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 an empty string (or anything

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

19

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

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

22 exponention of an L{Fsum} instance with a I{relative} C{residual} exceeding

23 the threshold, see methods L{Fsum.RESIDUAL}, L{Fsum.pow}, L{Fsum.__ipow__}

24 and L{Fsum.__itruediv__}.

25'''

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

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

28

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

30 signOf, _signOf

31 from pygeodesy.constants import INT0, _isfinite, isinf, isnan, NEG0, _pos_self, \

32 _0_0, _1_0, _N_1_0, Float, Int

33 from pygeodesy.errors import _OverflowError, _TypeError, _ValueError, _xError, \

34 _xError2, _xkwds_get, _ZeroDivisionError

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

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

37 _NOTEQUAL_, _not_finite_, _not_scalar_, _PERCENT_, \

38 _PLUS_, _R_, _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__ = '24.04.02'

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

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

77 '''

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

79 try:

80 v = float(v)

81 if _isfinite(v):

82 return v

83 raise ValueError(_not_finite_)

84 except Exception as e:

85 raise _xError(e, Fmt.INDEX(n, index), v)

86

87

88 def _2floats(xs, origin=0, neg=False):

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

90 '''

91 if neg:

92 def _X(X):

93 return X._ps_neg

94

95 def _x(x):

96 return -float(x)

97 else:

98 def _X(X): # PYCHOK re-def

99 return X._ps

100

101 _x = float

102

103 return _2yield(xs, origin, _X, _x)

104

105

106 def _1primed(xs): # in .fmath

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

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

109 '''

110 yield _1_0

111 for x in xs:

112 if x:

113 yield x

114 yield _N_1_0

115

116

117 def _2ps(s, r):

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

119 '''

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

121 s, r = r, s

122 return ((r, s) if s else (r,)) if r else (s,)

123

124

125 def _psum(ps): # PYCHOK used!

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

127 '''

128 # assert isinstance(ps, list)

129 i = len(ps) - 1 # len(ps) > 2

130 if i < 0:

131 return _0_0

132 s = ps[i]

133 _2s = _2sum

134 while i > 0:

135 i -= 1

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

137 if r: # sum(ps) became inexact

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

139 if i > 0:

140 p = ps[i-1] # round half-even

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 break

148 ps[i:] = s,

149 return s

150

151

152 def _2scalar(other, _raiser=None):

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

154 '''

155 if isinstance(other, Fsum):

156 s, r = other._fint2

157 if r:

158 s, r = other._fprs2

159 if r: # PYCHOK no cover

160 if _raiser and _raiser(r, s):

161 raise ValueError(_stresidual(_non_zero_, r))

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

163 else:

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

165 if isint(s, both=True):

166 s = int(s)

167 return s

168

169

170 def _strcomplex(s, *args):

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

172 '''

173 c = iscomplex.__name__[2:]

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

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

176 return unstr(t, *args)

177

178

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

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

181 '''

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

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

184 for n, v in itemsorted(name_values):

185 n = n.replace(_UNDER_, _SPACE_)

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

187 t = _COMMASPACE_(t, p)

188 return t

189

190

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

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

193 '''

194 s = a + b

195 if not _isfinite(s):

196 u = unstr(_2sum.__name__, a, b)

197 t = Fmt.PARENSPACED(_not_finite_, s)

198 raise _OverflowError(u, txt=t)

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

200 a, b = b, a

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

202

203

204 def _2yield(xs, i, _X_ps, _x):

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

206 '''

207 x = None

208 try:

209 _fin = _isfinite

210 _Fs = Fsum

211 for x in xs:

212 if isinstance(x, _Fs):

213 for p in _X_ps(x):

214 yield p

215 else:

216 f = _x(x)

217 if f:

218 if not _fin(f):

219 raise ValueError(_not_finite_)

220 yield f

221 i += 1

222 except Exception as e:

223 raise _xError(e, Fmt.INDEX(xs=i), x)

224

225

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

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

228

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

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

231 intermediate, I{running} summuation.

232

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

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

235

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

237 Python's C{math.fsum}.

238

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

240 393090_Binary_floating_point_summatiaccurate_full/recipe-393090.py>}, U{Kahan

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

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

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

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

245 '''

246 _math_fsum = None

247 _n = 0

248# _ps = [] # partial sums

249# _px = 0 # max(Fsum._px, len(Fsum._ps))

250 _ratio = None

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

252

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

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

255

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

257 or an L{Fsum} instance).

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

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

260

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

262 '''

263 if name_RESIDUAL:

264 n = _xkwds_get(name_RESIDUAL, name=NN)

265 if n: # set name before ...

266 self.name = n

267 r = _xkwds_get(name_RESIDUAL, RESIDUAL=None)

268 if r is not None:

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

270# self._n = 0

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

272 if len(xs) > 1:

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

274 elif xs: # len(xs) == 1

275 self._n = 1

276 self._ps[:] = _2float(x=xs[0]),

277

278 def __abs__(self):

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

280 '''

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

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

283

284 def __add__(self, other):

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

286

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

288

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

290

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

292 '''

293 f = self._copy_2(self.__add__)

294 return f._fadd(other, _add_op_)

295

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

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

298 '''

299 s, r = self._fprs2

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

301

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

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

304

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

306

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

308 '''

309 return self.ceil

310

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

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

313

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

315

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

317 '''

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

319 return _signOf(s, 0)

320

321 cmp = __cmp__

322

323 def __divmod__(self, other):

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

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

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

327

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

329

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

331 '''

332 f = self._copy_2(self.__divmod__)

333 return f._fdivmod2(other, _divmod_op_)

334

335 def __eq__(self, other):

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

337 '''

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

339

340 def __float__(self):

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

342

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

344 '''

345 return float(self._fprs)

346

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

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

349

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

351

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

353 '''

354 return self.floor

355

356 def __floordiv__(self, other):

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

358

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

360

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

362

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

364 '''

365 f = self._copy_2(self.__floordiv__)

366 return f._floordiv(other, _floordiv_op_)

367

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

369 '''Not implemented.'''

370 return _NotImplemented(self, *other)

371

372 def __ge__(self, other):

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

374 '''

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

376

377 def __gt__(self, other):

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

379 '''

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

381

382 def __hash__(self): # PYCHOK no cover

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

384 '''

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

386

387 def __iadd__(self, other):

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

389

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

391

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

393

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

395 C{scalar} nor L{Fsum}.

396

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

398 '''

399 return self._fadd(other, _iadd_op_)

400

401 def __ifloordiv__(self, other):

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

403

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

405

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

407

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

409

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

411

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

413

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

415

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

417 '''

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

419

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

421 '''Not implemented.'''

422 return _NotImplemented(self, other)

423

424 def __imod__(self, other):

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

426

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

428

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

430

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

432 '''

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

434

435 def __imul__(self, other):

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

437

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

439

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

441

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

443

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

445

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

447 '''

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

449

450 def __int__(self):

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

452

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

454 and L{Fsum.__floor__} and properties

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

456 '''

457 i, _ = self._fint2

458 return i

459

460 def __invert__(self): # PYCHOK no cover

461 '''Not implemented.'''

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

463 return _NotImplemented(self)

464

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

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

467

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

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

470 3-argument C{pow(B{self}, B{other}, B{mod})}

471 version.

472

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

474

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

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

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

478

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

480

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

482 env var C{PYGEODESY_FSUM_RESIDUAL}

483 set or this instance has a non-zero

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

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

486 is a negative or fractional C{scalar}.

487

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

489 C{pow} invocation failed.

490

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

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

493 is a fractional C{scalar} and this

494 instance is negative or has a non-zero

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

496

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

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

499 '''

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

501

502 def __isub__(self, other):

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

504

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

506

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

508

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

510

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

512 '''

513 return self._fsub(other, _isub_op_)

514

515 def __iter__(self):

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

517 '''

518 return iter(self.partials)

519

520 def __itruediv__(self, other):

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

522

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

524

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

526

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

528

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

530 env var C{PYGEODESY_FSUM_RESIDUAL} set.

531

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

533

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

535

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

537

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

539 '''

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

541

542 def __le__(self, other):

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

544 '''

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

546

547 def __len__(self):

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

549 '''

550 return self._n

551

552 def __lt__(self, other):

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

554 '''

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

556

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

558 '''Not implemented.'''

559 return _NotImplemented(self, other)

560

561 def __mod__(self, other):

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

563

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

565 '''

566 f = self._copy_2(self.__mod__)

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

568

569 def __mul__(self, other):

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

571

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

573 '''

574 f = self._copy_2(self.__mul__)

575 return f._fmul(other, _mul_op_)

576

577 def __ne__(self, other):

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

579 '''

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

581

582 def __neg__(self):

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

584 '''

585 f = self._copy_2(self.__neg__)

586 return f._fset(self._neg)

587

588 def __pos__(self):

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

590 '''

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

592

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

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

595

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

597 '''

598 f = self._copy_2(self.__pow__)

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

600

601 def __radd__(self, other):

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

603

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

605 '''

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

607 return f._fadd(self, _add_op_)

608

609 def __rdivmod__(self, other):

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

611 remainder)}.

612

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

614 '''

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

616 return f._fdivmod2(self, _divmod_op_)

617

618# def __repr__(self):

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

620# '''

621# return self.toRepr(lenc=True)

622

623 def __rfloordiv__(self, other):

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

625

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

627 '''

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

629 return f._floordiv(self, _floordiv_op_)

630

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

632 '''Not implemented.'''

633 return _NotImplemented(self, other)

634

635 def __rmod__(self, other):

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

637

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

639 '''

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

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

642

643 def __rmul__(self, other):

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

645

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

647 '''

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

649 return f._fmul(self, _mul_op_)

650

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

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

653

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

655 '''

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

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

658 name=self.__round__.__name__)

659

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

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

662

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

664 '''

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

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

667

668 def __rsub__(self, other):

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

670

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

672 '''

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

674 return f._fsub(self, _sub_op_)

675

676 def __rtruediv__(self, other):

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

678

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

680 '''

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

682 return f._ftruediv(self, _truediv_op_)

683

684 def __str__(self):

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

686 '''

687 return self.toStr(lenc=True)

688

689 def __sub__(self, other):

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

691

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

693

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

695

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

697 '''

698 f = self._copy_2(self.__sub__)

699 return f._fsub(other, _sub_op_)

700

701 def __truediv__(self, other):

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

703

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

705

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

707

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

709 '''

710 f = self._copy_2(self.__truediv__)

711 return f._ftruediv(other, _truediv_op_)

712

713 __trunc__ = __int__

714

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

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

717 __div__ = __truediv__

718 __idiv__ = __itruediv__

719 __long__ = __int__

720 __nonzero__ = __bool__

721 __rdiv__ = __rtruediv__

722

723 def as_integer_ratio(self):

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

725

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

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

728

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

730 '''

731 n, r = self._fint2

732 if r:

733 i, d = r.as_integer_ratio()

734 n *= d

735 n += i

736 else: # PYCHOK no cover

737 d = 1

738 return n, d

739

740 @property_RO

741 def ceil(self):

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

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

744

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

746

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

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

749 '''

750 s, r = self._fprs2

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

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

753 c += 1

754 return c

755

756 def _cmp_0(self, other, op):

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

758 '''

759 if isscalar(other):

760 if other:

761 s = _fsum(self._ps_1(other))

762 else:

763 s, r = self._fprs2

764 s = _signOf(s, -r)

765 elif isinstance(other, Fsum):

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

767 else:

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

769 return s

770

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

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

773

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

775 '''

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

777 f._n = self._n if deep else 1

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

779 return f

780

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

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

783 '''

784 n = name or which.__name__

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

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

787 # assert f._n == self._n

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

789 return f

790

791 def _copy_2r(self, other, which):

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

793 '''

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

795 Fsum(other, name=which.__name__)

796

797# def _copy_RESIDUAL(self, other):

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

799# '''

800# R = other._RESIDUAL

801# if R is not Fsum._RESIDUAL:

802# self._RESIDUAL = R

803

804 def divmod(self, other):

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

806 remainder)}.

807

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

809

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

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

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

813

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

815 '''

816 f = self._copy_2(self.divmod)

817 return f._fdivmod2(other, _divmod_op_)

818

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

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

821 '''

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

823

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

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

826 '''

827 E, t = _xError2(X)

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

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

830

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

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

833 '''

834 n, ps, _2s = 0, self._ps, _2sum

835 for x in xs: # _iter()

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

837 i = 0

838 for p in ps:

839 x, p = _2s(x, p)

840 if p:

841 ps[i] = p

842 i += 1

843 ps[i:] = x,

844 n += 1

845 # assert self._ps is ps

846 if n:

847 self._n += n

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

849 if up:

850 self._update()

851 return self

852

853 def _facc_(self, *xs, **up):

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

855 '''

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

857

858 def _facc_power(self, power, xs, which): # in .fmath

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

860 '''

861 if isinstance(power, Fsum):

862 if power.is_exact:

863 return self._facc_power(power._fprs, xs, which)

864 _Pow = Fsum._pow_any

865 elif isint(power, both=True) and power >= 0:

866 _Pow = Fsum._pow_int

867 power = int(power)

868 else:

869 _Pow = Fsum._pow_scalar

870 power = _2float(power=power)

871

872 if power:

873 from math import pow as _pow

874 op = which.__name__

875

876 def _X(X):

877 f = _Pow(X, power, power, op)

878 try: # isinstance(f, Fsum)

879 return f._ps

880 except AttributeError: # scalar

881 return f,

882

883 def _x(x):

884 return _pow(float(x), power)

885

886 self._facc(_2yield(xs, 1, _X, _x)) # PYCHOK yield

887 else:

888 self._facc_(float(len(xs))) # x**0 == 1

889 return self

890

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

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

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

894# '''

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

896# p = self._ps.pop()

897# if p:

898# n = self._n

899# self._facc_(p, up=False)

900# self._n = n

901# break

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

903

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

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

906 to this instance.

907

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

909 L{Fsum} instances).

910

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

912

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

914

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

916 nor L{Fsum}.

917

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

919 '''

920 if isinstance(xs, Fsum):

921 self._facc(xs._ps)

922 elif isscalar(xs): # for backward compatibility

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

924 elif xs:

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

926 return self

927

928 def fadd_(self, *xs):

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

930 to this instance.

931

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

933 all positional.

934

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

936

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

938

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

940 nor L{Fsum}.

941

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

943 '''

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

945

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

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

948 '''

949 if isinstance(other, Fsum):

950 if other is self:

951 self._facc_(*other._ps, **up) # == ._facc(tuple(other._ps))

952 elif other._ps:

953 self._facc(other._ps, **up)

954 elif not isscalar(other):

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

956 elif other:

957 self._facc_(other, **up)

958 return self

959

960 fcopy = copy # for backward compatibility

961 fdiv = __itruediv__ # for backward compatibility

962 fdivmod = __divmod__ # for backward compatibility

963

964 def _fdivmod2(self, other, op):

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

966 '''

967 # result mostly follows CPython function U{float_divmod

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

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

970 q = self._copy_2(self._fdivmod2)._ftruediv(other, op).floor

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

972 self -= other * q

973

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

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

976 self += other

977 q -= 1

978# t = self.signOf()

979# if t and t != s:

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

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

982

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

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

985 '''

986 if _isfinite(other):

987 return other

988 raise ValueError(_not_finite_) if not op else \

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

990

991 def fint(self, raiser=True, **name):

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

993

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

995 I{integer} residual is non-zero.

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

997

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

999

1000 @raise ResidualError: Non-zero I{integer} residual.

1001

1002 @see: Methods L{Fsum.int_float} and L{Fsum.is_integer}.

1003 '''

1004 i, r = self._fint2

1005 if r and raiser:

1006 t = _stresidual(_integer_, r)

1007 raise ResidualError(_integer_, i, txt=t)

1008 f = self._copy_2(self.fint, **name)

1009 return f._fset(i)

1010

1011 def fint2(self, **name):

1012 '''Return this instance' current running sum as C{int} and

1013 the I{integer} residual.

1014

1015 @kwarg name: Optional name (C{str}).

1016

1017 @return: An L{Fsum2Tuple}C{(fsum, residual)} with C{fsum}

1018 an C{int} and I{integer} C{residual} a C{float} or

1019 C{INT0} if the C{fsum} is considered to be I{exact}.

1020 '''

1021 return Fsum2Tuple(*self._fint2, **name)

1022

1023 @Property_RO

1024 def _fint2(self): # see ._fset

1025 '''(INTERNAL) Get 2-tuple (C{int}, I{integer} residual).

1026 '''

1027 s, r = self._fprs2

1028 i = int(s)

1029 r = _fsum(self._ps_1(i)) if r else float(s - i)

1030 return i, (r or INT0)

1031

1032 @deprecated_property_RO

1033 def float_int(self): # PYCHOK no cover

1034 '''DEPRECATED, use method C{Fsum.int_float}.'''

1035 return self.int_float() # raiser=False

1036

1037 @property_RO

1038 def floor(self):

1039 '''Get this instance' C{floor} (C{int} in Python 3+, but

1040 C{float} in Python 2-).

1041

1042 @note: The C{floor} takes the C{residual} into account.

1043

1044 @see: Method L{Fsum.int_float} and properties L{Fsum.ceil},

1045 L{Fsum.imag} and L{Fsum.real}.

1046 '''

1047 s, r = self._fprs2

1048 f = _floor(s) + _floor(r) + 1

1049 while (f - s) > r: # f > (s + r)

1050 f -= 1

1051 return f

1052

1053# floordiv = __floordiv__ # for naming consistency

1054

1055 def _floordiv(self, other, op): # rather _ffloordiv?

1056 '''Apply C{B{self} //= B{other}}.

1057 '''

1058 q = self._ftruediv(other, op) # == self

1059 return self._fset(q.floor) # floor(q)

1060

1061 fmul = __imul__ # for backward compatibility

1062

1063 def _fmul(self, other, op):

1064 '''(INTERNAL) Apply C{B{self} *= B{other}}.

1065 '''

1066 if isinstance(other, Fsum):

1067 if len(self._ps) != 1:

1068 f = self._mul_Fsum(other, op)

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

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

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

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

1073 elif isscalar(other):

1074 f = self._mul_scalar(other, op)

1075 else:

1076 raise self._TypeError(op, other) # txt=_invalid_

1077 return self._fset(f) # n=len(self) + 1

1078

1079 def fover(self, over):

1080 '''Apply C{B{self} /= B{over}} and summate.

1081

1082 @arg over: An L{Fsum} or C{scalar} denominator.

1083

1084 @return: Precision running sum (C{float}).

1085

1086 @see: Methods L{Fsum.fsum} and L{Fsum.__itruediv__}.

1087 '''

1088 return float(self.fdiv(over)._fprs)

1089

1090 fpow = __ipow__ # for backward compatibility

1091

1092 def _fpow(self, other, op, *mod):

1093 '''Apply C{B{self} **= B{other}}, optional B{C{mod}} or C{None}.

1094 '''

1095 if mod:

1096 if mod[0] is not None: # == 3-arg C{pow}

1097 f = self._pow_3(other, mod[0], op)

1098 elif self.is_integer():

1099 # return an exact C{int} for C{int}**C{int}

1100 x = _2scalar(other) # C{int}, C{float} or other

1101 i = self._fint2[0] # assert _fint2[1] == 0

1102 f = self._pow_2(i, x, other, op) if isscalar(x) else \

1103 _Fsum_ps(i)._pow_any(x, other, op)

1104 else: # mod[0] is None, power(self, other)

1105 f = self._pow_any(other, other, op)

1106 else: # pow(self, other) == pow(self, other, None)

1107 f = self._pow_any(other, other, op)

1108 return self._fset(f, asis=isint(f)) # n=max(len(self), 1)

1109

1110 @Property_RO

1111 def _fprs(self):

1112 '''(INTERNAL) Get and cache this instance' precision

1113 running sum (C{float} or C{int}), ignoring C{residual}.

1114

1115 @note: The precision running C{fsum} after a C{//=} or

1116 C{//} C{floor} division is C{int} in Python 3+.

1117 '''

1118 return self._fprs2.fsum

1119

1120 @Property_RO

1121 def _fprs2(self):

1122 '''(INTERNAL) Get and cache this instance' precision

1123 running sum and residual (L{Fsum2Tuple}).

1124 '''

1125 ps = self._ps

1126 n = len(ps)

1127 if n > 2: # len(ps) > 2

1128 s = _psum(ps)

1129 r = _fsum(self._ps_1(s)) or INT0

1130 elif n > 1: # len(ps) == 2

1131 ps[:] = _2ps(*_2sum(*ps))

1132 r, s = (INT0, ps[0]) if len(ps) != 2 else ps

1133 elif ps: # len(ps) == 1

1134 s, r = ps[0], INT0

1135 else: # len(ps) == 0

1136 s, r = _0_0, INT0

1137 ps[:] = s,

1138 # assert self._ps is ps

1139 return Fsum2Tuple(s, r)

1140

1141# def _fpsqz(self):

1142# '''(INTERNAL) Compress, squeeze the C{partials}.

1143# '''

1144# if len(self._ps) > 2:

1145# _ = self._fprs

1146# return self

1147

1148 def _fset(self, other, asis=True, n=0):

1149 '''(INTERNAL) Overwrite this instance with an other or a C{scalar}.

1150 '''

1151 if other is self:

1152 pass # from ._fmul, ._ftruediv and ._pow_scalar

1153 elif isinstance(other, Fsum):

1154 self._n = n or other._n

1155 self._ps[:] = other._ps

1156# self._copy_RESIDUAL(other)

1157 # use or zap the C{Property_RO} values

1158 Fsum._fint2._update_from(self, other)

1159 Fsum._fprs ._update_from(self, other)

1160 Fsum._fprs2._update_from(self, other)

1161 elif isscalar(other):

1162 s = other if asis else float(other)

1163 i = int(s) # see ._fint2

1164 t = i, ((s - i) or INT0)

1165 self._n = n or 1

1166 self._ps[:] = s,

1167 # Property_ROs _fint2, _fprs and _fprs2 can't be a Property:

1168 # Property's _fset zaps the value just set by the @setter

1169 self.__dict__.update(_fint2=t, _fprs=s, _fprs2=Fsum2Tuple(s, INT0))

1170 else: # PYCHOK no cover

1171 raise self._TypeError(_fset_op_, other) # txt=_invalid_

1172 return self

1173

1174 def _fset_ps(self, other, n=0): # in .fmath

1175 '''(INTERNAL) Set a known C{Fsum} or C{scalar}.

1176 '''

1177 if isinstance(other, Fsum):

1178 self._n = n or other._n

1179 self._ps[:] = other._ps

1180 else: # assert isscalar(other)

1181 self._n = n or 1

1182 self._ps[:] = other,

1183

1184 def fsub(self, xs=()):

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

1186 this instance.

1187

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

1189 instances).

1190

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

1192

1193 @see: Method L{Fsum.fadd}.

1194 '''

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

1196

1197 def fsub_(self, *xs):

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

1199 this instance.

1200

1201 @arg xs: Values to subtract (C{scalar} or L{Fsum} instances),

1202 all positional.

1203

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

1205

1206 @see: Method L{Fsum.fadd}.

1207 '''

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

1209

1210 def _fsub(self, other, op):

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

1212 '''

1213 if isinstance(other, Fsum):

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

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

1216 elif other._ps:

1217 self._facc(other._ps_neg)

1218 elif not isscalar(other):

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

1220 elif self._finite(other, op):

1221 self._facc_(-other)

1222 return self

1223

1224 def fsum(self, xs=()):

1225 '''Add more C{scalar} or L{Fsum} instances and summate.

1226

1227 @kwarg xs: Iterable, list, tuple, etc. (C{scalar} or

1228 L{Fsum} instances).

1229

1230 @return: Precision running sum (C{float} or C{int}).

1231

1232 @see: Method L{Fsum.fadd}.

1233

1234 @note: Accumulation can continue after summation.

1235 '''

1236 f = self._facc(_2floats(xs)) if xs else self # PYCHOK yield

1237 return f._fprs

1238

1239 def fsum_(self, *xs):

1240 '''Add all positional C{scalar} or L{Fsum} instances and summate.

1241

1242 @arg xs: Values to add (C{scalar} or L{Fsum} instances),

1243 all positional.

1244

1245 @return: Precision running sum (C{float} or C{int}).

1246

1247 @see: Methods L{Fsum.fsum} and L{Fsum.fsumf_}.

1248 '''

1249 f = self._facc(_2floats(xs, origin=1)) if xs else self # PYCHOK yield

1250 return f._fprs

1251

1252 def fsum2(self, xs=(), **name):

1253 '''Add more C{scalar} or L{Fsum} instances and return the

1254 current precision running sum and the C{residual}.

1255

1256 @kwarg xs: Iterable, list, tuple, etc. (C{scalar} or L{Fsum}

1257 instances).

1258 @kwarg name: Optional name (C{str}).

1259

1260 @return: L{Fsum2Tuple}C{(fsum, residual)} with C{fsum} the

1261 current precision running sum and C{residual}, the

1262 (precision) sum of the remaining C{partials}. The

1263 C{residual is INT0} if the C{fsum} is considered

1264 to be I{exact}.

1265

1266 @see: Methods L{Fsum.fint2}, L{Fsum.fsum} and L{Fsum.fsum2_}

1267 '''

1268 f = self._facc(_2floats(xs)) if xs else self # PYCHOK yield

1269 t = f._fprs2

1270 if name:

1271 n = _xkwds_get(name, name=NN)

1272 if n:

1273 t = t.dup(name=n)

1274 return t

1275

1276 def fsum2_(self, *xs):

1277 '''Add any positional C{scalar} or L{Fsum} instances and return

1278 the precision running sum and the C{differential}.

1279

1280 @arg xs: Values to add (C{scalar} or L{Fsum} instances),

1281 all positional.

1282

1283 @return: 2-Tuple C{(fsum, delta)} with the current precision

1284 running C{fsum} and C{delta}, the difference with

1285 the previous running C{fsum} (C{float}s).

1286

1287 @see: Methods L{Fsum.fsum_} and L{Fsum.fsum}.

1288 '''

1289 p, r = self._fprs2

1290 if xs:

1291 s, t = self._facc(_2floats(xs, origin=1))._fprs2 # PYCHOK yield

1292 return s, _fsum((s, -p, r, -t)) # ((s - p) + (r - t))

1293 else: # PYCHOK no cover

1294 return p, _0_0

1295

1296 def fsumf_(self, *xs):

1297 '''Like method L{Fsum.fsum_} but only for known C{float B{xs}}.

1298 '''

1299 f = self._facc(xs) if xs else self # PYCHOK yield

1300 return f._fprs

1301

1302# ftruediv = __itruediv__ # for naming consistency

1303

1304 def _ftruediv(self, other, op):

1305 '''(INTERNAL) Apply C{B{self} /= B{other}}.

1306 '''

1307 n = _1_0

1308 if isinstance(other, Fsum):

1309 if other is self or other._fprs2 == self._fprs2:

1310 return self._fset(_1_0) # n=len(self)

1311 d, r = other._fprs2

1312 if r:

1313 if not d: # PYCHOK no cover

1314 d = r

1315 elif self._raiser(r, d):

1316 raise self._ResidualError(op, other, r)

1317 else:

1318 d, n = other.as_integer_ratio()

1319 elif isscalar(other):

1320 d = other

1321 else: # PYCHOK no cover

1322 raise self._TypeError(op, other) # txt=_invalid_

1323 try:

1324 s = 0 if isinf(d) else (

1325 d if isnan(d) else self._finite(n / d))

1326 except Exception as x:

1327 E, t = _xError2(x)

1328 raise self._Error(op, other, E, txt=t)

1329 f = self._mul_scalar(s, _mul_op_) # handles 0, NAN, etc.

1330 return self._fset(f, asis=False)

1331

1332 @property_RO

1333 def imag(self):

1334 '''Get the C{imaginary} part of this instance (C{0.0}, always).

1335

1336 @see: Properties L{Fsum.ceil}, L{Fsum.floor} and L{Fsum.real}.

1337 '''

1338 return _0_0

1339

1340 def int_float(self, raiser=False):

1341 '''Return this instance' current running sum as C{int} or C{float}.

1342

1343 @kwarg raiser: If C{True} throw a L{ResidualError} if the

1344 residual is non-zero.

1345

1346 @return: This C{integer} sum if this instance C{is_integer},

1347 otherwise return the C{float} sum if the residual

1348 is zero or if C{B{raiser}=False}.

1349

1350 @raise ResidualError: Non-zero residual and C{B{raiser}=True}.

1351

1352 @see: Methods L{Fsum.fint} and L{Fsum.fint2}.

1353 '''

1354 s, r = self._fint2

1355 if r:

1356 s, r = self._fprs2

1357 if r and raiser: # PYCHOK no cover

1358 t = _stresidual(_non_zero_, r)

1359 raise ResidualError(int_float=s, txt=t)

1360 s = float(s) # redundant

1361 return s

1362

1363 def is_exact(self):

1364 '''Is this instance' current running C{fsum} considered to

1365 be exact? (C{bool}).

1366 '''

1367 return self.residual is INT0

1368

1369 def is_integer(self):

1370 '''Is this instance' current running sum C{integer}? (C{bool}).

1371

1372 @see: Methods L{Fsum.fint} and L{Fsum.fint2}.

1373 '''

1374 _, r = self._fint2

1375 return False if r else True

1376

1377 def is_math_fsum(self):

1378 '''Return whether functions L{fsum}, L{fsum_}, L{fsum1} and

1379 L{fsum1_} plus partials summation are based on Python's

1380 C{math.fsum} or not.

1381

1382 @return: C{2} if all functions and partials summation

1383 are based on C{math.fsum}, C{True} if only

1384 the functions are based on C{math.fsum} (and

1385 partials summation is not) or C{False} if

1386 none are.

1387 '''

1388 f = Fsum._math_fsum

1389 return 2 if _psum is f else bool(f)

1390

1391 def _mul_Fsum(self, other, op=_mul_op_): # in .fmath.Fhorner

1392 '''(INTERNAL) Return C{B{self} * Fsum B{other}} as L{Fsum} or C{0}.

1393 '''

1394 # assert isinstance(other, Fsum)

1395 if self._ps and other._ps:

1396 f = _Fsum_xs(self._ps_mul(op, *other._ps))

1397 else:

1398 f = _0_0

1399 return f

1400

1401 def _mul_scalar(self, factor, op): # in .fmath.Fhorner

1402 '''(INTERNAL) Return C{B{self} * scalar B{factor}} as L{Fsum}, C{0} or C{self}.

1403 '''

1404 # assert isscalar(factor)

1405 if self._ps and self._finite(factor, op):

1406 f = self if factor == _1_0 else (

1407 self._neg if factor == _N_1_0 else

1408 _Fsum_xs(self._ps_mul(op, factor))) # PYCHOK indent

1409 else:

1410 f = _0_0

1411 return f

1412

1413 @property_RO

1414 def _neg(self):

1415 '''(INTERNAL) Return C{-self}.

1416 '''

1417 return _Fsum_ps(*self._ps_neg) if self._ps else NEG0

1418

1419 @property_RO

1420 def partials(self):

1421 '''Get this instance' current partial sums (C{tuple} of C{float}s and/or C{int}s).

1422 '''

1423 return tuple(self._ps)

1424

1425 def pow(self, x, *mod):

1426 '''Return C{B{self}**B{x}} as L{Fsum}.

1427

1428 @arg x: The exponent (L{Fsum} or C{scalar}).

1429 @arg mod: Optional modulus (C{int} or C{None}) for the 3-argument

1430 C{pow(B{self}, B{other}, B{mod})} version.

1431

1432 @return: The C{pow(self, B{x})} or C{pow(self, B{x}, *B{mod})}

1433 result (L{Fsum}).

1434

1435 @note: If B{C{mod}} is given as C{None}, the result will be an

1436 C{integer} L{Fsum} provided this instance C{is_integer}

1437 or set to C{integer} with L{Fsum.fint}.

1438

1439 @see: Methods L{Fsum.__ipow__}, L{Fsum.fint} and L{Fsum.is_integer}.

1440 '''

1441 f = self._copy_2(self.pow)

1442 return f._fpow(x, _pow_op_, *mod) # f = pow(f, x, *mod)

1443

1444 def _pow_0_1(self, x, other):

1445 '''(INTERNAL) Return B{C{self}**1} or C{B{self}**0 == 1.0}.

1446 '''

1447 return self if x else (1 if self.is_integer() and isint(other) else _1_0)

1448

1449 def _pow_2(self, b, x, other, op):

1450 '''(INTERNAL) 2-arg C{pow(B{b}, scalar B{x})} embellishing errors.

1451 '''

1452 # assert isscalar(b) and isscalar(x)

1453 try: # type(s) == type(x) if x in (_1_0, 1)

1454 s = pow(b, x) # -1**2.3 == -(1**2.3)

1455 if not iscomplex(s):

1456 return self._finite(s) # 0**INF == 0.0, 1**INF==1.0

1457 # neg**frac == complex in Python 3+, but ValueError in 2-

1458 E, t = _ValueError, _strcomplex(s, b, x) # PYCHOK no cover

1459 except Exception as x:

1460 E, t = _xError2(x)

1461 raise self._Error(op, other, E, txt=t)

1462

1463 def _pow_3(self, other, mod, op):

1464 '''(INTERNAL) 3-arg C{pow(B{self}, B{other}, int B{mod} or C{None})}.

1465 '''

1466 b, r = self._fprs2 if mod is None else self._fint2

1467 if r and self._raiser(r, b):

1468 t = _non_zero_ if mod is None else _integer_

1469 E, t = ResidualError, _stresidual(t, r, mod=mod)

1470 else:

1471 try: # b, other, mod all C{int}, unless C{mod} is C{None}

1472 x = _2scalar(other, _raiser=self._raiser)

1473 s = pow(b, x, mod)

1474 if not iscomplex(s):

1475 return self._finite(s)

1476 # neg**frac == complex in Python 3+, but ValueError in 2-

1477 E, t = _ValueError, _strcomplex(s, b, x, mod) # PYCHOK no cover

1478 except Exception as x:

1479 E, t = _xError2(x)

1480 t = _COMMASPACE_(Fmt.PARENSPACED(mod=mod), t)

1481 raise self._Error(op, other, E, txt=t)

1482

1483 def _pow_any(self, other, unused, op):

1484 '''Return C{B{self} ** B{other}}.

1485 '''

1486 if isinstance(other, Fsum):

1487 x, r = other._fprs2

1488 f = self._pow_scalar(x, other, op)

1489 if r:

1490 if self._raiser(r, x):

1491 raise self._ResidualError(op, other, r)

1492 s = self._pow_scalar(r, other, op)

1493# s = _2scalar(s) # _raiser = None

1494 f *= s

1495 elif isscalar(other):

1496 x = self._finite(other, op)

1497 f = self._pow_scalar(x, other, op)

1498 else:

1499 raise self._TypeError(op, other) # txt=_invalid_

1500 return f

1501

1502 def _pow_int(self, x, other, op):

1503 '''(INTERNAL) Return C{B{self} **= B{x}} for C{int B{x} >= 0}.

1504 '''

1505 # assert isint(x) and x >= 0

1506 ps = self._ps

1507 if len(ps) > 1:

1508 f = self

1509 if x > 4:

1510 m = 1 # single-bit mask

1511 if (x & m):

1512 x -= m # x ^= m

1513 else:

1514 f = _Fsum_ps(_1_0)

1515 p = self

1516 while x:

1517 p = p._mul_Fsum(p, op) # p **= 2

1518 m += m # m <<= 1

1519 if (x & m):

1520 x -= m # x ^= m

1521 f = f._mul_Fsum(p, op) # f *= p

1522 elif x > 1: # self**2, 3 or 4

1523 f = f._mul_Fsum(f, op)

1524 if x > 2: # self**3 or 4

1525 p = self if x < 4 else f

1526 f = f._mul_Fsum(p, op)

1527 else: # self**1 or self**0 == 1 or _1_0

1528 f = f._pow_0_1(x, other)

1529 elif ps: # self._ps[0]**x

1530 f = self._pow_2(ps[0], x, other, op)

1531 else: # PYCHOK no cover

1532 # 0**pos_int == 0, but 0**0 == 1

1533 f = 0 if x else 1 # like ._fprs

1534 return f

1535

1536 def _pow_scalar(self, x, other, op):

1537 '''(INTERNAL) Return C{self**B{x}} for C{scalar B{x}}.

1538 '''

1539 s, r = self._fprs2

1540 if isint(x, both=True):

1541 x = int(x) # Fsum**int

1542 y = abs(x)

1543 if y > 1:

1544 if r:

1545 f = self._pow_int(y, other, op)

1546 if x > 0: # > 1

1547 return f

1548 # assert x < 0 # < -1

1549 s, r = f._fprs2 if isinstance(f, Fsum) else (f, 0)

1550 if r:

1551 return _Fsum_ps(_1_0)._ftruediv(f, op)

1552 # use **= -1 for the CPython float_pow

1553 # error if s is zero, and not s = 1 / s

1554 x = -1

1555 elif x < 0: # self**-1 == 1 / self

1556 if r:

1557 return _Fsum_ps(_1_0)._ftruediv(self, op)

1558 else: # self**1 or self**0

1559 return self._pow_0_1(x, other) # self, 1 or 1.0

1560 elif not isscalar(x): # assert ...

1561 raise self._TypeError(op, other, txt=_not_scalar_)

1562 elif r and self._raiser(r, s): # non-zero residual**fractional

1563 # raise self._ResidualError(op, other, r, fractional_power=x)

1564 t = _stresidual(_non_zero_, r, fractional_power=x)

1565 raise self._Error(op, other, ResidualError, txt=t)

1566 # assert isscalar(s) and isscalar(x)

1567 return self._pow_2(s, x, other, op)

1568

1569 def _ps_1(self, *less):

1570 '''(INTERNAL) Yield partials, 1-primed and subtract any C{less}.

1571 '''

1572 yield _1_0

1573 for p in self._ps:

1574 if p:

1575 yield p

1576 for p in less:

1577 if p:

1578 yield -p

1579 yield _N_1_0

1580

1581 def _ps_mul(self, op, *factors): # see .fmath.Fhorner

1582 '''(INTERNAL) Yield all C{partials} times each B{C{factor}},

1583 in total, up to C{len(partials) * len(factors)} items.

1584 '''

1585 ps = self._ps # tuple(self._ps)

1586 if len(ps) < len(factors):

1587 ps, factors = factors, ps

1588 _f = _isfinite

1589 for f in factors:

1590 for p in ps:

1591 p *= f

1592 yield p if _f(p) else self._finite(p, op)

1593

1594 @property_RO

1595 def _ps_neg(self):

1596 '''(INTERNAL) Yield the partials, I{negated}.

1597 '''

1598 for p in self._ps:

1599 yield -p

1600

1601 @property_RO

1602 def real(self):

1603 '''Get the C{real} part of this instance (C{float}).

1604

1605 @see: Methods L{Fsum.__float__} and L{Fsum.fsum}

1606 and properties L{Fsum.ceil}, L{Fsum.floor},

1607 L{Fsum.imag} and L{Fsum.residual}.

1608 '''

1609 return float(self._fprs)

1610

1611 @property_RO

1612 def residual(self):

1613 '''Get this instance' residual (C{float} or C{int}), the

1614 C{sum(partials)} less the precision running sum C{fsum}.

1615

1616 @note: If the C{residual is INT0}, the precision running

1617 C{fsum} is considered to be I{exact}.

1618

1619 @see: Methods L{Fsum.fsum}, L{Fsum.fsum2} and L{Fsum.is_exact}.

1620 '''

1621 return self._fprs2.residual

1622

1623 def _raiser(self, r, s):

1624 '''(INTERNAL) Does ratio C{r / s} exceed threshold?

1625 '''

1626 self._ratio = t = fabs((r / s) if s else r)

1627 return t > self._RESIDUAL

1628

1629 def RESIDUAL(self, *threshold):

1630 '''Get and set this instance' I{ratio} for raising L{ResidualError}s,

1631 overriding the default from env variable C{PYGEODESY_FSUM_RESIDUAL}.

1632

1633 @arg threshold: If C{scalar}, the I{ratio} to exceed for raising

1634 L{ResidualError}s in division and exponention, if

1635 C{None} restore the default set with env variable

1636 C{PYGEODESY_FSUM_RESIDUAL} or if omitted, keep the

1637 current setting.

1638

1639 @return: The previous C{RESIDUAL} setting (C{float}).

1640

1641 @raise ValueError: Negative B{C{threshold}}.

1642

1643 @note: A L{ResidualError} is thrown if the non-zero I{ratio}

1644 C{residual} / C{fsum} exceeds the B{C{threshold}}.

1645 '''

1646 r = self._RESIDUAL

1647 if threshold:

1648 t = threshold[0]

1649 t = Fsum._RESIDUAL if t is None else (

1650 float(t) if isscalar(t) else ( # for backward ...

1651 _0_0 if bool(t) else _1_0)) # ... compatibility

1652 if t < 0:

1653 u = _DOT_(self, unstr(self.RESIDUAL, *threshold))

1654 raise _ValueError(u, RESIDUAL=t, txt=_negative_)

1655 self._RESIDUAL = t

1656 return r

1657

1658 def _ResidualError(self, op, other, residual):

1659 '''(INTERNAL) Non-zero B{C{residual}} etc.

1660 '''

1661 t = _stresidual(_non_zero_, residual, ratio=self._ratio,

1662 RESIDUAL=self._RESIDUAL)

1663 t = t.replace(_COMMASPACE_R_, _exceeds_R_)

1664 return self._Error(op, other, ResidualError, txt=t)

1665

1666 def signOf(self, res=True):

1667 '''Determine the sign of this instance.

1668

1669 @kwarg res: If C{True} consider, otherwise

1670 ignore the residual (C{bool}).

1671

1672 @return: The sign (C{int}, -1, 0 or +1).

1673 '''

1674 s, r = self._fprs2 if res else (self._fprs, 0)

1675 return _signOf(s, -r)

1676

1677 def toRepr(self, **prec_sep_fmt_lenc): # PYCHOK signature

1678 '''Return this C{Fsum} instance as representation.

1679

1680 @kwarg prec_sep_fmt_lenc: Optional keyword arguments for

1681 method L{Fsum2Tuple.toRepr} plus C{B{lenc}=True}

1682 (C{bool}) to in-/exclude the current C{[len]}

1683 of this L{Fsum} enclosed in I{[brackets]}.

1684

1685 @return: This instance (C{repr}).

1686 '''

1687 return self._toT(self._fprs2.toRepr, **prec_sep_fmt_lenc)

1688

1689 def toStr(self, **prec_sep_fmt_lenc): # PYCHOK signature

1690 '''Return this C{Fsum} instance as string.

1691

1692 @kwarg prec_sep_fmt_lenc: Optional keyword arguments for

1693 method L{Fsum2Tuple.toStr} plus C{B{lenc}=True}

1694 (C{bool}) to in-/exclude the current C{[len]}

1695 of this L{Fsum} enclosed in I{[brackets]}.

1696

1697 @return: This instance (C{str}).

1698 '''

1699 return self._toT(self._fprs2.toStr, **prec_sep_fmt_lenc)

1700

1701 def _toT(self, toT, fmt=Fmt.g, lenc=True, **kwds):

1702 '''(INTERNAL) Helper for C{toRepr} and C{toStr}.

1703 '''

1704 n = self.named3

1705 if lenc:

1706 n = Fmt.SQUARE(n, len(self))

1707 return _SPACE_(n, toT(fmt=fmt, **kwds))

1708

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

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

1711 '''

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

1713

1714 def _update(self, updated=True): # see ._fset

1715 '''(INTERNAL) Zap all cached C{Property_RO} values.

1716 '''

1717 if updated:

1718 _pop = self.__dict__.pop

1719 for p in _ROs:

1720 _ = _pop(p, None)

1721# Fsum._fint2._update(self)

1722# Fsum._fprs ._update(self)

1723# Fsum._fprs2._update(self)

1724 return self

1725

1726 def _ValueError(self, op, other, **txt): # PYCHOK no cover

1727 '''(INTERNAL) Return a C{ValueError}.

1728 '''

1729 return self._Error(op, other, _ValueError, **txt)

1730

1731 def _ZeroDivisionError(self, op, other, **txt): # PYCHOK no cover

1732 '''(INTERNAL) Return a C{ZeroDivisionError}.

1733 '''

1734 return self._Error(op, other, _ZeroDivisionError, **txt)

1735

1736_ROs = _allPropertiesOf_n(3, Fsum, Property_RO) # PYCHOK assert, see Fsum._fset, -._update

1737

1738

1739 def _Float_Int(arg, **name_Error):

1740 '''(INTERNAL) Unit of L{Fsum2Tuple} items.

1741 '''

1742 U = Int if isint(arg) else Float

1743 return U(arg, **name_Error)

1744

1745

1746 class DivMod2Tuple(_NamedTuple):

1747 '''2-Tuple C{(div, mod)} with the quotient C{div} and remainder

1748 C{mod} results of a C{divmod} operation.

1749

1750 @note: Quotient C{div} an C{int} in Python 3+ or a C{float} in

1751 Python 2-. Remainder C{mod} an L{Fsum} instance.

1752 '''

1753 _Names_ = (_div_, _mod_)

1754 _Units_ = (_Float_Int, Fsum)

1755

1756

1757 class Fsum2Tuple(_NamedTuple):

1758 '''2-Tuple C{(fsum, residual)} with the precision running C{fsum}

1759 and the C{residual}, the sum of the remaining partials. Each

1760 item is either C{float} or C{int}.

1761

1762 @note: If the C{residual is INT0}, the C{fsum} is considered

1763 to be I{exact}, see method L{Fsum2Tuple.is_exact}.

1764 '''

1765 _Names_ = ( Fsum.fsum.__name__, Fsum.residual.name)

1766 _Units_ = (_Float_Int, _Float_Int)

1767

1768 @Property_RO

1769 def Fsum(self):

1770 '''Get this L{Fsum2Tuple} as an L{Fsum}.

1771 '''

1772 s, r = map(float, self)

1773 return _Fsum_ps(*_2ps(s, r), name=self.name)

1774

1775 def is_exact(self):

1776 '''Is this L{Fsum2Tuple} considered to be exact? (C{bool}).

1777 '''

1778 return self.Fsum.is_exact()

1779

1780 def is_integer(self):

1781 '''Is this L{Fsum2Tuple} C{integer}? (C{bool}).

1782 '''

1783 return self.Fsum.is_integer()

1784

1785

1786 class ResidualError(_ValueError):

1787 '''Error raised for an operation involving a L{pygeodesy.sums.Fsum}

1788 instance with a non-zero C{residual}, I{integer} or otherwise.

1789

1790 @see: Module L{pygeodesy.fsums} and method L{Fsum.RESIDUAL}.

1791 '''

1792 pass

1793

1794

1795 def _Fsum_ps(*ps, **name):

1796 '''(INTERNAL) Return an C{Fsum} from I{ordered} partials C{ps}.

1797 '''

1798 f = Fsum(**name) if name else Fsum()

1799 if ps:

1800 f._n = len(ps)

1801 f._ps[:] = ps

1802 return f

1803

1804

1805 def _Fsum_xs(xs, up=False, **name):

1806 '''(INTERNAL) Return an C{Fsum} from known floats C{xs}.

1807 '''

1808 f = Fsum(**name) if name else Fsum()

1809 return f._facc(xs, up=up)

1810

1811

1812 try:

1813 from math import fsum as _fsum # precision IEEE-754 sum, Python 2.6+

1814

1815 # make sure _fsum works as expected (XXX check

1816 # float.__getformat__('float')[:4] == 'IEEE'?)

1817 if _fsum((1, 1e101, 1, -1e101)) != 2: # PYCHOK no cover

1818 del _fsum # nope, remove _fsum ...

1819 raise ImportError # ... use _fsum below

1820

1821 Fsum._math_fsum = _sum = _fsum # PYCHOK exported

1822

1823 if _getenv('PYGEODESY_FSUM_PARTIALS', _fsum.__name__) == _fsum.__name__:

1824 _psum = _fsum # PYCHOK re-def

1825

1826 except ImportError:

1827 _sum = sum # Fsum(NAN) exception fall-back

1828

1829 def _fsum(xs):

1830 '''(INTERNAL) Precision summation, Python 2.5-.

1831 '''

1832 return Fsum(name=_fsum.__name__).fsum(xs) if xs else _0_0

1833

1834

1835 def fsum(xs, floats=False):

1836 '''Precision floating point summation based on or like Python's C{math.fsum}.

1837

1838 @arg xs: Iterable, list, tuple, etc. of values (C{scalar} or L{Fsum}

1839 instances).

1840 @kwarg floats: Optionally, use C{B{floats}=True} iff I{all} B{C{xs}}

1841 are known to be C{float}.

1842

1843 @return: Precision C{fsum} (C{float}).

1844

1845 @raise OverflowError: Partial C{2sum} overflow.

1846

1847 @raise TypeError: Non-scalar B{C{xs}} value.

1848

1849 @raise ValueError: Invalid or non-finite B{C{xs}} value.

1850

1851 @note: Exceptions and I{non-finite} handling may differ if not

1852 based on Python's C{math.fsum}.

1853

1854 @see: Class L{Fsum} and methods L{Fsum.fsum} and L{Fsum.fadd}.

1855 '''

1856 return _fsum(xs if floats else _2floats(xs)) if xs else _0_0 # PYCHOK yield

1857

1858

1859 def fsum_(*xs, **floats):

1860 '''Precision floating point summation of all positional arguments.

1861

1862 @arg xs: Values to be added (C{scalar} or L{Fsum} instances), all

1863 positional.

1864 @kwarg floats: Optionally, use C{B{floats}=True} iff I{all} B{C{xs}}

1865 are known to be C{float}.

1866

1867 @return: Precision C{fsum} (C{float}).

1868

1869 @see: Function C{fsum}.

1870 '''

1871 return _fsum(xs if _xkwds_get(floats, floats=False) else

1872 _2floats(xs, origin=1)) if xs else _0_0 # PYCHOK yield

1873

1874

1875 def fsumf_(*xs):

1876 '''Precision floating point summation L{fsum_}C{(*xs, floats=True)}.

1877 '''

1878 return _fsum(xs) if xs else _0_0

1879

1880

1881 def fsum1(xs, floats=False):

1882 '''Precision floating point summation of a few arguments, 1-primed.

1883

1884 @arg xs: Iterable, list, tuple, etc. of values (C{scalar} or L{Fsum}

1885 instances).

1886 @kwarg floats: Optionally, use C{B{floats}=True} iff I{all} B{C{xs}}

1887 are known to be C{float}.

1888

1889 @return: Precision C{fsum} (C{float}).

1890

1891 @see: Function C{fsum}.

1892 '''

1893 return _fsum(_1primed(xs if floats else _2floats(xs))) if xs else _0_0 # PYCHOK yield

1894

1895

1896 def fsum1_(*xs, **floats):

1897 '''Precision floating point summation of a few arguments, 1-primed.

1898

1899 @arg xs: Values to be added (C{scalar} or L{Fsum} instances), all

1900 positional.

1901 @kwarg floats: Optionally, use C{B{floats}=True} iff I{all} B{C{xs}}

1902 are known to be C{float}.

1903

1904 @return: Precision C{fsum} (C{float}).

1905

1906 @see: Function C{fsum}

1907 '''

1908 return _fsum(_1primed(xs if _xkwds_get(floats, floats=False) else

1909 _2floats(xs, origin=1))) if xs else _0_0 # PYCHOK yield

1910

1911

1912 def fsum1f_(*xs):

1913 '''Precision floating point summation L{fsum1_}C{(*xs, floats=True)}.

1914 '''

1915 return _fsum(_1primed(xs)) if xs else _0_0

1916

1917

1918# **) MIT License

1919#

1920# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.

1921#

1922# Permission is hereby granted, free of charge, to any person obtaining a

1923# copy of this software and associated documentation files (the "Software"),

1924# to deal in the Software without restriction, including without limitation

1925# the rights to use, copy, modify, merge, publish, distribute, sublicense,

1926# and/or sell copies of the Software, and to permit persons to whom the

1927# Software is furnished to do so, subject to the following conditions:

1928#

1929# The above copyright notice and this permission notice shall be included

1930# in all copies or substantial portions of the Software.

1931#

1932# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS

1933# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

1934# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL

1935# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR

1936# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,

1937# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR

1938# OTHER DEALINGS IN THE SOFTWARE.