Coverage for pygeodesy/fsums.py: 97%
873 statements
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2# -*- coding: utf-8 -*-
4u'''Class L{Fsum} for precision floating point summation and I{running}
5summation based on, respectively similar to Python's C{math.fsum}.
7Generally, an L{Fsum} instance is considered a C{float} plus a small or zero
8C{residual} value, see property L{Fsum.residual}. However, there are several
9C{integer} L{Fsum} cases, for example the result of C{ceil}, C{floor},
10C{Fsum.__floordiv__} and methods L{Fsum.fint} and L{Fsum.fint2}.
12Also, L{Fsum} methods L{Fsum.pow}, L{Fsum.__ipow__}, L{Fsum.__pow__} and
13L{Fsum.__rpow__} return a (very long) C{int} if invoked with optional argument
14C{mod} set to C{None}. The C{residual} of an C{integer} L{Fsum} may be between
15C{-1.0} and C{+1.0}, including C{INT0} if considered to be I{exact}.
17Set env variable C{PYGEODESY_FSUM_RESIDUAL} to a C{float} string greater than
18C{"0.0"} as the threshold to throw a L{ResidualError} for a division, power or
19root operation of an L{Fsum} instance with a C{residual} I{ratio} exceeding
20the threshold. See methods L{Fsum.RESIDUAL}, L{Fsum.pow}, L{Fsum.__ipow__}
21and L{Fsum.__itruediv__}.
22'''
23# make sure int/int division yields float quotient, see .basics
24from __future__ import division as _; del _ # PYCHOK semicolon
26from pygeodesy.basics import isbool, iscomplex, isint, isscalar, itemsorted, \
27 signOf, _signOf
28from pygeodesy.constants import INT0, _isfinite, NEG0, _pos_self, \
29 _0_0, _1_0, _N_1_0, Float, Int
30from pygeodesy.errors import _OverflowError, _TypeError, _ValueError, \
31 _xError, _xError2, _xkwds_get
32from pygeodesy.interns import NN, _arg_, _COMMASPACE_, _DASH_, _DOT_, \
33 _enquote, _EQUAL_, _from_, _LANGLE_, _NOTEQUAL_, \
34 _not_finite_, _PERCENT_, _PLUS_, _RANGLE_, \
35 _SLASH_, _SPACE_, _STAR_, _UNDER_
36from pygeodesy.lazily import _ALL_LAZY, _getenv, _sys_version_info2
37from pygeodesy.named import _Named, _NamedTuple, _NotImplemented
38from pygeodesy.props import _allPropertiesOf_n, deprecated_property_RO, \
39 Property_RO, property_RO
40from pygeodesy.streprs import Fmt, fstr, unstr
41# from pygeodesy.units import Float, Int # from .constants
43from math import ceil as _ceil, fabs, floor as _floor # PYCHOK used! .ltp
45__all__ = _ALL_LAZY.fsums
46__version__ = '24.05.08'
48_abs = abs
49_add_op_ = _PLUS_ # in .auxilats.auxAngle
50_eq_op_ = _EQUAL_ * 2 # _DEQUAL_
51_div_ = 'div'
52_Float = float # in .fstats
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_isAn = isinstance # in .fstats
60_le_op_ = _LANGLE_ + _EQUAL_
61_len = len
62_List = list
63_lt_op_ = _LANGLE_
64_mod_ = 'mod'
65_mod_op_ = _PERCENT_
66_mul_op_ = _STAR_
67_ne_op_ = _NOTEQUAL_
68_non_zero_ = 'non-zero'
69_pow_op_ = _STAR_ * 2 # _DSTAR_
70_significant_ = 'significant'
71_sub_op_ = _DASH_ # in .auxilats.auxAngle
72_threshold_ = 'threshold'
73_truediv_op_ = _SLASH_
74_Tuple = tuple # in .fstats
75_divmod_op_ = _floordiv_op_ + _mod_op_
76_isub_op_ = _sub_op_ + _fset_op_ # in .auxilats.auxAngle
79def _2delta(*ab):
80 '''(INTERNAL) Helper for C{Fsum._fsum2}.
81 '''
82 try:
83 a, b = _2sum(*ab)
84 except _OverflowError:
85 a, b = ab
86 return _Float(a if fabs(a) > fabs(b) else b)
89def _2error(unused): # in .fstats
90 '''(INTERNAL) Throw a C{not-finite} exception.
91 '''
92 raise ValueError(_not_finite_)
95def _2finite(x):
96 '''(INTERNAL) return C{float(x)} if finite.
97 '''
98 x = _Float(x)
99 return x if _isfinite(x) else _2error(x)
102def _2float(index=None, **name_value): # in .fmath, .fstats
103 '''(INTERNAL) Raise C{TypeError} or C{ValueError} if not scalar or infinite.
104 '''
105 n, v = name_value.popitem() # _xkwds_item2(name_value)
106 try:
107 return _2finite(v)
108 except Exception as X:
109 raise _xError(X, Fmt.INDEX(n, index), v)
112def _X_ps(X): # for _2floats only
113 return X._ps
116def _2floats(xs, origin=0, _X=_X_ps, _x=_Float):
117 '''(INTERNAL) Yield each B{C{xs}} as a C{float}.
118 '''
119 try:
120 i, x = origin, None
121 _fin = _isfinite
122 _FsT = _Fsum_Fsum2Tuple_types
123 _is = _isAn
124 for x in xs:
125 if _is(x, _FsT):
126 for p in _X(x._Fsum):
127 yield p
128 else:
129 f = _x(x)
130 yield f if _fin(f) else _2error(f)
131 i += 1
132 except Exception as X:
133 raise _xError(X, Fmt.INDEX(xs=i), x)
136def _Fsumf_(*xs): # floats=True, in .auxLat, ...
137 '''(INTERNAL) An C{Fsum} of I{known scalars}.
138 '''
139 return Fsum()._facc_scalar(xs, up=False)
142def _Fsum1f_(*xs): # floats=True, in .albers, ...
143 '''(INTERNAL) An C{Fsum} of I{known scalars}, 1-primed.
144 '''
145 return Fsum()._facc_scalar(_1primed(xs), up=False)
148def _2halfeven(s, r, p):
149 '''(INTERNAL) Round half-even.
150 '''
151 if (p > 0 and r > 0) or \
152 (p < 0 and r < 0): # signs match
153 r *= 2
154 t = s + r
155 if r == (t - s):
156 s = t
157 return s
160def _isFsum(x): # in .fmath
161 '''(INTERNAL) Is C{x} an C{Fsum} instance?
162 '''
163 return _isAn(x, Fsum)
166def _isFsumTuple(x): # in .fmath
167 '''(INTERNAL) Is C{x} an C{Fsum} or C{Fsum2Tuple} instance?
168 '''
169 return _isAn(x, _Fsum_Fsum2Tuple_types)
172def _1_Over(x, op, **raiser_RESIDUAL): # vs _1_over
173 '''(INTERNAL) Return C{Fsum(1) / B{x}}.
174 '''
175 return _Psum_(_1_0)._ftruediv(x, op, **raiser_RESIDUAL)
178def _1primed(xs): # in .fmath
179 '''(INTERNAL) 1-Primed summation of iterable C{xs}
180 items, all I{known} to be C{scalar}.
181 '''
182 yield _1_0
183 for x in xs:
184 yield x
185 yield _N_1_0
188def _psum(ps): # PYCHOK used!
189 '''(INTERNAL) Partials summation, updating C{ps}.
190 '''
191 # assert _isAn(ps, _List)
192 i = _len(ps) - 1
193 s = _0_0 if i < 0 else ps[i]
194 _2s = _2sum
195 while i > 0:
196 i -= 1
197 s, r = _2s(s, ps[i])
198 if r: # sum(ps) became inexact
199 if s:
200 ps[i:] = r, s
201 if i > 0:
202 s = _2halfeven(s, r, ps[i-1])
203 break # return s
204 s = r # PYCHOK no cover
205 ps[i:] = s,
206 return s
209def _Psum(ps, **name_RESIDUAL):
210 '''(INTERNAL) Return an C{Fsum} from I{ordered} partials C{ps}.
211 '''
212 f = Fsum(**name_RESIDUAL) if name_RESIDUAL else Fsum()
213 if ps:
214 f._ps[:] = ps
215 f._n = _len(f._ps)
216 return f
219def _Psum_(*ps, **name_RESIDUAL):
220 '''(INTERNAL) Return an C{Fsum} from 1 or 2 known scalar(s) C{ps}.
221 '''
222 return _Psum(ps, **name_RESIDUAL)
225def _2scalar2(other):
226 '''(INTERNAL) Return 2-tuple C{(other, r)} with C{other} as C{int},
227 C{float} or C{as-is} and C{r} the residual of C{as-is}.
228 '''
229 if _isFsumTuple(other):
230 s, r = other._fint2
231 if r:
232 s, r = other._fprs2
233 if r: # PYCHOK no cover
234 s = other # L{Fsum} as-is
235 else:
236 r = 0
237 s = other # C{type} as-is
238 if isint(s, both=True):
239 s = int(s)
240 return s, r
243def _s_r(s, r):
244 '''(INTERNAL) Return C{(s, r)}, I{ordered}.
245 '''
246 if r:
247 if fabs(s) < fabs(r):
248 s, r = r, (s or INT0)
249 else:
250 r = INT0
251 return s, r
254def _strcomplex(s, *args):
255 '''(INTERNAL) C{Complex} 2- or 3-arg C{pow} error as C{str}.
256 '''
257 c = _strcomplex.__name__[4:]
258 n = _DASH_(_len(args), _arg_)
259 t = unstr(pow, *args)
260 return _SPACE_(c, s, _from_, n, t)
263def _stresidual(prefix, residual, R=0, **mod_ratio):
264 '''(INTERNAL) Residual error txt C{str}.
265 '''
266 p = _stresidual.__name__[3:]
267 t = Fmt.PARENSPACED(p, Fmt(residual))
268 for n, v in itemsorted(mod_ratio):
269 p = Fmt.PARENSPACED(n, Fmt(v))
270 t = _COMMASPACE_(t, p)
271 return _SPACE_(prefix, t, Fmt.exceeds_R(R), _threshold_)
274def _2sum(a, b): # by .testFmath
275 '''(INTERNAL) Return C{a + b} as 2-tuple (sum, residual).
276 '''
277 s = a + b
278 if _isfinite(s):
279 if fabs(a) < fabs(b):
280 b, a = a, b
281 return s, (b - (s - a))
282 u = unstr(_2sum, a, b)
283 t = Fmt.PARENSPACED(_not_finite_, s)
284 raise _OverflowError(u, txt=t)
287def _threshold(threshold):
288 '''(INTERNAL) Get the L{ResidualError}s threshold.
289 '''
290 try:
291 t = _Float(threshold) or _0_0
292 return t if _isfinite(t) else _2error(t) # PYCHOK None
293 except Exception as x:
294 raise ResidualError(threshold=threshold, cause=x)
297class Fsum(_Named): # sync __methods__ with .vector3dBase.Vector3dBase
298 '''Precision floating point summation and I{running} summation.
300 Unlike Python's C{math.fsum}, this class accumulates values and provides intermediate,
301 I{running}, precision floating point summations. Accumulation may continue after any
302 intermediate, I{running} summuation.
304 @note: Values may be L{Fsum}, L{Fsum2Tuple}, C{int}, C{float} or C{scalar} instances,
305 any C{type} having method C{__float__} to convert the C{scalar} to a single
306 C{float}, except C{complex}.
308 @note: Handling of exceptions and C{inf}, C{INF}, C{nan} and C{NAN} differs from
309 Python's C{math.fsum}.
311 @see: U{Hettinger<https://GitHub.com/ActiveState/code/tree/master/recipes/Python/
312 393090_Binary_floating_point_summatiaccurate_full/recipe-393090.py>},
313 U{Kahan<https://WikiPedia.org/wiki/Kahan_summation_algorithm>}, U{Klein
314 <https://Link.Springer.com/article/10.1007/s00607-005-0139-x>}, Python 2.6+
315 file I{Modules/mathmodule.c} and the issue log U{Full precision summation
316 <https://Bugs.Python.org/issue2819>}.
317 '''
318 _math_fsum = None
319 _n = 0
320# _ps = [] # partial sums
321# _ps_max = 0 # max(Fsum._ps_max, _len(Fsum._ps))
322 _RESIDUAL = _threshold(_getenv('PYGEODESY_FSUM_RESIDUAL', _0_0))
324 def __init__(self, *xs, **name_RESIDUAL):
325 '''New L{Fsum} for I{running} precision floating point summation.
327 @arg xs: No, one or more items to add (each C{scalar} or an L{Fsum}
328 or L{Fsum2Tuple} instance), all positional.
329 @kwarg name_RESIDUAL: Optional C{B{name}=NN} for this L{Fsum} and
330 the C{B{RESIDUAL}=0.0} threshold for L{ResidualError}s.
332 @see: Methods L{Fsum.fadd} and L{Fsum.RESIDUAL}.
333 '''
334 if name_RESIDUAL:
336 def _n_R(name=NN, RESIDUAL=None):
337 return name, RESIDUAL
339 n, R = _n_R(**name_RESIDUAL)
340 if R is not None:
341 self.RESIDUAL(R)
342 if n:
343 self.name = n
345 self._ps = [] # [_0_0], see L{Fsum._fprs}
346 if xs:
347 self._facc_1(xs, up=False)
349 def __abs__(self):
350 '''Return this instance' absolute value as an L{Fsum}.
351 '''
352 s = self.signOf() # == self._cmp_0(0)
353 return (-self) if s < 0 else self._copy_2(self.__abs__)
355 def __add__(self, other):
356 '''Return C{B{self} + B{other}} as an L{Fsum}.
358 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar}.
360 @return: The sum (L{Fsum}).
362 @see: Methods L{Fsum.fadd_} and L{Fsum.fadd}.
363 '''
364 f = self._copy_2(self.__add__)
365 return f._fadd(other, _add_op_)
367 def __bool__(self): # PYCHOK Python 3+
368 '''Return C{True} if this instance is I{exactly} non-zero.
369 '''
370 s, r = self._fprs2
371 return bool(s or r) and s != -r # == self != 0
373 def __ceil__(self): # PYCHOK not special in Python 2-
374 '''Return this instance' C{math.ceil} as C{int} or C{float}.
376 @return: An C{int} in Python 3+, but C{float} in Python 2-.
378 @see: Methods L{Fsum.__floor__} and property L{Fsum.ceil}.
379 '''
380 return self.ceil
382 def __cmp__(self, other): # PYCHOK no cover
383 '''Compare this with an other instance or C{scalar}, Python 2-.
385 @return: -1, 0 or +1 (C{int}).
387 @raise TypeError: Incompatible B{C{other}} C{type}.
388 '''
389 s = self._cmp_0(other, self.cmp.__name__)
390 return _signOf(s, 0)
392 def __divmod__(self, other, **raiser_RESIDUAL):
393 '''Return C{divmod(B{self}, B{other})} as a L{DivMod2Tuple}
394 with quotient C{div} an C{int} in Python 3+ or C{float}
395 in Python 2- and remainder C{mod} an L{Fsum} instance.
397 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar} modulus.
398 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} (C{bool}) to
399 ignore L{ResidualError}s and C{B{RESIDUAL}=scalar}
400 to override the L{RESIDUAL<Fsum.RESIDUAL>}.
402 @raise ResidualError: Non-zero, significant residual or invalid
403 B{C{RESIDUAL}}.
405 @see: Method L{Fsum.fdiv}.
406 '''
407 f = self._copy_2(self.__divmod__)
408 return f._fdivmod2(other, _divmod_op_, **raiser_RESIDUAL)
410 def __eq__(self, other):
411 '''Compare this with an other instance or C{scalar}.
412 '''
413 return self._cmp_0(other, _eq_op_) == 0
415 def __float__(self):
416 '''Return this instance' current, precision running sum as C{float}.
418 @see: Methods L{Fsum.fsum} and L{Fsum.int_float}.
419 '''
420 return _Float(self._fprs)
422 def __floor__(self): # PYCHOK not special in Python 2-
423 '''Return this instance' C{math.floor} as C{int} or C{float}.
425 @return: An C{int} in Python 3+, but C{float} in Python 2-.
427 @see: Methods L{Fsum.__ceil__} and property L{Fsum.floor}.
428 '''
429 return self.floor
431 def __floordiv__(self, other):
432 '''Return C{B{self} // B{other}} as an L{Fsum}.
434 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar} divisor.
436 @return: The C{floor} quotient (L{Fsum}).
438 @see: Methods L{Fsum.__ifloordiv__}.
439 '''
440 f = self._copy_2(self.__floordiv__)
441 return f._floordiv(other, _floordiv_op_)
443 def __format__(self, *other): # PYCHOK no cover
444 '''Not implemented.'''
445 return _NotImplemented(self, *other)
447 def __ge__(self, other):
448 '''Compare this with an other instance or C{scalar}.
449 '''
450 return self._cmp_0(other, _ge_op_) >= 0
452 def __gt__(self, other):
453 '''Compare this with an other instance or C{scalar}.
454 '''
455 return self._cmp_0(other, _gt_op_) > 0
457 def __hash__(self): # PYCHOK no cover
458 '''Return this instance' C{hash}.
459 '''
460 return hash(self._ps) # XXX id(self)?
462 def __iadd__(self, other):
463 '''Apply C{B{self} += B{other}} to this instance.
465 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar} instance.
467 @return: This instance, updated (L{Fsum}).
469 @raise TypeError: Invalid B{C{other}}, not
470 C{scalar} nor L{Fsum}.
472 @see: Methods L{Fsum.fadd_} and L{Fsum.fadd}.
473 '''
474 return self._fadd(other, _iadd_op_)
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}.
583 @return: This instance, updated (L{Fsum}).
585 @raise TypeError: Invalid B{C{other}} type.
587 @see: Methods L{Fsum.fsub_} and L{Fsum.fsub}.
588 '''
589 return self._fsub(other, _isub_op_)
591 def __iter__(self):
592 '''Return an C{iter}ator over a C{partials} duplicate.
593 '''
594 return iter(self.partials)
596 def __itruediv__(self, other, **raiser_RESIDUAL):
597 '''Apply C{B{self} /= B{other}} to this instance.
599 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar} divisor.
600 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} (C{bool}) to
601 ignore L{ResidualError}s and C{B{RESIDUAL}=scalar}
602 to override the L{RESIDUAL<Fsum.RESIDUAL>}.
604 @return: This instance, updated (L{Fsum}).
606 @raise OverflowError: Partial C{2sum} overflow.
608 @raise ResidualError: Non-zero, significant residual or invalid
609 B{C{RESIDUAL}}.
611 @raise TypeError: Invalid B{C{other}} type.
613 @raise ValueError: Invalid or non-finite B{C{other}}.
615 @raise ZeroDivisionError: Zero B{C{other}}.
617 @see: Method L{Fsum.__ifloordiv__}.
618 '''
619 return self._ftruediv(other, _truediv_op_ + _fset_op_, **raiser_RESIDUAL)
621 def __le__(self, other):
622 '''Compare this with an other instance or C{scalar}.
623 '''
624 return self._cmp_0(other, _le_op_) <= 0
626 def __len__(self):
627 '''Return the number of values accumulated (C{int}).
628 '''
629 return self._n
631 def __lt__(self, other):
632 '''Compare this with an other instance or C{scalar}.
633 '''
634 return self._cmp_0(other, _lt_op_) < 0
636 def __matmul__(self, other): # PYCHOK no cover
637 '''Not implemented.'''
638 return _NotImplemented(self, other)
640 def __mod__(self, other):
641 '''Return C{B{self} % B{other}} as an L{Fsum}.
643 @see: Method L{Fsum.__imod__}.
644 '''
645 f = self._copy_2(self.__mod__)
646 return f._fdivmod2(other, _mod_op_).mod
648 def __mul__(self, other):
649 '''Return C{B{self} * B{other}} as an L{Fsum}.
651 @see: Method L{Fsum.__imul__}.
652 '''
653 f = self._copy_2(self.__mul__)
654 return f._fmul(other, _mul_op_)
656 def __ne__(self, other):
657 '''Compare this with an other instance or C{scalar}.
658 '''
659 return self._cmp_0(other, _ne_op_) != 0
661 def __neg__(self):
662 '''Return I{a copy of} this instance, I{negated}.
663 '''
664 f = self._copy_2(self.__neg__)
665 return f._fset(self._neg)
667 def __pos__(self):
668 '''Return this instance I{as-is}, like C{float.__pos__()}.
669 '''
670 return self if _pos_self else self._copy_2(self.__pos__)
672 def __pow__(self, other, *mod): # PYCHOK 2 vs 3 args
673 '''Return C{B{self}**B{other}} as an L{Fsum}.
675 @see: Method L{Fsum.__ipow__}.
676 '''
677 f = self._copy_2(self.__pow__)
678 return f._fpow(other, _pow_op_, *mod)
680 def __radd__(self, other):
681 '''Return C{B{other} + B{self}} as an L{Fsum}.
683 @see: Method L{Fsum.__iadd__}.
684 '''
685 f = self._copy_2r(other, self.__radd__)
686 return f._fadd(self, _add_op_)
688 def __rdivmod__(self, other):
689 '''Return C{divmod(B{other}, B{self})} as 2-tuple
690 C{(quotient, remainder)}.
692 @see: Method L{Fsum.__divmod__}.
693 '''
694 f = self._copy_2r(other, self.__rdivmod__)
695 return f._fdivmod2(self, _divmod_op_)
697# def __repr__(self):
698# '''Return the default C{repr(this)}.
699# '''
700# return self.toRepr(lenc=True)
702 def __rfloordiv__(self, other):
703 '''Return C{B{other} // B{self}} as an L{Fsum}.
705 @see: Method L{Fsum.__ifloordiv__}.
706 '''
707 f = self._copy_2r(other, self.__rfloordiv__)
708 return f._floordiv(self, _floordiv_op_)
710 def __rmatmul__(self, other): # PYCHOK no cover
711 '''Not implemented.'''
712 return _NotImplemented(self, other)
714 def __rmod__(self, other):
715 '''Return C{B{other} % B{self}} as an L{Fsum}.
717 @see: Method L{Fsum.__imod__}.
718 '''
719 f = self._copy_2r(other, self.__rmod__)
720 return f._fdivmod2(self, _mod_op_).mod
722 def __rmul__(self, other):
723 '''Return C{B{other} * B{self}} as an L{Fsum}.
725 @see: Method L{Fsum.__imul__}.
726 '''
727 f = self._copy_2r(other, self.__rmul__)
728 return f._fmul(self, _mul_op_)
730 def __round__(self, *ndigits): # PYCHOK Python 3+
731 '''Return C{round(B{self}, *B{ndigits}} as an L{Fsum}.
733 @arg ndigits: Optional number of digits (C{int}).
734 '''
735 f = self._copy_2(self.__round__)
736 # <https://docs.Python.org/3.12/reference/datamodel.html?#object.__round__>
737 return f._fset(round(_Float(self), *ndigits)) # can be C{int}
739 def __rpow__(self, other, *mod):
740 '''Return C{B{other}**B{self}} as an L{Fsum}.
742 @see: Method L{Fsum.__ipow__}.
743 '''
744 f = self._copy_2r(other, self.__rpow__)
745 return f._fpow(self, _pow_op_, *mod)
747 def __rsub__(self, other):
748 '''Return C{B{other} - B{self}} as L{Fsum}.
750 @see: Method L{Fsum.__isub__}.
751 '''
752 f = self._copy_2r(other, self.__rsub__)
753 return f._fsub(self, _sub_op_)
755 def __rtruediv__(self, other, **raiser_RESIDUAL):
756 '''Return C{B{other} / B{self}} as an L{Fsum}.
758 @see: Method L{Fsum.__itruediv__}.
759 '''
760 f = self._copy_2r(other, self.__rtruediv__)
761 return f._ftruediv(self, _truediv_op_, **raiser_RESIDUAL)
763 def __str__(self):
764 '''Return the default C{str(self)}.
765 '''
766 return self.toStr(lenc=True)
768 def __sub__(self, other):
769 '''Return C{B{self} - B{other}} as an L{Fsum}.
771 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar}.
773 @return: The difference (L{Fsum}).
775 @see: Method L{Fsum.__isub__}.
776 '''
777 f = self._copy_2(self.__sub__)
778 return f._fsub(other, _sub_op_)
780 def __truediv__(self, other, **raiser_RESIDUAL):
781 '''Return C{B{self} / B{other}} as an L{Fsum}.
783 @arg other: An L{Fsum}, L{Fsum2Tuple} or C{scalar} divisor.
784 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} (C{bool}) to
785 ignore L{ResidualError}s and C{B{RESIDUAL}=scalar}
786 to override the L{RESIDUAL<Fsum.RESIDUAL>}.
788 @return: The quotient (L{Fsum}).
790 @raise ResidualError: Non-zero, significant residual or invalid
791 B{C{RESIDUAL}}.
793 @see: Method L{Fsum.__itruediv__}.
794 '''
795 return self._truediv(other, _truediv_op_, **raiser_RESIDUAL)
797 __trunc__ = __int__
799 if _sys_version_info2 < (3, 0): # PYCHOK no cover
800 # <https://docs.Python.org/2/library/operator.html#mapping-operators-to-functions>
801 __div__ = __truediv__
802 __idiv__ = __itruediv__
803 __long__ = __int__
804 __nonzero__ = __bool__
805 __rdiv__ = __rtruediv__
807 def as_integer_ratio(self):
808 '''Return this instance as the ratio of 2 integers.
810 @return: 2-Tuple C{(numerator, denominator)} both C{int}
811 with C{numerator} signed and C{denominator}
812 non-zero, positive.
814 @see: Standard C{float.as_integer_ratio} in Python 2.7+.
815 '''
816 n, r = self._fint2
817 if r:
818 i, d = _Float(r).as_integer_ratio()
819 n *= d
820 n += i
821 else: # PYCHOK no cover
822 d = 1
823 return n, d
825 @property_RO
826 def as_iscalar(self):
827 '''Get this instance I{as-is} (L{Fsum} or C{scalar}), the
828 latter only if the C{residual} equals C{zero}.
829 '''
830 s, r = self._fprs2
831 return self if r else s
833 @property_RO
834 def ceil(self):
835 '''Get this instance' C{ceil} value (C{int} in Python 3+, but
836 C{float} in Python 2-).
838 @note: This C{ceil} takes the C{residual} into account.
840 @see: Method L{Fsum.int_float} and properties L{Fsum.floor},
841 L{Fsum.imag} and L{Fsum.real}.
842 '''
843 s, r = self._fprs2
844 c = _ceil(s) + int(r) - 1
845 while r > (c - s): # (s + r) > c
846 c += 1
847 return c # _ceil(self._n_d)
849 cmp = __cmp__
851 def _cmp_0(self, other, op):
852 '''(INTERNAL) Return C{scalar(self - B{other})} for 0-comparison.
853 '''
854 if _isFsumTuple(other):
855 s = self._ps_1sum(*other._ps)
856 elif self._scalar(other, op):
857 s = self._ps_1sum(other)
858 else:
859 s = self.signOf() # res=True
860 return s
862 def copy(self, deep=False, name=NN):
863 '''Copy this instance, C{shallow} or B{C{deep}}.
865 @return: The copy (L{Fsum}).
866 '''
867 f = _Named.copy(self, deep=deep, name=name)
868 if f._ps is self._ps:
869 f._ps = _List(self._ps) # separate list
870 if not deep:
871 f._n = 1
872 # assert f._Fsum is f
873 return f
875 def _copy_2(self, which, name=NN):
876 '''(INTERNAL) Copy for I{dyadic} operators.
877 '''
878 n = name or which.__name__
879 # NOT .classof due to .Fdot(a, *b) args, etc.
880 f = _Named.copy(self, deep=False, name=n)
881 f._ps = _List(self._ps) # separate list
882 # assert f._n == self._n
883 # assert f._Fsum is f
884 return f
886 def _copy_2r(self, other, which):
887 '''(INTERNAL) Copy for I{reverse-dyadic} operators.
888 '''
889 return other._copy_2(which) if _isFsum(other) else \
890 self._copy_2(which)._fset(other)
892# def _copy_RESIDUAL(self, other):
893# '''(INTERNAL) Copy C{other._RESIDUAL}.
894# '''
895# R = other._RESIDUAL
896# if R is not Fsum._RESIDUAL:
897# self._RESIDUAL = R
899 divmod = __divmod__
901 def _Error(self, op, other, Error, **txt_cause):
902 '''(INTERNAL) Format an B{C{Error}} for C{{self} B{op} B{other}}.
903 '''
904 return Error(_SPACE_(self.as_iscalar, op, other), **txt_cause)
906 def _ErrorX(self, X, op, other, *mod):
907 '''(INTERNAL) Format the caught exception C{X}.
908 '''
909 E, t = _xError2(X)
910 if mod:
911 t = _COMMASPACE_(Fmt.PARENSPACED(mod=mod[0]), t)
912 return self._Error(op, other, E, txt=t, cause=X)
914 def _ErrorXs(self, X, xs, **kwds): # in .fmath
915 '''(INTERNAL) Format the caught exception C{X}.
916 '''
917 E, t = _xError2(X)
918 u = unstr(self.named3, *xs[:3], _ELLIPSIS=_len(xs) > 3, **kwds)
919 return E(u, txt=t, cause=X)
921 def _facc(self, xs, up=True, **origin_X_x):
922 '''(INTERNAL) Accumulate more C{scalars} or L{Fsum}s.
923 '''
924 if xs:
925 _xs = _2floats(xs, **origin_X_x) # PYCHOK yield
926 ps = self._ps
927 ps[:] = self._ps_acc(_List(ps), _xs, up=up)
928 return self
930 def _facc_1(self, xs, **up):
931 '''(INTERNAL) Accumulate 0, 1 or more C{scalars} or L{Fsum}s,
932 all positional C{xs} in the caller of this method.
933 '''
934 return self._fadd(xs[0], _add_op_, **up) if _len(xs) == 1 else \
935 self._facc(xs, origin=1, **up)
937 def _facc_neg(self, xs, **up_origin):
938 '''(INTERNAL) Accumulate more C{scalars} or L{Fsum}s, negated.
939 '''
940 def _N(X):
941 return X._ps_neg
943 def _n(x):
944 return -_Float(x)
946 return self._facc(xs, _X=_N, _x=_n, **up_origin)
948 def _facc_power(self, power, xs, which, **raiser_RESIDUAL): # in .fmath
949 '''(INTERNAL) Add each C{xs} as C{float(x**power)}.
950 '''
951 def _Pow4(p):
952 r = 0
953 if _isFsumTuple(p):
954 s, r = p._fprs2
955 if r:
956 m = Fsum._pow
957 else: # scalar
958 return _Pow4(s)
959 elif isint(p, both=True) and int(p) >= 0:
960 p = s = int(p)
961 m = Fsum._pow_int
962 else:
963 p = s = _2float(power=p)
964 m = Fsum._pow_scalar
965 return m, p, s, r
967 _Pow, p, s, r = _Pow4(power)
968 if p: # and xs:
969 op = which.__name__
970 _Fs = Fsum
971 _is = _isAn
972 _pow = self._pow_2_3
974 def _P(X):
975 f = _Pow(X, p, power, op, **raiser_RESIDUAL)
976 return f._ps if _is(f, _Fs) else (f,)
978 def _p(x):
979 x = _Float(x)
980 f = _pow(x, s, power, op, **raiser_RESIDUAL)
981 if f and r:
982 f *= _pow(x, r, power, op, **raiser_RESIDUAL)
983 return f
985 f = self._facc(xs, origin=1, _X=_P, _x=_p)
986 else:
987 f = self._facc_scalar_(_Float(_len(xs))) # x**0 == 1
988 return f
990 def _facc_scalar(self, xs, **up):
991 '''(INTERNAL) Accumulate all C{xs}, known to be scalar.
992 '''
993 if xs:
994 _ = self._ps_acc(self._ps, xs, **up)
995 return self
997 def _facc_scalar_(self, *xs, **up):
998 '''(INTERNAL) Accumulate all positional C{xs}, known to be scalar.
999 '''
1000 if xs:
1001 _ = self._ps_acc(self._ps, xs, **up)
1002 return self
1004# def _facc_up(self, up=True):
1005# '''(INTERNAL) Update the C{partials}, by removing
1006# and re-accumulating the final C{partial}.
1007# '''
1008# ps = self._ps
1009# while _len(ps) > 1:
1010# p = ps.pop()
1011# if p:
1012# n = self._n
1013# _ = self._ps_acc(ps, (p,), up=False)
1014# self._n = n
1015# break
1016# return self._update() if up else self
1018 def fadd(self, xs=()):
1019 '''Add an iterable's items to this instance.
1021 @arg xs: Iterable of items to add (each C{scalar}
1022 or an L{Fsum} or L{Fsum2Tuple} instance).
1024 @return: This instance (L{Fsum}).
1026 @raise OverflowError: Partial C{2sum} overflow.
1028 @raise TypeError: An invalid B{C{xs}} item.
1030 @raise ValueError: Invalid or non-finite B{C{xs}} value.
1031 '''
1032 if _isFsumTuple(xs):
1033 self._facc_scalar(xs._ps) # _Tuple(xs._ps)
1034 elif isscalar(xs): # for backward compatibility
1035 self._facc_scalar_(_2float(x=xs)) # PYCHOK no cover
1036 elif xs: # assert isiterable(xs)
1037 self._facc(xs)
1038 return self
1040 def fadd_(self, *xs):
1041 '''Add all positional items to this instance.
1043 @arg xs: Values to add (each C{scalar} or an L{Fsum}
1044 or L{Fsum2Tuple} instance), all positional.
1046 @see: Method L{Fsum.fadd} for further details.
1047 '''
1048 return self._facc_1(xs)
1050 def _fadd(self, other, op, **up): # in .fmath.Fhorner
1051 '''(INTERNAL) Apply C{B{self} += B{other}}.
1052 '''
1053 if not self._ps: # new Fsum(x)
1054 self._fset(other, as_is=False, **up)
1055 elif _isFsumTuple(other):
1056 self._facc_scalar(other._ps, **up) # _Tuple
1057 elif self._scalar(other, op):
1058 self._facc_scalar_(other, **up)
1059 return self
1061 fcopy = copy # for backward compatibility
1062 fdiv = __itruediv__
1063 fdivmod = __divmod__
1065 def _fdivmod2(self, other, op, **raiser_RESIDUAL):
1066 '''(INTERNAL) Apply C{B{self} %= B{other}} and return a L{DivMod2Tuple}.
1067 '''
1068 # result mostly follows CPython function U{float_divmod
1069 # <https://GitHub.com/python/cpython/blob/main/Objects/floatobject.c>},
1070 # but at least divmod(-3, 2) equals Cpython's result (-2, 1).
1071 q = self._truediv(other, op, **raiser_RESIDUAL).floor
1072 if q: # == float // other == floor(float / other)
1073 self -= Fsum(q) * other # NOT other * q!
1075 s = signOf(other) # make signOf(self) == signOf(other)
1076 if s and self.signOf() == -s: # PYCHOK no cover
1077 self += other
1078 q -= 1
1079# t = self.signOf()
1080# if t and t != s:
1081# raise self._Error(op, other, _AssertionError, txt=signOf.__name__)
1082 return DivMod2Tuple(q, self) # q is C{int} in Python 3+, but C{float} in Python 2-
1084 def _finite(self, other, op=None):
1085 '''(INTERNAL) Return B{C{other}} if C{finite}.
1086 '''
1087 if _isfinite(other):
1088 return other
1089 raise ValueError(_not_finite_) if op is None else \
1090 self._Error(op, other, _ValueError, txt=_not_finite_)
1092 def fint(self, name=NN, **raiser_RESIDUAL):
1093 '''Return this instance' current running sum as C{integer}.
1095 @kwarg name: Optional name (C{str}), overriding C{"fint"}.
1096 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} (C{bool}) to
1097 ignore L{ResidualError}s and C{B{RESIDUAL}=scalar}
1098 to override the L{RESIDUAL<Fsum.RESIDUAL>}.
1100 @return: The C{integer} sum (L{Fsum}) if this instance C{is_integer}
1101 with a zero or insignificant I{integer} residual.
1103 @raise ResidualError: Non-zero, significant residual or invalid
1104 B{C{RESIDUAL}}.
1106 @see: Methods L{Fsum.fint2}, L{Fsum.int_float} and L{Fsum.is_integer}.
1107 '''
1108 i, r = self._fint2
1109 if r:
1110 R = self._raiser(r, i, **raiser_RESIDUAL)
1111 if R:
1112 t = _stresidual(_integer_, r, **R)
1113 raise ResidualError(_integer_, i, txt=t)
1114 f = self._copy_2(self.fint, name=name)
1115 return f._fset(i)
1117 def fint2(self, **name):
1118 '''Return this instance' current running sum as C{int} and the
1119 I{integer} residual.
1121 @kwarg name: Optional name (C{str}).
1123 @return: An L{Fsum2Tuple}C{(fsum, residual)} with C{fsum}
1124 an C{int} and I{integer} C{residual} a C{float} or
1125 C{INT0} if the C{fsum} is considered to be I{exact}.
1126 '''
1127 return Fsum2Tuple(*self._fint2, **name)
1129 @Property_RO
1130 def _fint2(self): # see ._fset
1131 '''(INTERNAL) Get 2-tuple (C{int}, I{integer} residual).
1132 '''
1133 s, r = self._fprs2
1134 i = int(s)
1135 n = _len(self._ps)
1136 r = self._ps_1sum(i) if r and n > 1 else _Float(s - i)
1137 return i, (r or INT0) # Fsum2Tuple?
1139 @deprecated_property_RO
1140 def float_int(self): # PYCHOK no cover
1141 '''DEPRECATED, use method C{Fsum.int_float}.'''
1142 return self.int_float() # raiser=False
1144 @property_RO
1145 def floor(self):
1146 '''Get this instance' C{floor} (C{int} in Python 3+, but
1147 C{float} in Python 2-).
1149 @note: This C{floor} takes the C{residual} into account.
1151 @see: Method L{Fsum.int_float} and properties L{Fsum.ceil},
1152 L{Fsum.imag} and L{Fsum.real}.
1153 '''
1154 s, r = self._fprs2
1155 f = _floor(s) + _floor(r) + 1
1156 while (f - s) > r: # f > (s + r)
1157 f -= 1
1158 return f # _floor(self._n_d)
1160# ffloordiv = __ifloordiv__ # for naming consistency
1161# floordiv = __floordiv__ # for naming consistency
1163 def _floordiv(self, other, op, **raiser_RESIDUAL): # rather _ffloordiv?
1164 '''Apply C{B{self} //= B{other}}.
1165 '''
1166 q = self._ftruediv(other, op, **raiser_RESIDUAL) # == self
1167 return self._fset(q.floor) # floor(q)
1169 fmul = __imul__
1171 def _fmul(self, other, op):
1172 '''(INTERNAL) Apply C{B{self} *= B{other}}.
1173 '''
1174 if _isFsumTuple(other):
1175 if _len(self._ps) != 1:
1176 f = self._mul_Fsum(other, op)
1177 elif _len(other._ps) != 1: # and _len(self._ps) == 1
1178 f = other._mul_scalar(self._ps[0], op)
1179 else: # _len(other._ps) == _len(self._ps) == 1
1180 f = self._finite(self._ps[0] * other._ps[0])
1181 else:
1182 s = self._scalar(other, op)
1183 f = self._mul_scalar(s, op)
1184 return self._fset(f) # n=_len(self) + 1
1186 def fover(self, over, **raiser_RESIDUAL):
1187 '''Apply C{B{self} /= B{over}} and summate.
1189 @arg over: An L{Fsum} or C{scalar} denominator.
1190 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} (C{bool}) to
1191 ignore L{ResidualError}s and C{B{RESIDUAL}=scalar}
1192 to override the L{RESIDUAL<Fsum.RESIDUAL>}.
1194 @return: Precision running sum (C{float}).
1196 @raise ResidualError: Non-zero, significant residual or invalid
1197 B{C{RESIDUAL}}.
1199 @see: Methods L{Fsum.fsum} and L{Fsum.__itruediv__}.
1200 '''
1201 return _Float(self.fdiv(over, **raiser_RESIDUAL)._fprs)
1203 fpow = __ipow__
1205 def _fpow(self, other, op, *mod, **raiser_RESIDUAL):
1206 '''Apply C{B{self} **= B{other}}, optional B{C{mod}} or C{None}.
1207 '''
1208 if mod:
1209 if mod[0] is not None: # == 3-arg C{pow}
1210 f = self._pow_2_3(self, other, other, op, *mod, **raiser_RESIDUAL)
1211 elif self.is_integer():
1212 # return an exact C{int} for C{int}**C{int}
1213 i, _ = self._fint2 # assert _ == 0
1214 x, r = _2scalar2(other) # C{int}, C{float} or other
1215 f = _Psum_(i)._pow_Fsum(other, op, **raiser_RESIDUAL) if r else \
1216 self._pow_2_3(i, x, other, op, **raiser_RESIDUAL)
1217 else: # mod[0] is None, power(self, other)
1218 f = self._pow(other, other, op, **raiser_RESIDUAL)
1219 else: # pow(self, other)
1220 f = self._pow(other, other, op, **raiser_RESIDUAL)
1221 return self._fset(f, as_is=isint(f)) # n=max(_len(self), 1)
1223 @Property_RO
1224 def _fprs(self):
1225 '''(INTERNAL) Get and cache this instance' precision
1226 running sum (C{float} or C{int}), ignoring C{residual}.
1228 @note: The precision running C{fsum} after a C{//=} or
1229 C{//} C{floor} division is C{int} in Python 3+.
1230 '''
1231 s, _ = self._fprs2
1232 return s # ._fprs2.fsum
1234 @Property_RO
1235 def _fprs2(self):
1236 '''(INTERNAL) Get and cache this instance' precision
1237 running sum and residual (L{Fsum2Tuple}).
1238 '''
1239 ps = self._ps
1240 n = _len(ps) - 2
1241 if n > 0: # _len(ps) > 2
1242 s = _psum(ps)
1243 n = _len(ps) - 2
1244 if n > 0:
1245 r = self._ps_1sum(s)
1246 return Fsum2Tuple(*_s_r(s, r))
1247 if n == 0: # _len(ps) == 2
1248 s, r = _s_r(*_2sum(*ps))
1249 ps[:] = (r, s) if r else (s,)
1250 elif ps: # _len(ps) == 1
1251 s, r = ps[0], INT0
1252 else: # _len(ps) == 0
1253 s, r = _0_0, INT0
1254 ps[:] = s,
1255 # assert self._ps is ps
1256 return Fsum2Tuple(s, r)
1258 def fset_(self, *xs):
1259 '''Replace this instance' value with all positional items.
1261 @arg xs: Optional, new values (each C{scalar} or
1262 an L{Fsum} or L{Fsum2Tuple} instance),
1263 all positional.
1265 @return: This instance, replaced (C{Fsum}).
1267 @see: Method L{Fsum.fadd} for further details.
1268 '''
1269 f = xs[0] if len(xs) == 1 else (
1270 Fsum(*xs) if xs else _0_0)
1271 return self._fset(f)
1273 def _fset(self, other, as_is=True, n=0, up=True):
1274 '''(INTERNAL) Overwrite this instance with an other or a C{scalar}.
1275 '''
1276 if other is self:
1277 pass # from ._fmul, ._ftruediv and ._pow_0_1
1278 elif _isFsumTuple(other):
1279 self._ps[:] = other._ps
1280 self._n = n or other._n
1281# self._copy_RESIDUAL(other)
1282 if up: # use or zap the C{Property_RO} values
1283 Fsum._fint2._update_from(self, other)
1284 Fsum._fprs ._update_from(self, other)
1285 Fsum._fprs2._update_from(self, other)
1286 elif isscalar(other):
1287 s = other if as_is else _Float(other)
1288 self._ps[:] = s,
1289 self._n = n or 1
1290 if up:
1291 i = int(s) # see ._fint2
1292 t = i, ((s - i) or INT0)
1293 # Property_ROs _fint2, _fprs and _fprs2 can't be a Property:
1294 # Property's _fset zaps the value just set by the @setter
1295 self.__dict__.update(_fint2=t, _fprs=s, _fprs2=Fsum2Tuple(s, INT0))
1296 else: # PYCHOK no cover
1297 raise self._Error(_fset_op_, other, _TypeError)
1298 return self
1300 def _fset_ps(self, other, n=0): # in .fmath
1301 '''(INTERNAL) Set partials from a known C{scalar}, L{Fsum} or L{Fsum2Tuple}.
1302 '''
1303 if _isFsumTuple(other):
1304 self._ps[:] = other._ps
1305 self._n = n or other._n
1306 else: # assert isscalar(other)
1307 self._ps[:] = other,
1308 self._n = n or 1
1309 return self
1311 def fsub(self, xs=()):
1312 '''Subtract an iterable's items from this instance.
1314 @see: Method L{Fsum.fadd} for further details.
1315 '''
1316 return self._facc_neg(xs)
1318 def fsub_(self, *xs):
1319 '''Subtract all positional items from this instance.
1321 @see: Method L{Fsum.fadd_} for further details.
1322 '''
1323 return self._fsub(xs[0], _sub_op_) if _len(xs) == 1 else \
1324 self._facc_neg(xs, origin=1)
1326 def _fsub(self, other, op):
1327 '''(INTERNAL) Apply C{B{self} -= B{other}}.
1328 '''
1329 if _isFsumTuple(other):
1330 if other is self: # or other._fprs2 == self._fprs2:
1331 self._fset(_0_0, n=_len(self) * 2)
1332 elif other._ps:
1333 self._facc_scalar(other._ps_neg)
1334 elif self._scalar(other, op):
1335 self._facc_scalar_(-other)
1336 return self
1338 def fsum(self, xs=()):
1339 '''Add an iterable's items, summate and return the
1340 current precision running sum.
1342 @arg xs: Iterable of items to add (each item C{scalar}
1343 or an L{Fsum} or L{Fsum2Tuple} instance).
1345 @return: Precision running sum (C{float} or C{int}).
1347 @see: Method L{Fsum.fadd}.
1349 @note: Accumulation can continue after summation.
1350 '''
1351 return self._facc(xs)._fprs
1353 def fsum_(self, *xs):
1354 '''Add any positional items, summate and return the
1355 current precision running sum.
1357 @arg xs: Items to add (each C{scalar} or an L{Fsum}
1358 or L{Fsum2Tuple} instance), all positional.
1360 @return: Precision running sum (C{float} or C{int}).
1362 @see: Methods L{Fsum.fsum}, L{Fsum.Fsum_} and L{Fsum.fsumf_}.
1363 '''
1364 return self._facc_1(xs)._fprs
1366 @property_RO
1367 def _Fsum(self): # like L{Fsum2Tuple._Fsum}, for C{_2floats}, .fstats
1368 return self # NOT @Property_RO, see .copy and ._copy_2
1370 def Fsum_(self, *xs, **name):
1371 '''Like method L{Fsum.fsum_} but returning a named L{Fsum}.
1373 @kwarg name: Optional name (C{str}).
1375 @return: Copy of this updated instance (L{Fsum}).
1376 '''
1377 return self._facc_1(xs)._copy_2(self.Fsum_, **name)
1379 def Fsum2Tuple_(self, *xs, **name):
1380 '''Like method L{Fsum.fsum_} but returning a named L{Fsum2Tuple}.
1382 @kwarg name: Optional name (C{str}).
1384 @return: Precision running sum (L{Fsum2Tuple}).
1385 '''
1386 return Fsum2Tuple(self._facc_1(xs)._fprs2, **name)
1388 def fsum2(self, xs=(), name=NN):
1389 '''Add an iterable's items, summate and return the
1390 current precision running sum I{and} the C{residual}.
1392 @arg xs: Iterable of items to add (each item C{scalar}
1393 or an L{Fsum} or L{Fsum2Tuple} instance).
1394 @kwarg name: Optional name (C{str}).
1396 @return: L{Fsum2Tuple}C{(fsum, residual)} with C{fsum} the
1397 current precision running sum and C{residual}, the
1398 (precision) sum of the remaining C{partials}. The
1399 C{residual is INT0} if the C{fsum} is considered
1400 to be I{exact}.
1402 @see: Methods L{Fsum.fint2}, L{Fsum.fsum} and L{Fsum.fsum2_}
1403 '''
1404 t = self._facc(xs)._fprs2
1405 return t.dup(name=name) if name else t
1407 def fsum2_(self, *xs):
1408 '''Add any positional items, summate and return the current
1409 precision running sum and the I{differential}.
1411 @arg xs: Values to add (each C{scalar} or an L{Fsum} or
1412 L{Fsum2Tuple} instance), all positional.
1414 @return: 2Tuple C{(fsum, delta)} with the current, precision
1415 running C{fsum} like method L{Fsum.fsum} and C{delta},
1416 the difference with previous running C{fsum}, C{float}.
1418 @see: Methods L{Fsum.fsum_} and L{Fsum.fsum}.
1419 '''
1420 return self._fsum2(xs, self._facc_1)
1422 def _fsum2(self, xs, _f, **origin):
1423 '''(INTERNAL) Helper for L{Fsum.fsum2_} and L{Fsum.fsum2f_}.
1424 '''
1425 p, q = self._fprs2
1426 if xs:
1427 s, r = _f(xs, **origin)._fprs2
1428 return s, _2delta(s - p, r - q) # _fsum(_1primed((s, -p, r, -q))
1429 else:
1430 return p, _0_0
1432 def fsumf_(self, *xs):
1433 '''Like method L{Fsum.fsum_} iff I{all} C{B{xs}} are I{known to be scalar}.
1434 '''
1435 return self._facc_scalar(xs)._fprs
1437 def Fsumf_(self, *xs):
1438 '''Like method L{Fsum.Fsum_} iff I{all} C{B{xs}} are I{known to be scalar}.
1439 '''
1440 return self._facc_scalar(xs)._copy_2(self.Fsumf_)
1442 def fsum2f_(self, *xs):
1443 '''Like method L{Fsum.fsum2_} iff I{all} C{B{xs}} are I{known to be scalar}.
1444 '''
1445 return self._fsum2(xs, self._facc_scalar, origin=1)
1447# ftruediv = __itruediv__ # for naming consistency?
1449 def _ftruediv(self, other, op, **raiser_RESIDUAL):
1450 '''(INTERNAL) Apply C{B{self} /= B{other}}.
1451 '''
1452 n = _1_0
1453 if _isFsumTuple(other):
1454 if other is self or self == other:
1455 return self._fset(n) # n=_len(self)
1456 d, r = other._fprs2
1457 if r:
1458 R = self._raiser(r, d, **raiser_RESIDUAL)
1459 if R:
1460 raise self._ResidualError(op, other, r, **R)
1461 d, n = other.as_integer_ratio()
1462 else:
1463 d = self._scalar(other, op)
1464 try:
1465 s = n / d
1466 except Exception as X:
1467 raise self._ErrorX(X, op, other)
1468 f = self._mul_scalar(s, _mul_op_) # handles 0, INF, NAN
1469 return self._fset(f) # as_is=False
1471 @property_RO
1472 def imag(self):
1473 '''Get the C{imaginary} part of this instance (C{0.0}, always).
1475 @see: Property L{Fsum.real}.
1476 '''
1477 return _0_0
1479 def int_float(self, **raiser_RESIDUAL):
1480 '''Return this instance' current running sum as C{int} or C{float}.
1482 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} (C{bool}) to
1483 ignore L{ResidualError}s and C{B{RESIDUAL}=scalar}
1484 to override the L{RESIDUAL<Fsum.RESIDUAL>}.
1486 @return: This C{integer} sum if this instance C{is_integer},
1487 otherwise return the C{float} sum if the residual is
1488 zero or not significant.
1490 @raise ResidualError: Non-zero, significant residual or invalid
1491 B{C{RESIDUAL}}.
1493 @see: Methods L{Fsum.fint}, L{Fsum.fint2}, L{Fsum.RESIDUAL} and
1494 property L{Fsum.as_iscalar}.
1495 '''
1496 s, r = self._fint2
1497 if r:
1498 s, r = self._fprs2
1499 if r: # PYCHOK no cover
1500 R = self._raiser(r, s, **raiser_RESIDUAL)
1501 if R:
1502 t = _stresidual(_non_zero_, r, **R)
1503 raise ResidualError(int_float=s, txt=t)
1504 s = _Float(s) # redundant
1505 return s
1507 def is_exact(self):
1508 '''Is this instance' running C{fsum} considered to be exact?
1509 (C{bool}), C{True} only if the C{residual is }L{INT0}.
1510 '''
1511 return self.residual is INT0
1513 def is_integer(self):
1514 '''Is this instance' running sum C{integer}? (C{bool}).
1516 @see: Methods L{Fsum.fint}, L{Fsum.fint2} and L{Fsum.is_scalar}.
1517 '''
1518 _, r = self._fint2
1519 return False if r else True
1521 def is_math_fsum(self):
1522 '''Return whether functions L{fsum}, L{fsum_}, L{fsum1} and
1523 L{fsum1_} plus partials summation are based on Python's
1524 C{math.fsum} or not.
1526 @return: C{2} if all functions and partials summation
1527 are based on C{math.fsum}, C{True} if only
1528 the functions are based on C{math.fsum} (and
1529 partials summation is not) or C{False} if
1530 none are.
1531 '''
1532 f = Fsum._math_fsum
1533 return 2 if _psum is f else bool(f)
1535 def is_scalar(self, **raiser_RESIDUAL):
1536 '''Is this instance' running sum C{scalar} without residual or with
1537 a residual I{ratio} not exceeding the RESIDUAL threshold?
1539 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} (C{bool}) to ignore
1540 L{ResidualError}s and C{B{RESIDUAL}=scalar} to override
1541 the L{RESIDUAL<Fsum.RESIDUAL>} threshold.
1543 @return: C{True} if this instance' non-zero residual C{ratio} exceeds
1544 the L{RESIDUAL<Fsum.RESIDUAL>} threshold (C{bool}).
1546 @raise ResidualError: Non-zero, significant residual or invalid
1547 B{C{RESIDUAL}}.
1549 @see: Method L{Fsum.RESIDUAL}, L{Fsum.is_integer} and property
1550 L{Fsum.as_iscalar}.
1551 '''
1552 s, r = self._fprs2
1553 return False if r and self._raiser(r, s, **raiser_RESIDUAL) else True
1555 def _mul_Fsum(self, other, op=_mul_op_): # in .fmath.Fhorner
1556 '''(INTERNAL) Return C{B{self} * B{other}} as L{Fsum} or C{0}.
1557 '''
1558 # assert _isFsumTuple(other)
1559 if self._ps and other._ps:
1560 f = self._ps_mul(op, *other._ps) # NO .as_iscalar!
1561 else:
1562 f = _0_0
1563 return f
1565 def _mul_scalar(self, factor, op): # in .fmath.Fhorner
1566 '''(INTERNAL) Return C{B{self} * scalar B{factor}} as L{Fsum}, C{0.0} or C{self}.
1567 '''
1568 # assert isscalar(factor)
1569 if self._ps and self._finite(factor, op):
1570 f = self if factor == _1_0 else (
1571 self._neg if factor == _N_1_0 else
1572 self._ps_mul(op, factor).as_iscalar)
1573 else:
1574 f = _0_0
1575 return f
1577# @property_RO
1578# def _n_d(self):
1579# n, d = self.as_integer_ratio()
1580# return n / d
1582 @property_RO
1583 def _neg(self):
1584 '''(INTERNAL) Return C{Fsum(-self)} or scalar C{NEG0}.
1585 '''
1586 return _Psum(self._ps_neg) if self._ps else NEG0
1588 @property_RO
1589 def partials(self):
1590 '''Get this instance' current, partial sums (C{tuple} of C{float}s).
1591 '''
1592 return _Tuple(self._ps)
1594 def pow(self, x, *mod, **raiser_RESIDUAL):
1595 '''Return C{B{self}**B{x}} as L{Fsum}.
1597 @arg x: The exponent (C{scalar} or L{Fsum}).
1598 @arg mod: Optional modulus (C{int} or C{None}) for the 3-argument
1599 C{pow(B{self}, B{other}, B{mod})} version.
1600 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} (C{bool}) to
1601 ignore L{ResidualError}s and C{B{RESIDUAL}=scalar}
1602 to override the L{RESIDUAL<Fsum.RESIDUAL>}.
1604 @return: The C{pow(self, B{x})} or C{pow(self, B{x}, *B{mod})}
1605 result (L{Fsum}).
1607 @raise ResidualError: Non-zero, significant residual or invalid
1608 B{C{RESIDUAL}}.
1610 @note: If B{C{mod}} is given as C{None}, the result will be an
1611 C{integer} L{Fsum} provided this instance C{is_integer}
1612 or set to C{integer} by an L{Fsum.fint} call.
1614 @see: Methods L{Fsum.__ipow__}, L{Fsum.fint}, L{Fsum.is_integer}
1615 and L{Fsum.root}.
1616 '''
1617 f = self._copy_2(self.pow)
1618 return f._fpow(x, _pow_op_, *mod, **raiser_RESIDUAL) # f = pow(f, x, *mod)
1620 def _pow(self, other, unused, op, **raiser_RESIDUAL):
1621 '''Return C{B{self} ** B{other}}.
1622 '''
1623 if _isFsumTuple(other):
1624 f = self._pow_Fsum(other, op, **raiser_RESIDUAL)
1625 elif self._scalar(other, op):
1626 x = self._finite(other, op)
1627 f = self._pow_scalar(x, other, op, **raiser_RESIDUAL)
1628 else:
1629 f = self._pow_0_1(0, other)
1630 return f
1632 def _pow_0_1(self, x, other):
1633 '''(INTERNAL) Return B{C{self}**1} or C{B{self}**0 == 1.0}.
1634 '''
1635 return self if x else (1 if isint(other) and self.is_integer() else _1_0)
1637 def _pow_2_3(self, b, x, other, op, *mod, **raiser_RESIDUAL):
1638 '''(INTERNAL) 2-arg C{pow(B{b}, scalar B{x})} and 3-arg C{pow(B{b},
1639 B{x}, int B{mod} or C{None})}, embellishing errors.
1640 '''
1642 if mod: # b, x, mod all C{int}, unless C{mod} is C{None}
1643 m = mod[0]
1644 # assert _isFsumTuple(b)
1646 def _s(s, r):
1647 R = self._raiser(r, s, **raiser_RESIDUAL)
1648 if R:
1649 raise self._ResidualError(op, other, r, mod=m, **R)
1650 return s
1652 b = _s(*(b._fprs2 if m is None else b._fint2))
1653 x = _s(*_2scalar2(x))
1655 try:
1656 # 0**INF == 0.0, 1**INF == 1.0, -1**2.3 == -(1**2.3)
1657 s = pow(b, x, *mod)
1658 if iscomplex(s):
1659 # neg**frac == complex in Python 3+, but ValueError in 2-
1660 raise ValueError(_strcomplex(s, b, x, *mod))
1661 return self._finite(s)
1662 except Exception as X:
1663 raise self._ErrorX(X, op, other, *mod)
1665 def _pow_Fsum(self, other, op, **raiser_RESIDUAL):
1666 '''(INTERNAL) Return C{B{self} **= B{other}} for C{_isFsumTuple(other)}.
1667 '''
1668 # assert _isFsumTuple(other)
1669 x, r = other._fprs2
1670 f = self._pow_scalar(x, other, op, **raiser_RESIDUAL)
1671 if f and r:
1672 f *= self._pow_scalar(r, other, op, **raiser_RESIDUAL)
1673 return f
1675 def _pow_int(self, x, other, op, **raiser_RESIDUAL):
1676 '''(INTERNAL) Return C{B{self} **= B{x}} for C{int B{x} >= 0}.
1677 '''
1678 # assert isint(x) and x >= 0
1679 ps = self._ps
1680 if _len(ps) > 1:
1681 _mul_Fsum = Fsum._mul_Fsum
1682 if x > 4:
1683 p = self
1684 f = self if (x & 1) else _Psum_(_1_0)
1685 m = x >> 1 # // 2
1686 while m:
1687 p = _mul_Fsum(p, p, op) # p **= 2
1688 if (m & 1):
1689 f = _mul_Fsum(f, p, op) # f *= p
1690 m >>= 1 # //= 2
1691 elif x > 1: # self**2, 3, or 4
1692 f = _mul_Fsum(self, self, op)
1693 if x > 2: # self**3 or 4
1694 p = self if x < 4 else f
1695 f = _mul_Fsum(f, p, op)
1696 else: # self**1 or self**0 == 1 or _1_0
1697 f = self._pow_0_1(x, other)
1698 elif ps: # self._ps[0]**x
1699 f = self._pow_2_3(ps[0], x, other, op, **raiser_RESIDUAL)
1700 else: # PYCHOK no cover
1701 # 0**pos_int == 0, but 0**0 == 1
1702 f = 0 if x else 1
1703 return f
1705 def _pow_scalar(self, x, other, op, **raiser_RESIDUAL):
1706 '''(INTERNAL) Return C{self**B{x}} for C{scalar B{x}}.
1707 '''
1708 s, r = self._fprs2
1709 if r:
1710 # assert s != 0
1711 if isint(x, both=True): # self**int
1712 x = int(x)
1713 y = _abs(x)
1714 if y > 1:
1715 f = self._pow_int(y, other, op, **raiser_RESIDUAL)
1716 if x > 0: # i.e. > 1
1717 return f # Fsum or scalar
1718 # assert x < 0 # i.e. < -1
1719 if _isFsum(f):
1720 s, r = f._fprs2
1721 if r:
1722 return _1_Over(f, op, **raiser_RESIDUAL)
1723 else: # scalar
1724 s = f
1725 # use s**(-1) to get the CPython
1726 # float_pow error iff s is zero
1727 x = -1
1728 elif x < 0: # self**(-1)
1729 return _1_Over(self, op, **raiser_RESIDUAL) # 1 / self
1730 else: # self**1 or self**0
1731 return self._pow_0_1(x, other) # self, 1 or 1.0
1732 else: # self**fractional
1733 R = self._raiser(r, s, **raiser_RESIDUAL)
1734 if R:
1735 raise self._ResidualError(op, other, r, **R)
1736 n, d = self.as_integer_ratio()
1737 if _abs(n) > _abs(d):
1738 n, d, x = d, n, (-x)
1739 s = n / d
1740 # assert isscalar(s) and isscalar(x)
1741 return self._pow_2_3(s, x, other, op, **raiser_RESIDUAL)
1743 def _ps_acc(self, ps, xs, up=True, **unused):
1744 '''(INTERNAL) Accumulate C{xs} scalars into list C{ps}.
1745 '''
1746 n = 0
1747 _2s = _2sum
1748 for x in (_Tuple(xs) if xs is ps else xs):
1749 # assert isscalar(x) and _isfinite(x)
1750 if x:
1751 i = 0
1752 for p in ps:
1753 x, p = _2s(x, p)
1754 if p:
1755 ps[i] = p
1756 i += 1
1757 ps[i:] = (x,) if x else ()
1758 n += 1
1759 if n:
1760 self._n += n
1761 # Fsum._ps_max = max(Fsum._ps_max, _len(ps))
1762 if up:
1763 self._update()
1764 return ps
1766 def _ps_mul(self, op, *factors):
1767 '''(INTERNAL) Multiply this instance' C{partials} with
1768 each scalar C{factor} and accumulate into an C{Fsum}.
1769 '''
1770 def _pfs(ps, fs):
1771 if _len(ps) < _len(fs):
1772 ps, fs = fs, ps
1773 _fin = _isfinite
1774 for f in fs:
1775 for p in ps:
1776 p *= f
1777 yield p if _fin(p) else self._finite(p, op)
1779 return Fsum()._facc_scalar(_pfs(self._ps, factors), up=False)
1781 @property_RO
1782 def _ps_neg(self):
1783 '''(INTERNAL) Yield the partials, I{negated}.
1784 '''
1785 for p in self._ps:
1786 yield -p
1788 def _ps_1sum(self, *less):
1789 '''(INTERNAL) Return the partials sum, 1-primed C{less} some scalars.
1790 '''
1791 def _1pls(ps, ls):
1792 yield _1_0
1793 for p in ps:
1794 yield p
1795 for p in ls:
1796 yield -p
1797 yield _N_1_0
1799 return _fsum(_1pls(self._ps, less))
1801 def _raiser(self, r, s, raiser=True, **RESIDUAL):
1802 '''(INTERNAL) Does ratio C{r / s} exceed the RESIDUAL threshold
1803 I{and} is residual C{r} I{non-zero} or I{significant} (for a
1804 negative respectively positive C{RESIDUAL} threshold)?
1805 '''
1806 if r and raiser:
1807 t = self._RESIDUAL
1808 if RESIDUAL:
1809 t = _threshold(_xkwds_get(RESIDUAL, RESIDUAL=t))
1810 if t < 0 or (s + r) != s:
1811 q = (r / s) if s else s # == 0.
1812 if fabs(q) > fabs(t):
1813 return dict(ratio=q, R=t)
1814 return {}
1816 rdiv = __rtruediv__
1818 @property_RO
1819 def real(self):
1820 '''Get the C{real} part of this instance (C{float}).
1822 @see: Methods L{Fsum.__float__} and L{Fsum.fsum}
1823 and properties L{Fsum.ceil}, L{Fsum.floor},
1824 L{Fsum.imag} and L{Fsum.residual}.
1825 '''
1826 return _Float(self._fprs)
1828 @property_RO
1829 def residual(self):
1830 '''Get this instance' residual (C{float} or C{int}): the
1831 C{sum(partials)} less the precision running sum C{fsum}.
1833 @note: The C{residual is INT0} iff the precision running
1834 C{fsum} is considered to be I{exact}.
1836 @see: Methods L{Fsum.fsum}, L{Fsum.fsum2} and L{Fsum.is_exact}.
1837 '''
1838 return self._fprs2.residual
1840 def RESIDUAL(self, *threshold):
1841 '''Get and set this instance' I{ratio} for raising L{ResidualError}s,
1842 overriding the default from env variable C{PYGEODESY_FSUM_RESIDUAL}.
1844 @arg threshold: If C{scalar}, the I{ratio} to exceed for raising
1845 L{ResidualError}s in division and exponention, if
1846 C{None} restore the default set with env variable
1847 C{PYGEODESY_FSUM_RESIDUAL} or if omitted, keep the
1848 current setting.
1850 @return: The previous C{RESIDUAL} setting (C{float}), default C{0.0}.
1852 @raise ResidualError: Invalid B{C{threshold}}.
1854 @note: L{ResidualError}s may be thrown if the non-zero I{ratio}
1855 C{residual / fsum} exceeds the given B{C{threshold}} and
1856 if the C{residual} is non-zero and I{significant} vs the
1857 C{fsum}, i.e. C{(fsum + residual) != fsum} and if optional
1858 keyword argument C{raiser=False} is missing. Specify a
1859 negative B{C{threshold}} for only non-zero C{residual}
1860 testing without I{significant}.
1861 '''
1862 r = self._RESIDUAL
1863 if threshold:
1864 t = threshold[0]
1865 self._RESIDUAL = Fsum._RESIDUAL if t is None else ( # for ...
1866 (_0_0 if t else _1_0) if isbool(t) else
1867 _threshold(t)) # ... backward compatibility
1868 return r
1870 def _ResidualError(self, op, other, residual, **mod_R):
1871 '''(INTERNAL) Non-zero B{C{residual}} etc.
1872 '''
1873 def _p(mod=None, R=0, **unused): # ratio=0
1874 return (_non_zero_ if R < 0 else _significant_) \
1875 if mod is None else _integer_
1877 t = _stresidual(_p(**mod_R), residual, **mod_R)
1878 return self._Error(op, other, ResidualError, txt=t)
1880 def root(self, root, **raiser_RESIDUAL):
1881 '''Return C{B{self}**(1 / B{root})} as L{Fsum}.
1883 @arg root: The order (C{scalar} or L{Fsum}), non-zero.
1884 @kwarg raiser_RESIDUAL: Use C{B{raiser}=False} (C{bool}) to
1885 ignore L{ResidualError}s and C{B{RESIDUAL}=scalar}
1886 to override the L{RESIDUAL<Fsum.RESIDUAL>}.
1888 @return: The C{self ** (1 / B{root})} result (L{Fsum}).
1890 @raise ResidualError: Non-zero, significant residual or invalid
1891 B{C{RESIDUAL}}.
1893 @see: Method L{Fsum.pow}.
1894 '''
1895 x = _1_Over(root, _truediv_op_, **raiser_RESIDUAL)
1896 f = self._copy_2(self.root)
1897 return f._fpow(x, f.name, **raiser_RESIDUAL) # == pow(f, x)
1899 def _scalar(self, other, op, **txt):
1900 '''(INTERNAL) Return scalar C{other}.
1901 '''
1902 if isscalar(other):
1903 return other
1904 raise self._Error(op, other, _TypeError, **txt) # _invalid_
1906 def signOf(self, res=True):
1907 '''Determine the sign of this instance.
1909 @kwarg res: If C{True} consider, otherwise
1910 ignore the residual (C{bool}).
1912 @return: The sign (C{int}, -1, 0 or +1).
1913 '''
1914 s, r = self._fprs2
1915 r = (-r) if res else 0
1916 return _signOf(s, r)
1918 def toRepr(self, **lenc_prec_sep_fmt): # PYCHOK signature
1919 '''Return this C{Fsum} instance as representation.
1921 @kwarg lenc_prec_sep_fmt: Optional keyword arguments
1922 for method L{Fsum.toStr}.
1924 @return: This instance (C{repr}).
1925 '''
1926 return Fmt.repr_at(self, self.toStr(**lenc_prec_sep_fmt))
1928 def toStr(self, lenc=True, **prec_sep_fmt): # PYCHOK signature
1929 '''Return this C{Fsum} instance as string.
1931 @kwarg lenc: If C{True} include the current C{[len]} of this
1932 L{Fsum} enclosed in I{[brackets]} (C{bool}).
1933 @kwarg prec_sep_fmt: Optional keyword arguments for method
1934 L{Fsum2Tuple.toStr}.
1936 @return: This instance (C{str}).
1937 '''
1938 p = self.classname
1939 if lenc:
1940 p = Fmt.SQUARE(p, _len(self))
1941 n = _enquote(self.name, white=_UNDER_)
1942 t = self._fprs2.toStr(**prec_sep_fmt)
1943 return NN(p, _SPACE_, n, t)
1945 def _truediv(self, other, op, **raiser_RESIDUAL):
1946 '''(INTERNAL) Return C{B{self} / B{other}} as an L{Fsum}.
1947 '''
1948 f = self._copy_2(self.__truediv__)
1949 return f._ftruediv(other, op, **raiser_RESIDUAL)
1951 def _update(self, updated=True): # see ._fset
1952 '''(INTERNAL) Zap all cached C{Property_RO} values.
1953 '''
1954 if updated:
1955 _pop = self.__dict__.pop
1956 for p in _ROs:
1957 _ = _pop(p, None)
1958# Fsum._fint2._update(self)
1959# Fsum._fprs ._update(self)
1960# Fsum._fprs2._update(self)
1961 return self # for .fset_
1963_ROs = _allPropertiesOf_n(3, Fsum, Property_RO) # PYCHOK see Fsum._update
1966def _Float_Int(arg, **name_Error):
1967 '''(INTERNAL) Unit of L{Fsum2Tuple} items.
1968 '''
1969 U = Int if isint(arg) else Float
1970 return U(arg, **name_Error)
1973class DivMod2Tuple(_NamedTuple):
1974 '''2-Tuple C{(div, mod)} with the quotient C{div} and remainder
1975 C{mod} results of a C{divmod} operation.
1977 @note: Quotient C{div} an C{int} in Python 3+ but a C{float}
1978 in Python 2-. Remainder C{mod} an L{Fsum} instance.
1979 '''
1980 _Names_ = (_div_, _mod_)
1981 _Units_ = (_Float_Int, Fsum)
1984class Fsum2Tuple(_NamedTuple): # in .fstats
1985 '''2-Tuple C{(fsum, residual)} with the precision running C{fsum}
1986 and the C{residual}, the sum of the remaining partials. Each
1987 item is C{float} or C{int}.
1989 @note: If the C{residual is INT0}, the C{fsum} is considered
1990 to be I{exact}, see method L{Fsum2Tuple.is_exact}.
1991 '''
1992 _Names_ = ( Fsum.fsum.__name__, Fsum.residual.name)
1993 _Units_ = (_Float_Int, _Float_Int)
1995 def __abs__(self): # in .fmath
1996 return self._Fsum.__abs__()
1998 def __bool__(self): # PYCHOK Python 3+
1999 return bool(self._Fsum)
2001 def __eq__(self, other):
2002 return self._other_op(other, self.__eq__)
2004 def __float__(self):
2005 return self._Fsum.__float__()
2007 def __ge__(self, other):
2008 return self._other_op(other, self.__ge__)
2010 def __gt__(self, other):
2011 return self._other_op(other, self.__gt__)
2013 def __le__(self, other):
2014 return self._other_op(other, self.__le__)
2016 def __lt__(self, other):
2017 return self._other_op(other, self.__lt__)
2019 def __int__(self):
2020 return self._Fsum.__int__()
2022 def __ne__(self, other):
2023 return self._other_op(other, self.__ne__)
2025 def __neg__(self):
2026 return self._Fsum.__neg__()
2028 __nonzero__ = __bool__ # Python 2-
2030 def __pos__(self):
2031 return self._Fsum.__pos__()
2033 def as_integer_ratio(self):
2034 '''Return this instance as the ratio of 2 integers.
2036 @see: Method L{Fsum.as_integer_ratio} for further details.
2037 '''
2038 return self._Fsum.as_integer_ratio()
2040 @property_RO
2041 def _fint2(self):
2042 return self._Fsum._fint2
2044 @property_RO
2045 def _fprs2(self):
2046 return self._Fsum._fprs2
2048 @Property_RO
2049 def _Fsum(self): # this C{Fsum2Tuple} as L{Fsum}, in .fstats
2050 s, r = _s_r(*self)
2051 ps = (r, s) if r else (s,)
2052 return _Psum(ps, name=self.name)
2054 def Fsum_(self, *xs, **name_RESIDUAL):
2055 '''Return this C{Fsum2Tuple} as an L{Fsum} plus some C{xs}.
2056 '''
2057 f = _Psum(self._Fsum._ps, **name_RESIDUAL)
2058 return f._facc_1(xs, up=False) if xs else f
2060 def is_exact(self):
2061 '''Is this L{Fsum2Tuple} considered to be exact? (C{bool}).
2062 '''
2063 return self._Fsum.is_exact()
2065 def is_integer(self):
2066 '''Is this L{Fsum2Tuple} C{integer}? (C{bool}).
2067 '''
2068 return self._Fsum.is_integer()
2070 def _mul_scalar(self, other, op): # for Fsum._fmul
2071 return self._Fsum._mul_scalar(other, op)
2073 @property_RO
2074 def _n(self):
2075 return self._Fsum._n
2077 def _other_op(self, other, which):
2078 C, s = (_Tuple, self) if _isAn(other, _Tuple) else (Fsum, self._Fsum)
2079 return getattr(C, which.__name__)(s, other)
2081 @property_RO
2082 def _ps(self):
2083 return self._Fsum._ps
2085 @property_RO
2086 def _ps_neg(self):
2087 return self._Fsum._ps_neg
2089 def signOf(self, **res):
2090 '''Like method L{Fsum.signOf}.
2091 '''
2092 return self._Fsum.signOf(**res)
2094 def toStr(self, fmt=Fmt.g, **prec_sep): # PYCHOK signature
2095 '''Return this L{Fsum2Tuple} as string (C{str}).
2097 @kwarg fmt: Optional C{float} format (C{letter}).
2098 @kwarg prec_sep: Optional keyword arguments for function
2099 L{fstr<streprs.fstr>}.
2100 '''
2101 return Fmt.PAREN(fstr(self, fmt=fmt, strepr=str, force=False, **prec_sep))
2103_Fsum_Fsum2Tuple_types = Fsum, Fsum2Tuple # PYCHOK lines
2106class ResidualError(_ValueError):
2107 '''Error raised for a division, power or root operation of
2108 an L{Fsum} instance with a C{residual} I{ratio} exceeding
2109 the L{RESIDUAL<Fsum.RESIDUAL>} threshold.
2111 @see: Module L{pygeodesy.fsums} and method L{Fsum.RESIDUAL}.
2112 '''
2113 pass
2116try:
2117 from math import fsum as _fsum # precision IEEE-754 sum, Python 2.6+
2119 # make sure _fsum works as expected (XXX check
2120 # float.__getformat__('float')[:4] == 'IEEE'?)
2121 if _fsum((1, 1e101, 1, -1e101)) != 2: # PYCHOK no cover
2122 del _fsum # nope, remove _fsum ...
2123 raise ImportError # ... use _fsum below
2125 Fsum._math_fsum = _sum = _fsum # PYCHOK exported
2126except ImportError:
2127 _sum = sum # Fsum(NAN) exception fall-back, in .elliptic
2129 def _fsum(xs):
2130 '''(INTERNAL) Precision summation, Python 2.5-.
2131 '''
2132 F = Fsum()
2133 F.name = _fsum.__name__
2134 return F._facc(xs, up=False)._fprs2.fsum
2137def fsum(xs, floats=False):
2138 '''Precision floating point summation based on/like Python's C{math.fsum}.
2140 @arg xs: Iterable of items to add (each C{scalar} or an L{Fsum} or L{Fsum2Tuple}
2141 instance).
2142 @kwarg floats: Use C{B{floats}=True} iff I{all} B{C{xs}} items are I{known to
2143 be scalar} (C{bool}).
2145 @return: Precision C{fsum} (C{float}).
2147 @raise OverflowError: Partial C{2sum} overflow.
2149 @raise TypeError: Non-scalar B{C{xs}} item.
2151 @raise ValueError: Invalid or non-finite B{C{xs}} item.
2153 @note: Exception and I{non-finite} handling may differ if not based
2154 on Python's C{math.fsum}.
2156 @see: Class L{Fsum} and methods L{Fsum.fsum} and L{Fsum.fadd}.
2157 '''
2158 return _fsum(xs if floats is True else _2floats(xs)) if xs else _0_0 # PYCHOK yield
2161def fsum_(*xs, **floats):
2162 '''Precision floating point summation of all positional items.
2164 @arg xs: Items to add (each C{scalar} or an L{Fsum} or L{Fsum2Tuple} instance),
2165 all positional.
2166 @kwarg floats: Use C{B{floats}=True} iff I{all} B{C{xs}} items are I{known to
2167 be scalar} (C{bool}).
2169 @see: Function L{fsum<fsums.fsum>} for further details.
2170 '''
2171 return _fsum(xs if _xkwds_get(floats, floats=False) is True else
2172 _2floats(xs, origin=1)) if xs else _0_0 # PYCHOK yield
2175def fsumf_(*xs):
2176 '''Precision floating point summation iff I{all} C{B{xs}} items are I{known to be scalar}.
2178 @see: Function L{fsum_<fsums.fsum_>} for further details.
2179 '''
2180 return _fsum(xs) if xs else _0_0
2183def fsum1(xs, floats=False):
2184 '''Precision floating point summation, 1-primed.
2186 @arg xs: Iterable of items to add (each C{scalar} or an L{Fsum} or L{Fsum2Tuple}
2187 instance).
2188 @kwarg floats: Use C{B{floats}=True} iff I{all} B{C{xs}} items are I{known to
2189 be scalar} (C{bool}).
2191 @see: Function L{fsum<fsums.fsum>} for further details.
2192 '''
2193 return _fsum(_1primed(xs if floats is True else _2floats(xs))) if xs else _0_0 # PYCHOK yield
2196def fsum1_(*xs, **floats):
2197 '''Precision floating point summation, 1-primed of all positional items.
2199 @arg xs: Items to add (each C{scalar} or an L{Fsum} or L{Fsum2Tuple} instance),
2200 all positional.
2201 @kwarg floats: Use C{B{floats}=True} iff I{all} B{C{xs}} items are I{known to
2202 be scalar} (C{bool}).
2204 @see: Function L{fsum_<fsums.fsum_>} for further details.
2205 '''
2206 return _fsum(_1primed(xs if _xkwds_get(floats, floats=False) is True else
2207 _2floats(xs, origin=1))) if xs else _0_0 # PYCHOK yield
2210def fsum1f_(*xs):
2211 '''Precision floating point summation iff I{all} C{B{xs}} items are I{known to be scalar}.
2213 @see: Function L{fsum_<fsums.fsum_>} for further details.
2214 '''
2215 return _fsum(_1primed(xs)) if xs else _0_0
2218if __name__ == '__main__':
2220 # usage: [env _psum=fsum] python3 -m pygeodesy.fsums
2222 if _getenv(_psum.__name__, NN) == _fsum.__name__:
2223 _psum = _fsum
2225 def _test(n):
2226 # copied from Hettinger, see L{Fsum} reference
2227 from pygeodesy import frandoms, printf
2229 printf(_fsum.__name__, end=_COMMASPACE_)
2230 printf(_psum.__name__, end=_COMMASPACE_)
2232 F = Fsum()
2233 if F.is_math_fsum():
2234 for t in frandoms(n, seeded=True):
2235 assert _Float(F.fset_(*t)) == _fsum(t)
2236 printf(_DOT_, end=NN)
2237 printf(NN)
2239 _test(128)
2241# **) MIT License
2242#
2243# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.
2244#
2245# Permission is hereby granted, free of charge, to any person obtaining a
2246# copy of this software and associated documentation files (the "Software"),
2247# to deal in the Software without restriction, including without limitation
2248# the rights to use, copy, modify, merge, publish, distribute, sublicense,
2249# and/or sell copies of the Software, and to permit persons to whom the
2250# Software is furnished to do so, subject to the following conditions:
2251#
2252# The above copyright notice and this permission notice shall be included
2253# in all copies or substantial portions of the Software.
2254#
2255# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
2256# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
2257# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
2258# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
2259# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
2260# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
2261# OTHER DEALINGS IN THE SOFTWARE.