Coverage for pygeodesy/fsums.py: 95%

949 statements  

« prev     ^ index     » next       coverage.py v7.6.0, created at 2024-09-11 15:06 -0400

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 

7Class L{Fsum} also supports accurate multiplication for Python 3.13 and 

8later, but as an option for older Python versions. For more details, see 

9method L{f2product<Fsum.f2product>}, class L{Fsum2product} and U{Accurate 

10Sum and Dot Product<https://www.TUHH.De/ti3/paper/rump/OgRuOi05.pdf>}. 

11 

12Generally, an L{Fsum} instance is considered a C{float} plus a small or zero 

13C{residual} value, see property L{Fsum.residual}. However, there are several 

14C{integer} L{Fsum} cases, for example the result of C{ceil}, C{floor}, 

15C{Fsum.__floordiv__} and methods L{Fsum.fint} and L{Fsum.fint2}. 

16 

17Also, L{Fsum} methods L{Fsum.pow}, L{Fsum.__ipow__}, L{Fsum.__pow__} and 

18L{Fsum.__rpow__} return a (very long) C{int} if invoked with optional argument 

19C{mod} set to C{None}. The C{residual} of an C{integer} L{Fsum} may be between 

20C{-1.0} and C{+1.0}, including C{INT0} if considered to be I{exact}. 

21 

22Set env variable C{PYGEODESY_FSUM_RESIDUAL} to a C{float} string greater than 

23C{"0.0"} as the threshold to throw a L{ResidualError} for a division, power or 

24root operation of an L{Fsum} instance with a C{residual} I{ratio} exceeding 

25the threshold. See methods L{Fsum.RESIDUAL}, L{Fsum.pow}, L{Fsum.__ipow__} 

26and L{Fsum.__itruediv__}. 

27''' 

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

29from __future__ import division as _; del _ # PYCHOK semicolon 

30 

31from pygeodesy.basics import isbool, iscomplex, isint, isscalar, \ 

32 _signOf, itemsorted, signOf, _xiterable, \ 

33 _xiterablen 

34from pygeodesy.constants import INT0, _isfinite, MANT_DIG, NEG0, _pos_self, \ 

35 _0_0, _1_0, _N_1_0, Float, Int 

36from pygeodesy.errors import _OverflowError, _TypeError, _UnexpectedError, \ 

37 _ValueError, _xError, _xError2, _xkwds_get1, \ 

38 _xkwds_pop2 

39from pygeodesy.internals import _enquote, _passarg 

40from pygeodesy.interns import NN, _arg_, _COMMASPACE_, _DASH_, _DOT_, \ 

41 _EQUAL_, _from_, _LANGLE_, _NOTEQUAL_, \ 

42 _not_finite_, _PERCENT_, _PLUS_, \ 

43 _RANGLE_, _SLASH_, _SPACE_, _STAR_, _UNDER_ 

44from pygeodesy.lazily import _ALL_LAZY, _getenv, _sys_version_info2 

45from pygeodesy.named import _name__, _name2__, _Named, _NamedTuple, \ 

46 _NotImplemented 

47from pygeodesy.props import _allPropertiesOf_n, deprecated_property_RO, \ 

48 Property, Property_RO, property_RO 

49from pygeodesy.streprs import Fmt, fstr, unstr 

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

51 

52from math import ceil as _ceil, fabs, floor as _floor # PYCHOK used! .ltp 

53 

54__all__ = _ALL_LAZY.fsums 

55__version__ = '24.09.10' 

56 

57_add_op_ = _PLUS_ # in .auxilats.auxAngle 

58_eq_op_ = _EQUAL_ * 2 # _DEQUAL_ 

59_div_ = 'div' 

60_floordiv_op_ = _SLASH_ * 2 # _DSLASH_ 

61_fset_op_ = _EQUAL_ 

62_ge_op_ = _RANGLE_ + _EQUAL_ 

63_gt_op_ = _RANGLE_ 

64_iadd_op_ = _add_op_ + _EQUAL_ # in .auxilats.auxAngle, .fstats 

65_integer_ = 'integer' 

66_le_op_ = _LANGLE_ + _EQUAL_ 

67_lt_op_ = _LANGLE_ 

68_mod_ = 'mod' 

69_mod_op_ = _PERCENT_ 

70_mul_op_ = _STAR_ 

71_ne_op_ = _NOTEQUAL_ 

72_non_zero_ = 'non-zero' 

73_pow_op_ = _STAR_ * 2 # _DSTAR_ 

74_significant_ = 'significant' 

75_sub_op_ = _DASH_ # in .auxilats.auxAngle 

76_threshold_ = 'threshold' 

77_truediv_op_ = _SLASH_ 

78_divmod_op_ = _floordiv_op_ + _mod_op_ 

79_isub_op_ = _sub_op_ + _fset_op_ # in .auxilats.auxAngle 

80 

81 

82def _2delta(*ab): 

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

84 ''' 

85 try: 

86 a, b = _2sum(*ab) 

87 except _OverflowError: 

88 a, b = ab 

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

90 

91 

92def _2error(unused): # in .fstats 

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

94 ''' 

95 raise ValueError(_not_finite_) 

96 

97 

98def _2finite(x): 

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

100 ''' 

101 x = float(x) 

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

103 

104 

105def _2float(index=None, **name_value): # in .fmath, .fstats 

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

107 ''' 

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

109 try: 

110 return _2finite(v) 

111 except Exception as X: 

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

113 

114 

115def _X_ps(X): # for _2floats only 

116 return X._ps 

117 

118 

119def _2floats(xs, origin=0, _X=_X_ps, _x=float): 

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

121 ''' 

122 try: 

123 i, x = origin, _X 

124 _fin = _isfinite 

125 _FsT = _Fsum_Fsum2Tuple_types 

126 _isa = isinstance 

127 for x in _xiterable(xs): 

128 if _isa(x, _FsT): 

129 for p in _X(x._Fsum): 

130 yield p 

131 else: 

132 f = _x(x) 

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

134 i += 1 

135 except Exception as X: 

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

137 _xError(X, Fmt.INDEX(xs=i), x) 

138 

139 

140try: # MCCABE 14 

141 from math import fma as _fma 

142 

143 def _2products(x, ys, **unused): 

144 # TwoProductFMA U{Algorithm 3.5 

145 # <https://www.TUHH.De/ti3/paper/rump/OgRuOi05.pdf>} 

146 for y in ys: 

147 f = x * y 

148 yield f 

149 yield _fma(x, y, -f) 

150 

151 _2split3s = _passarg # NOP 

152 

153except ImportError: # Python 3.12- 

154 

155 def _fma(*a_b_c): # in .fmath 

156 # mimick C{math.fma} from Python 3.13+ 

157 # <https://MomentsInGraphics.De/FMA.html> 

158 # >>> a = 1.00000011920929 

159 # >>> b = 53400708 

160 # >>> c = -b 

161 # >>> _fma(a, b, c) 

162 # 6.365860485903399 

163 # >>> (a * b) + c 

164 # 6.3658604845404625 

165 

166 def _as_n_d(x): 

167 try: 

168 if _isfinite(x): 

169 # int.as_integer_ratio since 3.8 

170 return x.as_integer_ratio() 

171 except (AttributeError, OverflowError, TypeError, ValueError): 

172 pass 

173 return float(x), 1 

174 

175 (na, da), (nb, db), (nc, dc) = map(_as_n_d, a_b_c) 

176 n = na * nb * dc + da * db * nc 

177 d = da * db * dc 

178 return float(n / d) 

179 

180 def _2products(x, y3s, two=False): # PYCHOK redef 

181 # TwoProduct U{Algorithm 3.3 

182 # <https://www.TUHH.De/ti3/paper/rump/OgRuOi05.pdf>} 

183 _, a, b = _2split3(x) 

184 for y, c, d in y3s: 

185 y *= x 

186 yield y 

187 if two: 

188 yield b * d - (((y - a * c) - b * c) - a * d) 

189# = b * d + (a * d - ((y - a * c) - b * c)) 

190# = b * d + (a * d + (b * c - (y - a * c))) 

191# = b * d + (a * d + (b * c + (a * c - y))) 

192 else: 

193 yield a * c - y 

194 yield b * c 

195 if d: 

196 yield a * d 

197 yield b * d 

198 

199 _2FACTOR = pow(2, (MANT_DIG + 1) // 2) + 1 

200 

201 def _2split3(x): 

202 # Split U{Algorithm 3.2 

203 # <ttps://www.TUHH.De/ti3/paper/rump/OgRuOi05.pdf>} 

204 a = c = x * _2FACTOR 

205 a -= c - x 

206 b = x - a 

207 return x, a, b 

208 

209 def _2split3s(xs): # PYCHOK redef 

210 return map(_2split3, xs) 

211 

212del MANT_DIG 

213 

214 

215def _Fsumf_(*xs): # floats=True, in .auxLat, ... 

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

217 ''' 

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

219 

220 

221def _Fsum1f_(*xs): # floats=True, in .albers, ... 

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

223 ''' 

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

225 

226 

227def _2halfeven(s, r, p): 

228 '''(INTERNAL) Round half-even. 

229 ''' 

230 if (p > 0 and r > 0) or \ 

231 (p < 0 and r < 0): # signs match 

232 r *= 2 

233 t = s + r 

234 if r == (t - s): 

235 s = t 

236 return s 

237 

238 

239def _isFsum(x): # in .fmath 

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

241 ''' 

242 return isinstance(x, Fsum) 

243 

244 

245def _isFsumTuple(x): # in .fmath 

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

247 ''' 

248 return isinstance(x, _Fsum_Fsum2Tuple_types) 

249 

250 

251def _1_Over(x, op, **raiser_RESIDUAL): # vs _1_over 

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

253 ''' 

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

255 

256 

257def _1primed(xs): # in .fmath 

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

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

260 ''' 

261 yield _1_0 

262 for x in xs: 

263 yield x 

264 yield _N_1_0 

265 

266 

267def _psum(ps): # PYCHOK used! 

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

269 ''' 

270 # assert isinstance(ps, list) 

271 i = len(ps) - 1 

272 s = _0_0 if i < 0 else ps[i] 

273 _2s = _2sum 

274 while i > 0: 

275 i -= 1 

276 s, r = _2s(s, ps[i]) 

277 if r: # sum(ps) became inexact 

278 if s: 

279 ps[i:] = r, s 

280 if i > 0: 

281 s = _2halfeven(s, r, ps[i-1]) 

282 break # return s 

283 s = r # PYCHOK no cover 

284 ps[i:] = s, 

285 return s 

286 

287 

288def _Psum(ps, **name_RESIDUAL): 

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

290 ''' 

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

292 if ps: 

293 f._ps[:] = ps 

294 f._n = len(f._ps) 

295 return f 

296 

297 

298def _Psum_(*ps, **name_RESIDUAL): 

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

300 ''' 

301 return _Psum(ps, **name_RESIDUAL) 

302 

303 

304def _2scalar2(other): 

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

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

307 ''' 

308 if _isFsumTuple(other): 

309 s, r = other._fint2 

310 if r: 

311 s, r = other._fprs2 

312 if r: # PYCHOK no cover 

313 s = other # L{Fsum} as-is 

314 else: 

315 r = 0 

316 s = other # C{type} as-is 

317 if isint(s, both=True): 

318 s = int(s) 

319 return s, r 

320 

321 

322def _s_r(s, r): 

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

324 ''' 

325 if r: 

326 if fabs(s) < fabs(r): 

327 s, r = r, (s or INT0) 

328 else: 

329 r = INT0 

330 return s, r 

331 

332 

333def _strcomplex(s, *args): 

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

335 ''' 

336 c = _strcomplex.__name__[4:] 

337 n = _DASH_(len(args), _arg_) 

338 t = unstr(pow, *args) 

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

340 

341 

342def _stresidual(prefix, residual, R=0, **mod_ratio): 

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

344 ''' 

345 p = _stresidual.__name__[3:] 

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

347 for n, v in itemsorted(mod_ratio): 

348 p = Fmt.PARENSPACED(n, Fmt(v)) 

349 t = _COMMASPACE_(t, p) 

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

351 

352 

353def _2sum(a, b): # by .testFmath 

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

355 ''' 

356 # Neumaier, A. U{Rundungsfehleranalyse einiger Verfahren zur Summation endlicher 

357 # Summen<https://OnlineLibrary.Wiley.com/doi/epdf/10.1002/zamm.19740540106>}, 

358 # 1974, Zeitschrift für Angewandte Mathmatik und Mechanik, vol 51, nr 1, p 39-51 

359 # <https://StackOverflow.com/questions/78633770/can-neumaier-summation-be-sped-up> 

360 s = a + b 

361 if _isfinite(s): 

362 if fabs(a) < fabs(b): 

363 r = (b - s) + a 

364 else: 

365 r = (a - s) + b 

366 return s, r 

367 u = unstr(_2sum, a, b) 

368 t = Fmt.PARENSPACED(_not_finite_, s) 

369 raise _OverflowError(u, txt=t) 

370 

371 

372def _threshold(threshold=_0_0, **kwds): 

373 '''(INTERNAL) Get the L{ResidualError}s threshold, 

374 optionally from single kwds C{B{RESIDUAL}=scalar}. 

375 ''' 

376 if kwds: 

377 threshold, kwds = _xkwds_pop2(kwds, RESIDUAL=threshold) 

378# threshold = kwds.pop('RESIDUAL', threshold) 

379 if kwds: 

380 raise _UnexpectedError(**kwds) 

381 try: 

382 return _2finite(threshold) # PYCHOK None 

383 except Exception as x: 

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

385 

386 

387class Fsum(_Named): # sync __methods__ with .vector3dBase.Vector3dBase 

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

389 

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

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

392 intermediate, I{running} summuation. 

393 

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

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

396 C{float}, except C{complex}. 

397 

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

399 Python's C{math.fsum}. 

400 

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

402 393090_Binary_floating_point_summatiaccurate_full/recipe-393090.py>}, 

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

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

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

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

407 ''' 

408 _f2product = _2split3s is _passarg # True for 3.13+ 

409 _math_fma = _fma if _f2product else None 

410 _math_fsum = None 

411 _n = 0 

412# _ps = [] # partial sums 

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

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

415 

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

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

418 

419 @arg xs: No, one or more initial items to add (each C{scalar} or 

420 an L{Fsum} or L{Fsum2Tuple} instance), all positional. 

421 @kwarg name_RESIDUAL: Optional C{B{name}=NN} (C{str}) for this 

422 L{Fsum} and the C{B{RESIDUAL}=0.0} threshold for 

423 L{ResidualError}s (C{scalar}). 

424 

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

426 ''' 

427 if name_RESIDUAL: 

428 n, kwds = _name2__(**name_RESIDUAL) 

429 if kwds: 

430 R = Fsum._RESIDUAL 

431 t = _threshold(R, **kwds) 

432 if t != R: 

433 self._RESIDUAL = t 

434 if n: 

435 self.name = n 

436 

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

438 if xs: 

439 self._facc_1(xs, up=False) 

440 

441 def __abs__(self): 

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

443 ''' 

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

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

446 

447 def __add__(self, other): 

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

449 

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

451 

452 @return: The sum (L{Fsum}). 

453 

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

455 ''' 

456 f = self._copy_2(self.__add__) 

457 return f._fadd(other, _add_op_) 

458 

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

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

461 ''' 

462 s, r = self._fprs2 

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

464 

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

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

467 

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

469 

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

471 ''' 

472 return self.ceil 

473 

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

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

476 

477 @return: -1, 0 or +1 (C{int}). 

478 

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

480 ''' 

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

482 return _signOf(s, 0) 

483 

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

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

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

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

488 

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

490 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore 

491 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar} 

492 to override the current L{RESIDUAL<Fsum.RESIDUAL>}. 

493 

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

495 B{C{RESIDUAL}}. 

496 

497 @see: Method L{Fsum.fdiv}. 

498 ''' 

499 f = self._copy_2(self.__divmod__) 

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

501 

502 def __eq__(self, other): 

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

504 ''' 

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

506 

507 def __float__(self): 

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

509 

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

511 ''' 

512 return float(self._fprs) 

513 

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

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

516 

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

518 

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

520 ''' 

521 return self.floor 

522 

523 def __floordiv__(self, other): 

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

525 

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

527 

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

529 

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

531 ''' 

532 f = self._copy_2(self.__floordiv__) 

533 return f._floordiv(other, _floordiv_op_) 

534 

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

536 '''Not implemented.''' 

537 return _NotImplemented(self, *other) 

538 

539 def __ge__(self, other): 

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

541 ''' 

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

543 

544 def __gt__(self, other): 

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

546 ''' 

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

548 

549 def __hash__(self): # PYCHOK no cover 

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

551 ''' 

552 # @see: U{Notes for type implementors<https://docs.Python.org/ 

553 # 3/library/numbers.html#numbers.Rational>} 

554 return hash(self.partials) # tuple.__hash__() 

555 

556 def __iadd__(self, other): 

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

558 

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

560 an iterable of several of the former. 

561 

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

563 

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

565 C{scalar} nor L{Fsum}. 

566 

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

568 ''' 

569 try: 

570 return self._fadd(other, _iadd_op_) 

571 except TypeError: 

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

573 

574 def __ifloordiv__(self, other): 

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

576 

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

578 

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

580 

581 @raise ResidualError: Non-zero, significant residual 

582 in B{C{other}}. 

583 

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

585 

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

587 

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

589 

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

591 ''' 

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

593 

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

595 '''Not implemented.''' 

596 return _NotImplemented(self, other) 

597 

598 def __imod__(self, other): 

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

600 

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

602 

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

604 

605 @see: Method L{Fsum.__divmod__}. 

606 ''' 

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

608 

609 def __imul__(self, other): 

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

611 

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

613 

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

615 

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

617 

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

619 

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

621 ''' 

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

623 

624 def __int__(self): 

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

626 

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

628 and L{Fsum.floor}. 

629 ''' 

630 i, _ = self._fint2 

631 return i 

632 

633 def __invert__(self): # PYCHOK no cover 

634 '''Not implemented.''' 

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

636 return _NotImplemented(self) 

637 

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

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

640 

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

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

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

644 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore 

645 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar} 

646 to override the current L{RESIDUAL<Fsum.RESIDUAL>}. 

647 

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

649 

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

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

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

653 

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

655 

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

657 is non-zero and significant and either 

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

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

660 C{None}. 

661 

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

663 invocation failed. 

664 

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

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

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

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

669 is given as C{0}. 

670 

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

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

673 ''' 

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

675 

676 def __isub__(self, other): 

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

678 

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

680 an iterable of several of the former. 

681 

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

683 

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

685 

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

687 ''' 

688 try: 

689 return self._fsub(other, _isub_op_) 

690 except TypeError: 

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

692 

693 def __iter__(self): 

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

695 ''' 

696 return iter(self.partials) 

697 

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

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

700 

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

702 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore 

703 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar} 

704 to override the current L{RESIDUAL<Fsum.RESIDUAL>}. 

705 

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

707 

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

709 

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

711 B{C{RESIDUAL}}. 

712 

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

714 

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

716 

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

718 

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

720 ''' 

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

722 

723 def __le__(self, other): 

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

725 ''' 

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

727 

728 def __len__(self): 

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

730 ''' 

731 return self._n 

732 

733 def __lt__(self, other): 

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

735 ''' 

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

737 

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

739 '''Not implemented.''' 

740 return _NotImplemented(self, other) 

741 

742 def __mod__(self, other): 

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

744 

745 @see: Method L{Fsum.__imod__}. 

746 ''' 

747 f = self._copy_2(self.__mod__) 

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

749 

750 def __mul__(self, other): 

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

752 

753 @see: Method L{Fsum.__imul__}. 

754 ''' 

755 f = self._copy_2(self.__mul__) 

756 return f._fmul(other, _mul_op_) 

757 

758 def __ne__(self, other): 

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

760 ''' 

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

762 

763 def __neg__(self): 

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

765 ''' 

766 f = self._copy_2(self.__neg__) 

767 return f._fset(self._neg) 

768 

769 def __pos__(self): 

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

771 ''' 

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

773 

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

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

776 

777 @see: Method L{Fsum.__ipow__}. 

778 ''' 

779 f = self._copy_2(self.__pow__) 

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

781 

782 def __radd__(self, other): 

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

784 

785 @see: Method L{Fsum.__iadd__}. 

786 ''' 

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

788 return f._fadd(self, _add_op_) 

789 

790 def __rdivmod__(self, other): 

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

792 C{(quotient, remainder)}. 

793 

794 @see: Method L{Fsum.__divmod__}. 

795 ''' 

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

797 return f._fdivmod2(self, _divmod_op_) 

798 

799# def __repr__(self): 

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

801# ''' 

802# return self.toRepr(lenc=True) 

803 

804 def __rfloordiv__(self, other): 

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

806 

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

808 ''' 

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

810 return f._floordiv(self, _floordiv_op_) 

811 

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

813 '''Not implemented.''' 

814 return _NotImplemented(self, other) 

815 

816 def __rmod__(self, other): 

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

818 

819 @see: Method L{Fsum.__imod__}. 

820 ''' 

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

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

823 

824 def __rmul__(self, other): 

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

826 

827 @see: Method L{Fsum.__imul__}. 

828 ''' 

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

830 return f._fmul(self, _mul_op_) 

831 

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

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

834 

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

836 ''' 

837 f = self._copy_2(self.__round__) 

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

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

840 

841 def __rpow__(self, other, *mod): 

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

843 

844 @see: Method L{Fsum.__ipow__}. 

845 ''' 

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

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

848 

849 def __rsub__(self, other): 

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

851 

852 @see: Method L{Fsum.__isub__}. 

853 ''' 

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

855 return f._fsub(self, _sub_op_) 

856 

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

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

859 

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

861 ''' 

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

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

864 

865 def __str__(self): 

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

867 ''' 

868 return self.toStr(lenc=True) 

869 

870 def __sub__(self, other): 

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

872 

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

874 

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

876 

877 @see: Method L{Fsum.__isub__}. 

878 ''' 

879 f = self._copy_2(self.__sub__) 

880 return f._fsub(other, _sub_op_) 

881 

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

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

884 

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

886 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore 

887 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar} 

888 to override the current L{RESIDUAL<Fsum.RESIDUAL>}. 

889 

890 @return: The quotient (L{Fsum}). 

891 

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

893 B{C{RESIDUAL}}. 

894 

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

896 ''' 

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

898 

899 __trunc__ = __int__ 

900 

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

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

903 __div__ = __truediv__ 

904 __idiv__ = __itruediv__ 

905 __long__ = __int__ 

906 __nonzero__ = __bool__ 

907 __rdiv__ = __rtruediv__ 

908 

909 def as_integer_ratio(self): 

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

911 

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

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

914 non-zero, positive. 

915 

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

917 ''' 

918 n, r = self._fint2 

919 if r: 

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

921 n *= d 

922 n += i 

923 else: # PYCHOK no cover 

924 d = 1 

925 return n, d 

926 

927 @property_RO 

928 def as_iscalar(self): 

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

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

931 ''' 

932 s, r = self._fprs2 

933 return self if r else s 

934 

935 @property_RO 

936 def ceil(self): 

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

938 C{float} in Python 2-). 

939 

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

941 

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

943 L{Fsum.imag} and L{Fsum.real}. 

944 ''' 

945 s, r = self._fprs2 

946 c = _ceil(s) + int(r) - 1 

947 while r > (c - s): # (s + r) > c 

948 c += 1 

949 return c # _ceil(self._n_d) 

950 

951 cmp = __cmp__ 

952 

953 def _cmp_0(self, other, op): 

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

955 ''' 

956 if _isFsumTuple(other): 

957 s = self._ps_1sum(*other._ps) 

958 elif self._scalar(other, op): 

959 s = self._ps_1sum(other) 

960 else: 

961 s = self.signOf() # res=True 

962 return s 

963 

964 def copy(self, deep=False, **name): 

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

966 

967 @kwarg name: Optional, overriding C{B{name}='"copy"} (C{str}). 

968 

969 @return: The copy (L{Fsum}). 

970 ''' 

971 n = _name__(name, name__=self.copy) 

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

973 if f._ps is self._ps: 

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

975 if not deep: 

976 f._n = 1 

977 # assert f._f2product == self._f2product 

978 # assert f._Fsum is f 

979 return f 

980 

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

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

983 ''' 

984 n = name or which.__name__ # _dunder_nameof 

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

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

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

988 # assert f._n == self._n 

989 # assert f._f2product == self._f2product 

990 # assert f._Fsum is f 

991 return f 

992 

993 def _copy_2r(self, other, which): 

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

995 ''' 

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

997 self._copy_2(which)._fset(other) 

998 

999# def _copy_RESIDUAL(self, other): 

1000# '''(INTERNAL) Copy C{other._RESIDUAL}. 

1001# ''' 

1002# R = other._RESIDUAL 

1003# if R is not Fsum._RESIDUAL: 

1004# self._RESIDUAL = R 

1005 

1006 divmod = __divmod__ 

1007 

1008 def _Error(self, op, other, Error, **txt_cause): 

1009 '''(INTERNAL) Format an B{C{Error}} for C{{self} B{op} B{other}}. 

1010 ''' 

1011 return Error(_SPACE_(self.as_iscalar, op, other), **txt_cause) 

1012 

1013 def _ErrorX(self, X, op, other, *mod): 

1014 '''(INTERNAL) Format the caught exception C{X}. 

1015 ''' 

1016 E, t = _xError2(X) 

1017 if mod: 

1018 t = _COMMASPACE_(Fmt.PARENSPACED(mod=mod[0]), t) 

1019 return self._Error(op, other, E, txt=t, cause=X) 

1020 

1021 def _ErrorXs(self, X, xs, **kwds): # in .fmath 

1022 '''(INTERNAL) Format the caught exception C{X}. 

1023 ''' 

1024 E, t = _xError2(X) 

1025 u = unstr(self.named3, *xs[:3], _ELLIPSIS=len(xs) > 3, **kwds) 

1026 return E(u, txt=t, cause=X) 

1027 

1028 def _facc(self, xs, up=True, **origin_X_x): 

1029 '''(INTERNAL) Accumulate more C{scalars} or L{Fsum}s. 

1030 ''' 

1031 if xs: 

1032 _xs = _2floats(xs, **origin_X_x) # PYCHOK yield 

1033 ps = self._ps 

1034 ps[:] = self._ps_acc(list(ps), _xs, up=up) 

1035 return self 

1036 

1037 def _facc_1(self, xs, **up): 

1038 '''(INTERNAL) Accumulate 0, 1 or more C{scalars} or L{Fsum}s, 

1039 all positional C{xs} in the caller of this method. 

1040 ''' 

1041 return self._fadd(xs[0], _add_op_, **up) if len(xs) == 1 else \ 

1042 self._facc(xs, origin=1, **up) 

1043 

1044 def _facc_inplace(self, other, op, _facc): 

1045 '''(INTERNAL) Accumulate from an iterable. 

1046 ''' 

1047 try: 

1048 return _facc(other, origin=1) if _xiterable(other) else self 

1049 except Exception as X: 

1050 raise self._ErrorX(X, op, other) 

1051 

1052 def _facc_neg(self, xs, **up_origin): 

1053 '''(INTERNAL) Accumulate more C{scalars} or L{Fsum}s, negated. 

1054 ''' 

1055 def _N(X): 

1056 return X._ps_neg 

1057 

1058 def _n(x): 

1059 return -float(x) 

1060 

1061 return self._facc(xs, _X=_N, _x=_n, **up_origin) 

1062 

1063 def _facc_power(self, power, xs, which, **raiser_RESIDUAL): # in .fmath 

1064 '''(INTERNAL) Add each C{xs} as C{float(x**power)}. 

1065 ''' 

1066 def _Pow4(p): 

1067 r = 0 

1068 if _isFsumTuple(p): 

1069 s, r = p._fprs2 

1070 if r: 

1071 m = Fsum._pow 

1072 else: # scalar 

1073 return _Pow4(s) 

1074 elif isint(p, both=True) and int(p) >= 0: 

1075 p = s = int(p) 

1076 m = Fsum._pow_int 

1077 else: 

1078 p = s = _2float(power=p) 

1079 m = Fsum._pow_scalar 

1080 return m, p, s, r 

1081 

1082 _Pow, p, s, r = _Pow4(power) 

1083 if p: # and xs: 

1084 op = which.__name__ 

1085 _flt = float 

1086 _Fs = Fsum 

1087 _isa = isinstance 

1088 _pow = self._pow_2_3 

1089 

1090 def _P(X): 

1091 f = _Pow(X, p, power, op, **raiser_RESIDUAL) 

1092 return f._ps if _isa(f, _Fs) else (f,) 

1093 

1094 def _p(x): 

1095 x = _flt(x) 

1096 f = _pow(x, s, power, op, **raiser_RESIDUAL) 

1097 if f and r: 

1098 f *= _pow(x, r, power, op, **raiser_RESIDUAL) 

1099 return f 

1100 

1101 f = self._facc(xs, origin=1, _X=_P, _x=_p) 

1102 else: 

1103 f = self._facc_scalar_(float(len(xs))) # x**0 == 1 

1104 return f 

1105 

1106 def _facc_scalar(self, xs, **up): 

1107 '''(INTERNAL) Accumulate all C{xs}, known to be scalar. 

1108 ''' 

1109 if xs: 

1110 _ = self._ps_acc(self._ps, xs, **up) 

1111 return self 

1112 

1113 def _facc_scalar_(self, *xs, **up): 

1114 '''(INTERNAL) Accumulate all positional C{xs}, known to be scalar. 

1115 ''' 

1116 if xs: 

1117 _ = self._ps_acc(self._ps, xs, **up) 

1118 return self 

1119 

1120# def _facc_up(self, up=True): 

1121# '''(INTERNAL) Update the C{partials}, by removing 

1122# and re-accumulating the final C{partial}. 

1123# ''' 

1124# ps = self._ps 

1125# while len(ps) > 1: 

1126# p = ps.pop() 

1127# if p: 

1128# n = self._n 

1129# _ = self._ps_acc(ps, (p,), up=False) 

1130# self._n = n 

1131# break 

1132# return self._update() if up else self 

1133 

1134 def fadd(self, xs=()): 

1135 '''Add an iterable's items to this instance. 

1136 

1137 @arg xs: Iterable of items to add (each C{scalar} 

1138 or an L{Fsum} or L{Fsum2Tuple} instance). 

1139 

1140 @return: This instance (L{Fsum}). 

1141 

1142 @raise OverflowError: Partial C{2sum} overflow. 

1143 

1144 @raise TypeError: An invalid B{C{xs}} item. 

1145 

1146 @raise ValueError: Invalid or non-finite B{C{xs}} value. 

1147 ''' 

1148 if _isFsumTuple(xs): 

1149 self._facc_scalar(xs._ps) 

1150 elif isscalar(xs): # for backward compatibility 

1151 self._facc_scalar_(_2float(x=xs)) # PYCHOK no cover 

1152 elif xs: # _xiterable(xs) 

1153 self._facc(xs) 

1154 return self 

1155 

1156 def fadd_(self, *xs): 

1157 '''Add all positional items to this instance. 

1158 

1159 @arg xs: Values to add (each C{scalar} or an L{Fsum} 

1160 or L{Fsum2Tuple} instance), all positional. 

1161 

1162 @see: Method L{Fsum.fadd} for further details. 

1163 ''' 

1164 return self._facc_1(xs) 

1165 

1166 def _fadd(self, other, op, **up): # in .fmath.Fhorner 

1167 '''(INTERNAL) Apply C{B{self} += B{other}}. 

1168 ''' 

1169 if not self._ps: # new Fsum(x) 

1170 self._fset(other, op=op, **up) 

1171 elif _isFsumTuple(other): 

1172 self._facc_scalar(other._ps, **up) 

1173 elif self._scalar(other, op): 

1174 self._facc_scalar_(other, **up) 

1175 return self 

1176 

1177 fcopy = copy # for backward compatibility 

1178 fdiv = __itruediv__ 

1179 fdivmod = __divmod__ 

1180 

1181 def _fdivmod2(self, other, op, **raiser_RESIDUAL): 

1182 '''(INTERNAL) Apply C{B{self} %= B{other}} and return a L{DivMod2Tuple}. 

1183 ''' 

1184 # result mostly follows CPython function U{float_divmod 

1185 # <https://GitHub.com/python/cpython/blob/main/Objects/floatobject.c>}, 

1186 # but at least divmod(-3, 2) equals Cpython's result (-2, 1). 

1187 q = self._truediv(other, op, **raiser_RESIDUAL).floor 

1188 if q: # == float // other == floor(float / other) 

1189 self -= Fsum(q) * other # NOT other * q! 

1190 

1191 s = signOf(other) # make signOf(self) == signOf(other) 

1192 if s and self.signOf() == -s: # PYCHOK no cover 

1193 self += other 

1194 q -= 1 

1195# t = self.signOf() 

1196# if t and t != s: 

1197# raise self._Error(op, other, _AssertionError, txt__=signOf) 

1198 return DivMod2Tuple(q, self) # q is C{int} in Python 3+, but C{float} in Python 2- 

1199 

1200 def _fhorner(self, x, cs, op, incx=True): # in .fmath 

1201 '''(INTERNAL) Add an L{Fhorner} evaluation of polynomial 

1202 C{sum(cs[i] * B{x}**i for i=0..len(cs)-1) if B{incx} 

1203 else sum(... i=len(cs)-1..0)}. 

1204 ''' 

1205 if _xiterablen(cs): 

1206 H = Fsum(name__=self._fhorner) 

1207 if _isFsumTuple(x): 

1208 _mul = H._mul_Fsum 

1209 else: 

1210 _mul = H._mul_scalar 

1211 x = _2float(x=x) 

1212 if len(cs) > 1 and x: 

1213 for c in (reversed(cs) if incx else cs): 

1214 H._fset_ps(_mul(x, op)) 

1215 H._fadd(c, op, up=False) 

1216 else: # x == 0 

1217 H = cs[0] if cs else _0_0 

1218 self._fadd(H, op) 

1219 return self 

1220 

1221 def _finite(self, other, op=None): 

1222 '''(INTERNAL) Return B{C{other}} if C{finite}. 

1223 ''' 

1224 if _isfinite(other): 

1225 return other 

1226 raise ValueError(_not_finite_) if op is None else \ 

1227 self._Error(op, other, _ValueError, txt=_not_finite_) 

1228 

1229 def fint(self, name=NN, **raiser_RESIDUAL): 

1230 '''Return this instance' current running sum as C{integer}. 

1231 

1232 @kwarg name: Optional, overriding C{B{name}="fint"} (C{str}). 

1233 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore 

1234 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar} 

1235 to override the current L{RESIDUAL<Fsum.RESIDUAL>}. 

1236 

1237 @return: The C{integer} sum (L{Fsum}) if this instance C{is_integer} 

1238 with a zero or insignificant I{integer} residual. 

1239 

1240 @raise ResidualError: Non-zero, significant residual or invalid 

1241 B{C{RESIDUAL}}. 

1242 

1243 @see: Methods L{Fsum.fint2}, L{Fsum.int_float} and L{Fsum.is_integer}. 

1244 ''' 

1245 i, r = self._fint2 

1246 if r: 

1247 R = self._raiser(r, i, **raiser_RESIDUAL) 

1248 if R: 

1249 t = _stresidual(_integer_, r, **R) 

1250 raise ResidualError(_integer_, i, txt=t) 

1251 return _Psum_(i, name=_name__(name, name__=self.fint)) 

1252 

1253 def fint2(self, **name): 

1254 '''Return this instance' current running sum as C{int} and the 

1255 I{integer} residual. 

1256 

1257 @kwarg name: Optional name (C{str}). 

1258 

1259 @return: An L{Fsum2Tuple}C{(fsum, residual)} with C{fsum} 

1260 an C{int} and I{integer} C{residual} a C{float} or 

1261 C{INT0} if the C{fsum} is considered to be I{exact}. 

1262 ''' 

1263 return Fsum2Tuple(*self._fint2, **name) 

1264 

1265 @Property 

1266 def _fint2(self): # see ._fset 

1267 '''(INTERNAL) Get 2-tuple (C{int}, I{integer} residual). 

1268 ''' 

1269 s, r = self._fprs2 

1270 i = int(s) 

1271 n = len(self._ps) 

1272 r = self._ps_1sum(i) if r and n > 1 else float(s - i) 

1273 return i, (r or INT0) # Fsum2Tuple? 

1274 

1275 @_fint2.setter_ # PYCHOK setter_underscore! 

1276 def _fint2(self, s): 

1277 '''(INTERNAL) Replace the C{_fint2} value. 

1278 ''' 

1279 i = int(s) 

1280 return i, ((s - i) or INT0) 

1281 

1282 @deprecated_property_RO 

1283 def float_int(self): # PYCHOK no cover 

1284 '''DEPRECATED, use method C{Fsum.int_float}.''' 

1285 return self.int_float() # raiser=False 

1286 

1287 @property_RO 

1288 def floor(self): 

1289 '''Get this instance' C{floor} (C{int} in Python 3+, but 

1290 C{float} in Python 2-). 

1291 

1292 @note: This C{floor} takes the C{residual} into account. 

1293 

1294 @see: Method L{Fsum.int_float} and properties L{Fsum.ceil}, 

1295 L{Fsum.imag} and L{Fsum.real}. 

1296 ''' 

1297 s, r = self._fprs2 

1298 f = _floor(s) + _floor(r) + 1 

1299 while (f - s) > r: # f > (s + r) 

1300 f -= 1 

1301 return f # _floor(self._n_d) 

1302 

1303# ffloordiv = __ifloordiv__ # for naming consistency 

1304# floordiv = __floordiv__ # for naming consistency 

1305 

1306 def _floordiv(self, other, op, **raiser_RESIDUAL): # rather _ffloordiv? 

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

1308 ''' 

1309 q = self._ftruediv(other, op, **raiser_RESIDUAL) # == self 

1310 return self._fset(q.floor) # floor(q) 

1311 

1312 def fma(self, other1, other2): # 

1313 '''Fused-multiply-add C{self *= B{other1}; self += B{other2}}. 

1314 

1315 @arg other1: A C{scalar}, an L{Fsum} or L{Fsum2Tuple} instance. 

1316 @arg other2: A C{scalar}, an L{Fsum} or L{Fsum2Tuple} instance. 

1317 

1318 @note: Uses C{math.fma} in Python 3.13+, provided C{self}, 

1319 B{C{other1}} and B{C{other2}} are all C{scalar}. 

1320 ''' 

1321 if len(self._ps) == 1 and isscalar(other1, both=True) \ 

1322 and isscalar(other2, both=True): 

1323 p = _fma(self._ps[0], other1, other2) 

1324 self._ps[:] = self._finite(p, self.fma.__name__), 

1325 if other2: 

1326 self._n += 1 

1327 else: 

1328 self._f2mul(self.fma.__name__, other1) 

1329 self += other2 

1330 return self 

1331 

1332# def _fma_scalar(self, op, x, *ys): # in .karney 

1333# '''(INTERNAL) Apply C{self.fma(B{x}, B{y}) for B{y} in B{ys}} 

1334# for scalar C{x} and C{y}s. 

1335# ''' 

1336# ps = self._ps 

1337# if ps and ys: 

1338# for y in ys: 

1339# ps[:] = self._ps_acc(list(y), _2products(x, _2split3s(ps))) 

1340# for p in (ps if op else()): 

1341# self._finite(p, op) 

1342# return self 

1343 

1344 fmul = __imul__ 

1345 

1346 def _fmul(self, other, op): 

1347 '''(INTERNAL) Apply C{B{self} *= B{other}}. 

1348 ''' 

1349 if _isFsumTuple(other): 

1350 if len(self._ps) != 1: 

1351 f = self._mul_Fsum(other, op) 

1352 elif len(other._ps) != 1: # and len(self._ps) == 1 

1353 f = other._mul_scalar(self._ps[0], op) 

1354 elif self._f2product: # len(other._ps) == 1 

1355 f = self._mul_scalar(other._ps[0], op) 

1356 else: # len(other._ps) == len(self._ps) == 1 

1357 f = self._finite(self._ps[0] * other._ps[0]) 

1358 else: 

1359 s = self._scalar(other, op) 

1360 f = self._mul_scalar(s, op) 

1361 return self._fset(f) # n=len(self) + 1 

1362 

1363 def f2mul(self, *others): 

1364 '''Apply C{B{self} *= B{other} for B{other} in B{others}} where each B{other} 

1365 is C{scalar}, an L{Fsum} or L{Fsum2Tuple} applying accurate multiplication 

1366 as if L{f2product<Fsum.f2product>}C{=True}. 

1367 

1368 @see: U{Equations 2.3<https://www.TUHH.De/ti3/paper/rump/OzOgRuOi06.pdf>} 

1369 ''' 

1370 return self._f2mul(self.f2mul.__name__, *others) 

1371 

1372 def _f2mul(self, op, *others): 

1373 '''(INTERNAL) See method C{f2mul}. 

1374 ''' 

1375 P = _Psum(self._ps) 

1376 ps = P._ps 

1377 if ps and others: 

1378 for p in self._ps_other(op, *others): 

1379 pfs = _2products(p, _2split3s(ps)) 

1380 ps[:] = P._ps_acc([], pfs, up=False) 

1381 for p in ps: 

1382 self._finite(p, op) 

1383 self._fset(P, op=op) 

1384 return self 

1385 

1386 def fover(self, over, **raiser_RESIDUAL): 

1387 '''Apply C{B{self} /= B{over}} and summate. 

1388 

1389 @arg over: An L{Fsum} or C{scalar} denominator. 

1390 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore 

1391 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar} 

1392 to override the current L{RESIDUAL<Fsum.RESIDUAL>}. 

1393 

1394 @return: Precision running sum (C{float}). 

1395 

1396 @raise ResidualError: Non-zero, significant residual or invalid 

1397 B{C{RESIDUAL}}. 

1398 

1399 @see: Methods L{Fsum.fsum} and L{Fsum.__itruediv__}. 

1400 ''' 

1401 return float(self.fdiv(over, **raiser_RESIDUAL)._fprs) 

1402 

1403 fpow = __ipow__ 

1404 

1405 def _fpow(self, other, op, *mod, **raiser_RESIDUAL): 

1406 '''Apply C{B{self} **= B{other}}, optional B{C{mod}} or C{None}. 

1407 ''' 

1408 if mod: 

1409 if mod[0] is not None: # == 3-arg C{pow} 

1410 f = self._pow_2_3(self, other, other, op, *mod, **raiser_RESIDUAL) 

1411 elif self.is_integer(): 

1412 # return an exact C{int} for C{int}**C{int} 

1413 i, _ = self._fint2 # assert _ == 0 

1414 x, r = _2scalar2(other) # C{int}, C{float} or other 

1415 f = _Psum_(i)._pow_Fsum(other, op, **raiser_RESIDUAL) if r else \ 

1416 self._pow_2_3(i, x, other, op, **raiser_RESIDUAL) 

1417 else: # mod[0] is None, power(self, other) 

1418 f = self._pow(other, other, op, **raiser_RESIDUAL) 

1419 else: # pow(self, other) 

1420 f = self._pow(other, other, op, **raiser_RESIDUAL) 

1421 return self._fset(f) # n=max(len(self), 1) 

1422 

1423 def f2product(self, *two): 

1424 '''Turn this instance' accurate I{TwoProduct} multiplication or or off. 

1425 

1426 @arg two: If C{True}, turn I{TwoProduct} on, if C{False} off or if 

1427 C{None} or if omitted, keep the current setting. 

1428 

1429 @return: The previous C{f2product} setting (C{bool}). 

1430 

1431 @see: On Python 3.13 and later I{TwoProduct} is based on I{TwoProductFMA} 

1432 U{Algorithm 3.5<https://www.TUHH.De/ti3/paper/rump/OgRuOi05.pdf>} 

1433 otherwise on the slower I{TwoProduct} and I{Split} U{Algorithms 

1434 3.3 and 3.2<https://www.TUHH.De/ti3/paper/rump/OgRuOi05.pdf>}. 

1435 ''' 

1436 t = self._f2product 

1437 if two and two[0] is not None: 

1438 self._f2product = bool(two[0]) 

1439 return t 

1440 

1441 @Property 

1442 def _fprs(self): 

1443 '''(INTERNAL) Get and cache this instance' precision 

1444 running sum (C{float} or C{int}), ignoring C{residual}. 

1445 

1446 @note: The precision running C{fsum} after a C{//=} or 

1447 C{//} C{floor} division is C{int} in Python 3+. 

1448 ''' 

1449 s, _ = self._fprs2 

1450 return s # ._fprs2.fsum 

1451 

1452 @_fprs.setter_ # PYCHOK setter_underscore! 

1453 def _fprs(self, s): 

1454 '''(INTERNAL) Replace the C{_fprs} value. 

1455 ''' 

1456 return s 

1457 

1458 @Property 

1459 def _fprs2(self): 

1460 '''(INTERNAL) Get and cache this instance' precision 

1461 running sum and residual (L{Fsum2Tuple}). 

1462 ''' 

1463 ps = self._ps 

1464 n = len(ps) - 2 

1465 if n > 0: # len(ps) > 2 

1466 s = _psum(ps) 

1467 n = len(ps) - 2 

1468 if n > 0: 

1469 r = self._ps_1sum(s) 

1470 return Fsum2Tuple(*_s_r(s, r)) 

1471 if n == 0: # len(ps) == 2 

1472 s, r = _s_r(*_2sum(*ps)) 

1473 ps[:] = (r, s) if r else (s,) 

1474 elif ps: # len(ps) == 1 

1475 s, r = ps[0], INT0 

1476 else: # len(ps) == 0 

1477 s, r = _0_0, INT0 

1478 ps[:] = s, 

1479 # assert self._ps is ps 

1480 return Fsum2Tuple(s, r) 

1481 

1482 @_fprs2.setter_ # PYCHOK setter_underscore! 

1483 def _fprs2(self, s_r): 

1484 '''(INTERNAL) Replace the C{_fprs2} value. 

1485 ''' 

1486 return Fsum2Tuple(s_r) 

1487 

1488 def fset_(self, *xs): 

1489 '''Replace this instance' value with all positional items. 

1490 

1491 @arg xs: Optional, new values (each C{scalar} or 

1492 an L{Fsum} or L{Fsum2Tuple} instance), 

1493 all positional. 

1494 

1495 @return: This instance, replaced (C{Fsum}). 

1496 

1497 @see: Method L{Fsum.fadd} for further details. 

1498 ''' 

1499 f = xs[0] if len(xs) == 1 else ( 

1500 Fsum(*xs) if xs else _0_0) 

1501 return self._fset(f) 

1502 

1503 def _fset(self, other, n=0, up=True, **op): 

1504 '''(INTERNAL) Overwrite this instance with an other or a C{scalar}. 

1505 ''' 

1506 if other is self: 

1507 pass # from ._fmul, ._ftruediv and ._pow_0_1 

1508 elif _isFsumTuple(other): 

1509 self._ps[:] = other._ps 

1510 self._n = n or other._n 

1511# self._copy_RESIDUAL(other) 

1512 if up: # use or zap the C{Property_RO} values 

1513 Fsum._fint2._update_from(self, other) 

1514 Fsum._fprs ._update_from(self, other) 

1515 Fsum._fprs2._update_from(self, other) 

1516 elif isscalar(other): 

1517 s = float(self._finite(other, **op)) if op else other 

1518 self._ps[:] = s, 

1519 self._n = n or 1 

1520 if up: # Property _fint2, _fprs and _fprs2 all have 

1521 # @.setter_underscore and NOT @.setter because the 

1522 # latter's _fset zaps the value set by @.setter 

1523 self._fint2 = s 

1524 self._fprs = s 

1525 self._fprs2 = s, INT0 

1526 # assert self._fprs is s 

1527 else: # PYCHOK no cover 

1528 op = _xkwds_get1(op, op=_fset_op_) 

1529 raise self._Error(op, other, _TypeError) 

1530 return self 

1531 

1532 def _fset_ps(self, other): # in .fmath 

1533 '''(INTERNAL) Set partials from a known C{scalar}, L{Fsum} or L{Fsum2Tuple}. 

1534 ''' 

1535 return self._fset(other, up=False) 

1536 

1537 def fsub(self, xs=()): 

1538 '''Subtract an iterable's items from this instance. 

1539 

1540 @see: Method L{Fsum.fadd} for further details. 

1541 ''' 

1542 return self._facc_neg(xs) 

1543 

1544 def fsub_(self, *xs): 

1545 '''Subtract all positional items from this instance. 

1546 

1547 @see: Method L{Fsum.fadd_} for further details. 

1548 ''' 

1549 return self._fsub(xs[0], _sub_op_) if len(xs) == 1 else \ 

1550 self._facc_neg(xs, origin=1) 

1551 

1552 def _fsub(self, other, op): 

1553 '''(INTERNAL) Apply C{B{self} -= B{other}}. 

1554 ''' 

1555 if _isFsumTuple(other): 

1556 if other is self: # or other._fprs2 == self._fprs2: 

1557 self._fset(_0_0, n=len(self) * 2) 

1558 elif other._ps: 

1559 self._facc_scalar(other._ps_neg) 

1560 elif self._scalar(other, op): 

1561 self._facc_scalar_(-other) 

1562 return self 

1563 

1564 def fsum(self, xs=()): 

1565 '''Add an iterable's items, summate and return the 

1566 current precision running sum. 

1567 

1568 @arg xs: Iterable of items to add (each item C{scalar} 

1569 or an L{Fsum} or L{Fsum2Tuple} instance). 

1570 

1571 @return: Precision running sum (C{float} or C{int}). 

1572 

1573 @see: Method L{Fsum.fadd}. 

1574 

1575 @note: Accumulation can continue after summation. 

1576 ''' 

1577 return self._facc(xs)._fprs 

1578 

1579 def fsum_(self, *xs): 

1580 '''Add any positional items, summate and return the 

1581 current precision running sum. 

1582 

1583 @arg xs: Items to add (each C{scalar} or an L{Fsum} 

1584 or L{Fsum2Tuple} instance), all positional. 

1585 

1586 @return: Precision running sum (C{float} or C{int}). 

1587 

1588 @see: Methods L{Fsum.fsum}, L{Fsum.Fsum_} and L{Fsum.fsumf_}. 

1589 ''' 

1590 return self._facc_1(xs)._fprs 

1591 

1592 @property_RO 

1593 def _Fsum(self): # like L{Fsum2Tuple._Fsum}, for C{_2floats}, .fstats 

1594 return self # NOT @Property_RO, see .copy and ._copy_2 

1595 

1596 def Fsum_(self, *xs, **name): 

1597 '''Like method L{Fsum.fsum_} but returning a named L{Fsum}. 

1598 

1599 @kwarg name: Optional name (C{str}). 

1600 

1601 @return: Copy of this updated instance (L{Fsum}). 

1602 ''' 

1603 return self._facc_1(xs)._copy_2(self.Fsum_, **name) 

1604 

1605 def Fsum2Tuple_(self, *xs, **name): 

1606 '''Like method L{Fsum.fsum_} but returning a named L{Fsum2Tuple}. 

1607 

1608 @kwarg name: Optional name (C{str}). 

1609 

1610 @return: Precision running sum (L{Fsum2Tuple}). 

1611 ''' 

1612 return Fsum2Tuple(self._facc_1(xs)._fprs2, **name) 

1613 

1614 def fsum2(self, xs=(), **name): 

1615 '''Add an iterable's items, summate and return the 

1616 current precision running sum I{and} the C{residual}. 

1617 

1618 @arg xs: Iterable of items to add (each item C{scalar} 

1619 or an L{Fsum} or L{Fsum2Tuple} instance). 

1620 @kwarg name: Optional C{B{name}=NN} (C{str}). 

1621 

1622 @return: L{Fsum2Tuple}C{(fsum, residual)} with C{fsum} the 

1623 current precision running sum and C{residual}, the 

1624 (precision) sum of the remaining C{partials}. The 

1625 C{residual is INT0} if the C{fsum} is considered 

1626 to be I{exact}. 

1627 

1628 @see: Methods L{Fsum.fint2}, L{Fsum.fsum} and L{Fsum.fsum2_} 

1629 ''' 

1630 t = self._facc(xs)._fprs2 

1631 return t.dup(name=name) if name else t 

1632 

1633 def fsum2_(self, *xs): 

1634 '''Add any positional items, summate and return the current 

1635 precision running sum and the I{differential}. 

1636 

1637 @arg xs: Values to add (each C{scalar} or an L{Fsum} or 

1638 L{Fsum2Tuple} instance), all positional. 

1639 

1640 @return: 2Tuple C{(fsum, delta)} with the current, precision 

1641 running C{fsum} like method L{Fsum.fsum} and C{delta}, 

1642 the difference with previous running C{fsum}, C{float}. 

1643 

1644 @see: Methods L{Fsum.fsum_} and L{Fsum.fsum}. 

1645 ''' 

1646 return self._fsum2(xs, self._facc_1) 

1647 

1648 def _fsum2(self, xs, _facc, **origin): 

1649 '''(INTERNAL) Helper for L{Fsum.fsum2_} and L{Fsum.fsum2f_}. 

1650 ''' 

1651 p, q = self._fprs2 

1652 if xs: 

1653 s, r = _facc(xs, **origin)._fprs2 

1654 return s, _2delta(s - p, r - q) # _fsum(_1primed((s, -p, r, -q)) 

1655 else: 

1656 return p, _0_0 

1657 

1658 def fsumf_(self, *xs): 

1659 '''Like method L{Fsum.fsum_} iff I{all} C{B{xs}} are I{known to be scalar}. 

1660 ''' 

1661 return self._facc_scalar(xs)._fprs 

1662 

1663 def Fsumf_(self, *xs): 

1664 '''Like method L{Fsum.Fsum_} iff I{all} C{B{xs}} are I{known to be scalar}. 

1665 ''' 

1666 return self._facc_scalar(xs)._copy_2(self.Fsumf_) 

1667 

1668 def fsum2f_(self, *xs): 

1669 '''Like method L{Fsum.fsum2_} iff I{all} C{B{xs}} are I{known to be scalar}. 

1670 ''' 

1671 return self._fsum2(xs, self._facc_scalar, origin=1) 

1672 

1673# ftruediv = __itruediv__ # for naming consistency? 

1674 

1675 def _ftruediv(self, other, op, **raiser_RESIDUAL): 

1676 '''(INTERNAL) Apply C{B{self} /= B{other}}. 

1677 ''' 

1678 n = _1_0 

1679 if _isFsumTuple(other): 

1680 if other is self or self == other: 

1681 return self._fset(n, n=len(self)) 

1682 d, r = other._fprs2 

1683 if r: 

1684 R = self._raiser(r, d, **raiser_RESIDUAL) 

1685 if R: 

1686 raise self._ResidualError(op, other, r, **R) 

1687 d, n = other.as_integer_ratio() 

1688 else: 

1689 d = self._scalar(other, op) 

1690 try: 

1691 s = n / d 

1692 except Exception as X: 

1693 raise self._ErrorX(X, op, other) 

1694 f = self._mul_scalar(s, _mul_op_) # handles 0, INF, NAN 

1695 return self._fset(f) 

1696 

1697 @property_RO 

1698 def imag(self): 

1699 '''Get the C{imaginary} part of this instance (C{0.0}, always). 

1700 

1701 @see: Property L{Fsum.real}. 

1702 ''' 

1703 return _0_0 

1704 

1705 def int_float(self, **raiser_RESIDUAL): 

1706 '''Return this instance' current running sum as C{int} or C{float}. 

1707 

1708 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore 

1709 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar} 

1710 to override the current L{RESIDUAL<Fsum.RESIDUAL>}. 

1711 

1712 @return: This C{integer} sum if this instance C{is_integer}, 

1713 otherwise return the C{float} sum if the residual is 

1714 zero or not significant. 

1715 

1716 @raise ResidualError: Non-zero, significant residual or invalid 

1717 B{C{RESIDUAL}}. 

1718 

1719 @see: Methods L{Fsum.fint}, L{Fsum.fint2}, L{Fsum.RESIDUAL} and 

1720 property L{Fsum.as_iscalar}. 

1721 ''' 

1722 s, r = self._fint2 

1723 if r: 

1724 s, r = self._fprs2 

1725 if r: # PYCHOK no cover 

1726 R = self._raiser(r, s, **raiser_RESIDUAL) 

1727 if R: 

1728 t = _stresidual(_non_zero_, r, **R) 

1729 raise ResidualError(int_float=s, txt=t) 

1730 s = float(s) 

1731 return s 

1732 

1733 def is_exact(self): 

1734 '''Is this instance' running C{fsum} considered to be exact? 

1735 (C{bool}), C{True} only if the C{residual is }L{INT0}. 

1736 ''' 

1737 return self.residual is INT0 

1738 

1739 def is_integer(self): 

1740 '''Is this instance' running sum C{integer}? (C{bool}). 

1741 

1742 @see: Methods L{Fsum.fint}, L{Fsum.fint2} and L{Fsum.is_scalar}. 

1743 ''' 

1744 _, r = self._fint2 

1745 return False if r else True 

1746 

1747 def is_math_fsum(self): 

1748 '''Return whether functions L{fsum}, L{fsum_}, L{fsum1} and 

1749 L{fsum1_} plus partials summation are based on Python's 

1750 C{math.fsum} or not. 

1751 

1752 @return: C{2} if all functions and partials summation 

1753 are based on C{math.fsum}, C{True} if only 

1754 the functions are based on C{math.fsum} (and 

1755 partials summation is not) or C{False} if 

1756 none are. 

1757 ''' 

1758 f = Fsum._math_fsum 

1759 return 2 if _psum is f else bool(f) 

1760 

1761 def is_scalar(self, **raiser_RESIDUAL): 

1762 '''Is this instance' running sum C{scalar} without residual or with 

1763 a residual I{ratio} not exceeding the RESIDUAL threshold? 

1764 

1765 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore 

1766 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar} 

1767 to override the current L{RESIDUAL<Fsum.RESIDUAL>}. 

1768 

1769 @return: C{True} if this instance' non-zero residual C{ratio} exceeds 

1770 the L{RESIDUAL<Fsum.RESIDUAL>} threshold (C{bool}). 

1771 

1772 @raise ResidualError: Non-zero, significant residual or invalid 

1773 B{C{RESIDUAL}}. 

1774 

1775 @see: Method L{Fsum.RESIDUAL}, L{Fsum.is_integer} and property 

1776 L{Fsum.as_iscalar}. 

1777 ''' 

1778 s, r = self._fprs2 

1779 return False if r and self._raiser(r, s, **raiser_RESIDUAL) else True 

1780 

1781 def _mul_Fsum(self, other, op=_mul_op_): # in .fmath.Fhorner 

1782 '''(INTERNAL) Return C{B{self} * B{other}} as L{Fsum} or C{0}. 

1783 ''' 

1784 # assert _isFsumTuple(other) 

1785 if self._ps and other._ps: 

1786 f = self._ps_mul(op, *other._ps) # NO .as_iscalar! 

1787 else: 

1788 f = _0_0 

1789 return f 

1790 

1791 def _mul_scalar(self, factor, op): # in .fmath.Fhorner 

1792 '''(INTERNAL) Return C{B{self} * scalar B{factor}} as L{Fsum}, C{0.0} or C{self}. 

1793 ''' 

1794 # assert isscalar(factor) 

1795 if self._ps and self._finite(factor, op): 

1796 f = self if factor == _1_0 else ( 

1797 self._neg if factor == _N_1_0 else 

1798 self._ps_mul(op, factor).as_iscalar) 

1799 else: 

1800 f = _0_0 

1801 return f 

1802 

1803# @property_RO 

1804# def _n_d(self): 

1805# n, d = self.as_integer_ratio() 

1806# return n / d 

1807 

1808 @property_RO 

1809 def _neg(self): 

1810 '''(INTERNAL) Return C{Fsum(-self)} or scalar C{NEG0}. 

1811 ''' 

1812 return _Psum(self._ps_neg) if self._ps else NEG0 

1813 

1814 @property_RO 

1815 def partials(self): 

1816 '''Get this instance' current, partial sums (C{tuple} of C{float}s). 

1817 ''' 

1818 return tuple(self._ps) 

1819 

1820 def pow(self, x, *mod, **raiser_RESIDUAL): 

1821 '''Return C{B{self}**B{x}} as L{Fsum}. 

1822 

1823 @arg x: The exponent (C{scalar} or L{Fsum}). 

1824 @arg mod: Optional modulus (C{int} or C{None}) for the 3-argument 

1825 C{pow(B{self}, B{other}, B{mod})} version. 

1826 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore 

1827 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar} 

1828 to override the current L{RESIDUAL<Fsum.RESIDUAL>}. 

1829 

1830 @return: The C{pow(self, B{x})} or C{pow(self, B{x}, *B{mod})} 

1831 result (L{Fsum}). 

1832 

1833 @raise ResidualError: Non-zero, significant residual or invalid 

1834 B{C{RESIDUAL}}. 

1835 

1836 @note: If B{C{mod}} is given and C{None}, the result will be an 

1837 C{integer} L{Fsum} provided this instance C{is_integer} 

1838 or set to C{integer} by an L{Fsum.fint} call. 

1839 

1840 @see: Methods L{Fsum.__ipow__}, L{Fsum.fint}, L{Fsum.is_integer} 

1841 and L{Fsum.root}. 

1842 ''' 

1843 f = self._copy_2(self.pow) 

1844 return f._fpow(x, _pow_op_, *mod, **raiser_RESIDUAL) # f = pow(f, x, *mod) 

1845 

1846 def _pow(self, other, unused, op, **raiser_RESIDUAL): 

1847 '''Return C{B{self} ** B{other}}. 

1848 ''' 

1849 if _isFsumTuple(other): 

1850 f = self._pow_Fsum(other, op, **raiser_RESIDUAL) 

1851 elif self._scalar(other, op): 

1852 x = self._finite(other, op) 

1853 f = self._pow_scalar(x, other, op, **raiser_RESIDUAL) 

1854 else: 

1855 f = self._pow_0_1(0, other) 

1856 return f 

1857 

1858 def _pow_0_1(self, x, other): 

1859 '''(INTERNAL) Return B{C{self}**1} or C{B{self}**0 == 1.0}. 

1860 ''' 

1861 return self if x else (1 if isint(other) and self.is_integer() else _1_0) 

1862 

1863 def _pow_2_3(self, b, x, other, op, *mod, **raiser_RESIDUAL): 

1864 '''(INTERNAL) 2-arg C{pow(B{b}, scalar B{x})} and 3-arg C{pow(B{b}, 

1865 B{x}, int B{mod} or C{None})}, embellishing errors. 

1866 ''' 

1867 

1868 if mod: # b, x, mod all C{int}, unless C{mod} is C{None} 

1869 m = mod[0] 

1870 # assert _isFsumTuple(b) 

1871 

1872 def _s(s, r): 

1873 R = self._raiser(r, s, **raiser_RESIDUAL) 

1874 if R: 

1875 raise self._ResidualError(op, other, r, mod=m, **R) 

1876 return s 

1877 

1878 b = _s(*(b._fprs2 if m is None else b._fint2)) 

1879 x = _s(*_2scalar2(x)) 

1880 

1881 try: 

1882 # 0**INF == 0.0, 1**INF == 1.0, -1**2.3 == -(1**2.3) 

1883 s = pow(b, x, *mod) 

1884 if iscomplex(s): 

1885 # neg**frac == complex in Python 3+, but ValueError in 2- 

1886 raise ValueError(_strcomplex(s, b, x, *mod)) 

1887 return self._finite(s) 

1888 except Exception as X: 

1889 raise self._ErrorX(X, op, other, *mod) 

1890 

1891 def _pow_Fsum(self, other, op, **raiser_RESIDUAL): 

1892 '''(INTERNAL) Return C{B{self} **= B{other}} for C{_isFsumTuple(other)}. 

1893 ''' 

1894 # assert _isFsumTuple(other) 

1895 x, r = other._fprs2 

1896 f = self._pow_scalar(x, other, op, **raiser_RESIDUAL) 

1897 if f and r: 

1898 f *= self._pow_scalar(r, other, op, **raiser_RESIDUAL) 

1899 return f 

1900 

1901 def _pow_int(self, x, other, op, **raiser_RESIDUAL): 

1902 '''(INTERNAL) Return C{B{self} **= B{x}} for C{int B{x} >= 0}. 

1903 ''' 

1904 # assert isint(x) and x >= 0 

1905 ps = self._ps 

1906 if len(ps) > 1: 

1907 _mul_Fsum = Fsum._mul_Fsum 

1908 if x > 4: 

1909 p = self 

1910 f = self if (x & 1) else _Psum_(_1_0) 

1911 m = x >> 1 # // 2 

1912 while m: 

1913 p = _mul_Fsum(p, p, op) # p **= 2 

1914 if (m & 1): 

1915 f = _mul_Fsum(f, p, op) # f *= p 

1916 m >>= 1 # //= 2 

1917 elif x > 1: # self**2, 3, or 4 

1918 f = _mul_Fsum(self, self, op) 

1919 if x > 2: # self**3 or 4 

1920 p = self if x < 4 else f 

1921 f = _mul_Fsum(f, p, op) 

1922 else: # self**1 or self**0 == 1 or _1_0 

1923 f = self._pow_0_1(x, other) 

1924 elif ps: # self._ps[0]**x 

1925 f = self._pow_2_3(ps[0], x, other, op, **raiser_RESIDUAL) 

1926 else: # PYCHOK no cover 

1927 # 0**pos_int == 0, but 0**0 == 1 

1928 f = 0 if x else 1 

1929 return f 

1930 

1931 def _pow_scalar(self, x, other, op, **raiser_RESIDUAL): 

1932 '''(INTERNAL) Return C{self**B{x}} for C{scalar B{x}}. 

1933 ''' 

1934 s, r = self._fprs2 

1935 if r: 

1936 # assert s != 0 

1937 if isint(x, both=True): # self**int 

1938 x = int(x) 

1939 y = abs(x) 

1940 if y > 1: 

1941 f = self._pow_int(y, other, op, **raiser_RESIDUAL) 

1942 if x > 0: # i.e. > 1 

1943 return f # Fsum or scalar 

1944 # assert x < 0 # i.e. < -1 

1945 if _isFsum(f): 

1946 s, r = f._fprs2 

1947 if r: 

1948 return _1_Over(f, op, **raiser_RESIDUAL) 

1949 else: # scalar 

1950 s = f 

1951 # use s**(-1) to get the CPython 

1952 # float_pow error iff s is zero 

1953 x = -1 

1954 elif x < 0: # self**(-1) 

1955 return _1_Over(self, op, **raiser_RESIDUAL) # 1 / self 

1956 else: # self**1 or self**0 

1957 return self._pow_0_1(x, other) # self, 1 or 1.0 

1958 else: # self**fractional 

1959 R = self._raiser(r, s, **raiser_RESIDUAL) 

1960 if R: 

1961 raise self._ResidualError(op, other, r, **R) 

1962 n, d = self.as_integer_ratio() 

1963 if abs(n) > abs(d): 

1964 n, d, x = d, n, (-x) 

1965 s = n / d 

1966 # assert isscalar(s) and isscalar(x) 

1967 return self._pow_2_3(s, x, other, op, **raiser_RESIDUAL) 

1968 

1969 def _ps_acc(self, ps, xs, up=True, **unused): 

1970 '''(INTERNAL) Accumulate C{xs} known scalars into list C{ps}. 

1971 ''' 

1972 n = 0 

1973 _2s = _2sum 

1974 for x in (tuple(xs) if xs is ps else xs): 

1975 # assert isscalar(x) and _isfinite(x) 

1976 if x: 

1977 i = 0 

1978 for p in ps: 

1979 x, p = _2s(x, p) 

1980 if p: 

1981 ps[i] = p 

1982 i += 1 

1983 ps[i:] = (x,) if x else () 

1984 n += 1 

1985 if n: 

1986 self._n += n 

1987 # Fsum._ps_max = max(Fsum._ps_max, len(ps)) 

1988 if up: 

1989 self._update() 

1990 return ps 

1991 

1992 def _ps_mul(self, op, *factors): 

1993 '''(INTERNAL) Multiply this instance' C{partials} with 

1994 each scalar C{factor} and accumulate into an C{Fsum}. 

1995 ''' 

1996 def _pfs(ps, fs): 

1997 if len(ps) < len(fs): 

1998 ps, fs = fs, ps 

1999 if self._f2product: 

2000 ps = tuple(_2split3s(ps)) 

2001 _xys = _2products 

2002 else: 

2003 def _xys(x, ys): 

2004 return (x * y for y in ys) 

2005 

2006 _fin = _isfinite 

2007 for f in fs: 

2008 for p in _xys(f, ps): 

2009 yield p if _fin(p) else self._finite(p, op) 

2010 

2011 return Fsum()._facc_scalar(_pfs(self._ps, factors), up=False) 

2012 

2013 @property_RO 

2014 def _ps_neg(self): 

2015 '''(INTERNAL) Yield the partials, I{negated}. 

2016 ''' 

2017 for p in self._ps: 

2018 yield -p 

2019 

2020 def _ps_other(self, op, *others): 

2021 '''(INTERNAL) Yield the partials of all C{other}s. 

2022 ''' 

2023 for other in others: 

2024 if _isFsumTuple(other): 

2025 for p in other._ps: 

2026 yield p 

2027 else: 

2028 yield self._scalar(other, op) 

2029 

2030 def _ps_1sum(self, *less): 

2031 '''(INTERNAL) Return the partials sum, 1-primed C{less} some scalars. 

2032 ''' 

2033 def _1pls(ps, ls): 

2034 yield _1_0 

2035 for p in ps: 

2036 yield p 

2037 for p in ls: 

2038 yield -p 

2039 yield _N_1_0 

2040 

2041 return _fsum(_1pls(self._ps, less)) 

2042 

2043 def _raiser(self, r, s, raiser=True, **RESIDUAL): 

2044 '''(INTERNAL) Does ratio C{r / s} exceed the RESIDUAL threshold 

2045 I{and} is residual C{r} I{non-zero} or I{significant} (for a 

2046 negative respectively positive C{RESIDUAL} threshold)? 

2047 ''' 

2048 if r and raiser: 

2049 t = self._RESIDUAL 

2050 if RESIDUAL: 

2051 t = _threshold(t, **RESIDUAL) 

2052 if t < 0 or (s + r) != s: 

2053 q = (r / s) if s else s # == 0. 

2054 if fabs(q) > fabs(t): 

2055 return dict(ratio=q, R=t) 

2056 return {} 

2057 

2058 rdiv = __rtruediv__ 

2059 

2060 @property_RO 

2061 def real(self): 

2062 '''Get the C{real} part of this instance (C{float}). 

2063 

2064 @see: Methods L{Fsum.__float__} and L{Fsum.fsum} 

2065 and properties L{Fsum.ceil}, L{Fsum.floor}, 

2066 L{Fsum.imag} and L{Fsum.residual}. 

2067 ''' 

2068 return float(self._fprs) 

2069 

2070 @property_RO 

2071 def residual(self): 

2072 '''Get this instance' residual (C{float} or C{int}): the 

2073 C{sum(partials)} less the precision running sum C{fsum}. 

2074 

2075 @note: The C{residual is INT0} iff the precision running 

2076 C{fsum} is considered to be I{exact}. 

2077 

2078 @see: Methods L{Fsum.fsum}, L{Fsum.fsum2} and L{Fsum.is_exact}. 

2079 ''' 

2080 return self._fprs2.residual 

2081 

2082 def RESIDUAL(self, *threshold): 

2083 '''Get and set this instance' I{ratio} for raising L{ResidualError}s, 

2084 overriding the default from env variable C{PYGEODESY_FSUM_RESIDUAL}. 

2085 

2086 @arg threshold: If C{scalar}, the I{ratio} to exceed for raising 

2087 L{ResidualError}s in division and exponention, if 

2088 C{None} restore the default set with env variable 

2089 C{PYGEODESY_FSUM_RESIDUAL} or if omitted, keep the 

2090 current setting. 

2091 

2092 @return: The previous C{RESIDUAL} setting (C{float}), default C{0.0}. 

2093 

2094 @raise ResidualError: Invalid B{C{threshold}}. 

2095 

2096 @note: L{ResidualError}s may be thrown if (1) the non-zero I{ratio} 

2097 C{residual / fsum} exceeds the given B{C{threshold}} and (2) 

2098 the C{residual} is non-zero and (3) I{significant} vs the 

2099 C{fsum}, i.e. C{(fsum + residual) != fsum} and (4) optional 

2100 keyword argument C{raiser=False} is missing. Specify a 

2101 negative B{C{threshold}} for only non-zero C{residual} 

2102 testing without I{significant}. 

2103 ''' 

2104 r = self._RESIDUAL 

2105 if threshold: 

2106 t = threshold[0] 

2107 self._RESIDUAL = Fsum._RESIDUAL if t is None else ( # for ... 

2108 (_0_0 if t else _1_0) if isbool(t) else 

2109 _threshold(t)) # ... backward compatibility 

2110 return r 

2111 

2112 def _ResidualError(self, op, other, residual, **mod_R): 

2113 '''(INTERNAL) Non-zero B{C{residual}} etc. 

2114 ''' 

2115 def _p(mod=None, R=0, **unused): # ratio=0 

2116 return (_non_zero_ if R < 0 else _significant_) \ 

2117 if mod is None else _integer_ 

2118 

2119 t = _stresidual(_p(**mod_R), residual, **mod_R) 

2120 return self._Error(op, other, ResidualError, txt=t) 

2121 

2122 def root(self, root, **raiser_RESIDUAL): 

2123 '''Return C{B{self}**(1 / B{root})} as L{Fsum}. 

2124 

2125 @arg root: The order (C{scalar} or L{Fsum}), non-zero. 

2126 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} to ignore 

2127 L{ResidualError}s (C{bool}) and C{B{RESIDUAL}=scalar} 

2128 to override the current L{RESIDUAL<Fsum.RESIDUAL>}. 

2129 

2130 @return: The C{self ** (1 / B{root})} result (L{Fsum}). 

2131 

2132 @raise ResidualError: Non-zero, significant residual or invalid 

2133 B{C{RESIDUAL}}. 

2134 

2135 @see: Method L{Fsum.pow}. 

2136 ''' 

2137 x = _1_Over(root, _truediv_op_, **raiser_RESIDUAL) 

2138 f = self._copy_2(self.root) 

2139 return f._fpow(x, f.name, **raiser_RESIDUAL) # == pow(f, x) 

2140 

2141 def _scalar(self, other, op, **txt): 

2142 '''(INTERNAL) Return scalar C{other}. 

2143 ''' 

2144 if isscalar(other): 

2145 return other 

2146 raise self._Error(op, other, _TypeError, **txt) # _invalid_ 

2147 

2148 def signOf(self, res=True): 

2149 '''Determine the sign of this instance. 

2150 

2151 @kwarg res: If C{True}, consider, otherwise ignore 

2152 the residual (C{bool}). 

2153 

2154 @return: The sign (C{int}, -1, 0 or +1). 

2155 ''' 

2156 s, r = self._fprs2 

2157 r = (-r) if res else 0 

2158 return _signOf(s, r) 

2159 

2160 def toRepr(self, **lenc_prec_sep_fmt): # PYCHOK signature 

2161 '''Return this C{Fsum} instance as representation. 

2162 

2163 @kwarg lenc_prec_sep_fmt: Optional keyword arguments 

2164 for method L{Fsum.toStr}. 

2165 

2166 @return: This instance (C{repr}). 

2167 ''' 

2168 return Fmt.repr_at(self, self.toStr(**lenc_prec_sep_fmt)) 

2169 

2170 def toStr(self, lenc=True, **prec_sep_fmt): # PYCHOK signature 

2171 '''Return this C{Fsum} instance as string. 

2172 

2173 @kwarg lenc: If C{True}, include the current C{[len]} of this 

2174 L{Fsum} enclosed in I{[brackets]} (C{bool}). 

2175 @kwarg prec_sep_fmt: Optional keyword arguments for method 

2176 L{Fsum2Tuple.toStr}. 

2177 

2178 @return: This instance (C{str}). 

2179 ''' 

2180 p = self.classname 

2181 if lenc: 

2182 p = Fmt.SQUARE(p, len(self)) 

2183 n = _enquote(self.name, white=_UNDER_) 

2184 t = self._fprs2.toStr(**prec_sep_fmt) 

2185 return NN(p, _SPACE_, n, t) 

2186 

2187 def _truediv(self, other, op, **raiser_RESIDUAL): 

2188 '''(INTERNAL) Return C{B{self} / B{other}} as an L{Fsum}. 

2189 ''' 

2190 f = self._copy_2(self.__truediv__) 

2191 return f._ftruediv(other, op, **raiser_RESIDUAL) 

2192 

2193 def _update(self, updated=True): # see ._fset 

2194 '''(INTERNAL) Zap all cached C{Property_RO} values. 

2195 ''' 

2196 if updated: 

2197 _pop = self.__dict__.pop 

2198 for p in _ROs: 

2199 _ = _pop(p, None) 

2200# Fsum._fint2._update(self) 

2201# Fsum._fprs ._update(self) 

2202# Fsum._fprs2._update(self) 

2203 return self # for .fset_ 

2204 

2205_ROs = _allPropertiesOf_n(3, Fsum, Property_RO) # PYCHOK see Fsum._update 

2206 

2207 

2208def _Float_Int(arg, **name_Error): 

2209 '''(INTERNAL) Unit of L{Fsum2Tuple} items. 

2210 ''' 

2211 U = Int if isint(arg) else Float 

2212 return U(arg, **name_Error) 

2213 

2214 

2215def Fsum2product(*xs, **name_RESIDUAL): 

2216 '''Return an L{Fsum} with L{f2product<Fsum.f2product>} accurate 

2217 multiplication I{turned on}. 

2218 ''' 

2219 F = Fsum(*xs, **name_RESIDUAL) 

2220 F.f2product(True) 

2221 return F 

2222 

2223 

2224class DivMod2Tuple(_NamedTuple): 

2225 '''2-Tuple C{(div, mod)} with the quotient C{div} and remainder 

2226 C{mod} results of a C{divmod} operation. 

2227 

2228 @note: Quotient C{div} an C{int} in Python 3+ but a C{float} 

2229 in Python 2-. Remainder C{mod} an L{Fsum} instance. 

2230 ''' 

2231 _Names_ = (_div_, _mod_) 

2232 _Units_ = (_Float_Int, Fsum) 

2233 

2234 

2235class Fsum2Tuple(_NamedTuple): # in .fstats 

2236 '''2-Tuple C{(fsum, residual)} with the precision running C{fsum} 

2237 and the C{residual}, the sum of the remaining partials. Each 

2238 item is C{float} or C{int}. 

2239 

2240 @note: If the C{residual is INT0}, the C{fsum} is considered 

2241 to be I{exact}, see method L{Fsum2Tuple.is_exact}. 

2242 ''' 

2243 _Names_ = ( Fsum.fsum.__name__, Fsum.residual.name) 

2244 _Units_ = (_Float_Int, _Float_Int) 

2245 

2246 def __abs__(self): # in .fmath 

2247 return self._Fsum.__abs__() 

2248 

2249 def __bool__(self): # PYCHOK Python 3+ 

2250 return bool(self._Fsum) 

2251 

2252 def __eq__(self, other): 

2253 return self._other_op(other, self.__eq__) 

2254 

2255 def __float__(self): 

2256 return self._Fsum.__float__() 

2257 

2258 def __ge__(self, other): 

2259 return self._other_op(other, self.__ge__) 

2260 

2261 def __gt__(self, other): 

2262 return self._other_op(other, self.__gt__) 

2263 

2264 def __le__(self, other): 

2265 return self._other_op(other, self.__le__) 

2266 

2267 def __lt__(self, other): 

2268 return self._other_op(other, self.__lt__) 

2269 

2270 def __int__(self): 

2271 return self._Fsum.__int__() 

2272 

2273 def __ne__(self, other): 

2274 return self._other_op(other, self.__ne__) 

2275 

2276 def __neg__(self): 

2277 return self._Fsum.__neg__() 

2278 

2279 __nonzero__ = __bool__ # Python 2- 

2280 

2281 def __pos__(self): 

2282 return self._Fsum.__pos__() 

2283 

2284 def as_integer_ratio(self): 

2285 '''Return this instance as the ratio of 2 integers. 

2286 

2287 @see: Method L{Fsum.as_integer_ratio} for further details. 

2288 ''' 

2289 return self._Fsum.as_integer_ratio() 

2290 

2291 @property_RO 

2292 def _fint2(self): 

2293 return self._Fsum._fint2 

2294 

2295 @property_RO 

2296 def _fprs2(self): 

2297 return self._Fsum._fprs2 

2298 

2299 @Property_RO 

2300 def _Fsum(self): # this C{Fsum2Tuple} as L{Fsum}, in .fstats 

2301 s, r = _s_r(*self) 

2302 ps = (r, s) if r else (s,) 

2303 return _Psum(ps, name=self.name) 

2304 

2305 def Fsum_(self, *xs, **name_RESIDUAL): 

2306 '''Return this C{Fsum2Tuple} as an L{Fsum} plus some C{xs}. 

2307 ''' 

2308 f = _Psum(self._Fsum._ps, **name_RESIDUAL) 

2309 return f._facc_1(xs, up=False) if xs else f 

2310 

2311 def is_exact(self): 

2312 '''Is this L{Fsum2Tuple} considered to be exact? (C{bool}). 

2313 ''' 

2314 return self._Fsum.is_exact() 

2315 

2316 def is_integer(self): 

2317 '''Is this L{Fsum2Tuple} C{integer}? (C{bool}). 

2318 ''' 

2319 return self._Fsum.is_integer() 

2320 

2321 def _mul_scalar(self, other, op): # for Fsum._fmul 

2322 return self._Fsum._mul_scalar(other, op) 

2323 

2324 @property_RO 

2325 def _n(self): 

2326 return self._Fsum._n 

2327 

2328 def _other_op(self, other, which): 

2329 C, s = (tuple, self) if isinstance(other, tuple) else (Fsum, self._Fsum) 

2330 return getattr(C, which.__name__)(s, other) 

2331 

2332 @property_RO 

2333 def _ps(self): 

2334 return self._Fsum._ps 

2335 

2336 @property_RO 

2337 def _ps_neg(self): 

2338 return self._Fsum._ps_neg 

2339 

2340 def signOf(self, **res): 

2341 '''Like method L{Fsum.signOf}. 

2342 ''' 

2343 return self._Fsum.signOf(**res) 

2344 

2345 def toStr(self, fmt=Fmt.g, **prec_sep): # PYCHOK signature 

2346 '''Return this L{Fsum2Tuple} as string (C{str}). 

2347 

2348 @kwarg fmt: Optional C{float} format (C{letter}). 

2349 @kwarg prec_sep: Optional keyword arguments for function 

2350 L{fstr<streprs.fstr>}. 

2351 ''' 

2352 return Fmt.PAREN(fstr(self, fmt=fmt, strepr=str, force=False, **prec_sep)) 

2353 

2354_Fsum_Fsum2Tuple_types = Fsum, Fsum2Tuple # PYCHOK lines 

2355 

2356 

2357class ResidualError(_ValueError): 

2358 '''Error raised for a division, power or root operation of 

2359 an L{Fsum} instance with a C{residual} I{ratio} exceeding 

2360 the L{RESIDUAL<Fsum.RESIDUAL>} threshold. 

2361 

2362 @see: Module L{pygeodesy.fsums} and method L{Fsum.RESIDUAL}. 

2363 ''' 

2364 pass 

2365 

2366 

2367try: 

2368 from math import fsum as _fsum # precision IEEE-754 sum, Python 2.6+ 

2369 

2370 # make sure _fsum works as expected (XXX check 

2371 # float.__getformat__('float')[:4] == 'IEEE'?) 

2372 if _fsum((1, 1e101, 1, -1e101)) != 2: # PYCHOK no cover 

2373 del _fsum # nope, remove _fsum ... 

2374 raise ImportError() # ... use _fsum below 

2375 

2376 Fsum._math_fsum = _sum = _fsum # PYCHOK exported 

2377except ImportError: 

2378 _sum = sum # Fsum(NAN) exception fall-back, in .elliptic 

2379 

2380 def _fsum(xs): 

2381 '''(INTERNAL) Precision summation, Python 2.5-. 

2382 ''' 

2383 F = Fsum() 

2384 F.name = _fsum.__name__ 

2385 return F._facc(xs, up=False)._fprs2.fsum 

2386 

2387 

2388def fsum(xs, floats=False): 

2389 '''Precision floating point summation based on/like Python's C{math.fsum}. 

2390 

2391 @arg xs: Iterable of items to add (each C{scalar} or an L{Fsum} or L{Fsum2Tuple} 

2392 instance). 

2393 @kwarg floats: Use C{B{floats}=True} iff I{all} B{C{xs}} items are I{known to 

2394 be scalar} (C{bool}). 

2395 

2396 @return: Precision C{fsum} (C{float}). 

2397 

2398 @raise OverflowError: Partial C{2sum} overflow. 

2399 

2400 @raise TypeError: Non-scalar B{C{xs}} item. 

2401 

2402 @raise ValueError: Invalid or non-finite B{C{xs}} item. 

2403 

2404 @note: Exception and I{non-finite} handling may differ if not based 

2405 on Python's C{math.fsum}. 

2406 

2407 @see: Class L{Fsum} and methods L{Fsum.fsum} and L{Fsum.fadd}. 

2408 ''' 

2409 return _fsum(xs if floats is True else _2floats(xs)) if xs else _0_0 # PYCHOK yield 

2410 

2411 

2412def fsum_(*xs, **floats): 

2413 '''Precision floating point summation of all positional items. 

2414 

2415 @arg xs: Items to add (each C{scalar} or an L{Fsum} or L{Fsum2Tuple} instance), 

2416 all positional. 

2417 @kwarg floats: Use C{B{floats}=True} iff I{all} B{C{xs}} items are I{known to 

2418 be scalar} (C{bool}). 

2419 

2420 @see: Function L{fsum<fsums.fsum>} for further details. 

2421 ''' 

2422 return _fsum(xs if _xkwds_get1(floats, floats=False) is True else 

2423 _2floats(xs, origin=1)) if xs else _0_0 # PYCHOK yield 

2424 

2425 

2426def fsumf_(*xs): 

2427 '''Precision floating point summation iff I{all} C{B{xs}} items are I{known to be scalar}. 

2428 

2429 @see: Function L{fsum_<fsums.fsum_>} for further details. 

2430 ''' 

2431 return _fsum(xs) if xs else _0_0 

2432 

2433 

2434def fsum1(xs, floats=False): 

2435 '''Precision floating point summation, 1-primed. 

2436 

2437 @arg xs: Iterable of items to add (each C{scalar} or an L{Fsum} or L{Fsum2Tuple} 

2438 instance). 

2439 @kwarg floats: Use C{B{floats}=True} iff I{all} B{C{xs}} items are I{known to 

2440 be scalar} (C{bool}). 

2441 

2442 @see: Function L{fsum<fsums.fsum>} for further details. 

2443 ''' 

2444 return _fsum(_1primed(xs if floats is True else _2floats(xs))) if xs else _0_0 # PYCHOK yield 

2445 

2446 

2447def fsum1_(*xs, **floats): 

2448 '''Precision floating point summation, 1-primed of all positional items. 

2449 

2450 @arg xs: Items to add (each C{scalar} or an L{Fsum} or L{Fsum2Tuple} instance), 

2451 all positional. 

2452 @kwarg floats: Use C{B{floats}=True} iff I{all} B{C{xs}} items are I{known to 

2453 be scalar} (C{bool}). 

2454 

2455 @see: Function L{fsum_<fsums.fsum_>} for further details. 

2456 ''' 

2457 return _fsum(_1primed(xs if _xkwds_get1(floats, floats=False) is True else 

2458 _2floats(xs, origin=1))) if xs else _0_0 # PYCHOK yield 

2459 

2460 

2461def fsum1f_(*xs): 

2462 '''Precision floating point summation iff I{all} C{B{xs}} items are I{known to be scalar}. 

2463 

2464 @see: Function L{fsum_<fsums.fsum_>} for further details. 

2465 ''' 

2466 return _fsum(_1primed(xs)) if xs else _0_0 

2467 

2468 

2469if __name__ == '__main__': 

2470 

2471 # usage: [env _psum=fsum] python3 -m pygeodesy.fsums 

2472 

2473 if _getenv(_psum.__name__, NN) == _fsum.__name__: 

2474 _psum = _fsum 

2475 

2476 def _test(n): 

2477 # copied from Hettinger, see L{Fsum} reference 

2478 from pygeodesy import frandoms, printf 

2479 

2480 printf(_fsum.__name__, end=_COMMASPACE_) 

2481 printf(_psum.__name__, end=_COMMASPACE_) 

2482 

2483 F = Fsum() 

2484 if F.is_math_fsum(): 

2485 for t in frandoms(n, seeded=True): 

2486 assert float(F.fset_(*t)) == _fsum(t) 

2487 printf(_DOT_, end=NN) 

2488 printf(NN) 

2489 

2490 _test(128) 

2491 

2492# **) MIT License 

2493# 

2494# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved. 

2495# 

2496# Permission is hereby granted, free of charge, to any person obtaining a 

2497# copy of this software and associated documentation files (the "Software"), 

2498# to deal in the Software without restriction, including without limitation 

2499# the rights to use, copy, modify, merge, publish, distribute, sublicense, 

2500# and/or sell copies of the Software, and to permit persons to whom the 

2501# Software is furnished to do so, subject to the following conditions: 

2502# 

2503# The above copyright notice and this permission notice shall be included 

2504# in all copies or substantial portions of the Software. 

2505# 

2506# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

2507# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

2508# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

2509# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

2510# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 

2511# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 

2512# OTHER DEALINGS IN THE SOFTWARE.