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rpn-mod-calculator.html
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<HTML>
<HEAD>
<SCRIPT LANGUAGE="JavaScript">
/*****
Demonstrates:
- If-Else
- For loops
- Array usage
- switch
- String building
- changing form elements
- Alert box
*****/
workwindow = null;
stack = new Array(6);
stack[0] = 0;
stackTop = 0;
modulo = 10;
changeable = true;
function checkMod(){
var test = document.modcalc.elements["Modulus"].value;
if(test != parseInt(test, 10)) {
document.modcalc.elements["Modulus"].value=modulo;
document.modcalc.elements["ErrorBox"].value="Modulus must be an integer";
}
else {
modulo=parseInt(test, 10);
document.modcalc.elements["ErrorBox"].value="";
}
}
function setMod(){
if(stackTop>=0) {
test = stack[stackTop];
if(test === 0) { return; }
modulo=test;
document.modcalc.elements["Modulus"].value=modulo;
if(stackTop >= 0) { stackTop--; }
else { stack[0]=0; }
changeable=false;
displayStack();
}
}
function displayStackLine(n){
document.modcalc.elements["ErrorBox"].value="";
var a = stackTop-n;
var elem = "Display" + n;
if(a>=0) { document.modcalc.elements[elem].value=stack[a]; }
else { document.modcalc.elements[elem].value=""; }
}
function displayStack(){
var i;
for(i=0;i<3;i++) {
displayStackLine(i);
}
}
function addDiget(value){
if(!changeable) { pushMe(); }
stack[stackTop] = stack[stackTop]*10 + value;
displayStackLine(0);
}
function performOpp(opp){
// performs opperation opp on appropriate values of the stack
var pop1, pop2;
var modon=document.modcalc.elements["ModOn"].checked;
if(opp==15){ // catch all to give more accurate alert if only one value on stack. Remove once implimented.
alert("not yet implimented");
return;
}
if(opp<=10){ // one pop opperations
pop1=stack[stackTop];
switch(opp){
case 1: // sign change
ans = changeSign(pop1, modon, modulo);
break;
case 2: // modulus
ans = pop1 % modulo;
break;
case 3: // mult. inverse
ans = multInv(pop1, modulo);
if(ans == 0) return;
break;
case 4: // square
ans = fastexp(pop1, 2);
break;
case 5: // cube
ans = fastexp(pop1, 3);
break;
case 6: // sqrt
ans = sqrt(pop1, modulo)
if (ans == 0) {
document.modcalc.elements["ErrorBox"].value="answer not found";
return;
}
break;
case 7: // cube root
ans = root(3, pop1, modulo)
if (ans == 0) {
document.modcalc.elements["ErrorBox"].value="answer not found";
return;
}
break;
case 8:
fermat();
return;
break;
case 9: // Miller-Rabin Test
MillerRabin();
return;
break;
}
stack[stackTop]=ans;
}
if(opp>10){ // two pop opperations
if(stackTop<1) {
document.modcalc.elements["ErrorBox"].value="not enough numbers for opperation";
return;
}
pop1=stack[stackTop];
pop2=stack[stackTop-1];
switch(opp) {
case 11: // addition
ans = pop2 + pop1;
if(modon) { ans = ans % modulo; }
break;
case 12: // subtraction
ans = pop2 - pop1;
if(modon) { ans = ans % modulo; }
break;
case 13: // multiplication
ans = pop2 * pop1;
if(modon) { ans = ans % modulo; }
break;
case 14: // nth powers
ans = fastexp(pop2, pop1);
break;
case 15: // nth roots
alert("not yet implimented");
return;
break;
case 16: // GCD
ans = GCD(pop2, pop1)
break;
}
stackTop--;
stack[stackTop]=ans;
}
changeable=false;
displayStack();
}
function changeSign(x, modon, base) {
var ans=0;
if(modon) {
if(x>0) { ans = x - base;}
if(x<0) { ans = x + base; }
}
else {ans = -x;}
return ans;
}
// If base is a prime%4=3
// Then x^( (base+1)/4) % base) is a possible sqrt of x
// Test: modulus=11, 3, 4, 5, 9 will work.
function sqrt(x, base) {
var ans=0;
if( (fermatTest(base-2, base) == 1) && ((base % 4) == 3)) {
ans = (fastexp(x, ((base+1)/4)) % base);
if(fastexp(ans, 2) != x) { ans=0; }
}
return ans
}
// x^n%base
function root(n, x, base) {
var ans=0;
var r=0;
// IF base is prime & gcd(n, base-1)=1
var gcd=GCD(base-1, n);
// need test case.
if( (fermatTest(base-2, base) == 1) && (gcd == 1) ) {
r = multInv(n, base); // let r=multiplicative inverse of n
//alert("r: "+r);
if(r != 0) {
ans = (fastexp(x, r) % base); // then (x^r)%base is a candidate
//alert("ans: "+ans);
if(fastexp(ans, n) == x) { return ans; }
}
}
// valid test: n=3, p=13, x={5, 8}
var testExp=0;
// if gcd(n, (p-1)/n) = 1
if ( (base-1)%n == 0) {
testExp=(base-1)/n;
gcd=GCD(testExp, n);
if (gcd == 1) {
// let r=n^(-1)%( (p-1)/n)
r = multInv(n, testExp);
// then (y^r)%p is a candidate
ans = (fastexp(x, r) % base);
if(fastexp(ans, n) == x) { return ans; }
}
}
return 0;
}
function fastexp(base, exp) {
var coef=1;
var work = "" + coef + "(" + base + ")^" + exp +"\n";
if(exp>3) { flag = true; }
else { flag = false; }
while(exp>0) {
if(exp%2==0) {
base *= base;
exp = exp / 2;
}
else {
coef *= base;
exp--;
}
if(document.modcalc.elements["ModOn"].checked) {
base = base%modulo;
coef = coef%modulo;
}
work += coef + "(" + base + ")^" + exp +"\n";
}
if(document.modcalc.elements["ShowWork"].checked && flag) {
document.modcalc.elements["work"].value=work;
}
return coef;
}
function euclidAlg(a, b, op){
var d = new Array(3);
var c1 = new Array(2);
var work = "";
var temp, ctemp;
var i=0;
if(a>b) {
d[0] = a;
d[1] = b;
}
else {
d[0] = b;
d[1] = a;
}
c1[0] = 1;
do {
c1[i+1]=-Math.floor(d[i]/d[i+1]);
d[i+2] = d[i] + c1[i+1] * d[i+1];
work += d[i] + " + (" + c1[i+1]+ ")" + d[i+1] + " = " + d[i+2] + "\n";
i++;
} while(d[i+1]!=0)
if(op == 1) {
if(document.modcalc.elements["ShowWork"].checked) {
document.modcalc.elements["work"].value=work;
}
return d[i];
} // gcd
if(op == 2 && d[i] !=1) { // if gcd != 1, mult inv does not exist
if(document.modcalc.elements["ShowWork"].checked) {
document.modcalc.elements["work"].value=work;
}
document.modcalc.elements["ErrorBox"].value="Mult. inv. does not exist";
return 0;
}
var c2 = new Array(c1.length);
i-=2;
c2[i] = 1;
c2[i+1] = c1[i+1];
do {
work += "1 = (" + c2[i] + ")"+d[i] + " + (" + c2[i+1]+ ")" + d[i+1] + "\n";
i--;
c2[i] = c2[i+2];
c2[i+1] += c2[i+2]*c1[i+1];
} while(i>=0)
if(document.modcalc.elements["ShowWork"].checked) {
document.modcalc.elements["work"].value=work;
}
return c2[1];
}
function GCD(a, b) {
return euclidAlg(a, b, 1);
}
function multInv(a, modulo) {
var ans=0;
if (a < 0) { a = changeSign(a, 1, modulo); }
if (a == 1) { return 1; }
ans=euclidAlg(modulo, a, 2);
if (ans < 0) { ans = changeSign(ans, 1, modulo); } // always force answer to be positive.
return ans;
}
function fermat(){
if(fermatTest(stack[stackTop], modulo) === 1) {
document.modcalc.elements["ErrorBox"].value="Modulus is a fermat psudo prime";
}
else {
document.modcalc.elements["ErrorBox"].value="fail";
}
changeable=false;
}
function fermatTest(n, modulo) {
if(fastexp(n, modulo-1) == 1) { return 1; }
else { return 0; }
}
function MillerRabin(){
changeable=false;
if(modulo%2==0) {
document.modcalc.elements["ErrorBox"].value="fail";
return;
}
var work="";
var s=0, r=0, m=modulo-1;
var b=stack[stackTop];
while(m%2==0) {
s++;
m=m/2;
}
b=fastexp(b, m);
work += "s=" + s + ", m=" + m + ", b^m=" + b + "\n";
if(b==1 || b == -1) {
document.modcalc.elements["ErrorBox"].value="fail";
document.modcalc.elements["work"].value=work;
return;
}
r=1;
while(r<s) {
b=fastexp(b, 2);
work += "b=" + b + ", r=" + r + "\n";
if(b==-1 || b==modulo-1) {
document.modcalc.elements["ErrorBox"].value="pass";
document.modcalc.elements["work"].value=work;
return;
}
if(b==1) {
document.modcalc.elements["ErrorBox"].value="fail";
document.modcalc.elements["work"].value=work;
return;
}
r++;
}
document.modcalc.elements["ErrorBox"].value="fail";
document.modcalc.elements["work"].value=work;
}
//--- end calc functions ---//
function pushMe(){
stackTop++;
stack[stackTop]=0;
displayStack();
changeable=true;
}
function clearMe(){
if(stackTop>=0) {
stackTop--;
displayStack();
changeable=false;
}
document.modcalc.elements["work"].value="";
}
function copyTop(){
if(stackTop>=0) {
pushMe();
stack[stackTop]=stack[stackTop-1];
displayStack();
changeable=false;
}
}
</SCRIPT>
<STYLE TYPE="text/css">
p.buttonFace { text-align: center; }
.buttonGroup1 { background: #FC0; }
.buttonGroup2 { background: #0CF; }
.buttonGroup3 { background: #9F9; }
.buttonGroup4 { background: #F99; }
.buttonGroup5 { background: #C00; }
</STYLE>
<TITLE>Calculator</TITLE>
</HEAD>
<BODY>
<FORM METHOD="POST" ENCTYPE="application/x-www-form-urlencoded" NAME="modcalc">
<P>
<table>
<tr><td>
<TABLE BORDER="0" >
<tr><td colspan="2">
<INPUT TYPE="TEXT" NAME="ErrorBox" SIZE="35" MAXLENGTH="35" VALUE="" readonly>
</td></tr>
<tr><td colspan="2">
<br>
</td></tr>
<tr><td colspan="2">
<INPUT TYPE="TEXT" NAME="Display0" SIZE="35" MAXLENGTH="32" VALUE="" readonly>
</td></tr>
<tr><td colspan="2">
<INPUT TYPE="TEXT" NAME="Display1" SIZE="35" MAXLENGTH="32" VALUE="" readonly>
</td></tr>
<tr><td colspan="2">
<INPUT TYPE="TEXT" NAME="Display2" SIZE="35" MAXLENGTH="32" VALUE="" readonly>
</td></tr>
<TR>
<TD WIDTH="70%"> </TD>
<TD WIDTH="30%"> </TD>
</TR>
<TR>
<TD WIDTH="70%">
<P ALIGN="RIGHT"><B>Working Modulus</B><BR>
<FONT SIZE="2"></FONT>
</TD>
<TD WIDTH="30%"> <INPUT TYPE="Text" NAME="Modulus" size="5" VALUE="10" onchange="checkMod()"></TD>
</TR>
<TR>
<TD WIDTH="70%">
<P ALIGN="RIGHT"> <B>Engadge Modulus</B><BR>
<FONT SIZE="2"></FONT>
</TD>
<TD WIDTH="30%"> <INPUT TYPE="CHECKBOX" NAME="ModOn" VALUE="ModOn" CHECKED></TD>
</TR>
<TR>
<TD WIDTH="70%">
<P ALIGN="RIGHT"> <B>Show Work</B><BR>
<FONT SIZE="2"></FONT>
</TD>
<TD WIDTH="30%"> <INPUT TYPE="CHECKBOX" NAME="ShowWork" VALUE="ShowWork" CHECKED></TD>
</TR>
<tr><td>
<br>
</td></tr>
<tr><td colspan="2">
<TEXTAREA NAME="work" ROWS="7" COLS="25" readonly></TEXTAREA>
</td></tr>
</TABLE>
</td><td>
<//---- begin calculator face >
<TABLE BORDER="1" WIDTH="100%">
<TR>
<TD WIDTH="100%">
<CENTER>
<P>
<TABLE BORDER="0" WIDTH="223">
<TR>
<TD class="buttonGroup1" WIDTH="52" HEIGHT="40" colspan="3">
<P class="buttonFace"><INPUT TYPE="BUTTON" NAME="click" VALUE=" Miller-Rabin test " onclick="performOpp(9)"> </P>
</TD>
<TD class="buttonGroup2" WIDTH="52" HEIGHT="40">
<P class="buttonFace"><INPUT TYPE="BUTTON" NAME="click" VALUE="set %" onclick="setMod()"> </P>
</TD>
</TR>
<TR>
<TD class="buttonGroup1" WIDTH="52" HEIGHT="40" colspan="2">
<P class="buttonFace"><INPUT TYPE="BUTTON" NAME="click" VALUE="Fermat test" onclick="fermat()"> </P>
</TD>
<TD class="buttonGroup1" WIDTH="49" HEIGHT="40">
<P class="buttonFace"><INPUT TYPE="BUTTON" NAME="click" VALUE="gcd" onclick="performOpp(16)"> </P>
</TD>
<TD class="buttonGroup2" WIDTH="52" HEIGHT="40">
<P class="buttonFace"><INPUT TYPE="BUTTON" NAME="click" VALUE="mod" onclick="performOpp(2)"> </P>
</TD>
</TR>
<TR>
<TD class="buttonGroup3" WIDTH="52" HEIGHT="40">
<P class="buttonFace"><INPUT TYPE="BUTTON" NAME="click" VALUE=" ^2 " onclick="performOpp(4)"> </P>
</TD>
<TD class="buttonGroup3" WIDTH="44" HEIGHT="40">
<P class="buttonFace"><INPUT TYPE="BUTTON" NAME="click" VALUE=" ^3 " onclick="performOpp(5)"> </P>
</TD>
<TD class="buttonGroup3" WIDTH="49" HEIGHT="40">
<P class="buttonFace"><INPUT TYPE="BUTTON" NAME="click" VALUE=" ^n " onclick="performOpp(14)"> </P>
</TD>
<TD class="buttonGroup2" WIDTH="52" HEIGHT="40">
<P class="buttonFace"><INPUT TYPE="BUTTON" NAME="click" VALUE="^-1" onclick="performOpp(3)"> </P>
</TD>
</TR>
<TR>
<TD class="buttonGroup3" WIDTH="52" HEIGHT="40">
<P class="buttonFace"><INPUT TYPE="BUTTON" NAME="click" VALUE=" sqrt " onclick="performOpp(6)"> </P>
</TD>
<TD class="buttonGroup3" WIDTH="44" HEIGHT="40">
<P class="buttonFace"><INPUT TYPE="BUTTON" NAME="click" VALUE=" c-rt " onclick="performOpp(7)"> </P>
</TD>
<TD class="buttonGroup3" WIDTH="49" HEIGHT="40">
<P class="buttonFace"><INPUT TYPE="BUTTON" NAME="click" VALUE=" n-rt " onclick="performOpp(15)"> </P>
</TD>
<TD class="buttonGroup2" WIDTH="52" HEIGHT="40">
<P class="buttonFace"><INPUT TYPE="BUTTON" NAME="click" VALUE=" × " onclick="performOpp(13)"> </P>
<// (÷) >
</TD>
</TR>
<TR>
<TD class="buttonGroup4" WIDTH="52" HEIGHT="40">
<P class="buttonFace"><INPUT TYPE="BUTTON" NAME="click" VALUE=" 7 " onclick="addDiget(7)"> </P>
</TD>
<TD class="buttonGroup4" WIDTH="44" HEIGHT="40">
<P class="buttonFace"><INPUT TYPE="BUTTON" NAME="click" VALUE=" 8 " onclick="addDiget(8)"> </P>
</TD>
<TD class="buttonGroup4" WIDTH="49" HEIGHT="40">
<P class="buttonFace"><INPUT TYPE="BUTTON" NAME="click" VALUE=" 9 " onclick="addDiget(9)"> </P>
</TD>
<TD class="buttonGroup2" WIDTH="52" HEIGHT="40">
<P class="buttonFace"><INPUT TYPE="BUTTON" NAME="click" VALUE=" - " onclick="performOpp(12)"> </P>
</TD>
</TR>
<TR>
<TD class="buttonGroup4" WIDTH="52" HEIGHT="40">
<P class="buttonFace"><INPUT TYPE="BUTTON" NAME="click" VALUE=" 4 " onclick="addDiget(4)"> </P>
</TD>
<TD class="buttonGroup4" WIDTH="44" HEIGHT="40">
<P class="buttonFace"><INPUT TYPE="BUTTON" NAME="click" VALUE=" 5 " onclick="addDiget(5)"> </P>
</TD>
<TD class="buttonGroup4" WIDTH="49" HEIGHT="40">
<P class="buttonFace"><INPUT TYPE="BUTTON" NAME="click" VALUE=" 6 " onclick="addDiget(6)"> </P>
</TD>
<TD class="buttonGroup2" WIDTH="52" HEIGHT="40">
<P class="buttonFace"><INPUT TYPE="BUTTON" NAME="click" VALUE=" + " onclick="performOpp(11)"> </P>
</TD>
</TR>
<TR>
<TD class="buttonGroup4" WIDTH="52" HEIGHT="40">
<P class="buttonFace"><INPUT TYPE="BUTTON" NAME="click" VALUE=" 1 " onclick="addDiget(1)"> </P>
</TD>
<TD class="buttonGroup4" WIDTH="44" HEIGHT="40">
<P class="buttonFace"><INPUT TYPE="BUTTON" NAME="click" VALUE=" 2 " onclick="addDiget(2)"> </P>
</TD>
<TD class="buttonGroup4" WIDTH="49" HEIGHT="40">
<P class="buttonFace"><INPUT TYPE="BUTTON" NAME="click" VALUE=" 3 " onclick="addDiget(3)"> </P>
</TD>
<TD class="buttonGroup2" WIDTH="52" HEIGHT="40">
<P class="buttonFace"><INPUT TYPE="BUTTON" NAME="click" VALUE="copy" onclick="copyTop()"> </P>
</TD>
</TR>
<TR>
<TD class="buttonGroup5" WIDTH="52" HEIGHT="40">
<P class="buttonFace"><INPUT TYPE="BUTTON" NAME="click" VALUE="ce/c" onclick="clearMe()"> </P>
</TD>
<TD class="buttonGroup4" WIDTH="44" HEIGHT="40">
<P class="buttonFace"><INPUT TYPE="BUTTON" NAME="click" VALUE=" 0 " onclick="addDiget(0)"> </P>
</TD>
<TD class="buttonGroup4" WIDTH="49" HEIGHT="40">
<P class="buttonFace"><INPUT TYPE="BUTTON" NAME="click" VALUE=" ± " onclick="performOpp(1)"> </P>
</TD>
<TD class="buttonGroup2" WIDTH="52" HEIGHT="40">
<P class="buttonFace"><INPUT TYPE="BUTTON" NAME="click" VALUE="push" onclick="pushMe()"> </P>
</TD>
</TR>
</TABLE>
</CENTER>
</TD>
</TR>
</TABLE>
<// end calculator face>
</td></tr>
</table>
</FORM>
</BODY>
</HTML>