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_, _LANGLE_, _negative_, \ 

37 _NOTEQUAL_, _not_finite_, _not_scalar_, \ 

38 _PERCENT_, _PLUS_, _R_, _RANGLE_, _SLASH_, \ 

39 _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__ = '23.06.04' 

51 

52_add_op_ = _PLUS_ 

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_ 

69_truediv_op_ = _SLASH_ 

70_divmod_op_ = _floordiv_op_ + _mod_op_ 

71 

72 

73def _2float(index=None, **name_value): # in .fmath, .fstats 

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

75 ''' 

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

77 try: 

78 v = float(v) 

79 if _isfinite(v): 

80 return v 

81 E, t = _ValueError, _not_finite_ 

82 except Exception as e: 

83 E, t = _xError2(e) 

84 if index is not None: 

85 n = Fmt.SQUARE(n, index) 

86 raise E(n, v, txt=t) 

87 

88 

89def _2floats(xs, origin=0, sub=False): 

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

91 ''' 

92 try: 

93 i, x = origin, None 

94 _fin = _isfinite 

95 _Fsum = Fsum 

96 for x in xs: 

97 if isinstance(x, _Fsum): 

98 for p in x._ps: 

99 yield (-p) if sub else p 

100 else: 

101 f = float(x) 

102 if not _fin(f): 

103 raise ValueError(_not_finite_) 

104 if f: 

105 yield (-f) if sub else f 

106 i += 1 

107 except Exception as e: 

108 E, t = _xError2(e) 

109 n = Fmt.SQUARE(xs=i) 

110 raise E(n, x, txt=t) 

111 

112 

113def _Powers(power, xs, origin=1): # in .fmath 

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

115 ''' 

116 if not isscalar(power): 

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

118 try: 

119 i, x = origin, None 

120 _fin = _isfinite 

121 _Fsum = Fsum 

122 _pow = pow # XXX math.pow 

123 for x in xs: 

124 if isinstance(x, _Fsum): 

125 P = x.pow(power) 

126 for p in P._ps: 

127 yield p 

128 else: 

129 p = _pow(float(x), power) 

130 if not _fin(p): 

131 raise ValueError(_not_finite_) 

132 yield p 

133 i += 1 

134 except Exception as e: 

135 E, t = _xError2(e) 

136 n = Fmt.SQUARE(xs=i) 

137 raise E(n, x, txt=t) 

138 

139 

140def _1primed(xs): 

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

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

143 ''' 

144 yield _1_0 

145 for x in xs: 

146 if x: 

147 yield x 

148 yield _N_1_0 

149 

150 

151def _psum(ps): # PYCHOK used! 

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

153 ''' 

154 i = len(ps) - 1 # len(ps) > 2 

155 s = ps[i] 

156 _2s = _2sum 

157 while i > 0: 

158 i -= 1 

159 s, r = _2s(s, ps[i]) 

160 if r: # sum(ps) became inexact 

161 ps[i:] = [s, r] if s else [r] 

162 if i > 0: 

163 p = ps[i-1] # round half-even 

164 if (p > 0 and r > 0) or \ 

165 (p < 0 and r < 0): # signs match 

166 r *= 2 

167 t = s + r 

168 if r == (t - s): 

169 s = t 

170 break 

171 ps[i:] = [s] 

172 return s 

173 

174 

175def _2scalar(other, _raiser=None): 

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

177 ''' 

178 if isinstance(other, Fsum): 

179 s, r = other._fint2 

180 if r: 

181 s, r = other._fprs2 

182 if r: # PYCHOK no cover 

183 if _raiser and _raiser(r, s): 

184 raise ValueError(_stresidual(_non_zero_, r)) 

185 s = other # L{Fsum} as-is 

186 else: 

187 s = other # C{type} as-is 

188 if isint(s, both=True): 

189 s = int(s) 

190 return s 

191 

192 

193def _strcomplex(s, *args): 

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

195 ''' 

196 c = iscomplex.__name__[2:] 

197 n = _DASH_(len(args), _arg_) 

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

199 return unstr(t, *args) 

200 

201 

202def _stresidual(prefix, residual, **name_values): 

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

204 ''' 

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

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

207 for n, v in itemsorted(name_values): 

208 n = n.replace(_UNDER_, _SPACE_) 

209 p = Fmt.PARENSPACED(n, Fmt(v)) 

210 t = _COMMASPACE_(t, p) 

211 return t 

212 

213 

214def _2sum(a, b): # by .testFmath 

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

216 ''' 

217 s = a + b 

218 if not _isfinite(s): 

219 u = unstr(_2sum.__name__, a, b) 

220 t = Fmt.PARENSPACED(_not_finite_, s) 

221 raise _OverflowError(u, txt=t) 

222 r = (a - (s - b)) if fabs(a) < fabs(b) else \ 

223 (b - (s - a)) # fabs(a) >= fabs(b) 

224 return s, r 

225 

226 

227class Fsum(_Named): # sync __methods__ with .vector3dBase.Vector3dBase 

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

229 

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

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

232 intermediate, I{running} summuation. 

233 

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

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

236 method C{__float__}. 

237 

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

239 Python's C{math.fsum}. 

240 

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

242 393090_Binary_floating_point_summatiaccurate_full/recipe-393090.py>}, U{Kahan 

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

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

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

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

247 ''' 

248 _math_fsum = None 

249 _n = 0 

250# _ps = [] # partial sums 

251# _px = 0 

252 _ratio = None 

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

254 

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

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

257 

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

259 L{Fsum} instance). 

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

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

262 L{ResidualError} threshold. 

263 

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

265 ''' 

266 if name_RESIDUAL: 

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

268 if n: # set name ... 

269 self.name = n 

270 if r is not None: 

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

272# self._n = 0 

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

274 if len(xs) > 1: 

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

276 elif xs: # len(xs) == 1 

277 self._ps = [_2float(x=xs[0])] 

278 self._n = 1 

279 

280 def __abs__(self): 

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

282 ''' 

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

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

285 self._copy_2(self.__abs__) 

286 

287 def __add__(self, other): 

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

289 

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

291 

292 @return: The sum (L{Fsum}). 

293 

294 @see: Method L{Fsum.__iadd__}. 

295 ''' 

296 f = self._copy_2(self.__add__) 

297 return f._fadd(other, _add_op_) 

298 

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

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

301 ''' 

302 s, r = self._fprs2 

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

304 

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

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

307 

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

309 

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

311 ''' 

312 return self.ceil 

313 

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

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

316 

317 @return: -1, 0 or +1 (C{int}). 

318 

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

320 ''' 

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

322 return _signOf(s, 0) 

323 

324 cmp = __cmp__ 

325 

326 def __divmod__(self, other): 

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

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

329 and an L{Fsum}. 

330 

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

332 

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

334 ''' 

335 f = self._copy_2(self.__divmod__) 

336 return f._fdivmod2(other, _divmod_op_) 

337 

338 def __eq__(self, other): 

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

340 ''' 

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

342 

343 def __float__(self): 

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

345 

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

347 ''' 

348 return float(self._fprs) 

349 

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

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

352 

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

354 

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

356 ''' 

357 return self.floor 

358 

359 def __floordiv__(self, other): 

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

361 

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

363 

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

365 

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

367 ''' 

368 f = self._copy_2(self.__floordiv__) 

369 return f._floordiv(other, _floordiv_op_) 

370 

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

372 '''Not implemented.''' 

373 return _NotImplemented(self, *other) 

374 

375 def __ge__(self, other): 

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

377 ''' 

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

379 

380 def __gt__(self, other): 

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

382 ''' 

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

384 

385 def __hash__(self): # PYCHOK no cover 

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

387 ''' 

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

389 

390 def __iadd__(self, other): 

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

392 

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

394 

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

396 

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

398 C{scalar} nor L{Fsum}. 

399 

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

401 ''' 

402 return self._fadd(other, _iadd_) 

403 

404 def __ifloordiv__(self, other): 

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

406 

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

408 

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

410 

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

412 

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

414 

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

416 

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

418 

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

420 ''' 

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

422 

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

424 '''Not implemented.''' 

425 return _NotImplemented(self, other) 

426 

427 def __imod__(self, other): 

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

429 

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

431 

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

433 

434 @see: Method L{Fsum.__divmod__}. 

435 ''' 

436 self._fdivmod2(other, _mod_op_ + _fset_op_) 

437 return self 

438 

439 def __imul__(self, other): 

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

441 

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

443 

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

445 

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

447 

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

449 

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

451 ''' 

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

453 

454 def __int__(self): 

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

456 

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

458 and L{Fsum.__floor__} and properties 

459 L{Fsum.ceil} and L{Fsum.floor}. 

460 ''' 

461 i, _ = self._fint2 

462 return i 

463 

464 def __invert__(self): # PYCHOK no cover 

465 '''Not implemented.''' 

466 # Luciano Ramalho, "Fluent Python", 2nd Ed, page 567, O'Reilly, 2022 

467 return _NotImplemented(self) 

468 

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

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

471 

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

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

474 3-argument C{pow(B{self}, B{other}, B{mod})} 

475 version. 

476 

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

478 

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

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

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

482 

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

484 

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

486 env var C{PYGEODESY_FSUM_RESIDUAL} 

487 set or this instance has a non-zero 

488 residual and either B{C{mod}} is 

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

490 is a negative or fractional C{scalar}. 

491 

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

493 C{pow} invocation failed. 

494 

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

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

497 is a fractional C{scalar} and this 

498 instance is negative or has a non-zero 

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

500 

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

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

503 ''' 

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

505 

506 def __isub__(self, other): 

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

508 

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

510 

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

512 

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

514 

515 @see: Method L{Fsum.fadd}. 

516 ''' 

517 return self._fsub(other, _sub_op_ + _fset_op_) 

518 

519 def __iter__(self): 

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

521 ''' 

522 return iter(self.partials) 

523 

524 def __itruediv__(self, other): 

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

526 

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

528 

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

530 

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

532 

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

534 env var C{PYGEODESY_FSUM_RESIDUAL} set. 

535 

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

537 

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

539 

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

541 

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

543 ''' 

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

545 

546 def __le__(self, other): 

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

548 ''' 

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

550 

551 def __len__(self): 

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

553 ''' 

554 return self._n 

555 

556 def __lt__(self, other): 

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

558 ''' 

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

560 

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

562 '''Not implemented.''' 

563 return _NotImplemented(self, other) 

564 

565 def __mod__(self, other): 

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

567 

568 @see: Method L{Fsum.__imod__}. 

569 ''' 

570 f = self._copy_2(self.__mod__) 

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

572 

573 def __mul__(self, other): 

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

575 

576 @see: Method L{Fsum.__imul__}. 

577 ''' 

578 f = self._copy_2(self.__mul__) 

579 return f._fmul(other, _mul_op_) 

580 

581 def __ne__(self, other): 

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

583 ''' 

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

585 

586 def __neg__(self): 

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

588 ''' 

589 return self._copy_n(self.__neg__) 

590 

591 def __pos__(self): 

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

593 ''' 

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

595 

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

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

598 

599 @see: Method L{Fsum.__ipow__}. 

600 ''' 

601 f = self._copy_2(self.__pow__) 

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

603 

604 def __radd__(self, other): 

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

606 

607 @see: Method L{Fsum.__iadd__}. 

608 ''' 

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

610 return f._fadd(self, _add_op_) 

611 

612 def __rdivmod__(self, other): 

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

614 remainder)}. 

615 

616 @see: Method L{Fsum.__divmod__}. 

617 ''' 

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

619 return f._fdivmod2(self, _divmod_op_) 

620 

621# def __repr__(self): 

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

623# ''' 

624# return self.toRepr(lenc=True) 

625 

626 def __rfloordiv__(self, other): 

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

628 

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

630 ''' 

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

632 return f._floordiv(self, _floordiv_op_) 

633 

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

635 '''Not implemented.''' 

636 return _NotImplemented(self, other) 

637 

638 def __rmod__(self, other): 

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

640 

641 @see: Method L{Fsum.__imod__}. 

642 ''' 

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

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

645 

646 def __rmul__(self, other): 

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

648 

649 @see: Method L{Fsum.__imul__}. 

650 ''' 

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

652 return f._fmul(self, _mul_op_) 

653 

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

655 '''Not implemented.''' 

656 return _NotImplemented(self, ndigits=ndigits) 

657 

658 def __rpow__(self, other, *mod): 

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

660 

661 @see: Method L{Fsum.__ipow__}. 

662 ''' 

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

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

665 

666 def __rsub__(self, other): 

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

668 

669 @see: Method L{Fsum.__isub__}. 

670 ''' 

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

672 return f._fsub(self, _sub_op_) 

673 

674 def __rtruediv__(self, other): 

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

676 

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

678 ''' 

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

680 return f._ftruediv(self, _truediv_op_) 

681 

682 def __str__(self): 

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

684 ''' 

685 return self.toStr(lenc=True) 

686 

687 def __sub__(self, other): 

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

689 

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

691 

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

693 

694 @see: Method L{Fsum.__isub__}. 

695 ''' 

696 f = self._copy_2(self.__sub__) 

697 return f._fsub(other, _sub_op_) 

698 

699 def __truediv__(self, other): 

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

701 

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

703 

704 @return: The quotient (L{Fsum}). 

705 

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

707 ''' 

708 f = self._copy_2(self.__truediv__) 

709 return f._ftruediv(other, _truediv_op_) 

710 

711 __trunc__ = __int__ 

712 

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

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

715 __div__ = __truediv__ 

716 __idiv__ = __itruediv__ 

717 __long__ = __int__ 

718 __nonzero__ = __bool__ 

719 __rdiv__ = __rtruediv__ 

720 

721 def as_integer_ratio(self): 

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

723 

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

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

726 

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

728 ''' 

729 n, r = self._fint2 

730 if r: 

731 i, d = r.as_integer_ratio() 

732 n *= d 

733 n += i 

734 else: # PYCHOK no cover 

735 d = 1 

736 return n, d 

737 

738 @property_RO 

739 def ceil(self): 

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

741 but C{float} in Python 2-). 

742 

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

744 

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

746 L{Fsum.imag} and L{Fsum.real}. 

747 ''' 

748 s, r = self._fprs2 

749 c = _ceil(s) + int(r) - 1 

750 while r > (c - s): # (s + r) > c 

751 c += 1 

752 return c 

753 

754 def _cmp_0(self, other, op): 

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

756 ''' 

757 if isscalar(other): 

758 if other: 

759 s = _fsum(self._ps_1(other)) 

760 else: 

761 s, r = self._fprs2 

762 s = _signOf(s, -r) 

763 elif isinstance(other, Fsum): 

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

765 else: 

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

767 return s 

768 

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

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

771 

772 @return: The copy (L{Fsum}). 

773 ''' 

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

775 f._n = self._n if deep else 1 

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

777 return f 

778 

779 def _copy_0(self, *xs): 

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

781 ''' 

782 # for x in xs: 

783 # assert isscalar(x) 

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

785 if self.name: 

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

787 return f 

788 

789 def _copy_2(self, which): 

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

791 ''' 

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

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

794 # assert f._n == self._n 

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

796 return f 

797 

798 def _copy_n(self, which): 

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

800 ''' 

801 if self._ps: 

802 f = self._Fsum(self._n) 

803 f._ps[:] = self._ps_n() 

804# f._facc_up(up=False) 

805 else: 

806 f = self._Fsum(self._n, _0_0) 

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

808 return f 

809 

810 def _copy_r2(self, other, which): 

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

812 ''' 

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

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

815 

816 def _copy_RESIDUAL(self, other): 

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

818 ''' 

819 R = other._RESIDUAL 

820 if R is not Fsum._RESIDUAL: 

821 self._RESIDUAL = R 

822 

823 def _copy_up(self, _fprs2=False): 

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

825 ''' 

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

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

828 Fsum._fprs2._update_from(f, self) 

829 return f 

830 

831 def divmod(self, other): 

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

833 remainder)}. 

834 

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

836 

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

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

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

840 

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

842 ''' 

843 f = self._copy_2(self.divmod) 

844 return f._fdivmod2(other, _divmod_op_) 

845 

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

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

848 ''' 

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

850 

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

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

853 ''' 

854 E, t = _xError2(X) 

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

856 return E(n, txt=t, cause=X) 

857 

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

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

860 ''' 

861 n, ps, _2s = 0, self._ps, _2sum 

862 for x in xs: # _iter() 

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

864 i = 0 

865 for p in ps: 

866 x, p = _2s(x, p) 

867 if p: 

868 ps[i] = p 

869 i += 1 

870 ps[i:] = [x] 

871 n += 1 

872 # assert self._ps is ps 

873 if n: 

874 self._n += n 

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

876 if up: 

877 self._update() 

878 return self 

879 

880 def _facc_(self, *xs, **up): 

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

882 ''' 

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

884 

885# def _facc_up(self, up=True): 

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

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

888# ''' 

889# while len(self._ps) > 1: 

890# p = self._ps.pop() 

891# if p: 

892# n = self._n 

893# self._facc_(p, up=False) 

894# self._n = n 

895# break 

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

897 

898 def fadd(self, xs=()): 

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

900 to this instance. 

901 

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

903 L{Fsum} instances). 

904 

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

906 

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

908 

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

910 nor L{Fsum}. 

911 

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

913 ''' 

914 if isinstance(xs, Fsum): 

915 self._facc(xs._ps) 

916 elif isscalar(xs): # for backward compatibility 

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

918 elif xs: 

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

920 return self 

921 

922 def fadd_(self, *xs): 

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

924 to this instance. 

925 

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

927 all positional. 

928 

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

930 

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

932 

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

934 nor L{Fsum}. 

935 

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

937 ''' 

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

939 

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

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

942 ''' 

943 if isinstance(other, Fsum): 

944 if other is self: 

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

946 elif other._ps: 

947 self._facc(other._ps) 

948 elif not isscalar(other): 

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

950 elif other: 

951 self._facc_(other) 

952 return self 

953 

954 fcopy = copy # for backward compatibility 

955 fdiv = __itruediv__ # for backward compatibility 

956 fdivmod = __divmod__ # for backward compatibility 

957 

958 def _fdivmod2(self, other, op): 

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

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

961 ''' 

962 # result mostly follows CPython function U{float_divmod 

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

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

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

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

967 self -= other * q 

968 

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

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

971 self += other 

972 q -= 1 

973 

974# t = self.signOf() 

975# if t and t != s: 

976# from pygeodesy.errors import _AssertionError 

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

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

979 

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

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

982 ''' 

983 if _isfinite(other): 

984 return other 

985 raise ValueError(_not_finite_) if not op else \ 

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

987 

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

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

990 

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

992 I{integer} residual is non-zero. 

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

994 

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

996 

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

998 

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

1000 ''' 

1001 i, r = self._fint2 

1002 if r and raiser: 

1003 t = _stresidual(_integer_, r) 

1004 raise ResidualError(_integer_, i, txt=t) 

1005 n = name or self.fint.__name__ 

1006 return Fsum(name=n)._fset(i, asis=True) 

1007 

1008 def fint2(self, **name): 

1009 '''Return this instance' current running sum as C{int} and 

1010 the I{integer} residual. 

1011 

1012 @kwarg name: Optional name (C{str}). 

1013 

1014 @return: An L{Fsum2Tuple}C{(fsum, residual)} with C{fsum} 

1015 an C{int} and I{integer} C{residual} a C{float} or 

1016 C{INT0} if the C{fsum} is considered to be I{exact}. 

1017 ''' 

1018 return Fsum2Tuple(*self._fint2, **name) 

1019 

1020 @Property_RO 

1021 def _fint2(self): # see ._fset 

1022 '''(INTERNAL) Get 2-tuple (C{int}, I{integer} residual). 

1023 ''' 

1024 i = int(self._fprs) # int(self) 

1025 r = _fsum(self._ps_1(i)) if len(self._ps) > 1 else ( 

1026 (self._ps[0] - i) if self._ps else -i) 

1027 return i, (r or INT0) 

1028 

1029 @deprecated_property_RO 

1030 def float_int(self): # PYCHOK no cover 

1031 '''DEPRECATED, use method C{Fsum.int_float}.''' 

1032 return self.int_float() # raiser=False 

1033 

1034 @property_RO 

1035 def floor(self): 

1036 '''Get this instance' C{floor} (C{int} in Python 3+, but 

1037 C{float} in Python 2-). 

1038 

1039 @note: The C{floor} takes the C{residual} into account. 

1040 

1041 @see: Method L{Fsum.int_float} and properties L{Fsum.ceil}, 

1042 L{Fsum.imag} and L{Fsum.real}. 

1043 ''' 

1044 s, r = self._fprs2 

1045 f = _floor(s) + _floor(r) + 1 

1046 while r < (f - s): # (s + r) < f 

1047 f -= 1 

1048 return f 

1049 

1050# floordiv = __floordiv__ # for naming consistency 

1051 

1052 def _floordiv(self, other, op): # rather _ffloordiv? 

1053 '''Apply C{B{self} //= B{other}}. 

1054 ''' 

1055 q = self._ftruediv(other, op) # == self 

1056 return self._fset(q.floor, asis=True) # floor(q) 

1057 

1058 fmul = __imul__ # for backward compatibility 

1059 

1060 def _fmul(self, other, op): 

1061 '''(INTERNAL) Apply C{B{self} *= B{other}}. 

1062 ''' 

1063 if isscalar(other): 

1064 f = self._mul_scalar(other, op) 

1065 elif not isinstance(other, Fsum): 

1066 raise self._TypeError(op, other) # txt=_invalid_ 

1067 elif len(self._ps) != 1: 

1068 f = self._mul_Fsum(other, op) 

1069 elif len(other._ps) != 1: # len(self._ps) == 1 

1070 f = other._copy_up()._mul_scalar(self._ps[0], op) 

1071 else: # len(other._ps) == len(self._ps) == 1 

1072 s = self._finite(self._ps[0] * other._ps[0]) 

1073 return self._fset(s, asis=True, n=len(self) + 1) 

1074 return self._fset(f) 

1075 

1076 def fover(self, over): 

1077 '''Apply C{B{self} /= B{over}} and summate. 

1078 

1079 @arg over: An L{Fsum} or C{scalar} denominator. 

1080 

1081 @return: Precision running sum (C{float}). 

1082 

1083 @see: Methods L{Fsum.fsum} and L{Fsum.__itruediv__}. 

1084 ''' 

1085 return float(self.fdiv(over)._fprs) 

1086 

1087 fpow = __ipow__ # for backward compatibility 

1088 

1089 def _fpow(self, other, op, *mod): 

1090 '''Apply C{B{self} **= B{other}}, optional B{C{mod}} or C{None}. 

1091 ''' 

1092 if mod and mod[0] is not None: # == 3-arg C{pow} 

1093 s = self._pow_3(other, mod[0], op) 

1094 elif mod and mod[0] is None and self.is_integer(): 

1095 # return an exact C{int} for C{int}**C{int} 

1096 i = self._copy_0(self._fint2[0]) # assert _fint2[1] == 0 

1097 x = _2scalar(other) # C{int}, C{float} or other 

1098 s = i._pow_2(x, other, op) if isscalar(x) else i._fpow(x, op) 

1099 else: # pow(self, other) == pow(self, other, None) 

1100 p = None 

1101 if isinstance(other, Fsum): 

1102 x, r = other._fprs2 

1103 if r: 

1104 if self._raiser(r, x): 

1105 raise self._ResidualError(op, other, r) 

1106 p = self._pow_scalar(r, other, op) 

1107# p = _2scalar(p) # _raiser = None 

1108 elif not isscalar(other): 

1109 raise self._TypeError(op, other) # txt=_invalid_ 

1110 else: 

1111 x = self._finite(other, op) 

1112 s = self._pow_scalar(x, other, op) 

1113 if p is not None: 

1114 s *= p 

1115 return self._fset(s, asis=isint(s), n=max(len(self), 1)) 

1116 

1117 @Property_RO 

1118 def _fprs(self): 

1119 '''(INTERNAL) Get and cache this instance' precision 

1120 running sum (C{float} or C{int}), ignoring C{residual}. 

1121 

1122 @note: The precision running C{fsum} after a C{//=} or 

1123 C{//} C{floor} division is C{int} in Python 3+. 

1124 ''' 

1125 ps = self._ps 

1126 n = len(ps) - 1 

1127 if n > 1: 

1128 s = _psum(ps) 

1129 elif n > 0: # len(ps) == 2 

1130 s, p = _2sum(*ps) if ps[1] else ps 

1131 ps[:] = ([p, s] if s else [p]) if p else [s] 

1132 elif n < 0: # see L{Fsum.__init__} 

1133 s = _0_0 

1134 ps[:] = [s] 

1135 else: # len(ps) == 1 

1136 s = ps[0] 

1137 # assert self._ps is ps 

1138 # assert Fsum._fprs2.name not in self.__dict__ 

1139 return s 

1140 

1141 @Property_RO 

1142 def _fprs2(self): 

1143 '''(INTERNAL) Get and cache this instance' precision 

1144 running sum and residual (L{Fsum2Tuple}). 

1145 ''' 

1146 s = self._fprs 

1147 r = _fsum(self._ps_1(s)) if len(self._ps) > 1 else INT0 

1148 return Fsum2Tuple(s, r) # name=Fsum.fsum2.__name__ 

1149 

1150# def _fpsqz(self): 

1151# '''(INTERNAL) Compress, squeeze the C{partials}. 

1152# ''' 

1153# if len(self._ps) > 2: 

1154# _ = self._fprs 

1155# return self 

1156 

1157 def _fset(self, other, asis=False, n=1): 

1158 '''(INTERNAL) Overwrite this instance with an other or a C{scalar}. 

1159 ''' 

1160 if other is self: 

1161 pass # from ._fmul, ._ftruediv and ._pow_scalar 

1162 elif isinstance(other, Fsum): 

1163 self._n = other._n 

1164 self._ps[:] = other._ps 

1165 self._copy_RESIDUAL(other) 

1166 # use or zap the C{Property_RO} values 

1167 Fsum._fint2._update_from(self, other) 

1168 Fsum._fprs ._update_from(self, other) 

1169 Fsum._fprs2._update_from(self, other) 

1170 elif isscalar(other): 

1171 s = other if asis else float(other) 

1172 i = int(s) # see ._fint2 

1173 t = i, ((s - i) or INT0) 

1174 self._n = n 

1175 self._ps[:] = [s] 

1176 # Property_RO _fint2, _fprs and _fprs2 can't be a Property: 

1177 # Property's _fset zaps the value just set by the @setter 

1178 self.__dict__.update(_fint2=t, _fprs=s, _fprs2=Fsum2Tuple(s, INT0)) 

1179 else: # PYCHOK no cover 

1180 raise self._TypeError(_fset_op_, other) # txt=_invalid_ 

1181 return self 

1182 

1183 def fsub(self, xs=()): 

1184 '''Subtract an iterable of C{scalar} or L{Fsum} instances 

1185 from this instance. 

1186 

1187 @arg xs: Iterable, list, tuple. etc. (C{scalar} 

1188 or L{Fsum} instances). 

1189 

1190 @return: This instance, updated (L{Fsum}). 

1191 

1192 @see: Method L{Fsum.fadd}. 

1193 ''' 

1194 return self._facc(_2floats(xs, sub=True)) if xs else self # PYCHOK yield 

1195 

1196 def fsub_(self, *xs): 

1197 '''Subtract all positional C{scalar} or L{Fsum} instances 

1198 from this instance. 

1199 

1200 @arg xs: Values to subtract (C{scalar} or 

1201 L{Fsum} instances), all positional. 

1202 

1203 @return: This instance, updated (L{Fsum}). 

1204 

1205 @see: Method L{Fsum.fadd}. 

1206 ''' 

1207 return self._facc(_2floats(xs, origin=1, sub=True)) if xs else self # PYCHOK yield 

1208 

1209 def _fsub(self, other, op): 

1210 '''(INTERNAL) Apply C{B{self} -= B{other}}. 

1211 ''' 

1212 if isinstance(other, Fsum): 

1213 if other is self: # or other._fprs2 == self._fprs2: 

1214 self._fset(_0_0, asis=True, n=len(self) * 2) # self -= self 

1215 elif other._ps: 

1216 self._facc(other._ps_n()) 

1217 elif not isscalar(other): 

1218 raise self._TypeError(op, other) # txt=_invalid_ 

1219 elif self._finite(other, op): 

1220 self._facc_(-other) 

1221 return self 

1222 

1223 def _Fsum(self, n, *ps): 

1224 '''(INTERNAL) New L{Fsum} instance. 

1225 ''' 

1226 f = Fsum() 

1227 f._n = n 

1228 if ps: 

1229 f._ps[:] = ps 

1230 f._copy_RESIDUAL(self) 

1231 return f 

1232 

1233 def fsum(self, xs=()): 

1234 '''Add more C{scalar} or L{Fsum} instances and summate. 

1235 

1236 @kwarg xs: Iterable, list, tuple, etc. (C{scalar} or 

1237 L{Fsum} instances). 

1238 

1239 @return: Precision running sum (C{float} or C{int}). 

1240 

1241 @see: Method L{Fsum.fadd}. 

1242 

1243 @note: Accumulation can continue after summation. 

1244 ''' 

1245 f = self._facc(_2floats(xs)) if xs else self # PYCHOK yield 

1246 return f._fprs 

1247 

1248 def fsum_(self, *xs): 

1249 '''Add all positional C{scalar} or L{Fsum} instances and summate. 

1250 

1251 @arg xs: Values to add (C{scalar} or L{Fsum} instances), 

1252 all positional. 

1253 

1254 @return: Precision running sum (C{float} or C{int}). 

1255 

1256 @see: Method L{Fsum.fsum}. 

1257 ''' 

1258 f = self._facc(_2floats(xs, origin=1)) if xs else self # PYCHOK yield 

1259 return f._fprs 

1260 

1261 def fsum2(self, xs=(), **name): 

1262 '''Add more C{scalar} or L{Fsum} instances and return the 

1263 current precision running sum and the C{residual}. 

1264 

1265 @kwarg xs: Iterable, list, tuple, etc. (C{scalar} or 

1266 L{Fsum} instances). 

1267 @kwarg name: Optional name (C{str}). 

1268 

1269 @return: L{Fsum2Tuple}C{(fsum, residual)} with C{fsum} the 

1270 current precision running sum and C{residual}, the 

1271 (precision) sum of the remaining C{partials}. The 

1272 C{residual is INT0} if the C{fsum} is considered 

1273 to be I{exact}. 

1274 

1275 @see: Methods L{Fsum.fint2}, L{Fsum.fsum} and L{Fsum.fsum2_} 

1276 ''' 

1277 f = self._facc(_2floats(xs)) if xs else self # PYCHOK yield 

1278 t = f._fprs2 

1279 if name: 

1280 t = t.dup(name=_xkwds_get(name, name=NN)) 

1281 return t 

1282 

1283 def fsum2_(self, *xs): 

1284 '''Add any positional C{scalar} or L{Fsum} instances and return 

1285 the precision running sum and the C{differential}. 

1286 

1287 @arg xs: Values to add (C{scalar} or L{Fsum} instances), 

1288 all positional. 

1289 

1290 @return: 2-Tuple C{(fsum, delta)} with the current precision 

1291 running C{fsum} and C{delta}, the difference with 

1292 the previous running C{fsum} (C{float}s). 

1293 

1294 @see: Methods L{Fsum.fsum_} and L{Fsum.fsum}. 

1295 ''' 

1296 p, r = self._fprs2 

1297 if xs: 

1298 s, t = self._facc(_2floats(xs, origin=1))._fprs2 # PYCHOK yield 

1299 return s, _fsum((s, -p, r, -t)) # ((s - p) + (r - t)) 

1300 else: # PYCHOK no cover 

1301 return p, _0_0 

1302 

1303# ftruediv = __itruediv__ # for naming consistency 

1304 

1305 def _ftruediv(self, other, op): 

1306 '''(INTERNAL) Apply C{B{self} /= B{other}}. 

1307 ''' 

1308 n = _1_0 

1309 if isinstance(other, Fsum): 

1310 if other is self or other._fprs2 == self._fprs2: 

1311 return self._fset(_1_0, asis=True, n=len(self)) 

1312 d, r = other._fprs2 

1313 if r: 

1314 if not d: # PYCHOK no cover 

1315 d = r 

1316 elif self._raiser(r, d): 

1317 raise self._ResidualError(op, other, r) 

1318 else: 

1319 d, n = other.as_integer_ratio() 

1320 elif isscalar(other): 

1321 d = other 

1322 else: # PYCHOK no cover 

1323 raise self._TypeError(op, other) # txt=_invalid_ 

1324 try: 

1325 s = 0 if isinf(d) else ( 

1326 d if isnan(d) else self._finite(n / d)) 

1327 except Exception as x: 

1328 E, t = _xError2(x) 

1329 raise self._Error(op, other, E, txt=t) 

1330 f = self._mul_scalar(s, _mul_op_) # handles 0, NAN, etc. 

1331 return self._fset(f) 

1332 

1333 @property_RO 

1334 def imag(self): 

1335 '''Get the C{imaginary} part of this instance (C{0.0}, always). 

1336 

1337 @see: Properties L{Fsum.ceil}, L{Fsum.floor} and L{Fsum.real}. 

1338 ''' 

1339 return _0_0 

1340 

1341 def int_float(self, raiser=False): 

1342 '''Return this instance' current running sum as C{int} or C{float}. 

1343 

1344 @kwarg raiser: If C{True} throw a L{ResidualError} if the 

1345 residual is non-zero. 

1346 

1347 @return: This C{integer} sum if this instance C{is_integer}, 

1348 otherwise return the C{float} sum if the residual 

1349 is zero or if C{B{raiser}=False}. 

1350 

1351 @raise ResidualError: Non-zero residual and C{B{raiser}=True}. 

1352 

1353 @see: Methods L{Fsum.fint} and L{Fsum.fint2}. 

1354 ''' 

1355 s, r = self._fint2 

1356 if r: 

1357 s, r = self._fprs2 

1358 if r and raiser: # PYCHOK no cover 

1359 t = _stresidual(_non_zero_, r) 

1360 raise ResidualError(int_float=s, txt=t) 

1361 s = float(s) # redundant 

1362 return s 

1363 

1364 def is_exact(self): 

1365 '''Is this instance' current running C{fsum} considered to 

1366 be exact? (C{bool}). 

1367 ''' 

1368 return self.residual is INT0 

1369 

1370 def is_integer(self): 

1371 '''Is this instance' current running sum C{integer}? (C{bool}). 

1372 

1373 @see: Methods L{Fsum.fint} and L{Fsum.fint2}. 

1374 ''' 

1375 _, r = self._fint2 

1376 return False if r else True 

1377 

1378 def is_math_fsum(self): 

1379 '''Return whether functions L{fsum}, L{fsum_}, L{fsum1} 

1380 and L{fsum1_} plus partials summation are based on 

1381 Python's C{math.fsum} or not. 

1382 

1383 @return: C{2} if all functions and partials summation 

1384 are based on C{math.fsum}, C{True} if only 

1385 the functions are based on C{math.fsum} (and 

1386 partials summation is not) or C{False} if 

1387 none are. 

1388 ''' 

1389 f = Fsum._math_fsum 

1390 return 2 if _psum is f else bool(f) 

1391 

1392 def _mul_Fsum(self, other, op=_mul_op_): 

1393 '''(INTERNAL) Return C{B{self} * Fsum B{other}} as L{Fsum}. 

1394 ''' 

1395 # assert isinstance(other, Fsum) 

1396 return self._copy_0()._facc(self._ps_x(op, *other._ps), up=False) 

1397 

1398 def _mul_scalar(self, factor, op): 

1399 '''(INTERNAL) Return C{B{self} * scalar B{factor}} as L{Fsum} or C{0}. 

1400 ''' 

1401 # assert isscalar(factor) 

1402 if self._finite(factor, op) and self._ps: 

1403 if factor == _1_0: 

1404 return self 

1405 f = self._copy_0()._facc(self._ps_x(op, factor), up=False) 

1406 else: 

1407 f = self._copy_0(_0_0) 

1408 return f 

1409 

1410 @property_RO 

1411 def partials(self): 

1412 '''Get this instance' current partial sums (C{tuple} of C{float}s and/or C{int}s). 

1413 ''' 

1414 return tuple(self._ps) 

1415 

1416 def pow(self, x, *mod): 

1417 '''Return C{B{self}**B{x}} as L{Fsum}. 

1418 

1419 @arg x: The exponent (L{Fsum} or C{scalar}). 

1420 @arg mod: Optional modulus (C{int} or C{None}) for the 3-argument 

1421 C{pow(B{self}, B{other}, B{mod})} version. 

1422 

1423 @return: The C{pow(self, B{x})} or C{pow(self, B{x}, *B{mod})} 

1424 result (L{Fsum}). 

1425 

1426 @note: If B{C{mod}} is given as C{None}, the result will be an 

1427 C{integer} L{Fsum} provided this instance C{is_integer} 

1428 or set C{integer} with L{Fsum.fint}. 

1429 

1430 @see: Methods L{Fsum.__ipow__}, L{Fsum.fint} and L{Fsum.is_integer}. 

1431 ''' 

1432 f = self._copy_2(self.pow) 

1433 if f and isint(x) and x >= 0 and not mod: 

1434 f._pow_int(x, x, _pow_op_) # f **= x 

1435 else: 

1436 f._fpow(x, _pow_op_, *mod) # f = pow(f, x, *mod) 

1437 return f 

1438 

1439 def _pow_0_1(self, x, other): 

1440 '''(INTERNAL) Return B{C{self}**1} or C{B{self}**0 == 1.0}. 

1441 ''' 

1442 return self if x else (1 if self.is_integer() and isint(other) else _1_0) 

1443 

1444 def _pow_2(self, x, other, op): 

1445 '''(INTERNAL) 2-arg C{pow(B{self}, scalar B{x})} embellishing errors. 

1446 ''' 

1447 # assert len(self._ps) == 1 and isscalar(x) 

1448 b = self._ps[0] # assert isscalar(b) 

1449 try: # type(s) == type(x) if x in (_1_0, 1) 

1450 s = pow(b, x) # -1**2.3 == -(1**2.3) 

1451 if not iscomplex(s): 

1452 return self._finite(s) # 0**INF == 0.0, 1**INF==1.0 

1453 # neg**frac == complex in Python 3+, but ValueError in 2- 

1454 E, t = _ValueError, _strcomplex(s, b, x) # PYCHOK no cover 

1455 except Exception as x: 

1456 E, t = _xError2(x) 

1457 raise self._Error(op, other, E, txt=t) 

1458 

1459 def _pow_3(self, other, mod, op): 

1460 '''(INTERNAL) 3-arg C{pow(B{self}, B{other}, int B{mod} or C{None})}. 

1461 ''' 

1462 b, r = self._fprs2 if mod is None else self._fint2 

1463 if r and self._raiser(r, b): 

1464 t = _non_zero_ if mod is None else _integer_ 

1465 E, t = ResidualError, _stresidual(t, r, mod=mod) 

1466 else: 

1467 try: # b, other, mod all C{int}, unless C{mod} is C{None} 

1468 x = _2scalar(other, _raiser=self._raiser) 

1469 s = pow(b, x, mod) 

1470 if not iscomplex(s): 

1471 return self._finite(s) 

1472 # neg**frac == complex in Python 3+, but ValueError in 2- 

1473 E, t = _ValueError, _strcomplex(s, b, x, mod) # PYCHOK no cover 

1474 except Exception as x: 

1475 E, t = _xError2(x) 

1476 t = _COMMASPACE_(Fmt.PARENSPACED(mod=mod), t) 

1477 raise self._Error(op, other, E, txt=t) 

1478 

1479 def _pow_int(self, x, other, op): 

1480 '''(INTERNAL) Return C{B{self} **= B{x}} for C{int B{x} >= 0}. 

1481 ''' 

1482 # assert isint(x) and x >= 0 

1483 if len(self._ps) > 1: 

1484 if x > 2: 

1485 p = self._copy_up() 

1486 m = 1 # single-bit mask 

1487 if x & m: 

1488 x -= m # x ^= m 

1489 f = p._copy_up() 

1490 else: 

1491 f = self._copy_0(_1_0) 

1492 while x: 

1493 p = p._mul_Fsum(p, op) # p **= 2 

1494 m += m # m <<= 1 

1495 if x & m: 

1496 x -= m # x ^= m 

1497 f = f._mul_Fsum(p, op) # f *= p 

1498 elif x > 1: # self**2 

1499 f = self._mul_Fsum(self, op) 

1500 else: # self**1 or self**0 

1501 f = self._pow_0_1(x, other) 

1502 elif self._ps: # self._ps[0]**x 

1503 f = self._pow_2(x, other, op) 

1504 else: # PYCHOK no cover 

1505 # 0**pos_int == 0, but 0**0 == 1 

1506 f = 0 if x else 1 # like ._fprs 

1507 return self._fset(f, asis=isint(f), n=len(self)) 

1508 

1509 def _pow_scalar(self, x, other, op): 

1510 '''(INTERNAL) Return C{self**B{x}} for C{scalar B{x}}. 

1511 ''' 

1512 s, r = self._fprs2 

1513 if isint(x, both=True): 

1514 x = int(x) # Fsum**int 

1515 y = abs(x) 

1516 if y > 1: 

1517 if r: 

1518 f = self._copy_up()._pow_int(y, other, op) 

1519 if x > 0: # > 1 

1520 return f 

1521 # assert x < 0 # < -1 

1522 s, r = f._fprs2 

1523 if r: 

1524 return self._copy_0(_1_0)._ftruediv(f, op) 

1525 # use **= -1 for the CPython float_pow 

1526 # error if s is zero, and not s = 1 / s 

1527 x = -1 

1528# elif y > 1: # self**2 or self**-2 

1529# f = self._mul_Fsum(self, op) 

1530# if x < 0: 

1531# f = f._copy_0(_1_0)._ftruediv(f, op) 

1532# return f 

1533 elif x < 0: # self**-1 == 1 / self 

1534 if r: 

1535 return self._copy_0(_1_0)._ftruediv(self, op) 

1536 else: # self**1 or self**0 

1537 return self._pow_0_1(x, other) # self or 0.0 

1538 elif not isscalar(x): # assert ... 

1539 raise self._TypeError(op, other, txt=_not_scalar_) 

1540 elif r and self._raiser(r, s): # non-zero residual**fractional 

1541 # raise self._ResidualError(op, other, r, fractional_power=x) 

1542 t = _stresidual(_non_zero_, r, fractional_power=x) 

1543 raise self._Error(op, other, ResidualError, txt=t) 

1544 # assert isscalar(s) and isscalar(x) 

1545 return self._copy_0(s)._pow_2(x, other, op) 

1546 

1547 def _ps_1(self, *less): 

1548 '''(INTERNAL) Yield partials, 1-primed and subtract any C{less}. 

1549 ''' 

1550 yield _1_0 

1551 for p in self._ps: 

1552 if p: 

1553 yield p 

1554 for p in less: 

1555 if p: 

1556 yield -p 

1557 yield _N_1_0 

1558 

1559 def _ps_n(self): 

1560 '''(INTERNAL) Yield partials, negated. 

1561 ''' 

1562 for p in self._ps: 

1563 if p: 

1564 yield -p 

1565 

1566 def _ps_x(self, op, *factors): # see .fmath.Fhorner 

1567 '''(INTERNAL) Yield all C{partials} times each B{C{factor}}, 

1568 in total, up to C{len(partials) * len(factors)} items. 

1569 ''' 

1570 ps = self._ps 

1571 if len(ps) < len(factors): 

1572 ps, factors = factors, ps 

1573 _f = _isfinite 

1574 for f in factors: 

1575 for p in ps: 

1576 p *= f 

1577 if _f(p): 

1578 yield p 

1579 else: # PYCHOK no cover 

1580 self._finite(p, op) # throw ValueError 

1581 

1582 @property_RO 

1583 def real(self): 

1584 '''Get the C{real} part of this instance (C{float}). 

1585 

1586 @see: Methods L{Fsum.__float__} and L{Fsum.fsum} 

1587 and properties L{Fsum.ceil}, L{Fsum.floor}, 

1588 L{Fsum.imag} and L{Fsum.residual}. 

1589 ''' 

1590 return float(self._fprs) 

1591 

1592 @property_RO 

1593 def residual(self): 

1594 '''Get this instance' residual (C{float} or C{int}), the 

1595 C{sum(partials)} less the precision running sum C{fsum}. 

1596 

1597 @note: If the C{residual is INT0}, the precision running 

1598 C{fsum} is considered to be I{exact}. 

1599 

1600 @see: Methods L{Fsum.fsum}, L{Fsum.fsum2} and L{Fsum.is_exact}. 

1601 ''' 

1602 return self._fprs2.residual 

1603 

1604 def _raiser(self, r, s): 

1605 '''(INTERNAL) Does the ratio C{r / s} exceed threshold? 

1606 ''' 

1607 self._ratio = t = fabs((r / s) if s else r) 

1608 return t > self._RESIDUAL 

1609 

1610 def RESIDUAL(self, *threshold): 

1611 '''Get and set this instance' I{ratio} for raising L{ResidualError}s, 

1612 overriding the default from env variable C{PYGEODESY_FSUM_RESIDUAL}. 

1613 

1614 @arg threshold: If C{scalar}, the I{ratio} to exceed for raising 

1615 L{ResidualError}s in division and exponention, if 

1616 C{None} restore the default set with env variable 

1617 C{PYGEODESY_FSUM_RESIDUAL} or if omitted, keep the 

1618 current setting. 

1619 

1620 @return: The previous C{RESIDUAL} setting (C{float}). 

1621 

1622 @raise ValueError: Negative B{C{threshold}}. 

1623 

1624 @note: A L{ResidualError} is thrown if the non-zero I{ratio} 

1625 C{residual} / C{fsum} exceeds the B{C{threshold}}. 

1626 ''' 

1627 r = self._RESIDUAL 

1628 if threshold: 

1629 t = threshold[0] 

1630 t = Fsum._RESIDUAL if t is None else ( 

1631 float(t) if isscalar(t) else ( # for backward ... 

1632 _0_0 if bool(t) else _1_0)) # ... compatibility 

1633 if t < 0: 

1634 u = self._unstr(self.RESIDUAL, *threshold) 

1635 raise _ValueError(u, RESIDUAL=t, txt=_negative_) 

1636 self._RESIDUAL = t 

1637 return r 

1638 

1639 def _ResidualError(self, op, other, residual): 

1640 '''(INTERNAL) Non-zero B{C{residual}} etc. 

1641 ''' 

1642 t = _stresidual(_non_zero_, residual, ratio=self._ratio, 

1643 RESIDUAL=self._RESIDUAL) 

1644 t = t.replace(_COMMASPACE_R_, _exceeds_R_) 

1645 return self._Error(op, other, ResidualError, txt=t) 

1646 

1647 def signOf(self, res=True): 

1648 '''Determine the sign of this instance. 

1649 

1650 @kwarg res: If C{True} consider, otherwise 

1651 ignore the residual (C{bool}). 

1652 

1653 @return: The sign (C{int}, -1, 0 or +1). 

1654 ''' 

1655 s, r = self._fprs2 if res else (self._fprs, 0) 

1656 return _signOf(s, -r) 

1657 

1658 def toRepr(self, **prec_sep_fmt_lenc): # PYCHOK signature 

1659 '''Return this C{Fsum} instance as representation. 

1660 

1661 @kwarg prec_sep_fmt_lenc: Optional keyword arguments for 

1662 method L{Fsum2Tuple.toRepr} plus C{B{lenc}=True} 

1663 (C{bool}) to in-/exclude the current C{[len]} 

1664 of this L{Fsum} enclosed in I{[brackets]}. 

1665 

1666 @return: This instance (C{repr}). 

1667 ''' 

1668 return self._toT(self._fprs2.toRepr, **prec_sep_fmt_lenc) 

1669 

1670 def toStr(self, **prec_sep_fmt_lenc): # PYCHOK signature 

1671 '''Return this C{Fsum} instance as string. 

1672 

1673 @kwarg prec_sep_fmt_lenc: Optional keyword arguments for 

1674 method L{Fsum2Tuple.toStr} plus C{B{lenc}=True} 

1675 (C{bool}) to in-/exclude the current C{[len]} 

1676 of this L{Fsum} enclosed in I{[brackets]}. 

1677 

1678 @return: This instance (C{str}). 

1679 ''' 

1680 return self._toT(self._fprs2.toStr, **prec_sep_fmt_lenc) 

1681 

1682 def _toT(self, toT, fmt=Fmt.g, lenc=True, **kwds): 

1683 '''(INTERNAL) Helper for C{toRepr} and C{toStr}. 

1684 ''' 

1685 n = self.named3 

1686 if lenc: 

1687 n = Fmt.SQUARE(n, len(self)) 

1688 return _SPACE_(n, toT(fmt=fmt, **kwds)) 

1689 

1690 def _TypeError(self, op, other, **txt): # PYCHOK no cover 

1691 '''(INTERNAL) Return a C{TypeError}. 

1692 ''' 

1693 return self._Error(op, other, _TypeError, **txt) 

1694 

1695 def _update(self): # see ._fset 

1696 '''(INTERNAL) Zap all cached C{Property_RO} values. 

1697 ''' 

1698 Fsum._fint2._update(self) 

1699 Fsum._fprs ._update(self) 

1700 Fsum._fprs2._update(self) 

1701 return self 

1702 

1703 def _ValueError(self, op, other, **txt): # PYCHOK no cover 

1704 '''(INTERNAL) Return a C{ValueError}. 

1705 ''' 

1706 return self._Error(op, other, _ValueError, **txt) 

1707 

1708 def _ZeroDivisionError(self, op, other, **txt): # PYCHOK no cover 

1709 '''(INTERNAL) Return a C{ZeroDivisionError}. 

1710 ''' 

1711 return self._Error(op, other, _ZeroDivisionError, **txt) 

1712 

1713_allPropertiesOf_n(3, Fsum, Property_RO) # PYCHOK assert, see Fsum._fset, -._update 

1714 

1715 

1716def _Float_Int(arg, **name_Error): 

1717 '''(INTERNAL) Unit of L{Fsum2Tuple} items. 

1718 ''' 

1719 U = Int if isint(arg) else Float 

1720 return U(arg, **name_Error) 

1721 

1722 

1723class Fsum2Tuple(_NamedTuple): 

1724 '''2-Tuple C{(fsum, residual)} with the precision running C{fsum} 

1725 and the C{residual}, the sum of the remaining partials. Each 

1726 item is either C{float} or C{int}. 

1727 

1728 @note: If the C{residual is INT0}, the C{fsum} is considered 

1729 to be I{exact}, see method L{Fsum2Tuple.is_exact}. 

1730 ''' 

1731 _Names_ = ( Fsum.fsum.__name__, Fsum.residual.name) 

1732 _Units_ = (_Float_Int, _Float_Int) 

1733 

1734 @Property_RO 

1735 def Fsum(self): 

1736 '''Get this L{Fsum2Tuple} as an L{Fsum}. 

1737 ''' 

1738 f = Fsum(name=self.name) 

1739 return f._copy_0(*(s for s in reversed(self) if s)) 

1740 

1741 def is_exact(self): 

1742 '''Is this L{Fsum2Tuple} considered to be exact? (C{bool}). 

1743 ''' 

1744 return self.Fsum.is_exact() 

1745 

1746 def is_integer(self): 

1747 '''Is this L{Fsum2Tuple} C{integer}? (C{bool}). 

1748 ''' 

1749 return self.Fsum.is_integer() 

1750 

1751 

1752class ResidualError(_ValueError): 

1753 '''Error raised for an operation involving a L{pygeodesy.sums.Fsum} 

1754 instance with a non-zero C{residual}, I{integer} or otherwise. 

1755 

1756 @see: Module L{pygeodesy.fsums} and method L{Fsum.RESIDUAL}. 

1757 ''' 

1758 pass 

1759 

1760 

1761try: 

1762 from math import fsum as _fsum # precision IEEE-754 sum, Python 2.6+ 

1763 

1764 # make sure _fsum works as expected (XXX check 

1765 # float.__getformat__('float')[:4] == 'IEEE'?) 

1766 if _fsum((1, 1e101, 1, -1e101)) != 2: # PYCHOK no cover 

1767 del _fsum # nope, remove _fsum ... 

1768 raise ImportError # ... use _fsum below 

1769 

1770 Fsum._math_fsum = _fsum 

1771 

1772 if _getenv('PYGEODESY_FSUM_PARTIALS', _fsum.__name__) == _fsum.__name__: 

1773 _psum = _fsum # PYCHOK redef 

1774 

1775except ImportError: 

1776 

1777 def _fsum(xs): 

1778 '''(INTERNAL) Precision summation, Python 2.5-. 

1779 ''' 

1780 return Fsum(name=_fsum.__name__)._facc(xs, up=False)._fprs 

1781 

1782 

1783def fsum(xs, floats=False): 

1784 '''Precision floating point summation based on or like Python's C{math.fsum}. 

1785 

1786 @arg xs: Iterable, list, tuple, etc. of values (C{scalar} or 

1787 L{Fsum} instances). 

1788 @kwarg floats: Optionally, use C{B{floats}=True} iff I{all} 

1789 B{C{xs}} are known to be C{float}. 

1790 

1791 @return: Precision C{fsum} (C{float}). 

1792 

1793 @raise OverflowError: Partial C{2sum} overflow. 

1794 

1795 @raise TypeError: Non-scalar B{C{xs}} value. 

1796 

1797 @raise ValueError: Invalid or non-finite B{C{xs}} value. 

1798 

1799 @note: Exceptions and I{non-finite} handling may differ if not 

1800 based on Python's C{math.fsum}. 

1801 

1802 @see: Class L{Fsum} and methods L{Fsum.fsum} and L{Fsum.fadd}. 

1803 ''' 

1804 return _fsum(xs if floats else _2floats(xs)) if xs else _0_0 # PYCHOK yield 

1805 

1806 

1807def fsum_(*xs, **floats): 

1808 '''Precision floating point summation of all positional arguments. 

1809 

1810 @arg xs: Values to be added (C{scalar} or L{Fsum} instances), 

1811 all positional. 

1812 @kwarg floats: Optionally, use C{B{floats}=True} iff I{all} 

1813 B{C{xs}} are known to be C{float}. 

1814 

1815 @return: Precision C{fsum} (C{float}). 

1816 

1817 @see: Function C{fsum}. 

1818 ''' 

1819 return _fsum(xs if _xkwds_get(floats, floats=False) else 

1820 _2floats(xs, origin=1)) if xs else _0_0 # PYCHOK yield 

1821 

1822 

1823def fsumf_(*xs): 

1824 '''Precision floating point summation L{fsum_}C{(*xs, floats=True)}. 

1825 ''' 

1826 return _fsum(xs) if xs else _0_0 

1827 

1828 

1829def fsum1(xs, floats=False): 

1830 '''Precision floating point summation of a few arguments, 1-primed. 

1831 

1832 @arg xs: Iterable, list, tuple, etc. of values (C{scalar} or 

1833 L{Fsum} instances). 

1834 @kwarg floats: Optionally, use C{B{floats}=True} iff I{all} 

1835 B{C{xs}} are known to be C{float}. 

1836 

1837 @return: Precision C{fsum} (C{float}). 

1838 

1839 @see: Function C{fsum}. 

1840 ''' 

1841 return _fsum(_1primed(xs if floats else _2floats(xs))) if xs else _0_0 # PYCHOK yield 

1842 

1843 

1844def fsum1_(*xs, **floats): 

1845 '''Precision floating point summation of a few arguments, 1-primed. 

1846 

1847 @arg xs: Values to be added (C{scalar} or L{Fsum} instances), 

1848 all positional. 

1849 @kwarg floats: Optionally, use C{B{floats}=True} iff I{all} 

1850 B{C{xs}} are known to be C{float}. 

1851 

1852 @return: Precision C{fsum} (C{float}). 

1853 

1854 @see: Function C{fsum} 

1855 ''' 

1856 return _fsum(_1primed(xs if _xkwds_get(floats, floats=False) else 

1857 _2floats(xs, origin=1))) if xs else _0_0 # PYCHOK yield 

1858 

1859 

1860def fsum1f_(*xs): 

1861 '''Precision floating point summation L{fsum1_}C{(*xs, floats=True)}. 

1862 ''' 

1863 return _fsum(_1primed(xs)) if xs else _0_0 

1864 

1865 

1866# **) MIT License 

1867# 

1868# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved. 

1869# 

1870# Permission is hereby granted, free of charge, to any person obtaining a 

1871# copy of this software and associated documentation files (the "Software"), 

1872# to deal in the Software without restriction, including without limitation 

1873# the rights to use, copy, modify, merge, publish, distribute, sublicense, 

1874# and/or sell copies of the Software, and to permit persons to whom the 

1875# Software is furnished to do so, subject to the following conditions: 

1876# 

1877# The above copyright notice and this permission notice shall be included 

1878# in all copies or substantial portions of the Software. 

1879# 

1880# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

1881# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

1882# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

1883# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

1884# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 

1885# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 

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