Coverage for pygeodesy/fsums.py: 97%
872 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, \
27 _signOf, itemsorted, signOf, _xiterable, \
28 _enquote
29from pygeodesy.constants import INT0, _isfinite, NEG0, _pos_self, \
30 _0_0, _1_0, _N_1_0, Float, Int
31from pygeodesy.errors import _OverflowError, _TypeError, _ValueError, \
32 _xError, _xError2, _xkwds_get
33# from pygeodesy.internals import _enquote # from .basics
34from pygeodesy.interns import NN, _arg_, _COMMASPACE_, _DASH_, _DOT_, \
35 _EQUAL_, _from_, _LANGLE_, _NOTEQUAL_, \
36 _not_finite_, _PERCENT_, _PLUS_, \
37 _RANGLE_, _SLASH_, _SPACE_, _STAR_, _UNDER_
38from pygeodesy.lazily import _ALL_LAZY, _getenv, _sys_version_info2
39from pygeodesy.named import _Named, _NamedTuple, _NotImplemented
40from pygeodesy.props import _allPropertiesOf_n, deprecated_property_RO, \
41 Property_RO, property_RO
42from pygeodesy.streprs import Fmt, fstr, unstr
43# from pygeodesy.units import Float, Int # from .constants
45from math import ceil as _ceil, fabs, floor as _floor # PYCHOK used! .ltp
47__all__ = _ALL_LAZY.fsums
48__version__ = '24.05.13'
50_add_op_ = _PLUS_ # in .auxilats.auxAngle
51_eq_op_ = _EQUAL_ * 2 # _DEQUAL_
52_div_ = 'div'
53_floordiv_op_ = _SLASH_ * 2 # _DSLASH_
54_fset_op_ = _EQUAL_
55_ge_op_ = _RANGLE_ + _EQUAL_
56_gt_op_ = _RANGLE_
57_iadd_op_ = _add_op_ + _EQUAL_ # in .auxilats.auxAngle, .fstats
58_integer_ = 'integer'
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): # in .fstats
86 '''(INTERNAL) Throw a C{not-finite} exception.
87 '''
88 raise ValueError(_not_finite_)
91def _2finite(x):
92 '''(INTERNAL) return C{float(x)} if finite.
93 '''
94 x = float(x)
95 return x if _isfinite(x) else _2error(x)
98def _2float(index=None, **name_value): # in .fmath, .fstats
99 '''(INTERNAL) Raise C{TypeError} or C{ValueError} if not scalar or infinite.
100 '''
101 n, v = name_value.popitem() # _xkwds_item2(name_value)
102 try:
103 return _2finite(v)
104 except Exception as X:
105 raise _xError(X, Fmt.INDEX(n, index), v)
108def _X_ps(X): # for _2floats only
109 return X._ps
112def _2floats(xs, origin=0, _X=_X_ps, _x=float):
113 '''(INTERNAL) Yield each B{C{xs}} as a C{float}.
114 '''
115 try:
116 i, x = origin, _X
117 _fin = _isfinite
118 _FsT = _Fsum_Fsum2Tuple_types
119 _isa = isinstance
120 for x in _xiterable(xs):
121 if _isa(x, _FsT):
122 for p in _X(x._Fsum):
123 yield p
124 else:
125 f = _x(x)
126 yield f if _fin(f) else _2error(f)
127 i += 1
128 except Exception as X:
129 raise _xError(X, xs=xs) if x is _X else \
130 _xError(X, Fmt.INDEX(xs=i), x)
133def _Fsumf_(*xs): # floats=True, in .auxLat, ...
134 '''(INTERNAL) An C{Fsum} of I{known scalars}.
135 '''
136 return Fsum()._facc_scalar(xs, up=False)
139def _Fsum1f_(*xs): # floats=True, in .albers, ...
140 '''(INTERNAL) An C{Fsum} of I{known scalars}, 1-primed.
141 '''
142 return Fsum()._facc_scalar(_1primed(xs), up=False)
145def _2halfeven(s, r, p):
146 '''(INTERNAL) Round half-even.
147 '''
148 if (p > 0 and r > 0) or \
149 (p < 0 and r < 0): # signs match
150 r *= 2
151 t = s + r
152 if r == (t - s):
153 s = t
154 return s
157def _isFsum(x): # in .fmath
158 '''(INTERNAL) Is C{x} an C{Fsum} instance?
159 '''
160 return isinstance(x, Fsum)
163def _isFsumTuple(x): # in .fmath
164 '''(INTERNAL) Is C{x} an C{Fsum} or C{Fsum2Tuple} instance?
165 '''
166 return isinstance(x, _Fsum_Fsum2Tuple_types)
169def _1_Over(x, op, **raiser_RESIDUAL): # vs _1_over
170 '''(INTERNAL) Return C{Fsum(1) / B{x}}.
171 '''
172 return _Psum_(_1_0)._ftruediv(x, op, **raiser_RESIDUAL)
175def _1primed(xs): # in .fmath
176 '''(INTERNAL) 1-Primed summation of iterable C{xs}
177 items, all I{known} to be C{scalar}.
178 '''
179 yield _1_0
180 for x in xs:
181 yield x
182 yield _N_1_0
185def _psum(ps): # PYCHOK used!
186 '''(INTERNAL) Partials summation, updating C{ps}.
187 '''
188 # assert isinstance(ps, list)
189 i = len(ps) - 1
190 s = _0_0 if i < 0 else ps[i]
191 _2s = _2sum
192 while i > 0:
193 i -= 1
194 s, r = _2s(s, ps[i])
195 if r: # sum(ps) became inexact
196 if s:
197 ps[i:] = r, s
198 if i > 0:
199 s = _2halfeven(s, r, ps[i-1])
200 break # return s
201 s = r # PYCHOK no cover
202 ps[i:] = s,
203 return s
206def _Psum(ps, **name_RESIDUAL):
207 '''(INTERNAL) Return an C{Fsum} from I{ordered} partials C{ps}.
208 '''
209 f = Fsum(**name_RESIDUAL) if name_RESIDUAL else Fsum()
210 if ps:
211 f._ps[:] = ps
212 f._n = len(f._ps)
213 return f
216def _Psum_(*ps, **name_RESIDUAL):
217 '''(INTERNAL) Return an C{Fsum} from 1 or 2 known scalar(s) C{ps}.
218 '''
219 return _Psum(ps, **name_RESIDUAL)
222def _2scalar2(other):
223 '''(INTERNAL) Return 2-tuple C{(other, r)} with C{other} as C{int},
224 C{float} or C{as-is} and C{r} the residual of C{as-is}.
225 '''
226 if _isFsumTuple(other):
227 s, r = other._fint2
228 if r:
229 s, r = other._fprs2
230 if r: # PYCHOK no cover
231 s = other # L{Fsum} as-is
232 else:
233 r = 0
234 s = other # C{type} as-is
235 if isint(s, both=True):
236 s = int(s)
237 return s, r
240def _s_r(s, r):
241 '''(INTERNAL) Return C{(s, r)}, I{ordered}.
242 '''
243 if r:
244 if fabs(s) < fabs(r):
245 s, r = r, (s or INT0)
246 else:
247 r = INT0
248 return s, r
251def _strcomplex(s, *args):
252 '''(INTERNAL) C{Complex} 2- or 3-arg C{pow} error as C{str}.
253 '''
254 c = _strcomplex.__name__[4:]
255 n = _DASH_(len(args), _arg_)
256 t = unstr(pow, *args)
257 return _SPACE_(c, s, _from_, n, t)
260def _stresidual(prefix, residual, R=0, **mod_ratio):
261 '''(INTERNAL) Residual error txt C{str}.
262 '''
263 p = _stresidual.__name__[3:]
264 t = Fmt.PARENSPACED(p, Fmt(residual))
265 for n, v in itemsorted(mod_ratio):
266 p = Fmt.PARENSPACED(n, Fmt(v))
267 t = _COMMASPACE_(t, p)
268 return _SPACE_(prefix, t, Fmt.exceeds_R(R), _threshold_)
271def _2sum(a, b): # by .testFmath
272 '''(INTERNAL) Return C{a + b} as 2-tuple (sum, residual).
273 '''
274 s = a + b
275 if _isfinite(s):
276 if fabs(a) < fabs(b):
277 b, a = a, b
278 return s, (b - (s - a))
279 u = unstr(_2sum, a, b)
280 t = Fmt.PARENSPACED(_not_finite_, s)
281 raise _OverflowError(u, txt=t)
284def _threshold(threshold):
285 '''(INTERNAL) Get the L{ResidualError}s threshold.
286 '''
287 try:
288 return _2finite(threshold) # PYCHOK None
289 except Exception as x:
290 raise ResidualError(threshold=threshold, cause=x)
293class Fsum(_Named): # sync __methods__ with .vector3dBase.Vector3dBase
294 '''Precision floating point summation and I{running} summation.
296 Unlike Python's C{math.fsum}, this class accumulates values and provides intermediate,
297 I{running}, precision floating point summations. Accumulation may continue after any
298 intermediate, I{running} summuation.
300 @note: Values may be L{Fsum}, L{Fsum2Tuple}, C{int}, C{float} or C{scalar} instances,
301 any C{type} having method C{__float__} to convert the C{scalar} to a single
302 C{float}, except C{complex}.
304 @note: Handling of exceptions and C{inf}, C{INF}, C{nan} and C{NAN} differs from
305 Python's C{math.fsum}.
307 @see: U{Hettinger<https://GitHub.com/ActiveState/code/tree/master/recipes/Python/
308 393090_Binary_floating_point_summatiaccurate_full/recipe-393090.py>},
309 U{Kahan<https://WikiPedia.org/wiki/Kahan_summation_algorithm>}, U{Klein
310 <https://Link.Springer.com/article/10.1007/s00607-005-0139-x>}, Python 2.6+
311 file I{Modules/mathmodule.c} and the issue log U{Full precision summation
312 <https://Bugs.Python.org/issue2819>}.
313 '''
314 _math_fsum = None
315 _n = 0
316# _ps = [] # partial sums
317# _ps_max = 0 # max(Fsum._ps_max, len(Fsum._ps))
318 _RESIDUAL = _threshold(_getenv('PYGEODESY_FSUM_RESIDUAL', _0_0))
320 def __init__(self, *xs, **name_RESIDUAL):
321 '''New L{Fsum} for I{running} precision floating point summation.
323 @arg xs: No, one or more items to add (each C{scalar} or an L{Fsum}
324 or L{Fsum2Tuple} instance), all positional.
325 @kwarg name_RESIDUAL: Optional C{B{name}=NN} for this L{Fsum} and
326 the C{B{RESIDUAL}=0.0} threshold for L{ResidualError}s.
328 @see: Methods L{Fsum.fadd} and L{Fsum.RESIDUAL}.
329 '''
330 if name_RESIDUAL:
332 def _n_R(name=NN, RESIDUAL=None):
333 return name, RESIDUAL
335 n, R = _n_R(**name_RESIDUAL)
336 if R is not None:
337 self.RESIDUAL(R)
338 if n:
339 self.name = n
341 self._ps = [] # [_0_0], see L{Fsum._fprs}
342 if xs:
343 self._facc_1(xs, up=False)
345 def __abs__(self):
346 '''Return this instance' absolute value as an L{Fsum}.
347 '''
348 s = self.signOf() # == self._cmp_0(0)
349 return (-self) if s < 0 else self._copy_2(self.__abs__)
351 def __add__(self, other):
352 '''Return C{B{self} + B{other}} as an L{Fsum}.
354 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar}.
356 @return: The sum (L{Fsum}).
358 @see: Methods L{Fsum.fadd_} and L{Fsum.fadd}.
359 '''
360 f = self._copy_2(self.__add__)
361 return f._fadd(other, _add_op_)
363 def __bool__(self): # PYCHOK Python 3+
364 '''Return C{True} if this instance is I{exactly} non-zero.
365 '''
366 s, r = self._fprs2
367 return bool(s or r) and s != -r # == self != 0
369 def __ceil__(self): # PYCHOK not special in Python 2-
370 '''Return this instance' C{math.ceil} as C{int} or C{float}.
372 @return: An C{int} in Python 3+, but C{float} in Python 2-.
374 @see: Methods L{Fsum.__floor__} and property L{Fsum.ceil}.
375 '''
376 return self.ceil
378 def __cmp__(self, other): # PYCHOK no cover
379 '''Compare this with an other instance or C{scalar}, Python 2-.
381 @return: -1, 0 or +1 (C{int}).
383 @raise TypeError: Incompatible B{C{other}} C{type}.
384 '''
385 s = self._cmp_0(other, self.cmp.__name__)
386 return _signOf(s, 0)
388 def __divmod__(self, other, **raiser_RESIDUAL):
389 '''Return C{divmod(B{self}, B{other})} as a L{DivMod2Tuple}
390 with quotient C{div} an C{int} in Python 3+ or C{float}
391 in Python 2- and remainder C{mod} an L{Fsum} instance.
393 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar} modulus.
394 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} (C{bool}) to
395 ignore L{ResidualError}s and C{B{RESIDUAL}=scalar}
396 to override the L{RESIDUAL<Fsum.RESIDUAL>}.
398 @raise ResidualError: Non-zero, significant residual or invalid
399 B{C{RESIDUAL}}.
401 @see: Method L{Fsum.fdiv}.
402 '''
403 f = self._copy_2(self.__divmod__)
404 return f._fdivmod2(other, _divmod_op_, **raiser_RESIDUAL)
406 def __eq__(self, other):
407 '''Compare this with an other instance or C{scalar}.
408 '''
409 return self._cmp_0(other, _eq_op_) == 0
411 def __float__(self):
412 '''Return this instance' current, precision running sum as C{float}.
414 @see: Methods L{Fsum.fsum} and L{Fsum.int_float}.
415 '''
416 return float(self._fprs)
418 def __floor__(self): # PYCHOK not special in Python 2-
419 '''Return this instance' C{math.floor} as C{int} or C{float}.
421 @return: An C{int} in Python 3+, but C{float} in Python 2-.
423 @see: Methods L{Fsum.__ceil__} and property L{Fsum.floor}.
424 '''
425 return self.floor
427 def __floordiv__(self, other):
428 '''Return C{B{self} // B{other}} as an L{Fsum}.
430 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar} divisor.
432 @return: The C{floor} quotient (L{Fsum}).
434 @see: Methods L{Fsum.__ifloordiv__}.
435 '''
436 f = self._copy_2(self.__floordiv__)
437 return f._floordiv(other, _floordiv_op_)
439 def __format__(self, *other): # PYCHOK no cover
440 '''Not implemented.'''
441 return _NotImplemented(self, *other)
443 def __ge__(self, other):
444 '''Compare this with an other instance or C{scalar}.
445 '''
446 return self._cmp_0(other, _ge_op_) >= 0
448 def __gt__(self, other):
449 '''Compare this with an other instance or C{scalar}.
450 '''
451 return self._cmp_0(other, _gt_op_) > 0
453 def __hash__(self): # PYCHOK no cover
454 '''Return this instance' C{hash}.
455 '''
456 return hash(self._ps) # XXX id(self)?
458 def __iadd__(self, other):
459 '''Apply C{B{self} += B{other}} to this instance.
461 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar} value or
462 an iterable of several of the former.
464 @return: This instance, updated (L{Fsum}).
466 @raise TypeError: Invalid B{C{other}}, not
467 C{scalar} nor L{Fsum}.
469 @see: Methods L{Fsum.fadd_} and L{Fsum.fadd}.
470 '''
471 try:
472 return self._fadd(other, _iadd_op_)
473 except TypeError:
474 return self._facc_inplace(other, _iadd_op_, self._facc)
476 def __ifloordiv__(self, other):
477 '''Apply C{B{self} //= B{other}} to this instance.
479 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar} divisor.
481 @return: This instance, updated (L{Fsum}).
483 @raise ResidualError: Non-zero, significant residual
484 in B{C{other}}.
486 @raise TypeError: Invalid B{C{other}} type.
488 @raise ValueError: Invalid or non-finite B{C{other}}.
490 @raise ZeroDivisionError: Zero B{C{other}}.
492 @see: Methods L{Fsum.__itruediv__}.
493 '''
494 return self._floordiv(other, _floordiv_op_ + _fset_op_)
496 def __imatmul__(self, other): # PYCHOK no cover
497 '''Not implemented.'''
498 return _NotImplemented(self, other)
500 def __imod__(self, other):
501 '''Apply C{B{self} %= B{other}} to this instance.
503 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar} modulus.
505 @return: This instance, updated (L{Fsum}).
507 @see: Method L{Fsum.__divmod__}.
508 '''
509 return self._fdivmod2(other, _mod_op_ + _fset_op_).mod
511 def __imul__(self, other):
512 '''Apply C{B{self} *= B{other}} to this instance.
514 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar} factor.
516 @return: This instance, updated (L{Fsum}).
518 @raise OverflowError: Partial C{2sum} overflow.
520 @raise TypeError: Invalid B{C{other}} type.
522 @raise ValueError: Invalid or non-finite B{C{other}}.
523 '''
524 return self._fmul(other, _mul_op_ + _fset_op_)
526 def __int__(self):
527 '''Return this instance as an C{int}.
529 @see: Method L{Fsum.int_float} and properties L{Fsum.ceil}
530 and L{Fsum.floor}.
531 '''
532 i, _ = self._fint2
533 return i
535 def __invert__(self): # PYCHOK no cover
536 '''Not implemented.'''
537 # Luciano Ramalho, "Fluent Python", O'Reilly, 2nd Ed, 2022 p. 567
538 return _NotImplemented(self)
540 def __ipow__(self, other, *mod, **raiser_RESIDUAL): # PYCHOK 2 vs 3 args
541 '''Apply C{B{self} **= B{other}} to this instance.
543 @arg other: The exponent (C{scalar}, L{Fsum} or L{Fsum2Tuple}).
544 @arg mod: Optional modulus (C{int} or C{None}) for the 3-argument
545 C{pow(B{self}, B{other}, B{mod})} version.
546 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} (C{bool}) to
547 ignore L{ResidualError}s and C{B{RESIDUAL}=scalar}
548 to override the L{RESIDUAL<Fsum.RESIDUAL>}.
550 @return: This instance, updated (L{Fsum}).
552 @note: If B{C{mod}} is given, the result will be an C{integer}
553 L{Fsum} in Python 3+ if this instance C{is_integer} or
554 set to C{as_integer} and B{C{mod}} is given as C{None}.
556 @raise OverflowError: Partial C{2sum} overflow.
558 @raise ResidualError: Invalid B{C{RESIDUAL}} or the residual
559 is non-zero and significant and either
560 B{C{other}} is a fractional or negative
561 C{scalar} or B{C{mod}} is given and not
562 C{None}.
564 @raise TypeError: Invalid B{C{other}} type or 3-argument C{pow}
565 invocation failed.
567 @raise ValueError: If B{C{other}} is a negative C{scalar} and this
568 instance is C{0} or B{C{other}} is a fractional
569 C{scalar} and this instance is negative or has a
570 non-zero and significant residual or B{C{mod}}
571 is given as C{0}.
573 @see: CPython function U{float_pow<https://GitHub.com/
574 python/cpython/blob/main/Objects/floatobject.c>}.
575 '''
576 return self._fpow(other, _pow_op_ + _fset_op_, *mod, **raiser_RESIDUAL)
578 def __isub__(self, other):
579 '''Apply C{B{self} -= B{other}} to this instance.
581 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar} value or
582 an iterable of several of the former.
584 @return: This instance, updated (L{Fsum}).
586 @raise TypeError: Invalid B{C{other}} type.
588 @see: Methods L{Fsum.fsub_} and L{Fsum.fsub}.
589 '''
590 try:
591 return self._fsub(other, _isub_op_)
592 except TypeError:
593 return self._facc_inplace(other, _isub_op_, self._facc_neg)
595 def __iter__(self):
596 '''Return an C{iter}ator over a C{partials} duplicate.
597 '''
598 return iter(self.partials)
600 def __itruediv__(self, other, **raiser_RESIDUAL):
601 '''Apply C{B{self} /= B{other}} to this instance.
603 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar} divisor.
604 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} (C{bool}) to
605 ignore L{ResidualError}s and C{B{RESIDUAL}=scalar}
606 to override the L{RESIDUAL<Fsum.RESIDUAL>}.
608 @return: This instance, updated (L{Fsum}).
610 @raise OverflowError: Partial C{2sum} overflow.
612 @raise ResidualError: Non-zero, significant residual or invalid
613 B{C{RESIDUAL}}.
615 @raise TypeError: Invalid B{C{other}} type.
617 @raise ValueError: Invalid or non-finite B{C{other}}.
619 @raise ZeroDivisionError: Zero B{C{other}}.
621 @see: Method L{Fsum.__ifloordiv__}.
622 '''
623 return self._ftruediv(other, _truediv_op_ + _fset_op_, **raiser_RESIDUAL)
625 def __le__(self, other):
626 '''Compare this with an other instance or C{scalar}.
627 '''
628 return self._cmp_0(other, _le_op_) <= 0
630 def __len__(self):
631 '''Return the number of values accumulated (C{int}).
632 '''
633 return self._n
635 def __lt__(self, other):
636 '''Compare this with an other instance or C{scalar}.
637 '''
638 return self._cmp_0(other, _lt_op_) < 0
640 def __matmul__(self, other): # PYCHOK no cover
641 '''Not implemented.'''
642 return _NotImplemented(self, other)
644 def __mod__(self, other):
645 '''Return C{B{self} % B{other}} as an L{Fsum}.
647 @see: Method L{Fsum.__imod__}.
648 '''
649 f = self._copy_2(self.__mod__)
650 return f._fdivmod2(other, _mod_op_).mod
652 def __mul__(self, other):
653 '''Return C{B{self} * B{other}} as an L{Fsum}.
655 @see: Method L{Fsum.__imul__}.
656 '''
657 f = self._copy_2(self.__mul__)
658 return f._fmul(other, _mul_op_)
660 def __ne__(self, other):
661 '''Compare this with an other instance or C{scalar}.
662 '''
663 return self._cmp_0(other, _ne_op_) != 0
665 def __neg__(self):
666 '''Return I{a copy of} this instance, I{negated}.
667 '''
668 f = self._copy_2(self.__neg__)
669 return f._fset(self._neg)
671 def __pos__(self):
672 '''Return this instance I{as-is}, like C{float.__pos__()}.
673 '''
674 return self if _pos_self else self._copy_2(self.__pos__)
676 def __pow__(self, other, *mod): # PYCHOK 2 vs 3 args
677 '''Return C{B{self}**B{other}} as an L{Fsum}.
679 @see: Method L{Fsum.__ipow__}.
680 '''
681 f = self._copy_2(self.__pow__)
682 return f._fpow(other, _pow_op_, *mod)
684 def __radd__(self, other):
685 '''Return C{B{other} + B{self}} as an L{Fsum}.
687 @see: Method L{Fsum.__iadd__}.
688 '''
689 f = self._copy_2r(other, self.__radd__)
690 return f._fadd(self, _add_op_)
692 def __rdivmod__(self, other):
693 '''Return C{divmod(B{other}, B{self})} as 2-tuple
694 C{(quotient, remainder)}.
696 @see: Method L{Fsum.__divmod__}.
697 '''
698 f = self._copy_2r(other, self.__rdivmod__)
699 return f._fdivmod2(self, _divmod_op_)
701# def __repr__(self):
702# '''Return the default C{repr(this)}.
703# '''
704# return self.toRepr(lenc=True)
706 def __rfloordiv__(self, other):
707 '''Return C{B{other} // B{self}} as an L{Fsum}.
709 @see: Method L{Fsum.__ifloordiv__}.
710 '''
711 f = self._copy_2r(other, self.__rfloordiv__)
712 return f._floordiv(self, _floordiv_op_)
714 def __rmatmul__(self, other): # PYCHOK no cover
715 '''Not implemented.'''
716 return _NotImplemented(self, other)
718 def __rmod__(self, other):
719 '''Return C{B{other} % B{self}} as an L{Fsum}.
721 @see: Method L{Fsum.__imod__}.
722 '''
723 f = self._copy_2r(other, self.__rmod__)
724 return f._fdivmod2(self, _mod_op_).mod
726 def __rmul__(self, other):
727 '''Return C{B{other} * B{self}} as an L{Fsum}.
729 @see: Method L{Fsum.__imul__}.
730 '''
731 f = self._copy_2r(other, self.__rmul__)
732 return f._fmul(self, _mul_op_)
734 def __round__(self, *ndigits): # PYCHOK Python 3+
735 '''Return C{round(B{self}, *B{ndigits}} as an L{Fsum}.
737 @arg ndigits: Optional number of digits (C{int}).
738 '''
739 f = self._copy_2(self.__round__)
740 # <https://docs.Python.org/3.12/reference/datamodel.html?#object.__round__>
741 return f._fset(round(float(self), *ndigits)) # can be C{int}
743 def __rpow__(self, other, *mod):
744 '''Return C{B{other}**B{self}} as an L{Fsum}.
746 @see: Method L{Fsum.__ipow__}.
747 '''
748 f = self._copy_2r(other, self.__rpow__)
749 return f._fpow(self, _pow_op_, *mod)
751 def __rsub__(self, other):
752 '''Return C{B{other} - B{self}} as L{Fsum}.
754 @see: Method L{Fsum.__isub__}.
755 '''
756 f = self._copy_2r(other, self.__rsub__)
757 return f._fsub(self, _sub_op_)
759 def __rtruediv__(self, other, **raiser_RESIDUAL):
760 '''Return C{B{other} / B{self}} as an L{Fsum}.
762 @see: Method L{Fsum.__itruediv__}.
763 '''
764 f = self._copy_2r(other, self.__rtruediv__)
765 return f._ftruediv(self, _truediv_op_, **raiser_RESIDUAL)
767 def __str__(self):
768 '''Return the default C{str(self)}.
769 '''
770 return self.toStr(lenc=True)
772 def __sub__(self, other):
773 '''Return C{B{self} - B{other}} as an L{Fsum}.
775 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar}.
777 @return: The difference (L{Fsum}).
779 @see: Method L{Fsum.__isub__}.
780 '''
781 f = self._copy_2(self.__sub__)
782 return f._fsub(other, _sub_op_)
784 def __truediv__(self, other, **raiser_RESIDUAL):
785 '''Return C{B{self} / B{other}} as an L{Fsum}.
787 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar} divisor.
788 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} (C{bool}) to
789 ignore L{ResidualError}s and C{B{RESIDUAL}=scalar}
790 to override the L{RESIDUAL<Fsum.RESIDUAL>}.
792 @return: The quotient (L{Fsum}).
794 @raise ResidualError: Non-zero, significant residual or invalid
795 B{C{RESIDUAL}}.
797 @see: Method L{Fsum.__itruediv__}.
798 '''
799 return self._truediv(other, _truediv_op_, **raiser_RESIDUAL)
801 __trunc__ = __int__
803 if _sys_version_info2 < (3, 0): # PYCHOK no cover
804 # <https://docs.Python.org/2/library/operator.html#mapping-operators-to-functions>
805 __div__ = __truediv__
806 __idiv__ = __itruediv__
807 __long__ = __int__
808 __nonzero__ = __bool__
809 __rdiv__ = __rtruediv__
811 def as_integer_ratio(self):
812 '''Return this instance as the ratio of 2 integers.
814 @return: 2-Tuple C{(numerator, denominator)} both C{int}
815 with C{numerator} signed and C{denominator}
816 non-zero, positive.
818 @see: Standard C{float.as_integer_ratio} in Python 2.7+.
819 '''
820 n, r = self._fint2
821 if r:
822 i, d = float(r).as_integer_ratio()
823 n *= d
824 n += i
825 else: # PYCHOK no cover
826 d = 1
827 return n, d
829 @property_RO
830 def as_iscalar(self):
831 '''Get this instance I{as-is} (L{Fsum} or C{scalar}), the
832 latter only if the C{residual} equals C{zero}.
833 '''
834 s, r = self._fprs2
835 return self if r else s
837 @property_RO
838 def ceil(self):
839 '''Get this instance' C{ceil} value (C{int} in Python 3+, but
840 C{float} in Python 2-).
842 @note: This C{ceil} takes the C{residual} into account.
844 @see: Method L{Fsum.int_float} and properties L{Fsum.floor},
845 L{Fsum.imag} and L{Fsum.real}.
846 '''
847 s, r = self._fprs2
848 c = _ceil(s) + int(r) - 1
849 while r > (c - s): # (s + r) > c
850 c += 1
851 return c # _ceil(self._n_d)
853 cmp = __cmp__
855 def _cmp_0(self, other, op):
856 '''(INTERNAL) Return C{scalar(self - B{other})} for 0-comparison.
857 '''
858 if _isFsumTuple(other):
859 s = self._ps_1sum(*other._ps)
860 elif self._scalar(other, op):
861 s = self._ps_1sum(other)
862 else:
863 s = self.signOf() # res=True
864 return s
866 def copy(self, deep=False, name=NN):
867 '''Copy this instance, C{shallow} or B{C{deep}}.
869 @return: The copy (L{Fsum}).
870 '''
871 f = _Named.copy(self, deep=deep, name=name)
872 if f._ps is self._ps:
873 f._ps = list(self._ps) # separate list
874 if not deep:
875 f._n = 1
876 # assert f._Fsum is f
877 return f
879 def _copy_2(self, which, name=NN):
880 '''(INTERNAL) Copy for I{dyadic} operators.
881 '''
882 n = name or which.__name__
883 # NOT .classof due to .Fdot(a, *b) args, etc.
884 f = _Named.copy(self, deep=False, name=n)
885 f._ps = list(self._ps) # separate list
886 # assert f._n == self._n
887 # assert f._Fsum is f
888 return f
890 def _copy_2r(self, other, which):
891 '''(INTERNAL) Copy for I{reverse-dyadic} operators.
892 '''
893 return other._copy_2(which) if _isFsum(other) else \
894 self._copy_2(which)._fset(other)
896# def _copy_RESIDUAL(self, other):
897# '''(INTERNAL) Copy C{other._RESIDUAL}.
898# '''
899# R = other._RESIDUAL
900# if R is not Fsum._RESIDUAL:
901# self._RESIDUAL = R
903 divmod = __divmod__
905 def _Error(self, op, other, Error, **txt_cause):
906 '''(INTERNAL) Format an B{C{Error}} for C{{self} B{op} B{other}}.
907 '''
908 return Error(_SPACE_(self.as_iscalar, op, other), **txt_cause)
910 def _ErrorX(self, X, op, other, *mod):
911 '''(INTERNAL) Format the caught exception C{X}.
912 '''
913 E, t = _xError2(X)
914 if mod:
915 t = _COMMASPACE_(Fmt.PARENSPACED(mod=mod[0]), t)
916 return self._Error(op, other, E, txt=t, cause=X)
918 def _ErrorXs(self, X, xs, **kwds): # in .fmath
919 '''(INTERNAL) Format the caught exception C{X}.
920 '''
921 E, t = _xError2(X)
922 u = unstr(self.named3, *xs[:3], _ELLIPSIS=len(xs) > 3, **kwds)
923 return E(u, txt=t, cause=X)
925 def _facc(self, xs, up=True, **origin_X_x):
926 '''(INTERNAL) Accumulate more C{scalars} or L{Fsum}s.
927 '''
928 if xs:
929 _xs = _2floats(xs, **origin_X_x) # PYCHOK yield
930 ps = self._ps
931 ps[:] = self._ps_acc(list(ps), _xs, up=up)
932 return self
934 def _facc_1(self, xs, **up):
935 '''(INTERNAL) Accumulate 0, 1 or more C{scalars} or L{Fsum}s,
936 all positional C{xs} in the caller of this method.
937 '''
938 return self._fadd(xs[0], _add_op_, **up) if len(xs) == 1 else \
939 self._facc(xs, origin=1, **up)
941 def _facc_inplace(self, other, op, _facc):
942 '''(INTERNAL) Accumulate from an iterable.
943 '''
944 try:
945 return _facc(other, origin=1) if _xiterable(other) else self
946 except Exception as X:
947 raise self._ErrorX(X, op, other)
949 def _facc_neg(self, xs, **up_origin):
950 '''(INTERNAL) Accumulate more C{scalars} or L{Fsum}s, negated.
951 '''
952 def _N(X):
953 return X._ps_neg
955 def _n(x):
956 return -float(x)
958 return self._facc(xs, _X=_N, _x=_n, **up_origin)
960 def _facc_power(self, power, xs, which, **raiser_RESIDUAL): # in .fmath
961 '''(INTERNAL) Add each C{xs} as C{float(x**power)}.
962 '''
963 def _Pow4(p):
964 r = 0
965 if _isFsumTuple(p):
966 s, r = p._fprs2
967 if r:
968 m = Fsum._pow
969 else: # scalar
970 return _Pow4(s)
971 elif isint(p, both=True) and int(p) >= 0:
972 p = s = int(p)
973 m = Fsum._pow_int
974 else:
975 p = s = _2float(power=p)
976 m = Fsum._pow_scalar
977 return m, p, s, r
979 _Pow, p, s, r = _Pow4(power)
980 if p: # and xs:
981 op = which.__name__
982 _flt = float
983 _Fs = Fsum
984 _isa = isinstance
985 _pow = self._pow_2_3
987 def _P(X):
988 f = _Pow(X, p, power, op, **raiser_RESIDUAL)
989 return f._ps if _isa(f, _Fs) else (f,)
991 def _p(x):
992 x = _flt(x)
993 f = _pow(x, s, power, op, **raiser_RESIDUAL)
994 if f and r:
995 f *= _pow(x, r, power, op, **raiser_RESIDUAL)
996 return f
998 f = self._facc(xs, origin=1, _X=_P, _x=_p)
999 else:
1000 f = self._facc_scalar_(float(len(xs))) # x**0 == 1
1001 return f
1003 def _facc_scalar(self, xs, **up):
1004 '''(INTERNAL) Accumulate all C{xs}, known to be scalar.
1005 '''
1006 if xs:
1007 _ = self._ps_acc(self._ps, xs, **up)
1008 return self
1010 def _facc_scalar_(self, *xs, **up):
1011 '''(INTERNAL) Accumulate all positional C{xs}, known to be scalar.
1012 '''
1013 if xs:
1014 _ = self._ps_acc(self._ps, xs, **up)
1015 return self
1017# def _facc_up(self, up=True):
1018# '''(INTERNAL) Update the C{partials}, by removing
1019# and re-accumulating the final C{partial}.
1020# '''
1021# ps = self._ps
1022# while len(ps) > 1:
1023# p = ps.pop()
1024# if p:
1025# n = self._n
1026# _ = self._ps_acc(ps, (p,), up=False)
1027# self._n = n
1028# break
1029# return self._update() if up else self
1031 def fadd(self, xs=()):
1032 '''Add an iterable's items to this instance.
1034 @arg xs: Iterable of items to add (each C{scalar}
1035 or an L{Fsum} or L{Fsum2Tuple} instance).
1037 @return: This instance (L{Fsum}).
1039 @raise OverflowError: Partial C{2sum} overflow.
1041 @raise TypeError: An invalid B{C{xs}} item.
1043 @raise ValueError: Invalid or non-finite B{C{xs}} value.
1044 '''
1045 if _isFsumTuple(xs):
1046 self._facc_scalar(xs._ps)
1047 elif isscalar(xs): # for backward compatibility
1048 self._facc_scalar_(_2float(x=xs)) # PYCHOK no cover
1049 elif xs: # _xiterable(xs)
1050 self._facc(xs)
1051 return self
1053 def fadd_(self, *xs):
1054 '''Add all positional items to this instance.
1056 @arg xs: Values to add (each C{scalar} or an L{Fsum}
1057 or L{Fsum2Tuple} instance), all positional.
1059 @see: Method L{Fsum.fadd} for further details.
1060 '''
1061 return self._facc_1(xs)
1063 def _fadd(self, other, op, **up): # in .fmath.Fhorner
1064 '''(INTERNAL) Apply C{B{self} += B{other}}.
1065 '''
1066 if not self._ps: # new Fsum(x)
1067 self._fset(other, op=op, **up)
1068 elif _isFsumTuple(other):
1069 self._facc_scalar(other._ps, **up)
1070 elif self._scalar(other, op):
1071 self._facc_scalar_(other, **up)
1072 return self
1074 fcopy = copy # for backward compatibility
1075 fdiv = __itruediv__
1076 fdivmod = __divmod__
1078 def _fdivmod2(self, other, op, **raiser_RESIDUAL):
1079 '''(INTERNAL) Apply C{B{self} %= B{other}} and return a L{DivMod2Tuple}.
1080 '''
1081 # result mostly follows CPython function U{float_divmod
1082 # <https://GitHub.com/python/cpython/blob/main/Objects/floatobject.c>},
1083 # but at least divmod(-3, 2) equals Cpython's result (-2, 1).
1084 q = self._truediv(other, op, **raiser_RESIDUAL).floor
1085 if q: # == float // other == floor(float / other)
1086 self -= Fsum(q) * other # NOT other * q!
1088 s = signOf(other) # make signOf(self) == signOf(other)
1089 if s and self.signOf() == -s: # PYCHOK no cover
1090 self += other
1091 q -= 1
1092# t = self.signOf()
1093# if t and t != s:
1094# raise self._Error(op, other, _AssertionError, txt=signOf.__name__)
1095 return DivMod2Tuple(q, self) # q is C{int} in Python 3+, but C{float} in Python 2-
1097 def _finite(self, other, op=None):
1098 '''(INTERNAL) Return B{C{other}} if C{finite}.
1099 '''
1100 if _isfinite(other):
1101 return other
1102 raise ValueError(_not_finite_) if op is None else \
1103 self._Error(op, other, _ValueError, txt=_not_finite_)
1105 def fint(self, name=NN, **raiser_RESIDUAL):
1106 '''Return this instance' current running sum as C{integer}.
1108 @kwarg name: Optional name (C{str}), overriding C{"fint"}.
1109 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} (C{bool}) to
1110 ignore L{ResidualError}s and C{B{RESIDUAL}=scalar}
1111 to override the L{RESIDUAL<Fsum.RESIDUAL>}.
1113 @return: The C{integer} sum (L{Fsum}) if this instance C{is_integer}
1114 with a zero or insignificant I{integer} residual.
1116 @raise ResidualError: Non-zero, significant residual or invalid
1117 B{C{RESIDUAL}}.
1119 @see: Methods L{Fsum.fint2}, L{Fsum.int_float} and L{Fsum.is_integer}.
1120 '''
1121 i, r = self._fint2
1122 if r:
1123 R = self._raiser(r, i, **raiser_RESIDUAL)
1124 if R:
1125 t = _stresidual(_integer_, r, **R)
1126 raise ResidualError(_integer_, i, txt=t)
1127 f = self._copy_2(self.fint, name=name)
1128 return f._fset(i)
1130 def fint2(self, **name):
1131 '''Return this instance' current running sum as C{int} and the
1132 I{integer} residual.
1134 @kwarg name: Optional name (C{str}).
1136 @return: An L{Fsum2Tuple}C{(fsum, residual)} with C{fsum}
1137 an C{int} and I{integer} C{residual} a C{float} or
1138 C{INT0} if the C{fsum} is considered to be I{exact}.
1139 '''
1140 return Fsum2Tuple(*self._fint2, **name)
1142 @Property_RO
1143 def _fint2(self): # see ._fset
1144 '''(INTERNAL) Get 2-tuple (C{int}, I{integer} residual).
1145 '''
1146 s, r = self._fprs2
1147 i = int(s)
1148 n = len(self._ps)
1149 r = self._ps_1sum(i) if r and n > 1 else float(s - i)
1150 return i, (r or INT0) # Fsum2Tuple?
1152 @deprecated_property_RO
1153 def float_int(self): # PYCHOK no cover
1154 '''DEPRECATED, use method C{Fsum.int_float}.'''
1155 return self.int_float() # raiser=False
1157 @property_RO
1158 def floor(self):
1159 '''Get this instance' C{floor} (C{int} in Python 3+, but
1160 C{float} in Python 2-).
1162 @note: This C{floor} takes the C{residual} into account.
1164 @see: Method L{Fsum.int_float} and properties L{Fsum.ceil},
1165 L{Fsum.imag} and L{Fsum.real}.
1166 '''
1167 s, r = self._fprs2
1168 f = _floor(s) + _floor(r) + 1
1169 while (f - s) > r: # f > (s + r)
1170 f -= 1
1171 return f # _floor(self._n_d)
1173# ffloordiv = __ifloordiv__ # for naming consistency
1174# floordiv = __floordiv__ # for naming consistency
1176 def _floordiv(self, other, op, **raiser_RESIDUAL): # rather _ffloordiv?
1177 '''Apply C{B{self} //= B{other}}.
1178 '''
1179 q = self._ftruediv(other, op, **raiser_RESIDUAL) # == self
1180 return self._fset(q.floor) # floor(q)
1182 fmul = __imul__
1184 def _fmul(self, other, op):
1185 '''(INTERNAL) Apply C{B{self} *= B{other}}.
1186 '''
1187 if _isFsumTuple(other):
1188 if len(self._ps) != 1:
1189 f = self._mul_Fsum(other, op)
1190 elif len(other._ps) != 1: # and len(self._ps) == 1
1191 f = other._mul_scalar(self._ps[0], op)
1192 else: # len(other._ps) == len(self._ps) == 1
1193 f = self._finite(self._ps[0] * other._ps[0])
1194 else:
1195 s = self._scalar(other, op)
1196 f = self._mul_scalar(s, op)
1197 return self._fset(f) # n=len(self) + 1
1199 def fover(self, over, **raiser_RESIDUAL):
1200 '''Apply C{B{self} /= B{over}} and summate.
1202 @arg over: An L{Fsum} or C{scalar} denominator.
1203 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} (C{bool}) to
1204 ignore L{ResidualError}s and C{B{RESIDUAL}=scalar}
1205 to override the L{RESIDUAL<Fsum.RESIDUAL>}.
1207 @return: Precision running sum (C{float}).
1209 @raise ResidualError: Non-zero, significant residual or invalid
1210 B{C{RESIDUAL}}.
1212 @see: Methods L{Fsum.fsum} and L{Fsum.__itruediv__}.
1213 '''
1214 return float(self.fdiv(over, **raiser_RESIDUAL)._fprs)
1216 fpow = __ipow__
1218 def _fpow(self, other, op, *mod, **raiser_RESIDUAL):
1219 '''Apply C{B{self} **= B{other}}, optional B{C{mod}} or C{None}.
1220 '''
1221 if mod:
1222 if mod[0] is not None: # == 3-arg C{pow}
1223 f = self._pow_2_3(self, other, other, op, *mod, **raiser_RESIDUAL)
1224 elif self.is_integer():
1225 # return an exact C{int} for C{int}**C{int}
1226 i, _ = self._fint2 # assert _ == 0
1227 x, r = _2scalar2(other) # C{int}, C{float} or other
1228 f = _Psum_(i)._pow_Fsum(other, op, **raiser_RESIDUAL) if r else \
1229 self._pow_2_3(i, x, other, op, **raiser_RESIDUAL)
1230 else: # mod[0] is None, power(self, other)
1231 f = self._pow(other, other, op, **raiser_RESIDUAL)
1232 else: # pow(self, other)
1233 f = self._pow(other, other, op, **raiser_RESIDUAL)
1234 return self._fset(f) # n=max(len(self), 1)
1236 @Property_RO
1237 def _fprs(self):
1238 '''(INTERNAL) Get and cache this instance' precision
1239 running sum (C{float} or C{int}), ignoring C{residual}.
1241 @note: The precision running C{fsum} after a C{//=} or
1242 C{//} C{floor} division is C{int} in Python 3+.
1243 '''
1244 s, _ = self._fprs2
1245 return s # ._fprs2.fsum
1247 @Property_RO
1248 def _fprs2(self):
1249 '''(INTERNAL) Get and cache this instance' precision
1250 running sum and residual (L{Fsum2Tuple}).
1251 '''
1252 ps = self._ps
1253 n = len(ps) - 2
1254 if n > 0: # len(ps) > 2
1255 s = _psum(ps)
1256 n = len(ps) - 2
1257 if n > 0:
1258 r = self._ps_1sum(s)
1259 return Fsum2Tuple(*_s_r(s, r))
1260 if n == 0: # len(ps) == 2
1261 s, r = _s_r(*_2sum(*ps))
1262 ps[:] = (r, s) if r else (s,)
1263 elif ps: # len(ps) == 1
1264 s, r = ps[0], INT0
1265 else: # len(ps) == 0
1266 s, r = _0_0, INT0
1267 ps[:] = s,
1268 # assert self._ps is ps
1269 return Fsum2Tuple(s, r)
1271 def fset_(self, *xs):
1272 '''Replace this instance' value with all positional items.
1274 @arg xs: Optional, new values (each C{scalar} or
1275 an L{Fsum} or L{Fsum2Tuple} instance),
1276 all positional.
1278 @return: This instance, replaced (C{Fsum}).
1280 @see: Method L{Fsum.fadd} for further details.
1281 '''
1282 f = xs[0] if len(xs) == 1 else (
1283 Fsum(*xs) if xs else _0_0)
1284 return self._fset(f)
1286 def _fset(self, other, n=0, up=True, **op):
1287 '''(INTERNAL) Overwrite this instance with an other or a C{scalar}.
1288 '''
1289 if other is self:
1290 pass # from ._fmul, ._ftruediv and ._pow_0_1
1291 elif _isFsumTuple(other):
1292 self._ps[:] = other._ps
1293 self._n = n or other._n
1294# self._copy_RESIDUAL(other)
1295 if up: # use or zap the C{Property_RO} values
1296 Fsum._fint2._update_from(self, other)
1297 Fsum._fprs ._update_from(self, other)
1298 Fsum._fprs2._update_from(self, other)
1299 elif isscalar(other):
1300 s = float(self._finite(other, **op)) if op else other
1301 self._ps[:] = s,
1302 self._n = n or 1
1303 if up:
1304 i = int(s) # see ._fint2
1305 t = i, ((s - i) or INT0)
1306 # Property_ROs _fint2, _fprs and _fprs2 can't be a Property:
1307 # Property's _fset zaps the value just set by the @setter
1308 self.__dict__.update(_fint2=t, _fprs=s, _fprs2=Fsum2Tuple(s, INT0))
1309 else: # PYCHOK no cover
1310 op = _xkwds_get(op, op=_fset_op_)
1311 raise self._Error(op, other, _TypeError)
1312 return self
1314 def _fset_ps(self, other, n=0): # in .fmath
1315 '''(INTERNAL) Set partials from a known C{scalar}, L{Fsum} or L{Fsum2Tuple}.
1316 '''
1317 if _isFsumTuple(other):
1318 self._ps[:] = other._ps
1319 self._n = n or other._n
1320 else: # assert isscalar(other)
1321 self._ps[:] = other,
1322 self._n = n or 1
1323 return self
1325 def fsub(self, xs=()):
1326 '''Subtract an iterable's items from this instance.
1328 @see: Method L{Fsum.fadd} for further details.
1329 '''
1330 return self._facc_neg(xs)
1332 def fsub_(self, *xs):
1333 '''Subtract all positional items from this instance.
1335 @see: Method L{Fsum.fadd_} for further details.
1336 '''
1337 return self._fsub(xs[0], _sub_op_) if len(xs) == 1 else \
1338 self._facc_neg(xs, origin=1)
1340 def _fsub(self, other, op):
1341 '''(INTERNAL) Apply C{B{self} -= B{other}}.
1342 '''
1343 if _isFsumTuple(other):
1344 if other is self: # or other._fprs2 == self._fprs2:
1345 self._fset(_0_0, n=len(self) * 2)
1346 elif other._ps:
1347 self._facc_scalar(other._ps_neg)
1348 elif self._scalar(other, op):
1349 self._facc_scalar_(-other)
1350 return self
1352 def fsum(self, xs=()):
1353 '''Add an iterable's items, summate and return the
1354 current precision running sum.
1356 @arg xs: Iterable of items to add (each item C{scalar}
1357 or an L{Fsum} or L{Fsum2Tuple} instance).
1359 @return: Precision running sum (C{float} or C{int}).
1361 @see: Method L{Fsum.fadd}.
1363 @note: Accumulation can continue after summation.
1364 '''
1365 return self._facc(xs)._fprs
1367 def fsum_(self, *xs):
1368 '''Add any positional items, summate and return the
1369 current precision running sum.
1371 @arg xs: Items to add (each C{scalar} or an L{Fsum}
1372 or L{Fsum2Tuple} instance), all positional.
1374 @return: Precision running sum (C{float} or C{int}).
1376 @see: Methods L{Fsum.fsum}, L{Fsum.Fsum_} and L{Fsum.fsumf_}.
1377 '''
1378 return self._facc_1(xs)._fprs
1380 @property_RO
1381 def _Fsum(self): # like L{Fsum2Tuple._Fsum}, for C{_2floats}, .fstats
1382 return self # NOT @Property_RO, see .copy and ._copy_2
1384 def Fsum_(self, *xs, **name):
1385 '''Like method L{Fsum.fsum_} but returning a named L{Fsum}.
1387 @kwarg name: Optional name (C{str}).
1389 @return: Copy of this updated instance (L{Fsum}).
1390 '''
1391 return self._facc_1(xs)._copy_2(self.Fsum_, **name)
1393 def Fsum2Tuple_(self, *xs, **name):
1394 '''Like method L{Fsum.fsum_} but returning a named L{Fsum2Tuple}.
1396 @kwarg name: Optional name (C{str}).
1398 @return: Precision running sum (L{Fsum2Tuple}).
1399 '''
1400 return Fsum2Tuple(self._facc_1(xs)._fprs2, **name)
1402 def fsum2(self, xs=(), name=NN):
1403 '''Add an iterable's items, summate and return the
1404 current precision running sum I{and} the C{residual}.
1406 @arg xs: Iterable of items to add (each item C{scalar}
1407 or an L{Fsum} or L{Fsum2Tuple} instance).
1408 @kwarg name: Optional name (C{str}).
1410 @return: L{Fsum2Tuple}C{(fsum, residual)} with C{fsum} the
1411 current precision running sum and C{residual}, the
1412 (precision) sum of the remaining C{partials}. The
1413 C{residual is INT0} if the C{fsum} is considered
1414 to be I{exact}.
1416 @see: Methods L{Fsum.fint2}, L{Fsum.fsum} and L{Fsum.fsum2_}
1417 '''
1418 t = self._facc(xs)._fprs2
1419 return t.dup(name=name) if name else t
1421 def fsum2_(self, *xs):
1422 '''Add any positional items, summate and return the current
1423 precision running sum and the I{differential}.
1425 @arg xs: Values to add (each C{scalar} or an L{Fsum} or
1426 L{Fsum2Tuple} instance), all positional.
1428 @return: 2Tuple C{(fsum, delta)} with the current, precision
1429 running C{fsum} like method L{Fsum.fsum} and C{delta},
1430 the difference with previous running C{fsum}, C{float}.
1432 @see: Methods L{Fsum.fsum_} and L{Fsum.fsum}.
1433 '''
1434 return self._fsum2(xs, self._facc_1)
1436 def _fsum2(self, xs, _facc, **origin):
1437 '''(INTERNAL) Helper for L{Fsum.fsum2_} and L{Fsum.fsum2f_}.
1438 '''
1439 p, q = self._fprs2
1440 if xs:
1441 s, r = _facc(xs, **origin)._fprs2
1442 return s, _2delta(s - p, r - q) # _fsum(_1primed((s, -p, r, -q))
1443 else:
1444 return p, _0_0
1446 def fsumf_(self, *xs):
1447 '''Like method L{Fsum.fsum_} iff I{all} C{B{xs}} are I{known to be scalar}.
1448 '''
1449 return self._facc_scalar(xs)._fprs
1451 def Fsumf_(self, *xs):
1452 '''Like method L{Fsum.Fsum_} iff I{all} C{B{xs}} are I{known to be scalar}.
1453 '''
1454 return self._facc_scalar(xs)._copy_2(self.Fsumf_)
1456 def fsum2f_(self, *xs):
1457 '''Like method L{Fsum.fsum2_} iff I{all} C{B{xs}} are I{known to be scalar}.
1458 '''
1459 return self._fsum2(xs, self._facc_scalar, origin=1)
1461# ftruediv = __itruediv__ # for naming consistency?
1463 def _ftruediv(self, other, op, **raiser_RESIDUAL):
1464 '''(INTERNAL) Apply C{B{self} /= B{other}}.
1465 '''
1466 n = _1_0
1467 if _isFsumTuple(other):
1468 if other is self or self == other:
1469 return self._fset(n, n=len(self))
1470 d, r = other._fprs2
1471 if r:
1472 R = self._raiser(r, d, **raiser_RESIDUAL)
1473 if R:
1474 raise self._ResidualError(op, other, r, **R)
1475 d, n = other.as_integer_ratio()
1476 else:
1477 d = self._scalar(other, op)
1478 try:
1479 s = n / d
1480 except Exception as X:
1481 raise self._ErrorX(X, op, other)
1482 f = self._mul_scalar(s, _mul_op_) # handles 0, INF, NAN
1483 return self._fset(f)
1485 @property_RO
1486 def imag(self):
1487 '''Get the C{imaginary} part of this instance (C{0.0}, always).
1489 @see: Property L{Fsum.real}.
1490 '''
1491 return _0_0
1493 def int_float(self, **raiser_RESIDUAL):
1494 '''Return this instance' current running sum as C{int} or C{float}.
1496 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} (C{bool}) to
1497 ignore L{ResidualError}s and C{B{RESIDUAL}=scalar}
1498 to override the L{RESIDUAL<Fsum.RESIDUAL>}.
1500 @return: This C{integer} sum if this instance C{is_integer},
1501 otherwise return the C{float} sum if the residual is
1502 zero or not significant.
1504 @raise ResidualError: Non-zero, significant residual or invalid
1505 B{C{RESIDUAL}}.
1507 @see: Methods L{Fsum.fint}, L{Fsum.fint2}, L{Fsum.RESIDUAL} and
1508 property L{Fsum.as_iscalar}.
1509 '''
1510 s, r = self._fint2
1511 if r:
1512 s, r = self._fprs2
1513 if r: # PYCHOK no cover
1514 R = self._raiser(r, s, **raiser_RESIDUAL)
1515 if R:
1516 t = _stresidual(_non_zero_, r, **R)
1517 raise ResidualError(int_float=s, txt=t)
1518 s = float(s)
1519 return s
1521 def is_exact(self):
1522 '''Is this instance' running C{fsum} considered to be exact?
1523 (C{bool}), C{True} only if the C{residual is }L{INT0}.
1524 '''
1525 return self.residual is INT0
1527 def is_integer(self):
1528 '''Is this instance' running sum C{integer}? (C{bool}).
1530 @see: Methods L{Fsum.fint}, L{Fsum.fint2} and L{Fsum.is_scalar}.
1531 '''
1532 _, r = self._fint2
1533 return False if r else True
1535 def is_math_fsum(self):
1536 '''Return whether functions L{fsum}, L{fsum_}, L{fsum1} and
1537 L{fsum1_} plus partials summation are based on Python's
1538 C{math.fsum} or not.
1540 @return: C{2} if all functions and partials summation
1541 are based on C{math.fsum}, C{True} if only
1542 the functions are based on C{math.fsum} (and
1543 partials summation is not) or C{False} if
1544 none are.
1545 '''
1546 f = Fsum._math_fsum
1547 return 2 if _psum is f else bool(f)
1549 def is_scalar(self, **raiser_RESIDUAL):
1550 '''Is this instance' running sum C{scalar} without residual or with
1551 a residual I{ratio} not exceeding the RESIDUAL threshold?
1553 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} (C{bool}) to ignore
1554 L{ResidualError}s and C{B{RESIDUAL}=scalar} to override
1555 the L{RESIDUAL<Fsum.RESIDUAL>} threshold.
1557 @return: C{True} if this instance' non-zero residual C{ratio} exceeds
1558 the L{RESIDUAL<Fsum.RESIDUAL>} threshold (C{bool}).
1560 @raise ResidualError: Non-zero, significant residual or invalid
1561 B{C{RESIDUAL}}.
1563 @see: Method L{Fsum.RESIDUAL}, L{Fsum.is_integer} and property
1564 L{Fsum.as_iscalar}.
1565 '''
1566 s, r = self._fprs2
1567 return False if r and self._raiser(r, s, **raiser_RESIDUAL) else True
1569 def _mul_Fsum(self, other, op=_mul_op_): # in .fmath.Fhorner
1570 '''(INTERNAL) Return C{B{self} * B{other}} as L{Fsum} or C{0}.
1571 '''
1572 # assert _isFsumTuple(other)
1573 if self._ps and other._ps:
1574 f = self._ps_mul(op, *other._ps) # NO .as_iscalar!
1575 else:
1576 f = _0_0
1577 return f
1579 def _mul_scalar(self, factor, op): # in .fmath.Fhorner
1580 '''(INTERNAL) Return C{B{self} * scalar B{factor}} as L{Fsum}, C{0.0} or C{self}.
1581 '''
1582 # assert isscalar(factor)
1583 if self._ps and self._finite(factor, op):
1584 f = self if factor == _1_0 else (
1585 self._neg if factor == _N_1_0 else
1586 self._ps_mul(op, factor).as_iscalar)
1587 else:
1588 f = _0_0
1589 return f
1591# @property_RO
1592# def _n_d(self):
1593# n, d = self.as_integer_ratio()
1594# return n / d
1596 @property_RO
1597 def _neg(self):
1598 '''(INTERNAL) Return C{Fsum(-self)} or scalar C{NEG0}.
1599 '''
1600 return _Psum(self._ps_neg) if self._ps else NEG0
1602 @property_RO
1603 def partials(self):
1604 '''Get this instance' current, partial sums (C{tuple} of C{float}s).
1605 '''
1606 return tuple(self._ps)
1608 def pow(self, x, *mod, **raiser_RESIDUAL):
1609 '''Return C{B{self}**B{x}} as L{Fsum}.
1611 @arg x: The exponent (C{scalar} or L{Fsum}).
1612 @arg mod: Optional modulus (C{int} or C{None}) for the 3-argument
1613 C{pow(B{self}, B{other}, B{mod})} version.
1614 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} (C{bool}) to
1615 ignore L{ResidualError}s and C{B{RESIDUAL}=scalar}
1616 to override the L{RESIDUAL<Fsum.RESIDUAL>}.
1618 @return: The C{pow(self, B{x})} or C{pow(self, B{x}, *B{mod})}
1619 result (L{Fsum}).
1621 @raise ResidualError: Non-zero, significant residual or invalid
1622 B{C{RESIDUAL}}.
1624 @note: If B{C{mod}} is given as C{None}, the result will be an
1625 C{integer} L{Fsum} provided this instance C{is_integer}
1626 or set to C{integer} by an L{Fsum.fint} call.
1628 @see: Methods L{Fsum.__ipow__}, L{Fsum.fint}, L{Fsum.is_integer}
1629 and L{Fsum.root}.
1630 '''
1631 f = self._copy_2(self.pow)
1632 return f._fpow(x, _pow_op_, *mod, **raiser_RESIDUAL) # f = pow(f, x, *mod)
1634 def _pow(self, other, unused, op, **raiser_RESIDUAL):
1635 '''Return C{B{self} ** B{other}}.
1636 '''
1637 if _isFsumTuple(other):
1638 f = self._pow_Fsum(other, op, **raiser_RESIDUAL)
1639 elif self._scalar(other, op):
1640 x = self._finite(other, op)
1641 f = self._pow_scalar(x, other, op, **raiser_RESIDUAL)
1642 else:
1643 f = self._pow_0_1(0, other)
1644 return f
1646 def _pow_0_1(self, x, other):
1647 '''(INTERNAL) Return B{C{self}**1} or C{B{self}**0 == 1.0}.
1648 '''
1649 return self if x else (1 if isint(other) and self.is_integer() else _1_0)
1651 def _pow_2_3(self, b, x, other, op, *mod, **raiser_RESIDUAL):
1652 '''(INTERNAL) 2-arg C{pow(B{b}, scalar B{x})} and 3-arg C{pow(B{b},
1653 B{x}, int B{mod} or C{None})}, embellishing errors.
1654 '''
1656 if mod: # b, x, mod all C{int}, unless C{mod} is C{None}
1657 m = mod[0]
1658 # assert _isFsumTuple(b)
1660 def _s(s, r):
1661 R = self._raiser(r, s, **raiser_RESIDUAL)
1662 if R:
1663 raise self._ResidualError(op, other, r, mod=m, **R)
1664 return s
1666 b = _s(*(b._fprs2 if m is None else b._fint2))
1667 x = _s(*_2scalar2(x))
1669 try:
1670 # 0**INF == 0.0, 1**INF == 1.0, -1**2.3 == -(1**2.3)
1671 s = pow(b, x, *mod)
1672 if iscomplex(s):
1673 # neg**frac == complex in Python 3+, but ValueError in 2-
1674 raise ValueError(_strcomplex(s, b, x, *mod))
1675 return self._finite(s)
1676 except Exception as X:
1677 raise self._ErrorX(X, op, other, *mod)
1679 def _pow_Fsum(self, other, op, **raiser_RESIDUAL):
1680 '''(INTERNAL) Return C{B{self} **= B{other}} for C{_isFsumTuple(other)}.
1681 '''
1682 # assert _isFsumTuple(other)
1683 x, r = other._fprs2
1684 f = self._pow_scalar(x, other, op, **raiser_RESIDUAL)
1685 if f and r:
1686 f *= self._pow_scalar(r, other, op, **raiser_RESIDUAL)
1687 return f
1689 def _pow_int(self, x, other, op, **raiser_RESIDUAL):
1690 '''(INTERNAL) Return C{B{self} **= B{x}} for C{int B{x} >= 0}.
1691 '''
1692 # assert isint(x) and x >= 0
1693 ps = self._ps
1694 if len(ps) > 1:
1695 _mul_Fsum = Fsum._mul_Fsum
1696 if x > 4:
1697 p = self
1698 f = self if (x & 1) else _Psum_(_1_0)
1699 m = x >> 1 # // 2
1700 while m:
1701 p = _mul_Fsum(p, p, op) # p **= 2
1702 if (m & 1):
1703 f = _mul_Fsum(f, p, op) # f *= p
1704 m >>= 1 # //= 2
1705 elif x > 1: # self**2, 3, or 4
1706 f = _mul_Fsum(self, self, op)
1707 if x > 2: # self**3 or 4
1708 p = self if x < 4 else f
1709 f = _mul_Fsum(f, p, op)
1710 else: # self**1 or self**0 == 1 or _1_0
1711 f = self._pow_0_1(x, other)
1712 elif ps: # self._ps[0]**x
1713 f = self._pow_2_3(ps[0], x, other, op, **raiser_RESIDUAL)
1714 else: # PYCHOK no cover
1715 # 0**pos_int == 0, but 0**0 == 1
1716 f = 0 if x else 1
1717 return f
1719 def _pow_scalar(self, x, other, op, **raiser_RESIDUAL):
1720 '''(INTERNAL) Return C{self**B{x}} for C{scalar B{x}}.
1721 '''
1722 s, r = self._fprs2
1723 if r:
1724 # assert s != 0
1725 if isint(x, both=True): # self**int
1726 x = int(x)
1727 y = abs(x)
1728 if y > 1:
1729 f = self._pow_int(y, other, op, **raiser_RESIDUAL)
1730 if x > 0: # i.e. > 1
1731 return f # Fsum or scalar
1732 # assert x < 0 # i.e. < -1
1733 if _isFsum(f):
1734 s, r = f._fprs2
1735 if r:
1736 return _1_Over(f, op, **raiser_RESIDUAL)
1737 else: # scalar
1738 s = f
1739 # use s**(-1) to get the CPython
1740 # float_pow error iff s is zero
1741 x = -1
1742 elif x < 0: # self**(-1)
1743 return _1_Over(self, op, **raiser_RESIDUAL) # 1 / self
1744 else: # self**1 or self**0
1745 return self._pow_0_1(x, other) # self, 1 or 1.0
1746 else: # self**fractional
1747 R = self._raiser(r, s, **raiser_RESIDUAL)
1748 if R:
1749 raise self._ResidualError(op, other, r, **R)
1750 n, d = self.as_integer_ratio()
1751 if abs(n) > abs(d):
1752 n, d, x = d, n, (-x)
1753 s = n / d
1754 # assert isscalar(s) and isscalar(x)
1755 return self._pow_2_3(s, x, other, op, **raiser_RESIDUAL)
1757 def _ps_acc(self, ps, xs, up=True, **unused):
1758 '''(INTERNAL) Accumulate C{xs} scalars into list C{ps}.
1759 '''
1760 n = 0
1761 _2s = _2sum
1762 for x in (tuple(xs) if xs is ps else xs):
1763 # assert isscalar(x) and _isfinite(x)
1764 if x:
1765 i = 0
1766 for p in ps:
1767 x, p = _2s(x, p)
1768 if p:
1769 ps[i] = p
1770 i += 1
1771 ps[i:] = (x,) if x else ()
1772 n += 1
1773 if n:
1774 self._n += n
1775 # Fsum._ps_max = max(Fsum._ps_max, len(ps))
1776 if up:
1777 self._update()
1778 return ps
1780 def _ps_mul(self, op, *factors):
1781 '''(INTERNAL) Multiply this instance' C{partials} with
1782 each scalar C{factor} and accumulate into an C{Fsum}.
1783 '''
1784 def _pfs(ps, fs):
1785 if len(ps) < len(fs):
1786 ps, fs = fs, ps
1787 _fin = _isfinite
1788 for f in fs:
1789 for p in ps:
1790 p *= f
1791 yield p if _fin(p) else self._finite(p, op)
1793 return Fsum()._facc_scalar(_pfs(self._ps, factors), up=False)
1795 @property_RO
1796 def _ps_neg(self):
1797 '''(INTERNAL) Yield the partials, I{negated}.
1798 '''
1799 for p in self._ps:
1800 yield -p
1802 def _ps_1sum(self, *less):
1803 '''(INTERNAL) Return the partials sum, 1-primed C{less} some scalars.
1804 '''
1805 def _1pls(ps, ls):
1806 yield _1_0
1807 for p in ps:
1808 yield p
1809 for p in ls:
1810 yield -p
1811 yield _N_1_0
1813 return _fsum(_1pls(self._ps, less))
1815 def _raiser(self, r, s, raiser=True, **RESIDUAL):
1816 '''(INTERNAL) Does ratio C{r / s} exceed the RESIDUAL threshold
1817 I{and} is residual C{r} I{non-zero} or I{significant} (for a
1818 negative respectively positive C{RESIDUAL} threshold)?
1819 '''
1820 if r and raiser:
1821 t = self._RESIDUAL
1822 if RESIDUAL:
1823 t = _threshold(_xkwds_get(RESIDUAL, RESIDUAL=t))
1824 if t < 0 or (s + r) != s:
1825 q = (r / s) if s else s # == 0.
1826 if fabs(q) > fabs(t):
1827 return dict(ratio=q, R=t)
1828 return {}
1830 rdiv = __rtruediv__
1832 @property_RO
1833 def real(self):
1834 '''Get the C{real} part of this instance (C{float}).
1836 @see: Methods L{Fsum.__float__} and L{Fsum.fsum}
1837 and properties L{Fsum.ceil}, L{Fsum.floor},
1838 L{Fsum.imag} and L{Fsum.residual}.
1839 '''
1840 return float(self._fprs)
1842 @property_RO
1843 def residual(self):
1844 '''Get this instance' residual (C{float} or C{int}): the
1845 C{sum(partials)} less the precision running sum C{fsum}.
1847 @note: The C{residual is INT0} iff the precision running
1848 C{fsum} is considered to be I{exact}.
1850 @see: Methods L{Fsum.fsum}, L{Fsum.fsum2} and L{Fsum.is_exact}.
1851 '''
1852 return self._fprs2.residual
1854 def RESIDUAL(self, *threshold):
1855 '''Get and set this instance' I{ratio} for raising L{ResidualError}s,
1856 overriding the default from env variable C{PYGEODESY_FSUM_RESIDUAL}.
1858 @arg threshold: If C{scalar}, the I{ratio} to exceed for raising
1859 L{ResidualError}s in division and exponention, if
1860 C{None} restore the default set with env variable
1861 C{PYGEODESY_FSUM_RESIDUAL} or if omitted, keep the
1862 current setting.
1864 @return: The previous C{RESIDUAL} setting (C{float}), default C{0.0}.
1866 @raise ResidualError: Invalid B{C{threshold}}.
1868 @note: L{ResidualError}s may be thrown if the non-zero I{ratio}
1869 C{residual / fsum} exceeds the given B{C{threshold}} and
1870 if the C{residual} is non-zero and I{significant} vs the
1871 C{fsum}, i.e. C{(fsum + residual) != fsum} and if optional
1872 keyword argument C{raiser=False} is missing. Specify a
1873 negative B{C{threshold}} for only non-zero C{residual}
1874 testing without I{significant}.
1875 '''
1876 r = self._RESIDUAL
1877 if threshold:
1878 t = threshold[0]
1879 self._RESIDUAL = Fsum._RESIDUAL if t is None else ( # for ...
1880 (_0_0 if t else _1_0) if isbool(t) else
1881 _threshold(t)) # ... backward compatibility
1882 return r
1884 def _ResidualError(self, op, other, residual, **mod_R):
1885 '''(INTERNAL) Non-zero B{C{residual}} etc.
1886 '''
1887 def _p(mod=None, R=0, **unused): # ratio=0
1888 return (_non_zero_ if R < 0 else _significant_) \
1889 if mod is None else _integer_
1891 t = _stresidual(_p(**mod_R), residual, **mod_R)
1892 return self._Error(op, other, ResidualError, txt=t)
1894 def root(self, root, **raiser_RESIDUAL):
1895 '''Return C{B{self}**(1 / B{root})} as L{Fsum}.
1897 @arg root: The order (C{scalar} or L{Fsum}), non-zero.
1898 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} (C{bool}) to
1899 ignore L{ResidualError}s and C{B{RESIDUAL}=scalar}
1900 to override the L{RESIDUAL<Fsum.RESIDUAL>}.
1902 @return: The C{self ** (1 / B{root})} result (L{Fsum}).
1904 @raise ResidualError: Non-zero, significant residual or invalid
1905 B{C{RESIDUAL}}.
1907 @see: Method L{Fsum.pow}.
1908 '''
1909 x = _1_Over(root, _truediv_op_, **raiser_RESIDUAL)
1910 f = self._copy_2(self.root)
1911 return f._fpow(x, f.name, **raiser_RESIDUAL) # == pow(f, x)
1913 def _scalar(self, other, op, **txt):
1914 '''(INTERNAL) Return scalar C{other}.
1915 '''
1916 if isscalar(other):
1917 return other
1918 raise self._Error(op, other, _TypeError, **txt) # _invalid_
1920 def signOf(self, res=True):
1921 '''Determine the sign of this instance.
1923 @kwarg res: If C{True} consider, otherwise
1924 ignore the residual (C{bool}).
1926 @return: The sign (C{int}, -1, 0 or +1).
1927 '''
1928 s, r = self._fprs2
1929 r = (-r) if res else 0
1930 return _signOf(s, r)
1932 def toRepr(self, **lenc_prec_sep_fmt): # PYCHOK signature
1933 '''Return this C{Fsum} instance as representation.
1935 @kwarg lenc_prec_sep_fmt: Optional keyword arguments
1936 for method L{Fsum.toStr}.
1938 @return: This instance (C{repr}).
1939 '''
1940 return Fmt.repr_at(self, self.toStr(**lenc_prec_sep_fmt))
1942 def toStr(self, lenc=True, **prec_sep_fmt): # PYCHOK signature
1943 '''Return this C{Fsum} instance as string.
1945 @kwarg lenc: If C{True} include the current C{[len]} of this
1946 L{Fsum} enclosed in I{[brackets]} (C{bool}).
1947 @kwarg prec_sep_fmt: Optional keyword arguments for method
1948 L{Fsum2Tuple.toStr}.
1950 @return: This instance (C{str}).
1951 '''
1952 p = self.classname
1953 if lenc:
1954 p = Fmt.SQUARE(p, len(self))
1955 n = _enquote(self.name, white=_UNDER_)
1956 t = self._fprs2.toStr(**prec_sep_fmt)
1957 return NN(p, _SPACE_, n, t)
1959 def _truediv(self, other, op, **raiser_RESIDUAL):
1960 '''(INTERNAL) Return C{B{self} / B{other}} as an L{Fsum}.
1961 '''
1962 f = self._copy_2(self.__truediv__)
1963 return f._ftruediv(other, op, **raiser_RESIDUAL)
1965 def _update(self, updated=True): # see ._fset
1966 '''(INTERNAL) Zap all cached C{Property_RO} values.
1967 '''
1968 if updated:
1969 _pop = self.__dict__.pop
1970 for p in _ROs:
1971 _ = _pop(p, None)
1972# Fsum._fint2._update(self)
1973# Fsum._fprs ._update(self)
1974# Fsum._fprs2._update(self)
1975 return self # for .fset_
1977_ROs = _allPropertiesOf_n(3, Fsum, Property_RO) # PYCHOK see Fsum._update
1980def _Float_Int(arg, **name_Error):
1981 '''(INTERNAL) Unit of L{Fsum2Tuple} items.
1982 '''
1983 U = Int if isint(arg) else Float
1984 return U(arg, **name_Error)
1987class DivMod2Tuple(_NamedTuple):
1988 '''2-Tuple C{(div, mod)} with the quotient C{div} and remainder
1989 C{mod} results of a C{divmod} operation.
1991 @note: Quotient C{div} an C{int} in Python 3+ but a C{float}
1992 in Python 2-. Remainder C{mod} an L{Fsum} instance.
1993 '''
1994 _Names_ = (_div_, _mod_)
1995 _Units_ = (_Float_Int, Fsum)
1998class Fsum2Tuple(_NamedTuple): # in .fstats
1999 '''2-Tuple C{(fsum, residual)} with the precision running C{fsum}
2000 and the C{residual}, the sum of the remaining partials. Each
2001 item is C{float} or C{int}.
2003 @note: If the C{residual is INT0}, the C{fsum} is considered
2004 to be I{exact}, see method L{Fsum2Tuple.is_exact}.
2005 '''
2006 _Names_ = ( Fsum.fsum.__name__, Fsum.residual.name)
2007 _Units_ = (_Float_Int, _Float_Int)
2009 def __abs__(self): # in .fmath
2010 return self._Fsum.__abs__()
2012 def __bool__(self): # PYCHOK Python 3+
2013 return bool(self._Fsum)
2015 def __eq__(self, other):
2016 return self._other_op(other, self.__eq__)
2018 def __float__(self):
2019 return self._Fsum.__float__()
2021 def __ge__(self, other):
2022 return self._other_op(other, self.__ge__)
2024 def __gt__(self, other):
2025 return self._other_op(other, self.__gt__)
2027 def __le__(self, other):
2028 return self._other_op(other, self.__le__)
2030 def __lt__(self, other):
2031 return self._other_op(other, self.__lt__)
2033 def __int__(self):
2034 return self._Fsum.__int__()
2036 def __ne__(self, other):
2037 return self._other_op(other, self.__ne__)
2039 def __neg__(self):
2040 return self._Fsum.__neg__()
2042 __nonzero__ = __bool__ # Python 2-
2044 def __pos__(self):
2045 return self._Fsum.__pos__()
2047 def as_integer_ratio(self):
2048 '''Return this instance as the ratio of 2 integers.
2050 @see: Method L{Fsum.as_integer_ratio} for further details.
2051 '''
2052 return self._Fsum.as_integer_ratio()
2054 @property_RO
2055 def _fint2(self):
2056 return self._Fsum._fint2
2058 @property_RO
2059 def _fprs2(self):
2060 return self._Fsum._fprs2
2062 @Property_RO
2063 def _Fsum(self): # this C{Fsum2Tuple} as L{Fsum}, in .fstats
2064 s, r = _s_r(*self)
2065 ps = (r, s) if r else (s,)
2066 return _Psum(ps, name=self.name)
2068 def Fsum_(self, *xs, **name_RESIDUAL):
2069 '''Return this C{Fsum2Tuple} as an L{Fsum} plus some C{xs}.
2070 '''
2071 f = _Psum(self._Fsum._ps, **name_RESIDUAL)
2072 return f._facc_1(xs, up=False) if xs else f
2074 def is_exact(self):
2075 '''Is this L{Fsum2Tuple} considered to be exact? (C{bool}).
2076 '''
2077 return self._Fsum.is_exact()
2079 def is_integer(self):
2080 '''Is this L{Fsum2Tuple} C{integer}? (C{bool}).
2081 '''
2082 return self._Fsum.is_integer()
2084 def _mul_scalar(self, other, op): # for Fsum._fmul
2085 return self._Fsum._mul_scalar(other, op)
2087 @property_RO
2088 def _n(self):
2089 return self._Fsum._n
2091 def _other_op(self, other, which):
2092 C, s = (tuple, self) if isinstance(other, tuple) else (Fsum, self._Fsum)
2093 return getattr(C, which.__name__)(s, other)
2095 @property_RO
2096 def _ps(self):
2097 return self._Fsum._ps
2099 @property_RO
2100 def _ps_neg(self):
2101 return self._Fsum._ps_neg
2103 def signOf(self, **res):
2104 '''Like method L{Fsum.signOf}.
2105 '''
2106 return self._Fsum.signOf(**res)
2108 def toStr(self, fmt=Fmt.g, **prec_sep): # PYCHOK signature
2109 '''Return this L{Fsum2Tuple} as string (C{str}).
2111 @kwarg fmt: Optional C{float} format (C{letter}).
2112 @kwarg prec_sep: Optional keyword arguments for function
2113 L{fstr<streprs.fstr>}.
2114 '''
2115 return Fmt.PAREN(fstr(self, fmt=fmt, strepr=str, force=False, **prec_sep))
2117_Fsum_Fsum2Tuple_types = Fsum, Fsum2Tuple # PYCHOK lines
2120class ResidualError(_ValueError):
2121 '''Error raised for a division, power or root operation of
2122 an L{Fsum} instance with a C{residual} I{ratio} exceeding
2123 the L{RESIDUAL<Fsum.RESIDUAL>} threshold.
2125 @see: Module L{pygeodesy.fsums} and method L{Fsum.RESIDUAL}.
2126 '''
2127 pass
2130try:
2131 from math import fsum as _fsum # precision IEEE-754 sum, Python 2.6+
2133 # make sure _fsum works as expected (XXX check
2134 # float.__getformat__('float')[:4] == 'IEEE'?)
2135 if _fsum((1, 1e101, 1, -1e101)) != 2: # PYCHOK no cover
2136 del _fsum # nope, remove _fsum ...
2137 raise ImportError # ... use _fsum below
2139 Fsum._math_fsum = _sum = _fsum # PYCHOK exported
2140except ImportError:
2141 _sum = sum # Fsum(NAN) exception fall-back, in .elliptic
2143 def _fsum(xs):
2144 '''(INTERNAL) Precision summation, Python 2.5-.
2145 '''
2146 F = Fsum()
2147 F.name = _fsum.__name__
2148 return F._facc(xs, up=False)._fprs2.fsum
2151def fsum(xs, floats=False):
2152 '''Precision floating point summation based on/like Python's C{math.fsum}.
2154 @arg xs: Iterable of items to add (each C{scalar} or an L{Fsum} or L{Fsum2Tuple}
2155 instance).
2156 @kwarg floats: Use C{B{floats}=True} iff I{all} B{C{xs}} items are I{known to
2157 be scalar} (C{bool}).
2159 @return: Precision C{fsum} (C{float}).
2161 @raise OverflowError: Partial C{2sum} overflow.
2163 @raise TypeError: Non-scalar B{C{xs}} item.
2165 @raise ValueError: Invalid or non-finite B{C{xs}} item.
2167 @note: Exception and I{non-finite} handling may differ if not based
2168 on Python's C{math.fsum}.
2170 @see: Class L{Fsum} and methods L{Fsum.fsum} and L{Fsum.fadd}.
2171 '''
2172 return _fsum(xs if floats is True else _2floats(xs)) if xs else _0_0 # PYCHOK yield
2175def fsum_(*xs, **floats):
2176 '''Precision floating point summation of all positional items.
2178 @arg xs: Items to add (each C{scalar} or an L{Fsum} or L{Fsum2Tuple} instance),
2179 all positional.
2180 @kwarg floats: Use C{B{floats}=True} iff I{all} B{C{xs}} items are I{known to
2181 be scalar} (C{bool}).
2183 @see: Function L{fsum<fsums.fsum>} for further details.
2184 '''
2185 return _fsum(xs if _xkwds_get(floats, floats=False) is True else
2186 _2floats(xs, origin=1)) if xs else _0_0 # PYCHOK yield
2189def fsumf_(*xs):
2190 '''Precision floating point summation iff I{all} C{B{xs}} items are I{known to be scalar}.
2192 @see: Function L{fsum_<fsums.fsum_>} for further details.
2193 '''
2194 return _fsum(xs) if xs else _0_0
2197def fsum1(xs, floats=False):
2198 '''Precision floating point summation, 1-primed.
2200 @arg xs: Iterable of items to add (each C{scalar} or an L{Fsum} or L{Fsum2Tuple}
2201 instance).
2202 @kwarg floats: Use C{B{floats}=True} iff I{all} B{C{xs}} items are I{known to
2203 be scalar} (C{bool}).
2205 @see: Function L{fsum<fsums.fsum>} for further details.
2206 '''
2207 return _fsum(_1primed(xs if floats is True else _2floats(xs))) if xs else _0_0 # PYCHOK yield
2210def fsum1_(*xs, **floats):
2211 '''Precision floating point summation, 1-primed of all positional items.
2213 @arg xs: Items to add (each C{scalar} or an L{Fsum} or L{Fsum2Tuple} instance),
2214 all positional.
2215 @kwarg floats: Use C{B{floats}=True} iff I{all} B{C{xs}} items are I{known to
2216 be scalar} (C{bool}).
2218 @see: Function L{fsum_<fsums.fsum_>} for further details.
2219 '''
2220 return _fsum(_1primed(xs if _xkwds_get(floats, floats=False) is True else
2221 _2floats(xs, origin=1))) if xs else _0_0 # PYCHOK yield
2224def fsum1f_(*xs):
2225 '''Precision floating point summation iff I{all} C{B{xs}} items are I{known to be scalar}.
2227 @see: Function L{fsum_<fsums.fsum_>} for further details.
2228 '''
2229 return _fsum(_1primed(xs)) if xs else _0_0
2232if __name__ == '__main__':
2234 # usage: [env _psum=fsum] python3 -m pygeodesy.fsums
2236 if _getenv(_psum.__name__, NN) == _fsum.__name__:
2237 _psum = _fsum
2239 def _test(n):
2240 # copied from Hettinger, see L{Fsum} reference
2241 from pygeodesy import frandoms, printf
2243 printf(_fsum.__name__, end=_COMMASPACE_)
2244 printf(_psum.__name__, end=_COMMASPACE_)
2246 F = Fsum()
2247 if F.is_math_fsum():
2248 for t in frandoms(n, seeded=True):
2249 assert float(F.fset_(*t)) == _fsum(t)
2250 printf(_DOT_, end=NN)
2251 printf(NN)
2253 _test(128)
2255# **) MIT License
2256#
2257# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.
2258#
2259# Permission is hereby granted, free of charge, to any person obtaining a
2260# copy of this software and associated documentation files (the "Software"),
2261# to deal in the Software without restriction, including without limitation
2262# the rights to use, copy, modify, merge, publish, distribute, sublicense,
2263# and/or sell copies of the Software, and to permit persons to whom the
2264# Software is furnished to do so, subject to the following conditions:
2265#
2266# The above copyright notice and this permission notice shall be included
2267# in all copies or substantial portions of the Software.
2268#
2269# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
2270# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
2271# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
2272# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
2273# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
2274# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
2275# OTHER DEALINGS IN THE SOFTWARE.