Coverage for pygeodesy/fsums.py: 96%

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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_PARTIALS} to string C{"fsum"}) for summation 

18of L{Fsum} partials by Python function C{math.fsum}. 

19 

20Set env variable C{PYGEODESY_FSUM_RESIDUAL} to a C{float} string greater 

21than C{"0.0"} as the threshold to throw a L{ResidualError} in division or 

22exponention of an L{Fsum} instance with a I{relative} C{residual} exceeding 

23the threshold, see methods L{Fsum.RESIDUAL}, L{Fsum.pow}, L{Fsum.__ipow__} 

24and L{Fsum.__itruediv__}. 

25''' 

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

27from __future__ import division as _; del _ # PYCHOK semicolon 

28 

29from pygeodesy.basics import iscomplex, isint, isscalar, itemsorted, \ 

30 signOf, _signOf 

31from pygeodesy.constants import INT0, _isfinite, isinf, isnan, NEG0, _pos_self, \ 

32 _0_0, _1_0, _N_1_0, Float, Int 

33from pygeodesy.errors import _OverflowError, _TypeError, _ValueError, _xError, \ 

34 _xError2, _xkwds_get, _ZeroDivisionError 

35from pygeodesy.interns import NN, _arg_, _COMMASPACE_, _DASH_, _DOT_, _EQUAL_, \ 

36 _exceeds_, _from_, _iadd_op_, _LANGLE_, _negative_, \ 

37 _NOTEQUAL_, _not_finite_, _not_scalar_, _PERCENT_, \ 

38 _PLUS_, _R_, _RANGLE_, _SLASH_, _SPACE_, _STAR_, _UNDER_ 

39from pygeodesy.lazily import _ALL_LAZY, _getenv, _sys_version_info2 

40from pygeodesy.named import _Named, _NamedTuple, _NotImplemented, Fmt, unstr 

41from pygeodesy.props import _allPropertiesOf_n, deprecated_property_RO, \ 

42 Property_RO, property_RO 

43# from pygeodesy.streprs import Fmt, unstr # from .named 

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

45 

46from math import ceil as _ceil, fabs, floor as _floor # PYCHOK used! .ltp 

47 

48__all__ = _ALL_LAZY.fsums 

49__version__ = '24.04.04' 

50 

51_add_op_ = _PLUS_ # in .auxilats.auxAngle 

52_eq_op_ = _EQUAL_ * 2 # _DEQUAL_ 

53_COMMASPACE_R_ = _COMMASPACE_ + _R_ 

54_div_ = 'div' 

55_exceeds_R_ = _SPACE_ + _exceeds_(_R_) 

56_floordiv_op_ = _SLASH_ * 2 # _DSLASH_ 

57_fset_op_ = _EQUAL_ 

58_ge_op_ = _RANGLE_ + _EQUAL_ 

59_gt_op_ = _RANGLE_ 

60_integer_ = 'integer' 

61_le_op_ = _LANGLE_ + _EQUAL_ 

62_lt_op_ = _LANGLE_ 

63_mod_ = 'mod' 

64_mod_op_ = _PERCENT_ 

65_mul_op_ = _STAR_ 

66_ne_op_ = _NOTEQUAL_ 

67_non_zero_ = 'non-zero' 

68_pow_op_ = _STAR_ * 2 # _DSTAR_, in .fmath 

69_sub_op_ = _DASH_ # in .auxilats.auxAngle, .fsums 

70_truediv_op_ = _SLASH_ 

71_divmod_op_ = _floordiv_op_ + _mod_op_ 

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

73 

74 

75def _2float(index=None, **name_value): # in .fmath, .fstats 

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

77 ''' 

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

79 try: 

80 v = float(v) 

81 if _isfinite(v): 

82 return v 

83 raise ValueError(_not_finite_) 

84 except Exception as X: 

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

86 

87 

88def _2floats(xs, origin=0, neg=False): 

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

90 ''' 

91 if neg: 

92 def _X(X): 

93 return X._ps_neg 

94 

95 def _x(x): 

96 return -float(x) 

97 else: 

98 def _X(X): # PYCHOK re-def 

99 return X._ps 

100 

101 _x = float 

102 

103 return _2yield(xs, origin, _X, _x) 

104 

105 

106def _1primed(xs): # in .fmath 

107 '''(INTERNAL) 1-Prime the summation of C{xs} 

108 arguments I{known} to be C{finite float}. 

109 ''' 

110 yield _1_0 

111 for x in xs: 

112 if x: 

113 yield x 

114 yield _N_1_0 

115 

116 

117def _2ps(s, r): 

118 '''(INTERNAL) Return a C{s} and C{r} pair, I{ps-ordered}. 

119 ''' 

120 if fabs(s) < fabs(r): 

121 s, r = r, s 

122 return ((r, s) if s else (r,)) if r else (s,) 

123 

124 

125def _psum(ps): # PYCHOK used! 

126 '''(INTERNAL) Partials sum, updating C{ps}, I{overridden below}. 

127 ''' 

128 # assert isinstance(ps, list) 

129 i = len(ps) - 1 

130 s = _0_0 if i < 0 else ps[i] 

131 _2s = _2sum 

132 while i > 0: 

133 i -= 1 

134 s, r = _2s(s, ps[i]) 

135 if r: # sum(ps) became inexact 

136 if s: 

137 ps[i:] = r, s 

138 if i > 0: 

139 p = ps[i-1] # round half-even 

140 if (p > 0 and r > 0) or \ 

141 (p < 0 and r < 0): # signs match 

142 r *= 2 

143 t = s + r 

144 if r == (t - s): 

145 s = t 

146 break # return s 

147 s = r # PYCHOK no cover 

148 ps[i:] = s, 

149 return s 

150 

151 

152def _2scalar(other, _raiser=None): 

153 '''(INTERNAL) Return B{C{other}} as C{int}, C{float} or C{as-is}. 

154 ''' 

155 if isinstance(other, Fsum): 

156 s, r = other._fint2 

157 if r: 

158 s, r = other._fprs2 

159 if r: # PYCHOK no cover 

160 if _raiser and _raiser(r, s): 

161 raise ValueError(_stresidual(_non_zero_, r)) 

162 s = other # L{Fsum} as-is 

163 else: 

164 s = other # C{type} as-is 

165 if isint(s, both=True): 

166 s = int(s) 

167 return s 

168 

169 

170def _strcomplex(s, *args): 

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

172 ''' 

173 c = _strcomplex.__name__[4:] 

174 n = _DASH_(len(args), _arg_) 

175 t = unstr(pow, *args) 

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

177 

178 

179def _stresidual(prefix, residual, **name_values): 

180 '''(INTERNAL) Residual error as C{str}. 

181 ''' 

182 p = _stresidual.__name__[3:] 

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

184 for n, v in itemsorted(name_values): 

185 n = n.replace(_UNDER_, _SPACE_) 

186 p = Fmt.PARENSPACED(n, Fmt(v)) 

187 t = _COMMASPACE_(t, p) 

188 return _SPACE_(prefix, t) 

189 

190 

191def _2sum(a, b): # by .testFmath 

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

193 ''' 

194 s = a + b 

195 if not _isfinite(s): 

196 u = unstr(_2sum.__name__, a, b) 

197 t = Fmt.PARENSPACED(_not_finite_, s) 

198 raise _OverflowError(u, txt=t) 

199 if fabs(a) < fabs(b): 

200 a, b = b, a 

201 return s, (b - (s - a)) 

202 

203 

204def _2yield(xs, i, _X_ps, _x): 

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

206 ''' 

207 x = None 

208 try: 

209 _fin = _isfinite 

210 _Fs = Fsum 

211 for x in xs: 

212 if isinstance(x, _Fs): 

213 for p in _X_ps(x): 

214 yield p 

215 else: 

216 f = _x(x) 

217 if f: 

218 if not _fin(f): 

219 raise ValueError(_not_finite_) 

220 yield f 

221 i += 1 

222 except Exception as X: 

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

224 

225 

226class Fsum(_Named): # sync __methods__ with .vector3dBase.Vector3dBase 

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

228 

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

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

231 intermediate, I{running} summuation. 

232 

233 @note: Accumulated values may be L{Fsum} or C{scalar} instances, any C{type} having 

234 method C{__float__} to convert the C{scalar} to a single C{float}. 

235 

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

237 Python's C{math.fsum}. 

238 

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

240 393090_Binary_floating_point_summatiaccurate_full/recipe-393090.py>}, U{Kahan 

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

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

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

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

245 ''' 

246 _math_fsum = None 

247 _n = 0 

248# _ps = [] # partial sums 

249# _px = 0 # max(Fsum._px, len(Fsum._ps)) 

250 _ratio = None 

251 _RESIDUAL = max(float(_getenv('PYGEODESY_FSUM_RESIDUAL', _0_0)), _0_0) 

252 

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

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

255 

256 @arg xs: No, one or more initial values, all positional (each C{scalar} 

257 or an L{Fsum} instance). 

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

259 C{B{RESIDUAL}=None} for the L{ResidualError} threshold. 

260 

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

262 ''' 

263 if name_RESIDUAL: 

264 n = _xkwds_get(name_RESIDUAL, name=NN) 

265 if n: # set name before ... 

266 self.name = n 

267 r = _xkwds_get(name_RESIDUAL, RESIDUAL=None) 

268 if r is not None: 

269 self.RESIDUAL(r) # ... ResidualError 

270# self._n = 0 

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

272 if len(xs) > 1: 

273 self._facc(_2floats(xs, origin=1), up=False) # PYCHOK yield 

274 elif xs: # len(xs) == 1 

275 self._n = 1 

276 self._ps[:] = _2float(x=xs[0]), 

277 

278 def __abs__(self): 

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

280 ''' 

281 s = _fsum(self._ps_1()) # == self._cmp_0(0, ...) 

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

283 

284 def __add__(self, other): 

285 '''Return the C{Fsum(B{self}, B{other})}. 

286 

287 @arg other: An L{Fsum} or C{scalar}. 

288 

289 @return: The sum (L{Fsum}). 

290 

291 @see: Method L{Fsum.__iadd__}. 

292 ''' 

293 f = self._copy_2(self.__add__) 

294 return f._fadd(other, _add_op_) 

295 

296 def __bool__(self): # PYCHOK not special in Python 2- 

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

298 ''' 

299 s, r = self._fprs2 

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

301 

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

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

304 

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

306 

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

308 ''' 

309 return self.ceil 

310 

311 def __cmp__(self, other): # Python 2- 

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

313 

314 @return: -1, 0 or +1 (C{int}). 

315 

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

317 ''' 

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

319 return _signOf(s, 0) 

320 

321 cmp = __cmp__ 

322 

323 def __divmod__(self, other): 

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

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

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

327 

328 @arg other: An L{Fsum} or C{scalar} modulus. 

329 

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

331 ''' 

332 f = self._copy_2(self.__divmod__) 

333 return f._fdivmod2(other, _divmod_op_) 

334 

335 def __eq__(self, other): 

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

337 ''' 

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

339 

340 def __float__(self): 

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

342 

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

344 ''' 

345 return float(self._fprs) 

346 

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

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

349 

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

351 

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

353 ''' 

354 return self.floor 

355 

356 def __floordiv__(self, other): 

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

358 

359 @arg other: An L{Fsum} or C{scalar} divisor. 

360 

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

362 

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

364 ''' 

365 f = self._copy_2(self.__floordiv__) 

366 return f._floordiv(other, _floordiv_op_) 

367 

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

369 '''Not implemented.''' 

370 return _NotImplemented(self, *other) 

371 

372 def __ge__(self, other): 

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

374 ''' 

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

376 

377 def __gt__(self, other): 

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

379 ''' 

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

381 

382 def __hash__(self): # PYCHOK no cover 

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

384 ''' 

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

386 

387 def __iadd__(self, other): 

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

389 

390 @arg other: An L{Fsum} or C{scalar} instance. 

391 

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

393 

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

395 C{scalar} nor L{Fsum}. 

396 

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

398 ''' 

399 return self._fadd(other, _iadd_op_) 

400 

401 def __ifloordiv__(self, other): 

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

403 

404 @arg other: An L{Fsum} or C{scalar} divisor. 

405 

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

407 

408 @raise ResidualError: Non-zero residual in B{C{other}}. 

409 

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

411 

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

413 

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

415 

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

417 ''' 

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

419 

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

421 '''Not implemented.''' 

422 return _NotImplemented(self, other) 

423 

424 def __imod__(self, other): 

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

426 

427 @arg other: An L{Fsum} or C{scalar} modulus. 

428 

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

430 

431 @see: Method L{Fsum.__divmod__}. 

432 ''' 

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

434 

435 def __imul__(self, other): 

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

437 

438 @arg other: An L{Fsum} or C{scalar} factor. 

439 

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

441 

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

443 

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

445 

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

447 ''' 

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

449 

450 def __int__(self): 

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

452 

453 @see: Methods L{Fsum.int_float}, L{Fsum.__ceil__} 

454 and L{Fsum.__floor__} and properties 

455 L{Fsum.ceil} and L{Fsum.floor}. 

456 ''' 

457 i, _ = self._fint2 

458 return i 

459 

460 def __invert__(self): # PYCHOK no cover 

461 '''Not implemented.''' 

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

463 return _NotImplemented(self) 

464 

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

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

467 

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

469 @arg mod: Optional modulus (C{int} or C{None}) for the 

470 3-argument C{pow(B{self}, B{other}, B{mod})} 

471 version. 

472 

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

474 

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

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

477 set to C{as_integer} if B{C{mod}} given as C{None}. 

478 

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

480 

481 @raise ResidualError: Non-zero residual in B{C{other}} and 

482 env var C{PYGEODESY_FSUM_RESIDUAL} 

483 set or this instance has a non-zero 

484 residual and either B{C{mod}} is 

485 given and non-C{None} or B{C{other}} 

486 is a negative or fractional C{scalar}. 

487 

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

489 C{pow} invocation failed. 

490 

491 @raise ValueError: If B{C{other}} is a negative C{scalar} 

492 and this instance is C{0} or B{C{other}} 

493 is a fractional C{scalar} and this 

494 instance is negative or has a non-zero 

495 residual or B{C{mod}} is given and C{0}. 

496 

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

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

499 ''' 

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

501 

502 def __isub__(self, other): 

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

504 

505 @arg other: An L{Fsum} or C{scalar}. 

506 

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

508 

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

510 

511 @see: Method L{Fsum.fadd}. 

512 ''' 

513 return self._fsub(other, _isub_op_) 

514 

515 def __iter__(self): 

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

517 ''' 

518 return iter(self.partials) 

519 

520 def __itruediv__(self, other): 

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

522 

523 @arg other: An L{Fsum} or C{scalar} divisor. 

524 

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

526 

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

528 

529 @raise ResidualError: Non-zero residual in B{C{other}} and 

530 env var C{PYGEODESY_FSUM_RESIDUAL} set. 

531 

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

533 

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

535 

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

537 

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

539 ''' 

540 return self._ftruediv(other, _truediv_op_ + _fset_op_) 

541 

542 def __le__(self, other): 

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

544 ''' 

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

546 

547 def __len__(self): 

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

549 ''' 

550 return self._n 

551 

552 def __lt__(self, other): 

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

554 ''' 

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

556 

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

558 '''Not implemented.''' 

559 return _NotImplemented(self, other) 

560 

561 def __mod__(self, other): 

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

563 

564 @see: Method L{Fsum.__imod__}. 

565 ''' 

566 f = self._copy_2(self.__mod__) 

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

568 

569 def __mul__(self, other): 

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

571 

572 @see: Method L{Fsum.__imul__}. 

573 ''' 

574 f = self._copy_2(self.__mul__) 

575 return f._fmul(other, _mul_op_) 

576 

577 def __ne__(self, other): 

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

579 ''' 

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

581 

582 def __neg__(self): 

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

584 ''' 

585 f = self._copy_2(self.__neg__) 

586 return f._fset(self._neg) 

587 

588 def __pos__(self): 

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

590 ''' 

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

592 

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

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

595 

596 @see: Method L{Fsum.__ipow__}. 

597 ''' 

598 f = self._copy_2(self.__pow__) 

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

600 

601 def __radd__(self, other): 

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

603 

604 @see: Method L{Fsum.__iadd__}. 

605 ''' 

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

607 return f._fadd(self, _add_op_) 

608 

609 def __rdivmod__(self, other): 

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

611 remainder)}. 

612 

613 @see: Method L{Fsum.__divmod__}. 

614 ''' 

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

616 return f._fdivmod2(self, _divmod_op_) 

617 

618# def __repr__(self): 

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

620# ''' 

621# return self.toRepr(lenc=True) 

622 

623 def __rfloordiv__(self, other): 

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

625 

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

627 ''' 

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

629 return f._floordiv(self, _floordiv_op_) 

630 

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

632 '''Not implemented.''' 

633 return _NotImplemented(self, other) 

634 

635 def __rmod__(self, other): 

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

637 

638 @see: Method L{Fsum.__imod__}. 

639 ''' 

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

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

642 

643 def __rmul__(self, other): 

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

645 

646 @see: Method L{Fsum.__imul__}. 

647 ''' 

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

649 return f._fmul(self, _mul_op_) 

650 

651 def __round__(self, *ndigits): # PYCHOK no cover 

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

653 

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

655 ''' 

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

657 return _Fsum_ps(round(float(self), *ndigits), # can be C{int} 

658 name=self.__round__.__name__) 

659 

660 def __rpow__(self, other, *mod): 

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

662 

663 @see: Method L{Fsum.__ipow__}. 

664 ''' 

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

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

667 

668 def __rsub__(self, other): 

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

670 

671 @see: Method L{Fsum.__isub__}. 

672 ''' 

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

674 return f._fsub(self, _sub_op_) 

675 

676 def __rtruediv__(self, other): 

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

678 

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

680 ''' 

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

682 return f._ftruediv(self, _truediv_op_) 

683 

684 def __str__(self): 

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

686 ''' 

687 return self.toStr(lenc=True) 

688 

689 def __sub__(self, other): 

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

691 

692 @arg other: An L{Fsum} or C{scalar}. 

693 

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

695 

696 @see: Method L{Fsum.__isub__}. 

697 ''' 

698 f = self._copy_2(self.__sub__) 

699 return f._fsub(other, _sub_op_) 

700 

701 def __truediv__(self, other): 

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

703 

704 @arg other: An L{Fsum} or C{scalar} divisor. 

705 

706 @return: The quotient (L{Fsum}). 

707 

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

709 ''' 

710 f = self._copy_2(self.__truediv__) 

711 return f._ftruediv(other, _truediv_op_) 

712 

713 __trunc__ = __int__ 

714 

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

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

717 __div__ = __truediv__ 

718 __idiv__ = __itruediv__ 

719 __long__ = __int__ 

720 __nonzero__ = __bool__ 

721 __rdiv__ = __rtruediv__ 

722 

723 def as_integer_ratio(self): 

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

725 

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

727 C{int} and with positive C{denominator}. 

728 

729 @see: Standard C{float.as_integer_ratio} in Python 3+. 

730 ''' 

731 n, r = self._fint2 

732 if r: 

733 i, d = r.as_integer_ratio() 

734 n *= d 

735 n += i 

736 else: # PYCHOK no cover 

737 d = 1 

738 return n, d 

739 

740 @property_RO 

741 def ceil(self): 

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

743 but C{float} in Python 2-). 

744 

745 @note: The C{ceil} takes the C{residual} into account. 

746 

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

748 L{Fsum.imag} and L{Fsum.real}. 

749 ''' 

750 s, r = self._fprs2 

751 c = _ceil(s) + int(r) - 1 

752 while r > (c - s): # (s + r) > c 

753 c += 1 

754 return c 

755 

756 def _cmp_0(self, other, op): 

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

758 ''' 

759 if isinstance(other, Fsum): 

760 s = _fsum(self._ps_1(*other._ps)) 

761 elif isscalar(other): 

762 if other: 

763 s = _fsum(self._ps_1(other)) 

764 else: 

765 s, r = self._fprs2 

766 s = _signOf(s, -r) 

767 else: 

768 raise self._TypeError(op, other) # txt=_invalid_ 

769 return s 

770 

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

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

773 

774 @return: The copy (L{Fsum}). 

775 ''' 

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

777 f._n = self._n if deep else 1 

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

779 return f 

780 

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

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

783 ''' 

784 n = name or which.__name__ 

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

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

787 # assert f._n == self._n 

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

789 return f 

790 

791 def _copy_2r(self, other, which): 

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

793 ''' 

794 return other._copy_2(which) if isinstance(other, Fsum) else \ 

795 Fsum(other, name=which.__name__) 

796 

797# def _copy_RESIDUAL(self, other): 

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

799# ''' 

800# R = other._RESIDUAL 

801# if R is not Fsum._RESIDUAL: 

802# self._RESIDUAL = R 

803 

804 def divmod(self, other): 

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

806 remainder)}. 

807 

808 @arg other: An L{Fsum} or C{scalar} divisor. 

809 

810 @return: A L{DivMod2Tuple}C{(div, mod)}, with quotient C{div} 

811 an C{int} in Python 3+ or C{float} in Python 2- and 

812 remainder C{mod} an L{Fsum} instance. 

813 

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

815 ''' 

816 f = self._copy_2(self.divmod) 

817 return f._fdivmod2(other, _divmod_op_) 

818 

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

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

821 ''' 

822 return Error(_SPACE_(self.toRepr(), op, repr(other)), **txt_cause) 

823 

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

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

826 ''' 

827 E, t = _xError2(X) 

828 if mod: 

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

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

831 

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

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

834 ''' 

835 E, t = _xError2(X) 

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

837 return E(n, txt=t, cause=X) 

838 

839 def _facc(self, xs, up=True): # from .elliptic._Defer.Fsum 

840 '''(INTERNAL) Accumulate more known C{scalar}s. 

841 ''' 

842 n, ps, _2s = 0, self._ps, _2sum 

843 for x in xs: # _iter() 

844 # assert isscalar(x) and isfinite(x) 

845 if x: 

846 i = 0 

847 for p in ps: 

848 x, p = _2s(x, p) 

849 if p: 

850 ps[i] = p 

851 i += 1 

852 ps[i:] = (x,) if x else () 

853 n += 1 

854 # assert self._ps is ps 

855 if n: 

856 self._n += n 

857 # Fsum._px = max(Fsum._px, len(ps)) 

858 if up: 

859 self._update() 

860 return self 

861 

862 def _facc_(self, *xs, **up): 

863 '''(INTERNAL) Accumulate all positional C{scalar}s. 

864 ''' 

865 return self._facc(xs, **up) if xs else self 

866 

867 def _facc_power(self, power, xs, which): # in .fmath 

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

869 ''' 

870 p = power 

871 if isinstance(p, Fsum): 

872 if p.is_exact: 

873 return self._facc_power(p._fprs, xs, which) 

874 _Pow = Fsum._pow_any 

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

876 _Pow, p = Fsum._pow_int, int(p) 

877 else: 

878 _Pow, p = Fsum._pow_scalar, _2float(power=p) 

879 

880 if p: 

881 from math import pow as _pow 

882 op = which.__name__ 

883 

884 def _X(X): 

885 f = _Pow(X, p, power, op) 

886 try: # isinstance(f, Fsum) 

887 return f._ps 

888 except AttributeError: # scalar 

889 return f, 

890 

891 def _x(x): 

892 return _pow(float(x), p) 

893 

894 self._facc(_2yield(xs, 1, _X, _x)) # PYCHOK yield 

895 else: 

896 self._facc_(float(len(xs))) # x**0 == 1 

897 return self 

898 

899# def _facc_up(self, up=True): 

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

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

902# ''' 

903# while len(self._ps) > 1: 

904# p = self._ps.pop() 

905# if p: 

906# n = self._n 

907# self._facc_(p, up=False) 

908# self._n = n 

909# break 

910# return self._update() if up else self # ._fpsqz() 

911 

912 def fadd(self, xs=()): 

913 '''Add an iterable of C{scalar} or L{Fsum} instances 

914 to this instance. 

915 

916 @arg xs: Iterable, list, tuple, etc. (C{scalar} or 

917 L{Fsum} instances). 

918 

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

920 

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

922 

923 @raise TypeError: An invalid B{C{xs}} type, not C{scalar} 

924 nor L{Fsum}. 

925 

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

927 ''' 

928 if isinstance(xs, Fsum): 

929 self._facc(xs._ps) 

930 elif isscalar(xs): # for backward compatibility 

931 self._facc_(_2float(x=xs)) # PYCHOK no cover 

932 elif xs: 

933 self._facc(_2floats(xs)) # PYCHOK yield 

934 return self 

935 

936 def fadd_(self, *xs): 

937 '''Add all positional C{scalar} or L{Fsum} instances 

938 to this instance. 

939 

940 @arg xs: Values to add (C{scalar} or L{Fsum} instances), 

941 all positional. 

942 

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

944 

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

946 

947 @raise TypeError: An invalid B{C{xs}} type, not C{scalar} 

948 nor L{Fsum}. 

949 

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

951 ''' 

952 return self._facc(_2floats(xs, origin=1)) # PYCHOK yield 

953 

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

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

956 ''' 

957 if isinstance(other, Fsum): 

958 if other is self: 

959 self._facc_(*other._ps, **up) # == ._facc(tuple(other._ps)) 

960 elif other._ps: 

961 self._facc(other._ps, **up) 

962 elif not isscalar(other): 

963 raise self._TypeError(op, other) # txt=_invalid_ 

964 elif other: 

965 self._facc_(other, **up) 

966 return self 

967 

968 fcopy = copy # for backward compatibility 

969 fdiv = __itruediv__ # for backward compatibility 

970 fdivmod = __divmod__ # for backward compatibility 

971 

972 def _fdivmod2(self, other, op): 

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

974 ''' 

975 # result mostly follows CPython function U{float_divmod 

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

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

978 q = self._copy_2(self._fdivmod2)._ftruediv(other, op).floor 

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

980 self -= other * q 

981 

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

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

984 self += other 

985 q -= 1 

986# t = self.signOf() 

987# if t and t != s: 

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

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

990 

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

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

993 ''' 

994 if _isfinite(other): 

995 return other 

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

997 self._ValueError(op, other, txt=_not_finite_) 

998 

999 def fint(self, raiser=True, **name): 

1000 '''Return this instance' current running sum as C{integer}. 

1001 

1002 @kwarg raiser: If C{True} throw a L{ResidualError} if the 

1003 I{integer} residual is non-zero. 

1004 @kwarg name: Optional name (C{str}), overriding C{"fint"}. 

1005 

1006 @return: The C{integer} (L{Fsum}). 

1007 

1008 @raise ResidualError: Non-zero I{integer} residual. 

1009 

1010 @see: Methods L{Fsum.int_float} and L{Fsum.is_integer}. 

1011 ''' 

1012 i, r = self._fint2 

1013 if r and raiser: 

1014 t = _stresidual(_integer_, r) 

1015 raise ResidualError(_integer_, i, txt=t) 

1016 f = self._copy_2(self.fint, **name) 

1017 return f._fset(i) 

1018 

1019 def fint2(self, **name): 

1020 '''Return this instance' current running sum as C{int} and 

1021 the I{integer} residual. 

1022 

1023 @kwarg name: Optional name (C{str}). 

1024 

1025 @return: An L{Fsum2Tuple}C{(fsum, residual)} with C{fsum} 

1026 an C{int} and I{integer} C{residual} a C{float} or 

1027 C{INT0} if the C{fsum} is considered to be I{exact}. 

1028 ''' 

1029 return Fsum2Tuple(*self._fint2, **name) 

1030 

1031 @Property_RO 

1032 def _fint2(self): # see ._fset 

1033 '''(INTERNAL) Get 2-tuple (C{int}, I{integer} residual). 

1034 ''' 

1035 s, r = self._fprs2 

1036 i = int(s) 

1037 r = _fsum(self._ps_1(i)) if r else float(s - i) 

1038 return i, (r or INT0) 

1039 

1040 @deprecated_property_RO 

1041 def float_int(self): # PYCHOK no cover 

1042 '''DEPRECATED, use method C{Fsum.int_float}.''' 

1043 return self.int_float() # raiser=False 

1044 

1045 @property_RO 

1046 def floor(self): 

1047 '''Get this instance' C{floor} (C{int} in Python 3+, but 

1048 C{float} in Python 2-). 

1049 

1050 @note: The C{floor} takes the C{residual} into account. 

1051 

1052 @see: Method L{Fsum.int_float} and properties L{Fsum.ceil}, 

1053 L{Fsum.imag} and L{Fsum.real}. 

1054 ''' 

1055 s, r = self._fprs2 

1056 f = _floor(s) + _floor(r) + 1 

1057 while (f - s) > r: # f > (s + r) 

1058 f -= 1 

1059 return f 

1060 

1061# floordiv = __floordiv__ # for naming consistency 

1062 

1063 def _floordiv(self, other, op): # rather _ffloordiv? 

1064 '''Apply C{B{self} //= B{other}}. 

1065 ''' 

1066 q = self._ftruediv(other, op) # == self 

1067 return self._fset(q.floor) # floor(q) 

1068 

1069 fmul = __imul__ # for backward compatibility 

1070 

1071 def _fmul(self, other, op): 

1072 '''(INTERNAL) Apply C{B{self} *= B{other}}. 

1073 ''' 

1074 if isinstance(other, Fsum): 

1075 if len(self._ps) != 1: 

1076 f = self._mul_Fsum(other, op) 

1077 elif len(other._ps) != 1: # and len(self._ps) == 1 

1078 f = other._mul_scalar(self._ps[0], op) 

1079 else: # len(other._ps) == len(self._ps) == 1 

1080 f = self._finite(self._ps[0] * other._ps[0]) 

1081 elif isscalar(other): 

1082 f = self._mul_scalar(other, op) 

1083 else: 

1084 raise self._TypeError(op, other) # txt=_invalid_ 

1085 return self._fset(f) # n=len(self) + 1 

1086 

1087 def fover(self, over): 

1088 '''Apply C{B{self} /= B{over}} and summate. 

1089 

1090 @arg over: An L{Fsum} or C{scalar} denominator. 

1091 

1092 @return: Precision running sum (C{float}). 

1093 

1094 @see: Methods L{Fsum.fsum} and L{Fsum.__itruediv__}. 

1095 ''' 

1096 return float(self.fdiv(over)._fprs) 

1097 

1098 fpow = __ipow__ # for backward compatibility 

1099 

1100 def _fpow(self, other, op, *mod): 

1101 '''Apply C{B{self} **= B{other}}, optional B{C{mod}} or C{None}. 

1102 ''' 

1103 if mod: 

1104 if mod[0] is not None: # == 3-arg C{pow} 

1105 f = self._pow_3(other, mod[0], op) 

1106 elif self.is_integer(): 

1107 # return an exact C{int} for C{int}**C{int} 

1108 x = _2scalar(other) # C{int}, C{float} or other 

1109 i = self._fint2[0] # assert _fint2[1] == 0 

1110 f = self._pow_2(i, x, other, op) if isscalar(x) else \ 

1111 _Fsum_ps(i)._pow_any(x, other, op) 

1112 else: # mod[0] is None, power(self, other) 

1113 f = self._pow_any(other, other, op) 

1114 else: # pow(self, other) == pow(self, other, None) 

1115 f = self._pow_any(other, other, op) 

1116 return self._fset(f, asis=isint(f)) # n=max(len(self), 1) 

1117 

1118 @Property_RO 

1119 def _fprs(self): 

1120 '''(INTERNAL) Get and cache this instance' precision 

1121 running sum (C{float} or C{int}), ignoring C{residual}. 

1122 

1123 @note: The precision running C{fsum} after a C{//=} or 

1124 C{//} C{floor} division is C{int} in Python 3+. 

1125 ''' 

1126 return self._fprs2.fsum 

1127 

1128 @Property_RO 

1129 def _fprs2(self): 

1130 '''(INTERNAL) Get and cache this instance' precision 

1131 running sum and residual (L{Fsum2Tuple}). 

1132 ''' 

1133 ps = self._ps 

1134 n = len(ps) - 2 

1135 if n > 0: # len(ps) > 2 

1136 s = _psum(ps) 

1137 r = _fsum(self._ps_1(s)) or INT0 

1138 elif n == 0: # len(ps) == 2 

1139 ps[:] = _2ps(*_2sum(*ps)) 

1140 r, s = (INT0, ps[0]) if len(ps) != 2 else ps 

1141 elif ps: # len(ps) == 1 

1142 s, r = ps[0], INT0 

1143 else: # len(ps) == 0 

1144 s, r = _0_0, INT0 

1145 ps[:] = s, 

1146 # assert self._ps is ps 

1147 return Fsum2Tuple(s, r) 

1148 

1149# def _fpsqz(self): 

1150# '''(INTERNAL) Compress, squeeze the C{partials}. 

1151# ''' 

1152# if len(self._ps) > 2: 

1153# _ = self._fprs 

1154# return self 

1155 

1156 def fset_(self, *xs): 

1157 '''Replace this instance' value with C{xs}. 

1158 

1159 @arg xs: Optional, new values (C{scalar} or L{Fsum} 

1160 instances), all positional. 

1161 

1162 @return: This instance (C{Fsum}). 

1163 

1164 @see: Method L{Fsum.fadd} for further details. 

1165 ''' 

1166 self._n = 0 

1167 self._ps[:] = 0, 

1168 return self.fadd(xs) if xs else self._update() 

1169 

1170 def _fset(self, other, asis=True, n=0): 

1171 '''(INTERNAL) Overwrite this instance with an other or a C{scalar}. 

1172 ''' 

1173 if other is self: 

1174 pass # from ._fmul, ._ftruediv and ._pow_scalar 

1175 elif isinstance(other, Fsum): 

1176 self._n = n or other._n 

1177 self._ps[:] = other._ps 

1178# self._copy_RESIDUAL(other) 

1179 # use or zap the C{Property_RO} values 

1180 Fsum._fint2._update_from(self, other) 

1181 Fsum._fprs ._update_from(self, other) 

1182 Fsum._fprs2._update_from(self, other) 

1183 elif isscalar(other): 

1184 s = other if asis else float(other) 

1185 i = int(s) # see ._fint2 

1186 t = i, ((s - i) or INT0) 

1187 self._n = n or 1 

1188 self._ps[:] = s, 

1189 # Property_ROs _fint2, _fprs and _fprs2 can't be a Property: 

1190 # Property's _fset zaps the value just set by the @setter 

1191 self.__dict__.update(_fint2=t, _fprs=s, _fprs2=Fsum2Tuple(s, INT0)) 

1192 else: # PYCHOK no cover 

1193 raise self._TypeError(_fset_op_, other) # txt=_invalid_ 

1194 return self 

1195 

1196 def _fset_ps(self, other, n=0): # in .fmath 

1197 '''(INTERNAL) Set a known C{Fsum} or C{scalar}. 

1198 ''' 

1199 if isinstance(other, Fsum): 

1200 self._n = n or other._n 

1201 self._ps[:] = other._ps 

1202 else: # assert isscalar(other) 

1203 self._n = n or 1 

1204 self._ps[:] = other, 

1205 

1206 def fsub(self, xs=()): 

1207 '''Subtract an iterable of C{scalar} or L{Fsum} instances from 

1208 this instance. 

1209 

1210 @arg xs: Iterable, list, tuple. etc. (C{scalar} or L{Fsum} 

1211 instances). 

1212 

1213 @return: This instance, updated (L{Fsum}). 

1214 

1215 @see: Method L{Fsum.fadd}. 

1216 ''' 

1217 return self._facc(_2floats(xs, neg=True)) if xs else self # PYCHOK yield 

1218 

1219 def fsub_(self, *xs): 

1220 '''Subtract all positional C{scalar} or L{Fsum} instances from 

1221 this instance. 

1222 

1223 @arg xs: Values to subtract (C{scalar} or L{Fsum} instances), 

1224 all positional. 

1225 

1226 @return: This instance, updated (L{Fsum}). 

1227 

1228 @see: Method L{Fsum.fadd}. 

1229 ''' 

1230 return self._facc(_2floats(xs, origin=1, neg=True)) if xs else self # PYCHOK yield 

1231 

1232 def _fsub(self, other, op): 

1233 '''(INTERNAL) Apply C{B{self} -= B{other}}. 

1234 ''' 

1235 if isinstance(other, Fsum): 

1236 if other is self: # or other._fprs2 == self._fprs2: 

1237 self._fset(_0_0) # n=len(self) * 2, self -= self 

1238 elif other._ps: 

1239 self._facc(other._ps_neg) 

1240 elif not isscalar(other): 

1241 raise self._TypeError(op, other) # txt=_invalid_ 

1242 elif self._finite(other, op): 

1243 self._facc_(-other) 

1244 return self 

1245 

1246 def fsum(self, xs=()): 

1247 '''Add more C{scalar} or L{Fsum} instances and summate. 

1248 

1249 @kwarg xs: Iterable, list, tuple, etc. (C{scalar} or 

1250 L{Fsum} instances). 

1251 

1252 @return: Precision running sum (C{float} or C{int}). 

1253 

1254 @see: Method L{Fsum.fadd}. 

1255 

1256 @note: Accumulation can continue after summation. 

1257 ''' 

1258 f = self._facc(_2floats(xs)) if xs else self # PYCHOK yield 

1259 return f._fprs 

1260 

1261 def fsum_(self, *xs): 

1262 '''Add all positional C{scalar} or L{Fsum} instances and summate. 

1263 

1264 @arg xs: Values to add (C{scalar} or L{Fsum} instances), 

1265 all positional. 

1266 

1267 @return: Precision running sum (C{float} or C{int}). 

1268 

1269 @see: Methods L{Fsum.fsum} and L{Fsum.fsumf_}. 

1270 ''' 

1271 f = self._facc(_2floats(xs, origin=1)) if xs else self # PYCHOK yield 

1272 return f._fprs 

1273 

1274 def fsum2(self, xs=(), name=NN): 

1275 '''Add more C{scalar} or L{Fsum} instances and return the 

1276 current precision running sum and the C{residual}. 

1277 

1278 @kwarg xs: Iterable, list, tuple, etc. (C{scalar} or L{Fsum} 

1279 instances). 

1280 @kwarg name: Optional name (C{str}). 

1281 

1282 @return: L{Fsum2Tuple}C{(fsum, residual)} with C{fsum} the 

1283 current precision running sum and C{residual}, the 

1284 (precision) sum of the remaining C{partials}. The 

1285 C{residual is INT0} if the C{fsum} is considered 

1286 to be I{exact}. 

1287 

1288 @see: Methods L{Fsum.fint2}, L{Fsum.fsum} and L{Fsum.fsum2_} 

1289 ''' 

1290 f = self._facc(_2floats(xs)) if xs else self # PYCHOK yield 

1291 t = f._fprs2 

1292 if name: 

1293 t = t.dup(name=name) 

1294 return t 

1295 

1296 def fsum2_(self, *xs): 

1297 '''Add any positional C{scalar} or L{Fsum} instances and return 

1298 the precision running sum and the C{differential}. 

1299 

1300 @arg xs: Values to add (C{scalar} or L{Fsum} instances), 

1301 all positional. 

1302 

1303 @return: 2-Tuple C{(fsum, delta)} with the current precision 

1304 running C{fsum} and C{delta}, the difference with 

1305 the previous running C{fsum} (C{float}s). 

1306 

1307 @see: Methods L{Fsum.fsum_} and L{Fsum.fsum}. 

1308 ''' 

1309 p, r = self._fprs2 

1310 if xs: 

1311 s, t = self._facc(_2floats(xs, origin=1))._fprs2 # PYCHOK yield 

1312 return s, _fsum((s, -p, r, -t)) # ((s - p) + (r - t)) 

1313 else: # PYCHOK no cover 

1314 return p, _0_0 

1315 

1316 def fsumf_(self, *xs): 

1317 '''Like method L{Fsum.fsum_} but only for known C{float B{xs}}. 

1318 ''' 

1319 f = self._facc(xs) if xs else self # PYCHOK yield 

1320 return f._fprs 

1321 

1322# ftruediv = __itruediv__ # for naming consistency 

1323 

1324 def _ftruediv(self, other, op): 

1325 '''(INTERNAL) Apply C{B{self} /= B{other}}. 

1326 ''' 

1327 n = _1_0 

1328 if isinstance(other, Fsum): 

1329 if other is self or other == self: 

1330 return self._fset(_1_0) # n=len(self) 

1331 d, r = other._fprs2 

1332 if r: 

1333 if d: 

1334 if self._raiser(r, d): 

1335 raise self._ResidualError(op, other, r) 

1336 d, n = other.as_integer_ratio() 

1337 else: # PYCHOK no cover 

1338 d = r 

1339 elif isscalar(other): 

1340 d = other 

1341 else: # PYCHOK no cover 

1342 raise self._TypeError(op, other) # txt=_invalid_ 

1343 try: 

1344 s = 0 if isinf(d) else ( 

1345 d if isnan(d) else self._finite(n / d)) 

1346 except Exception as X: 

1347 raise self._ErrorX(X, op, other) 

1348 f = self._mul_scalar(s, _mul_op_) # handles 0, NAN, etc. 

1349 return self._fset(f, asis=False) 

1350 

1351 @property_RO 

1352 def imag(self): 

1353 '''Get the C{imaginary} part of this instance (C{0.0}, always). 

1354 

1355 @see: Properties L{Fsum.ceil}, L{Fsum.floor} and L{Fsum.real}. 

1356 ''' 

1357 return _0_0 

1358 

1359 def int_float(self, raiser=False): 

1360 '''Return this instance' current running sum as C{int} or C{float}. 

1361 

1362 @kwarg raiser: If C{True} throw a L{ResidualError} if the 

1363 residual is non-zero. 

1364 

1365 @return: This C{integer} sum if this instance C{is_integer}, 

1366 otherwise return the C{float} sum if the residual 

1367 is zero or if C{B{raiser}=False}. 

1368 

1369 @raise ResidualError: Non-zero residual and C{B{raiser}=True}. 

1370 

1371 @see: Methods L{Fsum.fint} and L{Fsum.fint2}. 

1372 ''' 

1373 s, r = self._fint2 

1374 if r: 

1375 s, r = self._fprs2 

1376 if r and raiser: # PYCHOK no cover 

1377 t = _stresidual(_non_zero_, r) 

1378 raise ResidualError(int_float=s, txt=t) 

1379 s = float(s) # redundant 

1380 return s 

1381 

1382 def is_exact(self): 

1383 '''Is this instance' current running C{fsum} considered to 

1384 be exact? (C{bool}). 

1385 ''' 

1386 return self.residual is INT0 

1387 

1388 def is_integer(self): 

1389 '''Is this instance' current running sum C{integer}? (C{bool}). 

1390 

1391 @see: Methods L{Fsum.fint} and L{Fsum.fint2}. 

1392 ''' 

1393 _, r = self._fint2 

1394 return False if r else True 

1395 

1396 def is_math_fsum(self): 

1397 '''Return whether functions L{fsum}, L{fsum_}, L{fsum1} and 

1398 L{fsum1_} plus partials summation are based on Python's 

1399 C{math.fsum} or not. 

1400 

1401 @return: C{2} if all functions and partials summation 

1402 are based on C{math.fsum}, C{True} if only 

1403 the functions are based on C{math.fsum} (and 

1404 partials summation is not) or C{False} if 

1405 none are. 

1406 ''' 

1407 f = Fsum._math_fsum 

1408 return 2 if _psum is f else bool(f) 

1409 

1410 def _mul_Fsum(self, other, op=_mul_op_): # in .fmath.Fhorner 

1411 '''(INTERNAL) Return C{B{self} * Fsum B{other}} as L{Fsum} or C{0}. 

1412 ''' 

1413 # assert isinstance(other, Fsum) 

1414 if self._ps and other._ps: 

1415 f = _Fsum_xs(self._ps_mul(op, *other._ps)) 

1416 else: 

1417 f = _0_0 

1418 return f 

1419 

1420 def _mul_scalar(self, factor, op): # in .fmath.Fhorner 

1421 '''(INTERNAL) Return C{B{self} * scalar B{factor}} as L{Fsum}, C{0} or C{self}. 

1422 ''' 

1423 # assert isscalar(factor) 

1424 if self._ps and self._finite(factor, op): 

1425 f = self if factor == _1_0 else ( 

1426 self._neg if factor == _N_1_0 else 

1427 _Fsum_xs(self._ps_mul(op, factor))) # PYCHOK indent 

1428 else: 

1429 f = _0_0 

1430 return f 

1431 

1432 @property_RO 

1433 def _neg(self): 

1434 '''(INTERNAL) Return C{-self}. 

1435 ''' 

1436 return _Fsum_ps(*self._ps_neg) if self._ps else NEG0 

1437 

1438 @property_RO 

1439 def partials(self): 

1440 '''Get this instance' current partial sums (C{tuple} of C{float}s and/or C{int}s). 

1441 ''' 

1442 return tuple(self._ps) 

1443 

1444 def pow(self, x, *mod): 

1445 '''Return C{B{self}**B{x}} as L{Fsum}. 

1446 

1447 @arg x: The exponent (L{Fsum} or C{scalar}). 

1448 @arg mod: Optional modulus (C{int} or C{None}) for the 3-argument 

1449 C{pow(B{self}, B{other}, B{mod})} version. 

1450 

1451 @return: The C{pow(self, B{x})} or C{pow(self, B{x}, *B{mod})} 

1452 result (L{Fsum}). 

1453 

1454 @note: If B{C{mod}} is given as C{None}, the result will be an 

1455 C{integer} L{Fsum} provided this instance C{is_integer} 

1456 or set to C{integer} with L{Fsum.fint}. 

1457 

1458 @see: Methods L{Fsum.__ipow__}, L{Fsum.fint} and L{Fsum.is_integer}. 

1459 ''' 

1460 f = self._copy_2(self.pow) 

1461 return f._fpow(x, _pow_op_, *mod) # f = pow(f, x, *mod) 

1462 

1463 def _pow_0_1(self, x, other): 

1464 '''(INTERNAL) Return B{C{self}**1} or C{B{self}**0 == 1.0}. 

1465 ''' 

1466 return self if x else (1 if isint(other) and self.is_integer() else _1_0) 

1467 

1468 def _pow_2(self, b, x, other, op): 

1469 '''(INTERNAL) 2-arg C{pow(B{b}, scalar B{x})} embellishing errors. 

1470 ''' 

1471 # assert isscalar(b) and isscalar(x) 

1472 try: # type(s) == type(x) if x in (_1_0, 1) 

1473 s = pow(b, x) # -1**2.3 == -(1**2.3) 

1474 if not iscomplex(s): 

1475 return self._finite(s) # 0**INF == 0.0, 1**INF==1.0 

1476 # neg**frac == complex in Python 3+, but ValueError in 2- 

1477 raise ValueError(_strcomplex(s, b, x)) # PYCHOK no cover 

1478 except Exception as X: 

1479 raise self._ErrorX(X, op, other) 

1480 

1481 def _pow_3(self, other, mod, op): 

1482 '''(INTERNAL) 3-arg C{pow(B{self}, B{other}, int B{mod} or C{None})}. 

1483 ''' 

1484 b, r = self._fprs2 if mod is None else self._fint2 

1485 if r and self._raiser(r, b): 

1486 t = _non_zero_ if mod is None else _integer_ 

1487 t = _stresidual(t, r, mod=mod) 

1488 raise self._Error(op, other, ResidualError, txt=t) 

1489 

1490 try: # b, other, mod all C{int}, unless C{mod} is C{None} 

1491 x = _2scalar(other, _raiser=self._raiser) 

1492 s = pow(b, x, mod) 

1493 if not iscomplex(s): 

1494 return self._finite(s) 

1495 # neg**frac == complex in Python 3+, but ValueError in 2- 

1496 raise ValueError(_strcomplex(s, b, x, mod)) # PYCHOK no cover 

1497 except Exception as X: 

1498 raise self._ErrorX(X, op, other, mod) 

1499 

1500 def _pow_any(self, other, unused, op): 

1501 '''Return C{B{self} ** B{other}}. 

1502 ''' 

1503 if isinstance(other, Fsum): 

1504 x, r = other._fprs2 

1505 f = self._pow_scalar(x, other, op) 

1506 if r: 

1507 if self._raiser(r, x): 

1508 raise self._ResidualError(op, other, r) 

1509 s = self._pow_scalar(r, other, op) 

1510# s = _2scalar(s) # _raiser = None 

1511 f *= s 

1512 elif isscalar(other): 

1513 x = self._finite(other, op) 

1514 f = self._pow_scalar(x, other, op) 

1515 else: 

1516 raise self._TypeError(op, other) # txt=_invalid_ 

1517 return f 

1518 

1519 def _pow_int(self, x, other, op): 

1520 '''(INTERNAL) Return C{B{self} **= B{x}} for C{int B{x} >= 0}. 

1521 ''' 

1522 # assert isint(x) and x >= 0 

1523 ps = self._ps 

1524 if len(ps) > 1: 

1525 f = self 

1526 if x > 4: 

1527 m = 1 # single-bit mask 

1528 if (x & m): 

1529 x -= m # x ^= m 

1530 else: 

1531 f = _Fsum_ps(_1_0) 

1532 p = self 

1533 while x: 

1534 p = p._mul_Fsum(p, op) # p **= 2 

1535 m += m # m <<= 1 

1536 if (x & m): 

1537 x -= m # x ^= m 

1538 f = f._mul_Fsum(p, op) # f *= p 

1539 elif x > 1: # self**2, 3 or 4 

1540 f = f._mul_Fsum(f, op) 

1541 if x > 2: # self**3 or 4 

1542 p = self if x < 4 else f 

1543 f = f._mul_Fsum(p, op) 

1544 else: # self**1 or self**0 == 1 or _1_0 

1545 f = f._pow_0_1(x, other) 

1546 elif ps: # self._ps[0]**x 

1547 f = self._pow_2(ps[0], x, other, op) 

1548 else: # PYCHOK no cover 

1549 # 0**pos_int == 0, but 0**0 == 1 

1550 f = 0 if x else 1 # like ._fprs 

1551 return f 

1552 

1553 def _pow_scalar(self, x, other, op): 

1554 '''(INTERNAL) Return C{self**B{x}} for C{scalar B{x}}. 

1555 ''' 

1556 s, r = self._fprs2 

1557 if isint(x, both=True): 

1558 x = int(x) # Fsum**int 

1559 y = abs(x) 

1560 if y > 1: 

1561 if r: 

1562 f = self._pow_int(y, other, op) 

1563 if x > 0: # > 1 

1564 return f 

1565 # assert x < 0 # < -1 

1566 s, r = f._fprs2 if isinstance(f, Fsum) else (f, 0) 

1567 if r: 

1568 return _Fsum_ps(_1_0)._ftruediv(f, op) 

1569 # use **= -1 for the CPython float_pow 

1570 # error if s is zero, and not s = 1 / s 

1571 x = -1 

1572 elif x < 0: # self**-1 == 1 / self 

1573 if r: 

1574 return _Fsum_ps(_1_0)._ftruediv(self, op) 

1575 else: # self**1 or self**0 

1576 return self._pow_0_1(x, other) # self, 1 or 1.0 

1577 elif not isscalar(x): # assert ... 

1578 raise self._TypeError(op, other, txt=_not_scalar_) 

1579 elif r and self._raiser(r, s): # non-zero residual**fractional 

1580 # raise self._ResidualError(op, other, r, fractional_power=x) 

1581 t = _stresidual(_non_zero_, r, fractional_power=x) 

1582 raise self._Error(op, other, ResidualError, txt=t) 

1583 # assert isscalar(s) and isscalar(x) 

1584 return self._pow_2(s, x, other, op) 

1585 

1586 def _ps_1(self, *less): 

1587 '''(INTERNAL) Yield partials, 1-primed and subtract any C{less}. 

1588 ''' 

1589 n = len(self._ps) + len(less) - 4 

1590 if n < 0: 

1591 yield _1_0 

1592 for p in self._ps: 

1593 yield p 

1594 for p in less: 

1595 yield -p 

1596 if n < 0: 

1597 yield _N_1_0 

1598 

1599 def _ps_mul(self, op, *factors): # see .fmath.Fhorner 

1600 '''(INTERNAL) Yield all C{partials} times each B{C{factor}}, 

1601 in total, up to C{len(partials) * len(factors)} items. 

1602 ''' 

1603 ps = self._ps # tuple(self._ps) 

1604 if len(ps) < len(factors): 

1605 ps, factors = factors, ps 

1606 _f = _isfinite 

1607 for f in factors: 

1608 for p in ps: 

1609 p *= f 

1610 yield p if _f(p) else self._finite(p, op) 

1611 

1612 @property_RO 

1613 def _ps_neg(self): 

1614 '''(INTERNAL) Yield the partials, I{negated}. 

1615 ''' 

1616 for p in self._ps: 

1617 yield -p 

1618 

1619 @property_RO 

1620 def real(self): 

1621 '''Get the C{real} part of this instance (C{float}). 

1622 

1623 @see: Methods L{Fsum.__float__} and L{Fsum.fsum} 

1624 and properties L{Fsum.ceil}, L{Fsum.floor}, 

1625 L{Fsum.imag} and L{Fsum.residual}. 

1626 ''' 

1627 return float(self._fprs) 

1628 

1629 @property_RO 

1630 def residual(self): 

1631 '''Get this instance' residual (C{float} or C{int}), the 

1632 C{sum(partials)} less the precision running sum C{fsum}. 

1633 

1634 @note: If the C{residual is INT0}, the precision running 

1635 C{fsum} is considered to be I{exact}. 

1636 

1637 @see: Methods L{Fsum.fsum}, L{Fsum.fsum2} and L{Fsum.is_exact}. 

1638 ''' 

1639 return self._fprs2.residual 

1640 

1641 def _raiser(self, r, s): 

1642 '''(INTERNAL) Does ratio C{r / s} exceed threshold? 

1643 ''' 

1644 self._ratio = t = fabs((r / s) if s else r) 

1645 return t > self._RESIDUAL 

1646 

1647 def RESIDUAL(self, *threshold): 

1648 '''Get and set this instance' I{ratio} for raising L{ResidualError}s, 

1649 overriding the default from env variable C{PYGEODESY_FSUM_RESIDUAL}. 

1650 

1651 @arg threshold: If C{scalar}, the I{ratio} to exceed for raising 

1652 L{ResidualError}s in division and exponention, if 

1653 C{None} restore the default set with env variable 

1654 C{PYGEODESY_FSUM_RESIDUAL} or if omitted, keep the 

1655 current setting. 

1656 

1657 @return: The previous C{RESIDUAL} setting (C{float}), default C{0}. 

1658 

1659 @raise ValueError: Negative B{C{threshold}}. 

1660 

1661 @note: A L{ResidualError} is thrown if the non-zero I{ratio} 

1662 C{residual / fsum} exceeds the B{C{threshold}}. 

1663 ''' 

1664 r = self._RESIDUAL 

1665 if threshold: 

1666 t = threshold[0] 

1667 t = Fsum._RESIDUAL if t is None else ( 

1668 float(t) if isscalar(t) else ( # for backward ... 

1669 _0_0 if bool(t) else _1_0)) # ... compatibility 

1670 if t < 0: 

1671 u = _DOT_(self, unstr(self.RESIDUAL, *threshold)) 

1672 raise _ValueError(u, RESIDUAL=t, txt=_negative_) 

1673 self._RESIDUAL = t 

1674 return r 

1675 

1676 def _ResidualError(self, op, other, residual): 

1677 '''(INTERNAL) Non-zero B{C{residual}} etc. 

1678 ''' 

1679 t = _stresidual(_non_zero_, residual, ratio=self._ratio, 

1680 RESIDUAL=self._RESIDUAL) 

1681 t = t.replace(_COMMASPACE_R_, _exceeds_R_) 

1682 return self._Error(op, other, ResidualError, txt=t) 

1683 

1684 def signOf(self, res=True): 

1685 '''Determine the sign of this instance. 

1686 

1687 @kwarg res: If C{True} consider, otherwise 

1688 ignore the residual (C{bool}). 

1689 

1690 @return: The sign (C{int}, -1, 0 or +1). 

1691 ''' 

1692 s, r = self._fprs2 if res else (self._fprs, 0) 

1693 return _signOf(s, -r) 

1694 

1695 def toRepr(self, **prec_sep_fmt_lenc): # PYCHOK signature 

1696 '''Return this C{Fsum} instance as representation. 

1697 

1698 @kwarg prec_sep_fmt_lenc: Optional keyword arguments for 

1699 method L{Fsum2Tuple.toRepr} plus C{B{lenc}=True} 

1700 (C{bool}) to in-/exclude the current C{[len]} 

1701 of this L{Fsum} enclosed in I{[brackets]}. 

1702 

1703 @return: This instance (C{repr}). 

1704 ''' 

1705 return self._toT(self._fprs2.toRepr, **prec_sep_fmt_lenc) 

1706 

1707 def toStr(self, **prec_sep_fmt_lenc): # PYCHOK signature 

1708 '''Return this C{Fsum} instance as string. 

1709 

1710 @kwarg prec_sep_fmt_lenc: Optional keyword arguments for 

1711 method L{Fsum2Tuple.toStr} plus C{B{lenc}=True} 

1712 (C{bool}) to in-/exclude the current C{[len]} 

1713 of this L{Fsum} enclosed in I{[brackets]}. 

1714 

1715 @return: This instance (C{str}). 

1716 ''' 

1717 return self._toT(self._fprs2.toStr, **prec_sep_fmt_lenc) 

1718 

1719 def _toT(self, toT, fmt=Fmt.g, lenc=True, **kwds): 

1720 '''(INTERNAL) Helper for C{toRepr} and C{toStr}. 

1721 ''' 

1722 n = self.named3 

1723 if lenc: 

1724 n = Fmt.SQUARE(n, len(self)) 

1725 return _SPACE_(n, toT(fmt=fmt, **kwds)) 

1726 

1727 def _TypeError(self, op, other, **txt): # PYCHOK no cover 

1728 '''(INTERNAL) Return a C{TypeError}. 

1729 ''' 

1730 return self._Error(op, other, _TypeError, **txt) 

1731 

1732 def _update(self, updated=True): # see ._fset 

1733 '''(INTERNAL) Zap all cached C{Property_RO} values. 

1734 ''' 

1735 if updated: 

1736 _pop = self.__dict__.pop 

1737 for p in _ROs: 

1738 _ = _pop(p, None) 

1739# Fsum._fint2._update(self) 

1740# Fsum._fprs ._update(self) 

1741# Fsum._fprs2._update(self) 

1742 return self # for .fset_ 

1743 

1744 def _ValueError(self, op, other, **txt): # PYCHOK no cover 

1745 '''(INTERNAL) Return a C{ValueError}. 

1746 ''' 

1747 return self._Error(op, other, _ValueError, **txt) 

1748 

1749 def _ZeroDivisionError(self, op, other, **txt): # PYCHOK no cover 

1750 '''(INTERNAL) Return a C{ZeroDivisionError}. 

1751 ''' 

1752 return self._Error(op, other, _ZeroDivisionError, **txt) 

1753 

1754_ROs = _allPropertiesOf_n(3, Fsum, Property_RO) # PYCHOK assert, see Fsum._fset, -._update 

1755 

1756 

1757def _Float_Int(arg, **name_Error): 

1758 '''(INTERNAL) Unit of L{Fsum2Tuple} items. 

1759 ''' 

1760 U = Int if isint(arg) else Float 

1761 return U(arg, **name_Error) 

1762 

1763 

1764class DivMod2Tuple(_NamedTuple): 

1765 '''2-Tuple C{(div, mod)} with the quotient C{div} and remainder 

1766 C{mod} results of a C{divmod} operation. 

1767 

1768 @note: Quotient C{div} an C{int} in Python 3+ or a C{float} in 

1769 Python 2-. Remainder C{mod} an L{Fsum} instance. 

1770 ''' 

1771 _Names_ = (_div_, _mod_) 

1772 _Units_ = (_Float_Int, Fsum) 

1773 

1774 

1775class Fsum2Tuple(_NamedTuple): 

1776 '''2-Tuple C{(fsum, residual)} with the precision running C{fsum} 

1777 and the C{residual}, the sum of the remaining partials. Each 

1778 item is either C{float} or C{int}. 

1779 

1780 @note: If the C{residual is INT0}, the C{fsum} is considered 

1781 to be I{exact}, see method L{Fsum2Tuple.is_exact}. 

1782 ''' 

1783 _Names_ = ( Fsum.fsum.__name__, Fsum.residual.name) 

1784 _Units_ = (_Float_Int, _Float_Int) 

1785 

1786 @Property_RO 

1787 def Fsum(self): 

1788 '''Get this L{Fsum2Tuple} as an L{Fsum}. 

1789 ''' 

1790 s, r = map(float, self) 

1791 return _Fsum_ps(*_2ps(s, r), name=self.name) 

1792 

1793 def is_exact(self): 

1794 '''Is this L{Fsum2Tuple} considered to be exact? (C{bool}). 

1795 ''' 

1796 return self.Fsum.is_exact() 

1797 

1798 def is_integer(self): 

1799 '''Is this L{Fsum2Tuple} C{integer}? (C{bool}). 

1800 ''' 

1801 return self.Fsum.is_integer() 

1802 

1803 

1804class ResidualError(_ValueError): 

1805 '''Error raised for an operation involving a L{pygeodesy.sums.Fsum} 

1806 instance with a non-zero C{residual}, I{integer} or otherwise. 

1807 

1808 @see: Module L{pygeodesy.fsums} and method L{Fsum.RESIDUAL}. 

1809 ''' 

1810 pass 

1811 

1812 

1813def _Fsum_ps(*ps, **name): 

1814 '''(INTERNAL) Return an C{Fsum} from I{ordered} partials C{ps}. 

1815 ''' 

1816 f = Fsum(**name) if name else Fsum() 

1817 if ps: 

1818 f._n = len(ps) 

1819 f._ps[:] = ps 

1820 return f 

1821 

1822 

1823def _Fsum_xs(xs, up=False, **name): 

1824 '''(INTERNAL) Return an C{Fsum} from known floats C{xs}. 

1825 ''' 

1826 f = Fsum(**name) if name else Fsum() 

1827 return f._facc(xs, up=up) 

1828 

1829 

1830try: 

1831 from math import fsum as _fsum # precision IEEE-754 sum, Python 2.6+ 

1832 

1833 # make sure _fsum works as expected (XXX check 

1834 # float.__getformat__('float')[:4] == 'IEEE'?) 

1835 if _fsum((1, 1e101, 1, -1e101)) != 2: # PYCHOK no cover 

1836 del _fsum # nope, remove _fsum ... 

1837 raise ImportError # ... use _fsum below 

1838 

1839 Fsum._math_fsum = _sum = _fsum # PYCHOK exported 

1840 

1841 if _getenv('PYGEODESY_FSUM_PARTIALS', NN) == _fsum.__name__: 

1842 _psum = _fsum # PYCHOK re-def 

1843 

1844except ImportError: 

1845 _sum = sum # Fsum(NAN) exception fall-back 

1846 

1847 def _fsum(xs): 

1848 '''(INTERNAL) Precision summation, Python 2.5-. 

1849 ''' 

1850 return Fsum(name=_fsum.__name__).fsum(xs) if xs else _0_0 

1851 

1852 

1853def fsum(xs, floats=False): 

1854 '''Precision floating point summation based on or like Python's C{math.fsum}. 

1855 

1856 @arg xs: Iterable, list, tuple, etc. of values (C{scalar} or L{Fsum} 

1857 instances). 

1858 @kwarg floats: Optionally, use C{B{floats}=True} iff I{all} B{C{xs}} 

1859 are known to be C{float}. 

1860 

1861 @return: Precision C{fsum} (C{float}). 

1862 

1863 @raise OverflowError: Partial C{2sum} overflow. 

1864 

1865 @raise TypeError: Non-scalar B{C{xs}} value. 

1866 

1867 @raise ValueError: Invalid or non-finite B{C{xs}} value. 

1868 

1869 @note: Exceptions and I{non-finite} handling may differ if not 

1870 based on Python's C{math.fsum}. 

1871 

1872 @see: Class L{Fsum} and methods L{Fsum.fsum} and L{Fsum.fadd}. 

1873 ''' 

1874 return _fsum(xs if floats else _2floats(xs)) if xs else _0_0 # PYCHOK yield 

1875 

1876 

1877def fsum_(*xs, **floats): 

1878 '''Precision floating point summation of all positional arguments. 

1879 

1880 @arg xs: Values to be added (C{scalar} or L{Fsum} instances), all 

1881 positional. 

1882 @kwarg floats: Optionally, use C{B{floats}=True} iff I{all} B{C{xs}} 

1883 are known to be C{float}. 

1884 

1885 @return: Precision C{fsum} (C{float}). 

1886 

1887 @see: Function C{fsum}. 

1888 ''' 

1889 return _fsum(xs if _xkwds_get(floats, floats=False) else 

1890 _2floats(xs, origin=1)) if xs else _0_0 # PYCHOK yield 

1891 

1892 

1893def fsumf_(*xs): 

1894 '''Precision floating point summation L{fsum_}C{(*xs, floats=True)}. 

1895 ''' 

1896 return _fsum(xs) if xs else _0_0 

1897 

1898 

1899def fsum1(xs, floats=False): 

1900 '''Precision floating point summation of a few arguments, 1-primed. 

1901 

1902 @arg xs: Iterable, list, tuple, etc. of values (C{scalar} or L{Fsum} 

1903 instances). 

1904 @kwarg floats: Optionally, use C{B{floats}=True} iff I{all} B{C{xs}} 

1905 are known to be C{float}. 

1906 

1907 @return: Precision C{fsum} (C{float}). 

1908 

1909 @see: Function C{fsum}. 

1910 ''' 

1911 return _fsum(_1primed(xs if floats else _2floats(xs))) if xs else _0_0 # PYCHOK yield 

1912 

1913 

1914def fsum1_(*xs, **floats): 

1915 '''Precision floating point summation of a few arguments, 1-primed. 

1916 

1917 @arg xs: Values to be added (C{scalar} or L{Fsum} instances), all 

1918 positional. 

1919 @kwarg floats: Optionally, use C{B{floats}=True} iff I{all} B{C{xs}} 

1920 are known to be C{float}. 

1921 

1922 @return: Precision C{fsum} (C{float}). 

1923 

1924 @see: Function C{fsum} 

1925 ''' 

1926 return _fsum(_1primed(xs if _xkwds_get(floats, floats=False) else 

1927 _2floats(xs, origin=1))) if xs else _0_0 # PYCHOK yield 

1928 

1929 

1930def fsum1f_(*xs): 

1931 '''Precision floating point summation L{fsum1_}C{(*xs, floats=True)}. 

1932 ''' 

1933 return _fsum(_1primed(xs)) if xs else _0_0 

1934 

1935 

1936if __name__ == '__main__': 

1937 

1938 # usage: [env PYGEODESY_FSUM_PARTIALS=fsum] python3 -m pygeodesy.fsums 

1939 

1940 def _test(n): 

1941 # copied from Hettinger, see L{Fsum} reference 

1942 from pygeodesy import printf 

1943 from random import gauss, random, shuffle 

1944 

1945 printf(_fsum.__name__, end=_COMMASPACE_) 

1946 printf(_psum.__name__, end=_COMMASPACE_) 

1947 

1948 F = Fsum() 

1949 if F.is_math_fsum: 

1950 c = (7, 1e100, -7, -1e100, -9e-20, 8e-20) * 10 

1951 for _ in range(n): 

1952 t = list(c) 

1953 s = 0 

1954 for _ in range(n * 8): 

1955 v = gauss(0, random())**7 - s 

1956 t.append(v) 

1957 s += v 

1958 shuffle(t) 

1959 assert float(F.fset_(*t)) == _fsum(t) 

1960 printf(_DOT_, end=NN) 

1961 printf(NN) 

1962 

1963 _test(128) 

1964 

1965# **) MIT License 

1966# 

1967# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved. 

1968# 

1969# Permission is hereby granted, free of charge, to any person obtaining a 

1970# copy of this software and associated documentation files (the "Software"), 

1971# to deal in the Software without restriction, including without limitation 

1972# the rights to use, copy, modify, merge, publish, distribute, sublicense, 

1973# and/or sell copies of the Software, and to permit persons to whom the 

1974# Software is furnished to do so, subject to the following conditions: 

1975# 

1976# The above copyright notice and this permission notice shall be included 

1977# in all copies or substantial portions of the Software. 

1978# 

1979# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

1980# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

1981# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

1982# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

1983# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 

1984# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 

1985# OTHER DEALINGS IN THE SOFTWARE.