1 files changed, 130 insertions, 0 deletions
diff --git a/libtommath/bn_mp_n_root_ex.c b/libtommath/bn_mp_n_root_ex.c
new file mode 100644
index 0000000..9fd7098
--- /dev/null
+++ b/libtommath/bn_mp_n_root_ex.c
@@ -0,0 +1,130 @@
+#include "tommath_private.h"
+#ifdef BN_MP_N_ROOT_EX_C
+/* 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.
+ */
+
+/* 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_ex(const mp_int *a, mp_digit b, mp_int *c, int fast)
+{
+   mp_int  t1, t2, t3, a_;
+   int     res;
+
+   /* input must be positive if b is even */
+   if (((b & 1u) == 0u) && (a->sign == MP_NEG)) {
+      return MP_VAL;
+   }
+
+   if ((res = mp_init(&t1)) != MP_OKAY) {
+      return res;
+   }
+
+   if ((res = mp_init(&t2)) != MP_OKAY) {
+      goto LBL_T1;
+   }
+
+   if ((res = mp_init(&t3)) != MP_OKAY) {
+      goto LBL_T2;
+   }
+
+   /* if a is negative fudge the sign but keep track */
+   a_ = *a;
+   a_.sign = MP_ZPOS;
+
+   /* t2 = 2 */
+   mp_set(&t2, 2uL);
+
+   do {
+      /* t1 = t2 */
+      if ((res = mp_copy(&t2, &t1)) != MP_OKAY) {
+         goto LBL_T3;
+      }
+
+      /* t2 = t1 - ((t1**b - a) / (b * t1**(b-1))) */
+
+      /* t3 = t1**(b-1) */
+      if ((res = mp_expt_d_ex(&t1, b - 1u, &t3, fast)) != MP_OKAY) {
+         goto LBL_T3;
+      }
+
+      /* numerator */
+      /* t2 = t1**b */
+      if ((res = mp_mul(&t3, &t1, &t2)) != MP_OKAY) {
+         goto LBL_T3;
+      }
+
+      /* t2 = t1**b - a */
+      if ((res = mp_sub(&t2, &a_, &t2)) != MP_OKAY) {
+         goto LBL_T3;
+      }
+
+      /* denominator */
+      /* t3 = t1**(b-1) * b  */
+      if ((res = mp_mul_d(&t3, b, &t3)) != MP_OKAY) {
+         goto LBL_T3;
+      }
+
+      /* t3 = (t1**b - a)/(b * t1**(b-1)) */
+      if ((res = mp_div(&t2, &t3, &t3, NULL)) != MP_OKAY) {
+         goto LBL_T3;
+      }
+
+      if ((res = mp_sub(&t1, &t3, &t2)) != MP_OKAY) {
+         goto LBL_T3;
+      }
+   }  while (mp_cmp(&t1, &t2) != MP_EQ);
+
+   /* result can be off by a few so check */
+   for (;;) {
+      if ((res = mp_expt_d_ex(&t1, b, &t2, fast)) != MP_OKAY) {
+         goto LBL_T3;
+      }
+
+      if (mp_cmp(&t2, &a_) == MP_GT) {
+         if ((res = mp_sub_d(&t1, 1uL, &t1)) != MP_OKAY) {
+            goto LBL_T3;
+         }
+      } else {
+         break;
+      }
+   }
+
+   /* set the result */
+   mp_exch(&t1, c);
+
+   /* set the sign of the result */
+   c->sign = a->sign;
+
+   res = MP_OKAY;
+
+LBL_T3:
+   mp_clear(&t3);
+LBL_T2:
+   mp_clear(&t2);
+LBL_T1:
+   mp_clear(&t1);
+   return res;
+}
+#endif
+
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */