#
# Compute the romain notation of a number
# Compute the digital notation of a romain number
# Olivier Corby - Wimmics Inria I3S - 2015
#
prefix spqr: <http://ns.inria.fr/sparql-extension/spqr#>
select 

(99 as ?n)
(spqr:romain(?n) as ?r)
(spqr:digit(?r)  as ?d)

where {}


export {
function xt:romain(?n) {  spqr:spqr(?n) }
function xt:digit(?r)  { spqr:parse(?r) }

function spqr:romain(?n) {  spqr:spqr(?n) }
function spqr:digit(?r)  { spqr:parse(?r) }



function spqr:div(?a, ?b) {  xsd:integer(floor(?a / ?b)) }
function spqr:mod(?a, ?b) {  xsd:integer(?a - (?b * spqr:div(?a, ?b))) }

function spqr:rep(?s, ?n) { 
  if (?n = 0, "",
  if (?n = 1, ?s,
  concat(?s, spqr:rep(?s, ?n - 1))))
 }

function spqr:r1(?n) { 
    spqr:num(?n, "I", "V", "X")
 }

function spqr:r10(?n) { 
  spqr:num(?n, "X", "L", "C")
 }

function spqr:r100(?n) { 
  spqr:num(?n, "C", "D", "M")
 }

function spqr:r1000(?n) { 
  spqr:rep("M", ?n)
 }

function spqr:num(?n, ?u, ?f, ?t) { 
  if (?n <= 3, spqr:rep(?u, ?n),  
  if (?n = 4, concat(?u, ?f),
  if (?n < 9, concat(?f, spqr:rep(?u, ?n - 5)), 
  if (?n = 9, concat(?u, ?t), ""))))
 }

function spqr:spqr(?n) { 
  if (?n < 10, spqr:r1(?n),
  if (?n < 100, 
    let (?c = spqr:div(?n, 10), 
         ?r = spqr:mod(?n, 10)){ 
      concat(spqr:r10(?c), spqr:spqr(?r))
    },
    
  if (?n < 1000,
    let (?c = spqr:div(?n, 100),
         ?r = spqr:mod(?n, 100)){
      concat(spqr:r100(?c), spqr:spqr(?r))
    },
    
  if (?n < 10000,
    let (?c = spqr:div(?n, 1000),
         ?r = spqr:mod(?n, 1000)){
      concat(spqr:r1000(?c), spqr:spqr(?r))
    },       
    ?n))))
}

# parse romain number

function spqr:parse(?s) { 
  if (strlen(?s) = 0, 0,
    let (?f = substr(?s, 1, 1)){
      if (?f = "I", spqr:step(?s, "I", "V", "X", 1, 5, 10),
      if (?f = "V", 5 + spqr:parse(substr(?s, 2)),
      if (?f = "X", spqr:step(?s, "X", "L", "C", 10, 50, 100),
      if (?f = "L", 50 + spqr:parse(substr(?s, 2)),
      if (?f = "C", spqr:step(?s, "C", "D", "M", 100, 500, 1000),
      if (?f = "D", 500   + spqr:parse(substr(?s, 2)),
      if (?f = "M", 1000  + spqr:parse(substr(?s, 2)),
      0)))))))
      }
  )	      
}

function spqr:step(?s, ?su, ?sc, ?sd, ?u, ?c, ?d) { 
  if (strlen(?s) = 1, ?u,
    let (?r = substr(?s, 2, 1)){
      if (?r = ?sc,   ?c - ?u + spqr:parse(substr(?s, 3)),
	if (?r = ?sd, ?d - ?u + spqr:parse(substr(?s, 3)),
	  ?u + spqr:parse(substr(?s, 2))))
    }
  )
}


}