Coverage for pygeodesy/constants.py: 84%
228 statements
« prev ^ index » next coverage.py v7.6.0, created at 2024-09-25 17:40 -0400
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1# -*- coding: utf-8 -*-
3u'''Single-instance C{float} and C{int} constants across C{pygeodesy} modules and
4related functions L{pygeodesy.float_}, L{pygeodesy.isclose}, L{pygeodesy.isfinite},
5L{pygeodesy.isinf}, L{pygeodesy.isint0}, L{pygeodesy.isnan}, L{pygeodesy.isnear0},
6L{pygeodesy.isnear1}, L{pygeodesy.isnear90}, L{pygeodesy.isneg0}, L{pygeodesy.isninf},
7L{pygeodesy.isnon0} and L{pygeodesy.remainder}.
8'''
9# make sure int/int division yields float quotient, see .basics
10from __future__ import division as _; del _ # PYCHOK semicolon
12from pygeodesy.basics import _copysign, isbool, iscomplex, isint, _0_0
13from pygeodesy.errors import _xError, _xError2, _xkwds_get1, _xkwds_item2
14# from pygeodesy.internals import _0_0 # from .basics
15from pygeodesy.interns import _INF_, _NAN_, _UNDER_
16from pygeodesy.lazily import _ALL_MODS as _MODS, _ALL_LAZY
17# from pygeodesy.streprs import Fmt # from .unitsBase
18from pygeodesy.unitsBase import Float, Int, Radius, Fmt
20from math import fabs, isinf, isnan, pi as _pi, sqrt
21try:
22 from math import inf as _inf, nan as _nan # PYCHOK Python 3+
23except ImportError: # Python 2-
24 _inf, _nan = float(_INF_), float(_NAN_)
26__all__ = _ALL_LAZY.constants
27__version__ = '24.09.24'
30def _copysign_0_0(y):
31 '''(INTERNAL) copysign(0.0, y), only C{float}.
32 '''
33 return _N_0_0 if y < 0 else _0_0
36def _copysign_1_0(y):
37 '''(INTERNAL) copysign(1.0, y), only C{float}.
38 '''
39 return _N_1_0 if y < 0 else _1_0
42def _copysignINF(y):
43 '''(INTERNAL) copysign(INF, y), only C{float}.
44 '''
45 return NINF if y < 0 else INF
48def _Float(**name_arg):
49 '''(INTERNAL) New named, cached C{Float}.
50 '''
51 n, arg = _xkwds_item2(name_arg)
52 return Float(_float(arg), name=n)
55def _Radius(**name_arg):
56 '''(INTERNAL) New named, cached C{Radius}.
57 '''
58 n, arg = _xkwds_item2(name_arg)
59 return Radius(_float(arg), name=n)
62def float_(*fs, **sets): # sets=False
63 '''Get scalars as C{float} or I{intern}'ed C{float}.
65 @arg fs: One more values (C{scalar}), all positional.
66 @kwarg sets: Use C{B{sets}=True} to C{intern} each
67 B{C{fs}}, otherwise don't C{intern}.
69 @return: A single C{float} if only one B{C{fs}} is
70 given, otherwise a tuple of C{float}s.
72 @raise TypeError: Some B{C{fs}} is not C{scalar}.
73 '''
74 fl = []
75 _a = fl.append
76 _f = _floats.setdefault if _xkwds_get1(sets, sets=False) else \
77 _floats.get
78 try:
79 for i, f in enumerate(fs):
80 f = float(f)
81 _a(_f(f, f))
82 except Exception as x:
83 E, t = _xError2(x)
84 fs_i = Fmt.SQUARE(fs=i)
85 raise E(fs_i, f, txt=t)
86 return fl[0] if len(fl) == 1 else tuple(fl)
89def _float(f): # in .datums, .ellipsoids, ...
90 '''(INTERNAL) Cache initial C{float}s.
91 '''
92 f = float(f)
93 return _floats.setdefault(f, f) # PYCHOK del _floats
96def float0_(*xs):
97 '''Yield C{B{x}s} as a non-NEG0 C{float}.
98 '''
99 for x in xs:
100 yield float(x) if x else _0_0
103def _float0(f): # in .auxilats.auxily, .resections, .vector3dBase, ...
104 '''(INTERNAL) Return C{float(B{f})} or C{INT0}.
105 '''
106 if f:
107 f = float(f)
108 f = _floats.get(f, f)
109 elif f is not INT0:
110 f = float(f) or _0_0 # force None, NN error
111 return f
114def _floatuple(*fs):
115 '''(INTERNAL) Cache a tuple of C{float}s.
116 '''
117 return tuple(map(_float, fs))
120try:
121 from math import log2 as _log2
122except ImportError: # Python 3.3-
123 from math import log as _log
125 def _log2(x): # in .rhumb.aux_, .auxilats.auxLat
126 return _log(x, 2)
129def _naninf(p, *xs):
130 '''(INTERNAL) Return C{NAN}, C{NINF} or C{INF}.
131 '''
132 for x in xs:
133 p *= x # fmath.fprod(xs)
134 return _copysignINF(p) if isfinite(p) else p
137def _over(p, q):
138 '''(INTERNAL) Return C{B{p} / B{q}} avoiding C{ZeroDivisionError} exceptions.
139 '''
140 try:
141 return (p / q) # if p else _copysign_0_0(q)
142 except ZeroDivisionError:
143 return (_copysignINF(p) if isfinite(p) else NAN) if p else p
146def _1_over(x):
147 '''(INTERNAL) Return reciprocal C{1 / B{x}} avoiding C{ZeroDivisionError} exceptions.
148 '''
149 try:
150 return _1_0 / float(x)
151 except ZeroDivisionError:
152 return NINF if isneg0(x) else INF
155_floats = {} # PYCHOK floats cache, in .__main__
156# _float = float # PYCHOK expected
157# del _floats # XXX zap floats cache never
159_0_0 = _float( _0_0) # PYCHOK expected
160_0_0_1T = _0_0, # PYCHOK 1-tuple
161_0_0_9T = _0_0_1T * 9 # PYCHOK 9-tuple
162_0_0001 = _float( 0.0001) # PYCHOK expected
163_0_001 = _float( 0.001) # PYCHOK expected
164_0_01 = _float( 0.01) # PYCHOK expected
165_0_1 = _float( 0.1) # PYCHOK expected
166_0_125 = _float( 0.125) # PYCHOK expected
167_0_25 = _float( 0.25) # PYCHOK expected
168_0_5 = _float( 0.5) # PYCHOK expected
169_1_0 = _float( 1) # PYCHOK expected
170_1_0_1T = _1_0, # PYCHOK 1-tuple
171_1_5 = _float( 1.5) # PYCHOK expected
172_1_75 = _float( 1.75) # PYCHOK expected
173_2_0 = _float( 2) # PYCHOK expected
174_3_0 = _float( 3) # PYCHOK expected
175_4_0 = _float( 4) # PYCHOK expected
176_5_0 = _float( 5) # PYCHOK expected
177_6_0 = _float( 6) # PYCHOK expected
178_8_0 = _float( 8) # PYCHOK expected
179_9_0 = _float( 9) # PYCHOK expected
180_10_0 = _float( 10) # PYCHOK expected
181_16_0 = _float( 16) # PYCHOK expected
182_32_0 = _float( 32) # PYCHOK expected
183_60_0 = _float( 60) # PYCHOK expected
184_64_0 = _float( 64) # PYCHOK expected
185_90_0 = _float( 90) # PYCHOK expected
186_100_0 = _float( 100) # PYCHOK expected
187_180_0 = _float( 180) # PYCHOK expected
188_270_0 = _float( 270) # PYCHOK expected
189_360_0 = _float( 360) # PYCHOK expected
190_400_0 = _float( 400) # PYCHOK expected
191_720_0 = _float( 720) # PYCHOK expected
192_1000_0 = _float(1000) # PYCHOK expected
193_3600_0 = _float(3600) # PYCHOK expected
195_N_0_0 = float( '-0.0') # PYCHOK NOT _float!
196_N_0_5 = _float( -_0_5) # PYCHOK expected
197_N_1_0 = _float( -_1_0) # PYCHOK expected
198_N_2_0 = _float( -_2_0) # PYCHOK expected
199_N_90_0 = _float( -_90_0) # PYCHOK expected
200_N_180_0 = _float(-_180_0) # PYCHOK expected
202_M_KM = _1000_0 # meter per Kilo meter, see .utily
203_M_NM = _float(1852.0) # meter per Nautical Mile, exactly
204_M_SM = _float(1609.344) # meter per Statute Mile
206try:
207 from sys import float_info as _f_i
208 # @see: <https://NumPy.org/doc/stable/reference/generated/numpy.finfo.html>
209 DIG = Int( DIG =_f_i.dig) # PYCHOK system's float decimal digits
210 EPS = _Float(EPS =_f_i.epsilon) # PYCHOK system's EPSilon
211 MANT_DIG = Int( MANT_DIG=_f_i.mant_dig) # PYCHOK system's float mantissa bits
212 MAX = _Float(MAX =_f_i.max) # PYCHOK system's MAX float 1.7976931348623157e+308
213 MAX_EXP = Int( MAX_EXP =_f_i.max_exp) # PYTHON system's max base 2 exponent
214 MIN = _Float(MIN =_f_i.min) # PYCHOK system's MIN float 2.2250738585072014e-308
215 MIN_EXP = Int( MIN_EXP =_f_i.min_exp) # PYTHON system's min base 2 exponent
216# RADIX = Int( RADIX =_f_i.radix) # PYTHON system's float base
217 del _f_i
218except ImportError: # PYCHOK no cover
219 DIG = Int( DIG =15) # PYCHOK system's 64-bit float decimal digits
220 EPS = _Float(EPS =2.220446049250313e-16) # PYCHOK EPSilon 2**-52, M{EPS +/- 1 != 1}
221 MANT_DIG = Int( MANT_DIG=53) # PYCHOK float mantissa bits ≈ 53 (C{int})
222 MAX = _Float(MAX =pow(_2_0, 1023) * (_2_0 - EPS)) # PYCHOK ≈ 10**308
223 MAX_EXP = Int( MAX_ESP =_log2(MAX)) # 308 base 10
224 MIN = _Float(MIN =pow(_2_0, -1021)) # PYCHOK ≈ 10**-308
225 MIN_EXP = Int(MIN_EXP =_log2(MIN)) # -307 base 10
226# RADIX = Int(Radix =2) # base
228EPS0 = _Float( EPS0 = EPS**2) # PYCHOK near-/non-zero comparison 4.930381e-32, or EPS or EPS_2
229EPS02 = _Float( EPS02 = EPS**4) # PYCHOK near-zero-squared comparison 2.430865e-63
230EPS_2 = _Float( EPS_2 = EPS / _2_0) # PYCHOK ≈ 1.110223024625e-16
231EPS1 = _Float( EPS1 =_1_0 - EPS) # PYCHOK ≈ 0.9999999999999998
232EPS2 = _Float( EPS2 = EPS * _2_0) # PYCHOK ≈ 4.440892098501e-16
233EPS4 = _Float( EPS4 = EPS * _4_0) # PYCHOK ≈ 8.881784197001e-16
234# _1EPS = _Float(_1EPS =_1_0 + EPS) # PYCHOK ≈ 1.0000000000000002
235_1_EPS = _Float(_1_EPS =_1_0 / EPS) # PYCHOK = 4503599627370496.0
236# _2_EPS = _Float(_2_EPS =_2_0 / EPS) # PYCHOK = 9007199254740992.0
237_EPS2e4 = _Float(_EPS2e4= EPS2 * 1.e4) # PYCHOK ≈ 4.440892098501e-12
238_EPS4e8 = _Float(_EPS4e8= EPS4 * 1.e8) # PYCHOK ≈ 8.881784197001e-08
239_EPSjam = _Float(_EPSjam= pow(EPS, 0.75)) # PYCHOK = 1.818989403546e-12
240_EPSmin = _Float(_EPSmin= sqrt(MIN)) # PYCHOK = 1.49166814624e-154
241_EPSqrt = _Float(_EPSqrt= sqrt(EPS)) # PYCHOK = 1.49011611938e5-08
242_EPStol = _Float(_EPStol=_EPSqrt * _0_1) # PYCHOK = 1.49011611938e5-09 == sqrt(EPS * _0_01)
244_89_999 = _Float(_89_999=_90_0 * EPS1) # just below 90.0
245# <https://Numbers.Computation.Free.FR/Constants/Miscellaneous/digits.html>
246_1__90 = _Float(_1__90 =_1_0 / _90_0) # PYCHOK = 0.011_111_111_111_111_111_111_111_111_111_111_111_111_111_111_11111
247_2__PI = _Float(_2__PI =_2_0 / _pi) # PYCHOK = 0.636_619_772_367_581_343_075_535_053_490_057_448_137_838_582_96182
249_1_16th = _Float(_1_16th=_1_0 / _16_0) # PYCHOK in .ellipsoids, .karney
250_1_3rd = _Float(_1_3rd =_1_0 / _3_0) # PYCHOK in .fmath
251_1_6th = _Float(_1_6th =_1_0 / _6_0) # PYCHOK in .fmath
253_K0_UTM = _Float(_K0_UTM = 0.9996) # PYCHOK in .etm, .ktm, .utm, UTM scale at central meridian
254# sqrt(2) <https://WikiPedia.org/wiki/Square_root_of_2>
255# 1.414213562373095_048_801_688_724_209_698_078_569_671_875_376_948_073_176_679_737_99
256# _1SQRT2= _Float(_1SQRT2 =sqrt(_2_0) + 1)
257_SQRT2_2 = _Float(_SQRT2_2=sqrt(_0_5)) # PYCHOK = 0.707106781186547_6 == sqrt(2) / 2
259INF = Float(INF =_inf) # PYCHOK INFinity, see function L{isinf}, L{isfinite}, NOT _Float!
260INT0 = Int( INT0= 0) # PYCHOK unique int(0) instance, see .fsums, useZ=False
261NAN = Float(NAN =_nan) # PYCHOK Not-A-Number, see function L{isnan}, NOT _Float!
262NEG0 = Float(NEG0=_N_0_0) # PYCHOK NEGative 0.0, see function L{isneg0}, NOT _Float!
263NINF = Float(NINF=-INF) # PYCHOK Negative INFinity, NOT _Float!
265PI = _Float(PI =_pi) # 3.1415_9265_3589_7932_3846_2643_3832_795
266PI2 = _Float(PI2 =_pi * _2_0) # PYCHOK Two PI, M{PI * 2} aka I{Tau}
267PI_2 = _Float(PI_2 =_pi / _2_0) # PYCHOK Half PI, M{PI / 2}
268PI3 = _Float(PI3 =_pi * _3_0) # PYCHOK Three PI, M{PI * 3}
269PI3_2 = _Float(PI3_2=_pi * _1_5) # PYCHOK PI and a half, M{PI * 3 / 2}
270PI_3 = _Float(PI_3 =_pi / _3_0) # PYCHOK One third PI, M{PI / 3}
271PI4 = _Float(PI4 =_pi * _4_0) # PYCHOK Four PI, M{PI * 4}
272PI_4 = _Float(PI_4 =_pi / _4_0) # PYCHOK Quarter PI, M{PI / 4}
274R_MA = _Radius(R_MA=6378137.0) # PYCHOK equatorial earth radius (C{meter}), WGS84, EPSG:3785
275R_MB = _Radius(R_MB=6356752.3) # PYCHOK polar earth radius (C{meter}), WGS84, EPSG:3785
276R_M = _Radius(R_M =6371008.771415) # PYCHOK mean, spherical earth radius (C{meter})
277R_KM = _Radius(R_KM=R_M / _M_KM) # PYCHOK mean, spherical earth radius (C{KM}, Kilo meter)
278R_NM = _Radius(R_NM=R_M / _M_NM) # PYCHOK mean, spherical earth radius (C{NM}, nautical miles)
279R_SM = _Radius(R_SM=R_M / _M_SM) # PYCHOK mean, spherical earth radius (C{SM}, statute miles)
280# See <https://www.EdWilliams.org/avform.htm>, <https://www.DTIC.mil/dtic/tr/fulltext/u2/a216843.pdf>
281# and <https://GitHub.com/NASA/MultiDop/blob/master/src/share/man/man3/geog_lib.3> based on the
282# International Standard Nautical Mile of 1,852 meter (1' latitude)
283R_FM = _Radius(R_FM=6371000.0) # PYCHOK former FAI Sphere earth radius (C{meter})
284R_GM = _Radius(R_GM=6371230.0) # PYCHOK avg. radius, distance to geoid surface (C{meter})
285# <http://Wiki.GIS.com/wiki/index.php/Ellipsoidal_quadratic_mean_radius>
286R_QM = _Radius(R_QM=6372797.560856) # PYCHOK earth' quadratic mean radius (C{meter})
287# Rtri= _Radius(Rtri=6372797.5559594) # PYCHOK Rtriaxial quadratic mean radius (C{meter}), WGS84
288# Rbi = _Radius(Rbi =6367453.6345163) # PYCHOK Rbiaxial quadratic mean radius (C{meter}), WGS84
289R_VM = _Radius(R_VM=6366707.0194937) # PYCHOK aViation/naVigation earth radius (C{meter})
290# R_AU= Meter( R_AU=149597870700.0) # PYCHOK <https://WikiPedia.org/wiki/Astronomical_unit>
292_INF_NAN_NINF = INF, NAN, NINF
293_pos_self = _1_0.__pos__() is _1_0 # PYCHOK in .fsums, .vector3dBase
296def _0_0s(n):
297 '''(INTERNAL) Return an C{B{n}-tuple} of C{_0_0} zeros.
298 '''
299 return _0_0_9T[:n] if 0 <= n <= len(_0_0_9T) else (_0_0_1T * n)
302try:
303 from math import isclose as _isclose
304except ImportError: # Python 3.4-
306 def _isclose(a, b, rel_tol=1e-9, abs_tol=0):
307 '''Mimick Python 3.5+ C{math.isclose}.
308 '''
309 t, d = abs_tol, fabs(a - b)
310 if d > t:
311 r = max(fabs(a), fabs(b)) * rel_tol
312 t = max(r, t)
313 return d <= t
316def isclose(a, b, rel_tol=1e-12, abs_tol=EPS0):
317 '''Like C{math.isclose}, but with defaults such
318 that C{isclose(0, EPS0)} is C{True} by default.
319 '''
320 return _isclose(a, b, rel_tol=rel_tol, abs_tol=abs_tol)
323try:
324 from cmath import isfinite as _iscfinite
325except ImportError: # Python 3.1-
327 def _iscfinite(x): # PYCHOK not self?
328 '''Mimick Python 3.2+ C{cmath.isfinite}.
329 '''
330 return _isfinite(x.real) and _isfinite(x.imag)
332try:
333 from math import isfinite as _isfinite # in .ellipsoids, ...
334except ImportError: # Python 3.1-
336 def _isfinite(x): # PYCHOK not self?
337 '''Mimick Python 3.2+ C{math.isfinite}.
338 '''
339 return not (isinf(x) or isnan(x))
342def isfinite(obj):
343 '''Check a finite C{scalar}, C{complex}, ... value.
345 @arg obj: Value (C{scalar}, C{complex}, an L{Fsum} or
346 L{Fsum2Tuple}).
348 @return: C{False} if B{C{obj}} is C{INF}, C{NINF}
349 or C{NAN}, C{True} otherwise.
351 @raise TypeError: Non-scalar and non-complex B{C{obj}}.
352 '''
353 try:
354 return (obj not in _INF_NAN_NINF) and _isfinite(obj)
355 except Exception as x:
356 if iscomplex(obj): # _isfinite(complex) thows TypeError
357 return _iscfinite(obj)
358 if _MODS.fsums._isFsumTuple(obj): # OverflowError
359 return obj.is_finite()
360 raise _xError(x, Fmt.PAREN(isfinite.__name__, obj))
363def isint0(obj, both=False):
364 '''Check for L{INT0} or C{int(0)} value.
366 @arg obj: The object (any C{type}).
367 @kwarg both: If C{true}, also check C{float(0)} (C{bool}).
369 @return: C{True} if B{C{obj}} is L{INT0}, C{int(0)} or
370 C{float(0)}, C{False} otherwise.
371 '''
372 return (obj is INT0 or obj is int(0) or
373 bool(both and (not obj) and isint(obj, both=True))) and \
374 not isbool(obj)
377def isnear0(x, eps0=EPS0):
378 '''Is B{C{x}} near I{zero} within a tolerance?
380 @arg x: Value (C{scalar}).
381 @kwarg eps0: Near-I{zero} tolerance (C{EPS0}).
383 @return: C{True} if C{abs(B{x}) < B{eps0}},
384 C{False} otherwise.
386 @see: Function L{isnon0}.
387 '''
388 return bool(eps0 > x > -eps0)
391def isnear1(x, eps1=EPS0):
392 '''Is B{C{x}} near I{one} within a tolerance?
394 @arg x: Value (C{scalar}).
395 @kwarg eps1: Near-I{one} tolerance (C{EPS0}).
397 @return: C{isnear0(B{x} - 1, eps0=B{eps1})}.
399 @see: Function L{isnear0}.
400 '''
401 return bool(eps1 > (x - _1_0) > -eps1)
404def isnear90(x, eps90=EPS0):
405 '''Is B{C{x}} near I{90} within a tolerance?
407 @arg x: Value (C{scalar}).
408 @kwarg eps90: Near-I{90} tolerance (C{EPS0}).
410 @return: C{isnear0(B{x} - 90, eps0=eps90)}.
412 @see: Function L{isnear0}.
413 '''
414 return bool(eps90 > (x - _90_0) > -eps90)
417def isneg0(x):
418 '''Check for L{NEG0}, negative C{0.0}.
420 @arg x: Value (C{scalar}).
422 @return: C{True} if B{C{x}} is C{NEG0} or C{-0.0},
423 C{False} otherwise.
424 '''
425 return (not x) and _copysign(1, x) < 0
426# and str(x).startswith(_MINUS_)
429def isninf(x):
430 '''Check for L{NINF}, negative C{INF}.
432 @arg x: Value (C{scalar}).
434 @return: C{True} if B{C{x}} is C{NINF} or C{-inf},
435 C{False} otherwise.
436 '''
437 return x is NINF or (x < 0 and not isfinite(x))
440def isnon0(x, eps0=EPS0):
441 '''Is B{C{x}} non-zero with a tolerance?
443 @arg x: Value (C{scalar}).
444 @kwarg eps0: Non-zero tolerance (C{EPS0}).
446 @return: C{True} if C{abs(B{x}) > B{eps0}},
447 C{False} otherwise.
449 @see: Function L{isnear0}.
450 '''
451 return not bool(eps0 > x > -eps0) # not isnear0
454def _off90(lat):
455 '''(INTERNAL) Off 90.0 for .gars and .wgrs.
456 '''
457 return max(min(lat, _89_999), -_89_999)
460try:
461 from math import remainder
462except ImportError: # Python 3.6-
463 from math import fmod as _fmod
465 def remainder(x, y):
466 '''Mimick Python 3.7+ C{math.remainder}.
467 '''
468 if isnan(y):
469 x = NAN
470 elif x and not isnan(x):
471 y = fabs(y)
472 x = _fmod(x, y)
473 h = _0_5 * y
474 if x >= h:
475 x -= y
476 elif x < -h:
477 x += y
478 return x # keep signed 0.0
481def _umod_360(deg):
482 '''(INTERNAL) Non-negative C{deg} modulo 360, basic C{.utily.wrap360}.
483 '''
484 return (deg % _360_0) or _0_0
487def _umod_PI2(rad):
488 '''(INTERNAL) Non-negative C{rad} modulo PI2, basic C{.utily.wrapPI2}.
489 '''
490 return (rad % PI2) or _0_0
493if __name__ == '__main__':
495 from pygeodesy import itemsorted, printf
497 t = n = v = []
498 for n, v in itemsorted(locals()):
499 if isinstance(v, (Float, Int, Radius)):
500 printf('%9s: %r', n, v.toRepr(std=False))
501 if v.name != n:
502 raise AssertionError('%r != %r' % (n, v))
503 if v.name is not n:
504 raise AssertionError('%r is not %r' % (n, v))
505 if not n.startswith(_UNDER_):
506 t.append(n)
507 t.append(float_.__name__)
508 printf('__all__ = %r', tuple(t))
510# **) MIT License
511#
512# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.
513#
514# Permission is hereby granted, free of charge, to any person obtaining a
515# copy of this software and associated documentation files (the "Software"),
516# to deal in the Software without restriction, including without limitation
517# the rights to use, copy, modify, merge, publish, distribute, sublicense,
518# and/or sell copies of the Software, and to permit persons to whom the
519# Software is furnished to do so, subject to the following conditions:
520#
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