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 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__ = '24.12.02' 

68 

69from pygeodesy.interns import ( 

70 _PLUS_ as _add_op_, # in .auxilats.auxAngle 

71 _EQUAL_ as _fset_op_, 

72 _RANGLE_ as _gt_op_, 

73 _LANGLE_ as _lt_op_, 

74 _PERCENT_ as _mod_op_, 

75 _STAR_ as _mul_op_, 

76 _NOTEQUAL_ as _ne_op_, 

77 _DASH_ as _sub_op_, # in .auxilats.auxAngle 

78 _SLASH_ as _truediv_op_ 

79) 

80_floordiv_op_ = _truediv_op_ * 2 # _DSLASH_ 

81_divmod_op_ = _floordiv_op_ + _mod_op_ 

82_F2PRODUCT = _getPYGEODESY('FSUM_F2PRODUCT') 

83_iadd_op_ = _add_op_ + _fset_op_ # in .auxilats.auxAngle, .fstats 

84_integer_ = 'integer' 

85_isub_op_ = _sub_op_ + _fset_op_ # in .auxilats.auxAngle 

86_NONFINITEr = _0_0 # NOT INT0! 

87_NONFINITES = _getPYGEODESY('FSUM_NONFINITES') 

88_non_zero_ = 'non-zero' 

89_pow_op_ = _mul_op_ * 2 # _DSTAR_ 

90_RESIDUAL_0_0 = _getPYGEODESY('FSUM_RESIDUAL', _0_0) 

91_significant_ = 'significant' 

92_threshold_ = 'threshold' 

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 

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

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

138 # the same accuracy, but ~14x slower 

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

140 n = na * nb * dc 

141 n += da * db * nc 

142 d = da * db * dc 

143 try: 

144 n, d = _n_d2(n, d) 

145 r = float(n / d) 

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

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

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

149 

150 def _2n_d(x): # PYCHOK no cover 

151 try: # int.as_integer_ratio in 3.8+ 

152 return x.as_integer_ratio() 

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

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

155 else: 

156 

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

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

159 # the same accuracy, but ~13x slower 

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

161 r = _fsum(_2products(a, b3s, c)) 

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

163 

164 _2n_d = None # redef 

165 

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

167 # handle non-finite as Python 3.13+ C-function U{math_fma_impl<https:// 

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

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

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

171 if isnan(r): 

172 def _x(x): 

173 return not isnan(x) 

174 else: # non-NAN non-finite 

175 _x = _isfinite 

176 if all(map(_x, a_b_c)): 

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

178 return r 

179 

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

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

182 # TwoProduct U{Algorithm 3.3 

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

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

185 # #ifndef UNRELIABLE_FMA ... #else ... #endif 

186 _, a, b = _2split3(x) 

187 for y, c, d in y3s: 

188 y *= x 

189 yield y 

190 if _isfinite(y): 

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

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

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

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

195 yield a * c - y 

196 yield b * c 

197 if d: 

198 yield a * d 

199 yield b * d 

200 for z in zs: 

201 yield z 

202 

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

204 

205 def _2split3(x): 

206 # Split U{Algorithm 3.2 

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

208 a = c = x * _2FACTOR 

209 a -= c - x 

210 b = x - a 

211 return x, a, b 

212 

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

214 return map(_2split3, xs) 

215 

216 

217def f2product(two=None): 

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

219 

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

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

222 

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

224 

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

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

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

228 equivalent, slower implementation when not available. 

229 ''' 

230 t = Fsum._f2product 

231 if two is not None: 

232 Fsum._f2product = bool(two) 

233 return t 

234 

235 

236def _Fsumf_(*xs): # in .auxLat, ... 

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

238 ''' 

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

240 

241 

242def _Fsum1f_(*xs): # in .albers 

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

244 ''' 

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

246 

247 

248def _halfeven(s, r, p): 

249 '''(INTERNAL) Round half-even. 

250 ''' 

251 if (p > 0 and r > 0) or \ 

252 (p < 0 and r < 0): # signs match 

253 r *= 2 

254 t = s + r 

255 if r == (t - s): 

256 s = t 

257 return s 

258 

259 

260def _isFsum(x): # in .fmath 

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

262 ''' 

263 return isinstance(x, Fsum) 

264 

265 

266def _isFsum_2Tuple(x): # in .basics, .constants, .fmath, .fstats 

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

268 ''' 

269 return isinstance(x, _Fsum_2Tuple_types) 

270 

271 

272def _isOK(unused): 

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

274 ''' 

275 return True 

276 

277 

278def _isOK_or_finite(x, _isfine=_isfinite): 

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

280 ''' 

281 # assert _isfine in (_isOK, _isfinite) 

282 return _isfine(x) # C{bool} 

283 

284 

285try: 

286 from math import gcd as _gcd 

287 

288 def _n_d2(n, d): 

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

290 ''' 

291 if n and d: 

292 try: 

293 c = _gcd(n, d) 

294 if c > 1: 

295 n, d = (n // c), (d // c) 

296 except TypeError: # non-int float 

297 pass 

298 return n, d 

299 

300except ImportError: # 3.4- 

301 

302 def _n_d2(*n_d): # PYCHOK redef 

303 return n_d 

304 

305 

306def _nfError(x, *args): 

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

308 ''' 

309 E = _NonfiniteError(x) 

310 t = Fmt.PARENSPACED(_not_finite_, x) 

311 if args: # in _fmaX, _2sum 

312 return E(txt=t, *args) 

313 raise E(t, txt=None) 

314 

315 

316def _NonfiniteError(x): 

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

318 ''' 

319 return _OverflowError if isinf(x) else ( 

320 _ValueError if isnan(x) else _AssertionError) 

321 

322 

323def nonfiniterrors(raiser=None): 

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

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

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

327 

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

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

330 the setting unchanged. 

331 

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

333 

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

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

336 ''' 

337 d = Fsum._isfine 

338 if raiser is not None: 

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

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

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

342 

343 

344def _1primed(xs): # in .fmath 

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

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

347 ''' 

348 yield _1_0 

349 for x in xs: 

350 yield x 

351 yield _N_1_0 

352 

353 

354def _psum(ps, **_isfine): # PYCHOK used! 

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

356 ''' 

357 # assert isinstance(ps, list) 

358 i = len(ps) - 1 

359 s = _0_0 if i < 0 else ps[i] 

360 while i > 0: 

361 i -= 1 

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

363 if r: # sum(ps) became inexact 

364 if s: 

365 ps[i:] = r, s 

366 if i > 0: 

367 s = _halfeven(s, r, ps[i-1]) 

368 break # return s 

369 s = r # PYCHOK no cover 

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

371 i = 0 # collapse ps 

372 if ps: 

373 s += sum(ps) 

374 ps[i:] = s, 

375 return s 

376 

377 

378def _Psum(ps, **name_f2product_nonfinites_RESIDUAL): 

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

380 ''' 

381 F = Fsum(**name_f2product_nonfinites_RESIDUAL) 

382 if ps: 

383 F._ps[:] = ps 

384 F._n = len(F._ps) 

385 return F 

386 

387 

388def _Psum_(*ps, **name_f2product_nonfinites_RESIDUAL): # in .fmath 

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

390 ''' 

391 return _Psum(ps, **name_f2product_nonfinites_RESIDUAL) 

392 

393 

394def _residue(other): 

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

396 ''' 

397 try: 

398 r = other.residual 

399 except AttributeError: 

400 r = None # float, int, other 

401 return r 

402 

403 

404def _s_r2(s, r): 

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

406 ''' 

407 if _isfinite(s): 

408 if r: 

409 if fabs(s) < fabs(r): 

410 s, r = r, (s or INT0) 

411 else: 

412 r = INT0 

413 else: 

414 r = _NONFINITEr 

415 return s, r 

416 

417 

418def _strcomplex(s, *args): 

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

420 ''' 

421 c = _strcomplex.__name__[4:] 

422 n = _sub_op_(len(args), _arg_) 

423 t = unstr(pow, *args) 

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

425 

426 

427def _stresidual(prefix, residual, R=0, **mod_ratio): 

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

429 ''' 

430 p = _stresidual.__name__[3:] 

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

432 for n, v in itemsorted(mod_ratio): 

433 p = Fmt.PARENSPACED(n, Fmt(v)) 

434 t = _COMMASPACE_(t, p) 

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

436 

437 

438def _2sum(a, b, _isfine=_isfinite): # in .testFmath 

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

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

441 ''' 

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

443 

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

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

446 # 1974, Zeitschrift für Angewandte Mathmatik und Mechanik, vol 51, nr 1, p 39-51 

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

448 s = a + b 

449 if _isfinite(s): 

450 if fabs(a) < fabs(b): 

451 r = (b - s) + a 

452 else: 

453 r = (a - s) + b 

454 elif _isfine(s): 

455 r = _NONFINITEr 

456 else: # non-finite and not OK 

457 t = unstr(_2sum, a, b) 

458 raise _nfError(s, t) 

459 return s, r 

460 

461 

462def _threshold(threshold=_0_0, **kwds): 

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

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

465 ''' 

466 if kwds: 

467 threshold = _xkwds_get1(kwds, RESIDUAL=threshold) 

468 try: 

469 return _2finite(threshold) # PYCHOK None 

470 except Exception as x: 

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

472 

473 

474def _2tuple2(other): 

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

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

477 ''' 

478 if _isFsum_2Tuple(other): 

479 s, r = other._fint2 

480 if r: 

481 s, r = other._nfprs2 

482 if r: # PYCHOK no cover 

483 s = other # L{Fsum} as-is 

484 else: 

485 r = 0 

486 s = other # C{type} as-is 

487 if isint(s, both=True): 

488 s = int(s) 

489 return s, r 

490 

491 

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

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

494 

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

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

497 intermediate, I{running} summuation. 

498 

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

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

501 

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

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

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

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

506 exceptions by default. 

507 

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

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

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

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

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

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

514 

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

516 multiplication. 

517 

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

519 C{PYGEODESY_FSUM_NONFINITES} and C{PYGEODESY_FSUM_RESIDUAL}. 

520 ''' 

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

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

523 _n = 0 

524# _ps = [] # partial sums 

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

526 _RESIDUAL = _threshold(_RESIDUAL_0_0) 

527 

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

529 '''New L{Fsum}. 

530 

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

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

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

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

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

536 L{Fsum}. 

537 

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

539 L{Fsum.fadd} and L{Fsum.fadd_}. 

540 ''' 

541 if name_f2product_nonfinites_RESIDUAL: 

542 self._optionals(**name_f2product_nonfinites_RESIDUAL) 

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

544 if xs: 

545 self._facc_args(xs, up=False) 

546 

547 def __abs__(self): 

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

549 ''' 

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

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

552 

553 def __add__(self, other): 

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

555 

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

557 

558 @return: The sum (L{Fsum}). 

559 

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

561 ''' 

562 f = self._copy_2(self.__add__) 

563 return f._fadd(other) 

564 

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

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

567 ''' 

568 s, r = self._nfprs2 

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

570 

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

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

573 ''' 

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

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

576 return self 

577 

578 

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

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

581 

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

583 

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

585 ''' 

586 return self.ceil 

587 

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

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

590 

591 @return: -1, 0 or +1 (C{int}). 

592 

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

594 ''' 

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

596 return _signOf(s, 0) 

597 

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

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

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

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

602 

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

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

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

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

607 

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

609 B{C{RESIDUAL}}. 

610 

611 @see: Method L{Fsum.fdiv}. 

612 ''' 

613 f = self._copy_2(self.__divmod__) 

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

615 

616 def __eq__(self, other): 

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

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

619 ''' 

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

621 

622 def __float__(self): 

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

624 

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

626 ''' 

627 return float(self._fprs) 

628 

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

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

631 

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

633 

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

635 ''' 

636 return self.floor 

637 

638 def __floordiv__(self, other): 

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

640 

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

642 

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

644 

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

646 ''' 

647 f = self._copy_2(self.__floordiv__) 

648 return f._floordiv(other, _floordiv_op_) 

649 

650 def __ge__(self, other): 

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

652 ''' 

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

654 

655 def __gt__(self, other): 

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

657 ''' 

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

659 

660 def __hash__(self): # PYCHOK no cover 

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

662 ''' 

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

664 # 3/library/numbers.html#numbers.Rational>} 

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

666 

667 def __iadd__(self, other): 

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

669 

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

671 an iterable of several of the former. 

672 

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

674 

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

676 C{scalar} nor L{Fsum}. 

677 

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

679 ''' 

680 try: 

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

682 except TypeError: 

683 pass 

684 _xiterable(other) 

685 return self._facc(other) 

686 

687 def __ifloordiv__(self, other): 

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

689 

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

691 

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

693 

694 @raise ResidualError: Non-zero, significant residual 

695 in B{C{other}}. 

696 

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

698 

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

700 

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

702 

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

704 ''' 

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

706 

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

708 '''Not implemented.''' 

709 return _NotImplemented(self, other) 

710 

711 def __imod__(self, other): 

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

713 

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

715 

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

717 

718 @see: Method L{Fsum.__divmod__}. 

719 ''' 

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

721 

722 def __imul__(self, other): 

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

724 

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

726 

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

728 

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

730 

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

732 

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

734 ''' 

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

736 

737 def __int__(self): 

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

739 

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

741 and L{Fsum.floor}. 

742 ''' 

743 i, _ = self._fint2 

744 return i 

745 

746 def __invert__(self): # PYCHOK no cover 

747 '''Not implemented.''' 

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

749 return _NotImplemented(self) 

750 

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

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

753 

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

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

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

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

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

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

760 

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

762 

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

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

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

766 

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

768 

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

770 is non-zero and significant and either 

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

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

773 C{None}. 

774 

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

776 invocation failed. 

777 

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

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

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

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

782 is given as C{0}. 

783 

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

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

786 ''' 

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

788 

789 def __isub__(self, other): 

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

791 

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

793 an iterable of several of the former. 

794 

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

796 

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

798 

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

800 ''' 

801 try: 

802 return self._fsub(other, _isub_op_) 

803 except TypeError: 

804 pass 

805 _xiterable(other) 

806 return self._facc_neg(other) 

807 

808 def __iter__(self): 

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

810 ''' 

811 return iter(self.partials) 

812 

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

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

815 

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

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

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

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

820 

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

822 

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

824 

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

826 B{C{RESIDUAL}}. 

827 

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

829 

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

831 

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

833 

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

835 ''' 

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

837 

838 def __le__(self, other): 

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

840 ''' 

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

842 

843 def __len__(self): 

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

845 ''' 

846 return self._n 

847 

848 def __lt__(self, other): 

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

850 ''' 

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

852 

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

854 '''Not implemented.''' 

855 return _NotImplemented(self, other) 

856 

857 def __mod__(self, other): 

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

859 

860 @see: Method L{Fsum.__imod__}. 

861 ''' 

862 f = self._copy_2(self.__mod__) 

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

864 

865 def __mul__(self, other): 

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

867 

868 @see: Method L{Fsum.__imul__}. 

869 ''' 

870 f = self._copy_2(self.__mul__) 

871 return f._fmul(other, _mul_op_) 

872 

873 def __ne__(self, other): 

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

875 ''' 

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

877 

878 def __neg__(self): 

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

880 ''' 

881 f = self._copy_2(self.__neg__) 

882 return f._fset(self._neg) 

883 

884 def __pos__(self): 

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

886 ''' 

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

888 

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

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

891 

892 @see: Method L{Fsum.__ipow__}. 

893 ''' 

894 f = self._copy_2(self.__pow__) 

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

896 

897 def __radd__(self, other): 

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

899 

900 @see: Method L{Fsum.__iadd__}. 

901 ''' 

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

903 return f._fadd(self) 

904 

905 def __rdivmod__(self, other): 

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

907 C{(quotient, remainder)}. 

908 

909 @see: Method L{Fsum.__divmod__}. 

910 ''' 

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

912 return f._fdivmod2(self, _divmod_op_) 

913 

914# turned off, called by _deepcopy and _copy 

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

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

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

918# ''' 

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

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

921 

922# def __repr__(self): 

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

924# ''' 

925# return self.toRepr(lenc=True) 

926 

927 def __rfloordiv__(self, other): 

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

929 

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

931 ''' 

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

933 return f._floordiv(self, _floordiv_op_) 

934 

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

936 '''Not implemented.''' 

937 return _NotImplemented(self, other) 

938 

939 def __rmod__(self, other): 

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

941 

942 @see: Method L{Fsum.__imod__}. 

943 ''' 

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

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

946 

947 def __rmul__(self, other): 

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

949 

950 @see: Method L{Fsum.__imul__}. 

951 ''' 

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

953 return f._fmul(self, _mul_op_) 

954 

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

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

957 

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

959 ''' 

960 f = self._copy_2(self.__round__) 

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

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

963 

964 def __rpow__(self, other, *mod): 

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

966 

967 @see: Method L{Fsum.__ipow__}. 

968 ''' 

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

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

971 

972 def __rsub__(self, other): 

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

974 

975 @see: Method L{Fsum.__isub__}. 

976 ''' 

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

978 return f._fsub(self, _sub_op_) 

979 

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

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

982 

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

984 ''' 

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

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

987 

988 def __str__(self): 

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

990 ''' 

991 return self.toStr(lenc=True) 

992 

993 def __sub__(self, other): 

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

995 

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

997 

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

999 

1000 @see: Method L{Fsum.__isub__}. 

1001 ''' 

1002 f = self._copy_2(self.__sub__) 

1003 return f._fsub(other, _sub_op_) 

1004 

1005 def __truediv__(self, other, **raiser_RESIDUAL): 

1006 '''Return C{B{self} / B{other}} as an L{Fsum}. 

1007 

1008 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar} divisor. 

1009 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore 

1010 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar} 

1011 to override the current L{RESIDUAL<Fsum.RESIDUAL>}. 

1012 

1013 @return: The quotient (L{Fsum}). 

1014 

1015 @raise ResidualError: Non-zero, significant residual or invalid 

1016 B{C{RESIDUAL}}. 

1017 

1018 @see: Method L{Fsum.__itruediv__}. 

1019 ''' 

1020 return self._truediv(other, _truediv_op_, **raiser_RESIDUAL) 

1021 

1022 __trunc__ = __int__ 

1023 

1024 if _MODS.sys_version_info2 < (3, 0): # PYCHOK no cover 

1025 # <https://docs.Python.org/2/library/operator.html#mapping-operators-to-functions> 

1026 __div__ = __truediv__ 

1027 __idiv__ = __itruediv__ 

1028 __long__ = __int__ 

1029 __nonzero__ = __bool__ 

1030 __rdiv__ = __rtruediv__ 

1031 

1032 def as_integer_ratio(self): 

1033 '''Return this instance as the ratio of 2 integers. 

1034 

1035 @return: 2-Tuple C{(numerator, denominator)} both C{int} with 

1036 C{numerator} signed and C{denominator} non-zero and 

1037 positive. The C{numerator} is I{non-finite} if this 

1038 instance is. 

1039 

1040 @see: Method L{Fsum.fint2} and C{float.as_integer_ratio} in 

1041 Python 2.7+. 

1042 ''' 

1043 n, r = self._fint2 

1044 if r: 

1045 i, d = float(r).as_integer_ratio() 

1046 n, d = _n_d2(n * d + i, d) 

1047 else: # PYCHOK no cover 

1048 d = 1 

1049 return n, d 

1050 

1051 @property_RO 

1052 def as_iscalar(self): 

1053 '''Get this instance I{as-is} (L{Fsum} with C{non-zero residual}, 

1054 C{scalar} or I{non-finite}). 

1055 ''' 

1056 s, r = self._nfprs2 

1057 return self if r else s 

1058 

1059 @property_RO 

1060 def ceil(self): 

1061 '''Get this instance' C{ceil} value (C{int} in Python 3+, but 

1062 C{float} in Python 2-). 

1063 

1064 @note: This C{ceil} takes the C{residual} into account. 

1065 

1066 @see: Method L{Fsum.int_float} and properties L{Fsum.floor}, 

1067 L{Fsum.imag} and L{Fsum.real}. 

1068 ''' 

1069 s, r = self._fprs2 

1070 c = _ceil(s) + int(r) - 1 

1071 while r > (c - s): # (s + r) > c 

1072 c += 1 

1073 return c # _ceil(self._n_d) 

1074 

1075 cmp = __cmp__ 

1076 

1077 def _cmp_0(self, other, op): 

1078 '''(INTERNAL) Return C{scalar(self - B{other})} for 0-comparison. 

1079 ''' 

1080 if _isFsum_2Tuple(other): 

1081 s = self._ps_1sum(*other._ps) 

1082 elif self._scalar(other, op): 

1083 s = self._ps_1sum(other) 

1084 else: 

1085 s = self.signOf() # res=True 

1086 return s 

1087 

1088 def copy(self, deep=False, **name): 

1089 '''Copy this instance, C{shallow} or B{C{deep}}. 

1090 

1091 @kwarg name: Optional, overriding C{B{name}='"copy"} (C{str}). 

1092 

1093 @return: The copy (L{Fsum}). 

1094 ''' 

1095 n = _name__(name, name__=self.copy) 

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

1097 if f._ps is self._ps: 

1098 f._ps = list(self._ps) # separate list 

1099 if not deep: 

1100 f._n = 1 

1101 # assert f._f2product == self._f2product 

1102 # assert f._Fsum is f 

1103 # assert f._isfine is self._isfine 

1104 # assert f._RESIDUAL is self._RESIDUAL 

1105 return f 

1106 

1107 def _copy_2(self, which, name=NN): 

1108 '''(INTERNAL) Copy for I{dyadic} operators. 

1109 ''' 

1110 n = name or which.__name__ # _DUNDER_nameof 

1111 # NOT .classof due to .Fdot(a, *b) args, etc. 

1112 f = _Named.copy(self, deep=False, name=n) 

1113 f._ps = list(self._ps) # separate list 

1114 # assert f._n == self._n 

1115 # assert f._f2product == self._f2product 

1116 # assert f._Fsum is f 

1117 # assert f._isfine is self._isfine 

1118 # assert f._RESIDUAL is self._RESIDUAL 

1119 return f 

1120 

1121 def _copy_2r(self, other, which): 

1122 '''(INTERNAL) Copy for I{reverse-dyadic} operators. 

1123 ''' 

1124 return other._copy_2(which) if _isFsum(other) else \ 

1125 self._copy_2(which)._fset(other) 

1126 

1127 divmod = __divmod__ 

1128 

1129 def _Error(self, op, other, Error, **txt_cause): 

1130 '''(INTERNAL) Format an B{C{Error}} for C{{self} B{op} B{other}}. 

1131 ''' 

1132 # self.as_iscalar causes RecursionError for ._fprs2 errors 

1133 s = _Psum(self._ps, nonfinites=True, name=self.name) 

1134 return Error(_SPACE_(s.as_iscalar, op, other), **txt_cause) 

1135 

1136 def _ErrorX(self, X, op, other, *mod): 

1137 '''(INTERNAL) Format the caught exception C{X}. 

1138 ''' 

1139 E, t = _xError2(X) 

1140 if mod: 

1141 t = _COMMASPACE_(Fmt.PARENSPACED(mod=mod[0]), t) 

1142 return self._Error(op, other, E, txt=t, cause=X) 

1143 

1144 def _ErrorXs(self, X, xs, **kwds): # in .fmath 

1145 '''(INTERNAL) Format the caught exception C{X}. 

1146 ''' 

1147 E, t = _xError2(X) 

1148 u = unstr(self.named3, *xs, _ELLIPSIS=4, **kwds) 

1149 return E(u, txt=t, cause=X) 

1150 

1151 def _facc(self, xs, up=True, **_X_x_origin): 

1152 '''(INTERNAL) Accumulate more C{scalar}s or L{Fsum}s. 

1153 ''' 

1154 if xs: 

1155 kwds = self._isfine 

1156 if _X_x_origin: 

1157 kwds = _xkwds(_X_x_origin, **kwds) 

1158 fs = _xs(xs, **kwds) # PYCHOK yield 

1159 ps = self._ps 

1160 ps[:] = self._ps_acc(list(ps), fs, up=up) 

1161# if len(ps) > 16: 

1162# _ = _psum(ps, **self._isfine) 

1163 return self 

1164 

1165 def _facc_args(self, xs, **up): 

1166 '''(INTERNAL) Accumulate 0, 1 or more C{xs}, all positional 

1167 arguments in the caller of this method. 

1168 ''' 

1169 return self._fadd(xs[0], **up) if len(xs) == 1 else \ 

1170 self._facc(xs, **up) # origin=1? 

1171 

1172 def _facc_dot(self, n, xs, ys, **kwds): # in .fmath 

1173 '''(INTERNAL) Accumulate C{fdot(B{xs}, *B{ys})}. 

1174 ''' 

1175 if n > 0: 

1176 _f = Fsum(**kwds) 

1177 self._facc(_f(x).fmul(y) for x, y in zip(xs, ys)) # PYCHOK attr? 

1178 return self 

1179 

1180 def _facc_neg(self, xs, **up_origin): 

1181 '''(INTERNAL) Accumulate more C{xs}, negated. 

1182 ''' 

1183 def _N(X): 

1184 return X._ps_neg 

1185 

1186 def _n(x): 

1187 return -float(x) 

1188 

1189 return self._facc(xs, _X=_N, _x=_n, **up_origin) 

1190 

1191 def _facc_power(self, power, xs, which, **raiser_RESIDUAL): # in .fmath 

1192 '''(INTERNAL) Add each C{xs} as C{float(x**power)}. 

1193 ''' 

1194 def _Pow4(p): 

1195 r = 0 

1196 if _isFsum_2Tuple(p): 

1197 s, r = p._fprs2 

1198 if r: 

1199 m = Fsum._pow 

1200 else: # scalar 

1201 return _Pow4(s) 

1202 elif isint(p, both=True) and int(p) >= 0: 

1203 p = s = int(p) 

1204 m = Fsum._pow_int 

1205 else: 

1206 p = s = _2float(power=p, **self._isfine) 

1207 m = Fsum._pow_scalar 

1208 return m, p, s, r 

1209 

1210 _Pow, p, s, r = _Pow4(power) 

1211 if p: # and xs: 

1212 op = which.__name__ 

1213 _FsT = _Fsum_2Tuple_types 

1214 _pow = self._pow_2_3 

1215 

1216 def _P(X): 

1217 f = _Pow(X, p, power, op, **raiser_RESIDUAL) 

1218 return f._ps if isinstance(f, _FsT) else (f,) 

1219 

1220 def _p(x): 

1221 x = float(x) 

1222 f = _pow(x, s, power, op, **raiser_RESIDUAL) 

1223 if f and r: 

1224 f *= _pow(x, r, power, op, **raiser_RESIDUAL) 

1225 return f 

1226 

1227 f = self._facc(xs, _X=_P, _x=_p) # origin=1? 

1228 else: 

1229 f = self._facc_scalar_(float(len(xs))) # x**0 == 1 

1230 return f 

1231 

1232 def _facc_scalar(self, xs, **up): 

1233 '''(INTERNAL) Accumulate all C{xs}, each C{scalar}. 

1234 ''' 

1235 if xs: 

1236 ps = self._ps 

1237 ps[:] = self._ps_acc(list(ps), xs, **up) 

1238 return self 

1239 

1240 def _facc_scalar_(self, *xs, **up): 

1241 '''(INTERNAL) Accumulate all positional C{xs}, each C{scalar}. 

1242 ''' 

1243 return self._facc_scalar(xs, **up) 

1244 

1245 def _facc_scalarf(self, xs, up=True, **origin_which): 

1246 '''(INTERNAL) Accumulate all C{xs}, each C{scalar}, an L{Fsum} or 

1247 L{Fsum2Tuple}, like function C{_xsum}. 

1248 ''' 

1249 _C = self.__class__ 

1250 fs = _xs(xs, **_x_isfine(self.nonfinitesOK, _Cdot=_C, 

1251 **origin_which)) # PYCHOK yield 

1252 return self._facc_scalar(fs, up=up) 

1253 

1254# def _facc_up(self, up=True): 

1255# '''(INTERNAL) Update the C{partials}, by removing 

1256# and re-accumulating the final C{partial}. 

1257# ''' 

1258# ps = self._ps 

1259# while len(ps) > 1: 

1260# p = ps.pop() 

1261# if p: 

1262# n = self._n 

1263# _ = self._ps_acc(ps, (p,), up=False) 

1264# self._n = n 

1265# break 

1266# return self._update() if up else self 

1267 

1268 def fadd(self, xs=()): 

1269 '''Add an iterable's items to this instance. 

1270 

1271 @arg xs: Iterable of items to add (each C{scalar}, 

1272 an L{Fsum} or L{Fsum2Tuple}). 

1273 

1274 @return: This instance (L{Fsum}). 

1275 

1276 @raise OverflowError: Partial C{2sum} overflow. 

1277 

1278 @raise TypeError: An invalid B{C{xs}} item. 

1279 

1280 @raise ValueError: Invalid or I{non-finite} B{C{xs}} value. 

1281 ''' 

1282 if _isFsum_2Tuple(xs): 

1283 self._facc_scalar(xs._ps) 

1284 elif isscalar(xs): # for backward compatibility # PYCHOK no cover 

1285 x = _2float(x=xs, **self._isfine) 

1286 self._facc_scalar_(x) 

1287 elif xs: # _xiterable(xs) 

1288 self._facc(xs) 

1289 return self 

1290 

1291 def fadd_(self, *xs): 

1292 '''Add all positional items to this instance. 

1293 

1294 @arg xs: Values to add (each C{scalar}, an L{Fsum} 

1295 or L{Fsum2Tuple}), all positional. 

1296 

1297 @see: Method L{Fsum.fadd} for further details. 

1298 ''' 

1299 return self._facc_args(xs) 

1300 

1301 def _fadd(self, other, op=_add_op_, **up): 

1302 '''(INTERNAL) Apply C{B{self} += B{other}}. 

1303 ''' 

1304 if _isFsum_2Tuple(other): 

1305 self._facc_scalar(other._ps, **up) 

1306 elif self._scalar(other, op): 

1307 self._facc_scalar_(other, **up) 

1308 return self 

1309 

1310 fcopy = copy # for backward compatibility 

1311 fdiv = __itruediv__ 

1312 fdivmod = __divmod__ 

1313 

1314 def _fdivmod2(self, other, op, **raiser_RESIDUAL): 

1315 '''(INTERNAL) Apply C{B{self} %= B{other}} and return a L{DivMod2Tuple}. 

1316 ''' 

1317 # result mostly follows CPython function U{float_divmod 

1318 # <https://GitHub.com/python/cpython/blob/main/Objects/floatobject.c>}, 

1319 # but at least divmod(-3, 2) equals Cpython's result (-2, 1). 

1320 q = self._truediv(other, op, **raiser_RESIDUAL).floor 

1321 if q: # == float // other == floor(float / other) 

1322 self -= self._Fsum_as(q) * other # NOT other * q! 

1323 

1324 s = signOf(other) # make signOf(self) == signOf(other) 

1325 if s and self.signOf() == -s: # PYCHOK no cover 

1326 self += other 

1327 q -= 1 

1328# t = self.signOf() 

1329# if t and t != s: 

1330# raise self._Error(op, other, _AssertionError, txt__=signOf) 

1331 return DivMod2Tuple(q, self) # q is C{int} in Python 3+, but C{float} in Python 2- 

1332 

1333 def _fhorner(self, x, cs, where, incx=True): # in .fmath 

1334 '''(INTERNAL) Add an L{Fhorner} evaluation of polynomial 

1335 C{sum(cs[i] * B{x}**i for i=0..len(cs)-1) if B{incx} 

1336 else sum(... i=len(cs)-1..0)}. 

1337 ''' 

1338 # assert _xiterablen(cs) 

1339 try: 

1340 n = len(cs) 

1341 H = self._Fsum_as(name__=self._fhorner) 

1342 _m = H._mul_Fsum if _isFsum_2Tuple(x) else \ 

1343 H._mul_scalar 

1344 if _2finite(x, **self._isfine) and n > 1: 

1345 for c in (reversed(cs) if incx else cs): 

1346 H._fset(_m(x, _mul_op_), up=False) 

1347 H._fadd(c, up=False) 

1348 else: # x == 0 

1349 H = cs[0] if n else 0 

1350 self._fadd(H) 

1351 except Exception as X: 

1352 t = unstr(where, x, *cs, _ELLIPSIS=4, incx=incx) 

1353 raise self._ErrorX(X, _add_op_, t) 

1354 return self 

1355 

1356 def _finite(self, other, op=None): 

1357 '''(INTERNAL) Return B{C{other}} if C{finite}. 

1358 ''' 

1359 if _isOK_or_finite(other, **self._isfine): 

1360 return other 

1361 E = _NonfiniteError(other) 

1362 raise self._Error(op, other, E, txt=_not_finite_) 

1363 

1364 def fint(self, name=NN, **raiser_RESIDUAL): 

1365 '''Return this instance' current running sum as C{integer}. 

1366 

1367 @kwarg name: Optional, overriding C{B{name}="fint"} (C{str}). 

1368 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore 

1369 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar} 

1370 to override the current L{RESIDUAL<Fsum.RESIDUAL>}. 

1371 

1372 @return: The C{integer} sum (L{Fsum}) if this instance C{is_integer} 

1373 with a zero or insignificant I{integer} residual. 

1374 

1375 @raise ResidualError: Non-zero, significant residual or invalid 

1376 B{C{RESIDUAL}}. 

1377 

1378 @see: Methods L{Fsum.fint2}, L{Fsum.int_float} and L{Fsum.is_integer}. 

1379 ''' 

1380 i, r = self._fint2 

1381 if r: 

1382 R = self._raiser(r, i, **raiser_RESIDUAL) 

1383 if R: 

1384 t = _stresidual(_integer_, r, **R) 

1385 raise ResidualError(_integer_, i, txt=t) 

1386 return self._Fsum_as(i, name=_name__(name, name__=self.fint)) 

1387 

1388 def fint2(self, **name): 

1389 '''Return this instance' current running sum as C{int} and the 

1390 I{integer} residual. 

1391 

1392 @kwarg name: Optional name (C{str}). 

1393 

1394 @return: An L{Fsum2Tuple}C{(fsum, residual)} with C{fsum} 

1395 an C{int} and I{integer} C{residual} a C{float} or 

1396 C{INT0} if the C{fsum} is considered to be I{exact}. 

1397 The C{fsum} is I{non-finite} if this instance is. 

1398 ''' 

1399 return Fsum2Tuple(*self._fint2, **name) 

1400 

1401 @Property 

1402 def _fint2(self): # see ._fset 

1403 '''(INTERNAL) Get 2-tuple (C{int}, I{integer} residual). 

1404 ''' 

1405 s, r = self._nfprs2 

1406 if _isfinite(s): 

1407 i = int(s) 

1408 r = (self._ps_1sum(i) if len(self._ps) > 1 else 

1409 float(s - i)) or INT0 

1410 else: # INF, NAN, NINF 

1411 i = float(s) 

1412# r = _NONFINITEr 

1413 return i, r # Fsum2Tuple? 

1414 

1415 @_fint2.setter_ # PYCHOK setter_UNDERscore! 

1416 def _fint2(self, s): # in _fset 

1417 '''(INTERNAL) Replace the C{_fint2} value. 

1418 ''' 

1419 if _isfinite(s): 

1420 i = int(s) 

1421 r = (s - i) or INT0 

1422 else: # INF, NAN, NINF 

1423 i = float(s) 

1424 r = _NONFINITEr 

1425 return i, r # like _fint2.getter 

1426 

1427 @deprecated_property_RO 

1428 def float_int(self): # PYCHOK no cover 

1429 '''DEPRECATED, use method C{Fsum.int_float}.''' 

1430 return self.int_float() # raiser=False 

1431 

1432 @property_RO 

1433 def floor(self): 

1434 '''Get this instance' C{floor} (C{int} in Python 3+, but 

1435 C{float} in Python 2-). 

1436 

1437 @note: This C{floor} takes the C{residual} into account. 

1438 

1439 @see: Method L{Fsum.int_float} and properties L{Fsum.ceil}, 

1440 L{Fsum.imag} and L{Fsum.real}. 

1441 ''' 

1442 s, r = self._fprs2 

1443 f = _floor(s) + _floor(r) + 1 

1444 while (f - s) > r: # f > (s + r) 

1445 f -= 1 

1446 return f # _floor(self._n_d) 

1447 

1448# ffloordiv = __ifloordiv__ # for naming consistency? 

1449# floordiv = __floordiv__ # for naming consistency? 

1450 

1451 def _floordiv(self, other, op, **raiser_RESIDUAL): # rather _ffloordiv? 

1452 '''Apply C{B{self} //= B{other}}. 

1453 ''' 

1454 q = self._ftruediv(other, op, **raiser_RESIDUAL) # == self 

1455 return self._fset(q.floor) # floor(q) 

1456 

1457 def fma(self, other1, other2, **nonfinites): # in .fmath.fma 

1458 '''Fused-multiply-add C{self *= B{other1}; self += B{other2}}. 

1459 

1460 @arg other1: Multiplier (C{scalar}, an L{Fsum} or L{Fsum2Tuple}). 

1461 @arg other2: Addend (C{scalar}, an L{Fsum} or L{Fsum2Tuple}). 

1462 @kwarg nonfinites: Use C{B{nonfinites}=True} or C{False}, to 

1463 override L{nonfinites<Fsum.nonfinites>} and 

1464 L{nonfiniterrors} default (C{bool}). 

1465 ''' 

1466 op = self.fma.__name__ 

1467 _fs = self._ps_other 

1468 try: 

1469 s, r = self._fprs2 

1470 if r: 

1471 f = self._f2mul(self.fma, (other1,), **nonfinites) 

1472 f += other2 

1473 elif _residue(other1) or _residue(other2): 

1474 fs = _2split3s(_fs(op, other1)) 

1475 fs = _2products(s, fs, *_fs(op, other2)) 

1476 f = _Psum(self._ps_acc([], fs, up=False), name=op) 

1477 else: 

1478 f = _fma(s, other1, other2) 

1479 f = _2finite(f, **self._isfine) 

1480 except TypeError as X: 

1481 raise self._ErrorX(X, op, (other1, other2)) 

1482 except (OverflowError, ValueError) as X: # from math.fma 

1483 f = self._mul_reduce(s, other1) # INF, NAN, NINF 

1484 f += sum(_fs(op, other2)) 

1485 f = self._nonfiniteX(X, op, f, **nonfinites) 

1486 return self._fset(f) 

1487 

1488 fmul = __imul__ 

1489 

1490 def _fmul(self, other, op): 

1491 '''(INTERNAL) Apply C{B{self} *= B{other}}. 

1492 ''' 

1493 if _isFsum_2Tuple(other): 

1494 if len(self._ps) != 1: 

1495 f = self._mul_Fsum(other, op) 

1496 elif len(other._ps) != 1: # and len(self._ps) == 1 

1497 f = self._ps_mul(op, *other._ps) if other._ps else _0_0 

1498 elif self._f2product: # len(other._ps) == 1 

1499 f = self._mul_scalar(other._ps[0], op) 

1500 else: # len(other._ps) == len(self._ps) == 1 

1501 f = self._finite(self._ps[0] * other._ps[0], op=op) 

1502 else: 

1503 s = self._scalar(other, op) 

1504 f = self._mul_scalar(s, op) 

1505 return self._fset(f) # n=len(self) + 1 

1506 

1507 @deprecated_method 

1508 def f2mul(self, *others, **raiser): 

1509 '''DEPRECATED on 2024.09.13, use method L{f2mul_<Fsum.f2mul_>}.''' 

1510 return self._fset(self.f2mul_(others, **raiser)) 

1511 

1512 def f2mul_(self, *others, **f2product_nonfinites): # in .fmath.f2mul 

1513 '''Return C{B{self} * B{other} * B{other} ...} for all B{C{others}} using cascaded, 

1514 accurate multiplication like with L{f2product<Fsum.f2product>}C{(B{True})}. 

1515 

1516 @arg others: Multipliers (each C{scalar}, an L{Fsum} or L{Fsum2Tuple}), all 

1517 positional. 

1518 @kwarg f2product_nonfinites: Use C{B{f2product=False}} to override the default 

1519 C{True} and C{B{nonfinites}=True} or C{False}, to override 

1520 settings L{nonfinites<Fsum.nonfinites>} and L{nonfiniterrors}. 

1521 

1522 @return: The cascaded I{TwoProduct} (L{Fsum} or C{float}). 

1523 

1524 @see: U{Equations 2.3<https://www.TUHH.De/ti3/paper/rump/OzOgRuOi06.pdf>} 

1525 ''' 

1526 return self._f2mul(self.f2mul_, others, **f2product_nonfinites) 

1527 

1528 def _f2mul(self, where, others, f2product=True, **nonfinites_raiser): 

1529 '''(INTERNAL) See methods C{fma} and C{f2mul_}. 

1530 ''' 

1531 f = _Psum(self._ps, f2product=f2product, name=where.__name__) 

1532 if others and f: 

1533 if f.f2product(): 

1534 def _pfs(f, ps): 

1535 return _2products(f, _2split3s(ps)) 

1536 else: 

1537 def _pfs(f, ps): # PYCHOK redef 

1538 return (f * p for p in ps) 

1539 

1540 op, ps = where.__name__, f._ps 

1541 try: # as if self.f2product(True) 

1542 for other in others: # to pinpoint errors 

1543 for p in self._ps_other(op, other): 

1544 ps[:] = f._ps_acc([], _pfs(p, ps), update=False) 

1545 f._update() 

1546 except TypeError as X: 

1547 raise self._ErrorX(X, op, other) 

1548 except (OverflowError, ValueError) as X: 

1549 r = self._mul_reduce(sum(ps), other) # INF, NAN, NINF 

1550 r = self._nonfiniteX(X, op, r, **nonfinites_raiser) 

1551 f._fset(r) 

1552 return f 

1553 

1554 def fover(self, over, **raiser_RESIDUAL): 

1555 '''Apply C{B{self} /= B{over}} and summate. 

1556 

1557 @arg over: An L{Fsum} or C{scalar} denominator. 

1558 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore 

1559 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar} 

1560 to override the current L{RESIDUAL<Fsum.RESIDUAL>}. 

1561 

1562 @return: Precision running sum (C{float}). 

1563 

1564 @raise ResidualError: Non-zero, significant residual or invalid 

1565 B{C{RESIDUAL}}. 

1566 

1567 @see: Methods L{Fsum.fsum} and L{Fsum.__itruediv__}. 

1568 ''' 

1569 return float(self.fdiv(over, **raiser_RESIDUAL)._fprs) 

1570 

1571 fpow = __ipow__ 

1572 

1573 def _fpow(self, other, op, *mod, **raiser_RESIDUAL): 

1574 '''Apply C{B{self} **= B{other}}, optional B{C{mod}} or C{None}. 

1575 ''' 

1576 if mod: 

1577 if mod[0] is not None: # == 3-arg C{pow} 

1578 f = self._pow_2_3(self, other, other, op, *mod, **raiser_RESIDUAL) 

1579 elif self.is_integer(): 

1580 # return an exact C{int} for C{int}**C{int} 

1581 i, _ = self._fint2 # assert _ == 0 

1582 x, r = _2tuple2(other) # C{int}, C{float} or other 

1583 f = self._Fsum_as(i)._pow_Fsum(other, op, **raiser_RESIDUAL) if r else \ 

1584 self._pow_2_3(i, x, other, op, **raiser_RESIDUAL) 

1585 else: # mod[0] is None, power(self, other) 

1586 f = self._pow(other, other, op, **raiser_RESIDUAL) 

1587 else: # pow(self, other) 

1588 f = self._pow(other, other, op, **raiser_RESIDUAL) 

1589 return self._fset(f) # n=max(len(self), 1) 

1590 

1591 def f2product(self, *two): 

1592 '''Get and set accurate I{TwoProduct} multiplication for this 

1593 L{Fsum}, overriding the L{f2product} default. 

1594 

1595 @arg two: If omitted, leave the override unchanged, if C{True}, 

1596 turn I{TwoProduct} on, if C{False} off, if C{None}e 

1597 remove th override (C{bool} or C{None}). 

1598 

1599 @return: The previous setting (C{bool} or C{None} if not set). 

1600 

1601 @see: Function L{f2product<fsums.f2product>}. 

1602 

1603 @note: Use C{f.f2product() or f2product()} to determine whether 

1604 multiplication is accurate for L{Fsum} C{f}. 

1605 ''' 

1606 if two: # delattrof(self, _f2product=None) 

1607 t = _xkwds_pop(self.__dict__, _f2product=None) 

1608 if two[0] is not None: 

1609 self._f2product = bool(two[0]) 

1610 else: # getattrof(self, _f2product=None) 

1611 t = _xkwds_get(self.__dict__, _f2product=None) 

1612 return t 

1613 

1614 @Property 

1615 def _fprs(self): 

1616 '''(INTERNAL) Get and cache this instance' precision 

1617 running sum (C{float} or C{int}), ignoring C{residual}. 

1618 

1619 @note: The precision running C{fsum} after a C{//=} or 

1620 C{//} C{floor} division is C{int} in Python 3+. 

1621 ''' 

1622 s, _ = self._fprs2 

1623 return s # ._fprs2.fsum 

1624 

1625 @_fprs.setter_ # PYCHOK setter_UNDERscore! 

1626 def _fprs(self, s): 

1627 '''(INTERNAL) Replace the C{_fprs} value. 

1628 ''' 

1629 return s 

1630 

1631 @Property 

1632 def _fprs2(self): 

1633 '''(INTERNAL) Get and cache this instance' precision 

1634 running sum and residual (L{Fsum2Tuple}). 

1635 ''' 

1636 ps = self._ps 

1637 n = len(ps) 

1638 try: 

1639 if n > 2: 

1640 s = _psum(ps, **self._isfine) 

1641 if not _isfinite(s): 

1642 ps[:] = s, # collapse ps 

1643 return Fsum2Tuple(s, _NONFINITEr) 

1644 n = len(ps) 

1645# Fsum._ps_max = max(Fsum._ps_max, n) 

1646 if n > 2: 

1647 r = self._ps_1sum(s) 

1648 return Fsum2Tuple(*_s_r2(s, r)) 

1649 if n > 1: # len(ps) == 2 

1650 s, r = _s_r2(*_2sum(*ps, **self._isfine)) 

1651 ps[:] = (r, s) if r else (s,) 

1652 elif ps: # len(ps) == 1 

1653 s = ps[0] 

1654 r = INT0 if _isfinite(s) else _NONFINITEr 

1655 else: # len(ps) == 0 

1656 s = _0_0 

1657 r = INT0 if _isfinite(s) else _NONFINITEr 

1658 ps[:] = s, 

1659 except (OverflowError, ValueError) as X: 

1660 op = _fset_op_ # INF, NAN, NINF 

1661 ps[:] = sum(ps), # collapse ps 

1662 s = self._nonfiniteX(X, op, ps[0]) 

1663 r = _NONFINITEr 

1664 # assert self._ps is ps 

1665 return Fsum2Tuple(s, r) 

1666 

1667 @_fprs2.setter_ # PYCHOK setter_UNDERscore! 

1668 def _fprs2(self, s_r): 

1669 '''(INTERNAL) Replace the C{_fprs2} value. 

1670 ''' 

1671 return Fsum2Tuple(s_r) 

1672 

1673 def fset_(self, *xs): 

1674 '''Apply C{B{self}.partials = Fsum(*B{xs}).partials}. 

1675 

1676 @arg xs: Optional, new values (each C{scalar} or an L{Fsum} 

1677 or L{Fsum2Tuple} instance), all positional. 

1678 

1679 @return: This instance, replaced (C{Fsum}). 

1680 

1681 @see: Method L{Fsum.fadd} for further details. 

1682 ''' 

1683 f = (xs[0] if xs else _0_0) if len(xs) < 2 else \ 

1684 Fsum(*xs, nonfinites=self.nonfinites()) # self._Fsum_as(*xs) 

1685 return self._fset(f, op=_fset_op_) 

1686 

1687 def _fset(self, other, n=0, up=True, **op): 

1688 '''(INTERNAL) Overwrite this instance with an other or a C{scalar}. 

1689 ''' 

1690 if other is self: 

1691 pass # from ._fmul, ._ftruediv and ._pow_0_1 

1692 elif _isFsum_2Tuple(other): 

1693 if op: # and not self.nonfinitesOK: 

1694 self._finite(other._fprs, **op) 

1695 self._ps[:] = other._ps 

1696 self._n = n or other._n 

1697 if up: # use or zap the C{Property_RO} values 

1698 Fsum._fint2._update_from(self, other) 

1699 Fsum._fprs ._update_from(self, other) 

1700 Fsum._fprs2._update_from(self, other) 

1701 elif isscalar(other): 

1702 s = float(self._finite(other, **op)) if op else other 

1703 self._ps[:] = s, 

1704 self._n = n or 1 

1705 if up: # Property _fint2, _fprs and _fprs2 all have 

1706 # @.setter_underscore and NOT @.setter because the 

1707 # latter's _fset zaps the value set by @.setter 

1708 self._fint2 = s 

1709 self._fprs = s 

1710 self._fprs2 = s, INT0 

1711 # assert self._fprs is s 

1712 else: 

1713 op = _xkwds_get1(op, op=_fset_op_) 

1714 raise self._Error(op, other, _TypeError) 

1715 return self 

1716 

1717 def fsub(self, xs=()): 

1718 '''Subtract an iterable's items from this instance. 

1719 

1720 @see: Method L{Fsum.fadd} for further details. 

1721 ''' 

1722 return self._facc_neg(xs) 

1723 

1724 def fsub_(self, *xs): 

1725 '''Subtract all positional items from this instance. 

1726 

1727 @see: Method L{Fsum.fadd_} for further details. 

1728 ''' 

1729 return self._fsub(xs[0], _sub_op_) if len(xs) == 1 else \ 

1730 self._facc_neg(xs) # origin=1? 

1731 

1732 def _fsub(self, other, op): 

1733 '''(INTERNAL) Apply C{B{self} -= B{other}}. 

1734 ''' 

1735 if _isFsum_2Tuple(other): 

1736 if other is self: # or other._fprs2 == self._fprs2: 

1737 self._fset(_0_0, n=len(self) * 2) 

1738 elif other._ps: 

1739 self._facc_scalar(other._ps_neg) 

1740 elif self._scalar(other, op): 

1741 self._facc_scalar_(-other) 

1742 return self 

1743 

1744 def fsum(self, xs=()): 

1745 '''Add an iterable's items, summate and return the current 

1746 precision running sum. 

1747 

1748 @arg xs: Iterable of items to add (each item C{scalar}, 

1749 an L{Fsum} or L{Fsum2Tuple}). 

1750 

1751 @return: Precision running sum (C{float} or C{int}). 

1752 

1753 @see: Method L{Fsum.fadd}. 

1754 

1755 @note: Accumulation can continue after summation. 

1756 ''' 

1757 return self._facc(xs)._fprs 

1758 

1759 def fsum_(self, *xs): 

1760 '''Add any positional items, summate and return the current 

1761 precision running sum. 

1762 

1763 @arg xs: Items to add (each C{scalar}, an L{Fsum} or 

1764 L{Fsum2Tuple}), all positional. 

1765 

1766 @return: Precision running sum (C{float} or C{int}). 

1767 

1768 @see: Methods L{Fsum.fsum}, L{Fsum.Fsum_} and L{Fsum.fsumf_}. 

1769 ''' 

1770 return self._facc_args(xs)._fprs 

1771 

1772 def Fsum_(self, *xs, **name): 

1773 '''Like method L{Fsum.fsum_} but returning a named L{Fsum}. 

1774 

1775 @kwarg name: Optional name (C{str}). 

1776 

1777 @return: Copy of this updated instance (L{Fsum}). 

1778 ''' 

1779 return self._facc_args(xs)._copy_2(self.Fsum_, **name) 

1780 

1781 def Fsum2Tuple_(self, *xs, **name): 

1782 '''Like method L{Fsum.fsum_} but returning a named L{Fsum2Tuple}. 

1783 

1784 @kwarg name: Optional name (C{str}). 

1785 

1786 @return: Precision running sum (L{Fsum2Tuple}). 

1787 ''' 

1788 return Fsum2Tuple(self._facc_args(xs)._nfprs2, **name) 

1789 

1790 @property_RO 

1791 def _Fsum(self): # like L{Fsum2Tuple._Fsum}, in .fstats 

1792 return self # NOT @Property_RO, see .copy and ._copy_2 

1793 

1794 def _Fsum_as(self, *xs, **name_f2product_nonfinites_RESIDUAL): 

1795 '''(INTERNAL) Return an C{Fsum} with this C{Fsum}'s C{.f2product}, 

1796 C{.nonfinites} and C{.RESIDUAL} setting, optionally 

1797 overridden with C{name_f2product_nonfinites_RESIDUAL} and 

1798 with any C{xs} accumulated. 

1799 ''' 

1800 kwds = _xkwds_not(None, Fsum._RESIDUAL, f2product =self.f2product(), 

1801 nonfinites=self.nonfinites(), 

1802 RESIDUAL =self.RESIDUAL()) 

1803 if name_f2product_nonfinites_RESIDUAL: # overwrites 

1804 kwds.update(name_f2product_nonfinites_RESIDUAL) 

1805 f = Fsum(**kwds) 

1806 # assert all(v == self.__dict__[n] for n, v in f.__dict__.items()) 

1807 return f._fset(xs[0], op=_fset_op_) if len(xs) == 1 else ( 

1808 f._facc(xs, up=False) if xs else f) 

1809 

1810 def fsum2(self, xs=(), **name): 

1811 '''Add an iterable's items, summate and return the 

1812 current precision running sum I{and} the C{residual}. 

1813 

1814 @arg xs: Iterable of items to add (each item C{scalar}, 

1815 an L{Fsum} or L{Fsum2Tuple}). 

1816 @kwarg name: Optional C{B{name}=NN} (C{str}). 

1817 

1818 @return: L{Fsum2Tuple}C{(fsum, residual)} with C{fsum} the 

1819 current precision running sum and C{residual}, the 

1820 (precision) sum of the remaining C{partials}. The 

1821 C{residual is INT0} if the C{fsum} is considered 

1822 to be I{exact}. 

1823 

1824 @see: Methods L{Fsum.fint2}, L{Fsum.fsum} and L{Fsum.fsum2_} 

1825 ''' 

1826 t = self._facc(xs)._fprs2 

1827 return t.dup(name=name) if name else t 

1828 

1829 def fsum2_(self, *xs): 

1830 '''Add any positional items, summate and return the current 

1831 precision running sum and the I{differential}. 

1832 

1833 @arg xs: Values to add (each C{scalar}, an L{Fsum} or 

1834 L{Fsum2Tuple}), all positional. 

1835 

1836 @return: 2Tuple C{(fsum, delta)} with the current, precision 

1837 running C{fsum} like method L{Fsum.fsum} and C{delta}, 

1838 the difference with previous running C{fsum}, C{float}. 

1839 

1840 @see: Methods L{Fsum.fsum_} and L{Fsum.fsum}. 

1841 ''' 

1842 return self._fsum2(xs, self._facc_args) 

1843 

1844 def _fsum2(self, xs, _facc, **facc_kwds): 

1845 '''(INTERNAL) Helper for L{Fsum.fsum2_} and L{Fsum.fsum2f_}. 

1846 ''' 

1847 p, q = self._fprs2 

1848 if xs: 

1849 s, r = _facc(xs, **facc_kwds)._fprs2 

1850 if _isfinite(s): # _fsum(_1primed((s, -p, r, -q)) 

1851 d, r = _2sum(s - p, r - q, _isfine=_isOK) 

1852 r, _ = _s_r2(d, r) 

1853 return s, (r if _isfinite(r) else _NONFINITEr) 

1854 else: 

1855 return p, _0_0 

1856 

1857 def fsumf_(self, *xs): 

1858 '''Like method L{Fsum.fsum_} iff I{all} C{B{xs}}, each I{known to be} 

1859 C{scalar}, an L{Fsum} or L{Fsum2Tuple}. 

1860 ''' 

1861 return self._facc_scalarf(xs, which=self.fsumf_)._fprs # origin=1? 

1862 

1863 def Fsumf_(self, *xs): 

1864 '''Like method L{Fsum.Fsum_} iff I{all} C{B{xs}}, each I{known to be} 

1865 C{scalar}, an L{Fsum} or L{Fsum2Tuple}. 

1866 ''' 

1867 return self._facc_scalarf(xs, which=self.Fsumf_)._copy_2(self.Fsumf_) # origin=1? 

1868 

1869 def fsum2f_(self, *xs): 

1870 '''Like method L{Fsum.fsum2_} iff I{all} C{B{xs}}, each I{known to be} 

1871 C{scalar}, an L{Fsum} or L{Fsum2Tuple}. 

1872 ''' 

1873 return self._fsum2(xs, self._facc_scalarf, which=self.fsum2f_) # origin=1? 

1874 

1875# ftruediv = __itruediv__ # for naming consistency? 

1876 

1877 def _ftruediv(self, other, op, **raiser_RESIDUAL): 

1878 '''(INTERNAL) Apply C{B{self} /= B{other}}. 

1879 ''' 

1880 n = _1_0 

1881 if _isFsum_2Tuple(other): 

1882 if other is self or self == other: 

1883 return self._fset(n, n=len(self)) 

1884 d, r = other._fprs2 

1885 if r: 

1886 R = self._raiser(r, d, **raiser_RESIDUAL) 

1887 if R: 

1888 raise self._ResidualError(op, other, r, **R) 

1889 d, n = other.as_integer_ratio() 

1890 else: 

1891 d = self._scalar(other, op) 

1892 try: 

1893 s = n / d 

1894 except Exception as X: 

1895 raise self._ErrorX(X, op, other) 

1896 f = self._mul_scalar(s, _mul_op_) # handles 0, INF, NAN 

1897 return self._fset(f) 

1898 

1899 @property_RO 

1900 def imag(self): 

1901 '''Get the C{imaginary} part of this instance (C{0.0}, always). 

1902 

1903 @see: Property L{Fsum.real}. 

1904 ''' 

1905 return _0_0 

1906 

1907 def int_float(self, **raiser_RESIDUAL): 

1908 '''Return this instance' current running sum as C{int} or C{float}. 

1909 

1910 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore 

1911 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar} 

1912 to override the current L{RESIDUAL<Fsum.RESIDUAL>}. 

1913 

1914 @return: This C{int} sum if this instance C{is_integer} and 

1915 I{finite}, otherwise the C{float} sum if the residual 

1916 is zero or not significant. 

1917 

1918 @raise ResidualError: Non-zero, significant residual or invalid 

1919 B{C{RESIDUAL}}. 

1920 

1921 @see: Methods L{Fsum.fint}, L{Fsum.fint2}, L{Fsum.is_integer}, 

1922 L{Fsum.RESIDUAL} and property L{Fsum.as_iscalar}. 

1923 ''' 

1924 s, r = self._fint2 

1925 if r: 

1926 s, r = self._fprs2 

1927 if r: # PYCHOK no cover 

1928 R = self._raiser(r, s, **raiser_RESIDUAL) 

1929 if R: 

1930 t = _stresidual(_non_zero_, r, **R) 

1931 raise ResidualError(int_float=s, txt=t) 

1932 s = float(s) 

1933 return s 

1934 

1935 def is_exact(self): 

1936 '''Is this instance' running C{fsum} considered to be exact? 

1937 (C{bool}), C{True} only if the C{residual is }L{INT0}. 

1938 ''' 

1939 return self.residual is INT0 

1940 

1941 def is_finite(self): # in .constants 

1942 '''Is this instance C{finite}? (C{bool}). 

1943 

1944 @see: Function L{isfinite<pygeodesy.isfinite>}. 

1945 ''' 

1946 return _isfinite(sum(self._ps)) # == sum(self) 

1947 

1948 def is_integer(self): 

1949 '''Is this instance' running sum C{integer}? (C{bool}). 

1950 

1951 @see: Methods L{Fsum.fint}, L{Fsum.fint2} and L{Fsum.is_scalar}. 

1952 ''' 

1953 s, r = self._fint2 

1954 return False if r else (_isfinite(s) and isint(s)) 

1955 

1956 def is_math_fma(self): 

1957 '''Is accurate L{f2product} multiplication based on Python's C{math.fma}? 

1958 

1959 @return: C{True} if accurate multiplication uses C{math.fma}, C{False} 

1960 an C{fma} implementation as C{math.fma} or C{None}, a previous 

1961 C{PyGeodesy} implementation. 

1962 ''' 

1963 return (_2split3s is _passarg) or (False if _2n_d is None else None) 

1964 

1965 def is_math_fsum(self): 

1966 '''Are the summation functions L{fsum}, L{fsum_}, L{fsumf_}, L{fsum1}, 

1967 L{fsum1_} and L{fsum1f_} based on Python's C{math.fsum}? 

1968 

1969 @return: C{True} if summation functions use C{math.fsum}, C{False} 

1970 otherwise. 

1971 ''' 

1972 return _sum is _fsum # _fsum.__module__ is fabs.__module__ 

1973 

1974 def is_scalar(self, **raiser_RESIDUAL): 

1975 '''Is this instance' running sum C{scalar} with C{0} residual or with 

1976 a residual I{ratio} not exceeding the RESIDUAL threshold? 

1977 

1978 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore 

1979 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar} 

1980 to override the current L{RESIDUAL<Fsum.RESIDUAL>}. 

1981 

1982 @return: C{True} if this instance' residual is C{0} or C{insignificant}, 

1983 i.e. its residual C{ratio} doesn't exceed the L{RESIDUAL 

1984 <Fsum.RESIDUAL>} threshold (C{bool}). 

1985 

1986 @raise ResidualError: Non-zero, significant residual or invalid 

1987 B{C{RESIDUAL}}. 

1988 

1989 @see: Methods L{Fsum.RESIDUAL} and L{Fsum.is_integer} and property 

1990 L{Fsum.as_iscalar}. 

1991 ''' 

1992 s, r = self._fprs2 

1993 return False if r and self._raiser(r, s, **raiser_RESIDUAL) else True 

1994 

1995 def _mul_Fsum(self, other, op): 

1996 '''(INTERNAL) Return C{B{self} * B{other}} as L{Fsum} or C{0}. 

1997 ''' 

1998 # assert _isFsum_2Tuple(other) 

1999 if self._ps and other._ps: 

2000 try: 

2001 f = self._ps_mul(op, *other._ps) # NO .as_iscalar! 

2002 except Exception as X: 

2003 raise self._ErrorX(X, op, other) 

2004 else: 

2005 f = _0_0 

2006 return f 

2007 

2008 def _mul_reduce(self, *others): 

2009 '''(INTERNAL) Like fmath.fprod for I{non-finite} C{other}s. 

2010 ''' 

2011 r = _1_0 

2012 for f in others: 

2013 r *= sum(f._ps) if _isFsum_2Tuple(f) else float(f) 

2014 return r 

2015 

2016 def _mul_scalar(self, factor, op): 

2017 '''(INTERNAL) Return C{B{self} * scalar B{factor}} as L{Fsum}, C{0.0} or C{self}. 

2018 ''' 

2019 # assert isscalar(factor) 

2020 if self._ps and self._finite(factor, op=op): 

2021 f = self if factor == _1_0 else ( 

2022 self._neg if factor == _N_1_0 else 

2023 self._ps_mul(op, factor).as_iscalar) 

2024 else: 

2025 f = _0_0 

2026 return f 

2027 

2028# @property_RO 

2029# def _n_d(self): 

2030# n, d = self.as_integer_ratio() 

2031# return n / d 

2032 

2033 @property_RO 

2034 def _neg(self): 

2035 '''(INTERNAL) Return C{Fsum(-self)} or scalar C{NEG0}. 

2036 ''' 

2037 return _Psum(self._ps_neg) if self._ps else NEG0 

2038 

2039 @property_RO 

2040 def _nfprs2(self): 

2041 '''(INTERNAL) Handle I{non-finite} C{_fprs2}. 

2042 ''' 

2043 try: # to handle nonfiniterrors, etc. 

2044 t = self._fprs2 

2045 except (OverflowError, ValueError): 

2046 t = Fsum2Tuple(sum(self._ps), _NONFINITEr) 

2047 return t 

2048 

2049 def nonfinites(self, *OK): 

2050 '''Handle I{non-finite} C{float}s as C{inf}, C{INF}, C{NINF}, C{nan} 

2051 and C{NAN} for this L{Fsum} or throw C{OverflowError} respectively 

2052 C{ValueError} exceptions, overriding the L{nonfiniterrors} default. 

2053 

2054 @arg OK: If omitted, leave the override unchanged, if C{True}, 

2055 I{non-finites} are C{OK}, if C{False} throw exceptions 

2056 or if C{None} remove the override (C{bool} or C{None}). 

2057 

2058 @return: The previous setting (C{bool} or C{None} if not set). 

2059 

2060 @see: Function L{nonfiniterrors<fsums.nonfiniterrors>}. 

2061 

2062 @note: Use property L{nonfinitesOK<Fsum.nonfinitesOK>} to determine 

2063 whether I{non-finites} are C{OK} for this L{Fsum} and by the 

2064 L{nonfiniterrors} default. 

2065 ''' 

2066 _ks = Fsum._nonfinites_isfine_kwds 

2067 if OK: # delattrof(self, _isfine=None) 

2068 k = _xkwds_pop(self.__dict__, _isfine=None) 

2069 if OK[0] is not None: 

2070 self._isfine = _ks[bool(OK[0])] 

2071 self._update() 

2072 else: # getattrof(self, _isfine=None) 

2073 k = _xkwds_get(self.__dict__, _isfine=None) 

2074 # dict(map(reversed, _ks.items())).get(k, None) 

2075 # raises a TypeError: unhashable type: 'dict' 

2076 return True if k is _ks[True] else ( 

2077 False if k is _ks[False] else None) 

2078 

2079 _nonfinites_isfine_kwds = {True: dict(_isfine=_isOK), 

2080 False: dict(_isfine=_isfinite)} 

2081 

2082 @property_RO 

2083 def nonfinitesOK(self): 

2084 '''Are I{non-finites} C{OK} for this L{Fsum} or by default? (C{bool}). 

2085 ''' 

2086# nf = self.nonfinites() 

2087# if nf is None: 

2088# nf = not nonfiniterrors() 

2089 return _isOK_or_finite(INF, **self._isfine) 

2090 

2091 def _nonfiniteX(self, X, op, f, nonfinites=None, raiser=None): 

2092 '''(INTERNAL) Handle a I{non-finite} exception. 

2093 ''' 

2094 if nonfinites is None: 

2095 nonfinites = _isOK_or_finite(f, **self._isfine) if raiser is None else (not raiser) 

2096 if not nonfinites: 

2097 raise self._ErrorX(X, op, f) 

2098 return f 

2099 

2100 def _optionals(self, f2product=None, nonfinites=None, **name_RESIDUAL): 

2101 '''(INTERNAL) Re/set options from keyword arguments. 

2102 ''' 

2103 if f2product is not None: 

2104 self.f2product(f2product) 

2105 if nonfinites is not None: 

2106 self.nonfinites(nonfinites) 

2107 if name_RESIDUAL: # MUST be last 

2108 n, kwds = _name2__(**name_RESIDUAL) 

2109 if kwds: 

2110 R = Fsum._RESIDUAL 

2111 t = _threshold(R, **kwds) 

2112 if t != R: 

2113 self._RESIDUAL = t 

2114 if n: 

2115 self.name = n # self.rename(n) 

2116 

2117 def _1_Over(self, x, op, **raiser_RESIDUAL): # vs _1_over 

2118 '''(INTERNAL) Return C{Fsum(1) / B{x}}. 

2119 ''' 

2120 return self._Fsum_as(_1_0)._ftruediv(x, op, **raiser_RESIDUAL) 

2121 

2122 @property_RO 

2123 def partials(self): 

2124 '''Get this instance' current, partial sums (C{tuple} of C{float}s). 

2125 ''' 

2126 return tuple(self._ps) 

2127 

2128 def pow(self, x, *mod, **raiser_RESIDUAL): 

2129 '''Return C{B{self}**B{x}} as L{Fsum}. 

2130 

2131 @arg x: The exponent (C{scalar}, an L{Fsum} or L{Fsum2Tuple}). 

2132 @arg mod: Optional modulus (C{int} or C{None}) for the 3-argument 

2133 C{pow(B{self}, B{other}, B{mod})} version. 

2134 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore 

2135 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar} 

2136 to override the current L{RESIDUAL<Fsum.RESIDUAL>}. 

2137 

2138 @return: The C{pow(self, B{x})} or C{pow(self, B{x}, *B{mod})} 

2139 result (L{Fsum}). 

2140 

2141 @raise ResidualError: Non-zero, significant residual or invalid 

2142 B{C{RESIDUAL}}. 

2143 

2144 @note: If B{C{mod}} is given and C{None}, the result will be an 

2145 C{integer} L{Fsum} provided this instance C{is_integer} 

2146 or set to C{integer} by an L{Fsum.fint} call. 

2147 

2148 @see: Methods L{Fsum.__ipow__}, L{Fsum.fint}, L{Fsum.is_integer} 

2149 and L{Fsum.root}. 

2150 ''' 

2151 f = self._copy_2(self.pow) 

2152 return f._fpow(x, _pow_op_, *mod, **raiser_RESIDUAL) # f = pow(f, x, *mod) 

2153 

2154 def _pow(self, other, unused, op, **raiser_RESIDUAL): 

2155 '''Return C{B{self} ** B{other}}. 

2156 ''' 

2157 if _isFsum_2Tuple(other): 

2158 f = self._pow_Fsum(other, op, **raiser_RESIDUAL) 

2159 elif self._scalar(other, op): 

2160 x = self._finite(other, op=op) 

2161 f = self._pow_scalar(x, other, op, **raiser_RESIDUAL) 

2162 else: 

2163 f = self._pow_0_1(0, other) 

2164 return f 

2165 

2166 def _pow_0_1(self, x, other): 

2167 '''(INTERNAL) Return B{C{self}**1} or C{B{self}**0 == 1.0}. 

2168 ''' 

2169 return self if x else (1 if isint(other) and self.is_integer() else _1_0) 

2170 

2171 def _pow_2_3(self, b, x, other, op, *mod, **raiser_RESIDUAL): 

2172 '''(INTERNAL) 2-arg C{pow(B{b}, scalar B{x})} and 3-arg C{pow(B{b}, 

2173 B{x}, int B{mod} or C{None})}, embellishing errors. 

2174 ''' 

2175 

2176 if mod: # b, x, mod all C{int}, unless C{mod} is C{None} 

2177 m = mod[0] 

2178 # assert _isFsum_2Tuple(b) 

2179 

2180 def _s(s, r): 

2181 R = self._raiser(r, s, **raiser_RESIDUAL) 

2182 if R: 

2183 raise self._ResidualError(op, other, r, mod=m, **R) 

2184 return s 

2185 

2186 b = _s(*(b._fprs2 if m is None else b._fint2)) 

2187 x = _s(*_2tuple2(x)) 

2188 

2189 try: 

2190 # 0**INF == 0.0, 1**INF == 1.0, -1**2.3 == -(1**2.3) 

2191 s = pow(b, x, *mod) 

2192 if iscomplex(s): 

2193 # neg**frac == complex in Python 3+, but ValueError in 2- 

2194 raise ValueError(_strcomplex(s, b, x, *mod)) 

2195 _ = _2finite(s, **self._isfine) # ignore float 

2196 return s 

2197 except Exception as X: 

2198 raise self._ErrorX(X, op, other, *mod) 

2199 

2200 def _pow_Fsum(self, other, op, **raiser_RESIDUAL): 

2201 '''(INTERNAL) Return C{B{self} **= B{other}} for C{_isFsum_2Tuple(other)}. 

2202 ''' 

2203 # assert _isFsum_2Tuple(other) 

2204 x, r = other._fprs2 

2205 f = self._pow_scalar(x, other, op, **raiser_RESIDUAL) 

2206 if f and r: 

2207 f *= self._pow_scalar(r, other, op, **raiser_RESIDUAL) 

2208 return f 

2209 

2210 def _pow_int(self, x, other, op, **raiser_RESIDUAL): 

2211 '''(INTERNAL) Return C{B{self} **= B{x}} for C{int B{x} >= 0}. 

2212 ''' 

2213 # assert isint(x) and x >= 0 

2214 ps = self._ps 

2215 if len(ps) > 1: 

2216 _mul_Fsum = Fsum._mul_Fsum 

2217 if x > 4: 

2218 p = self 

2219 f = self if (x & 1) else self._Fsum_as(_1_0) 

2220 m = x >> 1 # // 2 

2221 while m: 

2222 p = _mul_Fsum(p, p, op) # p **= 2 

2223 if (m & 1): 

2224 f = _mul_Fsum(f, p, op) # f *= p 

2225 m >>= 1 # //= 2 

2226 elif x > 1: # self**2, 3, or 4 

2227 f = _mul_Fsum(self, self, op) 

2228 if x > 2: # self**3 or 4 

2229 p = self if x < 4 else f 

2230 f = _mul_Fsum(f, p, op) 

2231 else: # self**1 or self**0 == 1 or _1_0 

2232 f = self._pow_0_1(x, other) 

2233 elif ps: # self._ps[0]**x 

2234 f = self._pow_2_3(ps[0], x, other, op, **raiser_RESIDUAL) 

2235 else: # PYCHOK no cover 

2236 # 0**pos_int == 0, but 0**0 == 1 

2237 f = 0 if x else 1 

2238 return f 

2239 

2240 def _pow_scalar(self, x, other, op, **raiser_RESIDUAL): 

2241 '''(INTERNAL) Return C{self**B{x}} for C{scalar B{x}}. 

2242 ''' 

2243 s, r = self._fprs2 

2244 if r: 

2245 # assert s != 0 

2246 if isint(x, both=True): # self**int 

2247 x = int(x) 

2248 y = abs(x) 

2249 if y > 1: 

2250 f = self._pow_int(y, other, op, **raiser_RESIDUAL) 

2251 if x > 0: # i.e. > 1 

2252 return f # Fsum or scalar 

2253 # assert x < 0 # i.e. < -1 

2254 if _isFsum(f): 

2255 s, r = f._fprs2 

2256 if r: 

2257 return self._1_Over(f, op, **raiser_RESIDUAL) 

2258 else: # scalar 

2259 s = f 

2260 # use s**(-1) to get the CPython 

2261 # float_pow error iff s is zero 

2262 x = -1 

2263 elif x < 0: # self**(-1) 

2264 return self._1_Over(self, op, **raiser_RESIDUAL) # 1 / self 

2265 else: # self**1 or self**0 

2266 return self._pow_0_1(x, other) # self, 1 or 1.0 

2267 else: # self**fractional 

2268 R = self._raiser(r, s, **raiser_RESIDUAL) 

2269 if R: 

2270 raise self._ResidualError(op, other, r, **R) 

2271 n, d = self.as_integer_ratio() 

2272 if abs(n) > abs(d): 

2273 n, d, x = d, n, (-x) 

2274 s = n / d 

2275 # assert isscalar(s) and isscalar(x) 

2276 return self._pow_2_3(s, x, other, op, **raiser_RESIDUAL) 

2277 

2278 def _ps_acc(self, ps, xs, up=True, **unused): 

2279 '''(INTERNAL) Accumulate C{xs} known scalars into list C{ps}. 

2280 ''' 

2281 n = 0 

2282 _2s = _2sum 

2283 _fi = self._isfine 

2284 for x in (tuple(xs) if xs is ps else xs): 

2285 # assert isscalar(x) and _isOK_or_finite(x, **self._isfine) 

2286 if x: 

2287 i = 0 

2288 for p in ps: 

2289 x, p = _2s(x, p, **_fi) 

2290 if p: 

2291 ps[i] = p 

2292 i += 1 

2293 ps[i:] = (x,) if x else () 

2294 n += 1 

2295 if n: 

2296 self._n += n 

2297 # Fsum._ps_max = max(Fsum._ps_max, len(ps)) 

2298 if up: 

2299 self._update() 

2300# x = sum(ps) 

2301# if not _isOK_or_finite(x, **fi): 

2302# ps[:] = x, # collapse ps 

2303 return ps 

2304 

2305 def _ps_mul(self, op, *factors): 

2306 '''(INTERNAL) Multiply this instance' C{partials} with 

2307 each scalar C{factor} and accumulate into an C{Fsum}. 

2308 ''' 

2309 def _psfs(ps, fs, _isfine=_isfinite): 

2310 if len(ps) < len(fs): 

2311 ps, fs = fs, ps 

2312 if self._f2product: 

2313 fs, p = _2split3s(fs), fs 

2314 if len(ps) > 1 and fs is not p: 

2315 fs = tuple(fs) # several ps 

2316 _pfs = _2products 

2317 else: 

2318 def _pfs(p, fs): 

2319 return (p * f for f in fs) 

2320 

2321 for p in ps: 

2322 for x in _pfs(p, fs): 

2323 yield x if _isfine(x) else _nfError(x) 

2324 

2325 xs = _psfs(self._ps, factors, **self._isfine) 

2326 f = _Psum(self._ps_acc([], xs, up=False), name=op) 

2327 return f 

2328 

2329 @property_RO 

2330 def _ps_neg(self): 

2331 '''(INTERNAL) Yield the partials, I{negated}. 

2332 ''' 

2333 for p in self._ps: 

2334 yield -p 

2335 

2336 def _ps_other(self, op, other): 

2337 '''(INTERNAL) Yield C{other} as C{scalar}s. 

2338 ''' 

2339 if _isFsum_2Tuple(other): 

2340 for p in other._ps: 

2341 yield p 

2342 else: 

2343 yield self._scalar(other, op) 

2344 

2345 def _ps_1sum(self, *less): 

2346 '''(INTERNAL) Return the partials sum, 1-primed C{less} some scalars. 

2347 ''' 

2348 def _1psls(ps, ls): 

2349 yield _1_0 

2350 for p in ps: 

2351 yield p 

2352 for p in ls: 

2353 yield -p 

2354 yield _N_1_0 

2355 

2356 return _fsum(_1psls(self._ps, less)) 

2357 

2358 def _raiser(self, r, s, raiser=True, **RESIDUAL): 

2359 '''(INTERNAL) Does ratio C{r / s} exceed the RESIDUAL threshold 

2360 I{and} is residual C{r} I{non-zero} or I{significant} (for a 

2361 negative respectively positive C{RESIDUAL} threshold)? 

2362 ''' 

2363 if r and raiser: 

2364 t = self._RESIDUAL 

2365 if RESIDUAL: 

2366 t = _threshold(t, **RESIDUAL) 

2367 if t < 0 or (s + r) != s: 

2368 q = (r / s) if s else s # == 0. 

2369 if fabs(q) > fabs(t): 

2370 return dict(ratio=q, R=t) 

2371 return {} 

2372 

2373 rdiv = __rtruediv__ 

2374 

2375 @property_RO 

2376 def real(self): 

2377 '''Get the C{real} part of this instance (C{float}). 

2378 

2379 @see: Methods L{Fsum.__float__} and L{Fsum.fsum} 

2380 and properties L{Fsum.ceil}, L{Fsum.floor}, 

2381 L{Fsum.imag} and L{Fsum.residual}. 

2382 ''' 

2383 return float(self) 

2384 

2385 @property_RO 

2386 def residual(self): 

2387 '''Get this instance' residual or residue (C{float} or C{int}): 

2388 the C{sum(partials)} less the precision running sum C{fsum}. 

2389 

2390 @note: The C{residual is INT0} iff the precision running 

2391 C{fsum} is considered to be I{exact}. 

2392 

2393 @see: Methods L{Fsum.fsum}, L{Fsum.fsum2} and L{Fsum.is_exact}. 

2394 ''' 

2395 return self._fprs2.residual 

2396 

2397 def RESIDUAL(self, *threshold): 

2398 '''Get and set this instance' I{ratio} for raising L{ResidualError}s, 

2399 overriding the default from env variable C{PYGEODESY_FSUM_RESIDUAL}. 

2400 

2401 @arg threshold: If C{scalar}, the I{ratio} to exceed for raising 

2402 L{ResidualError}s in division and exponention, if 

2403 C{None}, restore the default set with env variable 

2404 C{PYGEODESY_FSUM_RESIDUAL} or if omitted, keep the 

2405 current setting. 

2406 

2407 @return: The previous C{RESIDUAL} setting (C{float}), default C{0.0}. 

2408 

2409 @raise ResidualError: Invalid B{C{threshold}}. 

2410 

2411 @note: L{ResidualError}s may be thrown if (1) the non-zero I{ratio} 

2412 C{residual / fsum} exceeds the given B{C{threshold}} and (2) 

2413 the C{residual} is non-zero and (3) is I{significant} vs the 

2414 C{fsum}, i.e. C{(fsum + residual) != fsum} and (4) optional 

2415 keyword argument C{raiser=False} is missing. Specify a 

2416 negative B{C{threshold}} for only non-zero C{residual} 

2417 testing without the I{significant} case. 

2418 ''' 

2419 r = self._RESIDUAL 

2420 if threshold: 

2421 t = threshold[0] 

2422 self._RESIDUAL = Fsum._RESIDUAL if t is None else ( # for ... 

2423 (_0_0 if t else _1_0) if isbool(t) else 

2424 _threshold(t)) # ... backward compatibility 

2425 return r 

2426 

2427 def _ResidualError(self, op, other, residual, **mod_R): 

2428 '''(INTERNAL) Non-zero B{C{residual}} etc. 

2429 ''' 

2430 def _p(mod=None, R=0, **unused): # ratio=0 

2431 return (_non_zero_ if R < 0 else _significant_) \ 

2432 if mod is None else _integer_ 

2433 

2434 t = _stresidual(_p(**mod_R), residual, **mod_R) 

2435 return self._Error(op, other, ResidualError, txt=t) 

2436 

2437 def root(self, root, **raiser_RESIDUAL): 

2438 '''Return C{B{self}**(1 / B{root})} as L{Fsum}. 

2439 

2440 @arg root: Non-zero order (C{scalar}, an L{Fsum} or L{Fsum2Tuple}). 

2441 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore any 

2442 L{ResidualError}s (C{bool}) or C{B{RESIDUAL}=scalar} 

2443 to override the current L{RESIDUAL<Fsum.RESIDUAL>}. 

2444 

2445 @return: The C{self ** (1 / B{root})} result (L{Fsum}). 

2446 

2447 @raise ResidualError: Non-zero, significant residual or invalid 

2448 B{C{RESIDUAL}}. 

2449 

2450 @see: Method L{Fsum.pow}. 

2451 ''' 

2452 x = self._1_Over(root, _truediv_op_, **raiser_RESIDUAL) 

2453 f = self._copy_2(self.root) 

2454 return f._fpow(x, f.name, **raiser_RESIDUAL) # == pow(f, x) 

2455 

2456 def _scalar(self, other, op, **txt): 

2457 '''(INTERNAL) Return scalar C{other} or throw a C{TypeError}. 

2458 ''' 

2459 if isscalar(other): 

2460 return other 

2461 raise self._Error(op, other, _TypeError, **txt) # _invalid_ 

2462 

2463 def signOf(self, res=True): 

2464 '''Determine the sign of this instance. 

2465 

2466 @kwarg res: If C{True}, consider the residual, 

2467 otherwise ignore the latter (C{bool}). 

2468 

2469 @return: The sign (C{int}, -1, 0 or +1). 

2470 ''' 

2471 s, r = self._nfprs2 

2472 r = (-r) if res else 0 

2473 return _signOf(s, r) 

2474 

2475 def toRepr(self, **lenc_prec_sep_fmt): # PYCHOK signature 

2476 '''Return this C{Fsum} instance as representation. 

2477 

2478 @kwarg lenc_prec_sep_fmt: Optional keyword arguments 

2479 for method L{Fsum.toStr}. 

2480 

2481 @return: This instance (C{repr}). 

2482 ''' 

2483 return Fmt.repr_at(self, self.toStr(**lenc_prec_sep_fmt)) 

2484 

2485 def toStr(self, lenc=True, **prec_sep_fmt): # PYCHOK signature 

2486 '''Return this C{Fsum} instance as string. 

2487 

2488 @kwarg lenc: If C{True}, include the current C{[len]} of this 

2489 L{Fsum} enclosed in I{[brackets]} (C{bool}). 

2490 @kwarg prec_sep_fmt: Optional keyword arguments for method 

2491 L{Fsum2Tuple.toStr}. 

2492 

2493 @return: This instance (C{str}). 

2494 ''' 

2495 p = self.classname 

2496 if lenc: 

2497 p = Fmt.SQUARE(p, len(self)) 

2498 n = _enquote(self.name, white=_UNDER_) 

2499 t = self._nfprs2.toStr(**prec_sep_fmt) 

2500 return NN(p, _SPACE_, n, t) 

2501 

2502 def _truediv(self, other, op, **raiser_RESIDUAL): 

2503 '''(INTERNAL) Return C{B{self} / B{other}} as an L{Fsum}. 

2504 ''' 

2505 f = self._copy_2(self.__truediv__) 

2506 return f._ftruediv(other, op, **raiser_RESIDUAL) 

2507 

2508 def _update(self, updated=True): # see ._fset 

2509 '''(INTERNAL) Zap all cached C{Property_RO} values. 

2510 ''' 

2511 if updated: 

2512 _pop = self.__dict__.pop 

2513 for p in _ROs: 

2514 _ = _pop(p, None) 

2515# Fsum._fint2._update(self) 

2516# Fsum._fprs ._update(self) 

2517# Fsum._fprs2._update(self) 

2518 return self # for .fset_ 

2519 

2520_ROs = _allPropertiesOf_n(3, Fsum, Property_RO) # PYCHOK see Fsum._update 

2521 

2522if _NONFINITES == _std_: # PYCHOK no cover 

2523 _ = nonfiniterrors(False) 

2524 

2525 

2526def _Float_Int(arg, **name_Error): 

2527 '''(INTERNAL) L{DivMod2Tuple}, L{Fsum2Tuple} Unit. 

2528 ''' 

2529 U = Int if isint(arg) else Float 

2530 return U(arg, **name_Error) 

2531 

2532 

2533class DivMod2Tuple(_NamedTuple): 

2534 '''2-Tuple C{(div, mod)} with the quotient C{div} and remainder 

2535 C{mod} results of a C{divmod} operation. 

2536 

2537 @note: Quotient C{div} an C{int} in Python 3+ but a C{float} 

2538 in Python 2-. Remainder C{mod} an L{Fsum} instance. 

2539 ''' 

2540 _Names_ = ('div', 'mod') 

2541 _Units_ = (_Float_Int, Fsum) 

2542 

2543 

2544class Fsum2Tuple(_NamedTuple): # in .fstats 

2545 '''2-Tuple C{(fsum, residual)} with the precision running C{fsum} 

2546 and the C{residual}, the sum of the remaining partials. Each 

2547 item is C{float} or C{int}. 

2548 

2549 @note: If the C{residual is INT0}, the C{fsum} is considered 

2550 to be I{exact}, see method L{Fsum2Tuple.is_exact}. 

2551 ''' 

2552 _Names_ = ( Fsum.fsum.__name__, Fsum.residual.name) 

2553 _Units_ = (_Float_Int, _Float_Int) 

2554 

2555 def __abs__(self): # in .fmath 

2556 return self._Fsum.__abs__() 

2557 

2558 def __bool__(self): # PYCHOK Python 3+ 

2559 return bool(self._Fsum) 

2560 

2561 def __eq__(self, other): 

2562 return self._other_op(other, self.__eq__) 

2563 

2564 def __float__(self): 

2565 return self._Fsum.__float__() 

2566 

2567 def __ge__(self, other): 

2568 return self._other_op(other, self.__ge__) 

2569 

2570 def __gt__(self, other): 

2571 return self._other_op(other, self.__gt__) 

2572 

2573 def __le__(self, other): 

2574 return self._other_op(other, self.__le__) 

2575 

2576 def __lt__(self, other): 

2577 return self._other_op(other, self.__lt__) 

2578 

2579 def __int__(self): 

2580 return self._Fsum.__int__() 

2581 

2582 def __ne__(self, other): 

2583 return self._other_op(other, self.__ne__) 

2584 

2585 def __neg__(self): 

2586 return self._Fsum.__neg__() 

2587 

2588 __nonzero__ = __bool__ # Python 2- 

2589 

2590 def __pos__(self): 

2591 return self._Fsum.__pos__() 

2592 

2593 def as_integer_ratio(self): 

2594 '''Return this instance as the ratio of 2 integers. 

2595 

2596 @see: Method L{Fsum.as_integer_ratio} for further details. 

2597 ''' 

2598 return self._Fsum.as_integer_ratio() 

2599 

2600 @property_RO 

2601 def _fint2(self): 

2602 return self._Fsum._fint2 

2603 

2604 @property_RO 

2605 def _fprs2(self): 

2606 return self._Fsum._fprs2 

2607 

2608 @Property_RO 

2609 def _Fsum(self): # this C{Fsum2Tuple} as L{Fsum}, in .fstats 

2610 s, r = _s_r2(*self) 

2611 ps = (r, s) if r else (s,) 

2612 return _Psum(ps, name=self.name) 

2613 

2614 def Fsum_(self, *xs, **name_f2product_nonfinites_RESIDUAL): 

2615 '''Return this C{Fsum2Tuple} as an L{Fsum} plus some C{xs}. 

2616 ''' 

2617 return Fsum(self, *xs, **name_f2product_nonfinites_RESIDUAL) 

2618 

2619 def is_exact(self): 

2620 '''Is this L{Fsum2Tuple} considered to be exact? (C{bool}). 

2621 ''' 

2622 return self._Fsum.is_exact() 

2623 

2624 def is_finite(self): # in .constants 

2625 '''Is this L{Fsum2Tuple} C{finite}? (C{bool}). 

2626 

2627 @see: Function L{isfinite<pygeodesy.isfinite>}. 

2628 ''' 

2629 return self._Fsum.is_finite() 

2630 

2631 def is_integer(self): 

2632 '''Is this L{Fsum2Tuple} C{integer}? (C{bool}). 

2633 ''' 

2634 return self._Fsum.is_integer() 

2635 

2636 def _mul_scalar(self, other, op): # for Fsum._fmul 

2637 return self._Fsum._mul_scalar(other, op) 

2638 

2639 @property_RO 

2640 def _n(self): 

2641 return self._Fsum._n 

2642 

2643 def _other_op(self, other, which): 

2644 C, s = (tuple, self) if isinstance(other, tuple) else (Fsum, self._Fsum) 

2645 return getattr(C, which.__name__)(s, other) 

2646 

2647 @property_RO 

2648 def _ps(self): 

2649 return self._Fsum._ps 

2650 

2651 @property_RO 

2652 def _ps_neg(self): 

2653 return self._Fsum._ps_neg 

2654 

2655 def signOf(self, **res): 

2656 '''Like method L{Fsum.signOf}. 

2657 ''' 

2658 return self._Fsum.signOf(**res) 

2659 

2660 def toStr(self, fmt=Fmt.g, **prec_sep): # PYCHOK signature 

2661 '''Return this L{Fsum2Tuple} as string (C{str}). 

2662 

2663 @kwarg fmt: Optional C{float} format (C{letter}). 

2664 @kwarg prec_sep: Optional keyword arguments for function 

2665 L{fstr<streprs.fstr>}. 

2666 ''' 

2667 return Fmt.PAREN(fstr(self, fmt=fmt, strepr=str, force=False, **prec_sep)) 

2668 

2669_Fsum_2Tuple_types = Fsum, Fsum2Tuple # PYCHOK lines 

2670 

2671 

2672class ResidualError(_ValueError): 

2673 '''Error raised for a division, power or root operation of 

2674 an L{Fsum} instance with a C{residual} I{ratio} exceeding 

2675 the L{RESIDUAL<Fsum.RESIDUAL>} threshold. 

2676 

2677 @see: Module L{pygeodesy.fsums} and method L{Fsum.RESIDUAL}. 

2678 ''' 

2679 pass 

2680 

2681 

2682try: 

2683 from math import fsum as _fsum # precision IEEE-754 sum, Python 2.6+ 

2684 

2685 # make sure _fsum works as expected (XXX check 

2686 # float.__getformat__('float')[:4] == 'IEEE'?) 

2687 if _fsum((1, 1e101, 1, -1e101)) != 2: # PYCHOK no cover 

2688 del _fsum # nope, remove _fsum ... 

2689 raise ImportError() # ... use _fsum below 

2690 

2691 _sum = _fsum # in .elliptic 

2692except ImportError: 

2693 _sum = sum # in .elliptic 

2694 

2695 def _fsum(xs): 

2696 '''(INTERNAL) Precision summation, Python 2.5-. 

2697 ''' 

2698 F = Fsum(name=_fsum.name, f2product=False, nonfinites=True) 

2699 return float(F._facc(xs, up=False)) 

2700 

2701 

2702def fsum(xs, nonfinites=None, **floats): 

2703 '''Precision floating point summation from Python's C{math.fsum}. 

2704 

2705 @arg xs: Iterable of items to add (each C{scalar}, an L{Fsum} or L{Fsum2Tuple}). 

2706 @kwarg nonfinites: Use C{B{nonfinites}=True} if I{non-finites} are C{OK}, if 

2707 C{False} I{non-finites} raise an Overflow-/ValueError or if 

2708 C{None}, L{nonfiniterrors} applies (C{bool} or C{None}). 

2709 @kwarg floats: DEPRECATED keyword argument C{B{floats}=False} (C{bool}), use 

2710 keyword argument C{B{nonfinites}=False} instead. 

2711 

2712 @return: Precision C{fsum} (C{float}). 

2713 

2714 @raise OverflowError: Infinite B{C{xs}} item or intermediate C{math.fsum} overflow. 

2715 

2716 @raise TypeError: Invalid B{C{xs}} item. 

2717 

2718 @raise ValueError: Invalid or C{NAN} B{C{xs}} item. 

2719 

2720 @see: Function L{nonfiniterrors}, class L{Fsum} and methods L{Fsum.nonfinites}, 

2721 L{Fsum.fsum}, L{Fsum.fadd} and L{Fsum.fadd_}. 

2722 ''' 

2723 return _xsum(fsum, xs, nonfinites=nonfinites, **floats) if xs else _0_0 

2724 

2725 

2726def fsum_(*xs, **nonfinites): 

2727 '''Precision floating point summation of all positional items. 

2728 

2729 @arg xs: Items to add (each C{scalar}, an L{Fsum} or L{Fsum2Tuple}), all positional. 

2730 @kwarg nonfinites: Use C{B{nonfinites}=True} if I{non-finites} are C{OK} (C{bool}). 

2731 

2732 @see: Function L{fsum<fsums.fsum>} for further details. 

2733 ''' 

2734 return _xsum(fsum_, xs, **nonfinites) if xs else _0_0 # origin=1? 

2735 

2736 

2737def fsumf_(*xs): 

2738 '''Precision floating point summation of all positional items with I{non-finites} C{OK}. 

2739 

2740 @arg xs: Items to add (each C{scalar}, an L{Fsum} or L{Fsum2Tuple}), 

2741 all positional. 

2742 

2743 @see: Function L{fsum_<fsums.fsum_>} for further details. 

2744 ''' 

2745 return _xsum(fsumf_, xs, nonfinites=True) if xs else _0_0 # origin=1? 

2746 

2747 

2748def fsum1(xs, **nonfinites): 

2749 '''Precision floating point summation, 1-primed. 

2750 

2751 @arg xs: Iterable of items to add (each C{scalar}, an L{Fsum} or L{Fsum2Tuple}). 

2752 @kwarg nonfinites: Use C{B{nonfinites}=True} if I{non-finites} are C{OK} (C{bool}). 

2753 

2754 @see: Function L{fsum<fsums.fsum>} for further details. 

2755 ''' 

2756 return _xsum(fsum1, xs, primed=1, **nonfinites) if xs else _0_0 

2757 

2758 

2759def fsum1_(*xs, **nonfinites): 

2760 '''Precision floating point summation of all positional items, 1-primed. 

2761 

2762 @arg xs: Items to add (each C{scalar}, an L{Fsum} or L{Fsum2Tuple}), all positional. 

2763 @kwarg nonfinites: Use C{B{nonfinites}=True} if I{non-finites} are C{OK} (C{bool}). 

2764 

2765 @see: Function L{fsum_<fsums.fsum_>} for further details. 

2766 ''' 

2767 return _xsum(fsum1_, xs, primed=1, **nonfinites) if xs else _0_0 # origin=1? 

2768 

2769 

2770def fsum1f_(*xs): 

2771 '''Precision floating point summation of all positional items, 1-primed and 

2772 with I{non-finites} C{OK}. 

2773 

2774 @see: Function L{fsum_<fsums.fsum_>} for further details. 

2775 ''' 

2776 return _xsum(fsum1f_, xs, nonfinites=True, primed=1) if xs else _0_0 

2777 

2778 

2779def _x_isfine(nfOK, **kwds): # get the C{_x} and C{_isfine} handlers. 

2780 _x_kwds = dict(_x= (_passarg if nfOK else _2finite), 

2781 _isfine=(_isOK if nfOK else _isfinite)) # PYCHOK kwds 

2782 _x_kwds.update(kwds) 

2783 return _x_kwds 

2784 

2785 

2786def _X_ps(X): # default C{_X} handler 

2787 return X._ps # lambda X: X._ps 

2788 

2789 

2790def _xs(xs, _X=_X_ps, _x=float, _isfine=_isfinite, # defaults for Fsum._facc 

2791 origin=0, which=None, **_Cdot): 

2792 '''(INTERNAL) Yield each C{xs} item as 1 or more C{float}s. 

2793 ''' 

2794 i, x = 0, xs 

2795 try: 

2796 for i, x in enumerate(_xiterable(xs)): 

2797 if _isFsum_2Tuple(x): 

2798 for p in _X(x): 

2799 yield p if _isfine(p) else _nfError(p) 

2800 else: 

2801 f = _x(x) 

2802 yield f if _isfine(f) else _nfError(f) 

2803 

2804 except (OverflowError, TypeError, ValueError) as X: 

2805 t = _xsError(X, xs, i + origin, x) 

2806 if which: # prefix invokation 

2807 w = unstr(which, *xs, _ELLIPSIS=4, **_Cdot) 

2808 t = _COMMASPACE_(w, t) 

2809 raise _xError(X, t, txt=None) 

2810 

2811 

2812def _xsum(which, xs, nonfinites=None, primed=0, **floats): # origin=0 

2813 '''(INTERNAL) Precision summation of C{xs} with conditions. 

2814 ''' 

2815 if floats: # for backward compatibility 

2816 nonfinites = _xkwds_get1(floats, floats=nonfinites) 

2817 elif nonfinites is None: 

2818 nonfinites = not nonfiniterrors() 

2819 fs = _xs(xs, **_x_isfine(nonfinites, which=which)) # PYCHOK yield 

2820 return _fsum(_1primed(fs) if primed else fs) 

2821 

2822 

2823# delete all decorators, etc. 

2824del _allPropertiesOf_n, deprecated_method, deprecated_property_RO, \ 

2825 Property, Property_RO, property_RO, _ALL_LAZY, _F2PRODUCT, \ 

2826 MANT_DIG, _NONFINITES, _RESIDUAL_0_0, _getPYGEODESY, _std_ 

2827 

2828if __name__ == '__main__': 

2829 

2830 # usage: python3 -m pygeodesy.fsums 

2831 

2832 def _test(n): 

2833 # copied from Hettinger, see L{Fsum} reference 

2834 from pygeodesy import frandoms, printf 

2835 

2836 printf(_fsum.__name__, end=_COMMASPACE_) 

2837 printf(_psum.__name__, end=_COMMASPACE_) 

2838 

2839 F = Fsum() 

2840 if F.is_math_fsum(): 

2841 for t in frandoms(n, seeded=True): 

2842 assert float(F.fset_(*t)) == _fsum(t) 

2843 printf(_DOT_, end=NN) 

2844 printf(NN) 

2845 

2846 _test(128) 

2847 

2848# **) MIT License 

2849# 

2850# Copyright (C) 2016-2025 -- mrJean1 at Gmail -- All Rights Reserved. 

2851# 

2852# Permission is hereby granted, free of charge, to any person obtaining a 

2853# copy of this software and associated documentation files (the "Software"), 

2854# to deal in the Software without restriction, including without limitation 

2855# the rights to use, copy, modify, merge, publish, distribute, sublicense, 

2856# and/or sell copies of the Software, and to permit persons to whom the 

2857# Software is furnished to do so, subject to the following conditions: 

2858# 

2859# The above copyright notice and this permission notice shall be included 

2860# in all copies or substantial portions of the Software. 

2861# 

2862# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

2863# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

2864# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

2865# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

2866# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 

2867# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 

2868# OTHER DEALINGS IN THE SOFTWARE.