function initialize!(integrator, cache::TanYam7ConstantCache)
    integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal
    OrdinaryDiffEqCore.increment_nf!(integrator.stats, 1)
    integrator.kshortsize = 2
    integrator.k = typeof(integrator.k)(undef, integrator.kshortsize)

    # Avoid undefined entries if k is an array of arrays
    integrator.fsallast = zero(integrator.fsalfirst)
    integrator.k[1] = integrator.fsalfirst
    return integrator.k[2] = integrator.fsallast
end

@muladd function perform_step!(integrator, cache::TanYam7ConstantCache, repeat_step = false)
    (; t, dt, uprev, u, f, p) = integrator
    (; c1, c2, c3, c4, c5, c6, c7, a21, a31, a32, a41, a43, a51, a53, a54, a61, a63, a64, a65, a71, a73, a74, a75, a76, a81, a83, a84, a85, a86, a87, a91, a93, a94, a95, a96, a97, a98, a101, a103, a104, a105, a106, a107, a108, b1, b4, b5, b6, b7, b8, b9, btilde1, btilde4, btilde5, btilde6, btilde7, btilde8, btilde9, btilde10) = cache
    k1 = integrator.fsalfirst
    a = dt * a21
    k2 = f(uprev + a * k1, p, t + c1 * dt)
    k3 = f(uprev + dt * (a31 * k1 + a32 * k2), p, t + c2 * dt)
    k4 = f(uprev + dt * (a41 * k1 + a43 * k3), p, t + c3 * dt)
    k5 = f(uprev + dt * (a51 * k1 + a53 * k3 + a54 * k4), p, t + c4 * dt)
    k6 = f(uprev + dt * (a61 * k1 + a63 * k3 + a64 * k4 + a65 * k5), p, t + c5 * dt)
    k7 = f(
        uprev + dt * (a71 * k1 + a73 * k3 + a74 * k4 + a75 * k5 + a76 * k6), p,
        t + c6 * dt
    )
    k8 = f(
        uprev + dt * (a81 * k1 + a83 * k3 + a84 * k4 + a85 * k5 + a86 * k6 + a87 * k7),
        p, t + c7 * dt
    )
    k9 = f(
        uprev +
            dt *
            (a91 * k1 + a93 * k3 + a94 * k4 + a95 * k5 + a96 * k6 + a97 * k7 + a98 * k8),
        p,
        t + dt
    )
    k10 = f(
        uprev +
            dt * (
            a101 * k1 + a103 * k3 + a104 * k4 + a105 * k5 + a106 * k6 + a107 * k7 +
                a108 * k8
        ),
        p,
        t + dt
    )
    OrdinaryDiffEqCore.increment_nf!(integrator.stats, 9)
    u = uprev + dt * (b1 * k1 + b4 * k4 + b5 * k5 + b6 * k6 + b7 * k7 + b8 * k8 + b9 * k9)
    if integrator.opts.adaptive
        utilde = dt *
            (
            btilde1 * k1 + btilde4 * k4 + btilde5 * k5 + btilde6 * k6 + btilde7 * k7 +
                btilde8 * k8 + btilde9 * k9 + btilde10 * k10
        )
        atmp = calculate_residuals(
            utilde, uprev, u, integrator.opts.abstol,
            integrator.opts.reltol, integrator.opts.internalnorm, t
        )
        OrdinaryDiffEqCore.set_EEst!(integrator, integrator.opts.internalnorm(atmp, t))
    end
    integrator.fsallast = f(u, p, t + dt) # For the interpolation, needs k at the updated point
    OrdinaryDiffEqCore.increment_nf!(integrator.stats, 1)
    integrator.k[1] = integrator.fsalfirst
    integrator.k[2] = integrator.fsallast
    integrator.u = u
end

function initialize!(integrator, cache::TanYam7Cache)
    integrator.kshortsize = 2
    resize!(integrator.k, integrator.kshortsize)
    integrator.k[1] = integrator.fsalfirst
    integrator.k[2] = integrator.fsallast
    integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) # Pre-start fsal
    return OrdinaryDiffEqCore.increment_nf!(integrator.stats, 1)
end

@muladd function perform_step!(integrator, cache::TanYam7Cache, repeat_step = false)
    (; t, dt, uprev, u, f, p) = integrator
    (; fsalfirst, k2, k3, k4, k5, k6, k7, k8, k9, k10, utilde, tmp, atmp, k, thread) = cache
    stage_limiter! = integrator.opts.stage_limiter!
    (; c1, c2, c3, c4, c5, c6, c7, a21, a31, a32, a41, a43, a51, a53, a54, a61, a63, a64, a65, a71, a73, a74, a75, a76, a81, a83, a84, a85, a86, a87, a91, a93, a94, a95, a96, a97, a98, a101, a103, a104, a105, a106, a107, a108, b1, b4, b5, b6, b7, b8, b9, btilde1, btilde4, btilde5, btilde6, btilde7, btilde8, btilde9, btilde10) = cache.tab
    k1 = fsalfirst
    f(k1, uprev, p, t)
    a = dt * a21
    @.. broadcast = false thread = thread tmp = uprev + a * k1
    stage_limiter!(tmp, integrator, p, t + c1 * dt)
    f(k2, tmp, p, t + c1 * dt)
    @.. broadcast = false thread = thread tmp = uprev + dt * (a31 * k1 + a32 * k2)
    stage_limiter!(tmp, integrator, p, t + c2 * dt)
    f(k3, tmp, p, t + c2 * dt)
    @.. broadcast = false thread = thread tmp = uprev + dt * (a41 * k1 + a43 * k3)
    stage_limiter!(tmp, integrator, p, t + c3 * dt)
    f(k4, tmp, p, t + c3 * dt)
    @.. broadcast = false thread = thread tmp = uprev + dt * (a51 * k1 + a53 * k3 + a54 * k4)
    stage_limiter!(tmp, integrator, p, t + c4 * dt)
    f(k5, tmp, p, t + c4 * dt)
    @.. broadcast = false thread = thread tmp = uprev +
        dt * (a61 * k1 + a63 * k3 + a64 * k4 + a65 * k5)
    stage_limiter!(tmp, integrator, p, t + c5 * dt)
    f(k6, tmp, p, t + c5 * dt)
    @.. broadcast = false thread = thread tmp = uprev +
        dt * (
        a71 * k1 + a73 * k3 + a74 * k4 + a75 * k5 +
            a76 * k6
    )
    stage_limiter!(tmp, integrator, p, t + c6 * dt)
    f(k7, tmp, p, t + c6 * dt)
    @.. broadcast = false thread = thread tmp = uprev +
        dt * (
        a81 * k1 + a83 * k3 + a84 * k4 + a85 * k5 +
            a86 * k6 +
            a87 * k7
    )
    stage_limiter!(tmp, integrator, p, t + c7 * dt)
    f(k8, tmp, p, t + c7 * dt)
    @.. broadcast = false thread = thread tmp = uprev +
        dt * (
        a91 * k1 + a93 * k3 + a94 * k4 + a95 * k5 +
            a96 * k6 +
            a97 * k7 + a98 * k8
    )
    stage_limiter!(tmp, integrator, p, t + dt)
    f(k9, tmp, p, t + dt)
    @.. broadcast = false thread = thread tmp = uprev +
        dt *
        (
        a101 * k1 + a103 * k3 + a104 * k4 + a105 * k5 +
            a106 * k6 +
            a107 * k7 + a108 * k8
    )
    stage_limiter!(tmp, integrator, p, t + dt)
    f(k10, tmp, p, t + dt)
    @.. broadcast = false thread = thread u = uprev +
        dt *
        (
        b1 * k1 + b4 * k4 + b5 * k5 + b6 * k6 + b7 * k7 +
            b8 * k8 +
            b9 * k9
    )
    stage_limiter!(u, integrator, p, t + dt)
    OrdinaryDiffEqCore.increment_nf!(integrator.stats, 10)
    if integrator.opts.adaptive
        @.. broadcast = false thread = thread utilde = dt * (
            btilde1 * k1 + btilde4 * k4 +
                btilde5 * k5 +
                btilde6 * k6 + btilde7 * k7 +
                btilde8 * k8 +
                btilde9 * k9 + btilde10 * k10
        )
        calculate_residuals!(
            atmp, utilde, uprev, u, integrator.opts.abstol,
            integrator.opts.reltol, integrator.opts.internalnorm, t,
            thread
        )
        OrdinaryDiffEqCore.set_EEst!(integrator, integrator.opts.internalnorm(atmp, t))
    end
    f(k, u, p, t + dt)
    OrdinaryDiffEqCore.increment_nf!(integrator.stats, 1)
    return nothing
end

#=
@muladd function perform_step!(integrator, cache::TanYam7Cache, repeat_step=false)
  (; t,dt,uprev,u,f,p) = integrator
  uidx = eachindex(integrator.uprev)
  (; fsalfirst,k2,k3,k4,k5,k6,k7,k8,k9,k10,utilde,tmp,atmp,k) = cache
  (; c1,c2,c3,c4,c5,c6,c7,a21,a31,a32,a41,a43,a51,a53,a54,a61,a63,a64,a65,a71,a73,a74,a75,a76,a81,a83,a84,a85,a86,a87,a91,a93,a94,a95,a96,a97,a98,a101,a103,a104,a105,a106,a107,a108,b1,b4,b5,b6,b7,b8,b9,btilde1,btilde4,btilde5,btilde6,btilde7,btilde8,btilde9,btilde10) = cache.tab
  k1 = fsalfirst
  f(k1, uprev, p, t)
  a = dt*a21
  @tight_loop_macros for i in uidx
    @inbounds tmp[i] = uprev[i]+a*k1[i]
  end
  f(k2, tmp, p, t + c1*dt)
  @tight_loop_macros for i in uidx
    @inbounds tmp[i] = uprev[i]+dt*(a31*k1[i]+a32*k2[i])
  end
  f(k3, tmp, p, t + c2*dt)
  @tight_loop_macros for i in uidx
    @inbounds tmp[i] = uprev[i]+dt*(a41*k1[i]+a43*k3[i])
  end
  f(k4, tmp, p, t + c3*dt)
  @tight_loop_macros for i in uidx
    @inbounds tmp[i] = uprev[i]+dt*(a51*k1[i]+a53*k3[i]+a54*k4[i])
  end
  f(k5, tmp, p, t + c4*dt)
  @tight_loop_macros for i in uidx
    @inbounds tmp[i] = uprev[i]+dt*(a61*k1[i]+a63*k3[i]+a64*k4[i]+a65*k5[i])
  end
  f(k6, tmp, p, t + c5*dt)
  @tight_loop_macros for i in uidx
    @inbounds tmp[i] = uprev[i]+dt*(a71*k1[i]+a73*k3[i]+a74*k4[i]+a75*k5[i]+a76*k6[i])
  end
  f(k7, tmp, p, t + c6*dt)
  @tight_loop_macros for i in uidx
    @inbounds tmp[i] = uprev[i]+dt*(a81*k1[i]+a83*k3[i]+a84*k4[i]+a85*k5[i]+a86*k6[i]+a87*k7[i])
  end
  f(k8, tmp, p, t + c7*dt)
  @tight_loop_macros for i in uidx
    @inbounds tmp[i] = uprev[i]+dt*(a91*k1[i]+a93*k3[i]+a94*k4[i]+a95*k5[i]+a96*k6[i]+a97*k7[i]+a98*k8[i])
  end
  f(k9, tmp, p, t+dt)
  @tight_loop_macros for i in uidx
    @inbounds tmp[i] = uprev[i]+dt*(a101*k1[i]+a103*k3[i]+a104*k4[i]+a105*k5[i]+a106*k6[i]+a107*k7[i]+a108*k8[i])
  end
  f(k10, tmp, p, t+dt)
  @tight_loop_macros for i in uidx
    @inbounds u[i] = uprev[i] + dt*(b1*k1[i]+b4*k4[i]+b5*k5[i]+b6*k6[i]+b7*k7[i]+b8*k8[i]+b9*k9[i])
  end
  OrdinaryDiffEqCore.increment_nf!(integrator.stats, 10)
  if integrator.opts.adaptive
    @tight_loop_macros for i in uidx
      @inbounds utilde[i] = dt*(btilde1*k1[i]+btilde4*k4[i]+btilde5*k5[i]+btilde6*k6[i]+btilde7*k7[i]+btilde8*k8[i]+btilde9*k9[i]+btilde10*k10[i])
    end
    calculate_residuals!(atmp, utilde, uprev, u, integrator.opts.abstol, integrator.opts.reltol,integrator.opts.internalnorm,t)
    OrdinaryDiffEqCore.set_EEst!(integrator, integrator.opts.internalnorm(atmp,t))
  end
  f(k, u, p, t+dt)
  OrdinaryDiffEqCore.increment_nf!(integrator.stats, 1)
end
=#

function initialize!(integrator, cache::TsitPap8ConstantCache)
    integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal
    OrdinaryDiffEqCore.increment_nf!(integrator.stats, 1)
    integrator.kshortsize = 2
    integrator.k = typeof(integrator.k)(undef, integrator.kshortsize)

    # Avoid undefined entries if k is an array of arrays
    integrator.fsallast = zero(integrator.fsalfirst)
    integrator.k[1] = integrator.fsalfirst
    return integrator.k[2] = integrator.fsallast
end

#=
@muladd function perform_step!(integrator, cache::TsitPap8ConstantCache, repeat_step=false)
  (; t,dt,uprev,u,f,p) = integrator
  (; c1,c2,c3,c4,c5,c6,c7,c8,c9,c10,a0201,a0301,a0302,a0401,a0403,a0501,a0503,a0504,a0601,a0604,a0605,a0701,a0704,a0705,a0706,a0801,a0804,a0805,a0806,a0807,a0901,a0904,a0905,a0906,a0907,a0908,a1001,a1004,a1005,a1006,a1007,a1008,a1009,a1101,a1104,a1105,a1106,a1107,a1108,a1109,a1110,a1201,a1204,a1205,a1206,a1207,a1208,a1209,a1210,a1211,a1301,a1304,a1305,a1306,a1307,a1308,a1309,a1310,b1,b6,b7,b8,b9,b10,b11,b12,btilde1,btilde6,btilde7,btilde8,btilde9,btilde10,btilde11,btilde12,btilde13) = cache
  k1 = integrator.fsalfirst
  a = dt*a0201
  k2 = f(t + c1*dt, @.. broadcast=false uprev+a*k1)
  k3 = f(t + c2*dt, @.. broadcast=false uprev+dt*(a0301*k1+a0302*k2))
  k4 = f(t + c3*dt, @.. broadcast=false uprev+dt*(a0401*k1       +a0403*k3))
  k5 = f(t + c4*dt, @.. broadcast=false uprev+dt*(a0501*k1       +a0503*k3+a0504*k4))
  k6 = f(t + c5*dt, @.. broadcast=false uprev+dt*(a0601*k1                +a0604*k4+a0605*k5))
  k7 = f(t + c6*dt, @.. broadcast=false uprev+dt*(a0701*k1                +a0704*k4+a0705*k5+a0706*k6))
  k8 = f(t + c7*dt, @.. broadcast=false uprev+dt*(a0801*k1                +a0804*k4+a0805*k5+a0806*k6+a0807*k7))
  k9 = f(t + c8*dt, @.. broadcast=false uprev+dt*(a0901*k1                +a0904*k4+a0905*k5+a0906*k6+a0907*k7+a0908*k8))
  k10 =f(t + c9*dt, @.. broadcast=false uprev+dt*(a1001*k1                +a1004*k4+a1005*k5+a1006*k6+a1007*k7+a1008*k8+a1009*k9))
  k11= f(t + c10*dt, @.. broadcast=false uprev+dt*(a1101*k1                +a1104*k4+a1105*k5+a1106*k6+a1107*k7+a1108*k8+a1109*k9+a1110*k10))
  k12= f(t+dt, @.. broadcast=false uprev+dt*(a1201*k1                +a1204*k4+a1205*k5+a1206*k6+a1207*k7+a1208*k8+a1209*k9+a1210*k10+a1211*k11))
  k13= f(t+dt, @.. broadcast=false uprev+dt*(a1301*k1                +a1304*k4+a1305*k5+a1306*k6+a1307*k7+a1308*k8+a1309*k9+a1310*k10))
  u = @.. broadcast=false uprev + dt*(b1*k1+b6*k6+b7*k7+b8*k8+b9*k9+b10*k10+b11*k11+b12*k12)
  if integrator.opts.adaptive
    utilde = @.. broadcast=false dt*(btilde1*k1 + btilde6*k6 + btilde7*k7 + btilde8*k8 + btilde9*k9 + btilde10*k10 + btilde11*k11 + btilde12*k12 + btilde13*k13)
    atmp = calculate_residuals(utilde, uprev, u, integrator.opts.abstol, integrator.opts.reltol,integrator.opts.internalnorm,t)
    OrdinaryDiffEqCore.set_EEst!(integrator, integrator.opts.internalnorm(atmp,t))
  end
  integrator.fsallast = f(u, p, t+dt)
  integrator.k[1] = integrator.fsalfirst
  integrator.k[2] = integrator.fsallast
  integrator.u = u
end
=#

@muladd function perform_step!(
        integrator, cache::TsitPap8ConstantCache,
        repeat_step = false
    )
    (; t, dt, uprev, u, f, p) = integrator
    (; c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, a0201, a0301, a0302, a0401, a0403, a0501, a0503, a0504, a0601, a0604, a0605, a0701, a0704, a0705, a0706, a0801, a0804, a0805, a0806, a0807, a0901, a0904, a0905, a0906, a0907, a0908, a1001, a1004, a1005, a1006, a1007, a1008, a1009, a1101, a1104, a1105, a1106, a1107, a1108, a1109, a1110, a1201, a1204, a1205, a1206, a1207, a1208, a1209, a1210, a1211, a1301, a1304, a1305, a1306, a1307, a1308, a1309, a1310, b1, b6, b7, b8, b9, b10, b11, b12, btilde1, btilde6, btilde7, btilde8, btilde9, btilde10, btilde11, btilde12, btilde13) = cache
    k1 = integrator.fsalfirst
    a = dt * a0201
    k2 = f(uprev + a * k1, p, t + c1 * dt)
    k3 = f(uprev + dt * (a0301 * k1 + a0302 * k2), p, t + c2 * dt)
    k4 = f(uprev + dt * (a0401 * k1 + a0403 * k3), p, t + c3 * dt)
    k5 = f(uprev + dt * (a0501 * k1 + a0503 * k3 + a0504 * k4), p, t + c4 * dt)
    k6 = f(uprev + dt * (a0601 * k1 + a0604 * k4 + a0605 * k5), p, t + c5 * dt)
    k7 = f(uprev + dt * (a0701 * k1 + a0704 * k4 + a0705 * k5 + a0706 * k6), p, t + c6 * dt)
    k8 = f(
        uprev + dt * (a0801 * k1 + a0804 * k4 + a0805 * k5 + a0806 * k6 + a0807 * k7), p,
        t + c7 * dt
    )
    k9 = f(
        uprev +
            dt *
            (a0901 * k1 + a0904 * k4 + a0905 * k5 + a0906 * k6 + a0907 * k7 + a0908 * k8),
        p,
        t + c8 * dt
    )
    k10 = f(
        uprev +
            dt *
            (
            a1001 * k1 + a1004 * k4 + a1005 * k5 + a1006 * k6 + a1007 * k7 + a1008 * k8 +
                a1009 * k9
        ),
        p,
        t + c9 * dt
    )
    k11 = f(
        uprev +
            dt *
            (
            a1101 * k1 + a1104 * k4 + a1105 * k5 + a1106 * k6 + a1107 * k7 + a1108 * k8 +
                a1109 * k9 + a1110 * k10
        ),
        p,
        t + c10 * dt
    )
    k12 = f(
        uprev +
            dt *
            (
            a1201 * k1 + a1204 * k4 + a1205 * k5 + a1206 * k6 + a1207 * k7 + a1208 * k8 +
                a1209 * k9 + a1210 * k10 + a1211 * k11
        ),
        p,
        t + dt
    )
    k13 = f(
        uprev +
            dt *
            (
            a1301 * k1 + a1304 * k4 + a1305 * k5 + a1306 * k6 + a1307 * k7 + a1308 * k8 +
                a1309 * k9 + a1310 * k10
        ),
        p,
        t + dt
    )
    OrdinaryDiffEqCore.increment_nf!(integrator.stats, 12)
    u = uprev +
        dt * (
        b1 * k1 + b6 * k6 + b7 * k7 + b8 * k8 + b9 * k9 + b10 * k10 + b11 * k11 +
            b12 * k12
    )
    if integrator.opts.adaptive
        utilde = dt *
            (
            btilde1 * k1 + btilde6 * k6 + btilde7 * k7 + btilde8 * k8 + btilde9 * k9 +
                btilde10 * k10 + btilde11 * k11 + btilde12 * k12 + btilde13 * k13
        )
        atmp = calculate_residuals(
            utilde, uprev, u, integrator.opts.abstol,
            integrator.opts.reltol, integrator.opts.internalnorm, t
        )
        OrdinaryDiffEqCore.set_EEst!(integrator, integrator.opts.internalnorm(atmp, t))
    end
    integrator.fsallast = f(u, p, t + dt)
    OrdinaryDiffEqCore.increment_nf!(integrator.stats, 1)
    integrator.k[1] = integrator.fsalfirst
    integrator.k[2] = integrator.fsallast
    integrator.u = u
end

function initialize!(integrator, cache::TsitPap8Cache)
    integrator.kshortsize = 2
    resize!(integrator.k, integrator.kshortsize)
    integrator.k[1] = integrator.fsalfirst
    integrator.k[2] = integrator.fsallast
    integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) # Pre-start fsal
    return OrdinaryDiffEqCore.increment_nf!(integrator.stats, 1)
end

@muladd function perform_step!(integrator, cache::TsitPap8Cache, repeat_step = false)
    (; t, dt, uprev, u, f, p) = integrator
    (; c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, a0201, a0301, a0302, a0401, a0403, a0501, a0503, a0504, a0601, a0604, a0605, a0701, a0704, a0705, a0706, a0801, a0804, a0805, a0806, a0807, a0901, a0904, a0905, a0906, a0907, a0908, a1001, a1004, a1005, a1006, a1007, a1008, a1009, a1101, a1104, a1105, a1106, a1107, a1108, a1109, a1110, a1201, a1204, a1205, a1206, a1207, a1208, a1209, a1210, a1211, a1301, a1304, a1305, a1306, a1307, a1308, a1309, a1310, b1, b6, b7, b8, b9, b10, b11, b12, btilde1, btilde6, btilde7, btilde8, btilde9, btilde10, btilde11, btilde12, btilde13) = cache.tab
    (; k2, k3, k4, k5, k6, k7, k8, k9, k10, k11, k12, k13, utilde, tmp, atmp, k, thread) = cache
    stage_limiter! = integrator.opts.stage_limiter!
    k1 = cache.fsalfirst
    f(k1, uprev, p, t)
    a = dt * a0201
    @.. broadcast = false thread = thread tmp = uprev + a * k1
    stage_limiter!(tmp, integrator, p, t + c1 * dt)
    f(k2, tmp, p, t + c1 * dt)
    @.. broadcast = false thread = thread tmp = uprev + dt * (a0301 * k1 + a0302 * k2)
    stage_limiter!(tmp, integrator, p, t + c2 * dt)
    f(k3, tmp, p, t + c2 * dt)
    @.. broadcast = false thread = thread tmp = uprev + dt * (a0401 * k1 + a0403 * k3)
    stage_limiter!(tmp, integrator, p, t + c3 * dt)
    f(k4, tmp, p, t + c3 * dt)
    @.. broadcast = false thread = thread tmp = uprev +
        dt * (a0501 * k1 + a0503 * k3 + a0504 * k4)
    stage_limiter!(tmp, integrator, p, t + c4 * dt)
    f(k5, tmp, p, t + c4 * dt)
    @.. broadcast = false thread = thread tmp = uprev +
        dt * (a0601 * k1 + a0604 * k4 + a0605 * k5)
    stage_limiter!(tmp, integrator, p, t + c5 * dt)
    f(k6, tmp, p, t + c5 * dt)
    @.. broadcast = false thread = thread tmp = uprev +
        dt * (
        a0701 * k1 + a0704 * k4 + a0705 * k5 +
            a0706 * k6
    )
    stage_limiter!(tmp, integrator, p, t + c6 * dt)
    f(k7, tmp, p, t + c6 * dt)
    @.. broadcast = false thread = thread tmp = uprev +
        dt *
        (
        a0801 * k1 + a0804 * k4 + a0805 * k5 +
            a0806 * k6 + a0807 * k7
    )
    stage_limiter!(tmp, integrator, p, t + c7 * dt)
    f(k8, tmp, p, t + c7 * dt)
    @.. broadcast = false thread = thread tmp = uprev +
        dt * (
        a0901 * k1 + a0904 * k4 + a0905 * k5 +
            a0906 * k6 +
            a0907 * k7 + a0908 * k8
    )
    stage_limiter!(tmp, integrator, p, t + c8 * dt)
    f(k9, tmp, p, t + c8 * dt)
    @.. broadcast = false thread = thread tmp = uprev +
        dt * (
        a1001 * k1 + a1004 * k4 + a1005 * k5 +
            a1006 * k6 +
            a1007 * k7 + a1008 * k8 + a1009 * k9
    )
    stage_limiter!(tmp, integrator, p, t + c9 * dt)
    f(k10, tmp, p, t + c9 * dt)
    @.. broadcast = false thread = thread tmp = uprev +
        dt * (
        a1101 * k1 + a1104 * k4 + a1105 * k5 +
            a1106 * k6 +
            a1107 * k7 + a1108 * k8 + a1109 * k9 +
            a1110 * k10
    )
    stage_limiter!(tmp, integrator, p, t + c10 * dt)
    f(k11, tmp, p, t + c10 * dt)
    @.. broadcast = false thread = thread tmp = uprev +
        dt * (
        a1201 * k1 + a1204 * k4 + a1205 * k5 +
            a1206 * k6 +
            a1207 * k7 + a1208 * k8 + a1209 * k9 +
            a1210 * k10 +
            a1211 * k11
    )
    stage_limiter!(tmp, integrator, p, t + dt)
    f(k12, tmp, p, t + dt)
    @.. broadcast = false thread = thread tmp = uprev +
        dt * (
        a1301 * k1 + a1304 * k4 + a1305 * k5 +
            a1306 * k6 +
            a1307 * k7 + a1308 * k8 + a1309 * k9 +
            a1310 * k10
    )
    stage_limiter!(tmp, integrator, p, t + dt)
    f(k13, tmp, p, t + dt)
    @.. broadcast = false thread = thread u = uprev +
        dt *
        (
        b1 * k1 + b6 * k6 + b7 * k7 + b8 * k8 + b9 * k9 +
            b10 * k10 +
            b11 * k11 + b12 * k12
    )
    stage_limiter!(u, integrator, p, t + dt)
    OrdinaryDiffEqCore.increment_nf!(integrator.stats, 13)
    if integrator.opts.adaptive
        @.. broadcast = false thread = thread utilde = dt * (
            btilde1 * k1 + btilde6 * k6 +
                btilde7 * k7 +
                btilde8 * k8 + btilde9 * k9 +
                btilde10 * k10 +
                btilde11 * k11 + btilde12 * k12 +
                btilde13 * k13
        )
        calculate_residuals!(
            atmp, utilde, uprev, u, integrator.opts.abstol,
            integrator.opts.reltol, integrator.opts.internalnorm, t,
            thread
        )
        OrdinaryDiffEqCore.set_EEst!(integrator, integrator.opts.internalnorm(atmp, t))
    end
    f(k, u, p, t + dt)
    OrdinaryDiffEqCore.increment_nf!(integrator.stats, 1)
    return nothing
end

#=
@muladd function perform_step!(integrator, cache::TsitPap8Cache, repeat_step=false)
  (; t,dt,uprev,u,f,p) = integrator
  uidx = eachindex(integrator.uprev)
  (; c1,c2,c3,c4,c5,c6,c7,c8,c9,c10,a0201,a0301,a0302,a0401,a0403,a0501,a0503,a0504,a0601,a0604,a0605,a0701,a0704,a0705,a0706,a0801,a0804,a0805,a0806,a0807,a0901,a0904,a0905,a0906,a0907,a0908,a1001,a1004,a1005,a1006,a1007,a1008,a1009,a1101,a1104,a1105,a1106,a1107,a1108,a1109,a1110,a1201,a1204,a1205,a1206,a1207,a1208,a1209,a1210,a1211,a1301,a1304,a1305,a1306,a1307,a1308,a1309,a1310,b1,b6,b7,b8,b9,b10,b11,b12,btilde1,btilde6,btilde7,btilde8,btilde9,btilde10,btilde11,btilde12,btilde13) = cache.tab
  (; k2,k3,k4,k5,k6,k7,k8,k9,k10,k11,k12,k13,utilde,tmp,atmp,k) = cache
  k1 = cache.fsalfirst
  f(k1, uprev, p, t)
  a = dt*a0201
  @tight_loop_macros for i in uidx
    @inbounds tmp[i] = uprev[i]+a*k1[i]
  end
  f(k2, tmp, p, t + c1*dt)
  @tight_loop_macros for i in uidx
    @inbounds tmp[i] = uprev[i]+dt*(a0301*k1[i]+a0302*k2[i])
  end
  f(k3, tmp, p, t + c2*dt)
  @tight_loop_macros for i in uidx
    @inbounds tmp[i] = uprev[i]+dt*(a0401*k1[i]+a0403*k3[i])
  end
  f(k4, tmp, p, t + c3*dt)
  @tight_loop_macros for i in uidx
    @inbounds tmp[i] = uprev[i]+dt*(a0501*k1[i]+a0503*k3[i]+a0504*k4[i])
  end
  f(k5, tmp, p, t + c4*dt)
  @tight_loop_macros for i in uidx
    @inbounds tmp[i] = uprev[i]+dt*(a0601*k1[i]+a0604*k4[i]+a0605*k5[i])
  end
  f(k6, tmp, p, t + c5*dt)
  @tight_loop_macros for i in uidx
    @inbounds tmp[i] = uprev[i]+dt*(a0701*k1[i]+a0704*k4[i]+a0705*k5[i]+a0706*k6[i])
  end
  f(k7, tmp, p, t + c6*dt)
  @tight_loop_macros for i in uidx
    @inbounds tmp[i] = uprev[i]+dt*(a0801*k1[i]+a0804*k4[i]+a0805*k5[i]+a0806*k6[i]+a0807*k7[i])
  end
  f(k8, tmp, p, t + c7*dt)
  @tight_loop_macros for i in uidx
    @inbounds tmp[i] = uprev[i]+dt*(a0901*k1[i]+a0904*k4[i]+a0905*k5[i]+a0906*k6[i]+a0907*k7[i]+a0908*k8[i])
  end
  f(k9, tmp, p, t + c8*dt)
  @tight_loop_macros for i in uidx
    @inbounds tmp[i] = uprev[i]+dt*(a1001*k1[i]+a1004*k4[i]+a1005*k5[i]+a1006*k6[i]+a1007*k7[i]+a1008*k8[i]+a1009*k9[i])
  end
  f(k10, tmp, p, t + c9*dt)
  @tight_loop_macros for i in uidx
    @inbounds tmp[i] = uprev[i]+dt*(a1101*k1[i]+a1104*k4[i]+a1105*k5[i]+a1106*k6[i]+a1107*k7[i]+a1108*k8[i]+a1109*k9[i]+a1110*k10[i])
  end
  f(k11, tmp, p, t + c10*dt)
  @tight_loop_macros for i in uidx
    @inbounds tmp[i] = uprev[i]+dt*(a1201*k1[i]+a1204*k4[i]+a1205*k5[i]+a1206*k6[i]+a1207*k7[i]+a1208*k8[i]+a1209*k9[i]+a1210*k10[i]+a1211*k11[i])
  end
  f(k12, tmp, p, t+dt)
  @tight_loop_macros for i in uidx
    @inbounds tmp[i] = uprev[i]+dt*(a1301*k1[i]+a1304*k4[i]+a1305*k5[i]+a1306*k6[i]+a1307*k7[i]+a1308*k8[i]+a1309*k9[i]+a1310*k10[i])
  end
  f(k13, tmp, p, t+dt)
  @tight_loop_macros for i in uidx
    @inbounds u[i] = uprev[i] + dt*(b1*k1[i]+b6*k6[i]+b7*k7[i]+b8*k8[i]+b9*k9[i]+b10*k10[i]+b11*k11[i]+b12*k12[i])
  end
  OrdinaryDiffEqCore.increment_nf!(integrator.stats, 13)
  if integrator.opts.adaptive
    @tight_loop_macros for i in uidx
      @inbounds utilde[i] = dt*(btilde1*k1[i] + btilde6*k6[i] + btilde7*k7[i] + btilde8*k8[i] + btilde9*k9[i] + btilde10*k10[i] + btilde11*k11[i] + btilde12*k12[i] + btilde13*k13[i])
    end
    calculate_residuals!(atmp, utilde, uprev, u, integrator.opts.abstol, integrator.opts.reltol,integrator.opts.internalnorm,t)
    OrdinaryDiffEqCore.set_EEst!(integrator, integrator.opts.internalnorm(atmp,t))
  end
  f(k, u, p, t+dt)
  OrdinaryDiffEqCore.increment_nf!(integrator.stats, 1)
end
=#

function initialize!(integrator, cache::DP8ConstantCache)
    integrator.kshortsize = 7
    integrator.k = typeof(integrator.k)(undef, integrator.kshortsize)
    integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal
    OrdinaryDiffEqCore.increment_nf!(integrator.stats, 1)

    # Avoid undefined entries if k is an array of arrays
    integrator.fsallast = zero(integrator.fsalfirst)
    return @inbounds for i in eachindex(integrator.k)
        integrator.k[i] = zero(integrator.fsalfirst)
    end
end

@muladd function perform_step!(integrator, cache::DP8ConstantCache, repeat_step = false)
    (; t, dt, uprev, u, f, p) = integrator
    (; c7, c8, c9, c10, c11, c6, c5, c4, c3, c2, b1, b6, b7, b8, b9, b10, b11, b12, btilde1, btilde6, btilde7, btilde8, btilde9, btilde10, btilde11, btilde12, er1, er6, er7, er8, er9, er10, er11, er12, a0201, a0301, a0302, a0401, a0403, a0501, a0503, a0504, a0601, a0604, a0605, a0701, a0704, a0705, a0706, a0801, a0804, a0805, a0806, a0807, a0901, a0904, a0905, a0906, a0907, a0908, a1001, a1004, a1005, a1006, a1007, a1008, a1009, a1101, a1104, a1105, a1106, a1107, a1108, a1109, a1110, a1201, a1204, a1205, a1206, a1207, a1208, a1209, a1210, a1211) = cache
    k1 = integrator.fsalfirst
    a = dt * a0201
    k2 = f(uprev + a * k1, p, t + c2 * dt)
    k3 = f(uprev + dt * (a0301 * k1 + a0302 * k2), p, t + c3 * dt)
    k4 = f(uprev + dt * (a0401 * k1 + a0403 * k3), p, t + c4 * dt)
    k5 = f(uprev + dt * (a0501 * k1 + a0503 * k3 + a0504 * k4), p, t + c5 * dt)
    k6 = f(uprev + dt * (a0601 * k1 + a0604 * k4 + a0605 * k5), p, t + c6 * dt)
    k7 = f(uprev + dt * (a0701 * k1 + a0704 * k4 + a0705 * k5 + a0706 * k6), p, t + c7 * dt)
    k8 = f(
        uprev + dt * (a0801 * k1 + a0804 * k4 + a0805 * k5 + a0806 * k6 + a0807 * k7), p,
        t + c8 * dt
    )
    k9 = f(
        uprev +
            dt *
            (a0901 * k1 + a0904 * k4 + a0905 * k5 + a0906 * k6 + a0907 * k7 + a0908 * k8),
        p,
        t + c9 * dt
    )
    k10 = f(
        uprev +
            dt *
            (
            a1001 * k1 + a1004 * k4 + a1005 * k5 + a1006 * k6 + a1007 * k7 + a1008 * k8 +
                a1009 * k9
        ),
        p,
        t + c10 * dt
    )
    k11 = f(
        uprev +
            dt *
            (
            a1101 * k1 + a1104 * k4 + a1105 * k5 + a1106 * k6 + a1107 * k7 + a1108 * k8 +
                a1109 * k9 + a1110 * k10
        ),
        p,
        t + c11 * dt
    )
    k12 = f(
        uprev +
            dt *
            (
            a1201 * k1 + a1204 * k4 + a1205 * k5 + a1206 * k6 + a1207 * k7 + a1208 * k8 +
                a1209 * k9 + a1210 * k10 + a1211 * k11
        ),
        p,
        t + dt
    )
    OrdinaryDiffEqCore.increment_nf!(integrator.stats, 11)
    kupdate = b1 * k1 + b6 * k6 + b7 * k7 + b8 * k8 + b9 * k9 + b10 * k10 + b11 * k11 +
        b12 * k12
    u = uprev + dt * kupdate
    if integrator.opts.adaptive
        utilde = dt * (
            k1 * er1 + k6 * er6 + k7 * er7 + k8 * er8 + k9 * er9 + k10 * er10 +
                k11 * er11 + k12 * er12
        )
        atmp = calculate_residuals(
            utilde, uprev, u, integrator.opts.abstol,
            integrator.opts.reltol, integrator.opts.internalnorm, t
        )
        err5 = integrator.opts.internalnorm(atmp, t) # Order 5
        utilde = dt *
            (
            btilde1 * k1 + btilde6 * k6 + btilde7 * k7 + btilde8 * k8 + btilde9 * k9 +
                btilde10 * k10 + btilde11 * k11 + btilde12 * k12
        )
        atmp = calculate_residuals(
            utilde, uprev, u, integrator.opts.abstol,
            integrator.opts.reltol, integrator.opts.internalnorm, t
        )
        err3 = integrator.opts.internalnorm(atmp, t) # Order 3
        err52 = err5 * err5
        if err5 ≈ 0 && err3 ≈ 0
            OrdinaryDiffEqCore.set_EEst!(integrator, zero(OrdinaryDiffEqCore.get_EEst(integrator)))
        else
            OrdinaryDiffEqCore.set_EEst!(integrator, err52 / sqrt(err52 + 0.01 * err3 * err3))
        end
    end
    k13 = f(u, p, t + dt)
    OrdinaryDiffEqCore.increment_nf!(integrator.stats, 1)
    integrator.fsallast = k13
    if integrator.opts.calck
        (; c14, c15, c16, a1401, a1407, a1408, a1409, a1410, a1411, a1412, a1413, a1501, a1506, a1507, a1508, a1511, a1512, a1513, a1514, a1601, a1606, a1607, a1608, a1609, a1613, a1614, a1615) = cache
        (; d401, d406, d407, d408, d409, d410, d411, d412, d413, d414, d415, d416, d501, d506, d507, d508, d509, d510, d511, d512, d513, d514, d515, d516, d601, d606, d607, d608, d609, d610, d611, d612, d613, d614, d615, d616, d701, d706, d707, d708, d709, d710, d711, d712, d713, d714, d715, d716) = cache
        k14 = f(
            uprev +
                dt * (
                a1401 * k1 + a1407 * k7 + a1408 * k8 + a1409 * k9 + a1410 * k10 +
                    a1411 * k11 + a1412 * k12 + a1413 * k13
            ),
            p,
            t + c14 * dt
        )
        k15 = f(
            uprev +
                dt * (
                a1501 * k1 + a1506 * k6 + a1507 * k7 + a1508 * k8 + a1511 * k11 +
                    a1512 * k12 + a1513 * k13 + a1514 * k14
            ),
            p,
            t + c15 * dt
        )
        k16 = f(
            uprev +
                dt * (
                a1601 * k1 + a1606 * k6 + a1607 * k7 + a1608 * k8 + a1609 * k9 +
                    a1613 * k13 + a1614 * k14 + a1615 * k15
            ),
            p,
            t + c16 * dt
        )
        OrdinaryDiffEqCore.increment_nf!(integrator.stats, 3)
        udiff = kupdate
        integrator.k[1] = udiff
        bspl = k1 - udiff
        integrator.k[2] = bspl
        integrator.k[3] = udiff - k13 - bspl
        integrator.k[4] = d401 * k1 + d406 * k6 + d407 * k7 + d408 * k8 + d409 * k9 +
            d410 * k10 + d411 * k11 + d412 * k12 + d413 * k13 + d414 * k14 +
            d415 * k15 + d416 * k16
        integrator.k[5] = d501 * k1 + d506 * k6 + d507 * k7 + d508 * k8 + d509 * k9 +
            d510 * k10 + d511 * k11 + d512 * k12 + d513 * k13 + d514 * k14 +
            d515 * k15 + d516 * k16
        integrator.k[6] = d601 * k1 + d606 * k6 + d607 * k7 + d608 * k8 + d609 * k9 +
            d610 * k10 + d611 * k11 + d612 * k12 + d613 * k13 + d614 * k14 +
            d615 * k15 + d616 * k16
        integrator.k[7] = d701 * k1 + d706 * k6 + d707 * k7 + d708 * k8 + d709 * k9 +
            d710 * k10 + d711 * k11 + d712 * k12 + d713 * k13 + d714 * k14 +
            d715 * k15 + d716 * k16
    end
    integrator.u = u
end

function initialize!(integrator, cache::DP8Cache)
    integrator.kshortsize = 7
    resize!(integrator.k, integrator.kshortsize)
    integrator.k .= [
        cache.udiff,
        cache.bspl,
        cache.dense_tmp3,
        cache.dense_tmp4,
        cache.dense_tmp5,
        cache.dense_tmp6,
        cache.dense_tmp7,
    ]
    integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) # Pre-start fsal
    return OrdinaryDiffEqCore.increment_nf!(integrator.stats, 1)
end

@muladd function perform_step!(integrator, cache::DP8Cache, repeat_step = false)
    (; t, dt, uprev, u, f, p) = integrator
    uidx = eachindex(integrator.uprev)
    (; c7, c8, c9, c10, c11, c6, c5, c4, c3, c2, b1, b6, b7, b8, b9, b10, b11, b12, btilde1, btilde6, btilde7, btilde8, btilde9, btilde10, btilde11, btilde12, er1, er6, er7, er8, er9, er10, er11, er12, a0201, a0301, a0302, a0401, a0403, a0501, a0503, a0504, a0601, a0604, a0605, a0701, a0704, a0705, a0706, a0801, a0804, a0805, a0806, a0807, a0901, a0904, a0905, a0906, a0907, a0908, a1001, a1004, a1005, a1006, a1007, a1008, a1009, a1101, a1104, a1105, a1106, a1107, a1108, a1109, a1110, a1201, a1204, a1205, a1206, a1207, a1208, a1209, a1210, a1211) = cache.tab
    (; k1, k2, k3, k4, k5, k6, k7, k8, k9, k10, k11, k12, k13, k14, k15, k16, udiff, bspl, dense_tmp3, dense_tmp4, dense_tmp5, dense_tmp6, dense_tmp7, kupdate, utilde, tmp, atmp, thread) = cache
    stage_limiter! = integrator.opts.stage_limiter!
    f(k1, uprev, p, t)
    a = dt * a0201
    @.. broadcast = false thread = thread tmp = uprev + a * k1
    stage_limiter!(tmp, integrator, p, t + c2 * dt)
    f(k2, tmp, p, t + c2 * dt)
    @.. broadcast = false thread = thread tmp = uprev + dt * (a0301 * k1 + a0302 * k2)
    stage_limiter!(tmp, integrator, p, t + c3 * dt)
    f(k3, tmp, p, t + c3 * dt)
    @.. broadcast = false thread = thread tmp = uprev + dt * (a0401 * k1 + a0403 * k3)
    stage_limiter!(tmp, integrator, p, t + c4 * dt)
    f(k4, tmp, p, t + c4 * dt)
    @.. broadcast = false thread = thread tmp = uprev +
        dt * (a0501 * k1 + a0503 * k3 + a0504 * k4)
    stage_limiter!(tmp, integrator, p, t + c5 * dt)
    f(k5, tmp, p, t + c5 * dt)
    @.. broadcast = false thread = thread tmp = uprev +
        dt * (a0601 * k1 + a0604 * k4 + a0605 * k5)
    stage_limiter!(tmp, integrator, p, t + c6 * dt)
    f(k6, tmp, p, t + c6 * dt)
    @.. broadcast = false thread = thread tmp = uprev +
        dt * (
        a0701 * k1 + a0704 * k4 + a0705 * k5 +
            a0706 * k6
    )
    stage_limiter!(tmp, integrator, p, t + c7 * dt)
    f(k7, tmp, p, t + c7 * dt)
    @.. broadcast = false thread = thread tmp = uprev +
        dt *
        (
        a0801 * k1 + a0804 * k4 + a0805 * k5 +
            a0806 * k6 + a0807 * k7
    )
    stage_limiter!(tmp, integrator, p, t + c8 * dt)
    f(k8, tmp, p, t + c8 * dt)
    @.. broadcast = false thread = thread tmp = uprev +
        dt * (
        a0901 * k1 + a0904 * k4 + a0905 * k5 +
            a0906 * k6 +
            a0907 * k7 + a0908 * k8
    )
    stage_limiter!(tmp, integrator, p, t + c9 * dt)
    f(k9, tmp, p, t + c9 * dt)
    @.. broadcast = false thread = thread tmp = uprev +
        dt * (
        a1001 * k1 + a1004 * k4 + a1005 * k5 +
            a1006 * k6 +
            a1007 * k7 + a1008 * k8 + a1009 * k9
    )
    stage_limiter!(tmp, integrator, p, t + c10 * dt)
    f(k10, tmp, p, t + c10 * dt)
    @.. broadcast = false thread = thread tmp = uprev +
        dt * (
        a1101 * k1 + a1104 * k4 + a1105 * k5 +
            a1106 * k6 +
            a1107 * k7 + a1108 * k8 + a1109 * k9 +
            a1110 * k10
    )
    stage_limiter!(tmp, integrator, p, t + c11 * dt)
    f(k11, tmp, p, t + c11 * dt)
    @.. broadcast = false thread = thread tmp = uprev +
        dt * (
        a1201 * k1 + a1204 * k4 + a1205 * k5 +
            a1206 * k6 +
            a1207 * k7 + a1208 * k8 + a1209 * k9 +
            a1210 * k10 +
            a1211 * k11
    )
    stage_limiter!(tmp, integrator, p, t + dt)
    f(k12, tmp, p, t + dt)
    @.. broadcast = false thread = thread kupdate = b1 * k1 + b6 * k6 + b7 * k7 + b8 * k8 +
        b9 * k9 +
        b10 * k10 + b11 * k11 + b12 * k12
    @.. broadcast = false thread = thread u = uprev + dt * kupdate
    stage_limiter!(u, integrator, p, t + dt)
    OrdinaryDiffEqCore.increment_nf!(integrator.stats, 12)
    if integrator.opts.adaptive
        @.. broadcast = false thread = thread utilde = dt *
            (
            k1 * er1 + k6 * er6 + k7 * er7 +
                k8 * er8 + k9 * er9 +
                k10 * er10 + k11 * er11 + k12 * er12
        )
        calculate_residuals!(
            atmp, utilde, uprev, u, integrator.opts.abstol,
            integrator.opts.reltol, integrator.opts.internalnorm, t,
            thread
        )
        err5 = integrator.opts.internalnorm(atmp, t) # Order 5
        @.. broadcast = false thread = thread utilde = dt * (
            btilde1 * k1 + btilde6 * k6 +
                btilde7 * k7 +
                btilde8 * k8 + btilde9 * k9 +
                btilde10 * k10 +
                btilde11 * k11 + btilde12 * k12
        )
        calculate_residuals!(
            atmp, utilde, uprev, u, integrator.opts.abstol,
            integrator.opts.reltol, integrator.opts.internalnorm, t,
            thread
        )
        err3 = integrator.opts.internalnorm(atmp, t) # Order 3
        err52 = err5 * err5
        if err5 ≈ 0 && err3 ≈ 0
            OrdinaryDiffEqCore.set_EEst!(integrator, zero(OrdinaryDiffEqCore.get_EEst(integrator)))
        else
            OrdinaryDiffEqCore.set_EEst!(integrator, err52 / sqrt(err52 + 0.01 * err3 * err3))
        end
    end
    f(k13, u, p, t + dt)
    OrdinaryDiffEqCore.increment_nf!(integrator.stats, 1)
    if integrator.opts.calck
        (; c14, c15, c16, a1401, a1407, a1408, a1409, a1410, a1411, a1412, a1413, a1501, a1506, a1507, a1508, a1511, a1512, a1513, a1514, a1601, a1606, a1607, a1608, a1609, a1613, a1614, a1615) = cache.tab
        (; d401, d406, d407, d408, d409, d410, d411, d412, d413, d414, d415, d416, d501, d506, d507, d508, d509, d510, d511, d512, d513, d514, d515, d516, d601, d606, d607, d608, d609, d610, d611, d612, d613, d614, d615, d616, d701, d706, d707, d708, d709, d710, d711, d712, d713, d714, d715, d716) = cache.tab
        @.. broadcast = false thread = thread tmp = uprev +
            dt * (
            a1401 * k1 + a1407 * k7 + a1408 * k8 +
                a1409 * k9 +
                a1410 * k10 + a1411 * k11 + a1412 * k12 +
                a1413 * k13
        )
        f(k14, tmp, p, t + c14 * dt)
        @.. broadcast = false thread = thread tmp = uprev +
            dt * (
            a1501 * k1 + a1506 * k6 + a1507 * k7 +
                a1508 * k8 +
                a1511 * k11 + a1512 * k12 + a1513 * k13 +
                a1514 * k14
        )
        f(k15, tmp, p, t + c15 * dt)
        @.. broadcast = false thread = thread tmp = uprev +
            dt * (
            a1601 * k1 + a1606 * k6 + a1607 * k7 +
                a1608 * k8 +
                a1609 * k9 + a1613 * k13 + a1614 * k14 +
                a1615 * k15
        )
        f(k16, tmp, p, t + c16 * dt)
        OrdinaryDiffEqCore.increment_nf!(integrator.stats, 3)
        @.. broadcast = false thread = thread udiff = kupdate
        @.. broadcast = false thread = thread bspl = k1 - udiff
        @.. broadcast = false thread = thread integrator.k[3] = udiff - k13 - bspl
        @.. broadcast = false thread = thread integrator.k[4] = d401 * k1 + d406 * k6 +
            d407 * k7 + d408 * k8 +
            d409 * k9 + d410 * k10 +
            d411 * k11 +
            d412 * k12 + d413 * k13 +
            d414 * k14 +
            d415 * k15 + d416 * k16
        @.. broadcast = false thread = thread integrator.k[5] = d501 * k1 + d506 * k6 +
            d507 * k7 + d508 * k8 +
            d509 * k9 + d510 * k10 +
            d511 * k11 +
            d512 * k12 + d513 * k13 +
            d514 * k14 +
            d515 * k15 + d516 * k16
        @.. broadcast = false thread = thread integrator.k[6] = d601 * k1 + d606 * k6 +
            d607 * k7 + d608 * k8 +
            d609 * k9 + d610 * k10 +
            d611 * k11 +
            d612 * k12 + d613 * k13 +
            d614 * k14 +
            d615 * k15 + d616 * k16
        @.. broadcast = false thread = thread integrator.k[7] = d701 * k1 + d706 * k6 +
            d707 * k7 + d708 * k8 +
            d709 * k9 + d710 * k10 +
            d711 * k11 +
            d712 * k12 + d713 * k13 +
            d714 * k14 +
            d715 * k15 + d716 * k16
    end
end

#=
@muladd function perform_step!(integrator, cache::DP8Cache, repeat_step=false)
  (; t,dt,uprev,u,f,p) = integrator
  uidx = eachindex(integrator.uprev)
  (; c7,c8,c9,c10,c11,c6,c5,c4,c3,c2,b1,b6,b7,b8,b9,b10,b11,b12,btilde1,btilde6,btilde7,btilde8,btilde9,btilde10,btilde11,btilde12,er1,er6,er7,er8,er9,er10,er11,er12,a0201,a0301,a0302,a0401,a0403,a0501,a0503,a0504,a0601,a0604,a0605,a0701,a0704,a0705,a0706,a0801,a0804,a0805,a0806,a0807,a0901,a0904,a0905,a0906,a0907,a0908,a1001,a1004,a1005,a1006,a1007,a1008,a1009,a1101,a1104,a1105,a1106,a1107,a1108,a1109,a1110,a1201,a1204,a1205,a1206,a1207,a1208,a1209,a1210,a1211) = cache.tab
  (; k1,k2,k3,k4,k5,k6,k7,k8,k9,k10,k11,k12,k13,k14,k15,k16,udiff,bspl,dense_tmp3,dense_tmp4,dense_tmp5,dense_tmp6,dense_tmp7,kupdate,utilde,tmp,atmp) = cache
  f(k1, uprev, p, t)
  a = dt*a0201
  @tight_loop_macros for i in uidx
    @inbounds tmp[i] = uprev[i]+a*k1[i]
  end
  f(k2, tmp, p, t + c2*dt)
  @tight_loop_macros for i in uidx
    @inbounds tmp[i] = uprev[i]+dt*(a0301*k1[i]+a0302*k2[i])
  end
  f(k3, tmp, p, t + c3*dt)
  @tight_loop_macros for i in uidx
    @inbounds tmp[i] = uprev[i]+dt*(a0401*k1[i]+a0403*k3[i])
  end
  f(k4, tmp, p, t + c4*dt)
  @tight_loop_macros for i in uidx
    @inbounds tmp[i] = uprev[i]+dt*(a0501*k1[i]+a0503*k3[i]+a0504*k4[i])
  end
  f(k5, tmp, p, t + c5*dt)
  @tight_loop_macros for i in uidx
    @inbounds tmp[i] = uprev[i]+dt*(a0601*k1[i]+a0604*k4[i]+a0605*k5[i])
  end
  f(k6, tmp, p, t + c6*dt)
  @tight_loop_macros for i in uidx
    @inbounds tmp[i] = uprev[i]+dt*(a0701*k1[i]+a0704*k4[i]+a0705*k5[i]+a0706*k6[i])
  end
  f(k7, tmp, p, t + c7*dt)
  @tight_loop_macros for i in uidx
    @inbounds tmp[i] = uprev[i]+dt*(a0801*k1[i]+a0804*k4[i]+a0805*k5[i]+a0806*k6[i]+a0807*k7[i])
  end
  f(k8, tmp, p, t + c8*dt)
  @tight_loop_macros for i in uidx
    @inbounds tmp[i] = uprev[i]+dt*(a0901*k1[i]+a0904*k4[i]+a0905*k5[i]+a0906*k6[i]+a0907*k7[i]+a0908*k8[i])
  end
  f(k9, tmp, p, t + c9*dt)
  @tight_loop_macros for i in uidx
    @inbounds tmp[i] = uprev[i]+dt*(a1001*k1[i]+a1004*k4[i]+a1005*k5[i]+a1006*k6[i]+a1007*k7[i]+a1008*k8[i]+a1009*k9[i])
  end
  f(k10, tmp, p, t + c10*dt)
  @tight_loop_macros for i in uidx
    @inbounds tmp[i] = uprev[i]+dt*(a1101*k1[i]+a1104*k4[i]+a1105*k5[i]+a1106*k6[i]+a1107*k7[i]+a1108*k8[i]+a1109*k9[i]+a1110*k10[i])
  end
  f(k11, tmp, p, t + c11*dt)
  @tight_loop_macros for i in uidx
    @inbounds tmp[i] = uprev[i]+dt*(a1201*k1[i]+a1204*k4[i]+a1205*k5[i]+a1206*k6[i]+a1207*k7[i]+a1208*k8[i]+a1209*k9[i]+a1210*k10[i]+a1211*k11[i])
  end
  f(k12, tmp, p, t+dt)
  @tight_loop_macros for i in uidx
    @inbounds kupdate[i] = b1*k1[i]+b6*k6[i]+b7*k7[i]+b8*k8[i]+b9*k9[i]+b10*k10[i]+b11*k11[i]+b12*k12[i]
    @inbounds u[i] = uprev[i] + dt*kupdate[i]
  end
  OrdinaryDiffEqCore.increment_nf!(integrator.stats, 12)
  if integrator.opts.adaptive
    @tight_loop_macros for i in uidx
      @inbounds utilde[i] = dt*(k1[i]*er1 + k6[i]*er6 + k7[i]*er7 + k8[i]*er8 + k9[i]*er9 + k10[i]*er10 + k11[i]*er11 + k12[i]*er12)
    end
    calculate_residuals!(atmp, utilde, uprev, u, integrator.opts.abstol, integrator.opts.reltol,integrator.opts.internalnorm,t)
    err5 = integrator.opts.internalnorm(atmp,t) # Order 5
    @tight_loop_macros for i in uidx
      @inbounds utilde[i]= dt*(btilde1*k1[i] + btilde6*k6[i] + btilde7*k7[i] + btilde8*k8[i] + btilde9*k9[i] + btilde10*k10[i] + btilde11*k11[i] + btilde12*k12[i])
    end
    calculate_residuals!(atmp, utilde, uprev, u, integrator.opts.abstol, integrator.opts.reltol,integrator.opts.internalnorm,t)
    err3 = integrator.opts.internalnorm(atmp,t) # Order 3
    err52 = err5*err5
    if err5 ≈ 0 && err3 ≈ 0
      OrdinaryDiffEqCore.set_EEst!(integrator, zero(OrdinaryDiffEqCore.get_EEst(integrator)))
    else
      OrdinaryDiffEqCore.set_EEst!(integrator, err52/sqrt(err52 + 0.01*err3*err3))
    end
  end
  f(k13, u, p, t+dt)
  OrdinaryDiffEqCore.increment_nf!(integrator.stats, 1)
  if integrator.opts.calck
    (; c14,c15,c16,a1401,a1407,a1408,a1409,a1410,a1411,a1412,a1413,a1501,a1506,a1507,a1508,a1511,a1512,a1513,a1514,a1601,a1606,a1607,a1608,a1609,a1613,a1614,a1615) = cache.tab
    (; d401,d406,d407,d408,d409,d410,d411,d412,d413,d414,d415,d416,d501,d506,d507,d508,d509,d510,d511,d512,d513,d514,d515,d516,d601,d606,d607,d608,d609,d610,d611,d612,d613,d614,d615,d616,d701,d706,d707,d708,d709,d710,d711,d712,d713,d714,d715,d716) = cache.tab
    @tight_loop_macros for i in uidx
      @inbounds tmp[i] = uprev[i]+dt*(a1401*k1[i]+a1407*k7[i]+a1408*k8[i]+a1409*k9[i]+a1410*k10[i]+a1411*k11[i]+a1412*k12[i]+a1413*k13[i])
    end
    f(k14, tmp, p, t + c14*dt)
    @tight_loop_macros for i in uidx
      @inbounds tmp[i] = uprev[i]+dt*(a1501*k1[i]+a1506*k6[i]+a1507*k7[i]+a1508*k8[i]+a1511*k11[i]+a1512*k12[i]+a1513*k13[i]+a1514*k14[i])
    end
    f(k15, tmp, p, t + c15*dt)
    @tight_loop_macros for i in uidx
      @inbounds tmp[i] = uprev[i]+dt*(a1601*k1[i]+a1606*k6[i]+a1607*k7[i]+a1608*k8[i]+a1609*k9[i]+a1613*k13[i]+a1614*k14[i]+a1615*k15[i])
    end
    f(k16, tmp, p, t + c16*dt)
    OrdinaryDiffEqCore.increment_nf!(integrator.stats, 3)
    @tight_loop_macros for i in uidx
      @inbounds udiff[i]= kupdate[i]
      @inbounds bspl[i] = k1[i] - udiff[i]
      @inbounds integrator.k[3][i] = udiff[i] - k13[i] - bspl[i]
      @inbounds integrator.k[4][i] = d401*k1[i]+d406*k6[i]+d407*k7[i]+d408*k8[i]+d409*k9[i]+d410*k10[i]+d411*k11[i]+d412*k12[i]+d413*k13[i]+d414*k14[i]+d415*k15[i]+d416*k16[i]
      @inbounds integrator.k[5][i] = d501*k1[i]+d506*k6[i]+d507*k7[i]+d508*k8[i]+d509*k9[i]+d510*k10[i]+d511*k11[i]+d512*k12[i]+d513*k13[i]+d514*k14[i]+d515*k15[i]+d516*k16[i]
      @inbounds integrator.k[6][i] = d601*k1[i]+d606*k6[i]+d607*k7[i]+d608*k8[i]+d609*k9[i]+d610*k10[i]+d611*k11[i]+d612*k12[i]+d613*k13[i]+d614*k14[i]+d615*k15[i]+d616*k16[i]
      @inbounds integrator.k[7][i] = d701*k1[i]+d706*k6[i]+d707*k7[i]+d708*k8[i]+d709*k9[i]+d710*k10[i]+d711*k11[i]+d712*k12[i]+d713*k13[i]+d714*k14[i]+d715*k15[i]+d716*k16[i]
    end
  end
end
=#

function initialize!(integrator, cache::PFRK87ConstantCache)
    integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal
    OrdinaryDiffEqCore.increment_nf!(integrator.stats, 1)
    integrator.kshortsize = 2
    integrator.k = typeof(integrator.k)(undef, integrator.kshortsize)

    # Avoid undefined entries if k is an array of arrays
    integrator.fsallast = zero(integrator.fsalfirst)
    integrator.k[1] = integrator.fsalfirst
    return integrator.k[2] = integrator.fsallast
end

@muladd function perform_step!(integrator, cache::PFRK87ConstantCache, repeat_step = false)
    (; t, dt, uprev, u, f, p) = integrator
    (; α0201, α0301, α0401, α0501, α0601, α0701, α0302, α0403, α0503, α0504, α0604, α0704, α0605, α0705, α0706, α0908, α1008, α1108, α1208, α1308, α1009, α1109, α1209, α1309, α1110, α1210, α1310, α1211, α1311, β1, β6, β7, β8, β9, β10, β11, β12, β13, β1tilde, β6tilde, β7tilde, β8tilde, β9tilde, β10tilde, β11tilde, β12tilde, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13) = cache
    alg = unwrap_alg(integrator, false)
    ν = alg.omega * dt
    νsq = ν^2

    c_ν = -0.19781108078634084 - (0.164050909125528499 * νsq) +
        (0.042578310088756321 * (νsq^2)) - (0.002300513610963998 * (νsq^3)) +
        (0.000033467244551879287 * (νsq^4)) -
        (7.8661142036921924 * (1 / 100000000) * (νsq^5))
    d_ν = 1 - (0.2964570921235674 * νsq) + (0.0015793885907465726 * (νsq^2)) -
        (0.00018913011771688527 * (νsq^3)) + (0.000017089234650765179 * (νsq^4)) -
        (1.2705211682518626 * (1 / 10000000) * (νsq^5))

    α0807 = c_ν / d_ν
    α0801 = 0.026876256 + 0.0576576 * α0807
    α0804 = 0.22464336 - 0.944944 * α0807
    α0805 = 0.000369024 - 0.2061696 * α0807
    α0806 = 0.21311136 + 0.093456 * α0807
    α0901 = 0.07239997637512857 + 0.01913119863380767 * α0807
    α0904 = -0.688400520601143 - 0.3135390887207368 * α0807
    α0905 = -0.17301267570583073 - 0.06840852844816077 * α0807
    α0906 = 0.1440060555560846 + 0.031009360422930017 * α0807
    α0907 = 0.9982362892760762 + 0.33180705811215994 * α0807
    α1001 = 0.16261514523236525 - 0.12125171966747463 * α0807
    α1004 = -2.1255544052061124 + 1.9871809612169453 * α0807
    α1005 = -0.216403903283323 + 0.43356675517460624 * α0807
    α1006 = -0.060417230254934076 - 0.1965343807796979 * α0807
    α1007 = 2.4846281621788395 - 2.102961615944379 * α0807
    α1101 = -1.0320124180911034 + 1.061943768952537 * α0807
    α1104 = 13.666683232895137 - 17.40407843561103 * α0807
    α1105 = 0.25990355211486116 - 3.797253476860588 * α0807
    α1106 = -5.759316475814002 + 1.7212824826428488 * α0807
    α1107 = -12.822511612651839 + 18.41810566087623 * α0807
    α1201 = 0.2478349764611783 - 0.06383934946543009 * α0807
    α1204 = -4.593782880309185 + 1.046256005127882 * α0807
    α1205 = -0.39566692537411896 + 0.22827403748244698 * α0807
    α1206 = -3.0673550479691665 - 0.10347586863902129 * α0807
    α1207 = 5.386688702227177 - 1.1072148245058775 * α0807
    α1301 = 0.7332242174431163 - 0.5164807626867616 * α0807
    α1304 = -10.196728938160977 + 8.464545832921925 * α0807
    α1305 = -0.43865244706547707 + 1.846809999910238 * α0807
    α1306 = 0.5693856884667226 - 0.8371528845746959 * α0807
    α1307 = 10.52865228002416 - 8.957722185570706 * α0807

    k1 = integrator.fsalfirst
    k2 = f(uprev + dt * α0201 * k1, p, t + c2 * dt)
    k3 = f(uprev + dt * (α0301 * k1 + α0302 * k2), p, t + c3 * dt)
    k4 = f(uprev + dt * (α0401 * k1 + α0403 * k3), p, t + c4 * dt)
    k5 = f(uprev + dt * (α0501 * k1 + α0503 * k3 + α0504 * k4), p, t + c5 * dt)
    k6 = f(uprev + dt * (α0601 * k1 + α0604 * k4 + α0605 * k5), p, t + c6 * dt)
    k7 = f(uprev + dt * (α0701 * k1 + α0704 * k4 + α0705 * k5 + α0706 * k6), p, t + c7 * dt)
    k8 = f(
        uprev + dt * (α0801 * k1 + α0804 * k4 + α0805 * k5 + α0806 * k6 + α0807 * k7), p,
        t + c8 * dt
    )
    k9 = f(
        uprev +
            dt *
            (α0901 * k1 + α0904 * k4 + α0905 * k5 + α0906 * k6 + α0907 * k7 + α0908 * k8),
        p,
        t + c9 * dt
    )
    k10 = f(
        uprev +
            dt *
            (
            α1001 * k1 + α1004 * k4 + α1005 * k5 + α1006 * k6 + α1007 * k7 + α1008 * k8 +
                α1009 * k9
        ),
        p,
        t + c10 * dt
    )
    k11 = f(
        uprev +
            dt *
            (
            α1101 * k1 + α1104 * k4 + α1105 * k5 + α1106 * k6 + α1107 * k7 + α1108 * k8 +
                α1109 * k9 + α1110 * k10
        ),
        p,
        t + c11 * dt
    )
    k12 = f(
        uprev +
            dt *
            (
            α1201 * k1 + α1204 * k4 + α1205 * k5 + α1206 * k6 + α1207 * k7 + α1208 * k8 +
                α1209 * k9 + α1210 * k10 + α1211 * k11
        ),
        p,
        t + c12 * dt
    )
    k13 = f(
        uprev +
            dt *
            (
            α1301 * k1 + α1304 * k4 + α1305 * k5 + α1306 * k6 + α1307 * k7 + α1308 * k8 +
                α1309 * k9 + α1310 * k10 + α1311 * k11
        ),
        p,
        t + c13 * dt
    )
    OrdinaryDiffEqCore.increment_nf!(integrator.stats, 12)
    u = uprev +
        dt * (
        β1 * k1 + β6 * k6 + β7 * k7 + β8 * k8 + β9 * k9 + β10 * k10 + β11 * k11 +
            β12 * k12 + β13 * k13
    )
    if integrator.opts.adaptive
        utilde = dt *
            (
            β1tilde * k1 + β6tilde * k6 + β7tilde * k7 + β8tilde * k8 + β9tilde * k9 +
                β10tilde * k10 + β11tilde * k11 + β12tilde * k12
        )
        atmp = calculate_residuals(
            utilde, uprev, u, integrator.opts.abstol,
            integrator.opts.reltol, integrator.opts.internalnorm, t
        )
        OrdinaryDiffEqCore.set_EEst!(integrator, integrator.opts.internalnorm(atmp, t))
    end
    integrator.fsallast = f(u, p, t + dt)
    OrdinaryDiffEqCore.increment_nf!(integrator.stats, 1)
    integrator.k[1] = integrator.fsalfirst
    integrator.k[2] = integrator.fsallast
    integrator.u = u
end

function initialize!(integrator, cache::PFRK87Cache)
    integrator.kshortsize = 2
    resize!(integrator.k, integrator.kshortsize)
    integrator.k[1] = integrator.fsalfirst
    integrator.k[2] = integrator.fsallast
    integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) # Pre-start fsal
    return OrdinaryDiffEqCore.increment_nf!(integrator.stats, 1)
end

@muladd function perform_step!(integrator, cache::PFRK87Cache, repeat_step = false)
    (; t, dt, uprev, u, f, p) = integrator
    (; α0201, α0301, α0401, α0501, α0601, α0701, α0302, α0403, α0503, α0504, α0604, α0704, α0605, α0705, α0706, α0908, α1008, α1108, α1208, α1308, α1009, α1109, α1209, α1309, α1110, α1210, α1310, α1211, α1311, β1, β6, β7, β8, β9, β10, β11, β12, β13, β1tilde, β6tilde, β7tilde, β8tilde, β9tilde, β10tilde, β11tilde, β12tilde, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13) = cache.tab
    (; k2, k3, k4, k5, k6, k7, k8, k9, k10, k11, k12, k13, utilde, tmp, atmp, k, thread) = cache
    stage_limiter! = integrator.opts.stage_limiter!

    alg = unwrap_alg(integrator, false)
    ν = alg.omega * dt
    νsq = ν^2

    c_ν = -0.19781108078634084 - (0.164050909125528499 * νsq) +
        (0.042578310088756321 * (νsq^2)) - (0.002300513610963998 * (νsq^3)) +
        (0.000033467244551879287 * (νsq^4)) - (7.8661142036921924 * (10^(-8)) * (νsq^5))
    d_ν = 1 - (0.2964570921235674 * νsq) + (0.0015793885907465726 * (νsq^2)) -
        (0.00018913011771688527 * (νsq^3)) + (0.000017089234650765179 * (νsq^4)) -
        (1.2705211682518626 * (10^(-7)) * (νsq^5))

    α0807 = c_ν / d_ν
    α0801 = 0.026876256 + 0.0576576 * α0807
    α0804 = 0.22464336 - 0.944944 * α0807
    α0805 = 0.000369024 - 0.2061696 * α0807
    α0806 = 0.21311136 + 0.093456 * α0807
    α0901 = 0.07239997637512857 + 0.01913119863380767 * α0807
    α0904 = -0.688400520601143 - 0.3135390887207368 * α0807
    α0905 = -0.17301267570583073 - 0.06840852844816077 * α0807
    α0906 = 0.1440060555560846 + 0.031009360422930017 * α0807
    α0907 = 0.9982362892760762 + 0.33180705811215994 * α0807
    α1001 = 0.16261514523236525 - 0.12125171966747463 * α0807
    α1004 = -2.1255544052061124 + 1.9871809612169453 * α0807
    α1005 = -0.216403903283323 + 0.43356675517460624 * α0807
    α1006 = -0.060417230254934076 - 0.1965343807796979 * α0807
    α1007 = 2.4846281621788395 - 2.102961615944379 * α0807
    α1101 = -1.0320124180911034 + 1.061943768952537 * α0807
    α1104 = 13.666683232895137 - 17.40407843561103 * α0807
    α1105 = 0.25990355211486116 - 3.797253476860588 * α0807
    α1106 = -5.759316475814002 + 1.7212824826428488 * α0807
    α1107 = -12.822511612651839 + 18.41810566087623 * α0807
    α1201 = 0.2478349764611783 - 0.06383934946543009 * α0807
    α1204 = -4.593782880309185 + 1.046256005127882 * α0807
    α1205 = -0.39566692537411896 + 0.22827403748244698 * α0807
    α1206 = -3.0673550479691665 - 0.10347586863902129 * α0807
    α1207 = 5.386688702227177 - 1.1072148245058775 * α0807
    α1301 = 0.7332242174431163 - 0.5164807626867616 * α0807
    α1304 = -10.196728938160977 + 8.464545832921925 * α0807
    α1305 = -0.43865244706547707 + 1.846809999910238 * α0807
    α1306 = 0.5693856884667226 - 0.8371528845746959 * α0807
    α1307 = 10.52865228002416 - 8.957722185570706 * α0807

    k1 = cache.fsalfirst
    f(k1, uprev, p, t)
    @.. broadcast = false thread = thread tmp = uprev + dt * α0201 * k1
    stage_limiter!(tmp, integrator, p, t + c2 * dt)
    f(k2, tmp, p, t + c2 * dt)
    @.. broadcast = false thread = thread tmp = uprev + dt * (α0301 * k1 + α0302 * k2)
    stage_limiter!(tmp, integrator, p, t + c3 * dt)
    f(k3, tmp, p, t + c3 * dt)
    @.. broadcast = false thread = thread tmp = uprev + dt * (α0401 * k1 + α0403 * k3)
    stage_limiter!(tmp, integrator, p, t + c4 * dt)
    f(k4, tmp, p, t + c4 * dt)
    @.. broadcast = false thread = thread tmp = uprev +
        dt * (α0501 * k1 + α0503 * k3 + α0504 * k4)
    stage_limiter!(tmp, integrator, p, t + c5 * dt)
    f(k5, tmp, p, t + c5 * dt)
    @.. broadcast = false thread = thread tmp = uprev +
        dt * (α0601 * k1 + α0604 * k4 + α0605 * k5)
    stage_limiter!(tmp, integrator, p, t + c6 * dt)
    f(k6, tmp, p, t + c6 * dt)
    @.. broadcast = false thread = thread tmp = uprev +
        dt * (
        α0701 * k1 + α0704 * k4 + α0705 * k5 +
            α0706 * k6
    )
    stage_limiter!(tmp, integrator, p, t + c7 * dt)
    f(k7, tmp, p, t + c7 * dt)
    @.. broadcast = false thread = thread tmp = uprev +
        dt *
        (
        α0801 * k1 + α0804 * k4 + α0805 * k5 +
            α0806 * k6 + α0807 * k7
    )
    stage_limiter!(tmp, integrator, p, t + c8 * dt)
    f(k8, tmp, p, t + c8 * dt)
    @.. broadcast = false thread = thread tmp = uprev +
        dt * (
        α0901 * k1 + α0904 * k4 + α0905 * k5 +
            α0906 * k6 +
            α0907 * k7 + α0908 * k8
    )
    stage_limiter!(tmp, integrator, p, t + c9 * dt)
    f(k9, tmp, p, t + c9 * dt)
    @.. broadcast = false thread = thread tmp = uprev +
        dt * (
        α1001 * k1 + α1004 * k4 + α1005 * k5 +
            α1006 * k6 +
            α1007 * k7 + α1008 * k8 + α1009 * k9
    )
    stage_limiter!(tmp, integrator, p, t + c10 * dt)
    f(k10, tmp, p, t + c10 * dt)
    @.. broadcast = false thread = thread tmp = uprev +
        dt * (
        α1101 * k1 + α1104 * k4 + α1105 * k5 +
            α1106 * k6 +
            α1107 * k7 + α1108 * k8 + α1109 * k9 +
            α1110 * k10
    )
    stage_limiter!(tmp, integrator, p, t + c11 * dt)
    f(k11, tmp, p, t + c11 * dt)
    @.. broadcast = false thread = thread tmp = uprev +
        dt * (
        α1201 * k1 + α1204 * k4 + α1205 * k5 +
            α1206 * k6 +
            α1207 * k7 + α1208 * k8 + α1209 * k9 +
            α1210 * k10 +
            α1211 * k11
    )
    stage_limiter!(tmp, integrator, p, t + c12 * dt)
    f(k12, tmp, p, t + c12 * dt)
    @.. broadcast = false thread = thread tmp = uprev +
        dt * (
        α1301 * k1 + α1304 * k4 + α1305 * k5 +
            α1306 * k6 +
            α1307 * k7 + α1308 * k8 + α1309 * k9 +
            α1310 * k10 +
            α1311 * k11
    )
    stage_limiter!(tmp, integrator, p, t + c13 * dt)
    f(k13, tmp, p, t + c13 * dt)
    @.. broadcast = false thread = thread u = uprev +
        dt *
        (
        β1 * k1 + β6 * k6 + β7 * k7 + β8 * k8 + β9 * k9 +
            β10 * k10 +
            β11 * k11 + β12 * k12 + β13 * k13
    )
    stage_limiter!(u, integrator, p, t + dt)
    OrdinaryDiffEqCore.increment_nf!(integrator.stats, 13)
    if integrator.opts.adaptive
        @.. broadcast = false thread = thread utilde = dt * (
            β1tilde * k1 + β6tilde * k6 +
                β7tilde * k7 +
                β8tilde * k8 + β9tilde * k9 +
                β10tilde * k10 +
                β11tilde * k11 + β12tilde * k12
        )
        calculate_residuals!(
            atmp, utilde, uprev, u, integrator.opts.abstol,
            integrator.opts.reltol, integrator.opts.internalnorm, t,
            thread
        )
        OrdinaryDiffEqCore.set_EEst!(integrator, integrator.opts.internalnorm(atmp, t))
    end
    f(k, u, p, t + dt)
    OrdinaryDiffEqCore.increment_nf!(integrator.stats, 1)
    return nothing
end
