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, \
34 _xError2, _xkwds_get, _ZeroDivisionError
35from pygeodesy.interns import NN, _arg_, _COMMASPACE_, _DASH_, _EQUAL_, \
36 _exceeds_, _from_, _iadd_op_, _LANGLE_, \
37 _negative_, _NOTEQUAL_, _not_finite_, \
38 _not_scalar_, _PERCENT_, _PLUS_, _R_, _RANGLE_, \
39 _SLASH_, _SPACE_, _STAR_, _UNDER_
40from pygeodesy.lazily import _ALL_LAZY, _getenv, _sys_version_info2
41from pygeodesy.named import _Named, _NamedTuple, _NotImplemented, Fmt, unstr
42from pygeodesy.props import _allPropertiesOf_n, deprecated_property_RO, \
43 Property_RO, property_RO
44# from pygeodesy.streprs import Fmt, unstr # from .named
45# from pygeodesy.units import Float, Int # from .constants
47from math import ceil as _ceil, fabs, floor as _floor # PYCHOK used! .ltp
49__all__ = _ALL_LAZY.fsums
50__version__ = '24.02.20'
52_add_op_ = _PLUS_ # in .auxilats.auxAngle
53_eq_op_ = _EQUAL_ * 2 # _DEQUAL_
54_COMMASPACE_R_ = _COMMASPACE_ + _R_
55_exceeds_R_ = _SPACE_ + _exceeds_(_R_)
56_floordiv_op_ = _SLASH_ * 2 # _DSLASH_
57_fset_op_ = _EQUAL_
58_ge_op_ = _RANGLE_ + _EQUAL_
59_gt_op_ = _RANGLE_
60_integer_ = 'integer'
61_le_op_ = _LANGLE_ + _EQUAL_
62_lt_op_ = _LANGLE_
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 _2float(index=None, **name_value): # in .fmath, .fstats
75 '''(INTERNAL) Raise C{TypeError} or C{ValueError} if not scalar or infinite.
76 '''
77 n, v = name_value.popitem() # _xkwds_item2(name_value)
78 try:
79 v = float(v)
80 if _isfinite(v):
81 return v
82 E, t = _ValueError, _not_finite_
83 except Exception as e:
84 E, t = _xError2(e)
85 raise E(Fmt.INDEX(n, index), v, txt=t)
88def _2floats(xs, origin=0, sub=False):
89 '''(INTERNAL) Yield each B{C{xs}} as a C{float}.
90 '''
91 try:
92 i, x = origin, None
93 _fin = _isfinite
94 _Fsum = Fsum
95 for x in xs:
96 if isinstance(x, _Fsum):
97 for p in x._ps:
98 yield (-p) if sub else p
99 else:
100 f = float(x)
101 if not _fin(f):
102 raise ValueError(_not_finite_)
103 if f:
104 yield (-f) if sub else f
105 i += 1
106 except Exception as e:
107 E, t = _xError2(e)
108 n = Fmt.SQUARE(xs=i)
109 raise E(n, x, txt=t)
112def _Powers(power, xs, origin=1): # in .fmath
113 '''(INTERNAL) Yield each C{xs} as C{float(x**power)}.
114 '''
115 _xisscalar(power=power)
116 try:
117 i, x = origin, None
118 _fin = _isfinite
119 _Fsum = Fsum
120 _pow = pow # XXX math.pow
121 for x in xs:
122 if isinstance(x, _Fsum):
123 P = x.pow(power)
124 for p in P._ps:
125 yield p
126 else:
127 p = _pow(float(x), power)
128 if not _fin(p):
129 raise ValueError(_not_finite_)
130 yield p
131 i += 1
132 except Exception as e:
133 E, t = _xError2(e)
134 n = Fmt.SQUARE(xs=i)
135 raise E(n, x, txt=t)
138def _1primed(xs):
139 '''(INTERNAL) 1-Prime the summation of C{xs}
140 arguments I{known} to be C{finite float}.
141 '''
142 yield _1_0
143 for x in xs:
144 if x:
145 yield x
146 yield _N_1_0
149def _psum(ps): # PYCHOK used!
150 '''(INTERNAL) Partials summation updating C{ps}, I{overridden below}.
151 '''
152 i = len(ps) - 1 # len(ps) > 2
153 s = ps[i]
154 _2s = _2sum
155 while i > 0:
156 i -= 1
157 s, r = _2s(s, ps[i])
158 if r: # sum(ps) became inexact
159 ps[i:] = [s, r] if s else [r]
160 if i > 0:
161 p = ps[i-1] # round half-even
162 if (p > 0 and r > 0) or \
163 (p < 0 and r < 0): # signs match
164 r *= 2
165 t = s + r
166 if r == (t - s):
167 s = t
168 break
169 ps[i:] = [s]
170 return s
173def _2scalar(other, _raiser=None):
174 '''(INTERNAL) Return B{C{other}} as C{int}, C{float} or C{as-is}.
175 '''
176 if isinstance(other, Fsum):
177 s, r = other._fint2
178 if r:
179 s, r = other._fprs2
180 if r: # PYCHOK no cover
181 if _raiser and _raiser(r, s):
182 raise ValueError(_stresidual(_non_zero_, r))
183 s = other # L{Fsum} as-is
184 else:
185 s = other # C{type} as-is
186 if isint(s, both=True):
187 s = int(s)
188 return s
191def _strcomplex(s, *args):
192 '''(INTERNAL) C{Complex} 2- or 3-arg C{pow} error C{str}.
193 '''
194 c = iscomplex.__name__[2:]
195 n = _DASH_(len(args), _arg_)
196 t = _SPACE_(c, s, _from_, n, pow.__name__)
197 return unstr(t, *args)
200def _stresidual(prefix, residual, **name_values):
201 '''(INTERNAL) Residual error C{str}.
202 '''
203 p = _SPACE_(prefix, Fsum.residual.name)
204 t = Fmt.PARENSPACED(p, Fmt(residual))
205 for n, v in itemsorted(name_values):
206 n = n.replace(_UNDER_, _SPACE_)
207 p = Fmt.PARENSPACED(n, Fmt(v))
208 t = _COMMASPACE_(t, p)
209 return t
212def _2sum(a, b): # by .testFmath
213 '''(INTERNAL) Return C{a + b} as 2-tuple (sum, residual).
214 '''
215 s = a + b
216 if not _isfinite(s):
217 u = unstr(_2sum.__name__, a, b)
218 t = Fmt.PARENSPACED(_not_finite_, s)
219 raise _OverflowError(u, txt=t)
220 if fabs(a) < fabs(b):
221 a, b = b, a
222 return s, (b - (s - a))
225class Fsum(_Named): # sync __methods__ with .vector3dBase.Vector3dBase
226 '''Precision floating point I{running} summation.
228 Unlike Python's C{math.fsum}, this class accumulates values and provides intermediate,
229 I{running} precision floating point summation. Accumulation may continue after
230 intermediate, I{running} summuation.
232 @note: Accumulated values may be L{Fsum} or C{scalar} instances with C{scalar} meaning
233 type C{float}, C{int} or any C{type} convertible to a single C{float}, having
234 method C{__float__}.
236 @note: Handling of exceptions and C{inf}, C{INF}, C{nan} and C{NAN} differs from
237 Python's C{math.fsum}.
239 @see: U{Hettinger<https://GitHub.com/ActiveState/code/blob/master/recipes/Python/
240 393090_Binary_floating_point_summatiaccurate_full/recipe-393090.py>}, U{Kahan
241 <https://WikiPedia.org/wiki/Kahan_summation_algorithm>}, U{Klein
242 <https://Link.Springer.com/article/10.1007/s00607-005-0139-x>}, Python 2.6+
243 file I{Modules/mathmodule.c} and the issue log U{Full precision summation
244 <https://Bugs.Python.org/issue2819>}.
245 '''
246 _math_fsum = None
247 _n = 0
248# _ps = [] # partial sums
249# _px = 0
250 _ratio = None
251 _RESIDUAL = max(float(_getenv('PYGEODESY_FSUM_RESIDUAL', _0_0)), _0_0)
253 def __init__(self, *xs, **name_RESIDUAL):
254 '''New L{Fsum} for precision floating point I{running} summation.
256 @arg xs: No, one or more initial values (each C{scalar} or an
257 L{Fsum} instance).
258 @kwarg name_RESIDUAL: Optional C{B{name}=NN} for this L{Fsum}
259 (C{str}) and C{B{RESIDUAL}=None} for the
260 L{ResidualError} threshold.
262 @see: Methods L{Fsum.fadd} and L{Fsum.RESIDUAL}.
263 '''
264 if name_RESIDUAL:
265 n = _xkwds_get(name_RESIDUAL, name=NN)
266 if n: # set name ...
267 self.name = n
268 r = _xkwds_get(name_RESIDUAL, RESIDUAL=None)
269 if r is not None:
270 self.RESIDUAL(r) # ... for ResidualError
271# self._n = 0
272 self._ps = [] # [_0_0], see L{Fsum._fprs}
273 if len(xs) > 1:
274 self._facc(_2floats(xs, origin=1), up=False) # PYCHOK yield
275 elif xs: # len(xs) == 1
276 self._ps = [_2float(x=xs[0])]
277 self._n = 1
279 def __abs__(self):
280 '''Return this instance' absolute value as an L{Fsum}.
281 '''
282 s = _fsum(self._ps_1()) # == self._cmp_0(0, ...)
283 return self._copy_n(self.__abs__) if s < 0 else \
284 self._copy_2(self.__abs__)
286 def __add__(self, other):
287 '''Return the C{Fsum(B{self}, B{other})}.
289 @arg other: An L{Fsum} or C{scalar}.
291 @return: The sum (L{Fsum}).
293 @see: Method L{Fsum.__iadd__}.
294 '''
295 f = self._copy_2(self.__add__)
296 return f._fadd(other, _add_op_)
298 def __bool__(self): # PYCHOK not special in Python 2-
299 '''Return C{True} if this instance is I{exactly} non-zero.
300 '''
301 s, r = self._fprs2
302 return bool(s or r) and s != -r # == self != 0
304 def __ceil__(self): # PYCHOK not special in Python 2-
305 '''Return this instance' C{math.ceil} as C{int} or C{float}.
307 @return: An C{int} in Python 3+, but C{float} in Python 2-.
309 @see: Methods L{Fsum.__floor__} and property L{Fsum.ceil}.
310 '''
311 return self.ceil
313 def __cmp__(self, other): # Python 2-
314 '''Compare this with an other instance or C{scalar}.
316 @return: -1, 0 or +1 (C{int}).
318 @raise TypeError: Incompatible B{C{other}} C{type}.
319 '''
320 s = self._cmp_0(other, self.cmp.__name__)
321 return _signOf(s, 0)
323 cmp = __cmp__
325 def __divmod__(self, other):
326 '''Return C{divmod(B{self}, B{other})} as 2-tuple C{(quotient,
327 remainder)}, an C{int} in Python 3+ or C{float} in Python 2-
328 and an L{Fsum}.
330 @arg other: An L{Fsum} or C{scalar} modulus.
332 @see: Method L{Fsum.__itruediv__}.
333 '''
334 f = self._copy_2(self.__divmod__)
335 return f._fdivmod2(other, _divmod_op_)
337 def __eq__(self, other):
338 '''Compare this with an other instance or C{scalar}.
339 '''
340 return self._cmp_0(other, _eq_op_) == 0
342 def __float__(self):
343 '''Return this instance' current precision running sum as C{float}.
345 @see: Methods L{Fsum.fsum} and L{Fsum.int_float}.
346 '''
347 return float(self._fprs)
349 def __floor__(self): # PYCHOK not special in Python 2-
350 '''Return this instance' C{math.floor} as C{int} or C{float}.
352 @return: An C{int} in Python 3+, but C{float} in Python 2-.
354 @see: Methods L{Fsum.__ceil__} and property L{Fsum.floor}.
355 '''
356 return self.floor
358 def __floordiv__(self, other):
359 '''Return C{B{self} // B{other}} as an L{Fsum}.
361 @arg other: An L{Fsum} or C{scalar} divisor.
363 @return: The C{floor} quotient (L{Fsum}).
365 @see: Methods L{Fsum.__ifloordiv__}.
366 '''
367 f = self._copy_2(self.__floordiv__)
368 return f._floordiv(other, _floordiv_op_)
370 def __format__(self, *other): # PYCHOK no cover
371 '''Not implemented.'''
372 return _NotImplemented(self, *other)
374 def __ge__(self, other):
375 '''Compare this with an other instance or C{scalar}.
376 '''
377 return self._cmp_0(other, _ge_op_) >= 0
379 def __gt__(self, other):
380 '''Compare this with an other instance or C{scalar}.
381 '''
382 return self._cmp_0(other, _gt_op_) > 0
384 def __hash__(self): # PYCHOK no cover
385 '''Return this instance' C{hash}.
386 '''
387 return hash(self._ps) # XXX id(self)?
389 def __iadd__(self, other):
390 '''Apply C{B{self} += B{other}} to this instance.
392 @arg other: An L{Fsum} or C{scalar} instance.
394 @return: This instance, updated (L{Fsum}).
396 @raise TypeError: Invalid B{C{other}}, not
397 C{scalar} nor L{Fsum}.
399 @see: Methods L{Fsum.fadd} and L{Fsum.fadd_}.
400 '''
401 return self._fadd(other, _iadd_op_)
403 def __ifloordiv__(self, other):
404 '''Apply C{B{self} //= B{other}} to this instance.
406 @arg other: An L{Fsum} or C{scalar} divisor.
408 @return: This instance, updated (L{Fsum}).
410 @raise ResidualError: Non-zero residual in B{C{other}}.
412 @raise TypeError: Invalid B{C{other}} type.
414 @raise ValueError: Invalid or non-finite B{C{other}}.
416 @raise ZeroDivisionError: Zero B{C{other}}.
418 @see: Methods L{Fsum.__itruediv__}.
419 '''
420 return self._floordiv(other, _floordiv_op_ + _fset_op_)
422 def __imatmul__(self, other): # PYCHOK no cover
423 '''Not implemented.'''
424 return _NotImplemented(self, other)
426 def __imod__(self, other):
427 '''Apply C{B{self} %= B{other}} to this instance.
429 @arg other: An L{Fsum} or C{scalar} modulus.
431 @return: This instance, updated (L{Fsum}).
433 @see: Method L{Fsum.__divmod__}.
434 '''
435 self._fdivmod2(other, _mod_op_ + _fset_op_)
436 return self
438 def __imul__(self, other):
439 '''Apply C{B{self} *= B{other}} to this instance.
441 @arg other: An L{Fsum} or C{scalar} factor.
443 @return: This instance, updated (L{Fsum}).
445 @raise OverflowError: Partial C{2sum} overflow.
447 @raise TypeError: Invalid B{C{other}} type.
449 @raise ValueError: Invalid or non-finite B{C{other}}.
450 '''
451 return self._fmul(other, _mul_op_ + _fset_op_)
453 def __int__(self):
454 '''Return this instance as an C{int}.
456 @see: Methods L{Fsum.int_float}, L{Fsum.__ceil__}
457 and L{Fsum.__floor__} and properties
458 L{Fsum.ceil} and L{Fsum.floor}.
459 '''
460 i, _ = self._fint2
461 return i
463 def __invert__(self): # PYCHOK no cover
464 '''Not implemented.'''
465 # Luciano Ramalho, "Fluent Python", O'Reilly, 2nd Ed, 2022 p. 567
466 return _NotImplemented(self)
468 def __ipow__(self, other, *mod): # PYCHOK 2 vs 3 args
469 '''Apply C{B{self} **= B{other}} to this instance.
471 @arg other: The exponent (L{Fsum} or C{scalar}).
472 @arg mod: Optional modulus (C{int} or C{None}) for the
473 3-argument C{pow(B{self}, B{other}, B{mod})}
474 version.
476 @return: This instance, updated (L{Fsum}).
478 @note: If B{C{mod}} is given, the result will be an C{integer}
479 L{Fsum} in Python 3+ if this instance C{is_integer} or
480 set to C{as_integer} if B{C{mod}} given as C{None}.
482 @raise OverflowError: Partial C{2sum} overflow.
484 @raise ResidualError: Non-zero residual in B{C{other}} and
485 env var C{PYGEODESY_FSUM_RESIDUAL}
486 set or this instance has a non-zero
487 residual and either B{C{mod}} is
488 given and non-C{None} or B{C{other}}
489 is a negative or fractional C{scalar}.
491 @raise TypeError: Invalid B{C{other}} type or 3-argument
492 C{pow} invocation failed.
494 @raise ValueError: If B{C{other}} is a negative C{scalar}
495 and this instance is C{0} or B{C{other}}
496 is a fractional C{scalar} and this
497 instance is negative or has a non-zero
498 residual or B{C{mod}} is given and C{0}.
500 @see: CPython function U{float_pow<https://GitHub.com/
501 python/cpython/blob/main/Objects/floatobject.c>}.
502 '''
503 return self._fpow(other, _pow_op_ + _fset_op_, *mod)
505 def __isub__(self, other):
506 '''Apply C{B{self} -= B{other}} to this instance.
508 @arg other: An L{Fsum} or C{scalar}.
510 @return: This instance, updated (L{Fsum}).
512 @raise TypeError: Invalid B{C{other}} type.
514 @see: Method L{Fsum.fadd}.
515 '''
516 return self._fsub(other, _isub_op_)
518 def __iter__(self):
519 '''Return an C{iter}ator over a C{partials} duplicate.
520 '''
521 return iter(self.partials)
523 def __itruediv__(self, other):
524 '''Apply C{B{self} /= B{other}} to this instance.
526 @arg other: An L{Fsum} or C{scalar} divisor.
528 @return: This instance, updated (L{Fsum}).
530 @raise OverflowError: Partial C{2sum} overflow.
532 @raise ResidualError: Non-zero residual in B{C{other}} and
533 env var C{PYGEODESY_FSUM_RESIDUAL} set.
535 @raise TypeError: Invalid B{C{other}} type.
537 @raise ValueError: Invalid or non-finite B{C{other}}.
539 @raise ZeroDivisionError: Zero B{C{other}}.
541 @see: Method L{Fsum.__ifloordiv__}.
542 '''
543 return self._ftruediv(other, _truediv_op_ + _fset_op_)
545 def __le__(self, other):
546 '''Compare this with an other instance or C{scalar}.
547 '''
548 return self._cmp_0(other, _le_op_) <= 0
550 def __len__(self):
551 '''Return the number of values accumulated (C{int}).
552 '''
553 return self._n
555 def __lt__(self, other):
556 '''Compare this with an other instance or C{scalar}.
557 '''
558 return self._cmp_0(other, _lt_op_) < 0
560 def __matmul__(self, other): # PYCHOK no cover
561 '''Not implemented.'''
562 return _NotImplemented(self, other)
564 def __mod__(self, other):
565 '''Return C{B{self} % B{other}} as an L{Fsum}.
567 @see: Method L{Fsum.__imod__}.
568 '''
569 f = self._copy_2(self.__mod__)
570 return f._fdivmod2(other, _mod_op_)[1]
572 def __mul__(self, other):
573 '''Return C{B{self} * B{other}} as an L{Fsum}.
575 @see: Method L{Fsum.__imul__}.
576 '''
577 f = self._copy_2(self.__mul__)
578 return f._fmul(other, _mul_op_)
580 def __ne__(self, other):
581 '''Compare this with an other instance or C{scalar}.
582 '''
583 return self._cmp_0(other, _ne_op_) != 0
585 def __neg__(self):
586 '''Return I{a copy of} this instance, negated.
587 '''
588 return self._copy_n(self.__neg__)
590 def __pos__(self):
591 '''Return this instance I{as-is}, like C{float.__pos__()}.
592 '''
593 return self if _pos_self else self._copy_2(self.__pos__)
595 def __pow__(self, other, *mod): # PYCHOK 2 vs 3 args
596 '''Return C{B{self}**B{other}} as an L{Fsum}.
598 @see: Method L{Fsum.__ipow__}.
599 '''
600 f = self._copy_2(self.__pow__)
601 return f._fpow(other, _pow_op_, *mod)
603 def __radd__(self, other):
604 '''Return C{B{other} + B{self}} as an L{Fsum}.
606 @see: Method L{Fsum.__iadd__}.
607 '''
608 f = self._copy_r2(other, self.__radd__)
609 return f._fadd(self, _add_op_)
611 def __rdivmod__(self, other):
612 '''Return C{divmod(B{other}, B{self})} as 2-tuple C{(quotient,
613 remainder)}.
615 @see: Method L{Fsum.__divmod__}.
616 '''
617 f = self._copy_r2(other, self.__rdivmod__)
618 return f._fdivmod2(self, _divmod_op_)
620# def __repr__(self):
621# '''Return the default C{repr(this)}.
622# '''
623# return self.toRepr(lenc=True)
625 def __rfloordiv__(self, other):
626 '''Return C{B{other} // B{self}} as an L{Fsum}.
628 @see: Method L{Fsum.__ifloordiv__}.
629 '''
630 f = self._copy_r2(other, self.__rfloordiv__)
631 return f._floordiv(self, _floordiv_op_)
633 def __rmatmul__(self, other): # PYCHOK no cover
634 '''Not implemented.'''
635 return _NotImplemented(self, other)
637 def __rmod__(self, other):
638 '''Return C{B{other} % B{self}} as an L{Fsum}.
640 @see: Method L{Fsum.__imod__}.
641 '''
642 f = self._copy_r2(other, self.__rmod__)
643 return f._fdivmod2(self, _mod_op_)[1]
645 def __rmul__(self, other):
646 '''Return C{B{other} * B{self}} as an L{Fsum}.
648 @see: Method L{Fsum.__imul__}.
649 '''
650 f = self._copy_r2(other, self.__rmul__)
651 return f._fmul(self, _mul_op_)
653 def __round__(self, *ndigits): # PYCHOK no cover
654 '''Return C{round(B{self}, *B{ndigits}} as an L{Fsum}.
656 @arg ndigits: Optional number of digits (C{int}).
657 '''
658 # <https://docs.Python.org/3.12/reference/datamodel.html?#object.__round__>
659 f = Fsum(name=self.__round__.__name__)
660 f._n = 1
661 f._ps = [round(float(self), *ndigits)] # can be C{int}
662 return f
664 def __rpow__(self, other, *mod):
665 '''Return C{B{other}**B{self}} as an L{Fsum}.
667 @see: Method L{Fsum.__ipow__}.
668 '''
669 f = self._copy_r2(other, self.__rpow__)
670 return f._fpow(self, _pow_op_, *mod)
672 def __rsub__(self, other):
673 '''Return C{B{other} - B{self}} as L{Fsum}.
675 @see: Method L{Fsum.__isub__}.
676 '''
677 f = self._copy_r2(other, self.__rsub__)
678 return f._fsub(self, _sub_op_)
680 def __rtruediv__(self, other):
681 '''Return C{B{other} / B{self}} as an L{Fsum}.
683 @see: Method L{Fsum.__itruediv__}.
684 '''
685 f = self._copy_r2(other, self.__rtruediv__)
686 return f._ftruediv(self, _truediv_op_)
688 def __str__(self):
689 '''Return the default C{str(self)}.
690 '''
691 return self.toStr(lenc=True)
693 def __sub__(self, other):
694 '''Return C{B{self} - B{other}} as an L{Fsum}.
696 @arg other: An L{Fsum} or C{scalar}.
698 @return: The difference (L{Fsum}).
700 @see: Method L{Fsum.__isub__}.
701 '''
702 f = self._copy_2(self.__sub__)
703 return f._fsub(other, _sub_op_)
705 def __truediv__(self, other):
706 '''Return C{B{self} / B{other}} as an L{Fsum}.
708 @arg other: An L{Fsum} or C{scalar} divisor.
710 @return: The quotient (L{Fsum}).
712 @see: Method L{Fsum.__itruediv__}.
713 '''
714 f = self._copy_2(self.__truediv__)
715 return f._ftruediv(other, _truediv_op_)
717 __trunc__ = __int__
719 if _sys_version_info2 < (3, 0): # PYCHOK no cover
720 # <https://docs.Python.org/2/library/operator.html#mapping-operators-to-functions>
721 __div__ = __truediv__
722 __idiv__ = __itruediv__
723 __long__ = __int__
724 __nonzero__ = __bool__
725 __rdiv__ = __rtruediv__
727 def as_integer_ratio(self):
728 '''Return this instance as the ratio of 2 integers.
730 @return: 2-Tuple C{(numerator, denominator)} both
731 C{int} and with positive C{denominator}.
733 @see: Standard C{float.as_integer_ratio} in Python 3+.
734 '''
735 n, r = self._fint2
736 if r:
737 i, d = r.as_integer_ratio()
738 n *= d
739 n += i
740 else: # PYCHOK no cover
741 d = 1
742 return n, d
744 @property_RO
745 def ceil(self):
746 '''Get this instance' C{ceil} value (C{int} in Python 3+,
747 but C{float} in Python 2-).
749 @note: The C{ceil} takes the C{residual} into account.
751 @see: Method L{Fsum.int_float} and properties L{Fsum.floor},
752 L{Fsum.imag} and L{Fsum.real}.
753 '''
754 s, r = self._fprs2
755 c = _ceil(s) + int(r) - 1
756 while r > (c - s): # (s + r) > c
757 c += 1
758 return c
760 def _cmp_0(self, other, op):
761 '''(INTERNAL) Return C{scalar(self - B{other})} for 0-comparison.
762 '''
763 if isscalar(other):
764 if other:
765 s = _fsum(self._ps_1(other))
766 else:
767 s, r = self._fprs2
768 s = _signOf(s, -r)
769 elif isinstance(other, Fsum):
770 s = _fsum(self._ps_1(*other._ps))
771 else:
772 raise self._TypeError(op, other) # txt=_invalid_
773 return s
775 def copy(self, deep=False, name=NN):
776 '''Copy this instance, C{shallow} or B{C{deep}}.
778 @return: The copy (L{Fsum}).
779 '''
780 f = _Named.copy(self, deep=deep, name=name)
781 f._n = self._n if deep else 1
782 f._ps = list(self._ps) # separate list
783 return f
785 def _copy_0(self, *xs):
786 '''(INTERNAL) Copy with/-out overriding C{partials}.
787 '''
788 # for x in xs:
789 # assert isscalar(x)
790 f = self._Fsum(self._n + len(xs), *xs)
791 if self.name:
792 f._name = self.name # .rename calls _update_attrs
793 return f
795 def _copy_2(self, which):
796 '''(INTERNAL) Copy for I{dyadic} operators.
797 '''
798 # NOT .classof due to .Fdot(a, *b) args, etc.
799 f = _Named.copy(self, deep=False, name=which.__name__)
800 # assert f._n == self._n
801 f._ps = list(self._ps) # separate list
802 return f
804 def _copy_n(self, which):
805 '''(INTERNAL) Negated copy for I{monadic} C{__abs__} and C{__neg__}.
806 '''
807 if self._ps:
808 f = self._Fsum(self._n)
809 f._ps[:] = self._ps_n()
810# f._facc_up(up=False)
811 else:
812 f = self._Fsum(self._n, _0_0)
813 f._name = which.__name__ # .rename calls _update_attrs
814 return f
816 def _copy_r2(self, other, which):
817 '''(INTERNAL) Copy for I{reverse-dyadic} operators.
818 '''
819 return other._copy_2(which) if isinstance(other, Fsum) else \
820 Fsum(other, name=which.__name__) # see ._copy_2
822 def _copy_RESIDUAL(self, other):
823 '''(INTERNAL) Copy C{other._RESIDUAL}.
824 '''
825 R = other._RESIDUAL
826 if R is not Fsum._RESIDUAL:
827 self._RESIDUAL = R
829 def _copy_up(self, _fprs2=False):
830 '''(INTERNAL) Minimal, anonymous copy.
831 '''
832 f = self._Fsum(self._n, *self._ps)
833 if _fprs2: # only the ._fprs2 2-tuple
834 Fsum._fprs2._update_from(f, self)
835 return f
837 def divmod(self, other):
838 '''Return C{divmod(B{self}, B{other})} as 2-tuple C{(quotient,
839 remainder)}.
841 @arg other: An L{Fsum} or C{scalar} divisor.
843 @return: 2-Tuple C{(quotient, remainder)}, with the C{quotient}
844 an C{int} in Python 3+ or a C{float} in Python 2- and
845 the C{remainder} an L{Fsum} instance.
847 @see: Method L{Fsum.__itruediv__}.
848 '''
849 f = self._copy_2(self.divmod)
850 return f._fdivmod2(other, _divmod_op_)
852 def _Error(self, op, other, Error, **txt):
853 '''(INTERNAL) Format an B{C{Error}} for C{{self} B{op} B{other}}.
854 '''
855 return Error(_SPACE_(self.toRepr(), op, repr(other)), **txt)
857 def _ErrorX(self, X, xs, **kwds): # in .fmath
858 '''(INTERNAL) Format a caught exception.
859 '''
860 E, t = _xError2(X)
861 n = unstr(self.named3, *xs[:3], _ELLIPSIS=len(xs) > 3, **kwds)
862 return E(n, txt=t, cause=X)
864 def _facc(self, xs, up=True): # from .elliptic._Defer.Fsum
865 '''(INTERNAL) Accumulate more known C{scalar}s.
866 '''
867 n, ps, _2s = 0, self._ps, _2sum
868 for x in xs: # _iter()
869 # assert isscalar(x) and isfinite(x)
870 i = 0
871 for p in ps:
872 x, p = _2s(x, p)
873 if p:
874 ps[i] = p
875 i += 1
876 ps[i:] = [x]
877 n += 1
878 # assert self._ps is ps
879 if n:
880 self._n += n
881 # Fsum._px = max(Fsum._px, len(ps))
882 if up:
883 self._update()
884 return self
886 def _facc_(self, *xs, **up):
887 '''(INTERNAL) Accumulate all positional C{scalar}s.
888 '''
889 return self._facc(xs, **up) if xs else self
891# def _facc_up(self, up=True):
892# '''(INTERNAL) Update the C{partials}, by removing
893# and re-accumulating the final C{partial}.
894# '''
895# while len(self._ps) > 1:
896# p = self._ps.pop()
897# if p:
898# n = self._n
899# self._facc_(p, up=False)
900# self._n = n
901# break
902# return self._update() if up else self # ._fpsqz()
904 def fadd(self, xs=()):
905 '''Add an iterable of C{scalar} or L{Fsum} instances
906 to this instance.
908 @arg xs: Iterable, list, tuple, etc. (C{scalar} or
909 L{Fsum} instances).
911 @return: This instance (L{Fsum}).
913 @raise OverflowError: Partial C{2sum} overflow.
915 @raise TypeError: An invalid B{C{xs}} type, not C{scalar}
916 nor L{Fsum}.
918 @raise ValueError: Invalid or non-finite B{C{xs}} value.
919 '''
920 if isinstance(xs, Fsum):
921 self._facc(xs._ps)
922 elif isscalar(xs): # for backward compatibility
923 self._facc_(_2float(x=xs)) # PYCHOK no cover
924 elif xs:
925 self._facc(_2floats(xs)) # PYCHOK yield
926 return self
928 def fadd_(self, *xs):
929 '''Add all positional C{scalar} or L{Fsum} instances
930 to this instance.
932 @arg xs: Values to add (C{scalar} or L{Fsum} instances),
933 all positional.
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 return self._facc(_2floats(xs, origin=1)) # PYCHOK yield
946 def _fadd(self, other, op): # in .fmath.Fhorner
947 '''(INTERNAL) Apply C{B{self} += B{other}}.
948 '''
949 if isinstance(other, Fsum):
950 if other is self:
951 self._facc_(*other._ps) # == ._facc(tuple(other._ps))
952 elif other._ps:
953 self._facc(other._ps)
954 elif not isscalar(other):
955 raise self._TypeError(op, other) # txt=_invalid_
956 elif other:
957 self._facc_(other)
958 return self
960 fcopy = copy # for backward compatibility
961 fdiv = __itruediv__ # for backward compatibility
962 fdivmod = __divmod__ # for backward compatibility
964 def _fdivmod2(self, other, op):
965 '''(INTERNAL) C{divmod(B{self}, B{other})} as 2-tuple
966 (C{int} or C{float}, remainder C{self}).
967 '''
968 # result mostly follows CPython function U{float_divmod
969 # <https://GitHub.com/python/cpython/blob/main/Objects/floatobject.c>},
970 # but at least divmod(-3, 2) equals Cpython's result (-2, 1).
971 q = self._copy_up(_fprs2=True)._ftruediv(other, op).floor
972 if q: # == float // other == floor(float / other)
973 self -= other * q
975 s = signOf(other) # make signOf(self) == signOf(other)
976 if s and self.signOf() == -s: # PYCHOK no cover
977 self += other
978 q -= 1
980# t = self.signOf()
981# if t and t != s:
982# from pygeodesy.errors import _AssertionError
983# raise self._Error(op, other, _AssertionError, txt=signOf.__name__)
984 return q, self # q is C{int} in Python 3+, but C{float} in Python 2-
986 def _finite(self, other, op=None):
987 '''(INTERNAL) Return B{C{other}} if C{finite}.
988 '''
989 if _isfinite(other):
990 return other
991 raise ValueError(_not_finite_) if not op else \
992 self._ValueError(op, other, txt=_not_finite_)
994 def fint(self, raiser=True, name=NN):
995 '''Return this instance' current running sum as C{integer}.
997 @kwarg raiser: If C{True} throw a L{ResidualError} if the
998 I{integer} residual is non-zero.
999 @kwarg name: Optional name (C{str}), overriding C{"fint"}.
1001 @return: The C{integer} (L{Fsum}).
1003 @raise ResidualError: Non-zero I{integer} residual.
1005 @see: Methods L{Fsum.int_float} and L{Fsum.is_integer}.
1006 '''
1007 i, r = self._fint2
1008 if r and raiser:
1009 t = _stresidual(_integer_, r)
1010 raise ResidualError(_integer_, i, txt=t)
1011 n = name or self.fint.__name__
1012 return Fsum(name=n)._fset(i, asis=True)
1014 def fint2(self, **name):
1015 '''Return this instance' current running sum as C{int} and
1016 the I{integer} residual.
1018 @kwarg name: Optional name (C{str}).
1020 @return: An L{Fsum2Tuple}C{(fsum, residual)} with C{fsum}
1021 an C{int} and I{integer} C{residual} a C{float} or
1022 C{INT0} if the C{fsum} is considered to be I{exact}.
1023 '''
1024 return Fsum2Tuple(*self._fint2, **name)
1026 @Property_RO
1027 def _fint2(self): # see ._fset
1028 '''(INTERNAL) Get 2-tuple (C{int}, I{integer} residual).
1029 '''
1030 i = int(self._fprs) # int(self)
1031 r = _fsum(self._ps_1(i)) if len(self._ps) > 1 else (
1032 (self._ps[0] - i) if self._ps else -i)
1033 return i, (r or INT0)
1035 @deprecated_property_RO
1036 def float_int(self): # PYCHOK no cover
1037 '''DEPRECATED, use method C{Fsum.int_float}.'''
1038 return self.int_float() # raiser=False
1040 @property_RO
1041 def floor(self):
1042 '''Get this instance' C{floor} (C{int} in Python 3+, but
1043 C{float} in Python 2-).
1045 @note: The C{floor} takes the C{residual} into account.
1047 @see: Method L{Fsum.int_float} and properties L{Fsum.ceil},
1048 L{Fsum.imag} and L{Fsum.real}.
1049 '''
1050 s, r = self._fprs2
1051 f = _floor(s) + _floor(r) + 1
1052 while r < (f - s): # (s + r) < f
1053 f -= 1
1054 return f
1056# floordiv = __floordiv__ # for naming consistency
1058 def _floordiv(self, other, op): # rather _ffloordiv?
1059 '''Apply C{B{self} //= B{other}}.
1060 '''
1061 q = self._ftruediv(other, op) # == self
1062 return self._fset(q.floor, asis=True) # floor(q)
1064 fmul = __imul__ # for backward compatibility
1066 def _fmul(self, other, op):
1067 '''(INTERNAL) Apply C{B{self} *= B{other}}.
1068 '''
1069 if isscalar(other):
1070 f = self._mul_scalar(other, op)
1071 elif not isinstance(other, Fsum):
1072 raise self._TypeError(op, other) # txt=_invalid_
1073 elif len(self._ps) != 1:
1074 f = self._mul_Fsum(other, op)
1075 elif len(other._ps) != 1: # len(self._ps) == 1
1076 f = other._copy_up()._mul_scalar(self._ps[0], op)
1077 else: # len(other._ps) == len(self._ps) == 1
1078 s = self._finite(self._ps[0] * other._ps[0])
1079 return self._fset(s, asis=True, n=len(self) + 1)
1080 return self._fset(f)
1082 def fover(self, over):
1083 '''Apply C{B{self} /= B{over}} and summate.
1085 @arg over: An L{Fsum} or C{scalar} denominator.
1087 @return: Precision running sum (C{float}).
1089 @see: Methods L{Fsum.fsum} and L{Fsum.__itruediv__}.
1090 '''
1091 return float(self.fdiv(over)._fprs)
1093 fpow = __ipow__ # for backward compatibility
1095 def _fpow(self, other, op, *mod):
1096 '''Apply C{B{self} **= B{other}}, optional B{C{mod}} or C{None}.
1097 '''
1098 if mod and mod[0] is not None: # == 3-arg C{pow}
1099 s = self._pow_3(other, mod[0], op)
1100 elif mod and mod[0] is None and self.is_integer():
1101 # return an exact C{int} for C{int}**C{int}
1102 i = self._copy_0(self._fint2[0]) # assert _fint2[1] == 0
1103 x = _2scalar(other) # C{int}, C{float} or other
1104 s = i._pow_2(x, other, op) if isscalar(x) else i._fpow(x, op)
1105 else: # pow(self, other) == pow(self, other, None)
1106 p = None
1107 if isinstance(other, Fsum):
1108 x, r = other._fprs2
1109 if r:
1110 if self._raiser(r, x):
1111 raise self._ResidualError(op, other, r)
1112 p = self._pow_scalar(r, other, op)
1113# p = _2scalar(p) # _raiser = None
1114 elif not isscalar(other):
1115 raise self._TypeError(op, other) # txt=_invalid_
1116 else:
1117 x = self._finite(other, op)
1118 s = self._pow_scalar(x, other, op)
1119 if p is not None:
1120 s *= p
1121 return self._fset(s, asis=isint(s), n=max(len(self), 1))
1123 @Property_RO
1124 def _fprs(self):
1125 '''(INTERNAL) Get and cache this instance' precision
1126 running sum (C{float} or C{int}), ignoring C{residual}.
1128 @note: The precision running C{fsum} after a C{//=} or
1129 C{//} C{floor} division is C{int} in Python 3+.
1130 '''
1131 ps = self._ps
1132 n = len(ps) - 1
1133 if n > 1:
1134 s = _psum(ps)
1135 elif n > 0: # len(ps) == 2
1136 s, p = _2sum(*ps) if ps[1] else ps
1137 ps[:] = ([p, s] if s else [p]) if p else [s]
1138 elif n < 0: # see L{Fsum.__init__}
1139 s = _0_0
1140 ps[:] = [s]
1141 else: # len(ps) == 1
1142 s = ps[0]
1143 # assert self._ps is ps
1144 # assert Fsum._fprs2.name not in self.__dict__
1145 return s
1147 @Property_RO
1148 def _fprs2(self):
1149 '''(INTERNAL) Get and cache this instance' precision
1150 running sum and residual (L{Fsum2Tuple}).
1151 '''
1152 s = self._fprs
1153 r = _fsum(self._ps_1(s)) if len(self._ps) > 1 else INT0
1154 return Fsum2Tuple(s, r) # name=Fsum.fsum2.__name__
1156# def _fpsqz(self):
1157# '''(INTERNAL) Compress, squeeze the C{partials}.
1158# '''
1159# if len(self._ps) > 2:
1160# _ = self._fprs
1161# return self
1163 def _fset(self, other, asis=False, n=1):
1164 '''(INTERNAL) Overwrite this instance with an other or a C{scalar}.
1165 '''
1166 if other is self:
1167 pass # from ._fmul, ._ftruediv and ._pow_scalar
1168 elif isinstance(other, Fsum):
1169 self._n = other._n
1170 self._ps[:] = other._ps
1171 self._copy_RESIDUAL(other)
1172 # use or zap the C{Property_RO} values
1173 Fsum._fint2._update_from(self, other)
1174 Fsum._fprs ._update_from(self, other)
1175 Fsum._fprs2._update_from(self, other)
1176 elif isscalar(other):
1177 s = other if asis else float(other)
1178 i = int(s) # see ._fint2
1179 t = i, ((s - i) or INT0)
1180 self._n = n
1181 self._ps[:] = [s]
1182 # Property_RO _fint2, _fprs and _fprs2 can't be a Property:
1183 # Property's _fset zaps the value just set by the @setter
1184 self.__dict__.update(_fint2=t, _fprs=s, _fprs2=Fsum2Tuple(s, INT0))
1185 else: # PYCHOK no cover
1186 raise self._TypeError(_fset_op_, other) # txt=_invalid_
1187 return self
1189 def fsub(self, xs=()):
1190 '''Subtract an iterable of C{scalar} or L{Fsum} instances
1191 from this instance.
1193 @arg xs: Iterable, list, tuple. etc. (C{scalar}
1194 or L{Fsum} instances).
1196 @return: This instance, updated (L{Fsum}).
1198 @see: Method L{Fsum.fadd}.
1199 '''
1200 return self._facc(_2floats(xs, sub=True)) if xs else self # PYCHOK yield
1202 def fsub_(self, *xs):
1203 '''Subtract all positional C{scalar} or L{Fsum} instances
1204 from this instance.
1206 @arg xs: Values to subtract (C{scalar} or
1207 L{Fsum} instances), all positional.
1209 @return: This instance, updated (L{Fsum}).
1211 @see: Method L{Fsum.fadd}.
1212 '''
1213 return self._facc(_2floats(xs, origin=1, sub=True)) if xs else self # PYCHOK yield
1215 def _fsub(self, other, op):
1216 '''(INTERNAL) Apply C{B{self} -= B{other}}.
1217 '''
1218 if isinstance(other, Fsum):
1219 if other is self: # or other._fprs2 == self._fprs2:
1220 self._fset(_0_0, asis=True, n=len(self) * 2) # self -= self
1221 elif other._ps:
1222 self._facc(other._ps_n())
1223 elif not isscalar(other):
1224 raise self._TypeError(op, other) # txt=_invalid_
1225 elif self._finite(other, op):
1226 self._facc_(-other)
1227 return self
1229 def _Fsum(self, n, *ps):
1230 '''(INTERNAL) New L{Fsum} instance.
1231 '''
1232 f = Fsum()
1233 f._n = n
1234 if ps:
1235 f._ps[:] = ps
1236 f._copy_RESIDUAL(self)
1237 return f
1239 def fsum(self, xs=()):
1240 '''Add more C{scalar} or L{Fsum} instances and summate.
1242 @kwarg xs: Iterable, list, tuple, etc. (C{scalar} or
1243 L{Fsum} instances).
1245 @return: Precision running sum (C{float} or C{int}).
1247 @see: Method L{Fsum.fadd}.
1249 @note: Accumulation can continue after summation.
1250 '''
1251 f = self._facc(_2floats(xs)) if xs else self # PYCHOK yield
1252 return f._fprs
1254 def fsum_(self, *xs):
1255 '''Add all positional C{scalar} or L{Fsum} instances and summate.
1257 @arg xs: Values to add (C{scalar} or L{Fsum} instances),
1258 all positional.
1260 @return: Precision running sum (C{float} or C{int}).
1262 @see: Methods L{Fsum.fsum} and L{Fsum.fsumf_}.
1263 '''
1264 f = self._facc(_2floats(xs, origin=1)) if xs else self # PYCHOK yield
1265 return f._fprs
1267 def fsum2(self, xs=(), **name):
1268 '''Add more C{scalar} or L{Fsum} instances and return the
1269 current precision running sum and the C{residual}.
1271 @kwarg xs: Iterable, list, tuple, etc. (C{scalar} or
1272 L{Fsum} instances).
1273 @kwarg name: Optional name (C{str}).
1275 @return: L{Fsum2Tuple}C{(fsum, residual)} with C{fsum} the
1276 current precision running sum and C{residual}, the
1277 (precision) sum of the remaining C{partials}. The
1278 C{residual is INT0} if the C{fsum} is considered
1279 to be I{exact}.
1281 @see: Methods L{Fsum.fint2}, L{Fsum.fsum} and L{Fsum.fsum2_}
1282 '''
1283 f = self._facc(_2floats(xs)) if xs else self # PYCHOK yield
1284 t = f._fprs2
1285 if name:
1286 t = t.dup(name=_xkwds_get(name, name=NN))
1287 return t
1289 def fsum2_(self, *xs):
1290 '''Add any positional C{scalar} or L{Fsum} instances and return
1291 the precision running sum and the C{differential}.
1293 @arg xs: Values to add (C{scalar} or L{Fsum} instances),
1294 all positional.
1296 @return: 2-Tuple C{(fsum, delta)} with the current precision
1297 running C{fsum} and C{delta}, the difference with
1298 the previous running C{fsum} (C{float}s).
1300 @see: Methods L{Fsum.fsum_} and L{Fsum.fsum}.
1301 '''
1302 p, r = self._fprs2
1303 if xs:
1304 s, t = self._facc(_2floats(xs, origin=1))._fprs2 # PYCHOK yield
1305 return s, _fsum((s, -p, r, -t)) # ((s - p) + (r - t))
1306 else: # PYCHOK no cover
1307 return p, _0_0
1309 def fsumf_(self, *xs):
1310 '''Like method L{Fsum.fsum_} but only for known C{float B{xs}}.
1311 '''
1312 f = self._facc(xs) if xs else self # PYCHOK yield
1313 return f._fprs
1315# ftruediv = __itruediv__ # for naming consistency
1317 def _ftruediv(self, other, op):
1318 '''(INTERNAL) Apply C{B{self} /= B{other}}.
1319 '''
1320 n = _1_0
1321 if isinstance(other, Fsum):
1322 if other is self or other._fprs2 == self._fprs2:
1323 return self._fset(_1_0, asis=True, n=len(self))
1324 d, r = other._fprs2
1325 if r:
1326 if not d: # PYCHOK no cover
1327 d = r
1328 elif self._raiser(r, d):
1329 raise self._ResidualError(op, other, r)
1330 else:
1331 d, n = other.as_integer_ratio()
1332 elif isscalar(other):
1333 d = other
1334 else: # PYCHOK no cover
1335 raise self._TypeError(op, other) # txt=_invalid_
1336 try:
1337 s = 0 if isinf(d) else (
1338 d if isnan(d) else self._finite(n / d))
1339 except Exception as x:
1340 E, t = _xError2(x)
1341 raise self._Error(op, other, E, txt=t)
1342 f = self._mul_scalar(s, _mul_op_) # handles 0, NAN, etc.
1343 return self._fset(f)
1345 @property_RO
1346 def imag(self):
1347 '''Get the C{imaginary} part of this instance (C{0.0}, always).
1349 @see: Properties L{Fsum.ceil}, L{Fsum.floor} and L{Fsum.real}.
1350 '''
1351 return _0_0
1353 def int_float(self, raiser=False):
1354 '''Return this instance' current running sum as C{int} or C{float}.
1356 @kwarg raiser: If C{True} throw a L{ResidualError} if the
1357 residual is non-zero.
1359 @return: This C{integer} sum if this instance C{is_integer},
1360 otherwise return the C{float} sum if the residual
1361 is zero or if C{B{raiser}=False}.
1363 @raise ResidualError: Non-zero residual and C{B{raiser}=True}.
1365 @see: Methods L{Fsum.fint} and L{Fsum.fint2}.
1366 '''
1367 s, r = self._fint2
1368 if r:
1369 s, r = self._fprs2
1370 if r and raiser: # PYCHOK no cover
1371 t = _stresidual(_non_zero_, r)
1372 raise ResidualError(int_float=s, txt=t)
1373 s = float(s) # redundant
1374 return s
1376 def is_exact(self):
1377 '''Is this instance' current running C{fsum} considered to
1378 be exact? (C{bool}).
1379 '''
1380 return self.residual is INT0
1382 def is_integer(self):
1383 '''Is this instance' current running sum C{integer}? (C{bool}).
1385 @see: Methods L{Fsum.fint} and L{Fsum.fint2}.
1386 '''
1387 _, r = self._fint2
1388 return False if r else True
1390 def is_math_fsum(self):
1391 '''Return whether functions L{fsum}, L{fsum_}, L{fsum1}
1392 and L{fsum1_} plus partials summation are based on
1393 Python's C{math.fsum} or not.
1395 @return: C{2} if all functions and partials summation
1396 are based on C{math.fsum}, C{True} if only
1397 the functions are based on C{math.fsum} (and
1398 partials summation is not) or C{False} if
1399 none are.
1400 '''
1401 f = Fsum._math_fsum
1402 return 2 if _psum is f else bool(f)
1404 def _mul_Fsum(self, other, op=_mul_op_):
1405 '''(INTERNAL) Return C{B{self} * Fsum B{other}} as L{Fsum}.
1406 '''
1407 # assert isinstance(other, Fsum)
1408 return self._copy_0()._facc(self._ps_x(op, *other._ps), up=False)
1410 def _mul_scalar(self, factor, op):
1411 '''(INTERNAL) Return C{B{self} * scalar B{factor}} as L{Fsum} or C{0}.
1412 '''
1413 # assert isscalar(factor)
1414 if self._finite(factor, op) and self._ps:
1415 if factor == _1_0:
1416 return self
1417 f = self._copy_0()._facc(self._ps_x(op, factor), up=False)
1418 else:
1419 f = self._copy_0(_0_0)
1420 return f
1422 @property_RO
1423 def partials(self):
1424 '''Get this instance' current partial sums (C{tuple} of C{float}s and/or C{int}s).
1425 '''
1426 return tuple(self._ps)
1428 def pow(self, x, *mod):
1429 '''Return C{B{self}**B{x}} as L{Fsum}.
1431 @arg x: The exponent (L{Fsum} or C{scalar}).
1432 @arg mod: Optional modulus (C{int} or C{None}) for the 3-argument
1433 C{pow(B{self}, B{other}, B{mod})} version.
1435 @return: The C{pow(self, B{x})} or C{pow(self, B{x}, *B{mod})}
1436 result (L{Fsum}).
1438 @note: If B{C{mod}} is given as C{None}, the result will be an
1439 C{integer} L{Fsum} provided this instance C{is_integer}
1440 or set C{integer} with L{Fsum.fint}.
1442 @see: Methods L{Fsum.__ipow__}, L{Fsum.fint} and L{Fsum.is_integer}.
1443 '''
1444 f = self._copy_2(self.pow)
1445 if f and isint(x) and x >= 0 and not mod:
1446 f._pow_int(x, x, _pow_op_) # f **= x
1447 else:
1448 f._fpow(x, _pow_op_, *mod) # f = pow(f, x, *mod)
1449 return f
1451 def _pow_0_1(self, x, other):
1452 '''(INTERNAL) Return B{C{self}**1} or C{B{self}**0 == 1.0}.
1453 '''
1454 return self if x else (1 if self.is_integer() and isint(other) else _1_0)
1456 def _pow_2(self, x, other, op):
1457 '''(INTERNAL) 2-arg C{pow(B{self}, scalar B{x})} embellishing errors.
1458 '''
1459 # assert len(self._ps) == 1 and isscalar(x)
1460 b = self._ps[0] # assert isscalar(b)
1461 try: # type(s) == type(x) if x in (_1_0, 1)
1462 s = pow(b, x) # -1**2.3 == -(1**2.3)
1463 if not iscomplex(s):
1464 return self._finite(s) # 0**INF == 0.0, 1**INF==1.0
1465 # neg**frac == complex in Python 3+, but ValueError in 2-
1466 E, t = _ValueError, _strcomplex(s, b, x) # PYCHOK no cover
1467 except Exception as x:
1468 E, t = _xError2(x)
1469 raise self._Error(op, other, E, txt=t)
1471 def _pow_3(self, other, mod, op):
1472 '''(INTERNAL) 3-arg C{pow(B{self}, B{other}, int B{mod} or C{None})}.
1473 '''
1474 b, r = self._fprs2 if mod is None else self._fint2
1475 if r and self._raiser(r, b):
1476 t = _non_zero_ if mod is None else _integer_
1477 E, t = ResidualError, _stresidual(t, r, mod=mod)
1478 else:
1479 try: # b, other, mod all C{int}, unless C{mod} is C{None}
1480 x = _2scalar(other, _raiser=self._raiser)
1481 s = pow(b, x, mod)
1482 if not iscomplex(s):
1483 return self._finite(s)
1484 # neg**frac == complex in Python 3+, but ValueError in 2-
1485 E, t = _ValueError, _strcomplex(s, b, x, mod) # PYCHOK no cover
1486 except Exception as x:
1487 E, t = _xError2(x)
1488 t = _COMMASPACE_(Fmt.PARENSPACED(mod=mod), t)
1489 raise self._Error(op, other, E, txt=t)
1491 def _pow_int(self, x, other, op):
1492 '''(INTERNAL) Return C{B{self} **= B{x}} for C{int B{x} >= 0}.
1493 '''
1494 # assert isint(x) and x >= 0
1495 if len(self._ps) > 1:
1496 if x > 2:
1497 p = self._copy_up()
1498 m = 1 # single-bit mask
1499 if x & m:
1500 x -= m # x ^= m
1501 f = p._copy_up()
1502 else:
1503 f = self._copy_0(_1_0)
1504 while x:
1505 p = p._mul_Fsum(p, op) # p **= 2
1506 m += m # m <<= 1
1507 if x & m:
1508 x -= m # x ^= m
1509 f = f._mul_Fsum(p, op) # f *= p
1510 elif x > 1: # self**2
1511 f = self._mul_Fsum(self, op)
1512 else: # self**1 or self**0
1513 f = self._pow_0_1(x, other)
1514 elif self._ps: # self._ps[0]**x
1515 f = self._pow_2(x, other, op)
1516 else: # PYCHOK no cover
1517 # 0**pos_int == 0, but 0**0 == 1
1518 f = 0 if x else 1 # like ._fprs
1519 return self._fset(f, asis=isint(f), n=len(self))
1521 def _pow_scalar(self, x, other, op):
1522 '''(INTERNAL) Return C{self**B{x}} for C{scalar B{x}}.
1523 '''
1524 s, r = self._fprs2
1525 if isint(x, both=True):
1526 x = int(x) # Fsum**int
1527 y = abs(x)
1528 if y > 1:
1529 if r:
1530 f = self._copy_up()._pow_int(y, other, op)
1531 if x > 0: # > 1
1532 return f
1533 # assert x < 0 # < -1
1534 s, r = f._fprs2
1535 if r:
1536 return self._copy_0(_1_0)._ftruediv(f, op)
1537 # use **= -1 for the CPython float_pow
1538 # error if s is zero, and not s = 1 / s
1539 x = -1
1540# elif y > 1: # self**2 or self**-2
1541# f = self._mul_Fsum(self, op)
1542# if x < 0:
1543# f = f._copy_0(_1_0)._ftruediv(f, op)
1544# return f
1545 elif x < 0: # self**-1 == 1 / self
1546 if r:
1547 return self._copy_0(_1_0)._ftruediv(self, op)
1548 else: # self**1 or self**0
1549 return self._pow_0_1(x, other) # self or 0.0
1550 elif not isscalar(x): # assert ...
1551 raise self._TypeError(op, other, txt=_not_scalar_)
1552 elif r and self._raiser(r, s): # non-zero residual**fractional
1553 # raise self._ResidualError(op, other, r, fractional_power=x)
1554 t = _stresidual(_non_zero_, r, fractional_power=x)
1555 raise self._Error(op, other, ResidualError, txt=t)
1556 # assert isscalar(s) and isscalar(x)
1557 return self._copy_0(s)._pow_2(x, other, op)
1559 def _ps_1(self, *less):
1560 '''(INTERNAL) Yield partials, 1-primed and subtract any C{less}.
1561 '''
1562 yield _1_0
1563 for p in self._ps:
1564 if p:
1565 yield p
1566 for p in less:
1567 if p:
1568 yield -p
1569 yield _N_1_0
1571 def _ps_n(self):
1572 '''(INTERNAL) Yield partials, negated.
1573 '''
1574 for p in self._ps:
1575 if p:
1576 yield -p
1578 def _ps_x(self, op, *factors): # see .fmath.Fhorner
1579 '''(INTERNAL) Yield all C{partials} times each B{C{factor}},
1580 in total, up to C{len(partials) * len(factors)} items.
1581 '''
1582 ps = self._ps
1583 if len(ps) < len(factors):
1584 ps, factors = factors, ps
1585 _f = _isfinite
1586 for f in factors:
1587 for p in ps:
1588 p *= f
1589 if _f(p):
1590 yield p
1591 else: # PYCHOK no cover
1592 self._finite(p, op) # throw ValueError
1594 @property_RO
1595 def real(self):
1596 '''Get the C{real} part of this instance (C{float}).
1598 @see: Methods L{Fsum.__float__} and L{Fsum.fsum}
1599 and properties L{Fsum.ceil}, L{Fsum.floor},
1600 L{Fsum.imag} and L{Fsum.residual}.
1601 '''
1602 return float(self._fprs)
1604 @property_RO
1605 def residual(self):
1606 '''Get this instance' residual (C{float} or C{int}), the
1607 C{sum(partials)} less the precision running sum C{fsum}.
1609 @note: If the C{residual is INT0}, the precision running
1610 C{fsum} is considered to be I{exact}.
1612 @see: Methods L{Fsum.fsum}, L{Fsum.fsum2} and L{Fsum.is_exact}.
1613 '''
1614 return self._fprs2.residual
1616 def _raiser(self, r, s):
1617 '''(INTERNAL) Does the ratio C{r / s} exceed threshold?
1618 '''
1619 self._ratio = t = fabs((r / s) if s else r)
1620 return t > self._RESIDUAL
1622 def RESIDUAL(self, *threshold):
1623 '''Get and set this instance' I{ratio} for raising L{ResidualError}s,
1624 overriding the default from env variable C{PYGEODESY_FSUM_RESIDUAL}.
1626 @arg threshold: If C{scalar}, the I{ratio} to exceed for raising
1627 L{ResidualError}s in division and exponention, if
1628 C{None} restore the default set with env variable
1629 C{PYGEODESY_FSUM_RESIDUAL} or if omitted, keep the
1630 current setting.
1632 @return: The previous C{RESIDUAL} setting (C{float}).
1634 @raise ValueError: Negative B{C{threshold}}.
1636 @note: A L{ResidualError} is thrown if the non-zero I{ratio}
1637 C{residual} / C{fsum} exceeds the B{C{threshold}}.
1638 '''
1639 r = self._RESIDUAL
1640 if threshold:
1641 t = threshold[0]
1642 t = Fsum._RESIDUAL if t is None else (
1643 float(t) if isscalar(t) else ( # for backward ...
1644 _0_0 if bool(t) else _1_0)) # ... compatibility
1645 if t < 0:
1646 u = self._unstr(self.RESIDUAL, *threshold)
1647 raise _ValueError(u, RESIDUAL=t, txt=_negative_)
1648 self._RESIDUAL = t
1649 return r
1651 def _ResidualError(self, op, other, residual):
1652 '''(INTERNAL) Non-zero B{C{residual}} etc.
1653 '''
1654 t = _stresidual(_non_zero_, residual, ratio=self._ratio,
1655 RESIDUAL=self._RESIDUAL)
1656 t = t.replace(_COMMASPACE_R_, _exceeds_R_)
1657 return self._Error(op, other, ResidualError, txt=t)
1659 def signOf(self, res=True):
1660 '''Determine the sign of this instance.
1662 @kwarg res: If C{True} consider, otherwise
1663 ignore the residual (C{bool}).
1665 @return: The sign (C{int}, -1, 0 or +1).
1666 '''
1667 s, r = self._fprs2 if res else (self._fprs, 0)
1668 return _signOf(s, -r)
1670 def toRepr(self, **prec_sep_fmt_lenc): # PYCHOK signature
1671 '''Return this C{Fsum} instance as representation.
1673 @kwarg prec_sep_fmt_lenc: Optional keyword arguments for
1674 method L{Fsum2Tuple.toRepr} plus C{B{lenc}=True}
1675 (C{bool}) to in-/exclude the current C{[len]}
1676 of this L{Fsum} enclosed in I{[brackets]}.
1678 @return: This instance (C{repr}).
1679 '''
1680 return self._toT(self._fprs2.toRepr, **prec_sep_fmt_lenc)
1682 def toStr(self, **prec_sep_fmt_lenc): # PYCHOK signature
1683 '''Return this C{Fsum} instance as string.
1685 @kwarg prec_sep_fmt_lenc: Optional keyword arguments for
1686 method L{Fsum2Tuple.toStr} plus C{B{lenc}=True}
1687 (C{bool}) to in-/exclude the current C{[len]}
1688 of this L{Fsum} enclosed in I{[brackets]}.
1690 @return: This instance (C{str}).
1691 '''
1692 return self._toT(self._fprs2.toStr, **prec_sep_fmt_lenc)
1694 def _toT(self, toT, fmt=Fmt.g, lenc=True, **kwds):
1695 '''(INTERNAL) Helper for C{toRepr} and C{toStr}.
1696 '''
1697 n = self.named3
1698 if lenc:
1699 n = Fmt.SQUARE(n, len(self))
1700 return _SPACE_(n, toT(fmt=fmt, **kwds))
1702 def _TypeError(self, op, other, **txt): # PYCHOK no cover
1703 '''(INTERNAL) Return a C{TypeError}.
1704 '''
1705 return self._Error(op, other, _TypeError, **txt)
1707 def _update(self): # see ._fset
1708 '''(INTERNAL) Zap all cached C{Property_RO} values.
1709 '''
1710 Fsum._fint2._update(self)
1711 Fsum._fprs ._update(self)
1712 Fsum._fprs2._update(self)
1713 return self
1715 def _ValueError(self, op, other, **txt): # PYCHOK no cover
1716 '''(INTERNAL) Return a C{ValueError}.
1717 '''
1718 return self._Error(op, other, _ValueError, **txt)
1720 def _ZeroDivisionError(self, op, other, **txt): # PYCHOK no cover
1721 '''(INTERNAL) Return a C{ZeroDivisionError}.
1722 '''
1723 return self._Error(op, other, _ZeroDivisionError, **txt)
1725_allPropertiesOf_n(3, Fsum, Property_RO) # PYCHOK assert, see Fsum._fset, -._update
1728def _Float_Int(arg, **name_Error):
1729 '''(INTERNAL) Unit of L{Fsum2Tuple} items.
1730 '''
1731 U = Int if isint(arg) else Float
1732 return U(arg, **name_Error)
1735class Fsum2Tuple(_NamedTuple):
1736 '''2-Tuple C{(fsum, residual)} with the precision running C{fsum}
1737 and the C{residual}, the sum of the remaining partials. Each
1738 item is either C{float} or C{int}.
1740 @note: If the C{residual is INT0}, the C{fsum} is considered
1741 to be I{exact}, see method L{Fsum2Tuple.is_exact}.
1742 '''
1743 _Names_ = ( Fsum.fsum.__name__, Fsum.residual.name)
1744 _Units_ = (_Float_Int, _Float_Int)
1746 @Property_RO
1747 def Fsum(self):
1748 '''Get this L{Fsum2Tuple} as an L{Fsum}.
1749 '''
1750 f = Fsum(name=self.name)
1751 return f._copy_0(*(s for s in reversed(self) if s))
1753 def is_exact(self):
1754 '''Is this L{Fsum2Tuple} considered to be exact? (C{bool}).
1755 '''
1756 return self.Fsum.is_exact()
1758 def is_integer(self):
1759 '''Is this L{Fsum2Tuple} C{integer}? (C{bool}).
1760 '''
1761 return self.Fsum.is_integer()
1764class ResidualError(_ValueError):
1765 '''Error raised for an operation involving a L{pygeodesy.sums.Fsum}
1766 instance with a non-zero C{residual}, I{integer} or otherwise.
1768 @see: Module L{pygeodesy.fsums} and method L{Fsum.RESIDUAL}.
1769 '''
1770 pass
1773try:
1774 from math import fsum as _fsum # precision IEEE-754 sum, Python 2.6+
1776 # make sure _fsum works as expected (XXX check
1777 # float.__getformat__('float')[:4] == 'IEEE'?)
1778 if _fsum((1, 1e101, 1, -1e101)) != 2: # PYCHOK no cover
1779 del _fsum # nope, remove _fsum ...
1780 raise ImportError # ... use _fsum below
1782 Fsum._math_fsum = _sum = _fsum # PYCHOK exported
1784 if _getenv('PYGEODESY_FSUM_PARTIALS', _fsum.__name__) == _fsum.__name__:
1785 _psum = _fsum # PYCHOK redef
1787except ImportError:
1788 _sum = sum # Fsum(NAN) exception fall-back
1790 def _fsum(xs):
1791 '''(INTERNAL) Precision summation, Python 2.5-.
1792 '''
1793 return Fsum(name=_fsum.__name__)._facc(xs, up=False)._fprs
1796def fsum(xs, floats=False):
1797 '''Precision floating point summation based on or like Python's C{math.fsum}.
1799 @arg xs: Iterable, list, tuple, etc. of values (C{scalar} or
1800 L{Fsum} instances).
1801 @kwarg floats: Optionally, use C{B{floats}=True} iff I{all}
1802 B{C{xs}} are known to be C{float}.
1804 @return: Precision C{fsum} (C{float}).
1806 @raise OverflowError: Partial C{2sum} overflow.
1808 @raise TypeError: Non-scalar B{C{xs}} value.
1810 @raise ValueError: Invalid or non-finite B{C{xs}} value.
1812 @note: Exceptions and I{non-finite} handling may differ if not
1813 based on Python's C{math.fsum}.
1815 @see: Class L{Fsum} and methods L{Fsum.fsum} and L{Fsum.fadd}.
1816 '''
1817 return _fsum(xs if floats else _2floats(xs)) if xs else _0_0 # PYCHOK yield
1820def fsum_(*xs, **floats):
1821 '''Precision floating point summation of all positional arguments.
1823 @arg xs: Values to be added (C{scalar} or L{Fsum} instances),
1824 all positional.
1825 @kwarg floats: Optionally, use C{B{floats}=True} iff I{all}
1826 B{C{xs}} are known to be C{float}.
1828 @return: Precision C{fsum} (C{float}).
1830 @see: Function C{fsum}.
1831 '''
1832 return _fsum(xs if _xkwds_get(floats, floats=False) else
1833 _2floats(xs, origin=1)) if xs else _0_0 # PYCHOK yield
1836def fsumf_(*xs):
1837 '''Precision floating point summation L{fsum_}C{(*xs, floats=True)}.
1838 '''
1839 return _fsum(xs) if xs else _0_0
1842def fsum1(xs, floats=False):
1843 '''Precision floating point summation of a few arguments, 1-primed.
1845 @arg xs: Iterable, list, tuple, etc. of values (C{scalar} or
1846 L{Fsum} instances).
1847 @kwarg floats: Optionally, use C{B{floats}=True} iff I{all}
1848 B{C{xs}} are known to be C{float}.
1850 @return: Precision C{fsum} (C{float}).
1852 @see: Function C{fsum}.
1853 '''
1854 return _fsum(_1primed(xs if floats else _2floats(xs))) if xs else _0_0 # PYCHOK yield
1857def fsum1_(*xs, **floats):
1858 '''Precision floating point summation of a few arguments, 1-primed.
1860 @arg xs: Values to be added (C{scalar} or L{Fsum} instances),
1861 all positional.
1862 @kwarg floats: Optionally, use C{B{floats}=True} iff I{all}
1863 B{C{xs}} are known to be C{float}.
1865 @return: Precision C{fsum} (C{float}).
1867 @see: Function C{fsum}
1868 '''
1869 return _fsum(_1primed(xs if _xkwds_get(floats, floats=False) else
1870 _2floats(xs, origin=1))) if xs else _0_0 # PYCHOK yield
1873def fsum1f_(*xs):
1874 '''Precision floating point summation L{fsum1_}C{(*xs, floats=True)}.
1875 '''
1876 return _fsum(_1primed(xs)) if xs else _0_0
1879# **) MIT License
1880#
1881# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.
1882#
1883# Permission is hereby granted, free of charge, to any person obtaining a
1884# copy of this software and associated documentation files (the "Software"),
1885# to deal in the Software without restriction, including without limitation
1886# the rights to use, copy, modify, merge, publish, distribute, sublicense,
1887# and/or sell copies of the Software, and to permit persons to whom the
1888# Software is furnished to do so, subject to the following conditions:
1889#
1890# The above copyright notice and this permission notice shall be included
1891# in all copies or substantial portions of the Software.
1892#
1893# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
1894# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
1895# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
1896# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
1897# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
1898# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
1899# OTHER DEALINGS IN THE SOFTWARE.