--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/bn_mp_n_root.c	Mon May 31 18:25:22 2004 +0000
@@ -0,0 +1,126 @@
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, [email protected], http://math.libtomcrypt.org
+ */
+#include <tommath.h>
+
+/* find the n'th root of an integer 
+ *
+ * Result found such that (c)**b <= a and (c+1)**b > a 
+ *
+ * This algorithm uses Newton's approximation 
+ * x[i+1] = x[i] - f(x[i])/f'(x[i]) 
+ * which will find the root in log(N) time where 
+ * each step involves a fair bit.  This is not meant to 
+ * find huge roots [square and cube, etc].
+ */
+int mp_n_root (mp_int * a, mp_digit b, mp_int * c)
+{
+  mp_int  t1, t2, t3;
+  int     res, neg;
+
+  /* input must be positive if b is even */
+  if ((b & 1) == 0 && a->sign == MP_NEG) {
+    return MP_VAL;
+  }
+
+  if ((res = mp_init (&t1)) != MP_OKAY) {
+    return res;
+  }
+
+  if ((res = mp_init (&t2)) != MP_OKAY) {
+    goto __T1;
+  }
+
+  if ((res = mp_init (&t3)) != MP_OKAY) {
+    goto __T2;
+  }
+
+  /* if a is negative fudge the sign but keep track */
+  neg     = a->sign;
+  a->sign = MP_ZPOS;
+
+  /* t2 = 2 */
+  mp_set (&t2, 2);
+
+  do {
+    /* t1 = t2 */
+    if ((res = mp_copy (&t2, &t1)) != MP_OKAY) {
+      goto __T3;
+    }
+
+    /* t2 = t1 - ((t1**b - a) / (b * t1**(b-1))) */
+    
+    /* t3 = t1**(b-1) */
+    if ((res = mp_expt_d (&t1, b - 1, &t3)) != MP_OKAY) {   
+      goto __T3;
+    }
+
+    /* numerator */
+    /* t2 = t1**b */
+    if ((res = mp_mul (&t3, &t1, &t2)) != MP_OKAY) {    
+      goto __T3;
+    }
+
+    /* t2 = t1**b - a */
+    if ((res = mp_sub (&t2, a, &t2)) != MP_OKAY) {  
+      goto __T3;
+    }
+
+    /* denominator */
+    /* t3 = t1**(b-1) * b  */
+    if ((res = mp_mul_d (&t3, b, &t3)) != MP_OKAY) {    
+      goto __T3;
+    }
+
+    /* t3 = (t1**b - a)/(b * t1**(b-1)) */
+    if ((res = mp_div (&t2, &t3, &t3, NULL)) != MP_OKAY) {  
+      goto __T3;
+    }
+
+    if ((res = mp_sub (&t1, &t3, &t2)) != MP_OKAY) {
+      goto __T3;
+    }
+  }  while (mp_cmp (&t1, &t2) != MP_EQ);
+
+  /* result can be off by a few so check */
+  for (;;) {
+    if ((res = mp_expt_d (&t1, b, &t2)) != MP_OKAY) {
+      goto __T3;
+    }
+
+    if (mp_cmp (&t2, a) == MP_GT) {
+      if ((res = mp_sub_d (&t1, 1, &t1)) != MP_OKAY) {
+         goto __T3;
+      }
+    } else {
+      break;
+    }
+  }
+
+  /* reset the sign of a first */
+  a->sign = neg;
+
+  /* set the result */
+  mp_exch (&t1, c);
+
+  /* set the sign of the result */
+  c->sign = neg;
+
+  res = MP_OKAY;
+
+__T3:mp_clear (&t3);
+__T2:mp_clear (&t2);
+__T1:mp_clear (&t1);
+  return res;
+}