root finding by bisection from http://ygc.cwsurf.de/2008/11/25/bisect-to-solve-equation/

bisection.r

bisect <- function(f, u, v, eps){
     if ( f(u) * f(v) > 0)
         stop (" error, select another value for u or v...")
     if ( f(u) < 0) {
         u1 <- u
         v1 <- v
     } else {
         u1 <- v
         v1 <- u
     }
     cnt <- 1
     step <- log2(abs(u1-v1)/eps)
     while ( cnt < step ){
         m <- (u1+v1)/2
         if ( f(m) == 0)
             break
         if ( f(m) < 0 ) {
             u1 <- m
         } else {
             v1 <- m
         }
         cnt <- cnt + 1
     }
     return (m)
 }