Coverage for pygeodesy/constants.py: 98%
194 statements
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« prev ^ index » next coverage.py v7.2.2, created at 2024-02-23 11:26 -0500
1# -*- coding: utf-8 -*-
3u'''Single-instance C{float} and C{int} constants across C{pygeodesy}
4modules and related functions L{pygeodesy.float_}, L{pygeodesy.isclose},
5L{pygeodesy.isfinite}, L{pygeodesy.isinf}, L{pygeodesy.isint0},
6L{pygeodesy.isnan}, L{pygeodesy.isnear0}, L{pygeodesy.isnear1},
7L{pygeodesy.isnear90}, L{pygeodesy.isneg0}, L{pygeodesy.isninf},
8L{pygeodesy.isnon0} and L{pygeodesy.remainder}.
9'''
10# make sure int/int division yields float quotient, see .basics
11from __future__ import division as _; del _ # PYCHOK semicolon
13from pygeodesy.basics import _0_0, _copysign, isbool, iscomplex, \
14 isint, _ALL_LAZY
15from pygeodesy.errors import _xError, _xError2, _xkwds_get
16from pygeodesy.interns import _INF_, _NAN_, _UNDER_
17# from pygeodesy.lazily import _ALL_LAZY # from .basics
18# from pygeodesy.streprs import Fmt # from .unitsBase
19from pygeodesy.unitsBase import Float, Int, Radius, Fmt
21from math import fabs, isinf, isnan, pi as _PI, sqrt
22try:
23 from math import inf as _inf, nan as _nan # PYCHOK Python 3+
24except ImportError: # Python 2-
25 _inf, _nan = float(_INF_), float(_NAN_)
27__all__ = _ALL_LAZY.constants
28__version__ = '24.02.20'
31def _copysign_0_0(y):
32 '''(INTERNAL) copysign(0.0, y), only C{float}.
33 '''
34 return _N_0_0 if y < 0 else _0_0
37def _copysign_1_0(y):
38 '''(INTERNAL) copysign(1.0, y), only C{float}.
39 '''
40 return _N_1_0 if y < 0 else _1_0
43def _copysignINF(y):
44 '''(INTERNAL) copysign(INF, y), only C{float}.
45 '''
46 return NINF if y < 0 else INF
49def _Float(**name_arg):
50 '''(INTERNAL) New named, cached C{Float}.
51 '''
52 n, arg = name_arg.popitem()
53 return Float(_float(arg), name=n)
56def _Radius(**name_arg):
57 '''(INTERNAL) New named, cached C{Radius}.
58 '''
59 n, arg = name_arg.popitem()
60 return Radius(_float(arg), name=n)
63def float_(*fs, **sets): # sets=False
64 '''Get scalars as C{float} or I{intern}'ed C{float}.
66 @arg fs: One more values (C{scalar}), all positional.
67 @kwarg sets: Use C{B{sets}=True} to C{intern} each
68 B{C{fs}}, otherwise don't C{intern}.
70 @return: A single C{float} if only one B{C{fs}} is
71 given, otherwise a tuple of C{float}s.
73 @raise TypeError: Some B{C{fs}} is not C{scalar}.
74 '''
75 fl = []
76 _a = fl.append
77 _f = _floats.setdefault if _xkwds_get(sets, sets=False) else \
78 _floats.get
79 try:
80 for i, f in enumerate(fs):
81 f = float(f)
82 _a(_f(f, f))
83 except Exception as x:
84 E, t = _xError2(x)
85 fs_i = Fmt.SQUARE(fs=i)
86 raise E(fs_i, f, txt=t)
87 return fl[0] if len(fl) == 1 else tuple(fl)
90def _float(f): # in .datums, .ellipsoids, ...
91 '''(INTERNAL) Cache initial C{float}s.
92 '''
93 f = float(f)
94 return _floats.setdefault(f, f) # PYCHOK del _floats
97def float0_(*xs):
98 '''Yield C{B{x}s} as a non-NEG0 C{float}.
99 '''
100 for x in xs:
101 yield float(x) if x else _0_0
104def _float0(f): # in .resections, .vector3dBase, ...
105 '''(INTERNAL) Return C{float(B{f})} or C{INT0}.
106 '''
107 if f:
108 f = float(f)
109 f = _floats.get(f, f)
110 elif f is not INT0:
111 f = float(f) or _0_0 # force None, NN error
112 return f
115def _floatuple(*fs):
116 '''(INTERNAL) Cache a tuple of C{float}s.
117 '''
118 return tuple(map(_float, fs))
121try:
122 from math import log2 as _log2
123except ImportError: # Python 3.3-
124 from math import log as _log
126 def _log2(x): # in .rhumb.aux_, .auxilats.auxLat
127 return _log(x, 2)
130def _naninf(p, *xs):
131 '''(INTERNAL) Return C{NAN}, C{NINF} or C{INF}.
132 '''
133 for x in xs:
134 p *= x # fmath.fprod(xs)
135 return _copysignINF(p) if isfinite(p) else p
138def _over(p, q):
139 '''(INTERNAL) Return C{B{p} / B{q}} avoiding C{ZeroDivisionError} exceptions.
140 '''
141 try:
142 return (p / q)
143 except ZeroDivisionError:
144 return (_copysignINF(p) if isfinite(p) else NAN) if p else p
147def _1_over(x):
148 '''(INTERNAL) Return reciprocal C{1 / B{x}} avoiding C{ZeroDivisionError} exceptions.
149 '''
150 try:
151 return _1_0 / float(x)
152 except ZeroDivisionError:
153 return NINF if isneg0(x) else INF
156_floats = {} # PYCHOK floats cache, in .__main__
157# _float = float # PYCHOK expected
158# del _floats # XXX zap floats cache never
160_0_0 = _float( _0_0) # PYCHOK expected
161_0_0_1T = _0_0, # PYCHOK 1-tuple
162_0_0_9T = _0_0_1T * 9 # PYCHOK 9-tuple
163_0_0001 = _float( 0.0001) # PYCHOK expected
164_0_001 = _float( 0.001) # PYCHOK expected
165_0_01 = _float( 0.01) # PYCHOK expected
166_0_1 = _float( 0.1) # PYCHOK expected
167_0_125 = _float( 0.125) # PYCHOK expected
168_0_25 = _float( 0.25) # PYCHOK expected
169_0_26 = _float( 0.26) # PYCHOK expected
170_0_5 = _float( 0.5) # PYCHOK expected
171_1_0 = _float( 1) # PYCHOK expected
172_1_0_1T = _1_0, # PYCHOK 1-tuple
173_1_5 = _float( 1.5) # PYCHOK expected
174_1_75 = _float( 1.75) # PYCHOK expected
175_2_0 = _float( 2) # PYCHOK expected
176_3_0 = _float( 3) # PYCHOK expected
177_4_0 = _float( 4) # PYCHOK expected
178_5_0 = _float( 5) # PYCHOK expected
179_6_0 = _float( 6) # PYCHOK expected
180_8_0 = _float( 8) # PYCHOK expected
181_9_0 = _float( 9) # PYCHOK expected
182_10_0 = _float( 10) # PYCHOK expected
183_16_0 = _float( 16) # PYCHOK expected
184_32_0 = _float( 32) # PYCHOK expected
185_60_0 = _float( 60) # PYCHOK expected
186_90_0 = _float( 90) # PYCHOK expected
187_100_0 = _float( 100) # PYCHOK expected
188_180_0 = _float( 180) # PYCHOK expected
189_270_0 = _float( 270) # PYCHOK expected
190_360_0 = _float( 360) # PYCHOK expected
191_400_0 = _float( 400) # PYCHOK expected
192_720_0 = _float( 720) # PYCHOK expected
193_1000_0 = _float(1000) # PYCHOK expected
194_3600_0 = _float(3600) # PYCHOK expected
196_N_0_0 = float( '-0.0') # PYCHOK NOT _float!
197_N_0_5 = _float( -_0_5) # PYCHOK expected
198_N_1_0 = _float( -_1_0) # PYCHOK expected
199_N_2_0 = _float( -_2_0) # PYCHOK expected
200_N_90_0 = _float( -_90_0) # PYCHOK expected
201_N_180_0 = _float(-_180_0) # PYCHOK expected
203_M_KM = _1000_0 # meter per Kilo meter, see .utily
204_M_NM = _float(1852.0) # meter per Nautical Mile, exactly
205_M_SM = _float(1609.344) # meter per Statute Mile
207try:
208 from sys import float_info as _f_i
209 # @see: <https://NumPy.org/doc/stable/reference/generated/numpy.finfo.html>
210 DIG = Int( DIG =_f_i.dig) # PYCHOK system's float decimal digits
211 EPS = _Float(EPS =_f_i.epsilon) # PYCHOK system's EPSilon
212 MANT_DIG = Int( MANT_DIG=_f_i.mant_dig) # PYCHOK system's float mantissa bits
213 MAX = _Float(MAX =_f_i.max) # PYCHOK system's MAX float 1.7976931348623157e+308
214 MAX_EXP = Int( MAX_EXP =_f_i.max_exp) # PYTHON system's max base 2 exponent
215 MIN = _Float(MIN =_f_i.min) # PYCHOK system's MIN float 2.2250738585072014e-308
216 MIN_EXP = Int( MIN_EXP =_f_i.min_exp) # PYTHON system's min base 2 exponent
217# RADIX = Int( RADIX =_f_i.radix) # PYTHON system's float base
218 del _f_i
219except ImportError: # PYCHOK no cover
220 DIG = Int( DIG =15) # PYCHOK system's 64-bit float decimal digits
221 EPS = _Float(EPS =2.220446049250313e-16) # PYCHOK EPSilon 2**-52, M{EPS +/- 1 != 1}
222 MANT_DIG = Int( MANT_DIG=53) # PYCHOK float mantissa bits ≈ 53 (C{int})
223 MAX = _Float(MAX =pow(_2_0, 1023) * (_2_0 - EPS)) # PYCHOK ≈ 10**308
224 MAX_EXP = Int( MAX_ESP =_log2(MAX)) # 308 base 10
225 MIN = _Float(MIN =pow(_2_0, -1021)) # PYCHOK ≈ 10**-308
226 MIN_EXP = Int(MIN_EXP =_log2(MIN)) # -307 base 10
227# RADIX = Int(Radix =2) # base
229EPS0 = _Float( EPS0 = EPS**2) # PYCHOK near-/non-zero comparison 4.930381e-32, or EPS or EPS_2
230EPS02 = _Float( EPS02 = EPS**4) # PYCHOK near-zero-squared comparison 2.430865e-63
231EPS_2 = _Float( EPS_2 = EPS / _2_0) # PYCHOK ≈ 1.110223024625e-16
232EPS1 = _Float( EPS1 =_1_0 - EPS) # PYCHOK ≈ 0.9999999999999998
233EPS2 = _Float( EPS2 = EPS * _2_0) # PYCHOK ≈ 4.440892098501e-16
234EPS4 = _Float( EPS4 = EPS * _4_0) # PYCHOK ≈ 8.881784197001e-16
235# _1EPS = _Float(_1EPS =_1_0 + EPS) # PYCHOK ≈ 1.0000000000000002
236_1_EPS = _Float(_1_EPS =_1_0 / EPS) # PYCHOK = 4503599627370496.0
237# _2_EPS = _Float(_2_EPS =_2_0 / EPS) # PYCHOK = 9007199254740992.0
238_EPS2e4 = _Float(_EPS2e4 = EPS2 * 1.e4) # PYCHOK ≈ 4.440892098501e-12
239_EPS4e8 = _Float(_EPS4e8 = EPS4 * 1.e8) # PYCHOK ≈ 8.881784197001e-08
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_= EPS1 * _90_0) # 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_64th = _Float(_1_64th =_1_0 / 64) # PYCHOK in .elliptic, pow(2.0, -6)
251_1_3rd = _Float(_1_3rd =_1_0 / _3_0) # PYCHOK in .fmath
252_1_6th = _Float(_1_6th =_1_0 / _6_0) # PYCHOK in .fmath
253_2_3rd = _Float(_2_3rd =_2_0 / _3_0) # PYCHOK in .fmath
255_K0_UTM = _Float(_K0_UTM = 0.9996) # PYCHOK in .etm, .ktm, .utm, UTM scale at central meridian
256# sqrt(2) <https://WikiPedia.org/wiki/Square_root_of_2>
257# 1.414213562373095_048_801_688_724_209_698_078_569_671_875_376_948_073_176_679_737_99
258# _1SQRT2= _Float(_1SQRT2 =sqrt(_2_0) + 1)
259_SQRT2_2 = _Float(_SQRT2_2=sqrt(_0_5)) # PYCHOK = 0.707106781186547_6 == sqrt(2) / 2
261INF = Float(INF =_inf) # PYCHOK INFinity, see function L{isinf}, L{isfinite}, NOT _Float!
262INT0 = Int( INT0= 0) # PYCHOK unique int(0) instance, see .fsums, useZ=False
263NAN = Float(NAN =_nan) # PYCHOK Not-A-Number, see function L{isnan}, NOT _Float!
264NEG0 = Float(NEG0=_N_0_0) # PYCHOK NEGative 0.0, see function L{isneg0}, NOT _Float!
265NINF = Float(NINF=-INF) # PYCHOK Negative INFinity, NOT _Float!
267PI = _Float(PI =_PI)
268PI2 = _Float(PI2 =_PI * _2_0) # PYCHOK Two PI, M{PI * 2} aka I{Tau}
269PI_2 = _Float(PI_2 =_PI / _2_0) # PYCHOK Half PI, M{PI / 2}
270PI3 = _Float(PI3 =_PI * _3_0) # PYCHOK Three PI, M{PI * 3}
271PI3_2 = _Float(PI3_2=_PI * _1_5) # PYCHOK PI and a half, M{PI * 3 / 2}
272PI_3 = _Float(PI_3 =_PI / _3_0) # PYCHOK One third PI, M{PI / 3}
273PI4 = _Float(PI4 =_PI * _4_0) # PYCHOK Four PI, M{PI * 4}
274PI_4 = _Float(PI_4 =_PI / _4_0) # PYCHOK Quarter PI, M{PI / 4}
276R_MA = _Radius(R_MA=6378137.0) # PYCHOK equatorial earth radius (C{meter}), WGS84, EPSG:3785
277R_MB = _Radius(R_MB=6356752.3) # PYCHOK polar earth radius (C{meter}), WGS84, EPSG:3785
278R_M = _Radius(R_M =6371008.771415) # PYCHOK mean, spherical earth radius (C{meter})
279R_KM = _Radius(R_KM=R_M / _M_KM) # PYCHOK mean, spherical earth radius (C{KM}, Kilo meter)
280R_NM = _Radius(R_NM=R_M / _M_NM) # PYCHOK mean, spherical earth radius (C{NM}, nautical miles)
281R_SM = _Radius(R_SM=R_M / _M_SM) # PYCHOK mean, spherical earth radius (C{SM}, statute miles)
282# See <https://www.EdWilliams.org/avform.htm>, <https://www.DTIC.mil/dtic/tr/fulltext/u2/a216843.pdf>
283# and <https://GitHub.com/NASA/MultiDop/blob/master/src/share/man/man3/geog_lib.3> based on the
284# International Standard Nautical Mile of 1,852 meter (1' latitude)
285R_FM = _Radius(R_FM=6371000.0) # PYCHOK former FAI Sphere earth radius (C{meter})
286R_GM = _Radius(R_GM=6371230.0) # PYCHOK avg. radius, distance to geoid surface (C{meter})
287# <http://Wiki.GIS.com/wiki/index.php/Ellipsoidal_quadratic_mean_radius>
288R_QM = _Radius(R_QM=6372797.560856) # PYCHOK earth' quadratic mean radius (C{meter})
289# Rtri= _Radius(Rtri=6372797.5559594) # PYCHOK Rtriaxial quadratic mean radius (C{meter}), WGS84
290# Rbi = _Radius(Rbi =6367453.6345163) # PYCHOK Rbiaxial quadratic mean radius (C{meter}), WGS84
291R_VM = _Radius(R_VM=6366707.0194937) # PYCHOK aViation/naVigation earth radius (C{meter})
292# R_AU= Meter( R_AU=149597870700.0) # PYCHOK <https://WikiPedia.org/wiki/Astronomical_unit>
294_INF_NAN_NINF = INF, NAN, NINF
295_pos_self = _1_0.__pos__() is _1_0 # PYCHOK in .fsums, .vector3dBase
298def _0_0s(n):
299 '''(INTERNAL) Return an C{B{n}-tuple} of C{_0_0} zeros.
300 '''
301 return _0_0_9T[:n] if 0 <= n <= len(_0_0_9T) else (_0_0_1T * n)
304try:
305 from math import isclose as _isclose
306except ImportError: # Python 3.4-
308 def _isclose(a, b, rel_tol=1e-9, abs_tol=0):
309 '''Mimick Python 3.5+ C{math.isclose}.
310 '''
311 t, d = abs_tol, fabs(a - b)
312 if d > t:
313 r = max(fabs(a), fabs(b)) * rel_tol
314 t = max(r, t)
315 return d <= t
318def isclose(a, b, rel_tol=1e-12, abs_tol=EPS0):
319 '''Like C{math.isclose}, but with defaults such
320 that C{isclose(0, EPS0)} is C{True} by default.
321 '''
322 return _isclose(a, b, rel_tol=rel_tol, abs_tol=abs_tol)
325try:
326 from math import isfinite as _isfinite # in .ellipsoids, ...
327except ImportError: # Python 3.1-
329 def _isfinite(x):
330 '''Mimick Python 3.2+ C{math.isfinite}.
331 '''
332 return not (isinf(x) or isnan(x))
335def isfinite(obj):
336 '''Check a finite C{scalar} or C{complex} value.
338 @arg obj: Value (C{scalar} or C{complex}).
340 @return: C{False} if B{C{obj}} is C{INF}, C{NINF}
341 or C{NAN}, C{True} otherwise.
343 @raise TypeError: Non-scalar and non-complex B{C{obj}}.
344 '''
345 try:
346 return (obj not in _INF_NAN_NINF) and _isfinite(obj)
347 except Exception as x:
348 if iscomplex(obj): # _isfinite(complex) thows TypeError
349 return isfinite(obj.real) and isfinite(obj.imag)
350 raise _xError(x, Fmt.PAREN(isfinite.__name__, obj))
353def isint0(obj, both=False):
354 '''Check for L{INT0} or C{int(0)} value.
356 @arg obj: The object (any C{type}).
357 @kwarg both: If C{true}, also check C{float(0)} (C{bool}).
359 @return: C{True} if B{C{obj}} is L{INT0}, C{int(0)} or
360 C{float(0)}, C{False} otherwise.
361 '''
362 return (obj is INT0 or obj is int(0) or bool(both and
363 (not obj) and isint(obj, both=True))) and not isbool(obj)
366def isnear0(x, eps0=EPS0):
367 '''Is B{C{x}} near I{zero} within a tolerance?
369 @arg x: Value (C{scalar}).
370 @kwarg eps0: Near-I{zero} tolerance (C{EPS0}).
372 @return: C{True} if C{abs(B{x}) < B{eps0}},
373 C{False} otherwise.
375 @see: Function L{isnon0}.
376 '''
377 return bool(eps0 > x > -eps0)
380def isnear1(x, eps1=EPS0):
381 '''Is B{C{x}} near I{one} within a tolerance?
383 @arg x: Value (C{scalar}).
384 @kwarg eps1: Near-I{one} tolerance (C{EPS0}).
386 @return: C{isnear0(B{x} - 1, eps0=B{eps1})}.
388 @see: Function L{isnear0}.
389 '''
390 return bool(eps1 > (x - _1_0) > -eps1)
393def isnear90(x, eps90=EPS0):
394 '''Is B{C{x}} near I{90} within a tolerance?
396 @arg x: Value (C{scalar}).
397 @kwarg eps90: Near-I{90} tolerance (C{EPS0}).
399 @return: C{isnear0(B{x} - 90, eps0=eps90)}.
401 @see: Function L{isnear0}.
402 '''
403 return bool(eps90 > (x - _90_0) > -eps90)
406def isneg0(x):
407 '''Check for L{NEG0}, negative C{0.0}.
409 @arg x: Value (C{scalar}).
411 @return: C{True} if B{C{x}} is C{NEG0} or C{-0.0},
412 C{False} otherwise.
413 '''
414 return (not x) and _copysign(1, x) < 0
415# and str(x).startswith(_MINUS_)
418def isninf(x):
419 '''Check for L{NINF}, negative C{INF}.
421 @arg x: Value (C{scalar}).
423 @return: C{True} if B{C{x}} is C{NINF} or C{-inf},
424 C{False} otherwise.
425 '''
426 return x is NINF or (x < 0 and not isfinite(x))
429def isnon0(x, eps0=EPS0):
430 '''Is B{C{x}} non-zero with a tolerance?
432 @arg x: Value (C{scalar}).
433 @kwarg eps0: Non-zero tolerance (C{EPS0}).
435 @return: C{True} if C{abs(B{x}) > B{eps0}},
436 C{False} otherwise.
438 @see: Function L{isnear0}.
439 '''
440 return not bool(eps0 > x > -eps0) # not isnear0
443def _off90(lat):
444 '''(INTERNAL) Off 90.0 for .gars and .wgrs.
445 '''
446 return max(min(lat, _89_999_), -_89_999_)
449try:
450 from math import remainder
451except ImportError: # Python 3.6-
452 from math import fmod as _fmod
454 def remainder(x, y):
455 '''Mimick Python 3.7+ C{math.remainder}.
456 '''
457 if isnan(y):
458 x = NAN
459 elif x and not isnan(x):
460 y = fabs(y)
461 x = _fmod(x, y)
462 h = _0_5 * y
463 if x >= h:
464 x -= y
465 elif x < -h:
466 x += y
467 return x # keep signed 0.0
470def _umod_360(deg):
471 '''(INTERNAL) Non-negative C{deg} modulo 360, basic C{.utily.wrap360}.
472 '''
473 return (deg % _360_0) or _0_0
476def _umod_PI2(rad):
477 '''(INTERNAL) Non-negative C{rad} modulo PI2, basic C{.utily.wrapPI2}.
478 '''
479 return (rad % PI2) or _0_0
482if __name__ == '__main__':
484 from pygeodesy import itemsorted, printf
486 t = n = v = []
487 for n, v in itemsorted(locals()):
488 if isinstance(v, (Float, Int, Radius)):
489 printf('%9s: %r', n, v.toRepr(std=False))
490 if v.name != n:
491 raise AssertionError('%r != %r' % (n, v))
492 if v.name is not n:
493 raise AssertionError('%r is not %r' % (n, v))
494 if not n.startswith(_UNDER_):
495 t.append(n)
496 t.append(float_.__name__)
497 printf('__all__ = %r', tuple(t))
499# **) MIT License
500#
501# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.
502#
503# Permission is hereby granted, free of charge, to any person obtaining a
504# copy of this software and associated documentation files (the "Software"),
505# to deal in the Software without restriction, including without limitation
506# the rights to use, copy, modify, merge, publish, distribute, sublicense,
507# and/or sell copies of the Software, and to permit persons to whom the
508# Software is furnished to do so, subject to the following conditions:
509#
510# The above copyright notice and this permission notice shall be included
511# in all copies or substantial portions of the Software.
512#
513# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
514# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
515# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
516# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
517# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
518# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
519# OTHER DEALINGS IN THE SOFTWARE.