In binb_sha256, extract processBlock_sha256 into a new function.  Use this in new class Sha256 where you can call multiple update(data) then finalize().  Added test to test-sh256.html.
diff --git a/js/securityLib/sha256.js b/js/securityLib/sha256.js
index 00ea8af..214ee4d 100644
--- a/js/securityLib/sha256.js
+++ b/js/securityLib/sha256.js
@@ -252,8 +252,10 @@
 {

   //console.log('Raw string comming is '+input);

   var output = Array(input.length >> 2);

+  /* JavaScript automatically zeroizes a new array.

   for(var i = 0; i < output.length; i++)

     output[i] = 0;

+   */

   for(var i = 0; i < input.length * 8; i += 8)

     output[i>>5] |= (input.charCodeAt(i / 8) & 0xFF) << (24 - i % 32);

   return output;

@@ -268,8 +270,10 @@
 function byteArray2binb(input){

 	//console.log("Byte array coming is " + input);

 	var output = Array(input.length >> 2);

+      /* JavaScript automatically zeroizes a new array.

 	  for(var i = 0; i < output.length; i++)

 	    output[i] = 0;

+       */

 	  for(var i = 0; i < input.length * 8; i += 8)

 	    output[i>>5] |= (input[i / 8] & 0xFF) << (24 - i % 32);

 	  return output;

@@ -322,15 +326,25 @@
   var HASH = new Array(1779033703, -1150833019, 1013904242, -1521486534,

                        1359893119, -1694144372, 528734635, 1541459225);

   var W = new Array(64);

-  var a, b, c, d, e, f, g, h;

-  var i, j, T1, T2;

 

   /* append padding */

   m[l >> 5] |= 0x80 << (24 - l % 32);

   m[((l + 64 >> 9) << 4) + 15] = l;

+ 

+  for(var offset = 0; offset < m.length; offset += 16)

+    processBlock_sha256(m, offset, HASH, W);

 

-  for(i = 0; i < m.length; i += 16)

-  {

+  return HASH;

+}

+

+/*

+ * Process a block of 16 4-byte words in m starting at offset and update HASH.  

+ * offset must be a multiple of 16 and less than m.length.  W is a scratchpad Array(64).

+ */

+function processBlock_sha256(m, offset, HASH, W) {

+    var a, b, c, d, e, f, g, h;

+    var j, T1, T2;

+    

     a = HASH[0];

     b = HASH[1];

     c = HASH[2];

@@ -342,7 +356,7 @@
 

     for(j = 0; j < 64; j++)

     {

-      if (j < 16) W[j] = m[j + i];

+      if (j < 16) W[j] = m[j + offset];

       else W[j] = safe_add(safe_add(safe_add(sha256_Gamma1256(W[j - 2]), W[j - 7]),

                                             sha256_Gamma0256(W[j - 15])), W[j - 16]);

 

@@ -367,8 +381,6 @@
     HASH[5] = safe_add(f, HASH[5]);

     HASH[6] = safe_add(g, HASH[6]);

     HASH[7] = safe_add(h, HASH[7]);

-  }

-  return HASH;

 }

 

 function safe_add (x, y)

@@ -377,3 +389,87 @@
   var msw = (x >> 16) + (y >> 16) + (lsw >> 16);

   return (msw << 16) | (lsw & 0xFFFF);

 }

+

+/*

+ * Create a Sha256, call update(data) multiple times, then call finalize().

+ */

+var Sha256 = function Sha256() {

+    this.W = new Array(64);

+    this.hash = new Array(1779033703, -1150833019, 1013904242, -1521486534,

+                          1359893119, -1694144372, 528734635, 1541459225);

+    this.nTotalBytes = 0;

+    this.buffer = new Uint8Array(16 * 4);

+    this.nBufferBytes = 0;

+}

+

+/*

+ * Update the hash with data, which is Uint8Array.

+ */

+Sha256.prototype.update = function(data) {

+    this.nTotalBytes += data.length;

+    

+    if (this.nBufferBytes > 0) {

+        // Fill up the buffer and process it first.

+        var bytesNeeded = this.buffer.length - this.nBufferBytes;

+        if (data.length < bytesNeeded) {

+            this.buffer.set(data, this.nBufferBytes);

+            this.nBufferBytes += data.length;

+            return;

+        }

+        else {

+            this.buffer.set(data.subarray(0, bytesNeeded), this.nBufferBytes);

+            processBlock_sha256(byteArray2binb(this.buffer), 0, this.hash, this.W);

+            this.nBufferBytes = 0;

+            // Consume the bytes from data.

+            data = data.subarray(bytesNeeded, data.length);

+            if (data.length == 0)

+                return;

+        }

+    }

+    

+    // 2^6 is 16 * 4.

+    var nBlocks = data.length >> 6;

+    if (nBlocks > 0) {

+        var nBytes = nBlocks * 16 * 4;

+        var m = byteArray2binb(data.subarray(0, nBytes));

+        for(var offset = 0; offset < m.length; offset += 16)

+            processBlock_sha256(m, offset, this.hash, this.W);

+

+        data = data.subarray(nBytes, data.length);

+    }

+    

+    if (data.length > 0) {

+        // Save the remainder in the buffer.

+        this.buffer.set(data);

+        this.nBufferBytes = data.length;

+    }

+}

+

+/*

+ * Finalize the hash and return the result as Uint8Array.

+ * Only call this once.  Return values on subsequent calls are undefined.

+ */

+Sha256.prototype.finalize = function() {

+    var m = byteArray2binb(this.buffer.subarray(0, this.nBufferBytes));

+    /* append padding */

+    var l = this.nBufferBytes * 8;

+    m[l >> 5] |= 0x80 << (24 - l % 32);

+    m[((l + 64 >> 9) << 4) + 15] = this.nTotalBytes * 8;

+

+    for(var offset = 0; offset < m.length; offset += 16)

+        processBlock_sha256(m, offset, this.hash, this.W);

+

+    return Sha256.binb2Uint8Array(this.hash);

+}

+

+/*

+ * Convert an array of big-endian words to Uint8Array.

+ */

+Sha256.binb2Uint8Array = function(input)

+{

+    var output = new Uint8Array(input.length * 4);

+    var iOutput = 0;

+    for (var i = 0; i < input.length * 32; i += 8)

+        output[iOutput++] = (input[i>>5] >>> (24 - i % 32)) & 0xFF;

+    return output;

+}

diff --git a/js/testing/test-sha256.html b/js/testing/test-sha256.html
index 4020f53..5980dac 100644
--- a/js/testing/test-sha256.html
+++ b/js/testing/test-sha256.html
@@ -11,11 +11,21 @@
 	<script src="http://crypto-js.googlecode.com/svn/tags/3.0.2/build/rollups/sha256.js"></script>

 	

 	<script type="text/javascript">

-		function hash(){			

+		function hash(){		

 			var input = document.getElementById('contentname').value;

 			

 			var output = "from string- " + hex_sha256(input) + "<br/>";

-			output += "from bytes-- " + hex_sha256_from_bytes(DataUtils.toNumbersFromString(input)) + "<br/>";			

+            

+            var sha256 = new Sha256();

+            var data = DataUtils.toNumbersFromString(input);

+            // Call update multiple times in small chunks to test the buffering.

+            var chunkSize = 3;

+            var nCalls = Math.floor(data / chunkSize);

+            for (var i = 0; i < nCalls; ++i)

+                sha256.update(data.subarray(i * chunkSize, chunkSize));

+            sha256.update(data.subarray(i * nCalls, data.length));

+			output += "from bytes-- " + DataUtils.toHex(sha256.finalize()) + "<br/>";			

+            

 			output += "reference---- " + CryptoJS.SHA256(input);

 			

 			document.getElementById('result').innerHTML = output;