Coverage for pygeodesy/fsums.py: 97%

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1 

2# -*- coding: utf-8 -*- 

3 

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

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

6 

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

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

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

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

11 

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

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

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

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

16 

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

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

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

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

21and L{Fsum.__itruediv__}. 

22''' 

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

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

25 

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

27 _signOf, itemsorted, signOf, _xiterable, \ 

28 _enquote 

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

30 _0_0, _1_0, _N_1_0, Float, Int 

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

32 _xError, _xError2, _xkwds_get 

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

34from pygeodesy.interns import NN, _arg_, _COMMASPACE_, _DASH_, _DOT_, \ 

35 _EQUAL_, _from_, _LANGLE_, _NOTEQUAL_, \ 

36 _not_finite_, _PERCENT_, _PLUS_, \ 

37 _RANGLE_, _SLASH_, _SPACE_, _STAR_, _UNDER_ 

38from pygeodesy.lazily import _ALL_LAZY, _getenv, _sys_version_info2 

39from pygeodesy.named import _Named, _NamedTuple, _NotImplemented 

40from pygeodesy.props import _allPropertiesOf_n, deprecated_property_RO, \ 

41 Property_RO, property_RO 

42from pygeodesy.streprs import Fmt, fstr, unstr 

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

44 

45from math import ceil as _ceil, fabs, floor as _floor # PYCHOK used! .ltp 

46 

47__all__ = _ALL_LAZY.fsums 

48__version__ = '24.05.13' 

49 

50_add_op_ = _PLUS_ # in .auxilats.auxAngle 

51_eq_op_ = _EQUAL_ * 2 # _DEQUAL_ 

52_div_ = 'div' 

53_floordiv_op_ = _SLASH_ * 2 # _DSLASH_ 

54_fset_op_ = _EQUAL_ 

55_ge_op_ = _RANGLE_ + _EQUAL_ 

56_gt_op_ = _RANGLE_ 

57_iadd_op_ = _add_op_ + _EQUAL_ # in .auxilats.auxAngle, .fstats 

58_integer_ = 'integer' 

59_le_op_ = _LANGLE_ + _EQUAL_ 

60_lt_op_ = _LANGLE_ 

61_mod_ = 'mod' 

62_mod_op_ = _PERCENT_ 

63_mul_op_ = _STAR_ 

64_ne_op_ = _NOTEQUAL_ 

65_non_zero_ = 'non-zero' 

66_pow_op_ = _STAR_ * 2 # _DSTAR_ 

67_significant_ = 'significant' 

68_sub_op_ = _DASH_ # in .auxilats.auxAngle 

69_threshold_ = 'threshold' 

70_truediv_op_ = _SLASH_ 

71_divmod_op_ = _floordiv_op_ + _mod_op_ 

72_isub_op_ = _sub_op_ + _fset_op_ # in .auxilats.auxAngle 

73 

74 

75def _2delta(*ab): 

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

77 ''' 

78 try: 

79 a, b = _2sum(*ab) 

80 except _OverflowError: 

81 a, b = ab 

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

83 

84 

85def _2error(unused): # in .fstats 

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

87 ''' 

88 raise ValueError(_not_finite_) 

89 

90 

91def _2finite(x): 

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

93 ''' 

94 x = float(x) 

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

96 

97 

98def _2float(index=None, **name_value): # in .fmath, .fstats 

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

100 ''' 

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

102 try: 

103 return _2finite(v) 

104 except Exception as X: 

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

106 

107 

108def _X_ps(X): # for _2floats only 

109 return X._ps 

110 

111 

112def _2floats(xs, origin=0, _X=_X_ps, _x=float): 

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

114 ''' 

115 try: 

116 i, x = origin, _X 

117 _fin = _isfinite 

118 _FsT = _Fsum_Fsum2Tuple_types 

119 _isa = isinstance 

120 for x in _xiterable(xs): 

121 if _isa(x, _FsT): 

122 for p in _X(x._Fsum): 

123 yield p 

124 else: 

125 f = _x(x) 

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

127 i += 1 

128 except Exception as X: 

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

130 _xError(X, Fmt.INDEX(xs=i), x) 

131 

132 

133def _Fsumf_(*xs): # floats=True, in .auxLat, ... 

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

135 ''' 

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

137 

138 

139def _Fsum1f_(*xs): # floats=True, in .albers, ... 

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

141 ''' 

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

143 

144 

145def _2halfeven(s, r, p): 

146 '''(INTERNAL) Round half-even. 

147 ''' 

148 if (p > 0 and r > 0) or \ 

149 (p < 0 and r < 0): # signs match 

150 r *= 2 

151 t = s + r 

152 if r == (t - s): 

153 s = t 

154 return s 

155 

156 

157def _isFsum(x): # in .fmath 

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

159 ''' 

160 return isinstance(x, Fsum) 

161 

162 

163def _isFsumTuple(x): # in .fmath 

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

165 ''' 

166 return isinstance(x, _Fsum_Fsum2Tuple_types) 

167 

168 

169def _1_Over(x, op, **raiser_RESIDUAL): # vs _1_over 

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

171 ''' 

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

173 

174 

175def _1primed(xs): # in .fmath 

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

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

178 ''' 

179 yield _1_0 

180 for x in xs: 

181 yield x 

182 yield _N_1_0 

183 

184 

185def _psum(ps): # PYCHOK used! 

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

187 ''' 

188 # assert isinstance(ps, list) 

189 i = len(ps) - 1 

190 s = _0_0 if i < 0 else ps[i] 

191 _2s = _2sum 

192 while i > 0: 

193 i -= 1 

194 s, r = _2s(s, ps[i]) 

195 if r: # sum(ps) became inexact 

196 if s: 

197 ps[i:] = r, s 

198 if i > 0: 

199 s = _2halfeven(s, r, ps[i-1]) 

200 break # return s 

201 s = r # PYCHOK no cover 

202 ps[i:] = s, 

203 return s 

204 

205 

206def _Psum(ps, **name_RESIDUAL): 

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

208 ''' 

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

210 if ps: 

211 f._ps[:] = ps 

212 f._n = len(f._ps) 

213 return f 

214 

215 

216def _Psum_(*ps, **name_RESIDUAL): 

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

218 ''' 

219 return _Psum(ps, **name_RESIDUAL) 

220 

221 

222def _2scalar2(other): 

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

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

225 ''' 

226 if _isFsumTuple(other): 

227 s, r = other._fint2 

228 if r: 

229 s, r = other._fprs2 

230 if r: # PYCHOK no cover 

231 s = other # L{Fsum} as-is 

232 else: 

233 r = 0 

234 s = other # C{type} as-is 

235 if isint(s, both=True): 

236 s = int(s) 

237 return s, r 

238 

239 

240def _s_r(s, r): 

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

242 ''' 

243 if r: 

244 if fabs(s) < fabs(r): 

245 s, r = r, (s or INT0) 

246 else: 

247 r = INT0 

248 return s, r 

249 

250 

251def _strcomplex(s, *args): 

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

253 ''' 

254 c = _strcomplex.__name__[4:] 

255 n = _DASH_(len(args), _arg_) 

256 t = unstr(pow, *args) 

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

258 

259 

260def _stresidual(prefix, residual, R=0, **mod_ratio): 

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

262 ''' 

263 p = _stresidual.__name__[3:] 

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

265 for n, v in itemsorted(mod_ratio): 

266 p = Fmt.PARENSPACED(n, Fmt(v)) 

267 t = _COMMASPACE_(t, p) 

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

269 

270 

271def _2sum(a, b): # by .testFmath 

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

273 ''' 

274 s = a + b 

275 if _isfinite(s): 

276 if fabs(a) < fabs(b): 

277 b, a = a, b 

278 return s, (b - (s - a)) 

279 u = unstr(_2sum, a, b) 

280 t = Fmt.PARENSPACED(_not_finite_, s) 

281 raise _OverflowError(u, txt=t) 

282 

283 

284def _threshold(threshold): 

285 '''(INTERNAL) Get the L{ResidualError}s threshold. 

286 ''' 

287 try: 

288 return _2finite(threshold) # PYCHOK None 

289 except Exception as x: 

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

291 

292 

293class Fsum(_Named): # sync __methods__ with .vector3dBase.Vector3dBase 

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

295 

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

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

298 intermediate, I{running} summuation. 

299 

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

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

302 C{float}, except C{complex}. 

303 

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

305 Python's C{math.fsum}. 

306 

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

308 393090_Binary_floating_point_summatiaccurate_full/recipe-393090.py>}, 

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

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

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

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

313 ''' 

314 _math_fsum = None 

315 _n = 0 

316# _ps = [] # partial sums 

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

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

319 

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

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

322 

323 @arg xs: No, one or more items to add (each C{scalar} or an L{Fsum} 

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

325 @kwarg name_RESIDUAL: Optional C{B{name}=NN} for this L{Fsum} and 

326 the C{B{RESIDUAL}=0.0} threshold for L{ResidualError}s. 

327 

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

329 ''' 

330 if name_RESIDUAL: 

331 

332 def _n_R(name=NN, RESIDUAL=None): 

333 return name, RESIDUAL 

334 

335 n, R = _n_R(**name_RESIDUAL) 

336 if R is not None: 

337 self.RESIDUAL(R) 

338 if n: 

339 self.name = n 

340 

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

342 if xs: 

343 self._facc_1(xs, up=False) 

344 

345 def __abs__(self): 

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

347 ''' 

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

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

350 

351 def __add__(self, other): 

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

353 

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

355 

356 @return: The sum (L{Fsum}). 

357 

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

359 ''' 

360 f = self._copy_2(self.__add__) 

361 return f._fadd(other, _add_op_) 

362 

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

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

365 ''' 

366 s, r = self._fprs2 

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

368 

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

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

371 

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

373 

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

375 ''' 

376 return self.ceil 

377 

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

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

380 

381 @return: -1, 0 or +1 (C{int}). 

382 

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

384 ''' 

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

386 return _signOf(s, 0) 

387 

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

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

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

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

392 

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

394 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} (C{bool}) to 

395 ignore L{ResidualError}s and C{B{RESIDUAL}=scalar} 

396 to override the L{RESIDUAL<Fsum.RESIDUAL>}. 

397 

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

399 B{C{RESIDUAL}}. 

400 

401 @see: Method L{Fsum.fdiv}. 

402 ''' 

403 f = self._copy_2(self.__divmod__) 

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

405 

406 def __eq__(self, other): 

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

408 ''' 

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

410 

411 def __float__(self): 

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

413 

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

415 ''' 

416 return float(self._fprs) 

417 

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

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

420 

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

422 

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

424 ''' 

425 return self.floor 

426 

427 def __floordiv__(self, other): 

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

429 

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

431 

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

433 

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

435 ''' 

436 f = self._copy_2(self.__floordiv__) 

437 return f._floordiv(other, _floordiv_op_) 

438 

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

440 '''Not implemented.''' 

441 return _NotImplemented(self, *other) 

442 

443 def __ge__(self, other): 

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

445 ''' 

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

447 

448 def __gt__(self, other): 

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

450 ''' 

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

452 

453 def __hash__(self): # PYCHOK no cover 

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

455 ''' 

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

457 

458 def __iadd__(self, other): 

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

460 

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

462 an iterable of several of the former. 

463 

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

465 

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

467 C{scalar} nor L{Fsum}. 

468 

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

470 ''' 

471 try: 

472 return self._fadd(other, _iadd_op_) 

473 except TypeError: 

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

475 

476 def __ifloordiv__(self, other): 

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

478 

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

480 

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

482 

483 @raise ResidualError: Non-zero, significant residual 

484 in B{C{other}}. 

485 

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

487 

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

489 

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

491 

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

493 ''' 

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

495 

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

497 '''Not implemented.''' 

498 return _NotImplemented(self, other) 

499 

500 def __imod__(self, other): 

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

502 

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

504 

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

506 

507 @see: Method L{Fsum.__divmod__}. 

508 ''' 

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

510 

511 def __imul__(self, other): 

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

513 

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

515 

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

517 

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

519 

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

521 

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

523 ''' 

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

525 

526 def __int__(self): 

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

528 

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

530 and L{Fsum.floor}. 

531 ''' 

532 i, _ = self._fint2 

533 return i 

534 

535 def __invert__(self): # PYCHOK no cover 

536 '''Not implemented.''' 

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

538 return _NotImplemented(self) 

539 

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

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

542 

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

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

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

546 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} (C{bool}) to 

547 ignore L{ResidualError}s and C{B{RESIDUAL}=scalar} 

548 to override the L{RESIDUAL<Fsum.RESIDUAL>}. 

549 

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

551 

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

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

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

555 

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

557 

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

559 is non-zero and significant and either 

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

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

562 C{None}. 

563 

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

565 invocation failed. 

566 

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

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

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

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

571 is given as C{0}. 

572 

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

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

575 ''' 

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

577 

578 def __isub__(self, other): 

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

580 

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

582 an iterable of several of the former. 

583 

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

585 

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

587 

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

589 ''' 

590 try: 

591 return self._fsub(other, _isub_op_) 

592 except TypeError: 

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

594 

595 def __iter__(self): 

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

597 ''' 

598 return iter(self.partials) 

599 

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

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

602 

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

604 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} (C{bool}) to 

605 ignore L{ResidualError}s and C{B{RESIDUAL}=scalar} 

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

607 

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

609 

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

611 

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

613 B{C{RESIDUAL}}. 

614 

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

616 

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

618 

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

620 

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

622 ''' 

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

624 

625 def __le__(self, other): 

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

627 ''' 

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

629 

630 def __len__(self): 

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

632 ''' 

633 return self._n 

634 

635 def __lt__(self, other): 

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

637 ''' 

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

639 

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

641 '''Not implemented.''' 

642 return _NotImplemented(self, other) 

643 

644 def __mod__(self, other): 

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

646 

647 @see: Method L{Fsum.__imod__}. 

648 ''' 

649 f = self._copy_2(self.__mod__) 

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

651 

652 def __mul__(self, other): 

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

654 

655 @see: Method L{Fsum.__imul__}. 

656 ''' 

657 f = self._copy_2(self.__mul__) 

658 return f._fmul(other, _mul_op_) 

659 

660 def __ne__(self, other): 

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

662 ''' 

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

664 

665 def __neg__(self): 

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

667 ''' 

668 f = self._copy_2(self.__neg__) 

669 return f._fset(self._neg) 

670 

671 def __pos__(self): 

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

673 ''' 

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

675 

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

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

678 

679 @see: Method L{Fsum.__ipow__}. 

680 ''' 

681 f = self._copy_2(self.__pow__) 

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

683 

684 def __radd__(self, other): 

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

686 

687 @see: Method L{Fsum.__iadd__}. 

688 ''' 

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

690 return f._fadd(self, _add_op_) 

691 

692 def __rdivmod__(self, other): 

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

694 C{(quotient, remainder)}. 

695 

696 @see: Method L{Fsum.__divmod__}. 

697 ''' 

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

699 return f._fdivmod2(self, _divmod_op_) 

700 

701# def __repr__(self): 

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

703# ''' 

704# return self.toRepr(lenc=True) 

705 

706 def __rfloordiv__(self, other): 

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

708 

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

710 ''' 

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

712 return f._floordiv(self, _floordiv_op_) 

713 

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

715 '''Not implemented.''' 

716 return _NotImplemented(self, other) 

717 

718 def __rmod__(self, other): 

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

720 

721 @see: Method L{Fsum.__imod__}. 

722 ''' 

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

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

725 

726 def __rmul__(self, other): 

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

728 

729 @see: Method L{Fsum.__imul__}. 

730 ''' 

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

732 return f._fmul(self, _mul_op_) 

733 

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

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

736 

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

738 ''' 

739 f = self._copy_2(self.__round__) 

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

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

742 

743 def __rpow__(self, other, *mod): 

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

745 

746 @see: Method L{Fsum.__ipow__}. 

747 ''' 

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

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

750 

751 def __rsub__(self, other): 

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

753 

754 @see: Method L{Fsum.__isub__}. 

755 ''' 

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

757 return f._fsub(self, _sub_op_) 

758 

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

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

761 

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

763 ''' 

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

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

766 

767 def __str__(self): 

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

769 ''' 

770 return self.toStr(lenc=True) 

771 

772 def __sub__(self, other): 

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

774 

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

776 

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

778 

779 @see: Method L{Fsum.__isub__}. 

780 ''' 

781 f = self._copy_2(self.__sub__) 

782 return f._fsub(other, _sub_op_) 

783 

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

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

786 

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

788 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} (C{bool}) to 

789 ignore L{ResidualError}s and C{B{RESIDUAL}=scalar} 

790 to override the L{RESIDUAL<Fsum.RESIDUAL>}. 

791 

792 @return: The quotient (L{Fsum}). 

793 

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

795 B{C{RESIDUAL}}. 

796 

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

798 ''' 

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

800 

801 __trunc__ = __int__ 

802 

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

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

805 __div__ = __truediv__ 

806 __idiv__ = __itruediv__ 

807 __long__ = __int__ 

808 __nonzero__ = __bool__ 

809 __rdiv__ = __rtruediv__ 

810 

811 def as_integer_ratio(self): 

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

813 

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

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

816 non-zero, positive. 

817 

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

819 ''' 

820 n, r = self._fint2 

821 if r: 

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

823 n *= d 

824 n += i 

825 else: # PYCHOK no cover 

826 d = 1 

827 return n, d 

828 

829 @property_RO 

830 def as_iscalar(self): 

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

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

833 ''' 

834 s, r = self._fprs2 

835 return self if r else s 

836 

837 @property_RO 

838 def ceil(self): 

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

840 C{float} in Python 2-). 

841 

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

843 

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

845 L{Fsum.imag} and L{Fsum.real}. 

846 ''' 

847 s, r = self._fprs2 

848 c = _ceil(s) + int(r) - 1 

849 while r > (c - s): # (s + r) > c 

850 c += 1 

851 return c # _ceil(self._n_d) 

852 

853 cmp = __cmp__ 

854 

855 def _cmp_0(self, other, op): 

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

857 ''' 

858 if _isFsumTuple(other): 

859 s = self._ps_1sum(*other._ps) 

860 elif self._scalar(other, op): 

861 s = self._ps_1sum(other) 

862 else: 

863 s = self.signOf() # res=True 

864 return s 

865 

866 def copy(self, deep=False, name=NN): 

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

868 

869 @return: The copy (L{Fsum}). 

870 ''' 

871 f = _Named.copy(self, deep=deep, name=name) 

872 if f._ps is self._ps: 

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

874 if not deep: 

875 f._n = 1 

876 # assert f._Fsum is f 

877 return f 

878 

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

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

881 ''' 

882 n = name or which.__name__ 

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

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

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

886 # assert f._n == self._n 

887 # assert f._Fsum is f 

888 return f 

889 

890 def _copy_2r(self, other, which): 

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

892 ''' 

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

894 self._copy_2(which)._fset(other) 

895 

896# def _copy_RESIDUAL(self, other): 

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

898# ''' 

899# R = other._RESIDUAL 

900# if R is not Fsum._RESIDUAL: 

901# self._RESIDUAL = R 

902 

903 divmod = __divmod__ 

904 

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

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

907 ''' 

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

909 

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

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

912 ''' 

913 E, t = _xError2(X) 

914 if mod: 

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

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

917 

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

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

920 ''' 

921 E, t = _xError2(X) 

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

923 return E(u, txt=t, cause=X) 

924 

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

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

927 ''' 

928 if xs: 

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

930 ps = self._ps 

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

932 return self 

933 

934 def _facc_1(self, xs, **up): 

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

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

937 ''' 

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

939 self._facc(xs, origin=1, **up) 

940 

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

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

943 ''' 

944 try: 

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

946 except Exception as X: 

947 raise self._ErrorX(X, op, other) 

948 

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

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

951 ''' 

952 def _N(X): 

953 return X._ps_neg 

954 

955 def _n(x): 

956 return -float(x) 

957 

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

959 

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

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

962 ''' 

963 def _Pow4(p): 

964 r = 0 

965 if _isFsumTuple(p): 

966 s, r = p._fprs2 

967 if r: 

968 m = Fsum._pow 

969 else: # scalar 

970 return _Pow4(s) 

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

972 p = s = int(p) 

973 m = Fsum._pow_int 

974 else: 

975 p = s = _2float(power=p) 

976 m = Fsum._pow_scalar 

977 return m, p, s, r 

978 

979 _Pow, p, s, r = _Pow4(power) 

980 if p: # and xs: 

981 op = which.__name__ 

982 _flt = float 

983 _Fs = Fsum 

984 _isa = isinstance 

985 _pow = self._pow_2_3 

986 

987 def _P(X): 

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

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

990 

991 def _p(x): 

992 x = _flt(x) 

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

994 if f and r: 

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

996 return f 

997 

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

999 else: 

1000 f = self._facc_scalar_(float(len(xs))) # x**0 == 1 

1001 return f 

1002 

1003 def _facc_scalar(self, xs, **up): 

1004 '''(INTERNAL) Accumulate all C{xs}, known to be scalar. 

1005 ''' 

1006 if xs: 

1007 _ = self._ps_acc(self._ps, xs, **up) 

1008 return self 

1009 

1010 def _facc_scalar_(self, *xs, **up): 

1011 '''(INTERNAL) Accumulate all positional C{xs}, known to be scalar. 

1012 ''' 

1013 if xs: 

1014 _ = self._ps_acc(self._ps, xs, **up) 

1015 return self 

1016 

1017# def _facc_up(self, up=True): 

1018# '''(INTERNAL) Update the C{partials}, by removing 

1019# and re-accumulating the final C{partial}. 

1020# ''' 

1021# ps = self._ps 

1022# while len(ps) > 1: 

1023# p = ps.pop() 

1024# if p: 

1025# n = self._n 

1026# _ = self._ps_acc(ps, (p,), up=False) 

1027# self._n = n 

1028# break 

1029# return self._update() if up else self 

1030 

1031 def fadd(self, xs=()): 

1032 '''Add an iterable's items to this instance. 

1033 

1034 @arg xs: Iterable of items to add (each C{scalar} 

1035 or an L{Fsum} or L{Fsum2Tuple} instance). 

1036 

1037 @return: This instance (L{Fsum}). 

1038 

1039 @raise OverflowError: Partial C{2sum} overflow. 

1040 

1041 @raise TypeError: An invalid B{C{xs}} item. 

1042 

1043 @raise ValueError: Invalid or non-finite B{C{xs}} value. 

1044 ''' 

1045 if _isFsumTuple(xs): 

1046 self._facc_scalar(xs._ps) 

1047 elif isscalar(xs): # for backward compatibility 

1048 self._facc_scalar_(_2float(x=xs)) # PYCHOK no cover 

1049 elif xs: # _xiterable(xs) 

1050 self._facc(xs) 

1051 return self 

1052 

1053 def fadd_(self, *xs): 

1054 '''Add all positional items to this instance. 

1055 

1056 @arg xs: Values to add (each C{scalar} or an L{Fsum} 

1057 or L{Fsum2Tuple} instance), all positional. 

1058 

1059 @see: Method L{Fsum.fadd} for further details. 

1060 ''' 

1061 return self._facc_1(xs) 

1062 

1063 def _fadd(self, other, op, **up): # in .fmath.Fhorner 

1064 '''(INTERNAL) Apply C{B{self} += B{other}}. 

1065 ''' 

1066 if not self._ps: # new Fsum(x) 

1067 self._fset(other, op=op, **up) 

1068 elif _isFsumTuple(other): 

1069 self._facc_scalar(other._ps, **up) 

1070 elif self._scalar(other, op): 

1071 self._facc_scalar_(other, **up) 

1072 return self 

1073 

1074 fcopy = copy # for backward compatibility 

1075 fdiv = __itruediv__ 

1076 fdivmod = __divmod__ 

1077 

1078 def _fdivmod2(self, other, op, **raiser_RESIDUAL): 

1079 '''(INTERNAL) Apply C{B{self} %= B{other}} and return a L{DivMod2Tuple}. 

1080 ''' 

1081 # result mostly follows CPython function U{float_divmod 

1082 # <https://GitHub.com/python/cpython/blob/main/Objects/floatobject.c>}, 

1083 # but at least divmod(-3, 2) equals Cpython's result (-2, 1). 

1084 q = self._truediv(other, op, **raiser_RESIDUAL).floor 

1085 if q: # == float // other == floor(float / other) 

1086 self -= Fsum(q) * other # NOT other * q! 

1087 

1088 s = signOf(other) # make signOf(self) == signOf(other) 

1089 if s and self.signOf() == -s: # PYCHOK no cover 

1090 self += other 

1091 q -= 1 

1092# t = self.signOf() 

1093# if t and t != s: 

1094# raise self._Error(op, other, _AssertionError, txt=signOf.__name__) 

1095 return DivMod2Tuple(q, self) # q is C{int} in Python 3+, but C{float} in Python 2- 

1096 

1097 def _finite(self, other, op=None): 

1098 '''(INTERNAL) Return B{C{other}} if C{finite}. 

1099 ''' 

1100 if _isfinite(other): 

1101 return other 

1102 raise ValueError(_not_finite_) if op is None else \ 

1103 self._Error(op, other, _ValueError, txt=_not_finite_) 

1104 

1105 def fint(self, name=NN, **raiser_RESIDUAL): 

1106 '''Return this instance' current running sum as C{integer}. 

1107 

1108 @kwarg name: Optional name (C{str}), overriding C{"fint"}. 

1109 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} (C{bool}) to 

1110 ignore L{ResidualError}s and C{B{RESIDUAL}=scalar} 

1111 to override the L{RESIDUAL<Fsum.RESIDUAL>}. 

1112 

1113 @return: The C{integer} sum (L{Fsum}) if this instance C{is_integer} 

1114 with a zero or insignificant I{integer} residual. 

1115 

1116 @raise ResidualError: Non-zero, significant residual or invalid 

1117 B{C{RESIDUAL}}. 

1118 

1119 @see: Methods L{Fsum.fint2}, L{Fsum.int_float} and L{Fsum.is_integer}. 

1120 ''' 

1121 i, r = self._fint2 

1122 if r: 

1123 R = self._raiser(r, i, **raiser_RESIDUAL) 

1124 if R: 

1125 t = _stresidual(_integer_, r, **R) 

1126 raise ResidualError(_integer_, i, txt=t) 

1127 f = self._copy_2(self.fint, name=name) 

1128 return f._fset(i) 

1129 

1130 def fint2(self, **name): 

1131 '''Return this instance' current running sum as C{int} and the 

1132 I{integer} residual. 

1133 

1134 @kwarg name: Optional name (C{str}). 

1135 

1136 @return: An L{Fsum2Tuple}C{(fsum, residual)} with C{fsum} 

1137 an C{int} and I{integer} C{residual} a C{float} or 

1138 C{INT0} if the C{fsum} is considered to be I{exact}. 

1139 ''' 

1140 return Fsum2Tuple(*self._fint2, **name) 

1141 

1142 @Property_RO 

1143 def _fint2(self): # see ._fset 

1144 '''(INTERNAL) Get 2-tuple (C{int}, I{integer} residual). 

1145 ''' 

1146 s, r = self._fprs2 

1147 i = int(s) 

1148 n = len(self._ps) 

1149 r = self._ps_1sum(i) if r and n > 1 else float(s - i) 

1150 return i, (r or INT0) # Fsum2Tuple? 

1151 

1152 @deprecated_property_RO 

1153 def float_int(self): # PYCHOK no cover 

1154 '''DEPRECATED, use method C{Fsum.int_float}.''' 

1155 return self.int_float() # raiser=False 

1156 

1157 @property_RO 

1158 def floor(self): 

1159 '''Get this instance' C{floor} (C{int} in Python 3+, but 

1160 C{float} in Python 2-). 

1161 

1162 @note: This C{floor} takes the C{residual} into account. 

1163 

1164 @see: Method L{Fsum.int_float} and properties L{Fsum.ceil}, 

1165 L{Fsum.imag} and L{Fsum.real}. 

1166 ''' 

1167 s, r = self._fprs2 

1168 f = _floor(s) + _floor(r) + 1 

1169 while (f - s) > r: # f > (s + r) 

1170 f -= 1 

1171 return f # _floor(self._n_d) 

1172 

1173# ffloordiv = __ifloordiv__ # for naming consistency 

1174# floordiv = __floordiv__ # for naming consistency 

1175 

1176 def _floordiv(self, other, op, **raiser_RESIDUAL): # rather _ffloordiv? 

1177 '''Apply C{B{self} //= B{other}}. 

1178 ''' 

1179 q = self._ftruediv(other, op, **raiser_RESIDUAL) # == self 

1180 return self._fset(q.floor) # floor(q) 

1181 

1182 fmul = __imul__ 

1183 

1184 def _fmul(self, other, op): 

1185 '''(INTERNAL) Apply C{B{self} *= B{other}}. 

1186 ''' 

1187 if _isFsumTuple(other): 

1188 if len(self._ps) != 1: 

1189 f = self._mul_Fsum(other, op) 

1190 elif len(other._ps) != 1: # and len(self._ps) == 1 

1191 f = other._mul_scalar(self._ps[0], op) 

1192 else: # len(other._ps) == len(self._ps) == 1 

1193 f = self._finite(self._ps[0] * other._ps[0]) 

1194 else: 

1195 s = self._scalar(other, op) 

1196 f = self._mul_scalar(s, op) 

1197 return self._fset(f) # n=len(self) + 1 

1198 

1199 def fover(self, over, **raiser_RESIDUAL): 

1200 '''Apply C{B{self} /= B{over}} and summate. 

1201 

1202 @arg over: An L{Fsum} or C{scalar} denominator. 

1203 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} (C{bool}) to 

1204 ignore L{ResidualError}s and C{B{RESIDUAL}=scalar} 

1205 to override the L{RESIDUAL<Fsum.RESIDUAL>}. 

1206 

1207 @return: Precision running sum (C{float}). 

1208 

1209 @raise ResidualError: Non-zero, significant residual or invalid 

1210 B{C{RESIDUAL}}. 

1211 

1212 @see: Methods L{Fsum.fsum} and L{Fsum.__itruediv__}. 

1213 ''' 

1214 return float(self.fdiv(over, **raiser_RESIDUAL)._fprs) 

1215 

1216 fpow = __ipow__ 

1217 

1218 def _fpow(self, other, op, *mod, **raiser_RESIDUAL): 

1219 '''Apply C{B{self} **= B{other}}, optional B{C{mod}} or C{None}. 

1220 ''' 

1221 if mod: 

1222 if mod[0] is not None: # == 3-arg C{pow} 

1223 f = self._pow_2_3(self, other, other, op, *mod, **raiser_RESIDUAL) 

1224 elif self.is_integer(): 

1225 # return an exact C{int} for C{int}**C{int} 

1226 i, _ = self._fint2 # assert _ == 0 

1227 x, r = _2scalar2(other) # C{int}, C{float} or other 

1228 f = _Psum_(i)._pow_Fsum(other, op, **raiser_RESIDUAL) if r else \ 

1229 self._pow_2_3(i, x, other, op, **raiser_RESIDUAL) 

1230 else: # mod[0] is None, power(self, other) 

1231 f = self._pow(other, other, op, **raiser_RESIDUAL) 

1232 else: # pow(self, other) 

1233 f = self._pow(other, other, op, **raiser_RESIDUAL) 

1234 return self._fset(f) # n=max(len(self), 1) 

1235 

1236 @Property_RO 

1237 def _fprs(self): 

1238 '''(INTERNAL) Get and cache this instance' precision 

1239 running sum (C{float} or C{int}), ignoring C{residual}. 

1240 

1241 @note: The precision running C{fsum} after a C{//=} or 

1242 C{//} C{floor} division is C{int} in Python 3+. 

1243 ''' 

1244 s, _ = self._fprs2 

1245 return s # ._fprs2.fsum 

1246 

1247 @Property_RO 

1248 def _fprs2(self): 

1249 '''(INTERNAL) Get and cache this instance' precision 

1250 running sum and residual (L{Fsum2Tuple}). 

1251 ''' 

1252 ps = self._ps 

1253 n = len(ps) - 2 

1254 if n > 0: # len(ps) > 2 

1255 s = _psum(ps) 

1256 n = len(ps) - 2 

1257 if n > 0: 

1258 r = self._ps_1sum(s) 

1259 return Fsum2Tuple(*_s_r(s, r)) 

1260 if n == 0: # len(ps) == 2 

1261 s, r = _s_r(*_2sum(*ps)) 

1262 ps[:] = (r, s) if r else (s,) 

1263 elif ps: # len(ps) == 1 

1264 s, r = ps[0], INT0 

1265 else: # len(ps) == 0 

1266 s, r = _0_0, INT0 

1267 ps[:] = s, 

1268 # assert self._ps is ps 

1269 return Fsum2Tuple(s, r) 

1270 

1271 def fset_(self, *xs): 

1272 '''Replace this instance' value with all positional items. 

1273 

1274 @arg xs: Optional, new values (each C{scalar} or 

1275 an L{Fsum} or L{Fsum2Tuple} instance), 

1276 all positional. 

1277 

1278 @return: This instance, replaced (C{Fsum}). 

1279 

1280 @see: Method L{Fsum.fadd} for further details. 

1281 ''' 

1282 f = xs[0] if len(xs) == 1 else ( 

1283 Fsum(*xs) if xs else _0_0) 

1284 return self._fset(f) 

1285 

1286 def _fset(self, other, n=0, up=True, **op): 

1287 '''(INTERNAL) Overwrite this instance with an other or a C{scalar}. 

1288 ''' 

1289 if other is self: 

1290 pass # from ._fmul, ._ftruediv and ._pow_0_1 

1291 elif _isFsumTuple(other): 

1292 self._ps[:] = other._ps 

1293 self._n = n or other._n 

1294# self._copy_RESIDUAL(other) 

1295 if up: # use or zap the C{Property_RO} values 

1296 Fsum._fint2._update_from(self, other) 

1297 Fsum._fprs ._update_from(self, other) 

1298 Fsum._fprs2._update_from(self, other) 

1299 elif isscalar(other): 

1300 s = float(self._finite(other, **op)) if op else other 

1301 self._ps[:] = s, 

1302 self._n = n or 1 

1303 if up: 

1304 i = int(s) # see ._fint2 

1305 t = i, ((s - i) or INT0) 

1306 # Property_ROs _fint2, _fprs and _fprs2 can't be a Property: 

1307 # Property's _fset zaps the value just set by the @setter 

1308 self.__dict__.update(_fint2=t, _fprs=s, _fprs2=Fsum2Tuple(s, INT0)) 

1309 else: # PYCHOK no cover 

1310 op = _xkwds_get(op, op=_fset_op_) 

1311 raise self._Error(op, other, _TypeError) 

1312 return self 

1313 

1314 def _fset_ps(self, other, n=0): # in .fmath 

1315 '''(INTERNAL) Set partials from a known C{scalar}, L{Fsum} or L{Fsum2Tuple}. 

1316 ''' 

1317 if _isFsumTuple(other): 

1318 self._ps[:] = other._ps 

1319 self._n = n or other._n 

1320 else: # assert isscalar(other) 

1321 self._ps[:] = other, 

1322 self._n = n or 1 

1323 return self 

1324 

1325 def fsub(self, xs=()): 

1326 '''Subtract an iterable's items from this instance. 

1327 

1328 @see: Method L{Fsum.fadd} for further details. 

1329 ''' 

1330 return self._facc_neg(xs) 

1331 

1332 def fsub_(self, *xs): 

1333 '''Subtract all positional items from this instance. 

1334 

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

1336 ''' 

1337 return self._fsub(xs[0], _sub_op_) if len(xs) == 1 else \ 

1338 self._facc_neg(xs, origin=1) 

1339 

1340 def _fsub(self, other, op): 

1341 '''(INTERNAL) Apply C{B{self} -= B{other}}. 

1342 ''' 

1343 if _isFsumTuple(other): 

1344 if other is self: # or other._fprs2 == self._fprs2: 

1345 self._fset(_0_0, n=len(self) * 2) 

1346 elif other._ps: 

1347 self._facc_scalar(other._ps_neg) 

1348 elif self._scalar(other, op): 

1349 self._facc_scalar_(-other) 

1350 return self 

1351 

1352 def fsum(self, xs=()): 

1353 '''Add an iterable's items, summate and return the 

1354 current precision running sum. 

1355 

1356 @arg xs: Iterable of items to add (each item C{scalar} 

1357 or an L{Fsum} or L{Fsum2Tuple} instance). 

1358 

1359 @return: Precision running sum (C{float} or C{int}). 

1360 

1361 @see: Method L{Fsum.fadd}. 

1362 

1363 @note: Accumulation can continue after summation. 

1364 ''' 

1365 return self._facc(xs)._fprs 

1366 

1367 def fsum_(self, *xs): 

1368 '''Add any positional items, summate and return the 

1369 current precision running sum. 

1370 

1371 @arg xs: Items to add (each C{scalar} or an L{Fsum} 

1372 or L{Fsum2Tuple} instance), all positional. 

1373 

1374 @return: Precision running sum (C{float} or C{int}). 

1375 

1376 @see: Methods L{Fsum.fsum}, L{Fsum.Fsum_} and L{Fsum.fsumf_}. 

1377 ''' 

1378 return self._facc_1(xs)._fprs 

1379 

1380 @property_RO 

1381 def _Fsum(self): # like L{Fsum2Tuple._Fsum}, for C{_2floats}, .fstats 

1382 return self # NOT @Property_RO, see .copy and ._copy_2 

1383 

1384 def Fsum_(self, *xs, **name): 

1385 '''Like method L{Fsum.fsum_} but returning a named L{Fsum}. 

1386 

1387 @kwarg name: Optional name (C{str}). 

1388 

1389 @return: Copy of this updated instance (L{Fsum}). 

1390 ''' 

1391 return self._facc_1(xs)._copy_2(self.Fsum_, **name) 

1392 

1393 def Fsum2Tuple_(self, *xs, **name): 

1394 '''Like method L{Fsum.fsum_} but returning a named L{Fsum2Tuple}. 

1395 

1396 @kwarg name: Optional name (C{str}). 

1397 

1398 @return: Precision running sum (L{Fsum2Tuple}). 

1399 ''' 

1400 return Fsum2Tuple(self._facc_1(xs)._fprs2, **name) 

1401 

1402 def fsum2(self, xs=(), name=NN): 

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

1404 current precision running sum I{and} the C{residual}. 

1405 

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

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

1408 @kwarg name: Optional name (C{str}). 

1409 

1410 @return: L{Fsum2Tuple}C{(fsum, residual)} with C{fsum} the 

1411 current precision running sum and C{residual}, the 

1412 (precision) sum of the remaining C{partials}. The 

1413 C{residual is INT0} if the C{fsum} is considered 

1414 to be I{exact}. 

1415 

1416 @see: Methods L{Fsum.fint2}, L{Fsum.fsum} and L{Fsum.fsum2_} 

1417 ''' 

1418 t = self._facc(xs)._fprs2 

1419 return t.dup(name=name) if name else t 

1420 

1421 def fsum2_(self, *xs): 

1422 '''Add any positional items, summate and return the current 

1423 precision running sum and the I{differential}. 

1424 

1425 @arg xs: Values to add (each C{scalar} or an L{Fsum} or 

1426 L{Fsum2Tuple} instance), all positional. 

1427 

1428 @return: 2Tuple C{(fsum, delta)} with the current, precision 

1429 running C{fsum} like method L{Fsum.fsum} and C{delta}, 

1430 the difference with previous running C{fsum}, C{float}. 

1431 

1432 @see: Methods L{Fsum.fsum_} and L{Fsum.fsum}. 

1433 ''' 

1434 return self._fsum2(xs, self._facc_1) 

1435 

1436 def _fsum2(self, xs, _facc, **origin): 

1437 '''(INTERNAL) Helper for L{Fsum.fsum2_} and L{Fsum.fsum2f_}. 

1438 ''' 

1439 p, q = self._fprs2 

1440 if xs: 

1441 s, r = _facc(xs, **origin)._fprs2 

1442 return s, _2delta(s - p, r - q) # _fsum(_1primed((s, -p, r, -q)) 

1443 else: 

1444 return p, _0_0 

1445 

1446 def fsumf_(self, *xs): 

1447 '''Like method L{Fsum.fsum_} iff I{all} C{B{xs}} are I{known to be scalar}. 

1448 ''' 

1449 return self._facc_scalar(xs)._fprs 

1450 

1451 def Fsumf_(self, *xs): 

1452 '''Like method L{Fsum.Fsum_} iff I{all} C{B{xs}} are I{known to be scalar}. 

1453 ''' 

1454 return self._facc_scalar(xs)._copy_2(self.Fsumf_) 

1455 

1456 def fsum2f_(self, *xs): 

1457 '''Like method L{Fsum.fsum2_} iff I{all} C{B{xs}} are I{known to be scalar}. 

1458 ''' 

1459 return self._fsum2(xs, self._facc_scalar, origin=1) 

1460 

1461# ftruediv = __itruediv__ # for naming consistency? 

1462 

1463 def _ftruediv(self, other, op, **raiser_RESIDUAL): 

1464 '''(INTERNAL) Apply C{B{self} /= B{other}}. 

1465 ''' 

1466 n = _1_0 

1467 if _isFsumTuple(other): 

1468 if other is self or self == other: 

1469 return self._fset(n, n=len(self)) 

1470 d, r = other._fprs2 

1471 if r: 

1472 R = self._raiser(r, d, **raiser_RESIDUAL) 

1473 if R: 

1474 raise self._ResidualError(op, other, r, **R) 

1475 d, n = other.as_integer_ratio() 

1476 else: 

1477 d = self._scalar(other, op) 

1478 try: 

1479 s = n / d 

1480 except Exception as X: 

1481 raise self._ErrorX(X, op, other) 

1482 f = self._mul_scalar(s, _mul_op_) # handles 0, INF, NAN 

1483 return self._fset(f) 

1484 

1485 @property_RO 

1486 def imag(self): 

1487 '''Get the C{imaginary} part of this instance (C{0.0}, always). 

1488 

1489 @see: Property L{Fsum.real}. 

1490 ''' 

1491 return _0_0 

1492 

1493 def int_float(self, **raiser_RESIDUAL): 

1494 '''Return this instance' current running sum as C{int} or C{float}. 

1495 

1496 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} (C{bool}) to 

1497 ignore L{ResidualError}s and C{B{RESIDUAL}=scalar} 

1498 to override the L{RESIDUAL<Fsum.RESIDUAL>}. 

1499 

1500 @return: This C{integer} sum if this instance C{is_integer}, 

1501 otherwise return the C{float} sum if the residual is 

1502 zero or not significant. 

1503 

1504 @raise ResidualError: Non-zero, significant residual or invalid 

1505 B{C{RESIDUAL}}. 

1506 

1507 @see: Methods L{Fsum.fint}, L{Fsum.fint2}, L{Fsum.RESIDUAL} and 

1508 property L{Fsum.as_iscalar}. 

1509 ''' 

1510 s, r = self._fint2 

1511 if r: 

1512 s, r = self._fprs2 

1513 if r: # PYCHOK no cover 

1514 R = self._raiser(r, s, **raiser_RESIDUAL) 

1515 if R: 

1516 t = _stresidual(_non_zero_, r, **R) 

1517 raise ResidualError(int_float=s, txt=t) 

1518 s = float(s) 

1519 return s 

1520 

1521 def is_exact(self): 

1522 '''Is this instance' running C{fsum} considered to be exact? 

1523 (C{bool}), C{True} only if the C{residual is }L{INT0}. 

1524 ''' 

1525 return self.residual is INT0 

1526 

1527 def is_integer(self): 

1528 '''Is this instance' running sum C{integer}? (C{bool}). 

1529 

1530 @see: Methods L{Fsum.fint}, L{Fsum.fint2} and L{Fsum.is_scalar}. 

1531 ''' 

1532 _, r = self._fint2 

1533 return False if r else True 

1534 

1535 def is_math_fsum(self): 

1536 '''Return whether functions L{fsum}, L{fsum_}, L{fsum1} and 

1537 L{fsum1_} plus partials summation are based on Python's 

1538 C{math.fsum} or not. 

1539 

1540 @return: C{2} if all functions and partials summation 

1541 are based on C{math.fsum}, C{True} if only 

1542 the functions are based on C{math.fsum} (and 

1543 partials summation is not) or C{False} if 

1544 none are. 

1545 ''' 

1546 f = Fsum._math_fsum 

1547 return 2 if _psum is f else bool(f) 

1548 

1549 def is_scalar(self, **raiser_RESIDUAL): 

1550 '''Is this instance' running sum C{scalar} without residual or with 

1551 a residual I{ratio} not exceeding the RESIDUAL threshold? 

1552 

1553 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} (C{bool}) to ignore 

1554 L{ResidualError}s and C{B{RESIDUAL}=scalar} to override 

1555 the L{RESIDUAL<Fsum.RESIDUAL>} threshold. 

1556 

1557 @return: C{True} if this instance' non-zero residual C{ratio} exceeds 

1558 the L{RESIDUAL<Fsum.RESIDUAL>} threshold (C{bool}). 

1559 

1560 @raise ResidualError: Non-zero, significant residual or invalid 

1561 B{C{RESIDUAL}}. 

1562 

1563 @see: Method L{Fsum.RESIDUAL}, L{Fsum.is_integer} and property 

1564 L{Fsum.as_iscalar}. 

1565 ''' 

1566 s, r = self._fprs2 

1567 return False if r and self._raiser(r, s, **raiser_RESIDUAL) else True 

1568 

1569 def _mul_Fsum(self, other, op=_mul_op_): # in .fmath.Fhorner 

1570 '''(INTERNAL) Return C{B{self} * B{other}} as L{Fsum} or C{0}. 

1571 ''' 

1572 # assert _isFsumTuple(other) 

1573 if self._ps and other._ps: 

1574 f = self._ps_mul(op, *other._ps) # NO .as_iscalar! 

1575 else: 

1576 f = _0_0 

1577 return f 

1578 

1579 def _mul_scalar(self, factor, op): # in .fmath.Fhorner 

1580 '''(INTERNAL) Return C{B{self} * scalar B{factor}} as L{Fsum}, C{0.0} or C{self}. 

1581 ''' 

1582 # assert isscalar(factor) 

1583 if self._ps and self._finite(factor, op): 

1584 f = self if factor == _1_0 else ( 

1585 self._neg if factor == _N_1_0 else 

1586 self._ps_mul(op, factor).as_iscalar) 

1587 else: 

1588 f = _0_0 

1589 return f 

1590 

1591# @property_RO 

1592# def _n_d(self): 

1593# n, d = self.as_integer_ratio() 

1594# return n / d 

1595 

1596 @property_RO 

1597 def _neg(self): 

1598 '''(INTERNAL) Return C{Fsum(-self)} or scalar C{NEG0}. 

1599 ''' 

1600 return _Psum(self._ps_neg) if self._ps else NEG0 

1601 

1602 @property_RO 

1603 def partials(self): 

1604 '''Get this instance' current, partial sums (C{tuple} of C{float}s). 

1605 ''' 

1606 return tuple(self._ps) 

1607 

1608 def pow(self, x, *mod, **raiser_RESIDUAL): 

1609 '''Return C{B{self}**B{x}} as L{Fsum}. 

1610 

1611 @arg x: The exponent (C{scalar} or L{Fsum}). 

1612 @arg mod: Optional modulus (C{int} or C{None}) for the 3-argument 

1613 C{pow(B{self}, B{other}, B{mod})} version. 

1614 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} (C{bool}) to 

1615 ignore L{ResidualError}s and C{B{RESIDUAL}=scalar} 

1616 to override the L{RESIDUAL<Fsum.RESIDUAL>}. 

1617 

1618 @return: The C{pow(self, B{x})} or C{pow(self, B{x}, *B{mod})} 

1619 result (L{Fsum}). 

1620 

1621 @raise ResidualError: Non-zero, significant residual or invalid 

1622 B{C{RESIDUAL}}. 

1623 

1624 @note: If B{C{mod}} is given as C{None}, the result will be an 

1625 C{integer} L{Fsum} provided this instance C{is_integer} 

1626 or set to C{integer} by an L{Fsum.fint} call. 

1627 

1628 @see: Methods L{Fsum.__ipow__}, L{Fsum.fint}, L{Fsum.is_integer} 

1629 and L{Fsum.root}. 

1630 ''' 

1631 f = self._copy_2(self.pow) 

1632 return f._fpow(x, _pow_op_, *mod, **raiser_RESIDUAL) # f = pow(f, x, *mod) 

1633 

1634 def _pow(self, other, unused, op, **raiser_RESIDUAL): 

1635 '''Return C{B{self} ** B{other}}. 

1636 ''' 

1637 if _isFsumTuple(other): 

1638 f = self._pow_Fsum(other, op, **raiser_RESIDUAL) 

1639 elif self._scalar(other, op): 

1640 x = self._finite(other, op) 

1641 f = self._pow_scalar(x, other, op, **raiser_RESIDUAL) 

1642 else: 

1643 f = self._pow_0_1(0, other) 

1644 return f 

1645 

1646 def _pow_0_1(self, x, other): 

1647 '''(INTERNAL) Return B{C{self}**1} or C{B{self}**0 == 1.0}. 

1648 ''' 

1649 return self if x else (1 if isint(other) and self.is_integer() else _1_0) 

1650 

1651 def _pow_2_3(self, b, x, other, op, *mod, **raiser_RESIDUAL): 

1652 '''(INTERNAL) 2-arg C{pow(B{b}, scalar B{x})} and 3-arg C{pow(B{b}, 

1653 B{x}, int B{mod} or C{None})}, embellishing errors. 

1654 ''' 

1655 

1656 if mod: # b, x, mod all C{int}, unless C{mod} is C{None} 

1657 m = mod[0] 

1658 # assert _isFsumTuple(b) 

1659 

1660 def _s(s, r): 

1661 R = self._raiser(r, s, **raiser_RESIDUAL) 

1662 if R: 

1663 raise self._ResidualError(op, other, r, mod=m, **R) 

1664 return s 

1665 

1666 b = _s(*(b._fprs2 if m is None else b._fint2)) 

1667 x = _s(*_2scalar2(x)) 

1668 

1669 try: 

1670 # 0**INF == 0.0, 1**INF == 1.0, -1**2.3 == -(1**2.3) 

1671 s = pow(b, x, *mod) 

1672 if iscomplex(s): 

1673 # neg**frac == complex in Python 3+, but ValueError in 2- 

1674 raise ValueError(_strcomplex(s, b, x, *mod)) 

1675 return self._finite(s) 

1676 except Exception as X: 

1677 raise self._ErrorX(X, op, other, *mod) 

1678 

1679 def _pow_Fsum(self, other, op, **raiser_RESIDUAL): 

1680 '''(INTERNAL) Return C{B{self} **= B{other}} for C{_isFsumTuple(other)}. 

1681 ''' 

1682 # assert _isFsumTuple(other) 

1683 x, r = other._fprs2 

1684 f = self._pow_scalar(x, other, op, **raiser_RESIDUAL) 

1685 if f and r: 

1686 f *= self._pow_scalar(r, other, op, **raiser_RESIDUAL) 

1687 return f 

1688 

1689 def _pow_int(self, x, other, op, **raiser_RESIDUAL): 

1690 '''(INTERNAL) Return C{B{self} **= B{x}} for C{int B{x} >= 0}. 

1691 ''' 

1692 # assert isint(x) and x >= 0 

1693 ps = self._ps 

1694 if len(ps) > 1: 

1695 _mul_Fsum = Fsum._mul_Fsum 

1696 if x > 4: 

1697 p = self 

1698 f = self if (x & 1) else _Psum_(_1_0) 

1699 m = x >> 1 # // 2 

1700 while m: 

1701 p = _mul_Fsum(p, p, op) # p **= 2 

1702 if (m & 1): 

1703 f = _mul_Fsum(f, p, op) # f *= p 

1704 m >>= 1 # //= 2 

1705 elif x > 1: # self**2, 3, or 4 

1706 f = _mul_Fsum(self, self, op) 

1707 if x > 2: # self**3 or 4 

1708 p = self if x < 4 else f 

1709 f = _mul_Fsum(f, p, op) 

1710 else: # self**1 or self**0 == 1 or _1_0 

1711 f = self._pow_0_1(x, other) 

1712 elif ps: # self._ps[0]**x 

1713 f = self._pow_2_3(ps[0], x, other, op, **raiser_RESIDUAL) 

1714 else: # PYCHOK no cover 

1715 # 0**pos_int == 0, but 0**0 == 1 

1716 f = 0 if x else 1 

1717 return f 

1718 

1719 def _pow_scalar(self, x, other, op, **raiser_RESIDUAL): 

1720 '''(INTERNAL) Return C{self**B{x}} for C{scalar B{x}}. 

1721 ''' 

1722 s, r = self._fprs2 

1723 if r: 

1724 # assert s != 0 

1725 if isint(x, both=True): # self**int 

1726 x = int(x) 

1727 y = abs(x) 

1728 if y > 1: 

1729 f = self._pow_int(y, other, op, **raiser_RESIDUAL) 

1730 if x > 0: # i.e. > 1 

1731 return f # Fsum or scalar 

1732 # assert x < 0 # i.e. < -1 

1733 if _isFsum(f): 

1734 s, r = f._fprs2 

1735 if r: 

1736 return _1_Over(f, op, **raiser_RESIDUAL) 

1737 else: # scalar 

1738 s = f 

1739 # use s**(-1) to get the CPython 

1740 # float_pow error iff s is zero 

1741 x = -1 

1742 elif x < 0: # self**(-1) 

1743 return _1_Over(self, op, **raiser_RESIDUAL) # 1 / self 

1744 else: # self**1 or self**0 

1745 return self._pow_0_1(x, other) # self, 1 or 1.0 

1746 else: # self**fractional 

1747 R = self._raiser(r, s, **raiser_RESIDUAL) 

1748 if R: 

1749 raise self._ResidualError(op, other, r, **R) 

1750 n, d = self.as_integer_ratio() 

1751 if abs(n) > abs(d): 

1752 n, d, x = d, n, (-x) 

1753 s = n / d 

1754 # assert isscalar(s) and isscalar(x) 

1755 return self._pow_2_3(s, x, other, op, **raiser_RESIDUAL) 

1756 

1757 def _ps_acc(self, ps, xs, up=True, **unused): 

1758 '''(INTERNAL) Accumulate C{xs} scalars into list C{ps}. 

1759 ''' 

1760 n = 0 

1761 _2s = _2sum 

1762 for x in (tuple(xs) if xs is ps else xs): 

1763 # assert isscalar(x) and _isfinite(x) 

1764 if x: 

1765 i = 0 

1766 for p in ps: 

1767 x, p = _2s(x, p) 

1768 if p: 

1769 ps[i] = p 

1770 i += 1 

1771 ps[i:] = (x,) if x else () 

1772 n += 1 

1773 if n: 

1774 self._n += n 

1775 # Fsum._ps_max = max(Fsum._ps_max, len(ps)) 

1776 if up: 

1777 self._update() 

1778 return ps 

1779 

1780 def _ps_mul(self, op, *factors): 

1781 '''(INTERNAL) Multiply this instance' C{partials} with 

1782 each scalar C{factor} and accumulate into an C{Fsum}. 

1783 ''' 

1784 def _pfs(ps, fs): 

1785 if len(ps) < len(fs): 

1786 ps, fs = fs, ps 

1787 _fin = _isfinite 

1788 for f in fs: 

1789 for p in ps: 

1790 p *= f 

1791 yield p if _fin(p) else self._finite(p, op) 

1792 

1793 return Fsum()._facc_scalar(_pfs(self._ps, factors), up=False) 

1794 

1795 @property_RO 

1796 def _ps_neg(self): 

1797 '''(INTERNAL) Yield the partials, I{negated}. 

1798 ''' 

1799 for p in self._ps: 

1800 yield -p 

1801 

1802 def _ps_1sum(self, *less): 

1803 '''(INTERNAL) Return the partials sum, 1-primed C{less} some scalars. 

1804 ''' 

1805 def _1pls(ps, ls): 

1806 yield _1_0 

1807 for p in ps: 

1808 yield p 

1809 for p in ls: 

1810 yield -p 

1811 yield _N_1_0 

1812 

1813 return _fsum(_1pls(self._ps, less)) 

1814 

1815 def _raiser(self, r, s, raiser=True, **RESIDUAL): 

1816 '''(INTERNAL) Does ratio C{r / s} exceed the RESIDUAL threshold 

1817 I{and} is residual C{r} I{non-zero} or I{significant} (for a 

1818 negative respectively positive C{RESIDUAL} threshold)? 

1819 ''' 

1820 if r and raiser: 

1821 t = self._RESIDUAL 

1822 if RESIDUAL: 

1823 t = _threshold(_xkwds_get(RESIDUAL, RESIDUAL=t)) 

1824 if t < 0 or (s + r) != s: 

1825 q = (r / s) if s else s # == 0. 

1826 if fabs(q) > fabs(t): 

1827 return dict(ratio=q, R=t) 

1828 return {} 

1829 

1830 rdiv = __rtruediv__ 

1831 

1832 @property_RO 

1833 def real(self): 

1834 '''Get the C{real} part of this instance (C{float}). 

1835 

1836 @see: Methods L{Fsum.__float__} and L{Fsum.fsum} 

1837 and properties L{Fsum.ceil}, L{Fsum.floor}, 

1838 L{Fsum.imag} and L{Fsum.residual}. 

1839 ''' 

1840 return float(self._fprs) 

1841 

1842 @property_RO 

1843 def residual(self): 

1844 '''Get this instance' residual (C{float} or C{int}): the 

1845 C{sum(partials)} less the precision running sum C{fsum}. 

1846 

1847 @note: The C{residual is INT0} iff the precision running 

1848 C{fsum} is considered to be I{exact}. 

1849 

1850 @see: Methods L{Fsum.fsum}, L{Fsum.fsum2} and L{Fsum.is_exact}. 

1851 ''' 

1852 return self._fprs2.residual 

1853 

1854 def RESIDUAL(self, *threshold): 

1855 '''Get and set this instance' I{ratio} for raising L{ResidualError}s, 

1856 overriding the default from env variable C{PYGEODESY_FSUM_RESIDUAL}. 

1857 

1858 @arg threshold: If C{scalar}, the I{ratio} to exceed for raising 

1859 L{ResidualError}s in division and exponention, if 

1860 C{None} restore the default set with env variable 

1861 C{PYGEODESY_FSUM_RESIDUAL} or if omitted, keep the 

1862 current setting. 

1863 

1864 @return: The previous C{RESIDUAL} setting (C{float}), default C{0.0}. 

1865 

1866 @raise ResidualError: Invalid B{C{threshold}}. 

1867 

1868 @note: L{ResidualError}s may be thrown if the non-zero I{ratio} 

1869 C{residual / fsum} exceeds the given B{C{threshold}} and 

1870 if the C{residual} is non-zero and I{significant} vs the 

1871 C{fsum}, i.e. C{(fsum + residual) != fsum} and if optional 

1872 keyword argument C{raiser=False} is missing. Specify a 

1873 negative B{C{threshold}} for only non-zero C{residual} 

1874 testing without I{significant}. 

1875 ''' 

1876 r = self._RESIDUAL 

1877 if threshold: 

1878 t = threshold[0] 

1879 self._RESIDUAL = Fsum._RESIDUAL if t is None else ( # for ... 

1880 (_0_0 if t else _1_0) if isbool(t) else 

1881 _threshold(t)) # ... backward compatibility 

1882 return r 

1883 

1884 def _ResidualError(self, op, other, residual, **mod_R): 

1885 '''(INTERNAL) Non-zero B{C{residual}} etc. 

1886 ''' 

1887 def _p(mod=None, R=0, **unused): # ratio=0 

1888 return (_non_zero_ if R < 0 else _significant_) \ 

1889 if mod is None else _integer_ 

1890 

1891 t = _stresidual(_p(**mod_R), residual, **mod_R) 

1892 return self._Error(op, other, ResidualError, txt=t) 

1893 

1894 def root(self, root, **raiser_RESIDUAL): 

1895 '''Return C{B{self}**(1 / B{root})} as L{Fsum}. 

1896 

1897 @arg root: The order (C{scalar} or L{Fsum}), non-zero. 

1898 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} (C{bool}) to 

1899 ignore L{ResidualError}s and C{B{RESIDUAL}=scalar} 

1900 to override the L{RESIDUAL<Fsum.RESIDUAL>}. 

1901 

1902 @return: The C{self ** (1 / B{root})} result (L{Fsum}). 

1903 

1904 @raise ResidualError: Non-zero, significant residual or invalid 

1905 B{C{RESIDUAL}}. 

1906 

1907 @see: Method L{Fsum.pow}. 

1908 ''' 

1909 x = _1_Over(root, _truediv_op_, **raiser_RESIDUAL) 

1910 f = self._copy_2(self.root) 

1911 return f._fpow(x, f.name, **raiser_RESIDUAL) # == pow(f, x) 

1912 

1913 def _scalar(self, other, op, **txt): 

1914 '''(INTERNAL) Return scalar C{other}. 

1915 ''' 

1916 if isscalar(other): 

1917 return other 

1918 raise self._Error(op, other, _TypeError, **txt) # _invalid_ 

1919 

1920 def signOf(self, res=True): 

1921 '''Determine the sign of this instance. 

1922 

1923 @kwarg res: If C{True} consider, otherwise 

1924 ignore the residual (C{bool}). 

1925 

1926 @return: The sign (C{int}, -1, 0 or +1). 

1927 ''' 

1928 s, r = self._fprs2 

1929 r = (-r) if res else 0 

1930 return _signOf(s, r) 

1931 

1932 def toRepr(self, **lenc_prec_sep_fmt): # PYCHOK signature 

1933 '''Return this C{Fsum} instance as representation. 

1934 

1935 @kwarg lenc_prec_sep_fmt: Optional keyword arguments 

1936 for method L{Fsum.toStr}. 

1937 

1938 @return: This instance (C{repr}). 

1939 ''' 

1940 return Fmt.repr_at(self, self.toStr(**lenc_prec_sep_fmt)) 

1941 

1942 def toStr(self, lenc=True, **prec_sep_fmt): # PYCHOK signature 

1943 '''Return this C{Fsum} instance as string. 

1944 

1945 @kwarg lenc: If C{True} include the current C{[len]} of this 

1946 L{Fsum} enclosed in I{[brackets]} (C{bool}). 

1947 @kwarg prec_sep_fmt: Optional keyword arguments for method 

1948 L{Fsum2Tuple.toStr}. 

1949 

1950 @return: This instance (C{str}). 

1951 ''' 

1952 p = self.classname 

1953 if lenc: 

1954 p = Fmt.SQUARE(p, len(self)) 

1955 n = _enquote(self.name, white=_UNDER_) 

1956 t = self._fprs2.toStr(**prec_sep_fmt) 

1957 return NN(p, _SPACE_, n, t) 

1958 

1959 def _truediv(self, other, op, **raiser_RESIDUAL): 

1960 '''(INTERNAL) Return C{B{self} / B{other}} as an L{Fsum}. 

1961 ''' 

1962 f = self._copy_2(self.__truediv__) 

1963 return f._ftruediv(other, op, **raiser_RESIDUAL) 

1964 

1965 def _update(self, updated=True): # see ._fset 

1966 '''(INTERNAL) Zap all cached C{Property_RO} values. 

1967 ''' 

1968 if updated: 

1969 _pop = self.__dict__.pop 

1970 for p in _ROs: 

1971 _ = _pop(p, None) 

1972# Fsum._fint2._update(self) 

1973# Fsum._fprs ._update(self) 

1974# Fsum._fprs2._update(self) 

1975 return self # for .fset_ 

1976 

1977_ROs = _allPropertiesOf_n(3, Fsum, Property_RO) # PYCHOK see Fsum._update 

1978 

1979 

1980def _Float_Int(arg, **name_Error): 

1981 '''(INTERNAL) Unit of L{Fsum2Tuple} items. 

1982 ''' 

1983 U = Int if isint(arg) else Float 

1984 return U(arg, **name_Error) 

1985 

1986 

1987class DivMod2Tuple(_NamedTuple): 

1988 '''2-Tuple C{(div, mod)} with the quotient C{div} and remainder 

1989 C{mod} results of a C{divmod} operation. 

1990 

1991 @note: Quotient C{div} an C{int} in Python 3+ but a C{float} 

1992 in Python 2-. Remainder C{mod} an L{Fsum} instance. 

1993 ''' 

1994 _Names_ = (_div_, _mod_) 

1995 _Units_ = (_Float_Int, Fsum) 

1996 

1997 

1998class Fsum2Tuple(_NamedTuple): # in .fstats 

1999 '''2-Tuple C{(fsum, residual)} with the precision running C{fsum} 

2000 and the C{residual}, the sum of the remaining partials. Each 

2001 item is C{float} or C{int}. 

2002 

2003 @note: If the C{residual is INT0}, the C{fsum} is considered 

2004 to be I{exact}, see method L{Fsum2Tuple.is_exact}. 

2005 ''' 

2006 _Names_ = ( Fsum.fsum.__name__, Fsum.residual.name) 

2007 _Units_ = (_Float_Int, _Float_Int) 

2008 

2009 def __abs__(self): # in .fmath 

2010 return self._Fsum.__abs__() 

2011 

2012 def __bool__(self): # PYCHOK Python 3+ 

2013 return bool(self._Fsum) 

2014 

2015 def __eq__(self, other): 

2016 return self._other_op(other, self.__eq__) 

2017 

2018 def __float__(self): 

2019 return self._Fsum.__float__() 

2020 

2021 def __ge__(self, other): 

2022 return self._other_op(other, self.__ge__) 

2023 

2024 def __gt__(self, other): 

2025 return self._other_op(other, self.__gt__) 

2026 

2027 def __le__(self, other): 

2028 return self._other_op(other, self.__le__) 

2029 

2030 def __lt__(self, other): 

2031 return self._other_op(other, self.__lt__) 

2032 

2033 def __int__(self): 

2034 return self._Fsum.__int__() 

2035 

2036 def __ne__(self, other): 

2037 return self._other_op(other, self.__ne__) 

2038 

2039 def __neg__(self): 

2040 return self._Fsum.__neg__() 

2041 

2042 __nonzero__ = __bool__ # Python 2- 

2043 

2044 def __pos__(self): 

2045 return self._Fsum.__pos__() 

2046 

2047 def as_integer_ratio(self): 

2048 '''Return this instance as the ratio of 2 integers. 

2049 

2050 @see: Method L{Fsum.as_integer_ratio} for further details. 

2051 ''' 

2052 return self._Fsum.as_integer_ratio() 

2053 

2054 @property_RO 

2055 def _fint2(self): 

2056 return self._Fsum._fint2 

2057 

2058 @property_RO 

2059 def _fprs2(self): 

2060 return self._Fsum._fprs2 

2061 

2062 @Property_RO 

2063 def _Fsum(self): # this C{Fsum2Tuple} as L{Fsum}, in .fstats 

2064 s, r = _s_r(*self) 

2065 ps = (r, s) if r else (s,) 

2066 return _Psum(ps, name=self.name) 

2067 

2068 def Fsum_(self, *xs, **name_RESIDUAL): 

2069 '''Return this C{Fsum2Tuple} as an L{Fsum} plus some C{xs}. 

2070 ''' 

2071 f = _Psum(self._Fsum._ps, **name_RESIDUAL) 

2072 return f._facc_1(xs, up=False) if xs else f 

2073 

2074 def is_exact(self): 

2075 '''Is this L{Fsum2Tuple} considered to be exact? (C{bool}). 

2076 ''' 

2077 return self._Fsum.is_exact() 

2078 

2079 def is_integer(self): 

2080 '''Is this L{Fsum2Tuple} C{integer}? (C{bool}). 

2081 ''' 

2082 return self._Fsum.is_integer() 

2083 

2084 def _mul_scalar(self, other, op): # for Fsum._fmul 

2085 return self._Fsum._mul_scalar(other, op) 

2086 

2087 @property_RO 

2088 def _n(self): 

2089 return self._Fsum._n 

2090 

2091 def _other_op(self, other, which): 

2092 C, s = (tuple, self) if isinstance(other, tuple) else (Fsum, self._Fsum) 

2093 return getattr(C, which.__name__)(s, other) 

2094 

2095 @property_RO 

2096 def _ps(self): 

2097 return self._Fsum._ps 

2098 

2099 @property_RO 

2100 def _ps_neg(self): 

2101 return self._Fsum._ps_neg 

2102 

2103 def signOf(self, **res): 

2104 '''Like method L{Fsum.signOf}. 

2105 ''' 

2106 return self._Fsum.signOf(**res) 

2107 

2108 def toStr(self, fmt=Fmt.g, **prec_sep): # PYCHOK signature 

2109 '''Return this L{Fsum2Tuple} as string (C{str}). 

2110 

2111 @kwarg fmt: Optional C{float} format (C{letter}). 

2112 @kwarg prec_sep: Optional keyword arguments for function 

2113 L{fstr<streprs.fstr>}. 

2114 ''' 

2115 return Fmt.PAREN(fstr(self, fmt=fmt, strepr=str, force=False, **prec_sep)) 

2116 

2117_Fsum_Fsum2Tuple_types = Fsum, Fsum2Tuple # PYCHOK lines 

2118 

2119 

2120class ResidualError(_ValueError): 

2121 '''Error raised for a division, power or root operation of 

2122 an L{Fsum} instance with a C{residual} I{ratio} exceeding 

2123 the L{RESIDUAL<Fsum.RESIDUAL>} threshold. 

2124 

2125 @see: Module L{pygeodesy.fsums} and method L{Fsum.RESIDUAL}. 

2126 ''' 

2127 pass 

2128 

2129 

2130try: 

2131 from math import fsum as _fsum # precision IEEE-754 sum, Python 2.6+ 

2132 

2133 # make sure _fsum works as expected (XXX check 

2134 # float.__getformat__('float')[:4] == 'IEEE'?) 

2135 if _fsum((1, 1e101, 1, -1e101)) != 2: # PYCHOK no cover 

2136 del _fsum # nope, remove _fsum ... 

2137 raise ImportError # ... use _fsum below 

2138 

2139 Fsum._math_fsum = _sum = _fsum # PYCHOK exported 

2140except ImportError: 

2141 _sum = sum # Fsum(NAN) exception fall-back, in .elliptic 

2142 

2143 def _fsum(xs): 

2144 '''(INTERNAL) Precision summation, Python 2.5-. 

2145 ''' 

2146 F = Fsum() 

2147 F.name = _fsum.__name__ 

2148 return F._facc(xs, up=False)._fprs2.fsum 

2149 

2150 

2151def fsum(xs, floats=False): 

2152 '''Precision floating point summation based on/like Python's C{math.fsum}. 

2153 

2154 @arg xs: Iterable of items to add (each C{scalar} or an L{Fsum} or L{Fsum2Tuple} 

2155 instance). 

2156 @kwarg floats: Use C{B{floats}=True} iff I{all} B{C{xs}} items are I{known to 

2157 be scalar} (C{bool}). 

2158 

2159 @return: Precision C{fsum} (C{float}). 

2160 

2161 @raise OverflowError: Partial C{2sum} overflow. 

2162 

2163 @raise TypeError: Non-scalar B{C{xs}} item. 

2164 

2165 @raise ValueError: Invalid or non-finite B{C{xs}} item. 

2166 

2167 @note: Exception and I{non-finite} handling may differ if not based 

2168 on Python's C{math.fsum}. 

2169 

2170 @see: Class L{Fsum} and methods L{Fsum.fsum} and L{Fsum.fadd}. 

2171 ''' 

2172 return _fsum(xs if floats is True else _2floats(xs)) if xs else _0_0 # PYCHOK yield 

2173 

2174 

2175def fsum_(*xs, **floats): 

2176 '''Precision floating point summation of all positional items. 

2177 

2178 @arg xs: Items to add (each C{scalar} or an L{Fsum} or L{Fsum2Tuple} instance), 

2179 all positional. 

2180 @kwarg floats: Use C{B{floats}=True} iff I{all} B{C{xs}} items are I{known to 

2181 be scalar} (C{bool}). 

2182 

2183 @see: Function L{fsum<fsums.fsum>} for further details. 

2184 ''' 

2185 return _fsum(xs if _xkwds_get(floats, floats=False) is True else 

2186 _2floats(xs, origin=1)) if xs else _0_0 # PYCHOK yield 

2187 

2188 

2189def fsumf_(*xs): 

2190 '''Precision floating point summation iff I{all} C{B{xs}} items are I{known to be scalar}. 

2191 

2192 @see: Function L{fsum_<fsums.fsum_>} for further details. 

2193 ''' 

2194 return _fsum(xs) if xs else _0_0 

2195 

2196 

2197def fsum1(xs, floats=False): 

2198 '''Precision floating point summation, 1-primed. 

2199 

2200 @arg xs: Iterable of items to add (each C{scalar} or an L{Fsum} or L{Fsum2Tuple} 

2201 instance). 

2202 @kwarg floats: Use C{B{floats}=True} iff I{all} B{C{xs}} items are I{known to 

2203 be scalar} (C{bool}). 

2204 

2205 @see: Function L{fsum<fsums.fsum>} for further details. 

2206 ''' 

2207 return _fsum(_1primed(xs if floats is True else _2floats(xs))) if xs else _0_0 # PYCHOK yield 

2208 

2209 

2210def fsum1_(*xs, **floats): 

2211 '''Precision floating point summation, 1-primed of all positional items. 

2212 

2213 @arg xs: Items to add (each C{scalar} or an L{Fsum} or L{Fsum2Tuple} instance), 

2214 all positional. 

2215 @kwarg floats: Use C{B{floats}=True} iff I{all} B{C{xs}} items are I{known to 

2216 be scalar} (C{bool}). 

2217 

2218 @see: Function L{fsum_<fsums.fsum_>} for further details. 

2219 ''' 

2220 return _fsum(_1primed(xs if _xkwds_get(floats, floats=False) is True else 

2221 _2floats(xs, origin=1))) if xs else _0_0 # PYCHOK yield 

2222 

2223 

2224def fsum1f_(*xs): 

2225 '''Precision floating point summation iff I{all} C{B{xs}} items are I{known to be scalar}. 

2226 

2227 @see: Function L{fsum_<fsums.fsum_>} for further details. 

2228 ''' 

2229 return _fsum(_1primed(xs)) if xs else _0_0 

2230 

2231 

2232if __name__ == '__main__': 

2233 

2234 # usage: [env _psum=fsum] python3 -m pygeodesy.fsums 

2235 

2236 if _getenv(_psum.__name__, NN) == _fsum.__name__: 

2237 _psum = _fsum 

2238 

2239 def _test(n): 

2240 # copied from Hettinger, see L{Fsum} reference 

2241 from pygeodesy import frandoms, printf 

2242 

2243 printf(_fsum.__name__, end=_COMMASPACE_) 

2244 printf(_psum.__name__, end=_COMMASPACE_) 

2245 

2246 F = Fsum() 

2247 if F.is_math_fsum(): 

2248 for t in frandoms(n, seeded=True): 

2249 assert float(F.fset_(*t)) == _fsum(t) 

2250 printf(_DOT_, end=NN) 

2251 printf(NN) 

2252 

2253 _test(128) 

2254 

2255# **) MIT License 

2256# 

2257# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved. 

2258# 

2259# Permission is hereby granted, free of charge, to any person obtaining a 

2260# copy of this software and associated documentation files (the "Software"), 

2261# to deal in the Software without restriction, including without limitation 

2262# the rights to use, copy, modify, merge, publish, distribute, sublicense, 

2263# and/or sell copies of the Software, and to permit persons to whom the 

2264# Software is furnished to do so, subject to the following conditions: 

2265# 

2266# The above copyright notice and this permission notice shall be included 

2267# in all copies or substantial portions of the Software. 

2268# 

2269# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

2270# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

2271# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

2272# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

2273# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 

2274# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 

2275# OTHER DEALINGS IN THE SOFTWARE.