Coverage for pygeodesy/fsums.py: 96%
745 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, isinf, isnan, 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_, _not_scalar_, _PERCENT_, \
37 _PLUS_, _R_, _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__ = '24.04.09'
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.fsum2f_}.
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 _2halfeven(s, r, p):
125 '''(INTERNAL) Round half-even.
126 '''
127 if (p > 0 and r > 0) or \
128 (p < 0 and r < 0): # signs match
129 r *= 2
130 t = s + r
131 if r == (t - s):
132 s = t
133 return s
136def _1primed(xs): # in .fmath
137 '''(INTERNAL) 1-Primed summation of iterable C{xs}
138 items, all I{known} to be C{finite float}.
139 '''
140 yield _1_0
141 for x in xs:
142 yield x
143 yield _N_1_0
146def _2ps(s, r):
147 '''(INTERNAL) Return a C{s} and C{r} pair, I{ps-ordered}.
148 '''
149 return (s, r) if fabs(s) < fabs(r) else (r, s)
152def _psum(ps): # PYCHOK used!
153 '''(INTERNAL) Partials sum, updating C{ps}, I{overridden below}.
154 '''
155 # assert isinstance(ps, list)
156 i = len(ps) - 1
157 s = _0_0 if i < 0 else ps[i]
158 _2s = _2sum
159 while i > 0:
160 i -= 1
161 s, r = _2s(s, ps[i])
162 if r: # sum(ps) became inexact
163 if s:
164 ps[i:] = r, s
165 if i > 0:
166 s = _2halfeven(s, r, ps[i-1])
167 break # return s
168 s = r # PYCHOK no cover
169 ps[i:] = s,
170 return s
173def _Psum(ps, **name):
174 '''(INTERNAL) Return an C{Fsum} from I{ordered} partials C{ps}.
175 '''
176 f = Fsum(**name) if name else Fsum()
177 if ps:
178 f._ps[:] = ps
179 f._n = len(f._ps)
180 return f
183def _Psum_1(p=_1_0, **name):
184 '''(INTERNAL) Return an C{Fsum} from a single partial C{p}.
185 '''
186 f = Fsum(**name) if name else Fsum()
187 f._ps[:] = p,
188 f._n = 1 # len(f._ps)
189 return f
192def _2scalar(other, _raiser=None, **mod):
193 '''(INTERNAL) Return B{C{other}} as C{int}, C{float} or C{as-is}.
194 '''
195 if isinstance(other, Fsum):
196 s, r = other._fint2
197 if r:
198 s, r = other._fprs2
199 if r: # PYCHOK no cover
200 if _raiser and _raiser(r, s):
201 t = _stresidual(_non_zero_, r, **mod)
202 raise ResidualError(t, txt=None)
203 s = other # L{Fsum} as-is
204 else:
205 s = other # C{type} as-is
206 if isint(s, both=True):
207 s = int(s)
208 return s
211def _strcomplex(s, *args):
212 '''(INTERNAL) C{Complex} 2- or 3-arg C{pow} error as C{str}.
213 '''
214 c = _strcomplex.__name__[4:]
215 n = _DASH_(len(args), _arg_)
216 t = unstr(pow, *args)
217 return _SPACE_(c, s, _from_, n, t)
220def _stresidual(prefix, residual, **name_values):
221 '''(INTERNAL) Residual error as C{str}.
222 '''
223 p = _stresidual.__name__[3:]
224 t = Fmt.PARENSPACED(p, Fmt(residual))
225 for n, v in itemsorted(name_values):
226 n = n.replace(_UNDER_, _SPACE_)
227 p = Fmt.PARENSPACED(n, Fmt(v))
228 t = _COMMASPACE_(t, p)
229 return _SPACE_(prefix, t)
232def _2sum(a, b): # by .testFmath
233 '''(INTERNAL) Return C{a + b} as 2-tuple (sum, residual).
234 '''
235 s = a + b
236 if not _isfinite(s):
237 u = unstr(_2sum, a, b)
238 t = Fmt.PARENSPACED(_not_finite_, s)
239 raise _OverflowError(u, txt=t)
240 if fabs(a) < fabs(b):
241 a, b = b, a
242 return s, (b - (s - a))
245class Fsum(_Named): # sync __methods__ with .vector3dBase.Vector3dBase
246 '''Precision floating point summation and I{running} summation.
248 Unlike Python's C{math.fsum}, this class accumulates values and provides intermediate,
249 I{running}, precision floating point summations. Accumulation may continue after any
250 intermediate, I{running} summuation.
252 @note: Accumulated values may be L{Fsum} or C{scalar} instances, any C{type} having
253 method C{__float__} to convert the C{scalar} to a single C{float}.
255 @note: Handling of exceptions and C{inf}, C{INF}, C{nan} and C{NAN} differs from
256 Python's C{math.fsum}.
258 @see: U{Hettinger<https://GitHub.com/ActiveState/code/blob/master/recipes/Python/
259 393090_Binary_floating_point_summatiaccurate_full/recipe-393090.py>}, U{Kahan
260 <https://WikiPedia.org/wiki/Kahan_summation_algorithm>}, U{Klein
261 <https://Link.Springer.com/article/10.1007/s00607-005-0139-x>}, Python 2.6+
262 file I{Modules/mathmodule.c} and the issue log U{Full precision summation
263 <https://Bugs.Python.org/issue2819>}.
264 '''
265 _math_fsum = None
266 _n = 0
267# _ps = [] # partial sums
268# _ps_max = 0 # max(Fsum._ps_max, len(Fsum._ps))
269 _ratio = None
270 _recursive = bool(_getenv('PYGEODESY_FSUM_RECURSIVE', NN))
271 _RESIDUAL = max(float(_getenv('PYGEODESY_FSUM_RESIDUAL', _0_0)), _0_0)
273 def __init__(self, *xs, **name_RESIDUAL):
274 '''New L{Fsum} for I{running} precision floating point summation.
276 @arg xs: No, one or more initial values, all positional (each C{scalar}
277 or an L{Fsum} instance).
278 @kwarg name_RESIDUAL: Optional C{B{name}=NN} for this L{Fsum} and
279 C{B{RESIDUAL}=None} for the L{ResidualError} threshold.
281 @see: Methods L{Fsum.fadd} and L{Fsum.RESIDUAL}.
282 '''
283 if name_RESIDUAL:
284 n = _xkwds_get(name_RESIDUAL, name=NN)
285 if n: # set name before ...
286 self.name = n
287 r = _xkwds_get(name_RESIDUAL, RESIDUAL=None)
288 if r is not None:
289 self.RESIDUAL(r) # ... ResidualError
290 self._ps = [] # [_0_0], see L{Fsum._fprs}
291 if xs:
292 self._facc_any(xs, origin=1, up=False)
294 def __abs__(self):
295 '''Return this instance' absolute value as an L{Fsum}.
296 '''
297 s = _fsum(self._ps_1()) # == self._cmp_0(0, ...)
298 return (-self) if s < 0 else self._copy_2(self.__abs__)
300 def __add__(self, other):
301 '''Return C{B{self} + B{other}} as an L{Fsum}.
303 @arg other: An L{Fsum} or C{scalar}.
305 @return: The sum (L{Fsum}).
307 @see: Method L{Fsum.__iadd__}.
308 '''
309 f = self._copy_2(self.__add__)
310 return f._fadd(other, _add_op_)
312 def __bool__(self): # PYCHOK not special in Python 2-
313 '''Return C{True} if this instance is I{exactly} non-zero.
314 '''
315 s, r = self._fprs2
316 return bool(s or r) and s != -r # == self != 0
318 def __ceil__(self): # PYCHOK not special in Python 2-
319 '''Return this instance' C{math.ceil} as C{int} or C{float}.
321 @return: An C{int} in Python 3+, but C{float} in Python 2-.
323 @see: Methods L{Fsum.__floor__} and property L{Fsum.ceil}.
324 '''
325 return self.ceil
327 def __cmp__(self, other): # Python 2-
328 '''Compare this with an other instance or C{scalar}.
330 @return: -1, 0 or +1 (C{int}).
332 @raise TypeError: Incompatible B{C{other}} C{type}.
333 '''
334 s = self._cmp_0(other, self.cmp.__name__)
335 return _signOf(s, 0)
337 cmp = __cmp__
339 def __divmod__(self, other):
340 '''Return C{divmod(B{self}, B{other})} as a L{DivMod2Tuple}
341 with quotient C{div} an C{int} in Python 3+ or C{float}
342 in Python 2- and remainder C{mod} an L{Fsum}.
344 @arg other: An L{Fsum} or C{scalar} modulus.
346 @see: Method L{Fsum.__itruediv__}.
347 '''
348 f = self._copy_2(self.__divmod__)
349 return f._fdivmod2(other, _divmod_op_)
351 def __eq__(self, other):
352 '''Compare this with an other instance or C{scalar}.
353 '''
354 return self._cmp_0(other, _eq_op_) == 0
356 def __float__(self):
357 '''Return this instance' current, precision running sum as C{float}.
359 @see: Methods L{Fsum.fsum} and L{Fsum.int_float}.
360 '''
361 return float(self._fprs)
363 def __floor__(self): # PYCHOK not special in Python 2-
364 '''Return this instance' C{math.floor} as C{int} or C{float}.
366 @return: An C{int} in Python 3+, but C{float} in Python 2-.
368 @see: Methods L{Fsum.__ceil__} and property L{Fsum.floor}.
369 '''
370 return self.floor
372 def __floordiv__(self, other):
373 '''Return C{B{self} // B{other}} as an L{Fsum}.
375 @arg other: An L{Fsum} or C{scalar} divisor.
377 @return: The C{floor} quotient (L{Fsum}).
379 @see: Methods L{Fsum.__ifloordiv__}.
380 '''
381 f = self._copy_2(self.__floordiv__)
382 return f._floordiv(other, _floordiv_op_)
384 def __format__(self, *other): # PYCHOK no cover
385 '''Not implemented.'''
386 return _NotImplemented(self, *other)
388 def __ge__(self, other):
389 '''Compare this with an other instance or C{scalar}.
390 '''
391 return self._cmp_0(other, _ge_op_) >= 0
393 def __gt__(self, other):
394 '''Compare this with an other instance or C{scalar}.
395 '''
396 return self._cmp_0(other, _gt_op_) > 0
398 def __hash__(self): # PYCHOK no cover
399 '''Return this instance' C{hash}.
400 '''
401 return hash(self._ps) # XXX id(self)?
403 def __iadd__(self, other):
404 '''Apply C{B{self} += B{other}} to this instance.
406 @arg other: An L{Fsum} or C{scalar} instance.
408 @return: This instance, updated (L{Fsum}).
410 @raise TypeError: Invalid B{C{other}}, not
411 C{scalar} nor L{Fsum}.
413 @see: Methods L{Fsum.fadd} and L{Fsum.fadd_}.
414 '''
415 return self._fadd(other, _iadd_op_)
417 def __ifloordiv__(self, other):
418 '''Apply C{B{self} //= B{other}} to this instance.
420 @arg other: An L{Fsum} or C{scalar} divisor.
422 @return: This instance, updated (L{Fsum}).
424 @raise ResidualError: Non-zero residual in B{C{other}}.
426 @raise TypeError: Invalid B{C{other}} type.
428 @raise ValueError: Invalid or non-finite B{C{other}}.
430 @raise ZeroDivisionError: Zero B{C{other}}.
432 @see: Methods L{Fsum.__itruediv__}.
433 '''
434 return self._floordiv(other, _floordiv_op_ + _fset_op_)
436 def __imatmul__(self, other): # PYCHOK no cover
437 '''Not implemented.'''
438 return _NotImplemented(self, other)
440 def __imod__(self, other):
441 '''Apply C{B{self} %= B{other}} to this instance.
443 @arg other: An L{Fsum} or C{scalar} modulus.
445 @return: This instance, updated (L{Fsum}).
447 @see: Method L{Fsum.__divmod__}.
448 '''
449 return self._fdivmod2(other, _mod_op_ + _fset_op_).mod
451 def __imul__(self, other):
452 '''Apply C{B{self} *= B{other}} to this instance.
454 @arg other: An L{Fsum} or C{scalar} factor.
456 @return: This instance, updated (L{Fsum}).
458 @raise OverflowError: Partial C{2sum} overflow.
460 @raise TypeError: Invalid B{C{other}} type.
462 @raise ValueError: Invalid or non-finite B{C{other}}.
463 '''
464 return self._fmul(other, _mul_op_ + _fset_op_)
466 def __int__(self):
467 '''Return this instance as an C{int}.
469 @see: Methods L{Fsum.int_float}, L{Fsum.__ceil__}
470 and L{Fsum.__floor__} and properties
471 L{Fsum.ceil} and L{Fsum.floor}.
472 '''
473 i, _ = self._fint2
474 return i
476 def __invert__(self): # PYCHOK no cover
477 '''Not implemented.'''
478 # Luciano Ramalho, "Fluent Python", O'Reilly, 2nd Ed, 2022 p. 567
479 return _NotImplemented(self)
481 def __ipow__(self, other, *mod): # PYCHOK 2 vs 3 args
482 '''Apply C{B{self} **= B{other}} to this instance.
484 @arg other: The exponent (L{Fsum} or C{scalar}).
485 @arg mod: Optional modulus (C{int} or C{None}) for the
486 3-argument C{pow(B{self}, B{other}, B{mod})}
487 version.
489 @return: This instance, updated (L{Fsum}).
491 @note: If B{C{mod}} is given, the result will be an C{integer}
492 L{Fsum} in Python 3+ if this instance C{is_integer} or
493 set to C{as_integer} if B{C{mod}} given as C{None}.
495 @raise OverflowError: Partial C{2sum} overflow.
497 @raise ResidualError: Non-zero residual in B{C{other}} and
498 env var C{PYGEODESY_FSUM_RESIDUAL}
499 set or this instance has a non-zero
500 residual and either B{C{mod}} is
501 given and non-C{None} or B{C{other}}
502 is a negative or fractional C{scalar}.
504 @raise TypeError: Invalid B{C{other}} type or 3-argument
505 C{pow} invocation failed.
507 @raise ValueError: If B{C{other}} is a negative C{scalar}
508 and this instance is C{0} or B{C{other}}
509 is a fractional C{scalar} and this
510 instance is negative or has a non-zero
511 residual or B{C{mod}} is given and C{0}.
513 @see: CPython function U{float_pow<https://GitHub.com/
514 python/cpython/blob/main/Objects/floatobject.c>}.
515 '''
516 return self._fpow(other, _pow_op_ + _fset_op_, *mod)
518 def __isub__(self, other):
519 '''Apply C{B{self} -= B{other}} to this instance.
521 @arg other: An L{Fsum} or C{scalar}.
523 @return: This instance, updated (L{Fsum}).
525 @raise TypeError: Invalid B{C{other}} type.
527 @see: Method L{Fsum.fadd}.
528 '''
529 return self._fsub(other, _isub_op_)
531 def __iter__(self):
532 '''Return an C{iter}ator over a C{partials} duplicate.
533 '''
534 return iter(self.partials)
536 def __itruediv__(self, other):
537 '''Apply C{B{self} /= B{other}} to this instance.
539 @arg other: An L{Fsum} or C{scalar} divisor.
541 @return: This instance, updated (L{Fsum}).
543 @raise OverflowError: Partial C{2sum} overflow.
545 @raise ResidualError: Non-zero residual in B{C{other}} and
546 env var C{PYGEODESY_FSUM_RESIDUAL} set.
548 @raise TypeError: Invalid B{C{other}} type.
550 @raise ValueError: Invalid or non-finite B{C{other}}.
552 @raise ZeroDivisionError: Zero B{C{other}}.
554 @see: Method L{Fsum.__ifloordiv__}.
555 '''
556 return self._ftruediv(other, _truediv_op_ + _fset_op_)
558 def __le__(self, other):
559 '''Compare this with an other instance or C{scalar}.
560 '''
561 return self._cmp_0(other, _le_op_) <= 0
563 def __len__(self):
564 '''Return the number of values accumulated (C{int}).
565 '''
566 return self._n
568 def __lt__(self, other):
569 '''Compare this with an other instance or C{scalar}.
570 '''
571 return self._cmp_0(other, _lt_op_) < 0
573 def __matmul__(self, other): # PYCHOK no cover
574 '''Not implemented.'''
575 return _NotImplemented(self, other)
577 def __mod__(self, other):
578 '''Return C{B{self} % B{other}} as an L{Fsum}.
580 @see: Method L{Fsum.__imod__}.
581 '''
582 f = self._copy_2(self.__mod__)
583 return f._fdivmod2(other, _mod_op_).mod
585 def __mul__(self, other):
586 '''Return C{B{self} * B{other}} as an L{Fsum}.
588 @see: Method L{Fsum.__imul__}.
589 '''
590 f = self._copy_2(self.__mul__)
591 return f._fmul(other, _mul_op_)
593 def __ne__(self, other):
594 '''Compare this with an other instance or C{scalar}.
595 '''
596 return self._cmp_0(other, _ne_op_) != 0
598 def __neg__(self):
599 '''Return I{a copy of} this instance, I{negated}.
600 '''
601 f = self._copy_2(self.__neg__)
602 return f._fset(self._neg)
604 def __pos__(self):
605 '''Return this instance I{as-is}, like C{float.__pos__()}.
606 '''
607 return self if _pos_self else self._copy_2(self.__pos__)
609 def __pow__(self, other, *mod): # PYCHOK 2 vs 3 args
610 '''Return C{B{self}**B{other}} as an L{Fsum}.
612 @see: Method L{Fsum.__ipow__}.
613 '''
614 f = self._copy_2(self.__pow__)
615 return f._fpow(other, _pow_op_, *mod)
617 def __radd__(self, other):
618 '''Return C{B{other} + B{self}} as an L{Fsum}.
620 @see: Method L{Fsum.__iadd__}.
621 '''
622 f = self._copy_2r(other, self.__radd__)
623 return f._fadd(self, _add_op_)
625 def __rdivmod__(self, other):
626 '''Return C{divmod(B{other}, B{self})} as 2-tuple C{(quotient,
627 remainder)}.
629 @see: Method L{Fsum.__divmod__}.
630 '''
631 f = self._copy_2r(other, self.__rdivmod__)
632 return f._fdivmod2(self, _divmod_op_)
634# def __repr__(self):
635# '''Return the default C{repr(this)}.
636# '''
637# return self.toRepr(lenc=True)
639 def __rfloordiv__(self, other):
640 '''Return C{B{other} // B{self}} as an L{Fsum}.
642 @see: Method L{Fsum.__ifloordiv__}.
643 '''
644 f = self._copy_2r(other, self.__rfloordiv__)
645 return f._floordiv(self, _floordiv_op_)
647 def __rmatmul__(self, other): # PYCHOK no cover
648 '''Not implemented.'''
649 return _NotImplemented(self, other)
651 def __rmod__(self, other):
652 '''Return C{B{other} % B{self}} as an L{Fsum}.
654 @see: Method L{Fsum.__imod__}.
655 '''
656 f = self._copy_2r(other, self.__rmod__)
657 return f._fdivmod2(self, _mod_op_).mod
659 def __rmul__(self, other):
660 '''Return C{B{other} * B{self}} as an L{Fsum}.
662 @see: Method L{Fsum.__imul__}.
663 '''
664 f = self._copy_2r(other, self.__rmul__)
665 return f._fmul(self, _mul_op_)
667 def __round__(self, *ndigits): # PYCHOK no cover
668 '''Return C{round(B{self}, *B{ndigits}} as an L{Fsum}.
670 @arg ndigits: Optional number of digits (C{int}).
671 '''
672 # <https://docs.Python.org/3.12/reference/datamodel.html?#object.__round__>
673 return _Psum_1(round(float(self), *ndigits), # can be C{int}
674 name=self.__round__.__name__)
676 def __rpow__(self, other, *mod):
677 '''Return C{B{other}**B{self}} as an L{Fsum}.
679 @see: Method L{Fsum.__ipow__}.
680 '''
681 f = self._copy_2r(other, self.__rpow__)
682 return f._fpow(self, _pow_op_, *mod)
684 def __rsub__(self, other):
685 '''Return C{B{other} - B{self}} as L{Fsum}.
687 @see: Method L{Fsum.__isub__}.
688 '''
689 f = self._copy_2r(other, self.__rsub__)
690 return f._fsub(self, _sub_op_)
692 def __rtruediv__(self, other):
693 '''Return C{B{other} / B{self}} as an L{Fsum}.
695 @see: Method L{Fsum.__itruediv__}.
696 '''
697 f = self._copy_2r(other, self.__rtruediv__)
698 return f._ftruediv(self, _truediv_op_)
700 def __str__(self):
701 '''Return the default C{str(self)}.
702 '''
703 return self.toStr(lenc=True)
705 def __sub__(self, other):
706 '''Return C{B{self} - B{other}} as an L{Fsum}.
708 @arg other: An L{Fsum} or C{scalar}.
710 @return: The difference (L{Fsum}).
712 @see: Method L{Fsum.__isub__}.
713 '''
714 f = self._copy_2(self.__sub__)
715 return f._fsub(other, _sub_op_)
717 def __truediv__(self, other):
718 '''Return C{B{self} / B{other}} as an L{Fsum}.
720 @arg other: An L{Fsum} or C{scalar} divisor.
722 @return: The quotient (L{Fsum}).
724 @see: Method L{Fsum.__itruediv__}.
725 '''
726 f = self._copy_2(self.__truediv__)
727 return f._ftruediv(other, _truediv_op_)
729 __trunc__ = __int__
731 if _sys_version_info2 < (3, 0): # PYCHOK no cover
732 # <https://docs.Python.org/2/library/operator.html#mapping-operators-to-functions>
733 __div__ = __truediv__
734 __idiv__ = __itruediv__
735 __long__ = __int__
736 __nonzero__ = __bool__
737 __rdiv__ = __rtruediv__
739 def as_integer_ratio(self):
740 '''Return this instance as the ratio of 2 integers.
742 @return: 2-Tuple C{(numerator, denominator)} both
743 C{int} and with positive C{denominator}.
745 @see: Standard C{float.as_integer_ratio} in Python 3+.
746 '''
747 n, r = self._fint2
748 if r:
749 i, d = r.as_integer_ratio()
750 n *= d
751 n += i
752 else: # PYCHOK no cover
753 d = 1
754 return n, d
756 @property_RO
757 def ceil(self):
758 '''Get this instance' C{ceil} value (C{int} in Python 3+,
759 but C{float} in Python 2-).
761 @note: The C{ceil} takes the C{residual} into account.
763 @see: Method L{Fsum.int_float} and properties L{Fsum.floor},
764 L{Fsum.imag} and L{Fsum.real}.
765 '''
766 s, r = self._fprs2
767 c = _ceil(s) + int(r) - 1
768 while r > (c - s): # (s + r) > c
769 c += 1
770 return c
772 def _cmp_0(self, other, op):
773 '''(INTERNAL) Return C{scalar(self - B{other})} for 0-comparison.
774 '''
775 if isinstance(other, Fsum):
776 s = _fsum(self._ps_1(*other._ps))
777 elif isscalar(other):
778 if other:
779 s = _fsum(self._ps_1(other))
780 else:
781 s, r = self._fprs2
782 s = _signOf(s, -r)
783 else:
784 raise self._TypeError(op, other) # txt=_invalid_
785 return s
787 def copy(self, deep=False, name=NN):
788 '''Copy this instance, C{shallow} or B{C{deep}}.
790 @return: The copy (L{Fsum}).
791 '''
792 f = _Named.copy(self, deep=deep, name=name)
793 f._ps = list(self._ps) # separate list
794 f._n = self._n if deep else 1
795 return f
797 def _copy_2(self, which, name=NN):
798 '''(INTERNAL) Copy for I{dyadic} operators.
799 '''
800 n = name or which.__name__
801 # NOT .classof due to .Fdot(a, *b) args, etc.
802 f = _Named.copy(self, deep=False, name=n)
803 # assert f._n == self._n
804 f._ps = list(self._ps) # separate list
805 return f
807 def _copy_2r(self, other, which):
808 '''(INTERNAL) Copy for I{reverse-dyadic} operators.
809 '''
810 return other._copy_2(which) if isinstance(other, Fsum) else \
811 Fsum(other, name=which.__name__)
813# def _copy_RESIDUAL(self, other):
814# '''(INTERNAL) Copy C{other._RESIDUAL}.
815# '''
816# R = other._RESIDUAL
817# if R is not Fsum._RESIDUAL:
818# self._RESIDUAL = R
820 def divmod(self, other):
821 '''Return C{divmod(B{self}, B{other})} as 2-tuple C{(quotient,
822 remainder)}.
824 @arg other: An L{Fsum} or C{scalar} divisor.
826 @return: A L{DivMod2Tuple}C{(div, mod)}, with quotient C{div}
827 an C{int} in Python 3+ or C{float} in Python 2- and
828 remainder C{mod} an L{Fsum} instance.
830 @see: Method L{Fsum.__itruediv__}.
831 '''
832 f = self._copy_2(self.divmod)
833 return f._fdivmod2(other, _divmod_op_)
835 def _Error(self, op, other, Error, **txt_cause):
836 '''(INTERNAL) Format an B{C{Error}} for C{{self} B{op} B{other}}.
837 '''
838 return Error(_SPACE_(self.toStr(), op, other), **txt_cause)
840 def _ErrorX(self, X, op, other, *mod):
841 '''(INTERNAL) Format the caught exception C{X}.
842 '''
843 E, t = _xError2(X)
844 if mod:
845 t = _COMMASPACE_(Fmt.PARENSPACED(mod=mod[0]), t)
846 return self._Error(op, other, E, txt=t, cause=X)
848 def _ErrorXs(self, X, xs, **kwds): # in .fmath
849 '''(INTERNAL) Format the caught exception C{X}.
850 '''
851 E, t = _xError2(X)
852 n = unstr(self.named3, *xs[:3], _ELLIPSIS=len(xs) > 3, **kwds)
853 return E(n, txt=t, cause=X)
855 def _facc(self, xs, **up):
856 '''(INTERNAL) Accumulate all C{xs}, known to be scalar.
857 '''
858 self._ps_acc(self._ps, xs, **up)
859 return self
861 def _facc_(self, *xs, **up):
862 '''(INTERNAL) Accumulate all positional C{xs}, known to be scalar.
863 '''
864 if xs:
865 self._ps_acc(self._ps, xs, **up)
866 return self
868 def _facc_any(self, xs, up=True, **origin_X_x):
869 '''(INTERNAL) Accumulate more C{scalars} or L{Fsum}s.
870 '''
871 self._ps[:] = self._ps_acc(list(self._ps),
872 _2floats(xs, **origin_X_x), up=up) # PYCHOK yield
873 return self
875 def _facc_any_neg(self, xs, up=True, **origin):
876 '''(INTERNAL) Accumulate more C{scalars} or L{Fsum}s, negated.
877 '''
878 def _neg(x):
879 return -x
881 self._ps[:] = self._ps_acc(list(self._ps), map(_neg,
882 _2floats(xs, **origin)), up=up) # PYCHOK yield
883 return self
885 def _facc_power(self, power, xs, which): # in .fmath
886 '''(INTERNAL) Add each C{xs} as C{float(x**power)}.
887 '''
888 p = power
889 if isinstance(p, Fsum):
890 if p.is_exact:
891 return self._facc_power(p._fprs, xs, which)
892 _Pow = Fsum._pow_any
893 elif isint(p, both=True) and p >= 0:
894 _Pow, p = Fsum._pow_int, int(p)
895 else:
896 _Pow, p = Fsum._pow_scalar, _2float(power=p)
898 if p:
899 from math import pow as _pow
900 op = which.__name__
901 _Fs = Fsum
903 def _X(X):
904 f = _Pow(X, p, power, op)
905 return f._ps if isinstance(f, _Fs) else (f,)
907 def _x(x):
908 return _pow(float(x), p)
910 f = self._facc_any(xs, origin=1, _X=_X, _x=_x)
911 else:
912 f = self._facc_(float(len(xs))) # x**0 == 1
913 return f
915# def _facc_up(self, up=True):
916# '''(INTERNAL) Update the C{partials}, by removing
917# and re-accumulating the final C{partial}.
918# '''
919# while len(self._ps) > 1:
920# p = self._ps.pop()
921# if p:
922# n = self._n
923# self._facc_(p, up=False)
924# self._n = n
925# break
926# return self._update() if up else self # ._fpsqz()
928 def fadd(self, xs=()):
929 '''Add an iterable of C{scalar} or L{Fsum} instances
930 to this instance.
932 @arg xs: Iterable, list, tuple, etc. (C{scalar} or
933 L{Fsum} instances).
935 @return: This instance (L{Fsum}).
937 @raise OverflowError: Partial C{2sum} overflow.
939 @raise TypeError: An invalid B{C{xs}} type, not C{scalar}
940 nor L{Fsum}.
942 @raise ValueError: Invalid or non-finite B{C{xs}} value.
943 '''
944 if isinstance(xs, Fsum):
945 self._facc(xs._ps) # tuple
946 elif isscalar(xs): # for backward compatibility
947 self._facc_(_2float(x=xs)) # PYCHOK no cover
948 elif xs:
949 self._facc_any(xs)
950 return self
952 def fadd_(self, *xs):
953 '''Add all positional C{scalar} or L{Fsum} instances
954 to this instance.
956 @arg xs: Values to add (C{scalar} or L{Fsum} instances),
957 all positional.
959 @return: This instance (L{Fsum}).
961 @raise OverflowError: Partial C{2sum} overflow.
963 @raise TypeError: An invalid B{C{xs}} type, not C{scalar}
964 nor L{Fsum}.
966 @raise ValueError: Invalid or non-finite B{C{xs}} value.
967 '''
968 return self._facc_any(xs, origin=1)
970 def _fadd(self, other, op, **up): # in .fmath.Fhorner
971 '''(INTERNAL) Apply C{B{self} += B{other}}.
972 '''
973 if isinstance(other, Fsum):
974 self._facc(other._ps, **up) # tuple
975 elif not isscalar(other):
976 raise self._TypeError(op, other) # txt=_invalid_
977 elif other:
978 self._facc_(other, **up)
979 return self
981 fcopy = copy # for backward compatibility
982 fdiv = __itruediv__ # for backward compatibility
983 fdivmod = __divmod__ # for backward compatibility
985 def _fdivmod2(self, other, op):
986 '''(INTERNAL) Apply C{B{self} %= B{other}} and return a L{DivMod2Tuple}.
987 '''
988 # result mostly follows CPython function U{float_divmod
989 # <https://GitHub.com/python/cpython/blob/main/Objects/floatobject.c>},
990 # but at least divmod(-3, 2) equals Cpython's result (-2, 1).
991 q = self._copy_2(self._fdivmod2)._ftruediv(other, op).floor
992 if q: # == float // other == floor(float / other)
993 self -= other * q
995 s = signOf(other) # make signOf(self) == signOf(other)
996 if s and self.signOf() == -s: # PYCHOK no cover
997 self += other
998 q -= 1
999# t = self.signOf()
1000# if t and t != s:
1001# raise self._Error(op, other, _AssertionError, txt=signOf.__name__)
1002 return DivMod2Tuple(q, self) # q is C{int} in Python 3+, but C{float} in Python 2-
1004 def _finite(self, other, op=None):
1005 '''(INTERNAL) Return B{C{other}} if C{finite}.
1006 '''
1007 if _isfinite(other):
1008 return other
1009 raise ValueError(_not_finite_) if op is None else \
1010 self._ValueError(op, other, txt=_not_finite_)
1012 def fint(self, raiser=True, **name):
1013 '''Return this instance' current running sum as C{integer}.
1015 @kwarg raiser: If C{True} throw a L{ResidualError} if the
1016 I{integer} residual is non-zero (C{bool}).
1017 @kwarg name: Optional name (C{str}), overriding C{"fint"}.
1019 @return: The C{integer} (L{Fsum}).
1021 @raise ResidualError: Non-zero I{integer} residual.
1023 @see: Methods L{Fsum.int_float} and L{Fsum.is_integer}.
1024 '''
1025 i, r = self._fint2
1026 if r and raiser:
1027 t = _stresidual(_integer_, r)
1028 raise ResidualError(_integer_, i, txt=t)
1029 f = self._copy_2(self.fint, **name)
1030 return f._fset(i)
1032 def fint2(self, **name):
1033 '''Return this instance' current running sum as C{int} and
1034 the I{integer} residual.
1036 @kwarg name: Optional name (C{str}).
1038 @return: An L{Fsum2Tuple}C{(fsum, residual)} with C{fsum}
1039 an C{int} and I{integer} C{residual} a C{float} or
1040 C{INT0} if the C{fsum} is considered to be I{exact}.
1041 '''
1042 return Fsum2Tuple(*self._fint2, **name)
1044 @Property_RO
1045 def _fint2(self): # see ._fset
1046 '''(INTERNAL) Get 2-tuple (C{int}, I{integer} residual).
1047 '''
1048 s, r = self._fprs2
1049 i = int(s)
1050 r = _fsum(self._ps_1(i)) if r else float(s - i)
1051 return i, (r or INT0) # Fsum2Tuple?
1053 @deprecated_property_RO
1054 def float_int(self): # PYCHOK no cover
1055 '''DEPRECATED, use method C{Fsum.int_float}.'''
1056 return self.int_float() # raiser=False
1058 @property_RO
1059 def floor(self):
1060 '''Get this instance' C{floor} (C{int} in Python 3+, but
1061 C{float} in Python 2-).
1063 @note: The C{floor} takes the C{residual} into account.
1065 @see: Method L{Fsum.int_float} and properties L{Fsum.ceil},
1066 L{Fsum.imag} and L{Fsum.real}.
1067 '''
1068 s, r = self._fprs2
1069 f = _floor(s) + _floor(r) + 1
1070 while (f - s) > r: # f > (s + r)
1071 f -= 1
1072 return f
1074# floordiv = __floordiv__ # for naming consistency
1076 def _floordiv(self, other, op): # rather _ffloordiv?
1077 '''Apply C{B{self} //= B{other}}.
1078 '''
1079 q = self._ftruediv(other, op) # == self
1080 return self._fset(q.floor) # floor(q)
1082 fmul = __imul__ # for backward compatibility
1084 def _fmul(self, other, op):
1085 '''(INTERNAL) Apply C{B{self} *= B{other}}.
1086 '''
1087 if isinstance(other, Fsum):
1088 if len(self._ps) != 1:
1089 f = self._mul_Fsum(other, op)
1090 elif len(other._ps) != 1: # and len(self._ps) == 1
1091 f = other._mul_scalar(self._ps[0], op)
1092 else: # len(other._ps) == len(self._ps) == 1
1093 f = self._finite(self._ps[0] * other._ps[0])
1094 elif isscalar(other):
1095 f = self._mul_scalar(other, op) if other != _1_0 else self
1096 else:
1097 raise self._TypeError(op, other) # txt=_invalid_
1098 return self._fset(f) # n=len(self) + 1
1100 def fover(self, over):
1101 '''Apply C{B{self} /= B{over}} and summate.
1103 @arg over: An L{Fsum} or C{scalar} denominator.
1105 @return: Precision running sum (C{float}).
1107 @see: Methods L{Fsum.fsum} and L{Fsum.__itruediv__}.
1108 '''
1109 return float(self.fdiv(over)._fprs)
1111 fpow = __ipow__ # for backward compatibility
1113 def _fpow(self, other, op, *mod):
1114 '''Apply C{B{self} **= B{other}}, optional B{C{mod}} or C{None}.
1115 '''
1116 if mod:
1117 if mod[0] is not None: # == 3-arg C{pow}
1118 f = self._pow_2_3(self, other, other, op, *mod)
1119 elif self.is_integer():
1120 # return an exact C{int} for C{int}**C{int}
1121 i, _ = self._fint2 # assert _ == 0
1122 x = _2scalar(other) # C{int}, C{float} or other
1123 f = self._pow_2_3(i, x, other, op) if isscalar(x) else \
1124 _Psum_1(i)._pow_any(x, other, op)
1125 else: # mod[0] is None, power(self, other)
1126 f = self._pow_any(other, other, op)
1127 else: # pow(self, other) == pow(self, other, None)
1128 f = self._pow_any(other, other, op)
1129 return self._fset(f, asis=isint(f)) # n=max(len(self), 1)
1131 @Property_RO
1132 def _fprs(self):
1133 '''(INTERNAL) Get and cache this instance' precision
1134 running sum (C{float} or C{int}), ignoring C{residual}.
1136 @note: The precision running C{fsum} after a C{//=} or
1137 C{//} C{floor} division is C{int} in Python 3+.
1138 '''
1139 return self._fprs2.fsum
1141 @Property_RO
1142 def _fprs2(self):
1143 '''(INTERNAL) Get and cache this instance' precision
1144 running sum and residual (L{Fsum2Tuple}).
1145 '''
1146 ps = self._ps
1147 n = len(ps) - 2
1148 if n > 0: # len(ps) > 2
1149 s = _psum(ps)
1150 n = len(ps) - 2
1151 if n > 0:
1152 r = _fsum(self._ps_1(s)) or INT0
1153 return Fsum2Tuple(s, r)
1154 if n == 0: # len(ps) == 2
1155 ps[:] = _2ps(*_2sum(*ps))
1156 r, s = (INT0, ps[0]) if len(ps) != 2 else ps
1157 elif ps: # len(ps) == 1
1158 s, r = ps[0], INT0
1159 else: # len(ps) == 0
1160 s, r = _0_0, INT0
1161 ps[:] = s,
1162 # assert self._ps is ps
1163 return Fsum2Tuple(s, r)
1165# def _fpsqz(self):
1166# '''(INTERNAL) Compress, squeeze the C{partials}.
1167# '''
1168# if len(self._ps) > 2:
1169# _ = self._fprs2
1170# return self
1172 def fset_(self, *xs):
1173 '''Replace this instance' value with C{xs}.
1175 @arg xs: Optional, new values (C{scalar} or L{Fsum}
1176 instances), all positional.
1178 @return: This instance (C{Fsum}).
1180 @see: Method L{Fsum.fadd} for further details.
1181 '''
1182 self._ps[:] = 0,
1183 self._n = 0
1184 return self.fadd(xs) if xs else self._update()
1186 def _fset(self, other, asis=True, n=0):
1187 '''(INTERNAL) Overwrite this instance with an other or a C{scalar}.
1188 '''
1189 if other is self:
1190 pass # from ._fmul, ._ftruediv and ._pow_scalar
1191 elif isinstance(other, Fsum):
1192 self._ps[:] = other._ps
1193 self._n = n or other._n
1194# self._copy_RESIDUAL(other)
1195 # use or zap the C{Property_RO} values
1196 Fsum._fint2._update_from(self, other)
1197 Fsum._fprs ._update_from(self, other)
1198 Fsum._fprs2._update_from(self, other)
1199 elif isscalar(other):
1200 s = other if asis else float(other)
1201 i = int(s) # see ._fint2
1202 t = i, ((s - i) or INT0)
1203 self._ps[:] = s,
1204 self._n = n or 1
1205 # Property_ROs _fint2, _fprs and _fprs2 can't be a Property:
1206 # Property's _fset zaps the value just set by the @setter
1207 self.__dict__.update(_fint2=t, _fprs=s, _fprs2=Fsum2Tuple(s, INT0))
1208 else: # PYCHOK no cover
1209 raise self._TypeError(_fset_op_, other) # txt=_invalid_
1210 return self
1212 def _fset_ps(self, other, n=0): # in .fmath
1213 '''(INTERNAL) Set partials from a known C{Fsum} or C{scalar}.
1214 '''
1215 if isinstance(other, Fsum):
1216 self._ps[:] = other._ps
1217 self._n = n or other._n
1218 else: # assert isscalar(other)
1219 self._ps[:] = other,
1220 self._n = n or 1
1221 return self
1223 def fsub(self, xs=()):
1224 '''Subtract an iterable of C{scalar} or L{Fsum} instances from
1225 this instance.
1227 @arg xs: Iterable, list, tuple. etc. (C{scalar} or L{Fsum}
1228 instances).
1230 @return: This instance, updated (L{Fsum}).
1232 @see: Method L{Fsum.fadd}.
1233 '''
1234 return self._facc_any_neg(xs) if xs else self
1236 def fsub_(self, *xs):
1237 '''Subtract all positional C{scalar} or L{Fsum} instances from
1238 this instance.
1240 @arg xs: Values to subtract (C{scalar} or L{Fsum} instances),
1241 all positional.
1243 @return: This instance, updated (L{Fsum}).
1245 @see: Method L{Fsum.fadd}.
1246 '''
1247 return self._facc_any_neg(xs, origin=1) if xs else self
1249 def _fsub(self, other, op):
1250 '''(INTERNAL) Apply C{B{self} -= B{other}}.
1251 '''
1252 if isinstance(other, Fsum):
1253 if other is self: # or other._fprs2 == self._fprs2:
1254 self._fset(_0_0) # n=len(self) * 2, self -= self
1255 elif other._ps:
1256 self._facc(other._ps_neg)
1257 elif not isscalar(other):
1258 raise self._TypeError(op, other) # txt=_invalid_
1259 elif self._finite(other, op):
1260 self._facc_(-other)
1261 return self
1263 def fsum(self, xs=()):
1264 '''Add more C{scalar} or L{Fsum} instances and summate.
1266 @kwarg xs: Iterable, list, tuple, etc. (C{scalar} or
1267 L{Fsum} instances).
1269 @return: Precision running sum (C{float} or C{int}).
1271 @see: Method L{Fsum.fadd}.
1273 @note: Accumulation can continue after summation.
1274 '''
1275 f = self._facc_any(xs) if xs else self
1276 return f._fprs
1278 def fsum_(self, *xs):
1279 '''Add all positional C{scalar} or L{Fsum} instances and summate.
1281 @arg xs: Values to add (C{scalar} or L{Fsum} instances), all
1282 positional.
1284 @return: Precision running sum (C{float} or C{int}).
1286 @see: Methods L{Fsum.fsum}, L{Fsum.Fsum_} and L{Fsum.fsumf_}.
1287 '''
1288 f = self._facc_any(xs, origin=1) if xs else self
1289 return f._fprs
1291 def Fsum_(self, *xs):
1292 '''Like method L{Fsum.fsum_} but returning an L{Fsum}.
1294 @return: Current, precision running sum (L{Fsum}).
1295 '''
1296 return self._facc_any(xs, origin=1)._copy_2(self.Fsum_)
1298 def fsum2(self, xs=(), name=NN):
1299 '''Add more C{scalar} or L{Fsum} instances and return the
1300 current precision running sum and the C{residual}.
1302 @kwarg xs: Iterable, list, tuple, etc. (C{scalar} or L{Fsum}
1303 instances).
1304 @kwarg name: Optional name (C{str}).
1306 @return: L{Fsum2Tuple}C{(fsum, residual)} with C{fsum} the
1307 current precision running sum and C{residual}, the
1308 (precision) sum of the remaining C{partials}. The
1309 C{residual is INT0} if the C{fsum} is considered
1310 to be I{exact}.
1312 @see: Methods L{Fsum.fint2}, L{Fsum.fsum} and L{Fsum.fsum2_}
1313 '''
1314 f = self._facc_any(xs) if xs else self
1315 t = f._fprs2
1316 if name:
1317 t = t.dup(name=name)
1318 return t
1320 def fsum2_(self, *xs):
1321 '''Add any positional C{scalar} or L{Fsum} instances and return
1322 the precision running sum and the C{differential}.
1324 @arg xs: Values to add (C{scalar} or L{Fsum} instances), all
1325 positional.
1327 @return: 2Tuple C{(fsum, delta)} with the current, precision
1328 running C{fsum} like method L{Fsum.fsum} and C{delta},
1329 the difference with previous running C{fsum}, C{float}.
1331 @see: Methods L{Fsum.fsum_} and L{Fsum.fsum}.
1332 '''
1333 return self._fsum2f_any(xs, self._facc_any, origin=1)
1335 def fsumf_(self, *xs):
1336 '''Like method L{Fsum.fsum_} but only for I{known} C{float B{xs}}.
1337 '''
1338 f = self._facc(xs) if xs else self
1339 return f._fprs
1341 def Fsumf_(self, *xs):
1342 '''Like method L{Fsum.Fsum_} but only for I{known} C{float B{xs}}.
1343 '''
1344 return self._facc(xs)._copy_2(self.Fsumf_)
1346 def fsum2f_(self, *xs):
1347 '''Like method L{Fsum.fsum2_} but only for I{known} C{float B{xs}}.
1348 '''
1349 return self._fsum2f_any(xs, self._facc)
1351 def _fsum2f_any(self, xs, _facc, **origin):
1352 '''(INTERNAL) Helper for L{Fsum.fsum2_} and L{Fsum.fsum2f_}.
1353 '''
1354 p, q = self._fprs2
1355 if xs:
1356 s, r = _facc(xs, **origin)._fprs2
1357 return s, _2delta(s - p, r - q) # _fsum(_1primed((s, -p, r, -q))
1358 else:
1359 return p, _0_0
1361# ftruediv = __itruediv__ # for naming consistency?
1363 def _ftruediv(self, other, op):
1364 '''(INTERNAL) Apply C{B{self} /= B{other}}.
1365 '''
1366 n = _1_0
1367 if isinstance(other, Fsum):
1368 if other is self or other == self:
1369 return self._fset(_1_0) # n=len(self)
1370 d, r = other._fprs2
1371 if r:
1372 if d:
1373 if self._raiser(r, d):
1374 raise self._ResidualError(op, other, r)
1375 d, n = other.as_integer_ratio()
1376 else: # PYCHOK no cover
1377 d = r
1378 elif isscalar(other):
1379 d = other
1380 else: # PYCHOK no cover
1381 raise self._TypeError(op, other) # txt=_invalid_
1382 try:
1383 s = 0 if isinf(d) else (
1384 d if isnan(d) else self._finite(n / d))
1385 except Exception as X:
1386 raise self._ErrorX(X, op, other)
1387 f = self._mul_scalar(s, _mul_op_) # handles 0, NAN, etc.
1388 return self._fset(f, asis=False)
1390 @property_RO
1391 def imag(self):
1392 '''Get the C{imaginary} part of this instance (C{0.0}, always).
1394 @see: Properties L{Fsum.ceil}, L{Fsum.floor} and L{Fsum.real}.
1395 '''
1396 return _0_0
1398 def int_float(self, raiser=False):
1399 '''Return this instance' current running sum as C{int} or C{float}.
1401 @kwarg raiser: If C{True} throw a L{ResidualError} if the
1402 residual is non-zero.
1404 @return: This C{integer} sum if this instance C{is_integer},
1405 otherwise return the C{float} sum if the residual
1406 is zero or if C{B{raiser}=False}.
1408 @raise ResidualError: Non-zero residual and C{B{raiser}=True}.
1410 @see: Methods L{Fsum.fint} and L{Fsum.fint2}.
1411 '''
1412 s, r = self._fint2
1413 if r:
1414 s, r = self._fprs2
1415 if r and raiser: # PYCHOK no cover
1416 t = _stresidual(_non_zero_, r)
1417 raise ResidualError(int_float=s, txt=t)
1418 s = float(s) # redundant
1419 return s
1421 def is_exact(self):
1422 '''Is this instance' running C{fsum} considered to be exact? (C{bool}).
1423 '''
1424 return self.residual is INT0
1426 def is_integer(self):
1427 '''Is this instance' running sum C{integer}? (C{bool}).
1429 @see: Methods L{Fsum.fint} and L{Fsum.fint2}.
1430 '''
1431 _, r = self._fint2
1432 return False if r else True
1434 def is_math_fsum(self):
1435 '''Return whether functions L{fsum}, L{fsum_}, L{fsum1} and
1436 L{fsum1_} plus partials summation are based on Python's
1437 C{math.fsum} or not.
1439 @return: C{2} if all functions and partials summation
1440 are based on C{math.fsum}, C{True} if only
1441 the functions are based on C{math.fsum} (and
1442 partials summation is not) or C{False} if
1443 none are.
1444 '''
1445 f = Fsum._math_fsum
1446 return 2 if _psum is f else bool(f)
1448 def _mul_Fsum(self, other, op=_mul_op_): # in .fmath.Fhorner
1449 '''(INTERNAL) Return C{B{self} * Fsum B{other}} as L{Fsum} or C{0}.
1450 '''
1451 # assert isinstance(other, Fsum)
1452 if self._ps and other._ps:
1453 f = self._ps_mul(op, *other._ps) # NO ._2scalar
1454 else:
1455 f = _0_0
1456 return f
1458 def _mul_scalar(self, factor, op): # in .fmath.Fhorner
1459 '''(INTERNAL) Return C{B{self} * scalar B{factor}} as L{Fsum}, C{0} or C{self}.
1460 '''
1461 # assert isscalar(factor)
1462 if self._ps and self._finite(factor, op):
1463 f = self if factor == _1_0 else (
1464 self._neg if factor == _N_1_0 else
1465 self._ps_mul(op, factor)._2scalar)
1466 else:
1467 f = _0_0
1468 return f
1470 @property_RO
1471 def _neg(self):
1472 '''(INTERNAL) Return C{Fsum(-self)} or scalar C{NEG0}.
1473 '''
1474 return _Psum(self._ps_neg) if self._ps else NEG0
1476 @property_RO
1477 def partials(self):
1478 '''Get this instance' current, partial sums (C{tuple} of C{float}s).
1479 '''
1480 return tuple(self._ps)
1482 def pow(self, x, *mod):
1483 '''Return C{B{self}**B{x}} as L{Fsum}.
1485 @arg x: The exponent (L{Fsum} or C{scalar}).
1486 @arg mod: Optional modulus (C{int} or C{None}) for the 3-argument
1487 C{pow(B{self}, B{other}, B{mod})} version.
1489 @return: The C{pow(self, B{x})} or C{pow(self, B{x}, *B{mod})}
1490 result (L{Fsum}).
1492 @note: If B{C{mod}} is given as C{None}, the result will be an
1493 C{integer} L{Fsum} provided this instance C{is_integer}
1494 or set to C{integer} by an L{Fsum.fint} call.
1496 @see: Methods L{Fsum.__ipow__}, L{Fsum.fint} and L{Fsum.is_integer}.
1497 '''
1498 f = self._copy_2(self.pow)
1499 return f._fpow(x, _pow_op_, *mod) # f = pow(f, x, *mod)
1501 def _pow_0_1(self, x, other):
1502 '''(INTERNAL) Return B{C{self}**1} or C{B{self}**0 == 1.0}.
1503 '''
1504 return self if x else (1 if isint(other) and self.is_integer() else _1_0)
1506 def _pow_2_3(self, b, x, other, op, *mod):
1507 '''(INTERNAL) 2-arg C{pow(B{b}, scalar B{x})} and 3-arg C{pow(B{b},
1508 B{x}, int B{mod} or C{None})}, embellishing errors.
1509 '''
1510 try:
1511 if mod: # b, x, mod all C{int}, unless C{mod} is C{None}
1512 m = mod[0]
1513 b, r = b._fprs2 if m is None else b._fint2
1514 if r and self._raiser(r, b):
1515 t = _non_zero_ if m is None else _integer_
1516 raise ResidualError(_stresidual(t, r, mod=m), txt=None)
1517 x = _2scalar(x, _raiser=self._raiser, mod=m)
1518 # 0**INF == 0.0, 1**INF == 1.0, -1**2.3 == -(1**2.3)
1519 s = pow(b, x, *mod)
1520 if iscomplex(s):
1521 # neg**frac == complex in Python 3+, but ValueError in 2-
1522 raise ValueError(_strcomplex(s, b, x, *mod))
1523 return self._finite(s)
1524 except Exception as X:
1525 raise self._ErrorX(X, op, other, *mod)
1527 def _pow_any(self, other, unused, op):
1528 '''Return C{B{self} ** B{other}}.
1529 '''
1530 if isinstance(other, Fsum):
1531 x, r = other._fprs2
1532 if r and self._raiser(r, x):
1533 raise self._ResidualError(op, other, r)
1534 f = self._pow_scalar(x, other, op)
1535 if r:
1536 f *= self._pow_scalar(r, other, op)
1537 elif isscalar(other):
1538 x = self._finite(other, op)
1539 f = self._pow_scalar(x, other, op)
1540 else:
1541 raise self._TypeError(op, other) # txt=_invalid_
1542 return f
1544 def _pow_int(self, x, other, op):
1545 '''(INTERNAL) Return C{B{self} **= B{x}} for C{int B{x} >= 0}.
1546 '''
1547 # assert isint(x) and x >= 0
1548 ps = self._ps
1549 if len(ps) > 1:
1550 _mul_Fsum = Fsum._mul_Fsum
1551 if x > 4:
1552 p = self
1553 f = self if (x & 1) else _Psum_1()
1554 m = x >> 1 # // 2
1555 while m:
1556 p = _mul_Fsum(p, p, op) # p **= 2
1557 if (m & 1):
1558 f = _mul_Fsum(f, p, op) # f *= p
1559 m >>= 1 # //= 2
1560 elif x > 1: # self**2, 3 or 4
1561 f = _mul_Fsum(self, self, op)
1562 if x > 2: # self**3 or 4
1563 p = self if x < 4 else f
1564 f = _mul_Fsum(f, p, op)._2scalar
1565 else: # self**1 or self**0 == 1 or _1_0
1566 f = self._pow_0_1(x, other)
1567 elif ps: # self._ps[0]**x
1568 f = self._pow_2_3(ps[0], x, other, op)
1569 else: # PYCHOK no cover
1570 # 0**pos_int == 0, but 0**0 == 1
1571 f = 0 if x else 1
1572 return f
1574 def _pow_scalar(self, x, other, op):
1575 '''(INTERNAL) Return C{self**B{x}} for C{scalar B{x}}.
1576 '''
1577 s, r = self._fprs2
1578 if isint(x, both=True):
1579 x = int(x) # Fsum**int
1580 y = abs(x)
1581 if y > 1:
1582 if r:
1583 f = self._pow_int(y, other, op)
1584 if x > 0: # > 1
1585 return f
1586 # assert x < 0 # < -1
1587 s, r = f._fprs2 if isinstance(f, Fsum) else (f, 0)
1588 if r:
1589 return _Psum_1()._ftruediv(f, op)
1590 # use **= -1 for the CPython float_pow
1591 # error if s is zero, and not s = 1 / s
1592 x = -1
1593 elif x < 0: # == -1: self**(-1) == 1 / self
1594 if r:
1595 return _Psum_1()._ftruediv(self, op)
1596 else: # self**1 or self**0
1597 return self._pow_0_1(x, other) # self, 1 or 1.0
1598 elif not isscalar(x): # assert ...
1599 raise self._TypeError(op, other, txt=_not_scalar_)
1600 elif r and self._raiser(r, s): # non-zero residual**fractional
1601 # raise self._ResidualError(op, other, r, fractional_power=x)
1602 t = _stresidual(_non_zero_, r, fractional_power=x)
1603 raise self._Error(op, other, ResidualError, txt=t)
1604 # assert isscalar(s) and isscalar(x)
1605 return self._pow_2_3(s, x, other, op)
1607 def _ps_1(self, *less):
1608 '''(INTERNAL) Yield partials, 1-primed and subtract any C{less}.
1609 '''
1610 yield _1_0
1611 for p in self._ps:
1612 yield p
1613 for p in less:
1614 yield -p
1615 yield _N_1_0
1617 def _ps_acc(self, ps, xs, up=True):
1618 '''(INTERNAL) Accumulate all scalar C{xs} into C{ps}.
1619 '''
1620 n = 0
1621 _2s = _2sum
1622 for x in (tuple(xs) if xs is ps else xs):
1623 # assert isscalar(x) and _isfinite(x)
1624 if x:
1625 i = 0
1626 for p in ps:
1627 x, p = _2s(x, p)
1628 if p:
1629 ps[i] = p
1630 i += 1
1631 ps[i:] = (x,) if x else ()
1632 n += 1
1633 if n:
1634 self._n += n
1635 # Fsum._ps_max = max(Fsum._ps_max, len(ps))
1636 if up:
1637 self._update()
1638 return ps
1640 def _ps_mul(self, op, *factors):
1641 '''(INTERNAL) Multiply this instance' C{partials} with
1642 each of the B{C{factors}}, all known to be scalar.
1643 '''
1644 def _pfs(ps, fs):
1645 if len(ps) < len(fs):
1646 ps, fs = fs, ps
1647 _fin = _isfinite
1648 for f in fs:
1649 for p in ps:
1650 p *= f
1651 yield p if _fin(p) else self._finite(p, op)
1653 return _Psum(self._ps_acc([], _pfs(self._ps, factors)))
1655 @property_RO
1656 def _ps_neg(self):
1657 '''(INTERNAL) Yield the partials, I{negated}.
1658 '''
1659 for p in self._ps:
1660 yield -p
1662 def _raiser(self, r, s):
1663 '''(INTERNAL) Does ratio C{r / s} exceed threshold?
1664 '''
1665 self._ratio = t = fabs((r / s) if s else r)
1666 return t > self._RESIDUAL
1668 @property_RO
1669 def real(self):
1670 '''Get the C{real} part of this instance (C{float}).
1672 @see: Methods L{Fsum.__float__} and L{Fsum.fsum}
1673 and properties L{Fsum.ceil}, L{Fsum.floor},
1674 L{Fsum.imag} and L{Fsum.residual}.
1675 '''
1676 return float(self._fprs)
1678 @property_RO
1679 def residual(self):
1680 '''Get this instance' residual (C{float} or C{int}), the
1681 C{sum(partials)} less the precision running sum C{fsum}.
1683 @note: If the C{residual is INT0}, the precision running
1684 C{fsum} is considered to be I{exact}.
1686 @see: Methods L{Fsum.fsum}, L{Fsum.fsum2} and L{Fsum.is_exact}.
1687 '''
1688 return self._fprs2.residual
1690 def RESIDUAL(self, *threshold):
1691 '''Get and set this instance' I{ratio} for raising L{ResidualError}s,
1692 overriding the default from env variable C{PYGEODESY_FSUM_RESIDUAL}.
1694 @arg threshold: If C{scalar}, the I{ratio} to exceed for raising
1695 L{ResidualError}s in division and exponention, if
1696 C{None} restore the default set with env variable
1697 C{PYGEODESY_FSUM_RESIDUAL} or if omitted, keep the
1698 current setting.
1700 @return: The previous C{RESIDUAL} setting (C{float}), default C{0}.
1702 @raise ValueError: Negative B{C{threshold}}.
1704 @note: L{ResidualError}s will be thrown if the non-zero I{ratio}
1705 C{residual / fsum} exceeds the B{C{threshold}}.
1706 '''
1707 r = self._RESIDUAL
1708 if threshold:
1709 t = threshold[0]
1710 t = Fsum._RESIDUAL if t is None else (
1711 float(t) if isscalar(t) else ( # for backward ...
1712 _0_0 if bool(t) else _1_0)) # ... compatibility
1713 if t < 0:
1714 u = _DOT_(self, unstr(self.RESIDUAL, *threshold))
1715 raise _ValueError(u, RESIDUAL=t, txt=_negative_)
1716 self._RESIDUAL = t
1717 return r
1719 def _ResidualError(self, op, other, residual):
1720 '''(INTERNAL) Non-zero B{C{residual}} etc.
1721 '''
1722 t = _stresidual(_non_zero_, residual, ratio=self._ratio,
1723 RESIDUAL=self._RESIDUAL)
1724 t = t.replace(_COMMASPACE_R_, _exceeds_R_)
1725 return self._Error(op, other, ResidualError, txt=t)
1727 @property_RO
1728 def _2scalar(self):
1729 '''(INTERNAL) Get this instance as C{scalar} or C{as-is}.
1730 '''
1731 s, r = self._fprs2
1732 return self if r else s
1734 def signOf(self, res=True):
1735 '''Determine the sign of this instance.
1737 @kwarg res: If C{True} consider, otherwise
1738 ignore the residual (C{bool}).
1740 @return: The sign (C{int}, -1, 0 or +1).
1741 '''
1742 s, r = self._fprs2
1743 return _signOf(s, (-r) if res else 0)
1745 def toRepr(self, **prec_sep_fmt_lenc): # PYCHOK signature
1746 '''Return this C{Fsum} instance as representation.
1748 @kwarg prec_sep_fmt_lenc: Optional keyword arguments for
1749 method L{Fsum2Tuple.toRepr} plus C{B{lenc}=True}
1750 (C{bool}) to in-/exclude the current C{[len]}
1751 of this L{Fsum} enclosed in I{[brackets]}.
1753 @return: This instance (C{repr}).
1754 '''
1755 return self._toT(self._fprs2.toRepr, **prec_sep_fmt_lenc)
1757 def toStr(self, **prec_sep_fmt_lenc): # PYCHOK signature
1758 '''Return this C{Fsum} instance as string.
1760 @kwarg prec_sep_fmt_lenc: Optional keyword arguments for
1761 method L{Fsum2Tuple.toStr} plus C{B{lenc}=True}
1762 (C{bool}) to in-/exclude the current C{[len]}
1763 of this L{Fsum} enclosed in I{[brackets]}.
1765 @return: This instance (C{str}).
1766 '''
1767 return self._toT(self._fprs2.toStr, **prec_sep_fmt_lenc)
1769 def _toT(self, toT, fmt=Fmt.g, lenc=True, **kwds):
1770 '''(INTERNAL) Helper for C{toRepr} and C{toStr}.
1771 '''
1772 n = self.named3
1773 if lenc:
1774 n = Fmt.SQUARE(n, len(self))
1775 return _SPACE_(n, toT(fmt=fmt, **kwds))
1777 def _TypeError(self, op, other, **txt): # PYCHOK no cover
1778 '''(INTERNAL) Return a C{TypeError}.
1779 '''
1780 return self._Error(op, other, _TypeError, **txt)
1782 def _update(self, updated=True): # see ._fset
1783 '''(INTERNAL) Zap all cached C{Property_RO} values.
1784 '''
1785 if updated:
1786 _pop = self.__dict__.pop
1787 for p in _ROs:
1788 _ = _pop(p, None)
1789# Fsum._fint2._update(self)
1790# Fsum._fprs ._update(self)
1791# Fsum._fprs2._update(self)
1792 return self # for .fset_
1794 def _ValueError(self, op, other, **txt): # PYCHOK no cover
1795 '''(INTERNAL) Return a C{ValueError}.
1796 '''
1797 return self._Error(op, other, _ValueError, **txt)
1799 def _ZeroDivisionError(self, op, other, **txt): # PYCHOK no cover
1800 '''(INTERNAL) Return a C{ZeroDivisionError}.
1801 '''
1802 return self._Error(op, other, _ZeroDivisionError, **txt)
1804_ROs = _allPropertiesOf_n(3, Fsum, Property_RO) # PYCHOK assert, see Fsum._fset, -._update
1807def _Float_Int(arg, **name_Error):
1808 '''(INTERNAL) Unit of L{Fsum2Tuple} items.
1809 '''
1810 U = Int if isint(arg) else Float
1811 return U(arg, **name_Error)
1814class DivMod2Tuple(_NamedTuple):
1815 '''2-Tuple C{(div, mod)} with the quotient C{div} and remainder
1816 C{mod} results of a C{divmod} operation.
1818 @note: Quotient C{div} an C{int} in Python 3+ or a C{float} in
1819 Python 2-. Remainder C{mod} an L{Fsum} instance.
1820 '''
1821 _Names_ = (_div_, _mod_)
1822 _Units_ = (_Float_Int, Fsum)
1825class Fsum2Tuple(_NamedTuple):
1826 '''2-Tuple C{(fsum, residual)} with the precision running C{fsum}
1827 and the C{residual}, the sum of the remaining partials. Each
1828 item is either C{float} or C{int}.
1830 @note: If the C{residual is INT0}, the C{fsum} is considered
1831 to be I{exact}, see method L{Fsum2Tuple.is_exact}.
1832 '''
1833 _Names_ = ( Fsum.fsum.__name__, Fsum.residual.name)
1834 _Units_ = (_Float_Int, _Float_Int)
1836 @Property_RO
1837 def _Fsum(self):
1838 '''(INTERNAL) Get this L{Fsum2Tuple} as an L{Fsum}.
1839 '''
1840 s, r = map(float, self)
1841 return _Psum(_2ps(s, r), name=self.name)
1843 def is_exact(self):
1844 '''Is this L{Fsum2Tuple} considered to be exact? (C{bool}).
1845 '''
1846 return self._Fsum.is_exact()
1848 def is_integer(self):
1849 '''Is this L{Fsum2Tuple} C{integer}? (C{bool}).
1850 '''
1851 return self._Fsum.is_integer()
1854class ResidualError(_ValueError):
1855 '''Error raised for an operation involving a L{pygeodesy.sums.Fsum}
1856 instance with a non-zero C{residual}, I{integer} or otherwise.
1858 @see: Module L{pygeodesy.fsums} and method L{Fsum.RESIDUAL}.
1859 '''
1860 pass
1863try:
1864 from math import fsum as _fsum # precision IEEE-754 sum, Python 2.6+
1866 # make sure _fsum works as expected (XXX check
1867 # float.__getformat__('float')[:4] == 'IEEE'?)
1868 if _fsum((1, 1e101, 1, -1e101)) != 2: # PYCHOK no cover
1869 del _fsum # nope, remove _fsum ...
1870 raise ImportError # ... use _fsum below
1872 Fsum._math_fsum = _sum = _fsum # PYCHOK exported
1874 if _getenv('PYGEODESY_FSUM_PARTIALS', NN) == _fsum.__name__:
1875 _psum = _fsum # PYCHOK re-def
1877except ImportError:
1878 _sum = sum # Fsum(NAN) exception fall-back, in .elliptic
1880 def _fsum(xs):
1881 '''(INTERNAL) Precision summation, Python 2.5-.
1882 '''
1883 f = Fsum()
1884 f.name = _fsum.__name__
1885 return f.fsum(xs)
1888def fsum(xs, floats=False):
1889 '''Precision floating point summation based on or like Python's C{math.fsum}.
1891 @arg xs: Iterable, list, tuple, etc. of values (C{scalar} or L{Fsum}
1892 instances).
1893 @kwarg floats: Use C{B{floats}=True} iff I{all} B{C{xs}} are known
1894 to be C{float} scalars (C{bool}).
1896 @return: Precision C{fsum} (C{float}).
1898 @raise OverflowError: Partial C{2sum} overflow.
1900 @raise TypeError: Non-scalar B{C{xs}} value.
1902 @raise ValueError: Invalid or non-finite B{C{xs}} value.
1904 @note: Exception and I{non-finite} handling may differ if not based
1905 on Python's C{math.fsum}.
1907 @see: Class L{Fsum} and methods L{Fsum.fsum} and L{Fsum.fadd}.
1908 '''
1909 return _fsum(xs if floats else _2floats(xs)) if xs else _0_0 # PYCHOK yield
1912def fsum_(*xs, **floats):
1913 '''Precision floating point summation of all positional arguments.
1915 @arg xs: Values to be added (C{scalar} or L{Fsum} instances), all
1916 positional.
1917 @kwarg floats: Use C{B{floats}=True} iff I{all} B{C{xs}} are known
1918 to be C{float} scalars (C{bool}).
1920 @return: Precision C{fsum} (C{float}).
1922 @see: Function C{fsum}.
1923 '''
1924 return _fsum(xs if _xkwds_get(floats, floats=False) else
1925 _2floats(xs, origin=1)) if xs else _0_0 # PYCHOK yield
1928def fsumf_(*xs):
1929 '''Precision floating point summation L{fsum_}C{(*xs, floats=True)}.
1930 '''
1931 return _fsum(xs) if xs else _0_0
1934def fsum1(xs, floats=False):
1935 '''Precision floating point summation, 1-primed.
1937 @arg xs: Iterable, list, tuple, etc. of values (C{scalar} or L{Fsum}
1938 instances).
1939 @kwarg floats: Use C{B{floats}=True} iff I{all} B{C{xs}} are known
1940 to be C{float}.
1942 @return: Precision C{fsum} (C{float}).
1944 @see: Function C{fsum}.
1945 '''
1946 return _fsum(_1primed(xs if floats else _2floats(xs))) if xs else _0_0 # PYCHOK yield
1949def fsum1_(*xs, **floats):
1950 '''Precision floating point summation, 1-primed.
1952 @arg xs: Values to be added (C{scalar} or L{Fsum} instances), all
1953 positional.
1954 @kwarg floats: Use C{B{floats}=True} iff I{all} B{C{xs}} are known
1955 to be C{float} scalars (C{bool}).
1957 @return: Precision C{fsum} (C{float}).
1959 @see: Function C{fsum}
1960 '''
1961 return _fsum(_1primed(xs if _xkwds_get(floats, floats=False) else
1962 _2floats(xs, origin=1))) if xs else _0_0 # PYCHOK yield
1965def fsum1f_(*xs):
1966 '''Precision floating point summation, L{fsum1_}C{(*xs, floats=True)}.
1967 '''
1968 return _fsum(_1primed(xs)) if xs else _0_0
1971if __name__ == '__main__':
1973 # usage: [env PYGEODESY_FSUM_PARTIALS=fsum] python3 -m pygeodesy.fsums
1975 def _test(n):
1976 # copied from Hettinger, see L{Fsum} reference
1977 from pygeodesy import printf
1978 from random import gauss, random, shuffle
1980 printf(_fsum.__name__, end=_COMMASPACE_)
1981 printf(_psum.__name__, end=_COMMASPACE_)
1983 F = Fsum()
1984 if F.is_math_fsum():
1985 c = (7, 1e100, -7, -1e100, -9e-20, 8e-20) * 10
1986 for _ in range(n):
1987 t = list(c)
1988 s = 0
1989 for _ in range(n * 8):
1990 v = gauss(0, random())**7 - s
1991 t.append(v)
1992 s += v
1993 shuffle(t)
1994 assert float(F.fset_(*t)) == _fsum(t)
1995 printf(_DOT_, end=NN)
1996 printf(NN)
1998 _test(128)
2000# **) MIT License
2001#
2002# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.
2003#
2004# Permission is hereby granted, free of charge, to any person obtaining a
2005# copy of this software and associated documentation files (the "Software"),
2006# to deal in the Software without restriction, including without limitation
2007# the rights to use, copy, modify, merge, publish, distribute, sublicense,
2008# and/or sell copies of the Software, and to permit persons to whom the
2009# Software is furnished to do so, subject to the following conditions:
2010#
2011# The above copyright notice and this permission notice shall be included
2012# in all copies or substantial portions of the Software.
2013#
2014# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
2015# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
2016# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
2017# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
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2019# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
2020# OTHER DEALINGS IN THE SOFTWARE.