Coverage for pygeodesy/fsums.py: 96%
778 statements
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2# -*- coding: utf-8 -*-
4u'''Class L{Fsum} for precision floating point summation and I{running}
5summation based on, respectively similar to Python's C{math.fsum}.
7Generally, an L{Fsum} instance is considered a C{float} plus a small or zero
8C{residual} value, see property L{Fsum.residual}. However, there are several
9C{integer} L{Fsum} cases, for example the result of C{ceil}, C{floor},
10C{Fsum.__floordiv__} and methods L{Fsum.fint} and L{Fsum.fint2}.
12Also, L{Fsum} methods L{Fsum.pow}, L{Fsum.__ipow__}, L{Fsum.__pow__} and
13L{Fsum.__rpow__} return a (very long) C{int} if invoked with optional argument
14C{mod} set to C{None}. The C{residual} of an C{integer} L{Fsum} may be between
15C{-1.0} and C{+1.0}, including C{INT0} if considered to be I{exact}.
17Set env variable C{PYGEODESY_FSUM_PARTIALS} to string C{"fsum"}) for summation
18of L{Fsum} partials by Python function C{math.fsum}.
20Set env variable C{PYGEODESY_FSUM_RESIDUAL} to a C{float} string greater than
21C{"0.0"} as the threshold to throw a L{ResidualError} in division or exponention
22of an L{Fsum} instance with a I{relative} C{residual} exceeding the threshold,
23see methods L{Fsum.RESIDUAL}, L{Fsum.pow}, L{Fsum.__ipow__} and L{Fsum.__itruediv__}.
24'''
25# make sure int/int division yields float quotient, see .basics
26from __future__ import division as _; del _ # PYCHOK semicolon
28from pygeodesy.basics import iscomplex, isint, isscalar, itemsorted, \
29 signOf, _signOf
30from pygeodesy.constants import INT0, _isfinite, NEG0, _pos_self, \
31 _0_0, _1_0, _N_1_0, Float, Int
32from pygeodesy.errors import _OverflowError, _TypeError, _ValueError, _xError, \
33 _xError2, _xkwds_get, _ZeroDivisionError
34from pygeodesy.interns import NN, _arg_, _COMMASPACE_, _DASH_, _DOT_, _EQUAL_, \
35 _exceeds_, _from_, _iadd_op_, _LANGLE_, _negative_, \
36 _NOTEQUAL_, _not_finite_, _PERCENT_, _PLUS_, _R_, \
37 _RANGLE_, _SLASH_, _SPACE_, _STAR_, _UNDER_
38from pygeodesy.lazily import _ALL_LAZY, _getenv, _sys_version_info2
39from pygeodesy.named import _Named, _NamedTuple, _NotImplemented, Fmt, unstr
40from pygeodesy.props import _allPropertiesOf_n, deprecated_property_RO, \
41 Property_RO, property_RO
42# from pygeodesy.streprs import Fmt, unstr # from .named
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__ = '24.04.18'
50_add_op_ = _PLUS_ # in .auxilats.auxAngle
51_eq_op_ = _EQUAL_ * 2 # _DEQUAL_
52_COMMASPACE_R_ = _COMMASPACE_ + _R_
53_div_ = 'div'
54_exceeds_R_ = _SPACE_ + _exceeds_(_R_)
55_floordiv_op_ = _SLASH_ * 2 # _DSLASH_
56_fset_op_ = _EQUAL_
57_ge_op_ = _RANGLE_ + _EQUAL_
58_gt_op_ = _RANGLE_
59_integer_ = 'integer'
60_le_op_ = _LANGLE_ + _EQUAL_
61_lt_op_ = _LANGLE_
62_mod_ = 'mod'
63_mod_op_ = _PERCENT_
64_mul_op_ = _STAR_
65_ne_op_ = _NOTEQUAL_
66_non_zero_ = 'non-zero'
67_pow_op_ = _STAR_ * 2 # _DSTAR_, in .fmath
68_sub_op_ = _DASH_ # in .auxilats.auxAngle, .fsums
69_truediv_op_ = _SLASH_
70_divmod_op_ = _floordiv_op_ + _mod_op_
71_isub_op_ = _sub_op_ + _fset_op_ # in .auxilats.auxAngle, .fsums
74def _2delta(*ab):
75 '''(INTERNAL) Helper for C{Fsum._fsum2}.
76 '''
77 try:
78 a, b = _2sum(*ab)
79 except _OverflowError:
80 a, b = ab
81 return float(a if fabs(a) > fabs(b) else b)
84def _2error(unused):
85 '''(INTERNAL) Throw a C{not finite} exception.
86 '''
87 raise ValueError(_not_finite_)
90def _2float(index=None, **name_value): # in .fmath, .fstats
91 '''(INTERNAL) Raise C{TypeError} or C{ValueError} if not scalar or infinite.
92 '''
93 n, v = name_value.popitem() # _xkwds_item2(name_value)
94 try:
95 v = float(v)
96 return v if _isfinite(v) else _2error(v)
97 except Exception as X:
98 raise _xError(X, Fmt.INDEX(n, index), v)
101def _X_ps(X): # for _2floats only
102 return X._ps
105def _2floats(xs, origin=0, _X=_X_ps, _x=float):
106 '''(INTERNAL) Yield each B{C{xs}} as a C{float}.
107 '''
108 try:
109 i, x = origin, None
110 _fin = _isfinite
111 _Fs = Fsum
112 for x in xs:
113 if isinstance(x, _Fs):
114 for p in _X(x):
115 yield p
116 else:
117 f = _x(x)
118 yield f if _fin(f) else _2error(f)
119 i += 1
120 except Exception as X:
121 raise _xError(X, Fmt.INDEX(xs=i), x)
124def _Fsumf_(*xs): # floats=True, in .auxLat, ...
125 '''(INTERNAL) An C{Fsum} of I{known scalars}.
126 '''
127 return Fsum()._facc_scalar(xs, up=False)
130def _Fsum1f_(*xs): # floats=True, in .albers, ...
131 '''(INTERNAL) An C{Fsum} of I{known scalars}, 1-primed.
132 '''
133 return Fsum()._facc_scalar(_1primed(xs), up=False)
136def _2halfeven(s, r, p):
137 '''(INTERNAL) Round half-even.
138 '''
139 if (p > 0 and r > 0) or \
140 (p < 0 and r < 0): # signs match
141 r *= 2
142 t = s + r
143 if r == (t - s):
144 s = t
145 return s
148def _1primed(xs): # in .fmath
149 '''(INTERNAL) 1-Primed summation of iterable C{xs}
150 items, all I{known} to be C{finite float}.
151 '''
152 yield _1_0
153 for x in xs:
154 yield x
155 yield _N_1_0
158def _2ps(s, r):
159 '''(INTERNAL) Return a C{s} and C{r} pair, I{ps-ordered}.
160 '''
161 return (s, r) if fabs(s) < fabs(r) else (r, s)
164def _psum(ps): # PYCHOK used!
165 '''(INTERNAL) Partials sum, updating C{ps}, I{overridden below}.
166 '''
167 # assert isinstance(ps, list)
168 i = len(ps) - 1
169 s = _0_0 if i < 0 else ps[i]
170 _2s = _2sum
171 while i > 0:
172 i -= 1
173 s, r = _2s(s, ps[i])
174 if r: # sum(ps) became inexact
175 if s:
176 ps[i:] = r, s
177 if i > 0:
178 s = _2halfeven(s, r, ps[i-1])
179 break # return s
180 s = r # PYCHOK no cover
181 ps[i:] = s,
182 return s
185def _Psum(ps, **name):
186 '''(INTERNAL) Return an C{Fsum} from I{ordered} partials C{ps}.
187 '''
188 F = Fsum(**name) if name else Fsum()
189 if ps:
190 F._ps[:] = ps
191 F._n = len(F._ps)
192 return F
195def _Psum_1(p=_1_0, **name):
196 '''(INTERNAL) Return an C{Fsum} from a single partial C{p}.
197 '''
198 F = Fsum(**name) if name else Fsum()
199 F._ps[:] = p,
200 F._n = 1 # len(F._ps)
201 return F
204def _2scalar(other, _raiser=None, **mod):
205 '''(INTERNAL) Return B{C{other}} as C{int}, C{float} or C{as-is}.
206 '''
207 if isinstance(other, Fsum):
208 s, r = other._fint2
209 if r:
210 s, r = other._fprs2
211 if r: # PYCHOK no cover
212 if _raiser and _raiser(r, s):
213 t = _stresidual(_non_zero_, r, **mod)
214 raise ResidualError(t, txt=None)
215 s = other # L{Fsum} as-is
216 else:
217 s = other # C{type} as-is
218 if isint(s, both=True):
219 s = int(s)
220 return s
223def _strcomplex(s, *args):
224 '''(INTERNAL) C{Complex} 2- or 3-arg C{pow} error as C{str}.
225 '''
226 c = _strcomplex.__name__[4:]
227 n = _DASH_(len(args), _arg_)
228 t = unstr(pow, *args)
229 return _SPACE_(c, s, _from_, n, t)
232def _stresidual(prefix, residual, **name_values):
233 '''(INTERNAL) Residual error as C{str}.
234 '''
235 p = _stresidual.__name__[3:]
236 t = Fmt.PARENSPACED(p, Fmt(residual))
237 for n, v in itemsorted(name_values):
238 n = n.replace(_UNDER_, _SPACE_)
239 p = Fmt.PARENSPACED(n, Fmt(v))
240 t = _COMMASPACE_(t, p)
241 return _SPACE_(prefix, t)
244def _2sum(a, b): # by .testFmath
245 '''(INTERNAL) Return C{a + b} as 2-tuple (sum, residual).
246 '''
247 s = a + b
248 if _isfinite(s):
249 if fabs(a) < fabs(b):
250 b, a = a, b
251 return s, (b - (s - a))
252 u = unstr(_2sum, a, b)
253 t = Fmt.PARENSPACED(_not_finite_, s)
254 raise _OverflowError(u, txt=t)
257class Fsum(_Named): # sync __methods__ with .vector3dBase.Vector3dBase
258 '''Precision floating point summation and I{running} summation.
260 Unlike Python's C{math.fsum}, this class accumulates values and provides intermediate,
261 I{running}, precision floating point summations. Accumulation may continue after any
262 intermediate, I{running} summuation.
264 @note: Accumulated values may be L{Fsum} or C{scalar} instances, any C{type} having
265 method C{__float__} to convert the C{scalar} to a single C{float}.
267 @note: Handling of exceptions and C{inf}, C{INF}, C{nan} and C{NAN} differs from
268 Python's C{math.fsum}.
270 @see: U{Hettinger<https://GitHub.com/ActiveState/code/blob/master/recipes/Python/
271 393090_Binary_floating_point_summatiaccurate_full/recipe-393090.py>}, U{Kahan
272 <https://WikiPedia.org/wiki/Kahan_summation_algorithm>}, U{Klein
273 <https://Link.Springer.com/article/10.1007/s00607-005-0139-x>}, Python 2.6+
274 file I{Modules/mathmodule.c} and the issue log U{Full precision summation
275 <https://Bugs.Python.org/issue2819>}.
276 '''
277 _math_fsum = None
278 _n = 0
279# _ps = [] # partial sums
280# _ps_max = 0 # max(Fsum._ps_max, len(Fsum._ps))
281 _ratio = None # see method _raiser
282 _recursive = bool(_getenv('PYGEODESY_FSUM_RECURSIVE', NN))
283 _RESIDUAL = max(float(_getenv('PYGEODESY_FSUM_RESIDUAL', _0_0)), _0_0)
285 def __init__(self, *xs, **name_RESIDUAL):
286 '''New L{Fsum} for I{running} precision floating point summation.
288 @arg xs: No, one or more initial values, all positional (each C{scalar}
289 or an L{Fsum} instance).
290 @kwarg name_RESIDUAL: Optional C{B{name}=NN} for this L{Fsum} and
291 C{B{RESIDUAL}=None} for the L{ResidualError} threshold.
293 @see: Methods L{Fsum.fadd} and L{Fsum.RESIDUAL}.
294 '''
295 if name_RESIDUAL:
296 n = _xkwds_get(name_RESIDUAL, name=NN)
297 if n: # set name before ...
298 self.name = n
299 r = _xkwds_get(name_RESIDUAL, RESIDUAL=None)
300 if r is not None:
301 self.RESIDUAL(r) # ... ResidualError
302 self._ps = [] # [_0_0], see L{Fsum._fprs}
303 if xs:
304 self._facc(xs, origin=1, up=False)
306 def __abs__(self):
307 '''Return this instance' absolute value as an L{Fsum}.
308 '''
309 s = _fsum(self._ps_1primed()) # == self._cmp_0(0, ...)
310 return (-self) if s < 0 else self._copy_2(self.__abs__)
312 def __add__(self, other):
313 '''Return C{B{self} + B{other}} as an L{Fsum}.
315 @arg other: An L{Fsum} or C{scalar}.
317 @return: The sum (L{Fsum}).
319 @see: Method L{Fsum.__iadd__}.
320 '''
321 f = self._copy_2(self.__add__)
322 return f._fadd(other, _add_op_)
324 def __bool__(self): # PYCHOK not special in Python 2-
325 '''Return C{True} if this instance is I{exactly} non-zero.
326 '''
327 s, r = self._fprs2
328 return bool(s or r) and s != -r # == self != 0
330 def __ceil__(self): # PYCHOK not special in Python 2-
331 '''Return this instance' C{math.ceil} as C{int} or C{float}.
333 @return: An C{int} in Python 3+, but C{float} in Python 2-.
335 @see: Methods L{Fsum.__floor__} and property L{Fsum.ceil}.
336 '''
337 return self.ceil
339 def __cmp__(self, other): # Python 2-
340 '''Compare this with an other instance or C{scalar}.
342 @return: -1, 0 or +1 (C{int}).
344 @raise TypeError: Incompatible B{C{other}} C{type}.
345 '''
346 s = self._cmp_0(other, self.cmp.__name__)
347 return _signOf(s, 0)
349 cmp = __cmp__
351 def __divmod__(self, other):
352 '''Return C{divmod(B{self}, B{other})} as a L{DivMod2Tuple}
353 with quotient C{div} an C{int} in Python 3+ or C{float}
354 in Python 2- and remainder C{mod} an L{Fsum}.
356 @arg other: An L{Fsum} or C{scalar} modulus.
358 @see: Method L{Fsum.__itruediv__}.
359 '''
360 f = self._copy_2(self.__divmod__)
361 return f._fdivmod2(other, _divmod_op_)
363 def __eq__(self, other):
364 '''Compare this with an other instance or C{scalar}.
365 '''
366 return self._cmp_0(other, _eq_op_) == 0
368 def __float__(self):
369 '''Return this instance' current, precision running sum as C{float}.
371 @see: Methods L{Fsum.fsum} and L{Fsum.int_float}.
372 '''
373 return float(self._fprs)
375 def __floor__(self): # PYCHOK not special in Python 2-
376 '''Return this instance' C{math.floor} as C{int} or C{float}.
378 @return: An C{int} in Python 3+, but C{float} in Python 2-.
380 @see: Methods L{Fsum.__ceil__} and property L{Fsum.floor}.
381 '''
382 return self.floor
384 def __floordiv__(self, other):
385 '''Return C{B{self} // B{other}} as an L{Fsum}.
387 @arg other: An L{Fsum} or C{scalar} divisor.
389 @return: The C{floor} quotient (L{Fsum}).
391 @see: Methods L{Fsum.__ifloordiv__}.
392 '''
393 f = self._copy_2(self.__floordiv__)
394 return f._floordiv(other, _floordiv_op_)
396 def __format__(self, *other): # PYCHOK no cover
397 '''Not implemented.'''
398 return _NotImplemented(self, *other)
400 def __ge__(self, other):
401 '''Compare this with an other instance or C{scalar}.
402 '''
403 return self._cmp_0(other, _ge_op_) >= 0
405 def __gt__(self, other):
406 '''Compare this with an other instance or C{scalar}.
407 '''
408 return self._cmp_0(other, _gt_op_) > 0
410 def __hash__(self): # PYCHOK no cover
411 '''Return this instance' C{hash}.
412 '''
413 return hash(self._ps) # XXX id(self)?
415 def __iadd__(self, other):
416 '''Apply C{B{self} += B{other}} to this instance.
418 @arg other: An L{Fsum} or C{scalar} instance.
420 @return: This instance, updated (L{Fsum}).
422 @raise TypeError: Invalid B{C{other}}, not
423 C{scalar} nor L{Fsum}.
425 @see: Methods L{Fsum.fadd} and L{Fsum.fadd_}.
426 '''
427 return self._fadd(other, _iadd_op_)
429 def __ifloordiv__(self, other):
430 '''Apply C{B{self} //= B{other}} to this instance.
432 @arg other: An L{Fsum} or C{scalar} divisor.
434 @return: This instance, updated (L{Fsum}).
436 @raise ResidualError: Non-zero residual in B{C{other}}.
438 @raise TypeError: Invalid B{C{other}} type.
440 @raise ValueError: Invalid or non-finite B{C{other}}.
442 @raise ZeroDivisionError: Zero B{C{other}}.
444 @see: Methods L{Fsum.__itruediv__}.
445 '''
446 return self._floordiv(other, _floordiv_op_ + _fset_op_)
448 def __imatmul__(self, other): # PYCHOK no cover
449 '''Not implemented.'''
450 return _NotImplemented(self, other)
452 def __imod__(self, other):
453 '''Apply C{B{self} %= B{other}} to this instance.
455 @arg other: An L{Fsum} or C{scalar} modulus.
457 @return: This instance, updated (L{Fsum}).
459 @see: Method L{Fsum.__divmod__}.
460 '''
461 return self._fdivmod2(other, _mod_op_ + _fset_op_).mod
463 def __imul__(self, other):
464 '''Apply C{B{self} *= B{other}} to this instance.
466 @arg other: An L{Fsum} or C{scalar} factor.
468 @return: This instance, updated (L{Fsum}).
470 @raise OverflowError: Partial C{2sum} overflow.
472 @raise TypeError: Invalid B{C{other}} type.
474 @raise ValueError: Invalid or non-finite B{C{other}}.
475 '''
476 return self._fmul(other, _mul_op_ + _fset_op_)
478 def __int__(self):
479 '''Return this instance as an C{int}.
481 @see: Methods L{Fsum.int_float}, L{Fsum.__ceil__}
482 and L{Fsum.__floor__} and properties
483 L{Fsum.ceil} and L{Fsum.floor}.
484 '''
485 i, _ = self._fint2
486 return i
488 def __invert__(self): # PYCHOK no cover
489 '''Not implemented.'''
490 # Luciano Ramalho, "Fluent Python", O'Reilly, 2nd Ed, 2022 p. 567
491 return _NotImplemented(self)
493 def __ipow__(self, other, *mod, **raiser): # PYCHOK 2 vs 3 args
494 '''Apply C{B{self} **= B{other}} to this instance.
496 @arg other: The exponent (L{Fsum} or C{scalar}).
497 @arg mod: Optional modulus (C{int} or C{None}) for the
498 3-argument C{pow(B{self}, B{other}, B{mod})}
499 version.
500 @kwarg raiser: Use C{B{raiser}=False} to ignore L{ResidualError}s
501 (C{bool}), see also method L{RESIDUAL}.
503 @return: This instance, updated (L{Fsum}).
505 @note: If B{C{mod}} is given, the result will be an C{integer}
506 L{Fsum} in Python 3+ if this instance C{is_integer} or
507 set to C{as_integer} if B{C{mod}} given as C{None}.
509 @raise OverflowError: Partial C{2sum} overflow.
511 @raise ResidualError: Non-zero residual in B{C{other}} and
512 env var C{PYGEODESY_FSUM_RESIDUAL}
513 set or this instance has a non-zero
514 residual and either B{C{mod}} is
515 given and non-C{None} or B{C{other}}
516 is a negative or fractional C{scalar}.
518 @raise TypeError: Invalid B{C{other}} type or 3-argument
519 C{pow} invocation failed.
521 @raise ValueError: If B{C{other}} is a negative C{scalar}
522 and this instance is C{0} or B{C{other}}
523 is a fractional C{scalar} and this
524 instance is negative or has a non-zero
525 residual or B{C{mod}} is given and C{0}.
527 @see: CPython function U{float_pow<https://GitHub.com/
528 python/cpython/blob/main/Objects/floatobject.c>}.
529 '''
530 return self._fpow(other, _pow_op_ + _fset_op_, *mod, **raiser)
532 def __isub__(self, other):
533 '''Apply C{B{self} -= B{other}} to this instance.
535 @arg other: An L{Fsum} or C{scalar}.
537 @return: This instance, updated (L{Fsum}).
539 @raise TypeError: Invalid B{C{other}} type.
541 @see: Method L{Fsum.fadd}.
542 '''
543 return self._fsub(other, _isub_op_)
545 def __iter__(self):
546 '''Return an C{iter}ator over a C{partials} duplicate.
547 '''
548 return iter(self.partials)
550 def __itruediv__(self, other, **raiser):
551 '''Apply C{B{self} /= B{other}} to this instance.
553 @arg other: An L{Fsum} or C{scalar} divisor.
554 @kwarg raiser: Use C{B{raiser}=False} to ignore L{ResidualError}s
555 (C{bool}), see also method L{RESIDUAL}.
557 @return: This instance, updated (L{Fsum}).
559 @raise OverflowError: Partial C{2sum} overflow.
561 @raise ResidualError: Non-zero residual in B{C{other}} and
562 env var C{PYGEODESY_FSUM_RESIDUAL} set.
564 @raise TypeError: Invalid B{C{other}} type.
566 @raise ValueError: Invalid or non-finite B{C{other}}.
568 @raise ZeroDivisionError: Zero B{C{other}}.
570 @see: Method L{Fsum.__ifloordiv__}.
571 '''
572 return self._ftruediv(other, _truediv_op_ + _fset_op_, **raiser)
574 def __le__(self, other):
575 '''Compare this with an other instance or C{scalar}.
576 '''
577 return self._cmp_0(other, _le_op_) <= 0
579 def __len__(self):
580 '''Return the number of values accumulated (C{int}).
581 '''
582 return self._n
584 def __lt__(self, other):
585 '''Compare this with an other instance or C{scalar}.
586 '''
587 return self._cmp_0(other, _lt_op_) < 0
589 def __matmul__(self, other): # PYCHOK no cover
590 '''Not implemented.'''
591 return _NotImplemented(self, other)
593 def __mod__(self, other):
594 '''Return C{B{self} % B{other}} as an L{Fsum}.
596 @see: Method L{Fsum.__imod__}.
597 '''
598 f = self._copy_2(self.__mod__)
599 return f._fdivmod2(other, _mod_op_).mod
601 def __mul__(self, other):
602 '''Return C{B{self} * B{other}} as an L{Fsum}.
604 @see: Method L{Fsum.__imul__}.
605 '''
606 f = self._copy_2(self.__mul__)
607 return f._fmul(other, _mul_op_)
609 def __ne__(self, other):
610 '''Compare this with an other instance or C{scalar}.
611 '''
612 return self._cmp_0(other, _ne_op_) != 0
614 def __neg__(self):
615 '''Return I{a copy of} this instance, I{negated}.
616 '''
617 f = self._copy_2(self.__neg__)
618 return f._fset(self._neg)
620 def __pos__(self):
621 '''Return this instance I{as-is}, like C{float.__pos__()}.
622 '''
623 return self if _pos_self else self._copy_2(self.__pos__)
625 def __pow__(self, other, *mod): # PYCHOK 2 vs 3 args
626 '''Return C{B{self}**B{other}} as an L{Fsum}.
628 @see: Method L{Fsum.__ipow__}.
629 '''
630 f = self._copy_2(self.__pow__)
631 return f._fpow(other, _pow_op_, *mod)
633 def __radd__(self, other):
634 '''Return C{B{other} + B{self}} as an L{Fsum}.
636 @see: Method L{Fsum.__iadd__}.
637 '''
638 f = self._copy_2r(other, self.__radd__)
639 return f._fadd(self, _add_op_)
641 def __rdivmod__(self, other):
642 '''Return C{divmod(B{other}, B{self})} as 2-tuple C{(quotient,
643 remainder)}.
645 @see: Method L{Fsum.__divmod__}.
646 '''
647 f = self._copy_2r(other, self.__rdivmod__)
648 return f._fdivmod2(self, _divmod_op_)
650# def __repr__(self):
651# '''Return the default C{repr(this)}.
652# '''
653# return self.toRepr(lenc=True)
655 def __rfloordiv__(self, other):
656 '''Return C{B{other} // B{self}} as an L{Fsum}.
658 @see: Method L{Fsum.__ifloordiv__}.
659 '''
660 f = self._copy_2r(other, self.__rfloordiv__)
661 return f._floordiv(self, _floordiv_op_)
663 def __rmatmul__(self, other): # PYCHOK no cover
664 '''Not implemented.'''
665 return _NotImplemented(self, other)
667 def __rmod__(self, other):
668 '''Return C{B{other} % B{self}} as an L{Fsum}.
670 @see: Method L{Fsum.__imod__}.
671 '''
672 f = self._copy_2r(other, self.__rmod__)
673 return f._fdivmod2(self, _mod_op_).mod
675 def __rmul__(self, other):
676 '''Return C{B{other} * B{self}} as an L{Fsum}.
678 @see: Method L{Fsum.__imul__}.
679 '''
680 f = self._copy_2r(other, self.__rmul__)
681 return f._fmul(self, _mul_op_)
683 def __round__(self, *ndigits): # PYCHOK no cover
684 '''Return C{round(B{self}, *B{ndigits}} as an L{Fsum}.
686 @arg ndigits: Optional number of digits (C{int}).
687 '''
688 # <https://docs.Python.org/3.12/reference/datamodel.html?#object.__round__>
689 return _Psum_1(round(float(self), *ndigits), # can be C{int}
690 name=self.__round__.__name__)
692 def __rpow__(self, other, *mod):
693 '''Return C{B{other}**B{self}} as an L{Fsum}.
695 @see: Method L{Fsum.__ipow__}.
696 '''
697 f = self._copy_2r(other, self.__rpow__)
698 return f._fpow(self, _pow_op_, *mod)
700 def __rsub__(self, other):
701 '''Return C{B{other} - B{self}} as L{Fsum}.
703 @see: Method L{Fsum.__isub__}.
704 '''
705 f = self._copy_2r(other, self.__rsub__)
706 return f._fsub(self, _sub_op_)
708 def __rtruediv__(self, other, **raiser):
709 '''Return C{B{other} / B{self}} as an L{Fsum}.
711 @see: Method L{Fsum.__itruediv__}.
712 '''
713 f = self._copy_2r(other, self.__rtruediv__)
714 return f._ftruediv(self, _truediv_op_, **raiser)
716 def __str__(self):
717 '''Return the default C{str(self)}.
718 '''
719 return self.toStr(lenc=True)
721 def __sub__(self, other):
722 '''Return C{B{self} - B{other}} as an L{Fsum}.
724 @arg other: An L{Fsum} or C{scalar}.
726 @return: The difference (L{Fsum}).
728 @see: Method L{Fsum.__isub__}.
729 '''
730 f = self._copy_2(self.__sub__)
731 return f._fsub(other, _sub_op_)
733 def __truediv__(self, other, **raiser):
734 '''Return C{B{self} / B{other}} as an L{Fsum}.
736 @arg other: An L{Fsum} or C{scalar} divisor.
737 @kwarg raiser: Use C{B{raiser}=False} to ignore L{ResidualError}s
738 (C{bool}), see also method L{RESIDUAL}.
740 @return: The quotient (L{Fsum}).
742 @see: Method L{Fsum.__itruediv__}.
743 '''
744 f = self._copy_2(self.__truediv__)
745 return f._ftruediv(other, _truediv_op_, **raiser)
747 __trunc__ = __int__
749 if _sys_version_info2 < (3, 0): # PYCHOK no cover
750 # <https://docs.Python.org/2/library/operator.html#mapping-operators-to-functions>
751 __div__ = __truediv__
752 __idiv__ = __itruediv__
753 __long__ = __int__
754 __nonzero__ = __bool__
755 __rdiv__ = __rtruediv__
757 def as_integer_ratio(self):
758 '''Return this instance as the ratio of 2 integers.
760 @return: 2-Tuple C{(numerator, denominator)} both
761 C{int} and with positive C{denominator}.
763 @see: Standard C{float.as_integer_ratio} in Python 3+.
764 '''
765 n, r = self._fint2
766 if r:
767 i, d = r.as_integer_ratio()
768 n *= d
769 n += i
770 else: # PYCHOK no cover
771 d = 1
772 return n, d
774 @property_RO
775 def ceil(self):
776 '''Get this instance' C{ceil} value (C{int} in Python 3+,
777 but C{float} in Python 2-).
779 @note: The C{ceil} takes the C{residual} into account.
781 @see: Method L{Fsum.int_float} and properties L{Fsum.floor},
782 L{Fsum.imag} and L{Fsum.real}.
783 '''
784 s, r = self._fprs2
785 c = _ceil(s) + int(r) - 1
786 while r > (c - s): # (s + r) > c
787 c += 1
788 return c
790 def _cmp_0(self, other, op):
791 '''(INTERNAL) Return C{scalar(self - B{other})} for 0-comparison.
792 '''
793 if isinstance(other, Fsum):
794 s = _fsum(self._ps_1primed(*other._ps))
795 elif self._scalar(other, op):
796 s = _fsum(self._ps_1primed(other))
797 else:
798 s, r = self._fprs2
799 s = _signOf(s, -r)
800 return s
802 def copy(self, deep=False, name=NN):
803 '''Copy this instance, C{shallow} or B{C{deep}}.
805 @return: The copy (L{Fsum}).
806 '''
807 f = _Named.copy(self, deep=deep, name=name)
808 if f._ps is self._ps:
809 f._ps = list(self._ps) # separate list
810 if not deep:
811 f._n = 1
812 return f
814 def _copy_2(self, which, name=NN):
815 '''(INTERNAL) Copy for I{dyadic} operators.
816 '''
817 n = name or which.__name__
818 # NOT .classof due to .Fdot(a, *b) args, etc.
819 f = _Named.copy(self, deep=False, name=n)
820 # assert f._n == self._n
821 f._ps = list(self._ps) # separate list
822 return f
824 def _copy_2r(self, other, which):
825 '''(INTERNAL) Copy for I{reverse-dyadic} operators.
826 '''
827 return other._copy_2(which) if isinstance(other, Fsum) else \
828 Fsum(other, name=which.__name__)
830# def _copy_RESIDUAL(self, other):
831# '''(INTERNAL) Copy C{other._RESIDUAL}.
832# '''
833# R = other._RESIDUAL
834# if R is not Fsum._RESIDUAL:
835# self._RESIDUAL = R
837 def divmod(self, other, **raiser):
838 '''Return C{divmod(B{self}, B{other})} as 2-tuple C{(quotient,
839 remainder)}.
841 @arg other: An L{Fsum} or C{scalar} divisor.
842 @kwarg raiser: Use C{B{raiser}=False} to ignore L{ResidualError}s
843 (C{bool}), see also method L{RESIDUAL}.
845 @return: A L{DivMod2Tuple}C{(div, mod)}, with quotient C{div}
846 an C{int} in Python 3+ or C{float} in Python 2- and
847 remainder C{mod} an L{Fsum} instance.
849 @see: Method L{Fsum.__itruediv__}.
850 '''
851 f = self._copy_2(self.divmod)
852 return f._fdivmod2(other, _divmod_op_, **raiser)
854 def _Error(self, op, other, Error, **txt_cause):
855 '''(INTERNAL) Format an B{C{Error}} for C{{self} B{op} B{other}}.
856 '''
857 return Error(_SPACE_(self.toStr(), op, other), **txt_cause)
859 def _ErrorX(self, X, op, other, *mod):
860 '''(INTERNAL) Format the caught exception C{X}.
861 '''
862 E, t = _xError2(X)
863 if mod:
864 t = _COMMASPACE_(Fmt.PARENSPACED(mod=mod[0]), t)
865 return self._Error(op, other, E, txt=t, cause=X)
867 def _ErrorXs(self, X, xs, **kwds): # in .fmath
868 '''(INTERNAL) Format the caught exception C{X}.
869 '''
870 E, t = _xError2(X)
871 n = unstr(self.named3, *xs[:3], _ELLIPSIS=len(xs) > 3, **kwds)
872 return E(n, txt=t, cause=X)
874 def _facc(self, xs, up=True, **origin_X_x):
875 '''(INTERNAL) Accumulate more C{scalars} or L{Fsum}s.
876 '''
877 if xs:
878 _x = _2floats(xs, **origin_X_x) # PYCHOK yield
879 ps = self._ps
880 ps[:] = self._ps_acc(list(ps), _x, up=up)
881 return self
883 def _facc_1(self, xs, **up):
884 '''(INTERNAL) Accumulate 0, 1 or more C{scalars} or L{Fsum}s,
885 all positional C{xs} in the caller of this method.
886 '''
887 # assert islistuple(xs)
888 return self._fadd(xs[0], _add_op_) if len(xs) == 1 else \
889 self._facc(xs, origin=1, **up)
891 def _facc_neg(self, xs, up=True, **origin):
892 '''(INTERNAL) Accumulate more C{scalars} or L{Fsum}s, negated.
893 '''
894 if xs:
895 def _neg(x):
896 return -x
898 _x = _2floats(xs, **origin) # PYCHOK yield
899 ps = self._ps
900 ps[:] = self._ps_acc(list(ps), map(_neg, _x), up=up)
901 return self
903 def _facc_power(self, power, xs, which, **raiser): # in .fmath
904 '''(INTERNAL) Add each C{xs} as C{float(x**power)}.
905 '''
906 def _Pow4(p):
907 r = 0
908 if isinstance(p, Fsum):
909 s, r = p._fprs2
910 if r:
911 return _Pow4(s)
912 m = Fsum._pow
913 elif isint(p, both=True) and int(p) >= 0:
914 p = s = int(p)
915 m = Fsum._pow_int
916 else:
917 p = s = _2float(power=p)
918 m = Fsum._pow_scalar
919 return m, p, s, r
921 _Pow, p, s, r = _Pow4(power)
922 if p: # and xs:
923 _pow = Fsum._pow_2_3
924 _Fs = Fsum
925 _Ps = _Psum_1()._fset_ps_
926 op = which.__name__
928 def _X(X):
929 f = _Pow(X, p, power, op, **raiser)
930 return f._ps if isinstance(f, _Fs) else (f,)
932 def _x(x):
933 x = float(x)
934 X = _Ps(x)
935 f = _pow(X, x, s, power, op, **raiser)
936 if r:
937 f *= _pow(X, x, r, power, op, **raiser)
938 return f
940 f = self._facc(xs, origin=1, _X=_X, _x=_x)
941 else:
942 f = self._facc_scalar_(float(len(xs))) # x**0 == 1
943 return f
945 def _facc_scalar(self, xs, **up):
946 '''(INTERNAL) Accumulate all C{xs}, known to be scalar.
947 '''
948 if xs:
949 self._ps_acc(self._ps, xs, **up)
950 return self
952 def _facc_scalar_(self, *xs, **up):
953 '''(INTERNAL) Accumulate all positional C{xs}, known to be scalar.
954 '''
955 if xs:
956 self._ps_acc(self._ps, xs, **up)
957 return self
959# def _facc_up(self, up=True):
960# '''(INTERNAL) Update the C{partials}, by removing
961# and re-accumulating the final C{partial}.
962# '''
963# while len(self._ps) > 1:
964# p = self._ps.pop()
965# if p:
966# n = self._n
967# self._facc_scalar_(p, up=False)
968# self._n = n
969# break
970# return self._update() if up else self # ._fpsqz()
972 def fadd(self, xs=()):
973 '''Add an iterable of C{scalar} or L{Fsum} instances
974 to this instance.
976 @arg xs: Iterable, list, tuple, etc. (C{scalar} or
977 L{Fsum} instances).
979 @return: This instance (L{Fsum}).
981 @raise OverflowError: Partial C{2sum} overflow.
983 @raise TypeError: An invalid B{C{xs}} type, not C{scalar}
984 nor L{Fsum}.
986 @raise ValueError: Invalid or non-finite B{C{xs}} value.
987 '''
988 if isinstance(xs, Fsum):
989 self._facc_scalar(xs._ps) # tuple
990 elif isscalar(xs): # for backward compatibility
991 self._facc_scalar_(_2float(x=xs)) # PYCHOK no cover
992 elif xs: # assert isiterable(xs)
993 self._facc(xs)
994 return self
996 def fadd_(self, *xs):
997 '''Add all positional C{scalar} or L{Fsum} instances
998 to this instance.
1000 @arg xs: Values to add (C{scalar} or L{Fsum} instances),
1001 all positional.
1003 @return: This instance (L{Fsum}).
1005 @raise OverflowError: Partial C{2sum} overflow.
1007 @raise TypeError: An invalid B{C{xs}} type, not C{scalar}
1008 nor L{Fsum}.
1010 @raise ValueError: Invalid or non-finite B{C{xs}} value.
1011 '''
1012 return self._facc_1(xs)
1014 def _fadd(self, other, op, **up): # in .fmath.Fhorner
1015 '''(INTERNAL) Apply C{B{self} += B{other}}.
1016 '''
1017 if isinstance(other, Fsum):
1018 self._facc_scalar(other._ps, **up) # tuple
1019 elif self._scalar(other, op):
1020 self._facc_scalar_(other, **up)
1021 return self
1023 fcopy = copy # for backward compatibility
1024 fdiv = __itruediv__ # for backward compatibility
1025 fdivmod = __divmod__ # for backward compatibility
1027 def _fdivmod2(self, other, op, **raiser):
1028 '''(INTERNAL) Apply C{B{self} %= B{other}} and return a L{DivMod2Tuple}.
1029 '''
1030 # result mostly follows CPython function U{float_divmod
1031 # <https://GitHub.com/python/cpython/blob/main/Objects/floatobject.c>},
1032 # but at least divmod(-3, 2) equals Cpython's result (-2, 1).
1033 f = self._copy_2(self._fdivmod2)
1034 q = f._ftruediv(other, op, **raiser).floor
1035 if q: # == float // other == floor(float / other)
1036 self -= other * q
1038 s = signOf(other) # make signOf(self) == signOf(other)
1039 if s and self.signOf() == -s: # PYCHOK no cover
1040 self += other
1041 q -= 1
1042# t = self.signOf()
1043# if t and t != s:
1044# raise self._Error(op, other, _AssertionError, txt=signOf.__name__)
1045 return DivMod2Tuple(q, self) # q is C{int} in Python 3+, but C{float} in Python 2-
1047 def _finite(self, other, op=None):
1048 '''(INTERNAL) Return B{C{other}} if C{finite}.
1049 '''
1050 if _isfinite(other):
1051 return other
1052 raise ValueError(_not_finite_) if op is None else \
1053 self._ValueError(op, other, txt=_not_finite_)
1055 def fint(self, raiser=True, **name):
1056 '''Return this instance' current running sum as C{integer}.
1058 @kwarg raiser: Use C{B{raiser}=False} to ignore L{ResidualError}s
1059 (C{bool}), see also method L{RESIDUAL}.
1060 @kwarg name: Optional name (C{str}), overriding C{"fint"}.
1062 @return: The C{integer} (L{Fsum}).
1064 @raise ResidualError: Non-zero I{integer} residual.
1066 @see: Methods L{Fsum.int_float} and L{Fsum.is_integer}.
1067 '''
1068 i, r = self._fint2
1069 if r and raiser:
1070 t = _stresidual(_integer_, r)
1071 raise ResidualError(_integer_, i, txt=t)
1072 f = self._copy_2(self.fint, **name)
1073 return f._fset(i)
1075 def fint2(self, **name):
1076 '''Return this instance' current running sum as C{int} and
1077 the I{integer} residual.
1079 @kwarg name: Optional name (C{str}).
1081 @return: An L{Fsum2Tuple}C{(fsum, residual)} with C{fsum}
1082 an C{int} and I{integer} C{residual} a C{float} or
1083 C{INT0} if the C{fsum} is considered to be I{exact}.
1084 '''
1085 return Fsum2Tuple(*self._fint2, **name)
1087 @Property_RO
1088 def _fint2(self): # see ._fset
1089 '''(INTERNAL) Get 2-tuple (C{int}, I{integer} residual).
1090 '''
1091 s, r = self._fprs2
1092 i = int(s)
1093 r = _fsum(self._ps_1primed(i)) if r else float(s - i)
1094 return i, (r or INT0) # Fsum2Tuple?
1096 @deprecated_property_RO
1097 def float_int(self): # PYCHOK no cover
1098 '''DEPRECATED, use method C{Fsum.int_float}.'''
1099 return self.int_float() # raiser=False
1101 @property_RO
1102 def floor(self):
1103 '''Get this instance' C{floor} (C{int} in Python 3+, but
1104 C{float} in Python 2-).
1106 @note: The C{floor} takes the C{residual} into account.
1108 @see: Method L{Fsum.int_float} and properties L{Fsum.ceil},
1109 L{Fsum.imag} and L{Fsum.real}.
1110 '''
1111 s, r = self._fprs2
1112 f = _floor(s) + _floor(r) + 1
1113 while (f - s) > r: # f > (s + r)
1114 f -= 1
1115 return f
1117# floordiv = __floordiv__ # for naming consistency
1119 def _floordiv(self, other, op, **raiser): # rather _ffloordiv?
1120 '''Apply C{B{self} //= B{other}}.
1121 '''
1122 q = self._ftruediv(other, op, **raiser) # == self
1123 return self._fset(q.floor) # floor(q)
1125 fmul = __imul__ # for backward compatibility
1127 def _fmul(self, other, op):
1128 '''(INTERNAL) Apply C{B{self} *= B{other}}.
1129 '''
1130 if isinstance(other, Fsum):
1131 if len(self._ps) != 1:
1132 f = self._mul_Fsum(other, op)
1133 elif len(other._ps) != 1: # and len(self._ps) == 1
1134 f = other._mul_scalar(self._ps[0], op)
1135 else: # len(other._ps) == len(self._ps) == 1
1136 f = self._finite(self._ps[0] * other._ps[0])
1137 else:
1138 s = self._scalar(other, op)
1139 f = self._mul_scalar(s, op)
1140 return self._fset(f) # n=len(self) + 1
1142 def fover(self, over, **raiser):
1143 '''Apply C{B{self} /= B{over}} and summate.
1145 @arg over: An L{Fsum} or C{scalar} denominator.
1146 @kwarg raiser: Use C{B{raiser}=False} to ignore L{ResidualError}s
1147 (C{bool}), see also method L{RESIDUAL}.
1149 @return: Precision running sum (C{float}).
1151 @see: Methods L{Fsum.fsum} and L{Fsum.__itruediv__}.
1152 '''
1153 return float(self.fdiv(over, **raiser)._fprs)
1155 fpow = __ipow__ # for backward compatibility
1157 def _fpow(self, other, op, *mod, **raiser):
1158 '''Apply C{B{self} **= B{other}}, optional B{C{mod}} or C{None}.
1159 '''
1160 if mod:
1161 if mod[0] is not None: # == 3-arg C{pow}
1162 f = self._pow_2_3(self, other, other, op, *mod, **raiser)
1163 elif self.is_integer():
1164 # return an exact C{int} for C{int}**C{int}
1165 i, _ = self._fint2 # assert _ == 0
1166 x = _2scalar(other) # C{int}, C{float} or other
1167 f = self._pow_2_3(i, x, other, op, **raiser) if isscalar(x) else \
1168 _Psum_1(i)._pow( x, other, op, **raiser) # x is Fsum
1169 else: # mod[0] is None, power(self, other)
1170 f = self._pow(other, other, op, **raiser)
1171 else: # pow(self, other)
1172 f = self._pow(other, other, op, **raiser)
1173 return self._fset(f, asis=isint(f)) # n=max(len(self), 1)
1175 @Property_RO
1176 def _fprs(self):
1177 '''(INTERNAL) Get and cache this instance' precision
1178 running sum (C{float} or C{int}), ignoring C{residual}.
1180 @note: The precision running C{fsum} after a C{//=} or
1181 C{//} C{floor} division is C{int} in Python 3+.
1182 '''
1183 return self._fprs2.fsum
1185 @Property_RO
1186 def _fprs2(self):
1187 '''(INTERNAL) Get and cache this instance' precision
1188 running sum and residual (L{Fsum2Tuple}).
1189 '''
1190 ps = self._ps
1191 n = len(ps) - 2
1192 if n > 0: # len(ps) > 2
1193 s = _psum(ps)
1194 n = len(ps) - 2
1195 if n > 0:
1196 r = _fsum(self._ps_1primed(s)) or INT0
1197 return Fsum2Tuple(s, r)
1198 if n == 0: # len(ps) == 2
1199 ps[:] = _2ps(*_2sum(*ps))
1200 r, s = (INT0, ps[0]) if len(ps) != 2 else ps
1201 elif ps: # len(ps) == 1
1202 s, r = ps[0], INT0
1203 else: # len(ps) == 0
1204 s, r = _0_0, INT0
1205 ps[:] = s,
1206 # assert self._ps is ps
1207 return Fsum2Tuple(s, r)
1209# def _fpsqz(self):
1210# '''(INTERNAL) Compress, squeeze the C{partials}.
1211# '''
1212# if len(self._ps) > 2:
1213# _ = self._fprs2
1214# return self
1216 def fset_(self, *xs):
1217 '''Replace this instance' value with C{xs}.
1219 @arg xs: Optional, new values (C{scalar} or L{Fsum}
1220 instances), all positional.
1222 @return: This instance (C{Fsum}).
1224 @see: Method L{Fsum.fadd} for further details.
1225 '''
1226 self._ps[:] = 0,
1227 self._n = 0
1228 return self.fadd(xs) if xs else self._update()
1230 def _fset(self, other, asis=True, n=0):
1231 '''(INTERNAL) Overwrite this instance with an other or a C{scalar}.
1232 '''
1233 if other is self:
1234 pass # from ._fmul, ._ftruediv and ._pow_0_1
1235 elif isinstance(other, Fsum):
1236 self._ps[:] = other._ps
1237 self._n = n or other._n
1238# self._copy_RESIDUAL(other)
1239 # use or zap the C{Property_RO} values
1240 Fsum._fint2._update_from(self, other)
1241 Fsum._fprs ._update_from(self, other)
1242 Fsum._fprs2._update_from(self, other)
1243 elif isscalar(other):
1244 s = other if asis else float(other)
1245 i = int(s) # see ._fint2
1246 t = i, ((s - i) or INT0)
1247 self._ps[:] = s,
1248 self._n = n or 1
1249 # Property_ROs _fint2, _fprs and _fprs2 can't be a Property:
1250 # Property's _fset zaps the value just set by the @setter
1251 self.__dict__.update(_fint2=t, _fprs=s, _fprs2=Fsum2Tuple(s, INT0))
1252 else: # PYCHOK no cover
1253 raise self._TypeError(_fset_op_, other) # AssertionError
1254 return self
1256 def _fset_ps(self, other, n=0): # in .fmath
1257 '''(INTERNAL) Set partials from a known C{Fsum} or C{scalar}.
1258 '''
1259 if isinstance(other, Fsum):
1260 self._ps[:] = other._ps
1261 self._n = n or other._n
1262 else: # assert isscalar(other)
1263 self._ps[:] = other,
1264 self._n = n or 1
1265 return self
1267 def _fset_ps_(self, *xs):
1268 '''(INTERNAL) Set partials to all known scalar C{xs}.
1269 '''
1270 self._ps[:] = xs
1271 self.n = len(xs)
1272 return self
1274 def fsub(self, xs=()):
1275 '''Subtract an iterable of C{scalar} or L{Fsum} instances from
1276 this instance.
1278 @arg xs: Iterable, list, tuple. etc. (C{scalar} or L{Fsum}
1279 instances).
1281 @return: This instance, updated (L{Fsum}).
1283 @see: Method L{Fsum.fadd}.
1284 '''
1285 return self._facc_neg(xs)
1287 def fsub_(self, *xs):
1288 '''Subtract all positional C{scalar} or L{Fsum} instances from
1289 this instance.
1291 @arg xs: Values to subtract (C{scalar} or L{Fsum} instances),
1292 all positional.
1294 @return: This instance, updated (L{Fsum}).
1296 @see: Method L{Fsum.fadd}.
1297 '''
1298 return self._fsub(xs[0], _sub_op_) if len(xs) == 1 else \
1299 self._facc_neg(xs, origin=1)
1301 def _fsub(self, other, op):
1302 '''(INTERNAL) Apply C{B{self} -= B{other}}.
1303 '''
1304 if isinstance(other, Fsum):
1305 if other is self: # or other._fprs2 == self._fprs2:
1306 self._fset(_0_0) # n=len(self) * 2, self -= self
1307 elif other._ps:
1308 self._facc_scalar(other._ps_neg)
1309 elif self._scalar(other, op):
1310 self._facc_scalar_(-self._finite(other, op))
1311 return self
1313 def fsum(self, xs=()):
1314 '''Add more C{scalar} or L{Fsum} instances and summate.
1316 @kwarg xs: Iterable, list, tuple, etc. (C{scalar} or
1317 L{Fsum} instances).
1319 @return: Precision running sum (C{float} or C{int}).
1321 @see: Method L{Fsum.fadd}.
1323 @note: Accumulation can continue after summation.
1324 '''
1325 return self._facc(xs)._fprs
1327 def fsum_(self, *xs):
1328 '''Add all positional C{scalar} or L{Fsum} instances and summate.
1330 @arg xs: Values to add (C{scalar} or L{Fsum} instances), all
1331 positional.
1333 @return: Precision running sum (C{float} or C{int}).
1335 @see: Methods L{Fsum.fsum}, L{Fsum.Fsum_} and L{Fsum.fsumf_}.
1336 '''
1337 return self._facc_1(xs)._fprs
1339 def Fsum_(self, *xs):
1340 '''Like method L{Fsum.fsum_} but returning an L{Fsum}.
1342 @return: Current, precision running sum (L{Fsum}).
1343 '''
1344 return self._facc_1(xs)._copy_2(self.Fsum_)
1346 def fsum2(self, xs=(), name=NN):
1347 '''Add more C{scalar} or L{Fsum} instances and return the
1348 current precision running sum and the C{residual}.
1350 @kwarg xs: Iterable, list, tuple, etc. (C{scalar} or L{Fsum}
1351 instances).
1352 @kwarg name: Optional name (C{str}).
1354 @return: L{Fsum2Tuple}C{(fsum, residual)} with C{fsum} the
1355 current precision running sum and C{residual}, the
1356 (precision) sum of the remaining C{partials}. The
1357 C{residual is INT0} if the C{fsum} is considered
1358 to be I{exact}.
1360 @see: Methods L{Fsum.fint2}, L{Fsum.fsum} and L{Fsum.fsum2_}
1361 '''
1362 t = self._facc(xs)._fprs2
1363 return t.dup(name=name) if name else t
1365 def fsum2_(self, *xs):
1366 '''Add any positional C{scalar} or L{Fsum} instances and return
1367 the precision running sum and the C{differential}.
1369 @arg xs: Values to add (C{scalar} or L{Fsum} instances), all
1370 positional.
1372 @return: 2Tuple C{(fsum, delta)} with the current, precision
1373 running C{fsum} like method L{Fsum.fsum} and C{delta},
1374 the difference with previous running C{fsum}, C{float}.
1376 @see: Methods L{Fsum.fsum_} and L{Fsum.fsum}.
1377 '''
1378 return self._fsum2(xs, self._facc_1)
1380 def _fsum2(self, xs, _f, **origin):
1381 '''(INTERNAL) Helper for L{Fsum.fsum2_} and L{Fsum.fsum2f_}.
1382 '''
1383 p, q = self._fprs2
1384 if xs:
1385 s, r = _f(xs, **origin)._fprs2
1386 return s, _2delta(s - p, r - q) # _fsum(_1primed((s, -p, r, -q))
1387 else:
1388 return p, _0_0
1390 def fsumf_(self, *xs):
1391 '''Like method L{Fsum.fsum_} but only for C{B{xs}}, I{known to be scalar}.
1392 '''
1393 return self._facc_scalar(xs)._fprs
1395 def Fsumf_(self, *xs):
1396 '''Like method L{Fsum.Fsum_} but only for C{B{xs}}, I{known to be scalar}.
1397 '''
1398 return self._facc_scalar(xs)._copy_2(self.Fsumf_)
1400 def fsum2f_(self, *xs):
1401 '''Like method L{Fsum.fsum2_} but only for C{B{xs}}, I{known to be scalar}.
1402 '''
1403 return self._fsum2(xs, self._facc_scalar, origin=1)
1405# ftruediv = __itruediv__ # for naming consistency?
1407 def _ftruediv(self, other, op, **raiser):
1408 '''(INTERNAL) Apply C{B{self} /= B{other}}.
1409 '''
1410 n = _1_0
1411 if isinstance(other, Fsum):
1412 if other is self or other == self:
1413 return self._fset(n) # n=len(self)
1414 d, r = other._fprs2
1415 if r:
1416 if d:
1417 if self._raiser(r, d, **raiser):
1418 raise self._ResidualError(op, other, r)
1419 d, n = other.as_integer_ratio()
1420 else: # PYCHOK no cover
1421 d = r
1422 else:
1423 d = self._scalar(other, op)
1424 try:
1425 s = n / d
1426 except Exception as X:
1427 raise self._ErrorX(X, op, other)
1428 f = self._mul_scalar(s, _mul_op_) # handles 0, INF, NAN
1429 return self._fset(f) # asis=False
1431 @property_RO
1432 def imag(self):
1433 '''Get the C{imaginary} part of this instance (C{0.0}, always).
1435 @see: Properties L{Fsum.ceil}, L{Fsum.floor} and L{Fsum.real}.
1436 '''
1437 return _0_0
1439 def int_float(self, raiser=False):
1440 '''Return this instance' current running sum as C{int} or C{float}.
1442 @kwarg raiser: If C{True} throw a L{ResidualError} if the
1443 residual is non-zero (C{bool}).
1445 @return: This C{integer} sum if this instance C{is_integer},
1446 otherwise return the C{float} sum if the residual
1447 is zero or if C{B{raiser}=False}.
1449 @raise ResidualError: Non-zero residual and C{B{raiser}=True}.
1451 @see: Methods L{Fsum.fint} and L{Fsum.fint2}.
1452 '''
1453 s, r = self._fint2
1454 if r:
1455 s, r = self._fprs2
1456 if r and raiser: # PYCHOK no cover
1457 t = _stresidual(_non_zero_, r)
1458 raise ResidualError(int_float=s, txt=t)
1459 s = float(s) # redundant
1460 return s
1462 def is_exact(self):
1463 '''Is this instance' running C{fsum} considered to be exact? (C{bool}).
1464 '''
1465 return self.residual is INT0
1467 def is_integer(self):
1468 '''Is this instance' running sum C{integer}? (C{bool}).
1470 @see: Methods L{Fsum.fint} and L{Fsum.fint2}.
1471 '''
1472 _, r = self._fint2
1473 return False if r else True
1475 def is_math_fsum(self):
1476 '''Return whether functions L{fsum}, L{fsum_}, L{fsum1} and
1477 L{fsum1_} plus partials summation are based on Python's
1478 C{math.fsum} or not.
1480 @return: C{2} if all functions and partials summation
1481 are based on C{math.fsum}, C{True} if only
1482 the functions are based on C{math.fsum} (and
1483 partials summation is not) or C{False} if
1484 none are.
1485 '''
1486 f = Fsum._math_fsum
1487 return 2 if _psum is f else bool(f)
1489 def _mul_Fsum(self, other, op=_mul_op_): # in .fmath.Fhorner
1490 '''(INTERNAL) Return C{B{self} * Fsum B{other}} as L{Fsum} or C{0}.
1491 '''
1492 # assert isinstance(other, Fsum)
1493 if self._ps and other._ps:
1494 f = self._ps_mul(op, *other._ps) # NO ._2scalar
1495 else:
1496 f = _0_0
1497 return f
1499 def _mul_scalar(self, factor, op): # in .fmath.Fhorner
1500 '''(INTERNAL) Return C{B{self} * scalar B{factor}} as L{Fsum}, C{0} or C{self}.
1501 '''
1502 # assert isscalar(factor)
1503 if self._ps and self._finite(factor, op):
1504 f = self if factor == _1_0 else (
1505 self._neg if factor == _N_1_0 else
1506 self._ps_mul(op, factor)._2scalar)
1507 else:
1508 f = _0_0
1509 return f
1511 @property_RO
1512 def _neg(self):
1513 '''(INTERNAL) Return C{Fsum(-self)} or scalar C{NEG0}.
1514 '''
1515 return _Psum(self._ps_neg) if self._ps else NEG0
1517 @property_RO
1518 def partials(self):
1519 '''Get this instance' current, partial sums (C{tuple} of C{float}s).
1520 '''
1521 return tuple(self._ps)
1523 def pow(self, x, *mod, **raiser):
1524 '''Return C{B{self}**B{x}} as L{Fsum}.
1526 @arg x: The exponent (L{Fsum} or C{scalar}).
1527 @arg mod: Optional modulus (C{int} or C{None}) for the 3-argument
1528 C{pow(B{self}, B{other}, B{mod})} version.
1529 @kwarg raiser: Use C{B{raiser}=False} to ignore L{ResidualError}s
1530 (C{bool}), see also method L{RESIDUAL}.
1532 @return: The C{pow(self, B{x})} or C{pow(self, B{x}, *B{mod})}
1533 result (L{Fsum}).
1535 @note: If B{C{mod}} is given as C{None}, the result will be an
1536 C{integer} L{Fsum} provided this instance C{is_integer}
1537 or set to C{integer} by an L{Fsum.fint} call.
1539 @see: Methods L{Fsum.__ipow__}, L{Fsum.fint}, L{Fsum.is_integer}
1540 and L{Fsum.root}.
1541 '''
1542 f = self._copy_2(self.pow)
1543 return f._fpow(x, _pow_op_, *mod, **raiser) # f = pow(f, x, *mod)
1545 def _pow(self, other, unused, op, **raiser):
1546 '''Return C{B{self} ** B{other}}.
1547 '''
1548 if isinstance(other, Fsum):
1549 x, r = other._fprs2
1550 if r and self._raiser(r, x, **raiser):
1551 raise self._ResidualError(op, other, r)
1552 f = self._pow_scalar(x, other, op, **raiser)
1553 if r:
1554 f *= self._pow_scalar(r, other, op, **raiser)
1555 elif self._scalar(other, op):
1556 x = self._finite(other, op)
1557 f = self._pow_scalar(x, other, op, **raiser)
1558 else:
1559 f = self._pow_0_1(0, other)
1560 return f
1562 def _pow_0_1(self, x, other):
1563 '''(INTERNAL) Return B{C{self}**1} or C{B{self}**0 == 1.0}.
1564 '''
1565 return self if x else (1 if isint(other) and self.is_integer() else _1_0)
1567 def _pow_2_3(self, b, x, other, op, *mod, **raiser):
1568 '''(INTERNAL) 2-arg C{pow(B{b}, scalar B{x})} and 3-arg C{pow(B{b},
1569 B{x}, int B{mod} or C{None})}, embellishing errors.
1570 '''
1571 try:
1572 if mod: # b, x, mod all C{int}, unless C{mod} is C{None}
1573 m = mod[0]
1574 b, r = b._fprs2 if m is None else b._fint2
1575 if r and self._raiser(r, b, **raiser):
1576 t = _non_zero_ if m is None else _integer_
1577 raise ResidualError(_stresidual(t, r, mod=m), txt=None)
1578 x = _2scalar(x, _raiser=self._raiser, mod=m)
1579 # 0**INF == 0.0, 1**INF == 1.0, -1**2.3 == -(1**2.3)
1580 s = pow(b, x, *mod)
1581 if iscomplex(s):
1582 # neg**frac == complex in Python 3+, but ValueError in 2-
1583 raise ValueError(_strcomplex(s, b, x, *mod))
1584 return self._finite(s)
1585 except Exception as X:
1586 raise self._ErrorX(X, op, other, *mod)
1588 def _pow_int(self, x, other, op, **raiser):
1589 '''(INTERNAL) Return C{B{self} **= B{x}} for C{int B{x} >= 0}.
1590 '''
1591 # assert isint(x) and x >= 0
1592 ps = self._ps
1593 if len(ps) > 1:
1594 _mul_Fsum = Fsum._mul_Fsum
1595 if x > 4:
1596 p = self
1597 f = self if (x & 1) else _Psum_1()
1598 m = x >> 1 # // 2
1599 while m:
1600 p = _mul_Fsum(p, p, op) # p **= 2
1601 if (m & 1):
1602 f = _mul_Fsum(f, p, op) # f *= p
1603 m >>= 1 # //= 2
1604 elif x > 1: # self**2, 3 or 4
1605 f = _mul_Fsum(self, self, op)
1606 if x > 2: # self**3 or 4
1607 p = self if x < 4 else f
1608 f = _mul_Fsum(f, p, op)._2scalar
1609 else: # self**1 or self**0 == 1 or _1_0
1610 f = self._pow_0_1(x, other)
1611 elif ps: # self._ps[0]**x
1612 f = self._pow_2_3(ps[0], x, other, op, **raiser)
1613 else: # PYCHOK no cover
1614 # 0**pos_int == 0, but 0**0 == 1
1615 f = 0 if x else 1
1616 return f
1618 def _pow_scalar(self, x, other, op, **raiser):
1619 '''(INTERNAL) Return C{self**B{x}} for C{scalar B{x}}.
1620 '''
1621 s, r = self._fprs2
1622 if isint(x, both=True):
1623 x = int(x) # Fsum**int
1624 y = abs(x)
1625 if y > 1:
1626 if r:
1627 f = self._pow_int(y, other, op, **raiser)
1628 if x > 0: # > 1
1629 return f
1630 # assert x < 0 # < -1
1631 s, r = f._fprs2 if isinstance(f, Fsum) else (f, 0)
1632 if r:
1633 return _Psum_1()._ftruediv(f, op, **raiser)
1634 # use **= -1 for the CPython float_pow
1635 # error if s is zero, and not s = 1 / s
1636 x = -1
1637 elif x < 0: # == -1: self**(-1) == 1 / self
1638 if r:
1639 return _Psum_1()._ftruediv(self, op, **raiser)
1640 else: # self**1 or self**0
1641 return self._pow_0_1(x, other) # self, 1 or 1.0
1642 elif r and self._raiser(r, s, **raiser): # non-zero residual**fractional
1643 # raise self._ResidualError(op, other, r, fractional_power=x)
1644 t = _stresidual(_non_zero_, r, fractional_power=x)
1645 raise self._Error(op, other, ResidualError, txt=t)
1646 # assert isscalar(s) and isscalar(x)
1647 return self._pow_2_3(s, x, other, op, **raiser)
1649 def _ps_acc(self, ps, xs, up=True, **unused):
1650 '''(INTERNAL) Accumulate all scalar C{xs} into C{ps}.
1651 '''
1652 n = 0
1653 _2s = _2sum
1654 for x in (tuple(xs) if xs is ps else xs):
1655 # assert isscalar(x) and _isfinite(x)
1656 if x:
1657 i = 0
1658 for p in ps:
1659 x, p = _2s(x, p)
1660 if p:
1661 ps[i] = p
1662 i += 1
1663 ps[i:] = (x,) if x else ()
1664 n += 1
1665 if n:
1666 self._n += n
1667 # Fsum._ps_max = max(Fsum._ps_max, len(ps))
1668 if up:
1669 self._update()
1670 return ps
1672 def _ps_mul(self, op, *factors):
1673 '''(INTERNAL) Multiply this instance' C{partials} with
1674 each of the scalar B{C{factors}} and accumulate.
1675 '''
1676 def _pfs(ps, fs):
1677 if len(ps) < len(fs):
1678 ps, fs = fs, ps
1679 _fin = _isfinite
1680 for f in fs:
1681 for p in ps:
1682 p *= f
1683 yield p if _fin(p) else self._finite(p, op)
1685 return _Psum(self._ps_acc([], _pfs(self._ps, factors)))
1687 @property_RO
1688 def _ps_neg(self):
1689 '''(INTERNAL) Yield the partials, I{negated}.
1690 '''
1691 for p in self._ps:
1692 yield -p
1694 def _ps_1primed(self, *less):
1695 '''(INTERNAL) Yield partials, 1-primed and subtract any C{less} scalars.
1696 '''
1697 yield _1_0
1698 for p in self._ps:
1699 yield p
1700 for p in less:
1701 yield -p
1702 yield _N_1_0
1704 def _raiser(self, r, s, raiser=True):
1705 '''(INTERNAL) Does ratio C{r / s} exceed the RESIDUAL threshold?
1706 '''
1707 self._ratio = t = fabs(r / s) if s else 0 # _0_0
1708 return raiser and (t > self._RESIDUAL)
1710 @property_RO
1711 def real(self):
1712 '''Get the C{real} part of this instance (C{float}).
1714 @see: Methods L{Fsum.__float__} and L{Fsum.fsum}
1715 and properties L{Fsum.ceil}, L{Fsum.floor},
1716 L{Fsum.imag} and L{Fsum.residual}.
1717 '''
1718 return float(self._fprs)
1720 @property_RO
1721 def residual(self):
1722 '''Get this instance' residual (C{float} or C{int}), the
1723 C{sum(partials)} less the precision running sum C{fsum}.
1725 @note: If the C{residual is INT0}, the precision running
1726 C{fsum} is considered to be I{exact}.
1728 @see: Methods L{Fsum.fsum}, L{Fsum.fsum2} and L{Fsum.is_exact}.
1729 '''
1730 return self._fprs2.residual
1732 def RESIDUAL(self, *threshold):
1733 '''Get and set this instance' I{ratio} for raising L{ResidualError}s,
1734 overriding the default from env variable C{PYGEODESY_FSUM_RESIDUAL}.
1736 @arg threshold: If C{scalar}, the I{ratio} to exceed for raising
1737 L{ResidualError}s in division and exponention, if
1738 C{None} restore the default set with env variable
1739 C{PYGEODESY_FSUM_RESIDUAL} or if omitted, keep the
1740 current setting.
1742 @return: The previous C{RESIDUAL} setting (C{float}), default C{0.}.
1744 @raise ValueError: Negative B{C{threshold}}.
1746 @note: L{ResidualError}s will be thrown if the non-zero I{ratio}
1747 C{residual / fsum} exceeds the B{C{threshold}}.
1748 '''
1749 r = self._RESIDUAL
1750 if threshold:
1751 t = threshold[0]
1752 t = Fsum._RESIDUAL if t is None else (
1753 float(t) if isscalar(t) else ( # for backward ...
1754 _0_0 if bool(t) else _1_0)) # ... compatibility
1755 if t < 0:
1756 u = _DOT_(self, unstr(self.RESIDUAL, *threshold))
1757 raise _ValueError(u, RESIDUAL=t, txt=_negative_)
1758 self._RESIDUAL = t
1759 return r
1761 def _ResidualError(self, op, other, residual):
1762 '''(INTERNAL) Non-zero B{C{residual}} etc.
1763 '''
1764 t = _stresidual(_non_zero_, residual, ratio=self._ratio,
1765 RESIDUAL=self._RESIDUAL)
1766 t = t.replace(_COMMASPACE_R_, _exceeds_R_)
1767 return self._Error(op, other, ResidualError, txt=t)
1769 def root(self, root, **raiser):
1770 '''Return C{B{self}**(1 / B{root})} as L{Fsum}.
1772 @arg root: The order (C{scalar} or C{Fsum}), non-zero.
1773 @kwarg raiser: Use C{B{raiser}=False} to ignore L{ResidualError}s
1774 (C{bool}), see also method L{RESIDUAL}.
1776 @return: The C{self ** (1 / B{root})} result (L{Fsum}).
1778 @see: Method L{Fsum.pow}.
1779 '''
1780 _root_ = self.root.__name__
1781 if isinstance(root, Fsum):
1782 x = root.__rtruediv__(_1_0, **raiser)
1783 else:
1784 try:
1785 x = _1_0 / _2float(root=root)
1786 except Exception as X:
1787 E, t = _xError2(X)
1788 n = _SPACE_(_1_0, _truediv_op_, _root_)
1789 raise E(n, root, txt=t, cause=X)
1790 f = self._copy_2(self.root)
1791 return f._fpow(x, _root_, **raiser) # == pow(f, x)
1793 def _scalar(self, other, op, **txt):
1794 '''(INTERNAL) Return scalar C{other}.
1795 '''
1796 if isscalar(other):
1797 return other
1798 raise self._TypeError(op, other, **txt) # _invalid_
1800 @property_RO
1801 def _2scalar(self):
1802 '''(INTERNAL) Get this instance as C{scalar} or C{as-is}.
1803 '''
1804 s, r = self._fprs2
1805 return self if r else s
1807 def signOf(self, res=True):
1808 '''Determine the sign of this instance.
1810 @kwarg res: If C{True} consider, otherwise
1811 ignore the residual (C{bool}).
1813 @return: The sign (C{int}, -1, 0 or +1).
1814 '''
1815 s, r = self._fprs2
1816 return _signOf(s, (-r) if res else 0)
1818 def toRepr(self, **prec_sep_fmt_lenc): # PYCHOK signature
1819 '''Return this C{Fsum} instance as representation.
1821 @kwarg prec_sep_fmt_lenc: Optional keyword arguments for
1822 method L{Fsum2Tuple.toRepr} plus C{B{lenc}=True}
1823 (C{bool}) to in-/exclude the current C{[len]}
1824 of this L{Fsum} enclosed in I{[brackets]}.
1826 @return: This instance (C{repr}).
1827 '''
1828 return self._toT(self._fprs2.toRepr, **prec_sep_fmt_lenc)
1830 def toStr(self, **prec_sep_fmt_lenc): # PYCHOK signature
1831 '''Return this C{Fsum} instance as string.
1833 @kwarg prec_sep_fmt_lenc: Optional keyword arguments for
1834 method L{Fsum2Tuple.toStr} plus C{B{lenc}=True}
1835 (C{bool}) to in-/exclude the current C{[len]}
1836 of this L{Fsum} enclosed in I{[brackets]}.
1838 @return: This instance (C{str}).
1839 '''
1840 return self._toT(self._fprs2.toStr, **prec_sep_fmt_lenc)
1842 def _toT(self, toT, fmt=Fmt.g, lenc=True, **kwds):
1843 '''(INTERNAL) Helper for C{toRepr} and C{toStr}.
1844 '''
1845 n = self.named3
1846 if lenc:
1847 n = Fmt.SQUARE(n, len(self))
1848 return _SPACE_(n, toT(fmt=fmt, **kwds))
1850 def _TypeError(self, op, other, **txt): # PYCHOK no cover
1851 '''(INTERNAL) Return a C{TypeError}.
1852 '''
1853 return self._Error(op, other, _TypeError, **txt)
1855 def _update(self, updated=True): # see ._fset
1856 '''(INTERNAL) Zap all cached C{Property_RO} values.
1857 '''
1858 if updated:
1859 _pop = self.__dict__.pop
1860 for p in _ROs:
1861 _ = _pop(p, None)
1862# Fsum._fint2._update(self)
1863# Fsum._fprs ._update(self)
1864# Fsum._fprs2._update(self)
1865 return self # for .fset_
1867 def _ValueError(self, op, other, **txt): # PYCHOK no cover
1868 '''(INTERNAL) Return a C{ValueError}.
1869 '''
1870 return self._Error(op, other, _ValueError, **txt)
1872 def _ZeroDivisionError(self, op, other, **txt): # PYCHOK no cover
1873 '''(INTERNAL) Return a C{ZeroDivisionError}.
1874 '''
1875 return self._Error(op, other, _ZeroDivisionError, **txt)
1877_ROs = _allPropertiesOf_n(3, Fsum, Property_RO) # PYCHOK assert, see Fsum._fset, -._update
1880def _Float_Int(arg, **name_Error):
1881 '''(INTERNAL) Unit of L{Fsum2Tuple} items.
1882 '''
1883 U = Int if isint(arg) else Float
1884 return U(arg, **name_Error)
1887class DivMod2Tuple(_NamedTuple):
1888 '''2-Tuple C{(div, mod)} with the quotient C{div} and remainder
1889 C{mod} results of a C{divmod} operation.
1891 @note: Quotient C{div} an C{int} in Python 3+ or a C{float} in
1892 Python 2-. Remainder C{mod} an L{Fsum} instance.
1893 '''
1894 _Names_ = (_div_, _mod_)
1895 _Units_ = (_Float_Int, Fsum)
1898class Fsum2Tuple(_NamedTuple):
1899 '''2-Tuple C{(fsum, residual)} with the precision running C{fsum}
1900 and the C{residual}, the sum of the remaining partials. Each
1901 item is either C{float} or C{int}.
1903 @note: If the C{residual is INT0}, the C{fsum} is considered
1904 to be I{exact}, see method L{Fsum2Tuple.is_exact}.
1905 '''
1906 _Names_ = ( Fsum.fsum.__name__, Fsum.residual.name)
1907 _Units_ = (_Float_Int, _Float_Int)
1909 @Property_RO
1910 def _Fsum(self):
1911 '''(INTERNAL) Get this L{Fsum2Tuple} as an L{Fsum}.
1912 '''
1913 s, r = map(float, self)
1914 return _Psum(_2ps(s, r), name=self.name)
1916 def is_exact(self):
1917 '''Is this L{Fsum2Tuple} considered to be exact? (C{bool}).
1918 '''
1919 return self._Fsum.is_exact()
1921 def is_integer(self):
1922 '''Is this L{Fsum2Tuple} C{integer}? (C{bool}).
1923 '''
1924 return self._Fsum.is_integer()
1927class ResidualError(_ValueError):
1928 '''Error raised for an operation involving a L{pygeodesy.sums.Fsum}
1929 instance with a non-zero C{residual}, I{integer} or otherwise.
1931 @see: Module L{pygeodesy.fsums} and method L{Fsum.RESIDUAL}.
1932 '''
1933 pass
1936try:
1937 from math import fsum as _fsum # precision IEEE-754 sum, Python 2.6+
1939 # make sure _fsum works as expected (XXX check
1940 # float.__getformat__('float')[:4] == 'IEEE'?)
1941 if _fsum((1, 1e101, 1, -1e101)) != 2: # PYCHOK no cover
1942 del _fsum # nope, remove _fsum ...
1943 raise ImportError # ... use _fsum below
1945 Fsum._math_fsum = _sum = _fsum # PYCHOK exported
1947 if _getenv('PYGEODESY_FSUM_PARTIALS', NN) == _fsum.__name__:
1948 _psum = _fsum # PYCHOK re-def
1950except ImportError:
1951 _sum = sum # Fsum(NAN) exception fall-back, in .elliptic
1953 def _fsum(xs):
1954 '''(INTERNAL) Precision summation, Python 2.5-.
1955 '''
1956 f = Fsum()
1957 f.name = _fsum.__name__
1958 return f.fsum(xs)
1961def fsum(xs, floats=False):
1962 '''Precision floating point summation based on or like Python's C{math.fsum}.
1964 @arg xs: Iterable, list, tuple, etc. of values (C{scalar} or L{Fsum}
1965 instances).
1966 @kwarg floats: Use C{B{floats}=True} iff I{all} B{C{xs}} are known
1967 to be C{float} scalars (C{bool}).
1969 @return: Precision C{fsum} (C{float}).
1971 @raise OverflowError: Partial C{2sum} overflow.
1973 @raise TypeError: Non-scalar B{C{xs}} value.
1975 @raise ValueError: Invalid or non-finite B{C{xs}} value.
1977 @note: Exception and I{non-finite} handling may differ if not based
1978 on Python's C{math.fsum}.
1980 @see: Class L{Fsum} and methods L{Fsum.fsum} and L{Fsum.fadd}.
1981 '''
1982 return _fsum(xs if floats else _2floats(xs)) if xs else _0_0 # PYCHOK yield
1985def fsum_(*xs, **floats):
1986 '''Precision floating point summation of all positional arguments.
1988 @arg xs: Values to be added (C{scalar} or L{Fsum} instances), all
1989 positional.
1990 @kwarg floats: Use C{B{floats}=True} iff I{all} B{C{xs}} are I{known
1991 to be scalar} (C{bool}).
1993 @return: Precision C{fsum} (C{float}).
1995 @see: Function C{fsum}.
1996 '''
1997 return _fsum(xs if _xkwds_get(floats, floats=False) else
1998 _2floats(xs, origin=1)) if xs else _0_0 # PYCHOK yield
2001def fsumf_(*xs):
2002 '''Precision floating point summation, L{fsum_}C{(*B{xs}, floats=True)},
2003 but only for C{B{xs}} I{known to be scalar}.
2004 '''
2005 return _fsum(xs) if xs else _0_0
2008def fsum1(xs, floats=False):
2009 '''Precision floating point summation, 1-primed.
2011 @arg xs: Iterable, list, tuple, etc. of values (C{scalar} or L{Fsum}
2012 instances).
2013 @kwarg floats: Use C{B{floats}=True} iff I{all} B{C{xs}} are known
2014 to be C{float}.
2016 @return: Precision C{fsum} (C{float}).
2018 @see: Function C{fsum}.
2019 '''
2020 return _fsum(_1primed(xs if floats else _2floats(xs))) if xs else _0_0 # PYCHOK yield
2023def fsum1_(*xs, **floats):
2024 '''Precision floating point summation, 1-primed.
2026 @arg xs: Values to be added (C{scalar} or L{Fsum} instances), all
2027 positional.
2028 @kwarg floats: Use C{B{floats}=True} iff I{all} B{C{xs}} are I{known
2029 to be scalar} (C{bool}).
2031 @return: Precision C{fsum} (C{float}).
2033 @see: Function C{fsum}
2034 '''
2035 return _fsum(_1primed(xs if _xkwds_get(floats, floats=False) else
2036 _2floats(xs, origin=1))) if xs else _0_0 # PYCHOK yield
2039def fsum1f_(*xs):
2040 '''Precision floating point summation, L{fsum1_}C{(*B{xs}, floats=True)},
2041 but only for C{B{xs}} I{known to be scalar}.
2042 '''
2043 return _fsum(_1primed(xs)) if xs else _0_0
2046if __name__ == '__main__':
2048 # usage: [env PYGEODESY_FSUM_PARTIALS=fsum] python3 -m pygeodesy.fsums
2050 def _test(n):
2051 # copied from Hettinger, see L{Fsum} reference
2052 from pygeodesy import printf
2053 from random import gauss, random, shuffle
2055 printf(_fsum.__name__, end=_COMMASPACE_)
2056 printf(_psum.__name__, end=_COMMASPACE_)
2058 F = Fsum()
2059 if F.is_math_fsum():
2060 c = (7, 1e100, -7, -1e100, -9e-20, 8e-20) * 10
2061 for _ in range(n):
2062 t = list(c)
2063 s = 0
2064 for _ in range(n * 8):
2065 v = gauss(0, random())**7 - s
2066 t.append(v)
2067 s += v
2068 shuffle(t)
2069 assert float(F.fset_(*t)) == _fsum(t)
2070 printf(_DOT_, end=NN)
2071 printf(NN)
2073 _test(128)
2075# **) MIT License
2076#
2077# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.
2078#
2079# Permission is hereby granted, free of charge, to any person obtaining a
2080# copy of this software and associated documentation files (the "Software"),
2081# to deal in the Software without restriction, including without limitation
2082# the rights to use, copy, modify, merge, publish, distribute, sublicense,
2083# and/or sell copies of the Software, and to permit persons to whom the
2084# Software is furnished to do so, subject to the following conditions:
2085#
2086# The above copyright notice and this permission notice shall be included
2087# in all copies or substantial portions of the Software.
2088#
2089# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
2090# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
2091# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
2092# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
2093# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
2094# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
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