Coverage for pygeodesy/fsums.py: 95%
700 statements
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« prev ^ index » next coverage.py v7.2.2, created at 2023-05-20 11:54 -0400
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, map1, signOf, _signOf
30from pygeodesy.constants import INT0, _isfinite, isinf, isnan, \
31 _0_0, _1_0, _N_1_0
32from pygeodesy.errors import itemsorted, _OverflowError, _TypeError, \
33 _ValueError, _xError2, _xkwds_get, _xkwds_get_, \
34 _ZeroDivisionError
35from pygeodesy.interns import NN, _arg_, _COMMASPACE_, _DASH_, _EQUAL_, \
36 _exceeds_, _from_, _iadd_, _LANGLE_, _negative_, \
37 _NOTEQUAL_, _not_finite_, _not_scalar_, \
38 _PERCENT_, _PLUS_, _R_, _RANGLE_, _SLASH_, \
39 _SPACE_, _STAR_, _UNDER_
40from pygeodesy.lazily import _ALL_LAZY, _getenv, _sys, _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
45from pygeodesy.units import Float, Int
47from math import ceil as _ceil, fabs, floor as _floor # PYCHOK used! .ltp
49__all__ = _ALL_LAZY.fsums
50__version__ = '23.05.18'
52_add_op_ = _PLUS_
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_
69_truediv_op_ = _SLASH_
70_divmod_op_ = _floordiv_op_ + _mod_op_
72_pos_self = _1_0.__pos__() is _1_0 # in .vector3dBase
75def _2float(index=None, **name_value): # in .fmath, .fstats
76 '''(INTERNAL) Raise C{TypeError} or C{ValueError} if not scalar or infinite.
77 '''
78 n, v = name_value.popitem() # _xkwds_popitem(name_value)
79 try:
80 v = float(v)
81 if _isfinite(v):
82 return v
83 E, t = _ValueError, _not_finite_
84 except Exception as e:
85 E, t = _xError2(e)
86 if index is not None:
87 n = Fmt.SQUARE(n, index)
88 raise E(n, v, txt=t)
91def _2floats(xs, origin=0, sub=False):
92 '''(INTERNAL) Yield each B{C{xs}} as a C{float}.
93 '''
94 try:
95 i, x = origin, None
96 _fin = _isfinite
97 _Fsum = Fsum
98 for x in xs:
99 if isinstance(x, _Fsum):
100 for p in x._ps:
101 yield (-p) if sub else p
102 else:
103 f = float(x)
104 if not _fin(f):
105 raise ValueError(_not_finite_)
106 if f:
107 yield (-f) if sub else f
108 i += 1
109 except Exception as e:
110 E, t = _xError2(e)
111 n = Fmt.SQUARE(xs=i)
112 raise E(n, x, txt=t)
115def _Powers(power, xs, origin=1): # in .fmath
116 '''(INTERNAL) Yield each C{xs} as C{float(x**power)}.
117 '''
118 if not isscalar(power):
119 raise _TypeError(power=power)
120 try:
121 i, x = origin, None
122 _fin = _isfinite
123 _Fsum = Fsum
124 _pow = pow # XXX math.pow
125 for x in xs:
126 if isinstance(x, _Fsum):
127 P = x.pow(power)
128 for p in P._ps:
129 yield p
130 else:
131 p = _pow(float(x), power)
132 if not _fin(p):
133 raise ValueError(_not_finite_)
134 yield p
135 i += 1
136 except Exception as e:
137 E, t = _xError2(e)
138 n = Fmt.SQUARE(xs=i)
139 raise E(n, x, txt=t)
142def _1primed(xs):
143 '''(INTERNAL) 1-Prime the summation of C{xs}
144 arguments I{known} to be C{finite float}.
145 '''
146 yield _1_0
147 for x in xs:
148 if x:
149 yield x
150 yield _N_1_0
153def _psum(ps): # PYCHOK used!
154 '''(INTERNAL) Partials summation updating C{ps}, I{overridden below}.
155 '''
156 i = len(ps) - 1 # len(ps) > 2
157 s = ps[i]
158 _2s = _2sum
159 while i > 0:
160 i -= 1
161 s, r = _2s(s, ps[i])
162 if r: # sum(ps) became inexact
163 ps[i:] = [s, r] if s else [r]
164 if i > 0:
165 p = ps[i-1] # round half-even
166 if (p > 0 and r > 0) or \
167 (p < 0 and r < 0): # signs match
168 r *= 2
169 t = s + r
170 if r == (t - s):
171 s = t
172 break
173 ps[i:] = [s]
174 return s
177def _2scalar(other, _raiser=None):
178 '''(INTERNAL) Return B{C{other}} as C{int}, C{float} or C{as-is}.
179 '''
180 if isinstance(other, Fsum):
181 s, r = other._fint2
182 if r:
183 s, r = other._fprs2
184 if r: # PYCHOK no cover
185 if _raiser and _raiser(r, s):
186 raise ValueError(_stresidual(_non_zero_, r))
187 s = other # L{Fsum} as-is
188 else:
189 s = other # C{type} as-is
190 if isint(s, both=True):
191 s = int(s)
192 return s
195def _strcomplex(s, *args):
196 '''(INTERNAL) C{Complex} 2- or 3-arg C{pow} error C{str}.
197 '''
198 c = iscomplex.__name__[2:]
199 n = _DASH_(len(args), _arg_)
200 t = _SPACE_(c, s, _from_, n, pow.__name__)
201 return unstr(t, *args)
204def _stresidual(prefix, residual, **name_values):
205 '''(INTERNAL) Residual error C{str}.
206 '''
207 p = _SPACE_(prefix, Fsum.residual.name)
208 t = Fmt.PARENSPACED(p, Fmt(residual))
209 for n, v in itemsorted(name_values):
210 n = n.replace(_UNDER_, _SPACE_)
211 p = Fmt.PARENSPACED(n, Fmt(v))
212 t = _COMMASPACE_(t, p)
213 return t
216def _2sum(a, b): # by .testFmath
217 '''(INTERNAL) Return C{a + b} as 2-tuple (sum, residual).
218 '''
219 s = a + b
220 if not _isfinite(s):
221 u = unstr(_2sum.__name__, a, b)
222 t = Fmt.PARENSPACED(_not_finite_, s)
223 raise _OverflowError(u, txt=t)
224 r = (a - (s - b)) if fabs(a) < fabs(b) else \
225 (b - (s - a)) # fabs(a) >= fabs(b)
226 return s, r
229class Fsum(_Named): # sync __methods__ with .vector3dBase.Vector3dBase
230 '''Precision floating point I{running} summation.
232 Unlike Python's C{math.fsum}, this class accumulates values and provides intermediate,
233 I{running} precision floating point summation. Accumulation may continue after
234 intermediate, I{running} summuation.
236 @note: Accumulated values may be L{Fsum} or C{scalar} instances with C{scalar} meaning
237 type C{float}, C{int} or any C{type} convertible to a single C{float}, having
238 method C{__float__}.
240 @note: Handling of exceptions and C{inf}, C{INF}, C{nan} and C{NAN} differs from
241 Python's C{math.fsum}.
243 @see: U{Hettinger<https://GitHub.com/ActiveState/code/blob/master/recipes/Python/
244 393090_Binary_floating_point_summatiaccurate_full/recipe-393090.py>}, U{Kahan
245 <https://WikiPedia.org/wiki/Kahan_summation_algorithm>}, U{Klein
246 <https://Link.Springer.com/article/10.1007/s00607-005-0139-x>}, Python 2.6+
247 file I{Modules/mathmodule.c} and the issue log U{Full precision summation
248 <https://Bugs.Python.org/issue2819>}.
249 '''
250 _math_fsum = None
251 _n = 0
252# _ps = [] # partial sums
253# _px = 0
254 _ratio = None
255 _RESIDUAL = max(float(_getenv('PYGEODESY_FSUM_RESIDUAL', _0_0)), _0_0)
257 def __init__(self, *xs, **name_RESIDUAL):
258 '''New L{Fsum} for precision floating point I{running} summation.
260 @arg xs: No, one or more initial values (each C{scalar} or an
261 L{Fsum} instance).
262 @kwarg name_RESIDUAL: Optional C{B{name}=NN} for this L{Fsum}
263 (C{str}) and C{B{RESIDUAL}=None} for the
264 L{ResidualError} threshold.
266 @see: Methods L{Fsum.fadd} and L{Fsum.RESIDUAL}.
267 '''
268 if name_RESIDUAL:
269 n, r = _xkwds_get_(name_RESIDUAL, name=NN, RESIDUAL=None)
270 if n: # set name ...
271 self.name = n
272 if r is not None:
273 self.RESIDUAL(r) # ... for ResidualError
274# self._n = 0
275 self._ps = [] # [_0_0], see L{Fsum._fprs}
276 if len(xs) > 1:
277 self._facc(_2floats(xs, origin=1), up=False) # PYCHOK yield
278 elif xs: # len(xs) == 1
279 self._ps = [_2float(x=xs[0])]
280 self._n = 1
282 def __abs__(self):
283 '''Return this instance' absolute value as an L{Fsum}.
284 '''
285 s = _fsum(self._ps_1()) # == self._cmp_0(0, ...)
286 return self._copy_n(self.__abs__) if s < 0 else \
287 self._copy_2(self.__abs__)
289 def __add__(self, other):
290 '''Return the C{Fsum(B{self}, B{other})}.
292 @arg other: An L{Fsum} or C{scalar}.
294 @return: The sum (L{Fsum}).
296 @see: Method L{Fsum.__iadd__}.
297 '''
298 f = self._copy_2(self.__add__)
299 return f._fadd(other, _add_op_)
301 def __bool__(self): # PYCHOK not special in Python 2-
302 '''Return C{True} if this instance is non-zero.
303 '''
304 return self != 0
306 def __ceil__(self): # PYCHOK not special in Python 2-
307 '''Return this instance' C{math.ceil} as C{int} or C{float}.
309 @return: An C{int} in Python 3+, but C{float} in Python 2-.
311 @see: Methods L{Fsum.__floor__} and property L{Fsum.ceil}.
312 '''
313 return self.ceil
315 def __cmp__(self, other): # Python 2-
316 '''Compare this with an other instance or scalar.
318 @return: -1, 0 or +1 (C{int}).
320 @raise TypeError: Incompatible B{C{other}} C{type}.
321 '''
322 s = self._cmp_0(other, self.cmp.__name__)
323 return -1 if s < 0 else (+1 if s > 0 else 0)
325 cmp = __cmp__
327 def __divmod__(self, other):
328 '''Return C{divmod(B{self}, B{other})} as 2-tuple C{(quotient,
329 remainder)}, an C{int} in Python 3+ or C{float} in Python 2-
330 and an L{Fsum}.
332 @arg other: An L{Fsum} or C{scalar} modulus.
334 @see: Method L{Fsum.__itruediv__}.
335 '''
336 f = self._copy_2(self.__divmod__)
337 return f._fdivmod2(other, _divmod_op_)
339 def __eq__(self, other):
340 '''Compare this with an other instance or scalar.
341 '''
342 return self._cmp_0(other, _eq_op_) == 0
344 def __float__(self):
345 '''Return this instance' current precision running sum as C{float}.
347 @see: Methods L{Fsum.fsum} and L{Fsum.int_float}.
348 '''
349 return float(self._fprs)
351 def __floor__(self): # PYCHOK not special in Python 2-
352 '''Return this instance' C{math.floor} as C{int} or C{float}.
354 @return: An C{int} in Python 3+, but C{float} in Python 2-.
356 @see: Methods L{Fsum.__ceil__} and property L{Fsum.floor}.
357 '''
358 return self.floor
360 def __floordiv__(self, other):
361 '''Return C{B{self} // B{other}} as an L{Fsum}.
363 @arg other: An L{Fsum} or C{scalar} divisor.
365 @return: The C{floor} quotient (L{Fsum}).
367 @see: Methods L{Fsum.__ifloordiv__}.
368 '''
369 f = self._copy_2(self.__floordiv__)
370 return f._floordiv(other, _floordiv_op_)
372 def __format__(self, *other): # PYCHOK no cover
373 '''Not implemented.'''
374 return _NotImplemented(self, *other)
376 def __ge__(self, other):
377 '''Compare this with an other instance or scalar.
378 '''
379 return self._cmp_0(other, _ge_op_) >= 0
381 def __gt__(self, other):
382 '''Compare this with an other instance or scalar.
383 '''
384 return self._cmp_0(other, _gt_op_) > 0
386 def __hash__(self): # PYCHOK no cover
387 '''Return this instance' C{hash}.
388 '''
389 return hash(self._ps) # XXX id(self)?
391 def __iadd__(self, other):
392 '''Apply C{B{self} += B{other}} to this instance.
394 @arg other: An L{Fsum} or C{scalar} instance.
396 @return: This instance, updated (L{Fsum}).
398 @raise TypeError: Invalid B{C{other}}, not
399 C{scalar} nor L{Fsum}.
401 @see: Methods L{Fsum.fadd} and L{Fsum.fadd_}.
402 '''
403 return self._fadd(other, _iadd_)
405 def __ifloordiv__(self, other):
406 '''Apply C{B{self} //= B{other}} to this instance.
408 @arg other: An L{Fsum} or C{scalar} divisor.
410 @return: This instance, updated (L{Fsum}).
412 @raise ResidualError: Non-zero residual in B{C{other}}.
414 @raise TypeError: Invalid B{C{other}} type.
416 @raise ValueError: Invalid or non-finite B{C{other}}.
418 @raise ZeroDivisionError: Zero B{C{other}}.
420 @see: Methods L{Fsum.__itruediv__}.
421 '''
422 return self._floordiv(other, _floordiv_op_ + _fset_op_)
424 def __imatmul__(self, other): # PYCHOK no cover
425 '''Not implemented.'''
426 return _NotImplemented(self, other)
428 def __imod__(self, other):
429 '''Apply C{B{self} %= B{other}} to this instance.
431 @arg other: An L{Fsum} or C{scalar} modulus.
433 @return: This instance, updated (L{Fsum}).
435 @see: Method L{Fsum.__divmod__}.
436 '''
437 self._fdivmod2(other, _mod_op_ + _fset_op_)
438 return self
440 def __imul__(self, other):
441 '''Apply C{B{self} *= B{other}} to this instance.
443 @arg other: An L{Fsum} or C{scalar} factor.
445 @return: This instance, updated (L{Fsum}).
447 @raise OverflowError: Partial C{2sum} overflow.
449 @raise TypeError: Invalid B{C{other}} type.
451 @raise ValueError: Invalid or non-finite B{C{other}}.
452 '''
453 return self._fmul(other, _mul_op_ + _fset_op_)
455 def __int__(self):
456 '''Return this instance as an C{int}.
458 @see: Methods L{Fsum.int_float}, L{Fsum.__ceil__}
459 and L{Fsum.__floor__} and properties
460 L{Fsum.ceil} and L{Fsum.floor}.
461 '''
462 i, _ = self._fint2
463 return i
465 def __invert__(self): # PYCHOK no cover
466 '''Not implemented.'''
467 # Luciano Ramalho, "Fluent Python", 2nd Ed, page 567, O'Reilly, 2022
468 return _NotImplemented(self)
470 def __ipow__(self, other, *mod): # PYCHOK 2 vs 3 args
471 '''Apply C{B{self} **= B{other}} to this instance.
473 @arg other: The exponent (L{Fsum} or C{scalar}).
474 @arg mod: Optional modulus (C{int} or C{None}) for the
475 3-argument C{pow(B{self}, B{other}, B{mod})}
476 version.
478 @return: This instance, updated (L{Fsum}).
480 @note: If B{C{mod}} is given, the result will be an C{integer}
481 L{Fsum} in Python 3+ if this instance C{is_integer} or
482 set to C{as_integer} if B{C{mod}} given as C{None}.
484 @raise OverflowError: Partial C{2sum} overflow.
486 @raise ResidualError: Non-zero residual in B{C{other}} and
487 env var C{PYGEODESY_FSUM_RESIDUAL}
488 set or this instance has a non-zero
489 residual and either B{C{mod}} is
490 given and non-C{None} or B{C{other}}
491 is a negative or fractional C{scalar}.
493 @raise TypeError: Invalid B{C{other}} type or 3-argument
494 C{pow} invocation failed.
496 @raise ValueError: If B{C{other}} is a negative C{scalar}
497 and this instance is C{0} or B{C{other}}
498 is a fractional C{scalar} and this
499 instance is negative or has a non-zero
500 residual or B{C{mod}} is given and C{0}.
502 @see: CPython function U{float_pow<https://GitHub.com/
503 python/cpython/blob/main/Objects/floatobject.c>}.
504 '''
505 return self._fpow(other, _pow_op_ + _fset_op_, *mod)
507 def __isub__(self, other):
508 '''Apply C{B{self} -= B{other}} to this instance.
510 @arg other: An L{Fsum} or C{scalar}.
512 @return: This instance, updated (L{Fsum}).
514 @raise TypeError: Invalid B{C{other}} type.
516 @see: Method L{Fsum.fadd}.
517 '''
518 return self._fsub(other, _sub_op_ + _fset_op_)
520 def __iter__(self):
521 '''Return an C{iter}ator over a C{partials} duplicate.
522 '''
523 return iter(self.partials)
525 def __itruediv__(self, other):
526 '''Apply C{B{self} /= B{other}} to this instance.
528 @arg other: An L{Fsum} or C{scalar} divisor.
530 @return: This instance, updated (L{Fsum}).
532 @raise OverflowError: Partial C{2sum} overflow.
534 @raise ResidualError: Non-zero residual in B{C{other}} and
535 env var C{PYGEODESY_FSUM_RESIDUAL} set.
537 @raise TypeError: Invalid B{C{other}} type.
539 @raise ValueError: Invalid or non-finite B{C{other}}.
541 @raise ZeroDivisionError: Zero B{C{other}}.
543 @see: Method L{Fsum.__ifloordiv__}.
544 '''
545 return self._ftruediv(other, _truediv_op_ + _fset_op_)
547 def __le__(self, other):
548 '''Compare this with an other instance or scalar.
549 '''
550 return self._cmp_0(other, _le_op_) <= 0
552 def __len__(self):
553 '''Return the I{total} number accumulations (C{int}).
554 '''
555 return self._n
557 def __lt__(self, other):
558 '''Compare this with an other instance or scalar.
559 '''
560 return self._cmp_0(other, _lt_op_) < 0
562 def __matmul__(self, other): # PYCHOK no cover
563 '''Not implemented.'''
564 return _NotImplemented(self, other)
566 def __mod__(self, other):
567 '''Return C{B{self} % B{other}} as an L{Fsum}.
569 @see: Method L{Fsum.__imod__}.
570 '''
571 f = self._copy_2(self.__mod__)
572 return f._fdivmod2(other, _mod_op_)[1]
574 def __mul__(self, other):
575 '''Return C{B{self} * B{other}} as an L{Fsum}.
577 @see: Method L{Fsum.__imul__}.
578 '''
579 f = self._copy_2(self.__mul__)
580 return f._fmul(other, _mul_op_)
582 def __ne__(self, other):
583 '''Compare this with an other instance or scalar.
584 '''
585 return self._cmp_0(other, _ne_op_) != 0
587 def __neg__(self):
588 '''Return I{a copy of} this instance, negated.
589 '''
590 return self._copy_n(self.__neg__)
592 def __pos__(self):
593 '''Return this instance I{as-is}, like C{float.__pos__()}.
594 '''
595 return self if _pos_self else self._copy_2(self.__pos__)
597 def __pow__(self, other, *mod): # PYCHOK 2 vs 3 args
598 '''Return C{B{self}**B{other}} as an L{Fsum}.
600 @see: Method L{Fsum.__ipow__}.
601 '''
602 f = self._copy_2(self.__pow__)
603 return f._fpow(other, _pow_op_, *mod)
605 def __radd__(self, other):
606 '''Return C{B{other} + B{self}} as an L{Fsum}.
608 @see: Method L{Fsum.__iadd__}.
609 '''
610 f = self._copy_r2(other, self.__radd__)
611 return f._fadd(self, _add_op_)
613 def __rdivmod__(self, other):
614 '''Return C{divmod(B{other}, B{self})} as 2-tuple C{(quotient,
615 remainder)}.
617 @see: Method L{Fsum.__divmod__}.
618 '''
619 f = self._copy_r2(other, self.__rdivmod__)
620 return f._fdivmod2(self, _divmod_op_)
622# def __repr__(self):
623# '''Return the default C{repr(this)}.
624# '''
625# return self.toRepr(lenc=True)
627 def __rfloordiv__(self, other):
628 '''Return C{B{other} // B{self}} as an L{Fsum}.
630 @see: Method L{Fsum.__ifloordiv__}.
631 '''
632 f = self._copy_r2(other, self.__rfloordiv__)
633 return f._floordiv(self, _floordiv_op_)
635 def __rmatmul__(self, other): # PYCHOK no cover
636 '''Not implemented.'''
637 return _NotImplemented(self, other)
639 def __rmod__(self, other):
640 '''Return C{B{other} % B{self}} as an L{Fsum}.
642 @see: Method L{Fsum.__imod__}.
643 '''
644 f = self._copy_r2(other, self.__rmod__)
645 return f._fdivmod2(self, _mod_op_)[1]
647 def __rmul__(self, other):
648 '''Return C{B{other} * B{self}} as an L{Fsum}.
650 @see: Method L{Fsum.__imul__}.
651 '''
652 f = self._copy_r2(other, self.__rmul__)
653 return f._fmul(self, _mul_op_)
655 def __round__(self, ndigits=None): # PYCHOK no cover
656 '''Not implemented.'''
657 return _NotImplemented(self, ndigits=ndigits)
659 def __rpow__(self, other, *mod):
660 '''Return C{B{other}**B{self}} as an L{Fsum}.
662 @see: Method L{Fsum.__ipow__}.
663 '''
664 f = self._copy_r2(other, self.__rpow__)
665 return f._fpow(self, _pow_op_, *mod)
667 def __rsub__(self, other):
668 '''Return C{B{other} - B{self}} as L{Fsum}.
670 @see: Method L{Fsum.__isub__}.
671 '''
672 f = self._copy_r2(other, self.__rsub__)
673 return f._fsub(self, _sub_op_)
675 def __rtruediv__(self, other):
676 '''Return C{B{other} / B{self}} as an L{Fsum}.
678 @see: Method L{Fsum.__itruediv__}.
679 '''
680 f = self._copy_r2(other, self.__rtruediv__)
681 return f._ftruediv(self, _truediv_op_)
683 def __sizeof__(self): # PYCHOK not special in Python 2-
684 '''Return the current size of this instance in C{bytes}.
685 '''
686 return sum(map1(_sys.getsizeof, self._fint2,
687 self._fint2[0],
688 self._fint2[1],
689 self._fprs,
690 self._fprs2,
691 self._fprs2.fsum,
692 self._fprs2.residual,
693 self._n,
694 self._ps, *self._ps))
696 def __str__(self):
697 '''Return the default C{str(self)}.
698 '''
699 return self.toStr(lenc=True)
701 def __sub__(self, other):
702 '''Return C{B{self} - B{other}} as an L{Fsum}.
704 @arg other: An L{Fsum} or C{scalar}.
706 @return: The difference (L{Fsum}).
708 @see: Method L{Fsum.__isub__}.
709 '''
710 f = self._copy_2(self.__sub__)
711 return f._fsub(other, _sub_op_)
713 def __truediv__(self, other):
714 '''Return C{B{self} / B{other}} as an L{Fsum}.
716 @arg other: An L{Fsum} or C{scalar} divisor.
718 @return: The quotient (L{Fsum}).
720 @see: Method L{Fsum.__itruediv__}.
721 '''
722 f = self._copy_2(self.__truediv__)
723 return f._ftruediv(other, _truediv_op_)
725 __trunc__ = __int__
727 if _sys_version_info2 < (3, 0): # PYCHOK no cover
728 # <https://docs.Python.org/2/library/operator.html#mapping-operators-to-functions>
729 __div__ = __truediv__
730 __idiv__ = __itruediv__
731 __long__ = __int__
732 __nonzero__ = __bool__
733 __rdiv__ = __rtruediv__
735 def as_integer_ratio(self):
736 '''Return this instance as the ratio of 2 integers.
738 @return: 2-Tuple C{(numerator, denominator)} both
739 C{int} and with positive C{denominator}.
741 @see: Standard C{float.as_integer_ratio} in Python 3+.
742 '''
743 n, r = self._fint2
744 if r:
745 i, d = r.as_integer_ratio()
746 n *= d
747 n += i
748 else: # PYCHOK no cover
749 d = 1
750 return n, d
752 @property_RO
753 def ceil(self):
754 '''Get this instance' C{ceil} value (C{int} in Python 3+,
755 but C{float} in Python 2-).
757 @note: The C{ceil} takes the C{residual} into account.
759 @see: Method L{Fsum.int_float} and properties L{Fsum.floor},
760 L{Fsum.imag} and L{Fsum.real}.
761 '''
762 s, r = self._fprs2
763 c = _ceil(s) + int(r) - 1
764 while r > (c - s): # (s + r) > c
765 c += 1
766 return c
768 def _cmp_0(self, other, op):
769 '''(INTERNAL) Return C{scalar(self - B{other})} for 0-comparison.
770 '''
771 if isscalar(other):
772 s = _fsum(self._ps_1(other))
773 elif isinstance(other, Fsum):
774 s = _fsum(self._ps_1(*other._ps))
775 else:
776 raise self._TypeError(op, other) # txt=_invalid_
777 return s
779 def copy(self, deep=False, name=NN):
780 '''Copy this instance, C{shallow} or B{C{deep}}.
782 @return: The copy (L{Fsum}).
783 '''
784 f = _Named.copy(self, deep=deep, name=name)
785 f._n = self._n if deep else 1
786 f._ps = list(self._ps) # separate list
787 return f
789 def _copy_0(self, *xs):
790 '''(INTERNAL) Copy with/-out overriding C{partials}.
791 '''
792 # for x in xs:
793 # assert isscalar(x)
794 f = self._Fsum(self._n + len(xs), *xs)
795 if self.name:
796 f._name = self.name # .rename calls _update_attrs
797 return f
799 def _copy_2(self, which):
800 '''(INTERNAL) Copy for I{dyadic} operators.
801 '''
802 # NOT .classof due to .Fdot(a, *b) args, etc.
803 f = _Named.copy(self, deep=False, name=which.__name__)
804 # assert f._n == self._n
805 f._ps = list(self._ps) # separate list
806 return f
808 def _copy_n(self, which):
809 '''(INTERNAL) Negated copy for I{monadic} C{__abs__} and C{__neg__}.
810 '''
811 if self._ps:
812 f = self._Fsum(self._n)
813 f._ps[:] = self._ps_n()
814# f._facc_up(up=False)
815 else:
816 f = self._Fsum(self._n, _0_0)
817 f._name = which.__name__ # .rename calls _update_attrs
818 return f
820 def _copy_r2(self, other, which):
821 '''(INTERNAL) Copy for I{reverse-dyadic} operators.
822 '''
823 return other._copy_2(which) if isinstance(other, Fsum) else \
824 Fsum(other, name=which.__name__) # see ._copy_2
826 def _copy_RESIDUAL(self, other):
827 '''(INTERNAL) Copy C{other._RESIDUAL}.
828 '''
829 R = other._RESIDUAL
830 if R is not Fsum._RESIDUAL:
831 self._RESIDUAL = R
833 def _copy_up(self, _fprs2=False):
834 '''(INTERNAL) Minimal, anonymous copy.
835 '''
836 f = self._Fsum(self._n, *self._ps)
837 if _fprs2: # only the ._fprs2 2-tuple
838 Fsum._fprs2._update_from(f, self)
839 return f
841 def divmod(self, other):
842 '''Return C{divmod(B{self}, B{other})} as 2-tuple C{(quotient,
843 remainder)}.
845 @arg other: An L{Fsum} or C{scalar} divisor.
847 @return: 2-Tuple C{(quotient, remainder)}, with the C{quotient}
848 an C{int} in Python 3+ or a C{float} in Python 2- and
849 the C{remainder} an L{Fsum} instance.
851 @see: Method L{Fsum.__itruediv__}.
852 '''
853 f = self._copy_2(self.divmod)
854 return f._fdivmod2(other, _divmod_op_)
856 def _Error(self, op, other, Error, **txt):
857 '''(INTERNAL) Format an B{C{Error}} for C{{self} B{op} B{other}}.
858 '''
859 return Error(_SPACE_(self.toRepr(), op, repr(other)), **txt)
861 def _ErrorX(self, X, xs, **kwds): # in .fmath
862 '''(INTERNAL) Format a caught exception.
863 '''
864 E, t = _xError2(X)
865 n = unstr(self.named3, *xs[:3], _ELLIPSIS=len(xs) > 3, **kwds)
866 return E(n, txt=t, cause=X)
868 def _facc(self, xs, up=True): # from .elliptic._Defer.Fsum
869 '''(INTERNAL) Accumulate more known C{scalar}s.
870 '''
871 n, ps, _2s = 0, self._ps, _2sum
872 for x in xs: # _iter()
873 # assert isscalar(x) and isfinite(x)
874 i = 0
875 for p in ps:
876 x, p = _2s(x, p)
877 if p:
878 ps[i] = p
879 i += 1
880 ps[i:] = [x]
881 n += 1
882 # assert self._ps is ps
883 if n:
884 self._n += n
885 # Fsum._px = max(Fsum._px, len(ps))
886 if up:
887 self._update()
888 return self
890 def _facc_(self, *xs, **up):
891 '''(INTERNAL) Accumulate all positional C{scalar}s.
892 '''
893 return self._facc(xs, **up) if xs else self
895# def _facc_up(self, up=True):
896# '''(INTERNAL) Update the C{partials}, by removing
897# and re-accumulating the final C{partial}.
898# '''
899# while len(self._ps) > 1:
900# p = self._ps.pop()
901# if p:
902# n = self._n
903# self._facc_(p, up=False)
904# self._n = n
905# break
906# return self._update() if up else self # ._fpsqz()
908 def fadd(self, xs=()):
909 '''Add an iterable of C{scalar} or L{Fsum} instances
910 to this instance.
912 @arg xs: Iterable, list, tuple, etc. (C{scalar} or
913 L{Fsum} instances).
915 @return: This instance (L{Fsum}).
917 @raise OverflowError: Partial C{2sum} overflow.
919 @raise TypeError: An invalid B{C{xs}} type, not C{scalar}
920 nor L{Fsum}.
922 @raise ValueError: Invalid or non-finite B{C{xs}} value.
923 '''
924 if isinstance(xs, Fsum):
925 self._facc(xs._ps)
926 elif isscalar(xs): # for backward compatibility
927 self._facc_(_2float(x=xs)) # PYCHOK no cover
928 elif xs:
929 self._facc(_2floats(xs)) # PYCHOK yield
930 return self
932 def fadd_(self, *xs):
933 '''Add all positional C{scalar} or L{Fsum} instances
934 to this instance.
936 @arg xs: Values to add (C{scalar} or L{Fsum} instances),
937 all positional.
939 @return: This instance (L{Fsum}).
941 @raise OverflowError: Partial C{2sum} overflow.
943 @raise TypeError: An invalid B{C{xs}} type, not C{scalar}
944 nor L{Fsum}.
946 @raise ValueError: Invalid or non-finite B{C{xs}} value.
947 '''
948 return self._facc(_2floats(xs, origin=1)) # PYCHOK yield
950 def _fadd(self, other, op): # in .fmath.Fhorner
951 '''(INTERNAL) Apply C{B{self} += B{other}}.
952 '''
953 if isinstance(other, Fsum):
954 if other is self:
955 self._facc_(*other._ps) # == ._facc(tuple(other._ps))
956 elif other._ps:
957 self._facc(other._ps)
958 elif not isscalar(other):
959 raise self._TypeError(op, other) # txt=_invalid_
960 elif other:
961 self._facc_(other)
962 return self
964 fcopy = copy # for backward compatibility
965 fdiv = __itruediv__ # for backward compatibility
966 fdivmod = __divmod__ # for backward compatibility
968 def _fdivmod2(self, other, op):
969 '''(INTERNAL) C{divmod(B{self}, B{other})} as 2-tuple
970 (C{int} or C{float}, remainder C{self}).
971 '''
972 # result mostly follows CPython function U{float_divmod
973 # <https://GitHub.com/python/cpython/blob/main/Objects/floatobject.c>},
974 # but at least divmod(-3, 2) equals Cpython's result (-2, 1).
975 q = self._copy_up(_fprs2=True)._ftruediv(other, op).floor
976 if q: # == float // other == floor(float / other)
977 self -= other * q
979 s = signOf(other) # make signOf(self) == signOf(other)
980 if s and self.signOf() == -s: # PYCHOK no cover
981 self += other
982 q -= 1
984# t = self.signOf()
985# if t and t != s:
986# from pygeodesy.errors import _AssertionError
987# raise self._Error(op, other, _AssertionError, txt=signOf.__name__)
988 return q, self # q is C{int} in Python 3+, but C{float} in Python 2-
990 def _finite(self, other, op=None):
991 '''(INTERNAL) Return B{C{other}} if C{finite}.
992 '''
993 if _isfinite(other):
994 return other
995 raise ValueError(_not_finite_) if not op else \
996 self._ValueError(op, other, txt=_not_finite_)
998 def fint(self, raiser=True, name=NN):
999 '''Return this instance' current running sum as C{integer}.
1001 @kwarg raiser: If C{True} throw a L{ResidualError} if the
1002 I{integer} residual is non-zero.
1003 @kwarg name: Optional name (C{str}), overriding C{"fint"}.
1005 @return: The C{integer} (L{Fsum}).
1007 @raise ResidualError: Non-zero I{integer} residual.
1009 @see: Methods L{Fsum.int_float} and L{Fsum.is_integer}.
1010 '''
1011 i, r = self._fint2
1012 if r and raiser:
1013 t = _stresidual(_integer_, r)
1014 raise ResidualError(_integer_, i, txt=t)
1015 n = name or self.fint.__name__
1016 return Fsum(name=n)._fset(i, asis=True)
1018 def fint2(self, **name):
1019 '''Return this instance' current running sum as C{int} and
1020 the I{integer} residual.
1022 @kwarg name: Optional name (C{str}).
1024 @return: An L{Fsum2Tuple}C{(fsum, residual)} with C{fsum}
1025 an C{int} and I{integer} C{residual} a C{float} or
1026 C{INT0} if the C{fsum} is considered to be I{exact}.
1027 '''
1028 return Fsum2Tuple(*self._fint2, **name)
1030 @Property_RO
1031 def _fint2(self): # see ._fset
1032 '''(INTERNAL) Get 2-tuple (C{int}, I{integer} residual).
1033 '''
1034 i = int(self._fprs) # int(self)
1035 r = _fsum(self._ps_1(i)) if len(self._ps) > 1 else (
1036 (self._ps[0] - i) if self._ps else -i)
1037 return i, (r or INT0)
1039 @deprecated_property_RO
1040 def float_int(self): # PYCHOK no cover
1041 '''DEPRECATED, use method C{Fsum.int_float}.'''
1042 return self.int_float() # raiser=False
1044 @property_RO
1045 def floor(self):
1046 '''Get this instance' C{floor} (C{int} in Python 3+, but
1047 C{float} in Python 2-).
1049 @note: The C{floor} takes the C{residual} into account.
1051 @see: Method L{Fsum.int_float} and properties L{Fsum.ceil},
1052 L{Fsum.imag} and L{Fsum.real}.
1053 '''
1054 s, r = self._fprs2
1055 f = _floor(s) + _floor(r) + 1
1056 while r < (f - s): # (s + r) < f
1057 f -= 1
1058 return f
1060# floordiv = __floordiv__ # for naming consistency
1062 def _floordiv(self, other, op): # rather _ffloordiv?
1063 '''Apply C{B{self} //= B{other}}.
1064 '''
1065 q = self._ftruediv(other, op) # == self
1066 return self._fset(q.floor, asis=True) # floor(q)
1068 fmul = __imul__ # for backward compatibility
1070 def _fmul(self, other, op):
1071 '''(INTERNAL) Apply C{B{self} *= B{other}}.
1072 '''
1073 if isscalar(other):
1074 f = self._mul_scalar(other, op)
1075 elif not isinstance(other, Fsum):
1076 raise self._TypeError(op, other) # txt=_invalid_
1077 elif len(self._ps) != 1:
1078 f = self._mul_Fsum(other, op)
1079 elif len(other._ps) != 1: # len(self._ps) == 1
1080 f = other._copy_up()._mul_scalar(self._ps[0], op)
1081 else: # len(other._ps) == len(self._ps) == 1
1082 s = self._finite(self._ps[0] * other._ps[0])
1083 return self._fset(s, asis=True, n=len(self) + 1)
1084 return self._fset(f)
1086 def fover(self, over):
1087 '''Apply C{B{self} /= B{over}} and summate.
1089 @arg over: An L{Fsum} or C{scalar} denominator.
1091 @return: Precision running sum (C{float}).
1093 @see: Methods L{Fsum.fsum} and L{Fsum.__itruediv__}.
1094 '''
1095 return float(self.fdiv(over)._fprs)
1097 fpow = __ipow__ # for backward compatibility
1099 def _fpow(self, other, op, *mod):
1100 '''Apply C{B{self} **= B{other}}, optional B{C{mod}} or C{None}.
1101 '''
1102 if mod and mod[0] is not None: # == 3-arg C{pow}
1103 s = self._pow_3(other, mod[0], op)
1104 elif mod and mod[0] is None and self.is_integer():
1105 # return an exact C{int} for C{int}**C{int}
1106 i = self._copy_0(self._fint2[0]) # assert _fint2[1] == 0
1107 x = _2scalar(other) # C{int}, C{float} or other
1108 s = i._pow_2(x, other, op) if isscalar(x) else i._fpow(x, op)
1109 else: # pow(self, other) == pow(self, other, None)
1110 p = None
1111 if isinstance(other, Fsum):
1112 x, r = other._fprs2
1113 if r:
1114 if self._raiser(r, x):
1115 raise self._ResidualError(op, other, r)
1116 p = self._pow_scalar(r, other, op)
1117# p = _2scalar(p) # _raiser = None
1118 elif not isscalar(other):
1119 raise self._TypeError(op, other) # txt=_invalid_
1120 else:
1121 x = self._finite(other, op)
1122 s = self._pow_scalar(x, other, op)
1123 if p is not None:
1124 s *= p
1125 return self._fset(s, asis=isint(s), n=max(len(self), 1))
1127 @Property_RO
1128 def _fprs(self):
1129 '''(INTERNAL) Get and cache this instance' precision
1130 running sum (C{float} or C{int}), ignoring C{residual}.
1132 @note: The precision running C{fsum} after a C{//=} or
1133 C{//} C{floor} division is C{int} in Python 3+.
1134 '''
1135 ps = self._ps
1136 n = len(ps) - 1
1137 if n > 1:
1138 s = _psum(ps)
1139 elif n > 0: # len(ps) == 2
1140 s, p = _2sum(*ps) if ps[1] else ps
1141 ps[:] = ([p, s] if s else [p]) if p else [s]
1142 elif n < 0: # see L{Fsum.__init__}
1143 s = _0_0
1144 ps[:] = [s]
1145 else: # len(ps) == 1
1146 s = ps[0]
1147 # assert self._ps is ps
1148 # assert Fsum._fprs2.name not in self.__dict__
1149 return s
1151 @Property_RO
1152 def _fprs2(self):
1153 '''(INTERNAL) Get and cache this instance' precision
1154 running sum and residual (L{Fsum2Tuple}).
1155 '''
1156 s = self._fprs
1157 r = _fsum(self._ps_1(s)) if len(self._ps) > 1 else INT0
1158 return Fsum2Tuple(s, r) # name=Fsum.fsum2.__name__
1160# def _fpsqz(self):
1161# '''(INTERNAL) Compress, squeeze the C{partials}.
1162# '''
1163# if len(self._ps) > 2:
1164# _ = self._fprs
1165# return self
1167 def _fset(self, other, asis=False, n=1):
1168 '''(INTERNAL) Overwrite this instance with an other or a C{scalar}.
1169 '''
1170 if other is self:
1171 pass # from ._fmul, ._ftruediv and ._pow_scalar
1172 elif isinstance(other, Fsum):
1173 self._n = other._n
1174 self._ps[:] = other._ps
1175 self._copy_RESIDUAL(other)
1176 # use or zap the C{Property_RO} values
1177 Fsum._fint2._update_from(self, other)
1178 Fsum._fprs ._update_from(self, other)
1179 Fsum._fprs2._update_from(self, other)
1180 elif isscalar(other):
1181 s = other if asis else float(other)
1182 i = int(s) # see ._fint2
1183 t = i, ((s - i) or INT0)
1184 self._n = n
1185 self._ps[:] = [s]
1186 # Property_RO _fint2, _fprs and _fprs2 can't be a Property:
1187 # Property's _fset zaps the value just set by the @setter
1188 self.__dict__.update(_fint2=t, _fprs=s, _fprs2=Fsum2Tuple(s, INT0))
1189 else: # PYCHOK no cover
1190 raise self._TypeError(_fset_op_, other) # txt=_invalid_
1191 return self
1193 def fsub(self, xs=()):
1194 '''Subtract an iterable of C{scalar} or L{Fsum} instances
1195 from this instance.
1197 @arg xs: Iterable, list, tuple. etc. (C{scalar}
1198 or L{Fsum} instances).
1200 @return: This instance, updated (L{Fsum}).
1202 @see: Method L{Fsum.fadd}.
1203 '''
1204 return self._facc(_2floats(xs, sub=True)) if xs else self # PYCHOK yield
1206 def fsub_(self, *xs):
1207 '''Subtract all positional C{scalar} or L{Fsum} instances
1208 from this instance.
1210 @arg xs: Values to subtract (C{scalar} or
1211 L{Fsum} instances), all positional.
1213 @return: This instance, updated (L{Fsum}).
1215 @see: Method L{Fsum.fadd}.
1216 '''
1217 return self._facc(_2floats(xs, origin=1, sub=True)) if xs else self # PYCHOK yield
1219 def _fsub(self, other, op):
1220 '''(INTERNAL) Apply C{B{self} -= B{other}}.
1221 '''
1222 if isinstance(other, Fsum):
1223 if other is self: # or other._fprs2 == self._fprs2:
1224 self._fset(_0_0, asis=True, n=len(self) * 2) # self -= self
1225 elif other._ps:
1226 self._facc(other._ps_n())
1227 elif not isscalar(other):
1228 raise self._TypeError(op, other) # txt=_invalid_
1229 elif self._finite(other, op):
1230 self._facc_(-other)
1231 return self
1233 def _Fsum(self, n, *ps):
1234 '''(INTERNAL) New L{Fsum} instance.
1235 '''
1236 f = Fsum()
1237 f._n = n
1238 if ps:
1239 f._ps[:] = ps
1240 f._copy_RESIDUAL(self)
1241 return f
1243 def fsum(self, xs=()):
1244 '''Add more C{scalar} or L{Fsum} instances and summate.
1246 @kwarg xs: Iterable, list, tuple, etc. (C{scalar} or
1247 L{Fsum} instances).
1249 @return: Precision running sum (C{float} or C{int}).
1251 @see: Method L{Fsum.fadd}.
1253 @note: Accumulation can continue after summation.
1254 '''
1255 f = self._facc(_2floats(xs)) if xs else self # PYCHOK yield
1256 return f._fprs
1258 def fsum_(self, *xs):
1259 '''Add all positional C{scalar} or L{Fsum} instances and summate.
1261 @arg xs: Values to add (C{scalar} or L{Fsum} instances),
1262 all positional.
1264 @return: Precision running sum (C{float} or C{int}).
1266 @see: Method L{Fsum.fsum}.
1267 '''
1268 f = self._facc(_2floats(xs, origin=1)) if xs else self # PYCHOK yield
1269 return f._fprs
1271 def fsum2(self, xs=(), **name):
1272 '''Add more C{scalar} or L{Fsum} instances and return the
1273 current precision running sum and the C{residual}.
1275 @kwarg xs: Iterable, list, tuple, etc. (C{scalar} or
1276 L{Fsum} instances).
1277 @kwarg name: Optional name (C{str}).
1279 @return: L{Fsum2Tuple}C{(fsum, residual)} with C{fsum} the
1280 current precision running sum and C{residual}, the
1281 (precision) sum of the remaining C{partials}. The
1282 C{residual is INT0} if the C{fsum} is considered
1283 to be I{exact}.
1285 @see: Methods L{Fsum.fint2}, L{Fsum.fsum} and L{Fsum.fsum2_}
1286 '''
1287 f = self._facc(_2floats(xs)) if xs else self # PYCHOK yield
1288 t = f._fprs2
1289 if name:
1290 t = t.dup(name=_xkwds_get(name, name=NN))
1291 return t
1293 def fsum2_(self, *xs):
1294 '''Add any positional C{scalar} or L{Fsum} instances and return
1295 the precision running sum and the C{differential}.
1297 @arg xs: Values to add (C{scalar} or L{Fsum} instances),
1298 all positional.
1300 @return: 2-Tuple C{(fsum, delta)} with the current precision
1301 running C{fsum} and C{delta}, the difference with
1302 the previous running C{fsum} (C{float}s).
1304 @see: Methods L{Fsum.fsum_} and L{Fsum.fsum}.
1305 '''
1306 p, r = self._fprs2
1307 if xs:
1308 s, t = self._facc(_2floats(xs, origin=1))._fprs2 # PYCHOK yield
1309 return s, _fsum((s, -p, r, -t)) # ((s - p) + (r - t))
1310 else: # PYCHOK no cover
1311 return p, _0_0
1313# ftruediv = __itruediv__ # for naming consistency
1315 def _ftruediv(self, other, op):
1316 '''(INTERNAL) Apply C{B{self} /= B{other}}.
1317 '''
1318 n = _1_0
1319 if isinstance(other, Fsum):
1320 if other is self or other._fprs2 == self._fprs2:
1321 return self._fset(_1_0, asis=True, n=len(self))
1322 d, r = other._fprs2
1323 if r:
1324 if not d: # PYCHOK no cover
1325 d = r
1326 elif self._raiser(r, d):
1327 raise self._ResidualError(op, other, r)
1328 else:
1329 d, n = other.as_integer_ratio()
1330 elif isscalar(other):
1331 d = other
1332 else: # PYCHOK no cover
1333 raise self._TypeError(op, other) # txt=_invalid_
1334 try:
1335 s = 0 if isinf(d) else (
1336 d if isnan(d) else self._finite(n / d))
1337 except Exception as x:
1338 E, t = _xError2(x)
1339 raise self._Error(op, other, E, txt=t)
1340 f = self._mul_scalar(s, _mul_op_) # handles 0, NAN, etc.
1341 return self._fset(f)
1343 @property_RO
1344 def imag(self):
1345 '''Get the C{imaginary} part of this instance (C{0.0}, always).
1347 @see: Properties L{Fsum.ceil}, L{Fsum.floor} and L{Fsum.real}.
1348 '''
1349 return _0_0
1351 def int_float(self, raiser=False):
1352 '''Return this instance' current running sum as C{int} or C{float}.
1354 @kwarg raiser: If C{True} throw a L{ResidualError} if the
1355 residual is non-zero.
1357 @return: This C{integer} sum if this instance C{is_integer},
1358 otherwise return the C{float} sum if the residual
1359 is zero or if C{B{raiser}=False}.
1361 @raise ResidualError: Non-zero residual and C{B{raiser}=True}.
1363 @see: Methods L{Fsum.fint} and L{Fsum.fint2}.
1364 '''
1365 s, r = self._fint2
1366 if r:
1367 s, r = self._fprs2
1368 if r and raiser: # PYCHOK no cover
1369 t = _stresidual(_non_zero_, r)
1370 raise ResidualError(int_float=s, txt=t)
1371 s = float(s) # redundant
1372 return s
1374 def is_exact(self):
1375 '''Is this instance' current running C{fsum} considered to
1376 be exact? (C{bool}).
1377 '''
1378 return self.residual is INT0
1380 def is_integer(self):
1381 '''Is this instance' current running sum C{integer}? (C{bool}).
1383 @see: Methods L{Fsum.fint} and L{Fsum.fint2}.
1384 '''
1385 _, r = self._fint2
1386 return False if r else True
1388 def is_math_fsum(self):
1389 '''Return whether functions L{fsum}, L{fsum_}, L{fsum1}
1390 and L{fsum1_} plus partials summation are based on
1391 Python's C{math.fsum} or not.
1393 @return: C{2} if all functions and partials summation
1394 are based on C{math.fsum}, C{True} if only
1395 the functions are based on C{math.fsum} (and
1396 partials summation is not) or C{False} if
1397 none are.
1398 '''
1399 f = Fsum._math_fsum
1400 return 2 if _psum is f else bool(f)
1402 def _mul_Fsum(self, other, op=_mul_op_):
1403 '''(INTERNAL) Return C{B{self} * Fsum B{other}} as L{Fsum}.
1404 '''
1405 # assert isinstance(other, Fsum)
1406 return self._copy_0()._facc(self._ps_x(op, *other._ps), up=False)
1408 def _mul_scalar(self, factor, op):
1409 '''(INTERNAL) Return C{B{self} * scalar B{factor}} as L{Fsum} or C{0}.
1410 '''
1411 # assert isscalar(factor)
1412 if self._finite(factor, op) and self._ps:
1413 if factor == _1_0:
1414 return self
1415 f = self._copy_0()._facc(self._ps_x(op, factor), up=False)
1416 else:
1417 f = self._copy_0(_0_0)
1418 return f
1420 @property_RO
1421 def partials(self):
1422 '''Get this instance' current partial sums (C{tuple} of C{float}s and/or C{int}s).
1423 '''
1424 return tuple(self._ps)
1426 def pow(self, x, *mod):
1427 '''Return C{B{self}**B{x}} as L{Fsum}.
1429 @arg x: The exponent (L{Fsum} or C{scalar}).
1430 @arg mod: Optional modulus (C{int} or C{None}) for the 3-argument
1431 C{pow(B{self}, B{other}, B{mod})} version.
1433 @return: The C{pow(self, B{x})} or C{pow(self, B{x}, *B{mod})}
1434 result (L{Fsum}).
1436 @note: If B{C{mod}} is given as C{None}, the result will be an
1437 C{integer} L{Fsum} provided this instance C{is_integer}
1438 or set C{integer} with L{Fsum.fint}.
1440 @see: Methods L{Fsum.__ipow__}, L{Fsum.fint} and L{Fsum.is_integer}.
1441 '''
1442 f = self._copy_2(self.pow)
1443 if f and isint(x) and x >= 0 and not mod:
1444 f._pow_int(x, x, _pow_op_) # f **= x
1445 else:
1446 f._fpow(x, _pow_op_, *mod) # f = pow(f, x, *mod)
1447 return f
1449 def _pow_0_1(self, x, other):
1450 '''(INTERNAL) Return B{C{self}**1} or C{B{self}**0 == 1.0}.
1451 '''
1452 return self if x else (1 if self.is_integer() and isint(other) else _1_0)
1454 def _pow_2(self, x, other, op):
1455 '''(INTERNAL) 2-arg C{pow(B{self}, scalar B{x})} embellishing errors.
1456 '''
1457 # assert len(self._ps) == 1 and isscalar(x)
1458 b = self._ps[0] # assert isscalar(b)
1459 try: # type(s) == type(x) if x in (_1_0, 1)
1460 s = pow(b, x) # -1**2.3 == -(1**2.3)
1461 if not iscomplex(s):
1462 return self._finite(s) # 0**INF == 0.0, 1**INF==1.0
1463 # neg**frac == complex in Python 3+, but ValueError in 2-
1464 E, t = _ValueError, _strcomplex(s, b, x) # PYCHOK no cover
1465 except Exception as x:
1466 E, t = _xError2(x)
1467 raise self._Error(op, other, E, txt=t)
1469 def _pow_3(self, other, mod, op):
1470 '''(INTERNAL) 3-arg C{pow(B{self}, B{other}, int B{mod} or C{None})}.
1471 '''
1472 b, r = self._fprs2 if mod is None else self._fint2
1473 if r and self._raiser(r, b):
1474 t = _non_zero_ if mod is None else _integer_
1475 E, t = ResidualError, _stresidual(t, r, mod=mod)
1476 else:
1477 try: # b, other, mod all C{int}, unless C{mod} is C{None}
1478 x = _2scalar(other, _raiser=self._raiser)
1479 s = pow(b, x, mod)
1480 if not iscomplex(s):
1481 return self._finite(s)
1482 # neg**frac == complex in Python 3+, but ValueError in 2-
1483 E, t = _ValueError, _strcomplex(s, b, x, mod) # PYCHOK no cover
1484 except Exception as x:
1485 E, t = _xError2(x)
1486 t = _COMMASPACE_(Fmt.PARENSPACED(mod=mod), t)
1487 raise self._Error(op, other, E, txt=t)
1489 def _pow_int(self, x, other, op):
1490 '''(INTERNAL) Return C{B{self} **= B{x}} for C{int B{x} >= 0}.
1491 '''
1492 # assert isint(x) and x >= 0
1493 if len(self._ps) > 1:
1494 if x > 2:
1495 p = self._copy_up()
1496 m = 1 # single-bit mask
1497 if x & m:
1498 x -= m # x ^= m
1499 f = p._copy_up()
1500 else:
1501 f = self._copy_0(_1_0)
1502 while x:
1503 p = p._mul_Fsum(p, op) # p **= 2
1504 m += m # m <<= 1
1505 if x & m:
1506 x -= m # x ^= m
1507 f = f._mul_Fsum(p, op) # f *= p
1508 elif x > 1: # self**2
1509 f = self._mul_Fsum(self, op)
1510 else: # self**1 or self**0
1511 f = self._pow_0_1(x, other)
1512 elif self._ps: # self._ps[0]**x
1513 f = self._pow_2(x, other, op)
1514 else: # PYCHOK no cover
1515 # 0**pos_int == 0, but 0**0 == 1
1516 f = 0 if x else 1 # like ._fprs
1517 return self._fset(f, asis=isint(f), n=len(self))
1519 def _pow_scalar(self, x, other, op):
1520 '''(INTERNAL) Return C{self**B{x}} for C{scalar B{x}}.
1521 '''
1522 s, r = self._fprs2
1523 if isint(x, both=True):
1524 x = int(x) # Fsum**int
1525 y = abs(x)
1526 if y > 1:
1527 if r:
1528 f = self._copy_up()._pow_int(y, other, op)
1529 if x > 0: # > 1
1530 return f
1531 # assert x < 0 # < -1
1532 s, r = f._fprs2
1533 if r:
1534 return self._copy_0(_1_0)._ftruediv(f, op)
1535 # use **= -1 for the CPython float_pow
1536 # error if s is zero, and not s = 1 / s
1537 x = -1
1538# elif y > 1: # self**2 or self**-2
1539# f = self._mul_Fsum(self, op)
1540# if x < 0:
1541# f = f._copy_0(_1_0)._ftruediv(f, op)
1542# return f
1543 elif x < 0: # self**-1 == 1 / self
1544 if r:
1545 return self._copy_0(_1_0)._ftruediv(self, op)
1546 else: # self**1 or self**0
1547 return self._pow_0_1(x, other) # self or 0.0
1548 elif not isscalar(x): # assert ...
1549 raise self._TypeError(op, other, txt=_not_scalar_)
1550 elif r and self._raiser(r, s): # non-zero residual**fractional
1551 # raise self._ResidualError(op, other, r, fractional_power=x)
1552 t = _stresidual(_non_zero_, r, fractional_power=x)
1553 raise self._Error(op, other, ResidualError, txt=t)
1554 # assert isscalar(s) and isscalar(x)
1555 return self._copy_0(s)._pow_2(x, other, op)
1557 def _ps_1(self, *less):
1558 '''(INTERNAL) Yield partials, 1-primed and subtract any C{less}.
1559 '''
1560 yield _1_0
1561 for p in self._ps:
1562 if p:
1563 yield p
1564 for p in less:
1565 if p:
1566 yield -p
1567 yield _N_1_0
1569 def _ps_n(self):
1570 '''(INTERNAL) Yield partials, negated.
1571 '''
1572 for p in self._ps:
1573 if p:
1574 yield -p
1576 def _ps_x(self, op, *factors): # see .fmath.Fhorner
1577 '''(INTERNAL) Yield all C{partials} times each B{C{factor}},
1578 in total, up to C{len(partials) * len(factors)} items.
1579 '''
1580 ps = self._ps
1581 if len(ps) < len(factors):
1582 ps, factors = factors, ps
1583 _f = _isfinite
1584 for f in factors:
1585 for p in ps:
1586 p *= f
1587 if _f(p):
1588 yield p
1589 else: # PYCHOK no cover
1590 self._finite(p, op) # throw ValueError
1592 @property_RO
1593 def real(self):
1594 '''Get the C{real} part of this instance (C{float}).
1596 @see: Methods L{Fsum.__float__} and L{Fsum.fsum}
1597 and properties L{Fsum.ceil}, L{Fsum.floor},
1598 L{Fsum.imag} and L{Fsum.residual}.
1599 '''
1600 return float(self._fprs)
1602 @property_RO
1603 def residual(self):
1604 '''Get this instance' residual (C{float} or C{int}), the
1605 C{sum(partials)} less the precision running sum C{fsum}.
1607 @note: If the C{residual is INT0}, the precision running
1608 C{fsum} is considered to be I{exact}.
1610 @see: Methods L{Fsum.fsum}, L{Fsum.fsum2} and L{Fsum.is_exact}.
1611 '''
1612 return self._fprs2.residual
1614 def _raiser(self, r, s):
1615 '''(INTERNAL) Does the ratio C{r / s} exceed threshold?
1616 '''
1617 self._ratio = t = fabs((r / s) if s else r)
1618 return t > self._RESIDUAL
1620 def RESIDUAL(self, *threshold):
1621 '''Get and set this instance' I{ratio} for raising L{ResidualError}s,
1622 overriding the default from env variable C{PYGEODESY_FSUM_RESIDUAL}.
1624 @arg threshold: If C{scalar}, the I{ratio} to exceed for raising
1625 L{ResidualError}s in division and exponention, if
1626 C{None} restore the default set with env variable
1627 C{PYGEODESY_FSUM_RESIDUAL} or if omitted, keep the
1628 current setting.
1630 @return: The previous C{RESIDUAL} setting (C{float}).
1632 @raise ValueError: Negative B{C{threshold}}.
1634 @note: A L{ResidualError} is thrown if the non-zero I{ratio}
1635 C{residual} / C{fsum} exceeds the B{C{threshold}}.
1636 '''
1637 r = self._RESIDUAL
1638 if threshold:
1639 t = threshold[0]
1640 t = Fsum._RESIDUAL if t is None else (
1641 float(t) if isscalar(t) else ( # for backward ...
1642 _0_0 if bool(t) else _1_0)) # ... compatibility
1643 if t < 0:
1644 u = self._unstr(self.RESIDUAL, *threshold)
1645 raise _ValueError(u, RESIDUAL=t, txt=_negative_)
1646 self._RESIDUAL = t
1647 return r
1649 def _ResidualError(self, op, other, residual):
1650 '''(INTERNAL) Non-zero B{C{residual}} etc.
1651 '''
1652 t = _stresidual(_non_zero_, residual, ratio=self._ratio,
1653 RESIDUAL=self._RESIDUAL)
1654 t = t.replace(_COMMASPACE_R_, _exceeds_R_)
1655 return self._Error(op, other, ResidualError, txt=t)
1657 def signOf(self, res=True):
1658 '''Determine the sign of this instance.
1660 @kwarg res: If C{True} consider, otherwise
1661 ignore the residual (C{bool}).
1663 @return: The sign (C{int}, -1, 0 or +1).
1664 '''
1665 s, r = self._fprs2 if res else (self._fprs, 0)
1666 return _signOf(r, -s)
1668 def toRepr(self, **prec_sep_fmt_lenc): # PYCHOK signature
1669 '''Return this C{Fsum} instance as representation.
1671 @kwarg prec_sep_fmt_lenc: Optional keyword arguments for
1672 method L{Fsum2Tuple.toRepr} plus C{B{lenc}=True}
1673 (C{bool}) to in-/exclude the current C{[len]}
1674 of this L{Fsum} enclosed in I{[brackets]}.
1676 @return: This instance (C{repr}).
1677 '''
1678 return self._toT(self._fprs2.toRepr, **prec_sep_fmt_lenc)
1680 def toStr(self, **prec_sep_fmt_lenc): # PYCHOK signature
1681 '''Return this C{Fsum} instance as string.
1683 @kwarg prec_sep_fmt_lenc: Optional keyword arguments for
1684 method L{Fsum2Tuple.toStr} plus C{B{lenc}=True}
1685 (C{bool}) to in-/exclude the current C{[len]}
1686 of this L{Fsum} enclosed in I{[brackets]}.
1688 @return: This instance (C{str}).
1689 '''
1690 return self._toT(self._fprs2.toStr, **prec_sep_fmt_lenc)
1692 def _toT(self, toT, fmt=Fmt.g, lenc=True, **kwds):
1693 '''(INTERNAL) Helper for C{toRepr} and C{toStr}.
1694 '''
1695 n = self.named3
1696 if lenc:
1697 n = Fmt.SQUARE(n, len(self))
1698 return _SPACE_(n, toT(fmt=fmt, **kwds))
1700 def _TypeError(self, op, other, **txt): # PYCHOK no cover
1701 '''(INTERNAL) Return a C{TypeError}.
1702 '''
1703 return self._Error(op, other, _TypeError, **txt)
1705 def _update(self): # see ._fset
1706 '''(INTERNAL) Zap all cached C{Property_RO} values.
1707 '''
1708 Fsum._fint2._update(self)
1709 Fsum._fprs ._update(self)
1710 Fsum._fprs2._update(self)
1711 return self
1713 def _ValueError(self, op, other, **txt): # PYCHOK no cover
1714 '''(INTERNAL) Return a C{ValueError}.
1715 '''
1716 return self._Error(op, other, _ValueError, **txt)
1718 def _ZeroDivisionError(self, op, other, **txt): # PYCHOK no cover
1719 '''(INTERNAL) Return a C{ZeroDivisionError}.
1720 '''
1721 return self._Error(op, other, _ZeroDivisionError, **txt)
1723_allPropertiesOf_n(3, Fsum, Property_RO) # PYCHOK assert, see Fsum._fset, -._update
1726def _Float_Int(arg, **name_Error):
1727 '''(INTERNAL) Unit of L{Fsum2Tuple} items.
1728 '''
1729 U = Int if isint(arg) else Float
1730 return U(arg, **name_Error)
1733class Fsum2Tuple(_NamedTuple):
1734 '''2-Tuple C{(fsum, residual)} with the precision running C{fsum}
1735 and the C{residual}, the sum of the remaining partials. Each
1736 item is either C{float} or C{int}.
1738 @note: If the C{residual is INT0}, the C{fsum} is considered
1739 to be I{exact}, see method L{Fsum2Tuple.is_exact}.
1740 '''
1741 _Names_ = ( Fsum.fsum.__name__, Fsum.residual.name)
1742 _Units_ = (_Float_Int, _Float_Int)
1744 @Property_RO
1745 def Fsum(self):
1746 '''Get this L{Fsum2Tuple} as an L{Fsum}.
1747 '''
1748 f = Fsum(name=self.name)
1749 return f._copy_0(*(s for s in reversed(self) if s))
1751 def is_exact(self):
1752 '''Is this L{Fsum2Tuple} considered to be exact? (C{bool}).
1753 '''
1754 return self.Fsum.is_exact()
1756 def is_integer(self):
1757 '''Is this L{Fsum2Tuple} C{integer}? (C{bool}).
1758 '''
1759 return self.Fsum.is_integer()
1762class ResidualError(_ValueError):
1763 '''Error raised for an operation involving a L{pygeodesy.sums.Fsum}
1764 instance with a non-zero C{residual}, I{integer} or otherwise.
1766 @see: Module L{pygeodesy.fsums} and method L{Fsum.RESIDUAL}.
1767 '''
1768 pass
1771try:
1772 from math import fsum as _fsum # precision IEEE-754 sum, Python 2.6+
1774 # make sure _fsum works as expected (XXX check
1775 # float.__getformat__('float')[:4] == 'IEEE'?)
1776 if _fsum((1, 1e101, 1, -1e101)) != 2: # PYCHOK no cover
1777 del _fsum # nope, remove _fsum ...
1778 raise ImportError # ... use _fsum below
1780 Fsum._math_fsum = _fsum
1782 if _getenv('PYGEODESY_FSUM_PARTIALS', _fsum.__name__) == _fsum.__name__:
1783 _psum = _fsum # PYCHOK redef
1785except ImportError:
1787 def _fsum(xs):
1788 '''(INTERNAL) Precision summation, Python 2.5-.
1789 '''
1790 return Fsum(name=_fsum.__name__)._facc(xs, up=False)._fprs
1793def fsum(xs, floats=False):
1794 '''Precision floating point summation based on or like Python's C{math.fsum}.
1796 @arg xs: Iterable, list, tuple, etc. of values (C{scalar} or
1797 L{Fsum} instances).
1798 @kwarg floats: Optionally, use C{B{floats}=True} iff I{all}
1799 B{C{xs}} are known to be C{float}.
1801 @return: Precision C{fsum} (C{float}).
1803 @raise OverflowError: Partial C{2sum} overflow.
1805 @raise TypeError: Non-scalar B{C{xs}} value.
1807 @raise ValueError: Invalid or non-finite B{C{xs}} value.
1809 @note: Exceptions and I{non-finite} handling may differ if not
1810 based on Python's C{math.fsum}.
1812 @see: Class L{Fsum} and methods L{Fsum.fsum} and L{Fsum.fadd}.
1813 '''
1814 return _fsum(xs if floats else _2floats(xs)) if xs else _0_0 # PYCHOK yield
1817def fsum_(*xs, **floats):
1818 '''Precision floating point summation of all positional arguments.
1820 @arg xs: Values to be added (C{scalar} or L{Fsum} instances),
1821 all positional.
1822 @kwarg floats: Optionally, use C{B{floats}=True} iff I{all}
1823 B{C{xs}} are known to be C{float}.
1825 @return: Precision C{fsum} (C{float}).
1827 @see: Function C{fsum}.
1828 '''
1829 return _fsum(xs if _xkwds_get(floats, floats=False) else
1830 _2floats(xs, origin=1)) if xs else _0_0 # PYCHOK yield
1833def fsumf_(*xs):
1834 '''Precision floating point summation L{fsum_}C{(*xs, floats=True)}.
1835 '''
1836 return _fsum(xs) if xs else _0_0
1839def fsum1(xs, floats=False):
1840 '''Precision floating point summation of a few arguments, 1-primed.
1842 @arg xs: Iterable, list, tuple, etc. of values (C{scalar} or
1843 L{Fsum} instances).
1844 @kwarg floats: Optionally, use C{B{floats}=True} iff I{all}
1845 B{C{xs}} are known to be C{float}.
1847 @return: Precision C{fsum} (C{float}).
1849 @see: Function C{fsum}.
1850 '''
1851 return _fsum(_1primed(xs if floats else _2floats(xs))) if xs else _0_0 # PYCHOK yield
1854def fsum1_(*xs, **floats):
1855 '''Precision floating point summation of a few arguments, 1-primed.
1857 @arg xs: Values to be added (C{scalar} or L{Fsum} instances),
1858 all positional.
1859 @kwarg floats: Optionally, use C{B{floats}=True} iff I{all}
1860 B{C{xs}} are known to be C{float}.
1862 @return: Precision C{fsum} (C{float}).
1864 @see: Function C{fsum}
1865 '''
1866 return _fsum(_1primed(xs if _xkwds_get(floats, floats=False) else
1867 _2floats(xs, origin=1))) if xs else _0_0 # PYCHOK yield
1870def fsum1f_(*xs):
1871 '''Precision floating point summation L{fsum1_}C{(*xs, floats=True)}.
1872 '''
1873 return _fsum(_1primed(xs)) if xs else _0_0
1876# **) MIT License
1877#
1878# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved.
1879#
1880# Permission is hereby granted, free of charge, to any person obtaining a
1881# copy of this software and associated documentation files (the "Software"),
1882# to deal in the Software without restriction, including without limitation
1883# the rights to use, copy, modify, merge, publish, distribute, sublicense,
1884# and/or sell copies of the Software, and to permit persons to whom the
1885# Software is furnished to do so, subject to the following conditions:
1886#
1887# The above copyright notice and this permission notice shall be included
1888# in all copies or substantial portions of the Software.
1889#
1890# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
1891# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
1892# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
1893# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
1894# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
1895# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
1896# OTHER DEALINGS IN THE SOFTWARE.