NAME
     MDevolve: Integrator framework for Molecular Dynamic evolutions

DESCRIPTION
     To use:
       1. Create individual integrators from update procedures,
          using one of the `newIntegratorPair`.
       2. Compose integrators using `mk...`.
       3. Start the integration with `evolve`.
       4. Finish the integration with `finish`.

SYNOPSIS
     const mdevolveVersion*:int = 1
     type
       Integrator* = ref object
       ParIntegrator* = ref object
         nonZeroStep*:float
         nonZeroStepWarn*:float
       Integrators* = ref object
     func `$`*(x:Integrator):string
     func `$`*(x:ParIntegrator):string
     proc steps*(x:Integrator):int
     proc steps*(x:ParIntegrator):int
     proc `steps=`*(x:Integrator, n:int)
     proc `steps=`*(x:ParIntegrator, n:int)
     proc forceGradient*(x:Integrator):Integrator
     proc `forceGradient=`*(x:Integrator, G:Integrator)
     proc `[]`*(xs:Integrators, n:int):Integrator
     template newIntegratorPair*(f,g:proc(t:float)):(Integrator,Integrator)
     template newIntegratorPair*(f:proc(ts:openarray[float]),g:proc(t:float)):(Integrators,Integrator)
     template newIntegratorPair*(f:proc(t:float),g:proc(ts:openarray[float])):(Integrator,Integrators)
     template newIntegratorPair*(f:proc(ts:openarray[float]),g:proc(ts:openarray[float])):(Integrators,Integrators)
     template newIntegratorPair*(f:proc(ts,ss:openarray[float]),g:proc(t:float)):(Integrators,Integrator)
     template newIntegratorPair*(f:proc(t:float),g:proc(ts,ss:openarray[float])):(Integrator,Integrators)
     macro newIntegratorPair*(fs:tuple, g:proc(t:float)):auto
     macro newIntegratorPair*(f:proc(t:float), gs:tuple):auto
     macro newIntegratorPair*(fs:tuple, gs:tuple):auto
     proc newSerialEvolution*(id:string, mds:seq[tuple[i:Integrator,f:float]], steps:int, order:int):Integrator
     proc add*(r:ParIntegrator, xs:varargs[Integrator])
     proc newParallelEvolution*(xs:varargs[Integrator]):ParIntegrator
     proc evolve*(x:Integrator, t:float)
     proc evolve*(x:ParIntegrator, t:float)
     proc finish*(x:Integrator)
     proc finish*(x:ParIntegrator)
     proc approximateFGcoeff*(cv,cg:float):tuple[tf:float,tg:float]
     proc approximateFGcoeff2*(cv,cg:float, b = 0.2):tuple[tf:array[2,float],tg:array[2,float]]
     proc mkLeapFrog*(T,V:Integrator, steps = 1):Integrator
     proc mkOmelyan2MN*(T,V:Integrator, steps = 1,
         lambda = 0.1931833275037836):Integrator
     proc mkSW92*(T,V:Integrator, steps = 1):Integrator
     proc mkOmelyan4MN4FP*(T,V:Integrator, steps = 1,
         rho = 0.1786178958448091,
         theta = -0.06626458266981843,
         lambda = 0.7123418310626056):Integrator
     proc mkOmelyan4MN5FV*(T,V:Integrator, steps = 1,
         rho = 0.2539785108410595,
         theta = -0.03230286765269967,
         vartheta = 0.08398315262876693,
         lambda = 0.6822365335719091):Integrator
     proc mkOmelyan4MN5FP*(T,V:Integrator, steps = 1,
         rho = 0.2750081212332419,
         theta = -0.1347950099106792,
         vartheta= -0.08442961950707149,
         lambda = 0.3549000571574260):Integrator
     proc mkOmelyan6MN7FV*(T,V:Integrator, steps = 1):Integrator
     proc mkOmelyan4MN2F2GV*(T,V:Integrator, steps = 1,
         xi = -17.0/18000.0):Integrator
     proc mkOmelyan4MN2F1GV*(T,V:Integrator, steps = 1):Integrator
     proc mkOmelyan4MN3F3GP*(T,V:Integrator, steps = 1,
         lambda = 0.2825633404177051,
         chi = 0.003035236056708454):Integrator
     proc mkOmelyan4MN3F2GP*(T,V:Integrator, steps = 1,
         lambda = 0.3152315246820299):Integrator
     proc mkOmelyan4MN3F1GP*(T,V:Integrator, steps = 1,
         lambda = 0.2470939580390842):Integrator
     proc mkOmelyan4MN3F3GV*(T,V:Integrator, steps = 1,
         theta = 0.2728983001988755,
         chi = 0.002960781208329478):Integrator
     proc mkOmelyan4MN3F2GV*(T,V:Integrator, steps = 1,
         theta = 0.2813980611667719):Integrator
     proc mkOmelyan4MN3F1GV*(T,V:Integrator, steps = 1,
         theta = 0.2409202729169543):Integrator
     proc mkOmelyan4MN4F2GVG*(T,V:Integrator, steps = 1):Integrator
     proc mkOmelyan4MN4F2GV*(T,V:Integrator, steps = 1):Integrator
     proc mkOmelyan4MN5F2GV*(T,V:Integrator, steps = 1):Integrator
     proc mkOmelyan4MN5F1GV*(T,V:Integrator, steps = 1):Integrator
     proc mkOmelyan4MN5F2GP*(T,V:Integrator, steps = 1):Integrator
     proc mkOmelyan4MN5F1GP*(T,V:Integrator, steps = 1):Integrator
     proc mkOmelyan6MN5F5GV*(T,V:Integrator, steps = 1):Integrator
     proc mkOmelyan6MN5F4GV*(T,V:Integrator, steps = 1):Integrator
     proc mkOmelyan6MN5F5GP*(T,V:Integrator, steps = 1):Integrator
     proc mkOmelyan6MN5F3GP*(T,V:Integrator, steps = 1):Integrator
     proc mkOmelyan8S11F11GP*(T,V:Integrator, steps = 1):Integrator
     proc mkCreutzGocksch*(S:Integrator, steps = 1):Integrator
     proc mkOmelyan8CK4P4*(S4:Integrator, steps = 1):Integrator
     proc mkOmelyan10CK4P7*(S4:Integrator, steps = 1):Integrator
     proc mkOmelyan12CK4P12*(S4:Integrator, steps = 1):Integrator
     proc mkOmelyan10CK6P4*(S6:Integrator, steps = 1):Integrator
     proc mkOmelyan12CK6P7*(S6:Integrator, steps = 1):Integrator

EXAMPLES
     See tests.

LICENSE
     This work is licensed under the MIT license.  See file
     LICENSE for details.

SEE ALSO
     Creutz and Gocksch, https://doi.org/10.1103/PhysRevLett.63.9
     Omelyan, Mryglod, and Folk, https://doi.org/10.1103/PhysRevE.66.026701
     Omelyan, Mryglod, and Folk, https://doi.org/10.1016/S0010-4655(02)00754-3
     Yin and Mawhinney, https://doi.org/10.22323/1.139.0051