mp_n_root: add mp_n_root_ex() with parameter 'fast' for mp_expt_d_ex()

This change is introduced to be able to choose the underlying
implementation of mp_expt_d_ex()

The implementation of the root_n functionality is now implemented in the
mp_n_root_ex() function.

The parameter 'fast' is just passed over to mp_expt_d_ex().

mp_n_root() defaults to the pre 921be35779
implementation

bn_mp_n_root.c

@@ -15,116 +15,14 @@
  * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
  */
 
-/* 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].
+/* wrapper function for mp_n_root_ex()
+ * computes c = (a)**(1/b) such that (c)**b <= a and (c+1)**b > a
  */
 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 LBL_T1;
-  }
-
-  if ((res = mp_init (&t3)) != MP_OKAY) {
-    goto LBL_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 LBL_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 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 (&t1, b, &t2)) != MP_OKAY) {
-      goto LBL_T3;
-    }
-
-    if (mp_cmp (&t2, a) == MP_GT) {
-      if ((res = mp_sub_d (&t1, 1, &t1)) != MP_OKAY) {
-         goto LBL_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;
-
-LBL_T3:mp_clear (&t3);
-LBL_T2:mp_clear (&t2);
-LBL_T1:mp_clear (&t1);
-  return res;
+  return mp_n_root_ex(a, b, c, 0);
 }
+
 #endif
 
 /* $Source$ */

bn_mp_n_root_ex.c

@@ -0,0 +1,132 @@
+#include <tommath.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.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* 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 (mp_int * a, mp_digit b, mp_int * c, int fast)
+{
+  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 LBL_T1;
+  }
+
+  if ((res = mp_init (&t3)) != MP_OKAY) {
+    goto LBL_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 LBL_T3;
+    }
+
+    /* t2 = t1 - ((t1**b - a) / (b * t1**(b-1))) */
+
+    /* t3 = t1**(b-1) */
+    if ((res = mp_expt_d_ex (&t1, b - 1, &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, 1, &t1)) != MP_OKAY) {
+         goto LBL_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;
+
+LBL_T3:mp_clear (&t3);
+LBL_T2:mp_clear (&t2);
+LBL_T1:mp_clear (&t1);
+  return res;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */

makefile

@@ -96,7 +96,7 @@ bn_mp_init_multi.o bn_mp_clear_multi.o bn_mp_exteuclid.o bn_mp_toradix_n.o \
 bn_mp_prime_random_ex.o bn_mp_get_int.o bn_mp_sqrt.o bn_mp_is_square.o bn_mp_init_set.o \
 bn_mp_init_set_int.o bn_mp_invmod_slow.o bn_mp_prime_rabin_miller_trials.o \
 bn_mp_to_signed_bin_n.o bn_mp_to_unsigned_bin_n.o bn_mp_import.o bn_mp_export.o \
-bn_mp_balance_mul.o bn_mp_expt_d_ex.o
+bn_mp_balance_mul.o bn_mp_expt_d_ex.o bn_mp_n_root_ex.o
 
 $(LIBNAME):  $(OBJECTS)
 	$(AR) $(ARFLAGS) $@ $(OBJECTS)

tommath.h

@@ -400,6 +400,7 @@ int mp_lcm(mp_int *a, mp_int *b, mp_int *c);
  * returns error if a < 0 and b is even
  */
 int mp_n_root(mp_int *a, mp_digit b, mp_int *c);
+int mp_n_root_ex (mp_int * a, mp_digit b, mp_int * c, int fast);
 
 /* special sqrt algo */
 int mp_sqrt(mp_int *arg, mp_int *ret);

tommath_class.h

@@ -77,6 +77,7 @@
 #define BN_MP_MUL_D_C
 #define BN_MP_MULMOD_C
 #define BN_MP_N_ROOT_C
+#define BN_MP_N_ROOT_EX_C
 #define BN_MP_NEG_C
 #define BN_MP_OR_C
 #define BN_MP_PRIME_FERMAT_C
@@ -614,10 +615,14 @@
 #endif
 
 #if defined(BN_MP_N_ROOT_C)
+   #define BN_MP_N_ROOT_EX_C
+#endif
+
+#if defined(BN_MP_N_ROOT_EX_C)
    #define BN_MP_INIT_C
    #define BN_MP_SET_C
    #define BN_MP_COPY_C
-   #define BN_MP_EXPT_D_C
+   #define BN_MP_EXPT_D_EX_C
    #define BN_MP_MUL_C
    #define BN_MP_SUB_C
    #define BN_MP_MUL_D_C
@@ -1023,7 +1028,3 @@
 #else
 #define LTM_LAST
 #endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */