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, itemsorted, \ 

27 signOf, _signOf 

28from pygeodesy.constants import INT0, _isfinite, NEG0, _pos_self, \ 

29 _0_0, _1_0, _N_1_0, Float, Int 

30from pygeodesy.errors import _OverflowError, _TypeError, _ValueError, \ 

31 _xError, _xError2, _xkwds_get 

32from pygeodesy.interns import NN, _arg_, _COMMASPACE_, _DASH_, _DOT_, \ 

33 _enquote, _EQUAL_, _from_, _LANGLE_, _NOTEQUAL_, \ 

34 _not_finite_, _PERCENT_, _PLUS_, _RANGLE_, \ 

35 _SLASH_, _SPACE_, _STAR_, _UNDER_ 

36from pygeodesy.lazily import _ALL_LAZY, _getenv, _sys_version_info2 

37from pygeodesy.named import _Named, _NamedTuple, _NotImplemented 

38from pygeodesy.props import _allPropertiesOf_n, deprecated_property_RO, \ 

39 Property_RO, property_RO 

40from pygeodesy.streprs import Fmt, fstr, unstr 

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

42 

43from math import ceil as _ceil, fabs, floor as _floor # PYCHOK used! .ltp 

44 

45__all__ = _ALL_LAZY.fsums 

46__version__ = '24.05.06' 

47 

48_abs = abs 

49_add_op_ = _PLUS_ # in .auxilats.auxAngle 

50_eq_op_ = _EQUAL_ * 2 # _DEQUAL_ 

51_div_ = 'div' 

52_Float = float # in .fstats 

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_isAn = isinstance # in .fstats 

60_le_op_ = _LANGLE_ + _EQUAL_ 

61_len = len 

62_List = list 

63_lt_op_ = _LANGLE_ 

64_mod_ = 'mod' 

65_mod_op_ = _PERCENT_ 

66_mul_op_ = _STAR_ 

67_ne_op_ = _NOTEQUAL_ 

68_non_zero_ = 'non-zero' 

69_pow_op_ = _STAR_ * 2 # _DSTAR_ 

70_significant_ = 'significant' 

71_sub_op_ = _DASH_ # in .auxilats.auxAngle 

72_threshold_ = 'threshold' 

73_truediv_op_ = _SLASH_ 

74_Tuple = tuple 

75_divmod_op_ = _floordiv_op_ + _mod_op_ 

76_isub_op_ = _sub_op_ + _fset_op_ # in .auxilats.auxAngle 

77 

78 

79def _2delta(*ab): 

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

81 ''' 

82 try: 

83 a, b = _2sum(*ab) 

84 except _OverflowError: 

85 a, b = ab 

86 return _Float(a if fabs(a) > fabs(b) else b) 

87 

88 

89def _2error(unused): 

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

91 ''' 

92 raise ValueError(_not_finite_) 

93 

94 

95def _2float(index=None, **name_value): # in .fmath, .fstats 

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

97 ''' 

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

99 try: 

100 v = _Float(v) 

101 return v if _isfinite(v) else _2error(v) 

102 except Exception as X: 

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

104 

105 

106def _X_ps(X): # for _2floats only 

107 return X._ps 

108 

109 

110def _2floats(xs, origin=0, _X=_X_ps, _x=_Float): 

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

112 ''' 

113 try: 

114 i, x = origin, None 

115 _fin = _isfinite 

116 _FsT = _Fsum_Fsum2Tuple_types 

117 _is = _isAn 

118 for x in xs: 

119 if _is(x, _FsT): 

120 for p in _X(x._Fsum): 

121 yield p 

122 else: 

123 f = _x(x) 

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

125 i += 1 

126 except Exception as X: 

127 raise _xError(X, Fmt.INDEX(xs=i), x) 

128 

129 

130def _Fsumf_(*xs): # floats=True, in .auxLat, ... 

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

132 ''' 

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

134 

135 

136def _Fsum1f_(*xs): # floats=True, in .albers, ... 

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

138 ''' 

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

140 

141 

142def _2halfeven(s, r, p): 

143 '''(INTERNAL) Round half-even. 

144 ''' 

145 if (p > 0 and r > 0) or \ 

146 (p < 0 and r < 0): # signs match 

147 r *= 2 

148 t = s + r 

149 if r == (t - s): 

150 s = t 

151 return s 

152 

153 

154def _isFsum(x): # in .fmath 

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

156 ''' 

157 return _isAn(x, Fsum) 

158 

159 

160def _isFsumTuple(x): # in .fmath 

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

162 ''' 

163 return _isAn(x, _Fsum_Fsum2Tuple_types) 

164 

165 

166def _1_Over(x, op, **raiser_RESIDUAL): # vs _1_over 

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

168 ''' 

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

170 

171 

172def _1primed(xs): # in .fmath 

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

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

175 ''' 

176 yield _1_0 

177 for x in xs: 

178 yield x 

179 yield _N_1_0 

180 

181 

182def _psum(ps): # PYCHOK used! 

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

184 ''' 

185 # assert _isAn(ps, _List) 

186 i = _len(ps) - 1 

187 s = _0_0 if i < 0 else ps[i] 

188 _2s = _2sum 

189 while i > 0: 

190 i -= 1 

191 s, r = _2s(s, ps[i]) 

192 if r: # sum(ps) became inexact 

193 if s: 

194 ps[i:] = r, s 

195 if i > 0: 

196 s = _2halfeven(s, r, ps[i-1]) 

197 break # return s 

198 s = r # PYCHOK no cover 

199 ps[i:] = s, 

200 return s 

201 

202 

203def _Psum(ps, **name_RESIDUAL): 

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

205 ''' 

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

207 if ps: 

208 f._ps[:] = ps 

209 f._n = _len(f._ps) 

210 return f 

211 

212 

213def _Psum_(*ps, **name_RESIDUAL): 

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

215 ''' 

216 return _Psum(ps, **name_RESIDUAL) 

217 

218 

219def _2scalar2(other): 

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

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

222 ''' 

223 if _isFsumTuple(other): 

224 s, r = other._fint2 

225 if r: 

226 s, r = other._fprs2 

227 if r: # PYCHOK no cover 

228 s = other # L{Fsum} as-is 

229 else: 

230 r = 0 

231 s = other # C{type} as-is 

232 if isint(s, both=True): 

233 s = int(s) 

234 return s, r 

235 

236 

237def _s_r(s, r): 

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

239 ''' 

240 if r: 

241 if fabs(s) < fabs(r): 

242 s, r = r, (s or INT0) 

243 else: 

244 r = INT0 

245 return s, r 

246 

247 

248def _strcomplex(s, *args): 

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

250 ''' 

251 c = _strcomplex.__name__[4:] 

252 n = _DASH_(_len(args), _arg_) 

253 t = unstr(pow, *args) 

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

255 

256 

257def _stresidual(prefix, residual, R=0, **mod_ratio): 

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

259 ''' 

260 p = _stresidual.__name__[3:] 

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

262 for n, v in itemsorted(mod_ratio): 

263 p = Fmt.PARENSPACED(n, Fmt(v)) 

264 t = _COMMASPACE_(t, p) 

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

266 

267 

268def _2sum(a, b): # by .testFmath 

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

270 ''' 

271 s = a + b 

272 if _isfinite(s): 

273 if fabs(a) < fabs(b): 

274 b, a = a, b 

275 return s, (b - (s - a)) 

276 u = unstr(_2sum, a, b) 

277 t = Fmt.PARENSPACED(_not_finite_, s) 

278 raise _OverflowError(u, txt=t) 

279 

280 

281def _threshold(threshold): 

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

283 ''' 

284 try: 

285 t = _Float(threshold) or _0_0 

286 return t if _isfinite(t) else _2error(t) # PYCHOK None 

287 except Exception as x: 

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

289 

290 

291class Fsum(_Named): # sync __methods__ with .vector3dBase.Vector3dBase 

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

293 

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

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

296 intermediate, I{running} summuation. 

297 

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

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

300 C{float}, except C{complex}. 

301 

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

303 Python's C{math.fsum}. 

304 

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

306 393090_Binary_floating_point_summatiaccurate_full/recipe-393090.py>}, 

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

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

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

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

311 ''' 

312 _math_fsum = None 

313 _n = 0 

314# _ps = [] # partial sums 

315# _ps_max = 0 # max(Fsum._ps_max, _len(Fsum._ps)) 

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

317 

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

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

320 

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

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

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

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

325 

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

327 ''' 

328 if name_RESIDUAL: 

329 

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

331 return name, RESIDUAL 

332 

333 n, R = _n_R(**name_RESIDUAL) 

334 if R is not None: 

335 self.RESIDUAL(R) 

336 if n: 

337 self.name = n 

338 

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

340 if xs: 

341 self._facc_1(xs, up=False) 

342 

343 def __abs__(self): 

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

345 ''' 

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

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

348 

349 def __add__(self, other): 

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

351 

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

353 

354 @return: The sum (L{Fsum}). 

355 

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

357 ''' 

358 f = self._copy_2(self.__add__) 

359 return f._fadd(other, _add_op_) 

360 

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

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

363 ''' 

364 s, r = self._fprs2 

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

366 

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

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

369 

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

371 

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

373 ''' 

374 return self.ceil 

375 

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

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

378 

379 @return: -1, 0 or +1 (C{int}). 

380 

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

382 ''' 

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

384 return _signOf(s, 0) 

385 

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

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

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

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

390 

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

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

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

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

395 

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

397 B{C{RESIDUAL}}. 

398 

399 @see: Method L{Fsum.fdiv}. 

400 ''' 

401 f = self._copy_2(self.__divmod__) 

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

403 

404 def __eq__(self, other): 

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

406 ''' 

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

408 

409 def __float__(self): 

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

411 

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

413 ''' 

414 return _Float(self._fprs) 

415 

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

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

418 

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

420 

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

422 ''' 

423 return self.floor 

424 

425 def __floordiv__(self, other): 

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

427 

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

429 

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

431 

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

433 ''' 

434 f = self._copy_2(self.__floordiv__) 

435 return f._floordiv(other, _floordiv_op_) 

436 

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

438 '''Not implemented.''' 

439 return _NotImplemented(self, *other) 

440 

441 def __ge__(self, other): 

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

443 ''' 

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

445 

446 def __gt__(self, other): 

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

448 ''' 

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

450 

451 def __hash__(self): # PYCHOK no cover 

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

453 ''' 

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

455 

456 def __iadd__(self, other): 

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

458 

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

460 

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

462 

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

464 C{scalar} nor L{Fsum}. 

465 

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

467 ''' 

468 return self._fadd(other, _iadd_op_) 

469 

470 def __ifloordiv__(self, other): 

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

472 

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

474 

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

476 

477 @raise ResidualError: Non-zero, significant residual 

478 in B{C{other}}. 

479 

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

481 

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

483 

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

485 

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

487 ''' 

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

489 

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

491 '''Not implemented.''' 

492 return _NotImplemented(self, other) 

493 

494 def __imod__(self, other): 

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

496 

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

498 

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

500 

501 @see: Method L{Fsum.__divmod__}. 

502 ''' 

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

504 

505 def __imul__(self, other): 

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

507 

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

509 

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

511 

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

513 

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

515 

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

517 ''' 

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

519 

520 def __int__(self): 

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

522 

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

524 and L{Fsum.floor}. 

525 ''' 

526 i, _ = self._fint2 

527 return i 

528 

529 def __invert__(self): # PYCHOK no cover 

530 '''Not implemented.''' 

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

532 return _NotImplemented(self) 

533 

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

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

536 

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

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

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

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

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

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

543 

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

545 

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

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

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

549 

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

551 

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

553 is non-zero and significant and either 

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

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

556 C{None}. 

557 

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

559 invocation failed. 

560 

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

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

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

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

565 is given as C{0}. 

566 

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

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

569 ''' 

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

571 

572 def __isub__(self, other): 

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

574 

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

576 

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

578 

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

580 

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

582 ''' 

583 return self._fsub(other, _isub_op_) 

584 

585 def __iter__(self): 

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

587 ''' 

588 return iter(self.partials) 

589 

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

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

592 

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

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

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

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

597 

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

599 

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

601 

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

603 B{C{RESIDUAL}}. 

604 

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

606 

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

608 

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

610 

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

612 ''' 

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

614 

615 def __le__(self, other): 

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

617 ''' 

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

619 

620 def __len__(self): 

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

622 ''' 

623 return self._n 

624 

625 def __lt__(self, other): 

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

627 ''' 

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

629 

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

631 '''Not implemented.''' 

632 return _NotImplemented(self, other) 

633 

634 def __mod__(self, other): 

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

636 

637 @see: Method L{Fsum.__imod__}. 

638 ''' 

639 f = self._copy_2(self.__mod__) 

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

641 

642 def __mul__(self, other): 

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

644 

645 @see: Method L{Fsum.__imul__}. 

646 ''' 

647 f = self._copy_2(self.__mul__) 

648 return f._fmul(other, _mul_op_) 

649 

650 def __ne__(self, other): 

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

652 ''' 

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

654 

655 def __neg__(self): 

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

657 ''' 

658 f = self._copy_2(self.__neg__) 

659 return f._fset(self._neg) 

660 

661 def __pos__(self): 

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

663 ''' 

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

665 

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

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

668 

669 @see: Method L{Fsum.__ipow__}. 

670 ''' 

671 f = self._copy_2(self.__pow__) 

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

673 

674 def __radd__(self, other): 

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

676 

677 @see: Method L{Fsum.__iadd__}. 

678 ''' 

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

680 return f._fadd(self, _add_op_) 

681 

682 def __rdivmod__(self, other): 

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

684 C{(quotient, remainder)}. 

685 

686 @see: Method L{Fsum.__divmod__}. 

687 ''' 

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

689 return f._fdivmod2(self, _divmod_op_) 

690 

691# def __repr__(self): 

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

693# ''' 

694# return self.toRepr(lenc=True) 

695 

696 def __rfloordiv__(self, other): 

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

698 

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

700 ''' 

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

702 return f._floordiv(self, _floordiv_op_) 

703 

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

705 '''Not implemented.''' 

706 return _NotImplemented(self, other) 

707 

708 def __rmod__(self, other): 

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

710 

711 @see: Method L{Fsum.__imod__}. 

712 ''' 

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

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

715 

716 def __rmul__(self, other): 

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

718 

719 @see: Method L{Fsum.__imul__}. 

720 ''' 

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

722 return f._fmul(self, _mul_op_) 

723 

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

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

726 

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

728 ''' 

729 f = self._copy_2(self.__round__) 

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

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

732 

733 def __rpow__(self, other, *mod): 

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

735 

736 @see: Method L{Fsum.__ipow__}. 

737 ''' 

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

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

740 

741 def __rsub__(self, other): 

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

743 

744 @see: Method L{Fsum.__isub__}. 

745 ''' 

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

747 return f._fsub(self, _sub_op_) 

748 

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

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

751 

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

753 ''' 

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

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

756 

757 def __str__(self): 

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

759 ''' 

760 return self.toStr(lenc=True) 

761 

762 def __sub__(self, other): 

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

764 

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

766 

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

768 

769 @see: Method L{Fsum.__isub__}. 

770 ''' 

771 f = self._copy_2(self.__sub__) 

772 return f._fsub(other, _sub_op_) 

773 

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

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

776 

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

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

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

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

781 

782 @return: The quotient (L{Fsum}). 

783 

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

785 B{C{RESIDUAL}}. 

786 

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

788 ''' 

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

790 

791 __trunc__ = __int__ 

792 

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

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

795 __div__ = __truediv__ 

796 __idiv__ = __itruediv__ 

797 __long__ = __int__ 

798 __nonzero__ = __bool__ 

799 __rdiv__ = __rtruediv__ 

800 

801 def as_integer_ratio(self): 

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

803 

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

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

806 non-zero, positive. 

807 

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

809 ''' 

810 n, r = self._fint2 

811 if r: 

812 i, d = _Float(r).as_integer_ratio() 

813 n *= d 

814 n += i 

815 else: # PYCHOK no cover 

816 d = 1 

817 return n, d 

818 

819 @property_RO 

820 def as_iscalar(self): 

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

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

823 ''' 

824 s, r = self._fprs2 

825 return self if r else s 

826 

827 @property_RO 

828 def ceil(self): 

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

830 C{float} in Python 2-). 

831 

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

833 

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

835 L{Fsum.imag} and L{Fsum.real}. 

836 ''' 

837 s, r = self._fprs2 

838 c = _ceil(s) + int(r) - 1 

839 while r > (c - s): # (s + r) > c 

840 c += 1 

841 return c 

842 

843 cmp = __cmp__ 

844 

845 def _cmp_0(self, other, op): 

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

847 ''' 

848 if _isFsumTuple(other): 

849 s = self._ps_1sum(*other._ps) 

850 elif self._scalar(other, op): 

851 s = self._ps_1sum(other) 

852 else: 

853 s = self.signOf() # res=True 

854 return s 

855 

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

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

858 

859 @return: The copy (L{Fsum}). 

860 ''' 

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

862 if f._ps is self._ps: 

863 f._ps = _List(self._ps) # separate list 

864 if not deep: 

865 f._n = 1 

866 # assert f._Fsum is f 

867 return f 

868 

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

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

871 ''' 

872 n = name or which.__name__ 

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

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

875 f._ps = _List(self._ps) # separate list 

876 # assert f._n == self._n 

877 # assert f._Fsum is f 

878 return f 

879 

880 def _copy_2r(self, other, which): 

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

882 ''' 

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

884 self._copy_2(which)._fset(other) 

885 

886# def _copy_RESIDUAL(self, other): 

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

888# ''' 

889# R = other._RESIDUAL 

890# if R is not Fsum._RESIDUAL: 

891# self._RESIDUAL = R 

892 

893 divmod = __divmod__ 

894 

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

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

897 ''' 

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

899 

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

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

902 ''' 

903 E, t = _xError2(X) 

904 if mod: 

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

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

907 

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

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

910 ''' 

911 E, t = _xError2(X) 

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

913 return E(u, txt=t, cause=X) 

914 

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

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

917 ''' 

918 if xs: 

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

920 ps = self._ps 

921 ps[:] = self._ps_acc(_List(ps), _xs, up=up) 

922 return self 

923 

924 def _facc_1(self, xs, **up): 

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

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

927 ''' 

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

929 self._facc(xs, origin=1, **up) 

930 

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

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

933 ''' 

934 def _N(X): 

935 return X._ps_neg 

936 

937 def _n(x): 

938 return -_Float(x) 

939 

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

941 

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

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

944 ''' 

945 def _Pow4(p): 

946 r = 0 

947 if _isFsumTuple(p): 

948 s, r = p._fprs2 

949 if r: 

950 m = Fsum._pow 

951 else: # scalar 

952 return _Pow4(s) 

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

954 p = s = int(p) 

955 m = Fsum._pow_int 

956 else: 

957 p = s = _2float(power=p) 

958 m = Fsum._pow_scalar 

959 return m, p, s, r 

960 

961 _Pow, p, s, r = _Pow4(power) 

962 if p: # and xs: 

963 op = which.__name__ 

964 _Fs = Fsum 

965 _is = _isAn 

966 _pow = self._pow_2_3 

967 

968 def _P(X): 

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

970 return f._ps if _is(f, _Fs) else (f,) 

971 

972 def _p(x): 

973 x = _Float(x) 

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

975 if f and r: 

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

977 return f 

978 

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

980 else: 

981 f = self._facc_scalar_(_Float(_len(xs))) # x**0 == 1 

982 return f 

983 

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

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

986 ''' 

987 if xs: 

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

989 return self 

990 

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

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

993 ''' 

994 if xs: 

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

996 return self 

997 

998# def _facc_up(self, up=True): 

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

1000# and re-accumulating the final C{partial}. 

1001# ''' 

1002# ps = self._ps 

1003# while _len(ps) > 1: 

1004# p = ps.pop() 

1005# if p: 

1006# n = self._n 

1007# _ = self._ps_acc(ps, (p,), up=False) 

1008# self._n = n 

1009# break 

1010# return self._update() if up else self 

1011 

1012 def fadd(self, xs=()): 

1013 '''Add an iterable's items to this instance. 

1014 

1015 @arg xs: Iterable of items to add (each C{scalar} 

1016 or an L{Fsum} or L{Fsum2Tuple} instance). 

1017 

1018 @return: This instance (L{Fsum}). 

1019 

1020 @raise OverflowError: Partial C{2sum} overflow. 

1021 

1022 @raise TypeError: An invalid B{C{xs}} item. 

1023 

1024 @raise ValueError: Invalid or non-finite B{C{xs}} value. 

1025 ''' 

1026 if _isFsumTuple(xs): 

1027 self._facc_scalar(xs._ps) # _Tuple(xs._ps) 

1028 elif isscalar(xs): # for backward compatibility 

1029 self._facc_scalar_(_2float(x=xs)) # PYCHOK no cover 

1030 elif xs: # assert isiterable(xs) 

1031 self._facc(xs) 

1032 return self 

1033 

1034 def fadd_(self, *xs): 

1035 '''Add all positional items to this instance. 

1036 

1037 @arg xs: Values to add (each C{scalar} or an L{Fsum} 

1038 or L{Fsum2Tuple} instance), all positional. 

1039 

1040 @see: Method L{Fsum.fadd} for further details. 

1041 ''' 

1042 return self._facc_1(xs) 

1043 

1044 def _fadd(self, other, op, **up): # in .fmath.Fhorner 

1045 '''(INTERNAL) Apply C{B{self} += B{other}}. 

1046 ''' 

1047 if not self._ps: # new Fsum(x) 

1048 self._fset(other, as_is=False, **up) 

1049 elif _isFsumTuple(other): 

1050 self._facc_scalar(other._ps, **up) # _Tuple 

1051 elif self._scalar(other, op): 

1052 self._facc_scalar_(other, **up) 

1053 return self 

1054 

1055 fcopy = copy # for backward compatibility 

1056 fdiv = __itruediv__ 

1057 fdivmod = __divmod__ 

1058 

1059 def _fdivmod2(self, other, op, **raiser_RESIDUAL): 

1060 '''(INTERNAL) Apply C{B{self} %= B{other}} and return a L{DivMod2Tuple}. 

1061 ''' 

1062 # result mostly follows CPython function U{float_divmod 

1063 # <https://GitHub.com/python/cpython/blob/main/Objects/floatobject.c>}, 

1064 # but at least divmod(-3, 2) equals Cpython's result (-2, 1). 

1065 q = self._truediv(other, op, **raiser_RESIDUAL).floor 

1066 if q: # == float // other == floor(float / other) 

1067 self -= Fsum(q) * other # NOT other * q! 

1068 

1069 s = signOf(other) # make signOf(self) == signOf(other) 

1070 if s and self.signOf() == -s: # PYCHOK no cover 

1071 self += other 

1072 q -= 1 

1073# t = self.signOf() 

1074# if t and t != s: 

1075# raise self._Error(op, other, _AssertionError, txt=signOf.__name__) 

1076 return DivMod2Tuple(q, self) # q is C{int} in Python 3+, but C{float} in Python 2- 

1077 

1078 def _finite(self, other, op=None): 

1079 '''(INTERNAL) Return B{C{other}} if C{finite}. 

1080 ''' 

1081 if _isfinite(other): 

1082 return other 

1083 raise ValueError(_not_finite_) if op is None else \ 

1084 self._Error(op, other, _ValueError, txt=_not_finite_) 

1085 

1086 def fint(self, name=NN, **raiser_RESIDUAL): 

1087 '''Return this instance' current running sum as C{integer}. 

1088 

1089 @kwarg name: Optional name (C{str}), overriding C{"fint"}. 

1090 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} (C{bool}) to 

1091 ignore L{ResidualError}s and C{B{RESIDUAL}=scalar} 

1092 to override the L{RESIDUAL<Fsum.RESIDUAL>}. 

1093 

1094 @return: The C{integer} sum (L{Fsum}) if this instance C{is_integer} 

1095 with a zero or insignificant I{integer} residual. 

1096 

1097 @raise ResidualError: Non-zero, significant residual or invalid 

1098 B{C{RESIDUAL}}. 

1099 

1100 @see: Methods L{Fsum.fint2}, L{Fsum.int_float} and L{Fsum.is_integer}. 

1101 ''' 

1102 i, r = self._fint2 

1103 if r: 

1104 R = self._raiser(r, i, **raiser_RESIDUAL) 

1105 if R: 

1106 t = _stresidual(_integer_, r, **R) 

1107 raise ResidualError(_integer_, i, txt=t) 

1108 f = self._copy_2(self.fint, name=name) 

1109 return f._fset(i) 

1110 

1111 def fint2(self, **name): 

1112 '''Return this instance' current running sum as C{int} and the 

1113 I{integer} residual. 

1114 

1115 @kwarg name: Optional name (C{str}). 

1116 

1117 @return: An L{Fsum2Tuple}C{(fsum, residual)} with C{fsum} 

1118 an C{int} and I{integer} C{residual} a C{float} or 

1119 C{INT0} if the C{fsum} is considered to be I{exact}. 

1120 ''' 

1121 return Fsum2Tuple(*self._fint2, **name) 

1122 

1123 @Property_RO 

1124 def _fint2(self): # see ._fset 

1125 '''(INTERNAL) Get 2-tuple (C{int}, I{integer} residual). 

1126 ''' 

1127 s, r = self._fprs2 

1128 i = int(s) 

1129 n = _len(self._ps) 

1130 r = self._ps_1sum(i) if r and n > 1 else _Float(s - i) 

1131 return i, (r or INT0) # Fsum2Tuple? 

1132 

1133 @deprecated_property_RO 

1134 def float_int(self): # PYCHOK no cover 

1135 '''DEPRECATED, use method C{Fsum.int_float}.''' 

1136 return self.int_float() # raiser=False 

1137 

1138 @property_RO 

1139 def floor(self): 

1140 '''Get this instance' C{floor} (C{int} in Python 3+, but 

1141 C{float} in Python 2-). 

1142 

1143 @note: This C{floor} takes the C{residual} into account. 

1144 

1145 @see: Method L{Fsum.int_float} and properties L{Fsum.ceil}, 

1146 L{Fsum.imag} and L{Fsum.real}. 

1147 ''' 

1148 s, r = self._fprs2 

1149 f = _floor(s) + _floor(r) + 1 

1150 while (f - s) > r: # f > (s + r) 

1151 f -= 1 

1152 return f 

1153 

1154# ffloordiv = __ifloordiv__ # for naming consistency 

1155# floordiv = __floordiv__ # for naming consistency 

1156 

1157 def _floordiv(self, other, op, **raiser_RESIDUAL): # rather _ffloordiv? 

1158 '''Apply C{B{self} //= B{other}}. 

1159 ''' 

1160 q = self._ftruediv(other, op, **raiser_RESIDUAL) # == self 

1161 return self._fset(q.floor) # floor(q) 

1162 

1163 fmul = __imul__ 

1164 

1165 def _fmul(self, other, op): 

1166 '''(INTERNAL) Apply C{B{self} *= B{other}}. 

1167 ''' 

1168 if _isFsumTuple(other): 

1169 if _len(self._ps) != 1: 

1170 f = self._mul_Fsum(other, op) 

1171 elif _len(other._ps) != 1: # and _len(self._ps) == 1 

1172 f = other._mul_scalar(self._ps[0], op) 

1173 else: # _len(other._ps) == _len(self._ps) == 1 

1174 f = self._finite(self._ps[0] * other._ps[0]) 

1175 else: 

1176 s = self._scalar(other, op) 

1177 f = self._mul_scalar(s, op) 

1178 return self._fset(f) # n=_len(self) + 1 

1179 

1180 def fover(self, over, **raiser_RESIDUAL): 

1181 '''Apply C{B{self} /= B{over}} and summate. 

1182 

1183 @arg over: An L{Fsum} or C{scalar} denominator. 

1184 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} (C{bool}) to 

1185 ignore L{ResidualError}s and C{B{RESIDUAL}=scalar} 

1186 to override the L{RESIDUAL<Fsum.RESIDUAL>}. 

1187 

1188 @return: Precision running sum (C{float}). 

1189 

1190 @raise ResidualError: Non-zero, significant residual or invalid 

1191 B{C{RESIDUAL}}. 

1192 

1193 @see: Methods L{Fsum.fsum} and L{Fsum.__itruediv__}. 

1194 ''' 

1195 return _Float(self.fdiv(over, **raiser_RESIDUAL)._fprs) 

1196 

1197 fpow = __ipow__ 

1198 

1199 def _fpow(self, other, op, *mod, **raiser_RESIDUAL): 

1200 '''Apply C{B{self} **= B{other}}, optional B{C{mod}} or C{None}. 

1201 ''' 

1202 if mod: 

1203 if mod[0] is not None: # == 3-arg C{pow} 

1204 f = self._pow_2_3(self, other, other, op, *mod, **raiser_RESIDUAL) 

1205 elif self.is_integer(): 

1206 # return an exact C{int} for C{int}**C{int} 

1207 i, _ = self._fint2 # assert _ == 0 

1208 x, r = _2scalar2(other) # C{int}, C{float} or other 

1209 f = _Psum_(i)._pow_Fsum(other, op, **raiser_RESIDUAL) if r else \ 

1210 self._pow_2_3(i, x, other, op, **raiser_RESIDUAL) 

1211 else: # mod[0] is None, power(self, other) 

1212 f = self._pow(other, other, op, **raiser_RESIDUAL) 

1213 else: # pow(self, other) 

1214 f = self._pow(other, other, op, **raiser_RESIDUAL) 

1215 return self._fset(f, as_is=isint(f)) # n=max(_len(self), 1) 

1216 

1217 @Property_RO 

1218 def _fprs(self): 

1219 '''(INTERNAL) Get and cache this instance' precision 

1220 running sum (C{float} or C{int}), ignoring C{residual}. 

1221 

1222 @note: The precision running C{fsum} after a C{//=} or 

1223 C{//} C{floor} division is C{int} in Python 3+. 

1224 ''' 

1225 return self._fprs2.fsum 

1226 

1227 @Property_RO 

1228 def _fprs2(self): 

1229 '''(INTERNAL) Get and cache this instance' precision 

1230 running sum and residual (L{Fsum2Tuple}). 

1231 ''' 

1232 ps = self._ps 

1233 n = _len(ps) - 2 

1234 if n > 0: # _len(ps) > 2 

1235 s = _psum(ps) 

1236 n = _len(ps) - 2 

1237 if n > 0: 

1238 r = self._ps_1sum(s) 

1239 return Fsum2Tuple(*_s_r(s, r)) 

1240 if n == 0: # _len(ps) == 2 

1241 s, r = _s_r(*_2sum(*ps)) 

1242 ps[:] = (r, s) if r else (s,) 

1243 elif ps: # _len(ps) == 1 

1244 s, r = ps[0], INT0 

1245 else: # _len(ps) == 0 

1246 s, r = _0_0, INT0 

1247 ps[:] = s, 

1248 # assert self._ps is ps 

1249 return Fsum2Tuple(s, r) 

1250 

1251 def fset_(self, *xs): 

1252 '''Replace this instance' value with all positional items. 

1253 

1254 @arg xs: Optional, new values (each C{scalar} or 

1255 an L{Fsum} or L{Fsum2Tuple} instance), 

1256 all positional. 

1257 

1258 @return: This instance, replaced (C{Fsum}). 

1259 

1260 @see: Method L{Fsum.fadd} for further details. 

1261 ''' 

1262 f = Fsum(*xs) if xs else _0_0 

1263 return self._fset(f) 

1264 

1265 def _fset(self, other, as_is=True, n=0, up=True): 

1266 '''(INTERNAL) Overwrite this instance with an other or a C{scalar}. 

1267 ''' 

1268 if other is self: 

1269 pass # from ._fmul, ._ftruediv and ._pow_0_1 

1270 elif _isFsumTuple(other): 

1271 self._ps[:] = other._ps 

1272 self._n = n or other._n 

1273# self._copy_RESIDUAL(other) 

1274 if up: # use or zap the C{Property_RO} values 

1275 Fsum._fint2._update_from(self, other) 

1276 Fsum._fprs ._update_from(self, other) 

1277 Fsum._fprs2._update_from(self, other) 

1278 elif isscalar(other): 

1279 s = other if as_is else _Float(other) 

1280 self._ps[:] = s, 

1281 self._n = n or 1 

1282 if up: 

1283 i = int(s) # see ._fint2 

1284 t = i, ((s - i) or INT0) 

1285 # Property_ROs _fint2, _fprs and _fprs2 can't be a Property: 

1286 # Property's _fset zaps the value just set by the @setter 

1287 self.__dict__.update(_fint2=t, _fprs=s, _fprs2=Fsum2Tuple(s, INT0)) 

1288 else: # PYCHOK no cover 

1289 raise self._Error(_fset_op_, other, _TypeError) 

1290 return self 

1291 

1292 def _fset_ps(self, other, n=0): # in .fmath 

1293 '''(INTERNAL) Set partials from a known C{scalar}, L{Fsum} or L{Fsum2Tuple}. 

1294 ''' 

1295 if _isFsumTuple(other): 

1296 self._ps[:] = other._ps 

1297 self._n = n or other._n 

1298 else: # assert isscalar(other) 

1299 self._ps[:] = other, 

1300 self._n = n or 1 

1301 return self 

1302 

1303 def fsub(self, xs=()): 

1304 '''Subtract an iterable's items from this instance. 

1305 

1306 @see: Method L{Fsum.fadd} for further details. 

1307 ''' 

1308 return self._facc_neg(xs) 

1309 

1310 def fsub_(self, *xs): 

1311 '''Subtract all positional items from this instance. 

1312 

1313 @see: Method L{Fsum.fadd_} for further details. 

1314 ''' 

1315 return self._fsub(xs[0], _sub_op_) if _len(xs) == 1 else \ 

1316 self._facc_neg(xs, origin=1) 

1317 

1318 def _fsub(self, other, op): 

1319 '''(INTERNAL) Apply C{B{self} -= B{other}}. 

1320 ''' 

1321 if _isFsumTuple(other): 

1322 if other is self: # or other._fprs2 == self._fprs2: 

1323 self._fset(_0_0, n=_len(self) * 2) 

1324 elif other._ps: 

1325 self._facc_scalar(other._ps_neg) 

1326 elif self._scalar(other, op): 

1327 self._facc_scalar_(-other) 

1328 return self 

1329 

1330 def fsum(self, xs=()): 

1331 '''Add an iterable's items, summate and return the 

1332 current precision running sum. 

1333 

1334 @arg xs: Iterable of items to add (each item C{scalar} 

1335 or an L{Fsum} or L{Fsum2Tuple} instance). 

1336 

1337 @return: Precision running sum (C{float} or C{int}). 

1338 

1339 @see: Method L{Fsum.fadd}. 

1340 

1341 @note: Accumulation can continue after summation. 

1342 ''' 

1343 return self._facc(xs)._fprs 

1344 

1345 def fsum_(self, *xs): 

1346 '''Add any positional items, summate and return the 

1347 current precision running sum. 

1348 

1349 @arg xs: Items to add (each C{scalar} or an L{Fsum} 

1350 or L{Fsum2Tuple} instance), all positional. 

1351 

1352 @return: Precision running sum (C{float} or C{int}). 

1353 

1354 @see: Methods L{Fsum.fsum}, L{Fsum.Fsum_} and L{Fsum.fsumf_}. 

1355 ''' 

1356 return self._facc_1(xs)._fprs 

1357 

1358 @property_RO 

1359 def _Fsum(self): # like L{Fsum2Tuple._Fsum}, for C{_2floats}. 

1360 return self # NOT @Property_RO, see .copy and ._copy_2 

1361 

1362 def Fsum_(self, *xs, **name): 

1363 '''Like method L{Fsum.fsum_} but returning a named L{Fsum}. 

1364 

1365 @kwarg name: Optional name (C{str}). 

1366 

1367 @return: Copy of this updated instance (L{Fsum}). 

1368 ''' 

1369 return self._facc_1(xs)._copy_2(self.Fsum_, **name) 

1370 

1371 def Fsum2Tuple_(self, *xs, **name): 

1372 '''Like method L{Fsum.fsum_} but returning a named L{Fsum2Tuple}. 

1373 

1374 @kwarg name: Optional name (C{str}). 

1375 

1376 @return: Precision running sum (L{Fsum2Tuple}). 

1377 ''' 

1378 return Fsum2Tuple(self._facc_1(xs)._fprs2, **name) 

1379 

1380 def fsum2(self, xs=(), name=NN): 

1381 '''Add an iterable's items, summate and return the 

1382 current precision running sum I{and} the C{residual}. 

1383 

1384 @arg xs: Iterable of items to add (each item C{scalar} 

1385 or an L{Fsum} or L{Fsum2Tuple} instance). 

1386 @kwarg name: Optional name (C{str}). 

1387 

1388 @return: L{Fsum2Tuple}C{(fsum, residual)} with C{fsum} the 

1389 current precision running sum and C{residual}, the 

1390 (precision) sum of the remaining C{partials}. The 

1391 C{residual is INT0} if the C{fsum} is considered 

1392 to be I{exact}. 

1393 

1394 @see: Methods L{Fsum.fint2}, L{Fsum.fsum} and L{Fsum.fsum2_} 

1395 ''' 

1396 t = self._facc(xs)._fprs2 

1397 return t.dup(name=name) if name else t 

1398 

1399 def fsum2_(self, *xs): 

1400 '''Add any positional items, summate and return the current 

1401 precision running sum and the I{differential}. 

1402 

1403 @arg xs: Values to add (each C{scalar} or an L{Fsum} or 

1404 L{Fsum2Tuple} instance), all positional. 

1405 

1406 @return: 2Tuple C{(fsum, delta)} with the current, precision 

1407 running C{fsum} like method L{Fsum.fsum} and C{delta}, 

1408 the difference with previous running C{fsum}, C{float}. 

1409 

1410 @see: Methods L{Fsum.fsum_} and L{Fsum.fsum}. 

1411 ''' 

1412 return self._fsum2(xs, self._facc_1) 

1413 

1414 def _fsum2(self, xs, _f, **origin): 

1415 '''(INTERNAL) Helper for L{Fsum.fsum2_} and L{Fsum.fsum2f_}. 

1416 ''' 

1417 p, q = self._fprs2 

1418 if xs: 

1419 s, r = _f(xs, **origin)._fprs2 

1420 return s, _2delta(s - p, r - q) # _fsum(_1primed((s, -p, r, -q)) 

1421 else: 

1422 return p, _0_0 

1423 

1424 def fsumf_(self, *xs): 

1425 '''Like method L{Fsum.fsum_} iff I{all} C{B{xs}} are I{known to be scalar}. 

1426 ''' 

1427 return self._facc_scalar(xs)._fprs 

1428 

1429 def Fsumf_(self, *xs): 

1430 '''Like method L{Fsum.Fsum_} iff I{all} C{B{xs}} are I{known to be scalar}. 

1431 ''' 

1432 return self._facc_scalar(xs)._copy_2(self.Fsumf_) 

1433 

1434 def fsum2f_(self, *xs): 

1435 '''Like method L{Fsum.fsum2_} iff I{all} C{B{xs}} are I{known to be scalar}. 

1436 ''' 

1437 return self._fsum2(xs, self._facc_scalar, origin=1) 

1438 

1439# ftruediv = __itruediv__ # for naming consistency? 

1440 

1441 def _ftruediv(self, other, op, **raiser_RESIDUAL): 

1442 '''(INTERNAL) Apply C{B{self} /= B{other}}. 

1443 ''' 

1444 n = _1_0 

1445 if _isFsumTuple(other): 

1446 if other is self or self == other: 

1447 return self._fset(n) # n=_len(self) 

1448 d, r = other._fprs2 

1449 if r: 

1450 R = self._raiser(r, d, **raiser_RESIDUAL) 

1451 if R: 

1452 raise self._ResidualError(op, other, r, **R) 

1453 d, n = other.as_integer_ratio() 

1454 else: 

1455 d = self._scalar(other, op) 

1456 try: 

1457 s = n / d 

1458 except Exception as X: 

1459 raise self._ErrorX(X, op, other) 

1460 f = self._mul_scalar(s, _mul_op_) # handles 0, INF, NAN 

1461 return self._fset(f) # as_is=False 

1462 

1463 @property_RO 

1464 def imag(self): 

1465 '''Get the C{imaginary} part of this instance (C{0.0}, always). 

1466 

1467 @see: Property L{Fsum.real}. 

1468 ''' 

1469 return _0_0 

1470 

1471 def int_float(self, **raiser_RESIDUAL): 

1472 '''Return this instance' current running sum as C{int} or C{float}. 

1473 

1474 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} (C{bool}) to 

1475 ignore L{ResidualError}s and C{B{RESIDUAL}=scalar} 

1476 to override the L{RESIDUAL<Fsum.RESIDUAL>}. 

1477 

1478 @return: This C{integer} sum if this instance C{is_integer}, 

1479 otherwise return the C{float} sum if the residual is 

1480 zero or not significant. 

1481 

1482 @raise ResidualError: Non-zero, significant residual or invalid 

1483 B{C{RESIDUAL}}. 

1484 

1485 @see: Methods L{Fsum.fint}, L{Fsum.fint2}, L{Fsum.RESIDUAL} and 

1486 property L{Fsum.as_iscalar}. 

1487 ''' 

1488 s, r = self._fint2 

1489 if r: 

1490 s, r = self._fprs2 

1491 if r: # PYCHOK no cover 

1492 R = self._raiser(r, s, **raiser_RESIDUAL) 

1493 if R: 

1494 t = _stresidual(_non_zero_, r, **R) 

1495 raise ResidualError(int_float=s, txt=t) 

1496 s = _Float(s) # redundant 

1497 return s 

1498 

1499 def is_exact(self): 

1500 '''Is this instance' running C{fsum} considered to be exact? 

1501 (C{bool}), C{True} only if the C{residual is }L{INT0}. 

1502 ''' 

1503 return self.residual is INT0 

1504 

1505 def is_integer(self): 

1506 '''Is this instance' running sum C{integer}? (C{bool}). 

1507 

1508 @see: Methods L{Fsum.fint}, L{Fsum.fint2} and L{Fsum.is_scalar}. 

1509 ''' 

1510 _, r = self._fint2 

1511 return False if r else True 

1512 

1513 def is_math_fsum(self): 

1514 '''Return whether functions L{fsum}, L{fsum_}, L{fsum1} and 

1515 L{fsum1_} plus partials summation are based on Python's 

1516 C{math.fsum} or not. 

1517 

1518 @return: C{2} if all functions and partials summation 

1519 are based on C{math.fsum}, C{True} if only 

1520 the functions are based on C{math.fsum} (and 

1521 partials summation is not) or C{False} if 

1522 none are. 

1523 ''' 

1524 f = Fsum._math_fsum 

1525 return 2 if _psum is f else bool(f) 

1526 

1527 def is_scalar(self, **raiser_RESIDUAL): 

1528 '''Is this instance' running sum C{scalar} without residual or with 

1529 a residual I{ratio} not exceeding the RESIDUAL threshold? 

1530 

1531 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} (C{bool}) to ignore 

1532 L{ResidualError}s and C{B{RESIDUAL}=scalar} to override 

1533 the L{RESIDUAL<Fsum.RESIDUAL>} threshold. 

1534 

1535 @return: C{True} if this instance' non-zero residual C{ratio} exceeds 

1536 the L{RESIDUAL<Fsum.RESIDUAL>} threshold (C{bool}). 

1537 

1538 @raise ResidualError: Non-zero, significant residual or invalid 

1539 B{C{RESIDUAL}}. 

1540 

1541 @see: Method L{Fsum.RESIDUAL}, L{Fsum.is_integer} and property 

1542 L{Fsum.as_iscalar}. 

1543 ''' 

1544 s, r = self._fprs2 

1545 return False if r and self._raiser(r, s, **raiser_RESIDUAL) else True 

1546 

1547 def _mul_Fsum(self, other, op=_mul_op_): # in .fmath.Fhorner 

1548 '''(INTERNAL) Return C{B{self} * B{other}} as L{Fsum} or C{0}. 

1549 ''' 

1550 # assert _isFsumTuple(other) 

1551 if self._ps and other._ps: 

1552 f = self._ps_mul(op, *other._ps) # NO .as_iscalar! 

1553 else: 

1554 f = _0_0 

1555 return f 

1556 

1557 def _mul_scalar(self, factor, op): # in .fmath.Fhorner 

1558 '''(INTERNAL) Return C{B{self} * scalar B{factor}} as L{Fsum}, C{0.0} or C{self}. 

1559 ''' 

1560 # assert isscalar(factor) 

1561 if self._ps and self._finite(factor, op): 

1562 f = self if factor == _1_0 else ( 

1563 self._neg if factor == _N_1_0 else 

1564 self._ps_mul(op, factor).as_iscalar) 

1565 else: 

1566 f = _0_0 

1567 return f 

1568 

1569 @property_RO 

1570 def _neg(self): 

1571 '''(INTERNAL) Return C{Fsum(-self)} or scalar C{NEG0}. 

1572 ''' 

1573 return _Psum(self._ps_neg) if self._ps else NEG0 

1574 

1575 @property_RO 

1576 def partials(self): 

1577 '''Get this instance' current, partial sums (C{tuple} of C{float}s). 

1578 ''' 

1579 return _Tuple(self._ps) 

1580 

1581 def pow(self, x, *mod, **raiser_RESIDUAL): 

1582 '''Return C{B{self}**B{x}} as L{Fsum}. 

1583 

1584 @arg x: The exponent (C{scalar} or L{Fsum}). 

1585 @arg mod: Optional modulus (C{int} or C{None}) for the 3-argument 

1586 C{pow(B{self}, B{other}, B{mod})} version. 

1587 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} (C{bool}) to 

1588 ignore L{ResidualError}s and C{B{RESIDUAL}=scalar} 

1589 to override the L{RESIDUAL<Fsum.RESIDUAL>}. 

1590 

1591 @return: The C{pow(self, B{x})} or C{pow(self, B{x}, *B{mod})} 

1592 result (L{Fsum}). 

1593 

1594 @raise ResidualError: Non-zero, significant residual or invalid 

1595 B{C{RESIDUAL}}. 

1596 

1597 @note: If B{C{mod}} is given as C{None}, the result will be an 

1598 C{integer} L{Fsum} provided this instance C{is_integer} 

1599 or set to C{integer} by an L{Fsum.fint} call. 

1600 

1601 @see: Methods L{Fsum.__ipow__}, L{Fsum.fint}, L{Fsum.is_integer} 

1602 and L{Fsum.root}. 

1603 ''' 

1604 f = self._copy_2(self.pow) 

1605 return f._fpow(x, _pow_op_, *mod, **raiser_RESIDUAL) # f = pow(f, x, *mod) 

1606 

1607 def _pow(self, other, unused, op, **raiser_RESIDUAL): 

1608 '''Return C{B{self} ** B{other}}. 

1609 ''' 

1610 if _isFsumTuple(other): 

1611 f = self._pow_Fsum(other, op, **raiser_RESIDUAL) 

1612 elif self._scalar(other, op): 

1613 x = self._finite(other, op) 

1614 f = self._pow_scalar(x, other, op, **raiser_RESIDUAL) 

1615 else: 

1616 f = self._pow_0_1(0, other) 

1617 return f 

1618 

1619 def _pow_0_1(self, x, other): 

1620 '''(INTERNAL) Return B{C{self}**1} or C{B{self}**0 == 1.0}. 

1621 ''' 

1622 return self if x else (1 if isint(other) and self.is_integer() else _1_0) 

1623 

1624 def _pow_2_3(self, b, x, other, op, *mod, **raiser_RESIDUAL): 

1625 '''(INTERNAL) 2-arg C{pow(B{b}, scalar B{x})} and 3-arg C{pow(B{b}, 

1626 B{x}, int B{mod} or C{None})}, embellishing errors. 

1627 ''' 

1628 

1629 if mod: # b, x, mod all C{int}, unless C{mod} is C{None} 

1630 m = mod[0] 

1631 # assert _isFsumTuple(b) 

1632 

1633 def _s(s, r): 

1634 R = self._raiser(r, s, **raiser_RESIDUAL) 

1635 if R: 

1636 raise self._ResidualError(op, other, r, mod=m, **R) 

1637 return s 

1638 

1639 b = _s(*(b._fprs2 if m is None else b._fint2)) 

1640 x = _s(*_2scalar2(x)) 

1641 

1642 try: 

1643 # 0**INF == 0.0, 1**INF == 1.0, -1**2.3 == -(1**2.3) 

1644 s = pow(b, x, *mod) 

1645 if iscomplex(s): 

1646 # neg**frac == complex in Python 3+, but ValueError in 2- 

1647 raise ValueError(_strcomplex(s, b, x, *mod)) 

1648 return self._finite(s) 

1649 except Exception as X: 

1650 raise self._ErrorX(X, op, other, *mod) 

1651 

1652 def _pow_Fsum(self, other, op, **raiser_RESIDUAL): 

1653 '''(INTERNAL) Return C{B{self} **= B{other}} for C{_isFsumTuple(other)}. 

1654 ''' 

1655 # assert _isFsumTuple(other) 

1656 x, r = other._fprs2 

1657 f = self._pow_scalar(x, other, op, **raiser_RESIDUAL) 

1658 if f and r: 

1659 f *= self._pow_scalar(r, other, op, **raiser_RESIDUAL) 

1660 return f 

1661 

1662 def _pow_int(self, x, other, op, **raiser_RESIDUAL): 

1663 '''(INTERNAL) Return C{B{self} **= B{x}} for C{int B{x} >= 0}. 

1664 ''' 

1665 # assert isint(x) and x >= 0 

1666 ps = self._ps 

1667 if _len(ps) > 1: 

1668 _mul_Fsum = Fsum._mul_Fsum 

1669 if x > 4: 

1670 p = self 

1671 f = self if (x & 1) else _Psum_(_1_0) 

1672 m = x >> 1 # // 2 

1673 while m: 

1674 p = _mul_Fsum(p, p, op) # p **= 2 

1675 if (m & 1): 

1676 f = _mul_Fsum(f, p, op) # f *= p 

1677 m >>= 1 # //= 2 

1678 elif x > 1: # self**2, 3, or 4 

1679 f = _mul_Fsum(self, self, op) 

1680 if x > 2: # self**3 or 4 

1681 p = self if x < 4 else f 

1682 f = _mul_Fsum(f, p, op) 

1683 else: # self**1 or self**0 == 1 or _1_0 

1684 f = self._pow_0_1(x, other) 

1685 elif ps: # self._ps[0]**x 

1686 f = self._pow_2_3(ps[0], x, other, op, **raiser_RESIDUAL) 

1687 else: # PYCHOK no cover 

1688 # 0**pos_int == 0, but 0**0 == 1 

1689 f = 0 if x else 1 

1690 return f 

1691 

1692 def _pow_scalar(self, x, other, op, **raiser_RESIDUAL): 

1693 '''(INTERNAL) Return C{self**B{x}} for C{scalar B{x}}. 

1694 ''' 

1695 s, r = self._fprs2 

1696 if r: 

1697 # assert s != 0 

1698 if isint(x, both=True): # self**int 

1699 x = int(x) 

1700 y = _abs(x) 

1701 if y > 1: 

1702 f = self._pow_int(y, other, op, **raiser_RESIDUAL) 

1703 if x > 0: # i.e. > 1 

1704 return f # Fsum or scalar 

1705 # assert x < 0 # i.e. < -1 

1706 if _isFsum(f): 

1707 s, r = f._fprs2 

1708 if r: 

1709 return _1_Over(f, op, **raiser_RESIDUAL) 

1710 else: # scalar 

1711 s = f 

1712 # use s**(-1) to get the CPython 

1713 # float_pow error iff s is zero 

1714 x = -1 

1715 elif x < 0: # self**(-1) 

1716 return _1_Over(self, op, **raiser_RESIDUAL) # 1 / self 

1717 else: # self**1 or self**0 

1718 return self._pow_0_1(x, other) # self, 1 or 1.0 

1719 else: # self**fractional 

1720 R = self._raiser(r, s, **raiser_RESIDUAL) 

1721 if R: 

1722 raise self._ResidualError(op, other, r, **R) 

1723 n, d = self.as_integer_ratio() 

1724 if _abs(n) > _abs(d): 

1725 n, d, x = d, n, (-x) 

1726 s = n / d 

1727 # assert isscalar(s) and isscalar(x) 

1728 return self._pow_2_3(s, x, other, op, **raiser_RESIDUAL) 

1729 

1730 def _ps_acc(self, ps, xs, up=True, **unused): 

1731 '''(INTERNAL) Accumulate C{xs} scalars into list C{ps}. 

1732 ''' 

1733 n = 0 

1734 _2s = _2sum 

1735 for x in (_Tuple(xs) if xs is ps else xs): 

1736 # assert isscalar(x) and _isfinite(x) 

1737 if x: 

1738 i = 0 

1739 for p in ps: 

1740 x, p = _2s(x, p) 

1741 if p: 

1742 ps[i] = p 

1743 i += 1 

1744 ps[i:] = (x,) if x else () 

1745 n += 1 

1746 if n: 

1747 self._n += n 

1748 # Fsum._ps_max = max(Fsum._ps_max, _len(ps)) 

1749 if up: 

1750 self._update() 

1751 return ps 

1752 

1753 def _ps_mul(self, op, *factors): 

1754 '''(INTERNAL) Multiply this instance' C{partials} with each 

1755 of the scalar B{C{factors}} and accumulate. 

1756 ''' 

1757 def _pfs(ps, fs): 

1758 if _len(ps) < _len(fs): 

1759 ps, fs = fs, ps 

1760 _fin = _isfinite 

1761 for f in fs: 

1762 for p in ps: 

1763 p *= f 

1764 yield p if _fin(p) else self._finite(p, op) 

1765 

1766 return _Psum(self._ps_acc([], _pfs(self._ps, factors), up=False)) 

1767 

1768 @property_RO 

1769 def _ps_neg(self): 

1770 '''(INTERNAL) Yield the partials, I{negated}. 

1771 ''' 

1772 for p in self._ps: 

1773 yield -p 

1774 

1775 def _ps_1sum(self, *less): 

1776 '''(INTERNAL) Return the partials sum, 1-primed C{less} any scalars. 

1777 ''' 

1778 def _1pls(ps, ls): 

1779 yield _1_0 

1780 for p in ps: 

1781 yield p 

1782 for p in ls: 

1783 yield -p 

1784 yield _N_1_0 

1785 

1786 return _fsum(_1pls(self._ps, less)) 

1787 

1788 def _raiser(self, r, s, raiser=True, **RESIDUAL): 

1789 '''(INTERNAL) Does ratio C{r / s} exceed the RESIDUAL threshold 

1790 I{and} is residual C{r} I{non-zero} or I{significant} (for a 

1791 negative respectively positive C{RESIDUAL} threshold)? 

1792 ''' 

1793 if r and raiser: 

1794 t = self._RESIDUAL 

1795 if RESIDUAL: 

1796 t = _threshold(_xkwds_get(RESIDUAL, RESIDUAL=t)) 

1797 if t < 0 or (s + r) != s: 

1798 q = (r / s) if s else s # == 0. 

1799 if fabs(q) > fabs(t): 

1800 return dict(ratio=q, R=t) 

1801 return {} 

1802 

1803 @property_RO 

1804 def real(self): 

1805 '''Get the C{real} part of this instance (C{float}). 

1806 

1807 @see: Methods L{Fsum.__float__} and L{Fsum.fsum} 

1808 and properties L{Fsum.ceil}, L{Fsum.floor}, 

1809 L{Fsum.imag} and L{Fsum.residual}. 

1810 ''' 

1811 return _Float(self._fprs) 

1812 

1813 @property_RO 

1814 def residual(self): 

1815 '''Get this instance' residual (C{float} or C{int}): the 

1816 C{sum(partials)} less the precision running sum C{fsum}. 

1817 

1818 @note: The C{residual is INT0} iff the precision running 

1819 C{fsum} is considered to be I{exact}. 

1820 

1821 @see: Methods L{Fsum.fsum}, L{Fsum.fsum2} and L{Fsum.is_exact}. 

1822 ''' 

1823 return self._fprs2.residual 

1824 

1825 def RESIDUAL(self, *threshold): 

1826 '''Get and set this instance' I{ratio} for raising L{ResidualError}s, 

1827 overriding the default from env variable C{PYGEODESY_FSUM_RESIDUAL}. 

1828 

1829 @arg threshold: If C{scalar}, the I{ratio} to exceed for raising 

1830 L{ResidualError}s in division and exponention, if 

1831 C{None} restore the default set with env variable 

1832 C{PYGEODESY_FSUM_RESIDUAL} or if omitted, keep the 

1833 current setting. 

1834 

1835 @return: The previous C{RESIDUAL} setting (C{float}), default C{0.0}. 

1836 

1837 @raise ResidualError: Invalid B{C{threshold}}. 

1838 

1839 @note: L{ResidualError}s may be thrown if the non-zero I{ratio} 

1840 C{residual / fsum} exceeds the given B{C{threshold}} and 

1841 if the C{residual} is non-zero and I{significant} vs the 

1842 C{fsum}, i.e. C{(fsum + residual) != fsum} and if optional 

1843 keyword argument C{raiser=False} is missing. Specify a 

1844 negative B{C{threshold}} for only non-zero C{residual} 

1845 testing without I{significant}. 

1846 ''' 

1847 r = self._RESIDUAL 

1848 if threshold: 

1849 t = threshold[0] 

1850 self._RESIDUAL = Fsum._RESIDUAL if t is None else ( # for ... 

1851 (_0_0 if t else _1_0) if isbool(t) else 

1852 _threshold(t)) # ... backward compatibility 

1853 return r 

1854 

1855 def _ResidualError(self, op, other, residual, **mod_R): 

1856 '''(INTERNAL) Non-zero B{C{residual}} etc. 

1857 ''' 

1858 def _p(mod=None, R=0, **unused): # ratio=0 

1859 return (_non_zero_ if R < 0 else _significant_) \ 

1860 if mod is None else _integer_ 

1861 

1862 t = _stresidual(_p(**mod_R), residual, **mod_R) 

1863 return self._Error(op, other, ResidualError, txt=t) 

1864 

1865 def root(self, root, **raiser_RESIDUAL): 

1866 '''Return C{B{self}**(1 / B{root})} as L{Fsum}. 

1867 

1868 @arg root: The order (C{scalar} or L{Fsum}), non-zero. 

1869 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} (C{bool}) to 

1870 ignore L{ResidualError}s and C{B{RESIDUAL}=scalar} 

1871 to override the L{RESIDUAL<Fsum.RESIDUAL>}. 

1872 

1873 @return: The C{self ** (1 / B{root})} result (L{Fsum}). 

1874 

1875 @raise ResidualError: Non-zero, significant residual or invalid 

1876 B{C{RESIDUAL}}. 

1877 

1878 @see: Method L{Fsum.pow}. 

1879 ''' 

1880 x = _1_Over(root, _truediv_op_, **raiser_RESIDUAL) 

1881 f = self._copy_2(self.root) 

1882 return f._fpow(x, f.name, **raiser_RESIDUAL) # == pow(f, x) 

1883 

1884 def _scalar(self, other, op, **txt): 

1885 '''(INTERNAL) Return scalar C{other}. 

1886 ''' 

1887 if isscalar(other): 

1888 return other 

1889 raise self._Error(op, other, _TypeError, **txt) # _invalid_ 

1890 

1891 def signOf(self, res=True): 

1892 '''Determine the sign of this instance. 

1893 

1894 @kwarg res: If C{True} consider, otherwise 

1895 ignore the residual (C{bool}). 

1896 

1897 @return: The sign (C{int}, -1, 0 or +1). 

1898 ''' 

1899 s, r = self._fprs2 

1900 r = (-r) if res else 0 

1901 return _signOf(s, r) 

1902 

1903 def toRepr(self, **lenc_prec_sep_fmt): # PYCHOK signature 

1904 '''Return this C{Fsum} instance as representation. 

1905 

1906 @kwarg lenc_prec_sep_fmt: Optional keyword arguments 

1907 for method L{Fsum.toStr}. 

1908 

1909 @return: This instance (C{repr}). 

1910 ''' 

1911 return Fmt.repr_at(self, self.toStr(**lenc_prec_sep_fmt)) 

1912 

1913 def toStr(self, lenc=True, **prec_sep_fmt): # PYCHOK signature 

1914 '''Return this C{Fsum} instance as string. 

1915 

1916 @kwarg lenc: If C{True} include the current C{[len]} of this 

1917 L{Fsum} enclosed in I{[brackets]} (C{bool}). 

1918 @kwarg prec_sep_fmt: Optional keyword arguments for method 

1919 L{Fsum2Tuple.toStr}. 

1920 

1921 @return: This instance (C{str}). 

1922 ''' 

1923 p = self.classname 

1924 if lenc: 

1925 p = Fmt.SQUARE(p, _len(self)) 

1926 n = _enquote(self.name, white=_UNDER_) 

1927 t = self._fprs2.toStr(**prec_sep_fmt) 

1928 return NN(p, _SPACE_, n, t) 

1929 

1930 def _truediv(self, other, op, **raiser_RESIDUAL): 

1931 '''(INTERNAL) Return C{B{self} / B{other}} as an L{Fsum}. 

1932 ''' 

1933 f = self._copy_2(self.__truediv__) 

1934 return f._ftruediv(other, op, **raiser_RESIDUAL) 

1935 

1936 def _update(self, updated=True): # see ._fset 

1937 '''(INTERNAL) Zap all cached C{Property_RO} values. 

1938 ''' 

1939 if updated: 

1940 _pop = self.__dict__.pop 

1941 for p in _ROs: 

1942 _ = _pop(p, None) 

1943# Fsum._fint2._update(self) 

1944# Fsum._fprs ._update(self) 

1945# Fsum._fprs2._update(self) 

1946 return self # for .fset_ 

1947 

1948_ROs = _allPropertiesOf_n(3, Fsum, Property_RO) # PYCHOK see Fsum._update 

1949 

1950 

1951def _Float_Int(arg, **name_Error): 

1952 '''(INTERNAL) Unit of L{Fsum2Tuple} items. 

1953 ''' 

1954 U = Int if isint(arg) else Float 

1955 return U(arg, **name_Error) 

1956 

1957 

1958class DivMod2Tuple(_NamedTuple): 

1959 '''2-Tuple C{(div, mod)} with the quotient C{div} and remainder 

1960 C{mod} results of a C{divmod} operation. 

1961 

1962 @note: Quotient C{div} an C{int} in Python 3+ but a C{float} 

1963 in Python 2-. Remainder C{mod} an L{Fsum} instance. 

1964 ''' 

1965 _Names_ = (_div_, _mod_) 

1966 _Units_ = (_Float_Int, Fsum) 

1967 

1968 

1969class Fsum2Tuple(_NamedTuple): 

1970 '''2-Tuple C{(fsum, residual)} with the precision running C{fsum} 

1971 and the C{residual}, the sum of the remaining partials. Each 

1972 item is C{float} or C{int}. 

1973 

1974 @note: If the C{residual is INT0}, the C{fsum} is considered 

1975 to be I{exact}, see method L{Fsum2Tuple.is_exact}. 

1976 ''' 

1977 _Names_ = ( Fsum.fsum.__name__, Fsum.residual.name) 

1978 _Units_ = (_Float_Int, _Float_Int) 

1979 

1980 def __abs__(self): # in .fmath 

1981 return self._Fsum.__abs__() 

1982 

1983 def __bool__(self): # PYCHOK Python 3+ 

1984 return bool(self._Fsum) 

1985 

1986 def __eq__(self, other): 

1987 return self._other_op(other, self.__eq__) 

1988 

1989 def __float__(self): 

1990 return self._Fsum.__float__() 

1991 

1992 def __ge__(self, other): 

1993 return self._other_op(other, self.__ge__) 

1994 

1995 def __gt__(self, other): 

1996 return self._other_op(other, self.__gt__) 

1997 

1998 def __le__(self, other): 

1999 return self._other_op(other, self.__le__) 

2000 

2001 def __lt__(self, other): 

2002 return self._other_op(other, self.__lt__) 

2003 

2004 def __int__(self): 

2005 return self._Fsum.__int__() 

2006 

2007 def __ne__(self, other): 

2008 return self._other_op(other, self.__ne__) 

2009 

2010 def __neg__(self): 

2011 return self._Fsum.__neg__() 

2012 

2013 __nonzero__ = __bool__ # Python 2- 

2014 

2015 def __pos__(self): 

2016 return self._Fsum.__pos__() 

2017 

2018 def as_integer_ratio(self): 

2019 '''Return this instance as the ratio of 2 integers. 

2020 

2021 @see: Method L{Fsum.as_integer_ratio} for further details. 

2022 ''' 

2023 return self._Fsum.as_integer_ratio() 

2024 

2025 @property_RO 

2026 def _fint2(self): 

2027 return self._Fsum._fint2 

2028 

2029 @property_RO 

2030 def _fprs2(self): 

2031 return self._Fsum._fprs2 

2032 

2033 @Property_RO 

2034 def _Fsum(self): # this C{Fsum2Tuple} as L{Fsum} 

2035 s, r = _s_r(*self) 

2036 ps = (r, s) if r else (s,) 

2037 return _Psum(ps, name=self.name) 

2038 

2039 def Fsum_(self, *xs, **name_RESIDUAL): 

2040 '''Return this C{Fsum2Tuple} as an L{Fsum} plus some C{xs}. 

2041 ''' 

2042 f = _Psum(self._Fsum._ps, **name_RESIDUAL) 

2043 return f._facc_1(xs, up=False) if xs else f 

2044 

2045 def is_exact(self): 

2046 '''Is this L{Fsum2Tuple} considered to be exact? (C{bool}). 

2047 ''' 

2048 return self._Fsum.is_exact() 

2049 

2050 def is_integer(self): 

2051 '''Is this L{Fsum2Tuple} C{integer}? (C{bool}). 

2052 ''' 

2053 return self._Fsum.is_integer() 

2054 

2055 def _mul_scalar(self, other, op): # for Fsum._fmul 

2056 return self._Fsum._mul_scalar(other, op) 

2057 

2058 @property_RO 

2059 def _n(self): 

2060 return self._Fsum._n 

2061 

2062 def _other_op(self, other, which): 

2063 C, s = (_Tuple, self) if _isAn(other, _Tuple) else (Fsum, self._Fsum) 

2064 return getattr(C, which.__name__)(s, other) 

2065 

2066 @property_RO 

2067 def _ps(self): 

2068 return self._Fsum._ps 

2069 

2070 @property_RO 

2071 def _ps_neg(self): 

2072 return self._Fsum._ps_neg 

2073 

2074 def signOf(self, **res): 

2075 '''Like method L{Fsum.signOf}. 

2076 ''' 

2077 return self._Fsum.signOf(**res) 

2078 

2079 def toStr(self, fmt=Fmt.g, **prec_sep): # PYCHOK signature 

2080 '''Return this L{Fsum2Tuple} as string (C{str}). 

2081 

2082 @kwarg fmt: Optional C{float} format (C{letter}). 

2083 @kwarg prec_sep: Optional keyword arguments for function 

2084 L{fstr<streprs.fstr>}. 

2085 ''' 

2086 return Fmt.PAREN(fstr(self, fmt=fmt, strepr=str, force=False, **prec_sep)) 

2087 

2088_Fsum_Fsum2Tuple_types = Fsum, Fsum2Tuple # PYCHOK in .fstats 

2089 

2090 

2091class ResidualError(_ValueError): 

2092 '''Error raised for a division, power or root operation of 

2093 an L{Fsum} instance with a C{residual} I{ratio} exceeding 

2094 the L{RESIDUAL<Fsum.RESIDUAL>} threshold. 

2095 

2096 @see: Module L{pygeodesy.fsums} and method L{Fsum.RESIDUAL}. 

2097 ''' 

2098 pass 

2099 

2100 

2101try: 

2102 from math import fsum as _fsum # precision IEEE-754 sum, Python 2.6+ 

2103 

2104 # make sure _fsum works as expected (XXX check 

2105 # float.__getformat__('float')[:4] == 'IEEE'?) 

2106 if _fsum((1, 1e101, 1, -1e101)) != 2: # PYCHOK no cover 

2107 del _fsum # nope, remove _fsum ... 

2108 raise ImportError # ... use _fsum below 

2109 

2110 Fsum._math_fsum = _sum = _fsum # PYCHOK exported 

2111except ImportError: 

2112 _sum = sum # Fsum(NAN) exception fall-back, in .elliptic 

2113 

2114 def _fsum(xs): 

2115 '''(INTERNAL) Precision summation, Python 2.5-. 

2116 ''' 

2117 F = Fsum() 

2118 F.name = _fsum.__name__ 

2119 return F._facc(xs, up=False)._fprs2.fsum 

2120 

2121 

2122def fsum(xs, floats=False): 

2123 '''Precision floating point summation based on/like Python's C{math.fsum}. 

2124 

2125 @arg xs: Iterable of items to add (each C{scalar} or an L{Fsum} or L{Fsum2Tuple} 

2126 instance). 

2127 @kwarg floats: Use C{B{floats}=True} iff I{all} B{C{xs}} items are I{known to 

2128 be scalar} (C{bool}). 

2129 

2130 @return: Precision C{fsum} (C{float}). 

2131 

2132 @raise OverflowError: Partial C{2sum} overflow. 

2133 

2134 @raise TypeError: Non-scalar B{C{xs}} item. 

2135 

2136 @raise ValueError: Invalid or non-finite B{C{xs}} item. 

2137 

2138 @note: Exception and I{non-finite} handling may differ if not based 

2139 on Python's C{math.fsum}. 

2140 

2141 @see: Class L{Fsum} and methods L{Fsum.fsum} and L{Fsum.fadd}. 

2142 ''' 

2143 return _fsum(xs if floats is True else _2floats(xs)) if xs else _0_0 # PYCHOK yield 

2144 

2145 

2146def fsum_(*xs, **floats): 

2147 '''Precision floating point summation of all positional items. 

2148 

2149 @arg xs: Items to add (each C{scalar} or an L{Fsum} or L{Fsum2Tuple} instance), 

2150 all positional. 

2151 @kwarg floats: Use C{B{floats}=True} iff I{all} B{C{xs}} items are I{known to 

2152 be scalar} (C{bool}). 

2153 

2154 @see: Function L{fsum<fsums.fsum>} for further details. 

2155 ''' 

2156 return _fsum(xs if _xkwds_get(floats, floats=False) is True else 

2157 _2floats(xs, origin=1)) if xs else _0_0 # PYCHOK yield 

2158 

2159 

2160def fsumf_(*xs): 

2161 '''Precision floating point summation iff I{all} C{B{xs}} items are I{known to be scalar}. 

2162 

2163 @see: Function L{fsum_<fsums.fsum_>} for further details. 

2164 ''' 

2165 return _fsum(xs) if xs else _0_0 

2166 

2167 

2168def fsum1(xs, floats=False): 

2169 '''Precision floating point summation, 1-primed. 

2170 

2171 @arg xs: Iterable of items to add (each C{scalar} or an L{Fsum} or L{Fsum2Tuple} 

2172 instance). 

2173 @kwarg floats: Use C{B{floats}=True} iff I{all} B{C{xs}} items are I{known to 

2174 be scalar} (C{bool}). 

2175 

2176 @see: Function L{fsum<fsums.fsum>} for further details. 

2177 ''' 

2178 return _fsum(_1primed(xs if floats is True else _2floats(xs))) if xs else _0_0 # PYCHOK yield 

2179 

2180 

2181def fsum1_(*xs, **floats): 

2182 '''Precision floating point summation, 1-primed of all positional items. 

2183 

2184 @arg xs: Items to add (each C{scalar} or an L{Fsum} or L{Fsum2Tuple} instance), 

2185 all positional. 

2186 @kwarg floats: Use C{B{floats}=True} iff I{all} B{C{xs}} items are I{known to 

2187 be scalar} (C{bool}). 

2188 

2189 @see: Function L{fsum_<fsums.fsum_>} for further details. 

2190 ''' 

2191 return _fsum(_1primed(xs if _xkwds_get(floats, floats=False) is True else 

2192 _2floats(xs, origin=1))) if xs else _0_0 # PYCHOK yield 

2193 

2194 

2195def fsum1f_(*xs): 

2196 '''Precision floating point summation iff I{all} C{B{xs}} items are I{known to be scalar}. 

2197 

2198 @see: Function L{fsum_<fsums.fsum_>} for further details. 

2199 ''' 

2200 return _fsum(_1primed(xs)) if xs else _0_0 

2201 

2202 

2203if __name__ == '__main__': 

2204 

2205 # usage: [env _psum=fsum] python3 -m pygeodesy.fsums 

2206 

2207 if _getenv(_psum.__name__, NN) == _fsum.__name__: 

2208 _psum = _fsum 

2209 

2210 def _test(n): 

2211 # copied from Hettinger, see L{Fsum} reference 

2212 from pygeodesy import frandoms, printf 

2213 

2214 printf(_fsum.__name__, end=_COMMASPACE_) 

2215 printf(_psum.__name__, end=_COMMASPACE_) 

2216 

2217 F = Fsum() 

2218 if F.is_math_fsum(): 

2219 for t in frandoms(n, seeded=True): 

2220 assert _Float(F.fset_(*t)) == _fsum(t) 

2221 printf(_DOT_, end=NN) 

2222 printf(NN) 

2223 

2224 _test(128) 

2225 

2226# **) MIT License 

2227# 

2228# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved. 

2229# 

2230# Permission is hereby granted, free of charge, to any person obtaining a 

2231# copy of this software and associated documentation files (the "Software"), 

2232# to deal in the Software without restriction, including without limitation 

2233# the rights to use, copy, modify, merge, publish, distribute, sublicense, 

2234# and/or sell copies of the Software, and to permit persons to whom the 

2235# Software is furnished to do so, subject to the following conditions: 

2236# 

2237# The above copyright notice and this permission notice shall be included 

2238# in all copies or substantial portions of the Software. 

2239# 

2240# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

2241# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

2242# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

2243# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

2244# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 

2245# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 

2246# OTHER DEALINGS IN THE SOFTWARE.