Function ReformingBondMassFraction

//Implement Eq. (2.25)

Let $m=$number of generations

If (m = 0) Let $f^{m-1}(t_{n+1})=1$

Else Let $f^{m-1}(t_{n+1})=F({\Xi }_m(t_{n+1}))$

For u = 0 to m – 1    $f^{m-1}(t_{n+1})$ $-=$

$f^{u-1}(t^u)g(\mathbf{F}(t^u),t_{n+1}-t^u)$     Return $f^{m-1}(t_{n+1})$

Function NewGeneration

//Implement Sec. 2.2.4

Let $f^{m-1}(t_{n+1})=$

ReformingBondMassFraction

If $f^{m-1}(t_{n+1})<w_{\min }$ Return false

//Implement Sec. 2.2.2

Evaluate $\Delta \mathbf{F}=\mathbf{F}(t_{n+1})·{\mathbf{F}}^{-1}(t^m)$

Evaluate e from Eq. (2.27)

If $e>e_{\min }$ Return True

Return False

Function CullGenerations

//Implement Sec. 2.2.3

Let $m=$number of generations

If m < 3 Return

Let $w^0(t_{n+1})=g(\mathbf{U}(t^0),t_{n+1}-t^0)$

If $w^0(t_{n+1})<w_{\min }$ Let $w^1(t_{n+1})=f^0(t^1)g(\mathbf{U}(t^1),t_{n+1}-t^1)$

Update t1, $f^0(t^1)$, $\mathbf{U}(t^1)$

and $F({\Xi }_m(t^1))$ per Eq. (2.28)

Pop t0, $\mathbf{U}(t^0)$, $f^{-\infty }(t^0)$

and $F({\Xi }_m(t^0))$ out of

$t^{u+1}$, $f^u(t^{u+1})$, $\mathbf{U}(t^{u+1})$

and $F({\Xi }_m(t^{u+1}))$ stacks

Return