Coverage for pygeodesy/utily.py: 94%
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« prev ^ index » next coverage.py v7.6.1, created at 2025-09-09 13:03 -0400
2# -*- coding: utf-8 -*-
4u'''Various utility functions.
6After I{Karney}'s C++ U{Math<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Math.html>}
7class and I{Veness}' U{Latitude/Longitude<https://www.Movable-Type.co.UK/scripts/latlong.html>}
8and U{Vector-based geodesy<https://www.Movable-Type.co.UK/scripts/latlong-vectors.html>}
9and published under the same MIT Licence**.
10'''
11# make sure int/int division yields float quotient, see .basics
12from __future__ import division as _; del _ # noqa: E702 ;
14from pygeodesy.basics import _copysign, isinstanceof, isint, isstr
15from pygeodesy.constants import EPS, EPS0, NAN, PI, PI2, PI_2, PI_4, PI_6, R_M, \
16 _M_KM, _M_NM, _M_SM, _0_0, _0_5, _1_0, _N_1_0, \
17 _10_0, _90_0, _180_0, _360_0, _copysign_0_0, \
18 _copysignINF, _float, _isfinite, isnan, isnear0, \
19 _over_1, _umod_360, _umod_PI2
20from pygeodesy.errors import _ValueError, _xkwds, _xkwds_get
21from pygeodesy.internals import _Enum, _passargs, typename
22from pygeodesy.interns import _edge_, _radians_, _semi_circular_, _SPACE_
23from pygeodesy.lazily import _ALL_LAZY, _ALL_MODS as _MODS
24from pygeodesy.units import Degrees, Degrees_, Feet, Float, Lam, Lamd, \
25 Meter, Meter2, Radians # Radians_
27from math import acos, asin, asinh, atan2 as _atan2, cos, degrees, fabs, \
28 radians, sin, sinh, tan as _tan # pow
30__all__ = _ALL_LAZY.utily
31__version__ = '25.09.09'
33# sqrt(3) <https://WikiPedia.org/wiki/Square_root_of_3>
34_COS_30, _SIN_30 = 0.86602540378443864676, _0_5 # sqrt(3) / 2
35_COS_45 = _SIN_45 = 0.70710678118654752440 # sqrt(2) / 2
37_G = _Enum( # grades per ...
38 DEG = _float( 400.0 / _360_0), # degree
39 RAD = _float( 400.0 / PI2)) # radian
41_M = _Enum( # meter per ...
42 ACRE = _float( 4046.8564224), # acre, chain2m(1) * furlong2m(1), squared
43 CHAIN = _float( 20.1168), # yard2m(1) * 22
44 FATHOM = _float( 1.8288), # yard2m(1) * 2 or _M.NM * 1e-3
45 FOOT = _float( 0.3048), # Int'l foot, 1 / 3.280_839_895_0131 = 10_000 / (254 * 12)
46 FOOT_GE = _float( 0.31608), # German Fuss, 1 / 3.163_756_011_1364
47 FOOT_FR = _float( 0.3248406), # French Pied-du-Roi or pied, 1 / 3.078_432_929_8739
48 FOOT_US = _float( 0.3048006096012192), # US Survey foot, 1_200 / 3_937
49 FURLONG = _float( 201.168), # furlong, 220 * yard2m(1) = 10 * m2chain(1)
50 HA = _float(10000.0), # hectare, 100 * 100, squared
51 KM = _M_KM, # kilo meter
52 NM = _M_NM, # nautical mile
53 SM = _M_SM, # statute mile
54 TOISE = _float( 1.9490436), # French toise, 6 pieds = 6 / 3.078_432_929_8739
55 YARD_UK = _float( 0.9144)) # yard, 254 * 12 * 3 / 10_000 = 3 * _M.FOOT
58def _abs1nan(x):
59 '''(INTERNAL) Bracket C{x}.
60 '''
61 return _N_1_0 < x < _1_0 or isnan(x)
64def acos1(x):
65 '''Return C{math.acos(max(-1, min(1, B{x})))}.
66 '''
67 return acos(x) if _abs1nan(x) else (PI if x < 0 else _0_0)
70def acre2ha(acres):
71 '''Convert acres to hectare.
73 @arg acres: Value in acres (C{scalar}).
75 @return: Value in C{hectare} (C{float}).
77 @raise ValueError: Invalid B{C{acres}}.
78 '''
79 return m2ha(acre2m2(acres))
82def acre2m2(acres):
83 '''Convert acres to I{square} meter.
85 @arg acres: Value in acres (C{scalar}).
87 @return: Value in C{meter^2} (C{float}).
89 @raise ValueError: Invalid B{C{acres}}.
90 '''
91 return Meter2(Float(acres=acres) * _M.ACRE)
94def agdf(phi):
95 '''Inverse U{Gudermannian function
96 <https://WikiPedia.org/wiki/Gudermannian_function>}.
98 @arg phi: Angle (C{radians}).
100 @return: Gudermannian (psi, C{float}).
102 @see: Function L{gdf}.
103 '''
104 return asinh(tan(phi))
107def asin1(x):
108 '''Return C{math.asin(max(-1, min(1, B{x})))}.
109 '''
110 return asin(x) if _abs1nan(x) else _copysign(PI_2, x)
113def atan1(y, x=_1_0):
114 '''Return C{atan(B{y} / B{x})} angle in C{radians} M{[-PI/2..+PI/2]}
115 using C{atan2} for consistency and to avoid C{ZeroDivisionError}.
116 '''
117 return _atan1u(y, x, atan2)
120def atan1d(y, x=_1_0):
121 '''Return C{atan(B{y} / B{x})} angle in C{degrees} M{[-90..+90]}
122 using C{atan2d} for consistency and to avoid C{ZeroDivisionError}.
124 @see: Function L{pygeodesy.atan2d}.
125 '''
126 return _atan1u(y, x, atan2d)
129def _atan1u(y, x, _2u):
130 '''(INTERNAL) Helper for functions C{atan1} and C{atan1d}.
131 '''
132 if x < 0:
133 x = -x
134 y = -y
135 return _2u(y, x or _0_0)
138atan2 = _atan2
139'''Return C{atan2(B{y}, B{x})} in radians M{[-PI..+PI]}.
141 @see: I{Karney}'s C++ function U{Math.atan2d
142 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Math.html>}.
143'''
146def atan2b(y, x):
147 '''Return C{atan2(B{y}, B{x})} in degrees M{[0..+360], counter-clockwise}.
149 @see: Function L{pygeodesy.atan2d}.
150 '''
151 b = atan2d(y, x)
152 if b < 0:
153 b += _360_0
154 return b or _0_0 # unsigned-0
157def atan2d(y, x, reverse=False):
158 '''Return C{atan2(B{y}, B{x})} in degrees M{[-180..+180]},
159 optionally I{reversed} (by 180 degrees for C{azimuth}s).
161 @see: I{Karney}'s C++ function U{Math.atan2d
162 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Math.html>}.
163 '''
164 d = degrees(_atan2(y, x)) # preserves signed-0
165 return _azireversed(d) if reverse else d
168def _azireversed(azi): # in .rhumbBase
169 '''(INTERNAL) Return the I{reverse} B{C{azi}} in degrees M{[-180..+180]}.
170 '''
171 return azi - _copysign(_180_0, azi)
174def chain2m(chains):
175 '''Convert I{UK} chains to meter.
177 @arg chains: Value in chains (C{scalar}).
179 @return: Value in C{meter} (C{float}).
181 @raise ValueError: Invalid B{C{chains}}.
182 '''
183 return Meter(Float(chains=chains) * _M.CHAIN)
186def circle4(earth, lat):
187 '''Get the equatorial or a parallel I{circle of latitude}.
189 @arg earth: The earth radius (C{meter}) or an ellipsoid or datum
190 (L{Ellipsoid}, L{Ellipsoid2}, L{Datum} or L{a_f2Tuple}).
191 @arg lat: Geodetic latitude (C{degrees90}, C{str}).
193 @return: A L{Circle4Tuple}C{(radius, height, lat, beta)}.
195 @raise RangeError: Latitude B{C{lat}} outside valid range and
196 L{rangerrors<pygeodesy.rangerrors>} is C{True}.
198 @raise TypeError: Invalid B{C{earth}}.
200 @raise ValueError: invalid B{C{earth}} or B{C{lat}}.
201 '''
202 E = _MODS.datums._earth_ellipsoid(earth)
203 return E.circle4(lat)
206def _circle4radius(earth, lat, **radius):
207 '''(INTERNAL) Get C{circle4(earth, lat).radius}.
208 '''
209 e = _xkwds_get(radius, radius=earth) if radius else earth
210 return e if e is R_M and not lat else circle4(e, lat).radius
213def cot(rad, **raiser_kwds):
214 '''Return the C{cotangent} of an angle in C{radians}.
216 @arg rad: Angle (C{radians}).
217 @kwarg raiser_kwds: Use C{B{raiser}=False} to avoid
218 ValueErrors and optional, additional
219 ValueError keyword argments.
221 @return: C{cot(B{rad})}.
223 @raise Error: If L{pygeodesy.isnear0}C{(sin(B{rad})}.
224 '''
225 try:
226 return _cotu(*sincos2(rad))
227 except ZeroDivisionError:
228 return _nonfinite(cot, rad, **raiser_kwds)
231def cot_(*rads, **raiser_kwds):
232 '''Yield the C{cotangent} of angle(s) in C{radians}.
234 @arg rads: One or more angles (each in C{radians}).
236 @return: Yield C{cot(B{rad})} for each angle.
238 @see: Function L{pygeodesy.cot} for further details.
239 '''
240 try:
241 for r in rads:
242 yield _cotu(*sincos2(r))
243 except ZeroDivisionError:
244 yield _nonfinite(cot_, r, **raiser_kwds)
247def cotd(deg, **raiser_kwds):
248 '''Return the C{cotangent} of an angle in C{degrees}.
250 @arg deg: Angle (C{degrees}).
251 @kwarg raiser_kwds: Use C{B{raiser}=False} to avoid
252 ValueErrors and optional, additional
253 ValueError keyword argments.
255 @return: C{cot(B{deg})}.
257 @raise Error: If L{pygeodesy.isnear0}C{(sin(B{deg})}.
258 '''
259 try:
260 return _cotu(*sincos2d(deg))
261 except ZeroDivisionError:
262 return _nonfinite(cotd, deg, **raiser_kwds)
265def cotd_(*degs, **raiser_kwds):
266 '''Yield the C{cotangent} of angle(s) in C{degrees}.
268 @arg degs: One or more angles (each in C{degrees}).
270 @return: Yield C{cotd(B{deg})} for each angle.
272 @see: Function L{pygeodesy.cotd} for further details.
273 '''
274 try:
275 for d in degs:
276 yield _cotu(*sincos2d(d))
277 except ZeroDivisionError:
278 yield _nonfinite(cotd_, d, **raiser_kwds)
281def _cotu(s, c):
282 '''(INTERNAL) Helper for functions C{cot}, C{cotd}, C{cot_} and C{cotd_}.
283 '''
284 return _tanu(c, s)
287def degrees90(rad):
288 '''Convert radians to degrees and wrap M{[-90..+90)}.
290 @arg rad: Angle (C{radians}).
292 @return: Angle, wrapped (C{degrees90}).
293 '''
294 return wrap90(degrees(rad))
297def degrees180(rad):
298 '''Convert radians to degrees and wrap M{[-180..+180)}.
300 @arg rad: Angle (C{radians}).
302 @return: Angle, wrapped (C{degrees180}).
303 '''
304 return wrap180(degrees(rad))
307def degrees360(rad):
308 '''Convert radians to degrees and wrap M{[0..+360)}.
310 @arg rad: Angle (C{radians}).
312 @return: Angle, wrapped (C{degrees360}).
313 '''
314 return _umod_360(degrees(rad))
317def degrees2grades(deg):
318 '''Convert degrees to I{grades} (aka I{gons} or I{gradians}).
320 @arg deg: Angle (C{degrees}).
322 @return: Angle (C{grades}).
323 '''
324 return Float(grades=Degrees(deg) * _G.DEG)
327def degrees2m(deg, earth=R_M, lat=0, **radius):
328 '''Convert an angle to a distance along the equator or along a parallel
329 at (geodetic) latitude.
331 @arg deg: The angle (C{degrees}).
332 @arg earth: The earth radius (C{meter}) or an ellipsoid or datum
333 (L{Ellipsoid}, L{Ellipsoid2}, L{Datum} or L{a_f2Tuple}).
334 @kwarg lat: Parallel latitude (C{degrees90}, C{str}).
335 @kwarg radius: For backward compatibility C{B{radius}=B{earth}}.
337 @return: Distance (C{meter}, same units as B{C{earth}} or polar and
338 equatorial radii) or C{0.0} for near-polar B{C{lat}}.
340 @raise RangeError: Latitude B{C{lat}} outside valid range and
341 L{rangerrors<pygeodesy.rangerrors>} is C{True}.
343 @raise TypeError: Invalid B{C{earth}} or B{C{radius}}.
345 @raise ValueError: Invalid B{C{deg}}, B{C{earth}} or B{C{lat}}.
347 @see: Function L{radians2m} and L{m2degrees}.
348 '''
349 m = _circle4radius(earth, lat, **radius)
350 return _Radians2m(Lamd(deg=deg, clip=0), m)
353def fathom2m(fathoms):
354 '''Convert I{Imperial} fathom to meter.
356 @arg fathoms: Value in fathoms (C{scalar}).
358 @return: Value in C{meter} (C{float}).
360 @raise ValueError: Invalid B{C{fathoms}}.
362 @see: Function L{toise2m}, U{Fathom<https://WikiPedia.org/wiki/Fathom>}
363 and U{Klafter<https://WikiPedia.org/wiki/Klafter>}.
364 '''
365 return Meter(Float(fathoms=fathoms) * _M.FATHOM)
368def ft2m(feet, usurvey=False, pied=False, fuss=False):
369 '''Convert I{International}, I{US Survey}, I{French} or I{German}
370 B{C{feet}} to C{meter}.
372 @arg feet: Value in feet (C{scalar}).
373 @kwarg usurvey: If C{True}, convert I{US Survey} foot else ...
374 @kwarg pied: If C{True}, convert French I{pied-du-Roi} else ...
375 @kwarg fuss: If C{True}, convert German I{Fuss}, otherwise
376 I{International} foot to C{meter}.
378 @return: Value in C{meter} (C{float}).
380 @raise ValueError: Invalid B{C{feet}}.
381 '''
382 return Meter(Feet(feet) * (_M.FOOT_US if usurvey else
383 (_M.FOOT_FR if pied else
384 (_M.FOOT_GE if fuss else _M.FOOT))))
387def furlong2m(furlongs):
388 '''Convert a furlong to meter.
390 @arg furlongs: Value in furlongs (C{scalar}).
392 @return: Value in C{meter} (C{float}).
394 @raise ValueError: Invalid B{C{furlongs}}.
395 '''
396 return Meter(Float(furlongs=furlongs) * _M.FURLONG)
399def gdf(psi):
400 '''U{Gudermannian function
401 <https://WikiPedia.org/wiki/Gudermannian_function>}.
403 @arg psi: Gudermannian (C{float}).
405 @return: Angle (C{radians}).
407 @see: Function L{agdf}.
408 '''
409 return atan1(sinh(psi))
412def grades(rad):
413 '''Convert radians to I{grades} (aka I{gons} or I{gradians}).
415 @arg rad: Angle (C{radians}).
417 @return: Angle (C{grades}).
418 '''
419 return Float(grades=Radians(rad) * _G.RAD)
422def grades400(rad):
423 '''Convert radians to I{grades} (aka I{gons} or I{gradians}) and wrap M{[0..+400)}.
425 @arg rad: Angle (C{radians}).
427 @return: Angle, wrapped (C{grades}).
428 '''
429 return Float(grades400=wrapPI2(rad) * _G.RAD)
432def grades2degrees(gon):
433 '''Convert I{grades} (aka I{gons} or I{gradians}) to C{degrees}.
435 @arg gon: Angle (C{grades}).
437 @return: Angle (C{degrees}).
438 '''
439 return Degrees(Float(gon=gon) / _G.DEG)
442def grades2radians(gon):
443 '''Convert I{grades} (aka I{gons} or I{gradians}) to C{radians}.
445 @arg gon: Angle (C{grades}).
447 @return: Angle (C{radians}).
448 '''
449 return Radians(Float(gon=gon) / _G.RAD)
452def ha2acre(ha):
453 '''Convert hectare to acre.
455 @arg ha: Value in hectare (C{scalar}).
457 @return: Value in acres (C{float}).
459 @raise ValueError: Invalid B{C{ha}}.
460 '''
461 return m2acre(ha2m2(ha))
464def ha2m2(ha):
465 '''Convert hectare to I{square} meter.
467 @arg ha: Value in hectare (C{scalar}).
469 @return: Value in C{meter^2} (C{float}).
471 @raise ValueError: Invalid B{C{ha}}.
472 '''
473 return Meter2(Float(ha=ha) * _M.HA)
476def hav(rad):
477 '''Return the U{haversine<https://WikiPedia.org/wiki/Haversine_formula>} of an angle.
479 @arg rad: Angle (C{radians}).
481 @return: C{sin(B{rad} / 2)**2}.
482 '''
483 return sin(rad * _0_5)**2
486def km2m(km):
487 '''Convert kilo meter to meter (m).
489 @arg km: Value in kilo meter (C{scalar}).
491 @return: Value in meter (C{float}).
493 @raise ValueError: Invalid B{C{km}}.
494 '''
495 return Meter(Float(km=km) * _M.KM)
498def _loneg(lon):
499 '''(INTERNAL) "Complement" of C{lon}.
500 '''
501 return _180_0 - lon
504def m2acre(meter2):
505 '''Convert I{square} meter to acres.
507 @arg meter2: Value in C{meter^2} (C{scalar}).
509 @return: Value in acres (C{float}).
511 @raise ValueError: Invalid B{C{meter2}}.
512 '''
513 return Float(acre=Meter2(meter2) / _M.ACRE)
516def m2chain(meter):
517 '''Convert meter to I{UK} chains.
519 @arg meter: Value in meter (C{scalar}).
521 @return: Value in C{chains} (C{float}).
523 @raise ValueError: Invalid B{C{meter}}.
524 '''
525 return Float(chain=Meter(meter) / _M.CHAIN) # * 0.049_709_695_378_986_715
528def m2degrees(distance, earth=R_M, lat=0, **radius):
529 '''Convert a distance to an angle along the equator or along a parallel
530 at (geodetic) latitude.
532 @arg distance: Distance (C{meter}, same units as B{C{radius}}).
533 @kwarg earth: Mean earth radius (C{meter}) or an ellipsoid or datum
534 (L{Ellipsoid}, L{Ellipsoid2}, L{Datum} or L{a_f2Tuple}).
535 @kwarg lat: Parallel latitude (C{degrees90}, C{str}).
536 @kwarg radius: For backward compatibility C{B{radius}=B{earth}}.
538 @return: Angle (C{degrees}) or C{INF} or C{NINF} for near-polar B{C{lat}}.
540 @raise RangeError: Latitude B{C{lat}} outside valid range and
541 L{rangerrors<pygeodesy.rangerrors>} is C{True}.
543 @raise TypeError: Invalid B{C{earth}} or B{C{radius}}.
545 @raise ValueError: Invalid B{C{distance}}, B{C{earth}} or B{C{lat}}.
547 @see: Function L{m2radians} and L{degrees2m}.
548 '''
549 return degrees(m2radians(distance, earth=earth, lat=lat, **radius))
552def m2fathom(meter):
553 '''Convert meter to I{Imperial} fathoms.
555 @arg meter: Value in meter (C{scalar}).
557 @return: Value in C{fathoms} (C{float}).
559 @raise ValueError: Invalid B{C{meter}}.
561 @see: Function L{m2toise}, U{Fathom<https://WikiPedia.org/wiki/Fathom>}
562 and U{Klafter<https://WikiPedia.org/wiki/Klafter>}.
563 '''
564 return Float(fathom=Meter(meter) / _M.FATHOM) # * 0.546_806_649
567def m2ft(meter, usurvey=False, pied=False, fuss=False):
568 '''Convert meter to I{International}, I{US Survey}, I{French} or
569 or I{German} feet (C{ft}).
571 @arg meter: Value in meter (C{scalar}).
572 @kwarg usurvey: If C{True}, convert to I{US Survey} foot else ...
573 @kwarg pied: If C{True}, convert to French I{pied-du-Roi} else ...
574 @kwarg fuss: If C{True}, convert to German I{Fuss}, otherwise to
575 I{International} foot.
577 @return: Value in C{feet} (C{float}).
579 @raise ValueError: Invalid B{C{meter}}.
580 '''
581 # * 3.280_833_333_333_3333, US Survey 3_937 / 1_200
582 # * 3.280_839_895_013_1235, Int'l 10_000 / (254 * 12)
583 return Float(feet=Meter(meter) / (_M.FOOT_US if usurvey else
584 (_M.FOOT_FR if pied else
585 (_M.FOOT_GE if fuss else _M.FOOT))))
588def m2furlong(meter):
589 '''Convert meter to furlongs.
591 @arg meter: Value in meter (C{scalar}).
593 @return: Value in C{furlongs} (C{float}).
595 @raise ValueError: Invalid B{C{meter}}.
596 '''
597 return Float(furlong=Meter(meter) / _M.FURLONG) # * 0.004_970_969_54
600def m2ha(meter2):
601 '''Convert I{square} meter to hectare.
603 @arg meter2: Value in C{meter^2} (C{scalar}).
605 @return: Value in hectare (C{float}).
607 @raise ValueError: Invalid B{C{meter2}}.
608 '''
609 return Float(ha=Meter2(meter2) / _M.HA)
612def m2km(meter):
613 '''Convert meter to kilo meter (Km).
615 @arg meter: Value in meter (C{scalar}).
617 @return: Value in Km (C{float}).
619 @raise ValueError: Invalid B{C{meter}}.
620 '''
621 return Float(km=Meter(meter) / _M.KM)
624def m2NM(meter):
625 '''Convert meter to nautical miles (NM).
627 @arg meter: Value in meter (C{scalar}).
629 @return: Value in C{NM} (C{float}).
631 @raise ValueError: Invalid B{C{meter}}.
632 '''
633 return Float(NM=Meter(meter) / _M.NM) # * 5.399_568_04e-4
636def m2radians(distance, earth=R_M, lat=0, **radius):
637 '''Convert a distance to an angle along the equator or along a parallel
638 at (geodetic) latitude.
640 @arg distance: Distance (C{meter}, same units as B{C{radius}}).
641 @kwarg earth: Mean earth radius (C{meter}) or an ellipsoid or datum
642 (L{Ellipsoid}, L{Ellipsoid2}, L{Datum} or L{a_f2Tuple}).
643 @kwarg lat: Parallel latitude (C{degrees90}, C{str}).
644 @kwarg radius: For backward compatibility C{B{radius}=B{earth}}.
646 @return: Angle (C{radians}) or C{INF} or C{NINF} for near-polar B{C{lat}}.
648 @raise RangeError: Latitude B{C{lat}} outside valid range and
649 L{rangerrors<pygeodesy.rangerrors>} is C{True}.
651 @raise TypeError: Invalid B{C{earth}} or B{C{radius}}.
653 @raise ValueError: Invalid B{C{distance}}, B{C{earth}} or B{C{lat}}.
655 @see: Function L{m2degrees} and L{radians2m}.
656 '''
657 m = _circle4radius(earth, lat, **radius)
658 return _copysign_0_0(distance) if m < EPS0 else \
659 Radians(Float(distance=distance) / m)
662def m2SM(meter):
663 '''Convert meter to statute miles (SM).
665 @arg meter: Value in meter (C{scalar}).
667 @return: Value in C{SM} (C{float}).
669 @raise ValueError: Invalid B{C{meter}}.
670 '''
671 return Float(SM=Meter(meter) / _M.SM) # * 6.213_699_49e-4 == 1 / 1_609.344
674def m2toise(meter):
675 '''Convert meter to French U{toises<https://WikiPedia.org/wiki/Toise>}.
677 @arg meter: Value in meter (C{scalar}).
679 @return: Value in C{toises} (C{float}).
681 @raise ValueError: Invalid B{C{meter}}.
683 @see: Function L{m2fathom}.
684 '''
685 return Float(toise=Meter(meter) / _M.TOISE) # * 0.513_083_632_632_119
688def m2yard(meter):
689 '''Convert meter to I{UK} yards.
691 @arg meter: Value in meter (C{scalar}).
693 @return: Value in C{yards} (C{float}).
695 @raise ValueError: Invalid B{C{meter}}.
696 '''
697 return Float(yard=Meter(meter) / _M.YARD_UK) # * 1.093_613_298_337_707_8
700def NM2m(nm):
701 '''Convert nautical miles to meter (m).
703 @arg nm: Value in nautical miles (C{scalar}).
705 @return: Value in meter (C{float}).
707 @raise ValueError: Invalid B{C{nm}}.
708 '''
709 return Meter(Float(nm=nm) * _M.NM)
712def _nonfinite(where, x, raiser=True, **kwds): # PYCHOK no cover
713 '''(INTERNAL) Raise a C{_ValueError} or return C{INF} or C{NINF}.
714 '''
715 if raiser:
716 t = typename(where)
717 t = _MODS.streprs.Fmt.PAREN(t, x)
718 raise _ValueError(t, **kwds)
719 return _copysignINF(x)
722def radians2m(rad, earth=R_M, lat=0, **radius):
723 '''Convert an angle to a distance along the equator or along a parallel
724 at (geodetic) latitude.
726 @arg rad: The angle (C{radians}).
727 @kwarg earth: Mean earth radius (C{meter}) or an ellipsoid or datum
728 (L{Ellipsoid}, L{Ellipsoid2}, L{Datum} or L{a_f2Tuple}).
729 @kwarg lat: Parallel latitude (C{degrees90}, C{str}).
730 @kwarg radius: For backward compatibility C{B{radius}=B{earth}}.
732 @return: Distance (C{meter}, same units as B{C{earth}} or polar and
733 equatorial radii) or C{0.0} for near-polar B{C{lat}}.
735 @raise RangeError: Latitude B{C{lat}} outside valid range and
736 L{rangerrors<pygeodesy.rangerrors>} is C{True}.
738 @raise TypeError: Invalid B{C{earth}} or B{C{radius}}.
740 @raise ValueError: Invalid B{C{rad}}, B{C{earth}} or B{C{lat}}.
742 @see: Function L{degrees2m} and L{m2radians}.
743 '''
744 m = _circle4radius(earth, lat, **radius)
745 return _Radians2m(Lam(rad=rad, clip=0), m)
748def _Radians2m(rad, m):
749 '''(INTERNAL) Helper for C{degrees2m} and C{radians2m}.
750 '''
751 return _copysign_0_0(rad) if m < EPS0 else (rad * m)
754def radiansPI(deg):
755 '''Convert and wrap degrees to radians M{[-PI..+PI]}.
757 @arg deg: Angle (C{degrees}).
759 @return: Radians, wrapped (C{radiansPI})
760 '''
761 return wrapPI(radians(deg))
764def radiansPI2(deg):
765 '''Convert and wrap degrees to radians M{[0..+2PI)}.
767 @arg deg: Angle (C{degrees}).
769 @return: Radians, wrapped (C{radiansPI2})
770 '''
771 return _umod_PI2(radians(deg))
774def radiansPI_2(deg):
775 '''Convert and wrap degrees to radians M{[-3PI/2..+PI/2]}.
777 @arg deg: Angle (C{degrees}).
779 @return: Radians, wrapped (C{radiansPI_2})
780 '''
781 return wrapPI_2(radians(deg))
784def _sin0cos2(q, r, sign):
785 '''(INTERNAL) 2-tuple (C{sin(r), cos(r)}) in quadrant C{0 <= B{q} <= 3} and
786 C{sin} zero I{signed} with B{C{sign}}, like Karney's U{Math.sind and .cosd
787 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Math.html>}
788 '''
789 q &= 3 # -1: 3, -2: 2, -3: 1, -4: 0 ...
790 if r < PI_2: # Quarter turn
791 a = fabs(r)
792 if a:
793 s = sin(r)
794 if a == PI_4:
795 s, c = _copysign(_SIN_45, s), _COS_45
796 elif a == PI_6:
797 s, c = _copysign(_SIN_30, s), _COS_30
798 else:
799 c = cos(r)
800 else:
801 s, c = _0_0, _1_0
802 else:
803 s, c = _1_0, _0_0
804 t = s, c, -s, -c, s
805 s = t[q] or _copysign_0_0(sign)
806 c = t[q + 1] or _0_0
807 return s, c
810def SinCos2(x):
811 '''Get C{sin} and C{cos} of I{typed} angle.
813 @arg x: Angle (L{Degrees}, L{Radians} or scalar C{radians}).
815 @return: 2-Tuple (C{sin(B{x})}, C{cos(B{x})}).
816 '''
817 return sincos2d(x) if isinstanceof(x, Degrees, Degrees_) else (
818# sincos2(x) if isinstanceof(x, Radians, Radians_) else
819 sincos2(Radians(x))) # assume C{radians}
822def sincos2(rad):
823 '''Return the C{sine} and C{cosine} of an angle in C{radians}.
825 @arg rad: Angle (C{radians}).
827 @return: 2-Tuple (C{sin(B{rad})}, C{cos(B{rad})}).
829 @see: U{GeographicLib<https://GeographicLib.SourceForge.io/C++/doc/
830 classGeographicLib_1_1Math.html#sincosd>} function U{sincosd
831 <https://SourceForge.net/p/geographiclib/code/ci/release/tree/
832 python/geographiclib/geomath.py#l155>} and C++ U{sincosd
833 <https://SourceForge.net/p/geographiclib/code/ci/release/tree/
834 include/GeographicLib/Math.hpp#l558>}.
835 '''
836 if _isfinite(rad):
837 q, r = divmod(rad, PI_2)
838 t = _sin0cos2(int(q), r, rad)
839 else:
840 t = NAN, NAN
841 return t
844def sincos2_(*rads):
845 '''Yield the C{sine} and C{cosine} of angle(s) in C{radians}.
847 @arg rads: One or more angles (C{radians}).
849 @return: Yield C{sin(B{rad})} and C{cos(B{rad})} for each angle.
851 @see: Function L{sincos2}.
852 '''
853 for r in rads:
854 s, c = sincos2(r)
855 yield s
856 yield c
859def sincos2d(deg, adeg=_0_0):
860 '''Return the C{sine} and C{cosine} of an angle in C{degrees}.
862 @arg deg: Angle (C{degrees}).
863 @kwarg adeg: Optional correction (C{degrees}).
865 @return: 2-Tuple (C{sin(B{deg_})}, C{cos(B{deg_})} with C{B{deg_} =
866 B{deg} + B{adeg}}).
868 @see: U{GeographicLib<https://GeographicLib.SourceForge.io/C++/doc/
869 classGeographicLib_1_1Math.html#sincosd>} function U{sincosd
870 <https://SourceForge.net/p/geographiclib/code/ci/release/tree/
871 python/geographiclib/geomath.py#l155>} and C++ U{sincosd
872 <https://SourceForge.net/p/geographiclib/code/ci/release/tree/
873 include/GeographicLib/Math.hpp#l558>}.
874 '''
875 if _isfinite(deg):
876 q, d = divmod(deg, _90_0)
877 if adeg:
878 d = _MODS.karney._around(d + adeg)
879 t = _sin0cos2(int(q), radians(d), deg)
880 else:
881 t = NAN, NAN
882 return t
885def sincos2d_(*degs):
886 '''Yield the C{sine} and C{cosine} of angle(s) in C{degrees}.
888 @arg degs: One or more angles (C{degrees}).
890 @return: Yield C{sind(B{deg})} and C{cosd(B{deg})} for each angle.
892 @see: Function L{sincos2d}.
893 '''
894 for d in degs:
895 s, c = sincos2d(d)
896 yield s
897 yield c
900def sincostan3(rad):
901 '''Return the C{sine}, C{cosine} and C{tangent} of an angle in C{radians}.
903 @arg rad: Angle (C{radians}).
905 @return: 3-Tuple (C{sin(B{rad})}, C{cos(B{rad})}, C{tan(B{rad})}).
907 @see: Function L{sincos2}.
908 '''
909 return _sincostan3(*sincos2(float(rad)))
912def _sincostan3(s, c):
913 '''(INTERNAL) Helper for C{sincostan3} and C{sincostan3d}.
914 '''
915 return s, c, _over_1(s, c) # _tanu(s, c, raiser=False)
918def sincostan3d(deg):
919 '''Return the C{sine}, C{cosine} and C{tangent} of an angle in C{degrees}.
921 @arg deg: Angle (C{degrees}).
923 @return: 3-Tuple (C{sind(B{deg})}, C{cosd(B{deg})}, C{tand(B{deg})}).
925 @see: Function L{sincos2d}.
926 '''
927 return _sincostan3(*sincos2d(float(deg)))
930def SM2m(sm):
931 '''Convert statute miles to meter (m).
933 @arg sm: Value in statute miles (C{scalar}).
935 @return: Value in meter (C{float}).
937 @raise ValueError: Invalid B{C{sm}}.
938 '''
939 return Meter(Float(sm=sm) * _M.SM)
942def tan_2(rad, **semi): # edge=1
943 '''Compute the tangent of half angle.
945 @arg rad: Angle (C{radians}).
946 @kwarg semi: Angle or edge name and index
947 for semi-circular error.
949 @return: M{tan(rad / 2)} (C{float}).
951 @raise ValueError: If B{C{rad}} is semi-circular
952 and B{C{semi}} is given.
953 '''
954 # .formy.excessKarney_, .sphericalTrigonometry.areaOf
955 if semi and isnear0(fabs(rad) - PI):
956 for n, v in semi.items():
957 break
958 n = _SPACE_(n, _radians_) if not isint(v) else \
959 _SPACE_(_MODS.streprs.Fmt.SQUARE(**semi), _edge_)
960 raise _ValueError(n, rad, txt=_semi_circular_)
962 return _tan(rad * _0_5) if _isfinite(rad) else NAN
965def tan(rad, **raiser_kwds):
966 '''Return the C{tangent} of an angle in C{radians}.
968 @arg rad: Angle (C{radians}).
969 @kwarg raiser_kwds: Use C{B{raiser}=False} to avoid
970 ValueErrors and optional, additional
971 ValueError keyword argments.
973 @return: C{tan(B{rad})}.
975 @raise Error: If L{pygeodesy.isnear0}C{(cos(B{rad})}.
976 '''
977 try:
978 return _tanu(*sincos2(rad))
979 except ZeroDivisionError:
980 return _nonfinite(tan, rad, **raiser_kwds)
983def tan_(*rads, **raiser_kwds):
984 '''Yield the C{tangent} of angle(s) in C{radians}.
986 @arg rads: One or more angles (each in C{radians}).
988 @return: Yield C{tan(B{rad})} for each angle.
990 @see: Function L{pygeodesy.tan} for futher details.
991 '''
992 try:
993 for r in rads:
994 yield _tanu(*sincos2(r))
995 except ZeroDivisionError:
996 yield _nonfinite(tan_, r, **raiser_kwds)
999def tand(deg, **raiser_kwds):
1000 '''Return the C{tangent} of an angle in C{degrees}.
1002 @arg deg: Angle (C{degrees}).
1003 @kwarg raiser_kwds: Use C{B{raiser}=False} to avoid
1004 ValueErrors and optional, additional
1005 ValueError keyword argments.
1007 @return: C{tan(B{deg})}.
1009 @raise Error: If L{pygeodesy.isnear0}C{(cos(B{deg})}.
1010 '''
1011 try:
1012 return _tanu(*sincos2d(deg))
1013 except ZeroDivisionError:
1014 return _nonfinite(tand, deg, **raiser_kwds)
1017def tand_(*degs, **raiser_kwds):
1018 '''Yield the C{tangent} of angle(s) in C{degrees}.
1020 @arg degs: One or more angles (each in C{degrees}).
1022 @return: Yield C{tand(B{deg})} for each angle.
1024 @see: Function L{pygeodesy.tand} for futher details.
1025 '''
1026 try:
1027 for d in degs:
1028 yield _tanu(*sincos2d(d))
1029 except ZeroDivisionError:
1030 yield _nonfinite(tand_, d, **raiser_kwds)
1033def tanPI_2_2(rad):
1034 '''Compute the tangent of half angle, 90 degrees rotated.
1036 @arg rad: Angle (C{radians}).
1038 @return: M{tan((rad + PI/2) / 2)} (C{float}).
1039 '''
1040 return _tan((rad + PI_2) * _0_5) if _isfinite(rad) else (
1041 NAN if isnan(rad) else _copysign(_90_0, rad))
1044def _tanu(s, c):
1045 '''(INTERNAL) Helper for functions C{_cotu}, C{sincostan3},
1046 C{sincostan3d}, C{tan}, C{tan_}, C{tand} and C{tand_}.
1047 '''
1048 if s is NAN or isnan(s):
1049 t = NAN
1050 elif isnear0(c):
1051 raise ZeroDivisionError()
1052 else:
1053 t = _over_1(s, c)
1054 return t
1057def toise2m(toises):
1058 '''Convert French U{toises<https://WikiPedia.org/wiki/Toise>} to meter.
1060 @arg toises: Value in toises (C{scalar}).
1062 @return: Value in C{meter} (C{float}).
1064 @raise ValueError: Invalid B{C{toises}}.
1066 @see: Function L{fathom2m}.
1067 '''
1068 return Meter(Float(toises=toises) * _M.TOISE)
1071def truncate(x, ndigits=None):
1072 '''Truncate to the given number of digits.
1074 @arg x: Value to truncate (C{scalar}).
1075 @kwarg ndigits: Number of digits (C{int}),
1076 aka I{precision}.
1078 @return: Truncated B{C{x}} (C{float}).
1080 @see: Python function C{round}.
1081 '''
1082 if isint(ndigits):
1083 p = _10_0**ndigits
1084 x = int(x * p) / p
1085 return x
1088def unroll180(lon1, lon2, wrap=True):
1089 '''Unroll longitudinal delta and wrap longitude in degrees.
1091 @arg lon1: Start longitude (C{degrees}).
1092 @arg lon2: End longitude (C{degrees}).
1093 @kwarg wrap: If C{True}, wrap and unroll to the M{(-180..+180]}
1094 range (C{bool}).
1096 @return: 2-Tuple C{(B{lon2}-B{lon1}, B{lon2})} unrolled (C{degrees},
1097 C{degrees}).
1099 @see: Capability C{LONG_UNROLL} in U{GeographicLib
1100 <https://GeographicLib.SourceForge.io/html/python/interface.html#outmask>}.
1101 '''
1102 d = lon2 - lon1
1103 if wrap:
1104 u = wrap180(d)
1105 if u != d:
1106 return u, (lon1 + u)
1107 return d, lon2
1110def _unrollon(p1, p2, wrap=False): # unroll180 == .karney._unroll2
1111 '''(INTERNAL) Wrap/normalize, unroll and replace longitude.
1112 '''
1113 lat, lon = p2.lat, p2.lon
1114 if wrap and _Wrap.normal:
1115 lat, lon = _Wrap.latlon(lat, lon)
1116 _, lon = unroll180(p1.lon, lon, wrap=True)
1117 if lat != p2.lat or fabs(lon - p2.lon) > EPS:
1118 p2 = p2.dup(lat=lat, lon=wrap180(lon))
1119 # p2 = p2.copy(); p2.latlon = lat, wrap180(lon)
1120 return p2
1123def _unrollon3(p1, p2, p3, wrap=False):
1124 '''(INTERNAL) Wrap/normalize, unroll 2 points.
1125 '''
1126 w = wrap
1127 if w: # PYCHOK no cover
1128 w = _Wrap.normal
1129 p2 = _unrollon(p1, p2, wrap=w)
1130 p3 = _unrollon(p1, p3, wrap=w)
1131 p2 = _unrollon(p2, p3)
1132 return p2, p3, w # was wrapped?
1135def unrollPI(rad1, rad2, wrap=True):
1136 '''Unroll longitudinal delta and wrap longitude in radians.
1138 @arg rad1: Start longitude (C{radians}).
1139 @arg rad2: End longitude (C{radians}).
1140 @kwarg wrap: If C{True}, wrap and unroll to the M{(-PI..+PI]}
1141 range (C{bool}).
1143 @return: 2-Tuple C{(B{rad2}-B{rad1}, B{rad2})} unrolled
1144 (C{radians}, C{radians}).
1146 @see: Capability C{LONG_UNROLL} in U{GeographicLib
1147 <https://GeographicLib.SourceForge.io/html/python/interface.html#outmask>}.
1148 '''
1149 r = rad2 - rad1
1150 if wrap:
1151 u = wrapPI(r)
1152 if u != r:
1153 return u, (rad1 + u)
1154 return r, rad2
1157class _Wrap(object):
1159 _normal = False # default
1161 @property
1162 def normal(self):
1163 '''Get the current L{normal} setting (C{True},
1164 C{False} or C{None}).
1165 '''
1166 return self._normal
1168 @normal.setter # PYCHOK setter!
1169 def normal(self, setting): # PYCHOK no cover
1170 '''Set L{normal} to C{True}, C{False} or C{None}.
1171 '''
1172 m = _MODS.formy
1173 t = {True: (m.normal, m.normal_),
1174 False: (self.wraplatlon, self.wraphilam),
1175 None: (_passargs, _passargs)}.get(setting, ())
1176 if t:
1177 self.latlon, self.philam = t
1178 self._normal = setting
1180 def latlonDMS2(self, lat, lon, **DMS2_kwds): # PYCHOK no cover
1181 if isstr(lat) or isstr(lon):
1182 kwds = _xkwds(DMS2_kwds, clipLon=0, clipLat=0)
1183 lat, lon = _MODS.dms.parseDMS2(lat, lon, **kwds)
1184 return self.latlon(lat, lon)
1186# def normalatlon(self, *latlon):
1187# return _MODS.formy.normal(*latlon)
1189# def normalamphi(self, *philam):
1190# return _MODS.formy.normal_(*philam)
1192 def wraplatlon(self, lat, lon):
1193 return wrap90(lat), wrap180(lon)
1195 latlon = wraplatlon # default
1197 def latlon3(self, lon1, lat2, lon2, wrap):
1198 if wrap:
1199 lat2, lon2 = self.latlon(lat2, lon2)
1200 lon21, lon2 = unroll180(lon1, lon2)
1201 else:
1202 lon21 = lon2 - lon1
1203 return lon21, lat2, lon2
1205 def _latlonop(self, wrap):
1206 if wrap and self._normal is not None:
1207 return self.latlon
1208 else:
1209 return _passargs
1211 def wraphilam(self, phi, lam):
1212 return wrapPI_2(phi), wrapPI(lam)
1214 philam = wraphilam # default
1216 def philam3(self, lam1, phi2, lam2, wrap):
1217 if wrap:
1218 phi2, lam2 = self.philam(phi2, lam2)
1219 lam21, lam2 = unrollPI(lam1, lam2)
1220 else:
1221 lam21 = lam2 - lam1
1222 return lam21, phi2, lam2
1224 def _philamop(self, wrap):
1225 if wrap and self._normal is not None:
1226 return self.philam
1227 else:
1228 return _passargs
1230 def point(self, ll, wrap=True): # in .points._fractional, -.PointsIter.iterate, ...
1231 '''Return C{ll} or a copy, I{normalized} or I{wrap}'d.
1232 '''
1233 if wrap and self._normal is not None:
1234 lat, lon = ll.latlon
1235 if fabs(lon) > _180_0 or fabs(lat) > _90_0:
1236 _n = self.latlon
1237 ll = ll.copy(name=typename(_n))
1238 ll.latlon = _n(lat, lon)
1239 return ll
1241_Wrap = _Wrap() # PYCHOK singleton
1244# def _wrap(angle, wrap, modulo):
1245# '''(INTERNAL) Angle wrapper M{((wrap-modulo)..+wrap]}.
1246#
1247# @arg angle: Angle (C{degrees}, C{radians} or C{grades}).
1248# @arg wrap: Range (C{degrees}, C{radians} or C{grades}).
1249# @arg modulo: Upper limit (360 C{degrees}, PI2 C{radians} or 400 C{grades}).
1250#
1251# @return: The B{C{angle}}, wrapped (C{degrees}, C{radians} or C{grades}).
1252# '''
1253# a = float(angle)
1254# if not (wrap - modulo) <= a < wrap:
1255# # math.fmod(-1.5, 3.14) == -1.5, but -1.5 % 3.14 == 1.64
1256# # math.fmod(-1.5, 360) == -1.5, but -1.5 % 360 == 358.5
1257# a %= modulo
1258# if a > wrap:
1259# a -= modulo
1260# return a
1263def wrap90(deg):
1264 '''Wrap degrees to M{[-90..+90]}.
1266 @arg deg: Angle (C{degrees}).
1268 @return: Degrees, wrapped (C{degrees90}).
1269 '''
1270 return _wrapu(wrap180(deg), _180_0, _90_0)
1273def wrap180(deg):
1274 '''Wrap degrees to M{[-180..+180]}.
1276 @arg deg: Angle (C{degrees}).
1278 @return: Degrees, wrapped (C{degrees180}).
1279 '''
1280 d = float(deg)
1281 w = _umod_360(d)
1282 if w > _180_0:
1283 w -= _360_0
1284 elif d < 0 and w == _180_0:
1285 w = -w
1286 return w
1289def wrap360(deg): # see .streprs._umod_360
1290 '''Wrap degrees to M{[0..+360)}.
1292 @arg deg: Angle (C{degrees}).
1294 @return: Degrees, wrapped (C{degrees360}).
1295 '''
1296 return _umod_360(float(deg))
1299def wrapPI(rad):
1300 '''Wrap radians to M{[-PI..+PI]}.
1302 @arg rad: Angle (C{radians}).
1304 @return: Radians, wrapped (C{radiansPI}).
1305 '''
1306 r = float(rad)
1307 w = _umod_PI2(r)
1308 if w > PI:
1309 w -= PI2
1310 elif r < 0 and w == PI:
1311 w = -PI
1312 return w
1315def wrapPI2(rad):
1316 '''Wrap radians to M{[0..+2PI)}.
1318 @arg rad: Angle (C{radians}).
1320 @return: Radians, wrapped (C{radiansPI2}).
1321 '''
1322 return _umod_PI2(float(rad))
1325def wrapPI_2(rad):
1326 '''Wrap radians to M{[-PI/2..+PI/2]}.
1328 @arg rad: Angle (C{radians}).
1330 @return: Radians, wrapped (C{radiansPI_2}).
1331 '''
1332 return _wrapu(wrapPI(rad), PI, PI_2)
1335# def wraplatlon(lat, lon):
1336# '''Both C{wrap90(B{lat})} and C{wrap180(B{lon})}.
1337# '''
1338# return wrap90(lat), wrap180(lon)
1341def wrap_normal(*normal):
1342 '''Define the operation for the keyword argument C{B{wrap}=True},
1343 across L{pygeodesy}: I{wrap}, I{normalize} or I{no-op}. For
1344 backward compatibility, the default is I{wrap}.
1346 @arg normal: If C{True}, I{normalize} lat- and longitude using
1347 L{normal} or L{normal_}, if C{False}, I{wrap} the
1348 lat- and longitude individually by L{wrap90} or
1349 L{wrapPI_2} respectively L{wrap180}, L{wrapPI} or
1350 if C{None}, leave lat- and longitude I{unchanged}.
1351 To get the current setting, do not specify.
1353 @return: The previous L{wrap_normal} setting (C{bool} or C{None}).
1354 '''
1355 t = _Wrap.normal
1356 if normal:
1357 _Wrap.normal = normal[0]
1358 return t
1361# def wraphilam(phi, lam,):
1362# '''Both C{wrapPI_2(B{phi})} and C{wrapPI(B{lam})}.
1363# '''
1364# return wrapPI_2(phi), wrapPI(lam)
1367def _wrapu(w, H, Q):
1368 '''(INTERNAL) Helper for functions C{wrap180} and C{wrapPI}.
1369 '''
1370 return (w - H) if w > Q else ((w + H) if w < (-Q) else w)
1373def yard2m(yards):
1374 '''Convert I{UK} yards to meter.
1376 @arg yards: Value in yards (C{scalar}).
1378 @return: Value in C{meter} (C{float}).
1380 @raise ValueError: Invalid B{C{yards}}.
1381 '''
1382 return Float(yards=yards) * _M.YARD_UK
1384# **) MIT License
1385#
1386# Copyright (C) 2016-2025 -- mrJean1 at Gmail -- All Rights Reserved.
1387#
1388# Permission is hereby granted, free of charge, to any person obtaining a
1389# copy of this software and associated documentation files (the "Software"),
1390# to deal in the Software without restriction, including without limitation
1391# the rights to use, copy, modify, merge, publish, distribute, sublicense,
1392# and/or sell copies of the Software, and to permit persons to whom the
1393# Software is furnished to do so, subject to the following conditions:
1394#
1395# The above copyright notice and this permission notice shall be included
1396# in all copies or substantial portions of the Software.
1397#
1398# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
1399# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
1400# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
1401# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
1402# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
1403# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
1404# OTHER DEALINGS IN THE SOFTWARE.