Added Jacobi functionality, more bn features - plus tests.

src/js/sjcl-custom/sjcl-extramath.js

@@ -45,8 +45,8 @@ sjcl.bn.prototype.div = function (that) {
 };
 
 sjcl.bn.prototype.sign = function () {
-      return this.greaterEquals(sjcl.bn.ZERO) ? 1 : -1;
-    };
+  return this.greaterEquals(sjcl.bn.ZERO) ? 1 : -1;
+};
 
 /** -this */
 sjcl.bn.prototype.neg = function () {
@@ -59,3 +59,79 @@ sjcl.bn.prototype.abs = function () {
     return this.neg();
   } else return this;
 };
+
+/** this >> that */
+sjcl.bn.prototype.shiftRight = function (that) {
+  if ("number" !== typeof that) {
+    throw new Error("shiftRight expects a number");
+  }
+
+  that = +that;
+
+  if (that < 0) {
+    return this.shiftLeft(that);
+  }
+
+  var a = new sjcl.bn(this);
+
+  while (that--) {
+    a.halveM();
+  }
+
+  return a;
+};
+
+/** this >> that */
+sjcl.bn.prototype.shiftLeft = function (that) {
+  if ("number" !== typeof that) {
+    throw new Error("shiftLeft expects a number");
+  }
+
+  that = +that;
+
+  if (that < 0) {
+    return this.shiftRight(that);
+  }
+
+  var a = new sjcl.bn(this);
+
+  while (that--) {
+    a.doubleM();
+  }
+
+  return a;
+};
+
+/** (int)this */
+// NOTE Truncates to 32-bit integer
+sjcl.bn.prototype.toNumber = function () {
+  return this.limbs[0] | 0;
+};
+
+/** find n-th bit, 0 = LSB */
+sjcl.bn.prototype.testBit = function (bitIndex) {
+  var limbIndex = Math.floor(bitIndex / this.radix);
+  var bitIndexInLimb = bitIndex % this.radix;
+
+  if (limbIndex >= this.limbs.length) return 0;
+
+  return (this.limbs[limbIndex] >>> bitIndexInLimb) & 1;
+};
+
+/** set n-th bit, 0 = LSB */
+sjcl.bn.prototype.setBitM = function (bitIndex) {
+  var limbIndex = Math.floor(bitIndex / this.radix);
+  var bitIndexInLimb = bitIndex % this.radix;
+
+  while (limbIndex >= this.limbs.length) this.limbs.push(0);
+
+  this.limbs[limbIndex] |= 1 << bitIndexInLimb;
+
+  this.cnormalize();
+
+  return this;
+};
+
+sjcl.bn.prototype.modInt = function (n) {
+  return this.toNumber() % n;
+};

src/js/sjcl-custom/sjcl-jacobi.js

@@ -0,0 +1,45 @@
+sjcl.bn.prototype.jacobi = function (that) {
+  var a = this;
+  that = new sjcl.bn(that);
+
+  if (that.sign() === -1) return;
+
+  // 1. If a = 0 then return(0).
+  if (a.equals(0)) { return 0; }
+
+  // 2. If a = 1 then return(1).
+  if (a.equals(1)) { return 1; }
+
+  var s = 0;
+
+  // 3. Write a = 2^e * a1, where a1 is odd.
+  var e = 0;
+  while (!a.testBit(e)) e++;
+  var a1 = a.shiftRight(e);
+
+  // 4. If e is even then set s ← 1.
+  if ((e & 1) === 0) {
+    s = 1;
+  } else {
+    var residue = that.modInt(8);
+
+    if (residue === 1 || residue === 7) {
+      // Otherwise set s ← 1 if n ≡ 1 or 7 (mod 8)
+      s = 1;
+    } else if (residue === 3 || residue === 5) {
+      // Or set s ← −1 if n ≡ 3 or 5 (mod 8).
+      s = -1;
+    }
+  }
+
+  // 5. If n ≡ 3 (mod 4) and a1 ≡ 3 (mod 4) then set s ← −s.
+  if (that.modInt(4) === 3 && a1.modInt(4) === 3) {
+    s = -s;
+  }
+
+  if (a1.equals(1)) {
+    return s;
+  } else {
+    return s * that.mod(a1).jacobi(a1);
+  }
+};