Expansion of mp_log to the full range together with the extension of mp_log to bigint bases.

Author: czurnieden

.gitignore

@@ -85,6 +85,16 @@ etc/tune
 tommath.tex
 libtommath.pc
 
+# ignore files generated by bibtex/biber
+83aea75e0c59d1de027747003151d53dcb2a51c9.bib
+*.bbl
+*.bcf
+*.blg
+*.loa
+*.lol
+*.run.xml
+
+
 # ignore files generated by testme.sh
 gcc_errors_*.txt
 test_*.txt

demo/test.c

@@ -1516,6 +1516,70 @@ static int test_mp_log_n(void)
    return EXIT_FAILURE;
 }
 
+static int test_mp_log(void)
+{
+   mp_int a, base, bn, t;
+   int lb, lb2, i, j;
+
+   DOR(mp_init_multi(&a, &base, &bn, &t, NULL));
+
+   /*
+      The small values got tested above for mp_log_n already, leaving the big stuff
+      with bases larger than INT_MAX.
+   */
+
+   /* Edgecases a^b and -1+a^b (floor(log_2(256^129)) = 1032) */
+   for (i = 2; i < 256; i++) {
+      mp_set_i32(&a,i);
+      for (j = 2; j < ((i/2)+1); j++) {
+         DO(mp_expt_n(&a, j, &bn));
+         mp_set_i32(&base,j);
+         /* i^j a perfect power */
+         DO(mp_log(&bn, &a, &lb));
+         DO(mp_expt_n(&a, lb, &t));
+         if (mp_cmp(&t, &bn) != MP_EQ) {
+            fprintf(stderr,"FAILURE mp_log for perf. power at i = %d, j = %d\n", i, j);
+            goto LBL_ERR;
+         }
+         /* -1 + i^j */
+         DO(mp_decr(&bn));
+         DO(mp_log(&bn, &a, &lb2));
+         if (lb != (lb2+1)) {
+            fprintf(stderr,"FAILURE mp_log for -1 + i^j at i = %d, j = %d\n", i, j);
+            goto LBL_ERR;
+         }
+      }
+   }
+
+   /* Random a, base */
+   for (i = 1; i < 256; i++) {
+      DO(mp_rand(&a, i));
+      for (j = 1; j < ((i/2)+1); j++) {
+         DO(mp_rand(&base, j));
+         DO(mp_log(&a, &base, &lb));
+         DO(mp_expt_n(&base, lb, &bn));
+         /* "bn" must be smaller than or equal to "a" at this point. */
+         if (mp_cmp(&bn, &a) == MP_GT) {
+            fprintf(stderr,"FAILURE mp_log random in GT check");
+            goto LBL_ERR;
+         }
+         DO(mp_mul(&bn, &base, &bn));
+         /* "bn" must be bigger than "a" at this point. */
+         if (mp_cmp(&bn, &a) != MP_GT) {
+            fprintf(stderr,"FAILURE mp_log random in NOT GT check");
+            goto LBL_ERR;
+         }
+      }
+   }
+
+   mp_clear_multi(&a, &base, &bn, &t, NULL);
+   return EXIT_SUCCESS;
+LBL_ERR:
+   mp_clear_multi(&a, &base, &bn, &t, NULL);
+   return EXIT_FAILURE;
+}
+
+
 static int test_mp_incr(void)
 {
    mp_int a, b;
@@ -2373,6 +2437,7 @@ static int unit_tests(int argc, char **argv)
       T1(mp_get_u64, MP_GET_I64),
       T1(mp_get_ul, MP_GET_L),
       T1(mp_log_n, MP_LOG_N),
+      T1(mp_log, MP_LOG),
       T1(mp_incr, MP_ADD_D),
       T1(mp_invmod, MP_INVMOD),
       T1(mp_is_square, MP_IS_SQUARE),

doc/bn.tex

@@ -1946,18 +1946,24 @@ \section{Root Finding}
 \begin{alltt}
 mp_err mp_sqrt(const mp_int *arg, mp_int *ret)
 \end{alltt}
-
 \chapter{Logarithm}
 \section{Integer Logarithm}
 A logarithm function for positive integer input \texttt{a, base} computing  $\floor{\log_bx}$ such
-that $(\log_b x)^b \le x$.
+that $(\log_b x)^b \le x$. The function \texttt{mp\_log\_n} is just a wrapper that converts \texttt{base}
+to a bigint and calls \texttt{mp\_log}.
+
+\index{mp\_log}
+\begin{alltt}
+mp_err mp_log(const mp_int *a, const mp_int *base, int *c)
+\end{alltt}
 
 \index{mp\_log\_n}
 \begin{alltt}
 mp_err mp_log_n(const mp_int *a, int base, int *c)
 \end{alltt}
 
 \subsection{Example}
+Example given for \texttt{mp\_log\_n} only because the single difference is the type of \texttt{base}.
 \begin{small}
   \begin{alltt}
 #include <stdlib.h>
@@ -1968,15 +1974,15 @@ \subsection{Example}
 
 int main(int argc, char **argv)
 {
-   mp_int x, output;
-   int base;
+   mp_int x;
+   int base, output;
    mp_err e;
 
    if (argc != 3) {
       fprintf(stderr,"Usage %s base x\textbackslash{}n", argv[0]);
       exit(EXIT_FAILURE);
    }
-   if ((e = mp_init_multi(&x, &output, NULL)) != MP_OKAY) {
+   if ((e = mp_init(&x)) != MP_OKAY) {
       fprintf(stderr,"mp_init failed: \textbackslash{}"%s\textbackslash{}"\textbackslash{}n",
                      mp_error_to_string(e));
               exit(EXIT_FAILURE);
@@ -1998,20 +2004,18 @@ \subsection{Example}
                       mp_error_to_string(e));
       exit(EXIT_FAILURE);
    }
+   printf("%d\n",output);
 
-   if ((e = mp_fwrite(&output, 10, stdout)) != MP_OKAY) {
-      fprintf(stderr,"mp_fwrite failed: \textbackslash{}"%s\textbackslash{}"\textbackslash{}n",
-                      mp_error_to_string(e));
-      exit(EXIT_FAILURE);
-   }
-   putchar('\textbackslash{}n');
-
-   mp_clear_multi(&x, &output, NULL);
+   mp_clear(&x);
    exit(EXIT_SUCCESS);
 }
 \end{alltt}
 \end{small}
 
+
+
+
+
 \chapter{Prime Numbers}
 
 \section{Fermat Test}

libtommath_VS2008.vcproj

@@ -544,6 +544,10 @@
 			RelativePath="mp_lcm.c"
 			>
 		</File>
+		<File
+			RelativePath="mp_log.c"
+			>
+		</File>
 		<File
 			RelativePath="mp_log_n.c"
 			>
@@ -829,27 +833,27 @@
 			>
 		</File>
 		<File
-			RelativePath="s_mp_get_bit.c"
+			RelativePath="s_mp_flog2_mp_word.c"
 			>
 		</File>
 		<File
-			RelativePath="s_mp_invmod.c"
+			RelativePath="s_mp_fp_log.c"
 			>
 		</File>
 		<File
-			RelativePath="s_mp_invmod_odd.c"
+			RelativePath="s_mp_get_bit.c"
 			>
 		</File>
 		<File
-			RelativePath="s_mp_log.c"
+			RelativePath="s_mp_invmod.c"
 			>
 		</File>
 		<File
-			RelativePath="s_mp_log_2expt.c"
+			RelativePath="s_mp_invmod_odd.c"
 			>
 		</File>
 		<File
-			RelativePath="s_mp_log_d.c"
+			RelativePath="s_mp_log_2expt.c"
 			>
 		</File>
 		<File

makefile

@@ -33,7 +33,7 @@ mp_error_to_string.o mp_exch.o mp_expt_n.o mp_exptmod.o mp_exteuclid.o mp_fread.
 mp_from_ubin.o mp_fwrite.o mp_gcd.o mp_get_double.o mp_get_i32.o mp_get_i64.o mp_get_l.o mp_get_mag_u32.o \
 mp_get_mag_u64.o mp_get_mag_ul.o mp_grow.o mp_hash.o mp_init.o mp_init_copy.o mp_init_i32.o mp_init_i64.o \
 mp_init_l.o mp_init_multi.o mp_init_set.o mp_init_size.o mp_init_u32.o mp_init_u64.o mp_init_ul.o \
-mp_invmod.o mp_is_square.o mp_kronecker.o mp_lcm.o mp_log_n.o mp_lshd.o mp_mod.o mp_mod_2d.o \
+mp_invmod.o mp_is_square.o mp_kronecker.o mp_lcm.o mp_log.o mp_log_n.o mp_lshd.o mp_mod.o mp_mod_2d.o \
 mp_montgomery_calc_normalization.o mp_montgomery_reduce.o mp_montgomery_setup.o mp_mul.o mp_mul_2.o \
 mp_mul_2d.o mp_mul_d.o mp_mulmod.o mp_neg.o mp_or.o mp_pack.o mp_pack_count.o mp_prime_fermat.o \
 mp_prime_frobenius_underwood.o mp_prime_is_prime.o mp_prime_miller_rabin.o mp_prime_next_prime.o \
@@ -44,8 +44,8 @@ mp_reduce_setup.o mp_root_n.o mp_rshd.o mp_sbin_size.o mp_set.o mp_set_double.o
 mp_set_l.o mp_set_u32.o mp_set_u64.o mp_set_ul.o mp_shrink.o mp_signed_rsh.o mp_sqrmod.o mp_sqrt.o \
 mp_sqrtmod_prime.o mp_sub.o mp_sub_d.o mp_submod.o mp_to_radix.o mp_to_sbin.o mp_to_ubin.o mp_ubin_size.o \
 mp_unpack.o mp_xor.o mp_zero.o s_mp_add.o s_mp_copy_digs.o s_mp_div_3.o s_mp_div_recursive.o \
-s_mp_div_school.o s_mp_div_small.o s_mp_exptmod.o s_mp_exptmod_fast.o s_mp_get_bit.o s_mp_invmod.o \
-s_mp_invmod_odd.o s_mp_log.o s_mp_log_2expt.o s_mp_log_d.o s_mp_montgomery_reduce_comba.o s_mp_mul.o \
+s_mp_div_school.o s_mp_div_small.o s_mp_exptmod.o s_mp_exptmod_fast.o s_mp_flog2_mp_word.o s_mp_fp_log.o \
+s_mp_get_bit.o s_mp_invmod.o s_mp_invmod_odd.o s_mp_log_2expt.o s_mp_montgomery_reduce_comba.o s_mp_mul.o \
 s_mp_mul_balance.o s_mp_mul_comba.o s_mp_mul_high.o s_mp_mul_high_comba.o s_mp_mul_karatsuba.o \
 s_mp_mul_toom.o s_mp_prime_is_divisible.o s_mp_prime_tab.o s_mp_radix_map.o \
 s_mp_radix_size_overestimate.o s_mp_rand_platform.o s_mp_sqr.o s_mp_sqr_comba.o s_mp_sqr_karatsuba.o \

makefile.mingw

@@ -35,7 +35,7 @@ mp_error_to_string.o mp_exch.o mp_expt_n.o mp_exptmod.o mp_exteuclid.o mp_fread.
 mp_from_ubin.o mp_fwrite.o mp_gcd.o mp_get_double.o mp_get_i32.o mp_get_i64.o mp_get_l.o mp_get_mag_u32.o \
 mp_get_mag_u64.o mp_get_mag_ul.o mp_grow.o mp_hash.o mp_init.o mp_init_copy.o mp_init_i32.o mp_init_i64.o \
 mp_init_l.o mp_init_multi.o mp_init_set.o mp_init_size.o mp_init_u32.o mp_init_u64.o mp_init_ul.o \
-mp_invmod.o mp_is_square.o mp_kronecker.o mp_lcm.o mp_log_n.o mp_lshd.o mp_mod.o mp_mod_2d.o \
+mp_invmod.o mp_is_square.o mp_kronecker.o mp_lcm.o mp_log.o mp_log_n.o mp_lshd.o mp_mod.o mp_mod_2d.o \
 mp_montgomery_calc_normalization.o mp_montgomery_reduce.o mp_montgomery_setup.o mp_mul.o mp_mul_2.o \
 mp_mul_2d.o mp_mul_d.o mp_mulmod.o mp_neg.o mp_or.o mp_pack.o mp_pack_count.o mp_prime_fermat.o \
 mp_prime_frobenius_underwood.o mp_prime_is_prime.o mp_prime_miller_rabin.o mp_prime_next_prime.o \
@@ -46,8 +46,8 @@ mp_reduce_setup.o mp_root_n.o mp_rshd.o mp_sbin_size.o mp_set.o mp_set_double.o
 mp_set_l.o mp_set_u32.o mp_set_u64.o mp_set_ul.o mp_shrink.o mp_signed_rsh.o mp_sqrmod.o mp_sqrt.o \
 mp_sqrtmod_prime.o mp_sub.o mp_sub_d.o mp_submod.o mp_to_radix.o mp_to_sbin.o mp_to_ubin.o mp_ubin_size.o \
 mp_unpack.o mp_xor.o mp_zero.o s_mp_add.o s_mp_copy_digs.o s_mp_div_3.o s_mp_div_recursive.o \
-s_mp_div_school.o s_mp_div_small.o s_mp_exptmod.o s_mp_exptmod_fast.o s_mp_get_bit.o s_mp_invmod.o \
-s_mp_invmod_odd.o s_mp_log.o s_mp_log_2expt.o s_mp_log_d.o s_mp_montgomery_reduce_comba.o s_mp_mul.o \
+s_mp_div_school.o s_mp_div_small.o s_mp_exptmod.o s_mp_exptmod_fast.o s_mp_flog2_mp_word.o s_mp_fp_log.o \
+s_mp_get_bit.o s_mp_invmod.o s_mp_invmod_odd.o s_mp_log_2expt.o s_mp_montgomery_reduce_comba.o s_mp_mul.o \
 s_mp_mul_balance.o s_mp_mul_comba.o s_mp_mul_high.o s_mp_mul_high_comba.o s_mp_mul_karatsuba.o \
 s_mp_mul_toom.o s_mp_prime_is_divisible.o s_mp_prime_tab.o s_mp_radix_map.o \
 s_mp_radix_size_overestimate.o s_mp_rand_platform.o s_mp_sqr.o s_mp_sqr_comba.o s_mp_sqr_karatsuba.o \

makefile.msvc

@@ -31,7 +31,7 @@ mp_error_to_string.obj mp_exch.obj mp_expt_n.obj mp_exptmod.obj mp_exteuclid.obj
 mp_from_ubin.obj mp_fwrite.obj mp_gcd.obj mp_get_double.obj mp_get_i32.obj mp_get_i64.obj mp_get_l.obj mp_get_mag_u32.obj \
 mp_get_mag_u64.obj mp_get_mag_ul.obj mp_grow.obj mp_hash.obj mp_init.obj mp_init_copy.obj mp_init_i32.obj mp_init_i64.obj \
 mp_init_l.obj mp_init_multi.obj mp_init_set.obj mp_init_size.obj mp_init_u32.obj mp_init_u64.obj mp_init_ul.obj \
-mp_invmod.obj mp_is_square.obj mp_kronecker.obj mp_lcm.obj mp_log_n.obj mp_lshd.obj mp_mod.obj mp_mod_2d.obj \
+mp_invmod.obj mp_is_square.obj mp_kronecker.obj mp_lcm.obj mp_log.obj mp_log_n.obj mp_lshd.obj mp_mod.obj mp_mod_2d.obj \
 mp_montgomery_calc_normalization.obj mp_montgomery_reduce.obj mp_montgomery_setup.obj mp_mul.obj mp_mul_2.obj \
 mp_mul_2d.obj mp_mul_d.obj mp_mulmod.obj mp_neg.obj mp_or.obj mp_pack.obj mp_pack_count.obj mp_prime_fermat.obj \
 mp_prime_frobenius_underwood.obj mp_prime_is_prime.obj mp_prime_miller_rabin.obj mp_prime_next_prime.obj \
@@ -42,8 +42,8 @@ mp_reduce_setup.obj mp_root_n.obj mp_rshd.obj mp_sbin_size.obj mp_set.obj mp_set
 mp_set_l.obj mp_set_u32.obj mp_set_u64.obj mp_set_ul.obj mp_shrink.obj mp_signed_rsh.obj mp_sqrmod.obj mp_sqrt.obj \
 mp_sqrtmod_prime.obj mp_sub.obj mp_sub_d.obj mp_submod.obj mp_to_radix.obj mp_to_sbin.obj mp_to_ubin.obj mp_ubin_size.obj \
 mp_unpack.obj mp_xor.obj mp_zero.obj s_mp_add.obj s_mp_copy_digs.obj s_mp_div_3.obj s_mp_div_recursive.obj \
-s_mp_div_school.obj s_mp_div_small.obj s_mp_exptmod.obj s_mp_exptmod_fast.obj s_mp_get_bit.obj s_mp_invmod.obj \
-s_mp_invmod_odd.obj s_mp_log.obj s_mp_log_2expt.obj s_mp_log_d.obj s_mp_montgomery_reduce_comba.obj s_mp_mul.obj \
+s_mp_div_school.obj s_mp_div_small.obj s_mp_exptmod.obj s_mp_exptmod_fast.obj s_mp_flog2_mp_word.obj s_mp_fp_log.obj \
+s_mp_get_bit.obj s_mp_invmod.obj s_mp_invmod_odd.obj s_mp_log_2expt.obj s_mp_montgomery_reduce_comba.obj s_mp_mul.obj \
 s_mp_mul_balance.obj s_mp_mul_comba.obj s_mp_mul_high.obj s_mp_mul_high_comba.obj s_mp_mul_karatsuba.obj \
 s_mp_mul_toom.obj s_mp_prime_is_divisible.obj s_mp_prime_tab.obj s_mp_radix_map.obj \
 s_mp_radix_size_overestimate.obj s_mp_rand_platform.obj s_mp_sqr.obj s_mp_sqr_comba.obj s_mp_sqr_karatsuba.obj \

makefile.shared

@@ -30,7 +30,7 @@ mp_error_to_string.o mp_exch.o mp_expt_n.o mp_exptmod.o mp_exteuclid.o mp_fread.
 mp_from_ubin.o mp_fwrite.o mp_gcd.o mp_get_double.o mp_get_i32.o mp_get_i64.o mp_get_l.o mp_get_mag_u32.o \
 mp_get_mag_u64.o mp_get_mag_ul.o mp_grow.o mp_hash.o mp_init.o mp_init_copy.o mp_init_i32.o mp_init_i64.o \
 mp_init_l.o mp_init_multi.o mp_init_set.o mp_init_size.o mp_init_u32.o mp_init_u64.o mp_init_ul.o \
-mp_invmod.o mp_is_square.o mp_kronecker.o mp_lcm.o mp_log_n.o mp_lshd.o mp_mod.o mp_mod_2d.o \
+mp_invmod.o mp_is_square.o mp_kronecker.o mp_lcm.o mp_log.o mp_log_n.o mp_lshd.o mp_mod.o mp_mod_2d.o \
 mp_montgomery_calc_normalization.o mp_montgomery_reduce.o mp_montgomery_setup.o mp_mul.o mp_mul_2.o \
 mp_mul_2d.o mp_mul_d.o mp_mulmod.o mp_neg.o mp_or.o mp_pack.o mp_pack_count.o mp_prime_fermat.o \
 mp_prime_frobenius_underwood.o mp_prime_is_prime.o mp_prime_miller_rabin.o mp_prime_next_prime.o \
@@ -41,8 +41,8 @@ mp_reduce_setup.o mp_root_n.o mp_rshd.o mp_sbin_size.o mp_set.o mp_set_double.o
 mp_set_l.o mp_set_u32.o mp_set_u64.o mp_set_ul.o mp_shrink.o mp_signed_rsh.o mp_sqrmod.o mp_sqrt.o \
 mp_sqrtmod_prime.o mp_sub.o mp_sub_d.o mp_submod.o mp_to_radix.o mp_to_sbin.o mp_to_ubin.o mp_ubin_size.o \
 mp_unpack.o mp_xor.o mp_zero.o s_mp_add.o s_mp_copy_digs.o s_mp_div_3.o s_mp_div_recursive.o \
-s_mp_div_school.o s_mp_div_small.o s_mp_exptmod.o s_mp_exptmod_fast.o s_mp_get_bit.o s_mp_invmod.o \
-s_mp_invmod_odd.o s_mp_log.o s_mp_log_2expt.o s_mp_log_d.o s_mp_montgomery_reduce_comba.o s_mp_mul.o \
+s_mp_div_school.o s_mp_div_small.o s_mp_exptmod.o s_mp_exptmod_fast.o s_mp_flog2_mp_word.o s_mp_fp_log.o \
+s_mp_get_bit.o s_mp_invmod.o s_mp_invmod_odd.o s_mp_log_2expt.o s_mp_montgomery_reduce_comba.o s_mp_mul.o \
 s_mp_mul_balance.o s_mp_mul_comba.o s_mp_mul_high.o s_mp_mul_high_comba.o s_mp_mul_karatsuba.o \
 s_mp_mul_toom.o s_mp_prime_is_divisible.o s_mp_prime_tab.o s_mp_radix_map.o \
 s_mp_radix_size_overestimate.o s_mp_rand_platform.o s_mp_sqr.o s_mp_sqr_comba.o s_mp_sqr_karatsuba.o \

makefile.unix

@@ -36,7 +36,7 @@ mp_error_to_string.o mp_exch.o mp_expt_n.o mp_exptmod.o mp_exteuclid.o mp_fread.
 mp_from_ubin.o mp_fwrite.o mp_gcd.o mp_get_double.o mp_get_i32.o mp_get_i64.o mp_get_l.o mp_get_mag_u32.o \
 mp_get_mag_u64.o mp_get_mag_ul.o mp_grow.o mp_hash.o mp_init.o mp_init_copy.o mp_init_i32.o mp_init_i64.o \
 mp_init_l.o mp_init_multi.o mp_init_set.o mp_init_size.o mp_init_u32.o mp_init_u64.o mp_init_ul.o \
-mp_invmod.o mp_is_square.o mp_kronecker.o mp_lcm.o mp_log_n.o mp_lshd.o mp_mod.o mp_mod_2d.o \
+mp_invmod.o mp_is_square.o mp_kronecker.o mp_lcm.o mp_log.o mp_log_n.o mp_lshd.o mp_mod.o mp_mod_2d.o \
 mp_montgomery_calc_normalization.o mp_montgomery_reduce.o mp_montgomery_setup.o mp_mul.o mp_mul_2.o \
 mp_mul_2d.o mp_mul_d.o mp_mulmod.o mp_neg.o mp_or.o mp_pack.o mp_pack_count.o mp_prime_fermat.o \
 mp_prime_frobenius_underwood.o mp_prime_is_prime.o mp_prime_miller_rabin.o mp_prime_next_prime.o \
@@ -47,8 +47,8 @@ mp_reduce_setup.o mp_root_n.o mp_rshd.o mp_sbin_size.o mp_set.o mp_set_double.o
 mp_set_l.o mp_set_u32.o mp_set_u64.o mp_set_ul.o mp_shrink.o mp_signed_rsh.o mp_sqrmod.o mp_sqrt.o \
 mp_sqrtmod_prime.o mp_sub.o mp_sub_d.o mp_submod.o mp_to_radix.o mp_to_sbin.o mp_to_ubin.o mp_ubin_size.o \
 mp_unpack.o mp_xor.o mp_zero.o s_mp_add.o s_mp_copy_digs.o s_mp_div_3.o s_mp_div_recursive.o \
-s_mp_div_school.o s_mp_div_small.o s_mp_exptmod.o s_mp_exptmod_fast.o s_mp_get_bit.o s_mp_invmod.o \
-s_mp_invmod_odd.o s_mp_log.o s_mp_log_2expt.o s_mp_log_d.o s_mp_montgomery_reduce_comba.o s_mp_mul.o \
+s_mp_div_school.o s_mp_div_small.o s_mp_exptmod.o s_mp_exptmod_fast.o s_mp_flog2_mp_word.o s_mp_fp_log.o \
+s_mp_get_bit.o s_mp_invmod.o s_mp_invmod_odd.o s_mp_log_2expt.o s_mp_montgomery_reduce_comba.o s_mp_mul.o \
 s_mp_mul_balance.o s_mp_mul_comba.o s_mp_mul_high.o s_mp_mul_high_comba.o s_mp_mul_karatsuba.o \
 s_mp_mul_toom.o s_mp_prime_is_divisible.o s_mp_prime_tab.o s_mp_radix_map.o \
 s_mp_radix_size_overestimate.o s_mp_rand_platform.o s_mp_sqr.o s_mp_sqr_comba.o s_mp_sqr_karatsuba.o \