Coverage for pygeodesy/fsums.py: 96%
822 statements
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2# -*- coding: utf-8 -*-
4u'''Class L{Fsum} for precision floating point summation and I{running}
5summation based on, respectively similar to Python's C{math.fsum}.
7Generally, an L{Fsum} instance is considered a C{float} plus a small or zero
8C{residual} value, see property L{Fsum.residual}. However, there are several
9C{integer} L{Fsum} cases, for example the result of C{ceil}, C{floor},
10C{Fsum.__floordiv__} and methods L{Fsum.fint} and L{Fsum.fint2}.
12Also, L{Fsum} methods L{Fsum.pow}, L{Fsum.__ipow__}, L{Fsum.__pow__} and
13L{Fsum.__rpow__} return a (very long) C{int} if invoked with optional argument
14C{mod} set to C{None}. The C{residual} of an C{integer} L{Fsum} may be between
15C{-1.0} and C{+1.0}, including C{INT0} if considered to be I{exact}.
17Set env variable C{PYGEODESY_FSUM_RESIDUAL} to a C{float} string greater than
18C{"0.0"} as the threshold to throw a L{ResidualError} for a division, power or
19root operation of an L{Fsum} instance with a C{residual} I{ratio} exceeding
20the threshold. See methods L{Fsum.RESIDUAL}, L{Fsum.pow}, L{Fsum.__ipow__}
21and L{Fsum.__itruediv__}.
22'''
23# make sure int/int division yields float quotient, see .basics
24from __future__ import division as _; del _ # PYCHOK semicolon
26from pygeodesy.basics import isbool, iscomplex, isint, isscalar, itemsorted, \
27 signOf, _signOf
28from pygeodesy.constants import INT0, _isfinite, NEG0, _pos_self, \
29 _0_0, _1_0, _N_1_0, Float, Int
30from pygeodesy.errors import _AssertionError, _OverflowError, _TypeError, \
31 _ValueError, _xError, _xError2, _xkwds_get, \
32 _ZeroDivisionError
33from pygeodesy.interns import NN, _arg_, _COMMASPACE_, _DASH_, _DOT_, \
34 _EQUAL_, _from_, _LANGLE_, _NOTEQUAL_, \
35 _not_finite_, _PERCENT_, _PLUS_, _RANGLE_, \
36 _SLASH_, _SPACE_, _STAR_, _UNDER_
37from pygeodesy.lazily import _ALL_LAZY, _getenv, _sys_version_info2
38from pygeodesy.named import _Named, _NamedTuple, _NotImplemented, Fmt, unstr
39from 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
44from math import ceil as _ceil, fabs, floor as _floor # PYCHOK used! .ltp
46__all__ = _ALL_LAZY.fsums
47__version__ = '24.05.02'
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
75def _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)
85def _2error(unused):
86 '''(INTERNAL) Throw a C{not-finite} exception.
87 '''
88 raise ValueError(_not_finite_)
91def _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)
102def _X_ps(X): # for _2floats only
103 return X._ps
106def _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)
126def _Fsumf_(*xs): # floats=True, in .auxLat, ...
127 '''(INTERNAL) An C{Fsum} of I{known scalars}.
128 '''
129 return Fsum()._facc_scalar(xs, up=False)
132def _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)
138def _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
150def _isFsum(x):
151 '''(INTERNAL) Is C{x} an C{Fsum} instance?
152 '''
153 return _isinstance(x, Fsum)
156def _isFsumTuple(x):
157 '''(INTERNAL) Is C{x} an C{Fsum} or C{Fsum2Tuple} instance?
158 '''
159 return _isinstance(x, _Fsum_Fsum2Tuple_types)
162def _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)
168def _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
178def _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
199def _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
209def _Psum_(*ps, **name):
210 '''(INTERNAL) Return an C{Fsum} from 1 or 2 known scalar(s) C{ps}.
211 '''
212 return _Psum(ps, **name)
215def _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
233def _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
244def _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)
253def _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_)
264def _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)
277def _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)
287class Fsum(_Named): # sync __methods__ with .vector3dBase.Vector3dBase
288 '''Precision floating point summation and I{running} summation.
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.
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}.
298 @note: Handling of exceptions and C{inf}, C{INF}, C{nan} and C{NAN} differs from
299 Python's C{math.fsum}.
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))
314 def __init__(self, *xs, **name_RESIDUAL):
315 '''New L{Fsum} for I{running} precision floating point summation.
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.
322 @see: Methods L{Fsum.fadd} and L{Fsum.RESIDUAL}.
323 '''
324 if name_RESIDUAL:
326 def _n_r(name=NN, RESIDUAL=None):
327 return name, RESIDUAL
329 n, r = _n_r(**name_RESIDUAL)
330 if r is not None:
331 self.RESIDUAL(r)
332 if n:
333 self.name = n
335 self._ps = [] # [_0_0], see L{Fsum._fprs}
336 if xs:
337 self._facc_1(xs, up=False)
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__)
345 def __add__(self, other):
346 '''Return C{B{self} + B{other}} as an L{Fsum}.
348 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar}.
350 @return: The sum (L{Fsum}).
352 @see: Method L{Fsum.__iadd__}.
353 '''
354 f = self._copy_2(self.__add__)
355 return f._fadd(other, _add_op_)
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
363 def __ceil__(self): # PYCHOK not special in Python 2-
364 '''Return this instance' C{math.ceil} as C{int} or C{float}.
366 @return: An C{int} in Python 3+, but C{float} in Python 2-.
368 @see: Methods L{Fsum.__floor__} and property L{Fsum.ceil}.
369 '''
370 return self.ceil
372 def __cmp__(self, other): # PYCHOK no cover
373 '''Compare this with an other instance or C{scalar}, Python 2-.
375 @return: -1, 0 or +1 (C{int}).
377 @raise TypeError: Incompatible B{C{other}} C{type}.
378 '''
379 s = self._cmp_0(other, self.cmp.__name__)
380 return _signOf(s, 0)
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.
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>}.
392 @raise ResidualError: Non-zero, significant residual or invalid
393 B{C{RESIDUAL}}.
395 @see: Method L{Fsum.__itruediv__}.
396 '''
397 f = self._copy_2(self.__divmod__)
398 return f._fdivmod2(other, _divmod_op_, **raiser_RESIDUAL)
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
405 def __float__(self):
406 '''Return this instance' current, precision running sum as C{float}.
408 @see: Methods L{Fsum.fsum} and L{Fsum.int_float}.
409 '''
410 return float(self._fprs)
412 def __floor__(self): # PYCHOK not special in Python 2-
413 '''Return this instance' C{math.floor} as C{int} or C{float}.
415 @return: An C{int} in Python 3+, but C{float} in Python 2-.
417 @see: Methods L{Fsum.__ceil__} and property L{Fsum.floor}.
418 '''
419 return self.floor
421 def __floordiv__(self, other):
422 '''Return C{B{self} // B{other}} as an L{Fsum}.
424 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar} divisor.
426 @return: The C{floor} quotient (L{Fsum}).
428 @see: Methods L{Fsum.__ifloordiv__}.
429 '''
430 f = self._copy_2(self.__floordiv__)
431 return f._floordiv(other, _floordiv_op_)
433 def __format__(self, *other): # PYCHOK no cover
434 '''Not implemented.'''
435 return _NotImplemented(self, *other)
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
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
447 def __hash__(self): # PYCHOK no cover
448 '''Return this instance' C{hash}.
449 '''
450 return hash(self._ps) # XXX id(self)?
452 def __iadd__(self, other):
453 '''Apply C{B{self} += B{other}} to this instance.
455 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar} instance.
457 @return: This instance, updated (L{Fsum}).
459 @raise TypeError: Invalid B{C{other}}, not
460 C{scalar} nor L{Fsum}.
462 @see: Methods L{Fsum.fadd} and L{Fsum.fadd_}.
463 '''
464 return self._fadd(other, _iadd_op_)
466 def __ifloordiv__(self, other):
467 '''Apply C{B{self} //= B{other}} to this instance.
469 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar} divisor.
471 @return: This instance, updated (L{Fsum}).
473 @raise ResidualError: Non-zero, significant residual
474 in B{C{other}}.
476 @raise TypeError: Invalid B{C{other}} type.
478 @raise ValueError: Invalid or non-finite B{C{other}}.
480 @raise ZeroDivisionError: Zero B{C{other}}.
482 @see: Methods L{Fsum.__itruediv__}.
483 '''
484 return self._floordiv(other, _floordiv_op_ + _fset_op_)
486 def __imatmul__(self, other): # PYCHOK no cover
487 '''Not implemented.'''
488 return _NotImplemented(self, other)
490 def __imod__(self, other):
491 '''Apply C{B{self} %= B{other}} to this instance.
493 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar} modulus.
495 @return: This instance, updated (L{Fsum}).
497 @see: Method L{Fsum.__divmod__}.
498 '''
499 return self._fdivmod2(other, _mod_op_ + _fset_op_).mod
501 def __imul__(self, other):
502 '''Apply C{B{self} *= B{other}} to this instance.
504 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar} factor.
506 @return: This instance, updated (L{Fsum}).
508 @raise OverflowError: Partial C{2sum} overflow.
510 @raise TypeError: Invalid B{C{other}} type.
512 @raise ValueError: Invalid or non-finite B{C{other}}.
513 '''
514 return self._fmul(other, _mul_op_ + _fset_op_)
516 def __int__(self):
517 '''Return this instance as an C{int}.
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
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)
531 def __ipow__(self, other, *mod, **raiser_RESIDUAL): # PYCHOK 2 vs 3 args
532 '''Apply C{B{self} **= B{other}} to this instance.
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>}.
541 @return: This instance, updated (L{Fsum}).
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}.
547 @raise OverflowError: Partial C{2sum} overflow.
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}.
555 @raise TypeError: Invalid B{C{other}} type or 3-argument C{pow}
556 invocation failed.
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}.
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)
569 def __isub__(self, other):
570 '''Apply C{B{self} -= B{other}} to this instance.
572 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar}.
574 @return: This instance, updated (L{Fsum}).
576 @raise TypeError: Invalid B{C{other}} type.
578 @see: Method L{Fsum.fadd}.
579 '''
580 return self._fsub(other, _isub_op_)
582 def __iter__(self):
583 '''Return an C{iter}ator over a C{partials} duplicate.
584 '''
585 return iter(self.partials)
587 def __itruediv__(self, other, **raiser_RESIDUAL):
588 '''Apply C{B{self} /= B{other}} to this instance.
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>}.
595 @return: This instance, updated (L{Fsum}).
597 @raise OverflowError: Partial C{2sum} overflow.
599 @raise ResidualError: Non-zero, significant residual or invalid
600 B{C{RESIDUAL}}.
602 @raise TypeError: Invalid B{C{other}} type.
604 @raise ValueError: Invalid or non-finite B{C{other}}.
606 @raise ZeroDivisionError: Zero B{C{other}}.
608 @see: Method L{Fsum.__ifloordiv__}.
609 '''
610 return self._ftruediv(other, _truediv_op_ + _fset_op_, **raiser_RESIDUAL)
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
617 def __len__(self):
618 '''Return the number of values accumulated (C{int}).
619 '''
620 return self._n
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
627 def __matmul__(self, other): # PYCHOK no cover
628 '''Not implemented.'''
629 return _NotImplemented(self, other)
631 def __mod__(self, other):
632 '''Return C{B{self} % B{other}} as an L{Fsum}.
634 @see: Method L{Fsum.__imod__}.
635 '''
636 f = self._copy_2(self.__mod__)
637 return f._fdivmod2(other, _mod_op_).mod
639 def __mul__(self, other):
640 '''Return C{B{self} * B{other}} as an L{Fsum}.
642 @see: Method L{Fsum.__imul__}.
643 '''
644 f = self._copy_2(self.__mul__)
645 return f._fmul(other, _mul_op_)
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
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)
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__)
663 def __pow__(self, other, *mod): # PYCHOK 2 vs 3 args
664 '''Return C{B{self}**B{other}} as an L{Fsum}.
666 @see: Method L{Fsum.__ipow__}.
667 '''
668 f = self._copy_2(self.__pow__)
669 return f._fpow(other, _pow_op_, *mod)
671 def __radd__(self, other):
672 '''Return C{B{other} + B{self}} as an L{Fsum}.
674 @see: Method L{Fsum.__iadd__}.
675 '''
676 f = self._copy_2r(other, self.__radd__)
677 return f._fadd(self, _add_op_)
679 def __rdivmod__(self, other):
680 '''Return C{divmod(B{other}, B{self})} as 2-tuple
681 C{(quotient, remainder)}.
683 @see: Method L{Fsum.__divmod__}.
684 '''
685 f = self._copy_2r(other, self.__rdivmod__)
686 return f._fdivmod2(self, _divmod_op_)
688# def __repr__(self):
689# '''Return the default C{repr(this)}.
690# '''
691# return self.toRepr(lenc=True)
693 def __rfloordiv__(self, other):
694 '''Return C{B{other} // B{self}} as an L{Fsum}.
696 @see: Method L{Fsum.__ifloordiv__}.
697 '''
698 f = self._copy_2r(other, self.__rfloordiv__)
699 return f._floordiv(self, _floordiv_op_)
701 def __rmatmul__(self, other): # PYCHOK no cover
702 '''Not implemented.'''
703 return _NotImplemented(self, other)
705 def __rmod__(self, other):
706 '''Return C{B{other} % B{self}} as an L{Fsum}.
708 @see: Method L{Fsum.__imod__}.
709 '''
710 f = self._copy_2r(other, self.__rmod__)
711 return f._fdivmod2(self, _mod_op_).mod
713 def __rmul__(self, other):
714 '''Return C{B{other} * B{self}} as an L{Fsum}.
716 @see: Method L{Fsum.__imul__}.
717 '''
718 f = self._copy_2r(other, self.__rmul__)
719 return f._fmul(self, _mul_op_)
721 def __round__(self, *ndigits): # PYCHOK Python 3+
722 '''Return C{round(B{self}, *B{ndigits}} as an L{Fsum}.
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}
730 def __rpow__(self, other, *mod):
731 '''Return C{B{other}**B{self}} as an L{Fsum}.
733 @see: Method L{Fsum.__ipow__}.
734 '''
735 f = self._copy_2r(other, self.__rpow__)
736 return f._fpow(self, _pow_op_, *mod)
738 def __rsub__(self, other):
739 '''Return C{B{other} - B{self}} as L{Fsum}.
741 @see: Method L{Fsum.__isub__}.
742 '''
743 f = self._copy_2r(other, self.__rsub__)
744 return f._fsub(self, _sub_op_)
746 def __rtruediv__(self, other, **raiser_RESIDUAL):
747 '''Return C{B{other} / B{self}} as an L{Fsum}.
749 @see: Method L{Fsum.__itruediv__}.
750 '''
751 f = self._copy_2r(other, self.__rtruediv__)
752 return f._ftruediv(self, _truediv_op_, **raiser_RESIDUAL)
754 def __str__(self):
755 '''Return the default C{str(self)}.
756 '''
757 return self.toStr(lenc=True)
759 def __sub__(self, other):
760 '''Return C{B{self} - B{other}} as an L{Fsum}.
762 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar}.
764 @return: The difference (L{Fsum}).
766 @see: Method L{Fsum.__isub__}.
767 '''
768 f = self._copy_2(self.__sub__)
769 return f._fsub(other, _sub_op_)
771 def __truediv__(self, other, **raiser_RESIDUAL):
772 '''Return C{B{self} / B{other}} as an L{Fsum}.
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>}.
779 @return: The quotient (L{Fsum}).
781 @raise ResidualError: Non-zero, significant residual or invalid
782 B{C{RESIDUAL}}.
784 @see: Method L{Fsum.__itruediv__}.
785 '''
786 f = self._copy_2(self.__truediv__)
787 return f._ftruediv(other, _truediv_op_, **raiser_RESIDUAL)
789 __trunc__ = __int__
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__
799 def as_integer_ratio(self):
800 '''Return this instance as the ratio of 2 integers.
802 @return: 2-Tuple C{(numerator, denominator)} both
803 C{int} and with positive C{denominator}.
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
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
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-).
828 @note: The C{ceil} takes the C{residual} into account.
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
839 cmp = __cmp__
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
852 def copy(self, deep=False, name=NN):
853 '''Copy this instance, C{shallow} or B{C{deep}}.
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
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
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)
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
887 divmod = __divmod__
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)
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)
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)
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
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)
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
931 def _n(x):
932 return -float(x)
934 return self._facc(xs, _X=_N, _x=_n, **up_origin)
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
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
961 def _P(X):
962 f = _Pow(X, p, power, op, **raiser_RESIDUAL)
963 return f._ps if _isF(f) else (f,)
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
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
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
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
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
1005 def fadd(self, xs=()):
1006 '''Add all items from an iterable to this instance.
1008 @arg xs: Iterable of items to add (each C{scalar}
1009 or an L{Fsum} or L{Fsum2Tuple} instance).
1011 @return: This instance (L{Fsum}).
1013 @raise OverflowError: Partial C{2sum} overflow.
1015 @raise TypeError: An invalid B{C{xs}} item.
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
1027 def fadd_(self, *xs):
1028 '''Add all positional arguments to this instance.
1030 @arg xs: Values to add (each C{scalar} or an L{Fsum}
1031 or L{Fsum2Tuple} instance), all positional.
1033 @see: Method L{Fsum.fadd} for further details.
1034 '''
1035 return self._facc_1(xs)
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
1046 fcopy = copy # for backward compatibility
1047 fdiv = __itruediv__ # for backward compatibility
1048 fdivmod = __divmod__ # for backward compatibility
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__!
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-
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_)
1078 def fint(self, name=NN, **raiser_RESIDUAL):
1079 '''Return this instance' current running sum as C{integer}.
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>}.
1086 @return: The C{integer} sum (L{Fsum}) if this instance C{is_integer}
1087 with a zero or insignificant I{integer} residual.
1089 @raise ResidualError: Non-zero, significant residual or invalid
1090 B{C{RESIDUAL}}.
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)
1103 def fint2(self, **name):
1104 '''Return this instance' current running sum as C{int} and the
1105 I{integer} residual.
1107 @kwarg name: Optional name (C{str}).
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)
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?
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
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-).
1134 @note: The C{floor} takes the C{residual} into account.
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
1145# floordiv = __floordiv__ # for naming consistency
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)
1153 fmul = __imul__ # for backward compatibility
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
1170 def fover(self, over, **raiser_RESIDUAL):
1171 '''Apply C{B{self} /= B{over}} and summate.
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>}.
1178 @return: Precision running sum (C{float}).
1180 @raise ResidualError: Non-zero, significant residual or invalid
1181 B{C{RESIDUAL}}.
1183 @see: Methods L{Fsum.fsum} and L{Fsum.__itruediv__}.
1184 '''
1185 return float(self.fdiv(over, **raiser_RESIDUAL)._fprs)
1187 fpow = __ipow__ # for backward compatibility
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)
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}.
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
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)
1241 def fset_(self, *xs):
1242 '''Replace this instance' value with C{xs}.
1244 @arg xs: Optional, new values (each C{scalar} or
1245 an L{Fsum} or L{Fsum2Tuple} instance),
1246 all positional.
1248 @return: This instance (C{Fsum}).
1250 @see: Method L{Fsum.fadd} for further details.
1251 '''
1252 f = Fsum(*xs) if xs else _0_0
1253 return self._fset(f)
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
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
1292 def fsub(self, xs=()):
1293 '''Subtract all items of an iterable from this instance.
1295 @see: Method L{Fsum.fadd} for further details.
1296 '''
1297 return self._facc_neg(xs)
1299 def fsub_(self, *xs):
1300 '''Subtract all positional arguments from this instance.
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)
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
1319 def fsum(self, xs=()):
1320 '''Add more items from an iterable, summate and return
1321 the current precision running sum.
1323 @arg xs: Iterable of items to add (each item C{scalar}
1324 or an L{Fsum} or L{Fsum2Tuple} instance).
1326 @return: Precision running sum (C{float} or C{int}).
1328 @see: Method L{Fsum.fadd}.
1330 @note: Accumulation can continue after summation.
1331 '''
1332 return self._facc(xs)._fprs
1334 def fsum_(self, *xs):
1335 '''Add any positional arguments, summate and return the
1336 current precision running sum.
1338 @arg xs: Values to add (each C{scalar} or an L{Fsum}
1339 or L{Fsum2Tuple} instance), all positional.
1341 @return: Precision running sum (C{float} or C{int}).
1343 @see: Methods L{Fsum.fsum}, L{Fsum.Fsum_} and L{Fsum.fsumf_}.
1344 '''
1345 return self._facc_1(xs)._fprs
1347 @property_RO
1348 def _Fsum(self):
1349 '''(INTERNAL) Like L{Fsum2Tuple._Fsum}, for C{_2floats}.
1350 '''
1351 return self
1353 def Fsum_(self, *xs, **name):
1354 '''Like method L{Fsum.fsum_} but returning a named L{Fsum}.
1356 @kwarg name: Optional name (C{str}).
1358 @return: Current, precision running sum (L{Fsum}).
1359 '''
1360 return self._facc_1(xs)._copy_2(self.Fsum_, **name)
1362 def Fsum2Tuple_(self, *xs, **name):
1363 '''Like method L{Fsum.fsum_} but returning a named L{Fsum2Tuple}.
1365 @kwarg name: Optional name (C{str}).
1367 @return: Current, precision running sum (L{Fsum2Tuple}).
1368 '''
1369 return Fsum2Tuple(self._facc_1(xs)._fprs2, **name)
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}.
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}).
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}.
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
1390 def fsum2_(self, *xs):
1391 '''Add any positional arguments, summate and return the current
1392 precision running sum I{and} the C{differential}.
1394 @arg xs: Values to add (each C{scalar} or an L{Fsum} or
1395 L{Fsum2Tuple} instance), all positional.
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}.
1401 @see: Methods L{Fsum.fsum_} and L{Fsum.fsum}.
1402 '''
1403 return self._fsum2(xs, self._facc_1)
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
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
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_)
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)
1430# ftruediv = __itruediv__ # for naming consistency?
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
1454 @property_RO
1455 def imag(self):
1456 '''Get the C{imaginary} part of this instance (C{0.0}, always).
1458 @see: Properties L{Fsum.ceil}, L{Fsum.floor} and L{Fsum.real}.
1459 '''
1460 return _0_0
1462 def int_float(self, **raiser_RESIDUAL):
1463 '''Return this instance' current running sum as C{int} or C{float}.
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>}.
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.
1473 @raise ResidualError: Non-zero, significant residual or invalid
1474 B{C{RESIDUAL}}.
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
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
1495 def is_integer(self):
1496 '''Is this instance' running sum C{integer}? (C{bool}).
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
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.
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)
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}).
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>}.
1526 @raise ResidualError: Non-zero, significant residual or invalid
1527 B{C{RESIDUAL}}.
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
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
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
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
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)
1569 def pow(self, x, *mod, **raiser_RESIDUAL):
1570 '''Return C{B{self}**B{x}} as L{Fsum}.
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>}.
1579 @return: The C{pow(self, B{x})} or C{pow(self, B{x}, *B{mod})}
1580 result (L{Fsum}).
1582 @raise ResidualError: Non-zero, significant residual or invalid
1583 B{C{RESIDUAL}}.
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.
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)
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
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)
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 '''
1617 if mod: # b, x, mod all C{int}, unless C{mod} is C{None}
1618 m = mod[0]
1619 # assert _isFsumTuple(b)
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
1627 b = _s(*(b._fprs2 if m is None else b._fint2))
1628 x = _s(*_2scalar2(x))
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)
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
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
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)
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
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)
1754 return _Psum(self._ps_acc([], _pfs(self._ps, factors), up=False))
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
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
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 {}
1788 @property_RO
1789 def real(self):
1790 '''Get the C{real} part of this instance (C{float}).
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)
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}.
1803 @note: The C{residual is INT0} iff the precision running
1804 C{fsum} is considered to be I{exact}.
1806 @see: Methods L{Fsum.fsum}, L{Fsum.fsum2} and L{Fsum.is_exact}.
1807 '''
1808 return self._fprs2.residual
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}.
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.
1820 @return: The previous C{RESIDUAL} setting (C{float}), default C{0.0}.
1822 @raise ResidualError: Invalid B{C{threshold}}.
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
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_
1847 t = _stresidual(_p(**mod_R), residual, **mod_R)
1848 return self._Error(op, other, ResidualError, txt=t)
1850 def root(self, root, **raiser_RESIDUAL):
1851 '''Return C{B{self}**(1 / B{root})} as L{Fsum}.
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>}.
1858 @return: The C{self ** (1 / B{root})} result (L{Fsum}).
1860 @raise ResidualError: Non-zero, significant residual or invalid
1861 B{C{RESIDUAL}}.
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)
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_
1876 def signOf(self, res=True):
1877 '''Determine the sign of this instance.
1879 @kwarg res: If C{True} consider, otherwise
1880 ignore the residual (C{bool}).
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)
1888 def toRepr(self, **prec_sep_fmt_lenc): # PYCHOK signature
1889 '''Return this C{Fsum} instance as representation.
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]}.
1896 @return: This instance (C{repr}).
1897 '''
1898 return self._toT(self._fprs2.toRepr, **prec_sep_fmt_lenc)
1900 def toStr(self, **prec_sep_fmt_lenc): # PYCHOK signature
1901 '''Return this C{Fsum} instance as string.
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]}.
1908 @return: This instance (C{str}).
1909 '''
1910 return self._toT(self._fprs2.toStr, **prec_sep_fmt_lenc)
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))
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)
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_
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)
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)
1950_ROs = _allPropertiesOf_n(3, Fsum, Property_RO) # PYCHOK see Fsum._update
1953def _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)
1960class DivMod2Tuple(_NamedTuple):
1961 '''2-Tuple C{(div, mod)} with the quotient C{div} and remainder
1962 C{mod} results of a C{divmod} operation.
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)
1971class 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}.
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)
1982 def as_integer_ratio(self):
1983 '''Return this instance as the ratio of 2 integers.
1985 @see: Method L{Fsum.as_integer_ratio} for further details.
1986 '''
1987 return self._Fsum.as_integer_ratio()
1989 @property_RO
1990 def _fint2(self):
1991 return self._Fsum.fint2
1993 @property_RO
1994 def _fprs2(self):
1995 return self._Fsum._fprs2
1997 @Property_RO
1998 def _Fsum(self):
1999 return Fsum(*self)
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
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)
2013 @property_RO
2014 def _n(self):
2015 return self._Fsum._n
2017 @property_RO
2018 def _ps(self):
2019 return self._Fsum._ps
2021 @property_RO
2022 def _ps_neg(self):
2023 return self._Fsum._ps_neg
2025 def signOf(self, **res):
2026 '''Like L{Fsum.signOf}.
2027 '''
2028 return self._Fsum.signOf(**res)
2030_Fsum_Fsum2Tuple_types = Fsum, Fsum2Tuple # PYCHOK line
2033class 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.
2038 @see: Module L{pygeodesy.fsums} and method L{Fsum.RESIDUAL}.
2039 '''
2040 pass
2043try:
2044 from math import fsum as _fsum # precision IEEE-754 sum, Python 2.6+
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
2052 Fsum._math_fsum = _sum = _fsum # PYCHOK exported
2053except ImportError:
2054 _sum = sum # Fsum(NAN) exception fall-back, in .elliptic
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
2064def fsum(xs, floats=False):
2065 '''Precision floating point summation based on/like Python's C{math.fsum}.
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}).
2072 @return: Precision C{fsum} (C{float}).
2074 @raise OverflowError: Partial C{2sum} overflow.
2076 @raise TypeError: Non-scalar B{C{xs}} item.
2078 @raise ValueError: Invalid or non-finite B{C{xs}} item.
2080 @note: Exception and I{non-finite} handling may differ if not based
2081 on Python's C{math.fsum}.
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
2088def fsum_(*xs, **floats):
2089 '''Precision floating point summation of all positional arguments.
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}).
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
2102def fsumf_(*xs):
2103 '''Precision floating point summation iff I{all} C{B{xs}} items are I{known to be scalar}.
2105 @see: Function L{fsum_<fsums.fsum_>} for further details.
2106 '''
2107 return _fsum(xs) if xs else _0_0
2110def fsum1(xs, floats=False):
2111 '''Precision floating point summation, 1-primed.
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}).
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
2123def fsum1_(*xs, **floats):
2124 '''Precision floating point summation, 1-primed of all positional arguments.
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}).
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
2137def fsum1f_(*xs):
2138 '''Precision floating point summation iff I{all} C{B{xs}} are I{known to be scalar}.
2140 @see: Function L{fsum_<fsums.fsum_>} for further details.
2141 '''
2142 return _fsum(_1primed(xs)) if xs else _0_0
2145if __name__ == '__main__':
2147 # usage: [env _psum=fsum] python3 -m pygeodesy.fsums
2149 if _getenv(_psum.__name__, NN) == _fsum.__name__:
2150 _psum = _fsum
2152 def _test(n):
2153 # copied from Hettinger, see L{Fsum} reference
2154 from pygeodesy import frandoms, printf
2156 printf(_fsum.__name__, end=_COMMASPACE_)
2157 printf(_psum.__name__, end=_COMMASPACE_)
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)
2166 _test(128)
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.