bugfix in correction

Author: Christoph Zurnieden

mp_root_n.c

@@ -196,16 +196,21 @@ mp_err mp_root_n(const mp_int *a, int b, mp_int *c)
    }
    /* log2(a), fixed point */
    if ((err = s_mp_fp_log(&a_, &t2)) != MP_OKAY)                              goto LBL_ERR;
+
+   /* This algorithm is sensitive to start-values that are too low. */
+   mp_set(&t1, 1);
+   if ((err = mp_mul_2d(&t1,MP_PRECISION_FIXED_LOG - 1, &t1)) != MP_OKAY)     goto LBL_ERR;
+   if ((err = mp_add(&t2, &t1, &t2)) != MP_OKAY)                              goto LBL_ERR;
+
    /* k = log2(a) / b, fixed point */
    mp_set_i64(&t1, b);
    if ((err = mp_mul_2d(&t1,MP_PRECISION_FIXED_LOG, &t1)) != MP_OKAY)         goto LBL_ERR;
    if ((err = mp_mul_2d(&t2,MP_PRECISION_FIXED_LOG, &t2)) != MP_OKAY)         goto LBL_ERR;
    if ((err = mp_div(&t2, &t1, &t2,NULL)) != MP_OKAY)                         goto LBL_ERR;
+
+
    /* 2^k, the start-value */
    if ((err = s_mp_fp_exp2(&t2, &t2)) != MP_OKAY)                             goto LBL_ERR;
-
-   /* This algorithm is sensitive to start-values that are too low. */
-   if ((err = mp_add_d(&t2, 2, &t2)) != MP_OKAY)                             goto LBL_ERR;
    do {
 
       /* t1 = t2 */
@@ -240,7 +245,6 @@ mp_err mp_root_n(const mp_int *a, int b, mp_int *c)
          break;
       }
    }  while (mp_cmp(&t1, &t2) != MP_EQ);
-
    /* result can be off by a few so check */
    /* Loop beneath can overshoot by one if root we found is smaller than the actual root */
    for (;;) {
@@ -249,7 +253,8 @@ mp_err mp_root_n(const mp_int *a, int b, mp_int *c)
       cmp = mp_cmp(&t2, &a_);
       if (cmp == MP_EQ) {
          err = MP_OKAY;
-         goto LBL_ERR;
+         /* On point, skip overshoot */
+         goto LBL_SET;
       }
       if (cmp == MP_LT) {
          if ((err = mp_add_d(&t1, 1uL, &t1)) != MP_OKAY)                      goto LBL_ERR;
@@ -266,7 +271,7 @@ mp_err mp_root_n(const mp_int *a, int b, mp_int *c)
          break;
       }
    }
-
+LBL_SET:
    /* set the result */
    mp_exch(&t1, c);