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_RESIDUAL} to a C{float} string greater than

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

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

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

21 and L{Fsum.__itruediv__}.

22'''

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

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

25

26 from pygeodesy.basics import isbool, iscomplex, isint, isscalar, itemsorted, \

27 signOf, _signOf

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

29 _0_0, _1_0, _N_1_0, Float, Int

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

31 _ValueError, _xError, _xError2, _xkwds_get, \

32 _ZeroDivisionError

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

34 _EQUAL_, _from_, _LANGLE_, _NOTEQUAL_, \

35 _not_finite_, _PERCENT_, _PLUS_, _RANGLE_, \

36 _SLASH_, _SPACE_, _STAR_, _UNDER_

37 from pygeodesy.lazily import _ALL_LAZY, _getenv, _sys_version_info2

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

39 from pygeodesy.props import _allPropertiesOf_n, deprecated_property_RO, \

40 Property_RO, property_RO

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

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

43

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

45

46__all__ = _ALL_LAZY.fsums

47__version__ = '24.05.02'

48

49_add_op_ = _PLUS_ # in .auxilats.auxAngle

50_eq_op_ = _EQUAL_ * 2 # _DEQUAL_

51_div_ = 'div'

52_floordiv_op_ = _SLASH_ * 2 # _DSLASH_

53_fset_op_ = _EQUAL_

54_ge_op_ = _RANGLE_ + _EQUAL_

55_gt_op_ = _RANGLE_

56_iadd_op_ = _add_op_ + _EQUAL_ # in .auxilats.auxAngle, .fstats

57_integer_ = 'integer'

58_isinstance = isinstance

59_le_op_ = _LANGLE_ + _EQUAL_

60_lt_op_ = _LANGLE_

61_mod_ = 'mod'

62_mod_op_ = _PERCENT_

63_mul_op_ = _STAR_

64_ne_op_ = _NOTEQUAL_

65_non_zero_ = 'non-zero'

66_pow_op_ = _STAR_ * 2 # _DSTAR_

67_significant_ = 'significant'

68_sub_op_ = _DASH_ # in .auxilats.auxAngle

69_threshold_ = 'threshold'

70_truediv_op_ = _SLASH_

71_divmod_op_ = _floordiv_op_ + _mod_op_

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

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 _FsT = _Fsum_Fsum2Tuple_types

113 _is = _isinstance

114 for x in xs:

115 if _is(x, _FsT):

116 for p in _X(x._Fsum):

117 yield p

118 else:

119 f = _x(x)

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

121 i += 1

122 except Exception as X:

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

124

125

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

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

128 '''

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

130

131

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

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

134 '''

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

136

137

138 def _2halfeven(s, r, p):

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

140 '''

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

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

143 r *= 2

144 t = s + r

145 if r == (t - s):

146 s = t

147 return s

148

149

150 def _isFsum(x):

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

152 '''

153 return _isinstance(x, Fsum)

154

155

156 def _isFsumTuple(x):

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

158 '''

159 return _isinstance(x, _Fsum_Fsum2Tuple_types)

160

161

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

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

164 '''

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

166

167

168 def _1primed(xs): # in .fmath

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

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

171 '''

172 yield _1_0

173 for x in xs:

174 yield x

175 yield _N_1_0

176

177

178 def _psum(ps): # PYCHOK used!

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

180 '''

181 # assert _isinstance(ps, list)

182 i = len(ps) - 1

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

184 _2s = _2sum

185 while i > 0:

186 i -= 1

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

188 if r: # sum(ps) became inexact

189 if s:

190 ps[i:] = r, s

191 if i > 0:

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

193 break # return s

194 s = r # PYCHOK no cover

195 ps[i:] = s,

196 return s

197

198

199 def _Psum(ps, **name):

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

201 '''

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

203 if ps:

204 F._ps[:] = ps

205 F._n = len(F._ps)

206 return F

207

208

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

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

211 '''

212 return _Psum(ps, **name)

213

214

215 def _2scalar2(other):

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

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

218 '''

219 if _isFsumTuple(other):

220 s, r = other._fint2

221 if r:

222 s, r = other._fprs2

223 if r: # PYCHOK no cover

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

225 else:

226 r = 0

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

228 if isint(s, both=True):

229 s = int(s)

230 return s, r

231

232

233 def _s_r(s, r):

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

235 '''

236 if r:

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

238 s, r = r, (s or INT0)

239 else:

240 r = INT0

241 return s, r

242

243

244 def _strcomplex(s, *args):

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

246 '''

247 c = _strcomplex.__name__[4:]

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

249 t = unstr(pow, *args)

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

251

252

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

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

255 '''

256 p = _stresidual.__name__[3:]

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

258 for n, v in itemsorted(mod_ratio):

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

260 t = _COMMASPACE_(t, p)

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

262

263

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

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

266 '''

267 s = a + b

268 if _isfinite(s):

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

270 b, a = a, b

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

272 u = unstr(_2sum, a, b)

273 t = Fmt.PARENSPACED(_not_finite_, s)

274 raise _OverflowError(u, txt=t)

275

276

277 def _threshold(threshold):

278 '''(INTERNAL) Get the L{ResidualError}s threshold.

279 '''

280 try:

281 t = float(threshold) or _0_0

282 return t if _isfinite(t) else _2error(t) # PYCHOK None

283 except Exception as x:

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

285

286

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

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

289

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

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

292 intermediate, I{running} summuation.

293

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

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

296 C{float}, except C{complex}.

297

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

299 Python's C{math.fsum}.

300

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

302 393090_Binary_floating_point_summatiaccurate_full/recipe-393090.py>},

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

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

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

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

307 '''

308 _math_fsum = None

309 _n = 0

310# _ps = [] # partial sums

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

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

313

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

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

316

317 @arg xs: No, one or more items to add (each C{scalar} or an L{Fsum}

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

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

320 the C{B{RESIDUAL}=0.0} threshold for L{ResidualError}s.

321

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

323 '''

324 if name_RESIDUAL:

325

326 def _n_r(name=NN, RESIDUAL=None):

327 return name, RESIDUAL

328

329 n, r = _n_r(**name_RESIDUAL)

330 if r is not None:

331 self.RESIDUAL(r)

332 if n:

333 self.name = n

334

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

336 if xs:

337 self._facc_1(xs, up=False)

338

339 def __abs__(self):

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

341 '''

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

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

344

345 def __add__(self, other):

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

347

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

349

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

351

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

353 '''

354 f = self._copy_2(self.__add__)

355 return f._fadd(other, _add_op_)

356

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

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

359 '''

360 s, r = self._fprs2

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

362

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

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

365

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

367

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

369 '''

370 return self.ceil

371

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

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

374

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

376

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

378 '''

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

380 return _signOf(s, 0)

381

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

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

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

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

386

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

388 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} (C{bool}) to

389 ignore L{ResidualError}s and C{B{RESIDUAL}=scalar}

390 to override the L{RESIDUAL<Fsum.RESIDUAL>}.

391

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

393 B{C{RESIDUAL}}.

394

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

396 '''

397 f = self._copy_2(self.__divmod__)

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

399

400 def __eq__(self, other):

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

402 '''

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

404

405 def __float__(self):

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

407

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

409 '''

410 return float(self._fprs)

411

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

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

414

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

416

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

418 '''

419 return self.floor

420

421 def __floordiv__(self, other):

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

423

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

425

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

427

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

429 '''

430 f = self._copy_2(self.__floordiv__)

431 return f._floordiv(other, _floordiv_op_)

432

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

434 '''Not implemented.'''

435 return _NotImplemented(self, *other)

436

437 def __ge__(self, other):

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

439 '''

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

441

442 def __gt__(self, other):

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

444 '''

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

446

447 def __hash__(self): # PYCHOK no cover

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

449 '''

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

451

452 def __iadd__(self, other):

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

454

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

456

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

458

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

460 C{scalar} nor L{Fsum}.

461

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

463 '''

464 return self._fadd(other, _iadd_op_)

465

466 def __ifloordiv__(self, other):

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

468

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

470

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

472

473 @raise ResidualError: Non-zero, significant residual

474 in B{C{other}}.

475

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

477

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

479

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

481

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

483 '''

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

485

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

487 '''Not implemented.'''

488 return _NotImplemented(self, other)

489

490 def __imod__(self, other):

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

492

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

494

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

496

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

498 '''

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

500

501 def __imul__(self, other):

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

503

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

505

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

507

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

509

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

511

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

513 '''

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

515

516 def __int__(self):

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

518

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

520 and L{Fsum.__floor__} and properties

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

522 '''

523 i, _ = self._fint2

524 return i

525

526 def __invert__(self): # PYCHOK no cover

527 '''Not implemented.'''

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

529 return _NotImplemented(self)

530

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

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

533

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

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

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

537 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} (C{bool}) to

538 ignore L{ResidualError}s and C{B{RESIDUAL}=scalar}

539 to override the L{RESIDUAL<Fsum.RESIDUAL>}.

540

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

542

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

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

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

546

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

548

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

550 is non-zero and significant and either

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

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

553 C{None}.

554

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

556 invocation failed.

557

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

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

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

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

562 is given as C{0}.

563

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

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

566 '''

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

568

569 def __isub__(self, other):

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

571

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

573

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

575

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

577

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

579 '''

580 return self._fsub(other, _isub_op_)

581

582 def __iter__(self):

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

584 '''

585 return iter(self.partials)

586

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

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

589

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

591 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} (C{bool}) to

592 ignore L{ResidualError}s and C{B{RESIDUAL}=scalar}

593 to override the L{RESIDUAL<Fsum.RESIDUAL>}.

594

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

596

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

598

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

600 B{C{RESIDUAL}}.

601

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

603

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

605

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

607

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

609 '''

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

611

612 def __le__(self, other):

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

614 '''

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

616

617 def __len__(self):

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

619 '''

620 return self._n

621

622 def __lt__(self, other):

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

624 '''

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

626

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

628 '''Not implemented.'''

629 return _NotImplemented(self, other)

630

631 def __mod__(self, other):

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

633

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

635 '''

636 f = self._copy_2(self.__mod__)

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

638

639 def __mul__(self, other):

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

641

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

643 '''

644 f = self._copy_2(self.__mul__)

645 return f._fmul(other, _mul_op_)

646

647 def __ne__(self, other):

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

649 '''

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

651

652 def __neg__(self):

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

654 '''

655 f = self._copy_2(self.__neg__)

656 return f._fset(self._neg)

657

658 def __pos__(self):

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

660 '''

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

662

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

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

665

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

667 '''

668 f = self._copy_2(self.__pow__)

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

670

671 def __radd__(self, other):

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

673

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

675 '''

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

677 return f._fadd(self, _add_op_)

678

679 def __rdivmod__(self, other):

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

681 C{(quotient, remainder)}.

682

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

684 '''

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

686 return f._fdivmod2(self, _divmod_op_)

687

688# def __repr__(self):

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

690# '''

691# return self.toRepr(lenc=True)

692

693 def __rfloordiv__(self, other):

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

695

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

697 '''

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

699 return f._floordiv(self, _floordiv_op_)

700

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

702 '''Not implemented.'''

703 return _NotImplemented(self, other)

704

705 def __rmod__(self, other):

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

707

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

709 '''

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

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

712

713 def __rmul__(self, other):

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

715

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

717 '''

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

719 return f._fmul(self, _mul_op_)

720

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

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

723

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

725 '''

726 f = self._copy_2(self.__round__)

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

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

729

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

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

732

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

734 '''

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

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

737

738 def __rsub__(self, other):

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

740

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

742 '''

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

744 return f._fsub(self, _sub_op_)

745

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

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

748

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

750 '''

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

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

753

754 def __str__(self):

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

756 '''

757 return self.toStr(lenc=True)

758

759 def __sub__(self, other):

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

761

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

763

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

765

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

767 '''

768 f = self._copy_2(self.__sub__)

769 return f._fsub(other, _sub_op_)

770

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

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

773

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

775 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} (C{bool}) to

776 ignore L{ResidualError}s and C{B{RESIDUAL}=scalar}

777 to override the L{RESIDUAL<Fsum.RESIDUAL>}.

778

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

780

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

782 B{C{RESIDUAL}}.

783

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

785 '''

786 f = self._copy_2(self.__truediv__)

787 return f._ftruediv(other, _truediv_op_, **raiser_RESIDUAL)

788

789 __trunc__ = __int__

790

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

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

793 __div__ = __truediv__

794 __idiv__ = __itruediv__

795 __long__ = __int__

796 __nonzero__ = __bool__

797 __rdiv__ = __rtruediv__

798

799 def as_integer_ratio(self):

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

801

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

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

804

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

806 '''

807 n, r = self._fint2

808 if r:

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

810 n *= d

811 n += i

812 else: # PYCHOK no cover

813 d = 1

814 return n, d

815

816 @property_RO

817 def as_iscalar(self):

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

819 '''

820 s, r = self._fprs2

821 return self if r else s

822

823 @property_RO

824 def ceil(self):

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

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

827

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

829

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

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

832 '''

833 s, r = self._fprs2

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

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

836 c += 1

837 return c

838

839 cmp = __cmp__

840

841 def _cmp_0(self, other, op):

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

843 '''

844 if _isFsumTuple(other):

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

846 elif self._scalar(other, op):

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

848 else:

849 s = self.signOf() # res=True

850 return s

851

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

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

854

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

856 '''

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

858 if f._ps is self._ps:

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

860 if not deep:

861 f._n = 1

862 return f

863

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

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

866 '''

867 n = name or which.__name__

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

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

870 # assert f._n == self._n

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

872 return f

873

874 def _copy_2r(self, other, which):

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

876 '''

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

878 self._copy_2(which)._fset(other)

879

880# def _copy_RESIDUAL(self, other):

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

882# '''

883# R = other._RESIDUAL

884# if R is not Fsum._RESIDUAL:

885# self._RESIDUAL = R

886

887 divmod = __divmod__

888

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

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

891 '''

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

893

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

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

896 '''

897 E, t = _xError2(X)

898 if mod:

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

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

901

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

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

904 '''

905 E, t = _xError2(X)

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

907 return E(u, txt=t, cause=X)

908

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

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

911 '''

912 if xs:

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

914 ps = self._ps

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

916 return self

917

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

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

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

921 '''

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

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

924

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

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

927 '''

928 def _N(X):

929 return X._ps_neg

930

931 def _n(x):

932 return -float(x)

933

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

935

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

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

938 '''

939 def _Pow4(p):

940 r = 0

941 if _isFsumTuple(p):

942 s, r = p._fprs2

943 if r:

944 m = Fsum._pow

945 else: # scalar

946 return _Pow4(s)

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

948 p = s = int(p)

949 m = Fsum._pow_int

950 else:

951 p = s = _2float(power=p)

952 m = Fsum._pow_scalar

953 return m, p, s, r

954

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

956 if p: # and xs:

957 op = which.__name__

958 _isF = _isFsum

959 _pow = self._pow_2_3

960

961 def _P(X):

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

963 return f._ps if _isF(f) else (f,)

964

965 def _p(x):

966 x = float(x)

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

968 if f and r:

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

970 return f

971

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

973 else:

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

975 return f

976

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

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

979 '''

980 if xs:

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

982 return self

983

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

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

986 '''

987 if xs:

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

989 return self

990

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

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

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

994# '''

995# ps = self._ps

996# while len(ps) > 1:

997# p = ps.pop()

998# if p:

999# n = self._n

1000# _ = self._ps_acc(ps, (p,), up=False)

1001# self._n = n

1002# break

1003# return self._update() if up else self

1004

1005 def fadd(self, xs=()):

1006 '''Add all items from an iterable to this instance.

1007

1008 @arg xs: Iterable of items to add (each C{scalar}

1009 or an L{Fsum} or L{Fsum2Tuple} instance).

1010

1011 @return: This instance (L{Fsum}).

1012

1013 @raise OverflowError: Partial C{2sum} overflow.

1014

1015 @raise TypeError: An invalid B{C{xs}} item.

1016

1017 @raise ValueError: Invalid or non-finite B{C{xs}} value.

1018 '''

1019 if _isFsumTuple(xs):

1020 self._facc_scalar(xs._ps) # tuple(xs._ps)

1021 elif isscalar(xs): # for backward compatibility

1022 self._facc_scalar_(_2float(x=xs)) # PYCHOK no cover

1023 elif xs: # assert isiterable(xs)

1024 self._facc(xs)

1025 return self

1026

1027 def fadd_(self, *xs):

1028 '''Add all positional arguments to this instance.

1029

1030 @arg xs: Values to add (each C{scalar} or an L{Fsum}

1031 or L{Fsum2Tuple} instance), all positional.

1032

1033 @see: Method L{Fsum.fadd} for further details.

1034 '''

1035 return self._facc_1(xs)

1036

1037 def _fadd(self, other, op, **up): # in .fmath.Fhorner

1038 '''(INTERNAL) Apply C{B{self} += B{other}}.

1039 '''

1040 if _isFsumTuple(other):

1041 self._facc_scalar(other._ps, **up) # tuple

1042 elif self._scalar(other, op):

1043 self._facc_scalar_(other, **up)

1044 return self

1045

1046 fcopy = copy # for backward compatibility

1047 fdiv = __itruediv__ # for backward compatibility

1048 fdivmod = __divmod__ # for backward compatibility

1049

1050 def _fdivmod2(self, other, op, **raiser_RESIDUAL):

1051 '''(INTERNAL) Apply C{B{self} %= B{other}} and return a L{DivMod2Tuple}.

1052 '''

1053 # result mostly follows CPython function U{float_divmod

1054 # <https://GitHub.com/python/cpython/blob/main/Objects/floatobject.c>},

1055 # but at least divmod(-3, 2) equals Cpython's result (-2, 1).

1056 q = self._copy_2(self._fdivmod2)

1057 q = q._ftruediv(other, op, **raiser_RESIDUAL).floor

1058 if q: # == float // other == floor(float / other)

1059 self -= Fsum(other) * q # NO Fsum2Tuple.__mul__!

1060

1061 s = signOf(other) # make signOf(self) == signOf(other)

1062 if s and self.signOf() == -s: # PYCHOK no cover

1063 self += other

1064 q -= 1

1065# t = self.signOf()

1066# if t and t != s:

1067# raise self._Error(op, other, _AssertionError, txt=signOf.__name__)

1068 return DivMod2Tuple(q, self) # q is C{int} in Python 3+, but C{float} in Python 2-

1069

1070 def _finite(self, other, op=None):

1071 '''(INTERNAL) Return B{C{other}} if C{finite}.

1072 '''

1073 if _isfinite(other):

1074 return other

1075 raise ValueError(_not_finite_) if op is None else \

1076 self._ValueError(op, other, txt=_not_finite_)

1077

1078 def fint(self, name=NN, **raiser_RESIDUAL):

1079 '''Return this instance' current running sum as C{integer}.

1080

1081 @kwarg name: Optional name (C{str}), overriding C{"fint"}.

1082 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} (C{bool}) to

1083 ignore L{ResidualError}s and C{B{RESIDUAL}=scalar}

1084 to override the L{RESIDUAL<Fsum.RESIDUAL>}.

1085

1086 @return: The C{integer} sum (L{Fsum}) if this instance C{is_integer}

1087 with a zero or insignificant I{integer} residual.

1088

1089 @raise ResidualError: Non-zero, significant residual or invalid

1090 B{C{RESIDUAL}}.

1091

1092 @see: Methods L{Fsum.int_float} and L{Fsum.is_integer}.

1093 '''

1094 i, r = self._fint2

1095 if r:

1096 R = self._raiser(r, i, **raiser_RESIDUAL)

1097 if R:

1098 t = _stresidual(_integer_, r, **R)

1099 raise ResidualError(_integer_, i, txt=t)

1100 f = self._copy_2(self.fint, name=name)

1101 return f._fset(i)

1102

1103 def fint2(self, **name):

1104 '''Return this instance' current running sum as C{int} and the

1105 I{integer} residual.

1106

1107 @kwarg name: Optional name (C{str}).

1108

1109 @return: An L{Fsum2Tuple}C{(fsum, residual)} with C{fsum}

1110 an C{int} and I{integer} C{residual} a C{float} or

1111 C{INT0} if the C{fsum} is considered to be I{exact}.

1112 '''

1113 return Fsum2Tuple(*self._fint2, **name)

1114

1115 @Property_RO

1116 def _fint2(self): # see ._fset

1117 '''(INTERNAL) Get 2-tuple (C{int}, I{integer} residual).

1118 '''

1119 s, r = self._fprs2

1120 i = int(s)

1121 r = _fsum(self._ps_1primed(i)) if r else float(s - i)

1122 return i, (r or INT0) # Fsum2Tuple?

1123

1124 @deprecated_property_RO

1125 def float_int(self): # PYCHOK no cover

1126 '''DEPRECATED, use method C{Fsum.int_float}.'''

1127 return self.int_float() # raiser=False

1128

1129 @property_RO

1130 def floor(self):

1131 '''Get this instance' C{floor} (C{int} in Python 3+, but

1132 C{float} in Python 2-).

1133

1134 @note: The C{floor} takes the C{residual} into account.

1135

1136 @see: Method L{Fsum.int_float} and properties L{Fsum.ceil},

1137 L{Fsum.imag} and L{Fsum.real}.

1138 '''

1139 s, r = self._fprs2

1140 f = _floor(s) + _floor(r) + 1

1141 while (f - s) > r: # f > (s + r)

1142 f -= 1

1143 return f

1144

1145# floordiv = __floordiv__ # for naming consistency

1146

1147 def _floordiv(self, other, op, **raiser_RESIDUAL): # rather _ffloordiv?

1148 '''Apply C{B{self} //= B{other}}.

1149 '''

1150 q = self._ftruediv(other, op, **raiser_RESIDUAL) # == self

1151 return self._fset(q.floor) # floor(q)

1152

1153 fmul = __imul__ # for backward compatibility

1154

1155 def _fmul(self, other, op):

1156 '''(INTERNAL) Apply C{B{self} *= B{other}}.

1157 '''

1158 if _isFsumTuple(other):

1159 if len(self._ps) != 1:

1160 f = self._mul_Fsum(other, op)

1161 elif len(other._ps) != 1: # and len(self._ps) == 1

1162 f = other._mul_scalar(self._ps[0], op)

1163 else: # len(other._ps) == len(self._ps) == 1

1164 f = self._finite(self._ps[0] * other._ps[0])

1165 else:

1166 s = self._scalar(other, op)

1167 f = self._mul_scalar(s, op)

1168 return self._fset(f) # n=len(self) + 1

1169

1170 def fover(self, over, **raiser_RESIDUAL):

1171 '''Apply C{B{self} /= B{over}} and summate.

1172

1173 @arg over: An L{Fsum} or C{scalar} denominator.

1174 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} (C{bool}) to

1175 ignore L{ResidualError}s and C{B{RESIDUAL}=scalar}

1176 to override the L{RESIDUAL<Fsum.RESIDUAL>}.

1177

1178 @return: Precision running sum (C{float}).

1179

1180 @raise ResidualError: Non-zero, significant residual or invalid

1181 B{C{RESIDUAL}}.

1182

1183 @see: Methods L{Fsum.fsum} and L{Fsum.__itruediv__}.

1184 '''

1185 return float(self.fdiv(over, **raiser_RESIDUAL)._fprs)

1186

1187 fpow = __ipow__ # for backward compatibility

1188

1189 def _fpow(self, other, op, *mod, **raiser_RESIDUAL):

1190 '''Apply C{B{self} **= B{other}}, optional B{C{mod}} or C{None}.

1191 '''

1192 if mod:

1193 if mod[0] is not None: # == 3-arg C{pow}

1194 f = self._pow_2_3(self, other, other, op, *mod, **raiser_RESIDUAL)

1195 elif self.is_integer():

1196 # return an exact C{int} for C{int}**C{int}

1197 i, _ = self._fint2 # assert _ == 0

1198 x, r = _2scalar2(other) # C{int}, C{float} or other

1199 f = _Psum_(i)._pow_Fsum(other, op, **raiser_RESIDUAL) if r else \

1200 self._pow_2_3(i, x, other, op, **raiser_RESIDUAL)

1201 else: # mod[0] is None, power(self, other)

1202 f = self._pow(other, other, op, **raiser_RESIDUAL)

1203 else: # pow(self, other)

1204 f = self._pow(other, other, op, **raiser_RESIDUAL)

1205 return self._fset(f, asis=isint(f)) # n=max(len(self), 1)

1206

1207 @Property_RO

1208 def _fprs(self):

1209 '''(INTERNAL) Get and cache this instance' precision

1210 running sum (C{float} or C{int}), ignoring C{residual}.

1211

1212 @note: The precision running C{fsum} after a C{//=} or

1213 C{//} C{floor} division is C{int} in Python 3+.

1214 '''

1215 return self._fprs2.fsum

1216

1217 @Property_RO

1218 def _fprs2(self):

1219 '''(INTERNAL) Get and cache this instance' precision

1220 running sum and residual (L{Fsum2Tuple}).

1221 '''

1222 ps = self._ps

1223 n = len(ps) - 2

1224 if n > 0: # len(ps) > 2

1225 s = _psum(ps)

1226 n = len(ps) - 2

1227 if n > 0:

1228 r = _fsum(self._ps_1primed(s))

1229 return Fsum2Tuple(*_s_r(s, r))

1230 if n == 0: # len(ps) == 2

1231 s, r = _s_r(*_2sum(*ps))

1232 ps[:] = (r, s) if r else (s,)

1233 elif ps: # len(ps) == 1

1234 s, r = ps[0], INT0

1235 else: # len(ps) == 0

1236 s, r = _0_0, INT0

1237 ps[:] = s,

1238 # assert self._ps is ps

1239 return Fsum2Tuple(s, r)

1240

1241 def fset_(self, *xs):

1242 '''Replace this instance' value with C{xs}.

1243

1244 @arg xs: Optional, new values (each C{scalar} or

1245 an L{Fsum} or L{Fsum2Tuple} instance),

1246 all positional.

1247

1248 @return: This instance (C{Fsum}).

1249

1250 @see: Method L{Fsum.fadd} for further details.

1251 '''

1252 f = Fsum(*xs) if xs else _0_0

1253 return self._fset(f)

1254

1255 def _fset(self, other, asis=True, n=0):

1256 '''(INTERNAL) Overwrite this instance with an other or a C{scalar}.

1257 '''

1258 if other is self:

1259 pass # from ._fmul, ._ftruediv and ._pow_0_1

1260 elif _isFsumTuple(other):

1261 self._ps[:] = other._ps

1262 self._n = n or other._n

1263# self._copy_RESIDUAL(other)

1264 # use or zap the C{Property_RO} values

1265 Fsum._fint2._update_from(self, other)

1266 Fsum._fprs ._update_from(self, other)

1267 Fsum._fprs2._update_from(self, other)

1268 elif isscalar(other):

1269 s = other if asis else float(other)

1270 i = int(s) # see ._fint2

1271 t = i, ((s - i) or INT0)

1272 self._ps[:] = s,

1273 self._n = n or 1

1274 # Property_ROs _fint2, _fprs and _fprs2 can't be a Property:

1275 # Property's _fset zaps the value just set by the @setter

1276 self.__dict__.update(_fint2=t, _fprs=s, _fprs2=Fsum2Tuple(s, INT0))

1277 else: # PYCHOK no cover

1278 raise self._Error(_fset_op_, other, _AssertionError)

1279 return self

1280

1281 def _fset_ps(self, other, n=0): # in .fmath

1282 '''(INTERNAL) Set partials from a known C{scalar}, L{Fsum} or L{Fsum2Tuple}.

1283 '''

1284 if _isFsumTuple(other):

1285 self._ps[:] = other._ps

1286 self._n = n or other._n

1287 else: # assert isscalar(other)

1288 self._ps[:] = other,

1289 self._n = n or 1

1290 return self

1291

1292 def fsub(self, xs=()):

1293 '''Subtract all items of an iterable from this instance.

1294

1295 @see: Method L{Fsum.fadd} for further details.

1296 '''

1297 return self._facc_neg(xs)

1298

1299 def fsub_(self, *xs):

1300 '''Subtract all positional arguments from this instance.

1301

1302 @see: Method L{Fsum.fadd_} for further details.

1303 '''

1304 return self._fsub(xs[0], _sub_op_) if len(xs) == 1 else \

1305 self._facc_neg(xs, origin=1)

1306

1307 def _fsub(self, other, op):

1308 '''(INTERNAL) Apply C{B{self} -= B{other}}.

1309 '''

1310 if _isFsumTuple(other):

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

1312 self._fset(_0_0, n=len(self) * 2)

1313 elif other._ps:

1314 self._facc_scalar(other._ps_neg)

1315 elif self._scalar(other, op):

1316 self._facc_scalar_(-other)

1317 return self

1318

1319 def fsum(self, xs=()):

1320 '''Add more items from an iterable, summate and return

1321 the current precision running sum.

1322

1323 @arg xs: Iterable of items to add (each item C{scalar}

1324 or an L{Fsum} or L{Fsum2Tuple} instance).

1325

1326 @return: Precision running sum (C{float} or C{int}).

1327

1328 @see: Method L{Fsum.fadd}.

1329

1330 @note: Accumulation can continue after summation.

1331 '''

1332 return self._facc(xs)._fprs

1333

1334 def fsum_(self, *xs):

1335 '''Add any positional arguments, summate and return the

1336 current precision running sum.

1337

1338 @arg xs: Values to add (each C{scalar} or an L{Fsum}

1339 or L{Fsum2Tuple} instance), all positional.

1340

1341 @return: Precision running sum (C{float} or C{int}).

1342

1343 @see: Methods L{Fsum.fsum}, L{Fsum.Fsum_} and L{Fsum.fsumf_}.

1344 '''

1345 return self._facc_1(xs)._fprs

1346

1347 @property_RO

1348 def _Fsum(self):

1349 '''(INTERNAL) Like L{Fsum2Tuple._Fsum}, for C{_2floats}.

1350 '''

1351 return self

1352

1353 def Fsum_(self, *xs, **name):

1354 '''Like method L{Fsum.fsum_} but returning a named L{Fsum}.

1355

1356 @kwarg name: Optional name (C{str}).

1357

1358 @return: Current, precision running sum (L{Fsum}).

1359 '''

1360 return self._facc_1(xs)._copy_2(self.Fsum_, **name)

1361

1362 def Fsum2Tuple_(self, *xs, **name):

1363 '''Like method L{Fsum.fsum_} but returning a named L{Fsum2Tuple}.

1364

1365 @kwarg name: Optional name (C{str}).

1366

1367 @return: Current, precision running sum (L{Fsum2Tuple}).

1368 '''

1369 return Fsum2Tuple(self._facc_1(xs)._fprs2, **name)

1370

1371 def fsum2(self, xs=(), name=NN):

1372 '''Add more items from an iterable, summate and return the

1373 current precision running sum I{and} the C{residual}.

1374

1375 @arg xs: Iterable of items to add (each item C{scalar}

1376 or an L{Fsum} or L{Fsum2Tuple} instance).

1377 @kwarg name: Optional name (C{str}).

1378

1379 @return: L{Fsum2Tuple}C{(fsum, residual)} with C{fsum} the

1380 current precision running sum and C{residual}, the

1381 (precision) sum of the remaining C{partials}. The

1382 C{residual is INT0} if the C{fsum} is considered

1383 to be I{exact}.

1384

1385 @see: Methods L{Fsum.fint2}, L{Fsum.fsum} and L{Fsum.fsum2_}

1386 '''

1387 t = self._facc(xs)._fprs2

1388 return t.dup(name=name) if name else t

1389

1390 def fsum2_(self, *xs):

1391 '''Add any positional arguments, summate and return the current

1392 precision running sum I{and} the C{differential}.

1393

1394 @arg xs: Values to add (each C{scalar} or an L{Fsum} or

1395 L{Fsum2Tuple} instance), all positional.

1396

1397 @return: 2Tuple C{(fsum, delta)} with the current, precision

1398 running C{fsum} like method L{Fsum.fsum} and C{delta},

1399 the difference with previous running C{fsum}, C{float}.

1400

1401 @see: Methods L{Fsum.fsum_} and L{Fsum.fsum}.

1402 '''

1403 return self._fsum2(xs, self._facc_1)

1404

1405 def _fsum2(self, xs, _f, **origin):

1406 '''(INTERNAL) Helper for L{Fsum.fsum2_} and L{Fsum.fsum2f_}.

1407 '''

1408 p, q = self._fprs2

1409 if xs:

1410 s, r = _f(xs, **origin)._fprs2

1411 return s, _2delta(s - p, r - q) # _fsum(_1primed((s, -p, r, -q))

1412 else:

1413 return p, _0_0

1414

1415 def fsumf_(self, *xs):

1416 '''Like method L{Fsum.fsum_} iff I{all} C{B{xs}} are I{known to be scalar}.

1417 '''

1418 return self._facc_scalar(xs)._fprs

1419

1420 def Fsumf_(self, *xs):

1421 '''Like method L{Fsum.Fsum_} iff I{all} C{B{xs}} are I{known to be scalar}.

1422 '''

1423 return self._facc_scalar(xs)._copy_2(self.Fsumf_)

1424

1425 def fsum2f_(self, *xs):

1426 '''Like method L{Fsum.fsum2_} iff I{all} C{B{xs}} are I{known to be scalar}.

1427 '''

1428 return self._fsum2(xs, self._facc_scalar, origin=1)

1429

1430# ftruediv = __itruediv__ # for naming consistency?

1431

1432 def _ftruediv(self, other, op, **raiser_RESIDUAL):

1433 '''(INTERNAL) Apply C{B{self} /= B{other}}.

1434 '''

1435 n = _1_0

1436 if _isFsumTuple(other):

1437 if other is self or self == other:

1438 return self._fset(n) # n=len(self)

1439 d, r = other._fprs2

1440 if r:

1441 R = self._raiser(r, d, **raiser_RESIDUAL)

1442 if R:

1443 raise self._ResidualError(op, other, r, **R)

1444 d, n = other.as_integer_ratio()

1445 else:

1446 d = self._scalar(other, op)

1447 try:

1448 s = n / d

1449 except Exception as X:

1450 raise self._ErrorX(X, op, other)

1451 f = self._mul_scalar(s, _mul_op_) # handles 0, INF, NAN

1452 return self._fset(f) # asis=False

1453

1454 @property_RO

1455 def imag(self):

1456 '''Get the C{imaginary} part of this instance (C{0.0}, always).

1457

1458 @see: Properties L{Fsum.ceil}, L{Fsum.floor} and L{Fsum.real}.

1459 '''

1460 return _0_0

1461

1462 def int_float(self, **raiser_RESIDUAL):

1463 '''Return this instance' current running sum as C{int} or C{float}.

1464

1465 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} (C{bool}) to

1466 ignore L{ResidualError}s and C{B{RESIDUAL}=scalar}

1467 to override the L{RESIDUAL<Fsum.RESIDUAL>}.

1468

1469 @return: This C{integer} sum if this instance C{is_integer},

1470 otherwise return the C{float} sum if the residual is

1471 zero or not significant.

1472

1473 @raise ResidualError: Non-zero, significant residual or invalid

1474 B{C{RESIDUAL}}.

1475

1476 @see: Methods L{Fsum.fint}, L{Fsum.fint2}, L{Fsum.RESIDUAL} and

1477 property L{Fsum.as_iscalar}.

1478 '''

1479 s, r = self._fint2

1480 if r:

1481 s, r = self._fprs2

1482 if r: # PYCHOK no cover

1483 R = self._raiser(r, s, **raiser_RESIDUAL)

1484 if R:

1485 t = _stresidual(_non_zero_, r, **R)

1486 raise ResidualError(int_float=s, txt=t)

1487 s = float(s) # redundant

1488 return s

1489

1490 def is_exact(self):

1491 '''Is this instance' running C{fsum} considered to be exact? (C{bool}).

1492 '''

1493 return self.residual is INT0

1494

1495 def is_integer(self):

1496 '''Is this instance' running sum C{integer}? (C{bool}).

1497

1498 @see: Methods L{Fsum.fint}, L{Fsum.fint2} and L{Fsum.is_scalar}.

1499 '''

1500 _, r = self._fint2

1501 return False if r else True

1502

1503 def is_math_fsum(self):

1504 '''Return whether functions L{fsum}, L{fsum_}, L{fsum1} and

1505 L{fsum1_} plus partials summation are based on Python's

1506 C{math.fsum} or not.

1507

1508 @return: C{2} if all functions and partials summation

1509 are based on C{math.fsum}, C{True} if only

1510 the functions are based on C{math.fsum} (and

1511 partials summation is not) or C{False} if

1512 none are.

1513 '''

1514 f = Fsum._math_fsum

1515 return 2 if _psum is f else bool(f)

1516

1517 def is_scalar(self, **raiser_RESIDUAL):

1518 '''Is this instance' running sum C{scalar} with an insignificant

1519 residual and the residual I{ratio} not exceeding the RESIDUAL

1520 threshold? (C{bool}).

1521

1522 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} (C{bool}) to

1523 ignore L{ResidualError}s and C{B{RESIDUAL}=scalar}

1524 to override the L{RESIDUAL<Fsum.RESIDUAL>}.

1525

1526 @raise ResidualError: Non-zero, significant residual or invalid

1527 B{C{RESIDUAL}}.

1528

1529 @see: Method L{Fsum.RESIDUAL}, L{Fsum.is_integer} and property

1530 L{Fsum.as_iscalar}.

1531 '''

1532 s, r = self._fprs2

1533 return False if r and self._raiser(r, s, **raiser_RESIDUAL) else True

1534

1535 def _mul_Fsum(self, other, op=_mul_op_): # in .fmath.Fhorner

1536 '''(INTERNAL) Return C{B{self} * B{other}} as L{Fsum} or C{0}.

1537 '''

1538 # assert _isFsumTuple(other)

1539 if self._ps and other._ps:

1540 f = self._ps_mul(op, *other._ps) # NO .as_iscalar

1541 else:

1542 f = _0_0

1543 return f

1544

1545 def _mul_scalar(self, factor, op): # in .fmath.Fhorner

1546 '''(INTERNAL) Return C{B{self} * scalar B{factor}} as L{Fsum}, C{0} or C{self}.

1547 '''

1548 # assert isscalar(factor)

1549 if self._ps and self._finite(factor, op):

1550 f = self if factor == _1_0 else (

1551 self._neg if factor == _N_1_0 else

1552 self._ps_mul(op, factor).as_iscalar)

1553 else:

1554 f = _0_0

1555 return f

1556

1557 @property_RO

1558 def _neg(self):

1559 '''(INTERNAL) Return C{Fsum(-self)} or scalar C{NEG0}.

1560 '''

1561 return _Psum(self._ps_neg) if self._ps else NEG0

1562

1563 @property_RO

1564 def partials(self):

1565 '''Get this instance' current, partial sums (C{tuple} of C{float}s).

1566 '''

1567 return tuple(self._ps)

1568

1569 def pow(self, x, *mod, **raiser_RESIDUAL):

1570 '''Return C{B{self}**B{x}} as L{Fsum}.

1571

1572 @arg x: The exponent (C{scalar} or L{Fsum}).

1573 @arg mod: Optional modulus (C{int} or C{None}) for the 3-argument

1574 C{pow(B{self}, B{other}, B{mod})} version.

1575 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} (C{bool}) to

1576 ignore L{ResidualError}s and C{B{RESIDUAL}=scalar}

1577 to override the L{RESIDUAL<Fsum.RESIDUAL>}.

1578

1579 @return: The C{pow(self, B{x})} or C{pow(self, B{x}, *B{mod})}

1580 result (L{Fsum}).

1581

1582 @raise ResidualError: Non-zero, significant residual or invalid

1583 B{C{RESIDUAL}}.

1584

1585 @note: If B{C{mod}} is given as C{None}, the result will be an

1586 C{integer} L{Fsum} provided this instance C{is_integer}

1587 or set to C{integer} by an L{Fsum.fint} call.

1588

1589 @see: Methods L{Fsum.__ipow__}, L{Fsum.fint}, L{Fsum.is_integer}

1590 and L{Fsum.root}.

1591 '''

1592 f = self._copy_2(self.pow)

1593 return f._fpow(x, _pow_op_, *mod, **raiser_RESIDUAL) # f = pow(f, x, *mod)

1594

1595 def _pow(self, other, unused, op, **raiser_RESIDUAL):

1596 '''Return C{B{self} ** B{other}}.

1597 '''

1598 if _isFsumTuple(other):

1599 f = self._pow_Fsum(other, op, **raiser_RESIDUAL)

1600 elif self._scalar(other, op):

1601 x = self._finite(other, op)

1602 f = self._pow_scalar(x, other, op, **raiser_RESIDUAL)

1603 else:

1604 f = self._pow_0_1(0, other)

1605 return f

1606

1607 def _pow_0_1(self, x, other):

1608 '''(INTERNAL) Return B{C{self}**1} or C{B{self}**0 == 1.0}.

1609 '''

1610 return self if x else (1 if isint(other) and self.is_integer() else _1_0)

1611

1612 def _pow_2_3(self, b, x, other, op, *mod, **raiser_RESIDUAL):

1613 '''(INTERNAL) 2-arg C{pow(B{b}, scalar B{x})} and 3-arg C{pow(B{b},

1614 B{x}, int B{mod} or C{None})}, embellishing errors.

1615 '''

1616

1617 if mod: # b, x, mod all C{int}, unless C{mod} is C{None}

1618 m = mod[0]

1619 # assert _isFsumTuple(b)

1620

1621 def _s(s, r):

1622 R = self._raiser(r, s, **raiser_RESIDUAL)

1623 if R:

1624 raise self._ResidualError(op, other, r, mod=m, **R)

1625 return s

1626

1627 b = _s(*(b._fprs2 if m is None else b._fint2))

1628 x = _s(*_2scalar2(x))

1629

1630 try:

1631 # 0**INF == 0.0, 1**INF == 1.0, -1**2.3 == -(1**2.3)

1632 s = pow(b, x, *mod)

1633 if iscomplex(s):

1634 # neg**frac == complex in Python 3+, but ValueError in 2-

1635 raise ValueError(_strcomplex(s, b, x, *mod))

1636 return self._finite(s)

1637 except Exception as X:

1638 raise self._ErrorX(X, op, other, *mod)

1639

1640 def _pow_Fsum(self, other, op, **raiser_RESIDUAL):

1641 '''(INTERNAL) Return C{B{self} **= B{other}} for C{_isFsumTuple(other)}.

1642 '''

1643 # assert _isFsumTuple(other)

1644 x, r = other._fprs2

1645 f = self._pow_scalar(x, other, op, **raiser_RESIDUAL)

1646 if f and r:

1647 f *= self._pow_scalar(r, other, op, **raiser_RESIDUAL)

1648 return f

1649

1650 def _pow_int(self, x, other, op, **raiser_RESIDUAL):

1651 '''(INTERNAL) Return C{B{self} **= B{x}} for C{int B{x} >= 0}.

1652 '''

1653 # assert isint(x) and x >= 0

1654 ps = self._ps

1655 if len(ps) > 1:

1656 _mul_Fsum = Fsum._mul_Fsum

1657 if x > 4:

1658 p = self

1659 f = self if (x & 1) else _Psum_(_1_0)

1660 m = x >> 1 # // 2

1661 while m:

1662 p = _mul_Fsum(p, p, op) # p **= 2

1663 if (m & 1):

1664 f = _mul_Fsum(f, p, op) # f *= p

1665 m >>= 1 # //= 2

1666 elif x > 1: # self**2, 3 or 4

1667 f = _mul_Fsum(self, self, op)

1668 if x > 2: # self**3 or 4

1669 p = self if x < 4 else f

1670 f = _mul_Fsum(f, p, op).as_iscalar

1671 else: # self**1 or self**0 == 1 or _1_0

1672 f = self._pow_0_1(x, other)

1673 elif ps: # self._ps[0]**x

1674 f = self._pow_2_3(ps[0], x, other, op, **raiser_RESIDUAL)

1675 else: # PYCHOK no cover

1676 # 0**pos_int == 0, but 0**0 == 1

1677 f = 0 if x else 1

1678 return f

1679

1680 def _pow_scalar(self, x, other, op, **raiser_RESIDUAL):

1681 '''(INTERNAL) Return C{self**B{x}} for C{scalar B{x}}.

1682 '''

1683 s, r = self._fprs2

1684 if r:

1685 # assert s != 0

1686 if isint(x, both=True): # self**int

1687 x = int(x)

1688 y = abs(x)

1689 if y > 1:

1690 f = self._pow_int(y, other, op, **raiser_RESIDUAL)

1691 if x > 0: # i.e. > 1

1692 return f # Fsum or scalar

1693 # assert x < 0 # i.e. < -1

1694 if _isFsum(f):

1695 s, r = f._fprs2

1696 if r:

1697 return _1_Over(f, op, **raiser_RESIDUAL)

1698 else: # scalar

1699 s = f

1700 # use s**(-1) to get the CPython

1701 # float_pow error iff s is zero

1702 x = -1

1703 elif x < 0: # self**(-1)

1704 return _1_Over(self, op, **raiser_RESIDUAL) # 1 / self

1705 else: # self**1 or self**0

1706 return self._pow_0_1(x, other) # self, 1 or 1.0

1707 else: # self**fractional

1708 R = self._raiser(r, s, **raiser_RESIDUAL)

1709 if R:

1710 raise self._ResidualError(op, other, r, **R)

1711 n, d = self.as_integer_ratio()

1712 if abs(n) > abs(d):

1713 n, d, x = d, n, (-x)

1714 s = n / d

1715 # assert isscalar(s) and isscalar(x)

1716 return self._pow_2_3(s, x, other, op, **raiser_RESIDUAL)

1717

1718 def _ps_acc(self, ps, xs, up=True, **unused):

1719 '''(INTERNAL) Accumulate all C{xs} scalars into list C{ps}.

1720 '''

1721 n = 0

1722 _2s = _2sum

1723 for x in (tuple(xs) if xs is ps else xs):

1724 # assert isscalar(x) and _isfinite(x)

1725 if x:

1726 i = 0

1727 for p in ps:

1728 x, p = _2s(x, p)

1729 if p:

1730 ps[i] = p

1731 i += 1

1732 ps[i:] = (x,) if x else ()

1733 n += 1

1734 if n:

1735 self._n += n

1736 # Fsum._ps_max = max(Fsum._ps_max, len(ps))

1737 if up:

1738 self._update()

1739 return ps

1740

1741 def _ps_mul(self, op, *factors):

1742 '''(INTERNAL) Multiply this instance' C{partials} with each

1743 of the scalar B{C{factors}} and accumulate.

1744 '''

1745 def _pfs(ps, fs):

1746 if len(ps) < len(fs):

1747 ps, fs = fs, ps

1748 _fin = _isfinite

1749 for f in fs:

1750 for p in ps:

1751 p *= f

1752 yield p if _fin(p) else self._finite(p, op)

1753

1754 return _Psum(self._ps_acc([], _pfs(self._ps, factors), up=False))

1755

1756 @property_RO

1757 def _ps_neg(self):

1758 '''(INTERNAL) Yield the partials, I{negated}.

1759 '''

1760 for p in self._ps:

1761 yield -p

1762

1763 def _ps_1primed(self, *less):

1764 '''(INTERNAL) Yield partials, 1-primed C{less} any scalars.

1765 '''

1766 yield _1_0

1767 for p in self._ps:

1768 yield p

1769 for p in less:

1770 yield -p

1771 yield _N_1_0

1772

1773 def _raiser(self, r, s, raiser=True, **RESIDUAL):

1774 '''(INTERNAL) Does ratio C{r / s} exceed the RESIDUAL threshold

1775 I{and} is residual C{r} I{non-zero} or I{significant} (for a

1776 negative respectively positive C{RESIDUAL} threshold)?

1777 '''

1778 if r and raiser:

1779 t = self._RESIDUAL

1780 if RESIDUAL:

1781 t = _threshold(_xkwds_get(RESIDUAL, RESIDUAL=t))

1782 if t < 0 or (s + r) != s:

1783 q = (r / s) if s else s # == 0.

1784 if fabs(q) > fabs(t):

1785 return dict(ratio=q, R=t)

1786 return {}

1787

1788 @property_RO

1789 def real(self):

1790 '''Get the C{real} part of this instance (C{float}).

1791

1792 @see: Methods L{Fsum.__float__} and L{Fsum.fsum}

1793 and properties L{Fsum.ceil}, L{Fsum.floor},

1794 L{Fsum.imag} and L{Fsum.residual}.

1795 '''

1796 return float(self._fprs)

1797

1798 @property_RO

1799 def residual(self):

1800 '''Get this instance' residual (C{float} or C{int}): the

1801 C{sum(partials)} less the precision running sum C{fsum}.

1802

1803 @note: The C{residual is INT0} iff the precision running

1804 C{fsum} is considered to be I{exact}.

1805

1806 @see: Methods L{Fsum.fsum}, L{Fsum.fsum2} and L{Fsum.is_exact}.

1807 '''

1808 return self._fprs2.residual

1809

1810 def RESIDUAL(self, *threshold):

1811 '''Get and set this instance' I{ratio} for raising L{ResidualError}s,

1812 overriding the default from env variable C{PYGEODESY_FSUM_RESIDUAL}.

1813

1814 @arg threshold: If C{scalar}, the I{ratio} to exceed for raising

1815 L{ResidualError}s in division and exponention, if

1816 C{None} restore the default set with env variable

1817 C{PYGEODESY_FSUM_RESIDUAL} or if omitted, keep the

1818 current setting.

1819

1820 @return: The previous C{RESIDUAL} setting (C{float}), default C{0.0}.

1821

1822 @raise ResidualError: Invalid B{C{threshold}}.

1823

1824 @note: L{ResidualError}s may be thrown if the non-zero I{ratio}

1825 C{residual / fsum} exceeds the given B{C{threshold}} and

1826 if the C{residual} is non-zero and I{significant} vs the

1827 C{fsum}, i.e. C{(fsum + residual) != fsum} and if optional

1828 keyword argument C{raiser=False} is missing. Specify a

1829 negative B{C{threshold}} for only non-zero C{residual}

1830 testing without I{significant}.

1831 '''

1832 r = self._RESIDUAL

1833 if threshold:

1834 t = threshold[0]

1835 self._RESIDUAL = Fsum._RESIDUAL if t is None else ( # for ...

1836 (_0_0 if t else _1_0) if isbool(t) else

1837 _threshold(t)) # ... backward compatibility

1838 return r

1839

1840 def _ResidualError(self, op, other, residual, **mod_R):

1841 '''(INTERNAL) Non-zero B{C{residual}} etc.

1842 '''

1843 def _p(mod=None, R=0, **unused): # ratio=0

1844 return (_non_zero_ if R < 0 else _significant_) \

1845 if mod is None else _integer_

1846

1847 t = _stresidual(_p(**mod_R), residual, **mod_R)

1848 return self._Error(op, other, ResidualError, txt=t)

1849

1850 def root(self, root, **raiser_RESIDUAL):

1851 '''Return C{B{self}**(1 / B{root})} as L{Fsum}.

1852

1853 @arg root: The order (C{scalar} or L{Fsum}), non-zero.

1854 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} (C{bool}) to

1855 ignore L{ResidualError}s and C{B{RESIDUAL}=scalar}

1856 to override the L{RESIDUAL<Fsum.RESIDUAL>}.

1857

1858 @return: The C{self ** (1 / B{root})} result (L{Fsum}).

1859

1860 @raise ResidualError: Non-zero, significant residual or invalid

1861 B{C{RESIDUAL}}.

1862

1863 @see: Method L{Fsum.pow}.

1864 '''

1865 x = _1_Over(root, _truediv_op_, **raiser_RESIDUAL)

1866 f = self._copy_2(self.root)

1867 return f._fpow(x, f.name, **raiser_RESIDUAL) # == pow(f, x)

1868

1869 def _scalar(self, other, op, **txt):

1870 '''(INTERNAL) Return scalar C{other}.

1871 '''

1872 if isscalar(other):

1873 return other

1874 raise self._TypeError(op, other, **txt) # _invalid_

1875

1876 def signOf(self, res=True):

1877 '''Determine the sign of this instance.

1878

1879 @kwarg res: If C{True} consider, otherwise

1880 ignore the residual (C{bool}).

1881

1882 @return: The sign (C{int}, -1, 0 or +1).

1883 '''

1884 s, r = self._fprs2

1885 r = (-r) if res else 0

1886 return _signOf(s, r)

1887

1888 def toRepr(self, **prec_sep_fmt_lenc): # PYCHOK signature

1889 '''Return this C{Fsum} instance as representation.

1890

1891 @kwarg prec_sep_fmt_lenc: Optional keyword arguments for

1892 method L{Fsum2Tuple.toRepr} plus C{B{lenc}=True}

1893 (C{bool}) to in-/exclude the current C{[len]}

1894 of this L{Fsum} enclosed in I{[brackets]}.

1895

1896 @return: This instance (C{repr}).

1897 '''

1898 return self._toT(self._fprs2.toRepr, **prec_sep_fmt_lenc)

1899

1900 def toStr(self, **prec_sep_fmt_lenc): # PYCHOK signature

1901 '''Return this C{Fsum} instance as string.

1902

1903 @kwarg prec_sep_fmt_lenc: Optional keyword arguments for

1904 method L{Fsum2Tuple.toStr} plus C{B{lenc}=True}

1905 (C{bool}) to in-/exclude the current C{[len]}

1906 of this L{Fsum} enclosed in I{[brackets]}.

1907

1908 @return: This instance (C{str}).

1909 '''

1910 return self._toT(self._fprs2.toStr, **prec_sep_fmt_lenc)

1911

1912 def _toT(self, toT, fmt=Fmt.g, lenc=True, **kwds):

1913 '''(INTERNAL) Helper for C{toRepr} and C{toStr}.

1914 '''

1915 p = self.classname

1916 if lenc:

1917 p = Fmt.SQUARE(p, len(self))

1918 n = self.name

1919 if n:

1920 n = _UNDER_(*n.split())

1921 return NN(p, _SPACE_, n, toT(fmt=fmt, **kwds))

1922

1923 def _TypeError(self, op, other, **txt): # PYCHOK no cover

1924 '''(INTERNAL) Return a C{TypeError}.

1925 '''

1926 return self._Error(op, other, _TypeError, **txt)

1927

1928 def _update(self, updated=True): # see ._fset

1929 '''(INTERNAL) Zap all cached C{Property_RO} values.

1930 '''

1931 if updated:

1932 _pop = self.__dict__.pop

1933 for p in _ROs:

1934 _ = _pop(p, None)

1935# Fsum._fint2._update(self)

1936# Fsum._fprs ._update(self)

1937# Fsum._fprs2._update(self)

1938 return self # for .fset_

1939

1940 def _ValueError(self, op, other, **txt): # PYCHOK no cover

1941 '''(INTERNAL) Return a C{ValueError}.

1942 '''

1943 return self._Error(op, other, _ValueError, **txt)

1944

1945 def _ZeroDivisionError(self, op, other, **txt): # PYCHOK no cover

1946 '''(INTERNAL) Return a C{ZeroDivisionError}.

1947 '''

1948 return self._Error(op, other, _ZeroDivisionError, **txt)

1949

1950_ROs = _allPropertiesOf_n(3, Fsum, Property_RO) # PYCHOK see Fsum._update

1951

1952

1953 def _Float_Int(arg, **name_Error):

1954 '''(INTERNAL) Unit of L{Fsum2Tuple} items.

1955 '''

1956 U = Int if isint(arg) else Float

1957 return U(arg, **name_Error)

1958

1959

1960 class DivMod2Tuple(_NamedTuple):

1961 '''2-Tuple C{(div, mod)} with the quotient C{div} and remainder

1962 C{mod} results of a C{divmod} operation.

1963

1964 @note: Quotient C{div} an C{int} in Python 3+ but a C{float}

1965 in Python 2-. Remainder C{mod} an L{Fsum} instance.

1966 '''

1967 _Names_ = (_div_, _mod_)

1968 _Units_ = (_Float_Int, Fsum)

1969

1970

1971 class Fsum2Tuple(_NamedTuple):

1972 '''2-Tuple C{(fsum, residual)} with the precision running C{fsum}

1973 and the C{residual}, the sum of the remaining partials. Each

1974 item is C{float} or C{int}.

1975

1976 @note: If the C{residual is INT0}, the C{fsum} is considered

1977 to be I{exact}, see method L{Fsum2Tuple.is_exact}.

1978 '''

1979 _Names_ = ( Fsum.fsum.__name__, Fsum.residual.name)

1980 _Units_ = (_Float_Int, _Float_Int)

1981

1982 def as_integer_ratio(self):

1983 '''Return this instance as the ratio of 2 integers.

1984

1985 @see: Method L{Fsum.as_integer_ratio} for further details.

1986 '''

1987 return self._Fsum.as_integer_ratio()

1988

1989 @property_RO

1990 def _fint2(self):

1991 return self._Fsum.fint2

1992

1993 @property_RO

1994 def _fprs2(self):

1995 return self._Fsum._fprs2

1996

1997 @Property_RO

1998 def _Fsum(self):

1999 return Fsum(*self)

2000

2001 def is_exact(self):

2002 '''Is this L{Fsum2Tuple} considered to be exact? (C{bool}).

2003 '''

2004 _, r = _s_r(*self)

2005 return False if r else True

2006

2007 def is_integer(self):

2008 '''Is this L{Fsum2Tuple} C{integer}? (C{bool}).

2009 '''

2010 s, r = _s_r(*self)

2011 return False if r else isint(s, both=True)

2012

2013 @property_RO

2014 def _n(self):

2015 return self._Fsum._n

2016

2017 @property_RO

2018 def _ps(self):

2019 return self._Fsum._ps

2020

2021 @property_RO

2022 def _ps_neg(self):

2023 return self._Fsum._ps_neg

2024

2025 def signOf(self, **res):

2026 '''Like L{Fsum.signOf}.

2027 '''

2028 return self._Fsum.signOf(**res)

2029

2030_Fsum_Fsum2Tuple_types = Fsum, Fsum2Tuple # PYCHOK line

2031

2032

2033 class ResidualError(_ValueError):

2034 '''Error raised for a division, power or root operation of

2035 an L{Fsum} instance with a C{residual} I{ratio} exceeding

2036 the L{RESIDUAL<Fsum.RESIDUAL>} threshold.

2037

2038 @see: Module L{pygeodesy.fsums} and method L{Fsum.RESIDUAL}.

2039 '''

2040 pass

2041

2042

2043 try:

2044 from math import fsum as _fsum # precision IEEE-754 sum, Python 2.6+

2045

2046 # make sure _fsum works as expected (XXX check

2047 # float.__getformat__('float')[:4] == 'IEEE'?)

2048 if _fsum((1, 1e101, 1, -1e101)) != 2: # PYCHOK no cover

2049 del _fsum # nope, remove _fsum ...

2050 raise ImportError # ... use _fsum below

2051

2052 Fsum._math_fsum = _sum = _fsum # PYCHOK exported

2053 except ImportError:

2054 _sum = sum # Fsum(NAN) exception fall-back, in .elliptic

2055

2056 def _fsum(xs):

2057 '''(INTERNAL) Precision summation, Python 2.5-.

2058 '''

2059 F = Fsum()

2060 F.name = _fsum.__name__

2061 return F._facc(xs, up=False)._fprs2.fsum

2062

2063

2064 def fsum(xs, floats=False):

2065 '''Precision floating point summation based on/like Python's C{math.fsum}.

2066

2067 @arg xs: Iterable of items to add (each C{scalar} or an L{Fsum} or

2068 L{Fsum2Tuple} instance).

2069 @kwarg floats: Use C{B{floats}=True} iff I{all} B{C{xs}} items are

2070 I{known to be scalar} (C{bool}).

2071

2072 @return: Precision C{fsum} (C{float}).

2073

2074 @raise OverflowError: Partial C{2sum} overflow.

2075

2076 @raise TypeError: Non-scalar B{C{xs}} item.

2077

2078 @raise ValueError: Invalid or non-finite B{C{xs}} item.

2079

2080 @note: Exception and I{non-finite} handling may differ if not based

2081 on Python's C{math.fsum}.

2082

2083 @see: Class L{Fsum} and methods L{Fsum.fsum} and L{Fsum.fadd}.

2084 '''

2085 return _fsum(xs if floats is True else _2floats(xs)) if xs else _0_0 # PYCHOK yield

2086

2087

2088 def fsum_(*xs, **floats):

2089 '''Precision floating point summation of all positional arguments.

2090

2091 @arg xs: Items to add (each C{scalar} or an L{Fsum} or L{Fsum2Tuple}

2092 instance), all positional.

2093 @kwarg floats: Use C{B{floats}=True} iff I{all} B{C{xs}} items are

2094 I{known to be scalar} (C{bool}).

2095

2096 @see: Function L{fsum<fsums.fsum>} for further details.

2097 '''

2098 return _fsum(xs if _xkwds_get(floats, floats=False) is True else

2099 _2floats(xs, origin=1)) if xs else _0_0 # PYCHOK yield

2100

2101

2102 def fsumf_(*xs):

2103 '''Precision floating point summation iff I{all} C{B{xs}} items are I{known to be scalar}.

2104

2105 @see: Function L{fsum_<fsums.fsum_>} for further details.

2106 '''

2107 return _fsum(xs) if xs else _0_0

2108

2109

2110 def fsum1(xs, floats=False):

2111 '''Precision floating point summation, 1-primed.

2112

2113 @arg xs: Iterable of items to add (each C{scalar} or an L{Fsum} or

2114 L{Fsum2Tuple} instance).

2115 @kwarg floats: Use C{B{floats}=True} iff I{all} B{C{xs}} items are

2116 I{known to be scalar} (C{bool}).

2117

2118 @see: Function L{fsum<fsums.fsum>} for further details.

2119 '''

2120 return _fsum(_1primed(xs if floats is True else _2floats(xs))) if xs else _0_0 # PYCHOK yield

2121

2122

2123 def fsum1_(*xs, **floats):

2124 '''Precision floating point summation, 1-primed of all positional arguments.

2125

2126 @arg xs: Items to add (each C{scalar} or an L{Fsum} or L{Fsum2Tuple}

2127 instance), all positional.

2128 @kwarg floats: Use C{B{floats}=True} iff I{all} B{C{xs}} items are

2129 I{known to be scalar} (C{bool}).

2130

2131 @see: Function L{fsum_<fsums.fsum_>} for further details.

2132 '''

2133 return _fsum(_1primed(xs if _xkwds_get(floats, floats=False) is True else

2134 _2floats(xs, origin=1))) if xs else _0_0 # PYCHOK yield

2135

2136

2137 def fsum1f_(*xs):

2138 '''Precision floating point summation iff I{all} C{B{xs}} are I{known to be scalar}.

2139

2140 @see: Function L{fsum_<fsums.fsum_>} for further details.

2141 '''

2142 return _fsum(_1primed(xs)) if xs else _0_0

2143

2144

2145 if __name__ == '__main__':

2146

2147 # usage: [env _psum=fsum] python3 -m pygeodesy.fsums

2148

2149 if _getenv(_psum.__name__, NN) == _fsum.__name__:

2150 _psum = _fsum

2151

2152 def _test(n):

2153 # copied from Hettinger, see L{Fsum} reference

2154 from pygeodesy import frandoms, printf

2155

2156 printf(_fsum.__name__, end=_COMMASPACE_)

2157 printf(_psum.__name__, end=_COMMASPACE_)

2158

2159 F = Fsum()

2160 if F.is_math_fsum():

2161 for t in frandoms(n, seeded=True):

2162 assert float(F.fset_(*t)) == _fsum(t)

2163 printf(_DOT_, end=NN)

2164 printf(NN)

2165

2166 _test(128)

2167

2168# **) MIT License

2169#

2170# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.

2171#

2172# Permission is hereby granted, free of charge, to any person obtaining a

2173# copy of this software and associated documentation files (the "Software"),

2174# to deal in the Software without restriction, including without limitation

2175# the rights to use, copy, modify, merge, publish, distribute, sublicense,

2176# and/or sell copies of the Software, and to permit persons to whom the

2177# Software is furnished to do so, subject to the following conditions:

2178#

2179# The above copyright notice and this permission notice shall be included

2180# in all copies or substantial portions of the Software.

2181#

2182# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS

2183# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

2184# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL

2185# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR

2186# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,

2187# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR

2188# OTHER DEALINGS IN THE SOFTWARE.