1527 for p in self._ps_other(op, other): 

1528 ps[:] = f._ps_acc([], _pfs(p, ps), update=False) 

1529 f._update() 

1530 except TypeError as X: 

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

1532 except (OverflowError, ValueError) as X: 

1533 r = self._mul_reduce(sum(ps), other) # INF, NAN, NINF 

1534 r = self._nonfiniteX(X, op, r, **nonfinites_raiser) 

1535 f._fset(r) 

1536 return f 

1537 

1538 def fover(self, over, **raiser_RESIDUAL): 

1539 '''Apply C{B{self} /= B{over}} and summate. 

1540 

1541 @arg over: An L{Fsum} or C{scalar} denominator. 

1542 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore 

1543 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar} 

1544 to override the current L{RESIDUAL<Fsum.RESIDUAL>}. 

1545 

1546 @return: Precision running sum (C{float}). 

1547 

1548 @raise ResidualError: Non-zero, significant residual or invalid 

1549 B{C{RESIDUAL}}. 

1550 

1551 @see: Methods L{Fsum.fsum} and L{Fsum.__itruediv__}. 

1552 ''' 

1553 return float(self.fdiv(over, **raiser_RESIDUAL)._fprs) 

1554 

1555 fpow = __ipow__ 

1556 

1557 def _fpow(self, other, op, *mod, **raiser_RESIDUAL): 

1558 '''Apply C{B{self} **= B{other}}, optional B{C{mod}} or C{None}. 

1559 ''' 

1560 if mod: 

1561 if mod[0] is not None: # == 3-arg C{pow} 

1562 f = self._pow_2_3(self, other, other, op, *mod, **raiser_RESIDUAL) 

1563 elif self.is_integer(): 

1564 # return an exact C{int} for C{int}**C{int} 

1565 i, _ = self._fint2 # assert _ == 0 

1566 x, r = _2tuple2(other) # C{int}, C{float} or other 

1567 f = self._Fsum_as(i)._pow_Fsum(other, op, **raiser_RESIDUAL) if r else \ 

1568 self._pow_2_3(i, x, other, op, **raiser_RESIDUAL) 

1569 else: # mod[0] is None, power(self, other) 

1570 f = self._pow(other, other, op, **raiser_RESIDUAL) 

1571 else: # pow(self, other) 

1572 f = self._pow(other, other, op, **raiser_RESIDUAL) 

1573 return self._fset(f) # n=max(len(self), 1) 

1574 

1575 def f2product(self, *two): 

1576 '''Get and set accurate I{TwoProduct} multiplication for this 

1577 L{Fsum}, overriding the L{f2product} default. 

1578 

1579 @arg two: If omitted, leave the override unchanged, if C{True}, 

1580 turn I{TwoProduct} on, if C{False} off, if C{None}e 

1581 remove th override (C{bool} or C{None}). 

1582 

1583 @return: The previous setting (C{bool} or C{None} if not set). 

1584 

1585 @see: Function L{f2product<fsums.f2product>}. 

1586 

1587 @note: Use C{f.f2product() or f2product()} to determine whether 

1588 multiplication is accurate for L{Fsum} C{f}. 

1589 ''' 

1590 if two: # delattrof(self, _f2product=None) 

1591 t = _xkwds_pop(self.__dict__, _f2product=None) 

1592 if two[0] is not None: 

1593 self._f2product = bool(two[0]) 

1594 else: # getattrof(self, _f2product=None) 

1595 t = _xkwds_get(self.__dict__, _f2product=None) 

1596 return t 

1597 

1598 @Property 

1599 def _fprs(self): 

1600 '''(INTERNAL) Get and cache this instance' precision 

1601 running sum (C{float} or C{int}), ignoring C{residual}. 

1602 

1603 @note: The precision running C{fsum} after a C{//=} or 

1604 C{//} C{floor} division is C{int} in Python 3+. 

1605 ''' 

1606 s, _ = self._fprs2 

1607 return s # ._fprs2.fsum 

1608 

1609 @_fprs.setter_ # PYCHOK setter_UNDERscore! 

1610 def _fprs(self, s): 

1611 '''(INTERNAL) Replace the C{_fprs} value. 

1612 ''' 

1613 return s 

1614 

1615 @Property 

1616 def _fprs2(self): 

1617 '''(INTERNAL) Get and cache this instance' precision 

1618 running sum and residual (L{Fsum2Tuple}). 

1619 ''' 

1620 ps = self._ps 

1621 n = len(ps) 

1622 try: 

1623 if n > 2: 

1624 s = _psum(ps, **self._isfine) 

1625 if not _isfinite(s): 

1626 ps[:] = s, # collapse ps 

1627 return Fsum2Tuple(s, _NONFINITEr) 

1628 n = len(ps) 

1629# Fsum._ps_max = max(Fsum._ps_max, n) 

1630 if n > 2: 

1631 r = self._ps_1sum(s) 

1632 return Fsum2Tuple(*_s_r2(s, r)) 

1633 if n > 1: # len(ps) == 2 

1634 s, r = _s_r2(*_2sum(*ps, **self._isfine)) 

1635 ps[:] = (r, s) if r else (s,) 

1636 elif ps: # len(ps) == 1 

1637 s = ps[0] 

1638 r = INT0 if _isfinite(s) else _NONFINITEr 

1639 else: # len(ps) == 0 

1640 s = _0_0 

1641 r = INT0 if _isfinite(s) else _NONFINITEr 

1642 ps[:] = s, 

1643 except (OverflowError, ValueError) as X: 

1644 op = _fset_op_ # INF, NAN, NINF 

1645 ps[:] = sum(ps), # collapse ps 

1646 s = self._nonfiniteX(X, op, ps[0]) 

1647 r = _NONFINITEr 

1648 # assert self._ps is ps 

1649 return Fsum2Tuple(s, r) 

1650 

1651 @_fprs2.setter_ # PYCHOK setter_UNDERscore! 

1652 def _fprs2(self, s_r): 

1653 '''(INTERNAL) Replace the C{_fprs2} value. 

1654 ''' 

1655 return Fsum2Tuple(s_r) 

1656 

1657 def fset_(self, *xs): 

1658 '''Apply C{B{self}.partials = Fsum(*B{xs}).partials}. 

1659 

1660 @arg xs: Optional, new values (each C{scalar} or an L{Fsum} 

1661 or L{Fsum2Tuple} instance), all positional. 

1662 

1663 @return: This instance, replaced (C{Fsum}). 

1664 

1665 @see: Method L{Fsum.fadd} for further details. 

1666 ''' 

1667 f = (xs[0] if xs else _0_0) if len(xs) < 2 else \ 

1668 Fsum(*xs, nonfinites=self.nonfinites()) # self._Fsum_as(*xs) 

1669 return self._fset(f, op=_fset_op_) 

1670 

1671 def _fset(self, other, n=0, up=True, **op): 

1672 '''(INTERNAL) Overwrite this instance with an other or a C{scalar}. 

1673 ''' 

1674 if other is self: 

1675 pass # from ._fmul, ._ftruediv and ._pow_0_1 

1676 elif _isFsum_2Tuple(other): 

1677 if op: # and not self.nonfinitesOK: 

1678 self._finite(other._fprs, **op) 

1679 self._ps[:] = other._ps 

1680 self._n = n or other._n 

1681 if up: # use or zap the C{Property_RO} values 

1682 Fsum._fint2._update_from(self, other) 

1683 Fsum._fprs ._update_from(self, other) 

1684 Fsum._fprs2._update_from(self, other) 

1685 elif isscalar(other): 

1686 s = float(self._finite(other, **op)) if op else other 

1687 self._ps[:] = s, 

1688 self._n = n or 1 

1689 if up: # Property _fint2, _fprs and _fprs2 all have 

1690 # @.setter_underscore and NOT @.setter because the 

1691 # latter's _fset zaps the value set by @.setter 

1692 self._fint2 = s 

1693 self._fprs = s 

1694 self._fprs2 = s, INT0 

1695 # assert self._fprs is s 

1696 else: 

1697 op = _xkwds_get1(op, op=_fset_op_) 

1698 raise self._Error(op, other, _TypeError) 

1699 return self 

1700 

1701 def fsub(self, xs=()): 

1702 '''Subtract an iterable's items from this instance. 

1703 

1704 @see: Method L{Fsum.fadd} for further details. 

1705 ''' 

1706 return self._facc_neg(xs) 

1707 

1708 def fsub_(self, *xs): 

1709 '''Subtract all positional items from this instance. 

1710 

1711 @see: Method L{Fsum.fadd_} for further details. 

1712 ''' 

1713 return self._fsub(xs[0], _sub_op_) if len(xs) == 1 else \ 

1714 self._facc_neg(xs) # origin=1? 

1715 

1716 def _fsub(self, other, op): 

1717 '''(INTERNAL) Apply C{B{self} -= B{other}}. 

1718 ''' 

1719 if _isFsum_2Tuple(other): 

1720 if other is self: # or other._fprs2 == self._fprs2: 

1721 self._fset(_0_0, n=len(self) * 2) 

1722 elif other._ps: 

1723 self._facc_scalar(other._ps_neg) 

1724 elif self._scalar(other, op): 

1725 self._facc_scalar_(-other) 

1726 return self 

1727 

1728 def fsum(self, xs=()): 

1729 '''Add an iterable's items, summate and return the current 

1730 precision running sum. 

1731 

1732 @arg xs: Iterable of items to add (each item C{scalar}, 

1733 an L{Fsum} or L{Fsum2Tuple}). 

1734 

1735 @return: Precision running sum (C{float} or C{int}). 

1736 

1737 @see: Method L{Fsum.fadd}. 

1738 

1739 @note: Accumulation can continue after summation. 

1740 ''' 

1741 return self._facc(xs)._fprs 

1742 

1743 def fsum_(self, *xs): 

1744 '''Add any positional items, summate and return the current 

1745 precision running sum. 

1746 

1747 @arg xs: Items to add (each C{scalar}, an L{Fsum} or 

1748 L{Fsum2Tuple}), all positional. 

1749 

1750 @return: Precision running sum (C{float} or C{int}). 

1751 

1752 @see: Methods L{Fsum.fsum}, L{Fsum.Fsum_} and L{Fsum.fsumf_}. 

1753 ''' 

1754 return self._facc_args(xs)._fprs 

1755 

1756 def Fsum_(self, *xs, **name): 

1757 '''Like method L{Fsum.fsum_} but returning a named L{Fsum}. 

1758 

1759 @kwarg name: Optional name (C{str}). 

1760 

1761 @return: Copy of this updated instance (L{Fsum}). 

1762 ''' 

1763 return self._facc_args(xs)._copy_2(self.Fsum_, **name) 

1764 

1765 def Fsum2Tuple_(self, *xs, **name): 

1766 '''Like method L{Fsum.fsum_} but returning a named L{Fsum2Tuple}. 

1767 

1768 @kwarg name: Optional name (C{str}). 

1769 

1770 @return: Precision running sum (L{Fsum2Tuple}). 

1771 ''' 

1772 return Fsum2Tuple(self._facc_args(xs)._nfprs2, **name) 

1773 

1774 @property_RO 

1775 def _Fsum(self): # like L{Fsum2Tuple._Fsum}, in .fstats 

1776 return self # NOT @Property_RO, see .copy and ._copy_2 

1777 

1778 def _Fsum_as(self, *xs, **name_f2product_nonfinites_RESIDUAL): 

1779 '''(INTERNAL) Return an C{Fsum} with this C{Fsum}'s C{.f2product}, 

1780 C{.nonfinites} and C{.RESIDUAL} setting, optionally 

1781 overridden with C{name_f2product_nonfinites_RESIDUAL} and 

1782 with any C{xs} accumulated. 

1783 ''' 

1784 kwds = _xkwds_not(None, Fsum._RESIDUAL, f2product =self.f2product(), 

1785 nonfinites=self.nonfinites(), 

1786 RESIDUAL =self.RESIDUAL()) 

1787 if name_f2product_nonfinites_RESIDUAL: # overwrites 

1788 kwds.update(name_f2product_nonfinites_RESIDUAL) 

1789 f = Fsum(**kwds) 

1790 # assert all(v == self.__dict__[n] for n, v in f.__dict__.items()) 

1791 return (f._facc(xs, up=False) if len(xs) > 1 else 

1792 f._fset(xs[0], op=_fset_op_)) if xs else f 

1793 

1794 def fsum2(self, xs=(), **name): 

1795 '''Add an iterable's items, summate and return the 

1796 current precision running sum I{and} the C{residual}. 

1797 

1798 @arg xs: Iterable of items to add (each item C{scalar}, 

1799 an L{Fsum} or L{Fsum2Tuple}). 

1800 @kwarg name: Optional C{B{name}=NN} (C{str}). 

1801 

1802 @return: L{Fsum2Tuple}C{(fsum, residual)} with C{fsum} the 

1803 current precision running sum and C{residual}, the 

1804 (precision) sum of the remaining C{partials}. The 

1805 C{residual is INT0} if the C{fsum} is considered 

1806 to be I{exact}. 

1807 

1808 @see: Methods L{Fsum.fint2}, L{Fsum.fsum} and L{Fsum.fsum2_} 

1809 ''' 

1810 t = self._facc(xs)._fprs2 

1811 return t.dup(name=name) if name else t 

1812 

1813 def fsum2_(self, *xs): 

1814 '''Add any positional items, summate and return the current 

1815 precision running sum and the I{differential}. 

1816 

1817 @arg xs: Values to add (each C{scalar}, an L{Fsum} or 

1818 L{Fsum2Tuple}), all positional. 

1819 

1820 @return: 2Tuple C{(fsum, delta)} with the current, precision 

1821 running C{fsum} like method L{Fsum.fsum} and C{delta}, 

1822 the difference with previous running C{fsum}, C{float}. 

1823 

1824 @see: Methods L{Fsum.fsum_} and L{Fsum.fsum}. 

1825 ''' 

1826 return self._fsum2(xs, self._facc_args) 

1827 

1828 def _fsum2(self, xs, _facc, **facc_kwds): 

1829 '''(INTERNAL) Helper for L{Fsum.fsum2_} and L{Fsum.fsum2f_}. 

1830 ''' 

1831 p, q = self._fprs2 

1832 if xs: 

1833 s, r = _facc(xs, **facc_kwds)._fprs2 

1834 if _isfinite(s): # _fsum(_1primed((s, -p, r, -q)) 

1835 d, r = _2sum(s - p, r - q, _isfine=_isOK) 

1836 r, _ = _s_r2(d, r) 

1837 return s, (r if _isfinite(r) else _NONFINITEr) 

1838 else: 

1839 return p, _0_0 

1840 

1841 def fsumf_(self, *xs): 

1842 '''Like method L{Fsum.fsum_} iff I{all} C{B{xs}}, each I{known to be} 

1843 C{scalar}, an L{Fsum} or L{Fsum2Tuple}. 

1844 ''' 

1845 return self._facc_scalarf(xs, which=self.fsumf_)._fprs # origin=1? 

1846 

1847 def Fsumf_(self, *xs): 

1848 '''Like method L{Fsum.Fsum_} iff I{all} C{B{xs}}, each I{known to be} 

1849 C{scalar}, an L{Fsum} or L{Fsum2Tuple}. 

1850 ''' 

1851 return self._facc_scalarf(xs, which=self.Fsumf_)._copy_2(self.Fsumf_) # origin=1? 

1852 

1853 def fsum2f_(self, *xs): 

1854 '''Like method L{Fsum.fsum2_} iff I{all} C{B{xs}}, each I{known to be} 

1855 C{scalar}, an L{Fsum} or L{Fsum2Tuple}. 

1856 ''' 

1857 return self._fsum2(xs, self._facc_scalarf, which=self.fsum2f_) # origin=1? 

1858 

1859# ftruediv = __itruediv__ # for naming consistency? 

1860 

1861 def _ftruediv(self, other, op, **raiser_RESIDUAL): 

1862 '''(INTERNAL) Apply C{B{self} /= B{other}}. 

1863 ''' 

1864 n = _1_0 

1865 if _isFsum_2Tuple(other): 

1866 if other is self or self == other: 

1867 return self._fset(n, n=len(self)) 

1868 d, r = other._fprs2 

1869 if r: 

1870 R = self._raiser(r, d, **raiser_RESIDUAL) 

1871 if R: 

1872 raise self._ResidualError(op, other, r, **R) 

1873 d, n = other.as_integer_ratio() 

1874 else: 

1875 d = self._scalar(other, op) 

1876 try: 

1877 s = n / d 

1878 except Exception as X: 

1879 raise self._ErrorX(X, op, other) 

1880 f = self._mul_scalar(s, _mul_op_) # handles 0, INF, NAN 

1881 return self._fset(f) 

1882 

1883 @property_RO 

1884 def imag(self): 

1885 '''Get the C{imaginary} part of this instance (C{0.0}, always). 

1886 

1887 @see: Property L{Fsum.real}. 

1888 ''' 

1889 return _0_0 

1890 

1891 def int_float(self, **raiser_RESIDUAL): 

1892 '''Return this instance' current running sum as C{int} or C{float}. 

1893 

1894 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore 

1895 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar} 

1896 to override the current L{RESIDUAL<Fsum.RESIDUAL>}. 

1897 

1898 @return: This C{int} sum if this instance C{is_integer} and 

1899 I{finite}, otherwise the C{float} sum if the residual 

1900 is zero or not significant. 

1901 

1902 @raise ResidualError: Non-zero, significant residual or invalid 

1903 B{C{RESIDUAL}}. 

1904 

1905 @see: Methods L{Fsum.fint}, L{Fsum.fint2}, L{Fsum.is_integer}, 

1906 L{Fsum.RESIDUAL} and property L{Fsum.as_iscalar}. 

1907 ''' 

1908 s, r = self._fint2 

1909 if r: 

1910 s, r = self._fprs2 

1911 if r: # PYCHOK no cover 

1912 R = self._raiser(r, s, **raiser_RESIDUAL) 

1913 if R: 

1914 t = _stresidual(_non_zero_, r, **R) 

1915 raise ResidualError(int_float=s, txt=t) 

1916 s = float(s) 

1917 return s 

1918 

1919 def is_exact(self): 

1920 '''Is this instance' running C{fsum} considered to be exact? 

1921 (C{bool}), C{True} only if the C{residual is }L{INT0}. 

1922 ''' 

1923 return self.residual is INT0 

1924 

1925 def is_finite(self): # in .constants 

1926 '''Is this instance C{finite}? (C{bool}). 

1927 

1928 @see: Function L{isfinite<pygeodesy.isfinite>}. 

1929 ''' 

1930 return _isfinite(sum(self._ps)) # == sum(self) 

1931 

1932 def is_integer(self): 

1933 '''Is this instance' running sum C{integer}? (C{bool}). 

1934 

1935 @see: Methods L{Fsum.fint}, L{Fsum.fint2} and L{Fsum.is_scalar}. 

1936 ''' 

1937 s, r = self._fint2 

1938 return False if r else (_isfinite(s) and isint(s)) 

1939 

1940 def is_math_fma(self): 

1941 '''Is accurate L{f2product} multiplication based on Python's C{math.fma}? 

1942 

1943 @return: C{True} if accurate multiplication uses C{math.fma}, C{False} 

1944 an C{fma} implementation as C{math.fma} or C{None}, a previous 

1945 C{PyGeodesy} implementation. 

1946 ''' 

1947 return (_2split3s is _passarg) or (False if _integer_ratio2 is None else None) 

1948 

1949 def is_math_fsum(self): 

1950 '''Are the summation functions L{fsum}, L{fsum_}, L{fsumf_}, L{fsum1}, 

1951 L{fsum1_} and L{fsum1f_} based on Python's C{math.fsum}? 

1952 

1953 @return: C{True} if summation functions use C{math.fsum}, C{False} 

1954 otherwise. 

1955 ''' 

1956 return _sum is _fsum # _fsum.__module__ is fabs.__module__ 

1957 

1958 def is_scalar(self, **raiser_RESIDUAL): 

1959 '''Is this instance' running sum C{scalar} with C{0} residual or with 

1960 a residual I{ratio} not exceeding the RESIDUAL threshold? 

1961 

1962 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore 

1963 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar} 

1964 to override the current L{RESIDUAL<Fsum.RESIDUAL>}. 

1965 

1966 @return: C{True} if this instance' residual is C{0} or C{insignificant}, 

1967 i.e. its residual C{ratio} doesn't exceed the L{RESIDUAL 

1968 <Fsum.RESIDUAL>} threshold (C{bool}). 

1969 

1970 @raise ResidualError: Non-zero, significant residual or invalid 

1971 B{C{RESIDUAL}}. 

1972 

1973 @see: Methods L{Fsum.RESIDUAL} and L{Fsum.is_integer} and property 

1974 L{Fsum.as_iscalar}. 

1975 ''' 

1976 s, r = self._fprs2 

1977 return False if r and self._raiser(r, s, **raiser_RESIDUAL) else True 

1978 

1979 def _mul_Fsum(self, other, op): 

1980 '''(INTERNAL) Return C{B{self} * B{other}} as L{Fsum} or C{0}. 

1981 ''' 

1982 # assert _isFsum_2Tuple(other) 

1983 if self._ps and other._ps: 

1984 try: 

1985 f = self._ps_mul(op, *other._ps) # NO .as_iscalar! 

1986 except Exception as X: 

1987 raise self._ErrorX(X, op, other) 

1988 else: 

1989 f = _0_0 

1990 return f 

1991 

1992 def _mul_reduce(self, *others): 

1993 '''(INTERNAL) Like fmath.fprod for I{non-finite} C{other}s. 

1994 ''' 

1995 r = _1_0 

1996 for f in others: 

1997 r *= sum(f._ps) if _isFsum_2Tuple(f) else float(f) 

1998 return r 

1999 

2000 def _mul_scalar(self, factor, op): 

2001 '''(INTERNAL) Return C{B{self} * scalar B{factor}} as L{Fsum}, C{0.0} or C{self}. 

2002 ''' 

2003 # assert isscalar(factor) 

2004 if self._ps and self._finite(factor, op=op): 

2005 f = self if factor == _1_0 else ( 

2006 self._neg if factor == _N_1_0 else 

2007 self._ps_mul(op, factor).as_iscalar) 

2008 else: 

2009 f = _0_0 

2010 return f 

2011 

2012# @property_RO 

2013# def _n_d(self): 

2014# n, d = self.as_integer_ratio() 

2015# return n / d 

2016 

2017 @property_RO 

2018 def _neg(self): 

2019 '''(INTERNAL) Return C{Fsum(-self)} or scalar C{NEG0}. 

2020 ''' 

2021 return _Psum(self._ps_neg) if self._ps else NEG0 

2022 

2023 @property_RO 

2024 def _nfprs2(self): 

2025 '''(INTERNAL) Handle I{non-finite} C{_fprs2}. 

2026 ''' 

2027 try: # to handle nonfiniterrors, etc. 

2028 t = self._fprs2 

2029 except (OverflowError, ValueError): 

2030 t = Fsum2Tuple(sum(self._ps), _NONFINITEr) 

2031 return t 

2032 

2033 def nonfinites(self, *OK): 

2034 '''Handle I{non-finite} C{float}s as C{inf}, C{INF}, C{NINF}, C{nan} 

2035 and C{NAN} for this L{Fsum} or throw C{OverflowError} respectively 

2036 C{ValueError} exceptions, overriding the L{nonfiniterrors} default. 

2037 

2038 @arg OK: If omitted, leave the override unchanged, if C{True}, 

2039 I{non-finites} are C{OK}, if C{False} throw exceptions 

2040 or if C{None} remove the override (C{bool} or C{None}). 

2041 

2042 @return: The previous setting (C{bool} or C{None} if not set). 

2043 

2044 @see: Function L{nonfiniterrors<fsums.nonfiniterrors>}. 

2045 

2046 @note: Use property L{nonfinitesOK<Fsum.nonfinitesOK>} to determine 

2047 whether I{non-finites} are C{OK} for this L{Fsum} and by the 

2048 L{nonfiniterrors} default. 

2049 ''' 

2050 _ks = Fsum._nonfinites_isfine_kwds 

2051 if OK: # delattrof(self, _isfine=None) 

2052 k = _xkwds_pop(self.__dict__, _isfine=None) 

2053 if OK[0] is not None: 

2054 self._isfine = _ks[bool(OK[0])] 

2055 self._update() 

2056 else: # getattrof(self, _isfine=None) 

2057 k = _xkwds_get(self.__dict__, _isfine=None) 

2058 # dict(map(reversed, _ks.items())).get(k, None) 

2059 # raises a TypeError: unhashable type: 'dict' 

2060 return True if k is _ks[True] else ( 

2061 False if k is _ks[False] else None) 

2062 

2063 _nonfinites_isfine_kwds = {True: dict(_isfine=_isOK), 

2064 False: dict(_isfine=_isfinite)} 

2065 

2066 @property_RO 

2067 def nonfinitesOK(self): 

2068 '''Are I{non-finites} C{OK} for this L{Fsum} or by default? (C{bool}). 

2069 ''' 

2070# nf = self.nonfinites() 

2071# if nf is None: 

2072# nf = not nonfiniterrors() 

2073 return _isOK_or_finite(INF, **self._isfine) 

2074 

2075 def _nonfiniteX(self, X, op, f, nonfinites=None, raiser=None): 

2076 '''(INTERNAL) Handle a I{non-finite} exception. 

2077 ''' 

2078 if nonfinites is None: 

2079 nonfinites = _isOK_or_finite(f, **self._isfine) if raiser is None else (not raiser) 

2080 if not nonfinites: 

2081 raise self._ErrorX(X, op, f) 

2082 return f 

2083 

2084 def _optionals(self, f2product=None, nonfinites=None, **name_RESIDUAL): 

2085 '''(INTERNAL) Re/set options from keyword arguments. 

2086 ''' 

2087 if f2product is not None: 

2088 self.f2product(f2product) 

2089 if nonfinites is not None: 

2090 self.nonfinites(nonfinites) 

2091 if name_RESIDUAL: # MUST be last 

2092 n, kwds = _name2__(**name_RESIDUAL) 

2093 if kwds: 

2094 R = Fsum._RESIDUAL 

2095 t = _threshold(R, **kwds) 

2096 if t != R: 

2097 self._RESIDUAL = t 

2098 if n: 

2099 self.name = n # self.rename(n) 

2100 

2101 def _1_Over(self, x, op, **raiser_RESIDUAL): # vs _1_over 

2102 '''(INTERNAL) Return C{Fsum(1) / B{x}}. 

2103 ''' 

2104 return self._Fsum_as(_1_0)._ftruediv(x, op, **raiser_RESIDUAL) 

2105 

2106 @property_RO 

2107 def partials(self): 

2108 '''Get this instance' current, partial sums (C{tuple} of C{float}s). 

2109 ''' 

2110 return tuple(self._ps) 

2111 

2112 def pow(self, x, *mod, **raiser_RESIDUAL): 

2113 '''Return C{B{self}**B{x}} as L{Fsum}. 

2114 

2115 @arg x: The exponent (C{scalar}, an L{Fsum} or L{Fsum2Tuple}). 

2116 @arg mod: Optional modulus (C{int} or C{None}) for the 3-argument 

2117 C{pow(B{self}, B{other}, B{mod})} version. 

2118 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore 

2119 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar} 

2120 to override the current L{RESIDUAL<Fsum.RESIDUAL>}. 

2121 

2122 @return: The C{pow(self, B{x})} or C{pow(self, B{x}, *B{mod})} 

2123 result (L{Fsum}). 

2124 

2125 @raise ResidualError: Non-zero, significant residual or invalid 

2126 B{C{RESIDUAL}}. 

2127 

2128 @note: If B{C{mod}} is given and C{None}, the result will be an 

2129 C{integer} L{Fsum} provided this instance C{is_integer} 

2130 or set to C{integer} by an L{Fsum.fint} call. 

2131 

2132 @see: Methods L{Fsum.__ipow__}, L{Fsum.fint}, L{Fsum.is_integer} 

2133 and L{Fsum.root}. 

2134 ''' 

2135 f = self._copy_2(self.pow) 

2136 return f._fpow(x, _pow_op_, *mod, **raiser_RESIDUAL) # f = pow(f, x, *mod) 

2137 

2138 def _pow(self, other, unused, op, **raiser_RESIDUAL): 

2139 '''Return C{B{self} ** B{other}}. 

2140 ''' 

2141 if _isFsum_2Tuple(other): 

2142 f = self._pow_Fsum(other, op, **raiser_RESIDUAL) 

2143 elif self._scalar(other, op): 

2144 x = self._finite(other, op=op) 

2145 f = self._pow_scalar(x, other, op, **raiser_RESIDUAL) 

2146 else: 

2147 f = self._pow_0_1(0, other) 

2148 return f 

2149 

2150 def _pow_0_1(self, x, other): 

2151 '''(INTERNAL) Return B{C{self}**1} or C{B{self}**0 == 1.0}. 

2152 ''' 

2153 return self if x else (1 if isint(other) and self.is_integer() else _1_0) 

2154 

2155 def _pow_2_3(self, b, x, other, op, *mod, **raiser_RESIDUAL): 

2156 '''(INTERNAL) 2-arg C{pow(B{b}, scalar B{x})} and 3-arg C{pow(B{b}, 

2157 B{x}, int B{mod} or C{None})}, embellishing errors. 

2158 ''' 

2159 

2160 if mod: # b, x, mod all C{int}, unless C{mod} is C{None} 

2161 m = mod[0] 

2162 # assert _isFsum_2Tuple(b) 

2163 

2164 def _s(s, r): 

2165 R = self._raiser(r, s, **raiser_RESIDUAL) 

2166 if R: 

2167 raise self._ResidualError(op, other, r, mod=m, **R) 

2168 return s 

2169 

2170 b = _s(*(b._fprs2 if m is None else b._fint2)) 

2171 x = _s(*_2tuple2(x)) 

2172 

2173 try: 

2174 # 0**INF == 0.0, 1**INF == 1.0, -1**2.3 == -(1**2.3) 

2175 s = pow(b, x, *mod) 

2176 if iscomplex(s): 

2177 # neg**frac == complex in Python 3+, but ValueError in 2- 

2178 raise ValueError(_strcomplex(s, b, x, *mod)) 

2179 _ = _2finite(s, **self._isfine) # ignore float 

2180 return s 

2181 except Exception as X: 

2182 raise self._ErrorX(X, op, other, *mod) 

2183 

2184 def _pow_Fsum(self, other, op, **raiser_RESIDUAL): 

2185 '''(INTERNAL) Return C{B{self} **= B{other}} for C{_isFsum_2Tuple(other)}. 

2186 ''' 

2187 # assert _isFsum_2Tuple(other) 

2188 x, r = other._fprs2 

2189 f = self._pow_scalar(x, other, op, **raiser_RESIDUAL) 

2190 if f and r: 

2191 f *= self._pow_scalar(r, other, op, **raiser_RESIDUAL) 

2192 return f 

2193 

2194 def _pow_int(self, x, other, op, **raiser_RESIDUAL): 

2195 '''(INTERNAL) Return C{B{self} **= B{x}} for C{int B{x} >= 0}. 

2196 ''' 

2197 # assert isint(x) and x >= 0 

2198 ps = self._ps 

2199 if len(ps) > 1: 

2200 _mul_Fsum = Fsum._mul_Fsum 

2201 if x > 4: 

2202 p = self 

2203 f = self if (x & 1) else self._Fsum_as(_1_0) 

2204 m = x >> 1 # // 2 

2205 while m: 

2206 p = _mul_Fsum(p, p, op) # p **= 2 

2207 if (m & 1): 

2208 f = _mul_Fsum(f, p, op) # f *= p 

2209 m >>= 1 # //= 2 

2210 elif x > 1: # self**2, 3, or 4 

2211 f = _mul_Fsum(self, self, op) 

2212 if x > 2: # self**3 or 4 

2213 p = self if x < 4 else f 

2214 f = _mul_Fsum(f, p, op) 

2215 else: # self**1 or self**0 == 1 or _1_0 

2216 f = self._pow_0_1(x, other) 

2217 elif ps: # self._ps[0]**x 

2218 f = self._pow_2_3(ps[0], x, other, op, **raiser_RESIDUAL) 

2219 else: # PYCHOK no cover 

2220 # 0**pos_int == 0, but 0**0 == 1 

2221 f = 0 if x else 1 

2222 return f 

2223 

2224 def _pow_scalar(self, x, other, op, **raiser_RESIDUAL): 

2225 '''(INTERNAL) Return C{self**B{x}} for C{scalar B{x}}. 

2226 ''' 

2227 s, r = self._fprs2 

2228 if r: 

2229 # assert s != 0 

2230 if isint(x, both=True): # self**int 

2231 x = int(x) 

2232 y = abs(x) 

2233 if y > 1: 

2234 f = self._pow_int(y, other, op, **raiser_RESIDUAL) 

2235 if x > 0: # i.e. > 1 

2236 return f # Fsum or scalar 

2237 # assert x < 0 # i.e. < -1 

2238 if _isFsum(f): 

2239 s, r = f._fprs2 

2240 if r: 

2241 return self._1_Over(f, op, **raiser_RESIDUAL) 

2242 else: # scalar 

2243 s = f 

2244 # use s**(-1) to get the CPython 

2245 # float_pow error iff s is zero 

2246 x = -1 

2247 elif x < 0: # self**(-1) 

2248 return self._1_Over(self, op, **raiser_RESIDUAL) # 1 / self 

2249 else: # self**1 or self**0 

2250 return self._pow_0_1(x, other) # self, 1 or 1.0 

2251 else: # self**fractional 

2252 R = self._raiser(r, s, **raiser_RESIDUAL) 

2253 if R: 

2254 raise self._ResidualError(op, other, r, **R) 

2255 n, d = self.as_integer_ratio() 

2256 if abs(n) > abs(d): 

2257 n, d, x = d, n, (-x) 

2258 s = n / d 

2259 # assert isscalar(s) and isscalar(x) 

2260 return self._pow_2_3(s, x, other, op, **raiser_RESIDUAL) 

2261 

2262 def _ps_acc(self, ps, xs, up=True, **unused): 

2263 '''(INTERNAL) Accumulate C{xs} known scalars into list C{ps}. 

2264 ''' 

2265 n = 0 

2266 _2s = _2sum 

2267 _fi = self._isfine 

2268 for x in (tuple(xs) if xs is ps else xs): 

2269 # assert isscalar(x) and _isOK_or_finite(x, **self._isfine) 

2270 if x: 

2271 i = 0 

2272 for p in ps: 

2273 x, p = _2s(x, p, **_fi) 

2274 if p: 

2275 ps[i] = p 

2276 i += 1 

2277 ps[i:] = (x,) if x else () 

2278 n += 1 

2279 if n: 

2280 self._n += n 

2281 # Fsum._ps_max = max(Fsum._ps_max, len(ps)) 

2282 if up: 

2283 self._update() 

2284# x = sum(ps) 

2285# if not _isOK_or_finite(x, **fi): 

2286# ps[:] = x, # collapse ps 

2287 return ps 

2288 

2289 def _ps_mul(self, op, *factors): 

2290 '''(INTERNAL) Multiply this instance' C{partials} with 

2291 each scalar C{factor} and accumulate into an C{Fsum}. 

2292 ''' 

2293 def _psfs(ps, fs, _isfine=_isfinite): 

2294 if len(ps) < len(fs): 

2295 ps, fs = fs, ps 

2296 if self._f2product: 

2297 fs, p = _2split3s(fs), fs 

2298 if len(ps) > 1 and fs is not p: 

2299 fs = tuple(fs) # several ps 

2300 _pfs = _2products 

2301 else: 

2302 def _pfs(p, fs): 

2303 return (p * f for f in fs) 

2304 

2305 for p in ps: 

2306 for x in _pfs(p, fs): 

2307 yield x if _isfine(x) else _nfError(x) 

2308 

2309 xs = _psfs(self._ps, factors, **self._isfine) 

2310 f = _Psum(self._ps_acc([], xs, up=False), name=op) 

2311 return f 

2312 

2313 @property_RO 

2314 def _ps_neg(self): 

2315 '''(INTERNAL) Yield the partials, I{negated}. 

2316 ''' 

2317 for p in self._ps: 

2318 yield -p 

2319 

2320 def _ps_other(self, op, other): 

2321 '''(INTERNAL) Yield C{other} as C{scalar}s. 

2322 ''' 

2323 if _isFsum_2Tuple(other): 

2324 for p in other._ps: 

2325 yield p 

2326 else: 

2327 yield self._scalar(other, op) 

2328 

2329 def _ps_1sum(self, *less): 

2330 '''(INTERNAL) Return the partials sum, 1-primed C{less} some scalars. 

2331 ''' 

2332 def _1psls(ps, ls): 

2333 yield _1_0 

2334 for p in ps: 

2335 yield p 

2336 for p in ls: 

2337 yield -p 

2338 yield _N_1_0 

2339 

2340 return _fsum(_1psls(self._ps, less)) 

2341 

2342 def _raiser(self, r, s, raiser=True, **RESIDUAL): 

2343 '''(INTERNAL) Does ratio C{r / s} exceed the RESIDUAL threshold 

2344 I{and} is residual C{r} I{non-zero} or I{significant} (for a 

2345 negative respectively positive C{RESIDUAL} threshold)? 

2346 ''' 

2347 if r and raiser: 

2348 t = self._RESIDUAL 

2349 if RESIDUAL: 

2350 t = _threshold(t, **RESIDUAL) 

2351 if t < 0 or (s + r) != s: 

2352 q = (r / s) if s else s # == 0. 

2353 if fabs(q) > fabs(t): 

2354 return dict(ratio=q, R=t) 

2355 return {} 

2356 

2357 rdiv = __rtruediv__ 

2358 

2359 @property_RO 

2360 def real(self): 

2361 '''Get the C{real} part of this instance (C{float}). 

2362 

2363 @see: Methods L{Fsum.__float__} and L{Fsum.fsum} 

2364 and properties L{Fsum.ceil}, L{Fsum.floor}, 

2365 L{Fsum.imag} and L{Fsum.residual}. 

2366 ''' 

2367 return float(self) 

2368 

2369 @property_RO 

2370 def residual(self): 

2371 '''Get this instance' residual or residue (C{float} or C{int}): 

2372 the C{sum(partials)} less the precision running sum C{fsum}. 

2373 

2374 @note: The C{residual is INT0} iff the precision running 

2375 C{fsum} is considered to be I{exact}. 

2376 

2377 @see: Methods L{Fsum.fsum}, L{Fsum.fsum2} and L{Fsum.is_exact}. 

2378 ''' 

2379 return self._fprs2.residual 

2380 

2381 def RESIDUAL(self, *threshold): 

2382 '''Get and set this instance' I{ratio} for raising L{ResidualError}s, 

2383 overriding the default from env variable C{PYGEODESY_FSUM_RESIDUAL}. 

2384 

2385 @arg threshold: If C{scalar}, the I{ratio} to exceed for raising 

2386 L{ResidualError}s in division and exponention, if 

2387 C{None}, restore the default set with env variable 

2388 C{PYGEODESY_FSUM_RESIDUAL} or if omitted, keep the 

2389 current setting. 

2390 

2391 @return: The previous C{RESIDUAL} setting (C{float}), default C{0.0}. 

2392 

2393 @raise ResidualError: Invalid B{C{threshold}}. 

2394 

2395 @note: L{ResidualError}s may be thrown if (1) the non-zero I{ratio} 

2396 C{residual / fsum} exceeds the given B{C{threshold}} and (2) 

2397 the C{residual} is non-zero and (3) is I{significant} vs the 

2398 C{fsum}, i.e. C{(fsum + residual) != fsum} and (4) optional 

2399 keyword argument C{raiser=False} is missing. Specify a 

2400 negative B{C{threshold}} for only non-zero C{residual} 

2401 testing without the I{significant} case. 

2402 ''' 

2403 r = self._RESIDUAL 

2404 if threshold: 

2405 t = threshold[0] 

2406 self._RESIDUAL = Fsum._RESIDUAL if t is None else ( # for ... 

2407 (_0_0 if t else _1_0) if isbool(t) else 

2408 _threshold(t)) # ... backward compatibility 

2409 return r 

2410 

2411 def _ResidualError(self, op, other, residual, **mod_R): 

2412 '''(INTERNAL) Non-zero B{C{residual}} etc. 

2413 ''' 

2414 def _p(mod=None, R=0, **unused): # ratio=0 

2415 return (_non_zero_ if R < 0 else _significant_) \ 

2416 if mod is None else _integer_ 

2417 

2418 t = _stresidual(_p(**mod_R), residual, **mod_R) 

2419 return self._Error(op, other, ResidualError, txt=t) 

2420 

2421 def root(self, root, **raiser_RESIDUAL): 

2422 '''Return C{B{self}**(1 / B{root})} as L{Fsum}. 

2423 

2424 @arg root: Non-zero order (C{scalar}, an L{Fsum} or L{Fsum2Tuple}). 

2425 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore any 

2426 L{ResidualError}s (C{bool}) or C{B{RESIDUAL}=scalar} 

2427 to override the current L{RESIDUAL<Fsum.RESIDUAL>}. 

2428 

2429 @return: The C{self ** (1 / B{root})} result (L{Fsum}). 

2430 

2431 @raise ResidualError: Non-zero, significant residual or invalid 

2432 B{C{RESIDUAL}}. 

2433 

2434 @see: Method L{Fsum.pow}. 

2435 ''' 

2436 x = self._1_Over(root, _truediv_op_, **raiser_RESIDUAL) 

2437 f = self._copy_2(self.root) 

2438 return f._fpow(x, f.name, **raiser_RESIDUAL) # == pow(f, x) 

2439 

2440 def _scalar(self, other, op, **txt): 

2441 '''(INTERNAL) Return scalar C{other} or throw a C{TypeError}. 

2442 ''' 

2443 if isscalar(other): 

2444 return other 

2445 raise self._Error(op, other, _TypeError, **txt) # _invalid_ 

2446 

2447 def signOf(self, res=True): 

2448 '''Determine the sign of this instance. 

2449 

2450 @kwarg res: If C{True}, consider the residual, 

2451 otherwise ignore the latter (C{bool}). 

2452 

2453 @return: The sign (C{int}, -1, 0 or +1). 

2454 ''' 

2455 s, r = self._nfprs2 

2456 r = (-r) if res else 0 

2457 return _signOf(s, r) 

2458 

2459 def toRepr(self, **lenc_prec_sep_fmt): # PYCHOK signature 

2460 '''Return this C{Fsum} instance as representation. 

2461 

2462 @kwarg lenc_prec_sep_fmt: Optional keyword arguments 

2463 for method L{Fsum.toStr}. 

2464 

2465 @return: This instance (C{repr}). 

2466 ''' 

2467 return Fmt.repr_at(self, self.toStr(**lenc_prec_sep_fmt)) 

2468 

2469 def toStr(self, lenc=True, **prec_sep_fmt): # PYCHOK signature 

2470 '''Return this C{Fsum} instance as string. 

2471 

2472 @kwarg lenc: If C{True}, include the current C{[len]} of this 

2473 L{Fsum} enclosed in I{[brackets]} (C{bool}). 

2474 @kwarg prec_sep_fmt: Optional keyword arguments for method 

2475 L{Fsum2Tuple.toStr}. 

2476 

2477 @return: This instance (C{str}). 

2478 ''' 

2479 p = self.classname 

2480 if lenc: 

2481 p = Fmt.SQUARE(p, len(self)) 

2482 n = _enquote(self.name, white=_UNDER_) 

2483 t = self._nfprs2.toStr(**prec_sep_fmt) 

2484 return NN(p, _SPACE_, n, t) 

2485 

2486 def _truediv(self, other, op, **raiser_RESIDUAL): 

2487 '''(INTERNAL) Return C{B{self} / B{other}} as an L{Fsum}. 

2488 ''' 

2489 f = self._copy_2(self.__truediv__) 

2490 return f._ftruediv(other, op, **raiser_RESIDUAL) 

2491 

2492 def _update(self, updated=True): # see ._fset 

2493 '''(INTERNAL) Zap all cached C{Property_RO} values. 

2494 ''' 

2495 if updated: 

2496 _pop = self.__dict__.pop 

2497 for p in _ROs: 

2498 _ = _pop(p, None) 

2499# Fsum._fint2._update(self) 

2500# Fsum._fprs ._update(self) 

2501# Fsum._fprs2._update(self) 

2502 return self # for .fset_ 

2503 

2504_ROs = _allPropertiesOf_n(3, Fsum, Property_RO) # PYCHOK see Fsum._update 

2505 

2506if _NONFINITES == _std_: # PYCHOK no cover 

2507 _ = nonfiniterrors(False) 

2508 

2509 

2510def _Float_Int(arg, **name_Error): 

2511 '''(INTERNAL) L{DivMod2Tuple}, L{Fsum2Tuple} Unit. 

2512 ''' 

2513 U = Int if isint(arg) else Float 

2514 return U(arg, **name_Error) 

2515 

2516 

2517class DivMod2Tuple(_NamedTuple): 

2518 '''2-Tuple C{(div, mod)} with the quotient C{div} and remainder 

2519 C{mod} results of a C{divmod} operation. 

2520 

2521 @note: Quotient C{div} an C{int} in Python 3+ but a C{float} 

2522 in Python 2-. Remainder C{mod} an L{Fsum} instance. 

2523 ''' 

2524 _Names_ = ('div', 'mod') 

2525 _Units_ = (_Float_Int, Fsum) 

2526 

2527 

2528class Fsum2Tuple(_NamedTuple): # in .fstats 

2529 '''2-Tuple C{(fsum, residual)} with the precision running C{fsum} 

2530 and the C{residual}, the sum of the remaining partials. Each 

2531 item is C{float} or C{int}. 

2532 

2533 @note: If the C{residual is INT0}, the C{fsum} is considered 

2534 to be I{exact}, see method L{Fsum2Tuple.is_exact}. 

2535 ''' 

2536 _Names_ = ( Fsum.fsum.__name__, Fsum.residual.name) 

2537 _Units_ = (_Float_Int, _Float_Int) 

2538 

2539 def __abs__(self): # in .fmath 

2540 return self._Fsum.__abs__() 

2541 

2542 def __bool__(self): # PYCHOK Python 3+ 

2543 return bool(self._Fsum) 

2544 

2545 def __eq__(self, other): 

2546 return self._other_op(other, self.__eq__) 

2547 

2548 def __float__(self): 

2549 return self._Fsum.__float__() 

2550 

2551 def __ge__(self, other): 

2552 return self._other_op(other, self.__ge__) 

2553 

2554 def __gt__(self, other): 

2555 return self._other_op(other, self.__gt__) 

2556 

2557 def __le__(self, other): 

2558 return self._other_op(other, self.__le__) 

2559 

2560 def __lt__(self, other): 

2561 return self._other_op(other, self.__lt__) 

2562 

2563 def __int__(self): 

2564 return self._Fsum.__int__() 

2565 

2566 def __ne__(self, other): 

2567 return self._other_op(other, self.__ne__) 

2568 

2569 def __neg__(self): 

2570 return self._Fsum.__neg__() 

2571 

2572 __nonzero__ = __bool__ # Python 2- 

2573 

2574 def __pos__(self): 

2575 return self._Fsum.__pos__() 

2576 

2577 def as_integer_ratio(self): 

2578 '''Return this instance as the ratio of 2 integers. 

2579 

2580 @see: Method L{Fsum.as_integer_ratio} for further details. 

2581 ''' 

2582 return self._Fsum.as_integer_ratio() 

2583 

2584 @property_RO 

2585 def _fint2(self): 

2586 return self._Fsum._fint2 

2587 

2588 @property_RO 

2589 def _fprs2(self): 

2590 return self._Fsum._fprs2 

2591 

2592 @Property_RO 

2593 def _Fsum(self): # this C{Fsum2Tuple} as L{Fsum}, in .fstats 

2594 s, r = _s_r2(*self) 

2595 ps = (r, s) if r else (s,) 

2596 return _Psum(ps, name=self.name) 

2597 

2598 def Fsum_(self, *xs, **name_f2product_nonfinites_RESIDUAL): 

2599 '''Return this C{Fsum2Tuple} as an L{Fsum} plus some C{xs}. 

2600 ''' 

2601 return Fsum(self, *xs, **name_f2product_nonfinites_RESIDUAL) 

2602 

2603 def is_exact(self): 

2604 '''Is this L{Fsum2Tuple} considered to be exact? (C{bool}). 

2605 ''' 

2606 return self._Fsum.is_exact() 

2607 

2608 def is_finite(self): # in .constants 

2609 '''Is this L{Fsum2Tuple} C{finite}? (C{bool}). 

2610 

2611 @see: Function L{isfinite<pygeodesy.isfinite>}. 

2612 ''' 

2613 return self._Fsum.is_finite() 

2614 

2615 def is_integer(self): 

2616 '''Is this L{Fsum2Tuple} C{integer}? (C{bool}). 

2617 ''' 

2618 return self._Fsum.is_integer() 

2619 

2620 def _mul_scalar(self, other, op): # for Fsum._fmul 

2621 return self._Fsum._mul_scalar(other, op) 

2622 

2623 @property_RO 

2624 def _n(self): 

2625 return self._Fsum._n 

2626 

2627 def _other_op(self, other, which): 

2628 C, s = (tuple, self) if isinstance(other, tuple) else (Fsum, self._Fsum) 

2629 return getattr(C, which.__name__)(s, other) 

2630 

2631 @property_RO 

2632 def _ps(self): 

2633 return self._Fsum._ps 

2634 

2635 @property_RO 

2636 def _ps_neg(self): 

2637 return self._Fsum._ps_neg 

2638 

2639 def signOf(self, **res): 

2640 '''Like method L{Fsum.signOf}. 

2641 ''' 

2642 return self._Fsum.signOf(**res) 

2643 

2644 def toStr(self, fmt=Fmt.g, **prec_sep): # PYCHOK signature 

2645 '''Return this L{Fsum2Tuple} as string (C{str}). 

2646 

2647 @kwarg fmt: Optional C{float} format (C{letter}). 

2648 @kwarg prec_sep: Optional keyword arguments for function 

2649 L{fstr<streprs.fstr>}. 

2650 ''' 

2651 return Fmt.PAREN(fstr(self, fmt=fmt, strepr=str, force=False, **prec_sep)) 

2652 

2653_Fsum_2Tuple_types = Fsum, Fsum2Tuple # PYCHOK lines 

2654 

2655 

2656class ResidualError(_ValueError): 

2657 '''Error raised for a division, power or root operation of 

2658 an L{Fsum} instance with a C{residual} I{ratio} exceeding 

2659 the L{RESIDUAL<Fsum.RESIDUAL>} threshold. 

2660 

2661 @see: Module L{pygeodesy.fsums} and method L{Fsum.RESIDUAL}. 

2662 ''' 

2663 pass 

2664 

2665 

2666try: 

2667 from math import fsum as _fsum # precision IEEE-754 sum, Python 2.6+ 

2668 

2669 # make sure _fsum works as expected (XXX check 

2670 # float.__getformat__('float')[:4] == 'IEEE'?) 

2671 if _fsum((1, 1e101, 1, -1e101)) != 2: # PYCHOK no cover 

2672 del _fsum # nope, remove _fsum ... 

2673 raise ImportError() # ... use _fsum below 

2674 

2675 _sum = _fsum # in .elliptic 

2676except ImportError: 

2677 _sum = sum # in .elliptic 

2678 

2679 def _fsum(xs): 

2680 '''(INTERNAL) Precision summation, Python 2.5-. 

2681 ''' 

2682 F = Fsum(name=_fsum.name, f2product=False, nonfinites=True) 

2683 return float(F._facc(xs, up=False)) 

2684 

2685 

2686def fsum(xs, nonfinites=None, **floats): 

2687 '''Precision floating point summation from Python's C{math.fsum}. 

2688 

2689 @arg xs: Iterable of items to add (each C{scalar}, an L{Fsum} or L{Fsum2Tuple}). 

2690 @kwarg nonfinites: Use C{B{nonfinites}=True} if I{non-finites} are C{OK}, if 

2691 C{False} I{non-finites} raise an Overflow-/ValueError or if 

2692 C{None}, L{nonfiniterrors} applies (C{bool} or C{None}). 

2693 @kwarg floats: DEPRECATED keyword argument C{B{floats}=False} (C{bool}), use 

2694 keyword argument C{B{nonfinites}=False} instead. 

2695 

2696 @return: Precision C{fsum} (C{float}). 

2697 

2698 @raise OverflowError: Infinite B{C{xs}} item or intermediate C{math.fsum} overflow. 

2699 

2700 @raise TypeError: Invalid B{C{xs}} item. 

2701 

2702 @raise ValueError: Invalid or C{NAN} B{C{xs}} item. 

2703 

2704 @see: Function L{nonfiniterrors}, class L{Fsum} and methods L{Fsum.nonfinites}, 

2705 L{Fsum.fsum}, L{Fsum.fadd} and L{Fsum.fadd_}. 

2706 ''' 

2707 return _xsum(fsum, xs, nonfinites=nonfinites, **floats) if xs else _0_0 

2708 

2709 

2710def fsum_(*xs, **nonfinites): 

2711 '''Precision floating point summation of all positional items. 

2712 

2713 @arg xs: Items to add (each C{scalar}, an L{Fsum} or L{Fsum2Tuple}), all positional. 

2714 @kwarg nonfinites: Use C{B{nonfinites}=True} if I{non-finites} are C{OK} (C{bool}). 

2715 

2716 @see: Function L{fsum<fsums.fsum>} for further details. 

2717 ''' 

2718 return _xsum(fsum_, xs, **nonfinites) if xs else _0_0 # origin=1? 

2719 

2720 

2721def fsumf_(*xs): 

2722 '''Precision floating point summation of all positional items with I{non-finites} C{OK}. 

2723 

2724 @arg xs: Items to add (each C{scalar}, an L{Fsum} or L{Fsum2Tuple}), 

2725 all positional. 

2726 

2727 @see: Function L{fsum_<fsums.fsum_>} for further details. 

2728 ''' 

2729 return _xsum(fsumf_, xs, nonfinites=True) if xs else _0_0 # origin=1? 

2730 

2731 

2732def fsum1(xs, **nonfinites): 

2733 '''Precision floating point summation, 1-primed. 

2734 

2735 @arg xs: Iterable of items to add (each C{scalar}, an L{Fsum} or L{Fsum2Tuple}). 

2736 @kwarg nonfinites: Use C{B{nonfinites}=True} if I{non-finites} are C{OK} (C{bool}). 

2737 

2738 @see: Function L{fsum<fsums.fsum>} for further details. 

2739 ''' 

2740 return _xsum(fsum1, xs, primed=1, **nonfinites) if xs else _0_0 

2741 

2742 

2743def fsum1_(*xs, **nonfinites): 

2744 '''Precision floating point summation of all positional items, 1-primed. 

2745 

2746 @arg xs: Items to add (each C{scalar}, an L{Fsum} or L{Fsum2Tuple}), all positional. 

2747 @kwarg nonfinites: Use C{B{nonfinites}=True} if I{non-finites} are C{OK} (C{bool}). 

2748 

2749 @see: Function L{fsum_<fsums.fsum_>} for further details. 

2750 ''' 

2751 return _xsum(fsum1_, xs, primed=1, **nonfinites) if xs else _0_0 # origin=1? 

2752 

2753 

2754def fsum1f_(*xs): 

2755 '''Precision floating point summation of all positional items, 1-primed and 

2756 with I{non-finites} C{OK}. 

2757 

2758 @see: Function L{fsum_<fsums.fsum_>} for further details. 

2759 ''' 

2760 return _xsum(fsum1f_, xs, nonfinites=True, primed=1) if xs else _0_0 

2761 

2762 

2763def _x_isfine(nfOK, **kwds): # get the C{_x} and C{_isfine} handlers. 

2764 _x_kwds = dict(_x= (_passarg if nfOK else _2finite), 

2765 _isfine=(_isOK if nfOK else _isfinite)) # PYCHOK kwds 

2766 _x_kwds.update(kwds) 

2767 return _x_kwds 

2768 

2769 

2770def _X_ps(X): # default C{_X} handler 

2771 return X._ps # lambda X: X._ps 

2772 

2773 

2774def _xs(xs, _X=_X_ps, _x=float, _isfine=_isfinite, # defaults for Fsum._facc 

2775 origin=0, which=None, **_Cdot): 

2776 '''(INTERNAL) Yield each C{xs} item as 1 or more C{float}s. 

2777 ''' 

2778 i, x = 0, xs 

2779 try: 

2780 for i, x in enumerate(_xiterable(xs)): 

2781 if _isFsum_2Tuple(x): 

2782 for p in _X(x): 

2783 yield p if _isfine(p) else _nfError(p) 

2784 else: 

2785 f = _x(x) 

2786 yield f if _isfine(f) else _nfError(f) 

2787 

2788 except (OverflowError, TypeError, ValueError) as X: 

2789 t = _xsError(X, xs, i + origin, x) 

2790 if which: # prefix invokation 

2791 w = unstr(which, *xs, _ELLIPSIS=4, **_Cdot) 

2792 t = _COMMASPACE_(w, t) 

2793 raise _xError(X, t, txt=None) 

2794 

2795 

2796def _xsum(which, xs, nonfinites=None, primed=0, **floats): # origin=0 

2797 '''(INTERNAL) Precision summation of C{xs} with conditions. 

2798 ''' 

2799 if floats: # for backward compatibility 

2800 nonfinites = _xkwds_get1(floats, floats=nonfinites) 

2801 elif nonfinites is None: 

2802 nonfinites = not nonfiniterrors() 

2803 fs = _xs(xs, **_x_isfine(nonfinites, which=which)) # PYCHOK yield 

2804 return _fsum(_1primed(fs) if primed else fs) 

2805 

2806 

2807# delete all decorators, etc. 

2808del _allPropertiesOf_n, deprecated_method, deprecated_property_RO, \ 

2809 Property, Property_RO, property_RO, _ALL_LAZY, _F2PRODUCT, \ 

2810 MANT_DIG, _NONFINITES, _RESIDUAL_0_0, _getPYGEODESY, _std_ 

2811 

2812if __name__ == '__main__': 

2813 

2814 # usage: python3 -m pygeodesy.fsums 

2815 

2816 def _test(n): 

2817 # copied from Hettinger, see L{Fsum} reference 

2818 from pygeodesy import frandoms, printf 

2819 

2820 printf(_fsum.__name__, end=_COMMASPACE_) 

2821 printf(_psum.__name__, end=_COMMASPACE_) 

2822 

2823 F = Fsum() 

2824 if F.is_math_fsum(): 

2825 for t in frandoms(n, seeded=True): 

2826 assert float(F.fset_(*t)) == _fsum(t) 

2827 printf(_DOT_, end=NN) 

2828 printf(NN) 

2829 

2830 _test(128) 

2831 

2832# **) MIT License 

2833# 

2834# Copyright (C) 2016-2025 -- mrJean1 at Gmail -- All Rights Reserved. 

2835# 

2836# Permission is hereby granted, free of charge, to any person obtaining a 

2837# copy of this software and associated documentation files (the "Software"), 

2838# to deal in the Software without restriction, including without limitation 

2839# the rights to use, copy, modify, merge, publish, distribute, sublicense, 

2840# and/or sell copies of the Software, and to permit persons to whom the 

2841# Software is furnished to do so, subject to the following conditions: 

2842# 

2843# The above copyright notice and this permission notice shall be included 

2844# in all copies or substantial portions of the Software. 

2845# 

2846# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

2847# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

2848# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

2849# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

2850# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 

2851# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 

2852# OTHER DEALINGS IN THE SOFTWARE.