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[Version: 8 September 2017] Added "bits" column.
Decoding column: Negative values are in their two's complement form. Sign of values is represented with plus or minus symbol.
var expvalue = {
"0": function(){
return 1;
},
"1": function(){
return 2;
},
"2": function(){
return 4;
},
"3": function(){
return 8;
},
"4": function(){
return 16;
}
};
function convertDToP(){ var decimal = document.getElementById("decimal").value;
var positkeys = Object.keys(positMax);
var msg = "Posit format Binary Value Relative Error Decimals of Accuracy\n";
for (i=0; i<positkeys.length; i++){
var positInfo = positkeys[i].split("_");
var ps = parseInt(positInfo[0]);
var es = parseInt(positInfo[1]);
//Within range
var p_max = positMax[positkeys[i]]();
var useed = Math.pow(2, expvalue[es]());
var usigned_decimal = Math.abs(decimal);
var sign = Math.sign(decimal);
var posit = "";
var temp = usigned_decimal;
var value =0;
// handling so that there is no overflow
if (usigned_decimal > p_max){
if(sign<0){
posit = "1";
k = ps -2;
while(k>0){
posit += "0";
k--;
}
posit += "1";
}
else{
posit = "0";
k = ps-1;
while(k>0){
posit += "1";
k--;
}
}
}
else if (usigned_decimal==0){
k = ps;
while(k>0){
posit += "0";
k--;
}
}
else if (usigned_decimal < 1){
//regime<1 => k<0
posit += "0";
while(true){
temp2=temp*useed;
if (temp2>useed){
break;
}
else{
temp = temp2;
posit += "0";
}
}
posit += "1";
}
else if (usigned_decimal >=1 && usigned_decimal < useed){
//regime = 1 => k=1 => regime is 01 or 10
posit = "010";
}
else if (usigned_decimal>=useed ){
//regime > 1
var j=0;
posit +="01";
while (temp>=useed){
temp = temp/useed;
j++;
posit += "1";
}
posit +="0";
}
if(usigned_decimal>0 && usigned_decimal <= p_max){
//value is in exponential and fraction
var j=0;
while (temp>=2){
temp = temp/2;
j++;
}
if(es>0){
var e_binary = dec2bin(j);
while (e_binary.length<es){
e_binary = "0"+e_binary;
}
posit += e_binary;
}
f_fraction=temp.toString( 2 );
posit += f_fraction.substring(2, f_fraction.length);
while (posit.length < ps){
posit += "0";
}
//console.log("<"+ps+", " + es + ">");
//console.log(posit);
if (posit.length>ps){
//Need to round
//faster method
var roundPlusOne = false;
if (posit.charAt(ps) == "1"){
var n = ps+1;
while(n<posit.length){
if (posit.charAt(n) == "1"){
roundPlusOne = true;
break;
}
n++;
}
if (!roundPlusOne){
//round to nearest even.
if (posit.charAt(ps-1)=="1"){
roundPlusOne = true;
}
}
}
if(roundPlusOne){
posit = posit.substring(0,ps);
var posit2 = parseInt(posit, 2) +1;
posit2= posit2.toString(2);
while(posit2.length<posit.length){
posit2 = "0"+posit2
}
var value2 = calculatePositValue(posit2, ps, es);
if (value2 == "INF"){
//Prevent overflow
var value1 = calculatePositValue(posit, ps, es);
value = value1;
}
else{
posit = posit2;
value = value2;
}
}
else{
posit = posit.substring(0,ps);
var value1 = calculatePositValue(posit, ps, es);
value = value1;
//prevent underflow
if (value=="0"){
var posit2 = parseInt(posit, 2) +1;
posit2= posit2.toString(2);
while(posit2.length<posit.length){
posit2 = "0"+posit2
}
var value2 = calculatePositValue(posit2, ps, es);
posit = posit2;
value = value2;
}
}
}
if(sign<0){
var twoComplement = parseInt(posit, 2);
posit = dec2bin(-twoComplement).substring(32-ps,32);
value = -value;
}
}
if (value ==0){
if(usigned_decimal==0)
value=0;
else
value = calculatePositValue(posit, ps, es);
}
var error = 0;
error = Math.abs((decimal-value)/decimal);
msg += "Posit<"+ps+","+es+"> " + colouredCodedPosit(posit, es) + " " ;
var no_whitespace = "Binary".length+32 - posit.toString().length;
while (no_whitespace>0){
msg += " ";
no_whitespace --;
}
if (posit.toString().length<8){
msg += " ";
}
msg += value;
no_whitespace = "Binary".length+28 - value.toString().length;// 5-Math.ceil(value.toString().length/8);
/*if (value.toString().length%8 == 0){
no_whitespace --;
}*/
while (no_whitespace>0){
//msg += " " ;
msg+=" ";
no_whitespace --;
}
msg += error;
var accuracy = -Math.log10(Math.abs(error));
no_whitespace = 5-Math.ceil(error.toString().length/8);
if (error.toString().length%8 == 0){
no_whitespace --;
}
while (no_whitespace>0){
msg += " " ;
no_whitespace --;
}
msg += accuracy;
msg += "\n";
}
document.getElementById('output').innerHTML = msg;
}
function dec2bin(dec){ return (dec >>> 0).toString(2); }
function calculatePositValue(binary, posit, expo){
sign = 0;
regimesign = 0;
isRegime = true;
runlength = 0;
expo_bitvalue = 0;
fraction_bitvalue = 0;
fractionlength =0;
var i=parseInt(binary,2);
var INF = "1";
j= binary.length -1;
while(j>0){
INF+="0"
j--;
}
if (binary == INF.toString(2)){
value = "INF"
}
else if(i==0){
value = 0;
}
else{
for(j=0; j<binary.length; j++){
if (j==0){
sign = parseInt(binary.charAt(j));
if(sign==0){
sign = 1;
}
else if (sign==1){
sign = -1;
//Two's complements
binary = dec2bin(-i).substring(32-posit,32);
while(binary.length<posit){
binary="0" + binary;
}
}
}
else if (j==1){
regimesign = parseInt(binary.charAt(j));
runlength++
}
else{
if (isRegime){
if(parseInt(binary.charAt(j)) == regimesign){
runlength++;
}
else{
isRegime = false;
expo_start = runlength +2;
expoLength_max = expo_start +parseInt(expo);
if (parseInt(expo) > 0 && (expo_start)<binary.length){
tmp_expo = binary.substring(expo_start, binary.length);
if (tmp_expo.length>expo){
tmp_expo = tmp_expo.substring(0, expo);
}
else if (tmp_expo.length<expo){
missingzero = expo-tmp_expo.length;
while(missingzero>0){
tmp_expo += "0";
missingzero --;
}
}
expo_bitvalue = parseInt(tmp_expo,2);
}
//Check fraction
if(expoLength_max<binary.length){
fractionlength = binary.length - expoLength_max;
tmp_frac = binary.substring(expoLength_max, binary.length);
fraction_bitvalue = parseInt(tmp_frac, 2);
}
break;
}
}
}
}
k = 0;
if (regimesign==0){
k=-(runlength);
}
else{
k=runlength-1;
}
regime = Math.pow(Math.pow(2, Math.pow(2, expo)), k);
expo_value = Math.pow(2, expo_bitvalue);
fraction_max = Math.pow(2, fractionlength);
fraction_value = 1+ (parseInt(fraction_bitvalue)/fraction_max);
value = sign * regime * expo_value * fraction_value;
}
return value;
}
function colouredCodedPosit(posit, es){
var signchar = "+";
if(posit.charAt(0)=="1"){
signchar = "-";
}
var colouredPosit = ""+signchar+"";
var isRegime = true;
var regime = "";
var terminateRegime = "";
var expo = "";
var fraction = "";
var regimeBit = "0";
for (v=1; v<posit.length; v++){
if(v==1 && posit.charAt(v)=="1"){
regimeBit = "1";
}
if(isRegime){
if(regimeBit==posit.charAt(v)){
regime += posit.charAt(v);
}
else{
isRegime = false;
terminateRegime = ""+posit.charAt(v)+"";
}
}
else{
if (v+es>=posit.length){
expo += ""+posit.substring(v, posit.length) +"";
}
else{
expo += ""+posit.substring(v, v+es) +"";
if(v+es<posit.length){
fraction += posit.substring(v+es, posit.length);
}
}
break;
}
}
colouredPosit += "<font color='#CC9933'>"+regime+"</font>" + terminateRegime + expo + fraction;
return colouredPosit;
BIP: Title: Author: <list of authors' real names and optionally, email addrs> Discussions-To: Status: <Draft | Active | Accepted | Deferred | Rejected | Withdrawn | Final | Superseded> Type: <Standards Track | Informational | Process> Created: <date created on, in ISO 8601 (yyyy-mm-dd) format> Replaces: Superseded-By: Resolution:
==Abstract==
==Motivation==
==Specification==
==Rationale==
==Implementation==
BIP: Title: Author: <list of authors' real names and optionally, email addrs> Discussions-To: Status: <Draft | Active | Accepted | Deferred | Rejected | Withdrawn | Final | Superseded> Type: <Standards Track | Informational | Process> Created: <date created on, in ISO 8601 (yyyy-mm-dd) format> Replaces: Superseded-By: Resolution:
==Abstract==
==Motivation==
==Specification==
==Rationale==