using LinearAlgebra

struct ValueOne; end
ValueOne()

# Compute X <- a X + b I.
function matfun_axpby!(X,a,b,Y::UniformScaling)
    m,n=size(X)
    if ~(a isa ValueOne)
        rmul!(X,a)
    end
    @inbounds for i=1:n
        X[i,i]+=(b isa ValueOne) ? 1 : b
    end
end

@inline function exp_sastre_opt_rho1_9(A)
    T=promote_type(eltype(A),Float64)
    A_copy=similar(A,T); A_copy .= A;
    return exp_sastre_opt_rho1_9!(A_copy)
end

@inline function exp_sastre_opt_rho1_9!(A)
    T=promote_type(eltype(A),Float64) # Make it work for many 'bigger' types (matrices and scalars)
    # max_memslots=8
    n=size(A,1)
    # The first slots are precomputed nodes [:A]
    memslots2 = similar(A,T)
    memslots3 = similar(A,T)
    memslots4 = similar(A,T)
    memslots5 = similar(A,T)
    memslots6 = similar(A,T)
    memslots7 = similar(A,T)
    memslots8 = similar(A,T)
    # Assign precomputed nodes memslots 
    memslots1=A # overwrite A
    # Uniform scaling is exploited.
    # No matrix I explicitly allocated.
    # Computation order: Bb2 Ba2 B2 Ba3 Bb3 B3 Ba4 Bb4 B4 Ba5 Bb5 B5 Ba6 Bb6 B6 T2k8
    # Computing Bb2 = x*I+x*A
    coeff1=-4.479293476259415
    coeff2=-1.965591461532149
    memslots2 .= coeff2.*memslots1
    mul!(memslots2,true,I*coeff1,true,true)
    # Computing Ba2 = x*I+x*A
    coeff1=-4.479293476259415
    coeff2=-1.965591461532149
    memslots3 .= coeff2.*memslots1
    mul!(memslots3,true,I*coeff1,true,true)
    # Computing B2 with operation: mult
    mul!(memslots4,memslots3,memslots2)
    # Deallocating Ba2 in slot 3
    # Deallocating Bb2 in slot 2
    # Computing Ba3 = x*I+x*A+x*B2
    coeff1=0.5431852019042509
    coeff2=2.808044477000553
    coeff3=3.072468368540587
    memslots2 .= coeff2.*memslots1 .+ coeff3.*memslots4
    mul!(memslots2,true,I*coeff1,true,true)
    # Computing Bb3 = x*I+x*A+x*B2
    coeff1=1.8758020055089961
    coeff2=-4.077994868395093
    coeff3=-0.5726777535092064
    memslots3 .= coeff2.*memslots1 .+ coeff3.*memslots4
    mul!(memslots3,true,I*coeff1,true,true)
    # Computing B3 with operation: mult
    mul!(memslots5,memslots2,memslots3)
    # Deallocating Ba3 in slot 2
    # Deallocating Bb3 in slot 3
    # Computing Ba4 = x*I+x*A+x*B2+x*B3
    coeff1=3.513744518233991
    coeff2=3.480716229698247
    coeff3=-7.395064443323127
    coeff4=3.9135175595994687
    memslots2 .= coeff2.*memslots1 .+ coeff3.*memslots4 .+ coeff4.*memslots5
    mul!(memslots2,true,I*coeff1,true,true)
    # Computing Bb4 = x*I+x*A+x*B2+x*B3
    coeff1=0.02417939999948854
    coeff2=0.013482072269100465
    coeff3=-0.0015522395764164978
    coeff4=-2.310576048441552e-6
    memslots3 .= coeff2.*memslots1 .+ coeff3.*memslots4 .+ coeff4.*memslots5
    mul!(memslots3,true,I*coeff1,true,true)
    # Computing B4 with operation: mult
    mul!(memslots6,memslots2,memslots3)
    # Deallocating Ba4 in slot 2
    # Deallocating Bb4 in slot 3
    # Computing Ba5 = x*I+x*A+x*B2+x*B3+x*B4
    coeff1=-2.7514538554861674
    coeff2=28.533085265354913
    coeff3=-32.70207976001747
    coeff4=15.117957339910209
    coeff5=-31.69337657641421
    memslots2 .= coeff2.*memslots1 .+ coeff3.*memslots4 .+ coeff4.*memslots5 .+ coeff5.*memslots6
    mul!(memslots2,true,I*coeff1,true,true)
    # Computing Bb5 = x*I+x*A+x*B2+x*B3+x*B4
    coeff1=1.4649998087002614
    coeff2=-1.1631539168725962
    coeff3=18.10426755193074
    coeff4=-13.187053051683513
    coeff5=27.426929433347695
    memslots3 .= coeff2.*memslots1 .+ coeff3.*memslots4 .+ coeff4.*memslots5 .+ coeff5.*memslots6
    mul!(memslots3,true,I*coeff1,true,true)
    # Computing B5 with operation: mult
    mul!(memslots7,memslots2,memslots3)
    # Deallocating Ba5 in slot 2
    # Deallocating Bb5 in slot 3
    # Computing Ba6 = x*I+x*A+x*B2+x*B3+x*B4+x*B5
    coeff1=-2.57802584497714
    coeff2=-1.9681270306651504
    coeff3=-0.5172562598353871
    coeff4=0.2838459715474883
    coeff5=-0.0930303538906508
    coeff6=-0.17367745193891393
    memslots2 .= coeff2.*memslots1 .+ coeff3.*memslots4 .+ coeff4.*memslots5 .+ coeff5.*memslots6 .+ coeff6.*memslots7
    mul!(memslots2,true,I*coeff1,true,true)
    # Computing Bb6 = x*I+x*A+x*B2+x*B3+x*B4+x*B5
    coeff1=2.7927443516334343
    coeff2=-2.5111253025765686e-6
    coeff3=1.1720013130685409e-7
    coeff4=2.1593312631548876e-10
    coeff5=2.7906362162645103e-10
    coeff6=-5.055543522880249e-19
    memslots3 .= coeff2.*memslots1 .+ coeff3.*memslots4 .+ coeff4.*memslots5 .+ coeff5.*memslots6 .+ coeff6.*memslots7
    mul!(memslots3,true,I*coeff1,true,true)
    # Computing B6 with operation: mult
    mul!(memslots8,memslots2,memslots3)
    # Deallocating Ba6 in slot 2
    # Deallocating Bb6 in slot 3
    # Computing T2k8 = x*I+x*A+x*B2+x*B3+x*B4+x*B5+x*B6
    coeff1=9.679532976243642
    coeff2=3.9359833423253106
    coeff3=6.090302916482898
    coeff4=-2.7031124428719058
    coeff5=-2.542481119421314
    coeff6=1.6620101377768384
    coeff7=3.4265640842763014
    # Smart lincomb recycle A
    memslots1 .= coeff2.*memslots1 .+ coeff3.*memslots4 .+ coeff4.*memslots5 .+ coeff5.*memslots6 .+ coeff6.*memslots7 .+ coeff7.*memslots8
    mul!(memslots1,true,I*coeff1,true,true)
    # Deallocating B2 in slot 4
    # Deallocating B3 in slot 5
    # Deallocating B4 in slot 6
    # Deallocating B5 in slot 7
    # Deallocating B6 in slot 8
    return memslots1 # Returning T2k8
end

