Coverage for pygeodesy/constants.py: 98%

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1 

2# -*- coding: utf-8 -*- 

3 

4u'''Single-instance C{float} and C{int} constants across C{pygeodesy} modules and 

5related functions L{pygeodesy.float_}, L{pygeodesy.isclose}, L{pygeodesy.isfinite}, 

6L{pygeodesy.isinf}, L{pygeodesy.isint0}, L{pygeodesy.isnan}, L{pygeodesy.isnear0}, 

7L{pygeodesy.isnear1}, L{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 

12 

13from pygeodesy.basics import _copysign, isbool, iscomplex, isint 

14from pygeodesy.errors import _xError, _xError2, _xkwds_get1, _xkwds_item2 

15# from pygeodesy.fsums import _isFsum_2Tuple # _MODS 

16from pygeodesy.internals import _0_0, _100_0 

17from pygeodesy.interns import _INF_, _NAN_, _UNDER_ 

18from pygeodesy.lazily import _ALL_MODS as _MODS, _ALL_LAZY 

19# from pygeodesy.streprs import Fmt # from .unitsBase 

20from pygeodesy.unitsBase import Float, Int, Radius, Fmt 

21 

22from math import fabs, isinf, isnan, pi as _pi, sqrt 

23try: 

24 from math import inf as _inf, nan as _nan # PYCHOK Python 3+ 

25except ImportError: # Python 2- 

26 _inf, _nan = float(_INF_), float(_NAN_) 

27 

28__all__ = _ALL_LAZY.constants 

29__version__ = '24.12.22' 

30 

31 

32def _copysign_0_0(y): 

33 '''(INTERNAL) copysign(0.0, y), only C{float}. 

34 ''' 

35 return _N_0_0 if y < 0 else _0_0 

36 

37 

38def _copysign_1_0(y): 

39 '''(INTERNAL) copysign(1.0, y), only C{float}. 

40 ''' 

41 return _N_1_0 if y < 0 else _1_0 

42 

43 

44def _copysignINF(y): 

45 '''(INTERNAL) copysign(INF, y), only C{float}. 

46 ''' 

47 return NINF if y < 0 else INF 

48 

49 

50def _Float(**name_arg): 

51 '''(INTERNAL) New named, cached C{Float}. 

52 ''' 

53 n, arg = _xkwds_item2(name_arg) 

54 return Float(_float(arg), name=n) 

55 

56 

57def _Radius(**name_arg): 

58 '''(INTERNAL) New named, cached C{Radius}. 

59 ''' 

60 n, arg = _xkwds_item2(name_arg) 

61 return Radius(_float(arg), name=n) 

62 

63 

64def float_(*fs, **sets): # sets=False 

65 '''Get scalars as C{float} or I{intern}'ed C{float}. 

66 

67 @arg fs: One more values (C{scalar}), all positional. 

68 @kwarg sets: Use C{B{sets}=True} to C{intern} each 

69 B{C{fs}}, otherwise don't C{intern}. 

70 

71 @return: A single C{float} if only one B{C{fs}} is 

72 given, otherwise a tuple of C{float}s. 

73 

74 @raise TypeError: Some B{C{fs}} is not C{scalar}. 

75 ''' 

76 fl = [] 

77 _a = fl.append 

78 _f = _floats.setdefault if _xkwds_get1(sets, sets=False) else \ 

79 _floats.get 

80 try: 

81 for i, f in enumerate(fs): 

82 f = float(f) 

83 _a(_f(f, f)) 

84 except Exception as x: 

85 E, t = _xError2(x) 

86 fs_i = Fmt.SQUARE(fs=i) 

87 raise E(fs_i, f, txt=t) 

88 return fl[0] if len(fl) == 1 else tuple(fl) 

89 

90 

91def _float(f): # in .datums, .ellipsoids, ... 

92 '''(INTERNAL) Cache initial C{float}s. 

93 ''' 

94 f = float(f) 

95 return _floats.setdefault(f, f) # PYCHOK del _floats 

96 

97 

98def float0_(*xs): 

99 '''Yield C{B{x}s} as a non-NEG0 C{float}. 

100 ''' 

101 for x in xs: 

102 yield float(x) if x else _0_0 

103 

104 

105def _float0(f): # in .auxilats.auxily, .resections, .vector3dBase, ... 

106 '''(INTERNAL) Return C{float(B{f})} or C{INT0}. 

107 ''' 

108 if f: 

109 f = float(f) 

110 f = _floats.get(f, f) 

111 elif f is not INT0: 

112 f = float(f) or _0_0 # force None, NN error 

113 return f 

114 

115 

116def _floatuple(*fs): 

117 '''(INTERNAL) Cache a tuple of C{float}s. 

118 ''' 

119 return tuple(map(_float, fs)) 

120 

121 

122try: 

123 from math import log2 as _log2 

124except ImportError: # Python 3.3- 

125 from math import log as _log 

126 

127 def _log2(x): # in .rhumb.aux_, .auxilats.auxLat 

128 return _log(x, 2) 

129 

130 

131def _naninf(p, *xs): 

132 '''(INTERNAL) Return C{NAN}, C{NINF} or C{INF}. 

133 ''' 

134 for x in xs: 

135 p *= x # fmath.fprod(xs) 

136 return _copysignINF(p) if isfinite(p) else p 

137 

138 

139def _over(p, q): 

140 '''(INTERNAL) Return C{B{p} / B{q}} avoiding C{ZeroDivisionError} exceptions. 

141 ''' 

142 try: 

143 return (p / q) # if p else _copysign_0_0(q) 

144 except ZeroDivisionError: 

145 return (_copysignINF(p) if isfinite(p) else NAN) if p else p 

146 

147 

148def _1_over(x): 

149 '''(INTERNAL) Return reciprocal C{1 / B{x}} avoiding C{ZeroDivisionError} exceptions. 

150 ''' 

151 try: 

152 return _1_0 / float(x) 

153 except ZeroDivisionError: 

154 return NINF if isneg0(x) else INF 

155 

156 

157_floats = {} # PYCHOK floats cache, in .__main__ 

158# _float = float # PYCHOK expected 

159# del _floats # XXX zap floats cache never 

160 

161_0_0 = _float( _0_0) # PYCHOK expected 

162_0_0_1T = _0_0, # PYCHOK 1-tuple 

163_0_0_9T = _0_0_1T * 9 # PYCHOK 9-tuple 

164_0_0001 = _float( 0.0001) # PYCHOK expected 

165_0_001 = _float( 0.001) # PYCHOK expected 

166_0_01 = _float( 0.01) # PYCHOK expected 

167_0_1 = _float( 0.1) # PYCHOK expected 

168_0_125 = _float( 0.125) # PYCHOK expected 

169_0_25 = _float( 0.25) # 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_45_0 = _float( 45) # PYCHOK expected 

186_60_0 = _float( 60) # PYCHOK expected 

187_64_0 = _float( 64) # PYCHOK expected 

188_90_0 = _float( 90) # PYCHOK expected 

189_100_0 = _float(_100_0) # PYCHOK expected 

190_180_0 = _float( 180) # PYCHOK expected 

191_270_0 = _float( 270) # PYCHOK expected 

192_360_0 = _float( 360) # PYCHOK expected 

193_720_0 = _float( 720) # PYCHOK expected 

194_1000_0 = _float(1000) # PYCHOK expected 

195_3600_0 = _float(3600) # PYCHOK expected 

196 

197_N_0_0 = float( '-0.0') # PYCHOK NOT _float! 

198_N_0_5 = _float( -_0_5) # PYCHOK expected 

199_N_1_0 = _float( -_1_0) # PYCHOK expected 

200_N_2_0 = _float( -_2_0) # PYCHOK expected 

201_N_90_0 = _float( -_90_0) # PYCHOK expected 

202_N_180_0 = _float(-_180_0) # PYCHOK expected 

203 

204_M_KM = _1000_0 # meter per Kilo meter, see .utily 

205_M_NM = _float(1852.0) # meter per Nautical Mile, exactly 

206_M_SM = _float(1609.344) # meter per Statute Mile 

207 

208try: 

209 from sys import float_info as _f_i 

210 # @see: <https://NumPy.org/doc/stable/reference/generated/numpy.finfo.html> 

211 DIG = Int( DIG =_f_i.dig) # PYCHOK system's float decimal digits 

212 EPS = _Float(EPS =_f_i.epsilon) # PYCHOK system's EPSilon 

213 MANT_DIG = Int( MANT_DIG=_f_i.mant_dig) # PYCHOK system's float mantissa bits 

214 MAX = _Float(MAX =_f_i.max) # PYCHOK system's MAX float 1.7976931348623157e+308 

215 MAX_EXP = Int( MAX_EXP =_f_i.max_exp) # PYTHON system's max base 2 exponent 

216 MIN = _Float(MIN =_f_i.min) # PYCHOK system's MIN float 2.2250738585072014e-308 

217 MIN_EXP = Int( MIN_EXP =_f_i.min_exp) # PYTHON system's min base 2 exponent 

218# RADIX = Int( RADIX =_f_i.radix) # PYTHON system's float base 

219 del _f_i 

220except ImportError: # PYCHOK no cover 

221 DIG = Int( DIG =15) # PYCHOK system's 64-bit float decimal digits 

222 EPS = _Float(EPS =2.220446049250313e-16) # PYCHOK EPSilon 2**-52, M{EPS +/- 1 != 1} 

223 MANT_DIG = Int( MANT_DIG=53) # PYCHOK float mantissa bits ≈ 53 (C{int}) 

224 MAX = _Float(MAX =pow(_2_0, 1023) * (_2_0 - EPS)) # PYCHOK ≈ 10**308 

225 MAX_EXP = Int( MAX_ESP =_log2(MAX)) # 308 base 10 

226 MIN = _Float(MIN =pow(_2_0, -1021)) # PYCHOK ≈ 10**-308 

227 MIN_EXP = Int(MIN_EXP =_log2(MIN)) # -307 base 10 

228# RADIX = Int(Radix =2) # base 

229 

230EPS0 = _Float( EPS0 = EPS**2) # PYCHOK near-/non-zero comparison 4.930381e-32, or EPS or EPS_2 

231EPS02 = _Float( EPS02 = EPS**4) # PYCHOK near-zero-squared comparison 2.430865e-63 

232EPS_2 = _Float( EPS_2 = EPS / _2_0) # PYCHOK ≈ 1.110223024625e-16 

233EPS1 = _Float( EPS1 =_1_0 - EPS) # PYCHOK ≈ 0.9999999999999998 

234EPS2 = _Float( EPS2 = EPS * _2_0) # PYCHOK ≈ 4.440892098501e-16 

235EPS4 = _Float( EPS4 = EPS * _4_0) # PYCHOK ≈ 8.881784197001e-16 

236# _1EPS = _Float(_1EPS =_1_0 + EPS) # PYCHOK ≈ 1.0000000000000002 

237_1_EPS = _Float(_1_EPS =_1_0 / EPS) # PYCHOK = 4503599627370496.0 

238# _2_EPS = _Float(_2_EPS =_2_0 / EPS) # PYCHOK = 9007199254740992.0 

239_EPS2e4 = _Float(_EPS2e4= EPS2 * 1.e4) # PYCHOK ≈ 4.440892098501e-12 

240_EPS4e8 = _Float(_EPS4e8= EPS4 * 1.e8) # PYCHOK ≈ 8.881784197001e-08 

241_EPSjam = _Float(_EPSjam= pow(EPS, 0.75)) # PYCHOK = 1.818989403546e-12 

242_EPSmin = _Float(_EPSmin= sqrt(MIN)) # PYCHOK = 1.49166814624e-154 

243_EPSqrt = _Float(_EPSqrt= sqrt(EPS)) # PYCHOK = 1.49011611938e5-08 

244_EPStol = _Float(_EPStol=_EPSqrt * _0_1) # PYCHOK = 1.49011611938e5-09 == sqrt(EPS * _0_01) 

245 

246_89_999 = _Float(_89_999=_90_0 * EPS1) # just below 90.0 

247# <https://Numbers.Computation.Free.FR/Constants/Miscellaneous/digits.html> 

248_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 

249_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 

250 

251_1_16th = _Float(_1_16th=_1_0 / _16_0) # PYCHOK in .ellipsoids, .karney 

252_1_3rd = _Float(_1_3rd =_1_0 / _3_0) # PYCHOK in .fmath 

253_1_6th = _Float(_1_6th =_1_0 / _6_0) # PYCHOK in .fmath 

254 

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# 0.707106781186547_524_400_844_362_104_849_039_284_835_937_688_474_036_588_339_868_99 

260_SQRT2_2 = _Float(_SQRT2_2=sqrt(_0_5)) # PYCHOK = 0.707106781186547_5 == sqrt(2) / 2 

261 

262INF = Float(INF =_inf) # PYCHOK INFinity, see function L{isinf}, L{isfinite}, NOT _Float! 

263INT0 = Int( INT0= 0) # PYCHOK unique int(0) instance, see .fsums, useZ=False 

264NAN = Float(NAN =_nan) # PYCHOK Not-A-Number, see function L{isnan}, NOT _Float! 

265NEG0 = Float(NEG0=_N_0_0) # PYCHOK NEGative 0.0, see function L{isneg0}, NOT _Float! 

266NINF = Float(NINF=-INF) # PYCHOK Negative INFinity, NOT _Float! 

267 

268PI = _Float(PI =_pi) # 3.1415_9265_3589_7932_3846_2643_3832_795 

269PI2 = _Float(PI2 =_pi * _2_0) # PYCHOK Two PI, M{PI * 2} aka I{Tau} 

270PI_2 = _Float(PI_2 =_pi / _2_0) # PYCHOK Half PI, M{PI / 2} 

271PI3 = _Float(PI3 =_pi * _3_0) # PYCHOK Three PI, M{PI * 3} 

272PI3_2 = _Float(PI3_2=_pi * _1_5) # PYCHOK PI and a half, M{PI * 3 / 2} 

273PI_3 = _Float(PI_3 =_pi / _3_0) # PYCHOK One third PI, M{PI / 3} 

274PI4 = _Float(PI4 =_pi * _4_0) # PYCHOK Four PI, M{PI * 4} 

275PI_4 = _Float(PI_4 =_pi / _4_0) # PYCHOK Quarter PI, M{PI / 4} 

276 

277R_MA = _Radius(R_MA=6378137.0) # PYCHOK equatorial earth radius (C{meter}), WGS84, EPSG:3785 

278R_MB = _Radius(R_MB=6356752.3) # PYCHOK polar earth radius (C{meter}), WGS84, EPSG:3785 

279R_M = _Radius(R_M =6371008.771415) # PYCHOK mean, spherical earth radius (C{meter}) 

280R_KM = _Radius(R_KM=R_M / _M_KM) # PYCHOK mean, spherical earth radius (C{KM}, Kilo meter) 

281R_NM = _Radius(R_NM=R_M / _M_NM) # PYCHOK mean, spherical earth radius (C{NM}, nautical miles) 

282R_SM = _Radius(R_SM=R_M / _M_SM) # PYCHOK mean, spherical earth radius (C{SM}, statute miles) 

283# See <https://www.EdWilliams.org/avform.htm>, <https://www.DTIC.mil/dtic/tr/fulltext/u2/a216843.pdf> 

284# and <https://GitHub.com/NASA/MultiDop/blob/master/src/share/man/man3/geog_lib.3> based on the 

285# International Standard Nautical Mile of 1,852 meter (1' latitude) 

286R_FM = _Radius(R_FM=6371000.0) # PYCHOK former FAI Sphere earth radius (C{meter}) 

287R_GM = _Radius(R_GM=6371230.0) # PYCHOK avg. radius, distance to geoid surface (C{meter}) 

288# <http://Wiki.GIS.com/wiki/index.php/Ellipsoidal_quadratic_mean_radius> 

289R_QM = _Radius(R_QM=6372797.560856) # PYCHOK earth' quadratic mean radius (C{meter}) 

290# Rtri= _Radius(Rtri=6372797.5559594) # PYCHOK Rtriaxial quadratic mean radius (C{meter}), WGS84 

291# Rbi = _Radius(Rbi =6367453.6345163) # PYCHOK Rbiaxial quadratic mean radius (C{meter}), WGS84 

292R_VM = _Radius(R_VM=6366707.0194937) # PYCHOK aViation/naVigation earth radius (C{meter}) 

293# R_AU= Meter( R_AU=149597870700.0) # PYCHOK <https://WikiPedia.org/wiki/Astronomical_unit> 

294 

295_INF_NAN_NINF = INF, NAN, NINF 

296_pos_self = _1_0.__pos__() is _1_0 # PYCHOK in .fsums, .vector3dBase 

297 

298 

299def _0_0s(n): 

300 '''(INTERNAL) Return an C{B{n}-tuple} of C{_0_0} zeros. 

301 ''' 

302 return _0_0_9T[:n] if 0 <= n <= len(_0_0_9T) else (_0_0_1T * n) 

303 

304 

305try: 

306 from math import isclose as _isclose 

307except ImportError: # Python 3.4- 

308 

309 def _isclose(a, b, rel_tol=1e-9, abs_tol=0): 

310 '''Mimick Python 3.5+ C{math.isclose}. 

311 ''' 

312 t, d = abs_tol, fabs(a - b) 

313 if d > t: 

314 r = max(fabs(a), fabs(b)) * rel_tol 

315 t = max(r, t) 

316 return d <= t 

317 

318 

319def isclose(a, b, rel_tol=1e-12, abs_tol=EPS0): 

320 '''Like C{math.isclose}, but with defaults such 

321 that C{isclose(0, EPS0)} is C{True} by default. 

322 ''' 

323 return _isclose(a, b, rel_tol=rel_tol, abs_tol=abs_tol) 

324 

325 

326try: 

327 from cmath import isfinite as _iscfinite 

328except ImportError: # Python 3.1- 

329 

330 def _iscfinite(x): # PYCHOK not self? 

331 '''Mimick Python 3.2+ C{cmath.isfinite}. 

332 ''' 

333 return _isfinite(x.real) and _isfinite(x.imag) 

334 

335try: 

336 from math import isfinite as _isfinite # in .ellipsoids, ... 

337except ImportError: # Python 3.1- 

338 

339 def _isfinite(x): # PYCHOK not self? 

340 '''Mimick Python 3.2+ C{math.isfinite}. 

341 ''' 

342 return not (isinf(x) or isnan(x)) 

343 

344 

345def isfinite(obj): 

346 '''Check a finite C{scalar}, C{complex}, ... value. 

347 

348 @arg obj: Value (C{scalar}, C{complex}, an L{Fsum} or 

349 L{Fsum2Tuple}). 

350 

351 @return: C{False} if B{C{obj}} is C{INF}, C{NINF} or 

352 C{NAN}, C{True} otherwise. 

353 

354 @raise TypeError: Non-scalar and non-complex B{C{obj}}. 

355 ''' 

356 try: 

357 return (obj not in _INF_NAN_NINF) and _isfinite(obj) 

358 except Exception as x: 

359 if iscomplex(obj): # _isfinite(complex) thows TypeError 

360 return _iscfinite(obj) 

361 if _MODS.fsums._isFsum_2Tuple(obj): # OverflowError 

362 return obj.is_finite() 

363 raise _xError(x, Fmt.PAREN(isfinite.__name__, obj)) 

364 

365 

366def isint0(obj, both=False): 

367 '''Check for L{INT0} or C{int(0)} value. 

368 

369 @arg obj: The object (any C{type}). 

370 @kwarg both: If C{true}, also check C{float(0)} (C{bool}). 

371 

372 @return: C{True} if B{C{obj}} is L{INT0}, C{int(0)} or 

373 C{float(0)}, C{False} otherwise. 

374 ''' 

375 return (obj is INT0 or obj is int(0) or 

376 bool(both and (not obj) and isint(obj, both=True))) and \ 

377 not isbool(obj) 

378 

379 

380def isnear0(x, eps0=EPS0): 

381 '''Is B{C{x}} near I{zero} within a tolerance? 

382 

383 @arg x: Value (C{scalar}). 

384 @kwarg eps0: Near-I{zero} tolerance (C{EPS0}). 

385 

386 @return: C{True} if C{abs(B{x}) < B{eps0}}, 

387 C{False} otherwise. 

388 

389 @see: Function L{isnon0}. 

390 ''' 

391 return bool(eps0 > x > -eps0) 

392 

393 

394def isnear1(x, eps1=EPS0): 

395 '''Is B{C{x}} near I{one} within a tolerance? 

396 

397 @arg x: Value (C{scalar}). 

398 @kwarg eps1: Near-I{one} tolerance (C{EPS0}). 

399 

400 @return: C{isnear0(B{x} - 1, eps0=B{eps1})}. 

401 

402 @see: Function L{isnear0}. 

403 ''' 

404 return bool(eps1 > (x - _1_0) > -eps1) 

405 

406 

407def isnear90(x, eps90=EPS0): 

408 '''Is B{C{x}} near I{90} within a tolerance? 

409 

410 @arg x: Value (C{scalar}). 

411 @kwarg eps90: Near-I{90} tolerance (C{EPS0}). 

412 

413 @return: C{isnear0(B{x} - 90, eps0=eps90)}. 

414 

415 @see: Function L{isnear0}. 

416 ''' 

417 return bool(eps90 > (x - _90_0) > -eps90) 

418 

419 

420def isneg0(x): 

421 '''Check for L{NEG0}, negative C{0.0}. 

422 

423 @arg x: Value (C{scalar}). 

424 

425 @return: C{True} if B{C{x}} is C{NEG0} or C{-0.0}, 

426 C{False} otherwise. 

427 ''' 

428 return (not x) and _copysign(1, x) < 0 

429# and str(x).startswith(_MINUS_) 

430 

431 

432def isninf(x): 

433 '''Check for L{NINF}, negative C{INF}. 

434 

435 @arg x: Value (C{scalar}). 

436 

437 @return: C{True} if B{C{x}} is C{NINF} or C{-inf}, 

438 C{False} otherwise. 

439 ''' 

440 return x is NINF or (x < 0 and not isfinite(x)) 

441 

442 

443def isnon0(x, eps0=EPS0): 

444 '''Is B{C{x}} non-zero with a tolerance? 

445 

446 @arg x: Value (C{scalar}). 

447 @kwarg eps0: Non-zero tolerance (C{EPS0}). 

448 

449 @return: C{True} if C{abs(B{x}) > B{eps0}}, 

450 C{False} otherwise. 

451 

452 @see: Function L{isnear0}. 

453 ''' 

454 return not bool(eps0 > x > -eps0) # not isnear0 

455 

456 

457def _off90(lat): 

458 '''(INTERNAL) Off 90.0 for .gars and .wgrs. 

459 ''' 

460 return max(min(lat, _89_999), -_89_999) 

461 

462 

463try: 

464 from math import remainder 

465except ImportError: # Python 3.6- 

466 from math import fmod as _fmod 

467 

468 def remainder(x, y): 

469 '''Mimick Python 3.7+ C{math.remainder}. 

470 ''' 

471 if isnan(y): 

472 x = NAN 

473 elif x and not isnan(x): 

474 y = fabs(y) 

475 x = _fmod(x, y) 

476 h = _0_5 * y 

477 if x >= h: 

478 x -= y 

479 elif x < -h: 

480 x += y 

481 return x # keep signed 0.0 

482 

483 

484def _umod_360(deg): 

485 '''(INTERNAL) Non-negative C{deg} modulo 360, basic C{.utily.wrap360}. 

486 ''' 

487 return (deg % _360_0) or _0_0 

488 

489 

490def _umod_PI2(rad): 

491 '''(INTERNAL) Non-negative C{rad} modulo PI2, basic C{.utily.wrapPI2}. 

492 ''' 

493 return (rad % PI2) or _0_0 

494 

495 

496if __name__ == '__main__': 

497 

498 def _main(): 

499 from pygeodesy import itemsorted, printf 

500 

501 t = n = v = [] 

502 for n, v in itemsorted(locals()): 

503 if isinstance(v, (Float, Int, Radius)): 

504 printf('%9s: %r', n, v.toRepr(std=False)) 

505 if v.name != n: 

506 raise AssertionError('%r != %r' % (n, v)) 

507 if v.name is not n: 

508 raise AssertionError('%r is not %r' % (n, v)) 

509 if not n.startswith(_UNDER_): 

510 t.append(n) 

511 t.append(float_.__name__) 

512 printf('__all__ = %r', tuple(t)) 

513 

514 _main() 

515 

516# **) MIT License 

517# 

518# Copyright (C) 2016-2025 -- mrJean1 at Gmail -- All Rights Reserved. 

519# 

520# Permission is hereby granted, free of charge, to any person obtaining a 

521# copy of this software and associated documentation files (the "Software"), 

522# to deal in the Software without restriction, including without limitation 

523# the rights to use, copy, modify, merge, publish, distribute, sublicense, 

524# and/or sell copies of the Software, and to permit persons to whom the 

525# Software is furnished to do so, subject to the following conditions: 

526# 

527# The above copyright notice and this permission notice shall be included 

528# in all copies or substantial portions of the Software. 

529# 

530# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

531# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

532# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

533# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

534# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 

535# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 

536# OTHER DEALINGS IN THE SOFTWARE.