Coverage for pygeodesy/fsums.py: 96%
783 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_PARTIALS} to string C{"fsum"}) for summation
18of L{Fsum} partials by Python function C{math.fsum}.
20Set env variable C{PYGEODESY_FSUM_RESIDUAL} to a C{float} string greater than
21C{"0.0"} as the threshold to throw a L{ResidualError} in division or exponention
22of an L{Fsum} instance with a I{relative} C{residual} exceeding the threshold,
23see methods L{Fsum.RESIDUAL}, L{Fsum.pow}, L{Fsum.__ipow__} and L{Fsum.__itruediv__}.
24'''
25# make sure int/int division yields float quotient, see .basics
26from __future__ import division as _; del _ # PYCHOK semicolon
28from pygeodesy.basics import iscomplex, isint, isscalar, itemsorted, \
29 signOf, _signOf
30from pygeodesy.constants import INT0, _isfinite, NEG0, _pos_self, \
31 _0_0, _1_0, _N_1_0, Float, Int
32from pygeodesy.errors import _AssertionError, _OverflowError, _TypeError, \
33 _ValueError, _xError, _xError2, _xkwds_get, \
34 _ZeroDivisionError
35from pygeodesy.interns import NN, _arg_, _COMMASPACE_, _DASH_, _DOT_, _EQUAL_, \
36 _exceeds_, _from_, _iadd_op_, _LANGLE_, _negative_, \
37 _NOTEQUAL_, _not_finite_, _PERCENT_, _PLUS_, _R_, \
38 _RANGLE_, _SLASH_, _SPACE_, _STAR_, _UNDER_
39from pygeodesy.lazily import _ALL_LAZY, _getenv, _sys_version_info2
40from pygeodesy.named import _Named, _NamedTuple, _NotImplemented, Fmt, unstr
41from 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
46from math import ceil as _ceil, fabs, floor as _floor # PYCHOK used! .ltp
48__all__ = _ALL_LAZY.fsums
49__version__ = '24.04.24'
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
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 _Fs = Fsum
113 for x in xs:
114 if isinstance(x, _Fs):
115 for p in _X(x):
116 yield p
117 else:
118 f = _x(x)
119 yield f if _fin(f) else _2error(f)
120 i += 1
121 except Exception as X:
122 raise _xError(X, Fmt.INDEX(xs=i), x)
125def _Fsumf_(*xs): # floats=True, in .auxLat, ...
126 '''(INTERNAL) An C{Fsum} of I{known scalars}.
127 '''
128 return Fsum()._facc_scalar(xs, up=False)
131def _Fsum1f_(*xs): # floats=True, in .albers, ...
132 '''(INTERNAL) An C{Fsum} of I{known scalars}, 1-primed.
133 '''
134 return Fsum()._facc_scalar(_1primed(xs), up=False)
137def _2halfeven(s, r, p):
138 '''(INTERNAL) Round half-even.
139 '''
140 if (p > 0 and r > 0) or \
141 (p < 0 and r < 0): # signs match
142 r *= 2
143 t = s + r
144 if r == (t - s):
145 s = t
146 return s
149def _1_over(x, op=_truediv_op_, **raiser):
150 '''(INTERNAL) Return C{Fsum(1) /= B{x}}.
151 '''
152 return _Psum_(_1_0)._ftruediv(x, op, **raiser)
155def _1primed(xs): # in .fmath
156 '''(INTERNAL) 1-Primed summation of iterable C{xs}
157 items, all I{known} to be C{finite float}.
158 '''
159 yield _1_0
160 for x in xs:
161 yield x
162 yield _N_1_0
165def _2ps(s, r):
166 '''(INTERNAL) Return an C{s} and C{r} pair, I{ps-ordered}.
167 '''
168 if fabs(s) < fabs(r):
169 s, r = r, s
170 return (r, s) if r else (s,) # PYCHOK types
173def _psum(ps): # PYCHOK used!
174 '''(INTERNAL) Partials sum, updating C{ps}, I{overridden below}.
175 '''
176 # assert isinstance(ps, list)
177 i = len(ps) - 1
178 s = _0_0 if i < 0 else ps[i]
179 _2s = _2sum
180 while i > 0:
181 i -= 1
182 s, r = _2s(s, ps[i])
183 if r: # sum(ps) became inexact
184 if s:
185 ps[i:] = r, s
186 if i > 0:
187 s = _2halfeven(s, r, ps[i-1])
188 break # return s
189 s = r # PYCHOK no cover
190 ps[i:] = s,
191 return s
194def _Psum(ps, **name):
195 '''(INTERNAL) Return an C{Fsum} from I{ordered} partials C{ps}.
196 '''
197 F = Fsum(**name) if name else Fsum()
198 if ps:
199 F._ps[:] = ps
200 F._n = len(F._ps)
201 return F
204def _Psum_(*ps, **name):
205 '''(INTERNAL) Return an C{Fsum} from 1 or 2 known scalar(s) C{ps}.
206 '''
207 return _Psum(ps, **name)
210def _2scalar(other, _raiser=None, **mod):
211 '''(INTERNAL) Return B{C{other}} as C{int}, C{float} or C{as-is}.
212 '''
213 if isinstance(other, Fsum):
214 s, r = other._fint2
215 if r:
216 s, r = other._fprs2
217 if r: # PYCHOK no cover
218 if _raiser and _raiser(r, s):
219 t = _stresidual(_non_zero_, r, **mod)
220 raise ResidualError(t, txt=None)
221 s = other # L{Fsum} as-is
222 else:
223 s = other # C{type} as-is
224 if isint(s, both=True):
225 s = int(s)
226 return s
229def _strcomplex(s, *args):
230 '''(INTERNAL) C{Complex} 2- or 3-arg C{pow} error as C{str}.
231 '''
232 c = _strcomplex.__name__[4:]
233 n = _DASH_(len(args), _arg_)
234 t = unstr(pow, *args)
235 return _SPACE_(c, s, _from_, n, t)
238def _stresidual(prefix, residual, **name_values):
239 '''(INTERNAL) Residual error as C{str}.
240 '''
241 p = _stresidual.__name__[3:]
242 t = Fmt.PARENSPACED(p, Fmt(residual))
243 for n, v in itemsorted(name_values):
244 n = n.replace(_UNDER_, _SPACE_)
245 p = Fmt.PARENSPACED(n, Fmt(v))
246 t = _COMMASPACE_(t, p)
247 return _SPACE_(prefix, t)
250def _2sum(a, b): # by .testFmath
251 '''(INTERNAL) Return C{a + b} as 2-tuple (sum, residual).
252 '''
253 s = a + b
254 if _isfinite(s):
255 if fabs(a) < fabs(b):
256 b, a = a, b
257 return s, (b - (s - a))
258 u = unstr(_2sum, a, b)
259 t = Fmt.PARENSPACED(_not_finite_, s)
260 raise _OverflowError(u, txt=t)
263class Fsum(_Named): # sync __methods__ with .vector3dBase.Vector3dBase
264 '''Precision floating point summation and I{running} summation.
266 Unlike Python's C{math.fsum}, this class accumulates values and provides intermediate,
267 I{running}, precision floating point summations. Accumulation may continue after any
268 intermediate, I{running} summuation.
270 @note: Accumulated values may be L{Fsum} or C{scalar} instances, any C{type} having
271 method C{__float__} to convert the C{scalar} to a single C{float}.
273 @note: Handling of exceptions and C{inf}, C{INF}, C{nan} and C{NAN} differs from
274 Python's C{math.fsum}.
276 @see: U{Hettinger<https://GitHub.com/ActiveState/code/tree/master/recipes/Python/
277 393090_Binary_floating_point_summatiaccurate_full/recipe-393090.py>},
278 U{Kahan<https://WikiPedia.org/wiki/Kahan_summation_algorithm>}, U{Klein
279 <https://Link.Springer.com/article/10.1007/s00607-005-0139-x>}, Python 2.6+
280 file I{Modules/mathmodule.c} and the issue log U{Full precision summation
281 <https://Bugs.Python.org/issue2819>}.
282 '''
283 _math_fsum = None
284 _n = 0
285# _ps = [] # partial sums
286# _ps_max = 0 # max(Fsum._ps_max, len(Fsum._ps))
287 _ratio = None # see method _raiser
288 _recursive = bool(_getenv('PYGEODESY_FSUM_RECURSIVE', NN))
289 _RESIDUAL = max(float(_getenv('PYGEODESY_FSUM_RESIDUAL', _0_0)), _0_0)
291 def __init__(self, *xs, **name_RESIDUAL):
292 '''New L{Fsum} for I{running} precision floating point summation.
294 @arg xs: No, one or more initial values, all positional (each C{scalar}
295 or an L{Fsum} instance).
296 @kwarg name_RESIDUAL: Optional C{B{name}=NN} for this L{Fsum} and
297 C{B{RESIDUAL}=None} for the L{ResidualError} threshold.
299 @see: Methods L{Fsum.fadd} and L{Fsum.RESIDUAL}.
300 '''
301 if name_RESIDUAL:
302 n = _xkwds_get(name_RESIDUAL, name=NN)
303 if n: # set name before ...
304 self.name = n
305 r = _xkwds_get(name_RESIDUAL, RESIDUAL=None)
306 if r is not None:
307 self.RESIDUAL(r) # ... ResidualError
308 self._ps = [] # [_0_0], see L{Fsum._fprs}
309 if xs:
310 self._facc(xs, origin=1, up=False)
312 def __abs__(self):
313 '''Return this instance' absolute value as an L{Fsum}.
314 '''
315 s = _fsum(self._ps_1primed()) # == self._cmp_0(0, ...)
316 return (-self) if s < 0 else self._copy_2(self.__abs__)
318 def __add__(self, other):
319 '''Return C{B{self} + B{other}} as an L{Fsum}.
321 @arg other: An L{Fsum} or C{scalar}.
323 @return: The sum (L{Fsum}).
325 @see: Method L{Fsum.__iadd__}.
326 '''
327 f = self._copy_2(self.__add__)
328 return f._fadd(other, _add_op_)
330 def __bool__(self): # PYCHOK not special in Python 2-
331 '''Return C{True} if this instance is I{exactly} non-zero.
332 '''
333 s, r = self._fprs2
334 return bool(s or r) and s != -r # == self != 0
336 def __ceil__(self): # PYCHOK not special in Python 2-
337 '''Return this instance' C{math.ceil} as C{int} or C{float}.
339 @return: An C{int} in Python 3+, but C{float} in Python 2-.
341 @see: Methods L{Fsum.__floor__} and property L{Fsum.ceil}.
342 '''
343 return self.ceil
345 def __cmp__(self, other): # PYCHOK no cover
346 '''Compare this with an other instance or C{scalar}, Python 2-.
348 @return: -1, 0 or +1 (C{int}).
350 @raise TypeError: Incompatible B{C{other}} C{type}.
351 '''
352 s = self._cmp_0(other, self.cmp.__name__)
353 return _signOf(s, 0)
355 cmp = __cmp__
357 def __divmod__(self, other):
358 '''Return C{divmod(B{self}, B{other})} as a L{DivMod2Tuple}
359 with quotient C{div} an C{int} in Python 3+ or C{float}
360 in Python 2- and remainder C{mod} an L{Fsum}.
362 @arg other: An L{Fsum} or C{scalar} modulus.
364 @see: Method L{Fsum.__itruediv__}.
365 '''
366 f = self._copy_2(self.__divmod__)
367 return f._fdivmod2(other, _divmod_op_)
369 def __eq__(self, other):
370 '''Compare this with an other instance or C{scalar}.
371 '''
372 return self._cmp_0(other, _eq_op_) == 0
374 def __float__(self):
375 '''Return this instance' current, precision running sum as C{float}.
377 @see: Methods L{Fsum.fsum} and L{Fsum.int_float}.
378 '''
379 return float(self._fprs)
381 def __floor__(self): # PYCHOK not special in Python 2-
382 '''Return this instance' C{math.floor} as C{int} or C{float}.
384 @return: An C{int} in Python 3+, but C{float} in Python 2-.
386 @see: Methods L{Fsum.__ceil__} and property L{Fsum.floor}.
387 '''
388 return self.floor
390 def __floordiv__(self, other):
391 '''Return C{B{self} // B{other}} as an L{Fsum}.
393 @arg other: An L{Fsum} or C{scalar} divisor.
395 @return: The C{floor} quotient (L{Fsum}).
397 @see: Methods L{Fsum.__ifloordiv__}.
398 '''
399 f = self._copy_2(self.__floordiv__)
400 return f._floordiv(other, _floordiv_op_)
402 def __format__(self, *other): # PYCHOK no cover
403 '''Not implemented.'''
404 return _NotImplemented(self, *other)
406 def __ge__(self, other):
407 '''Compare this with an other instance or C{scalar}.
408 '''
409 return self._cmp_0(other, _ge_op_) >= 0
411 def __gt__(self, other):
412 '''Compare this with an other instance or C{scalar}.
413 '''
414 return self._cmp_0(other, _gt_op_) > 0
416 def __hash__(self): # PYCHOK no cover
417 '''Return this instance' C{hash}.
418 '''
419 return hash(self._ps) # XXX id(self)?
421 def __iadd__(self, other):
422 '''Apply C{B{self} += B{other}} to this instance.
424 @arg other: An L{Fsum} or C{scalar} instance.
426 @return: This instance, updated (L{Fsum}).
428 @raise TypeError: Invalid B{C{other}}, not
429 C{scalar} nor L{Fsum}.
431 @see: Methods L{Fsum.fadd} and L{Fsum.fadd_}.
432 '''
433 return self._fadd(other, _iadd_op_)
435 def __ifloordiv__(self, other):
436 '''Apply C{B{self} //= B{other}} to this instance.
438 @arg other: An L{Fsum} or C{scalar} divisor.
440 @return: This instance, updated (L{Fsum}).
442 @raise ResidualError: Non-zero residual in B{C{other}}.
444 @raise TypeError: Invalid B{C{other}} type.
446 @raise ValueError: Invalid or non-finite B{C{other}}.
448 @raise ZeroDivisionError: Zero B{C{other}}.
450 @see: Methods L{Fsum.__itruediv__}.
451 '''
452 return self._floordiv(other, _floordiv_op_ + _fset_op_)
454 def __imatmul__(self, other): # PYCHOK no cover
455 '''Not implemented.'''
456 return _NotImplemented(self, other)
458 def __imod__(self, other):
459 '''Apply C{B{self} %= B{other}} to this instance.
461 @arg other: An L{Fsum} or C{scalar} modulus.
463 @return: This instance, updated (L{Fsum}).
465 @see: Method L{Fsum.__divmod__}.
466 '''
467 return self._fdivmod2(other, _mod_op_ + _fset_op_).mod
469 def __imul__(self, other):
470 '''Apply C{B{self} *= B{other}} to this instance.
472 @arg other: An L{Fsum} or C{scalar} factor.
474 @return: This instance, updated (L{Fsum}).
476 @raise OverflowError: Partial C{2sum} overflow.
478 @raise TypeError: Invalid B{C{other}} type.
480 @raise ValueError: Invalid or non-finite B{C{other}}.
481 '''
482 return self._fmul(other, _mul_op_ + _fset_op_)
484 def __int__(self):
485 '''Return this instance as an C{int}.
487 @see: Methods L{Fsum.int_float}, L{Fsum.__ceil__}
488 and L{Fsum.__floor__} and properties
489 L{Fsum.ceil} and L{Fsum.floor}.
490 '''
491 i, _ = self._fint2
492 return i
494 def __invert__(self): # PYCHOK no cover
495 '''Not implemented.'''
496 # Luciano Ramalho, "Fluent Python", O'Reilly, 2nd Ed, 2022 p. 567
497 return _NotImplemented(self)
499 def __ipow__(self, other, *mod, **raiser): # PYCHOK 2 vs 3 args
500 '''Apply C{B{self} **= B{other}} to this instance.
502 @arg other: The exponent (L{Fsum} or C{scalar}).
503 @arg mod: Optional modulus (C{int} or C{None}) for the
504 3-argument C{pow(B{self}, B{other}, B{mod})}
505 version.
506 @kwarg raiser: Use C{B{raiser}=False} to ignore L{ResidualError}s
507 (C{bool}), see also method L{RESIDUAL}.
509 @return: This instance, updated (L{Fsum}).
511 @note: If B{C{mod}} is given, the result will be an C{integer}
512 L{Fsum} in Python 3+ if this instance C{is_integer} or
513 set to C{as_integer} if B{C{mod}} given as C{None}.
515 @raise OverflowError: Partial C{2sum} overflow.
517 @raise ResidualError: Non-zero residual in B{C{other}} and
518 env var C{PYGEODESY_FSUM_RESIDUAL}
519 set or this instance has a non-zero
520 residual and either B{C{mod}} is
521 given and non-C{None} or B{C{other}}
522 is a negative or fractional C{scalar}.
524 @raise TypeError: Invalid B{C{other}} type or 3-argument
525 C{pow} invocation failed.
527 @raise ValueError: If B{C{other}} is a negative C{scalar}
528 and this instance is C{0} or B{C{other}}
529 is a fractional C{scalar} and this
530 instance is negative or has a non-zero
531 residual or B{C{mod}} is given and C{0}.
533 @see: CPython function U{float_pow<https://GitHub.com/
534 python/cpython/blob/main/Objects/floatobject.c>}.
535 '''
536 return self._fpow(other, _pow_op_ + _fset_op_, *mod, **raiser)
538 def __isub__(self, other):
539 '''Apply C{B{self} -= B{other}} to this instance.
541 @arg other: An L{Fsum} or C{scalar}.
543 @return: This instance, updated (L{Fsum}).
545 @raise TypeError: Invalid B{C{other}} type.
547 @see: Method L{Fsum.fadd}.
548 '''
549 return self._fsub(other, _isub_op_)
551 def __iter__(self):
552 '''Return an C{iter}ator over a C{partials} duplicate.
553 '''
554 return iter(self.partials)
556 def __itruediv__(self, other, **raiser):
557 '''Apply C{B{self} /= B{other}} to this instance.
559 @arg other: An L{Fsum} or C{scalar} divisor.
560 @kwarg raiser: Use C{B{raiser}=False} to ignore L{ResidualError}s
561 (C{bool}), see also method L{RESIDUAL}.
563 @return: This instance, updated (L{Fsum}).
565 @raise OverflowError: Partial C{2sum} overflow.
567 @raise ResidualError: Non-zero residual in B{C{other}} and
568 env var C{PYGEODESY_FSUM_RESIDUAL} set.
570 @raise TypeError: Invalid B{C{other}} type.
572 @raise ValueError: Invalid or non-finite B{C{other}}.
574 @raise ZeroDivisionError: Zero B{C{other}}.
576 @see: Method L{Fsum.__ifloordiv__}.
577 '''
578 return self._ftruediv(other, _truediv_op_ + _fset_op_, **raiser)
580 def __le__(self, other):
581 '''Compare this with an other instance or C{scalar}.
582 '''
583 return self._cmp_0(other, _le_op_) <= 0
585 def __len__(self):
586 '''Return the number of values accumulated (C{int}).
587 '''
588 return self._n
590 def __lt__(self, other):
591 '''Compare this with an other instance or C{scalar}.
592 '''
593 return self._cmp_0(other, _lt_op_) < 0
595 def __matmul__(self, other): # PYCHOK no cover
596 '''Not implemented.'''
597 return _NotImplemented(self, other)
599 def __mod__(self, other):
600 '''Return C{B{self} % B{other}} as an L{Fsum}.
602 @see: Method L{Fsum.__imod__}.
603 '''
604 f = self._copy_2(self.__mod__)
605 return f._fdivmod2(other, _mod_op_).mod
607 def __mul__(self, other):
608 '''Return C{B{self} * B{other}} as an L{Fsum}.
610 @see: Method L{Fsum.__imul__}.
611 '''
612 f = self._copy_2(self.__mul__)
613 return f._fmul(other, _mul_op_)
615 def __ne__(self, other):
616 '''Compare this with an other instance or C{scalar}.
617 '''
618 return self._cmp_0(other, _ne_op_) != 0
620 def __neg__(self):
621 '''Return I{a copy of} this instance, I{negated}.
622 '''
623 f = self._copy_2(self.__neg__)
624 return f._fset(self._neg)
626 def __pos__(self):
627 '''Return this instance I{as-is}, like C{float.__pos__()}.
628 '''
629 return self if _pos_self else self._copy_2(self.__pos__)
631 def __pow__(self, other, *mod): # PYCHOK 2 vs 3 args
632 '''Return C{B{self}**B{other}} as an L{Fsum}.
634 @see: Method L{Fsum.__ipow__}.
635 '''
636 f = self._copy_2(self.__pow__)
637 return f._fpow(other, _pow_op_, *mod)
639 def __radd__(self, other):
640 '''Return C{B{other} + B{self}} as an L{Fsum}.
642 @see: Method L{Fsum.__iadd__}.
643 '''
644 f = self._copy_2r(other, self.__radd__)
645 return f._fadd(self, _add_op_)
647 def __rdivmod__(self, other):
648 '''Return C{divmod(B{other}, B{self})} as 2-tuple C{(quotient,
649 remainder)}.
651 @see: Method L{Fsum.__divmod__}.
652 '''
653 f = self._copy_2r(other, self.__rdivmod__)
654 return f._fdivmod2(self, _divmod_op_)
656# def __repr__(self):
657# '''Return the default C{repr(this)}.
658# '''
659# return self.toRepr(lenc=True)
661 def __rfloordiv__(self, other):
662 '''Return C{B{other} // B{self}} as an L{Fsum}.
664 @see: Method L{Fsum.__ifloordiv__}.
665 '''
666 f = self._copy_2r(other, self.__rfloordiv__)
667 return f._floordiv(self, _floordiv_op_)
669 def __rmatmul__(self, other): # PYCHOK no cover
670 '''Not implemented.'''
671 return _NotImplemented(self, other)
673 def __rmod__(self, other):
674 '''Return C{B{other} % B{self}} as an L{Fsum}.
676 @see: Method L{Fsum.__imod__}.
677 '''
678 f = self._copy_2r(other, self.__rmod__)
679 return f._fdivmod2(self, _mod_op_).mod
681 def __rmul__(self, other):
682 '''Return C{B{other} * B{self}} as an L{Fsum}.
684 @see: Method L{Fsum.__imul__}.
685 '''
686 f = self._copy_2r(other, self.__rmul__)
687 return f._fmul(self, _mul_op_)
689 def __round__(self, *ndigits): # PYCHOK no cover
690 '''Return C{round(B{self}, *B{ndigits}} as an L{Fsum}.
692 @arg ndigits: Optional number of digits (C{int}).
693 '''
694 # <https://docs.Python.org/3.12/reference/datamodel.html?#object.__round__>
695 return _Psum_(round(float(self), *ndigits), # can be C{int}
696 name=self.__round__.__name__)
698 def __rpow__(self, other, *mod):
699 '''Return C{B{other}**B{self}} as an L{Fsum}.
701 @see: Method L{Fsum.__ipow__}.
702 '''
703 f = self._copy_2r(other, self.__rpow__)
704 return f._fpow(self, _pow_op_, *mod)
706 def __rsub__(self, other):
707 '''Return C{B{other} - B{self}} as L{Fsum}.
709 @see: Method L{Fsum.__isub__}.
710 '''
711 f = self._copy_2r(other, self.__rsub__)
712 return f._fsub(self, _sub_op_)
714 def __rtruediv__(self, other, **raiser):
715 '''Return C{B{other} / B{self}} as an L{Fsum}.
717 @see: Method L{Fsum.__itruediv__}.
718 '''
719 f = self._copy_2r(other, self.__rtruediv__)
720 return f._ftruediv(self, _truediv_op_, **raiser)
722 def __str__(self):
723 '''Return the default C{str(self)}.
724 '''
725 return self.toStr(lenc=True)
727 def __sub__(self, other):
728 '''Return C{B{self} - B{other}} as an L{Fsum}.
730 @arg other: An L{Fsum} or C{scalar}.
732 @return: The difference (L{Fsum}).
734 @see: Method L{Fsum.__isub__}.
735 '''
736 f = self._copy_2(self.__sub__)
737 return f._fsub(other, _sub_op_)
739 def __truediv__(self, other, **raiser):
740 '''Return C{B{self} / B{other}} as an L{Fsum}.
742 @arg other: An L{Fsum} or C{scalar} divisor.
743 @kwarg raiser: Use C{B{raiser}=False} to ignore L{ResidualError}s
744 (C{bool}), see also method L{RESIDUAL}.
746 @return: The quotient (L{Fsum}).
748 @see: Method L{Fsum.__itruediv__}.
749 '''
750 f = self._copy_2(self.__truediv__)
751 return f._ftruediv(other, _truediv_op_, **raiser)
753 __trunc__ = __int__
755 if _sys_version_info2 < (3, 0): # PYCHOK no cover
756 # <https://docs.Python.org/2/library/operator.html#mapping-operators-to-functions>
757 __div__ = __truediv__
758 __idiv__ = __itruediv__
759 __long__ = __int__
760 __nonzero__ = __bool__
761 __rdiv__ = __rtruediv__
763 def as_integer_ratio(self):
764 '''Return this instance as the ratio of 2 integers.
766 @return: 2-Tuple C{(numerator, denominator)} both
767 C{int} and with positive C{denominator}.
769 @see: Standard C{float.as_integer_ratio} in Python 3+.
770 '''
771 n, r = self._fint2
772 if r:
773 i, d = r.as_integer_ratio()
774 n *= d
775 n += i
776 else: # PYCHOK no cover
777 d = 1
778 return n, d
780 @property_RO
781 def as_iscalar(self):
782 '''Get this instance I{as-is} (L{Fsum}) or C{scalar} iff scalar.
783 '''
784 s, r = self._fprs2
785 return self if r else s
787 @property_RO
788 def ceil(self):
789 '''Get this instance' C{ceil} value (C{int} in Python 3+,
790 but C{float} in Python 2-).
792 @note: The C{ceil} takes the C{residual} into account.
794 @see: Method L{Fsum.int_float} and properties L{Fsum.floor},
795 L{Fsum.imag} and L{Fsum.real}.
796 '''
797 s, r = self._fprs2
798 c = _ceil(s) + int(r) - 1
799 while r > (c - s): # (s + r) > c
800 c += 1
801 return c
803 def _cmp_0(self, other, op):
804 '''(INTERNAL) Return C{scalar(self - B{other})} for 0-comparison.
805 '''
806 if isinstance(other, Fsum):
807 s = _fsum(self._ps_1primed(*other._ps))
808 elif self._scalar(other, op):
809 s = _fsum(self._ps_1primed(other))
810 else:
811 s, r = self._fprs2
812 s = _signOf(s, -r)
813 return s
815 def copy(self, deep=False, name=NN):
816 '''Copy this instance, C{shallow} or B{C{deep}}.
818 @return: The copy (L{Fsum}).
819 '''
820 f = _Named.copy(self, deep=deep, name=name)
821 if f._ps is self._ps:
822 f._ps = list(self._ps) # separate list
823 if not deep:
824 f._n = 1
825 return f
827 def _copy_2(self, which, name=NN):
828 '''(INTERNAL) Copy for I{dyadic} operators.
829 '''
830 n = name or which.__name__
831 # NOT .classof due to .Fdot(a, *b) args, etc.
832 f = _Named.copy(self, deep=False, name=n)
833 # assert f._n == self._n
834 f._ps = list(self._ps) # separate list
835 return f
837 def _copy_2r(self, other, which):
838 '''(INTERNAL) Copy for I{reverse-dyadic} operators.
839 '''
840 return other._copy_2(which) if isinstance(other, Fsum) else \
841 Fsum(other, name=which.__name__)
843# def _copy_RESIDUAL(self, other):
844# '''(INTERNAL) Copy C{other._RESIDUAL}.
845# '''
846# R = other._RESIDUAL
847# if R is not Fsum._RESIDUAL:
848# self._RESIDUAL = R
850 def divmod(self, other, **raiser):
851 '''Return C{divmod(B{self}, B{other})} as 2-tuple C{(quotient,
852 remainder)}.
854 @arg other: An L{Fsum} or C{scalar} divisor.
855 @kwarg raiser: Use C{B{raiser}=False} to ignore L{ResidualError}s
856 (C{bool}), see also method L{RESIDUAL}.
858 @return: A L{DivMod2Tuple}C{(div, mod)}, with quotient C{div}
859 an C{int} in Python 3+ or C{float} in Python 2- and
860 remainder C{mod} an L{Fsum} instance.
862 @see: Method L{Fsum.__itruediv__}.
863 '''
864 f = self._copy_2(self.divmod)
865 return f._fdivmod2(other, _divmod_op_, **raiser)
867 def _Error(self, op, other, Error, **txt_cause):
868 '''(INTERNAL) Format an B{C{Error}} for C{{self} B{op} B{other}}.
869 '''
870 return Error(_SPACE_(self.as_iscalar, op, other), **txt_cause)
872 def _ErrorX(self, X, op, other, *mod):
873 '''(INTERNAL) Format the caught exception C{X}.
874 '''
875 E, t = _xError2(X)
876 if mod:
877 t = _COMMASPACE_(Fmt.PARENSPACED(mod=mod[0]), t)
878 return self._Error(op, other, E, txt=t, cause=X)
880 def _ErrorXs(self, X, xs, **kwds): # in .fmath
881 '''(INTERNAL) Format the caught exception C{X}.
882 '''
883 E, t = _xError2(X)
884 n = unstr(self.named3, *xs[:3], _ELLIPSIS=len(xs) > 3, **kwds)
885 return E(n, txt=t, cause=X)
887 def _facc(self, xs, up=True, **origin_X_x):
888 '''(INTERNAL) Accumulate more C{scalars} or L{Fsum}s.
889 '''
890 if xs:
891 _xs = _2floats(xs, **origin_X_x) # PYCHOK yield
892 ps = self._ps
893 ps[:] = self._ps_acc(list(ps), _xs, up=up)
894 return self
896 def _facc_1(self, xs, **up):
897 '''(INTERNAL) Accumulate 0, 1 or more C{scalars} or L{Fsum}s,
898 all positional C{xs} in the caller of this method.
899 '''
900 # assert islistuple(xs)
901 return self._fadd(xs[0], _add_op_) if len(xs) == 1 else \
902 self._facc(xs, origin=1, **up)
904 def _facc_neg(self, xs, up=True, **origin):
905 '''(INTERNAL) Accumulate more C{scalars} or L{Fsum}s, negated.
906 '''
907 if xs:
908 def _neg(x):
909 return -x
911 _x = _2floats(xs, **origin) # PYCHOK yield
912 ps = self._ps
913 ps[:] = self._ps_acc(list(ps), map(_neg, _x), up=up)
914 return self
916 def _facc_power(self, power, xs, which, **raiser): # in .fmath
917 '''(INTERNAL) Add each C{xs} as C{float(x**power)}.
918 '''
919 def _Pow4(p):
920 r = 0
921 if isinstance(p, Fsum):
922 s, r = p._fprs2
923 if r == 0:
924 return _Pow4(s)
925 m = Fsum._pow
926 elif isint(p, both=True) and int(p) >= 0:
927 p = s = int(p)
928 m = Fsum._pow_int
929 else:
930 p = s = _2float(power=p)
931 m = Fsum._pow_scalar
932 return m, p, s, r
934 _Pow, p, s, r = _Pow4(power)
935 if p: # and xs:
936 _pow = Fsum._pow_2_3
937 _Fs = Fsum
938 _Ps = _Psum_ # ()._fset_ps_
939 op = which.__name__
941 def _X(X):
942 f = _Pow(X, p, power, op, **raiser)
943 return f._ps if isinstance(f, _Fs) else (f,)
945 def _x(x):
946 x = float(x)
947 X = _Ps(x)
948 f = _pow(X, x, s, power, op, **raiser)
949 if r:
950 f *= _pow(X, x, r, power, op, **raiser)
951 return f
953 f = self._facc(xs, origin=1, _X=_X, _x=_x)
954 else:
955 f = self._facc_scalar_(float(len(xs))) # x**0 == 1
956 return f
958 def _facc_scalar(self, xs, **up):
959 '''(INTERNAL) Accumulate all C{xs}, known to be scalar.
960 '''
961 if xs:
962 self._ps_acc(self._ps, xs, **up)
963 return self
965 def _facc_scalar_(self, *xs, **up):
966 '''(INTERNAL) Accumulate all positional C{xs}, known to be scalar.
967 '''
968 if xs:
969 self._ps_acc(self._ps, xs, **up)
970 return self
972# def _facc_up(self, up=True):
973# '''(INTERNAL) Update the C{partials}, by removing
974# and re-accumulating the final C{partial}.
975# '''
976# while len(self._ps) > 1:
977# p = self._ps.pop()
978# if p:
979# n = self._n
980# self._facc_scalar_(p, up=False)
981# self._n = n
982# break
983# return self._update() if up else self # ._fpsqz()
985 def fadd(self, xs=()):
986 '''Add an iterable of C{scalar} or L{Fsum} instances
987 to this instance.
989 @arg xs: Iterable, list, tuple, etc. (C{scalar} or
990 L{Fsum} instances).
992 @return: This instance (L{Fsum}).
994 @raise OverflowError: Partial C{2sum} overflow.
996 @raise TypeError: An invalid B{C{xs}} type, not C{scalar}
997 nor L{Fsum}.
999 @raise ValueError: Invalid or non-finite B{C{xs}} value.
1000 '''
1001 if isinstance(xs, Fsum):
1002 self._facc_scalar(xs._ps) # tuple
1003 elif isscalar(xs): # for backward compatibility
1004 self._facc_scalar_(_2float(x=xs)) # PYCHOK no cover
1005 elif xs: # assert isiterable(xs)
1006 self._facc(xs)
1007 return self
1009 def fadd_(self, *xs):
1010 '''Add all positional C{scalar} or L{Fsum} instances
1011 to this instance.
1013 @arg xs: Values to add (C{scalar} or L{Fsum} instances),
1014 all positional.
1016 @return: This instance (L{Fsum}).
1018 @raise OverflowError: Partial C{2sum} overflow.
1020 @raise TypeError: An invalid B{C{xs}} type, not C{scalar}
1021 nor L{Fsum}.
1023 @raise ValueError: Invalid or non-finite B{C{xs}} value.
1024 '''
1025 return self._facc_1(xs)
1027 def _fadd(self, other, op, **up): # in .fmath.Fhorner
1028 '''(INTERNAL) Apply C{B{self} += B{other}}.
1029 '''
1030 if isinstance(other, Fsum):
1031 self._facc_scalar(other._ps, **up) # tuple
1032 elif self._scalar(other, op):
1033 self._facc_scalar_(other, **up)
1034 return self
1036 fcopy = copy # for backward compatibility
1037 fdiv = __itruediv__ # for backward compatibility
1038 fdivmod = __divmod__ # for backward compatibility
1040 def _fdivmod2(self, other, op, **raiser):
1041 '''(INTERNAL) Apply C{B{self} %= B{other}} and return a L{DivMod2Tuple}.
1042 '''
1043 # result mostly follows CPython function U{float_divmod
1044 # <https://GitHub.com/python/cpython/blob/main/Objects/floatobject.c>},
1045 # but at least divmod(-3, 2) equals Cpython's result (-2, 1).
1046 f = self._copy_2(self._fdivmod2)
1047 q = f._ftruediv(other, op, **raiser).floor
1048 if q: # == float // other == floor(float / other)
1049 self -= other * q
1051 s = signOf(other) # make signOf(self) == signOf(other)
1052 if s and self.signOf() == -s: # PYCHOK no cover
1053 self += other
1054 q -= 1
1055# t = self.signOf()
1056# if t and t != s:
1057# raise self._Error(op, other, _AssertionError, txt=signOf.__name__)
1058 return DivMod2Tuple(q, self) # q is C{int} in Python 3+, but C{float} in Python 2-
1060 def _finite(self, other, op=None):
1061 '''(INTERNAL) Return B{C{other}} if C{finite}.
1062 '''
1063 if _isfinite(other):
1064 return other
1065 raise ValueError(_not_finite_) if op is None else \
1066 self._ValueError(op, other, txt=_not_finite_)
1068 def fint(self, raiser=True, name=NN, **RESIDUAL):
1069 '''Return this instance' current running sum as C{integer}.
1071 @kwarg raiser: Use C{B{raiser}=False} to ignore L{ResidualError}s
1072 (C{bool}), see also method L{RESIDUAL}.
1073 @kwarg name: Optional name (C{str}), overriding C{"fint"}.
1074 @kwarg RESIDUAL: Optional threshold, overriding the current
1075 L{RESIDUAL<Fsum.RESIDUAL>} (C{scalar}).
1077 @return: The C{integer} sum (L{Fsum}) if this instance
1078 C{is_integer} and the residual is zero or
1079 insignificant or if C{B{raiser}=False}.
1081 @raise ResidualError: Non-zero I{integer} residual.
1083 @see: Methods L{Fsum.int_float} and L{Fsum.is_integer}.
1084 '''
1085 i, r = self._fint2
1086 if r and raiser and self._raiser2sum(r, i, **RESIDUAL):
1087 t = _stresidual(_integer_, r)
1088 raise ResidualError(_integer_, i, txt=t)
1089 f = self._copy_2(self.fint, name=name)
1090 return f._fset(i)
1092 def fint2(self, **name):
1093 '''Return this instance' current running sum as C{int} and
1094 the I{integer} residual.
1096 @kwarg name: Optional name (C{str}).
1098 @return: An L{Fsum2Tuple}C{(fsum, residual)} with C{fsum}
1099 an C{int} and I{integer} C{residual} a C{float} or
1100 C{INT0} if the C{fsum} is considered to be I{exact}.
1101 '''
1102 return Fsum2Tuple(*self._fint2, **name)
1104 @Property_RO
1105 def _fint2(self): # see ._fset
1106 '''(INTERNAL) Get 2-tuple (C{int}, I{integer} residual).
1107 '''
1108 s, r = self._fprs2
1109 i = int(s)
1110 r = _fsum(self._ps_1primed(i)) if r else float(s - i)
1111 return i, (r or INT0) # Fsum2Tuple?
1113 @deprecated_property_RO
1114 def float_int(self): # PYCHOK no cover
1115 '''DEPRECATED, use method C{Fsum.int_float}.'''
1116 return self.int_float() # raiser=False
1118 @property_RO
1119 def floor(self):
1120 '''Get this instance' C{floor} (C{int} in Python 3+, but
1121 C{float} in Python 2-).
1123 @note: The C{floor} takes the C{residual} into account.
1125 @see: Method L{Fsum.int_float} and properties L{Fsum.ceil},
1126 L{Fsum.imag} and L{Fsum.real}.
1127 '''
1128 s, r = self._fprs2
1129 f = _floor(s) + _floor(r) + 1
1130 while (f - s) > r: # f > (s + r)
1131 f -= 1
1132 return f
1134# floordiv = __floordiv__ # for naming consistency
1136 def _floordiv(self, other, op, **raiser): # rather _ffloordiv?
1137 '''Apply C{B{self} //= B{other}}.
1138 '''
1139 q = self._ftruediv(other, op, **raiser) # == self
1140 return self._fset(q.floor) # floor(q)
1142 fmul = __imul__ # for backward compatibility
1144 def _fmul(self, other, op):
1145 '''(INTERNAL) Apply C{B{self} *= B{other}}.
1146 '''
1147 if isinstance(other, Fsum):
1148 if len(self._ps) != 1:
1149 f = self._mul_Fsum(other, op)
1150 elif len(other._ps) != 1: # and len(self._ps) == 1
1151 f = other._mul_scalar(self._ps[0], op)
1152 else: # len(other._ps) == len(self._ps) == 1
1153 f = self._finite(self._ps[0] * other._ps[0])
1154 else:
1155 s = self._scalar(other, op)
1156 f = self._mul_scalar(s, op)
1157 return self._fset(f) # n=len(self) + 1
1159 def fover(self, over, **raiser):
1160 '''Apply C{B{self} /= B{over}} and summate.
1162 @arg over: An L{Fsum} or C{scalar} denominator.
1163 @kwarg raiser: Use C{B{raiser}=False} to ignore L{ResidualError}s
1164 (C{bool}), see also method L{RESIDUAL}.
1166 @return: Precision running sum (C{float}).
1168 @see: Methods L{Fsum.fsum} and L{Fsum.__itruediv__}.
1169 '''
1170 return float(self.fdiv(over, **raiser)._fprs)
1172 fpow = __ipow__ # for backward compatibility
1174 def _fpow(self, other, op, *mod, **raiser):
1175 '''Apply C{B{self} **= B{other}}, optional B{C{mod}} or C{None}.
1176 '''
1177 if mod:
1178 if mod[0] is not None: # == 3-arg C{pow}
1179 f = self._pow_2_3(self, other, other, op, *mod, **raiser)
1180 elif self.is_integer():
1181 # return an exact C{int} for C{int}**C{int}
1182 i, _ = self._fint2 # assert _ == 0
1183 x = _2scalar(other) # C{int}, C{float} or other
1184 f = self._pow_2_3(i, x, other, op, **raiser) if isscalar(x) else \
1185 _Psum_(i)._pow( x, other, op, **raiser) # x is Fsum
1186 else: # mod[0] is None, power(self, other)
1187 f = self._pow(other, other, op, **raiser)
1188 else: # pow(self, other)
1189 f = self._pow(other, other, op, **raiser)
1190 return self._fset(f, asis=isint(f)) # n=max(len(self), 1)
1192 @Property_RO
1193 def _fprs(self):
1194 '''(INTERNAL) Get and cache this instance' precision
1195 running sum (C{float} or C{int}), ignoring C{residual}.
1197 @note: The precision running C{fsum} after a C{//=} or
1198 C{//} C{floor} division is C{int} in Python 3+.
1199 '''
1200 return self._fprs2.fsum
1202 @Property_RO
1203 def _fprs2(self):
1204 '''(INTERNAL) Get and cache this instance' precision
1205 running sum and residual (L{Fsum2Tuple}).
1206 '''
1207 ps = self._ps
1208 n = len(ps) - 2
1209 if n > 0: # len(ps) > 2
1210 s = _psum(ps)
1211 n = len(ps) - 2
1212 if n > 0:
1213 r = _fsum(self._ps_1primed(s)) or INT0
1214 return Fsum2Tuple(s, r)
1215 if n == 0: # len(ps) == 2
1216 ps[:] = _2ps(*_2sum(*ps))
1217 r, s = (INT0, ps[0]) if len(ps) != 2 else ps
1218 elif ps: # len(ps) == 1
1219 s, r = ps[0], INT0
1220 else: # len(ps) == 0
1221 s, r = _0_0, INT0
1222 ps[:] = s,
1223 # assert self._ps is ps
1224 return Fsum2Tuple(s, r)
1226# def _fpsqz(self):
1227# '''(INTERNAL) Compress, squeeze the C{partials}.
1228# '''
1229# if len(self._ps) > 2:
1230# _ = self._fprs2
1231# return self
1233 def fset_(self, *xs):
1234 '''Replace this instance' value with C{xs}.
1236 @arg xs: Optional, new values (C{scalar} or L{Fsum}
1237 instances), all positional.
1239 @return: This instance (C{Fsum}).
1241 @see: Method L{Fsum.fadd} for further details.
1242 '''
1243 self._ps[:] = 0,
1244 self._n = 0
1245 return self.fadd(xs) if xs else self._update()
1247 def _fset(self, other, asis=True, n=0):
1248 '''(INTERNAL) Overwrite this instance with an other or a C{scalar}.
1249 '''
1250 if other is self:
1251 pass # from ._fmul, ._ftruediv and ._pow_0_1
1252 elif isinstance(other, Fsum):
1253 self._ps[:] = other._ps
1254 self._n = n or other._n
1255# self._copy_RESIDUAL(other)
1256 # use or zap the C{Property_RO} values
1257 Fsum._fint2._update_from(self, other)
1258 Fsum._fprs ._update_from(self, other)
1259 Fsum._fprs2._update_from(self, other)
1260 elif isscalar(other):
1261 s = other if asis else float(other)
1262 i = int(s) # see ._fint2
1263 t = i, ((s - i) or INT0)
1264 self._ps[:] = s,
1265 self._n = n or 1
1266 # Property_ROs _fint2, _fprs and _fprs2 can't be a Property:
1267 # Property's _fset zaps the value just set by the @setter
1268 self.__dict__.update(_fint2=t, _fprs=s, _fprs2=Fsum2Tuple(s, INT0))
1269 else: # PYCHOK no cover
1270 raise self._Error(_fset_op_, other, _AssertionError)
1271 return self
1273 def _fset_ps(self, other, n=0): # in .fmath
1274 '''(INTERNAL) Set partials from a known C{Fsum} or C{scalar}.
1275 '''
1276 if isinstance(other, Fsum):
1277 self._ps[:] = other._ps
1278 self._n = n or other._n
1279 else: # assert isscalar(other)
1280 self._ps[:] = other,
1281 self._n = n or 1
1282 return self
1284# def _fset_ps_(self, *xs):
1285# '''(INTERNAL) Set partials to all known scalar C{xs}.
1286# '''
1287# self._ps[:] = xs
1288# self.n = len(xs)
1289# return self
1291 def fsub(self, xs=()):
1292 '''Subtract an iterable of C{scalar} or L{Fsum} instances from
1293 this instance.
1295 @arg xs: Iterable, list, tuple. etc. (C{scalar} or L{Fsum}
1296 instances).
1298 @return: This instance, updated (L{Fsum}).
1300 @see: Method L{Fsum.fadd}.
1301 '''
1302 return self._facc_neg(xs)
1304 def fsub_(self, *xs):
1305 '''Subtract all positional C{scalar} or L{Fsum} instances from
1306 this instance.
1308 @arg xs: Values to subtract (C{scalar} or L{Fsum} instances),
1309 all positional.
1311 @return: This instance, updated (L{Fsum}).
1313 @see: Method L{Fsum.fadd}.
1314 '''
1315 return self._fsub(xs[0], _sub_op_) if len(xs) == 1 else \
1316 self._facc_neg(xs, origin=1)
1318 def _fsub(self, other, op):
1319 '''(INTERNAL) Apply C{B{self} -= B{other}}.
1320 '''
1321 if isinstance(other, Fsum):
1322 if other is self: # or other._fprs2 == self._fprs2:
1323 self._fset(_0_0) # n=len(self) * 2, self -= self
1324 elif other._ps:
1325 self._facc_scalar(other._ps_neg)
1326 elif self._scalar(other, op):
1327 self._facc_scalar_(-self._finite(other, op))
1328 return self
1330 def fsum(self, xs=()):
1331 '''Add more C{scalar} or L{Fsum} instances and summate.
1333 @kwarg xs: Iterable, list, tuple, etc. (C{scalar} or
1334 L{Fsum} instances).
1336 @return: Precision running sum (C{float} or C{int}).
1338 @see: Method L{Fsum.fadd}.
1340 @note: Accumulation can continue after summation.
1341 '''
1342 return self._facc(xs)._fprs
1344 def fsum_(self, *xs):
1345 '''Add all positional C{scalar} or L{Fsum} instances and summate.
1347 @arg xs: Values to add (C{scalar} or L{Fsum} instances), all
1348 positional.
1350 @return: Precision running sum (C{float} or C{int}).
1352 @see: Methods L{Fsum.fsum}, L{Fsum.Fsum_} and L{Fsum.fsumf_}.
1353 '''
1354 return self._facc_1(xs)._fprs
1356 def Fsum_(self, *xs):
1357 '''Like method L{Fsum.fsum_} but returning an L{Fsum}.
1359 @return: Current, precision running sum (L{Fsum}).
1360 '''
1361 return self._facc_1(xs)._copy_2(self.Fsum_)
1363 def fsum2(self, xs=(), name=NN):
1364 '''Add more C{scalar} or L{Fsum} instances and return the
1365 current precision running sum and the C{residual}.
1367 @kwarg xs: Iterable, list, tuple, etc. (C{scalar} or L{Fsum}
1368 instances).
1369 @kwarg name: Optional name (C{str}).
1371 @return: L{Fsum2Tuple}C{(fsum, residual)} with C{fsum} the
1372 current precision running sum and C{residual}, the
1373 (precision) sum of the remaining C{partials}. The
1374 C{residual is INT0} if the C{fsum} is considered
1375 to be I{exact}.
1377 @see: Methods L{Fsum.fint2}, L{Fsum.fsum} and L{Fsum.fsum2_}
1378 '''
1379 t = self._facc(xs)._fprs2
1380 return t.dup(name=name) if name else t
1382 def fsum2_(self, *xs):
1383 '''Add any positional C{scalar} or L{Fsum} instances and return
1384 the precision running sum and the C{differential}.
1386 @arg xs: Values to add (C{scalar} or L{Fsum} instances), all
1387 positional.
1389 @return: 2Tuple C{(fsum, delta)} with the current, precision
1390 running C{fsum} like method L{Fsum.fsum} and C{delta},
1391 the difference with previous running C{fsum}, C{float}.
1393 @see: Methods L{Fsum.fsum_} and L{Fsum.fsum}.
1394 '''
1395 return self._fsum2(xs, self._facc_1)
1397 def _fsum2(self, xs, _f, **origin):
1398 '''(INTERNAL) Helper for L{Fsum.fsum2_} and L{Fsum.fsum2f_}.
1399 '''
1400 p, q = self._fprs2
1401 if xs:
1402 s, r = _f(xs, **origin)._fprs2
1403 return s, _2delta(s - p, r - q) # _fsum(_1primed((s, -p, r, -q))
1404 else:
1405 return p, _0_0
1407 def fsumf_(self, *xs):
1408 '''Like method L{Fsum.fsum_} but only for C{B{xs}}, I{known to be scalar}.
1409 '''
1410 return self._facc_scalar(xs)._fprs
1412 def Fsumf_(self, *xs):
1413 '''Like method L{Fsum.Fsum_} but only for C{B{xs}}, I{known to be scalar}.
1414 '''
1415 return self._facc_scalar(xs)._copy_2(self.Fsumf_)
1417 def fsum2f_(self, *xs):
1418 '''Like method L{Fsum.fsum2_} but only for C{B{xs}}, I{known to be scalar}.
1419 '''
1420 return self._fsum2(xs, self._facc_scalar, origin=1)
1422# ftruediv = __itruediv__ # for naming consistency?
1424 def _ftruediv(self, other, op, **raiser):
1425 '''(INTERNAL) Apply C{B{self} /= B{other}}.
1426 '''
1427 n = _1_0
1428 if isinstance(other, Fsum):
1429 if other is self or other == self:
1430 return self._fset(n) # n=len(self)
1431 d, r = other._fprs2
1432 if r:
1433 if d:
1434 if self._raiser(r, d, **raiser):
1435 raise self._ResidualError(op, other, r)
1436 d, n = other.as_integer_ratio()
1437 else: # PYCHOK no cover
1438 d = r
1439 else:
1440 d = self._scalar(other, op)
1441 try:
1442 s = n / d
1443 except Exception as X:
1444 raise self._ErrorX(X, op, other)
1445 f = self._mul_scalar(s, _mul_op_) # handles 0, INF, NAN
1446 return self._fset(f) # asis=False
1448 @property_RO
1449 def imag(self):
1450 '''Get the C{imaginary} part of this instance (C{0.0}, always).
1452 @see: Properties L{Fsum.ceil}, L{Fsum.floor} and L{Fsum.real}.
1453 '''
1454 return _0_0
1456 def int_float(self, raiser=False, **RESIDUAL):
1457 '''Return this instance' current running sum as C{int} or C{float}.
1459 @kwarg raiser: If C{True} throw a L{ResidualError} if the
1460 residual exceeds the C{RESIDUAL} (C{bool}).
1461 @kwarg RESIDUAL: Optional threshold, overriding the current
1462 L{RESIDUAL<Fsum.RESIDUAL>} (C{scalar}).
1464 @return: This C{integer} sum if this instance C{is_integer},
1465 otherwise return the C{float} sum if the residual is
1466 zero or insignificant or if C{B{raiser}=False}.
1468 @raise ResidualError: Non-zero residual and C{B{raiser}=True}.
1470 @see: Methods L{Fsum.fint} and L{Fsum.fint2} and property L{Fsum.as_iscalar}.
1471 '''
1472 s, r = self._fint2
1473 if r:
1474 s, r = self._fprs2
1475 if r and raiser and self._raiser2sum(r, s, **RESIDUAL): # PYCHOK no cover
1476 t = _stresidual(_non_zero_, r)
1477 raise ResidualError(int_float=s, txt=t)
1478 s = float(s) # redundant
1479 return s
1481 def is_exact(self):
1482 '''Is this instance' running C{fsum} considered to be exact? (C{bool}).
1483 '''
1484 return self.residual is INT0
1486 def is_integer(self):
1487 '''Is this instance' running sum C{integer}? (C{bool}).
1489 @see: Methods L{Fsum.fint}, L{Fsum.fint2} and L{Fsum.is_scalar}.
1490 '''
1491 _, r = self._fint2
1492 return False if r else True
1494 def is_math_fsum(self):
1495 '''Return whether functions L{fsum}, L{fsum_}, L{fsum1} and
1496 L{fsum1_} plus partials summation are based on Python's
1497 C{math.fsum} or not.
1499 @return: C{2} if all functions and partials summation
1500 are based on C{math.fsum}, C{True} if only
1501 the functions are based on C{math.fsum} (and
1502 partials summation is not) or C{False} if
1503 none are.
1504 '''
1505 f = Fsum._math_fsum
1506 return 2 if _psum is f else bool(f)
1508 def is_scalar(self):
1509 '''Is this instance' running sum C{scalar}? (C{bool}).
1511 @see: Method L{Fsum.is_integer} and property L{Fsum.as_iscalar}.
1512 '''
1513 s, r = t = self._fprs2
1514 return False if r and _2sum(s, r) != t else True
1516 def _mul_Fsum(self, other, op=_mul_op_): # in .fmath.Fhorner
1517 '''(INTERNAL) Return C{B{self} * Fsum B{other}} as L{Fsum} or C{0}.
1518 '''
1519 # assert isinstance(other, Fsum)
1520 if self._ps and other._ps:
1521 f = self._ps_mul(op, *other._ps) # NO .as_iscalar
1522 else:
1523 f = _0_0
1524 return f
1526 def _mul_scalar(self, factor, op): # in .fmath.Fhorner
1527 '''(INTERNAL) Return C{B{self} * scalar B{factor}} as L{Fsum}, C{0} or C{self}.
1528 '''
1529 # assert isscalar(factor)
1530 if self._ps and self._finite(factor, op):
1531 f = self if factor == _1_0 else (
1532 self._neg if factor == _N_1_0 else
1533 self._ps_mul(op, factor).as_iscalar)
1534 else:
1535 f = _0_0
1536 return f
1538 @property_RO
1539 def _neg(self):
1540 '''(INTERNAL) Return C{Fsum(-self)} or scalar C{NEG0}.
1541 '''
1542 return _Psum(self._ps_neg) if self._ps else NEG0
1544 @property_RO
1545 def partials(self):
1546 '''Get this instance' current, partial sums (C{tuple} of C{float}s).
1547 '''
1548 return tuple(self._ps)
1550 def pow(self, x, *mod, **raiser):
1551 '''Return C{B{self}**B{x}} as L{Fsum}.
1553 @arg x: The exponent (L{Fsum} or C{scalar}).
1554 @arg mod: Optional modulus (C{int} or C{None}) for the 3-argument
1555 C{pow(B{self}, B{other}, B{mod})} version.
1556 @kwarg raiser: Use C{B{raiser}=False} to ignore L{ResidualError}s
1557 (C{bool}), see also method L{RESIDUAL}.
1559 @return: The C{pow(self, B{x})} or C{pow(self, B{x}, *B{mod})}
1560 result (L{Fsum}).
1562 @note: If B{C{mod}} is given as C{None}, the result will be an
1563 C{integer} L{Fsum} provided this instance C{is_integer}
1564 or set to C{integer} by an L{Fsum.fint} call.
1566 @see: Methods L{Fsum.__ipow__}, L{Fsum.fint}, L{Fsum.is_integer}
1567 and L{Fsum.root}.
1568 '''
1569 f = self._copy_2(self.pow)
1570 return f._fpow(x, _pow_op_, *mod, **raiser) # f = pow(f, x, *mod)
1572 def _pow(self, other, unused, op, **raiser):
1573 '''Return C{B{self} ** B{other}}.
1574 '''
1575 if isinstance(other, Fsum):
1576 x, r = other._fprs2
1577 if r and self._raiser(r, x, **raiser):
1578 raise self._ResidualError(op, other, r)
1579 f = self._pow_scalar(x, other, op, **raiser)
1580 if r:
1581 f *= self._pow_scalar(r, other, op, **raiser)
1582 elif self._scalar(other, op):
1583 x = self._finite(other, op)
1584 f = self._pow_scalar(x, other, op, **raiser)
1585 else:
1586 f = self._pow_0_1(0, other)
1587 return f
1589 def _pow_0_1(self, x, other):
1590 '''(INTERNAL) Return B{C{self}**1} or C{B{self}**0 == 1.0}.
1591 '''
1592 return self if x else (1 if isint(other) and self.is_integer() else _1_0)
1594 def _pow_2_3(self, b, x, other, op, *mod, **raiser):
1595 '''(INTERNAL) 2-arg C{pow(B{b}, scalar B{x})} and 3-arg C{pow(B{b},
1596 B{x}, int B{mod} or C{None})}, embellishing errors.
1597 '''
1598 try:
1599 if mod: # b, x, mod all C{int}, unless C{mod} is C{None}
1600 m = mod[0]
1601 b, r = b._fprs2 if m is None else b._fint2
1602 if r and self._raiser(r, b, **raiser):
1603 t = _non_zero_ if m is None else _integer_
1604 raise ResidualError(_stresidual(t, r, mod=m), txt=None)
1605 x = _2scalar(x, _raiser=self._raiser, mod=m)
1606 # 0**INF == 0.0, 1**INF == 1.0, -1**2.3 == -(1**2.3)
1607 s = pow(b, x, *mod)
1608 if iscomplex(s):
1609 # neg**frac == complex in Python 3+, but ValueError in 2-
1610 raise ValueError(_strcomplex(s, b, x, *mod))
1611 return self._finite(s)
1612 except Exception as X:
1613 raise self._ErrorX(X, op, other, *mod)
1615 def _pow_int(self, x, other, op, **raiser):
1616 '''(INTERNAL) Return C{B{self} **= B{x}} for C{int B{x} >= 0}.
1617 '''
1618 # assert isint(x) and x >= 0
1619 ps = self._ps
1620 if len(ps) > 1:
1621 _mul_Fsum = Fsum._mul_Fsum
1622 if x > 4:
1623 p = self
1624 f = self if (x & 1) else _Psum_(_1_0)
1625 m = x >> 1 # // 2
1626 while m:
1627 p = _mul_Fsum(p, p, op) # p **= 2
1628 if (m & 1):
1629 f = _mul_Fsum(f, p, op) # f *= p
1630 m >>= 1 # //= 2
1631 elif x > 1: # self**2, 3 or 4
1632 f = _mul_Fsum(self, self, op)
1633 if x > 2: # self**3 or 4
1634 p = self if x < 4 else f
1635 f = _mul_Fsum(f, p, op).as_iscalar
1636 else: # self**1 or self**0 == 1 or _1_0
1637 f = self._pow_0_1(x, other)
1638 elif ps: # self._ps[0]**x
1639 f = self._pow_2_3(ps[0], x, other, op, **raiser)
1640 else: # PYCHOK no cover
1641 # 0**pos_int == 0, but 0**0 == 1
1642 f = 0 if x else 1
1643 return f
1645 def _pow_scalar(self, x, other, op, **raiser):
1646 '''(INTERNAL) Return C{self**B{x}} for C{scalar B{x}}.
1647 '''
1648 s, r = self._fprs2
1649 if isint(x, both=True):
1650 x = int(x) # Fsum**int
1651 y = abs(x)
1652 if y > 1:
1653 if r:
1654 f = self._pow_int(y, other, op, **raiser)
1655 if x > 0: # > 1
1656 return f
1657 # assert x < 0 # < -1
1658 s, r = f._fprs2 if isinstance(f, Fsum) else (f, 0)
1659 if r:
1660 return _1_over(f, op, **raiser) # PYCHOK 2 args
1661 # use **= -1 for the CPython float_pow
1662 # error if s is zero, and not s = 1 / s
1663 x = -1
1664 elif x < 0: # == -1: self**(-1) == 1 / self
1665 if r:
1666 return _1_over(self, op, **raiser) # PYCHOK 2 args
1667 else: # self**1 or self**0
1668 return self._pow_0_1(x, other) # self, 1 or 1.0
1669 elif r: # non-zero residual**fractional
1670 if s:
1671 n, d = self.as_integer_ratio()
1672 if abs(n) > abs(d):
1673 n, d, x = d, n, (-x)
1674 s = n / d
1675 else:
1676 s = r
1677 # assert isscalar(s) and isscalar(x)
1678 return self._pow_2_3(s, x, other, op, **raiser)
1680 def _ps_acc(self, ps, xs, up=True, **unused):
1681 '''(INTERNAL) Accumulate all scalar C{xs} into C{ps}.
1682 '''
1683 n = 0
1684 _2s = _2sum
1685 for x in (tuple(xs) if xs is ps else xs):
1686 # assert isscalar(x) and _isfinite(x)
1687 if x:
1688 i = 0
1689 for p in ps:
1690 x, p = _2s(x, p)
1691 if p:
1692 ps[i] = p
1693 i += 1
1694 ps[i:] = (x,) if x else ()
1695 n += 1
1696 if n:
1697 self._n += n
1698 # Fsum._ps_max = max(Fsum._ps_max, len(ps))
1699 if up:
1700 self._update()
1701 return ps
1703 def _ps_mul(self, op, *factors):
1704 '''(INTERNAL) Multiply this instance' C{partials} with
1705 each of the scalar B{C{factors}} and accumulate.
1706 '''
1707 def _pfs(ps, fs):
1708 if len(ps) < len(fs):
1709 ps, fs = fs, ps
1710 _fin = _isfinite
1711 for f in fs:
1712 for p in ps:
1713 p *= f
1714 yield p if _fin(p) else self._finite(p, op)
1716 return _Psum(self._ps_acc([], _pfs(self._ps, factors)))
1718 @property_RO
1719 def _ps_neg(self):
1720 '''(INTERNAL) Yield the partials, I{negated}.
1721 '''
1722 for p in self._ps:
1723 yield -p
1725 def _ps_1primed(self, *less):
1726 '''(INTERNAL) Yield partials, 1-primed and subtract any C{less} scalars.
1727 '''
1728 yield _1_0
1729 for p in self._ps:
1730 yield p
1731 for p in less:
1732 yield -p
1733 yield _N_1_0
1735 def _raiser(self, r, s, raiser=True, **RESIDUAL):
1736 '''(INTERNAL) Does ratio C{r / s} exceed the RESIDUAL threshold?
1737 '''
1738 self._ratio = r = (r / s) if s else s # == 0.
1739 if r and raiser:
1740 R = self._RESIDUAL
1741 if RESIDUAL:
1742 R = _xkwds_get(RESIDUAL, RESIDUAL=R)
1743 return fabs(r) > R
1744 return False
1746 def _raiser2sum(self, r, s, **raiser_RESIDUAL):
1747 '''(INTERNAL) Does ratio C{r / s} exceed the RESIDUAL threshold
1748 I{and} is the residual B{C{r}} significant vs sum B{C{s}}?
1749 '''
1750 return self._raiser(r, s, **raiser_RESIDUAL) and _2sum(s, r) != (s, r)
1752 @property_RO
1753 def real(self):
1754 '''Get the C{real} part of this instance (C{float}).
1756 @see: Methods L{Fsum.__float__} and L{Fsum.fsum}
1757 and properties L{Fsum.ceil}, L{Fsum.floor},
1758 L{Fsum.imag} and L{Fsum.residual}.
1759 '''
1760 return float(self._fprs)
1762 @property_RO
1763 def residual(self):
1764 '''Get this instance' residual (C{float} or C{int}), the
1765 C{sum(partials)} less the precision running sum C{fsum}.
1767 @note: If the C{residual is INT0}, the precision running
1768 C{fsum} is considered to be I{exact}.
1770 @see: Methods L{Fsum.fsum}, L{Fsum.fsum2} and L{Fsum.is_exact}.
1771 '''
1772 return self._fprs2.residual
1774 def RESIDUAL(self, *threshold):
1775 '''Get and set this instance' I{ratio} for raising L{ResidualError}s,
1776 overriding the default from env variable C{PYGEODESY_FSUM_RESIDUAL}.
1778 @arg threshold: If C{scalar}, the I{ratio} to exceed for raising
1779 L{ResidualError}s in division and exponention, if
1780 C{None} restore the default set with env variable
1781 C{PYGEODESY_FSUM_RESIDUAL} or if omitted, keep the
1782 current setting.
1784 @return: The previous C{RESIDUAL} setting (C{float}), default C{0.0}.
1786 @raise ValueError: Negative B{C{threshold}}.
1788 @note: L{ResidualError}s will be thrown if the non-zero I{ratio}
1789 C{residual / fsum} exceeds the B{C{threshold}}.
1790 '''
1791 r = self._RESIDUAL
1792 if threshold:
1793 t = threshold[0]
1794 t = Fsum._RESIDUAL if t is None else (
1795 float(t) if isscalar(t) else ( # for backward ...
1796 _0_0 if bool(t) else _1_0)) # ... compatibility
1797 if t < 0:
1798 u = _DOT_(self, unstr(self.RESIDUAL, *threshold))
1799 raise _ValueError(u, RESIDUAL=t, txt=_negative_)
1800 self._RESIDUAL = t
1801 return r
1803 def _ResidualError(self, op, other, residual):
1804 '''(INTERNAL) Non-zero B{C{residual}} etc.
1805 '''
1806 t = _stresidual(_non_zero_, residual, ratio=self._ratio,
1807 RESIDUAL=self._RESIDUAL)
1808 t = t.replace(_COMMASPACE_R_, _exceeds_R_)
1809 return self._Error(op, other, ResidualError, txt=t)
1811 def root(self, root, **raiser):
1812 '''Return C{B{self}**(1 / B{root})} as L{Fsum}.
1814 @arg root: The order (C{scalar} or C{Fsum}), non-zero.
1815 @kwarg raiser: Use C{B{raiser}=False} to ignore L{ResidualError}s
1816 (C{bool}), see also method L{RESIDUAL}.
1818 @return: The C{self ** (1 / B{root})} result (L{Fsum}).
1820 @see: Method L{Fsum.pow}.
1821 '''
1822 x = _1_over(root, **raiser)
1823 f = self._copy_2(self.root)
1824 return f._fpow(x, f.name, **raiser) # == pow(f, x)
1826 def _scalar(self, other, op, **txt):
1827 '''(INTERNAL) Return scalar C{other}.
1828 '''
1829 if isscalar(other):
1830 return other
1831 raise self._TypeError(op, other, **txt) # _invalid_
1833 def signOf(self, res=True):
1834 '''Determine the sign of this instance.
1836 @kwarg res: If C{True} consider, otherwise
1837 ignore the residual (C{bool}).
1839 @return: The sign (C{int}, -1, 0 or +1).
1840 '''
1841 s, r = self._fprs2
1842 return _signOf(s, (-r) if res else 0)
1844 def toRepr(self, **prec_sep_fmt_lenc): # PYCHOK signature
1845 '''Return this C{Fsum} instance as representation.
1847 @kwarg prec_sep_fmt_lenc: Optional keyword arguments for
1848 method L{Fsum2Tuple.toRepr} plus C{B{lenc}=True}
1849 (C{bool}) to in-/exclude the current C{[len]}
1850 of this L{Fsum} enclosed in I{[brackets]}.
1852 @return: This instance (C{repr}).
1853 '''
1854 return self._toT(self._fprs2.toRepr, **prec_sep_fmt_lenc)
1856 def toStr(self, **prec_sep_fmt_lenc): # PYCHOK signature
1857 '''Return this C{Fsum} instance as string.
1859 @kwarg prec_sep_fmt_lenc: Optional keyword arguments for
1860 method L{Fsum2Tuple.toStr} plus C{B{lenc}=True}
1861 (C{bool}) to in-/exclude the current C{[len]}
1862 of this L{Fsum} enclosed in I{[brackets]}.
1864 @return: This instance (C{str}).
1865 '''
1866 return self._toT(self._fprs2.toStr, **prec_sep_fmt_lenc)
1868 def _toT(self, toT, fmt=Fmt.g, lenc=True, **kwds):
1869 '''(INTERNAL) Helper for C{toRepr} and C{toStr}.
1870 '''
1871 n = self.named3
1872 if lenc:
1873 n = Fmt.SQUARE(n, len(self))
1874 return _SPACE_(n, toT(fmt=fmt, **kwds))
1876 def _TypeError(self, op, other, **txt): # PYCHOK no cover
1877 '''(INTERNAL) Return a C{TypeError}.
1878 '''
1879 return self._Error(op, other, _TypeError, **txt)
1881 def _update(self, updated=True): # see ._fset
1882 '''(INTERNAL) Zap all cached C{Property_RO} values.
1883 '''
1884 if updated:
1885 _pop = self.__dict__.pop
1886 for p in _ROs:
1887 _ = _pop(p, None)
1888# Fsum._fint2._update(self)
1889# Fsum._fprs ._update(self)
1890# Fsum._fprs2._update(self)
1891 return self # for .fset_
1893 def _ValueError(self, op, other, **txt): # PYCHOK no cover
1894 '''(INTERNAL) Return a C{ValueError}.
1895 '''
1896 return self._Error(op, other, _ValueError, **txt)
1898 def _ZeroDivisionError(self, op, other, **txt): # PYCHOK no cover
1899 '''(INTERNAL) Return a C{ZeroDivisionError}.
1900 '''
1901 return self._Error(op, other, _ZeroDivisionError, **txt)
1903_ROs = _allPropertiesOf_n(3, Fsum, Property_RO) # PYCHOK assert, see Fsum._fset, -._update
1906def _Float_Int(arg, **name_Error):
1907 '''(INTERNAL) Unit of L{Fsum2Tuple} items.
1908 '''
1909 U = Int if isint(arg) else Float
1910 return U(arg, **name_Error)
1913class DivMod2Tuple(_NamedTuple):
1914 '''2-Tuple C{(div, mod)} with the quotient C{div} and remainder
1915 C{mod} results of a C{divmod} operation.
1917 @note: Quotient C{div} an C{int} in Python 3+ or a C{float} in
1918 Python 2-. Remainder C{mod} an L{Fsum} instance.
1919 '''
1920 _Names_ = (_div_, _mod_)
1921 _Units_ = (_Float_Int, Fsum)
1924class Fsum2Tuple(_NamedTuple):
1925 '''2-Tuple C{(fsum, residual)} with the precision running C{fsum}
1926 and the C{residual}, the sum of the remaining partials. Each
1927 item is either C{float} or C{int}.
1929 @note: If the C{residual is INT0}, the C{fsum} is considered
1930 to be I{exact}, see method L{Fsum2Tuple.is_exact}.
1931 '''
1932 _Names_ = ( Fsum.fsum.__name__, Fsum.residual.name)
1933 _Units_ = (_Float_Int, _Float_Int)
1935 @Property_RO
1936 def _Fsum(self):
1937 '''(INTERNAL) Get this L{Fsum2Tuple} as an L{Fsum}.
1938 '''
1939 s, r = map(float, self)
1940 return _Psum(_2ps(s, r), name=self.name)
1942 def is_exact(self):
1943 '''Is this L{Fsum2Tuple} considered to be exact? (C{bool}).
1944 '''
1945 return self._Fsum.is_exact()
1947 def is_integer(self):
1948 '''Is this L{Fsum2Tuple} C{integer}? (C{bool}).
1949 '''
1950 return self._Fsum.is_integer()
1953class ResidualError(_ValueError):
1954 '''Error raised for an operation involving a L{pygeodesy.sums.Fsum}
1955 instance with a non-zero C{residual}, I{integer} or otherwise.
1957 @see: Module L{pygeodesy.fsums} and method L{Fsum.RESIDUAL}.
1958 '''
1959 pass
1962try:
1963 from math import fsum as _fsum # precision IEEE-754 sum, Python 2.6+
1965 # make sure _fsum works as expected (XXX check
1966 # float.__getformat__('float')[:4] == 'IEEE'?)
1967 if _fsum((1, 1e101, 1, -1e101)) != 2: # PYCHOK no cover
1968 del _fsum # nope, remove _fsum ...
1969 raise ImportError # ... use _fsum below
1971 Fsum._math_fsum = _sum = _fsum # PYCHOK exported
1973 if _getenv('PYGEODESY_FSUM_PARTIALS', NN) == _fsum.__name__:
1974 _psum = _fsum # PYCHOK re-def
1976except ImportError:
1977 _sum = sum # Fsum(NAN) exception fall-back, in .elliptic
1979 def _fsum(xs):
1980 '''(INTERNAL) Precision summation, Python 2.5-.
1981 '''
1982 f = Fsum()
1983 f.name = _fsum.__name__
1984 return f.fsum(xs)
1987def fsum(xs, floats=False):
1988 '''Precision floating point summation based on or like Python's C{math.fsum}.
1990 @arg xs: Iterable, list, tuple, etc. of values (C{scalar} or L{Fsum}
1991 instances).
1992 @kwarg floats: Use C{B{floats}=True} iff I{all} B{C{xs}} are known
1993 to be C{float} scalars (C{bool}).
1995 @return: Precision C{fsum} (C{float}).
1997 @raise OverflowError: Partial C{2sum} overflow.
1999 @raise TypeError: Non-scalar B{C{xs}} value.
2001 @raise ValueError: Invalid or non-finite B{C{xs}} value.
2003 @note: Exception and I{non-finite} handling may differ if not based
2004 on Python's C{math.fsum}.
2006 @see: Class L{Fsum} and methods L{Fsum.fsum} and L{Fsum.fadd}.
2007 '''
2008 return _fsum(xs if floats else _2floats(xs)) if xs else _0_0 # PYCHOK yield
2011def fsum_(*xs, **floats):
2012 '''Precision floating point summation of all positional arguments.
2014 @arg xs: Values to be added (C{scalar} or L{Fsum} instances), all
2015 positional.
2016 @kwarg floats: Use C{B{floats}=True} iff I{all} B{C{xs}} are I{known
2017 to be scalar} (C{bool}).
2019 @return: Precision C{fsum} (C{float}).
2021 @see: Function C{fsum}.
2022 '''
2023 return _fsum(xs if _xkwds_get(floats, floats=False) else
2024 _2floats(xs, origin=1)) if xs else _0_0 # PYCHOK yield
2027def fsumf_(*xs):
2028 '''Precision floating point summation, L{fsum_}C{(*B{xs}, floats=True)},
2029 but only for C{B{xs}} I{known to be scalar}.
2030 '''
2031 return _fsum(xs) if xs else _0_0
2034def fsum1(xs, floats=False):
2035 '''Precision floating point summation, 1-primed.
2037 @arg xs: Iterable, list, tuple, etc. of values (C{scalar} or L{Fsum}
2038 instances).
2039 @kwarg floats: Use C{B{floats}=True} iff I{all} B{C{xs}} are known
2040 to be C{float}.
2042 @return: Precision C{fsum} (C{float}).
2044 @see: Function C{fsum}.
2045 '''
2046 return _fsum(_1primed(xs if floats else _2floats(xs))) if xs else _0_0 # PYCHOK yield
2049def fsum1_(*xs, **floats):
2050 '''Precision floating point summation, 1-primed.
2052 @arg xs: Values to be added (C{scalar} or L{Fsum} instances), all
2053 positional.
2054 @kwarg floats: Use C{B{floats}=True} iff I{all} B{C{xs}} are I{known
2055 to be scalar} (C{bool}).
2057 @return: Precision C{fsum} (C{float}).
2059 @see: Function C{fsum}
2060 '''
2061 return _fsum(_1primed(xs if _xkwds_get(floats, floats=False) else
2062 _2floats(xs, origin=1))) if xs else _0_0 # PYCHOK yield
2065def fsum1f_(*xs):
2066 '''Precision floating point summation, L{fsum1_}C{(*B{xs}, floats=True)},
2067 but only for C{B{xs}} I{known to be scalar}.
2068 '''
2069 return _fsum(_1primed(xs)) if xs else _0_0
2072if __name__ == '__main__':
2074 # usage: [env PYGEODESY_FSUM_PARTIALS=fsum] python3 -m pygeodesy.fsums
2076 def _test(n):
2077 # copied from Hettinger, see L{Fsum} reference
2078 from pygeodesy import frandoms, printf
2080 printf(_fsum.__name__, end=_COMMASPACE_)
2081 printf(_psum.__name__, end=_COMMASPACE_)
2083 F = Fsum()
2084 if F.is_math_fsum():
2085 for t in frandoms(n, seeded=True):
2086 assert float(F.fset_(*t)) == _fsum(t)
2087 printf(_DOT_, end=NN)
2088 printf(NN)
2090 _test(128)
2092# **) MIT License
2093#
2094# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.
2095#
2096# Permission is hereby granted, free of charge, to any person obtaining a
2097# copy of this software and associated documentation files (the "Software"),
2098# to deal in the Software without restriction, including without limitation
2099# the rights to use, copy, modify, merge, publish, distribute, sublicense,
2100# and/or sell copies of the Software, and to permit persons to whom the
2101# Software is furnished to do so, subject to the following conditions:
2102#
2103# The above copyright notice and this permission notice shall be included
2104# in all copies or substantial portions of the Software.
2105#
2106# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
2107# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
2108# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
2109# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
2110# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
2111# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
2112# OTHER DEALINGS IN THE SOFTWARE.