Add 1 (one) unconditionally to the start value

Author: Christoph Zurnieden

mp_root_n.c

@@ -108,28 +108,21 @@ static mp_err s_mp_fp_exp2(const mp_int *a, mp_int *c)
    if ((err = mp_init_multi(&tmp, &int_part, &fract_part, NULL)) != MP_OKAY) {
       return err;
    }
-
    /* Cut fore and aft to get the integer part */
    if ((err = mp_div_2d(a, MP_PRECISION_FIXED_LOG, &int_part, NULL)) != MP_OKAY)          goto LBL_ERR;
    if ((err = mp_mul_2d(&int_part, MP_PRECISION_FIXED_LOG, &int_part)) != MP_OKAY)        goto LBL_ERR;
-
    /* Fractional part */
    if ((err = mp_sub(a, &int_part, &fract_part)) != MP_OKAY)                              goto LBL_ERR;
-
    /* 2^{fractional part} */
    if ((err = s_mp_fp_exp2_fract(&fract_part, &fract_part)) != MP_OKAY)                   goto LBL_ERR;
-
    /* A = 1 << normalized integer part */
    mp_set(&tmp,1);
    if ((err = mp_div_2d(&int_part, MP_PRECISION_FIXED_LOG, &int_part, NULL)) != MP_OKAY)  goto LBL_ERR;
    if ((err = mp_mul_2d(&tmp, (int)mp_get_l(&int_part), &int_part)) != MP_OKAY)           goto LBL_ERR;
-
    /* B = A * fractional part */
    if ((err = mp_mul(&int_part, &fract_part, &tmp)) != MP_OKAY)                           goto LBL_ERR;
-
    /* normalize B */
    if ((err = mp_div_2d(&tmp, MP_PRECISION_FIXED_LOG, &tmp, NULL)) != MP_OKAY)            goto LBL_ERR;
-
    /* C = 2^a (Roughly. Very, very roughly) */
    if (c != NULL) {
       mp_exch(&tmp, c);
@@ -219,38 +212,27 @@ mp_err mp_root_n(const mp_int *a, int b, mp_int *c)
    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;
-   if (mp_isone(&t2)) {
-      if ((err = mp_incr(&t2)) != MP_OKAY)                                   goto LBL_ERR;
-   }
+   /* Add 1 (one) unconditionally for the small roots.  */
+   if ((err = mp_incr(&t2)) != MP_OKAY)                                       goto LBL_ERR;
    do {
-
       /* t1 = t2 */
       if ((err = mp_copy(&t2, &t1)) != MP_OKAY)                               goto LBL_ERR;
-
       /* t2 = t1 - ((t1**b - a) / (b * t1**(b-1))) */
-
       /* t3 = t1**(b-1) */
       if ((err = mp_expt_n(&t1, b - 1, &t3)) != MP_OKAY)                      goto LBL_ERR;
-
       /* numerator */
       /* t2 = t1**b */
       if ((err = mp_mul(&t3, &t1, &t2)) != MP_OKAY)                           goto LBL_ERR;
-
       /* t2 = t1**b - a */
       if ((err = mp_sub(&t2, &a_, &t2)) != MP_OKAY)                           goto LBL_ERR;
-
       /* denominator */
       /* t3 = t1**(b-1) * b  */
       if ((err = mp_mul_d(&t3, (mp_digit)b, &t3)) != MP_OKAY)                 goto LBL_ERR;
-
       /* t3 = (t1**b - a)/(b * t1**(b-1)) */
       if ((err = mp_div(&t2, &t3, &t3, NULL)) != MP_OKAY)                     goto LBL_ERR;
-
       if ((err = mp_sub(&t1, &t3, &t2)) != MP_OKAY)                           goto LBL_ERR;
-
       /*
           Number of rounds is at most log_2(root). If it is more it
           got stuck, so break out of the loop and do the rest manually.