1

2# -*- coding: utf-8 -*-

3

4 u'''Class L{Fsum} for precision floating point summation and I{running}

5 summation based on, respectively similar to Python's C{math.fsum}.

6

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

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

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

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

11

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

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

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

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

16

17 Set env variable C{PYGEODESY_FSUM_PARTIALS} to string C{"fsum"}) for summation

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

19

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

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

22 of an L{Fsum} instance with a I{relative} C{residual} exceeding the threshold,

23 see methods L{Fsum.RESIDUAL}, L{Fsum.pow}, L{Fsum.__ipow__} and L{Fsum.__itruediv__}.

24'''

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

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

27

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

29 signOf, _signOf

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

31 _0_0, _1_0, _N_1_0, Float, Int

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

33 _ValueError, _xError, _xError2, _xkwds_get, \

34 _ZeroDivisionError

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

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

37 _NOTEQUAL_, _not_finite_, _PERCENT_, _PLUS_, _R_, \

38 _RANGLE_, _SLASH_, _SPACE_, _STAR_, _UNDER_

39 from pygeodesy.lazily import _ALL_LAZY, _getenv, _sys_version_info2

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

41 from pygeodesy.props import _allPropertiesOf_n, deprecated_property_RO, \

42 Property_RO, property_RO

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

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

45

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

47

48__all__ = _ALL_LAZY.fsums

49__version__ = '24.04.24'

50

51_add_op_ = _PLUS_ # in .auxilats.auxAngle

52_eq_op_ = _EQUAL_ * 2 # _DEQUAL_

53_COMMASPACE_R_ = _COMMASPACE_ + _R_

54_div_ = 'div'

55_exceeds_R_ = _SPACE_ + _exceeds_(_R_)

56_floordiv_op_ = _SLASH_ * 2 # _DSLASH_

57_fset_op_ = _EQUAL_

58_ge_op_ = _RANGLE_ + _EQUAL_

59_gt_op_ = _RANGLE_

60_integer_ = 'integer'

61_le_op_ = _LANGLE_ + _EQUAL_

62_lt_op_ = _LANGLE_

63_mod_ = 'mod'

64_mod_op_ = _PERCENT_

65_mul_op_ = _STAR_

66_ne_op_ = _NOTEQUAL_

67_non_zero_ = 'non-zero'

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

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

70_truediv_op_ = _SLASH_

71_divmod_op_ = _floordiv_op_ + _mod_op_

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

73

74

75 def _2delta(*ab):

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

77 '''

78 try:

79 a, b = _2sum(*ab)

80 except _OverflowError:

81 a, b = ab

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

83

84

85 def _2error(unused):

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

87 '''

88 raise ValueError(_not_finite_)

89

90

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

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

93 '''

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

95 try:

96 v = float(v)

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

98 except Exception as X:

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

100

101

102 def _X_ps(X): # for _2floats only

103 return X._ps

104

105

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

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

108 '''

109 try:

110 i, x = origin, None

111 _fin = _isfinite

112 _Fs = Fsum

113 for x in xs:

114 if isinstance(x, _Fs):

115 for p in _X(x):

116 yield p

117 else:

118 f = _x(x)

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

120 i += 1

121 except Exception as X:

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

123

124

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

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

127 '''

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

129

130

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

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

133 '''

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

135

136

137 def _2halfeven(s, r, p):

138 '''(INTERNAL) Round half-even.

139 '''

140 if (p > 0 and r > 0) or \

141 (p < 0 and r < 0): # signs match

142 r *= 2

143 t = s + r

144 if r == (t - s):

145 s = t

146 return s

147

148

149 def _1_over(x, op=_truediv_op_, **raiser):

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

151 '''

152 return _Psum_(_1_0)._ftruediv(x, op, **raiser)

153

154

155 def _1primed(xs): # in .fmath

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

157 items, all I{known} to be C{finite float}.

158 '''

159 yield _1_0

160 for x in xs:

161 yield x

162 yield _N_1_0

163

164

165 def _2ps(s, r):

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

167 '''

168 if fabs(s) < fabs(r):

169 s, r = r, s

170 return (r, s) if r else (s,) # PYCHOK types

171

172

173 def _psum(ps): # PYCHOK used!

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

175 '''

176 # assert isinstance(ps, list)

177 i = len(ps) - 1

178 s = _0_0 if i < 0 else ps[i]

179 _2s = _2sum

180 while i > 0:

181 i -= 1

182 s, r = _2s(s, ps[i])

183 if r: # sum(ps) became inexact

184 if s:

185 ps[i:] = r, s

186 if i > 0:

187 s = _2halfeven(s, r, ps[i-1])

188 break # return s

189 s = r # PYCHOK no cover

190 ps[i:] = s,

191 return s

192

193

194 def _Psum(ps, **name):

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

196 '''

197 F = Fsum(**name) if name else Fsum()

198 if ps:

199 F._ps[:] = ps

200 F._n = len(F._ps)

201 return F

202

203

204 def _Psum_(*ps, **name):

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

206 '''

207 return _Psum(ps, **name)

208

209

210 def _2scalar(other, _raiser=None, **mod):

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

212 '''

213 if isinstance(other, Fsum):

214 s, r = other._fint2

215 if r:

216 s, r = other._fprs2

217 if r: # PYCHOK no cover

218 if _raiser and _raiser(r, s):

219 t = _stresidual(_non_zero_, r, **mod)

220 raise ResidualError(t, txt=None)

221 s = other # L{Fsum} as-is

222 else:

223 s = other # C{type} as-is

224 if isint(s, both=True):

225 s = int(s)

226 return s

227

228

229 def _strcomplex(s, *args):

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

231 '''

232 c = _strcomplex.__name__[4:]

233 n = _DASH_(len(args), _arg_)

234 t = unstr(pow, *args)

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

236

237

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

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

240 '''

241 p = _stresidual.__name__[3:]

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

243 for n, v in itemsorted(name_values):

244 n = n.replace(_UNDER_, _SPACE_)

245 p = Fmt.PARENSPACED(n, Fmt(v))

246 t = _COMMASPACE_(t, p)

247 return _SPACE_(prefix, t)

248

249

250 def _2sum(a, b): # by .testFmath

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

252 '''

253 s = a + b

254 if _isfinite(s):

255 if fabs(a) < fabs(b):

256 b, a = a, b

257 return s, (b - (s - a))

258 u = unstr(_2sum, a, b)

259 t = Fmt.PARENSPACED(_not_finite_, s)

260 raise _OverflowError(u, txt=t)

261

262

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

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

265

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

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

268 intermediate, I{running} summuation.

269

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

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

272

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

274 Python's C{math.fsum}.

275

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

277 393090_Binary_floating_point_summatiaccurate_full/recipe-393090.py>},

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

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

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

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

282 '''

283 _math_fsum = None

284 _n = 0

285# _ps = [] # partial sums

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

287 _ratio = None # see method _raiser

288 _recursive = bool(_getenv('PYGEODESY_FSUM_RECURSIVE', NN))

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

290

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

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

293

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

295 or an L{Fsum} instance).

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

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

298

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

300 '''

301 if name_RESIDUAL:

302 n = _xkwds_get(name_RESIDUAL, name=NN)

303 if n: # set name before ...

304 self.name = n

305 r = _xkwds_get(name_RESIDUAL, RESIDUAL=None)

306 if r is not None:

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

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

309 if xs:

310 self._facc(xs, origin=1, up=False)

311

312 def __abs__(self):

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

314 '''

315 s = _fsum(self._ps_1primed()) # == self._cmp_0(0, ...)

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

317

318 def __add__(self, other):

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

320

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

322

323 @return: The sum (L{Fsum}).

324

325 @see: Method L{Fsum.__iadd__}.

326 '''

327 f = self._copy_2(self.__add__)

328 return f._fadd(other, _add_op_)

329

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

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

332 '''

333 s, r = self._fprs2

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

335

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

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

338

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

340

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

342 '''

343 return self.ceil

344

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

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

347

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

349

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

351 '''

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

353 return _signOf(s, 0)

354

355 cmp = __cmp__

356

357 def __divmod__(self, other):

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

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

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

361

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

363

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

365 '''

366 f = self._copy_2(self.__divmod__)

367 return f._fdivmod2(other, _divmod_op_)

368

369 def __eq__(self, other):

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

371 '''

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

373

374 def __float__(self):

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

376

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

378 '''

379 return float(self._fprs)

380

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

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

383

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

385

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

387 '''

388 return self.floor

389

390 def __floordiv__(self, other):

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

392

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

394

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

396

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

398 '''

399 f = self._copy_2(self.__floordiv__)

400 return f._floordiv(other, _floordiv_op_)

401

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

403 '''Not implemented.'''

404 return _NotImplemented(self, *other)

405

406 def __ge__(self, other):

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

408 '''

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

410

411 def __gt__(self, other):

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

413 '''

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

415

416 def __hash__(self): # PYCHOK no cover

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

418 '''

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

420

421 def __iadd__(self, other):

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

423

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

425

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

427

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

429 C{scalar} nor L{Fsum}.

430

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

432 '''

433 return self._fadd(other, _iadd_op_)

434

435 def __ifloordiv__(self, other):

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

437

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

439

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

441

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

443

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

445

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

447

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

449

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

451 '''

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

453

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

455 '''Not implemented.'''

456 return _NotImplemented(self, other)

457

458 def __imod__(self, other):

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

460

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

462

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

464

465 @see: Method L{Fsum.__divmod__}.

466 '''

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

468

469 def __imul__(self, other):

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

471

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

473

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

475

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

477

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

479

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

481 '''

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

483

484 def __int__(self):

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

486

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

488 and L{Fsum.__floor__} and properties

489 L{Fsum.ceil} and L{Fsum.floor}.

490 '''

491 i, _ = self._fint2

492 return i

493

494 def __invert__(self): # PYCHOK no cover

495 '''Not implemented.'''

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

497 return _NotImplemented(self)

498

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

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

501

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

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

504 3-argument C{pow(B{self}, B{other}, B{mod})}

505 version.

506 @kwarg raiser: Use C{B{raiser}=False} to ignore L{ResidualError}s

507 (C{bool}), see also method L{RESIDUAL}.

508

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

510

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

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

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

514

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

516

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

518 env var C{PYGEODESY_FSUM_RESIDUAL}

519 set or this instance has a non-zero

520 residual and either B{C{mod}} is

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

522 is a negative or fractional C{scalar}.

523

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

525 C{pow} invocation failed.

526

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

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

529 is a fractional C{scalar} and this

530 instance is negative or has a non-zero

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

532

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

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

535 '''

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

537

538 def __isub__(self, other):

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

540

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

542

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

544

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

546

547 @see: Method L{Fsum.fadd}.

548 '''

549 return self._fsub(other, _isub_op_)

550

551 def __iter__(self):

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

553 '''

554 return iter(self.partials)

555

556 def __itruediv__(self, other, **raiser):

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

558

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

560 @kwarg raiser: Use C{B{raiser}=False} to ignore L{ResidualError}s

561 (C{bool}), see also method L{RESIDUAL}.

562

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

564

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

566

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

568 env var C{PYGEODESY_FSUM_RESIDUAL} set.

569

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

571

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

573

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

575

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

577 '''

578 return self._ftruediv(other, _truediv_op_ + _fset_op_, **raiser)

579

580 def __le__(self, other):

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

582 '''

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

584

585 def __len__(self):

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

587 '''

588 return self._n

589

590 def __lt__(self, other):

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

592 '''

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

594

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

596 '''Not implemented.'''

597 return _NotImplemented(self, other)

598

599 def __mod__(self, other):

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

601

602 @see: Method L{Fsum.__imod__}.

603 '''

604 f = self._copy_2(self.__mod__)

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

606

607 def __mul__(self, other):

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

609

610 @see: Method L{Fsum.__imul__}.

611 '''

612 f = self._copy_2(self.__mul__)

613 return f._fmul(other, _mul_op_)

614

615 def __ne__(self, other):

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

617 '''

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

619

620 def __neg__(self):

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

622 '''

623 f = self._copy_2(self.__neg__)

624 return f._fset(self._neg)

625

626 def __pos__(self):

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

628 '''

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

630

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

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

633

634 @see: Method L{Fsum.__ipow__}.

635 '''

636 f = self._copy_2(self.__pow__)

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

638

639 def __radd__(self, other):

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

641

642 @see: Method L{Fsum.__iadd__}.

643 '''

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

645 return f._fadd(self, _add_op_)

646

647 def __rdivmod__(self, other):

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

649 remainder)}.

650

651 @see: Method L{Fsum.__divmod__}.

652 '''

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

654 return f._fdivmod2(self, _divmod_op_)

655

656# def __repr__(self):

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

658# '''

659# return self.toRepr(lenc=True)

660

661 def __rfloordiv__(self, other):

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

663

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

665 '''

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

667 return f._floordiv(self, _floordiv_op_)

668

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

670 '''Not implemented.'''

671 return _NotImplemented(self, other)

672

673 def __rmod__(self, other):

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

675

676 @see: Method L{Fsum.__imod__}.

677 '''

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

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

680

681 def __rmul__(self, other):

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

683

684 @see: Method L{Fsum.__imul__}.

685 '''

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

687 return f._fmul(self, _mul_op_)

688

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

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

691

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

693 '''

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

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

696 name=self.__round__.__name__)

697

698 def __rpow__(self, other, *mod):

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

700

701 @see: Method L{Fsum.__ipow__}.

702 '''

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

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

705

706 def __rsub__(self, other):

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

708

709 @see: Method L{Fsum.__isub__}.

710 '''

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

712 return f._fsub(self, _sub_op_)

713

714 def __rtruediv__(self, other, **raiser):

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

716

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

718 '''

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

720 return f._ftruediv(self, _truediv_op_, **raiser)

721

722 def __str__(self):

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

724 '''

725 return self.toStr(lenc=True)

726

727 def __sub__(self, other):

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

729

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

731

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

733

734 @see: Method L{Fsum.__isub__}.

735 '''

736 f = self._copy_2(self.__sub__)

737 return f._fsub(other, _sub_op_)

738

739 def __truediv__(self, other, **raiser):

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

741

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

743 @kwarg raiser: Use C{B{raiser}=False} to ignore L{ResidualError}s

744 (C{bool}), see also method L{RESIDUAL}.

745

746 @return: The quotient (L{Fsum}).

747

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

749 '''

750 f = self._copy_2(self.__truediv__)

751 return f._ftruediv(other, _truediv_op_, **raiser)

752

753 __trunc__ = __int__

754

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

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

757 __div__ = __truediv__

758 __idiv__ = __itruediv__

759 __long__ = __int__

760 __nonzero__ = __bool__

761 __rdiv__ = __rtruediv__

762

763 def as_integer_ratio(self):

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

765

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

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

768

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

770 '''

771 n, r = self._fint2

772 if r:

773 i, d = r.as_integer_ratio()

774 n *= d

775 n += i

776 else: # PYCHOK no cover

777 d = 1

778 return n, d

779

780 @property_RO

781 def as_iscalar(self):

782 '''Get this instance I{as-is} (L{Fsum}) or C{scalar} iff scalar.

783 '''

784 s, r = self._fprs2

785 return self if r else s

786

787 @property_RO

788 def ceil(self):

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

790 but C{float} in Python 2-).

791

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

793

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

795 L{Fsum.imag} and L{Fsum.real}.

796 '''

797 s, r = self._fprs2

798 c = _ceil(s) + int(r) - 1

799 while r > (c - s): # (s + r) > c

800 c += 1

801 return c

802

803 def _cmp_0(self, other, op):

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

805 '''

806 if isinstance(other, Fsum):

807 s = _fsum(self._ps_1primed(*other._ps))

808 elif self._scalar(other, op):

809 s = _fsum(self._ps_1primed(other))

810 else:

811 s, r = self._fprs2

812 s = _signOf(s, -r)

813 return s

814

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

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

817

818 @return: The copy (L{Fsum}).

819 '''

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

821 if f._ps is self._ps:

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

823 if not deep:

824 f._n = 1

825 return f

826

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

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

829 '''

830 n = name or which.__name__

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

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

833 # assert f._n == self._n

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

835 return f

836

837 def _copy_2r(self, other, which):

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

839 '''

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

841 Fsum(other, name=which.__name__)

842

843# def _copy_RESIDUAL(self, other):

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

845# '''

846# R = other._RESIDUAL

847# if R is not Fsum._RESIDUAL:

848# self._RESIDUAL = R

849

850 def divmod(self, other, **raiser):

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

852 remainder)}.

853

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

855 @kwarg raiser: Use C{B{raiser}=False} to ignore L{ResidualError}s

856 (C{bool}), see also method L{RESIDUAL}.

857

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

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

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

861

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

863 '''

864 f = self._copy_2(self.divmod)

865 return f._fdivmod2(other, _divmod_op_, **raiser)

866

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

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

869 '''

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

871

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

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

874 '''

875 E, t = _xError2(X)

876 if mod:

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

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

879

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

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

882 '''

883 E, t = _xError2(X)

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

885 return E(n, txt=t, cause=X)

886

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

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

889 '''

890 if xs:

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

892 ps = self._ps

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

894 return self

895

896 def _facc_1(self, xs, **up):

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

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

899 '''

900 # assert islistuple(xs)

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

902 self._facc(xs, origin=1, **up)

903

904 def _facc_neg(self, xs, up=True, **origin):

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

906 '''

907 if xs:

908 def _neg(x):

909 return -x

910

911 _x = _2floats(xs, **origin) # PYCHOK yield

912 ps = self._ps

913 ps[:] = self._ps_acc(list(ps), map(_neg, _x), up=up)

914 return self

915

916 def _facc_power(self, power, xs, which, **raiser): # in .fmath

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

918 '''

919 def _Pow4(p):

920 r = 0

921 if isinstance(p, Fsum):

922 s, r = p._fprs2

923 if r == 0:

924 return _Pow4(s)

925 m = Fsum._pow

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

927 p = s = int(p)

928 m = Fsum._pow_int

929 else:

930 p = s = _2float(power=p)

931 m = Fsum._pow_scalar

932 return m, p, s, r

933

934 _Pow, p, s, r = _Pow4(power)

935 if p: # and xs:

936 _pow = Fsum._pow_2_3

937 _Fs = Fsum

938 _Ps = _Psum_ # ()._fset_ps_

939 op = which.__name__

940

941 def _X(X):

942 f = _Pow(X, p, power, op, **raiser)

943 return f._ps if isinstance(f, _Fs) else (f,)

944

945 def _x(x):

946 x = float(x)

947 X = _Ps(x)

948 f = _pow(X, x, s, power, op, **raiser)

949 if r:

950 f *= _pow(X, x, r, power, op, **raiser)

951 return f

952

953 f = self._facc(xs, origin=1, _X=_X, _x=_x)

954 else:

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

956 return f

957

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

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

960 '''

961 if xs:

962 self._ps_acc(self._ps, xs, **up)

963 return self

964

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

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

967 '''

968 if xs:

969 self._ps_acc(self._ps, xs, **up)

970 return self

971

972# def _facc_up(self, up=True):

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

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

975# '''

976# while len(self._ps) > 1:

977# p = self._ps.pop()

978# if p:

979# n = self._n

980# self._facc_scalar_(p, up=False)

981# self._n = n

982# break

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

984

985 def fadd(self, xs=()):

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

987 to this instance.

988

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

990 L{Fsum} instances).

991

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

993

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

995

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

997 nor L{Fsum}.

998

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

1000 '''

1001 if isinstance(xs, Fsum):

1002 self._facc_scalar(xs._ps) # tuple

1003 elif isscalar(xs): # for backward compatibility

1004 self._facc_scalar_(_2float(x=xs)) # PYCHOK no cover

1005 elif xs: # assert isiterable(xs)

1006 self._facc(xs)

1007 return self

1008

1009 def fadd_(self, *xs):

1010 '''Add all positional C{scalar} or L{Fsum} instances

1011 to this instance.

1012

1013 @arg xs: Values to add (C{scalar} or L{Fsum} instances),

1014 all positional.

1015

1016 @return: This instance (L{Fsum}).

1017

1018 @raise OverflowError: Partial C{2sum} overflow.

1019

1020 @raise TypeError: An invalid B{C{xs}} type, not C{scalar}

1021 nor L{Fsum}.

1022

1023 @raise ValueError: Invalid or non-finite B{C{xs}} value.

1024 '''

1025 return self._facc_1(xs)

1026

1027 def _fadd(self, other, op, **up): # in .fmath.Fhorner

1028 '''(INTERNAL) Apply C{B{self} += B{other}}.

1029 '''

1030 if isinstance(other, Fsum):

1031 self._facc_scalar(other._ps, **up) # tuple

1032 elif self._scalar(other, op):

1033 self._facc_scalar_(other, **up)

1034 return self

1035

1036 fcopy = copy # for backward compatibility

1037 fdiv = __itruediv__ # for backward compatibility

1038 fdivmod = __divmod__ # for backward compatibility

1039

1040 def _fdivmod2(self, other, op, **raiser):

1041 '''(INTERNAL) Apply C{B{self} %= B{other}} and return a L{DivMod2Tuple}.

1042 '''

1043 # result mostly follows CPython function U{float_divmod

1044 # <https://GitHub.com/python/cpython/blob/main/Objects/floatobject.c>},

1045 # but at least divmod(-3, 2) equals Cpython's result (-2, 1).

1046 f = self._copy_2(self._fdivmod2)

1047 q = f._ftruediv(other, op, **raiser).floor

1048 if q: # == float // other == floor(float / other)

1049 self -= other * q

1050

1051 s = signOf(other) # make signOf(self) == signOf(other)

1052 if s and self.signOf() == -s: # PYCHOK no cover

1053 self += other

1054 q -= 1

1055# t = self.signOf()

1056# if t and t != s:

1057# raise self._Error(op, other, _AssertionError, txt=signOf.__name__)

1058 return DivMod2Tuple(q, self) # q is C{int} in Python 3+, but C{float} in Python 2-

1059

1060 def _finite(self, other, op=None):

1061 '''(INTERNAL) Return B{C{other}} if C{finite}.

1062 '''

1063 if _isfinite(other):

1064 return other

1065 raise ValueError(_not_finite_) if op is None else \

1066 self._ValueError(op, other, txt=_not_finite_)

1067

1068 def fint(self, raiser=True, name=NN, **RESIDUAL):

1069 '''Return this instance' current running sum as C{integer}.

1070

1071 @kwarg raiser: Use C{B{raiser}=False} to ignore L{ResidualError}s

1072 (C{bool}), see also method L{RESIDUAL}.

1073 @kwarg name: Optional name (C{str}), overriding C{"fint"}.

1074 @kwarg RESIDUAL: Optional threshold, overriding the current

1075 L{RESIDUAL<Fsum.RESIDUAL>} (C{scalar}).

1076

1077 @return: The C{integer} sum (L{Fsum}) if this instance

1078 C{is_integer} and the residual is zero or

1079 insignificant or if C{B{raiser}=False}.

1080

1081 @raise ResidualError: Non-zero I{integer} residual.

1082

1083 @see: Methods L{Fsum.int_float} and L{Fsum.is_integer}.

1084 '''

1085 i, r = self._fint2

1086 if r and raiser and self._raiser2sum(r, i, **RESIDUAL):

1087 t = _stresidual(_integer_, r)

1088 raise ResidualError(_integer_, i, txt=t)

1089 f = self._copy_2(self.fint, name=name)

1090 return f._fset(i)

1091

1092 def fint2(self, **name):

1093 '''Return this instance' current running sum as C{int} and

1094 the I{integer} residual.

1095

1096 @kwarg name: Optional name (C{str}).

1097

1098 @return: An L{Fsum2Tuple}C{(fsum, residual)} with C{fsum}

1099 an C{int} and I{integer} C{residual} a C{float} or

1100 C{INT0} if the C{fsum} is considered to be I{exact}.

1101 '''

1102 return Fsum2Tuple(*self._fint2, **name)

1103

1104 @Property_RO

1105 def _fint2(self): # see ._fset

1106 '''(INTERNAL) Get 2-tuple (C{int}, I{integer} residual).

1107 '''

1108 s, r = self._fprs2

1109 i = int(s)

1110 r = _fsum(self._ps_1primed(i)) if r else float(s - i)

1111 return i, (r or INT0) # Fsum2Tuple?

1112

1113 @deprecated_property_RO

1114 def float_int(self): # PYCHOK no cover

1115 '''DEPRECATED, use method C{Fsum.int_float}.'''

1116 return self.int_float() # raiser=False

1117

1118 @property_RO

1119 def floor(self):

1120 '''Get this instance' C{floor} (C{int} in Python 3+, but

1121 C{float} in Python 2-).

1122

1123 @note: The C{floor} takes the C{residual} into account.

1124

1125 @see: Method L{Fsum.int_float} and properties L{Fsum.ceil},

1126 L{Fsum.imag} and L{Fsum.real}.

1127 '''

1128 s, r = self._fprs2

1129 f = _floor(s) + _floor(r) + 1

1130 while (f - s) > r: # f > (s + r)

1131 f -= 1

1132 return f

1133

1134# floordiv = __floordiv__ # for naming consistency

1135

1136 def _floordiv(self, other, op, **raiser): # rather _ffloordiv?

1137 '''Apply C{B{self} //= B{other}}.

1138 '''

1139 q = self._ftruediv(other, op, **raiser) # == self

1140 return self._fset(q.floor) # floor(q)

1141

1142 fmul = __imul__ # for backward compatibility

1143

1144 def _fmul(self, other, op):

1145 '''(INTERNAL) Apply C{B{self} *= B{other}}.

1146 '''

1147 if isinstance(other, Fsum):

1148 if len(self._ps) != 1:

1149 f = self._mul_Fsum(other, op)

1150 elif len(other._ps) != 1: # and len(self._ps) == 1

1151 f = other._mul_scalar(self._ps[0], op)

1152 else: # len(other._ps) == len(self._ps) == 1

1153 f = self._finite(self._ps[0] * other._ps[0])

1154 else:

1155 s = self._scalar(other, op)

1156 f = self._mul_scalar(s, op)

1157 return self._fset(f) # n=len(self) + 1

1158

1159 def fover(self, over, **raiser):

1160 '''Apply C{B{self} /= B{over}} and summate.

1161

1162 @arg over: An L{Fsum} or C{scalar} denominator.

1163 @kwarg raiser: Use C{B{raiser}=False} to ignore L{ResidualError}s

1164 (C{bool}), see also method L{RESIDUAL}.

1165

1166 @return: Precision running sum (C{float}).

1167

1168 @see: Methods L{Fsum.fsum} and L{Fsum.__itruediv__}.

1169 '''

1170 return float(self.fdiv(over, **raiser)._fprs)

1171

1172 fpow = __ipow__ # for backward compatibility

1173

1174 def _fpow(self, other, op, *mod, **raiser):

1175 '''Apply C{B{self} **= B{other}}, optional B{C{mod}} or C{None}.

1176 '''

1177 if mod:

1178 if mod[0] is not None: # == 3-arg C{pow}

1179 f = self._pow_2_3(self, other, other, op, *mod, **raiser)

1180 elif self.is_integer():

1181 # return an exact C{int} for C{int}**C{int}

1182 i, _ = self._fint2 # assert _ == 0

1183 x = _2scalar(other) # C{int}, C{float} or other

1184 f = self._pow_2_3(i, x, other, op, **raiser) if isscalar(x) else \

1185 _Psum_(i)._pow( x, other, op, **raiser) # x is Fsum

1186 else: # mod[0] is None, power(self, other)

1187 f = self._pow(other, other, op, **raiser)

1188 else: # pow(self, other)

1189 f = self._pow(other, other, op, **raiser)

1190 return self._fset(f, asis=isint(f)) # n=max(len(self), 1)

1191

1192 @Property_RO

1193 def _fprs(self):

1194 '''(INTERNAL) Get and cache this instance' precision

1195 running sum (C{float} or C{int}), ignoring C{residual}.

1196

1197 @note: The precision running C{fsum} after a C{//=} or

1198 C{//} C{floor} division is C{int} in Python 3+.

1199 '''

1200 return self._fprs2.fsum

1201

1202 @Property_RO

1203 def _fprs2(self):

1204 '''(INTERNAL) Get and cache this instance' precision

1205 running sum and residual (L{Fsum2Tuple}).

1206 '''

1207 ps = self._ps

1208 n = len(ps) - 2

1209 if n > 0: # len(ps) > 2

1210 s = _psum(ps)

1211 n = len(ps) - 2

1212 if n > 0:

1213 r = _fsum(self._ps_1primed(s)) or INT0

1214 return Fsum2Tuple(s, r)

1215 if n == 0: # len(ps) == 2

1216 ps[:] = _2ps(*_2sum(*ps))

1217 r, s = (INT0, ps[0]) if len(ps) != 2 else ps

1218 elif ps: # len(ps) == 1

1219 s, r = ps[0], INT0

1220 else: # len(ps) == 0

1221 s, r = _0_0, INT0

1222 ps[:] = s,

1223 # assert self._ps is ps

1224 return Fsum2Tuple(s, r)

1225

1226# def _fpsqz(self):

1227# '''(INTERNAL) Compress, squeeze the C{partials}.

1228# '''

1229# if len(self._ps) > 2:

1230# _ = self._fprs2

1231# return self

1232

1233 def fset_(self, *xs):

1234 '''Replace this instance' value with C{xs}.

1235

1236 @arg xs: Optional, new values (C{scalar} or L{Fsum}

1237 instances), all positional.

1238

1239 @return: This instance (C{Fsum}).

1240

1241 @see: Method L{Fsum.fadd} for further details.

1242 '''

1243 self._ps[:] = 0,

1244 self._n = 0

1245 return self.fadd(xs) if xs else self._update()

1246

1247 def _fset(self, other, asis=True, n=0):

1248 '''(INTERNAL) Overwrite this instance with an other or a C{scalar}.

1249 '''

1250 if other is self:

1251 pass # from ._fmul, ._ftruediv and ._pow_0_1

1252 elif isinstance(other, Fsum):

1253 self._ps[:] = other._ps

1254 self._n = n or other._n

1255# self._copy_RESIDUAL(other)

1256 # use or zap the C{Property_RO} values

1257 Fsum._fint2._update_from(self, other)

1258 Fsum._fprs ._update_from(self, other)

1259 Fsum._fprs2._update_from(self, other)

1260 elif isscalar(other):

1261 s = other if asis else float(other)

1262 i = int(s) # see ._fint2

1263 t = i, ((s - i) or INT0)

1264 self._ps[:] = s,

1265 self._n = n or 1

1266 # Property_ROs _fint2, _fprs and _fprs2 can't be a Property:

1267 # Property's _fset zaps the value just set by the @setter

1268 self.__dict__.update(_fint2=t, _fprs=s, _fprs2=Fsum2Tuple(s, INT0))

1269 else: # PYCHOK no cover

1270 raise self._Error(_fset_op_, other, _AssertionError)

1271 return self

1272

1273 def _fset_ps(self, other, n=0): # in .fmath

1274 '''(INTERNAL) Set partials from a known C{Fsum} or C{scalar}.

1275 '''

1276 if isinstance(other, Fsum):

1277 self._ps[:] = other._ps

1278 self._n = n or other._n

1279 else: # assert isscalar(other)

1280 self._ps[:] = other,

1281 self._n = n or 1

1282 return self

1283

1284# def _fset_ps_(self, *xs):

1285# '''(INTERNAL) Set partials to all known scalar C{xs}.

1286# '''

1287# self._ps[:] = xs

1288# self.n = len(xs)

1289# return self

1290

1291 def fsub(self, xs=()):

1292 '''Subtract an iterable of C{scalar} or L{Fsum} instances from

1293 this instance.

1294

1295 @arg xs: Iterable, list, tuple. etc. (C{scalar} or L{Fsum}

1296 instances).

1297

1298 @return: This instance, updated (L{Fsum}).

1299

1300 @see: Method L{Fsum.fadd}.

1301 '''

1302 return self._facc_neg(xs)

1303

1304 def fsub_(self, *xs):

1305 '''Subtract all positional C{scalar} or L{Fsum} instances from

1306 this instance.

1307

1308 @arg xs: Values to subtract (C{scalar} or L{Fsum} instances),

1309 all positional.

1310

1311 @return: This instance, updated (L{Fsum}).

1312

1313 @see: Method L{Fsum.fadd}.

1314 '''

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

1316 self._facc_neg(xs, origin=1)

1317

1318 def _fsub(self, other, op):

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

1320 '''

1321 if isinstance(other, Fsum):

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

1323 self._fset(_0_0) # n=len(self) * 2, self -= self

1324 elif other._ps:

1325 self._facc_scalar(other._ps_neg)

1326 elif self._scalar(other, op):

1327 self._facc_scalar_(-self._finite(other, op))

1328 return self

1329

1330 def fsum(self, xs=()):

1331 '''Add more C{scalar} or L{Fsum} instances and summate.

1332

1333 @kwarg xs: Iterable, list, tuple, etc. (C{scalar} or

1334 L{Fsum} instances).

1335

1336 @return: Precision running sum (C{float} or C{int}).

1337

1338 @see: Method L{Fsum.fadd}.

1339

1340 @note: Accumulation can continue after summation.

1341 '''

1342 return self._facc(xs)._fprs

1343

1344 def fsum_(self, *xs):

1345 '''Add all positional C{scalar} or L{Fsum} instances and summate.

1346

1347 @arg xs: Values to add (C{scalar} or L{Fsum} instances), all

1348 positional.

1349

1350 @return: Precision running sum (C{float} or C{int}).

1351

1352 @see: Methods L{Fsum.fsum}, L{Fsum.Fsum_} and L{Fsum.fsumf_}.

1353 '''

1354 return self._facc_1(xs)._fprs

1355

1356 def Fsum_(self, *xs):

1357 '''Like method L{Fsum.fsum_} but returning an L{Fsum}.

1358

1359 @return: Current, precision running sum (L{Fsum}).

1360 '''

1361 return self._facc_1(xs)._copy_2(self.Fsum_)

1362

1363 def fsum2(self, xs=(), name=NN):

1364 '''Add more C{scalar} or L{Fsum} instances and return the

1365 current precision running sum and the C{residual}.

1366

1367 @kwarg xs: Iterable, list, tuple, etc. (C{scalar} or L{Fsum}

1368 instances).

1369 @kwarg name: Optional name (C{str}).

1370

1371 @return: L{Fsum2Tuple}C{(fsum, residual)} with C{fsum} the

1372 current precision running sum and C{residual}, the

1373 (precision) sum of the remaining C{partials}. The

1374 C{residual is INT0} if the C{fsum} is considered

1375 to be I{exact}.

1376

1377 @see: Methods L{Fsum.fint2}, L{Fsum.fsum} and L{Fsum.fsum2_}

1378 '''

1379 t = self._facc(xs)._fprs2

1380 return t.dup(name=name) if name else t

1381

1382 def fsum2_(self, *xs):

1383 '''Add any positional C{scalar} or L{Fsum} instances and return

1384 the precision running sum and the C{differential}.

1385

1386 @arg xs: Values to add (C{scalar} or L{Fsum} instances), all

1387 positional.

1388

1389 @return: 2Tuple C{(fsum, delta)} with the current, precision

1390 running C{fsum} like method L{Fsum.fsum} and C{delta},

1391 the difference with previous running C{fsum}, C{float}.

1392

1393 @see: Methods L{Fsum.fsum_} and L{Fsum.fsum}.

1394 '''

1395 return self._fsum2(xs, self._facc_1)

1396

1397 def _fsum2(self, xs, _f, **origin):

1398 '''(INTERNAL) Helper for L{Fsum.fsum2_} and L{Fsum.fsum2f_}.

1399 '''

1400 p, q = self._fprs2

1401 if xs:

1402 s, r = _f(xs, **origin)._fprs2

1403 return s, _2delta(s - p, r - q) # _fsum(_1primed((s, -p, r, -q))

1404 else:

1405 return p, _0_0

1406

1407 def fsumf_(self, *xs):

1408 '''Like method L{Fsum.fsum_} but only for C{B{xs}}, I{known to be scalar}.

1409 '''

1410 return self._facc_scalar(xs)._fprs

1411

1412 def Fsumf_(self, *xs):

1413 '''Like method L{Fsum.Fsum_} but only for C{B{xs}}, I{known to be scalar}.

1414 '''

1415 return self._facc_scalar(xs)._copy_2(self.Fsumf_)

1416

1417 def fsum2f_(self, *xs):

1418 '''Like method L{Fsum.fsum2_} but only for C{B{xs}}, I{known to be scalar}.

1419 '''

1420 return self._fsum2(xs, self._facc_scalar, origin=1)

1421

1422# ftruediv = __itruediv__ # for naming consistency?

1423

1424 def _ftruediv(self, other, op, **raiser):

1425 '''(INTERNAL) Apply C{B{self} /= B{other}}.

1426 '''

1427 n = _1_0

1428 if isinstance(other, Fsum):

1429 if other is self or other == self:

1430 return self._fset(n) # n=len(self)

1431 d, r = other._fprs2

1432 if r:

1433 if d:

1434 if self._raiser(r, d, **raiser):

1435 raise self._ResidualError(op, other, r)

1436 d, n = other.as_integer_ratio()

1437 else: # PYCHOK no cover

1438 d = r

1439 else:

1440 d = self._scalar(other, op)

1441 try:

1442 s = n / d

1443 except Exception as X:

1444 raise self._ErrorX(X, op, other)

1445 f = self._mul_scalar(s, _mul_op_) # handles 0, INF, NAN

1446 return self._fset(f) # asis=False

1447

1448 @property_RO

1449 def imag(self):

1450 '''Get the C{imaginary} part of this instance (C{0.0}, always).

1451

1452 @see: Properties L{Fsum.ceil}, L{Fsum.floor} and L{Fsum.real}.

1453 '''

1454 return _0_0

1455

1456 def int_float(self, raiser=False, **RESIDUAL):

1457 '''Return this instance' current running sum as C{int} or C{float}.

1458

1459 @kwarg raiser: If C{True} throw a L{ResidualError} if the

1460 residual exceeds the C{RESIDUAL} (C{bool}).

1461 @kwarg RESIDUAL: Optional threshold, overriding the current

1462 L{RESIDUAL<Fsum.RESIDUAL>} (C{scalar}).

1463

1464 @return: This C{integer} sum if this instance C{is_integer},

1465 otherwise return the C{float} sum if the residual is

1466 zero or insignificant or if C{B{raiser}=False}.

1467

1468 @raise ResidualError: Non-zero residual and C{B{raiser}=True}.

1469

1470 @see: Methods L{Fsum.fint} and L{Fsum.fint2} and property L{Fsum.as_iscalar}.

1471 '''

1472 s, r = self._fint2

1473 if r:

1474 s, r = self._fprs2

1475 if r and raiser and self._raiser2sum(r, s, **RESIDUAL): # PYCHOK no cover

1476 t = _stresidual(_non_zero_, r)

1477 raise ResidualError(int_float=s, txt=t)

1478 s = float(s) # redundant

1479 return s

1480

1481 def is_exact(self):

1482 '''Is this instance' running C{fsum} considered to be exact? (C{bool}).

1483 '''

1484 return self.residual is INT0

1485

1486 def is_integer(self):

1487 '''Is this instance' running sum C{integer}? (C{bool}).

1488

1489 @see: Methods L{Fsum.fint}, L{Fsum.fint2} and L{Fsum.is_scalar}.

1490 '''

1491 _, r = self._fint2

1492 return False if r else True

1493

1494 def is_math_fsum(self):

1495 '''Return whether functions L{fsum}, L{fsum_}, L{fsum1} and

1496 L{fsum1_} plus partials summation are based on Python's

1497 C{math.fsum} or not.

1498

1499 @return: C{2} if all functions and partials summation

1500 are based on C{math.fsum}, C{True} if only

1501 the functions are based on C{math.fsum} (and

1502 partials summation is not) or C{False} if

1503 none are.

1504 '''

1505 f = Fsum._math_fsum

1506 return 2 if _psum is f else bool(f)

1507

1508 def is_scalar(self):

1509 '''Is this instance' running sum C{scalar}? (C{bool}).

1510

1511 @see: Method L{Fsum.is_integer} and property L{Fsum.as_iscalar}.

1512 '''

1513 s, r = t = self._fprs2

1514 return False if r and _2sum(s, r) != t else True

1515

1516 def _mul_Fsum(self, other, op=_mul_op_): # in .fmath.Fhorner

1517 '''(INTERNAL) Return C{B{self} * Fsum B{other}} as L{Fsum} or C{0}.

1518 '''

1519 # assert isinstance(other, Fsum)

1520 if self._ps and other._ps:

1521 f = self._ps_mul(op, *other._ps) # NO .as_iscalar

1522 else:

1523 f = _0_0

1524 return f

1525

1526 def _mul_scalar(self, factor, op): # in .fmath.Fhorner

1527 '''(INTERNAL) Return C{B{self} * scalar B{factor}} as L{Fsum}, C{0} or C{self}.

1528 '''

1529 # assert isscalar(factor)

1530 if self._ps and self._finite(factor, op):

1531 f = self if factor == _1_0 else (

1532 self._neg if factor == _N_1_0 else

1533 self._ps_mul(op, factor).as_iscalar)

1534 else:

1535 f = _0_0

1536 return f

1537

1538 @property_RO

1539 def _neg(self):

1540 '''(INTERNAL) Return C{Fsum(-self)} or scalar C{NEG0}.

1541 '''

1542 return _Psum(self._ps_neg) if self._ps else NEG0

1543

1544 @property_RO

1545 def partials(self):

1546 '''Get this instance' current, partial sums (C{tuple} of C{float}s).

1547 '''

1548 return tuple(self._ps)

1549

1550 def pow(self, x, *mod, **raiser):

1551 '''Return C{B{self}**B{x}} as L{Fsum}.

1552

1553 @arg x: The exponent (L{Fsum} or C{scalar}).

1554 @arg mod: Optional modulus (C{int} or C{None}) for the 3-argument

1555 C{pow(B{self}, B{other}, B{mod})} version.

1556 @kwarg raiser: Use C{B{raiser}=False} to ignore L{ResidualError}s

1557 (C{bool}), see also method L{RESIDUAL}.

1558

1559 @return: The C{pow(self, B{x})} or C{pow(self, B{x}, *B{mod})}

1560 result (L{Fsum}).

1561

1562 @note: If B{C{mod}} is given as C{None}, the result will be an

1563 C{integer} L{Fsum} provided this instance C{is_integer}

1564 or set to C{integer} by an L{Fsum.fint} call.

1565

1566 @see: Methods L{Fsum.__ipow__}, L{Fsum.fint}, L{Fsum.is_integer}

1567 and L{Fsum.root}.

1568 '''

1569 f = self._copy_2(self.pow)

1570 return f._fpow(x, _pow_op_, *mod, **raiser) # f = pow(f, x, *mod)

1571

1572 def _pow(self, other, unused, op, **raiser):

1573 '''Return C{B{self} ** B{other}}.

1574 '''

1575 if isinstance(other, Fsum):

1576 x, r = other._fprs2

1577 if r and self._raiser(r, x, **raiser):

1578 raise self._ResidualError(op, other, r)

1579 f = self._pow_scalar(x, other, op, **raiser)

1580 if r:

1581 f *= self._pow_scalar(r, other, op, **raiser)

1582 elif self._scalar(other, op):

1583 x = self._finite(other, op)

1584 f = self._pow_scalar(x, other, op, **raiser)

1585 else:

1586 f = self._pow_0_1(0, other)

1587 return f

1588

1589 def _pow_0_1(self, x, other):

1590 '''(INTERNAL) Return B{C{self}**1} or C{B{self}**0 == 1.0}.

1591 '''

1592 return self if x else (1 if isint(other) and self.is_integer() else _1_0)

1593

1594 def _pow_2_3(self, b, x, other, op, *mod, **raiser):

1595 '''(INTERNAL) 2-arg C{pow(B{b}, scalar B{x})} and 3-arg C{pow(B{b},

1596 B{x}, int B{mod} or C{None})}, embellishing errors.

1597 '''

1598 try:

1599 if mod: # b, x, mod all C{int}, unless C{mod} is C{None}

1600 m = mod[0]

1601 b, r = b._fprs2 if m is None else b._fint2

1602 if r and self._raiser(r, b, **raiser):

1603 t = _non_zero_ if m is None else _integer_

1604 raise ResidualError(_stresidual(t, r, mod=m), txt=None)

1605 x = _2scalar(x, _raiser=self._raiser, mod=m)

1606 # 0**INF == 0.0, 1**INF == 1.0, -1**2.3 == -(1**2.3)

1607 s = pow(b, x, *mod)

1608 if iscomplex(s):

1609 # neg**frac == complex in Python 3+, but ValueError in 2-

1610 raise ValueError(_strcomplex(s, b, x, *mod))

1611 return self._finite(s)

1612 except Exception as X:

1613 raise self._ErrorX(X, op, other, *mod)

1614

1615 def _pow_int(self, x, other, op, **raiser):

1616 '''(INTERNAL) Return C{B{self} **= B{x}} for C{int B{x} >= 0}.

1617 '''

1618 # assert isint(x) and x >= 0

1619 ps = self._ps

1620 if len(ps) > 1:

1621 _mul_Fsum = Fsum._mul_Fsum

1622 if x > 4:

1623 p = self

1624 f = self if (x & 1) else _Psum_(_1_0)

1625 m = x >> 1 # // 2

1626 while m:

1627 p = _mul_Fsum(p, p, op) # p **= 2

1628 if (m & 1):

1629 f = _mul_Fsum(f, p, op) # f *= p

1630 m >>= 1 # //= 2

1631 elif x > 1: # self**2, 3 or 4

1632 f = _mul_Fsum(self, self, op)

1633 if x > 2: # self**3 or 4

1634 p = self if x < 4 else f

1635 f = _mul_Fsum(f, p, op).as_iscalar

1636 else: # self**1 or self**0 == 1 or _1_0

1637 f = self._pow_0_1(x, other)

1638 elif ps: # self._ps[0]**x

1639 f = self._pow_2_3(ps[0], x, other, op, **raiser)

1640 else: # PYCHOK no cover

1641 # 0**pos_int == 0, but 0**0 == 1

1642 f = 0 if x else 1

1643 return f

1644

1645 def _pow_scalar(self, x, other, op, **raiser):

1646 '''(INTERNAL) Return C{self**B{x}} for C{scalar B{x}}.

1647 '''

1648 s, r = self._fprs2

1649 if isint(x, both=True):

1650 x = int(x) # Fsum**int

1651 y = abs(x)

1652 if y > 1:

1653 if r:

1654 f = self._pow_int(y, other, op, **raiser)

1655 if x > 0: # > 1

1656 return f

1657 # assert x < 0 # < -1

1658 s, r = f._fprs2 if isinstance(f, Fsum) else (f, 0)

1659 if r:

1660 return _1_over(f, op, **raiser) # PYCHOK 2 args

1661 # use **= -1 for the CPython float_pow

1662 # error if s is zero, and not s = 1 / s

1663 x = -1

1664 elif x < 0: # == -1: self**(-1) == 1 / self

1665 if r:

1666 return _1_over(self, op, **raiser) # PYCHOK 2 args

1667 else: # self**1 or self**0

1668 return self._pow_0_1(x, other) # self, 1 or 1.0

1669 elif r: # non-zero residual**fractional

1670 if s:

1671 n, d = self.as_integer_ratio()

1672 if abs(n) > abs(d):

1673 n, d, x = d, n, (-x)

1674 s = n / d

1675 else:

1676 s = r

1677 # assert isscalar(s) and isscalar(x)

1678 return self._pow_2_3(s, x, other, op, **raiser)

1679

1680 def _ps_acc(self, ps, xs, up=True, **unused):

1681 '''(INTERNAL) Accumulate all scalar C{xs} into C{ps}.

1682 '''

1683 n = 0

1684 _2s = _2sum

1685 for x in (tuple(xs) if xs is ps else xs):

1686 # assert isscalar(x) and _isfinite(x)

1687 if x:

1688 i = 0

1689 for p in ps:

1690 x, p = _2s(x, p)

1691 if p:

1692 ps[i] = p

1693 i += 1

1694 ps[i:] = (x,) if x else ()

1695 n += 1

1696 if n:

1697 self._n += n

1698 # Fsum._ps_max = max(Fsum._ps_max, len(ps))

1699 if up:

1700 self._update()

1701 return ps

1702

1703 def _ps_mul(self, op, *factors):

1704 '''(INTERNAL) Multiply this instance' C{partials} with

1705 each of the scalar B{C{factors}} and accumulate.

1706 '''

1707 def _pfs(ps, fs):

1708 if len(ps) < len(fs):

1709 ps, fs = fs, ps

1710 _fin = _isfinite

1711 for f in fs:

1712 for p in ps:

1713 p *= f

1714 yield p if _fin(p) else self._finite(p, op)

1715

1716 return _Psum(self._ps_acc([], _pfs(self._ps, factors)))

1717

1718 @property_RO

1719 def _ps_neg(self):

1720 '''(INTERNAL) Yield the partials, I{negated}.

1721 '''

1722 for p in self._ps:

1723 yield -p

1724

1725 def _ps_1primed(self, *less):

1726 '''(INTERNAL) Yield partials, 1-primed and subtract any C{less} scalars.

1727 '''

1728 yield _1_0

1729 for p in self._ps:

1730 yield p

1731 for p in less:

1732 yield -p

1733 yield _N_1_0

1734

1735 def _raiser(self, r, s, raiser=True, **RESIDUAL):

1736 '''(INTERNAL) Does ratio C{r / s} exceed the RESIDUAL threshold?

1737 '''

1738 self._ratio = r = (r / s) if s else s # == 0.

1739 if r and raiser:

1740 R = self._RESIDUAL

1741 if RESIDUAL:

1742 R = _xkwds_get(RESIDUAL, RESIDUAL=R)

1743 return fabs(r) > R

1744 return False

1745

1746 def _raiser2sum(self, r, s, **raiser_RESIDUAL):

1747 '''(INTERNAL) Does ratio C{r / s} exceed the RESIDUAL threshold

1748 I{and} is the residual B{C{r}} significant vs sum B{C{s}}?

1749 '''

1750 return self._raiser(r, s, **raiser_RESIDUAL) and _2sum(s, r) != (s, r)

1751

1752 @property_RO

1753 def real(self):

1754 '''Get the C{real} part of this instance (C{float}).

1755

1756 @see: Methods L{Fsum.__float__} and L{Fsum.fsum}

1757 and properties L{Fsum.ceil}, L{Fsum.floor},

1758 L{Fsum.imag} and L{Fsum.residual}.

1759 '''

1760 return float(self._fprs)

1761

1762 @property_RO

1763 def residual(self):

1764 '''Get this instance' residual (C{float} or C{int}), the

1765 C{sum(partials)} less the precision running sum C{fsum}.

1766

1767 @note: If the C{residual is INT0}, the precision running

1768 C{fsum} is considered to be I{exact}.

1769

1770 @see: Methods L{Fsum.fsum}, L{Fsum.fsum2} and L{Fsum.is_exact}.

1771 '''

1772 return self._fprs2.residual

1773

1774 def RESIDUAL(self, *threshold):

1775 '''Get and set this instance' I{ratio} for raising L{ResidualError}s,

1776 overriding the default from env variable C{PYGEODESY_FSUM_RESIDUAL}.

1777

1778 @arg threshold: If C{scalar}, the I{ratio} to exceed for raising

1779 L{ResidualError}s in division and exponention, if

1780 C{None} restore the default set with env variable

1781 C{PYGEODESY_FSUM_RESIDUAL} or if omitted, keep the

1782 current setting.

1783

1784 @return: The previous C{RESIDUAL} setting (C{float}), default C{0.0}.

1785

1786 @raise ValueError: Negative B{C{threshold}}.

1787

1788 @note: L{ResidualError}s will be thrown if the non-zero I{ratio}

1789 C{residual / fsum} exceeds the B{C{threshold}}.

1790 '''

1791 r = self._RESIDUAL

1792 if threshold:

1793 t = threshold[0]

1794 t = Fsum._RESIDUAL if t is None else (

1795 float(t) if isscalar(t) else ( # for backward ...

1796 _0_0 if bool(t) else _1_0)) # ... compatibility

1797 if t < 0:

1798 u = _DOT_(self, unstr(self.RESIDUAL, *threshold))

1799 raise _ValueError(u, RESIDUAL=t, txt=_negative_)

1800 self._RESIDUAL = t

1801 return r

1802

1803 def _ResidualError(self, op, other, residual):

1804 '''(INTERNAL) Non-zero B{C{residual}} etc.

1805 '''

1806 t = _stresidual(_non_zero_, residual, ratio=self._ratio,

1807 RESIDUAL=self._RESIDUAL)

1808 t = t.replace(_COMMASPACE_R_, _exceeds_R_)

1809 return self._Error(op, other, ResidualError, txt=t)

1810

1811 def root(self, root, **raiser):

1812 '''Return C{B{self}**(1 / B{root})} as L{Fsum}.

1813

1814 @arg root: The order (C{scalar} or C{Fsum}), non-zero.

1815 @kwarg raiser: Use C{B{raiser}=False} to ignore L{ResidualError}s

1816 (C{bool}), see also method L{RESIDUAL}.

1817

1818 @return: The C{self ** (1 / B{root})} result (L{Fsum}).

1819

1820 @see: Method L{Fsum.pow}.

1821 '''

1822 x = _1_over(root, **raiser)

1823 f = self._copy_2(self.root)

1824 return f._fpow(x, f.name, **raiser) # == pow(f, x)

1825

1826 def _scalar(self, other, op, **txt):

1827 '''(INTERNAL) Return scalar C{other}.

1828 '''

1829 if isscalar(other):

1830 return other

1831 raise self._TypeError(op, other, **txt) # _invalid_

1832

1833 def signOf(self, res=True):

1834 '''Determine the sign of this instance.

1835

1836 @kwarg res: If C{True} consider, otherwise

1837 ignore the residual (C{bool}).

1838

1839 @return: The sign (C{int}, -1, 0 or +1).

1840 '''

1841 s, r = self._fprs2

1842 return _signOf(s, (-r) if res else 0)

1843

1844 def toRepr(self, **prec_sep_fmt_lenc): # PYCHOK signature

1845 '''Return this C{Fsum} instance as representation.

1846

1847 @kwarg prec_sep_fmt_lenc: Optional keyword arguments for

1848 method L{Fsum2Tuple.toRepr} plus C{B{lenc}=True}

1849 (C{bool}) to in-/exclude the current C{[len]}

1850 of this L{Fsum} enclosed in I{[brackets]}.

1851

1852 @return: This instance (C{repr}).

1853 '''

1854 return self._toT(self._fprs2.toRepr, **prec_sep_fmt_lenc)

1855

1856 def toStr(self, **prec_sep_fmt_lenc): # PYCHOK signature

1857 '''Return this C{Fsum} instance as string.

1858

1859 @kwarg prec_sep_fmt_lenc: Optional keyword arguments for

1860 method L{Fsum2Tuple.toStr} plus C{B{lenc}=True}

1861 (C{bool}) to in-/exclude the current C{[len]}

1862 of this L{Fsum} enclosed in I{[brackets]}.

1863

1864 @return: This instance (C{str}).

1865 '''

1866 return self._toT(self._fprs2.toStr, **prec_sep_fmt_lenc)

1867

1868 def _toT(self, toT, fmt=Fmt.g, lenc=True, **kwds):

1869 '''(INTERNAL) Helper for C{toRepr} and C{toStr}.

1870 '''

1871 n = self.named3

1872 if lenc:

1873 n = Fmt.SQUARE(n, len(self))

1874 return _SPACE_(n, toT(fmt=fmt, **kwds))

1875

1876 def _TypeError(self, op, other, **txt): # PYCHOK no cover

1877 '''(INTERNAL) Return a C{TypeError}.

1878 '''

1879 return self._Error(op, other, _TypeError, **txt)

1880

1881 def _update(self, updated=True): # see ._fset

1882 '''(INTERNAL) Zap all cached C{Property_RO} values.

1883 '''

1884 if updated:

1885 _pop = self.__dict__.pop

1886 for p in _ROs:

1887 _ = _pop(p, None)

1888# Fsum._fint2._update(self)

1889# Fsum._fprs ._update(self)

1890# Fsum._fprs2._update(self)

1891 return self # for .fset_

1892

1893 def _ValueError(self, op, other, **txt): # PYCHOK no cover

1894 '''(INTERNAL) Return a C{ValueError}.

1895 '''

1896 return self._Error(op, other, _ValueError, **txt)

1897

1898 def _ZeroDivisionError(self, op, other, **txt): # PYCHOK no cover

1899 '''(INTERNAL) Return a C{ZeroDivisionError}.

1900 '''

1901 return self._Error(op, other, _ZeroDivisionError, **txt)

1902

1903_ROs = _allPropertiesOf_n(3, Fsum, Property_RO) # PYCHOK assert, see Fsum._fset, -._update

1904

1905

1906 def _Float_Int(arg, **name_Error):

1907 '''(INTERNAL) Unit of L{Fsum2Tuple} items.

1908 '''

1909 U = Int if isint(arg) else Float

1910 return U(arg, **name_Error)

1911

1912

1913 class DivMod2Tuple(_NamedTuple):

1914 '''2-Tuple C{(div, mod)} with the quotient C{div} and remainder

1915 C{mod} results of a C{divmod} operation.

1916

1917 @note: Quotient C{div} an C{int} in Python 3+ or a C{float} in

1918 Python 2-. Remainder C{mod} an L{Fsum} instance.

1919 '''

1920 _Names_ = (_div_, _mod_)

1921 _Units_ = (_Float_Int, Fsum)

1922

1923

1924 class Fsum2Tuple(_NamedTuple):

1925 '''2-Tuple C{(fsum, residual)} with the precision running C{fsum}

1926 and the C{residual}, the sum of the remaining partials. Each

1927 item is either C{float} or C{int}.

1928

1929 @note: If the C{residual is INT0}, the C{fsum} is considered

1930 to be I{exact}, see method L{Fsum2Tuple.is_exact}.

1931 '''

1932 _Names_ = ( Fsum.fsum.__name__, Fsum.residual.name)

1933 _Units_ = (_Float_Int, _Float_Int)

1934

1935 @Property_RO

1936 def _Fsum(self):

1937 '''(INTERNAL) Get this L{Fsum2Tuple} as an L{Fsum}.

1938 '''

1939 s, r = map(float, self)

1940 return _Psum(_2ps(s, r), name=self.name)

1941

1942 def is_exact(self):

1943 '''Is this L{Fsum2Tuple} considered to be exact? (C{bool}).

1944 '''

1945 return self._Fsum.is_exact()

1946

1947 def is_integer(self):

1948 '''Is this L{Fsum2Tuple} C{integer}? (C{bool}).

1949 '''

1950 return self._Fsum.is_integer()

1951

1952

1953 class ResidualError(_ValueError):

1954 '''Error raised for an operation involving a L{pygeodesy.sums.Fsum}

1955 instance with a non-zero C{residual}, I{integer} or otherwise.

1956

1957 @see: Module L{pygeodesy.fsums} and method L{Fsum.RESIDUAL}.

1958 '''

1959 pass

1960

1961

1962 try:

1963 from math import fsum as _fsum # precision IEEE-754 sum, Python 2.6+

1964

1965 # make sure _fsum works as expected (XXX check

1966 # float.__getformat__('float')[:4] == 'IEEE'?)

1967 if _fsum((1, 1e101, 1, -1e101)) != 2: # PYCHOK no cover

1968 del _fsum # nope, remove _fsum ...

1969 raise ImportError # ... use _fsum below

1970

1971 Fsum._math_fsum = _sum = _fsum # PYCHOK exported

1972

1973 if _getenv('PYGEODESY_FSUM_PARTIALS', NN) == _fsum.__name__:

1974 _psum = _fsum # PYCHOK re-def

1975

1976 except ImportError:

1977 _sum = sum # Fsum(NAN) exception fall-back, in .elliptic

1978

1979 def _fsum(xs):

1980 '''(INTERNAL) Precision summation, Python 2.5-.

1981 '''

1982 f = Fsum()

1983 f.name = _fsum.__name__

1984 return f.fsum(xs)

1985

1986

1987 def fsum(xs, floats=False):

1988 '''Precision floating point summation based on or like Python's C{math.fsum}.

1989

1990 @arg xs: Iterable, list, tuple, etc. of values (C{scalar} or L{Fsum}

1991 instances).

1992 @kwarg floats: Use C{B{floats}=True} iff I{all} B{C{xs}} are known

1993 to be C{float} scalars (C{bool}).

1994

1995 @return: Precision C{fsum} (C{float}).

1996

1997 @raise OverflowError: Partial C{2sum} overflow.

1998

1999 @raise TypeError: Non-scalar B{C{xs}} value.

2000

2001 @raise ValueError: Invalid or non-finite B{C{xs}} value.

2002

2003 @note: Exception and I{non-finite} handling may differ if not based

2004 on Python's C{math.fsum}.

2005

2006 @see: Class L{Fsum} and methods L{Fsum.fsum} and L{Fsum.fadd}.

2007 '''

2008 return _fsum(xs if floats else _2floats(xs)) if xs else _0_0 # PYCHOK yield

2009

2010

2011 def fsum_(*xs, **floats):

2012 '''Precision floating point summation of all positional arguments.

2013

2014 @arg xs: Values to be added (C{scalar} or L{Fsum} instances), all

2015 positional.

2016 @kwarg floats: Use C{B{floats}=True} iff I{all} B{C{xs}} are I{known

2017 to be scalar} (C{bool}).

2018

2019 @return: Precision C{fsum} (C{float}).

2020

2021 @see: Function C{fsum}.

2022 '''

2023 return _fsum(xs if _xkwds_get(floats, floats=False) else

2024 _2floats(xs, origin=1)) if xs else _0_0 # PYCHOK yield

2025

2026

2027 def fsumf_(*xs):

2028 '''Precision floating point summation, L{fsum_}C{(*B{xs}, floats=True)},

2029 but only for C{B{xs}} I{known to be scalar}.

2030 '''

2031 return _fsum(xs) if xs else _0_0

2032

2033

2034 def fsum1(xs, floats=False):

2035 '''Precision floating point summation, 1-primed.

2036

2037 @arg xs: Iterable, list, tuple, etc. of values (C{scalar} or L{Fsum}

2038 instances).

2039 @kwarg floats: Use C{B{floats}=True} iff I{all} B{C{xs}} are known

2040 to be C{float}.

2041

2042 @return: Precision C{fsum} (C{float}).

2043

2044 @see: Function C{fsum}.

2045 '''

2046 return _fsum(_1primed(xs if floats else _2floats(xs))) if xs else _0_0 # PYCHOK yield

2047

2048

2049 def fsum1_(*xs, **floats):

2050 '''Precision floating point summation, 1-primed.

2051

2052 @arg xs: Values to be added (C{scalar} or L{Fsum} instances), all

2053 positional.

2054 @kwarg floats: Use C{B{floats}=True} iff I{all} B{C{xs}} are I{known

2055 to be scalar} (C{bool}).

2056

2057 @return: Precision C{fsum} (C{float}).

2058

2059 @see: Function C{fsum}

2060 '''

2061 return _fsum(_1primed(xs if _xkwds_get(floats, floats=False) else

2062 _2floats(xs, origin=1))) if xs else _0_0 # PYCHOK yield

2063

2064

2065 def fsum1f_(*xs):

2066 '''Precision floating point summation, L{fsum1_}C{(*B{xs}, floats=True)},

2067 but only for C{B{xs}} I{known to be scalar}.

2068 '''

2069 return _fsum(_1primed(xs)) if xs else _0_0

2070

2071

2072 if __name__ == '__main__':

2073

2074 # usage: [env PYGEODESY_FSUM_PARTIALS=fsum] python3 -m pygeodesy.fsums

2075

2076 def _test(n):

2077 # copied from Hettinger, see L{Fsum} reference

2078 from pygeodesy import frandoms, printf

2079

2080 printf(_fsum.__name__, end=_COMMASPACE_)

2081 printf(_psum.__name__, end=_COMMASPACE_)

2082

2083 F = Fsum()

2084 if F.is_math_fsum():

2085 for t in frandoms(n, seeded=True):

2086 assert float(F.fset_(*t)) == _fsum(t)

2087 printf(_DOT_, end=NN)

2088 printf(NN)

2089

2090 _test(128)

2091

2092# **) MIT License

2093#

2094# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.

2095#

2096# Permission is hereby granted, free of charge, to any person obtaining a

2097# copy of this software and associated documentation files (the "Software"),

2098# to deal in the Software without restriction, including without limitation

2099# the rights to use, copy, modify, merge, publish, distribute, sublicense,

2100# and/or sell copies of the Software, and to permit persons to whom the

2101# Software is furnished to do so, subject to the following conditions:

2102#

2103# The above copyright notice and this permission notice shall be included

2104# in all copies or substantial portions of the Software.

2105#

2106# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS

2107# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

2108# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL

2109# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR

2110# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,

2111# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR

2112# OTHER DEALINGS IN THE SOFTWARE.