Coverage for pygeodesy/fsums.py: 95%

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1 

2# -*- coding: utf-8 -*- 

3 

4u'''Class L{Fsum} for precision floating point summation 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 an empty string (or anything 

18other than C{"fsum"}) for backward compatible summation of L{Fsum} partials. 

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, signOf, _signOf 

30from pygeodesy.constants import INT0, _isfinite, isinf, isnan, _pos_self, \ 

31 _0_0, _1_0, _N_1_0, Float, Int 

32from pygeodesy.errors import itemsorted, _OverflowError, _TypeError, \ 

33 _ValueError, _xError2, _xkwds_get, _xkwds_get_, \ 

34 _ZeroDivisionError 

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

36 _exceeds_, _from_, _iadd_op_, _LANGLE_, \ 

37 _negative_, _NOTEQUAL_, _not_finite_, \ 

38 _not_scalar_, _PERCENT_, _PLUS_, _R_, _RANGLE_, \ 

39 _SLASH_, _SPACE_, _STAR_, _UNDER_ 

40from pygeodesy.lazily import _ALL_LAZY, _getenv, _sys_version_info2 

41from pygeodesy.named import _Named, _NamedTuple, _NotImplemented, Fmt, unstr 

42from pygeodesy.props import _allPropertiesOf_n, deprecated_property_RO, \ 

43 Property_RO, property_RO 

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

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

46 

47from math import ceil as _ceil, fabs, floor as _floor # PYCHOK used! .ltp 

48 

49__all__ = _ALL_LAZY.fsums 

50__version__ = '23.08.23' 

51 

52_add_op_ = _PLUS_ # in .auxilats.auxAngle 

53_eq_op_ = _EQUAL_ * 2 # _DEQUAL_ 

54_COMMASPACE_R_ = _COMMASPACE_ + _R_ 

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_op_ = _PERCENT_ 

64_mul_op_ = _STAR_ 

65_ne_op_ = _NOTEQUAL_ 

66_non_zero_ = 'non-zero' 

67_pow_op_ = _STAR_ * 2 # _DSTAR_, in .fmath 

68_sub_op_ = _DASH_ # in .auxilats.auxAngle, .fsums 

69_truediv_op_ = _SLASH_ 

70_divmod_op_ = _floordiv_op_ + _mod_op_ 

71_isub_op_ = _sub_op_ + _fset_op_ # in .auxilats.auxAngle, .fsums 

72 

73 

74def _2float(index=None, **name_value): # in .fmath, .fstats 

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

76 ''' 

77 n, v = name_value.popitem() # _xkwds_popitem(name_value) 

78 try: 

79 v = float(v) 

80 if _isfinite(v): 

81 return v 

82 E, t = _ValueError, _not_finite_ 

83 except Exception as e: 

84 E, t = _xError2(e) 

85 if index is not None: 

86 n = Fmt.SQUARE(n, index) 

87 raise E(n, v, txt=t) 

88 

89 

90def _2floats(xs, origin=0, sub=False): 

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

92 ''' 

93 try: 

94 i, x = origin, None 

95 _fin = _isfinite 

96 _Fsum = Fsum 

97 for x in xs: 

98 if isinstance(x, _Fsum): 

99 for p in x._ps: 

100 yield (-p) if sub else p 

101 else: 

102 f = float(x) 

103 if not _fin(f): 

104 raise ValueError(_not_finite_) 

105 if f: 

106 yield (-f) if sub else f 

107 i += 1 

108 except Exception as e: 

109 E, t = _xError2(e) 

110 n = Fmt.SQUARE(xs=i) 

111 raise E(n, x, txt=t) 

112 

113 

114def _Powers(power, xs, origin=1): # in .fmath 

115 '''(INTERNAL) Yield each C{xs} as C{float(x**power)}. 

116 ''' 

117 if not isscalar(power): 

118 raise _TypeError(power=power, txt=_not_scalar_) 

119 try: 

120 i, x = origin, None 

121 _fin = _isfinite 

122 _Fsum = Fsum 

123 _pow = pow # XXX math.pow 

124 for x in xs: 

125 if isinstance(x, _Fsum): 

126 P = x.pow(power) 

127 for p in P._ps: 

128 yield p 

129 else: 

130 p = _pow(float(x), power) 

131 if not _fin(p): 

132 raise ValueError(_not_finite_) 

133 yield p 

134 i += 1 

135 except Exception as e: 

136 E, t = _xError2(e) 

137 n = Fmt.SQUARE(xs=i) 

138 raise E(n, x, txt=t) 

139 

140 

141def _1primed(xs): 

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

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

144 ''' 

145 yield _1_0 

146 for x in xs: 

147 if x: 

148 yield x 

149 yield _N_1_0 

150 

151 

152def _psum(ps): # PYCHOK used! 

153 '''(INTERNAL) Partials summation updating C{ps}, I{overridden below}. 

154 ''' 

155 i = len(ps) - 1 # len(ps) > 2 

156 s = ps[i] 

157 _2s = _2sum 

158 while i > 0: 

159 i -= 1 

160 s, r = _2s(s, ps[i]) 

161 if r: # sum(ps) became inexact 

162 ps[i:] = [s, r] if s else [r] 

163 if i > 0: 

164 p = ps[i-1] # round half-even 

165 if (p > 0 and r > 0) or \ 

166 (p < 0 and r < 0): # signs match 

167 r *= 2 

168 t = s + r 

169 if r == (t - s): 

170 s = t 

171 break 

172 ps[i:] = [s] 

173 return s 

174 

175 

176def _2scalar(other, _raiser=None): 

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

178 ''' 

179 if isinstance(other, Fsum): 

180 s, r = other._fint2 

181 if r: 

182 s, r = other._fprs2 

183 if r: # PYCHOK no cover 

184 if _raiser and _raiser(r, s): 

185 raise ValueError(_stresidual(_non_zero_, r)) 

186 s = other # L{Fsum} as-is 

187 else: 

188 s = other # C{type} as-is 

189 if isint(s, both=True): 

190 s = int(s) 

191 return s 

192 

193 

194def _strcomplex(s, *args): 

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

196 ''' 

197 c = iscomplex.__name__[2:] 

198 n = _DASH_(len(args), _arg_) 

199 t = _SPACE_(c, s, _from_, n, pow.__name__) 

200 return unstr(t, *args) 

201 

202 

203def _stresidual(prefix, residual, **name_values): 

204 '''(INTERNAL) Residual error C{str}. 

205 ''' 

206 p = _SPACE_(prefix, Fsum.residual.name) 

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

208 for n, v in itemsorted(name_values): 

209 n = n.replace(_UNDER_, _SPACE_) 

210 p = Fmt.PARENSPACED(n, Fmt(v)) 

211 t = _COMMASPACE_(t, p) 

212 return t 

213 

214 

215def _2sum(a, b): # by .testFmath 

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

217 ''' 

218 s = a + b 

219 if not _isfinite(s): 

220 u = unstr(_2sum.__name__, a, b) 

221 t = Fmt.PARENSPACED(_not_finite_, s) 

222 raise _OverflowError(u, txt=t) 

223 if fabs(a) < fabs(b): 

224 a, b = b, a 

225 return s, (b - (s - a)) 

226 

227 

228class Fsum(_Named): # sync __methods__ with .vector3dBase.Vector3dBase 

229 '''Precision floating point I{running} summation. 

230 

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

232 I{running} precision floating point summation. Accumulation may continue after 

233 intermediate, I{running} summuation. 

234 

235 @note: Accumulated values may be L{Fsum} or C{scalar} instances with C{scalar} meaning 

236 type C{float}, C{int} or any C{type} convertible to a single C{float}, having 

237 method C{__float__}. 

238 

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

240 Python's C{math.fsum}. 

241 

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

243 393090_Binary_floating_point_summatiaccurate_full/recipe-393090.py>}, U{Kahan 

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

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

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

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

248 ''' 

249 _math_fsum = None 

250 _n = 0 

251# _ps = [] # partial sums 

252# _px = 0 

253 _ratio = None 

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

255 

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

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

258 

259 @arg xs: No, one or more initial values (each C{scalar} or an 

260 L{Fsum} instance). 

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

262 (C{str}) and C{B{RESIDUAL}=None} for the 

263 L{ResidualError} threshold. 

264 

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

266 ''' 

267 if name_RESIDUAL: 

268 n, r = _xkwds_get_(name_RESIDUAL, name=NN, RESIDUAL=None) 

269 if n: # set name ... 

270 self.name = n 

271 if r is not None: 

272 self.RESIDUAL(r) # ... for ResidualError 

273# self._n = 0 

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

275 if len(xs) > 1: 

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

277 elif xs: # len(xs) == 1 

278 self._ps = [_2float(x=xs[0])] 

279 self._n = 1 

280 

281 def __abs__(self): 

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

283 ''' 

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

285 return self._copy_n(self.__abs__) if s < 0 else \ 

286 self._copy_2(self.__abs__) 

287 

288 def __add__(self, other): 

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

290 

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

292 

293 @return: The sum (L{Fsum}). 

294 

295 @see: Method L{Fsum.__iadd__}. 

296 ''' 

297 f = self._copy_2(self.__add__) 

298 return f._fadd(other, _add_op_) 

299 

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

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

302 ''' 

303 s, r = self._fprs2 

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

305 

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

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

308 

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

310 

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

312 ''' 

313 return self.ceil 

314 

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

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

317 

318 @return: -1, 0 or +1 (C{int}). 

319 

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

321 ''' 

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

323 return _signOf(s, 0) 

324 

325 cmp = __cmp__ 

326 

327 def __divmod__(self, other): 

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

329 remainder)}, an C{int} in Python 3+ or C{float} in Python 2- 

330 and an L{Fsum}. 

331 

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

333 

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

335 ''' 

336 f = self._copy_2(self.__divmod__) 

337 return f._fdivmod2(other, _divmod_op_) 

338 

339 def __eq__(self, other): 

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

341 ''' 

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

343 

344 def __float__(self): 

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

346 

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

348 ''' 

349 return float(self._fprs) 

350 

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

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

353 

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

355 

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

357 ''' 

358 return self.floor 

359 

360 def __floordiv__(self, other): 

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

362 

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

364 

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

366 

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

368 ''' 

369 f = self._copy_2(self.__floordiv__) 

370 return f._floordiv(other, _floordiv_op_) 

371 

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

373 '''Not implemented.''' 

374 return _NotImplemented(self, *other) 

375 

376 def __ge__(self, other): 

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

378 ''' 

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

380 

381 def __gt__(self, other): 

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

383 ''' 

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

385 

386 def __hash__(self): # PYCHOK no cover 

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

388 ''' 

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

390 

391 def __iadd__(self, other): 

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

393 

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

395 

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

397 

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

399 C{scalar} nor L{Fsum}. 

400 

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

402 ''' 

403 return self._fadd(other, _iadd_op_) 

404 

405 def __ifloordiv__(self, other): 

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

407 

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

409 

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

411 

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

413 

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

415 

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

417 

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

419 

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

421 ''' 

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

423 

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

425 '''Not implemented.''' 

426 return _NotImplemented(self, other) 

427 

428 def __imod__(self, other): 

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

430 

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

432 

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

434 

435 @see: Method L{Fsum.__divmod__}. 

436 ''' 

437 self._fdivmod2(other, _mod_op_ + _fset_op_) 

438 return self 

439 

440 def __imul__(self, other): 

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

442 

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

444 

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

446 

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

448 

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

450 

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

452 ''' 

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

454 

455 def __int__(self): 

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

457 

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

459 and L{Fsum.__floor__} and properties 

460 L{Fsum.ceil} and L{Fsum.floor}. 

461 ''' 

462 i, _ = self._fint2 

463 return i 

464 

465 def __invert__(self): # PYCHOK no cover 

466 '''Not implemented.''' 

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

468 return _NotImplemented(self) 

469 

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

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

472 

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

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

475 3-argument C{pow(B{self}, B{other}, B{mod})} 

476 version. 

477 

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

479 

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

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

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

483 

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

485 

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

487 env var C{PYGEODESY_FSUM_RESIDUAL} 

488 set or this instance has a non-zero 

489 residual and either B{C{mod}} is 

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

491 is a negative or fractional C{scalar}. 

492 

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

494 C{pow} invocation failed. 

495 

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

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

498 is a fractional C{scalar} and this 

499 instance is negative or has a non-zero 

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

501 

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

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

504 ''' 

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

506 

507 def __isub__(self, other): 

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

509 

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

511 

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

513 

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

515 

516 @see: Method L{Fsum.fadd}. 

517 ''' 

518 return self._fsub(other, _isub_op_) 

519 

520 def __iter__(self): 

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

522 ''' 

523 return iter(self.partials) 

524 

525 def __itruediv__(self, other): 

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

527 

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

529 

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

531 

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

533 

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

535 env var C{PYGEODESY_FSUM_RESIDUAL} set. 

536 

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

538 

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

540 

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

542 

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

544 ''' 

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

546 

547 def __le__(self, other): 

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

549 ''' 

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

551 

552 def __len__(self): 

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

554 ''' 

555 return self._n 

556 

557 def __lt__(self, other): 

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

559 ''' 

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

561 

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

563 '''Not implemented.''' 

564 return _NotImplemented(self, other) 

565 

566 def __mod__(self, other): 

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

568 

569 @see: Method L{Fsum.__imod__}. 

570 ''' 

571 f = self._copy_2(self.__mod__) 

572 return f._fdivmod2(other, _mod_op_)[1] 

573 

574 def __mul__(self, other): 

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

576 

577 @see: Method L{Fsum.__imul__}. 

578 ''' 

579 f = self._copy_2(self.__mul__) 

580 return f._fmul(other, _mul_op_) 

581 

582 def __ne__(self, other): 

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

584 ''' 

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

586 

587 def __neg__(self): 

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

589 ''' 

590 return self._copy_n(self.__neg__) 

591 

592 def __pos__(self): 

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

594 ''' 

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

596 

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

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

599 

600 @see: Method L{Fsum.__ipow__}. 

601 ''' 

602 f = self._copy_2(self.__pow__) 

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

604 

605 def __radd__(self, other): 

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

607 

608 @see: Method L{Fsum.__iadd__}. 

609 ''' 

610 f = self._copy_r2(other, self.__radd__) 

611 return f._fadd(self, _add_op_) 

612 

613 def __rdivmod__(self, other): 

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

615 remainder)}. 

616 

617 @see: Method L{Fsum.__divmod__}. 

618 ''' 

619 f = self._copy_r2(other, self.__rdivmod__) 

620 return f._fdivmod2(self, _divmod_op_) 

621 

622# def __repr__(self): 

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

624# ''' 

625# return self.toRepr(lenc=True) 

626 

627 def __rfloordiv__(self, other): 

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

629 

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

631 ''' 

632 f = self._copy_r2(other, self.__rfloordiv__) 

633 return f._floordiv(self, _floordiv_op_) 

634 

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

636 '''Not implemented.''' 

637 return _NotImplemented(self, other) 

638 

639 def __rmod__(self, other): 

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

641 

642 @see: Method L{Fsum.__imod__}. 

643 ''' 

644 f = self._copy_r2(other, self.__rmod__) 

645 return f._fdivmod2(self, _mod_op_)[1] 

646 

647 def __rmul__(self, other): 

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

649 

650 @see: Method L{Fsum.__imul__}. 

651 ''' 

652 f = self._copy_r2(other, self.__rmul__) 

653 return f._fmul(self, _mul_op_) 

654 

655 def __round__(self, ndigits=None): # PYCHOK no cover 

656 '''Not implemented.''' 

657 return _NotImplemented(self, ndigits=ndigits) 

658 

659 def __rpow__(self, other, *mod): 

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

661 

662 @see: Method L{Fsum.__ipow__}. 

663 ''' 

664 f = self._copy_r2(other, self.__rpow__) 

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

666 

667 def __rsub__(self, other): 

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

669 

670 @see: Method L{Fsum.__isub__}. 

671 ''' 

672 f = self._copy_r2(other, self.__rsub__) 

673 return f._fsub(self, _sub_op_) 

674 

675 def __rtruediv__(self, other): 

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

677 

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

679 ''' 

680 f = self._copy_r2(other, self.__rtruediv__) 

681 return f._ftruediv(self, _truediv_op_) 

682 

683 def __str__(self): 

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

685 ''' 

686 return self.toStr(lenc=True) 

687 

688 def __sub__(self, other): 

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

690 

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

692 

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

694 

695 @see: Method L{Fsum.__isub__}. 

696 ''' 

697 f = self._copy_2(self.__sub__) 

698 return f._fsub(other, _sub_op_) 

699 

700 def __truediv__(self, other): 

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

702 

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

704 

705 @return: The quotient (L{Fsum}). 

706 

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

708 ''' 

709 f = self._copy_2(self.__truediv__) 

710 return f._ftruediv(other, _truediv_op_) 

711 

712 __trunc__ = __int__ 

713 

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

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

716 __div__ = __truediv__ 

717 __idiv__ = __itruediv__ 

718 __long__ = __int__ 

719 __nonzero__ = __bool__ 

720 __rdiv__ = __rtruediv__ 

721 

722 def as_integer_ratio(self): 

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

724 

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

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

727 

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

729 ''' 

730 n, r = self._fint2 

731 if r: 

732 i, d = r.as_integer_ratio() 

733 n *= d 

734 n += i 

735 else: # PYCHOK no cover 

736 d = 1 

737 return n, d 

738 

739 @property_RO 

740 def ceil(self): 

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

742 but C{float} in Python 2-). 

743 

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

745 

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

747 L{Fsum.imag} and L{Fsum.real}. 

748 ''' 

749 s, r = self._fprs2 

750 c = _ceil(s) + int(r) - 1 

751 while r > (c - s): # (s + r) > c 

752 c += 1 

753 return c 

754 

755 def _cmp_0(self, other, op): 

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

757 ''' 

758 if isscalar(other): 

759 if other: 

760 s = _fsum(self._ps_1(other)) 

761 else: 

762 s, r = self._fprs2 

763 s = _signOf(s, -r) 

764 elif isinstance(other, Fsum): 

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

766 else: 

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

768 return s 

769 

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

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

772 

773 @return: The copy (L{Fsum}). 

774 ''' 

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

776 f._n = self._n if deep else 1 

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

778 return f 

779 

780 def _copy_0(self, *xs): 

781 '''(INTERNAL) Copy with/-out overriding C{partials}. 

782 ''' 

783 # for x in xs: 

784 # assert isscalar(x) 

785 f = self._Fsum(self._n + len(xs), *xs) 

786 if self.name: 

787 f._name = self.name # .rename calls _update_attrs 

788 return f 

789 

790 def _copy_2(self, which): 

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

792 ''' 

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

794 f = _Named.copy(self, deep=False, name=which.__name__) 

795 # assert f._n == self._n 

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

797 return f 

798 

799 def _copy_n(self, which): 

800 '''(INTERNAL) Negated copy for I{monadic} C{__abs__} and C{__neg__}. 

801 ''' 

802 if self._ps: 

803 f = self._Fsum(self._n) 

804 f._ps[:] = self._ps_n() 

805# f._facc_up(up=False) 

806 else: 

807 f = self._Fsum(self._n, _0_0) 

808 f._name = which.__name__ # .rename calls _update_attrs 

809 return f 

810 

811 def _copy_r2(self, other, which): 

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

813 ''' 

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

815 Fsum(other, name=which.__name__) # see ._copy_2 

816 

817 def _copy_RESIDUAL(self, other): 

818 '''(INTERNAL) Copy C{other._RESIDUAL}. 

819 ''' 

820 R = other._RESIDUAL 

821 if R is not Fsum._RESIDUAL: 

822 self._RESIDUAL = R 

823 

824 def _copy_up(self, _fprs2=False): 

825 '''(INTERNAL) Minimal, anonymous copy. 

826 ''' 

827 f = self._Fsum(self._n, *self._ps) 

828 if _fprs2: # only the ._fprs2 2-tuple 

829 Fsum._fprs2._update_from(f, self) 

830 return f 

831 

832 def divmod(self, other): 

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

834 remainder)}. 

835 

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

837 

838 @return: 2-Tuple C{(quotient, remainder)}, with the C{quotient} 

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

840 the C{remainder} an L{Fsum} instance. 

841 

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

843 ''' 

844 f = self._copy_2(self.divmod) 

845 return f._fdivmod2(other, _divmod_op_) 

846 

847 def _Error(self, op, other, Error, **txt): 

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

849 ''' 

850 return Error(_SPACE_(self.toRepr(), op, repr(other)), **txt) 

851 

852 def _ErrorX(self, X, xs, **kwds): # in .fmath 

853 '''(INTERNAL) Format a caught exception. 

854 ''' 

855 E, t = _xError2(X) 

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

857 return E(n, txt=t, cause=X) 

858 

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

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

861 ''' 

862 n, ps, _2s = 0, self._ps, _2sum 

863 for x in xs: # _iter() 

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

865 i = 0 

866 for p in ps: 

867 x, p = _2s(x, p) 

868 if p: 

869 ps[i] = p 

870 i += 1 

871 ps[i:] = [x] 

872 n += 1 

873 # assert self._ps is ps 

874 if n: 

875 self._n += n 

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

877 if up: 

878 self._update() 

879 return self 

880 

881 def _facc_(self, *xs, **up): 

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

883 ''' 

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

885 

886# def _facc_up(self, up=True): 

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

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

889# ''' 

890# while len(self._ps) > 1: 

891# p = self._ps.pop() 

892# if p: 

893# n = self._n 

894# self._facc_(p, up=False) 

895# self._n = n 

896# break 

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

898 

899 def fadd(self, xs=()): 

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

901 to this instance. 

902 

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

904 L{Fsum} instances). 

905 

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

907 

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

909 

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

911 nor L{Fsum}. 

912 

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

914 ''' 

915 if isinstance(xs, Fsum): 

916 self._facc(xs._ps) 

917 elif isscalar(xs): # for backward compatibility 

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

919 elif xs: 

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

921 return self 

922 

923 def fadd_(self, *xs): 

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

925 to this instance. 

926 

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

928 all positional. 

929 

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

931 

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

933 

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

935 nor L{Fsum}. 

936 

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

938 ''' 

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

940 

941 def _fadd(self, other, op): # in .fmath.Fhorner 

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

943 ''' 

944 if isinstance(other, Fsum): 

945 if other is self: 

946 self._facc_(*other._ps) # == ._facc(tuple(other._ps)) 

947 elif other._ps: 

948 self._facc(other._ps) 

949 elif not isscalar(other): 

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

951 elif other: 

952 self._facc_(other) 

953 return self 

954 

955 fcopy = copy # for backward compatibility 

956 fdiv = __itruediv__ # for backward compatibility 

957 fdivmod = __divmod__ # for backward compatibility 

958 

959 def _fdivmod2(self, other, op): 

960 '''(INTERNAL) C{divmod(B{self}, B{other})} as 2-tuple 

961 (C{int} or C{float}, remainder C{self}). 

962 ''' 

963 # result mostly follows CPython function U{float_divmod 

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

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

966 q = self._copy_up(_fprs2=True)._ftruediv(other, op).floor 

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

968 self -= other * q 

969 

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

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

972 self += other 

973 q -= 1 

974 

975# t = self.signOf() 

976# if t and t != s: 

977# from pygeodesy.errors import _AssertionError 

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

979 return q, self # q is C{int} in Python 3+, but C{float} in Python 2- 

980 

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

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

983 ''' 

984 if _isfinite(other): 

985 return other 

986 raise ValueError(_not_finite_) if not op else \ 

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

988 

989 def fint(self, raiser=True, name=NN): 

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

991 

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

993 I{integer} residual is non-zero. 

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

995 

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

997 

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

999 

1000 @see: Methods L{Fsum.int_float} and L{Fsum.is_integer}. 

1001 ''' 

1002 i, r = self._fint2 

1003 if r and raiser: 

1004 t = _stresidual(_integer_, r) 

1005 raise ResidualError(_integer_, i, txt=t) 

1006 n = name or self.fint.__name__ 

1007 return Fsum(name=n)._fset(i, asis=True) 

1008 

1009 def fint2(self, **name): 

1010 '''Return this instance' current running sum as C{int} and 

1011 the I{integer} residual. 

1012 

1013 @kwarg name: Optional name (C{str}). 

1014 

1015 @return: An L{Fsum2Tuple}C{(fsum, residual)} with C{fsum} 

1016 an C{int} and I{integer} C{residual} a C{float} or 

1017 C{INT0} if the C{fsum} is considered to be I{exact}. 

1018 ''' 

1019 return Fsum2Tuple(*self._fint2, **name) 

1020 

1021 @Property_RO 

1022 def _fint2(self): # see ._fset 

1023 '''(INTERNAL) Get 2-tuple (C{int}, I{integer} residual). 

1024 ''' 

1025 i = int(self._fprs) # int(self) 

1026 r = _fsum(self._ps_1(i)) if len(self._ps) > 1 else ( 

1027 (self._ps[0] - i) if self._ps else -i) 

1028 return i, (r or INT0) 

1029 

1030 @deprecated_property_RO 

1031 def float_int(self): # PYCHOK no cover 

1032 '''DEPRECATED, use method C{Fsum.int_float}.''' 

1033 return self.int_float() # raiser=False 

1034 

1035 @property_RO 

1036 def floor(self): 

1037 '''Get this instance' C{floor} (C{int} in Python 3+, but 

1038 C{float} in Python 2-). 

1039 

1040 @note: The C{floor} takes the C{residual} into account. 

1041 

1042 @see: Method L{Fsum.int_float} and properties L{Fsum.ceil}, 

1043 L{Fsum.imag} and L{Fsum.real}. 

1044 ''' 

1045 s, r = self._fprs2 

1046 f = _floor(s) + _floor(r) + 1 

1047 while r < (f - s): # (s + r) < f 

1048 f -= 1 

1049 return f 

1050 

1051# floordiv = __floordiv__ # for naming consistency 

1052 

1053 def _floordiv(self, other, op): # rather _ffloordiv? 

1054 '''Apply C{B{self} //= B{other}}. 

1055 ''' 

1056 q = self._ftruediv(other, op) # == self 

1057 return self._fset(q.floor, asis=True) # floor(q) 

1058 

1059 fmul = __imul__ # for backward compatibility 

1060 

1061 def _fmul(self, other, op): 

1062 '''(INTERNAL) Apply C{B{self} *= B{other}}. 

1063 ''' 

1064 if isscalar(other): 

1065 f = self._mul_scalar(other, op) 

1066 elif not isinstance(other, Fsum): 

1067 raise self._TypeError(op, other) # txt=_invalid_ 

1068 elif len(self._ps) != 1: 

1069 f = self._mul_Fsum(other, op) 

1070 elif len(other._ps) != 1: # len(self._ps) == 1 

1071 f = other._copy_up()._mul_scalar(self._ps[0], op) 

1072 else: # len(other._ps) == len(self._ps) == 1 

1073 s = self._finite(self._ps[0] * other._ps[0]) 

1074 return self._fset(s, asis=True, n=len(self) + 1) 

1075 return self._fset(f) 

1076 

1077 def fover(self, over): 

1078 '''Apply C{B{self} /= B{over}} and summate. 

1079 

1080 @arg over: An L{Fsum} or C{scalar} denominator. 

1081 

1082 @return: Precision running sum (C{float}). 

1083 

1084 @see: Methods L{Fsum.fsum} and L{Fsum.__itruediv__}. 

1085 ''' 

1086 return float(self.fdiv(over)._fprs) 

1087 

1088 fpow = __ipow__ # for backward compatibility 

1089 

1090 def _fpow(self, other, op, *mod): 

1091 '''Apply C{B{self} **= B{other}}, optional B{C{mod}} or C{None}. 

1092 ''' 

1093 if mod and mod[0] is not None: # == 3-arg C{pow} 

1094 s = self._pow_3(other, mod[0], op) 

1095 elif mod and mod[0] is None and self.is_integer(): 

1096 # return an exact C{int} for C{int}**C{int} 

1097 i = self._copy_0(self._fint2[0]) # assert _fint2[1] == 0 

1098 x = _2scalar(other) # C{int}, C{float} or other 

1099 s = i._pow_2(x, other, op) if isscalar(x) else i._fpow(x, op) 

1100 else: # pow(self, other) == pow(self, other, None) 

1101 p = None 

1102 if isinstance(other, Fsum): 

1103 x, r = other._fprs2 

1104 if r: 

1105 if self._raiser(r, x): 

1106 raise self._ResidualError(op, other, r) 

1107 p = self._pow_scalar(r, other, op) 

1108# p = _2scalar(p) # _raiser = None 

1109 elif not isscalar(other): 

1110 raise self._TypeError(op, other) # txt=_invalid_ 

1111 else: 

1112 x = self._finite(other, op) 

1113 s = self._pow_scalar(x, other, op) 

1114 if p is not None: 

1115 s *= p 

1116 return self._fset(s, asis=isint(s), 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 ps = self._ps 

1127 n = len(ps) - 1 

1128 if n > 1: 

1129 s = _psum(ps) 

1130 elif n > 0: # len(ps) == 2 

1131 s, p = _2sum(*ps) if ps[1] else ps 

1132 ps[:] = ([p, s] if s else [p]) if p else [s] 

1133 elif n < 0: # see L{Fsum.__init__} 

1134 s = _0_0 

1135 ps[:] = [s] 

1136 else: # len(ps) == 1 

1137 s = ps[0] 

1138 # assert self._ps is ps 

1139 # assert Fsum._fprs2.name not in self.__dict__ 

1140 return s 

1141 

1142 @Property_RO 

1143 def _fprs2(self): 

1144 '''(INTERNAL) Get and cache this instance' precision 

1145 running sum and residual (L{Fsum2Tuple}). 

1146 ''' 

1147 s = self._fprs 

1148 r = _fsum(self._ps_1(s)) if len(self._ps) > 1 else INT0 

1149 return Fsum2Tuple(s, r) # name=Fsum.fsum2.__name__ 

1150 

1151# def _fpsqz(self): 

1152# '''(INTERNAL) Compress, squeeze the C{partials}. 

1153# ''' 

1154# if len(self._ps) > 2: 

1155# _ = self._fprs 

1156# return self 

1157 

1158 def _fset(self, other, asis=False, n=1): 

1159 '''(INTERNAL) Overwrite this instance with an other or a C{scalar}. 

1160 ''' 

1161 if other is self: 

1162 pass # from ._fmul, ._ftruediv and ._pow_scalar 

1163 elif isinstance(other, Fsum): 

1164 self._n = other._n 

1165 self._ps[:] = other._ps 

1166 self._copy_RESIDUAL(other) 

1167 # use or zap the C{Property_RO} values 

1168 Fsum._fint2._update_from(self, other) 

1169 Fsum._fprs ._update_from(self, other) 

1170 Fsum._fprs2._update_from(self, other) 

1171 elif isscalar(other): 

1172 s = other if asis else float(other) 

1173 i = int(s) # see ._fint2 

1174 t = i, ((s - i) or INT0) 

1175 self._n = n 

1176 self._ps[:] = [s] 

1177 # Property_RO _fint2, _fprs and _fprs2 can't be a Property: 

1178 # Property's _fset zaps the value just set by the @setter 

1179 self.__dict__.update(_fint2=t, _fprs=s, _fprs2=Fsum2Tuple(s, INT0)) 

1180 else: # PYCHOK no cover 

1181 raise self._TypeError(_fset_op_, other) # txt=_invalid_ 

1182 return self 

1183 

1184 def fsub(self, xs=()): 

1185 '''Subtract an iterable of C{scalar} or L{Fsum} instances 

1186 from this instance. 

1187 

1188 @arg xs: Iterable, list, tuple. etc. (C{scalar} 

1189 or L{Fsum} instances). 

1190 

1191 @return: This instance, updated (L{Fsum}). 

1192 

1193 @see: Method L{Fsum.fadd}. 

1194 ''' 

1195 return self._facc(_2floats(xs, sub=True)) if xs else self # PYCHOK yield 

1196 

1197 def fsub_(self, *xs): 

1198 '''Subtract all positional C{scalar} or L{Fsum} instances 

1199 from this instance. 

1200 

1201 @arg xs: Values to subtract (C{scalar} or 

1202 L{Fsum} instances), all positional. 

1203 

1204 @return: This instance, updated (L{Fsum}). 

1205 

1206 @see: Method L{Fsum.fadd}. 

1207 ''' 

1208 return self._facc(_2floats(xs, origin=1, sub=True)) if xs else self # PYCHOK yield 

1209 

1210 def _fsub(self, other, op): 

1211 '''(INTERNAL) Apply C{B{self} -= B{other}}. 

1212 ''' 

1213 if isinstance(other, Fsum): 

1214 if other is self: # or other._fprs2 == self._fprs2: 

1215 self._fset(_0_0, asis=True, n=len(self) * 2) # self -= self 

1216 elif other._ps: 

1217 self._facc(other._ps_n()) 

1218 elif not isscalar(other): 

1219 raise self._TypeError(op, other) # txt=_invalid_ 

1220 elif self._finite(other, op): 

1221 self._facc_(-other) 

1222 return self 

1223 

1224 def _Fsum(self, n, *ps): 

1225 '''(INTERNAL) New L{Fsum} instance. 

1226 ''' 

1227 f = Fsum() 

1228 f._n = n 

1229 if ps: 

1230 f._ps[:] = ps 

1231 f._copy_RESIDUAL(self) 

1232 return f 

1233 

1234 def fsum(self, xs=()): 

1235 '''Add more C{scalar} or L{Fsum} instances and summate. 

1236 

1237 @kwarg xs: Iterable, list, tuple, etc. (C{scalar} or 

1238 L{Fsum} instances). 

1239 

1240 @return: Precision running sum (C{float} or C{int}). 

1241 

1242 @see: Method L{Fsum.fadd}. 

1243 

1244 @note: Accumulation can continue after summation. 

1245 ''' 

1246 f = self._facc(_2floats(xs)) if xs else self # PYCHOK yield 

1247 return f._fprs 

1248 

1249 def fsum_(self, *xs): 

1250 '''Add all positional C{scalar} or L{Fsum} instances and summate. 

1251 

1252 @arg xs: Values to add (C{scalar} or L{Fsum} instances), 

1253 all positional. 

1254 

1255 @return: Precision running sum (C{float} or C{int}). 

1256 

1257 @see: Method L{Fsum.fsum}. 

1258 ''' 

1259 f = self._facc(_2floats(xs, origin=1)) if xs else self # PYCHOK yield 

1260 return f._fprs 

1261 

1262 def fsum2(self, xs=(), **name): 

1263 '''Add more C{scalar} or L{Fsum} instances and return the 

1264 current precision running sum and the C{residual}. 

1265 

1266 @kwarg xs: Iterable, list, tuple, etc. (C{scalar} or 

1267 L{Fsum} instances). 

1268 @kwarg name: Optional name (C{str}). 

1269 

1270 @return: L{Fsum2Tuple}C{(fsum, residual)} with C{fsum} the 

1271 current precision running sum and C{residual}, the 

1272 (precision) sum of the remaining C{partials}. The 

1273 C{residual is INT0} if the C{fsum} is considered 

1274 to be I{exact}. 

1275 

1276 @see: Methods L{Fsum.fint2}, L{Fsum.fsum} and L{Fsum.fsum2_} 

1277 ''' 

1278 f = self._facc(_2floats(xs)) if xs else self # PYCHOK yield 

1279 t = f._fprs2 

1280 if name: 

1281 t = t.dup(name=_xkwds_get(name, name=NN)) 

1282 return t 

1283 

1284 def fsum2_(self, *xs): 

1285 '''Add any positional C{scalar} or L{Fsum} instances and return 

1286 the precision running sum and the C{differential}. 

1287 

1288 @arg xs: Values to add (C{scalar} or L{Fsum} instances), 

1289 all positional. 

1290 

1291 @return: 2-Tuple C{(fsum, delta)} with the current precision 

1292 running C{fsum} and C{delta}, the difference with 

1293 the previous running C{fsum} (C{float}s). 

1294 

1295 @see: Methods L{Fsum.fsum_} and L{Fsum.fsum}. 

1296 ''' 

1297 p, r = self._fprs2 

1298 if xs: 

1299 s, t = self._facc(_2floats(xs, origin=1))._fprs2 # PYCHOK yield 

1300 return s, _fsum((s, -p, r, -t)) # ((s - p) + (r - t)) 

1301 else: # PYCHOK no cover 

1302 return p, _0_0 

1303 

1304# ftruediv = __itruediv__ # for naming consistency 

1305 

1306 def _ftruediv(self, other, op): 

1307 '''(INTERNAL) Apply C{B{self} /= B{other}}. 

1308 ''' 

1309 n = _1_0 

1310 if isinstance(other, Fsum): 

1311 if other is self or other._fprs2 == self._fprs2: 

1312 return self._fset(_1_0, asis=True, n=len(self)) 

1313 d, r = other._fprs2 

1314 if r: 

1315 if not d: # PYCHOK no cover 

1316 d = r 

1317 elif self._raiser(r, d): 

1318 raise self._ResidualError(op, other, r) 

1319 else: 

1320 d, n = other.as_integer_ratio() 

1321 elif isscalar(other): 

1322 d = other 

1323 else: # PYCHOK no cover 

1324 raise self._TypeError(op, other) # txt=_invalid_ 

1325 try: 

1326 s = 0 if isinf(d) else ( 

1327 d if isnan(d) else self._finite(n / d)) 

1328 except Exception as x: 

1329 E, t = _xError2(x) 

1330 raise self._Error(op, other, E, txt=t) 

1331 f = self._mul_scalar(s, _mul_op_) # handles 0, NAN, etc. 

1332 return self._fset(f) 

1333 

1334 @property_RO 

1335 def imag(self): 

1336 '''Get the C{imaginary} part of this instance (C{0.0}, always). 

1337 

1338 @see: Properties L{Fsum.ceil}, L{Fsum.floor} and L{Fsum.real}. 

1339 ''' 

1340 return _0_0 

1341 

1342 def int_float(self, raiser=False): 

1343 '''Return this instance' current running sum as C{int} or C{float}. 

1344 

1345 @kwarg raiser: If C{True} throw a L{ResidualError} if the 

1346 residual is non-zero. 

1347 

1348 @return: This C{integer} sum if this instance C{is_integer}, 

1349 otherwise return the C{float} sum if the residual 

1350 is zero or if C{B{raiser}=False}. 

1351 

1352 @raise ResidualError: Non-zero residual and C{B{raiser}=True}. 

1353 

1354 @see: Methods L{Fsum.fint} and L{Fsum.fint2}. 

1355 ''' 

1356 s, r = self._fint2 

1357 if r: 

1358 s, r = self._fprs2 

1359 if r and raiser: # PYCHOK no cover 

1360 t = _stresidual(_non_zero_, r) 

1361 raise ResidualError(int_float=s, txt=t) 

1362 s = float(s) # redundant 

1363 return s 

1364 

1365 def is_exact(self): 

1366 '''Is this instance' current running C{fsum} considered to 

1367 be exact? (C{bool}). 

1368 ''' 

1369 return self.residual is INT0 

1370 

1371 def is_integer(self): 

1372 '''Is this instance' current running sum C{integer}? (C{bool}). 

1373 

1374 @see: Methods L{Fsum.fint} and L{Fsum.fint2}. 

1375 ''' 

1376 _, r = self._fint2 

1377 return False if r else True 

1378 

1379 def is_math_fsum(self): 

1380 '''Return whether functions L{fsum}, L{fsum_}, L{fsum1} 

1381 and L{fsum1_} plus partials summation are based on 

1382 Python's C{math.fsum} or not. 

1383 

1384 @return: C{2} if all functions and partials summation 

1385 are based on C{math.fsum}, C{True} if only 

1386 the functions are based on C{math.fsum} (and 

1387 partials summation is not) or C{False} if 

1388 none are. 

1389 ''' 

1390 f = Fsum._math_fsum 

1391 return 2 if _psum is f else bool(f) 

1392 

1393 def _mul_Fsum(self, other, op=_mul_op_): 

1394 '''(INTERNAL) Return C{B{self} * Fsum B{other}} as L{Fsum}. 

1395 ''' 

1396 # assert isinstance(other, Fsum) 

1397 return self._copy_0()._facc(self._ps_x(op, *other._ps), up=False) 

1398 

1399 def _mul_scalar(self, factor, op): 

1400 '''(INTERNAL) Return C{B{self} * scalar B{factor}} as L{Fsum} or C{0}. 

1401 ''' 

1402 # assert isscalar(factor) 

1403 if self._finite(factor, op) and self._ps: 

1404 if factor == _1_0: 

1405 return self 

1406 f = self._copy_0()._facc(self._ps_x(op, factor), up=False) 

1407 else: 

1408 f = self._copy_0(_0_0) 

1409 return f 

1410 

1411 @property_RO 

1412 def partials(self): 

1413 '''Get this instance' current partial sums (C{tuple} of C{float}s and/or C{int}s). 

1414 ''' 

1415 return tuple(self._ps) 

1416 

1417 def pow(self, x, *mod): 

1418 '''Return C{B{self}**B{x}} as L{Fsum}. 

1419 

1420 @arg x: The exponent (L{Fsum} or C{scalar}). 

1421 @arg mod: Optional modulus (C{int} or C{None}) for the 3-argument 

1422 C{pow(B{self}, B{other}, B{mod})} version. 

1423 

1424 @return: The C{pow(self, B{x})} or C{pow(self, B{x}, *B{mod})} 

1425 result (L{Fsum}). 

1426 

1427 @note: If B{C{mod}} is given as C{None}, the result will be an 

1428 C{integer} L{Fsum} provided this instance C{is_integer} 

1429 or set C{integer} with L{Fsum.fint}. 

1430 

1431 @see: Methods L{Fsum.__ipow__}, L{Fsum.fint} and L{Fsum.is_integer}. 

1432 ''' 

1433 f = self._copy_2(self.pow) 

1434 if f and isint(x) and x >= 0 and not mod: 

1435 f._pow_int(x, x, _pow_op_) # f **= x 

1436 else: 

1437 f._fpow(x, _pow_op_, *mod) # f = pow(f, x, *mod) 

1438 return f 

1439 

1440 def _pow_0_1(self, x, other): 

1441 '''(INTERNAL) Return B{C{self}**1} or C{B{self}**0 == 1.0}. 

1442 ''' 

1443 return self if x else (1 if self.is_integer() and isint(other) else _1_0) 

1444 

1445 def _pow_2(self, x, other, op): 

1446 '''(INTERNAL) 2-arg C{pow(B{self}, scalar B{x})} embellishing errors. 

1447 ''' 

1448 # assert len(self._ps) == 1 and isscalar(x) 

1449 b = self._ps[0] # assert isscalar(b) 

1450 try: # type(s) == type(x) if x in (_1_0, 1) 

1451 s = pow(b, x) # -1**2.3 == -(1**2.3) 

1452 if not iscomplex(s): 

1453 return self._finite(s) # 0**INF == 0.0, 1**INF==1.0 

1454 # neg**frac == complex in Python 3+, but ValueError in 2- 

1455 E, t = _ValueError, _strcomplex(s, b, x) # PYCHOK no cover 

1456 except Exception as x: 

1457 E, t = _xError2(x) 

1458 raise self._Error(op, other, E, txt=t) 

1459 

1460 def _pow_3(self, other, mod, op): 

1461 '''(INTERNAL) 3-arg C{pow(B{self}, B{other}, int B{mod} or C{None})}. 

1462 ''' 

1463 b, r = self._fprs2 if mod is None else self._fint2 

1464 if r and self._raiser(r, b): 

1465 t = _non_zero_ if mod is None else _integer_ 

1466 E, t = ResidualError, _stresidual(t, r, mod=mod) 

1467 else: 

1468 try: # b, other, mod all C{int}, unless C{mod} is C{None} 

1469 x = _2scalar(other, _raiser=self._raiser) 

1470 s = pow(b, x, mod) 

1471 if not iscomplex(s): 

1472 return self._finite(s) 

1473 # neg**frac == complex in Python 3+, but ValueError in 2- 

1474 E, t = _ValueError, _strcomplex(s, b, x, mod) # PYCHOK no cover 

1475 except Exception as x: 

1476 E, t = _xError2(x) 

1477 t = _COMMASPACE_(Fmt.PARENSPACED(mod=mod), t) 

1478 raise self._Error(op, other, E, txt=t) 

1479 

1480 def _pow_int(self, x, other, op): 

1481 '''(INTERNAL) Return C{B{self} **= B{x}} for C{int B{x} >= 0}. 

1482 ''' 

1483 # assert isint(x) and x >= 0 

1484 if len(self._ps) > 1: 

1485 if x > 2: 

1486 p = self._copy_up() 

1487 m = 1 # single-bit mask 

1488 if x & m: 

1489 x -= m # x ^= m 

1490 f = p._copy_up() 

1491 else: 

1492 f = self._copy_0(_1_0) 

1493 while x: 

1494 p = p._mul_Fsum(p, op) # p **= 2 

1495 m += m # m <<= 1 

1496 if x & m: 

1497 x -= m # x ^= m 

1498 f = f._mul_Fsum(p, op) # f *= p 

1499 elif x > 1: # self**2 

1500 f = self._mul_Fsum(self, op) 

1501 else: # self**1 or self**0 

1502 f = self._pow_0_1(x, other) 

1503 elif self._ps: # self._ps[0]**x 

1504 f = self._pow_2(x, other, op) 

1505 else: # PYCHOK no cover 

1506 # 0**pos_int == 0, but 0**0 == 1 

1507 f = 0 if x else 1 # like ._fprs 

1508 return self._fset(f, asis=isint(f), n=len(self)) 

1509 

1510 def _pow_scalar(self, x, other, op): 

1511 '''(INTERNAL) Return C{self**B{x}} for C{scalar B{x}}. 

1512 ''' 

1513 s, r = self._fprs2 

1514 if isint(x, both=True): 

1515 x = int(x) # Fsum**int 

1516 y = abs(x) 

1517 if y > 1: 

1518 if r: 

1519 f = self._copy_up()._pow_int(y, other, op) 

1520 if x > 0: # > 1 

1521 return f 

1522 # assert x < 0 # < -1 

1523 s, r = f._fprs2 

1524 if r: 

1525 return self._copy_0(_1_0)._ftruediv(f, op) 

1526 # use **= -1 for the CPython float_pow 

1527 # error if s is zero, and not s = 1 / s 

1528 x = -1 

1529# elif y > 1: # self**2 or self**-2 

1530# f = self._mul_Fsum(self, op) 

1531# if x < 0: 

1532# f = f._copy_0(_1_0)._ftruediv(f, op) 

1533# return f 

1534 elif x < 0: # self**-1 == 1 / self 

1535 if r: 

1536 return self._copy_0(_1_0)._ftruediv(self, op) 

1537 else: # self**1 or self**0 

1538 return self._pow_0_1(x, other) # self or 0.0 

1539 elif not isscalar(x): # assert ... 

1540 raise self._TypeError(op, other, txt=_not_scalar_) 

1541 elif r and self._raiser(r, s): # non-zero residual**fractional 

1542 # raise self._ResidualError(op, other, r, fractional_power=x) 

1543 t = _stresidual(_non_zero_, r, fractional_power=x) 

1544 raise self._Error(op, other, ResidualError, txt=t) 

1545 # assert isscalar(s) and isscalar(x) 

1546 return self._copy_0(s)._pow_2(x, other, op) 

1547 

1548 def _ps_1(self, *less): 

1549 '''(INTERNAL) Yield partials, 1-primed and subtract any C{less}. 

1550 ''' 

1551 yield _1_0 

1552 for p in self._ps: 

1553 if p: 

1554 yield p 

1555 for p in less: 

1556 if p: 

1557 yield -p 

1558 yield _N_1_0 

1559 

1560 def _ps_n(self): 

1561 '''(INTERNAL) Yield partials, negated. 

1562 ''' 

1563 for p in self._ps: 

1564 if p: 

1565 yield -p 

1566 

1567 def _ps_x(self, op, *factors): # see .fmath.Fhorner 

1568 '''(INTERNAL) Yield all C{partials} times each B{C{factor}}, 

1569 in total, up to C{len(partials) * len(factors)} items. 

1570 ''' 

1571 ps = self._ps 

1572 if len(ps) < len(factors): 

1573 ps, factors = factors, ps 

1574 _f = _isfinite 

1575 for f in factors: 

1576 for p in ps: 

1577 p *= f 

1578 if _f(p): 

1579 yield p 

1580 else: # PYCHOK no cover 

1581 self._finite(p, op) # throw ValueError 

1582 

1583 @property_RO 

1584 def real(self): 

1585 '''Get the C{real} part of this instance (C{float}). 

1586 

1587 @see: Methods L{Fsum.__float__} and L{Fsum.fsum} 

1588 and properties L{Fsum.ceil}, L{Fsum.floor}, 

1589 L{Fsum.imag} and L{Fsum.residual}. 

1590 ''' 

1591 return float(self._fprs) 

1592 

1593 @property_RO 

1594 def residual(self): 

1595 '''Get this instance' residual (C{float} or C{int}), the 

1596 C{sum(partials)} less the precision running sum C{fsum}. 

1597 

1598 @note: If the C{residual is INT0}, the precision running 

1599 C{fsum} is considered to be I{exact}. 

1600 

1601 @see: Methods L{Fsum.fsum}, L{Fsum.fsum2} and L{Fsum.is_exact}. 

1602 ''' 

1603 return self._fprs2.residual 

1604 

1605 def _raiser(self, r, s): 

1606 '''(INTERNAL) Does the ratio C{r / s} exceed threshold? 

1607 ''' 

1608 self._ratio = t = fabs((r / s) if s else r) 

1609 return t > self._RESIDUAL 

1610 

1611 def RESIDUAL(self, *threshold): 

1612 '''Get and set this instance' I{ratio} for raising L{ResidualError}s, 

1613 overriding the default from env variable C{PYGEODESY_FSUM_RESIDUAL}. 

1614 

1615 @arg threshold: If C{scalar}, the I{ratio} to exceed for raising 

1616 L{ResidualError}s in division and exponention, if 

1617 C{None} restore the default set with env variable 

1618 C{PYGEODESY_FSUM_RESIDUAL} or if omitted, keep the 

1619 current setting. 

1620 

1621 @return: The previous C{RESIDUAL} setting (C{float}). 

1622 

1623 @raise ValueError: Negative B{C{threshold}}. 

1624 

1625 @note: A L{ResidualError} is thrown if the non-zero I{ratio} 

1626 C{residual} / C{fsum} exceeds the B{C{threshold}}. 

1627 ''' 

1628 r = self._RESIDUAL 

1629 if threshold: 

1630 t = threshold[0] 

1631 t = Fsum._RESIDUAL if t is None else ( 

1632 float(t) if isscalar(t) else ( # for backward ... 

1633 _0_0 if bool(t) else _1_0)) # ... compatibility 

1634 if t < 0: 

1635 u = self._unstr(self.RESIDUAL, *threshold) 

1636 raise _ValueError(u, RESIDUAL=t, txt=_negative_) 

1637 self._RESIDUAL = t 

1638 return r 

1639 

1640 def _ResidualError(self, op, other, residual): 

1641 '''(INTERNAL) Non-zero B{C{residual}} etc. 

1642 ''' 

1643 t = _stresidual(_non_zero_, residual, ratio=self._ratio, 

1644 RESIDUAL=self._RESIDUAL) 

1645 t = t.replace(_COMMASPACE_R_, _exceeds_R_) 

1646 return self._Error(op, other, ResidualError, txt=t) 

1647 

1648 def signOf(self, res=True): 

1649 '''Determine the sign of this instance. 

1650 

1651 @kwarg res: If C{True} consider, otherwise 

1652 ignore the residual (C{bool}). 

1653 

1654 @return: The sign (C{int}, -1, 0 or +1). 

1655 ''' 

1656 s, r = self._fprs2 if res else (self._fprs, 0) 

1657 return _signOf(s, -r) 

1658 

1659 def toRepr(self, **prec_sep_fmt_lenc): # PYCHOK signature 

1660 '''Return this C{Fsum} instance as representation. 

1661 

1662 @kwarg prec_sep_fmt_lenc: Optional keyword arguments for 

1663 method L{Fsum2Tuple.toRepr} plus C{B{lenc}=True} 

1664 (C{bool}) to in-/exclude the current C{[len]} 

1665 of this L{Fsum} enclosed in I{[brackets]}. 

1666 

1667 @return: This instance (C{repr}). 

1668 ''' 

1669 return self._toT(self._fprs2.toRepr, **prec_sep_fmt_lenc) 

1670 

1671 def toStr(self, **prec_sep_fmt_lenc): # PYCHOK signature 

1672 '''Return this C{Fsum} instance as string. 

1673 

1674 @kwarg prec_sep_fmt_lenc: Optional keyword arguments for 

1675 method L{Fsum2Tuple.toStr} plus C{B{lenc}=True} 

1676 (C{bool}) to in-/exclude the current C{[len]} 

1677 of this L{Fsum} enclosed in I{[brackets]}. 

1678 

1679 @return: This instance (C{str}). 

1680 ''' 

1681 return self._toT(self._fprs2.toStr, **prec_sep_fmt_lenc) 

1682 

1683 def _toT(self, toT, fmt=Fmt.g, lenc=True, **kwds): 

1684 '''(INTERNAL) Helper for C{toRepr} and C{toStr}. 

1685 ''' 

1686 n = self.named3 

1687 if lenc: 

1688 n = Fmt.SQUARE(n, len(self)) 

1689 return _SPACE_(n, toT(fmt=fmt, **kwds)) 

1690 

1691 def _TypeError(self, op, other, **txt): # PYCHOK no cover 

1692 '''(INTERNAL) Return a C{TypeError}. 

1693 ''' 

1694 return self._Error(op, other, _TypeError, **txt) 

1695 

1696 def _update(self): # see ._fset 

1697 '''(INTERNAL) Zap all cached C{Property_RO} values. 

1698 ''' 

1699 Fsum._fint2._update(self) 

1700 Fsum._fprs ._update(self) 

1701 Fsum._fprs2._update(self) 

1702 return self 

1703 

1704 def _ValueError(self, op, other, **txt): # PYCHOK no cover 

1705 '''(INTERNAL) Return a C{ValueError}. 

1706 ''' 

1707 return self._Error(op, other, _ValueError, **txt) 

1708 

1709 def _ZeroDivisionError(self, op, other, **txt): # PYCHOK no cover 

1710 '''(INTERNAL) Return a C{ZeroDivisionError}. 

1711 ''' 

1712 return self._Error(op, other, _ZeroDivisionError, **txt) 

1713 

1714_allPropertiesOf_n(3, Fsum, Property_RO) # PYCHOK assert, see Fsum._fset, -._update 

1715 

1716 

1717def _Float_Int(arg, **name_Error): 

1718 '''(INTERNAL) Unit of L{Fsum2Tuple} items. 

1719 ''' 

1720 U = Int if isint(arg) else Float 

1721 return U(arg, **name_Error) 

1722 

1723 

1724class Fsum2Tuple(_NamedTuple): 

1725 '''2-Tuple C{(fsum, residual)} with the precision running C{fsum} 

1726 and the C{residual}, the sum of the remaining partials. Each 

1727 item is either C{float} or C{int}. 

1728 

1729 @note: If the C{residual is INT0}, the C{fsum} is considered 

1730 to be I{exact}, see method L{Fsum2Tuple.is_exact}. 

1731 ''' 

1732 _Names_ = ( Fsum.fsum.__name__, Fsum.residual.name) 

1733 _Units_ = (_Float_Int, _Float_Int) 

1734 

1735 @Property_RO 

1736 def Fsum(self): 

1737 '''Get this L{Fsum2Tuple} as an L{Fsum}. 

1738 ''' 

1739 f = Fsum(name=self.name) 

1740 return f._copy_0(*(s for s in reversed(self) if s)) 

1741 

1742 def is_exact(self): 

1743 '''Is this L{Fsum2Tuple} considered to be exact? (C{bool}). 

1744 ''' 

1745 return self.Fsum.is_exact() 

1746 

1747 def is_integer(self): 

1748 '''Is this L{Fsum2Tuple} C{integer}? (C{bool}). 

1749 ''' 

1750 return self.Fsum.is_integer() 

1751 

1752 

1753class ResidualError(_ValueError): 

1754 '''Error raised for an operation involving a L{pygeodesy.sums.Fsum} 

1755 instance with a non-zero C{residual}, I{integer} or otherwise. 

1756 

1757 @see: Module L{pygeodesy.fsums} and method L{Fsum.RESIDUAL}. 

1758 ''' 

1759 pass 

1760 

1761 

1762try: 

1763 from math import fsum as _fsum # precision IEEE-754 sum, Python 2.6+ 

1764 

1765 # make sure _fsum works as expected (XXX check 

1766 # float.__getformat__('float')[:4] == 'IEEE'?) 

1767 if _fsum((1, 1e101, 1, -1e101)) != 2: # PYCHOK no cover 

1768 del _fsum # nope, remove _fsum ... 

1769 raise ImportError # ... use _fsum below 

1770 

1771 Fsum._math_fsum = _fsum 

1772 

1773 if _getenv('PYGEODESY_FSUM_PARTIALS', _fsum.__name__) == _fsum.__name__: 

1774 _psum = _fsum # PYCHOK redef 

1775 

1776except ImportError: 

1777 

1778 def _fsum(xs): 

1779 '''(INTERNAL) Precision summation, Python 2.5-. 

1780 ''' 

1781 return Fsum(name=_fsum.__name__)._facc(xs, up=False)._fprs 

1782 

1783 

1784def fsum(xs, floats=False): 

1785 '''Precision floating point summation based on or like Python's C{math.fsum}. 

1786 

1787 @arg xs: Iterable, list, tuple, etc. of values (C{scalar} or 

1788 L{Fsum} instances). 

1789 @kwarg floats: Optionally, use C{B{floats}=True} iff I{all} 

1790 B{C{xs}} are known to be C{float}. 

1791 

1792 @return: Precision C{fsum} (C{float}). 

1793 

1794 @raise OverflowError: Partial C{2sum} overflow. 

1795 

1796 @raise TypeError: Non-scalar B{C{xs}} value. 

1797 

1798 @raise ValueError: Invalid or non-finite B{C{xs}} value. 

1799 

1800 @note: Exceptions and I{non-finite} handling may differ if not 

1801 based on Python's C{math.fsum}. 

1802 

1803 @see: Class L{Fsum} and methods L{Fsum.fsum} and L{Fsum.fadd}. 

1804 ''' 

1805 return _fsum(xs if floats else _2floats(xs)) if xs else _0_0 # PYCHOK yield 

1806 

1807 

1808def fsum_(*xs, **floats): 

1809 '''Precision floating point summation of all positional arguments. 

1810 

1811 @arg xs: Values to be added (C{scalar} or L{Fsum} instances), 

1812 all positional. 

1813 @kwarg floats: Optionally, use C{B{floats}=True} iff I{all} 

1814 B{C{xs}} are known to be C{float}. 

1815 

1816 @return: Precision C{fsum} (C{float}). 

1817 

1818 @see: Function C{fsum}. 

1819 ''' 

1820 return _fsum(xs if _xkwds_get(floats, floats=False) else 

1821 _2floats(xs, origin=1)) if xs else _0_0 # PYCHOK yield 

1822 

1823 

1824def fsumf_(*xs): 

1825 '''Precision floating point summation L{fsum_}C{(*xs, floats=True)}. 

1826 ''' 

1827 return _fsum(xs) if xs else _0_0 

1828 

1829 

1830def fsum1(xs, floats=False): 

1831 '''Precision floating point summation of a few arguments, 1-primed. 

1832 

1833 @arg xs: Iterable, list, tuple, etc. of values (C{scalar} or 

1834 L{Fsum} instances). 

1835 @kwarg floats: Optionally, use C{B{floats}=True} iff I{all} 

1836 B{C{xs}} are known to be C{float}. 

1837 

1838 @return: Precision C{fsum} (C{float}). 

1839 

1840 @see: Function C{fsum}. 

1841 ''' 

1842 return _fsum(_1primed(xs if floats else _2floats(xs))) if xs else _0_0 # PYCHOK yield 

1843 

1844 

1845def fsum1_(*xs, **floats): 

1846 '''Precision floating point summation of a few arguments, 1-primed. 

1847 

1848 @arg xs: Values to be added (C{scalar} or L{Fsum} instances), 

1849 all positional. 

1850 @kwarg floats: Optionally, use C{B{floats}=True} iff I{all} 

1851 B{C{xs}} are known to be C{float}. 

1852 

1853 @return: Precision C{fsum} (C{float}). 

1854 

1855 @see: Function C{fsum} 

1856 ''' 

1857 return _fsum(_1primed(xs if _xkwds_get(floats, floats=False) else 

1858 _2floats(xs, origin=1))) if xs else _0_0 # PYCHOK yield 

1859 

1860 

1861def fsum1f_(*xs): 

1862 '''Precision floating point summation L{fsum1_}C{(*xs, floats=True)}. 

1863 ''' 

1864 return _fsum(_1primed(xs)) if xs else _0_0 

1865 

1866 

1867# **) MIT License 

1868# 

1869# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved. 

1870# 

1871# Permission is hereby granted, free of charge, to any person obtaining a 

1872# copy of this software and associated documentation files (the "Software"), 

1873# to deal in the Software without restriction, including without limitation 

1874# the rights to use, copy, modify, merge, publish, distribute, sublicense, 

1875# and/or sell copies of the Software, and to permit persons to whom the 

1876# Software is furnished to do so, subject to the following conditions: 

1877# 

1878# The above copyright notice and this permission notice shall be included 

1879# in all copies or substantial portions of the Software. 

1880# 

1881# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

1882# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

1883# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

1884# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

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