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ieee754.js
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ieee754.js
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/*
* A script that operates a form in which a user can
*
* (1) type in a hexadecimal value for an IEEE-754 single- or double-precision value and have
* it shown in binary (with sign, exponent, and mantissa highlighted) and its approximate
* decimal value; and
* (2) type in a decimal value and see its IEEE-754 hexadecimal encodings in both single- and
* double-precision.
*/
$(function () {
// The big.js defaults are too lame for us. We need more precision!
Big.DP = 100000;
// It's little endian if integer 1 is encoded as 01.00.00.00
var littleEndian = !!(new Uint8Array((new Uint32Array([1])).buffer))[0];
var allZeros = /^0+$/;
var allOnes = /^1+$/;
var UP_ARROW = 38;
var DOWN_ARROW = 40;
// I probably should just use .toString(2) for these....
var translate = [
"0000", "0001", "0010", "0011", "0100", "0101", "0110", "0111",
"1000", "1001", "1010", "1011", "1100", "1101", "1110", "1111"
];
/*
* Return a string of the form "(1.f)_2 x 2^e" where the fractional part has no trailing
* zeros.
*/
var formatExactValue = function (fraction, exponent) {
return "(1." + (fraction.replace(/0+$/, "") || "0") + ")<sub>2</sub>" +
" × 2<sup>" + exponent + "</sup>";
};
/*
* Produces a hexidecimal string for a Uint8Array.
*/
var byteArrayToHex = function (b) {
var array = [];
for (var i = 0; i < b.length; i++) {
array[littleEndian ? "unshift" : "push"](b[i]); // couldn't resist writing this.
}
return array.map(function (byte) {
var hex = byte.toString(16);
return hex.length === 1 ? "0" + hex : "" + hex;
}).join("");
};
/*
* Determine the decimal representation of a hexidecimal character
*/
var hexToDec = function (hexString, charLoc) {
return "0123456789ABCDEF".indexOf(hexString.charAt(charLoc));
};
var binToHex = function (binString) {
if (binString.length % 4 != 0) {
throw new Error("Invalid binary string");
}
var hex = [];
for (var i = 0; i < binString.length; i+=4) {
var hexMap = {
'0000': '0',
'0001': '1',
'0010': '2',
'0011': '3',
'0100': '4',
'0101': '5',
'0110': '6',
'0111': '7',
'1000': '8',
'1001': '9',
'1010': 'A',
'1011': 'B',
'1100': 'C',
'1101': 'D',
'1110': 'E',
'1111': 'F',
};
hex.push(hexMap[binString.substr(i, 4)]);
}
return hex.join('');
};
/*
* Determine the various interpretations of the given hex value and render them into the
* document.
*/
var decodeAndUpdate = function (h, data) {
data = data || {};
// Render in binary. Hackish.
var b = "";
for (var i = 0, n = h.length; i < n; i++) {
b += translate[hexToDec(h,i)];
}
// Determine configuration. This could have all been precomputed but it is fast enough.
var exponentBits = h.length === 8 ? 8 : 11;
var mantissaBits = (h.length * 4) - exponentBits - 1;
var bias = Math.pow(2, exponentBits - 1) - 1;
var minExponent = 1 - bias - mantissaBits;
// Break up the binary representation into its pieces for easier processing.
var s = data.sign || b[0];
var e = data.exponent || b.substring(1, exponentBits + 1);
var m = data.mantissa || b.substring(exponentBits + 1);
var value = 0;
var text = (s === "0" ? "+" : "-");
var multiplier = (s === "0" ? 1 : -1);
var exactDecimal = (s === "0" ? "" : "-");
if (allZeros.test(e)) {
// Zero or denormalized
if (allZeros.test(m)) {
text += " Zero";
exactDecimal += "0";
} else {
var firstOneIndex = m.indexOf("1");
text += formatExactValue(m.substring(firstOneIndex + 1), -bias-firstOneIndex);
value = parseInt(m, 2) * Math.pow(2, minExponent);
exactDecimal += new Big(parseInt(m, 2)).times(new Big(2).pow(minExponent)).toFixed();
}
} else if (allOnes.test(e)) {
// Infinity or NaN
if (allZeros.test(m)) {
text += "∞";
value = Infinity;
} else {
text = "NaN";
value = NaN;
}
exactDecimal = text;
} else {
// Normalized
var exponent = parseInt(e, 2) - bias;
var mantissa = parseInt(m, 2);
text += formatExactValue(m, exponent);
value = (1 + (mantissa * Math.pow(2, -mantissaBits))) * Math.pow(2, exponent);
exactDecimal += new Big(1).
plus(new Big(mantissa).times(new Big(2).pow(-mantissaBits))).
times(new Big(2).pow(exponent)).
toFixed();
}
// All done computing, render everything.
$("#sign").unbind();
$("#sign").html(s);
$("#sign").click(function(event) {
var newSign = $(this).text() === '0' ? '1' : '0';
data.sign = newSign;
decodeAndUpdate(h, data);
event.preventDefault();
event.stopPropagation();
});
//$("#exp").html(e);
$("#exp").empty();
for (var i = 0; i < e.length; i++) {
var bit = $("<div></div>").text(e[i]);
bit.data({
'index': i,
'exponent': e
});
bit.click(function(event) {
var eindex = $(this).data('index');
var exponent = $(this).data('exponent');
var thisBit = exponent[eindex] === '0' ? '1' : '0';
exponent = exponent.substr(0, eindex) + thisBit + exponent.substr(eindex + 1);
data.exponent = exponent
decodeAndUpdate(h, data);
event.preventDefault();
});
$("#exp").append(bit);
}
//$("#mantissa").html(m);
$("#mantissa").empty();
for (var i = 0; i < m.length; i++) {
var mbit = $("<div></div>").text(m[i]);
mbit.data({
'index': i,
'mantissa': m
});
mbit.click(function(event) {
var mindex = $(this).data('index');
var mantissa = $(this).data('mantissa');
var thisBit = mantissa[mindex] === '0' ? '1' : '0';
mantissa = mantissa.substr(0, mindex) + thisBit + mantissa.substr(mindex + 1);
data.mantissa = mantissa
decodeAndUpdate(h, data);
event.preventDefault();
});
$("#mantissa").append(mbit);
}
$("#description").html(text);
$("#decimal").html(value * multiplier);
$("#exact-decoded-decimal").html(exactDecimal);
$("#hex").val(binToHex(s + e + m));
};
var isValidLength = function (h) {
return (h.length===8 || h.length===16);
}
/**
* Here's the code for encoding decimal values into hex. Here we let JavaScript do all
* the work.
*/
var encodeAndUpdate = function (d) {
$("#32hex").html(byteArrayToHex(new Uint8Array((new Float32Array([d])).buffer)));
$("#64hex").html(byteArrayToHex(new Uint8Array((new Float64Array([d])).buffer)));
$("#printed").html(+d);
};
/**
* Change the hex text box 'h' given relevant information. Assumes input is already sanitized.
*/
var changeHexValue = function(h, operationToPerform, lastCharDecValue, charToAppend) {
var charIndex = h.length - 1;
while (hexToDec(h, charIndex) === lastCharDecValue) {
charIndex--;
}
var endString = "";
for (var i = charIndex; i < h.length-1; i++) {
endString += charToAppend
}
var decCharValue = hexToDec(h, charIndex);
decCharValue += operationToPerform;
var newH = h.substring(0,charIndex) + "0123456789ABCDEF".charAt(decCharValue) + endString
decodeAndUpdate(newH);
$("#hex").val(newH);
}
// Prohibit non-hex digits from even being entered into the textfield.
$("#hex").keypress(function (e) {
var char = String.fromCharCode(e.which);
if (! /[\dA-Fa-f]/.test(char)) {
e.preventDefault();
}
});
// Up and down arrows for hex
$("#hex").keydown(function (e) {
var h = $("#hex").val().toUpperCase();
if (isValidLength(h)){
if (e.keyCode === UP_ARROW) {
if (h != "FFFFFFFF" && h != "FFFFFFFFFFFFFFFF") {
changeHexValue(h, 1, 15, "0");
}
}
else if (e.keyCode === DOWN_ARROW) {
if (h != "00000000" && h != "0000000000000000") {
changeHexValue(h, -1, 0, "F");
}
}
}
});
// Update the display after something has been entered in the decoding section.
$("#hex").keyup(function (e) {
var h = $("#hex").val().toUpperCase();
if (isValidLength(h)) {
decodeAndUpdate(h);
} else {
// Erase all the computed fields from the section
$("#decoder div").html("");
$("#decoder span").html("");
}
});
// Update the display after something has been entered in the encoding section.
$("#dec").keyup(function (e) {
var d = $("#dec").val();
if (/^-?\d+(\.\d*)?([Ee][+-]?\d+)?$/.test(d)) {
encodeAndUpdate(d);
} else {
// Erase all the computed fields from the section
$("#encoder div").html("");
$("#encoder span").html("");
}
});
});