Coverage for pygeodesy/fsums.py: 98%
704 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 an empty string (or anything
18other than C{"fsum"}) for backward compatible summation of L{Fsum} partials.
20Set env variable C{PYGEODESY_FSUM_RESIDUAL} to a C{float} string greater
21than C{"0.0"} as the threshold to throw a L{ResidualError} in division or
22exponention of an L{Fsum} instance with a I{relative} C{residual} exceeding
23the threshold, see methods L{Fsum.RESIDUAL}, L{Fsum.pow}, L{Fsum.__ipow__}
24and L{Fsum.__itruediv__}.
25'''
26# make sure int/int division yields float quotient, see .basics
27from __future__ import division as _; del _ # PYCHOK semicolon
29from pygeodesy.basics import iscomplex, isint, isscalar, itemsorted, \
30 signOf, _signOf, _xisscalar
31from pygeodesy.constants import INT0, _isfinite, isinf, isnan, _pos_self, \
32 _0_0, _1_0, _N_1_0, Float, Int
33from pygeodesy.errors import _OverflowError, _TypeError, _ValueError, _xError2, \
34 _xkwds_get, _ZeroDivisionError
35from pygeodesy.interns import NN, _arg_, _COMMASPACE_, _DASH_, _DOT_, _EQUAL_, \
36 _exceeds_, _from_, _iadd_op_, _LANGLE_, _negative_, \
37 _NOTEQUAL_, _not_finite_, _not_scalar_, _PERCENT_, \
38 _PLUS_, _R_, _RANGLE_, _SLASH_, _SPACE_, _STAR_, _UNDER_
39from pygeodesy.lazily import _ALL_LAZY, _getenv, _sys_version_info2
40from pygeodesy.named import _Named, _NamedTuple, _NotImplemented, Fmt, unstr
41from pygeodesy.props import _allPropertiesOf_n, deprecated_property_RO, \
42 Property_RO, property_RO
43# from pygeodesy.streprs import Fmt, unstr # from .named
44# from pygeodesy.units import Float, Int # from .constants
46from math import ceil as _ceil, fabs, floor as _floor # PYCHOK used! .ltp
48__all__ = _ALL_LAZY.fsums
49__version__ = '24.03.18'
51_add_op_ = _PLUS_ # in .auxilats.auxAngle
52_eq_op_ = _EQUAL_ * 2 # _DEQUAL_
53_COMMASPACE_R_ = _COMMASPACE_ + _R_
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_op_ = _PERCENT_
63_mul_op_ = _STAR_
64_ne_op_ = _NOTEQUAL_
65_non_zero_ = 'non-zero'
66_pow_op_ = _STAR_ * 2 # _DSTAR_, in .fmath
67_sub_op_ = _DASH_ # in .auxilats.auxAngle, .fsums
68_truediv_op_ = _SLASH_
69_divmod_op_ = _floordiv_op_ + _mod_op_
70_isub_op_ = _sub_op_ + _fset_op_ # in .auxilats.auxAngle, .fsums
73def _2float(index=None, **name_value): # in .fmath, .fstats
74 '''(INTERNAL) Raise C{TypeError} or C{ValueError} if not scalar or infinite.
75 '''
76 n, v = name_value.popitem() # _xkwds_item2(name_value)
77 try:
78 v = float(v)
79 if _isfinite(v):
80 return v
81 E, t = _ValueError, _not_finite_
82 except Exception as e:
83 E, t = _xError2(e)
84 raise E(Fmt.INDEX(n, index), v, txt=t)
87def _2floats(xs, origin=0, sub=False):
88 '''(INTERNAL) Yield each B{C{xs}} as a C{float}.
89 '''
90 try:
91 i, x = origin, None
92 _fin = _isfinite
93 _Fsum = Fsum
94 for x in xs:
95 if isinstance(x, _Fsum):
96 for p in x._ps:
97 yield (-p) if sub else p
98 else:
99 f = float(x)
100 if not _fin(f):
101 raise ValueError(_not_finite_)
102 if f:
103 yield (-f) if sub else f
104 i += 1
105 except Exception as e:
106 E, t = _xError2(e)
107 n = Fmt.SQUARE(xs=i)
108 raise E(n, x, txt=t)
111def _Powers(power, xs, origin=1): # in .fmath
112 '''(INTERNAL) Yield each C{xs} as C{float(x**power)}.
113 '''
114 _xisscalar(power=power)
115 try:
116 i, x = origin, None
117 _fin = _isfinite
118 _Fsum = Fsum
119 _pow = pow # XXX math.pow
120 for x in xs:
121 if isinstance(x, _Fsum):
122 P = x.pow(power)
123 for p in P._ps:
124 yield p
125 else:
126 p = _pow(float(x), power)
127 if not _fin(p):
128 raise ValueError(_not_finite_)
129 yield p
130 i += 1
131 except Exception as e:
132 E, t = _xError2(e)
133 n = Fmt.SQUARE(xs=i)
134 raise E(n, x, txt=t)
137def _1primed(xs):
138 '''(INTERNAL) 1-Prime the summation of C{xs}
139 arguments I{known} to be C{finite float}.
140 '''
141 yield _1_0
142 for x in xs:
143 if x:
144 yield x
145 yield _N_1_0
148def _psum(ps): # PYCHOK used!
149 '''(INTERNAL) Partials summation updating C{ps}, I{overridden below}.
150 '''
151 i = len(ps) - 1 # len(ps) > 2
152 s = ps[i]
153 _2s = _2sum
154 while i > 0:
155 i -= 1
156 s, r = _2s(s, ps[i])
157 if r: # sum(ps) became inexact
158 ps[i:] = [s, r] if s else [r]
159 if i > 0:
160 p = ps[i-1] # round half-even
161 if (p > 0 and r > 0) or \
162 (p < 0 and r < 0): # signs match
163 r *= 2
164 t = s + r
165 if r == (t - s):
166 s = t
167 break
168 ps[i:] = [s]
169 return s
172def _2scalar(other, _raiser=None):
173 '''(INTERNAL) Return B{C{other}} as C{int}, C{float} or C{as-is}.
174 '''
175 if isinstance(other, Fsum):
176 s, r = other._fint2
177 if r:
178 s, r = other._fprs2
179 if r: # PYCHOK no cover
180 if _raiser and _raiser(r, s):
181 raise ValueError(_stresidual(_non_zero_, r))
182 s = other # L{Fsum} as-is
183 else:
184 s = other # C{type} as-is
185 if isint(s, both=True):
186 s = int(s)
187 return s
190def _strcomplex(s, *args):
191 '''(INTERNAL) C{Complex} 2- or 3-arg C{pow} error C{str}.
192 '''
193 c = iscomplex.__name__[2:]
194 n = _DASH_(len(args), _arg_)
195 t = _SPACE_(c, s, _from_, n, pow.__name__)
196 return unstr(t, *args)
199def _stresidual(prefix, residual, **name_values):
200 '''(INTERNAL) Residual error C{str}.
201 '''
202 p = _SPACE_(prefix, Fsum.residual.name)
203 t = Fmt.PARENSPACED(p, Fmt(residual))
204 for n, v in itemsorted(name_values):
205 n = n.replace(_UNDER_, _SPACE_)
206 p = Fmt.PARENSPACED(n, Fmt(v))
207 t = _COMMASPACE_(t, p)
208 return t
211def _2sum(a, b): # by .testFmath
212 '''(INTERNAL) Return C{a + b} as 2-tuple (sum, residual).
213 '''
214 s = a + b
215 if not _isfinite(s):
216 u = unstr(_2sum.__name__, a, b)
217 t = Fmt.PARENSPACED(_not_finite_, s)
218 raise _OverflowError(u, txt=t)
219 if fabs(a) < fabs(b):
220 a, b = b, a
221 return s, (b - (s - a))
224class Fsum(_Named): # sync __methods__ with .vector3dBase.Vector3dBase
225 '''Precision floating point I{running} summation.
227 Unlike Python's C{math.fsum}, this class accumulates values and provides intermediate,
228 I{running} precision floating point summation. Accumulation may continue after
229 intermediate, I{running} summuation.
231 @note: Accumulated values may be L{Fsum} or C{scalar} instances with C{scalar} meaning
232 type C{float}, C{int} or any C{type} convertible to a single C{float}, having
233 method C{__float__}.
235 @note: Handling of exceptions and C{inf}, C{INF}, C{nan} and C{NAN} differs from
236 Python's C{math.fsum}.
238 @see: U{Hettinger<https://GitHub.com/ActiveState/code/blob/master/recipes/Python/
239 393090_Binary_floating_point_summatiaccurate_full/recipe-393090.py>}, U{Kahan
240 <https://WikiPedia.org/wiki/Kahan_summation_algorithm>}, U{Klein
241 <https://Link.Springer.com/article/10.1007/s00607-005-0139-x>}, Python 2.6+
242 file I{Modules/mathmodule.c} and the issue log U{Full precision summation
243 <https://Bugs.Python.org/issue2819>}.
244 '''
245 _math_fsum = None
246 _n = 0
247# _ps = [] # partial sums
248# _px = 0
249 _ratio = None
250 _RESIDUAL = max(float(_getenv('PYGEODESY_FSUM_RESIDUAL', _0_0)), _0_0)
252 def __init__(self, *xs, **name_RESIDUAL):
253 '''New L{Fsum} for precision floating point I{running} summation.
255 @arg xs: No, one or more initial values (each C{scalar} or an
256 L{Fsum} instance).
257 @kwarg name_RESIDUAL: Optional C{B{name}=NN} for this L{Fsum}
258 (C{str}) and C{B{RESIDUAL}=None} for the
259 L{ResidualError} threshold.
261 @see: Methods L{Fsum.fadd} and L{Fsum.RESIDUAL}.
262 '''
263 if name_RESIDUAL:
264 n = _xkwds_get(name_RESIDUAL, name=NN)
265 if n: # set name ...
266 self.name = n
267 r = _xkwds_get(name_RESIDUAL, RESIDUAL=None)
268 if r is not None:
269 self.RESIDUAL(r) # ... for ResidualError
270# self._n = 0
271 self._ps = [] # [_0_0], see L{Fsum._fprs}
272 if len(xs) > 1:
273 self._facc(_2floats(xs, origin=1), up=False) # PYCHOK yield
274 elif xs: # len(xs) == 1
275 self._ps = [_2float(x=xs[0])]
276 self._n = 1
278 def __abs__(self):
279 '''Return this instance' absolute value as an L{Fsum}.
280 '''
281 s = _fsum(self._ps_1()) # == self._cmp_0(0, ...)
282 return self._copy_n(self.__abs__) if s < 0 else \
283 self._copy_2(self.__abs__)
285 def __add__(self, other):
286 '''Return the C{Fsum(B{self}, B{other})}.
288 @arg other: An L{Fsum} or C{scalar}.
290 @return: The sum (L{Fsum}).
292 @see: Method L{Fsum.__iadd__}.
293 '''
294 f = self._copy_2(self.__add__)
295 return f._fadd(other, _add_op_)
297 def __bool__(self): # PYCHOK not special in Python 2-
298 '''Return C{True} if this instance is I{exactly} non-zero.
299 '''
300 s, r = self._fprs2
301 return bool(s or r) and s != -r # == self != 0
303 def __ceil__(self): # PYCHOK not special in Python 2-
304 '''Return this instance' C{math.ceil} as C{int} or C{float}.
306 @return: An C{int} in Python 3+, but C{float} in Python 2-.
308 @see: Methods L{Fsum.__floor__} and property L{Fsum.ceil}.
309 '''
310 return self.ceil
312 def __cmp__(self, other): # Python 2-
313 '''Compare this with an other instance or C{scalar}.
315 @return: -1, 0 or +1 (C{int}).
317 @raise TypeError: Incompatible B{C{other}} C{type}.
318 '''
319 s = self._cmp_0(other, self.cmp.__name__)
320 return _signOf(s, 0)
322 cmp = __cmp__
324 def __divmod__(self, other):
325 '''Return C{divmod(B{self}, B{other})} as 2-tuple C{(quotient,
326 remainder)}, an C{int} in Python 3+ or C{float} in Python 2-
327 and an L{Fsum}.
329 @arg other: An L{Fsum} or C{scalar} modulus.
331 @see: Method L{Fsum.__itruediv__}.
332 '''
333 f = self._copy_2(self.__divmod__)
334 return f._fdivmod2(other, _divmod_op_)
336 def __eq__(self, other):
337 '''Compare this with an other instance or C{scalar}.
338 '''
339 return self._cmp_0(other, _eq_op_) == 0
341 def __float__(self):
342 '''Return this instance' current precision running sum as C{float}.
344 @see: Methods L{Fsum.fsum} and L{Fsum.int_float}.
345 '''
346 return float(self._fprs)
348 def __floor__(self): # PYCHOK not special in Python 2-
349 '''Return this instance' C{math.floor} as C{int} or C{float}.
351 @return: An C{int} in Python 3+, but C{float} in Python 2-.
353 @see: Methods L{Fsum.__ceil__} and property L{Fsum.floor}.
354 '''
355 return self.floor
357 def __floordiv__(self, other):
358 '''Return C{B{self} // B{other}} as an L{Fsum}.
360 @arg other: An L{Fsum} or C{scalar} divisor.
362 @return: The C{floor} quotient (L{Fsum}).
364 @see: Methods L{Fsum.__ifloordiv__}.
365 '''
366 f = self._copy_2(self.__floordiv__)
367 return f._floordiv(other, _floordiv_op_)
369 def __format__(self, *other): # PYCHOK no cover
370 '''Not implemented.'''
371 return _NotImplemented(self, *other)
373 def __ge__(self, other):
374 '''Compare this with an other instance or C{scalar}.
375 '''
376 return self._cmp_0(other, _ge_op_) >= 0
378 def __gt__(self, other):
379 '''Compare this with an other instance or C{scalar}.
380 '''
381 return self._cmp_0(other, _gt_op_) > 0
383 def __hash__(self): # PYCHOK no cover
384 '''Return this instance' C{hash}.
385 '''
386 return hash(self._ps) # XXX id(self)?
388 def __iadd__(self, other):
389 '''Apply C{B{self} += B{other}} to this instance.
391 @arg other: An L{Fsum} or C{scalar} instance.
393 @return: This instance, updated (L{Fsum}).
395 @raise TypeError: Invalid B{C{other}}, not
396 C{scalar} nor L{Fsum}.
398 @see: Methods L{Fsum.fadd} and L{Fsum.fadd_}.
399 '''
400 return self._fadd(other, _iadd_op_)
402 def __ifloordiv__(self, other):
403 '''Apply C{B{self} //= B{other}} to this instance.
405 @arg other: An L{Fsum} or C{scalar} divisor.
407 @return: This instance, updated (L{Fsum}).
409 @raise ResidualError: Non-zero residual in B{C{other}}.
411 @raise TypeError: Invalid B{C{other}} type.
413 @raise ValueError: Invalid or non-finite B{C{other}}.
415 @raise ZeroDivisionError: Zero B{C{other}}.
417 @see: Methods L{Fsum.__itruediv__}.
418 '''
419 return self._floordiv(other, _floordiv_op_ + _fset_op_)
421 def __imatmul__(self, other): # PYCHOK no cover
422 '''Not implemented.'''
423 return _NotImplemented(self, other)
425 def __imod__(self, other):
426 '''Apply C{B{self} %= B{other}} to this instance.
428 @arg other: An L{Fsum} or C{scalar} modulus.
430 @return: This instance, updated (L{Fsum}).
432 @see: Method L{Fsum.__divmod__}.
433 '''
434 self._fdivmod2(other, _mod_op_ + _fset_op_)
435 return self
437 def __imul__(self, other):
438 '''Apply C{B{self} *= B{other}} to this instance.
440 @arg other: An L{Fsum} or C{scalar} factor.
442 @return: This instance, updated (L{Fsum}).
444 @raise OverflowError: Partial C{2sum} overflow.
446 @raise TypeError: Invalid B{C{other}} type.
448 @raise ValueError: Invalid or non-finite B{C{other}}.
449 '''
450 return self._fmul(other, _mul_op_ + _fset_op_)
452 def __int__(self):
453 '''Return this instance as an C{int}.
455 @see: Methods L{Fsum.int_float}, L{Fsum.__ceil__}
456 and L{Fsum.__floor__} and properties
457 L{Fsum.ceil} and L{Fsum.floor}.
458 '''
459 i, _ = self._fint2
460 return i
462 def __invert__(self): # PYCHOK no cover
463 '''Not implemented.'''
464 # Luciano Ramalho, "Fluent Python", O'Reilly, 2nd Ed, 2022 p. 567
465 return _NotImplemented(self)
467 def __ipow__(self, other, *mod): # PYCHOK 2 vs 3 args
468 '''Apply C{B{self} **= B{other}} to this instance.
470 @arg other: The exponent (L{Fsum} or C{scalar}).
471 @arg mod: Optional modulus (C{int} or C{None}) for the
472 3-argument C{pow(B{self}, B{other}, B{mod})}
473 version.
475 @return: This instance, updated (L{Fsum}).
477 @note: If B{C{mod}} is given, the result will be an C{integer}
478 L{Fsum} in Python 3+ if this instance C{is_integer} or
479 set to C{as_integer} if B{C{mod}} given as C{None}.
481 @raise OverflowError: Partial C{2sum} overflow.
483 @raise ResidualError: Non-zero residual in B{C{other}} and
484 env var C{PYGEODESY_FSUM_RESIDUAL}
485 set or this instance has a non-zero
486 residual and either B{C{mod}} is
487 given and non-C{None} or B{C{other}}
488 is a negative or fractional C{scalar}.
490 @raise TypeError: Invalid B{C{other}} type or 3-argument
491 C{pow} invocation failed.
493 @raise ValueError: If B{C{other}} is a negative C{scalar}
494 and this instance is C{0} or B{C{other}}
495 is a fractional C{scalar} and this
496 instance is negative or has a non-zero
497 residual or B{C{mod}} is given and C{0}.
499 @see: CPython function U{float_pow<https://GitHub.com/
500 python/cpython/blob/main/Objects/floatobject.c>}.
501 '''
502 return self._fpow(other, _pow_op_ + _fset_op_, *mod)
504 def __isub__(self, other):
505 '''Apply C{B{self} -= B{other}} to this instance.
507 @arg other: An L{Fsum} or C{scalar}.
509 @return: This instance, updated (L{Fsum}).
511 @raise TypeError: Invalid B{C{other}} type.
513 @see: Method L{Fsum.fadd}.
514 '''
515 return self._fsub(other, _isub_op_)
517 def __iter__(self):
518 '''Return an C{iter}ator over a C{partials} duplicate.
519 '''
520 return iter(self.partials)
522 def __itruediv__(self, other):
523 '''Apply C{B{self} /= B{other}} to this instance.
525 @arg other: An L{Fsum} or C{scalar} divisor.
527 @return: This instance, updated (L{Fsum}).
529 @raise OverflowError: Partial C{2sum} overflow.
531 @raise ResidualError: Non-zero residual in B{C{other}} and
532 env var C{PYGEODESY_FSUM_RESIDUAL} set.
534 @raise TypeError: Invalid B{C{other}} type.
536 @raise ValueError: Invalid or non-finite B{C{other}}.
538 @raise ZeroDivisionError: Zero B{C{other}}.
540 @see: Method L{Fsum.__ifloordiv__}.
541 '''
542 return self._ftruediv(other, _truediv_op_ + _fset_op_)
544 def __le__(self, other):
545 '''Compare this with an other instance or C{scalar}.
546 '''
547 return self._cmp_0(other, _le_op_) <= 0
549 def __len__(self):
550 '''Return the number of values accumulated (C{int}).
551 '''
552 return self._n
554 def __lt__(self, other):
555 '''Compare this with an other instance or C{scalar}.
556 '''
557 return self._cmp_0(other, _lt_op_) < 0
559 def __matmul__(self, other): # PYCHOK no cover
560 '''Not implemented.'''
561 return _NotImplemented(self, other)
563 def __mod__(self, other):
564 '''Return C{B{self} % B{other}} as an L{Fsum}.
566 @see: Method L{Fsum.__imod__}.
567 '''
568 f = self._copy_2(self.__mod__)
569 return f._fdivmod2(other, _mod_op_)[1]
571 def __mul__(self, other):
572 '''Return C{B{self} * B{other}} as an L{Fsum}.
574 @see: Method L{Fsum.__imul__}.
575 '''
576 f = self._copy_2(self.__mul__)
577 return f._fmul(other, _mul_op_)
579 def __ne__(self, other):
580 '''Compare this with an other instance or C{scalar}.
581 '''
582 return self._cmp_0(other, _ne_op_) != 0
584 def __neg__(self):
585 '''Return I{a copy of} this instance, negated.
586 '''
587 return self._copy_n(self.__neg__)
589 def __pos__(self):
590 '''Return this instance I{as-is}, like C{float.__pos__()}.
591 '''
592 return self if _pos_self else self._copy_2(self.__pos__)
594 def __pow__(self, other, *mod): # PYCHOK 2 vs 3 args
595 '''Return C{B{self}**B{other}} as an L{Fsum}.
597 @see: Method L{Fsum.__ipow__}.
598 '''
599 f = self._copy_2(self.__pow__)
600 return f._fpow(other, _pow_op_, *mod)
602 def __radd__(self, other):
603 '''Return C{B{other} + B{self}} as an L{Fsum}.
605 @see: Method L{Fsum.__iadd__}.
606 '''
607 f = self._copy_r2(other, self.__radd__)
608 return f._fadd(self, _add_op_)
610 def __rdivmod__(self, other):
611 '''Return C{divmod(B{other}, B{self})} as 2-tuple C{(quotient,
612 remainder)}.
614 @see: Method L{Fsum.__divmod__}.
615 '''
616 f = self._copy_r2(other, self.__rdivmod__)
617 return f._fdivmod2(self, _divmod_op_)
619# def __repr__(self):
620# '''Return the default C{repr(this)}.
621# '''
622# return self.toRepr(lenc=True)
624 def __rfloordiv__(self, other):
625 '''Return C{B{other} // B{self}} as an L{Fsum}.
627 @see: Method L{Fsum.__ifloordiv__}.
628 '''
629 f = self._copy_r2(other, self.__rfloordiv__)
630 return f._floordiv(self, _floordiv_op_)
632 def __rmatmul__(self, other): # PYCHOK no cover
633 '''Not implemented.'''
634 return _NotImplemented(self, other)
636 def __rmod__(self, other):
637 '''Return C{B{other} % B{self}} as an L{Fsum}.
639 @see: Method L{Fsum.__imod__}.
640 '''
641 f = self._copy_r2(other, self.__rmod__)
642 return f._fdivmod2(self, _mod_op_)[1]
644 def __rmul__(self, other):
645 '''Return C{B{other} * B{self}} as an L{Fsum}.
647 @see: Method L{Fsum.__imul__}.
648 '''
649 f = self._copy_r2(other, self.__rmul__)
650 return f._fmul(self, _mul_op_)
652 def __round__(self, *ndigits): # PYCHOK no cover
653 '''Return C{round(B{self}, *B{ndigits}} as an L{Fsum}.
655 @arg ndigits: Optional number of digits (C{int}).
656 '''
657 # <https://docs.Python.org/3.12/reference/datamodel.html?#object.__round__>
658 f = Fsum(name=self.__round__.__name__)
659 f._n = 1
660 f._ps = [round(float(self), *ndigits)] # can be C{int}
661 return f
663 def __rpow__(self, other, *mod):
664 '''Return C{B{other}**B{self}} as an L{Fsum}.
666 @see: Method L{Fsum.__ipow__}.
667 '''
668 f = self._copy_r2(other, self.__rpow__)
669 return f._fpow(self, _pow_op_, *mod)
671 def __rsub__(self, other):
672 '''Return C{B{other} - B{self}} as L{Fsum}.
674 @see: Method L{Fsum.__isub__}.
675 '''
676 f = self._copy_r2(other, self.__rsub__)
677 return f._fsub(self, _sub_op_)
679 def __rtruediv__(self, other):
680 '''Return C{B{other} / B{self}} as an L{Fsum}.
682 @see: Method L{Fsum.__itruediv__}.
683 '''
684 f = self._copy_r2(other, self.__rtruediv__)
685 return f._ftruediv(self, _truediv_op_)
687 def __str__(self):
688 '''Return the default C{str(self)}.
689 '''
690 return self.toStr(lenc=True)
692 def __sub__(self, other):
693 '''Return C{B{self} - B{other}} as an L{Fsum}.
695 @arg other: An L{Fsum} or C{scalar}.
697 @return: The difference (L{Fsum}).
699 @see: Method L{Fsum.__isub__}.
700 '''
701 f = self._copy_2(self.__sub__)
702 return f._fsub(other, _sub_op_)
704 def __truediv__(self, other):
705 '''Return C{B{self} / B{other}} as an L{Fsum}.
707 @arg other: An L{Fsum} or C{scalar} divisor.
709 @return: The quotient (L{Fsum}).
711 @see: Method L{Fsum.__itruediv__}.
712 '''
713 f = self._copy_2(self.__truediv__)
714 return f._ftruediv(other, _truediv_op_)
716 __trunc__ = __int__
718 if _sys_version_info2 < (3, 0): # PYCHOK no cover
719 # <https://docs.Python.org/2/library/operator.html#mapping-operators-to-functions>
720 __div__ = __truediv__
721 __idiv__ = __itruediv__
722 __long__ = __int__
723 __nonzero__ = __bool__
724 __rdiv__ = __rtruediv__
726 def as_integer_ratio(self):
727 '''Return this instance as the ratio of 2 integers.
729 @return: 2-Tuple C{(numerator, denominator)} both
730 C{int} and with positive C{denominator}.
732 @see: Standard C{float.as_integer_ratio} in Python 3+.
733 '''
734 n, r = self._fint2
735 if r:
736 i, d = r.as_integer_ratio()
737 n *= d
738 n += i
739 else: # PYCHOK no cover
740 d = 1
741 return n, d
743 @property_RO
744 def ceil(self):
745 '''Get this instance' C{ceil} value (C{int} in Python 3+,
746 but C{float} in Python 2-).
748 @note: The C{ceil} takes the C{residual} into account.
750 @see: Method L{Fsum.int_float} and properties L{Fsum.floor},
751 L{Fsum.imag} and L{Fsum.real}.
752 '''
753 s, r = self._fprs2
754 c = _ceil(s) + int(r) - 1
755 while r > (c - s): # (s + r) > c
756 c += 1
757 return c
759 def _cmp_0(self, other, op):
760 '''(INTERNAL) Return C{scalar(self - B{other})} for 0-comparison.
761 '''
762 if isscalar(other):
763 if other:
764 s = _fsum(self._ps_1(other))
765 else:
766 s, r = self._fprs2
767 s = _signOf(s, -r)
768 elif isinstance(other, Fsum):
769 s = _fsum(self._ps_1(*other._ps))
770 else:
771 raise self._TypeError(op, other) # txt=_invalid_
772 return s
774 def copy(self, deep=False, name=NN):
775 '''Copy this instance, C{shallow} or B{C{deep}}.
777 @return: The copy (L{Fsum}).
778 '''
779 f = _Named.copy(self, deep=deep, name=name)
780 f._n = self._n if deep else 1
781 f._ps = list(self._ps) # separate list
782 return f
784 def _copy_0(self, *xs):
785 '''(INTERNAL) Copy with/-out overriding C{partials}.
786 '''
787 # for x in xs:
788 # assert isscalar(x)
789 f = self._Fsum(self._n + len(xs), *xs)
790 if self.name:
791 f._name = self.name # .rename calls _update_attrs
792 return f
794 def _copy_2(self, which):
795 '''(INTERNAL) Copy for I{dyadic} operators.
796 '''
797 # NOT .classof due to .Fdot(a, *b) args, etc.
798 f = _Named.copy(self, deep=False, name=which.__name__)
799 # assert f._n == self._n
800 f._ps = list(self._ps) # separate list
801 return f
803 def _copy_n(self, which):
804 '''(INTERNAL) Negated copy for I{monadic} C{__abs__} and C{__neg__}.
805 '''
806 if self._ps:
807 f = self._Fsum(self._n)
808 f._ps[:] = self._ps_n()
809# f._facc_up(up=False)
810 else:
811 f = self._Fsum(self._n, _0_0)
812 f._name = which.__name__ # .rename calls _update_attrs
813 return f
815 def _copy_r2(self, other, which):
816 '''(INTERNAL) Copy for I{reverse-dyadic} operators.
817 '''
818 return other._copy_2(which) if isinstance(other, Fsum) else \
819 Fsum(other, name=which.__name__) # see ._copy_2
821 def _copy_RESIDUAL(self, other):
822 '''(INTERNAL) Copy C{other._RESIDUAL}.
823 '''
824 R = other._RESIDUAL
825 if R is not Fsum._RESIDUAL:
826 self._RESIDUAL = R
828 def _copy_up(self, _fprs2=False):
829 '''(INTERNAL) Minimal, anonymous copy.
830 '''
831 f = self._Fsum(self._n, *self._ps)
832 if _fprs2: # only the ._fprs2 2-tuple
833 Fsum._fprs2._update_from(f, self)
834 return f
836 def divmod(self, other):
837 '''Return C{divmod(B{self}, B{other})} as 2-tuple C{(quotient,
838 remainder)}.
840 @arg other: An L{Fsum} or C{scalar} divisor.
842 @return: 2-Tuple C{(quotient, remainder)}, with the C{quotient}
843 an C{int} in Python 3+ or a C{float} in Python 2- and
844 the C{remainder} an L{Fsum} instance.
846 @see: Method L{Fsum.__itruediv__}.
847 '''
848 f = self._copy_2(self.divmod)
849 return f._fdivmod2(other, _divmod_op_)
851 def _Error(self, op, other, Error, **txt):
852 '''(INTERNAL) Format an B{C{Error}} for C{{self} B{op} B{other}}.
853 '''
854 return Error(_SPACE_(self.toRepr(), op, repr(other)), **txt)
856 def _ErrorX(self, X, xs, **kwds): # in .fmath
857 '''(INTERNAL) Format a caught exception.
858 '''
859 E, t = _xError2(X)
860 n = unstr(self.named3, *xs[:3], _ELLIPSIS=len(xs) > 3, **kwds)
861 return E(n, txt=t, cause=X)
863 def _facc(self, xs, up=True): # from .elliptic._Defer.Fsum
864 '''(INTERNAL) Accumulate more known C{scalar}s.
865 '''
866 n, ps, _2s = 0, self._ps, _2sum
867 for x in xs: # _iter()
868 # assert isscalar(x) and isfinite(x)
869 i = 0
870 for p in ps:
871 x, p = _2s(x, p)
872 if p:
873 ps[i] = p
874 i += 1
875 ps[i:] = [x]
876 n += 1
877 # assert self._ps is ps
878 if n:
879 self._n += n
880 # Fsum._px = max(Fsum._px, len(ps))
881 if up:
882 self._update()
883 return self
885 def _facc_(self, *xs, **up):
886 '''(INTERNAL) Accumulate all positional C{scalar}s.
887 '''
888 return self._facc(xs, **up) if xs else self
890# def _facc_up(self, up=True):
891# '''(INTERNAL) Update the C{partials}, by removing
892# and re-accumulating the final C{partial}.
893# '''
894# while len(self._ps) > 1:
895# p = self._ps.pop()
896# if p:
897# n = self._n
898# self._facc_(p, up=False)
899# self._n = n
900# break
901# return self._update() if up else self # ._fpsqz()
903 def fadd(self, xs=()):
904 '''Add an iterable of C{scalar} or L{Fsum} instances
905 to this instance.
907 @arg xs: Iterable, list, tuple, etc. (C{scalar} or
908 L{Fsum} instances).
910 @return: This instance (L{Fsum}).
912 @raise OverflowError: Partial C{2sum} overflow.
914 @raise TypeError: An invalid B{C{xs}} type, not C{scalar}
915 nor L{Fsum}.
917 @raise ValueError: Invalid or non-finite B{C{xs}} value.
918 '''
919 if isinstance(xs, Fsum):
920 self._facc(xs._ps)
921 elif isscalar(xs): # for backward compatibility
922 self._facc_(_2float(x=xs)) # PYCHOK no cover
923 elif xs:
924 self._facc(_2floats(xs)) # PYCHOK yield
925 return self
927 def fadd_(self, *xs):
928 '''Add all positional C{scalar} or L{Fsum} instances
929 to this instance.
931 @arg xs: Values to add (C{scalar} or L{Fsum} instances),
932 all positional.
934 @return: This instance (L{Fsum}).
936 @raise OverflowError: Partial C{2sum} overflow.
938 @raise TypeError: An invalid B{C{xs}} type, not C{scalar}
939 nor L{Fsum}.
941 @raise ValueError: Invalid or non-finite B{C{xs}} value.
942 '''
943 return self._facc(_2floats(xs, origin=1)) # PYCHOK yield
945 def _fadd(self, other, op): # in .fmath.Fhorner
946 '''(INTERNAL) Apply C{B{self} += B{other}}.
947 '''
948 if isinstance(other, Fsum):
949 if other is self:
950 self._facc_(*other._ps) # == ._facc(tuple(other._ps))
951 elif other._ps:
952 self._facc(other._ps)
953 elif not isscalar(other):
954 raise self._TypeError(op, other) # txt=_invalid_
955 elif other:
956 self._facc_(other)
957 return self
959 fcopy = copy # for backward compatibility
960 fdiv = __itruediv__ # for backward compatibility
961 fdivmod = __divmod__ # for backward compatibility
963 def _fdivmod2(self, other, op):
964 '''(INTERNAL) C{divmod(B{self}, B{other})} as 2-tuple
965 (C{int} or C{float}, remainder C{self}).
966 '''
967 # result mostly follows CPython function U{float_divmod
968 # <https://GitHub.com/python/cpython/blob/main/Objects/floatobject.c>},
969 # but at least divmod(-3, 2) equals Cpython's result (-2, 1).
970 q = self._copy_up(_fprs2=True)._ftruediv(other, op).floor
971 if q: # == float // other == floor(float / other)
972 self -= other * q
974 s = signOf(other) # make signOf(self) == signOf(other)
975 if s and self.signOf() == -s: # PYCHOK no cover
976 self += other
977 q -= 1
979# t = self.signOf()
980# if t and t != s:
981# from pygeodesy.errors import _AssertionError
982# raise self._Error(op, other, _AssertionError, txt=signOf.__name__)
983 return q, self # q is C{int} in Python 3+, but C{float} in Python 2-
985 def _finite(self, other, op=None):
986 '''(INTERNAL) Return B{C{other}} if C{finite}.
987 '''
988 if _isfinite(other):
989 return other
990 raise ValueError(_not_finite_) if not op else \
991 self._ValueError(op, other, txt=_not_finite_)
993 def fint(self, raiser=True, name=NN):
994 '''Return this instance' current running sum as C{integer}.
996 @kwarg raiser: If C{True} throw a L{ResidualError} if the
997 I{integer} residual is non-zero.
998 @kwarg name: Optional name (C{str}), overriding C{"fint"}.
1000 @return: The C{integer} (L{Fsum}).
1002 @raise ResidualError: Non-zero I{integer} residual.
1004 @see: Methods L{Fsum.int_float} and L{Fsum.is_integer}.
1005 '''
1006 i, r = self._fint2
1007 if r and raiser:
1008 t = _stresidual(_integer_, r)
1009 raise ResidualError(_integer_, i, txt=t)
1010 n = name or self.fint.__name__
1011 return Fsum(name=n)._fset(i, asis=True)
1013 def fint2(self, **name):
1014 '''Return this instance' current running sum as C{int} and
1015 the I{integer} residual.
1017 @kwarg name: Optional name (C{str}).
1019 @return: An L{Fsum2Tuple}C{(fsum, residual)} with C{fsum}
1020 an C{int} and I{integer} C{residual} a C{float} or
1021 C{INT0} if the C{fsum} is considered to be I{exact}.
1022 '''
1023 return Fsum2Tuple(*self._fint2, **name)
1025 @Property_RO
1026 def _fint2(self): # see ._fset
1027 '''(INTERNAL) Get 2-tuple (C{int}, I{integer} residual).
1028 '''
1029 i = int(self._fprs) # int(self)
1030 r = _fsum(self._ps_1(i)) if len(self._ps) > 1 else (
1031 (self._ps[0] - i) if self._ps else -i)
1032 return i, (r or INT0)
1034 @deprecated_property_RO
1035 def float_int(self): # PYCHOK no cover
1036 '''DEPRECATED, use method C{Fsum.int_float}.'''
1037 return self.int_float() # raiser=False
1039 @property_RO
1040 def floor(self):
1041 '''Get this instance' C{floor} (C{int} in Python 3+, but
1042 C{float} in Python 2-).
1044 @note: The C{floor} takes the C{residual} into account.
1046 @see: Method L{Fsum.int_float} and properties L{Fsum.ceil},
1047 L{Fsum.imag} and L{Fsum.real}.
1048 '''
1049 s, r = self._fprs2
1050 f = _floor(s) + _floor(r) + 1
1051 while r < (f - s): # (s + r) < f
1052 f -= 1
1053 return f
1055# floordiv = __floordiv__ # for naming consistency
1057 def _floordiv(self, other, op): # rather _ffloordiv?
1058 '''Apply C{B{self} //= B{other}}.
1059 '''
1060 q = self._ftruediv(other, op) # == self
1061 return self._fset(q.floor, asis=True) # floor(q)
1063 fmul = __imul__ # for backward compatibility
1065 def _fmul(self, other, op):
1066 '''(INTERNAL) Apply C{B{self} *= B{other}}.
1067 '''
1068 if isscalar(other):
1069 f = self._mul_scalar(other, op)
1070 elif not isinstance(other, Fsum):
1071 raise self._TypeError(op, other) # txt=_invalid_
1072 elif len(self._ps) != 1:
1073 f = self._mul_Fsum(other, op)
1074 elif len(other._ps) != 1: # len(self._ps) == 1
1075 f = other._copy_up()._mul_scalar(self._ps[0], op)
1076 else: # len(other._ps) == len(self._ps) == 1
1077 s = self._finite(self._ps[0] * other._ps[0])
1078 return self._fset(s, asis=True, n=len(self) + 1)
1079 return self._fset(f)
1081 def fover(self, over):
1082 '''Apply C{B{self} /= B{over}} and summate.
1084 @arg over: An L{Fsum} or C{scalar} denominator.
1086 @return: Precision running sum (C{float}).
1088 @see: Methods L{Fsum.fsum} and L{Fsum.__itruediv__}.
1089 '''
1090 return float(self.fdiv(over)._fprs)
1092 fpow = __ipow__ # for backward compatibility
1094 def _fpow(self, other, op, *mod):
1095 '''Apply C{B{self} **= B{other}}, optional B{C{mod}} or C{None}.
1096 '''
1097 if mod and mod[0] is not None: # == 3-arg C{pow}
1098 s = self._pow_3(other, mod[0], op)
1099 elif mod and mod[0] is None and self.is_integer():
1100 # return an exact C{int} for C{int}**C{int}
1101 i = self._copy_0(self._fint2[0]) # assert _fint2[1] == 0
1102 x = _2scalar(other) # C{int}, C{float} or other
1103 s = i._pow_2(x, other, op) if isscalar(x) else i._fpow(x, op)
1104 else: # pow(self, other) == pow(self, other, None)
1105 p = None
1106 if isinstance(other, Fsum):
1107 x, r = other._fprs2
1108 if r:
1109 if self._raiser(r, x):
1110 raise self._ResidualError(op, other, r)
1111 p = self._pow_scalar(r, other, op)
1112# p = _2scalar(p) # _raiser = None
1113 elif not isscalar(other):
1114 raise self._TypeError(op, other) # txt=_invalid_
1115 else:
1116 x = self._finite(other, op)
1117 s = self._pow_scalar(x, other, op)
1118 if p is not None:
1119 s *= p
1120 return self._fset(s, asis=isint(s), n=max(len(self), 1))
1122 @Property_RO
1123 def _fprs(self):
1124 '''(INTERNAL) Get and cache this instance' precision
1125 running sum (C{float} or C{int}), ignoring C{residual}.
1127 @note: The precision running C{fsum} after a C{//=} or
1128 C{//} C{floor} division is C{int} in Python 3+.
1129 '''
1130 ps = self._ps
1131 n = len(ps) - 1
1132 if n > 1:
1133 s = _psum(ps)
1134 elif n > 0: # len(ps) == 2
1135 s, p = _2sum(*ps) if ps[1] else ps
1136 ps[:] = ([p, s] if s else [p]) if p else [s]
1137 elif n < 0: # see L{Fsum.__init__}
1138 s = _0_0
1139 ps[:] = [s]
1140 else: # len(ps) == 1
1141 s = ps[0]
1142 # assert self._ps is ps
1143 # assert Fsum._fprs2.name not in self.__dict__
1144 return s
1146 @Property_RO
1147 def _fprs2(self):
1148 '''(INTERNAL) Get and cache this instance' precision
1149 running sum and residual (L{Fsum2Tuple}).
1150 '''
1151 s = self._fprs
1152 r = _fsum(self._ps_1(s)) if len(self._ps) > 1 else INT0
1153 return Fsum2Tuple(s, r) # name=Fsum.fsum2.__name__
1155# def _fpsqz(self):
1156# '''(INTERNAL) Compress, squeeze the C{partials}.
1157# '''
1158# if len(self._ps) > 2:
1159# _ = self._fprs
1160# return self
1162 def _fset(self, other, asis=False, n=1):
1163 '''(INTERNAL) Overwrite this instance with an other or a C{scalar}.
1164 '''
1165 if other is self:
1166 pass # from ._fmul, ._ftruediv and ._pow_scalar
1167 elif isinstance(other, Fsum):
1168 self._n = other._n
1169 self._ps[:] = other._ps
1170 self._copy_RESIDUAL(other)
1171 # use or zap the C{Property_RO} values
1172 Fsum._fint2._update_from(self, other)
1173 Fsum._fprs ._update_from(self, other)
1174 Fsum._fprs2._update_from(self, other)
1175 elif isscalar(other):
1176 s = other if asis else float(other)
1177 i = int(s) # see ._fint2
1178 t = i, ((s - i) or INT0)
1179 self._n = n
1180 self._ps[:] = [s]
1181 # Property_RO _fint2, _fprs and _fprs2 can't be a Property:
1182 # Property's _fset zaps the value just set by the @setter
1183 self.__dict__.update(_fint2=t, _fprs=s, _fprs2=Fsum2Tuple(s, INT0))
1184 else: # PYCHOK no cover
1185 raise self._TypeError(_fset_op_, other) # txt=_invalid_
1186 return self
1188 def fsub(self, xs=()):
1189 '''Subtract an iterable of C{scalar} or L{Fsum} instances
1190 from this instance.
1192 @arg xs: Iterable, list, tuple. etc. (C{scalar}
1193 or L{Fsum} instances).
1195 @return: This instance, updated (L{Fsum}).
1197 @see: Method L{Fsum.fadd}.
1198 '''
1199 return self._facc(_2floats(xs, sub=True)) if xs else self # PYCHOK yield
1201 def fsub_(self, *xs):
1202 '''Subtract all positional C{scalar} or L{Fsum} instances
1203 from this instance.
1205 @arg xs: Values to subtract (C{scalar} or
1206 L{Fsum} instances), all positional.
1208 @return: This instance, updated (L{Fsum}).
1210 @see: Method L{Fsum.fadd}.
1211 '''
1212 return self._facc(_2floats(xs, origin=1, sub=True)) if xs else self # PYCHOK yield
1214 def _fsub(self, other, op):
1215 '''(INTERNAL) Apply C{B{self} -= B{other}}.
1216 '''
1217 if isinstance(other, Fsum):
1218 if other is self: # or other._fprs2 == self._fprs2:
1219 self._fset(_0_0, asis=True, n=len(self) * 2) # self -= self
1220 elif other._ps:
1221 self._facc(other._ps_n())
1222 elif not isscalar(other):
1223 raise self._TypeError(op, other) # txt=_invalid_
1224 elif self._finite(other, op):
1225 self._facc_(-other)
1226 return self
1228 def _Fsum(self, n, *ps):
1229 '''(INTERNAL) New L{Fsum} instance.
1230 '''
1231 f = Fsum()
1232 f._n = n
1233 if ps:
1234 f._ps[:] = ps
1235 f._copy_RESIDUAL(self)
1236 return f
1238 def fsum(self, xs=()):
1239 '''Add more C{scalar} or L{Fsum} instances and summate.
1241 @kwarg xs: Iterable, list, tuple, etc. (C{scalar} or
1242 L{Fsum} instances).
1244 @return: Precision running sum (C{float} or C{int}).
1246 @see: Method L{Fsum.fadd}.
1248 @note: Accumulation can continue after summation.
1249 '''
1250 f = self._facc(_2floats(xs)) if xs else self # PYCHOK yield
1251 return f._fprs
1253 def fsum_(self, *xs):
1254 '''Add all positional C{scalar} or L{Fsum} instances and summate.
1256 @arg xs: Values to add (C{scalar} or L{Fsum} instances),
1257 all positional.
1259 @return: Precision running sum (C{float} or C{int}).
1261 @see: Methods L{Fsum.fsum} and L{Fsum.fsumf_}.
1262 '''
1263 f = self._facc(_2floats(xs, origin=1)) if xs else self # PYCHOK yield
1264 return f._fprs
1266 def fsum2(self, xs=(), **name):
1267 '''Add more C{scalar} or L{Fsum} instances and return the
1268 current precision running sum and the C{residual}.
1270 @kwarg xs: Iterable, list, tuple, etc. (C{scalar} or
1271 L{Fsum} instances).
1272 @kwarg name: Optional name (C{str}).
1274 @return: L{Fsum2Tuple}C{(fsum, residual)} with C{fsum} the
1275 current precision running sum and C{residual}, the
1276 (precision) sum of the remaining C{partials}. The
1277 C{residual is INT0} if the C{fsum} is considered
1278 to be I{exact}.
1280 @see: Methods L{Fsum.fint2}, L{Fsum.fsum} and L{Fsum.fsum2_}
1281 '''
1282 f = self._facc(_2floats(xs)) if xs else self # PYCHOK yield
1283 t = f._fprs2
1284 if name:
1285 t = t.dup(name=_xkwds_get(name, name=NN))
1286 return t
1288 def fsum2_(self, *xs):
1289 '''Add any positional C{scalar} or L{Fsum} instances and return
1290 the precision running sum and the C{differential}.
1292 @arg xs: Values to add (C{scalar} or L{Fsum} instances),
1293 all positional.
1295 @return: 2-Tuple C{(fsum, delta)} with the current precision
1296 running C{fsum} and C{delta}, the difference with
1297 the previous running C{fsum} (C{float}s).
1299 @see: Methods L{Fsum.fsum_} and L{Fsum.fsum}.
1300 '''
1301 p, r = self._fprs2
1302 if xs:
1303 s, t = self._facc(_2floats(xs, origin=1))._fprs2 # PYCHOK yield
1304 return s, _fsum((s, -p, r, -t)) # ((s - p) + (r - t))
1305 else: # PYCHOK no cover
1306 return p, _0_0
1308 def fsumf_(self, *xs):
1309 '''Like method L{Fsum.fsum_} but only for known C{float B{xs}}.
1310 '''
1311 f = self._facc(xs) if xs else self # PYCHOK yield
1312 return f._fprs
1314# ftruediv = __itruediv__ # for naming consistency
1316 def _ftruediv(self, other, op):
1317 '''(INTERNAL) Apply C{B{self} /= B{other}}.
1318 '''
1319 n = _1_0
1320 if isinstance(other, Fsum):
1321 if other is self or other._fprs2 == self._fprs2:
1322 return self._fset(_1_0, asis=True, n=len(self))
1323 d, r = other._fprs2
1324 if r:
1325 if not d: # PYCHOK no cover
1326 d = r
1327 elif self._raiser(r, d):
1328 raise self._ResidualError(op, other, r)
1329 else:
1330 d, n = other.as_integer_ratio()
1331 elif isscalar(other):
1332 d = other
1333 else: # PYCHOK no cover
1334 raise self._TypeError(op, other) # txt=_invalid_
1335 try:
1336 s = 0 if isinf(d) else (
1337 d if isnan(d) else self._finite(n / d))
1338 except Exception as x:
1339 E, t = _xError2(x)
1340 raise self._Error(op, other, E, txt=t)
1341 f = self._mul_scalar(s, _mul_op_) # handles 0, NAN, etc.
1342 return self._fset(f)
1344 @property_RO
1345 def imag(self):
1346 '''Get the C{imaginary} part of this instance (C{0.0}, always).
1348 @see: Properties L{Fsum.ceil}, L{Fsum.floor} and L{Fsum.real}.
1349 '''
1350 return _0_0
1352 def int_float(self, raiser=False):
1353 '''Return this instance' current running sum as C{int} or C{float}.
1355 @kwarg raiser: If C{True} throw a L{ResidualError} if the
1356 residual is non-zero.
1358 @return: This C{integer} sum if this instance C{is_integer},
1359 otherwise return the C{float} sum if the residual
1360 is zero or if C{B{raiser}=False}.
1362 @raise ResidualError: Non-zero residual and C{B{raiser}=True}.
1364 @see: Methods L{Fsum.fint} and L{Fsum.fint2}.
1365 '''
1366 s, r = self._fint2
1367 if r:
1368 s, r = self._fprs2
1369 if r and raiser: # PYCHOK no cover
1370 t = _stresidual(_non_zero_, r)
1371 raise ResidualError(int_float=s, txt=t)
1372 s = float(s) # redundant
1373 return s
1375 def is_exact(self):
1376 '''Is this instance' current running C{fsum} considered to
1377 be exact? (C{bool}).
1378 '''
1379 return self.residual is INT0
1381 def is_integer(self):
1382 '''Is this instance' current running sum C{integer}? (C{bool}).
1384 @see: Methods L{Fsum.fint} and L{Fsum.fint2}.
1385 '''
1386 _, r = self._fint2
1387 return False if r else True
1389 def is_math_fsum(self):
1390 '''Return whether functions L{fsum}, L{fsum_}, L{fsum1}
1391 and L{fsum1_} plus partials summation are based on
1392 Python's C{math.fsum} or not.
1394 @return: C{2} if all functions and partials summation
1395 are based on C{math.fsum}, C{True} if only
1396 the functions are based on C{math.fsum} (and
1397 partials summation is not) or C{False} if
1398 none are.
1399 '''
1400 f = Fsum._math_fsum
1401 return 2 if _psum is f else bool(f)
1403 def _mul_Fsum(self, other, op=_mul_op_):
1404 '''(INTERNAL) Return C{B{self} * Fsum B{other}} as L{Fsum}.
1405 '''
1406 # assert isinstance(other, Fsum)
1407 return self._copy_0()._facc(self._ps_x(op, *other._ps), up=False)
1409 def _mul_scalar(self, factor, op):
1410 '''(INTERNAL) Return C{B{self} * scalar B{factor}} as L{Fsum} or C{0}.
1411 '''
1412 # assert isscalar(factor)
1413 if self._finite(factor, op) and self._ps:
1414 if factor == _1_0:
1415 return self
1416 f = self._copy_0()._facc(self._ps_x(op, factor), up=False)
1417 else:
1418 f = self._copy_0(_0_0)
1419 return f
1421 @property_RO
1422 def partials(self):
1423 '''Get this instance' current partial sums (C{tuple} of C{float}s and/or C{int}s).
1424 '''
1425 return tuple(self._ps)
1427 def pow(self, x, *mod):
1428 '''Return C{B{self}**B{x}} as L{Fsum}.
1430 @arg x: The exponent (L{Fsum} or C{scalar}).
1431 @arg mod: Optional modulus (C{int} or C{None}) for the 3-argument
1432 C{pow(B{self}, B{other}, B{mod})} version.
1434 @return: The C{pow(self, B{x})} or C{pow(self, B{x}, *B{mod})}
1435 result (L{Fsum}).
1437 @note: If B{C{mod}} is given as C{None}, the result will be an
1438 C{integer} L{Fsum} provided this instance C{is_integer}
1439 or set C{integer} with L{Fsum.fint}.
1441 @see: Methods L{Fsum.__ipow__}, L{Fsum.fint} and L{Fsum.is_integer}.
1442 '''
1443 f = self._copy_2(self.pow)
1444 if f and isint(x) and x >= 0 and not mod:
1445 f._pow_int(x, x, _pow_op_) # f **= x
1446 else:
1447 f._fpow(x, _pow_op_, *mod) # f = pow(f, x, *mod)
1448 return f
1450 def _pow_0_1(self, x, other):
1451 '''(INTERNAL) Return B{C{self}**1} or C{B{self}**0 == 1.0}.
1452 '''
1453 return self if x else (1 if self.is_integer() and isint(other) else _1_0)
1455 def _pow_2(self, x, other, op):
1456 '''(INTERNAL) 2-arg C{pow(B{self}, scalar B{x})} embellishing errors.
1457 '''
1458 # assert len(self._ps) == 1 and isscalar(x)
1459 b = self._ps[0] # assert isscalar(b)
1460 try: # type(s) == type(x) if x in (_1_0, 1)
1461 s = pow(b, x) # -1**2.3 == -(1**2.3)
1462 if not iscomplex(s):
1463 return self._finite(s) # 0**INF == 0.0, 1**INF==1.0
1464 # neg**frac == complex in Python 3+, but ValueError in 2-
1465 E, t = _ValueError, _strcomplex(s, b, x) # PYCHOK no cover
1466 except Exception as x:
1467 E, t = _xError2(x)
1468 raise self._Error(op, other, E, txt=t)
1470 def _pow_3(self, other, mod, op):
1471 '''(INTERNAL) 3-arg C{pow(B{self}, B{other}, int B{mod} or C{None})}.
1472 '''
1473 b, r = self._fprs2 if mod is None else self._fint2
1474 if r and self._raiser(r, b):
1475 t = _non_zero_ if mod is None else _integer_
1476 E, t = ResidualError, _stresidual(t, r, mod=mod)
1477 else:
1478 try: # b, other, mod all C{int}, unless C{mod} is C{None}
1479 x = _2scalar(other, _raiser=self._raiser)
1480 s = pow(b, x, mod)
1481 if not iscomplex(s):
1482 return self._finite(s)
1483 # neg**frac == complex in Python 3+, but ValueError in 2-
1484 E, t = _ValueError, _strcomplex(s, b, x, mod) # PYCHOK no cover
1485 except Exception as x:
1486 E, t = _xError2(x)
1487 t = _COMMASPACE_(Fmt.PARENSPACED(mod=mod), t)
1488 raise self._Error(op, other, E, txt=t)
1490 def _pow_int(self, x, other, op):
1491 '''(INTERNAL) Return C{B{self} **= B{x}} for C{int B{x} >= 0}.
1492 '''
1493 # assert isint(x) and x >= 0
1494 if len(self._ps) > 1:
1495 if x > 2:
1496 p = self._copy_up()
1497 m = 1 # single-bit mask
1498 if x & m:
1499 x -= m # x ^= m
1500 f = p._copy_up()
1501 else:
1502 f = self._copy_0(_1_0)
1503 while x:
1504 p = p._mul_Fsum(p, op) # p **= 2
1505 m += m # m <<= 1
1506 if x & m:
1507 x -= m # x ^= m
1508 f = f._mul_Fsum(p, op) # f *= p
1509 elif x > 1: # self**2
1510 f = self._mul_Fsum(self, op)
1511 else: # self**1 or self**0
1512 f = self._pow_0_1(x, other)
1513 elif self._ps: # self._ps[0]**x
1514 f = self._pow_2(x, other, op)
1515 else: # PYCHOK no cover
1516 # 0**pos_int == 0, but 0**0 == 1
1517 f = 0 if x else 1 # like ._fprs
1518 return self._fset(f, asis=isint(f), n=len(self))
1520 def _pow_scalar(self, x, other, op):
1521 '''(INTERNAL) Return C{self**B{x}} for C{scalar B{x}}.
1522 '''
1523 s, r = self._fprs2
1524 if isint(x, both=True):
1525 x = int(x) # Fsum**int
1526 y = abs(x)
1527 if y > 1:
1528 if r:
1529 f = self._copy_up()._pow_int(y, other, op)
1530 if x > 0: # > 1
1531 return f
1532 # assert x < 0 # < -1
1533 s, r = f._fprs2
1534 if r:
1535 return self._copy_0(_1_0)._ftruediv(f, op)
1536 # use **= -1 for the CPython float_pow
1537 # error if s is zero, and not s = 1 / s
1538 x = -1
1539# elif y > 1: # self**2 or self**-2
1540# f = self._mul_Fsum(self, op)
1541# if x < 0:
1542# f = f._copy_0(_1_0)._ftruediv(f, op)
1543# return f
1544 elif x < 0: # self**-1 == 1 / self
1545 if r:
1546 return self._copy_0(_1_0)._ftruediv(self, op)
1547 else: # self**1 or self**0
1548 return self._pow_0_1(x, other) # self or 0.0
1549 elif not isscalar(x): # assert ...
1550 raise self._TypeError(op, other, txt=_not_scalar_)
1551 elif r and self._raiser(r, s): # non-zero residual**fractional
1552 # raise self._ResidualError(op, other, r, fractional_power=x)
1553 t = _stresidual(_non_zero_, r, fractional_power=x)
1554 raise self._Error(op, other, ResidualError, txt=t)
1555 # assert isscalar(s) and isscalar(x)
1556 return self._copy_0(s)._pow_2(x, other, op)
1558 def _ps_1(self, *less):
1559 '''(INTERNAL) Yield partials, 1-primed and subtract any C{less}.
1560 '''
1561 yield _1_0
1562 for p in self._ps:
1563 if p:
1564 yield p
1565 for p in less:
1566 if p:
1567 yield -p
1568 yield _N_1_0
1570 def _ps_n(self):
1571 '''(INTERNAL) Yield partials, negated.
1572 '''
1573 for p in self._ps:
1574 if p:
1575 yield -p
1577 def _ps_x(self, op, *factors): # see .fmath.Fhorner
1578 '''(INTERNAL) Yield all C{partials} times each B{C{factor}},
1579 in total, up to C{len(partials) * len(factors)} items.
1580 '''
1581 ps = self._ps
1582 if len(ps) < len(factors):
1583 ps, factors = factors, ps
1584 _f = _isfinite
1585 for f in factors:
1586 for p in ps:
1587 p *= f
1588 if _f(p):
1589 yield p
1590 else: # PYCHOK no cover
1591 self._finite(p, op) # throw ValueError
1593 @property_RO
1594 def real(self):
1595 '''Get the C{real} part of this instance (C{float}).
1597 @see: Methods L{Fsum.__float__} and L{Fsum.fsum}
1598 and properties L{Fsum.ceil}, L{Fsum.floor},
1599 L{Fsum.imag} and L{Fsum.residual}.
1600 '''
1601 return float(self._fprs)
1603 @property_RO
1604 def residual(self):
1605 '''Get this instance' residual (C{float} or C{int}), the
1606 C{sum(partials)} less the precision running sum C{fsum}.
1608 @note: If the C{residual is INT0}, the precision running
1609 C{fsum} is considered to be I{exact}.
1611 @see: Methods L{Fsum.fsum}, L{Fsum.fsum2} and L{Fsum.is_exact}.
1612 '''
1613 return self._fprs2.residual
1615 def _raiser(self, r, s):
1616 '''(INTERNAL) Does the ratio C{r / s} exceed threshold?
1617 '''
1618 self._ratio = t = fabs((r / s) if s else r)
1619 return t > self._RESIDUAL
1621 def RESIDUAL(self, *threshold):
1622 '''Get and set this instance' I{ratio} for raising L{ResidualError}s,
1623 overriding the default from env variable C{PYGEODESY_FSUM_RESIDUAL}.
1625 @arg threshold: If C{scalar}, the I{ratio} to exceed for raising
1626 L{ResidualError}s in division and exponention, if
1627 C{None} restore the default set with env variable
1628 C{PYGEODESY_FSUM_RESIDUAL} or if omitted, keep the
1629 current setting.
1631 @return: The previous C{RESIDUAL} setting (C{float}).
1633 @raise ValueError: Negative B{C{threshold}}.
1635 @note: A L{ResidualError} is thrown if the non-zero I{ratio}
1636 C{residual} / C{fsum} exceeds the B{C{threshold}}.
1637 '''
1638 r = self._RESIDUAL
1639 if threshold:
1640 t = threshold[0]
1641 t = Fsum._RESIDUAL if t is None else (
1642 float(t) if isscalar(t) else ( # for backward ...
1643 _0_0 if bool(t) else _1_0)) # ... compatibility
1644 if t < 0:
1645 u = _DOT_(self, unstr(self.RESIDUAL, *threshold))
1646 raise _ValueError(u, RESIDUAL=t, txt=_negative_)
1647 self._RESIDUAL = t
1648 return r
1650 def _ResidualError(self, op, other, residual):
1651 '''(INTERNAL) Non-zero B{C{residual}} etc.
1652 '''
1653 t = _stresidual(_non_zero_, residual, ratio=self._ratio,
1654 RESIDUAL=self._RESIDUAL)
1655 t = t.replace(_COMMASPACE_R_, _exceeds_R_)
1656 return self._Error(op, other, ResidualError, txt=t)
1658 def signOf(self, res=True):
1659 '''Determine the sign of this instance.
1661 @kwarg res: If C{True} consider, otherwise
1662 ignore the residual (C{bool}).
1664 @return: The sign (C{int}, -1, 0 or +1).
1665 '''
1666 s, r = self._fprs2 if res else (self._fprs, 0)
1667 return _signOf(s, -r)
1669 def toRepr(self, **prec_sep_fmt_lenc): # PYCHOK signature
1670 '''Return this C{Fsum} instance as representation.
1672 @kwarg prec_sep_fmt_lenc: Optional keyword arguments for
1673 method L{Fsum2Tuple.toRepr} plus C{B{lenc}=True}
1674 (C{bool}) to in-/exclude the current C{[len]}
1675 of this L{Fsum} enclosed in I{[brackets]}.
1677 @return: This instance (C{repr}).
1678 '''
1679 return self._toT(self._fprs2.toRepr, **prec_sep_fmt_lenc)
1681 def toStr(self, **prec_sep_fmt_lenc): # PYCHOK signature
1682 '''Return this C{Fsum} instance as string.
1684 @kwarg prec_sep_fmt_lenc: Optional keyword arguments for
1685 method L{Fsum2Tuple.toStr} plus C{B{lenc}=True}
1686 (C{bool}) to in-/exclude the current C{[len]}
1687 of this L{Fsum} enclosed in I{[brackets]}.
1689 @return: This instance (C{str}).
1690 '''
1691 return self._toT(self._fprs2.toStr, **prec_sep_fmt_lenc)
1693 def _toT(self, toT, fmt=Fmt.g, lenc=True, **kwds):
1694 '''(INTERNAL) Helper for C{toRepr} and C{toStr}.
1695 '''
1696 n = self.named3
1697 if lenc:
1698 n = Fmt.SQUARE(n, len(self))
1699 return _SPACE_(n, toT(fmt=fmt, **kwds))
1701 def _TypeError(self, op, other, **txt): # PYCHOK no cover
1702 '''(INTERNAL) Return a C{TypeError}.
1703 '''
1704 return self._Error(op, other, _TypeError, **txt)
1706 def _update(self): # see ._fset
1707 '''(INTERNAL) Zap all cached C{Property_RO} values.
1708 '''
1709 Fsum._fint2._update(self)
1710 Fsum._fprs ._update(self)
1711 Fsum._fprs2._update(self)
1712 return self
1714 def _ValueError(self, op, other, **txt): # PYCHOK no cover
1715 '''(INTERNAL) Return a C{ValueError}.
1716 '''
1717 return self._Error(op, other, _ValueError, **txt)
1719 def _ZeroDivisionError(self, op, other, **txt): # PYCHOK no cover
1720 '''(INTERNAL) Return a C{ZeroDivisionError}.
1721 '''
1722 return self._Error(op, other, _ZeroDivisionError, **txt)
1724_allPropertiesOf_n(3, Fsum, Property_RO) # PYCHOK assert, see Fsum._fset, -._update
1727def _Float_Int(arg, **name_Error):
1728 '''(INTERNAL) Unit of L{Fsum2Tuple} items.
1729 '''
1730 U = Int if isint(arg) else Float
1731 return U(arg, **name_Error)
1734class Fsum2Tuple(_NamedTuple):
1735 '''2-Tuple C{(fsum, residual)} with the precision running C{fsum}
1736 and the C{residual}, the sum of the remaining partials. Each
1737 item is either C{float} or C{int}.
1739 @note: If the C{residual is INT0}, the C{fsum} is considered
1740 to be I{exact}, see method L{Fsum2Tuple.is_exact}.
1741 '''
1742 _Names_ = ( Fsum.fsum.__name__, Fsum.residual.name)
1743 _Units_ = (_Float_Int, _Float_Int)
1745 @Property_RO
1746 def Fsum(self):
1747 '''Get this L{Fsum2Tuple} as an L{Fsum}.
1748 '''
1749 f = Fsum(name=self.name)
1750 return f._copy_0(*(s for s in reversed(self) if s))
1752 def is_exact(self):
1753 '''Is this L{Fsum2Tuple} considered to be exact? (C{bool}).
1754 '''
1755 return self.Fsum.is_exact()
1757 def is_integer(self):
1758 '''Is this L{Fsum2Tuple} C{integer}? (C{bool}).
1759 '''
1760 return self.Fsum.is_integer()
1763class ResidualError(_ValueError):
1764 '''Error raised for an operation involving a L{pygeodesy.sums.Fsum}
1765 instance with a non-zero C{residual}, I{integer} or otherwise.
1767 @see: Module L{pygeodesy.fsums} and method L{Fsum.RESIDUAL}.
1768 '''
1769 pass
1772try:
1773 from math import fsum as _fsum # precision IEEE-754 sum, Python 2.6+
1775 # make sure _fsum works as expected (XXX check
1776 # float.__getformat__('float')[:4] == 'IEEE'?)
1777 if _fsum((1, 1e101, 1, -1e101)) != 2: # PYCHOK no cover
1778 del _fsum # nope, remove _fsum ...
1779 raise ImportError # ... use _fsum below
1781 Fsum._math_fsum = _sum = _fsum # PYCHOK exported
1783 if _getenv('PYGEODESY_FSUM_PARTIALS', _fsum.__name__) == _fsum.__name__:
1784 _psum = _fsum # PYCHOK redef
1786except ImportError:
1787 _sum = sum # Fsum(NAN) exception fall-back
1789 def _fsum(xs):
1790 '''(INTERNAL) Precision summation, Python 2.5-.
1791 '''
1792 return Fsum(name=_fsum.__name__)._facc(xs, up=False)._fprs
1795def fsum(xs, floats=False):
1796 '''Precision floating point summation based on or like Python's C{math.fsum}.
1798 @arg xs: Iterable, list, tuple, etc. of values (C{scalar} or
1799 L{Fsum} instances).
1800 @kwarg floats: Optionally, use C{B{floats}=True} iff I{all}
1801 B{C{xs}} are known to be C{float}.
1803 @return: Precision C{fsum} (C{float}).
1805 @raise OverflowError: Partial C{2sum} overflow.
1807 @raise TypeError: Non-scalar B{C{xs}} value.
1809 @raise ValueError: Invalid or non-finite B{C{xs}} value.
1811 @note: Exceptions and I{non-finite} handling may differ if not
1812 based on Python's C{math.fsum}.
1814 @see: Class L{Fsum} and methods L{Fsum.fsum} and L{Fsum.fadd}.
1815 '''
1816 return _fsum(xs if floats else _2floats(xs)) if xs else _0_0 # PYCHOK yield
1819def fsum_(*xs, **floats):
1820 '''Precision floating point summation of all positional arguments.
1822 @arg xs: Values to be added (C{scalar} or L{Fsum} instances),
1823 all positional.
1824 @kwarg floats: Optionally, use C{B{floats}=True} iff I{all}
1825 B{C{xs}} are known to be C{float}.
1827 @return: Precision C{fsum} (C{float}).
1829 @see: Function C{fsum}.
1830 '''
1831 return _fsum(xs if _xkwds_get(floats, floats=False) else
1832 _2floats(xs, origin=1)) if xs else _0_0 # PYCHOK yield
1835def fsumf_(*xs):
1836 '''Precision floating point summation L{fsum_}C{(*xs, floats=True)}.
1837 '''
1838 return _fsum(xs) if xs else _0_0
1841def fsum1(xs, floats=False):
1842 '''Precision floating point summation of a few arguments, 1-primed.
1844 @arg xs: Iterable, list, tuple, etc. of values (C{scalar} or
1845 L{Fsum} instances).
1846 @kwarg floats: Optionally, use C{B{floats}=True} iff I{all}
1847 B{C{xs}} are known to be C{float}.
1849 @return: Precision C{fsum} (C{float}).
1851 @see: Function C{fsum}.
1852 '''
1853 return _fsum(_1primed(xs if floats else _2floats(xs))) if xs else _0_0 # PYCHOK yield
1856def fsum1_(*xs, **floats):
1857 '''Precision floating point summation of a few arguments, 1-primed.
1859 @arg xs: Values to be added (C{scalar} or L{Fsum} instances),
1860 all positional.
1861 @kwarg floats: Optionally, use C{B{floats}=True} iff I{all}
1862 B{C{xs}} are known to be C{float}.
1864 @return: Precision C{fsum} (C{float}).
1866 @see: Function C{fsum}
1867 '''
1868 return _fsum(_1primed(xs if _xkwds_get(floats, floats=False) else
1869 _2floats(xs, origin=1))) if xs else _0_0 # PYCHOK yield
1872def fsum1f_(*xs):
1873 '''Precision floating point summation L{fsum1_}C{(*xs, floats=True)}.
1874 '''
1875 return _fsum(_1primed(xs)) if xs else _0_0
1878# **) MIT License
1879#
1880# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.
1881#
1882# Permission is hereby granted, free of charge, to any person obtaining a
1883# copy of this software and associated documentation files (the "Software"),
1884# to deal in the Software without restriction, including without limitation
1885# the rights to use, copy, modify, merge, publish, distribute, sublicense,
1886# and/or sell copies of the Software, and to permit persons to whom the
1887# Software is furnished to do so, subject to the following conditions:
1888#
1889# The above copyright notice and this permission notice shall be included
1890# in all copies or substantial portions of the Software.
1891#
1892# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
1893# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
1894# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
1895# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
1896# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
1897# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
1898# OTHER DEALINGS IN THE SOFTWARE.