rbs<-function(f,a,b,tol=1.0e-10,...){
    if( abs(b-a)<tol ) stop("starting values to close together")
    fa<-f(a,...)
    fb<-f(b,...)
    if( fa*fb > 0 ) stop("try new starting points")
    if( fa > 0 )
    {
    tmp<-b
    b<-a
    a<-tmp
    }
    if(abs(fa) < abs(fb)) midold<-a else midold<-b
       while(T) {
        fb<-f(b,...)
        fa<-f(a,...)
        mid<-((fb*a-fa*b))/(fb-fa)
        if(abs(mid-midold)<tol) return(mid)
        midold<-mid
        fc<-f(mid,...)
        if( fc > 0 ) {
            b<-mid
        }
        else {
            a<-mid
        }
    }
}


#The Poisson case, this works nicely... but now we need another function.
(Note this is the upper tail value)

rbspois <- function(x,lambda,p){log(p)-newpois(x,lambda)}
newpois <-function(q,lambda) pgamma(q=lambda,shape=q,rate=1,log.p=T)

#newpois(q,lambda)= P(X>=q,lambda) = 1-ppois(q-1,lambda)