r - Estimating distance difference between rows (genetic markers)

Question

I would like to calculate the distance between the markers (Name) in a given chromosome (Chr). The objects dist1.alldown (distance downstream) and dist1.allup (distance upstream) have exactly what I want. However, the below script is computationally inefficient (my real data could contain a milion of markers and this loop is time consuming).

  df <-  'Name  Chr Position
  GGaluGA001820 chr1    34388
  Gga_rs16686671 chr1    67781
  GGaluGA001841 chr1    80477
  Gga_rs15995401 chr1   111556
  Gga_rs15995393 chr1   112481
  GGaluGA001890 chr1   149690
  GGaluGA001902 chr1   176450
  Gga_rs14688751 chr1   185573
  GGaluGA001921 chr1   202425
  GGaluGA001945 chr1   235155'
df <- read.table(text=df, header=T)
probes <- df   
probes.split <- split(probes, probes$Chr)

####### Loop to infer distance upstream #####
{dist1.all <- NULL
 for(k in 1:length(probes.split)){
   probescx <- probes.split[[k]]
   probescx <- probescx[order(probescx$Position, decreasing=F),]
   for(i in 1:nrow(probescx)){
     v <- vector()
     v[k] <- k^2; print(paste(k,i)) 
     rowx <- probescx[i,]
     rowxm1 <- probescx[i-1,]
     if(nrow(rowxm1) > 0){
       lab <- rowx[1,1:2]
       dist1 <- rowx[1,3] - rowxm1[1,3]
       dist1 <- as.data.frame(dist1)
       dist1 <- cbind(lab, dist1)
       dist1.all <- rbind(dist1.all, dist1)
     }
   }
 }
}
### Save a different object
dist1.allup <- dist1.all
##background of up object
dist1.allupback <- dist1.allup

### Loop to infer distance downstream
{dist1.all <- NULL
 for(k in 1:length(probes.split)){
   probescx <- probes.split[[k]]
   probescx <- probescx[order(probescx$Position, decreasing=F),]
   for(i in 1:nrow(probescx)){
     v <- vector()
     v[k] <- k^2; print(paste(k,i)) 
     rowx <- probescx[i,]
     rowxm1 <- probescx[i+1,]
     if(nrow(rowxm1) > 0){
       lab <- rowx[1,1:2]
       dist1 <- rowx[1,3] - rowxm1[1,3]
       dist1 <- as.data.frame(dist1)
       dist1 <- cbind(lab, dist1)
       dist1.all <- rbind(dist1.all, dist1)
     }
   }
 }
}
### Save a different object
dist1.alldown <- dist1.all
##background of down object
dist1.alldownback <- dist1.alldown
## Turn distance in positive integers
dist1.alldown$dist1 <- dist1.alldown$dist1 * -1

Some ideas or known tools to obtain an efficiently approach? Thank you!