Coverage for pygeodesy/fsums.py: 95%
702 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, signOf, _signOf
30from pygeodesy.constants import INT0, _isfinite, isinf, isnan, _pos_self, \
31 _0_0, _1_0, _N_1_0, Float, Int
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_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__ = '23.08.27'
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_popitem(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 if index is not None:
86 n = Fmt.SQUARE(n, index)
87 raise E(n, v, txt=t)
90def _2floats(xs, origin=0, sub=False):
91 '''(INTERNAL) Yield each B{C{xs}} as a C{float}.
92 '''
93 try:
94 i, x = origin, None
95 _fin = _isfinite
96 _Fsum = Fsum
97 for x in xs:
98 if isinstance(x, _Fsum):
99 for p in x._ps:
100 yield (-p) if sub else p
101 else:
102 f = float(x)
103 if not _fin(f):
104 raise ValueError(_not_finite_)
105 if f:
106 yield (-f) if sub else f
107 i += 1
108 except Exception as e:
109 E, t = _xError2(e)
110 n = Fmt.SQUARE(xs=i)
111 raise E(n, x, txt=t)
114def _Powers(power, xs, origin=1): # in .fmath
115 '''(INTERNAL) Yield each C{xs} as C{float(x**power)}.
116 '''
117 if not isscalar(power):
118 raise _TypeError(power=power, txt=_not_scalar_)
119 try:
120 i, x = origin, None
121 _fin = _isfinite
122 _Fsum = Fsum
123 _pow = pow # XXX math.pow
124 for x in xs:
125 if isinstance(x, _Fsum):
126 P = x.pow(power)
127 for p in P._ps:
128 yield p
129 else:
130 p = _pow(float(x), power)
131 if not _fin(p):
132 raise ValueError(_not_finite_)
133 yield p
134 i += 1
135 except Exception as e:
136 E, t = _xError2(e)
137 n = Fmt.SQUARE(xs=i)
138 raise E(n, x, txt=t)
141def _1primed(xs):
142 '''(INTERNAL) 1-Prime the summation of C{xs}
143 arguments I{known} to be C{finite float}.
144 '''
145 yield _1_0
146 for x in xs:
147 if x:
148 yield x
149 yield _N_1_0
152def _psum(ps): # PYCHOK used!
153 '''(INTERNAL) Partials summation updating C{ps}, I{overridden below}.
154 '''
155 i = len(ps) - 1 # len(ps) > 2
156 s = ps[i]
157 _2s = _2sum
158 while i > 0:
159 i -= 1
160 s, r = _2s(s, ps[i])
161 if r: # sum(ps) became inexact
162 ps[i:] = [s, r] if s else [r]
163 if i > 0:
164 p = ps[i-1] # round half-even
165 if (p > 0 and r > 0) or \
166 (p < 0 and r < 0): # signs match
167 r *= 2
168 t = s + r
169 if r == (t - s):
170 s = t
171 break
172 ps[i:] = [s]
173 return s
176def _2scalar(other, _raiser=None):
177 '''(INTERNAL) Return B{C{other}} as C{int}, C{float} or C{as-is}.
178 '''
179 if isinstance(other, Fsum):
180 s, r = other._fint2
181 if r:
182 s, r = other._fprs2
183 if r: # PYCHOK no cover
184 if _raiser and _raiser(r, s):
185 raise ValueError(_stresidual(_non_zero_, r))
186 s = other # L{Fsum} as-is
187 else:
188 s = other # C{type} as-is
189 if isint(s, both=True):
190 s = int(s)
191 return s
194def _strcomplex(s, *args):
195 '''(INTERNAL) C{Complex} 2- or 3-arg C{pow} error C{str}.
196 '''
197 c = iscomplex.__name__[2:]
198 n = _DASH_(len(args), _arg_)
199 t = _SPACE_(c, s, _from_, n, pow.__name__)
200 return unstr(t, *args)
203def _stresidual(prefix, residual, **name_values):
204 '''(INTERNAL) Residual error C{str}.
205 '''
206 p = _SPACE_(prefix, Fsum.residual.name)
207 t = Fmt.PARENSPACED(p, Fmt(residual))
208 for n, v in itemsorted(name_values):
209 n = n.replace(_UNDER_, _SPACE_)
210 p = Fmt.PARENSPACED(n, Fmt(v))
211 t = _COMMASPACE_(t, p)
212 return t
215def _2sum(a, b): # by .testFmath
216 '''(INTERNAL) Return C{a + b} as 2-tuple (sum, residual).
217 '''
218 s = a + b
219 if not _isfinite(s):
220 u = unstr(_2sum.__name__, a, b)
221 t = Fmt.PARENSPACED(_not_finite_, s)
222 raise _OverflowError(u, txt=t)
223 if fabs(a) < fabs(b):
224 a, b = b, a
225 return s, (b - (s - a))
228class Fsum(_Named): # sync __methods__ with .vector3dBase.Vector3dBase
229 '''Precision floating point I{running} summation.
231 Unlike Python's C{math.fsum}, this class accumulates values and provides intermediate,
232 I{running} precision floating point summation. Accumulation may continue after
233 intermediate, I{running} summuation.
235 @note: Accumulated values may be L{Fsum} or C{scalar} instances with C{scalar} meaning
236 type C{float}, C{int} or any C{type} convertible to a single C{float}, having
237 method C{__float__}.
239 @note: Handling of exceptions and C{inf}, C{INF}, C{nan} and C{NAN} differs from
240 Python's C{math.fsum}.
242 @see: U{Hettinger<https://GitHub.com/ActiveState/code/blob/master/recipes/Python/
243 393090_Binary_floating_point_summatiaccurate_full/recipe-393090.py>}, U{Kahan
244 <https://WikiPedia.org/wiki/Kahan_summation_algorithm>}, U{Klein
245 <https://Link.Springer.com/article/10.1007/s00607-005-0139-x>}, Python 2.6+
246 file I{Modules/mathmodule.c} and the issue log U{Full precision summation
247 <https://Bugs.Python.org/issue2819>}.
248 '''
249 _math_fsum = None
250 _n = 0
251# _ps = [] # partial sums
252# _px = 0
253 _ratio = None
254 _RESIDUAL = max(float(_getenv('PYGEODESY_FSUM_RESIDUAL', _0_0)), _0_0)
256 def __init__(self, *xs, **name_RESIDUAL):
257 '''New L{Fsum} for precision floating point I{running} summation.
259 @arg xs: No, one or more initial values (each C{scalar} or an
260 L{Fsum} instance).
261 @kwarg name_RESIDUAL: Optional C{B{name}=NN} for this L{Fsum}
262 (C{str}) and C{B{RESIDUAL}=None} for the
263 L{ResidualError} threshold.
265 @see: Methods L{Fsum.fadd} and L{Fsum.RESIDUAL}.
266 '''
267 if name_RESIDUAL:
268 n, r = _xkwds_get_(name_RESIDUAL, name=NN, RESIDUAL=None)
269 if n: # set name ...
270 self.name = n
271 if r is not None:
272 self.RESIDUAL(r) # ... for ResidualError
273# self._n = 0
274 self._ps = [] # [_0_0], see L{Fsum._fprs}
275 if len(xs) > 1:
276 self._facc(_2floats(xs, origin=1), up=False) # PYCHOK yield
277 elif xs: # len(xs) == 1
278 self._ps = [_2float(x=xs[0])]
279 self._n = 1
281 def __abs__(self):
282 '''Return this instance' absolute value as an L{Fsum}.
283 '''
284 s = _fsum(self._ps_1()) # == self._cmp_0(0, ...)
285 return self._copy_n(self.__abs__) if s < 0 else \
286 self._copy_2(self.__abs__)
288 def __add__(self, other):
289 '''Return the C{Fsum(B{self}, B{other})}.
291 @arg other: An L{Fsum} or C{scalar}.
293 @return: The sum (L{Fsum}).
295 @see: Method L{Fsum.__iadd__}.
296 '''
297 f = self._copy_2(self.__add__)
298 return f._fadd(other, _add_op_)
300 def __bool__(self): # PYCHOK not special in Python 2-
301 '''Return C{True} if this instance is I{exactly} non-zero.
302 '''
303 s, r = self._fprs2
304 return bool(s or r) and s != -r # == 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 C{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 _signOf(s, 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 C{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 C{scalar}.
378 '''
379 return self._cmp_0(other, _ge_op_) >= 0
381 def __gt__(self, other):
382 '''Compare this with an other instance or C{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_op_)
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", O'Reilly, 2nd Ed, 2022 p. 567
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, _isub_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 C{scalar}.
549 '''
550 return self._cmp_0(other, _le_op_) <= 0
552 def __len__(self):
553 '''Return the number of values accumulated (C{int}).
554 '''
555 return self._n
557 def __lt__(self, other):
558 '''Compare this with an other instance or C{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 C{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 __str__(self):
684 '''Return the default C{str(self)}.
685 '''
686 return self.toStr(lenc=True)
688 def __sub__(self, other):
689 '''Return C{B{self} - B{other}} as an L{Fsum}.
691 @arg other: An L{Fsum} or C{scalar}.
693 @return: The difference (L{Fsum}).
695 @see: Method L{Fsum.__isub__}.
696 '''
697 f = self._copy_2(self.__sub__)
698 return f._fsub(other, _sub_op_)
700 def __truediv__(self, other):
701 '''Return C{B{self} / B{other}} as an L{Fsum}.
703 @arg other: An L{Fsum} or C{scalar} divisor.
705 @return: The quotient (L{Fsum}).
707 @see: Method L{Fsum.__itruediv__}.
708 '''
709 f = self._copy_2(self.__truediv__)
710 return f._ftruediv(other, _truediv_op_)
712 __trunc__ = __int__
714 if _sys_version_info2 < (3, 0): # PYCHOK no cover
715 # <https://docs.Python.org/2/library/operator.html#mapping-operators-to-functions>
716 __div__ = __truediv__
717 __idiv__ = __itruediv__
718 __long__ = __int__
719 __nonzero__ = __bool__
720 __rdiv__ = __rtruediv__
722 def as_integer_ratio(self):
723 '''Return this instance as the ratio of 2 integers.
725 @return: 2-Tuple C{(numerator, denominator)} both
726 C{int} and with positive C{denominator}.
728 @see: Standard C{float.as_integer_ratio} in Python 3+.
729 '''
730 n, r = self._fint2
731 if r:
732 i, d = r.as_integer_ratio()
733 n *= d
734 n += i
735 else: # PYCHOK no cover
736 d = 1
737 return n, d
739 @property_RO
740 def ceil(self):
741 '''Get this instance' C{ceil} value (C{int} in Python 3+,
742 but C{float} in Python 2-).
744 @note: The C{ceil} takes the C{residual} into account.
746 @see: Method L{Fsum.int_float} and properties L{Fsum.floor},
747 L{Fsum.imag} and L{Fsum.real}.
748 '''
749 s, r = self._fprs2
750 c = _ceil(s) + int(r) - 1
751 while r > (c - s): # (s + r) > c
752 c += 1
753 return c
755 def _cmp_0(self, other, op):
756 '''(INTERNAL) Return C{scalar(self - B{other})} for 0-comparison.
757 '''
758 if isscalar(other):
759 if other:
760 s = _fsum(self._ps_1(other))
761 else:
762 s, r = self._fprs2
763 s = _signOf(s, -r)
764 elif isinstance(other, Fsum):
765 s = _fsum(self._ps_1(*other._ps))
766 else:
767 raise self._TypeError(op, other) # txt=_invalid_
768 return s
770 def copy(self, deep=False, name=NN):
771 '''Copy this instance, C{shallow} or B{C{deep}}.
773 @return: The copy (L{Fsum}).
774 '''
775 f = _Named.copy(self, deep=deep, name=name)
776 f._n = self._n if deep else 1
777 f._ps = list(self._ps) # separate list
778 return f
780 def _copy_0(self, *xs):
781 '''(INTERNAL) Copy with/-out overriding C{partials}.
782 '''
783 # for x in xs:
784 # assert isscalar(x)
785 f = self._Fsum(self._n + len(xs), *xs)
786 if self.name:
787 f._name = self.name # .rename calls _update_attrs
788 return f
790 def _copy_2(self, which):
791 '''(INTERNAL) Copy for I{dyadic} operators.
792 '''
793 # NOT .classof due to .Fdot(a, *b) args, etc.
794 f = _Named.copy(self, deep=False, name=which.__name__)
795 # assert f._n == self._n
796 f._ps = list(self._ps) # separate list
797 return f
799 def _copy_n(self, which):
800 '''(INTERNAL) Negated copy for I{monadic} C{__abs__} and C{__neg__}.
801 '''
802 if self._ps:
803 f = self._Fsum(self._n)
804 f._ps[:] = self._ps_n()
805# f._facc_up(up=False)
806 else:
807 f = self._Fsum(self._n, _0_0)
808 f._name = which.__name__ # .rename calls _update_attrs
809 return f
811 def _copy_r2(self, other, which):
812 '''(INTERNAL) Copy for I{reverse-dyadic} operators.
813 '''
814 return other._copy_2(which) if isinstance(other, Fsum) else \
815 Fsum(other, name=which.__name__) # see ._copy_2
817 def _copy_RESIDUAL(self, other):
818 '''(INTERNAL) Copy C{other._RESIDUAL}.
819 '''
820 R = other._RESIDUAL
821 if R is not Fsum._RESIDUAL:
822 self._RESIDUAL = R
824 def _copy_up(self, _fprs2=False):
825 '''(INTERNAL) Minimal, anonymous copy.
826 '''
827 f = self._Fsum(self._n, *self._ps)
828 if _fprs2: # only the ._fprs2 2-tuple
829 Fsum._fprs2._update_from(f, self)
830 return f
832 def divmod(self, other):
833 '''Return C{divmod(B{self}, B{other})} as 2-tuple C{(quotient,
834 remainder)}.
836 @arg other: An L{Fsum} or C{scalar} divisor.
838 @return: 2-Tuple C{(quotient, remainder)}, with the C{quotient}
839 an C{int} in Python 3+ or a C{float} in Python 2- and
840 the C{remainder} an L{Fsum} instance.
842 @see: Method L{Fsum.__itruediv__}.
843 '''
844 f = self._copy_2(self.divmod)
845 return f._fdivmod2(other, _divmod_op_)
847 def _Error(self, op, other, Error, **txt):
848 '''(INTERNAL) Format an B{C{Error}} for C{{self} B{op} B{other}}.
849 '''
850 return Error(_SPACE_(self.toRepr(), op, repr(other)), **txt)
852 def _ErrorX(self, X, xs, **kwds): # in .fmath
853 '''(INTERNAL) Format a caught exception.
854 '''
855 E, t = _xError2(X)
856 n = unstr(self.named3, *xs[:3], _ELLIPSIS=len(xs) > 3, **kwds)
857 return E(n, txt=t, cause=X)
859 def _facc(self, xs, up=True): # from .elliptic._Defer.Fsum
860 '''(INTERNAL) Accumulate more known C{scalar}s.
861 '''
862 n, ps, _2s = 0, self._ps, _2sum
863 for x in xs: # _iter()
864 # assert isscalar(x) and isfinite(x)
865 i = 0
866 for p in ps:
867 x, p = _2s(x, p)
868 if p:
869 ps[i] = p
870 i += 1
871 ps[i:] = [x]
872 n += 1
873 # assert self._ps is ps
874 if n:
875 self._n += n
876 # Fsum._px = max(Fsum._px, len(ps))
877 if up:
878 self._update()
879 return self
881 def _facc_(self, *xs, **up):
882 '''(INTERNAL) Accumulate all positional C{scalar}s.
883 '''
884 return self._facc(xs, **up) if xs else self
886# def _facc_up(self, up=True):
887# '''(INTERNAL) Update the C{partials}, by removing
888# and re-accumulating the final C{partial}.
889# '''
890# while len(self._ps) > 1:
891# p = self._ps.pop()
892# if p:
893# n = self._n
894# self._facc_(p, up=False)
895# self._n = n
896# break
897# return self._update() if up else self # ._fpsqz()
899 def fadd(self, xs=()):
900 '''Add an iterable of C{scalar} or L{Fsum} instances
901 to this instance.
903 @arg xs: Iterable, list, tuple, etc. (C{scalar} or
904 L{Fsum} instances).
906 @return: This instance (L{Fsum}).
908 @raise OverflowError: Partial C{2sum} overflow.
910 @raise TypeError: An invalid B{C{xs}} type, not C{scalar}
911 nor L{Fsum}.
913 @raise ValueError: Invalid or non-finite B{C{xs}} value.
914 '''
915 if isinstance(xs, Fsum):
916 self._facc(xs._ps)
917 elif isscalar(xs): # for backward compatibility
918 self._facc_(_2float(x=xs)) # PYCHOK no cover
919 elif xs:
920 self._facc(_2floats(xs)) # PYCHOK yield
921 return self
923 def fadd_(self, *xs):
924 '''Add all positional C{scalar} or L{Fsum} instances
925 to this instance.
927 @arg xs: Values to add (C{scalar} or L{Fsum} instances),
928 all positional.
930 @return: This instance (L{Fsum}).
932 @raise OverflowError: Partial C{2sum} overflow.
934 @raise TypeError: An invalid B{C{xs}} type, not C{scalar}
935 nor L{Fsum}.
937 @raise ValueError: Invalid or non-finite B{C{xs}} value.
938 '''
939 return self._facc(_2floats(xs, origin=1)) # PYCHOK yield
941 def _fadd(self, other, op): # in .fmath.Fhorner
942 '''(INTERNAL) Apply C{B{self} += B{other}}.
943 '''
944 if isinstance(other, Fsum):
945 if other is self:
946 self._facc_(*other._ps) # == ._facc(tuple(other._ps))
947 elif other._ps:
948 self._facc(other._ps)
949 elif not isscalar(other):
950 raise self._TypeError(op, other) # txt=_invalid_
951 elif other:
952 self._facc_(other)
953 return self
955 fcopy = copy # for backward compatibility
956 fdiv = __itruediv__ # for backward compatibility
957 fdivmod = __divmod__ # for backward compatibility
959 def _fdivmod2(self, other, op):
960 '''(INTERNAL) C{divmod(B{self}, B{other})} as 2-tuple
961 (C{int} or C{float}, remainder C{self}).
962 '''
963 # result mostly follows CPython function U{float_divmod
964 # <https://GitHub.com/python/cpython/blob/main/Objects/floatobject.c>},
965 # but at least divmod(-3, 2) equals Cpython's result (-2, 1).
966 q = self._copy_up(_fprs2=True)._ftruediv(other, op).floor
967 if q: # == float // other == floor(float / other)
968 self -= other * q
970 s = signOf(other) # make signOf(self) == signOf(other)
971 if s and self.signOf() == -s: # PYCHOK no cover
972 self += other
973 q -= 1
975# t = self.signOf()
976# if t and t != s:
977# from pygeodesy.errors import _AssertionError
978# raise self._Error(op, other, _AssertionError, txt=signOf.__name__)
979 return q, self # q is C{int} in Python 3+, but C{float} in Python 2-
981 def _finite(self, other, op=None):
982 '''(INTERNAL) Return B{C{other}} if C{finite}.
983 '''
984 if _isfinite(other):
985 return other
986 raise ValueError(_not_finite_) if not op else \
987 self._ValueError(op, other, txt=_not_finite_)
989 def fint(self, raiser=True, name=NN):
990 '''Return this instance' current running sum as C{integer}.
992 @kwarg raiser: If C{True} throw a L{ResidualError} if the
993 I{integer} residual is non-zero.
994 @kwarg name: Optional name (C{str}), overriding C{"fint"}.
996 @return: The C{integer} (L{Fsum}).
998 @raise ResidualError: Non-zero I{integer} residual.
1000 @see: Methods L{Fsum.int_float} and L{Fsum.is_integer}.
1001 '''
1002 i, r = self._fint2
1003 if r and raiser:
1004 t = _stresidual(_integer_, r)
1005 raise ResidualError(_integer_, i, txt=t)
1006 n = name or self.fint.__name__
1007 return Fsum(name=n)._fset(i, asis=True)
1009 def fint2(self, **name):
1010 '''Return this instance' current running sum as C{int} and
1011 the I{integer} residual.
1013 @kwarg name: Optional name (C{str}).
1015 @return: An L{Fsum2Tuple}C{(fsum, residual)} with C{fsum}
1016 an C{int} and I{integer} C{residual} a C{float} or
1017 C{INT0} if the C{fsum} is considered to be I{exact}.
1018 '''
1019 return Fsum2Tuple(*self._fint2, **name)
1021 @Property_RO
1022 def _fint2(self): # see ._fset
1023 '''(INTERNAL) Get 2-tuple (C{int}, I{integer} residual).
1024 '''
1025 i = int(self._fprs) # int(self)
1026 r = _fsum(self._ps_1(i)) if len(self._ps) > 1 else (
1027 (self._ps[0] - i) if self._ps else -i)
1028 return i, (r or INT0)
1030 @deprecated_property_RO
1031 def float_int(self): # PYCHOK no cover
1032 '''DEPRECATED, use method C{Fsum.int_float}.'''
1033 return self.int_float() # raiser=False
1035 @property_RO
1036 def floor(self):
1037 '''Get this instance' C{floor} (C{int} in Python 3+, but
1038 C{float} in Python 2-).
1040 @note: The C{floor} takes the C{residual} into account.
1042 @see: Method L{Fsum.int_float} and properties L{Fsum.ceil},
1043 L{Fsum.imag} and L{Fsum.real}.
1044 '''
1045 s, r = self._fprs2
1046 f = _floor(s) + _floor(r) + 1
1047 while r < (f - s): # (s + r) < f
1048 f -= 1
1049 return f
1051# floordiv = __floordiv__ # for naming consistency
1053 def _floordiv(self, other, op): # rather _ffloordiv?
1054 '''Apply C{B{self} //= B{other}}.
1055 '''
1056 q = self._ftruediv(other, op) # == self
1057 return self._fset(q.floor, asis=True) # floor(q)
1059 fmul = __imul__ # for backward compatibility
1061 def _fmul(self, other, op):
1062 '''(INTERNAL) Apply C{B{self} *= B{other}}.
1063 '''
1064 if isscalar(other):
1065 f = self._mul_scalar(other, op)
1066 elif not isinstance(other, Fsum):
1067 raise self._TypeError(op, other) # txt=_invalid_
1068 elif len(self._ps) != 1:
1069 f = self._mul_Fsum(other, op)
1070 elif len(other._ps) != 1: # len(self._ps) == 1
1071 f = other._copy_up()._mul_scalar(self._ps[0], op)
1072 else: # len(other._ps) == len(self._ps) == 1
1073 s = self._finite(self._ps[0] * other._ps[0])
1074 return self._fset(s, asis=True, n=len(self) + 1)
1075 return self._fset(f)
1077 def fover(self, over):
1078 '''Apply C{B{self} /= B{over}} and summate.
1080 @arg over: An L{Fsum} or C{scalar} denominator.
1082 @return: Precision running sum (C{float}).
1084 @see: Methods L{Fsum.fsum} and L{Fsum.__itruediv__}.
1085 '''
1086 return float(self.fdiv(over)._fprs)
1088 fpow = __ipow__ # for backward compatibility
1090 def _fpow(self, other, op, *mod):
1091 '''Apply C{B{self} **= B{other}}, optional B{C{mod}} or C{None}.
1092 '''
1093 if mod and mod[0] is not None: # == 3-arg C{pow}
1094 s = self._pow_3(other, mod[0], op)
1095 elif mod and mod[0] is None and self.is_integer():
1096 # return an exact C{int} for C{int}**C{int}
1097 i = self._copy_0(self._fint2[0]) # assert _fint2[1] == 0
1098 x = _2scalar(other) # C{int}, C{float} or other
1099 s = i._pow_2(x, other, op) if isscalar(x) else i._fpow(x, op)
1100 else: # pow(self, other) == pow(self, other, None)
1101 p = None
1102 if isinstance(other, Fsum):
1103 x, r = other._fprs2
1104 if r:
1105 if self._raiser(r, x):
1106 raise self._ResidualError(op, other, r)
1107 p = self._pow_scalar(r, other, op)
1108# p = _2scalar(p) # _raiser = None
1109 elif not isscalar(other):
1110 raise self._TypeError(op, other) # txt=_invalid_
1111 else:
1112 x = self._finite(other, op)
1113 s = self._pow_scalar(x, other, op)
1114 if p is not None:
1115 s *= p
1116 return self._fset(s, asis=isint(s), n=max(len(self), 1))
1118 @Property_RO
1119 def _fprs(self):
1120 '''(INTERNAL) Get and cache this instance' precision
1121 running sum (C{float} or C{int}), ignoring C{residual}.
1123 @note: The precision running C{fsum} after a C{//=} or
1124 C{//} C{floor} division is C{int} in Python 3+.
1125 '''
1126 ps = self._ps
1127 n = len(ps) - 1
1128 if n > 1:
1129 s = _psum(ps)
1130 elif n > 0: # len(ps) == 2
1131 s, p = _2sum(*ps) if ps[1] else ps
1132 ps[:] = ([p, s] if s else [p]) if p else [s]
1133 elif n < 0: # see L{Fsum.__init__}
1134 s = _0_0
1135 ps[:] = [s]
1136 else: # len(ps) == 1
1137 s = ps[0]
1138 # assert self._ps is ps
1139 # assert Fsum._fprs2.name not in self.__dict__
1140 return s
1142 @Property_RO
1143 def _fprs2(self):
1144 '''(INTERNAL) Get and cache this instance' precision
1145 running sum and residual (L{Fsum2Tuple}).
1146 '''
1147 s = self._fprs
1148 r = _fsum(self._ps_1(s)) if len(self._ps) > 1 else INT0
1149 return Fsum2Tuple(s, r) # name=Fsum.fsum2.__name__
1151# def _fpsqz(self):
1152# '''(INTERNAL) Compress, squeeze the C{partials}.
1153# '''
1154# if len(self._ps) > 2:
1155# _ = self._fprs
1156# return self
1158 def _fset(self, other, asis=False, n=1):
1159 '''(INTERNAL) Overwrite this instance with an other or a C{scalar}.
1160 '''
1161 if other is self:
1162 pass # from ._fmul, ._ftruediv and ._pow_scalar
1163 elif isinstance(other, Fsum):
1164 self._n = other._n
1165 self._ps[:] = other._ps
1166 self._copy_RESIDUAL(other)
1167 # use or zap the C{Property_RO} values
1168 Fsum._fint2._update_from(self, other)
1169 Fsum._fprs ._update_from(self, other)
1170 Fsum._fprs2._update_from(self, other)
1171 elif isscalar(other):
1172 s = other if asis else float(other)
1173 i = int(s) # see ._fint2
1174 t = i, ((s - i) or INT0)
1175 self._n = n
1176 self._ps[:] = [s]
1177 # Property_RO _fint2, _fprs and _fprs2 can't be a Property:
1178 # Property's _fset zaps the value just set by the @setter
1179 self.__dict__.update(_fint2=t, _fprs=s, _fprs2=Fsum2Tuple(s, INT0))
1180 else: # PYCHOK no cover
1181 raise self._TypeError(_fset_op_, other) # txt=_invalid_
1182 return self
1184 def fsub(self, xs=()):
1185 '''Subtract an iterable of C{scalar} or L{Fsum} instances
1186 from this instance.
1188 @arg xs: Iterable, list, tuple. etc. (C{scalar}
1189 or L{Fsum} instances).
1191 @return: This instance, updated (L{Fsum}).
1193 @see: Method L{Fsum.fadd}.
1194 '''
1195 return self._facc(_2floats(xs, sub=True)) if xs else self # PYCHOK yield
1197 def fsub_(self, *xs):
1198 '''Subtract all positional C{scalar} or L{Fsum} instances
1199 from this instance.
1201 @arg xs: Values to subtract (C{scalar} or
1202 L{Fsum} instances), all positional.
1204 @return: This instance, updated (L{Fsum}).
1206 @see: Method L{Fsum.fadd}.
1207 '''
1208 return self._facc(_2floats(xs, origin=1, sub=True)) if xs else self # PYCHOK yield
1210 def _fsub(self, other, op):
1211 '''(INTERNAL) Apply C{B{self} -= B{other}}.
1212 '''
1213 if isinstance(other, Fsum):
1214 if other is self: # or other._fprs2 == self._fprs2:
1215 self._fset(_0_0, asis=True, n=len(self) * 2) # self -= self
1216 elif other._ps:
1217 self._facc(other._ps_n())
1218 elif not isscalar(other):
1219 raise self._TypeError(op, other) # txt=_invalid_
1220 elif self._finite(other, op):
1221 self._facc_(-other)
1222 return self
1224 def _Fsum(self, n, *ps):
1225 '''(INTERNAL) New L{Fsum} instance.
1226 '''
1227 f = Fsum()
1228 f._n = n
1229 if ps:
1230 f._ps[:] = ps
1231 f._copy_RESIDUAL(self)
1232 return f
1234 def fsum(self, xs=()):
1235 '''Add more C{scalar} or L{Fsum} instances and summate.
1237 @kwarg xs: Iterable, list, tuple, etc. (C{scalar} or
1238 L{Fsum} instances).
1240 @return: Precision running sum (C{float} or C{int}).
1242 @see: Method L{Fsum.fadd}.
1244 @note: Accumulation can continue after summation.
1245 '''
1246 f = self._facc(_2floats(xs)) if xs else self # PYCHOK yield
1247 return f._fprs
1249 def fsum_(self, *xs):
1250 '''Add all positional C{scalar} or L{Fsum} instances and summate.
1252 @arg xs: Values to add (C{scalar} or L{Fsum} instances),
1253 all positional.
1255 @return: Precision running sum (C{float} or C{int}).
1257 @see: Method L{Fsum.fsum}.
1258 '''
1259 f = self._facc(_2floats(xs, origin=1)) if xs else self # PYCHOK yield
1260 return f._fprs
1262 def fsum2(self, xs=(), **name):
1263 '''Add more C{scalar} or L{Fsum} instances and return the
1264 current precision running sum and the C{residual}.
1266 @kwarg xs: Iterable, list, tuple, etc. (C{scalar} or
1267 L{Fsum} instances).
1268 @kwarg name: Optional name (C{str}).
1270 @return: L{Fsum2Tuple}C{(fsum, residual)} with C{fsum} the
1271 current precision running sum and C{residual}, the
1272 (precision) sum of the remaining C{partials}. The
1273 C{residual is INT0} if the C{fsum} is considered
1274 to be I{exact}.
1276 @see: Methods L{Fsum.fint2}, L{Fsum.fsum} and L{Fsum.fsum2_}
1277 '''
1278 f = self._facc(_2floats(xs)) if xs else self # PYCHOK yield
1279 t = f._fprs2
1280 if name:
1281 t = t.dup(name=_xkwds_get(name, name=NN))
1282 return t
1284 def fsum2_(self, *xs):
1285 '''Add any positional C{scalar} or L{Fsum} instances and return
1286 the precision running sum and the C{differential}.
1288 @arg xs: Values to add (C{scalar} or L{Fsum} instances),
1289 all positional.
1291 @return: 2-Tuple C{(fsum, delta)} with the current precision
1292 running C{fsum} and C{delta}, the difference with
1293 the previous running C{fsum} (C{float}s).
1295 @see: Methods L{Fsum.fsum_} and L{Fsum.fsum}.
1296 '''
1297 p, r = self._fprs2
1298 if xs:
1299 s, t = self._facc(_2floats(xs, origin=1))._fprs2 # PYCHOK yield
1300 return s, _fsum((s, -p, r, -t)) # ((s - p) + (r - t))
1301 else: # PYCHOK no cover
1302 return p, _0_0
1304# ftruediv = __itruediv__ # for naming consistency
1306 def _ftruediv(self, other, op):
1307 '''(INTERNAL) Apply C{B{self} /= B{other}}.
1308 '''
1309 n = _1_0
1310 if isinstance(other, Fsum):
1311 if other is self or other._fprs2 == self._fprs2:
1312 return self._fset(_1_0, asis=True, n=len(self))
1313 d, r = other._fprs2
1314 if r:
1315 if not d: # PYCHOK no cover
1316 d = r
1317 elif self._raiser(r, d):
1318 raise self._ResidualError(op, other, r)
1319 else:
1320 d, n = other.as_integer_ratio()
1321 elif isscalar(other):
1322 d = other
1323 else: # PYCHOK no cover
1324 raise self._TypeError(op, other) # txt=_invalid_
1325 try:
1326 s = 0 if isinf(d) else (
1327 d if isnan(d) else self._finite(n / d))
1328 except Exception as x:
1329 E, t = _xError2(x)
1330 raise self._Error(op, other, E, txt=t)
1331 f = self._mul_scalar(s, _mul_op_) # handles 0, NAN, etc.
1332 return self._fset(f)
1334 @property_RO
1335 def imag(self):
1336 '''Get the C{imaginary} part of this instance (C{0.0}, always).
1338 @see: Properties L{Fsum.ceil}, L{Fsum.floor} and L{Fsum.real}.
1339 '''
1340 return _0_0
1342 def int_float(self, raiser=False):
1343 '''Return this instance' current running sum as C{int} or C{float}.
1345 @kwarg raiser: If C{True} throw a L{ResidualError} if the
1346 residual is non-zero.
1348 @return: This C{integer} sum if this instance C{is_integer},
1349 otherwise return the C{float} sum if the residual
1350 is zero or if C{B{raiser}=False}.
1352 @raise ResidualError: Non-zero residual and C{B{raiser}=True}.
1354 @see: Methods L{Fsum.fint} and L{Fsum.fint2}.
1355 '''
1356 s, r = self._fint2
1357 if r:
1358 s, r = self._fprs2
1359 if r and raiser: # PYCHOK no cover
1360 t = _stresidual(_non_zero_, r)
1361 raise ResidualError(int_float=s, txt=t)
1362 s = float(s) # redundant
1363 return s
1365 def is_exact(self):
1366 '''Is this instance' current running C{fsum} considered to
1367 be exact? (C{bool}).
1368 '''
1369 return self.residual is INT0
1371 def is_integer(self):
1372 '''Is this instance' current running sum C{integer}? (C{bool}).
1374 @see: Methods L{Fsum.fint} and L{Fsum.fint2}.
1375 '''
1376 _, r = self._fint2
1377 return False if r else True
1379 def is_math_fsum(self):
1380 '''Return whether functions L{fsum}, L{fsum_}, L{fsum1}
1381 and L{fsum1_} plus partials summation are based on
1382 Python's C{math.fsum} or not.
1384 @return: C{2} if all functions and partials summation
1385 are based on C{math.fsum}, C{True} if only
1386 the functions are based on C{math.fsum} (and
1387 partials summation is not) or C{False} if
1388 none are.
1389 '''
1390 f = Fsum._math_fsum
1391 return 2 if _psum is f else bool(f)
1393 def _mul_Fsum(self, other, op=_mul_op_):
1394 '''(INTERNAL) Return C{B{self} * Fsum B{other}} as L{Fsum}.
1395 '''
1396 # assert isinstance(other, Fsum)
1397 return self._copy_0()._facc(self._ps_x(op, *other._ps), up=False)
1399 def _mul_scalar(self, factor, op):
1400 '''(INTERNAL) Return C{B{self} * scalar B{factor}} as L{Fsum} or C{0}.
1401 '''
1402 # assert isscalar(factor)
1403 if self._finite(factor, op) and self._ps:
1404 if factor == _1_0:
1405 return self
1406 f = self._copy_0()._facc(self._ps_x(op, factor), up=False)
1407 else:
1408 f = self._copy_0(_0_0)
1409 return f
1411 @property_RO
1412 def partials(self):
1413 '''Get this instance' current partial sums (C{tuple} of C{float}s and/or C{int}s).
1414 '''
1415 return tuple(self._ps)
1417 def pow(self, x, *mod):
1418 '''Return C{B{self}**B{x}} as L{Fsum}.
1420 @arg x: The exponent (L{Fsum} or C{scalar}).
1421 @arg mod: Optional modulus (C{int} or C{None}) for the 3-argument
1422 C{pow(B{self}, B{other}, B{mod})} version.
1424 @return: The C{pow(self, B{x})} or C{pow(self, B{x}, *B{mod})}
1425 result (L{Fsum}).
1427 @note: If B{C{mod}} is given as C{None}, the result will be an
1428 C{integer} L{Fsum} provided this instance C{is_integer}
1429 or set C{integer} with L{Fsum.fint}.
1431 @see: Methods L{Fsum.__ipow__}, L{Fsum.fint} and L{Fsum.is_integer}.
1432 '''
1433 f = self._copy_2(self.pow)
1434 if f and isint(x) and x >= 0 and not mod:
1435 f._pow_int(x, x, _pow_op_) # f **= x
1436 else:
1437 f._fpow(x, _pow_op_, *mod) # f = pow(f, x, *mod)
1438 return f
1440 def _pow_0_1(self, x, other):
1441 '''(INTERNAL) Return B{C{self}**1} or C{B{self}**0 == 1.0}.
1442 '''
1443 return self if x else (1 if self.is_integer() and isint(other) else _1_0)
1445 def _pow_2(self, x, other, op):
1446 '''(INTERNAL) 2-arg C{pow(B{self}, scalar B{x})} embellishing errors.
1447 '''
1448 # assert len(self._ps) == 1 and isscalar(x)
1449 b = self._ps[0] # assert isscalar(b)
1450 try: # type(s) == type(x) if x in (_1_0, 1)
1451 s = pow(b, x) # -1**2.3 == -(1**2.3)
1452 if not iscomplex(s):
1453 return self._finite(s) # 0**INF == 0.0, 1**INF==1.0
1454 # neg**frac == complex in Python 3+, but ValueError in 2-
1455 E, t = _ValueError, _strcomplex(s, b, x) # PYCHOK no cover
1456 except Exception as x:
1457 E, t = _xError2(x)
1458 raise self._Error(op, other, E, txt=t)
1460 def _pow_3(self, other, mod, op):
1461 '''(INTERNAL) 3-arg C{pow(B{self}, B{other}, int B{mod} or C{None})}.
1462 '''
1463 b, r = self._fprs2 if mod is None else self._fint2
1464 if r and self._raiser(r, b):
1465 t = _non_zero_ if mod is None else _integer_
1466 E, t = ResidualError, _stresidual(t, r, mod=mod)
1467 else:
1468 try: # b, other, mod all C{int}, unless C{mod} is C{None}
1469 x = _2scalar(other, _raiser=self._raiser)
1470 s = pow(b, x, mod)
1471 if not iscomplex(s):
1472 return self._finite(s)
1473 # neg**frac == complex in Python 3+, but ValueError in 2-
1474 E, t = _ValueError, _strcomplex(s, b, x, mod) # PYCHOK no cover
1475 except Exception as x:
1476 E, t = _xError2(x)
1477 t = _COMMASPACE_(Fmt.PARENSPACED(mod=mod), t)
1478 raise self._Error(op, other, E, txt=t)
1480 def _pow_int(self, x, other, op):
1481 '''(INTERNAL) Return C{B{self} **= B{x}} for C{int B{x} >= 0}.
1482 '''
1483 # assert isint(x) and x >= 0
1484 if len(self._ps) > 1:
1485 if x > 2:
1486 p = self._copy_up()
1487 m = 1 # single-bit mask
1488 if x & m:
1489 x -= m # x ^= m
1490 f = p._copy_up()
1491 else:
1492 f = self._copy_0(_1_0)
1493 while x:
1494 p = p._mul_Fsum(p, op) # p **= 2
1495 m += m # m <<= 1
1496 if x & m:
1497 x -= m # x ^= m
1498 f = f._mul_Fsum(p, op) # f *= p
1499 elif x > 1: # self**2
1500 f = self._mul_Fsum(self, op)
1501 else: # self**1 or self**0
1502 f = self._pow_0_1(x, other)
1503 elif self._ps: # self._ps[0]**x
1504 f = self._pow_2(x, other, op)
1505 else: # PYCHOK no cover
1506 # 0**pos_int == 0, but 0**0 == 1
1507 f = 0 if x else 1 # like ._fprs
1508 return self._fset(f, asis=isint(f), n=len(self))
1510 def _pow_scalar(self, x, other, op):
1511 '''(INTERNAL) Return C{self**B{x}} for C{scalar B{x}}.
1512 '''
1513 s, r = self._fprs2
1514 if isint(x, both=True):
1515 x = int(x) # Fsum**int
1516 y = abs(x)
1517 if y > 1:
1518 if r:
1519 f = self._copy_up()._pow_int(y, other, op)
1520 if x > 0: # > 1
1521 return f
1522 # assert x < 0 # < -1
1523 s, r = f._fprs2
1524 if r:
1525 return self._copy_0(_1_0)._ftruediv(f, op)
1526 # use **= -1 for the CPython float_pow
1527 # error if s is zero, and not s = 1 / s
1528 x = -1
1529# elif y > 1: # self**2 or self**-2
1530# f = self._mul_Fsum(self, op)
1531# if x < 0:
1532# f = f._copy_0(_1_0)._ftruediv(f, op)
1533# return f
1534 elif x < 0: # self**-1 == 1 / self
1535 if r:
1536 return self._copy_0(_1_0)._ftruediv(self, op)
1537 else: # self**1 or self**0
1538 return self._pow_0_1(x, other) # self or 0.0
1539 elif not isscalar(x): # assert ...
1540 raise self._TypeError(op, other, txt=_not_scalar_)
1541 elif r and self._raiser(r, s): # non-zero residual**fractional
1542 # raise self._ResidualError(op, other, r, fractional_power=x)
1543 t = _stresidual(_non_zero_, r, fractional_power=x)
1544 raise self._Error(op, other, ResidualError, txt=t)
1545 # assert isscalar(s) and isscalar(x)
1546 return self._copy_0(s)._pow_2(x, other, op)
1548 def _ps_1(self, *less):
1549 '''(INTERNAL) Yield partials, 1-primed and subtract any C{less}.
1550 '''
1551 yield _1_0
1552 for p in self._ps:
1553 if p:
1554 yield p
1555 for p in less:
1556 if p:
1557 yield -p
1558 yield _N_1_0
1560 def _ps_n(self):
1561 '''(INTERNAL) Yield partials, negated.
1562 '''
1563 for p in self._ps:
1564 if p:
1565 yield -p
1567 def _ps_x(self, op, *factors): # see .fmath.Fhorner
1568 '''(INTERNAL) Yield all C{partials} times each B{C{factor}},
1569 in total, up to C{len(partials) * len(factors)} items.
1570 '''
1571 ps = self._ps
1572 if len(ps) < len(factors):
1573 ps, factors = factors, ps
1574 _f = _isfinite
1575 for f in factors:
1576 for p in ps:
1577 p *= f
1578 if _f(p):
1579 yield p
1580 else: # PYCHOK no cover
1581 self._finite(p, op) # throw ValueError
1583 @property_RO
1584 def real(self):
1585 '''Get the C{real} part of this instance (C{float}).
1587 @see: Methods L{Fsum.__float__} and L{Fsum.fsum}
1588 and properties L{Fsum.ceil}, L{Fsum.floor},
1589 L{Fsum.imag} and L{Fsum.residual}.
1590 '''
1591 return float(self._fprs)
1593 @property_RO
1594 def residual(self):
1595 '''Get this instance' residual (C{float} or C{int}), the
1596 C{sum(partials)} less the precision running sum C{fsum}.
1598 @note: If the C{residual is INT0}, the precision running
1599 C{fsum} is considered to be I{exact}.
1601 @see: Methods L{Fsum.fsum}, L{Fsum.fsum2} and L{Fsum.is_exact}.
1602 '''
1603 return self._fprs2.residual
1605 def _raiser(self, r, s):
1606 '''(INTERNAL) Does the ratio C{r / s} exceed threshold?
1607 '''
1608 self._ratio = t = fabs((r / s) if s else r)
1609 return t > self._RESIDUAL
1611 def RESIDUAL(self, *threshold):
1612 '''Get and set this instance' I{ratio} for raising L{ResidualError}s,
1613 overriding the default from env variable C{PYGEODESY_FSUM_RESIDUAL}.
1615 @arg threshold: If C{scalar}, the I{ratio} to exceed for raising
1616 L{ResidualError}s in division and exponention, if
1617 C{None} restore the default set with env variable
1618 C{PYGEODESY_FSUM_RESIDUAL} or if omitted, keep the
1619 current setting.
1621 @return: The previous C{RESIDUAL} setting (C{float}).
1623 @raise ValueError: Negative B{C{threshold}}.
1625 @note: A L{ResidualError} is thrown if the non-zero I{ratio}
1626 C{residual} / C{fsum} exceeds the B{C{threshold}}.
1627 '''
1628 r = self._RESIDUAL
1629 if threshold:
1630 t = threshold[0]
1631 t = Fsum._RESIDUAL if t is None else (
1632 float(t) if isscalar(t) else ( # for backward ...
1633 _0_0 if bool(t) else _1_0)) # ... compatibility
1634 if t < 0:
1635 u = self._unstr(self.RESIDUAL, *threshold)
1636 raise _ValueError(u, RESIDUAL=t, txt=_negative_)
1637 self._RESIDUAL = t
1638 return r
1640 def _ResidualError(self, op, other, residual):
1641 '''(INTERNAL) Non-zero B{C{residual}} etc.
1642 '''
1643 t = _stresidual(_non_zero_, residual, ratio=self._ratio,
1644 RESIDUAL=self._RESIDUAL)
1645 t = t.replace(_COMMASPACE_R_, _exceeds_R_)
1646 return self._Error(op, other, ResidualError, txt=t)
1648 def signOf(self, res=True):
1649 '''Determine the sign of this instance.
1651 @kwarg res: If C{True} consider, otherwise
1652 ignore the residual (C{bool}).
1654 @return: The sign (C{int}, -1, 0 or +1).
1655 '''
1656 s, r = self._fprs2 if res else (self._fprs, 0)
1657 return _signOf(s, -r)
1659 def toRepr(self, **prec_sep_fmt_lenc): # PYCHOK signature
1660 '''Return this C{Fsum} instance as representation.
1662 @kwarg prec_sep_fmt_lenc: Optional keyword arguments for
1663 method L{Fsum2Tuple.toRepr} plus C{B{lenc}=True}
1664 (C{bool}) to in-/exclude the current C{[len]}
1665 of this L{Fsum} enclosed in I{[brackets]}.
1667 @return: This instance (C{repr}).
1668 '''
1669 return self._toT(self._fprs2.toRepr, **prec_sep_fmt_lenc)
1671 def toStr(self, **prec_sep_fmt_lenc): # PYCHOK signature
1672 '''Return this C{Fsum} instance as string.
1674 @kwarg prec_sep_fmt_lenc: Optional keyword arguments for
1675 method L{Fsum2Tuple.toStr} plus C{B{lenc}=True}
1676 (C{bool}) to in-/exclude the current C{[len]}
1677 of this L{Fsum} enclosed in I{[brackets]}.
1679 @return: This instance (C{str}).
1680 '''
1681 return self._toT(self._fprs2.toStr, **prec_sep_fmt_lenc)
1683 def _toT(self, toT, fmt=Fmt.g, lenc=True, **kwds):
1684 '''(INTERNAL) Helper for C{toRepr} and C{toStr}.
1685 '''
1686 n = self.named3
1687 if lenc:
1688 n = Fmt.SQUARE(n, len(self))
1689 return _SPACE_(n, toT(fmt=fmt, **kwds))
1691 def _TypeError(self, op, other, **txt): # PYCHOK no cover
1692 '''(INTERNAL) Return a C{TypeError}.
1693 '''
1694 return self._Error(op, other, _TypeError, **txt)
1696 def _update(self): # see ._fset
1697 '''(INTERNAL) Zap all cached C{Property_RO} values.
1698 '''
1699 Fsum._fint2._update(self)
1700 Fsum._fprs ._update(self)
1701 Fsum._fprs2._update(self)
1702 return self
1704 def _ValueError(self, op, other, **txt): # PYCHOK no cover
1705 '''(INTERNAL) Return a C{ValueError}.
1706 '''
1707 return self._Error(op, other, _ValueError, **txt)
1709 def _ZeroDivisionError(self, op, other, **txt): # PYCHOK no cover
1710 '''(INTERNAL) Return a C{ZeroDivisionError}.
1711 '''
1712 return self._Error(op, other, _ZeroDivisionError, **txt)
1714_allPropertiesOf_n(3, Fsum, Property_RO) # PYCHOK assert, see Fsum._fset, -._update
1717def _Float_Int(arg, **name_Error):
1718 '''(INTERNAL) Unit of L{Fsum2Tuple} items.
1719 '''
1720 U = Int if isint(arg) else Float
1721 return U(arg, **name_Error)
1724class Fsum2Tuple(_NamedTuple):
1725 '''2-Tuple C{(fsum, residual)} with the precision running C{fsum}
1726 and the C{residual}, the sum of the remaining partials. Each
1727 item is either C{float} or C{int}.
1729 @note: If the C{residual is INT0}, the C{fsum} is considered
1730 to be I{exact}, see method L{Fsum2Tuple.is_exact}.
1731 '''
1732 _Names_ = ( Fsum.fsum.__name__, Fsum.residual.name)
1733 _Units_ = (_Float_Int, _Float_Int)
1735 @Property_RO
1736 def Fsum(self):
1737 '''Get this L{Fsum2Tuple} as an L{Fsum}.
1738 '''
1739 f = Fsum(name=self.name)
1740 return f._copy_0(*(s for s in reversed(self) if s))
1742 def is_exact(self):
1743 '''Is this L{Fsum2Tuple} considered to be exact? (C{bool}).
1744 '''
1745 return self.Fsum.is_exact()
1747 def is_integer(self):
1748 '''Is this L{Fsum2Tuple} C{integer}? (C{bool}).
1749 '''
1750 return self.Fsum.is_integer()
1753class ResidualError(_ValueError):
1754 '''Error raised for an operation involving a L{pygeodesy.sums.Fsum}
1755 instance with a non-zero C{residual}, I{integer} or otherwise.
1757 @see: Module L{pygeodesy.fsums} and method L{Fsum.RESIDUAL}.
1758 '''
1759 pass
1762try:
1763 from math import fsum as _fsum # precision IEEE-754 sum, Python 2.6+
1765 # make sure _fsum works as expected (XXX check
1766 # float.__getformat__('float')[:4] == 'IEEE'?)
1767 if _fsum((1, 1e101, 1, -1e101)) != 2: # PYCHOK no cover
1768 del _fsum # nope, remove _fsum ...
1769 raise ImportError # ... use _fsum below
1771 Fsum._math_fsum = _sum = _fsum # PYCHOK exported
1773 if _getenv('PYGEODESY_FSUM_PARTIALS', _fsum.__name__) == _fsum.__name__:
1774 _psum = _fsum # PYCHOK redef
1776except ImportError:
1777 _sum = sum # Fsum(NAN) exception fall-back
1779 def _fsum(xs):
1780 '''(INTERNAL) Precision summation, Python 2.5-.
1781 '''
1782 return Fsum(name=_fsum.__name__)._facc(xs, up=False)._fprs
1785def fsum(xs, floats=False):
1786 '''Precision floating point summation based on or like Python's C{math.fsum}.
1788 @arg xs: Iterable, list, tuple, etc. of values (C{scalar} or
1789 L{Fsum} instances).
1790 @kwarg floats: Optionally, use C{B{floats}=True} iff I{all}
1791 B{C{xs}} are known to be C{float}.
1793 @return: Precision C{fsum} (C{float}).
1795 @raise OverflowError: Partial C{2sum} overflow.
1797 @raise TypeError: Non-scalar B{C{xs}} value.
1799 @raise ValueError: Invalid or non-finite B{C{xs}} value.
1801 @note: Exceptions and I{non-finite} handling may differ if not
1802 based on Python's C{math.fsum}.
1804 @see: Class L{Fsum} and methods L{Fsum.fsum} and L{Fsum.fadd}.
1805 '''
1806 return _fsum(xs if floats else _2floats(xs)) if xs else _0_0 # PYCHOK yield
1809def fsum_(*xs, **floats):
1810 '''Precision floating point summation of all positional arguments.
1812 @arg xs: Values to be added (C{scalar} or L{Fsum} instances),
1813 all positional.
1814 @kwarg floats: Optionally, use C{B{floats}=True} iff I{all}
1815 B{C{xs}} are known to be C{float}.
1817 @return: Precision C{fsum} (C{float}).
1819 @see: Function C{fsum}.
1820 '''
1821 return _fsum(xs if _xkwds_get(floats, floats=False) else
1822 _2floats(xs, origin=1)) if xs else _0_0 # PYCHOK yield
1825def fsumf_(*xs):
1826 '''Precision floating point summation L{fsum_}C{(*xs, floats=True)}.
1827 '''
1828 return _fsum(xs) if xs else _0_0
1831def fsum1(xs, floats=False):
1832 '''Precision floating point summation of a few arguments, 1-primed.
1834 @arg xs: Iterable, list, tuple, etc. of values (C{scalar} or
1835 L{Fsum} instances).
1836 @kwarg floats: Optionally, use C{B{floats}=True} iff I{all}
1837 B{C{xs}} are known to be C{float}.
1839 @return: Precision C{fsum} (C{float}).
1841 @see: Function C{fsum}.
1842 '''
1843 return _fsum(_1primed(xs if floats else _2floats(xs))) if xs else _0_0 # PYCHOK yield
1846def fsum1_(*xs, **floats):
1847 '''Precision floating point summation of a few arguments, 1-primed.
1849 @arg xs: Values to be added (C{scalar} or L{Fsum} instances),
1850 all positional.
1851 @kwarg floats: Optionally, use C{B{floats}=True} iff I{all}
1852 B{C{xs}} are known to be C{float}.
1854 @return: Precision C{fsum} (C{float}).
1856 @see: Function C{fsum}
1857 '''
1858 return _fsum(_1primed(xs if _xkwds_get(floats, floats=False) else
1859 _2floats(xs, origin=1))) if xs else _0_0 # PYCHOK yield
1862def fsum1f_(*xs):
1863 '''Precision floating point summation L{fsum1_}C{(*xs, floats=True)}.
1864 '''
1865 return _fsum(_1primed(xs)) if xs else _0_0
1868# **) MIT License
1869#
1870# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved.
1871#
1872# Permission is hereby granted, free of charge, to any person obtaining a
1873# copy of this software and associated documentation files (the "Software"),
1874# to deal in the Software without restriction, including without limitation
1875# the rights to use, copy, modify, merge, publish, distribute, sublicense,
1876# and/or sell copies of the Software, and to permit persons to whom the
1877# Software is furnished to do so, subject to the following conditions:
1878#
1879# The above copyright notice and this permission notice shall be included
1880# in all copies or substantial portions of the Software.
1881#
1882# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
1883# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
1884# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
1885# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
1886# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
1887# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
1888# OTHER DEALINGS IN THE SOFTWARE.