Don't remove ~ files on make clean (and find -type was wrong anyway)

--HG-- branch : libtommath extra : convert_revision : 38ad9968c111d9364b88e0098afc3e8e794e67e3
Update Makefile.in for dropbear
2025-06-26 18:17:32 +00:00 · 2005-05-11 16:27:28 +00:00 · 2005-05-11 16:25:34 +00:00 · 2005-05-11 16:23:24 +00:00 · 2005-05-11 16:15:27 +00:00 · 2005-05-06 08:59:30 +00:00
80 changed files with 6694 additions and 4009 deletions
--- a/Makefile.in
+++ b/Makefile.in
@@ -2,6 +2,9 @@
 #
 #Tom St Denis

+#version of library 
+VERSION=0.35
+
 VPATH=@srcdir@
 srcdir=@srcdir@

@@ -11,7 +14,7 @@ CFLAGS += -I$(srcdir)
 #CFLAGS  +=  -I./ -Wall -W -Wshadow -Wsign-compare

 #for speed 
-#CFLAGS += -O3 -funroll-loops
+#CFLAGS += -O3 -funroll-all-loops

 #for size 
 #CFLAGS += -Os
@@ -22,13 +25,15 @@ CFLAGS += -I$(srcdir)
 #debug
 #CFLAGS += -g3

-VERSION=0.32
+#install as this user
+USER=root
+GROUP=root

 default: libtommath.a

 #default files to install
 LIBNAME=libtommath.a
-HEADERS=tommath.h
+HEADERS=tommath.h tommath_class.h tommath_superclass.h

 #LIBPATH-The directory for libtommath to be installed to.
 #INCPATH-The directory to install the header files for libtommath.
@@ -58,17 +63,18 @@ bn_mp_prime_is_prime.o bn_mp_prime_next_prime.o bn_mp_dr_reduce.o \
 bn_mp_dr_is_modulus.o bn_mp_dr_setup.o bn_mp_reduce_setup.o \
 bn_mp_toom_mul.o bn_mp_toom_sqr.o bn_mp_div_3.o bn_s_mp_exptmod.o \
 bn_mp_reduce_2k.o bn_mp_reduce_is_2k.o bn_mp_reduce_2k_setup.o \
+bn_mp_reduce_2k_l.o bn_mp_reduce_is_2k_l.o bn_mp_reduce_2k_setup_l.o \
 bn_mp_radix_smap.o bn_mp_read_radix.o bn_mp_toradix.o bn_mp_radix_size.o \
 bn_mp_fread.o bn_mp_fwrite.o bn_mp_cnt_lsb.o bn_error.o \
 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_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

 libtommath.a:  $(OBJECTS)
 	$(AR) $(ARFLAGS) libtommath.a $(OBJECTS)
 	$(RANLIB) libtommath.a

-
 #make a profiled library (takes a while!!!)
 #
 # This will build the library with profile generation
@@ -93,19 +99,19 @@ profiled_single:
 	ranlib libtommath.a	

 install: libtommath.a
-	install -d -g root -o root $(DESTDIR)$(LIBPATH)
-	install -d -g root -o root $(DESTDIR)$(INCPATH)
-	install -g root -o root $(LIBNAME) $(DESTDIR)$(LIBPATH)
-	install -g root -o root $(HEADERS) $(DESTDIR)$(INCPATH)
+	install -d -g $(GROUP) -o $(USER) $(DESTDIR)$(LIBPATH)
+	install -d -g $(GROUP) -o $(USER) $(DESTDIR)$(INCPATH)
+	install -g $(GROUP) -o $(USER) $(LIBNAME) $(DESTDIR)$(LIBPATH)
+	install -g $(GROUP) -o $(USER) $(HEADERS) $(DESTDIR)$(INCPATH)

 test: libtommath.a demo/demo.o
-	$(CC) demo/demo.o libtommath.a -o test
+	$(CC) $(CFLAGS) demo/demo.o libtommath.a -o test
 	
 mtest: test	
-	cd mtest ; $(CC) $(CFLAGS) mtest.c -o mtest -s
+	cd mtest ; $(CC) $(CFLAGS) mtest.c -o mtest
        
 timing: libtommath.a
-	$(CC) $(CFLAGS) -DTIMER demo/timing.c libtommath.a -o ltmtest -s
+	$(CC) $(CFLAGS) -DTIMER demo/timing.c libtommath.a -o ltmtest

 # makes the LTM book DVI file, requires tetex, perl and makeindex [part of tetex I think]
 docdvi: tommath.src
@@ -145,11 +151,11 @@ pretty:
 	perl pretty.build

 clean:
-	-rm -f *.bat *.pdf *.o *.a *.obj *.lib *.exe *.dll etclib/*.o demo/demo.o test ltmtest mpitest mtest/mtest mtest/mtest.exe \
-        *.idx *.toc *.log *.aux *.dvi *.lof *.ind *.ilg *.ps *.log *.s mpi.c *.da *.dyn *.dpi tommath.tex `find . -type f | grep [~] | xargs` *.lo *.la
-	-rm -rf .libs
-	-cd etc && make clean
-	-cd pics && make clean
+	rm -f *.bat *.pdf *.o *.a *.obj *.lib *.exe *.dll etclib/*.o demo/demo.o test ltmtest mpitest mtest/mtest mtest/mtest.exe \
+        *.idx *.toc *.log *.aux *.dvi *.lof *.ind *.ilg *.ps *.log *.s mpi.c *.da *.dyn *.dpi tommath.tex *.lo *.la
+	rm -rf .libs
+	cd etc && make clean
+	cd pics && make clean

 zipup: clean manual poster docs
 	perl gen.pl ; mv mpi.c pre_gen/ ; \
--- a/16
+++ b/16
@@ -0,0 +1,16 @@
+things for book in order of importance...
+
+- Fix up pseudo-code [only] for combas that are not consistent with source
+- Start in chapter 3 [basics] and work up...
+   - re-write to prose [less abrupt]
+   - clean up pseudo code [spacing]
+   - more examples where appropriate and figures
+
+Goal:
+   - Get sync done by mid January [roughly 8-12 hours work]
+   - Finish ch3-6 by end of January [roughly 12-16 hours of work]
+   - Finish ch7-end by mid Feb [roughly 20-24 hours of work].
+
+Goal isn't "first edition" but merely cleaner to read.
+
+
--- a/bn.tex
+++ b/bn.tex
@@ -49,7 +49,7 @@
 \begin{document}
 \frontmatter
 \pagestyle{empty}
-\title{LibTomMath User Manual \\ v0.32}
+\title{LibTomMath User Manual \\ v0.35}
 \author{Tom St Denis \\ tomstdenis@iahu.ca}
 \maketitle
 This text, the library and the accompanying textbook are all hereby placed in the public domain.  This book has been 
@@ -263,12 +263,12 @@ are the pros and cons of LibTomMath by comparing it to the math routines from Gn
 \begin{center}
 \begin{tabular}{|l|c|c|l|}
 \hline \textbf{Criteria} & \textbf{Pro} & \textbf{Con} & \textbf{Notes} \\
-\hline Few lines of code per file & X & & GnuPG $ = 300.9$, LibTomMath  $ = 76.04$ \\
+\hline Few lines of code per file & X & & GnuPG $ = 300.9$, LibTomMath  $ = 71.97$ \\
 \hline Commented function prototypes & X && GnuPG function names are cryptic. \\
 \hline Speed && X & LibTomMath is slower.  \\
 \hline Totally free & X & & GPL has unfavourable restrictions.\\
 \hline Large function base & X & & GnuPG is barebones. \\
-\hline Four modular reduction algorithms & X & & Faster modular exponentiation. \\
+\hline Five modular reduction algorithms & X & & Faster modular exponentiation for a variety of moduli. \\
 \hline Portable & X & & GnuPG requires configuration to build. \\
 \hline
 \end{tabular}
@@ -284,9 +284,12 @@ would require when working with large integers.
 So it may feel tempting to just rip the math code out of GnuPG (or GnuMP where it was taken from originally) in your
 own application but I think there are reasons not to.  While LibTomMath is slower than libraries such as GnuMP it is
 not normally significantly slower.  On x86 machines the difference is normally a factor of two when performing modular
-exponentiations.
+exponentiations.  It depends largely on the processor, compiler and the moduli being used.

-Essentially the only time you wouldn't use LibTomMath is when blazing speed is the primary concern.
+Essentially the only time you wouldn't use LibTomMath is when blazing speed is the primary concern.  However,
+on the other side of the coin LibTomMath offers you a totally free (public domain) well structured math library
+that is very flexible, complete and performs well in resource contrained environments.  Fast RSA for example can
+be performed with as little as 8KB of ram for data (again depending on build options).  

 \chapter{Getting Started with LibTomMath}
 \section{Building Programs}
@@ -809,7 +812,7 @@ mp\_int variables based on their digits only.

 \index{mp\_cmp\_mag}
 \begin{alltt}
-int mp_cmp(mp_int * a, mp_int * b);
+int mp_cmp_mag(mp_int * a, mp_int * b);
 \end{alltt}
 This will compare $a$ to $b$ placing $a$ to the left of $b$.  This function cannot fail and will return one of the
 three compare codes listed in figure \ref{fig:CMP}.
@@ -1220,12 +1223,13 @@ int mp_sqr (mp_int * a, mp_int * b);
 \end{alltt}

 Will square $a$ and store it in $b$.  Like the case of multiplication there are four different squaring
-algorithms all which can be called from mp\_sqr().  It is ideal to use mp\_sqr over mp\_mul when squaring terms.
+algorithms all which can be called from mp\_sqr().  It is ideal to use mp\_sqr over mp\_mul when squaring terms because
+of the speed difference.  

 \section{Tuning Polynomial Basis Routines}

 Both of the Toom-Cook and Karatsuba multiplication algorithms are faster than the traditional $O(n^2)$ approach that
-the Comba and baseline algorithms use.  At $O(n^{1.464973})$ and $O(n^{1.584962})$ running times respectfully they require 
+the Comba and baseline algorithms use.  At $O(n^{1.464973})$ and $O(n^{1.584962})$ running times respectively they require 
 considerably less work.  For example, a 10000-digit multiplication would take roughly 724,000 single precision
 multiplications with Toom-Cook or 100,000,000 single precision multiplications with the standard Comba (a factor
 of 138).
@@ -1297,14 +1301,14 @@ of $b$.  This algorithm accepts an input $a$ of any range and is not limited by
 \section{Barrett Reduction}

 Barrett reduction is a generic optimized reduction algorithm that requires pre--computation to achieve
-a decent speedup over straight division.  First a $mu$ value must be precomputed with the following function.
+a decent speedup over straight division.  First a $\mu$ value must be precomputed with the following function.

 \index{mp\_reduce\_setup}
 \begin{alltt}
 int mp_reduce_setup(mp_int *a, mp_int *b);
 \end{alltt}

-Given a modulus in $b$ this produces the required $mu$ value in $a$.  For any given modulus this only has to
+Given a modulus in $b$ this produces the required $\mu$ value in $a$.  For any given modulus this only has to
 be computed once.  Modular reduction can now be performed with the following.

 \index{mp\_reduce}
@@ -1312,7 +1316,7 @@ be computed once.  Modular reduction can now be performed with the following.
 int mp_reduce(mp_int *a, mp_int *b, mp_int *c);
 \end{alltt}

-This will reduce $a$ in place modulo $b$ with the precomputed $mu$ value in $c$.  $a$ must be in the range
+This will reduce $a$ in place modulo $b$ with the precomputed $\mu$ value in $c$.  $a$ must be in the range
 $0 \le a < b^2$.

 \begin{alltt}
@@ -1578,7 +1582,8 @@ will return $-2$.
 This algorithm uses the ``Newton Approximation'' method and will converge on the correct root fairly quickly.  Since
 the algorithm requires raising $a$ to the power of $b$ it is not ideal to attempt to find roots for large
 values of $b$.  If particularly large roots are required then a factor method could be used instead.  For example,
-$a^{1/16}$ is equivalent to $\left (a^{1/4} \right)^{1/4}$.
+$a^{1/16}$ is equivalent to $\left (a^{1/4} \right)^{1/4}$ or simply 
+$\left ( \left ( \left ( a^{1/2} \right )^{1/2} \right )^{1/2} \right )^{1/2}$

 \chapter{Prime Numbers}
 \section{Trial Division}
--- a/bn_fast_mp_invmod.c
+++ b/bn_fast_mp_invmod.c
@@ -21,8 +21,7 @@
 * Based on slow invmod except this is optimized for the case where b is 
 * odd as per HAC Note 14.64 on pp. 610
 */
-int
-fast_mp_invmod (mp_int * a, mp_int * b, mp_int * c)
+int fast_mp_invmod (mp_int * a, mp_int * b, mp_int * c)
 {
  mp_int  x, y, u, v, B, D;
  int     res, neg;
@@ -39,20 +38,20 @@ fast_mp_invmod (mp_int * a, mp_int * b, mp_int * c)

  /* x == modulus, y == value to invert */
  if ((res = mp_copy (b, &x)) != MP_OKAY) {
-    goto __ERR;
+    goto LBL_ERR;
  }

  /* we need y = |a| */
-  if ((res = mp_abs (a, &y)) != MP_OKAY) {
-    goto __ERR;
+  if ((res = mp_mod (a, b, &y)) != MP_OKAY) {
+    goto LBL_ERR;
  }

  /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
  if ((res = mp_copy (&x, &u)) != MP_OKAY) {
-    goto __ERR;
+    goto LBL_ERR;
  }
  if ((res = mp_copy (&y, &v)) != MP_OKAY) {
-    goto __ERR;
+    goto LBL_ERR;
  }
  mp_set (&D, 1);

@@ -61,17 +60,17 @@ top:
  while (mp_iseven (&u) == 1) {
    /* 4.1 u = u/2 */
    if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
-      goto __ERR;
+      goto LBL_ERR;
    }
    /* 4.2 if B is odd then */
    if (mp_isodd (&B) == 1) {
      if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
-        goto __ERR;
+        goto LBL_ERR;
      }
    }
    /* B = B/2 */
    if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
-      goto __ERR;
+      goto LBL_ERR;
    }
  }

@@ -79,18 +78,18 @@ top:
  while (mp_iseven (&v) == 1) {
    /* 5.1 v = v/2 */
    if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
-      goto __ERR;
+      goto LBL_ERR;
    }
    /* 5.2 if D is odd then */
    if (mp_isodd (&D) == 1) {
      /* D = (D-x)/2 */
      if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
-        goto __ERR;
+        goto LBL_ERR;
      }
    }
    /* D = D/2 */
    if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
-      goto __ERR;
+      goto LBL_ERR;
    }
  }

@@ -98,20 +97,20 @@ top:
  if (mp_cmp (&u, &v) != MP_LT) {
    /* u = u - v, B = B - D */
    if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) {
-      goto __ERR;
+      goto LBL_ERR;
    }

    if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
-      goto __ERR;
+      goto LBL_ERR;
    }
  } else {
    /* v - v - u, D = D - B */
    if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
-      goto __ERR;
+      goto LBL_ERR;
    }

    if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
-      goto __ERR;
+      goto LBL_ERR;
    }
  }

@@ -125,21 +124,21 @@ top:
  /* if v != 1 then there is no inverse */
  if (mp_cmp_d (&v, 1) != MP_EQ) {
    res = MP_VAL;
-    goto __ERR;
+    goto LBL_ERR;
  }

  /* b is now the inverse */
  neg = a->sign;
  while (D.sign == MP_NEG) {
    if ((res = mp_add (&D, b, &D)) != MP_OKAY) {
-      goto __ERR;
+      goto LBL_ERR;
    }
  }
  mp_exch (&D, c);
  c->sign = neg;
  res = MP_OKAY;

-__ERR:mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL);
+LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL);
  return res;
 }
 #endif
--- a/bn_fast_mp_montgomery_reduce.c
+++ b/bn_fast_mp_montgomery_reduce.c
@@ -23,8 +23,7 @@
 *
 * Based on Algorithm 14.32 on pp.601 of HAC.
 */
-int
-fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
+int fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
 {
  int     ix, res, olduse;
  mp_word W[MP_WARRAY];
--- a/bn_fast_s_mp_mul_digs.c
+++ b/bn_fast_s_mp_mul_digs.c
@@ -31,8 +31,7 @@
 * Based on Algorithm 14.12 on pp.595 of HAC.
 *
 */
-int
-fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
+int fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
 {
  int     olduse, res, pa, ix, iz;
  mp_digit W[MP_WARRAY];
@@ -50,7 +49,7 @@ fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)

  /* clear the carry */
  _W = 0;
-  for (ix = 0; ix <= pa; ix++) { 
+  for (ix = 0; ix < pa; ix++) { 
      int      tx, ty;
      int      iy;
      mp_digit *tmpx, *tmpy;
@@ -63,7 +62,7 @@ fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
      tmpx = a->dp + tx;
      tmpy = b->dp + ty;

-      /* this is the number of times the loop will iterrate, essentially its 
+      /* this is the number of times the loop will iterrate, essentially 
         while (tx++ < a->used && ty-- >= 0) { ... }
       */
      iy = MIN(a->used-tx, ty+1);
@@ -80,14 +79,17 @@ fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
      _W = _W >> ((mp_word)DIGIT_BIT);
  }

+  /* store final carry */
+  W[ix] = (mp_digit)(_W & MP_MASK);
+
  /* setup dest */
  olduse  = c->used;
-  c->used = digs;
+  c->used = pa;

  {
    register mp_digit *tmpc;
    tmpc = c->dp;
-    for (ix = 0; ix < digs; ix++) {
+    for (ix = 0; ix < pa+1; ix++) {
      /* now extract the previous digit [below the carry] */
      *tmpc++ = W[ix];
    }
--- a/bn_fast_s_mp_mul_high_digs.c
+++ b/bn_fast_s_mp_mul_high_digs.c
@@ -24,8 +24,7 @@
 *
 * Based on Algorithm 14.12 on pp.595 of HAC.
 */
-int
-fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
+int fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
 {
  int     olduse, res, pa, ix, iz;
  mp_digit W[MP_WARRAY];
@@ -42,7 +41,7 @@ fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
  /* number of output digits to produce */
  pa = a->used + b->used;
  _W = 0;
-  for (ix = digs; ix <= pa; ix++) { 
+  for (ix = digs; ix < pa; ix++) { 
      int      tx, ty, iy;
      mp_digit *tmpx, *tmpy;

@@ -70,6 +69,9 @@ fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
      /* make next carry */
      _W = _W >> ((mp_word)DIGIT_BIT);
  }
+  
+  /* store final carry */
+  W[ix] = (mp_digit)(_W & MP_MASK);

  /* setup dest */
  olduse  = c->used;
--- a/bn_fast_s_mp_sqr.c
+++ b/bn_fast_s_mp_sqr.c
@@ -15,33 +15,14 @@
 * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
 */

-/* fast squaring
- *
- * This is the comba method where the columns of the product
- * are computed first then the carries are computed.  This
- * has the effect of making a very simple inner loop that
- * is executed the most
- *
- * W2 represents the outer products and W the inner.
- *
- * A further optimizations is made because the inner
- * products are of the form "A * B * 2".  The *2 part does
- * not need to be computed until the end which is good
- * because 64-bit shifts are slow!
- *
- * Based on Algorithm 14.16 on pp.597 of HAC.
- *
- */
 /* the jist of squaring...
-
-you do like mult except the offset of the tmpx [one that starts closer to zero]
-can't equal the offset of tmpy.  So basically you set up iy like before then you min it with
-(ty-tx) so that it never happens.  You double all those you add in the inner loop
+ * you do like mult except the offset of the tmpx [one that 
+ * starts closer to zero] can't equal the offset of tmpy.  
+ * So basically you set up iy like before then you min it with
+ * (ty-tx) so that it never happens.  You double all those 
+ * you add in the inner loop

 After that loop you do the squares and add them in.
-
-Remove W2 and don't memset W
-
 */

 int fast_s_mp_sqr (mp_int * a, mp_int * b)
@@ -60,7 +41,7 @@ int fast_s_mp_sqr (mp_int * a, mp_int * b)

  /* number of output digits to produce */
  W1 = 0;
-  for (ix = 0; ix <= pa; ix++) { 
+  for (ix = 0; ix < pa; ix++) { 
      int      tx, ty, iy;
      mp_word  _W;
      mp_digit *tmpy;
@@ -76,7 +57,7 @@ int fast_s_mp_sqr (mp_int * a, mp_int * b)
      tmpx = a->dp + tx;
      tmpy = a->dp + ty;

-      /* this is the number of times the loop will iterrate, essentially its 
+      /* this is the number of times the loop will iterrate, essentially
         while (tx++ < a->used && ty-- >= 0) { ... }
       */
      iy = MIN(a->used-tx, ty+1);
@@ -101,7 +82,7 @@ int fast_s_mp_sqr (mp_int * a, mp_int * b)
      }

      /* store it */
-      W[ix] = _W;
+      W[ix] = (mp_digit)(_W & MP_MASK);

      /* make next carry */
      W1 = _W >> ((mp_word)DIGIT_BIT);
--- a/bn_mp_div.c
+++ b/bn_mp_div.c
@@ -49,23 +49,23 @@ int mp_div(mp_int * a, mp_int * b, mp_int * c, mp_int * d)

  mp_set(&tq, 1);
  n = mp_count_bits(a) - mp_count_bits(b);
-  if (((res = mp_copy(a, &ta)) != MP_OKAY) ||
-      ((res = mp_copy(b, &tb)) != MP_OKAY) || 
+  if (((res = mp_abs(a, &ta)) != MP_OKAY) ||
+      ((res = mp_abs(b, &tb)) != MP_OKAY) || 
      ((res = mp_mul_2d(&tb, n, &tb)) != MP_OKAY) ||
      ((res = mp_mul_2d(&tq, n, &tq)) != MP_OKAY)) {
-      goto __ERR;
+      goto LBL_ERR;
  }

  while (n-- >= 0) {
     if (mp_cmp(&tb, &ta) != MP_GT) {
        if (((res = mp_sub(&ta, &tb, &ta)) != MP_OKAY) ||
            ((res = mp_add(&q, &tq, &q)) != MP_OKAY)) {
-           goto __ERR;
+           goto LBL_ERR;
        }
     }
     if (((res = mp_div_2d(&tb, 1, &tb, NULL)) != MP_OKAY) ||
         ((res = mp_div_2d(&tq, 1, &tq, NULL)) != MP_OKAY)) {
-           goto __ERR;
+           goto LBL_ERR;
     }
  }

@@ -74,13 +74,13 @@ int mp_div(mp_int * a, mp_int * b, mp_int * c, mp_int * d)
  n2 = (a->sign == b->sign ? MP_ZPOS : MP_NEG);
  if (c != NULL) {
     mp_exch(c, &q);
-     c->sign  = n2;
+     c->sign  = (mp_iszero(c) == MP_YES) ? MP_ZPOS : n2;
  }
  if (d != NULL) {
     mp_exch(d, &ta);
-     d->sign = n;
+     d->sign = (mp_iszero(d) == MP_YES) ? MP_ZPOS : n;
  }
-__ERR:
+LBL_ERR:
   mp_clear_multi(&ta, &tb, &tq, &q, NULL);
   return res;
 }
@@ -129,19 +129,19 @@ int mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
  q.used = a->used + 2;

  if ((res = mp_init (&t1)) != MP_OKAY) {
-    goto __Q;
+    goto LBL_Q;
  }

  if ((res = mp_init (&t2)) != MP_OKAY) {
-    goto __T1;
+    goto LBL_T1;
  }

  if ((res = mp_init_copy (&x, a)) != MP_OKAY) {
-    goto __T2;
+    goto LBL_T2;
  }

  if ((res = mp_init_copy (&y, b)) != MP_OKAY) {
-    goto __X;
+    goto LBL_X;
  }

  /* fix the sign */
@@ -153,10 +153,10 @@ int mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
  if (norm < (int)(DIGIT_BIT-1)) {
     norm = (DIGIT_BIT-1) - norm;
     if ((res = mp_mul_2d (&x, norm, &x)) != MP_OKAY) {
-       goto __Y;
+       goto LBL_Y;
     }
     if ((res = mp_mul_2d (&y, norm, &y)) != MP_OKAY) {
-       goto __Y;
+       goto LBL_Y;
     }
  } else {
     norm = 0;
@@ -168,13 +168,13 @@ int mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d)

  /* while (x >= y*b**n-t) do { q[n-t] += 1; x -= y*b**{n-t} } */
  if ((res = mp_lshd (&y, n - t)) != MP_OKAY) { /* y = y*b**{n-t} */
-    goto __Y;
+    goto LBL_Y;
  }

  while (mp_cmp (&x, &y) != MP_LT) {
    ++(q.dp[n - t]);
    if ((res = mp_sub (&x, &y, &x)) != MP_OKAY) {
-      goto __Y;
+      goto LBL_Y;
    }
  }

@@ -216,7 +216,7 @@ int mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
      t1.dp[1] = y.dp[t];
      t1.used = 2;
      if ((res = mp_mul_d (&t1, q.dp[i - t - 1], &t1)) != MP_OKAY) {
-        goto __Y;
+        goto LBL_Y;
      }

      /* find right hand */
@@ -228,27 +228,27 @@ int mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d)

    /* step 3.3 x = x - q{i-t-1} * y * b**{i-t-1} */
    if ((res = mp_mul_d (&y, q.dp[i - t - 1], &t1)) != MP_OKAY) {
-      goto __Y;
+      goto LBL_Y;
    }

    if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) {
-      goto __Y;
+      goto LBL_Y;
    }

    if ((res = mp_sub (&x, &t1, &x)) != MP_OKAY) {
-      goto __Y;
+      goto LBL_Y;
    }

    /* if x < 0 then { x = x + y*b**{i-t-1}; q{i-t-1} -= 1; } */
    if (x.sign == MP_NEG) {
      if ((res = mp_copy (&y, &t1)) != MP_OKAY) {
-        goto __Y;
+        goto LBL_Y;
      }
      if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) {
-        goto __Y;
+        goto LBL_Y;
      }
      if ((res = mp_add (&x, &t1, &x)) != MP_OKAY) {
-        goto __Y;
+        goto LBL_Y;
      }

      q.dp[i - t - 1] = (q.dp[i - t - 1] - 1UL) & MP_MASK;
@@ -275,11 +275,11 @@ int mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d)

  res = MP_OKAY;

-__Y:mp_clear (&y);
-__X:mp_clear (&x);
-__T2:mp_clear (&t2);
-__T1:mp_clear (&t1);
-__Q:mp_clear (&q);
+LBL_Y:mp_clear (&y);
+LBL_X:mp_clear (&x);
+LBL_T2:mp_clear (&t2);
+LBL_T1:mp_clear (&t1);
+LBL_Q:mp_clear (&q);
  return res;
 }

--- a/bn_mp_dr_reduce.c
+++ b/bn_mp_dr_reduce.c
@@ -20,7 +20,7 @@
 * Based on algorithm from the paper
 *
 * "Generating Efficient Primes for Discrete Log Cryptosystems"
- *                 Chae Hoon Lim, Pil Loong Lee,
+ *                 Chae Hoon Lim, Pil Joong Lee,
 *          POSTECH Information Research Laboratories
 *
 * The modulus must be of a special format [see manual]
--- a/bn_mp_exptmod.c
+++ b/bn_mp_exptmod.c
@@ -61,25 +61,33 @@ int mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
     return err;
 #else 
     /* no invmod */
-     return MP_VAL
+     return MP_VAL;
 #endif
  }

+/* modified diminished radix reduction */
+#if defined(BN_MP_REDUCE_IS_2K_L_C) && defined(BN_MP_REDUCE_2K_L_C)
+  if (mp_reduce_is_2k_l(P) == MP_YES) {
+     return s_mp_exptmod(G, X, P, Y, 1);
+  }
+#endif
+
 #ifdef BN_MP_DR_IS_MODULUS_C
  /* is it a DR modulus? */
  dr = mp_dr_is_modulus(P);
 #else
+  /* default to no */
  dr = 0;
 #endif

 #ifdef BN_MP_REDUCE_IS_2K_C
-  /* if not, is it a uDR modulus? */
+  /* if not, is it a unrestricted DR modulus? */
  if (dr == 0) {
     dr = mp_reduce_is_2k(P) << 1;
  }
 #endif
    
-  /* if the modulus is odd or dr != 0 use the fast method */
+  /* if the modulus is odd or dr != 0 use the montgomery method */
 #ifdef BN_MP_EXPTMOD_FAST_C
  if (mp_isodd (P) == 1 || dr !=  0) {
    return mp_exptmod_fast (G, X, P, Y, dr);
@@ -87,7 +95,7 @@ int mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
 #endif
 #ifdef BN_S_MP_EXPTMOD_C
    /* otherwise use the generic Barrett reduction technique */
-    return s_mp_exptmod (G, X, P, Y);
+    return s_mp_exptmod (G, X, P, Y, 0);
 #else
    /* no exptmod for evens */
    return MP_VAL;
--- a/bn_mp_exptmod_fast.c
+++ b/bn_mp_exptmod_fast.c
@@ -29,8 +29,7 @@
   #define TAB_SIZE 256
 #endif

-int
-mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
+int mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
 {
  mp_int  M[TAB_SIZE], res;
  mp_digit buf, mp;
@@ -88,11 +87,11 @@ mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
 #ifdef BN_MP_MONTGOMERY_SETUP_C     
     /* now setup montgomery  */
     if ((err = mp_montgomery_setup (P, &mp)) != MP_OKAY) {
-        goto __M;
+        goto LBL_M;
     }
 #else
     err = MP_VAL;
-     goto __M;
+     goto LBL_M;
 #endif

     /* automatically pick the comba one if available (saves quite a few calls/ifs) */
@@ -108,7 +107,7 @@ mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
        redux = mp_montgomery_reduce;
 #else
        err = MP_VAL;
-        goto __M;
+        goto LBL_M;
 #endif
     }
  } else if (redmode == 1) {
@@ -118,24 +117,24 @@ mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
     redux = mp_dr_reduce;
 #else
     err = MP_VAL;
-     goto __M;
+     goto LBL_M;
 #endif
  } else {
 #if defined(BN_MP_REDUCE_2K_SETUP_C) && defined(BN_MP_REDUCE_2K_C)
     /* setup DR reduction for moduli of the form 2**k - b */
     if ((err = mp_reduce_2k_setup(P, &mp)) != MP_OKAY) {
-        goto __M;
+        goto LBL_M;
     }
     redux = mp_reduce_2k;
 #else
     err = MP_VAL;
-     goto __M;
+     goto LBL_M;
 #endif
  }

  /* setup result */
  if ((err = mp_init (&res)) != MP_OKAY) {
-    goto __M;
+    goto LBL_M;
  }

  /* create M table
@@ -149,45 +148,45 @@ mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
 #ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
     /* now we need R mod m */
     if ((err = mp_montgomery_calc_normalization (&res, P)) != MP_OKAY) {
-       goto __RES;
+       goto LBL_RES;
     }
 #else 
     err = MP_VAL;
-     goto __RES;
+     goto LBL_RES;
 #endif

     /* now set M[1] to G * R mod m */
     if ((err = mp_mulmod (G, &res, P, &M[1])) != MP_OKAY) {
-       goto __RES;
+       goto LBL_RES;
     }
  } else {
     mp_set(&res, 1);
     if ((err = mp_mod(G, P, &M[1])) != MP_OKAY) {
-        goto __RES;
+        goto LBL_RES;
     }
  }

  /* compute the value at M[1<<(winsize-1)] by squaring M[1] (winsize-1) times */
  if ((err = mp_copy (&M[1], &M[1 << (winsize - 1)])) != MP_OKAY) {
-    goto __RES;
+    goto LBL_RES;
  }

  for (x = 0; x < (winsize - 1); x++) {
    if ((err = mp_sqr (&M[1 << (winsize - 1)], &M[1 << (winsize - 1)])) != MP_OKAY) {
-      goto __RES;
+      goto LBL_RES;
    }
    if ((err = redux (&M[1 << (winsize - 1)], P, mp)) != MP_OKAY) {
-      goto __RES;
+      goto LBL_RES;
    }
  }

  /* create upper table */
  for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) {
    if ((err = mp_mul (&M[x - 1], &M[1], &M[x])) != MP_OKAY) {
-      goto __RES;
+      goto LBL_RES;
    }
    if ((err = redux (&M[x], P, mp)) != MP_OKAY) {
-      goto __RES;
+      goto LBL_RES;
    }
  }

@@ -227,10 +226,10 @@ mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
    /* if the bit is zero and mode == 1 then we square */
    if (mode == 1 && y == 0) {
      if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
-        goto __RES;
+        goto LBL_RES;
      }
      if ((err = redux (&res, P, mp)) != MP_OKAY) {
-        goto __RES;
+        goto LBL_RES;
      }
      continue;
    }
@@ -244,19 +243,19 @@ mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
      /* square first */
      for (x = 0; x < winsize; x++) {
        if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
-          goto __RES;
+          goto LBL_RES;
        }
        if ((err = redux (&res, P, mp)) != MP_OKAY) {
-          goto __RES;
+          goto LBL_RES;
        }
      }

      /* then multiply */
      if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) {
-        goto __RES;
+        goto LBL_RES;
      }
      if ((err = redux (&res, P, mp)) != MP_OKAY) {
-        goto __RES;
+        goto LBL_RES;
      }

      /* empty window and reset */
@@ -271,10 +270,10 @@ mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
    /* square then multiply if the bit is set */
    for (x = 0; x < bitcpy; x++) {
      if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
-        goto __RES;
+        goto LBL_RES;
      }
      if ((err = redux (&res, P, mp)) != MP_OKAY) {
-        goto __RES;
+        goto LBL_RES;
      }

      /* get next bit of the window */
@@ -282,10 +281,10 @@ mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
      if ((bitbuf & (1 << winsize)) != 0) {
        /* then multiply */
        if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) {
-          goto __RES;
+          goto LBL_RES;
        }
        if ((err = redux (&res, P, mp)) != MP_OKAY) {
-          goto __RES;
+          goto LBL_RES;
        }
      }
    }
@@ -299,15 +298,15 @@ mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
      * of R.
      */
     if ((err = redux(&res, P, mp)) != MP_OKAY) {
-       goto __RES;
+       goto LBL_RES;
     }
  }

  /* swap res with Y */
  mp_exch (&res, Y);
  err = MP_OKAY;
-__RES:mp_clear (&res);
-__M:
+LBL_RES:mp_clear (&res);
+LBL_M:
  mp_clear(&M[1]);
  for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
    mp_clear (&M[x]);
--- a/bn_mp_exteuclid.c
+++ b/bn_mp_exteuclid.c
@@ -59,6 +59,13 @@ int mp_exteuclid(mp_int *a, mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3)
       if ((err = mp_copy(&t3, &v3)) != MP_OKAY)                                  { goto _ERR; }
   }

+   /* make sure U3 >= 0 */
+   if (u3.sign == MP_NEG) {
+      mp_neg(&u1, &u1);
+      mp_neg(&u2, &u2);
+      mp_neg(&u3, &u3);
+   }
+
   /* copy result out */
   if (U1 != NULL) { mp_exch(U1, &u1); }
   if (U2 != NULL) { mp_exch(U2, &u2); }
--- a/bn_mp_gcd.c
+++ b/bn_mp_gcd.c
@@ -43,7 +43,7 @@ int mp_gcd (mp_int * a, mp_int * b, mp_int * c)
  }

  if ((res = mp_init_copy (&v, b)) != MP_OKAY) {
-    goto __U;
+    goto LBL_U;
  }

  /* must be positive for the remainder of the algorithm */
@@ -57,24 +57,24 @@ int mp_gcd (mp_int * a, mp_int * b, mp_int * c)
  if (k > 0) {
     /* divide the power of two out */
     if ((res = mp_div_2d(&u, k, &u, NULL)) != MP_OKAY) {
-        goto __V;
+        goto LBL_V;
     }

     if ((res = mp_div_2d(&v, k, &v, NULL)) != MP_OKAY) {
-        goto __V;
+        goto LBL_V;
     }
  }

  /* divide any remaining factors of two out */
  if (u_lsb != k) {
     if ((res = mp_div_2d(&u, u_lsb - k, &u, NULL)) != MP_OKAY) {
-        goto __V;
+        goto LBL_V;
     }
  }

  if (v_lsb != k) {
     if ((res = mp_div_2d(&v, v_lsb - k, &v, NULL)) != MP_OKAY) {
-        goto __V;
+        goto LBL_V;
     }
  }

@@ -87,23 +87,23 @@ int mp_gcd (mp_int * a, mp_int * b, mp_int * c)
     
     /* subtract smallest from largest */
     if ((res = s_mp_sub(&v, &u, &v)) != MP_OKAY) {
-        goto __V;
+        goto LBL_V;
     }
     
     /* Divide out all factors of two */
     if ((res = mp_div_2d(&v, mp_cnt_lsb(&v), &v, NULL)) != MP_OKAY) {
-        goto __V;
+        goto LBL_V;
     } 
  } 

  /* multiply by 2**k which we divided out at the beginning */
  if ((res = mp_mul_2d (&u, k, c)) != MP_OKAY) {
-     goto __V;
+     goto LBL_V;
  }
  c->sign = MP_ZPOS;
  res = MP_OKAY;
-__V:mp_clear (&u);
-__U:mp_clear (&v);
+LBL_V:mp_clear (&u);
+LBL_U:mp_clear (&v);
  return res;
 }
 #endif
--- a/bn_mp_invmod_slow.c
+++ b/bn_mp_invmod_slow.c
@@ -33,25 +33,25 @@ int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c)
  }

  /* x = a, y = b */
-  if ((res = mp_copy (a, &x)) != MP_OKAY) {
-    goto __ERR;
+  if ((res = mp_mod(a, b, &x)) != MP_OKAY) {
+      goto LBL_ERR;
  }
  if ((res = mp_copy (b, &y)) != MP_OKAY) {
-    goto __ERR;
+    goto LBL_ERR;
  }

  /* 2. [modified] if x,y are both even then return an error! */
  if (mp_iseven (&x) == 1 && mp_iseven (&y) == 1) {
    res = MP_VAL;
-    goto __ERR;
+    goto LBL_ERR;
  }

  /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
  if ((res = mp_copy (&x, &u)) != MP_OKAY) {
-    goto __ERR;
+    goto LBL_ERR;
  }
  if ((res = mp_copy (&y, &v)) != MP_OKAY) {
-    goto __ERR;
+    goto LBL_ERR;
  }
  mp_set (&A, 1);
  mp_set (&D, 1);
@@ -61,24 +61,24 @@ top:
  while (mp_iseven (&u) == 1) {
    /* 4.1 u = u/2 */
    if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
-      goto __ERR;
+      goto LBL_ERR;
    }
    /* 4.2 if A or B is odd then */
    if (mp_isodd (&A) == 1 || mp_isodd (&B) == 1) {
      /* A = (A+y)/2, B = (B-x)/2 */
      if ((res = mp_add (&A, &y, &A)) != MP_OKAY) {
-         goto __ERR;
+         goto LBL_ERR;
      }
      if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
-         goto __ERR;
+         goto LBL_ERR;
      }
    }
    /* A = A/2, B = B/2 */
    if ((res = mp_div_2 (&A, &A)) != MP_OKAY) {
-      goto __ERR;
+      goto LBL_ERR;
    }
    if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
-      goto __ERR;
+      goto LBL_ERR;
    }
  }

@@ -86,24 +86,24 @@ top:
  while (mp_iseven (&v) == 1) {
    /* 5.1 v = v/2 */
    if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
-      goto __ERR;
+      goto LBL_ERR;
    }
    /* 5.2 if C or D is odd then */
    if (mp_isodd (&C) == 1 || mp_isodd (&D) == 1) {
      /* C = (C+y)/2, D = (D-x)/2 */
      if ((res = mp_add (&C, &y, &C)) != MP_OKAY) {
-         goto __ERR;
+         goto LBL_ERR;
      }
      if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
-         goto __ERR;
+         goto LBL_ERR;
      }
    }
    /* C = C/2, D = D/2 */
    if ((res = mp_div_2 (&C, &C)) != MP_OKAY) {
-      goto __ERR;
+      goto LBL_ERR;
    }
    if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
-      goto __ERR;
+      goto LBL_ERR;
    }
  }

@@ -111,28 +111,28 @@ top:
  if (mp_cmp (&u, &v) != MP_LT) {
    /* u = u - v, A = A - C, B = B - D */
    if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) {
-      goto __ERR;
+      goto LBL_ERR;
    }

    if ((res = mp_sub (&A, &C, &A)) != MP_OKAY) {
-      goto __ERR;
+      goto LBL_ERR;
    }

    if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
-      goto __ERR;
+      goto LBL_ERR;
    }
  } else {
    /* v - v - u, C = C - A, D = D - B */
    if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
-      goto __ERR;
+      goto LBL_ERR;
    }

    if ((res = mp_sub (&C, &A, &C)) != MP_OKAY) {
-      goto __ERR;
+      goto LBL_ERR;
    }

    if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
-      goto __ERR;
+      goto LBL_ERR;
    }
  }

@@ -145,27 +145,27 @@ top:
  /* if v != 1 then there is no inverse */
  if (mp_cmp_d (&v, 1) != MP_EQ) {
    res = MP_VAL;
-    goto __ERR;
+    goto LBL_ERR;
  }

  /* if its too low */
  while (mp_cmp_d(&C, 0) == MP_LT) {
      if ((res = mp_add(&C, b, &C)) != MP_OKAY) {
-         goto __ERR;
+         goto LBL_ERR;
      }
  }
  
  /* too big */
  while (mp_cmp_mag(&C, b) != MP_LT) {
      if ((res = mp_sub(&C, b, &C)) != MP_OKAY) {
-         goto __ERR;
+         goto LBL_ERR;
      }
  }
  
  /* C is now the inverse */
  mp_exch (&C, c);
  res = MP_OKAY;
-__ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL);
+LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL);
  return res;
 }
 #endif
--- a/bn_mp_jacobi.c
+++ b/bn_mp_jacobi.c
@@ -50,13 +50,13 @@ int mp_jacobi (mp_int * a, mp_int * p, int *c)
  }

  if ((res = mp_init (&p1)) != MP_OKAY) {
-    goto __A1;
+    goto LBL_A1;
  }

  /* divide out larger power of two */
  k = mp_cnt_lsb(&a1);
  if ((res = mp_div_2d(&a1, k, &a1, NULL)) != MP_OKAY) {
-     goto __P1;
+     goto LBL_P1;
  }

  /* step 4.  if e is even set s=1 */
@@ -84,18 +84,18 @@ int mp_jacobi (mp_int * a, mp_int * p, int *c)
  } else {
    /* n1 = n mod a1 */
    if ((res = mp_mod (p, &a1, &p1)) != MP_OKAY) {
-      goto __P1;
+      goto LBL_P1;
    }
    if ((res = mp_jacobi (&p1, &a1, &r)) != MP_OKAY) {
-      goto __P1;
+      goto LBL_P1;
    }
    *c = s * r;
  }

  /* done */
  res = MP_OKAY;
-__P1:mp_clear (&p1);
-__A1:mp_clear (&a1);
+LBL_P1:mp_clear (&p1);
+LBL_A1:mp_clear (&a1);
  return res;
 }
 #endif
--- a/bn_mp_lcm.c
+++ b/bn_mp_lcm.c
@@ -28,20 +28,20 @@ int mp_lcm (mp_int * a, mp_int * b, mp_int * c)

  /* t1 = get the GCD of the two inputs */
  if ((res = mp_gcd (a, b, &t1)) != MP_OKAY) {
-    goto __T;
+    goto LBL_T;
  }

  /* divide the smallest by the GCD */
  if (mp_cmp_mag(a, b) == MP_LT) {
     /* store quotient in t2 such that t2 * b is the LCM */
     if ((res = mp_div(a, &t1, &t2, NULL)) != MP_OKAY) {
-        goto __T;
+        goto LBL_T;
     }
     res = mp_mul(b, &t2, c);
  } else {
     /* store quotient in t2 such that t2 * a is the LCM */
     if ((res = mp_div(b, &t1, &t2, NULL)) != MP_OKAY) {
-        goto __T;
+        goto LBL_T;
     }
     res = mp_mul(a, &t2, c);
  }
@@ -49,7 +49,7 @@ int mp_lcm (mp_int * a, mp_int * b, mp_int * c)
  /* fix the sign to positive */
  c->sign = MP_ZPOS;

-__T:
+LBL_T:
  mp_clear_multi (&t1, &t2, NULL);
  return res;
 }
--- a/bn_mp_mod_2d.c
+++ b/bn_mp_mod_2d.c
@@ -28,7 +28,7 @@ mp_mod_2d (mp_int * a, int b, mp_int * c)
  }

  /* if the modulus is larger than the value than return */
-  if (b > (int) (a->used * DIGIT_BIT)) {
+  if (b >= (int) (a->used * DIGIT_BIT)) {
    res = mp_copy (a, c);
    return res;
  }
--- a/bn_mp_montgomery_calc_normalization.c
+++ b/bn_mp_montgomery_calc_normalization.c
@@ -28,7 +28,6 @@ int mp_montgomery_calc_normalization (mp_int * a, mp_int * b)
  /* how many bits of last digit does b use */
  bits = mp_count_bits (b) % DIGIT_BIT;

-
  if (b->used > 1) {
     if ((res = mp_2expt (a, (b->used - 1) * DIGIT_BIT + bits - 1)) != MP_OKAY) {
        return res;
--- a/bn_mp_mul_d.c
+++ b/bn_mp_mul_d.c
@@ -57,8 +57,9 @@ mp_mul_d (mp_int * a, mp_digit b, mp_int * c)
    u       = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
  }

-  /* store final carry [if any] */
+  /* store final carry [if any] and increment ix offset  */
  *tmpc++ = u;
+  ++ix;

  /* now zero digits above the top */
  while (ix++ < olduse) {
--- a/bn_mp_n_root.c
+++ b/bn_mp_n_root.c
@@ -40,11 +40,11 @@ int mp_n_root (mp_int * a, mp_digit b, mp_int * c)
  }

  if ((res = mp_init (&t2)) != MP_OKAY) {
-    goto __T1;
+    goto LBL_T1;
  }

  if ((res = mp_init (&t3)) != MP_OKAY) {
-    goto __T2;
+    goto LBL_T2;
  }

  /* if a is negative fudge the sign but keep track */
@@ -57,52 +57,52 @@ int mp_n_root (mp_int * a, mp_digit b, mp_int * c)
  do {
    /* t1 = t2 */
    if ((res = mp_copy (&t2, &t1)) != MP_OKAY) {
-      goto __T3;
+      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 __T3;
+      goto LBL_T3;
    }

    /* numerator */
    /* t2 = t1**b */
    if ((res = mp_mul (&t3, &t1, &t2)) != MP_OKAY) {    
-      goto __T3;
+      goto LBL_T3;
    }

    /* t2 = t1**b - a */
    if ((res = mp_sub (&t2, a, &t2)) != MP_OKAY) {  
-      goto __T3;
+      goto LBL_T3;
    }

    /* denominator */
    /* t3 = t1**(b-1) * b  */
    if ((res = mp_mul_d (&t3, b, &t3)) != MP_OKAY) {    
-      goto __T3;
+      goto LBL_T3;
    }

    /* t3 = (t1**b - a)/(b * t1**(b-1)) */
    if ((res = mp_div (&t2, &t3, &t3, NULL)) != MP_OKAY) {  
-      goto __T3;
+      goto LBL_T3;
    }

    if ((res = mp_sub (&t1, &t3, &t2)) != MP_OKAY) {
-      goto __T3;
+      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 __T3;
+      goto LBL_T3;
    }

    if (mp_cmp (&t2, a) == MP_GT) {
      if ((res = mp_sub_d (&t1, 1, &t1)) != MP_OKAY) {
-         goto __T3;
+         goto LBL_T3;
      }
    } else {
      break;
@@ -120,9 +120,9 @@ int mp_n_root (mp_int * a, mp_digit b, mp_int * c)

  res = MP_OKAY;

-__T3:mp_clear (&t3);
-__T2:mp_clear (&t2);
-__T1:mp_clear (&t1);
+LBL_T3:mp_clear (&t3);
+LBL_T2:mp_clear (&t2);
+LBL_T1:mp_clear (&t1);
  return res;
 }
 #endif
--- a/bn_mp_neg.c
+++ b/bn_mp_neg.c
@@ -19,12 +19,18 @@
 int mp_neg (mp_int * a, mp_int * b)
 {
  int     res;
-  if ((res = mp_copy (a, b)) != MP_OKAY) {
-    return res;
+  if (a != b) {
+     if ((res = mp_copy (a, b)) != MP_OKAY) {
+        return res;
+     }
  }
+
  if (mp_iszero(b) != MP_YES) {
     b->sign = (a->sign == MP_ZPOS) ? MP_NEG : MP_ZPOS;
+  } else {
+     b->sign = MP_ZPOS;
  }
+
  return MP_OKAY;
 }
 #endif
--- a/bn_mp_prime_fermat.c
+++ b/bn_mp_prime_fermat.c
@@ -43,7 +43,7 @@ int mp_prime_fermat (mp_int * a, mp_int * b, int *result)

  /* compute t = b**a mod a */
  if ((err = mp_exptmod (b, a, a, &t)) != MP_OKAY) {
-    goto __T;
+    goto LBL_T;
  }

  /* is it equal to b? */
@@ -52,7 +52,7 @@ int mp_prime_fermat (mp_int * a, mp_int * b, int *result)
  }

  err = MP_OKAY;
-__T:mp_clear (&t);
+LBL_T:mp_clear (&t);
  return err;
 }
 #endif
--- a/bn_mp_prime_is_divisible.c
+++ b/bn_mp_prime_is_divisible.c
@@ -29,8 +29,8 @@ int mp_prime_is_divisible (mp_int * a, int *result)
  *result = MP_NO;

  for (ix = 0; ix < PRIME_SIZE; ix++) {
-    /* what is a mod __prime_tab[ix] */
-    if ((err = mp_mod_d (a, __prime_tab[ix], &res)) != MP_OKAY) {
+    /* what is a mod LBL_prime_tab[ix] */
+    if ((err = mp_mod_d (a, ltm_prime_tab[ix], &res)) != MP_OKAY) {
      return err;
    }

--- a/bn_mp_prime_is_prime.c
+++ b/bn_mp_prime_is_prime.c
@@ -37,7 +37,7 @@ int mp_prime_is_prime (mp_int * a, int t, int *result)

  /* is the input equal to one of the primes in the table? */
  for (ix = 0; ix < PRIME_SIZE; ix++) {
-      if (mp_cmp_d(a, __prime_tab[ix]) == MP_EQ) {
+      if (mp_cmp_d(a, ltm_prime_tab[ix]) == MP_EQ) {
         *result = 1;
         return MP_OKAY;
      }
@@ -60,20 +60,20 @@ int mp_prime_is_prime (mp_int * a, int t, int *result)

  for (ix = 0; ix < t; ix++) {
    /* set the prime */
-    mp_set (&b, __prime_tab[ix]);
+    mp_set (&b, ltm_prime_tab[ix]);

    if ((err = mp_prime_miller_rabin (a, &b, &res)) != MP_OKAY) {
-      goto __B;
+      goto LBL_B;
    }

    if (res == MP_NO) {
-      goto __B;
+      goto LBL_B;
    }
  }

  /* passed the test */
  *result = MP_YES;
-__B:mp_clear (&b);
+LBL_B:mp_clear (&b);
  return err;
 }
 #endif
--- a/bn_mp_prime_miller_rabin.c
+++ b/bn_mp_prime_miller_rabin.c
@@ -40,12 +40,12 @@ int mp_prime_miller_rabin (mp_int * a, mp_int * b, int *result)
    return err;
  }
  if ((err = mp_sub_d (&n1, 1, &n1)) != MP_OKAY) {
-    goto __N1;
+    goto LBL_N1;
  }

  /* set 2**s * r = n1 */
  if ((err = mp_init_copy (&r, &n1)) != MP_OKAY) {
-    goto __N1;
+    goto LBL_N1;
  }

  /* count the number of least significant bits
@@ -55,15 +55,15 @@ int mp_prime_miller_rabin (mp_int * a, mp_int * b, int *result)

  /* now divide n - 1 by 2**s */
  if ((err = mp_div_2d (&r, s, &r, NULL)) != MP_OKAY) {
-    goto __R;
+    goto LBL_R;
  }

  /* compute y = b**r mod a */
  if ((err = mp_init (&y)) != MP_OKAY) {
-    goto __R;
+    goto LBL_R;
  }
  if ((err = mp_exptmod (b, &r, a, &y)) != MP_OKAY) {
-    goto __Y;
+    goto LBL_Y;
  }

  /* if y != 1 and y != n1 do */
@@ -72,12 +72,12 @@ int mp_prime_miller_rabin (mp_int * a, mp_int * b, int *result)
    /* while j <= s-1 and y != n1 */
    while ((j <= (s - 1)) && mp_cmp (&y, &n1) != MP_EQ) {
      if ((err = mp_sqrmod (&y, a, &y)) != MP_OKAY) {
-         goto __Y;
+         goto LBL_Y;
      }

      /* if y == 1 then composite */
      if (mp_cmp_d (&y, 1) == MP_EQ) {
-         goto __Y;
+         goto LBL_Y;
      }

      ++j;
@@ -85,15 +85,15 @@ int mp_prime_miller_rabin (mp_int * a, mp_int * b, int *result)

    /* if y != n1 then composite */
    if (mp_cmp (&y, &n1) != MP_EQ) {
-      goto __Y;
+      goto LBL_Y;
    }
  }

  /* probably prime now */
  *result = MP_YES;
-__Y:mp_clear (&y);
-__R:mp_clear (&r);
-__N1:mp_clear (&n1);
+LBL_Y:mp_clear (&y);
+LBL_R:mp_clear (&r);
+LBL_N1:mp_clear (&n1);
  return err;
 }
 #endif
--- a/bn_mp_prime_next_prime.c
+++ b/bn_mp_prime_next_prime.c
@@ -35,10 +35,10 @@ int mp_prime_next_prime(mp_int *a, int t, int bbs_style)
   a->sign = MP_ZPOS;

   /* simple algo if a is less than the largest prime in the table */
-   if (mp_cmp_d(a, __prime_tab[PRIME_SIZE-1]) == MP_LT) {
+   if (mp_cmp_d(a, ltm_prime_tab[PRIME_SIZE-1]) == MP_LT) {
      /* find which prime it is bigger than */
      for (x = PRIME_SIZE - 2; x >= 0; x--) {
-          if (mp_cmp_d(a, __prime_tab[x]) != MP_LT) {
+          if (mp_cmp_d(a, ltm_prime_tab[x]) != MP_LT) {
             if (bbs_style == 1) {
                /* ok we found a prime smaller or
                 * equal [so the next is larger]
@@ -46,17 +46,17 @@ int mp_prime_next_prime(mp_int *a, int t, int bbs_style)
                 * however, the prime must be
                 * congruent to 3 mod 4
                 */
-                if ((__prime_tab[x + 1] & 3) != 3) {
+                if ((ltm_prime_tab[x + 1] & 3) != 3) {
                   /* scan upwards for a prime congruent to 3 mod 4 */
                   for (y = x + 1; y < PRIME_SIZE; y++) {
-                       if ((__prime_tab[y] & 3) == 3) {
-                          mp_set(a, __prime_tab[y]);
+                       if ((ltm_prime_tab[y] & 3) == 3) {
+                          mp_set(a, ltm_prime_tab[y]);
                          return MP_OKAY;
                       }
                   }
                }
             } else {
-                mp_set(a, __prime_tab[x + 1]);
+                mp_set(a, ltm_prime_tab[x + 1]);
                return MP_OKAY;
             }
          }
@@ -94,7 +94,7 @@ int mp_prime_next_prime(mp_int *a, int t, int bbs_style)

   /* generate the restable */
   for (x = 1; x < PRIME_SIZE; x++) {
-      if ((err = mp_mod_d(a, __prime_tab[x], res_tab + x)) != MP_OKAY) {
+      if ((err = mp_mod_d(a, ltm_prime_tab[x], res_tab + x)) != MP_OKAY) {
         return err;
      }
   }
@@ -120,8 +120,8 @@ int mp_prime_next_prime(mp_int *a, int t, int bbs_style)
             res_tab[x] += kstep;

             /* subtract the modulus [instead of using division] */
-             if (res_tab[x] >= __prime_tab[x]) {
-                res_tab[x]  -= __prime_tab[x];
+             if (res_tab[x] >= ltm_prime_tab[x]) {
+                res_tab[x]  -= ltm_prime_tab[x];
             }

             /* set flag if zero */
@@ -133,7 +133,7 @@ int mp_prime_next_prime(mp_int *a, int t, int bbs_style)

      /* add the step */
      if ((err = mp_add_d(a, step, a)) != MP_OKAY) {
-         goto __ERR;
+         goto LBL_ERR;
      }

      /* if didn't pass sieve and step == MAX then skip test */
@@ -143,9 +143,9 @@ int mp_prime_next_prime(mp_int *a, int t, int bbs_style)

      /* is this prime? */
      for (x = 0; x < t; x++) {
-          mp_set(&b, __prime_tab[t]);
+          mp_set(&b, ltm_prime_tab[t]);
          if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) {
-             goto __ERR;
+             goto LBL_ERR;
          }
          if (res == MP_NO) {
             break;
@@ -158,7 +158,7 @@ int mp_prime_next_prime(mp_int *a, int t, int bbs_style)
   }

   err = MP_OKAY;
-__ERR:
+LBL_ERR:
   mp_clear(&b);
   return err;
 }
--- a/bn_mp_prime_random_ex.c
+++ b/bn_mp_prime_random_ex.c
@@ -47,7 +47,7 @@ int mp_prime_random_ex(mp_int *a, int t, int size, int flags, ltm_prime_callback
   }

   /* calc the byte size */
-   bsize = (size>>3)+(size&7?1:0);
+   bsize = (size>>3) + ((size&7)?1:0);

   /* we need a buffer of bsize bytes */
   tmp = OPT_CAST(unsigned char) XMALLOC(bsize);
@@ -56,19 +56,19 @@ int mp_prime_random_ex(mp_int *a, int t, int size, int flags, ltm_prime_callback
   }

   /* calc the maskAND value for the MSbyte*/
-   maskAND = 0xFF >> (8 - (size & 7));
+   maskAND = ((size&7) == 0) ? 0xFF : (0xFF >> (8 - (size & 7)));

   /* calc the maskOR_msb */
   maskOR_msb        = 0;
-   maskOR_msb_offset = (size - 2) >> 3;
+   maskOR_msb_offset = ((size & 7) == 1) ? 1 : 0;
   if (flags & LTM_PRIME_2MSB_ON) {
      maskOR_msb     |= 1 << ((size - 2) & 7);
   } else if (flags & LTM_PRIME_2MSB_OFF) {
      maskAND        &= ~(1 << ((size - 2) & 7));
-   }
+   } 

   /* get the maskOR_lsb */
-   maskOR_lsb         = 0;
+   maskOR_lsb         = 1;
   if (flags & LTM_PRIME_BBS) {
      maskOR_lsb     |= 3;
   }
--- a/bn_mp_radix_size.c
+++ b/bn_mp_radix_size.c
@@ -35,22 +35,29 @@ int mp_radix_size (mp_int * a, int radix, int *size)
    return MP_VAL;
  }

-  /* init a copy of the input */
-  if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
-    return res;
+  if (mp_iszero(a) == MP_YES) {
+     *size = 2;
+    return MP_OKAY;
  }

  /* digs is the digit count */
  digs = 0;

  /* if it's negative add one for the sign */
-  if (t.sign == MP_NEG) {
+  if (a->sign == MP_NEG) {
    ++digs;
-    t.sign = MP_ZPOS;
  }

+  /* init a copy of the input */
+  if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
+    return res;
+  }
+
+  /* force temp to positive */
+  t.sign = MP_ZPOS; 
+
  /* fetch out all of the digits */
-  while (mp_iszero (&t) == 0) {
+  while (mp_iszero (&t) == MP_NO) {
    if ((res = mp_div_d (&t, (mp_digit) radix, &t, &d)) != MP_OKAY) {
      mp_clear (&t);
      return res;
--- a/bn_mp_rand.c
+++ b/bn_mp_rand.c
@@ -29,14 +29,14 @@ mp_rand (mp_int * a, int digits)

  /* first place a random non-zero digit */
  do {
-    d = ((mp_digit) abs (rand ()));
+    d = ((mp_digit) abs (rand ())) & MP_MASK;
  } while (d == 0);

  if ((res = mp_add_d (a, d, a)) != MP_OKAY) {
    return res;
  }

-  while (digits-- > 0) {
+  while (--digits > 0) {
    if ((res = mp_lshd (a, 1)) != MP_OKAY) {
      return res;
    }
--- a/bn_mp_read_radix.c
+++ b/bn_mp_read_radix.c
@@ -16,7 +16,7 @@
 */

 /* read a string [ASCII] in a given radix */
-int mp_read_radix (mp_int * a, char *str, int radix)
+int mp_read_radix (mp_int * a, const char *str, int radix)
 {
  int     y, res, neg;
  char    ch;
--- a/bn_mp_reduce.c
+++ b/bn_mp_reduce.c
@@ -19,8 +19,7 @@
 * precomputed via mp_reduce_setup.
 * From HAC pp.604 Algorithm 14.42
 */
-int
-mp_reduce (mp_int * x, mp_int * m, mp_int * mu)
+int mp_reduce (mp_int * x, mp_int * m, mp_int * mu)
 {
  mp_int  q;
  int     res, um = m->used;
@@ -40,11 +39,11 @@ mp_reduce (mp_int * x, mp_int * m, mp_int * mu)
    }
  } else {
 #ifdef BN_S_MP_MUL_HIGH_DIGS_C
-    if ((res = s_mp_mul_high_digs (&q, mu, &q, um - 1)) != MP_OKAY) {
+    if ((res = s_mp_mul_high_digs (&q, mu, &q, um)) != MP_OKAY) {
      goto CLEANUP;
    }
 #elif defined(BN_FAST_S_MP_MUL_HIGH_DIGS_C)
-    if ((res = fast_s_mp_mul_high_digs (&q, mu, &q, um - 1)) != MP_OKAY) {
+    if ((res = fast_s_mp_mul_high_digs (&q, mu, &q, um)) != MP_OKAY) {
      goto CLEANUP;
    }
 #else 
--- a/bn_mp_reduce_2k.c
+++ b/bn_mp_reduce_2k.c
@@ -16,8 +16,7 @@
 */

 /* reduces a modulo n where n is of the form 2**p - d */
-int
-mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d)
+int mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d)
 {
   mp_int q;
   int    p, res;
--- a/bn_mp_reduce_2k_l.c
+++ b/bn_mp_reduce_2k_l.c
@@ -0,0 +1,58 @@
+#include <tommath.h>
+#ifdef BN_MP_REDUCE_2K_L_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@iahu.ca, http://math.libtomcrypt.org
+ */
+
+/* reduces a modulo n where n is of the form 2**p - d 
+   This differs from reduce_2k since "d" can be larger
+   than a single digit.
+*/
+int mp_reduce_2k_l(mp_int *a, mp_int *n, mp_int *d)
+{
+   mp_int q;
+   int    p, res;
+   
+   if ((res = mp_init(&q)) != MP_OKAY) {
+      return res;
+   }
+   
+   p = mp_count_bits(n);    
+top:
+   /* q = a/2**p, a = a mod 2**p */
+   if ((res = mp_div_2d(a, p, &q, a)) != MP_OKAY) {
+      goto ERR;
+   }
+   
+   /* q = q * d */
+   if ((res = mp_mul(&q, d, &q)) != MP_OKAY) { 
+      goto ERR;
+   }
+   
+   /* a = a + q */
+   if ((res = s_mp_add(a, &q, a)) != MP_OKAY) {
+      goto ERR;
+   }
+   
+   if (mp_cmp_mag(a, n) != MP_LT) {
+      s_mp_sub(a, n, a);
+      goto top;
+   }
+   
+ERR:
+   mp_clear(&q);
+   return res;
+}
+
+#endif
--- a/bn_mp_reduce_2k_setup.c
+++ b/bn_mp_reduce_2k_setup.c
@@ -16,8 +16,7 @@
 */

 /* determines the setup value */
-int 
-mp_reduce_2k_setup(mp_int *a, mp_digit *d)
+int mp_reduce_2k_setup(mp_int *a, mp_digit *d)
 {
   int res, p;
   mp_int tmp;
--- a/bn_mp_reduce_2k_setup_l.c
+++ b/bn_mp_reduce_2k_setup_l.c
@@ -0,0 +1,40 @@
+#include <tommath.h>
+#ifdef BN_MP_REDUCE_2K_SETUP_L_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@iahu.ca, http://math.libtomcrypt.org
+ */
+
+/* determines the setup value */
+int mp_reduce_2k_setup_l(mp_int *a, mp_int *d)
+{
+   int    res;
+   mp_int tmp;
+   
+   if ((res = mp_init(&tmp)) != MP_OKAY) {
+      return res;
+   }
+   
+   if ((res = mp_2expt(&tmp, mp_count_bits(a))) != MP_OKAY) {
+      goto ERR;
+   }
+   
+   if ((res = s_mp_sub(&tmp, a, d)) != MP_OKAY) {
+      goto ERR;
+   }
+   
+ERR:
+   mp_clear(&tmp);
+   return res;
+}
+#endif
--- a/bn_mp_reduce_is_2k.c
+++ b/bn_mp_reduce_is_2k.c
@@ -22,9 +22,9 @@ int mp_reduce_is_2k(mp_int *a)
   mp_digit iz;
   
   if (a->used == 0) {
-      return 0;
+      return MP_NO;
   } else if (a->used == 1) {
-      return 1;
+      return MP_YES;
   } else if (a->used > 1) {
      iy = mp_count_bits(a);
      iz = 1;
@@ -33,7 +33,7 @@ int mp_reduce_is_2k(mp_int *a)
      /* Test every bit from the second digit up, must be 1 */
      for (ix = DIGIT_BIT; ix < iy; ix++) {
          if ((a->dp[iw] & iz) == 0) {
-             return 0;
+             return MP_NO;
          }
          iz <<= 1;
          if (iz > (mp_digit)MP_MASK) {
@@ -42,7 +42,7 @@ int mp_reduce_is_2k(mp_int *a)
          }
      }
   }
-   return 1;
+   return MP_YES;
 }

 #endif
--- a/bn_mp_reduce_is_2k_l.c
+++ b/bn_mp_reduce_is_2k_l.c
@@ -0,0 +1,40 @@
+#include <tommath.h>
+#ifdef BN_MP_REDUCE_IS_2K_L_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@iahu.ca, http://math.libtomcrypt.org
+ */
+
+/* determines if reduce_2k_l can be used */
+int mp_reduce_is_2k_l(mp_int *a)
+{
+   int ix, iy;
+   
+   if (a->used == 0) {
+      return MP_NO;
+   } else if (a->used == 1) {
+      return MP_YES;
+   } else if (a->used > 1) {
+      /* if more than half of the digits are -1 we're sold */
+      for (iy = ix = 0; ix < a->used; ix++) {
+          if (a->dp[ix] == MP_MASK) {
+              ++iy;
+          }
+      }
+      return (iy >= (a->used/2)) ? MP_YES : MP_NO;
+      
+   }
+   return MP_NO;
+}
+
+#endif
--- a/bn_mp_to_signed_bin.c
+++ b/bn_mp_to_signed_bin.c
@@ -16,8 +16,7 @@
 */

 /* store in signed [big endian] format */
-int
-mp_to_signed_bin (mp_int * a, unsigned char *b)
+int mp_to_signed_bin (mp_int * a, unsigned char *b)
 {
  int     res;

--- a/bn_mp_to_signed_bin_n.c
+++ b/bn_mp_to_signed_bin_n.c
@@ -0,0 +1,27 @@
+#include <tommath.h>
+#ifdef BN_MP_TO_SIGNED_BIN_N_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@iahu.ca, http://math.libtomcrypt.org
+ */
+
+/* store in signed [big endian] format */
+int mp_to_signed_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen)
+{
+   if (*outlen < (unsigned long)mp_signed_bin_size(a)) {
+      return MP_VAL;
+   }
+   *outlen = mp_signed_bin_size(a);
+   return mp_to_signed_bin(a, b);
+}
+#endif
--- a/bn_mp_to_unsigned_bin.c
+++ b/bn_mp_to_unsigned_bin.c
@@ -16,8 +16,7 @@
 */

 /* store in unsigned [big endian] format */
-int
-mp_to_unsigned_bin (mp_int * a, unsigned char *b)
+int mp_to_unsigned_bin (mp_int * a, unsigned char *b)
 {
  int     x, res;
  mp_int  t;
--- a/bn_mp_to_unsigned_bin_n.c
+++ b/bn_mp_to_unsigned_bin_n.c
@@ -0,0 +1,27 @@
+#include <tommath.h>
+#ifdef BN_MP_TO_UNSIGNED_BIN_N_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@iahu.ca, http://math.libtomcrypt.org
+ */
+
+/* store in unsigned [big endian] format */
+int mp_to_unsigned_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen)
+{
+   if (*outlen < (unsigned long)mp_unsigned_bin_size(a)) {
+      return MP_VAL;
+   }
+   *outlen = mp_unsigned_bin_size(a);
+   return mp_to_unsigned_bin(a, b);
+}
+#endif
--- a/bn_mp_toom_mul.c
+++ b/bn_mp_toom_mul.c
@@ -17,9 +17,10 @@

 /* multiplication using the Toom-Cook 3-way algorithm 
 *
- * Much more complicated than Karatsuba but has a lower asymptotic running time of 
- * O(N**1.464).  This algorithm is only particularly useful on VERY large
- * inputs (we're talking 1000s of digits here...).
+ * Much more complicated than Karatsuba but has a lower 
+ * asymptotic running time of O(N**1.464).  This algorithm is 
+ * only particularly useful on VERY large inputs 
+ * (we're talking 1000s of digits here...).
 */
 int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c)
 {
--- a/bn_mp_unsigned_bin_size.c
+++ b/bn_mp_unsigned_bin_size.c
@@ -16,8 +16,7 @@
 */

 /* get the size for an unsigned equivalent */
-int
-mp_unsigned_bin_size (mp_int * a)
+int mp_unsigned_bin_size (mp_int * a)
 {
  int     size = mp_count_bits (a);
  return (size / 8 + ((size & 7) != 0 ? 1 : 0));
--- a/bn_mp_xor.c
+++ b/bn_mp_xor.c
@@ -37,7 +37,7 @@ mp_xor (mp_int * a, mp_int * b, mp_int * c)
  }

  for (ix = 0; ix < px; ix++) {
-
+     t.dp[ix] ^= x->dp[ix];
  }
  mp_clamp (&t);
  mp_exch (c, &t);
--- a/bn_mp_zero.c
+++ b/bn_mp_zero.c
@@ -16,11 +16,17 @@
 */

 /* set to zero */
-void
-mp_zero (mp_int * a)
+void mp_zero (mp_int * a)
 {
+  int       n;
+  mp_digit *tmp;
+
  a->sign = MP_ZPOS;
  a->used = 0;
-  memset (a->dp, 0, sizeof (mp_digit) * a->alloc);
+
+  tmp = a->dp;
+  for (n = 0; n < a->alloc; n++) {
+     *tmp++ = 0;
+  }
 }
 #endif
--- a/bn_prime_tab.c
+++ b/bn_prime_tab.c
@@ -14,7 +14,7 @@
 *
 * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
 */
-const mp_digit __prime_tab[] = {
+const mp_digit ltm_prime_tab[] = {
  0x0002, 0x0003, 0x0005, 0x0007, 0x000B, 0x000D, 0x0011, 0x0013,
  0x0017, 0x001D, 0x001F, 0x0025, 0x0029, 0x002B, 0x002F, 0x0035,
  0x003B, 0x003D, 0x0043, 0x0047, 0x0049, 0x004F, 0x0053, 0x0059,
--- a/bn_s_mp_exptmod.c
+++ b/bn_s_mp_exptmod.c
@@ -21,11 +21,12 @@
   #define TAB_SIZE 256
 #endif

-int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
+int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
 {
  mp_int  M[TAB_SIZE], res, mu;
  mp_digit buf;
  int     err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
+  int (*redux)(mp_int*,mp_int*,mp_int*);

  /* find window size */
  x = mp_count_bits (X);
@@ -70,11 +71,20 @@ int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)

  /* create mu, used for Barrett reduction */
  if ((err = mp_init (&mu)) != MP_OKAY) {
-    goto __M;
-  }
-  if ((err = mp_reduce_setup (&mu, P)) != MP_OKAY) {
-    goto __MU;
+    goto LBL_M;
  }
+  
+  if (redmode == 0) {
+     if ((err = mp_reduce_setup (&mu, P)) != MP_OKAY) {
+        goto LBL_MU;
+     }
+     redux = mp_reduce;
+  } else {
+     if ((err = mp_reduce_2k_setup_l (P, &mu)) != MP_OKAY) {
+        goto LBL_MU;
+     }
+     redux = mp_reduce_2k_l;
+  }    

  /* create M table
   *
@@ -85,23 +95,26 @@ int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
   * computed though accept for M[0] and M[1]
   */
  if ((err = mp_mod (G, P, &M[1])) != MP_OKAY) {
-    goto __MU;
+    goto LBL_MU;
  }

  /* compute the value at M[1<<(winsize-1)] by squaring 
   * M[1] (winsize-1) times 
   */
  if ((err = mp_copy (&M[1], &M[1 << (winsize - 1)])) != MP_OKAY) {
-    goto __MU;
+    goto LBL_MU;
  }

  for (x = 0; x < (winsize - 1); x++) {
+    /* square it */
    if ((err = mp_sqr (&M[1 << (winsize - 1)], 
                       &M[1 << (winsize - 1)])) != MP_OKAY) {
-      goto __MU;
+      goto LBL_MU;
    }
-    if ((err = mp_reduce (&M[1 << (winsize - 1)], P, &mu)) != MP_OKAY) {
-      goto __MU;
+
+    /* reduce modulo P */
+    if ((err = redux (&M[1 << (winsize - 1)], P, &mu)) != MP_OKAY) {
+      goto LBL_MU;
    }
  }

@@ -110,16 +123,16 @@ int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
   */
  for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) {
    if ((err = mp_mul (&M[x - 1], &M[1], &M[x])) != MP_OKAY) {
-      goto __MU;
+      goto LBL_MU;
    }
-    if ((err = mp_reduce (&M[x], P, &mu)) != MP_OKAY) {
-      goto __MU;
+    if ((err = redux (&M[x], P, &mu)) != MP_OKAY) {
+      goto LBL_MU;
    }
  }

  /* setup result */
  if ((err = mp_init (&res)) != MP_OKAY) {
-    goto __MU;
+    goto LBL_MU;
  }
  mp_set (&res, 1);

@@ -159,10 +172,10 @@ int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
    /* if the bit is zero and mode == 1 then we square */
    if (mode == 1 && y == 0) {
      if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
-        goto __RES;
+        goto LBL_RES;
      }
-      if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) {
-        goto __RES;
+      if ((err = redux (&res, P, &mu)) != MP_OKAY) {
+        goto LBL_RES;
      }
      continue;
    }
@@ -176,19 +189,19 @@ int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
      /* square first */
      for (x = 0; x < winsize; x++) {
        if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
-          goto __RES;
+          goto LBL_RES;
        }
-        if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) {
-          goto __RES;
+        if ((err = redux (&res, P, &mu)) != MP_OKAY) {
+          goto LBL_RES;
        }
      }

      /* then multiply */
      if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) {
-        goto __RES;
+        goto LBL_RES;
      }
-      if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) {
-        goto __RES;
+      if ((err = redux (&res, P, &mu)) != MP_OKAY) {
+        goto LBL_RES;
      }

      /* empty window and reset */
@@ -203,20 +216,20 @@ int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
    /* square then multiply if the bit is set */
    for (x = 0; x < bitcpy; x++) {
      if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
-        goto __RES;
+        goto LBL_RES;
      }
-      if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) {
-        goto __RES;
+      if ((err = redux (&res, P, &mu)) != MP_OKAY) {
+        goto LBL_RES;
      }

      bitbuf <<= 1;
      if ((bitbuf & (1 << winsize)) != 0) {
        /* then multiply */
        if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) {
-          goto __RES;
+          goto LBL_RES;
        }
-        if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) {
-          goto __RES;
+        if ((err = redux (&res, P, &mu)) != MP_OKAY) {
+          goto LBL_RES;
        }
      }
    }
@@ -224,9 +237,9 @@ int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)

  mp_exch (&res, Y);
  err = MP_OKAY;
-__RES:mp_clear (&res);
-__MU:mp_clear (&mu);
-__M:
+LBL_RES:mp_clear (&res);
+LBL_MU:mp_clear (&mu);
+LBL_M:
  mp_clear(&M[1]);
  for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
    mp_clear (&M[x]);
--- a/bn_s_mp_mul_digs.c
+++ b/bn_s_mp_mul_digs.c
@@ -19,8 +19,7 @@
 * HAC pp. 595, Algorithm 14.12  Modified so you can control how 
 * many digits of output are created.
 */
-int
-s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
+int s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
 {
  mp_int  t;
  int     res, pa, pb, ix, iy;
--- a/bn_s_mp_sqr.c
+++ b/bn_s_mp_sqr.c
@@ -16,8 +16,7 @@
 */

 /* low level squaring, b = a*a, HAC pp.596-597, Algorithm 14.16 */
-int
-s_mp_sqr (mp_int * a, mp_int * b)
+int s_mp_sqr (mp_int * a, mp_int * b)
 {
  mp_int  t;
  int     res, ix, iy, pa;
--- a/bncore.c
+++ b/bncore.c
@@ -20,11 +20,12 @@
 CPU                    /Compiler     /MUL CUTOFF/SQR CUTOFF
 -------------------------------------------------------------
 Intel P4 Northwood     /GCC v3.4.1   /        88/       128/LTM 0.32 ;-)
+ AMD Athlon64           /GCC v3.4.4   /        74/       124/LTM 0.34
 
 */

-int     KARATSUBA_MUL_CUTOFF = 88,      /* Min. number of digits before Karatsuba multiplication is used. */
-        KARATSUBA_SQR_CUTOFF = 128,     /* Min. number of digits before Karatsuba squaring is used. */
+int     KARATSUBA_MUL_CUTOFF = 74,      /* Min. number of digits before Karatsuba multiplication is used. */
+        KARATSUBA_SQR_CUTOFF = 124,     /* Min. number of digits before Karatsuba squaring is used. */
        
        TOOM_MUL_CUTOFF      = 350,      /* no optimal values of these are known yet so set em high */
        TOOM_SQR_CUTOFF      = 400; 
--- a/callgraph.txt
+++ b/callgraph.txt
--- a/changes.txt
+++ b/changes.txt
@@ -1,3 +1,35 @@
+March 12th, 2005
+v0.35  -- Stupid XOR function missing line again... oops.
+       -- Fixed bug in invmod not handling negative inputs correctly [Wolfgang Ehrhardt]
+       -- Made exteuclid always give positive u3 output...[ Wolfgang Ehrhardt ]
+       -- [Wolfgang Ehrhardt] Suggested a fix for mp_reduce() which avoided underruns.  ;-)
+       -- mp_rand() would emit one too many digits and it was possible to get a 0 out of it ... oops
+       -- Added montgomery to the testing to make sure it handles 1..10 digit moduli correctly
+       -- Fixed bug in comba that would lead to possible erroneous outputs when "pa < digs" 
+       -- Fixed bug in mp_toradix_size for "0" [Kevin Kenny]
+       -- Updated chapters 1-5 of the textbook ;-) It now talks about the new comba code!
+
+February 12th, 2005
+v0.34  -- Fixed two more small errors in mp_prime_random_ex()
+       -- Fixed overflow in mp_mul_d() [Kevin Kenny]
+       -- Added mp_to_(un)signed_bin_n() functions which do bounds checking for ya [and report the size]
+       -- Added "large" diminished radix support.  Speeds up things like DSA where the moduli is of the form 2^k - P for some P < 2^(k/2) or so
+          Actually is faster than Montgomery on my AMD64 (and probably much faster on a P4)
+       -- Updated the manual a bit
+       -- Ok so I haven't done the textbook work yet... My current freelance gig has landed me in France till the 
+          end of Feb/05.  Once I get back I'll have tons of free time and I plan to go to town on the book.
+          As of this release the API will freeze.  At least until the book catches up with all the changes.  I welcome
+          bug reports but new algorithms will have to wait.
+
+December 23rd, 2004
+v0.33  -- Fixed "small" variant for mp_div() which would munge with negative dividends...
+       -- Fixed bug in mp_prime_random_ex() which would set the most significant byte to zero when
+          no special flags were set
+       -- Fixed overflow [minor] bug in fast_s_mp_sqr()
+       -- Made the makefiles easier to configure the group/user that ltm will install as
+       -- Fixed "final carry" bug in comba multipliers. (Volkan Ceylan)
+       -- Matt Johnston pointed out a missing semi-colon in mp_exptmod
+
 October 29th, 2004
 v0.32  -- Added "makefile.shared" for shared object support
       -- Added more to the build options/configs in the manual
--- a/demo/demo.c
+++ b/demo/demo.c
--- a/demo/timing.c
+++ b/demo/timing.c
@@ -11,15 +11,16 @@ ulong64 _tt;
 #endif


-void ndraw(mp_int *a, char *name)
+void ndraw(mp_int * a, char *name)
 {
   char buf[4096];
+
   printf("%s: ", name);
   mp_toradix(a, buf, 64);
   printf("%s\n", buf);
 }

-static void draw(mp_int *a)
+static void draw(mp_int * a)
 {
   ndraw(a, "");
 }
@@ -38,40 +39,39 @@ int lbit(void)
   }
 }

-#if defined(__i386__) || defined(_M_IX86) || defined(_M_AMD64)
 /* RDTSC from Scott Duplichan */
-static ulong64 TIMFUNC (void)
-   {
-   #if defined __GNUC__
-      #ifdef __i386__
-         ulong64 a;
-         __asm__ __volatile__ ("rdtsc ":"=A" (a));
-         return a;
-      #else /* gcc-IA64 version */
-         unsigned long result;
-         __asm__ __volatile__("mov %0=ar.itc" : "=r"(result) :: "memory");
-         while (__builtin_expect ((int) result == -1, 0))
-         __asm__ __volatile__("mov %0=ar.itc" : "=r"(result) :: "memory");
-         return result;
-      #endif
+static ulong64 TIMFUNC(void)
+{
+#if defined __GNUC__
+#if defined(__i386__) || defined(__x86_64__)
+   unsigned long long a;
+   __asm__ __volatile__("rdtsc\nmovl %%eax,%0\nmovl %%edx,4+%0\n"::
+			"m"(a):"%eax", "%edx");
+   return a;
+#else /* gcc-IA64 version */
+   unsigned long result;
+   __asm__ __volatile__("mov %0=ar.itc":"=r"(result)::"memory");
+
+   while (__builtin_expect((int) result == -1, 0))
+      __asm__ __volatile__("mov %0=ar.itc":"=r"(result)::"memory");
+
+   return result;
+#endif

   // Microsoft and Intel Windows compilers
-   #elif defined _M_IX86
-     __asm rdtsc
-   #elif defined _M_AMD64
-     return __rdtsc ();
-   #elif defined _M_IA64
-     #if defined __INTEL_COMPILER
-       #include <ia64intrin.h>
-     #endif
-      return __getReg (3116);
-   #else
-     #error need rdtsc function for this build
-   #endif
-   }
-#else
-#define TIMFUNC clock
+#elif defined _M_IX86
+   __asm rdtsc
+#elif defined _M_AMD64
+   return __rdtsc();
+#elif defined _M_IA64
+#if defined __INTEL_COMPILER
+#include <ia64intrin.h>
 #endif
+   return __getReg(3116);
+#else
+#error need rdtsc function for this build
+#endif
+}

 #define DO(x) x; x;
 //#define DO4(x) DO2(x); DO2(x);
@@ -81,7 +81,7 @@ static ulong64 TIMFUNC (void)
 int main(void)
 {
   ulong64 tt, gg, CLK_PER_SEC;
-   FILE *log, *logb, *logc;
+   FILE *log, *logb, *logc, *logd;
   mp_int a, b, c, d, e, f;
   int n, cnt, ix, old_kara_m, old_kara_s;
   unsigned rr;
@@ -94,168 +94,191 @@ int main(void)
   mp_init(&f);

   srand(time(NULL));
- 

-      /* temp. turn off TOOM */
-      TOOM_MUL_CUTOFF = TOOM_SQR_CUTOFF = 100000;

-      CLK_PER_SEC = TIMFUNC();
-      sleep(1);
-      CLK_PER_SEC = TIMFUNC() - CLK_PER_SEC;
+   /* temp. turn off TOOM */
+   TOOM_MUL_CUTOFF = TOOM_SQR_CUTOFF = 100000;

-      printf("CLK_PER_SEC == %llu\n", CLK_PER_SEC);
-      
-      log = fopen("logs/add.log", "w");
-      for (cnt = 8; cnt <= 128; cnt += 8) {
-         SLEEP;
-         mp_rand(&a, cnt);
-         mp_rand(&b, cnt);
-         rr = 0;
-         tt = -1;
-         do {
-            gg = TIMFUNC();
-            DO(mp_add(&a,&b,&c));
-            gg = (TIMFUNC() - gg)>>1;
-            if (tt > gg) tt = gg;
-         } while (++rr < 100000);
-         printf("Adding\t\t%4d-bit => %9llu/sec, %9llu cycles\n", mp_count_bits(&a), CLK_PER_SEC/tt, tt);
-         fprintf(log, "%d %9llu\n", cnt*DIGIT_BIT, tt); fflush(log);
-      }
-      fclose(log);
+   CLK_PER_SEC = TIMFUNC();
+   sleep(1);
+   CLK_PER_SEC = TIMFUNC() - CLK_PER_SEC;

-      log = fopen("logs/sub.log", "w");
-      for (cnt = 8; cnt <= 128; cnt += 8) {
-         SLEEP;
-         mp_rand(&a, cnt);
-         mp_rand(&b, cnt);
-         rr = 0;
-         tt = -1;
-         do {
-            gg = TIMFUNC();
-            DO(mp_sub(&a,&b,&c));
-            gg = (TIMFUNC() - gg)>>1;
-            if (tt > gg) tt = gg;
-         } while (++rr < 100000);
+   printf("CLK_PER_SEC == %llu\n", CLK_PER_SEC);
+   goto exptmod;
+   log = fopen("logs/add.log", "w");
+   for (cnt = 8; cnt <= 128; cnt += 8) {
+      SLEEP;
+      mp_rand(&a, cnt);
+      mp_rand(&b, cnt);
+      rr = 0;
+      tt = -1;
+      do {
+	 gg = TIMFUNC();
+	 DO(mp_add(&a, &b, &c));
+	 gg = (TIMFUNC() - gg) >> 1;
+	 if (tt > gg)
+	    tt = gg;
+      } while (++rr < 100000);
+      printf("Adding\t\t%4d-bit => %9llu/sec, %9llu cycles\n",
+	     mp_count_bits(&a), CLK_PER_SEC / tt, tt);
+      fprintf(log, "%d %9llu\n", cnt * DIGIT_BIT, tt);
+      fflush(log);
+   }
+   fclose(log);

-         printf("Subtracting\t\t%4d-bit => %9llu/sec, %9llu cycles\n", mp_count_bits(&a), CLK_PER_SEC/tt, tt);
-         fprintf(log, "%d %9llu\n", cnt*DIGIT_BIT, tt);  fflush(log);
-      }
-      fclose(log);
+   log = fopen("logs/sub.log", "w");
+   for (cnt = 8; cnt <= 128; cnt += 8) {
+      SLEEP;
+      mp_rand(&a, cnt);
+      mp_rand(&b, cnt);
+      rr = 0;
+      tt = -1;
+      do {
+	 gg = TIMFUNC();
+	 DO(mp_sub(&a, &b, &c));
+	 gg = (TIMFUNC() - gg) >> 1;
+	 if (tt > gg)
+	    tt = gg;
+      } while (++rr < 100000);
+
+      printf("Subtracting\t\t%4d-bit => %9llu/sec, %9llu cycles\n",
+	     mp_count_bits(&a), CLK_PER_SEC / tt, tt);
+      fprintf(log, "%d %9llu\n", cnt * DIGIT_BIT, tt);
+      fflush(log);
+   }
+   fclose(log);

   /* do mult/square twice, first without karatsuba and second with */
+ multtest:
   old_kara_m = KARATSUBA_MUL_CUTOFF;
   old_kara_s = KARATSUBA_SQR_CUTOFF;
-   for (ix = 0; ix < 1; ix++) {
-      printf("With%s Karatsuba\n", (ix==0)?"out":"");
+   for (ix = 0; ix < 2; ix++) {
+      printf("With%s Karatsuba\n", (ix == 0) ? "out" : "");

-      KARATSUBA_MUL_CUTOFF = (ix==0)?9999:old_kara_m;
-      KARATSUBA_SQR_CUTOFF = (ix==0)?9999:old_kara_s;
+      KARATSUBA_MUL_CUTOFF = (ix == 0) ? 9999 : old_kara_m;
+      KARATSUBA_SQR_CUTOFF = (ix == 0) ? 9999 : old_kara_s;

-      log = fopen((ix==0)?"logs/mult.log":"logs/mult_kara.log", "w");
-      for (cnt = 4; cnt <= 288; cnt += 2) {
-         SLEEP;
-         mp_rand(&a, cnt);
-         mp_rand(&b, cnt);
-         rr = 0;
-         tt = -1;
-         do {
-            gg = TIMFUNC();
-            DO(mp_mul(&a, &b, &c));
-            gg = (TIMFUNC() - gg)>>1;
-            if (tt > gg) tt = gg;
-         } while (++rr < 100);
-         printf("Multiplying\t%4d-bit => %9llu/sec, %9llu cycles\n", mp_count_bits(&a), CLK_PER_SEC/tt, tt);
-         fprintf(log, "%d %9llu\n", mp_count_bits(&a), tt);  fflush(log);
+      log = fopen((ix == 0) ? "logs/mult.log" : "logs/mult_kara.log", "w");
+      for (cnt = 4; cnt <= 10240 / DIGIT_BIT; cnt += 2) {
+	 SLEEP;
+	 mp_rand(&a, cnt);
+	 mp_rand(&b, cnt);
+	 rr = 0;
+	 tt = -1;
+	 do {
+	    gg = TIMFUNC();
+	    DO(mp_mul(&a, &b, &c));
+	    gg = (TIMFUNC() - gg) >> 1;
+	    if (tt > gg)
+	       tt = gg;
+	 } while (++rr < 100);
+	 printf("Multiplying\t%4d-bit => %9llu/sec, %9llu cycles\n",
+		mp_count_bits(&a), CLK_PER_SEC / tt, tt);
+	 fprintf(log, "%d %9llu\n", mp_count_bits(&a), tt);
+	 fflush(log);
      }
      fclose(log);

-      log = fopen((ix==0)?"logs/sqr.log":"logs/sqr_kara.log", "w");
-      for (cnt = 4; cnt <= 288; cnt += 2) {
-         SLEEP;
-         mp_rand(&a, cnt);
-         rr = 0;
-         tt = -1;
-         do {
-            gg = TIMFUNC();
-            DO(mp_sqr(&a, &b));
-            gg = (TIMFUNC() - gg)>>1;
-            if (tt > gg) tt = gg;
-         } while (++rr < 100);
-         printf("Squaring\t%4d-bit => %9llu/sec, %9llu cycles\n", mp_count_bits(&a), CLK_PER_SEC/tt, tt);
-         fprintf(log, "%d %9llu\n", mp_count_bits(&a), tt);  fflush(log);
+      log = fopen((ix == 0) ? "logs/sqr.log" : "logs/sqr_kara.log", "w");
+      for (cnt = 4; cnt <= 10240 / DIGIT_BIT; cnt += 2) {
+	 SLEEP;
+	 mp_rand(&a, cnt);
+	 rr = 0;
+	 tt = -1;
+	 do {
+	    gg = TIMFUNC();
+	    DO(mp_sqr(&a, &b));
+	    gg = (TIMFUNC() - gg) >> 1;
+	    if (tt > gg)
+	       tt = gg;
+	 } while (++rr < 100);
+	 printf("Squaring\t%4d-bit => %9llu/sec, %9llu cycles\n",
+		mp_count_bits(&a), CLK_PER_SEC / tt, tt);
+	 fprintf(log, "%d %9llu\n", mp_count_bits(&a), tt);
+	 fflush(log);
      }
      fclose(log);

   }
+ exptmod:

-  {
+   {
      char *primes[] = {
-         /* 2K moduli mersenne primes */
-         "6864797660130609714981900799081393217269435300143305409394463459185543183397656052122559640661454554977296311391480858037121987999716643812574028291115057151",
-         "531137992816767098689588206552468627329593117727031923199444138200403559860852242739162502265229285668889329486246501015346579337652707239409519978766587351943831270835393219031728127",
-         "10407932194664399081925240327364085538615262247266704805319112350403608059673360298012239441732324184842421613954281007791383566248323464908139906605677320762924129509389220345773183349661583550472959420547689811211693677147548478866962501384438260291732348885311160828538416585028255604666224831890918801847068222203140521026698435488732958028878050869736186900714720710555703168729087",
-         "1475979915214180235084898622737381736312066145333169775147771216478570297878078949377407337049389289382748507531496480477281264838760259191814463365330269540496961201113430156902396093989090226259326935025281409614983499388222831448598601834318536230923772641390209490231836446899608210795482963763094236630945410832793769905399982457186322944729636418890623372171723742105636440368218459649632948538696905872650486914434637457507280441823676813517852099348660847172579408422316678097670224011990280170474894487426924742108823536808485072502240519452587542875349976558572670229633962575212637477897785501552646522609988869914013540483809865681250419497686697771007",
-         "259117086013202627776246767922441530941818887553125427303974923161874019266586362086201209516800483406550695241733194177441689509238807017410377709597512042313066624082916353517952311186154862265604547691127595848775610568757931191017711408826252153849035830401185072116424747461823031471398340229288074545677907941037288235820705892351068433882986888616658650280927692080339605869308790500409503709875902119018371991620994002568935113136548829739112656797303241986517250116412703509705427773477972349821676443446668383119322540099648994051790241624056519054483690809616061625743042361721863339415852426431208737266591962061753535748892894599629195183082621860853400937932839420261866586142503251450773096274235376822938649407127700846077124211823080804139298087057504713825264571448379371125032081826126566649084251699453951887789613650248405739378594599444335231188280123660406262468609212150349937584782292237144339628858485938215738821232393687046160677362909315071",
-         "190797007524439073807468042969529173669356994749940177394741882673528979787005053706368049835514900244303495954950709725762186311224148828811920216904542206960744666169364221195289538436845390250168663932838805192055137154390912666527533007309292687539092257043362517857366624699975402375462954490293259233303137330643531556539739921926201438606439020075174723029056838272505051571967594608350063404495977660656269020823960825567012344189908927956646011998057988548630107637380993519826582389781888135705408653045219655801758081251164080554609057468028203308718724654081055323215860189611391296030471108443146745671967766308925858547271507311563765171008318248647110097614890313562856541784154881743146033909602737947385055355960331855614540900081456378659068370317267696980001187750995491090350108417050917991562167972281070161305972518044872048331306383715094854938415738549894606070722584737978176686422134354526989443028353644037187375385397838259511833166416134323695660367676897722287918773420968982326089026150031515424165462111337527431154890666327374921446276833564519776797633875503548665093914556482031482248883127023777039667707976559857333357013727342079099064400455741830654320379350833236245819348824064783585692924881021978332974949906122664421376034687815350484991",
+	 /* 2K large moduli */
+	 "179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586239334100047359817950870678242457666208137217",
+	 "32317006071311007300714876688669951960444102669715484032130345427524655138867890893197201411522913463688717960921898019494119559150490921095088152386448283120630877367300996091750197750389652106796057638384067568276792218642619756161838094338476170470581645852036305042887575891541065808607552399123930385521914333389668342420684974786564569494856176035326322058077805659331026192708460314150258592864177116725943603718461857357598351152301645904403697613233287231227125684710820209725157101726931323469678542580656697935045997268352998638099733077152121140120031150424541696791951097529546801429027668869927491725169",
+	 "1044388881413152506691752710716624382579964249047383780384233483283953907971557456848826811934997558340890106714439262837987573438185793607263236087851365277945956976543709998340361590134383718314428070011855946226376318839397712745672334684344586617496807908705803704071284048740118609114467977783598029006686938976881787785946905630190260940599579453432823469303026696443059025015972399867714215541693835559885291486318237914434496734087811872639496475100189041349008417061675093668333850551032972088269550769983616369411933015213796825837188091833656751221318492846368125550225998300412344784862595674492194617023806505913245610825731835380087608622102834270197698202313169017678006675195485079921636419370285375124784014907159135459982790513399611551794271106831134090584272884279791554849782954323534517065223269061394905987693002122963395687782878948440616007412945674919823050571642377154816321380631045902916136926708342856440730447899971901781465763473223850267253059899795996090799469201774624817718449867455659250178329070473119433165550807568221846571746373296884912819520317457002440926616910874148385078411929804522981857338977648103126085902995208257421855249796721729039744118165938433694823325696642096892124547425283",
+	 /* 2K moduli mersenne primes */
+	 "6864797660130609714981900799081393217269435300143305409394463459185543183397656052122559640661454554977296311391480858037121987999716643812574028291115057151",
+	 "531137992816767098689588206552468627329593117727031923199444138200403559860852242739162502265229285668889329486246501015346579337652707239409519978766587351943831270835393219031728127",
+	 "10407932194664399081925240327364085538615262247266704805319112350403608059673360298012239441732324184842421613954281007791383566248323464908139906605677320762924129509389220345773183349661583550472959420547689811211693677147548478866962501384438260291732348885311160828538416585028255604666224831890918801847068222203140521026698435488732958028878050869736186900714720710555703168729087",
+	 "1475979915214180235084898622737381736312066145333169775147771216478570297878078949377407337049389289382748507531496480477281264838760259191814463365330269540496961201113430156902396093989090226259326935025281409614983499388222831448598601834318536230923772641390209490231836446899608210795482963763094236630945410832793769905399982457186322944729636418890623372171723742105636440368218459649632948538696905872650486914434637457507280441823676813517852099348660847172579408422316678097670224011990280170474894487426924742108823536808485072502240519452587542875349976558572670229633962575212637477897785501552646522609988869914013540483809865681250419497686697771007",
+	 "259117086013202627776246767922441530941818887553125427303974923161874019266586362086201209516800483406550695241733194177441689509238807017410377709597512042313066624082916353517952311186154862265604547691127595848775610568757931191017711408826252153849035830401185072116424747461823031471398340229288074545677907941037288235820705892351068433882986888616658650280927692080339605869308790500409503709875902119018371991620994002568935113136548829739112656797303241986517250116412703509705427773477972349821676443446668383119322540099648994051790241624056519054483690809616061625743042361721863339415852426431208737266591962061753535748892894599629195183082621860853400937932839420261866586142503251450773096274235376822938649407127700846077124211823080804139298087057504713825264571448379371125032081826126566649084251699453951887789613650248405739378594599444335231188280123660406262468609212150349937584782292237144339628858485938215738821232393687046160677362909315071",
+	 "190797007524439073807468042969529173669356994749940177394741882673528979787005053706368049835514900244303495954950709725762186311224148828811920216904542206960744666169364221195289538436845390250168663932838805192055137154390912666527533007309292687539092257043362517857366624699975402375462954490293259233303137330643531556539739921926201438606439020075174723029056838272505051571967594608350063404495977660656269020823960825567012344189908927956646011998057988548630107637380993519826582389781888135705408653045219655801758081251164080554609057468028203308718724654081055323215860189611391296030471108443146745671967766308925858547271507311563765171008318248647110097614890313562856541784154881743146033909602737947385055355960331855614540900081456378659068370317267696980001187750995491090350108417050917991562167972281070161305972518044872048331306383715094854938415738549894606070722584737978176686422134354526989443028353644037187375385397838259511833166416134323695660367676897722287918773420968982326089026150031515424165462111337527431154890666327374921446276833564519776797633875503548665093914556482031482248883127023777039667707976559857333357013727342079099064400455741830654320379350833236245819348824064783585692924881021978332974949906122664421376034687815350484991",

-         /* DR moduli */
-         "14059105607947488696282932836518693308967803494693489478439861164411992439598399594747002144074658928593502845729752797260025831423419686528151609940203368612079",
-         "101745825697019260773923519755878567461315282017759829107608914364075275235254395622580447400994175578963163918967182013639660669771108475957692810857098847138903161308502419410142185759152435680068435915159402496058513611411688900243039",
-         "736335108039604595805923406147184530889923370574768772191969612422073040099331944991573923112581267542507986451953227192970402893063850485730703075899286013451337291468249027691733891486704001513279827771740183629161065194874727962517148100775228363421083691764065477590823919364012917984605619526140821797602431",
-         "38564998830736521417281865696453025806593491967131023221754800625044118265468851210705360385717536794615180260494208076605798671660719333199513807806252394423283413430106003596332513246682903994829528690198205120921557533726473585751382193953592127439965050261476810842071573684505878854588706623484573925925903505747545471088867712185004135201289273405614415899438276535626346098904241020877974002916168099951885406379295536200413493190419727789712076165162175783",
-         "542189391331696172661670440619180536749994166415993334151601745392193484590296600979602378676624808129613777993466242203025054573692562689251250471628358318743978285860720148446448885701001277560572526947619392551574490839286458454994488665744991822837769918095117129546414124448777033941223565831420390846864429504774477949153794689948747680362212954278693335653935890352619041936727463717926744868338358149568368643403037768649616778526013610493696186055899318268339432671541328195724261329606699831016666359440874843103020666106568222401047720269951530296879490444224546654729111504346660859907296364097126834834235287147",
-         "1487259134814709264092032648525971038895865645148901180585340454985524155135260217788758027400478312256339496385275012465661575576202252063145698732079880294664220579764848767704076761853197216563262660046602703973050798218246170835962005598561669706844469447435461092542265792444947706769615695252256130901271870341005768912974433684521436211263358097522726462083917939091760026658925757076733484173202927141441492573799914240222628795405623953109131594523623353044898339481494120112723445689647986475279242446083151413667587008191682564376412347964146113898565886683139407005941383669325997475076910488086663256335689181157957571445067490187939553165903773554290260531009121879044170766615232300936675369451260747671432073394867530820527479172464106442450727640226503746586340279816318821395210726268291535648506190714616083163403189943334431056876038286530365757187367147446004855912033137386225053275419626102417236133948503",
-         "1095121115716677802856811290392395128588168592409109494900178008967955253005183831872715423151551999734857184538199864469605657805519106717529655044054833197687459782636297255219742994736751541815269727940751860670268774903340296040006114013971309257028332849679096824800250742691718610670812374272414086863715763724622797509437062518082383056050144624962776302147890521249477060215148275163688301275847155316042279405557632639366066847442861422164832655874655824221577849928863023018366835675399949740429332468186340518172487073360822220449055340582568461568645259954873303616953776393853174845132081121976327462740354930744487429617202585015510744298530101547706821590188733515880733527449780963163909830077616357506845523215289297624086914545378511082534229620116563260168494523906566709418166011112754529766183554579321224940951177394088465596712620076240067370589036924024728375076210477267488679008016579588696191194060127319035195370137160936882402244399699172017835144537488486396906144217720028992863941288217185353914991583400421682751000603596655790990815525126154394344641336397793791497068253936771017031980867706707490224041075826337383538651825493679503771934836094655802776331664261631740148281763487765852746577808019633679",
+	 /* DR moduli */
+	 "14059105607947488696282932836518693308967803494693489478439861164411992439598399594747002144074658928593502845729752797260025831423419686528151609940203368612079",
+	 "101745825697019260773923519755878567461315282017759829107608914364075275235254395622580447400994175578963163918967182013639660669771108475957692810857098847138903161308502419410142185759152435680068435915159402496058513611411688900243039",
+	 "736335108039604595805923406147184530889923370574768772191969612422073040099331944991573923112581267542507986451953227192970402893063850485730703075899286013451337291468249027691733891486704001513279827771740183629161065194874727962517148100775228363421083691764065477590823919364012917984605619526140821797602431",
+	 "38564998830736521417281865696453025806593491967131023221754800625044118265468851210705360385717536794615180260494208076605798671660719333199513807806252394423283413430106003596332513246682903994829528690198205120921557533726473585751382193953592127439965050261476810842071573684505878854588706623484573925925903505747545471088867712185004135201289273405614415899438276535626346098904241020877974002916168099951885406379295536200413493190419727789712076165162175783",
+	 "542189391331696172661670440619180536749994166415993334151601745392193484590296600979602378676624808129613777993466242203025054573692562689251250471628358318743978285860720148446448885701001277560572526947619392551574490839286458454994488665744991822837769918095117129546414124448777033941223565831420390846864429504774477949153794689948747680362212954278693335653935890352619041936727463717926744868338358149568368643403037768649616778526013610493696186055899318268339432671541328195724261329606699831016666359440874843103020666106568222401047720269951530296879490444224546654729111504346660859907296364097126834834235287147",
+	 "1487259134814709264092032648525971038895865645148901180585340454985524155135260217788758027400478312256339496385275012465661575576202252063145698732079880294664220579764848767704076761853197216563262660046602703973050798218246170835962005598561669706844469447435461092542265792444947706769615695252256130901271870341005768912974433684521436211263358097522726462083917939091760026658925757076733484173202927141441492573799914240222628795405623953109131594523623353044898339481494120112723445689647986475279242446083151413667587008191682564376412347964146113898565886683139407005941383669325997475076910488086663256335689181157957571445067490187939553165903773554290260531009121879044170766615232300936675369451260747671432073394867530820527479172464106442450727640226503746586340279816318821395210726268291535648506190714616083163403189943334431056876038286530365757187367147446004855912033137386225053275419626102417236133948503",
+	 "1095121115716677802856811290392395128588168592409109494900178008967955253005183831872715423151551999734857184538199864469605657805519106717529655044054833197687459782636297255219742994736751541815269727940751860670268774903340296040006114013971309257028332849679096824800250742691718610670812374272414086863715763724622797509437062518082383056050144624962776302147890521249477060215148275163688301275847155316042279405557632639366066847442861422164832655874655824221577849928863023018366835675399949740429332468186340518172487073360822220449055340582568461568645259954873303616953776393853174845132081121976327462740354930744487429617202585015510744298530101547706821590188733515880733527449780963163909830077616357506845523215289297624086914545378511082534229620116563260168494523906566709418166011112754529766183554579321224940951177394088465596712620076240067370589036924024728375076210477267488679008016579588696191194060127319035195370137160936882402244399699172017835144537488486396906144217720028992863941288217185353914991583400421682751000603596655790990815525126154394344641336397793791497068253936771017031980867706707490224041075826337383538651825493679503771934836094655802776331664261631740148281763487765852746577808019633679",

-         /* generic unrestricted moduli */
-         "17933601194860113372237070562165128350027320072176844226673287945873370751245439587792371960615073855669274087805055507977323024886880985062002853331424203",
-         "2893527720709661239493896562339544088620375736490408468011883030469939904368086092336458298221245707898933583190713188177399401852627749210994595974791782790253946539043962213027074922559572312141181787434278708783207966459019479487",
-         "347743159439876626079252796797422223177535447388206607607181663903045907591201940478223621722118173270898487582987137708656414344685816179420855160986340457973820182883508387588163122354089264395604796675278966117567294812714812796820596564876450716066283126720010859041484786529056457896367683122960411136319",
-         "47266428956356393164697365098120418976400602706072312735924071745438532218237979333351774907308168340693326687317443721193266215155735814510792148768576498491199122744351399489453533553203833318691678263241941706256996197460424029012419012634671862283532342656309677173602509498417976091509154360039893165037637034737020327399910409885798185771003505320583967737293415979917317338985837385734747478364242020380416892056650841470869294527543597349250299539682430605173321029026555546832473048600327036845781970289288898317888427517364945316709081173840186150794397479045034008257793436817683392375274635794835245695887",
-         "436463808505957768574894870394349739623346440601945961161254440072143298152040105676491048248110146278752857839930515766167441407021501229924721335644557342265864606569000117714935185566842453630868849121480179691838399545644365571106757731317371758557990781880691336695584799313313687287468894148823761785582982549586183756806449017542622267874275103877481475534991201849912222670102069951687572917937634467778042874315463238062009202992087620963771759666448266532858079402669920025224220613419441069718482837399612644978839925207109870840278194042158748845445131729137117098529028886770063736487420613144045836803985635654192482395882603511950547826439092832800532152534003936926017612446606135655146445620623395788978726744728503058670046885876251527122350275750995227",
-         "11424167473351836398078306042624362277956429440521137061889702611766348760692206243140413411077394583180726863277012016602279290144126785129569474909173584789822341986742719230331946072730319555984484911716797058875905400999504305877245849119687509023232790273637466821052576859232452982061831009770786031785669030271542286603956118755585683996118896215213488875253101894663403069677745948305893849505434201763745232895780711972432011344857521691017896316861403206449421332243658855453435784006517202894181640562433575390821384210960117518650374602256601091379644034244332285065935413233557998331562749140202965844219336298970011513882564935538704289446968322281451907487362046511461221329799897350993370560697505809686438782036235372137015731304779072430260986460269894522159103008260495503005267165927542949439526272736586626709581721032189532726389643625590680105784844246152702670169304203783072275089194754889511973916207",
-         "1214855636816562637502584060163403830270705000634713483015101384881871978446801224798536155406895823305035467591632531067547890948695117172076954220727075688048751022421198712032848890056357845974246560748347918630050853933697792254955890439720297560693579400297062396904306270145886830719309296352765295712183040773146419022875165382778007040109957609739589875590885701126197906063620133954893216612678838507540777138437797705602453719559017633986486649523611975865005712371194067612263330335590526176087004421363598470302731349138773205901447704682181517904064735636518462452242791676541725292378925568296858010151852326316777511935037531017413910506921922450666933202278489024521263798482237150056835746454842662048692127173834433089016107854491097456725016327709663199738238442164843147132789153725513257167915555162094970853584447993125488607696008169807374736711297007473812256272245489405898470297178738029484459690836250560495461579533254473316340608217876781986188705928270735695752830825527963838355419762516246028680280988020401914551825487349990306976304093109384451438813251211051597392127491464898797406789175453067960072008590614886532333015881171367104445044718144312416815712216611576221546455968770801413440778423979",
-         NULL
+	 /* generic unrestricted moduli */
+	 "17933601194860113372237070562165128350027320072176844226673287945873370751245439587792371960615073855669274087805055507977323024886880985062002853331424203",
+	 "2893527720709661239493896562339544088620375736490408468011883030469939904368086092336458298221245707898933583190713188177399401852627749210994595974791782790253946539043962213027074922559572312141181787434278708783207966459019479487",
+	 "347743159439876626079252796797422223177535447388206607607181663903045907591201940478223621722118173270898487582987137708656414344685816179420855160986340457973820182883508387588163122354089264395604796675278966117567294812714812796820596564876450716066283126720010859041484786529056457896367683122960411136319",
+	 "47266428956356393164697365098120418976400602706072312735924071745438532218237979333351774907308168340693326687317443721193266215155735814510792148768576498491199122744351399489453533553203833318691678263241941706256996197460424029012419012634671862283532342656309677173602509498417976091509154360039893165037637034737020327399910409885798185771003505320583967737293415979917317338985837385734747478364242020380416892056650841470869294527543597349250299539682430605173321029026555546832473048600327036845781970289288898317888427517364945316709081173840186150794397479045034008257793436817683392375274635794835245695887",
+	 "436463808505957768574894870394349739623346440601945961161254440072143298152040105676491048248110146278752857839930515766167441407021501229924721335644557342265864606569000117714935185566842453630868849121480179691838399545644365571106757731317371758557990781880691336695584799313313687287468894148823761785582982549586183756806449017542622267874275103877481475534991201849912222670102069951687572917937634467778042874315463238062009202992087620963771759666448266532858079402669920025224220613419441069718482837399612644978839925207109870840278194042158748845445131729137117098529028886770063736487420613144045836803985635654192482395882603511950547826439092832800532152534003936926017612446606135655146445620623395788978726744728503058670046885876251527122350275750995227",
+	 "11424167473351836398078306042624362277956429440521137061889702611766348760692206243140413411077394583180726863277012016602279290144126785129569474909173584789822341986742719230331946072730319555984484911716797058875905400999504305877245849119687509023232790273637466821052576859232452982061831009770786031785669030271542286603956118755585683996118896215213488875253101894663403069677745948305893849505434201763745232895780711972432011344857521691017896316861403206449421332243658855453435784006517202894181640562433575390821384210960117518650374602256601091379644034244332285065935413233557998331562749140202965844219336298970011513882564935538704289446968322281451907487362046511461221329799897350993370560697505809686438782036235372137015731304779072430260986460269894522159103008260495503005267165927542949439526272736586626709581721032189532726389643625590680105784844246152702670169304203783072275089194754889511973916207",
+	 "1214855636816562637502584060163403830270705000634713483015101384881871978446801224798536155406895823305035467591632531067547890948695117172076954220727075688048751022421198712032848890056357845974246560748347918630050853933697792254955890439720297560693579400297062396904306270145886830719309296352765295712183040773146419022875165382778007040109957609739589875590885701126197906063620133954893216612678838507540777138437797705602453719559017633986486649523611975865005712371194067612263330335590526176087004421363598470302731349138773205901447704682181517904064735636518462452242791676541725292378925568296858010151852326316777511935037531017413910506921922450666933202278489024521263798482237150056835746454842662048692127173834433089016107854491097456725016327709663199738238442164843147132789153725513257167915555162094970853584447993125488607696008169807374736711297007473812256272245489405898470297178738029484459690836250560495461579533254473316340608217876781986188705928270735695752830825527963838355419762516246028680280988020401914551825487349990306976304093109384451438813251211051597392127491464898797406789175453067960072008590614886532333015881171367104445044718144312416815712216611576221546455968770801413440778423979",
+	 NULL
      };
-   log = fopen("logs/expt.log", "w");
-   logb = fopen("logs/expt_dr.log", "w");
-   logc = fopen("logs/expt_2k.log", "w");
-   for (n = 0; primes[n]; n++) {
-      SLEEP;
-      mp_read_radix(&a, primes[n], 10);
-      mp_zero(&b);
-      for (rr = 0; rr < (unsigned)mp_count_bits(&a); rr++) {
-         mp_mul_2(&b, &b);
-         b.dp[0] |= lbit();
-         b.used  += 1;
+      log = fopen("logs/expt.log", "w");
+      logb = fopen("logs/expt_dr.log", "w");
+      logc = fopen("logs/expt_2k.log", "w");
+      logd = fopen("logs/expt_2kl.log", "w");
+      for (n = 0; primes[n]; n++) {
+	 SLEEP;
+	 mp_read_radix(&a, primes[n], 10);
+	 mp_zero(&b);
+	 for (rr = 0; rr < (unsigned) mp_count_bits(&a); rr++) {
+	    mp_mul_2(&b, &b);
+	    b.dp[0] |= lbit();
+	    b.used += 1;
+	 }
+	 mp_sub_d(&a, 1, &c);
+	 mp_mod(&b, &c, &b);
+	 mp_set(&c, 3);
+	 rr = 0;
+	 tt = -1;
+	 do {
+	    gg = TIMFUNC();
+	    DO(mp_exptmod(&c, &b, &a, &d));
+	    gg = (TIMFUNC() - gg) >> 1;
+	    if (tt > gg)
+	       tt = gg;
+	 } while (++rr < 10);
+	 mp_sub_d(&a, 1, &e);
+	 mp_sub(&e, &b, &b);
+	 mp_exptmod(&c, &b, &a, &e);	/* c^(p-1-b) mod a */
+	 mp_mulmod(&e, &d, &a, &d);	/* c^b * c^(p-1-b) == c^p-1 == 1 */
+	 if (mp_cmp_d(&d, 1)) {
+	    printf("Different (%d)!!!\n", mp_count_bits(&a));
+	    draw(&d);
+	    exit(0);
+	 }
+	 printf("Exponentiating\t%4d-bit => %9llu/sec, %9llu cycles\n",
+		mp_count_bits(&a), CLK_PER_SEC / tt, tt);
+	 fprintf(n < 4 ? logd : (n < 9) ? logc : (n < 16) ? logb : log,
+		 "%d %9llu\n", mp_count_bits(&a), tt);
      }
-      mp_sub_d(&a, 1, &c);
-      mp_mod(&b, &c, &b);
-      mp_set(&c, 3);
-         rr = 0;
-         tt = -1;
-         do {
-            gg = TIMFUNC();
-            DO(mp_exptmod(&c, &b, &a, &d));
-            gg = (TIMFUNC() - gg)>>1;
-            if (tt > gg) tt = gg;
-         } while (++rr < 10);
-      mp_sub_d(&a, 1, &e);
-      mp_sub(&e, &b, &b);
-      mp_exptmod(&c, &b, &a, &e);  /* c^(p-1-b) mod a */
-      mp_mulmod(&e, &d, &a, &d);   /* c^b * c^(p-1-b) == c^p-1 == 1 */
-      if (mp_cmp_d(&d, 1)) {
-         printf("Different (%d)!!!\n", mp_count_bits(&a));
-         draw(&d);
-         exit(0);
-      }
-      printf("Exponentiating\t%4d-bit => %9llu/sec, %9llu cycles\n", mp_count_bits(&a), CLK_PER_SEC/tt, tt);
-      fprintf((n < 6) ? logc : (n < 13) ? logb : log, "%d %9llu\n", mp_count_bits(&a), tt);
-   }
   }
   fclose(log);
   fclose(logb);
   fclose(logc);
+   fclose(logd);

   log = fopen("logs/invmod.log", "w");
   for (cnt = 4; cnt <= 128; cnt += 4) {
@@ -264,28 +287,29 @@ int main(void)
      mp_rand(&b, cnt);

      do {
-         mp_add_d(&b, 1, &b);
-         mp_gcd(&a, &b, &c);
+	 mp_add_d(&b, 1, &b);
+	 mp_gcd(&a, &b, &c);
      } while (mp_cmp_d(&c, 1) != MP_EQ);

-         rr = 0;
-         tt = -1;
+      rr = 0;
+      tt = -1;
      do {
-         gg = TIMFUNC();
-         DO(mp_invmod(&b, &a, &c));
-         gg = (TIMFUNC() - gg)>>1;
-         if (tt > gg) tt = gg;
+	 gg = TIMFUNC();
+	 DO(mp_invmod(&b, &a, &c));
+	 gg = (TIMFUNC() - gg) >> 1;
+	 if (tt > gg)
+	    tt = gg;
      } while (++rr < 1000);
      mp_mulmod(&b, &c, &a, &d);
      if (mp_cmp_d(&d, 1) != MP_EQ) {
-         printf("Failed to invert\n");
-         return 0;
+	 printf("Failed to invert\n");
+	 return 0;
      }
-      printf("Inverting mod\t%4d-bit => %9llu/sec, %9llu cycles\n", mp_count_bits(&a), CLK_PER_SEC/tt, tt);
-      fprintf(log, "%d %9llu\n", cnt*DIGIT_BIT, tt);
+      printf("Inverting mod\t%4d-bit => %9llu/sec, %9llu cycles\n",
+	     mp_count_bits(&a), CLK_PER_SEC / tt, tt);
+      fprintf(log, "%d %9llu\n", cnt * DIGIT_BIT, tt);
   }
   fclose(log);

   return 0;
 }
-
--- a/dep.pl
+++ b/dep.pl
@@ -13,6 +13,8 @@ print CLASS "#if !(defined(LTM1) && defined(LTM2) && defined(LTM3))\n#if defined
 foreach my $filename (glob "bn*.c") {
   my $define = $filename;

+print "Processing $filename\n";
+
   # convert filename to upper case so we can use it as a define 
   $define =~ tr/[a-z]/[A-Z]/;
   $define =~ tr/\./_/;
--- a/etc/mersenne.c
+++ b/etc/mersenne.c
@@ -18,15 +18,15 @@ is_mersenne (long s, int *pp)
  }

  if ((res = mp_init (&u)) != MP_OKAY) {
-    goto __N;
+    goto LBL_N;
  }

  /* n = 2^s - 1 */
  if ((res = mp_2expt(&n, s)) != MP_OKAY) {
-     goto __MU;
+     goto LBL_MU;
  }
  if ((res = mp_sub_d (&n, 1, &n)) != MP_OKAY) {
-    goto __MU;
+    goto LBL_MU;
  }

  /* set u=4 */
@@ -36,22 +36,22 @@ is_mersenne (long s, int *pp)
  for (k = 1; k <= s - 2; k++) {
    /* u = u^2 - 2 mod n */
    if ((res = mp_sqr (&u, &u)) != MP_OKAY) {
-      goto __MU;
+      goto LBL_MU;
    }
    if ((res = mp_sub_d (&u, 2, &u)) != MP_OKAY) {
-      goto __MU;
+      goto LBL_MU;
    }

    /* make sure u is positive */
    while (u.sign == MP_NEG) {
      if ((res = mp_add (&u, &n, &u)) != MP_OKAY) {
-         goto __MU;
+         goto LBL_MU;
      }
    }

    /* reduce */
    if ((res = mp_reduce_2k (&u, &n, 1)) != MP_OKAY) {
-      goto __MU;
+      goto LBL_MU;
    }
  }

@@ -62,8 +62,8 @@ is_mersenne (long s, int *pp)
  }

  res = MP_OKAY;
-__MU:mp_clear (&u);
-__N:mp_clear (&n);
+LBL_MU:mp_clear (&u);
+LBL_N:mp_clear (&n);
  return res;
 }

--- a/etc/pprime.c
+++ b/etc/pprime.c
@@ -189,7 +189,7 @@ pprime (int k, int li, mp_int * p, mp_int * q)
  }

  if ((res = mp_init (&v)) != MP_OKAY) {
-    goto __C;
+    goto LBL_C;
  }

  /* product of first 50 primes */
@@ -197,34 +197,34 @@ pprime (int k, int li, mp_int * p, mp_int * q)
       mp_read_radix (&v,
 		      "19078266889580195013601891820992757757219839668357012055907516904309700014933909014729740190",
 		      10)) != MP_OKAY) {
-    goto __V;
+    goto LBL_V;
  }

  if ((res = mp_init (&a)) != MP_OKAY) {
-    goto __V;
+    goto LBL_V;
  }

  /* set the prime */
  mp_set (&a, prime_digit ());

  if ((res = mp_init (&b)) != MP_OKAY) {
-    goto __A;
+    goto LBL_A;
  }

  if ((res = mp_init (&n)) != MP_OKAY) {
-    goto __B;
+    goto LBL_B;
  }

  if ((res = mp_init (&x)) != MP_OKAY) {
-    goto __N;
+    goto LBL_N;
  }

  if ((res = mp_init (&y)) != MP_OKAY) {
-    goto __X;
+    goto LBL_X;
  }

  if ((res = mp_init (&z)) != MP_OKAY) {
-    goto __Y;
+    goto LBL_Y;
  }

  /* now loop making the single digit */
@@ -236,25 +236,25 @@ pprime (int k, int li, mp_int * p, mp_int * q)

    /* now compute z = a * b * 2 */
    if ((res = mp_mul (&a, &b, &z)) != MP_OKAY) {	/* z = a * b */
-      goto __Z;
+      goto LBL_Z;
    }

    if ((res = mp_copy (&z, &c)) != MP_OKAY) {	/* c = a * b */
-      goto __Z;
+      goto LBL_Z;
    }

    if ((res = mp_mul_2 (&z, &z)) != MP_OKAY) {	/* z = 2 * a * b */
-      goto __Z;
+      goto LBL_Z;
    }

    /* n = z + 1 */
    if ((res = mp_add_d (&z, 1, &n)) != MP_OKAY) {	/* n = z + 1 */
-      goto __Z;
+      goto LBL_Z;
    }

    /* check (n, v) == 1 */
    if ((res = mp_gcd (&n, &v, &y)) != MP_OKAY) {	/* y = (n, v) */
-      goto __Z;
+      goto LBL_Z;
    }

    if (mp_cmp_d (&y, 1) != MP_EQ)
@@ -266,7 +266,7 @@ pprime (int k, int li, mp_int * p, mp_int * q)

      /* compute x^a mod n */
      if ((res = mp_exptmod (&x, &a, &n, &y)) != MP_OKAY) {	/* y = x^a mod n */
-	goto __Z;
+	goto LBL_Z;
      }

      /* if y == 1 loop */
@@ -275,7 +275,7 @@ pprime (int k, int li, mp_int * p, mp_int * q)

      /* now x^2a mod n */
      if ((res = mp_sqrmod (&y, &n, &y)) != MP_OKAY) {	/* y = x^2a mod n */
-	goto __Z;
+	goto LBL_Z;
      }

      if (mp_cmp_d (&y, 1) == MP_EQ)
@@ -283,7 +283,7 @@ pprime (int k, int li, mp_int * p, mp_int * q)

      /* compute x^b mod n */
      if ((res = mp_exptmod (&x, &b, &n, &y)) != MP_OKAY) {	/* y = x^b mod n */
-	goto __Z;
+	goto LBL_Z;
      }

      /* if y == 1 loop */
@@ -292,7 +292,7 @@ pprime (int k, int li, mp_int * p, mp_int * q)

      /* now x^2b mod n */
      if ((res = mp_sqrmod (&y, &n, &y)) != MP_OKAY) {	/* y = x^2b mod n */
-	goto __Z;
+	goto LBL_Z;
      }

      if (mp_cmp_d (&y, 1) == MP_EQ)
@@ -300,7 +300,7 @@ pprime (int k, int li, mp_int * p, mp_int * q)

      /* compute x^c mod n == x^ab mod n */
      if ((res = mp_exptmod (&x, &c, &n, &y)) != MP_OKAY) {	/* y = x^ab mod n */
-	goto __Z;
+	goto LBL_Z;
      }

      /* if y == 1 loop */
@@ -309,7 +309,7 @@ pprime (int k, int li, mp_int * p, mp_int * q)

      /* now compute (x^c mod n)^2 */
      if ((res = mp_sqrmod (&y, &n, &y)) != MP_OKAY) {	/* y = x^2ab mod n */
-	goto __Z;
+	goto LBL_Z;
      }

      /* y should be 1 */
@@ -346,14 +346,14 @@ pprime (int k, int li, mp_int * p, mp_int * q)
  mp_exch (&n, p);

  res = MP_OKAY;
-__Z:mp_clear (&z);
-__Y:mp_clear (&y);
-__X:mp_clear (&x);
-__N:mp_clear (&n);
-__B:mp_clear (&b);
-__A:mp_clear (&a);
-__V:mp_clear (&v);
-__C:mp_clear (&c);
+LBL_Z:mp_clear (&z);
+LBL_Y:mp_clear (&y);
+LBL_X:mp_clear (&x);
+LBL_N:mp_clear (&n);
+LBL_B:mp_clear (&b);
+LBL_A:mp_clear (&a);
+LBL_V:mp_clear (&v);
+LBL_C:mp_clear (&c);
  return res;
 }

--- a/etc/tune.c
+++ b/etc/tune.c
@@ -10,13 +10,44 @@
 */
 #define TIMES (1UL<<14UL)

+/* RDTSC from Scott Duplichan */
+static ulong64 TIMFUNC (void)
+   {
+   #if defined __GNUC__
+      #if defined(__i386__) || defined(__x86_64__)
+         unsigned long long a;
+         __asm__ __volatile__ ("rdtsc\nmovl %%eax,%0\nmovl %%edx,4+%0\n"::"m"(a):"%eax","%edx");
+         return a;
+      #else /* gcc-IA64 version */
+         unsigned long result;
+         __asm__ __volatile__("mov %0=ar.itc" : "=r"(result) :: "memory");
+         while (__builtin_expect ((int) result == -1, 0))
+         __asm__ __volatile__("mov %0=ar.itc" : "=r"(result) :: "memory");
+         return result;
+      #endif
+
+   // Microsoft and Intel Windows compilers
+   #elif defined _M_IX86
+     __asm rdtsc
+   #elif defined _M_AMD64
+     return __rdtsc ();
+   #elif defined _M_IA64
+     #if defined __INTEL_COMPILER
+       #include <ia64intrin.h>
+     #endif
+      return __getReg (3116);
+   #else
+     #error need rdtsc function for this build
+   #endif
+   }
+

 #ifndef X86_TIMER

 /* generic ISO C timer */
-ulong64 __T;
-void t_start(void) { __T = clock(); }
-ulong64 t_read(void) { return clock() - __T; }
+ulong64 LBL_T;
+void t_start(void) { LBL_T = TIMFUNC(); }
+ulong64 t_read(void) { return TIMFUNC() - LBL_T; }

 #else
 extern void t_start(void);
--- a/logs/add.log
+++ b/logs/add.log
@@ -1,16 +1,16 @@
-224       222
-448       330
-672       436
-896       520
-1120       612
-1344       696
-1568       810
-1792       912
-2016      1006
-2240      1116
-2464      1152
-2688      1284
-2912      1348
-3136      1486
-3360      1580
-3584      1636
+480        87
+960       111
+1440       135
+1920       159
+2400       200
+2880       224
+3360       248
+3840       272
+4320       296
+4800       320
+5280       344
+5760       368
+6240       392
+6720       416
+7200       440
+7680       464
--- a/logs/expt.log
+++ b/logs/expt.log
@@ -0,0 +1,7 @@
+513   1489160
+769   3688476
+1025   8162061
+2049  49260015
+2561  89579052
+3073 148797060
+4097 324449263
--- a/logs/expt_2k.log
+++ b/logs/expt_2k.log
@@ -0,0 +1,5 @@
+607   2272809
+1279   9557382
+2203  36250309
+3217  87666486
+4253 174168369
--- a/logs/expt_2kl.log
+++ b/logs/expt_2kl.log
@@ -0,0 +1,4 @@
+1024   6954080
+2048  35993987
+4096 176068521
+521   1683720
--- a/logs/expt_dr.log
+++ b/logs/expt_dr.log
@@ -0,0 +1,7 @@
+532   1989592
+784   3898697
+1036   6519700
+1540  15676650
+2072  33128187
+3080  82963362
+4116 168358337
--- a/logs/mult.log
+++ b/logs/mult.log
@@ -1,143 +1,84 @@
-140      1272
-195      1428
-252      1996
-307      2586
-364      3464
-420      4420
-476      5260
-532      6430
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+10228    203298
--- a/logs/mult_kara.log
+++ b/logs/mult_kara.log
@@ -1,33 +1,84 @@
-924     16686
-1146     25334
-1371     35304
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+10231    176412
--- a/logs/sqr.log
+++ b/logs/sqr.log
@@ -1,143 +1,84 @@
-139       806
-195      1212
-252      1604
-307      2260
-364      2892
-420      3308
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-6524    994088
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-6636   1027178
-6692   1045466
-6747   1056910
-6804   1083784
-6860   1104706
-6915   1116450
-6972   1137894
-7028   1154670
-7084   1158064
-7138   1188734
-7196   1214218
-7249   1226822
-7307   1247528
-7363   1255338
-7420   1291104
-7475   1297940
-7532   1324994
-7587   1340274
-7644   1342596
-7698   1381418
-7756   1382904
-7812   1432588
-7867   1443632
-7922   1465092
-7979   1496804
-8036   1520142
-8092   1539566
+265       562
+389       882
+509      1207
+631      1572
+750      1990
+859      2433
+991      2894
+1109      3555
+1230      4228
+1350      5018
+1471      5805
+1591      6579
+1709      7415
+1829      8329
+1949      9225
+2071     10139
+2188     11239
+2309     12178
+2431     13212
+2551     14294
+2671     15551
+2791     16512
+2911     17718
+3030     18876
+3150     20259
+3270     21374
+3391     22650
+3511     23948
+3631     25493
+3750     26756
+3870     28225
+3989     29705
+4110     31409
+4230     32834
+4351     34327
+4471     35818
+4591     37636
+4711     39228
+4830     40868
+4949     42393
+5070     44541
+5191     46269
+5310     48162
+5429     49728
+5548     51985
+5671     53948
+5791     55885
+5910     57584
+6031     60082
+6150     62239
+6270     64309
+6390     66014
+6511     68766
+6631     71012
+6750     73172
+6871     74952
+6991     77909
+7111     80371
+7231     82666
+7351     84531
+7469     87698
+7589     90318
+7711    225384
+7830    232428
+7950    240009
+8070    246522
+8190    253662
+8310    260961
+8431    269253
+8549    275743
+8671    283769
+8789    290811
+8911    300034
+9030    306873
+9149    315085
+9270    323944
+9390    332390
+9508    337519
+9631    348986
+9749    356904
+9871    367013
+9989    373831
+10108    381033
+10230    393475
--- a/logs/sqr_kara.log
+++ b/logs/sqr_kara.log
@@ -1,33 +1,84 @@
-922     11272
-1148     16004
-1370     21958
-1596     28684
-1817     37832
-2044     46386
-2262     56218
-2492     66388
-2716     77478
-2940     89380
-3163    103680
-3385    116274
-3612    135334
-3836    151332
-4057    164938
-4284    183178
-4508    198864
-4731    215222
-4954    231986
-5180    251660
-5404    269414
-5626    288454
-5850    307806
-6076    329458
-6299    347726
-6523    369864
-6748    387832
-6971    413010
-7194    453310
-7415    476936
-7643    497118
-7867    521394
-8091    540224
+271       560
+388       878
+511      1179
+629      1625
+751      1988
+871      2423
+989      2896
+1111      3561
+1231      4209
+1350      5015
+1470      5804
+1591      6556
+1709      7420
+1831      8263
+1951      9173
+2070     10153
+2191     11229
+2310     12167
+2431     13211
+2550     14309
+2671     15524
+2788     16525
+2910     17712
+3028     18822
+3148     20220
+3271     21343
+3391     22652
+3511     23944
+3630     25485
+3750     26778
+3868     28201
+3990     29653
+4111     31393
+4225     32841
+4350     34328
+4471     35786
+4590     37652
+4711     39245
+4830     40876
+4951     42433
+5068     44547
+5191     46321
+5311     48140
+5430     49727
+5550     52034
+5671     53954
+5791     55921
+5908     57597
+6031     60084
+6148     62226
+6270     64295
+6390     66045
+6511     68779
+6629     71003
+6751     73169
+6871     74992
+6991     77895
+7110     80376
+7231     82628
+7351     84468
+7470     87664
+7591     90284
+7711     91352
+7828     93995
+7950     96276
+8071     98691
+8190    101256
+8308    103631
+8431    105222
+8550    108343
+8671    110281
+8787    112764
+8911    115397
+9031    117690
+9151    120266
+9271    122715
+9391    124624
+9510    127937
+9630    130313
+9750    132914
+9871    136129
+9991    138517
+10108    141525
+10231    144225
--- a/logs/sub.log
+++ b/logs/sub.log
@@ -1,16 +1,16 @@
-224       216
-448       324
-672       428
-896       532
-1120       648
-1344       766
-1568       862
-1792       928
-2016      1070
-2240      1128
-2464      1250
-2688      1344
-2912      1436
-3136      1542
-3360      1628
-3584      1696
+480        94
+960       116
+1440       140
+1920       164
+2400       205
+2880       229
+3360       253
+3840       277
+4320       299
+4800       321
+5280       345
+5760       371
+6240       395
+6720       419
+7200       441
+7680       465
--- a/makefile.bcc
+++ b/makefile.bcc
@@ -27,11 +27,13 @@ bn_mp_prime_is_prime.obj bn_mp_prime_next_prime.obj bn_mp_dr_reduce.obj \
 bn_mp_dr_is_modulus.obj bn_mp_dr_setup.obj bn_mp_reduce_setup.obj \
 bn_mp_toom_mul.obj bn_mp_toom_sqr.obj bn_mp_div_3.obj bn_s_mp_exptmod.obj \
 bn_mp_reduce_2k.obj bn_mp_reduce_is_2k.obj bn_mp_reduce_2k_setup.obj \
+bn_mp_reduce_2k_l.obj bn_mp_reduce_is_2k_l.obj bn_mp_reduce_2k_setup_l.obj \
 bn_mp_radix_smap.obj bn_mp_read_radix.obj bn_mp_toradix.obj bn_mp_radix_size.obj \
 bn_mp_fread.obj bn_mp_fwrite.obj bn_mp_cnt_lsb.obj bn_error.obj \
 bn_mp_init_multi.obj bn_mp_clear_multi.obj bn_mp_exteuclid.obj bn_mp_toradix_n.obj \
 bn_mp_prime_random_ex.obj bn_mp_get_int.obj bn_mp_sqrt.obj bn_mp_is_square.obj \
-bn_mp_init_set.obj bn_mp_init_set_int.obj bn_mp_invmod_slow.obj bn_mp_prime_rabin_miller_trials.obj
+bn_mp_init_set.obj bn_mp_init_set_int.obj bn_mp_invmod_slow.obj bn_mp_prime_rabin_miller_trials.obj \
+bn_mp_to_signed_bin_n.obj bn_mp_to_unsigned_bin_n.obj

 TARGET = libtommath.lib

--- a/makefile.cygwin_dll
+++ b/makefile.cygwin_dll
@@ -32,11 +32,13 @@ bn_mp_prime_is_prime.o bn_mp_prime_next_prime.o bn_mp_dr_reduce.o \
 bn_mp_dr_is_modulus.o bn_mp_dr_setup.o bn_mp_reduce_setup.o \
 bn_mp_toom_mul.o bn_mp_toom_sqr.o bn_mp_div_3.o bn_s_mp_exptmod.o \
 bn_mp_reduce_2k.o bn_mp_reduce_is_2k.o bn_mp_reduce_2k_setup.o \
+bn_mp_reduce_2k_l.o bn_mp_reduce_is_2k_l.o bn_mp_reduce_2k_setup_l.o \
 bn_mp_radix_smap.o bn_mp_read_radix.o bn_mp_toradix.o bn_mp_radix_size.o \
 bn_mp_fread.o bn_mp_fwrite.o bn_mp_cnt_lsb.o bn_error.o \
 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_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

 # make a Windows DLL via Cygwin
 windll:  $(OBJECTS)
--- a/makefile.icc
+++ b/makefile.icc
@@ -21,6 +21,10 @@ CFLAGS  +=  -I./
 # Default to just generic max opts
 CFLAGS += -O3 -xN

+#install as this user
+USER=root
+GROUP=root
+
 default: libtommath.a

 #default files to install
@@ -55,11 +59,13 @@ bn_mp_prime_is_prime.o bn_mp_prime_next_prime.o bn_mp_dr_reduce.o \
 bn_mp_dr_is_modulus.o bn_mp_dr_setup.o bn_mp_reduce_setup.o \
 bn_mp_toom_mul.o bn_mp_toom_sqr.o bn_mp_div_3.o bn_s_mp_exptmod.o \
 bn_mp_reduce_2k.o bn_mp_reduce_is_2k.o bn_mp_reduce_2k_setup.o \
+bn_mp_reduce_2k_l.o bn_mp_reduce_is_2k_l.o bn_mp_reduce_2k_setup_l.o \
 bn_mp_radix_smap.o bn_mp_read_radix.o bn_mp_toradix.o bn_mp_radix_size.o \
 bn_mp_fread.o bn_mp_fwrite.o bn_mp_cnt_lsb.o bn_error.o \
 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_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

 libtommath.a:  $(OBJECTS)
 	$(AR) $(ARFLAGS) libtommath.a $(OBJECTS)
@@ -89,10 +95,10 @@ profiled_single:
 	ranlib libtommath.a	

 install: libtommath.a
-	install -d -g root -o root $(DESTDIR)$(LIBPATH)
-	install -d -g root -o root $(DESTDIR)$(INCPATH)
-	install -g root -o root $(LIBNAME) $(DESTDIR)$(LIBPATH)
-	install -g root -o root $(HEADERS) $(DESTDIR)$(INCPATH)
+	install -d -g $(GROUP) -o $(USER) $(DESTDIR)$(LIBPATH)
+	install -d -g $(GROUP) -o $(USER) $(DESTDIR)$(INCPATH)
+	install -g $(GROUP) -o $(USER) $(LIBNAME) $(DESTDIR)$(LIBPATH)
+	install -g $(GROUP) -o $(USER) $(HEADERS) $(DESTDIR)$(INCPATH)

 test: libtommath.a demo/demo.o
 	$(CC) demo/demo.o libtommath.a -o test
--- a/makefile.msvc
+++ b/makefile.msvc
@@ -26,11 +26,13 @@ bn_mp_prime_is_prime.obj bn_mp_prime_next_prime.obj bn_mp_dr_reduce.obj \
 bn_mp_dr_is_modulus.obj bn_mp_dr_setup.obj bn_mp_reduce_setup.obj \
 bn_mp_toom_mul.obj bn_mp_toom_sqr.obj bn_mp_div_3.obj bn_s_mp_exptmod.obj \
 bn_mp_reduce_2k.obj bn_mp_reduce_is_2k.obj bn_mp_reduce_2k_setup.obj \
+bn_mp_reduce_2k_l.obj bn_mp_reduce_is_2k_l.obj bn_mp_reduce_2k_setup_l.obj \
 bn_mp_radix_smap.obj bn_mp_read_radix.obj bn_mp_toradix.obj bn_mp_radix_size.obj \
 bn_mp_fread.obj bn_mp_fwrite.obj bn_mp_cnt_lsb.obj bn_error.obj \
 bn_mp_init_multi.obj bn_mp_clear_multi.obj bn_mp_exteuclid.obj bn_mp_toradix_n.obj \
 bn_mp_prime_random_ex.obj bn_mp_get_int.obj bn_mp_sqrt.obj bn_mp_is_square.obj \
-bn_mp_init_set.obj bn_mp_init_set_int.obj bn_mp_invmod_slow.obj bn_mp_prime_rabin_miller_trials.obj
+bn_mp_init_set.obj bn_mp_init_set_int.obj bn_mp_invmod_slow.obj bn_mp_prime_rabin_miller_trials.obj \
+bn_mp_to_signed_bin_n.obj bn_mp_to_unsigned_bin_n.obj

 library: $(OBJECTS)
 	lib /out:tommath.lib $(OBJECTS)
--- a/makefile.shared
+++ b/makefile.shared
@@ -1,10 +1,9 @@
 #Makefile for GCC
 #
 #Tom St Denis
-VERSION=0:32
+VERSION=0:35

 CC = libtool --mode=compile gcc
-
 CFLAGS  +=  -I./ -Wall -W -Wshadow -Wsign-compare

 #for speed 
@@ -16,11 +15,15 @@ CFLAGS += -O3 -funroll-loops
 #x86 optimizations [should be valid for any GCC install though]
 CFLAGS  += -fomit-frame-pointer

+#install as this user
+USER=root
+GROUP=root
+
 default: libtommath.la

 #default files to install
 LIBNAME=libtommath.la
-HEADERS=tommath.h
+HEADERS=tommath.h tommath_class.h tommath_superclass.h

 #LIBPATH-The directory for libtommath to be installed to.
 #INCPATH-The directory to install the header files for libtommath.
@@ -50,18 +53,21 @@ bn_mp_prime_is_prime.o bn_mp_prime_next_prime.o bn_mp_dr_reduce.o \
 bn_mp_dr_is_modulus.o bn_mp_dr_setup.o bn_mp_reduce_setup.o \
 bn_mp_toom_mul.o bn_mp_toom_sqr.o bn_mp_div_3.o bn_s_mp_exptmod.o \
 bn_mp_reduce_2k.o bn_mp_reduce_is_2k.o bn_mp_reduce_2k_setup.o \
+bn_mp_reduce_2k_l.o bn_mp_reduce_is_2k_l.o bn_mp_reduce_2k_setup_l.o \
 bn_mp_radix_smap.o bn_mp_read_radix.o bn_mp_toradix.o bn_mp_radix_size.o \
 bn_mp_fread.o bn_mp_fwrite.o bn_mp_cnt_lsb.o bn_error.o \
 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_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
+

 libtommath.la:  $(OBJECTS)
 	libtool --mode=link gcc *.lo -o libtommath.la -rpath $(LIBPATH) -version-info $(VERSION)
 	libtool --mode=link gcc *.o -o libtommath.a 
 	libtool --mode=install install -c libtommath.la $(LIBPATH)/libtommath.la
-	install -d -g root -o root $(DESTDIR)$(INCPATH)
-	install -g root -o root $(HEADERS) $(DESTDIR)$(INCPATH)
+	install -d -g $(GROUP) -o $(USER) $(DESTDIR)$(INCPATH)
+	install -g $(GROUP) -o $(USER) $(HEADERS) $(DESTDIR)$(INCPATH)

 test: libtommath.a demo/demo.o
 	gcc $(CFLAGS) -c demo/demo.c -o demo/demo.o
--- a/mtest/mtest.c
+++ b/mtest/mtest.c
@@ -46,7 +46,7 @@ void rand_num(mp_int *a)
   int n, size;
   unsigned char buf[2048];

-   size = 1 + ((fgetc(rng)<<8) + fgetc(rng)) % 1031;
+   size = 1 + ((fgetc(rng)<<8) + fgetc(rng)) % 101;
   buf[0] = (fgetc(rng)&1)?1:0;
   fread(buf+1, 1, size, rng);
   while (buf[1] == 0) buf[1] = fgetc(rng);
@@ -58,7 +58,7 @@ void rand_num2(mp_int *a)
   int n, size;
   unsigned char buf[2048];

-   size = 10 + ((fgetc(rng)<<8) + fgetc(rng)) % 97;
+   size = 10 + ((fgetc(rng)<<8) + fgetc(rng)) % 101;
   buf[0] = (fgetc(rng)&1)?1:0;
   fread(buf+1, 1, size, rng);
   while (buf[1] == 0) buf[1] = fgetc(rng);
--- a/pre_gen/mpi.c
+++ b/pre_gen/mpi.c
--- a/tombc/grammar.txt
+++ b/tombc/grammar.txt
@@ -0,0 +1,35 @@
+program       := program statement | statement | empty
+statement     := { statement }                                                                              | 
+                 identifier = numexpression;                                                                | 
+                 identifier[numexpression] = numexpression;                                                 |
+                 function(expressionlist);                                                                  | 
+                 for (identifer = numexpression; numexpression; identifier = numexpression) { statement }   |
+                 while (numexpression) { statement }                                                        | 
+                 if (numexpresion) { statement } elif                                                       | 
+                 break;                                                                                     | 
+                 continue;                                                                                  
+                 
+elif          := else statement | empty
+function      := abs | countbits | exptmod | jacobi | print | isprime | nextprime | issquare | readinteger | exit
+expressionlist := expressionlist, expression | expression
+
+// LR(1) !!!?
+expression    := string | numexpression
+numexpression := cmpexpr && cmpexpr | cmpexpr \|\| cmpexpr | cmpexpr
+cmpexpr       := boolexpr  < boolexpr | boolexpr  > boolexpr | boolexpr == boolexpr | 
+                 boolexpr <= boolexpr | boolexpr >= boolexpr | boolexpr
+boolexpr      := shiftexpr & shiftexpr | shiftexpr ^ shiftexpr | shiftexpr \| shiftexpr | shiftexpr
+shiftexpr     := addsubexpr << addsubexpr | addsubexpr >> addsubexpr | addsubexpr
+addsubexpr    := mulexpr + mulexpr | mulexpr - mulexpr | mulexpr
+mulexpr       := expr * expr       | expr / expr | expr % expr | expr
+expr          := -nexpr | nexpr 
+nexpr         := integer | identifier | ( numexpression ) | identifier[numexpression] 
+
+identifier    := identifer digits | identifier alpha | alpha
+alpha         := a ... z | A ... Z
+integer       := hexnumber | digits 
+hexnumber     := 0xhexdigits
+hexdigits     := hexdigits hexdigit | hexdigit
+hexdigit      := 0 ... 9 | a ... f | A ... F
+digits        := digits digit | digit 
+digit         := 0 ... 9
--- a/tommath.h
+++ b/tommath.h
@@ -429,6 +429,15 @@ int mp_reduce_2k_setup(mp_int *a, mp_digit *d);
 /* reduces a modulo b where b is of the form 2**p - k [0 <= a] */
 int mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d);

+/* returns true if a can be reduced with mp_reduce_2k_l */
+int mp_reduce_is_2k_l(mp_int *a);
+
+/* determines k value for 2k reduction */
+int mp_reduce_2k_setup_l(mp_int *a, mp_int *d);
+
+/* reduces a modulo b where b is of the form 2**p - k [0 <= a] */
+int mp_reduce_2k_l(mp_int *a, mp_int *n, mp_int *d);
+
 /* d = a**b (mod c) */
 int mp_exptmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d);

@@ -442,7 +451,7 @@ int mp_exptmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d);
 #endif

 /* table of first PRIME_SIZE primes */
-extern const mp_digit __prime_tab[];
+extern const mp_digit ltm_prime_tab[];

 /* result=1 if a is divisible by one of the first PRIME_SIZE primes */
 int mp_prime_is_divisible(mp_int *a, int *result);
@@ -511,12 +520,14 @@ int mp_count_bits(mp_int *a);
 int mp_unsigned_bin_size(mp_int *a);
 int mp_read_unsigned_bin(mp_int *a, unsigned char *b, int c);
 int mp_to_unsigned_bin(mp_int *a, unsigned char *b);
+int mp_to_unsigned_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen);

 int mp_signed_bin_size(mp_int *a);
 int mp_read_signed_bin(mp_int *a, unsigned char *b, int c);
 int mp_to_signed_bin(mp_int *a, unsigned char *b);
+int mp_to_signed_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen);

-int mp_read_radix(mp_int *a, char *str, int radix);
+int mp_read_radix(mp_int *a, const char *str, int radix);
 int mp_toradix(mp_int *a, char *str, int radix);
 int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen);
 int mp_radix_size(mp_int *a, int radix, int *size);
@@ -554,7 +565,7 @@ int fast_mp_invmod(mp_int *a, mp_int *b, mp_int *c);
 int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c);
 int fast_mp_montgomery_reduce(mp_int *a, mp_int *m, mp_digit mp);
 int mp_exptmod_fast(mp_int *G, mp_int *X, mp_int *P, mp_int *Y, int mode);
-int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y);
+int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int mode);
 void bn_reverse(unsigned char *s, int len);

 extern const char *mp_s_rmap;
--- a/tommath.src
+++ b/tommath.src
@@ -49,7 +49,7 @@
 \begin{document}
 \frontmatter
 \pagestyle{empty}
-\title{Implementing Multiple Precision Arithmetic \\ ~ \\ Draft Edition }
+\title{Multi--Precision Math}
 \author{\mbox{
 %\begin{small}
 \begin{tabular}{c}
@@ -66,7 +66,7 @@ QUALCOMM Australia \\
 }
 }
 \maketitle
-This text has been placed in the public domain.  This text corresponds to the v0.30 release of the 
+This text has been placed in the public domain.  This text corresponds to the v0.35 release of the 
 LibTomMath project.

 \begin{alltt}
@@ -85,66 +85,32 @@ This text is formatted to the international B5 paper size of 176mm wide by 250mm

 \tableofcontents
 \listoffigures
-\chapter*{Prefaces to the Draft Edition}
-I started this text in April 2003 to complement my LibTomMath library.  That is, explain how to implement the functions
-contained in LibTomMath.  The goal is to have a textbook that any Computer Science student can use when implementing their
-own multiple precision arithmetic.  The plan I wanted to follow was flesh out all the
-ideas and concepts I had floating around in my head and then work on it afterwards refining a little bit at a time.  Chance
-would have it that I ended up with my summer off from Algonquin College and I was given four months solid to work on the
-text.  
+\chapter*{Prefaces}
+When I tell people about my LibTom projects and that I release them as public domain they are often puzzled.  
+They ask why I did it and especially why I continue to work on them for free.  The best I can explain it is ``Because I can.''  
+Which seems odd and perhaps too terse for adult conversation. I often qualify it with ``I am able, I am willing.'' which 
+perhaps explains it better.  I am the first to admit there is not anything that special with what I have done.  Perhaps
+others can see that too and then we would have a society to be proud of.  My LibTom projects are what I am doing to give 
+back to society in the form of tools and knowledge that can help others in their endeavours.

-Choosing to not waste any time I dove right into the project even before my spring semester was finished.  I wrote a bit
-off and on at first.  The moment my exams were finished I jumped into long 12 to 16 hour days.  The result after only
-a couple of months was a ten chapter, three hundred page draft that I quickly had distributed to anyone who wanted
-to read it.  I had Jean-Luc Cooke print copies for me and I brought them to Crypto'03 in Santa Barbara.  So far I have
-managed to grab a certain level of attention having people from around the world ask me for copies of the text was certain
-rewarding.
+I started writing this book because it was the most logical task to further my goal of open academia.  The LibTomMath source
+code itself was written to be easy to follow and learn from.  There are times, however, where pure C source code does not
+explain the algorithms properly.  Hence this book.  The book literally starts with the foundation of the library and works
+itself outwards to the more complicated algorithms.  The use of both pseudo--code and verbatim source code provides a duality
+of ``theory'' and ``practice'' that the computer science students of the world shall appreciate.  I never deviate too far
+from relatively straightforward algebra and I hope that this book can be a valuable learning asset.

-Now we are past December 2003.  By this time I had pictured that I would have at least finished my second draft of the text.  
-Currently I am far off from this goal.  I've done partial re-writes of chapters one, two and three but they are not even
-finished yet.  I haven't given up on the project, only had some setbacks.  First O'Reilly declined to publish the text then
-Addison-Wesley and Greg is tried another which I don't know the name of.  However, at this point I want to focus my energy
-onto finishing the book not securing a contract.
+This book and indeed much of the LibTom projects would not exist in their current form if it was not for a plethora
+of kind people donating their time, resources and kind words to help support my work.  Writing a text of significant
+length (along with the source code) is a tiresome and lengthy process.  Currently the LibTom project is four years old,
+comprises of literally thousands of users and over 100,000 lines of source code, TeX and other material.  People like Mads and Greg 
+were there at the beginning to encourage me to work well.  It is amazing how timely validation from others can boost morale to 
+continue the project. Definitely my parents were there for me by providing room and board during the many months of work in 2003.  

-So why am I writing this text?  It seems like a lot of work right?  Most certainly it is a lot of work writing a textbook.  
-Even the simplest introductory material has to be lined with references and figures.  A lot of the text has to be re-written
-from point form to prose form to ensure an easier read.  Why am I doing all this work for free then?  Simple. My philosophy
-is quite simply ``Open Source.  Open Academia.  Open Minds'' which means that to achieve a goal of open minds, that is,
-people willing to accept new ideas and explore the unknown you have to make available material they can access freely 
-without hinderance.  
+To my many friends whom I have met through the years I thank you for the good times and the words of encouragement.  I hope I
+honour your kind gestures with this project.

-I've been writing free software since I was about sixteen but only recently have I hit upon software that people have come
-to depend upon.  I started LibTomCrypt in December 2001 and now several major companies use it as integral portions of their
-software.  Several educational institutions use it as a matter of course and many freelance developers use it as
-part of their projects.  To further my contributions I started the LibTomMath project in December 2002 aimed at providing
-multiple precision arithmetic routines that students could learn from.  That is write routines that are not only easy
-to understand and follow but provide quite impressive performance considering they are all in standard portable ISO C.  
-
-The second leg of my philosophy is ``Open Academia'' which is where this textbook comes in.  In the end, when all is
-said and done the text will be useable by educational institutions as a reference on multiple precision arithmetic.  
-
-At this time I feel I should share a little information about myself.  The most common question I was asked at 
-Crypto'03, perhaps just out of professional courtesy, was which school I either taught at or attended.  The unfortunate
-truth is that I neither teach at or attend a school of academic reputation.  I'm currently at Algonquin College which 
-is what I'd like to call ``somewhat academic but mostly vocational'' college.  In otherwords, job training.
-
-I'm a 21 year old computer science student mostly self-taught in the areas I am aware of (which includes a half-dozen
-computer science fields, a few fields of mathematics and some English).  I look forward to teaching someday but I am
-still far off from that goal.  
-
-Now it would be improper for me to not introduce the rest of the texts co-authors.  While they are only contributing 
-corrections and editorial feedback their support has been tremendously helpful in presenting the concepts laid out
-in the text so far.  Greg has always been there for me.  He has tracked my LibTom projects since their inception and even
-sent cheques to help pay tuition from time to time.  His background has provided a wonderful source to bounce ideas off
-of and improve the quality of my writing.  Mads is another fellow who has just ``been there''.  I don't even recall what
-his interest in the LibTom projects is but I'm definitely glad he has been around.  His ability to catch logical errors
-in my written English have saved me on several occasions to say the least.
-
-What to expect next?  Well this is still a rough draft.  I've only had the chance to update a few chapters.  However, I've
-been getting the feeling that people are starting to use my text and I owe them some updated material.  My current tenative
-plan is to edit one chapter every two weeks starting January 4th.  It seems insane but my lower course load at college
-should provide ample time.  By Crypto'04 I plan to have a 2nd draft of the text polished and ready to hand out to as many
-people who will take it.
+Open Source.  Open Academia.  Open Minds.

 \begin{flushright} Tom St Denis \end{flushright}

@@ -937,7 +903,7 @@ assumed to contain undefined values they are initially set to zero.

 EXAM,bn_mp_grow.c

-A quick optimization is to first determine if a memory re-allocation is required at all.  The if statement (line @23,if@) checks
+A quick optimization is to first determine if a memory re-allocation is required at all.  The if statement (line @24,alloc@) checks
 if the \textbf{alloc} member of the mp\_int is smaller than the requested digit count.  If the count is not larger than \textbf{alloc}
 the function skips the re-allocation part thus saving time.

@@ -1310,7 +1276,7 @@ After the function is completed, all of the digits are zeroed, the \textbf{used}
 With the mp\_int representation of an integer, calculating the absolute value is trivial.  The mp\_abs algorithm will compute
 the absolute value of an mp\_int.

-\newpage\begin{figure}[here]
+\begin{figure}[here]
 \begin{center}
 \begin{tabular}{l}
 \hline Algorithm \textbf{mp\_abs}. \\
@@ -1335,6 +1301,9 @@ logic to handle it.

 EXAM,bn_mp_abs.c

+This fairly trivial algorithm first eliminates non--required duplications (line @27,a != b@) and then sets the
+\textbf{sign} flag to \textbf{MP\_ZPOS}.
+
 \subsection{Integer Negation}
 With the mp\_int representation of an integer, calculating the negation is also trivial.  The mp\_neg algorithm will compute
 the negative of an mp\_int input.
@@ -1368,11 +1337,15 @@ zero as negative.

 EXAM,bn_mp_neg.c

+Like mp\_abs() this function avoids non--required duplications (line @21,a != b@) and then sets the sign.  We
+have to make sure that only non--zero values get a \textbf{sign} of \textbf{MP\_NEG}.  If the mp\_int is zero
+than the \textbf{sign} is hard--coded to \textbf{MP\_ZPOS}.
+
 \section{Small Constants}
 \subsection{Setting Small Constants}
 Often a mp\_int must be set to a relatively small value such as $1$ or $2$.  For these cases the mp\_set algorithm is useful.

-\begin{figure}[here]
+\newpage\begin{figure}[here]
 \begin{center}
 \begin{tabular}{l}
 \hline Algorithm \textbf{mp\_set}. \\
@@ -1397,11 +1370,14 @@ single digit is set (\textit{modulo $\beta$}) and the \textbf{used} count is adj

 EXAM,bn_mp_set.c

-Line @21,mp_zero@ calls mp\_zero() to clear the mp\_int and reset the sign.  Line @22,MP_MASK@ copies the digit 
-into the least significant location.  Note the usage of a new constant \textbf{MP\_MASK}.  This constant is used to quickly
-reduce an integer modulo $\beta$.  Since $\beta$ is of the form $2^k$ for any suitable $k$ it suffices to perform a binary AND with 
-$MP\_MASK = 2^k - 1$ to perform the reduction.  Finally line @23,a->used@ will set the \textbf{used} member with respect to the 
-digit actually set. This function will always make the integer positive.
+First we zero (line @21,mp_zero@) the mp\_int to make sure that the other members are initialized for a 
+small positive constant.  mp\_zero() ensures that the \textbf{sign} is positive and the \textbf{used} count
+is zero.  Next we set the digit and reduce it modulo $\beta$ (line @22,MP_MASK@).  After this step we have to 
+check if the resulting digit is zero or not.  If it is not then we set the \textbf{used} count to one, otherwise
+to zero.
+
+We can quickly reduce modulo $\beta$ since it is of the form $2^k$ and a quick binary AND operation with 
+$2^k - 1$ will perform the same operation.

 One important limitation of this function is that it will only set one digit.  The size of a digit is not fixed, meaning source that uses 
 this function should take that into account.  Only trivially small constants can be set using this function.
@@ -1503,10 +1479,12 @@ the zero'th digit.  If after all of the digits have been compared, no difference

 EXAM,bn_mp_cmp_mag.c

-The two if statements on lines @24,if@ and @28,if@ compare the number of digits in the two inputs.  These two are performed before all of the digits
-are compared since it is a very cheap test to perform and can potentially save considerable time.  The implementation given is also not valid 
-without those two statements.  $b.alloc$ may be smaller than $a.used$, meaning that undefined values will be read from $b$ past the end of the 
-array of digits.
+The two if statements (lines @24,if@ and @28,if@) compare the number of digits in the two inputs.  These two are 
+performed before all of the digits are compared since it is a very cheap test to perform and can potentially save 
+considerable time.  The implementation given is also not valid without those two statements.  $b.alloc$ may be 
+smaller than $a.used$, meaning that undefined values will be read from $b$ past the end of the array of digits.
+
+

 \subsection{Signed Comparisons}
 Comparing with sign considerations is also fairly critical in several routines (\textit{division for example}).  Based on an unsigned magnitude 
@@ -1539,9 +1517,9 @@ $\vert a \vert < \vert b \vert$.  Step number four will compare the two when the

 EXAM,bn_mp_cmp.c

-The two if statements on lines @22,if@ and @26,if@ perform the initial sign comparison.  If the signs are not the equal then which ever
-has the positive sign is larger.   At line @30,if@, the inputs are compared based on magnitudes.  If the signs were both negative then 
-the unsigned comparison is performed in the opposite direction (\textit{line @31,mp_cmp_mag@}).  Otherwise, the signs are assumed to 
+The two if statements (lines @22,if@ and @26,if@) perform the initial sign comparison.  If the signs are not the equal then which ever
+has the positive sign is larger.   The inputs are compared (line @30,if@) based on magnitudes.  If the signs were both 
+negative then the unsigned comparison is performed in the opposite direction (line @31,mp_cmp_mag@).  Otherwise, the signs are assumed to 
 be both positive and a forward direction unsigned comparison is performed.

 \section*{Exercises}
@@ -1664,19 +1642,21 @@ The final carry is stored in $c_{max}$ and digits above $max$ upto $oldused$ are

 EXAM,bn_s_mp_add.c

-Lines @27,if@ to @35,}@ perform the initial sorting of the inputs and determine the $min$ and $max$ variables.  Note that $x$ is a pointer to a 
-mp\_int assigned to the largest input, in effect it is a local alias.  Lines @37,init@ to @42,}@ ensure that the destination is grown to 
-accomodate the result of the addition. 
+We first sort (lines @27,if@ to @35,}@) the inputs based on magnitude and determine the $min$ and $max$ variables.
+Note that $x$ is a pointer to an mp\_int assigned to the largest input, in effect it is a local alias.  Next we
+grow the destination (@37,init@ to @42,}@) ensure that it can accomodate the result of the addition. 

 Similar to the implementation of mp\_copy this function uses the braced code and local aliases coding style.  The three aliases that are on 
 lines @56,tmpa@, @59,tmpb@ and @62,tmpc@ represent the two inputs and destination variables respectively.  These aliases are used to ensure the
 compiler does not have to dereference $a$, $b$ or $c$ (respectively) to access the digits of the respective mp\_int.

-The initial carry $u$ is cleared on line @65,u = 0@, note that $u$ is of type mp\_digit which ensures type compatibility within the 
-implementation.  The initial addition loop begins on line @66,for@ and ends on line @75,}@.  Similarly the conditional addition loop
-begins on line @81,for@ and ends on line @90,}@.  The addition is finished with the final carry being stored in $tmpc$ on line @94,tmpc++@.  
-Note the ``++'' operator on the same line.  After line @94,tmpc++@ $tmpc$ will point to the $c.used$'th digit of the mp\_int $c$.  This is useful
-for the next loop on lines @97,for@ to @99,}@ which set any old upper digits to zero.
+The initial carry $u$ will be cleared (line @65,u = 0@), note that $u$ is of type mp\_digit which ensures type 
+compatibility within the implementation.  The initial addition (line @66,for@ to @75,}@) adds digits from
+both inputs until the smallest input runs out of digits.  Similarly the conditional addition loop
+(line @81,for@ to @90,}@) adds the remaining digits from the larger of the two inputs.  The addition is finished 
+with the final carry being stored in $tmpc$ (line @94,tmpc++@).  Note the ``++'' operator within the same expression.
+After line @94,tmpc++@, $tmpc$ will point to the $c.used$'th digit of the mp\_int $c$.  This is useful
+for the next loop (line @97,for@ to @99,}@) which set any old upper digits to zero.

 \subsection{Low Level Subtraction}
 The low level unsigned subtraction algorithm is very similar to the low level unsigned addition algorithm.  The principle difference is that the
@@ -1692,7 +1672,7 @@ this algorithm we will assume that the variable $\gamma$ represents the number o
 mp\_digit (\textit{this implies $2^{\gamma} > \beta$}).  

 For example, the default for LibTomMath is to use a ``unsigned long'' for the mp\_digit ``type'' while $\beta = 2^{28}$.  In ISO C an ``unsigned long''
-data type must be able to represent $0 \le x < 2^{32}$ meaning that in this case $\gamma = 32$.
+data type must be able to represent $0 \le x < 2^{32}$ meaning that in this case $\gamma \ge 32$.

 \newpage\begin{figure}[!here]
 \begin{center}
@@ -1759,20 +1739,23 @@ If $b$ has a smaller magnitude than $a$ then step 9 will force the carry and cop

 EXAM,bn_s_mp_sub.c

-Line @24,min@ and @25,max@ perform the initial hardcoded sorting of the inputs.  In reality the $min$ and $max$ variables are only aliases and are only 
-used to make the source code easier to read.  Again the pointer alias optimization is used within this algorithm.  Lines @42,tmpa@, @43,tmpb@ and @44,tmpc@ initialize the aliases for 
-$a$, $b$ and $c$ respectively.
+Like low level addition we ``sort'' the inputs.  Except in this case the sorting is hardcoded 
+(lines @24,min@ and @25,max@).  In reality the $min$ and $max$ variables are only aliases and are only 
+used to make the source code easier to read.  Again the pointer alias optimization is used 
+within this algorithm.  The aliases $tmpa$, $tmpb$ and $tmpc$ are initialized
+(lines @42,tmpa@, @43,tmpb@ and @44,tmpc@) for $a$, $b$ and $c$ respectively.

-The first subtraction loop occurs on lines @47,u = 0@ through @61,}@.  The theory behind the subtraction loop is exactly the same as that for
-the addition loop.  As remarked earlier there is an implementation reason for using the ``awkward'' method of extracting the carry 
-(\textit{see line @57, >>@}).  The traditional method for extracting the carry would be to shift by $lg(\beta)$ positions and logically AND 
-the least significant bit.  The AND operation is required because all of the bits above the $\lg(\beta)$'th bit will be set to one after a carry
-occurs from subtraction.  This carry extraction requires two relatively cheap operations to extract the carry.  The other method is to simply 
-shift the most significant bit to the least significant bit thus extracting the carry with a single cheap operation.  This optimization only works on
-twos compliment machines which is a safe assumption to make.
+The first subtraction loop (lines @47,u = 0@ through @61,}@) subtract digits from both inputs until the smaller of
+the two inputs has been exhausted.  As remarked earlier there is an implementation reason for using the ``awkward'' 
+method of extracting the carry (line @57, >>@).  The traditional method for extracting the carry would be to shift 
+by $lg(\beta)$ positions and logically AND the least significant bit.  The AND operation is required because all of 
+the bits above the $\lg(\beta)$'th bit will be set to one after a carry occurs from subtraction.  This carry 
+extraction requires two relatively cheap operations to extract the carry.  The other method is to simply shift the 
+most significant bit to the least significant bit thus extracting the carry with a single cheap operation.  This 
+optimization only works on twos compliment machines which is a safe assumption to make.

-If $a$ has a larger magnitude than $b$ an additional loop (\textit{see lines @64,for@ through @73,}@}) is required to propagate the carry through
-$a$ and copy the result to $c$.  
+If $a$ has a larger magnitude than $b$ an additional loop (lines @64,for@ through @73,}@) is required to propagate 
+the carry through $a$ and copy the result to $c$.  

 \subsection{High Level Addition}
 Now that both lower level addition and subtraction algorithms have been established an effective high level signed addition algorithm can be
@@ -2098,10 +2081,11 @@ FIGU,sliding_window,Sliding Window Movement

 EXAM,bn_mp_lshd.c

-The if statement on line @24,if@ ensures that the $b$ variable is greater than zero.  The \textbf{used} count is incremented by $b$ before
-the copy loop begins.  This elminates the need for an additional variable in the for loop.  The variable $top$ on line @42,top@ is an alias
-for the leading digit while $bottom$ on line @45,bottom@ is an alias for the trailing edge.  The aliases form a window of exactly $b$ digits
-over the input.  
+The if statement (line @24,if@) ensures that the $b$ variable is greater than zero since we do not interpret negative
+shift counts properly.  The \textbf{used} count is incremented by $b$ before the copy loop begins.  This elminates 
+the need for an additional variable in the for loop.  The variable $top$ (line @42,top@) is an alias
+for the leading digit while $bottom$ (line @45,bottom@) is an alias for the trailing edge.  The aliases form a 
+window of exactly $b$ digits over the input.  

 \subsection{Division by $x$}

@@ -2151,9 +2135,9 @@ Once the window copy is complete the upper digits must be zeroed and the \textbf

 EXAM,bn_mp_rshd.c

-The only noteworthy element of this routine is the lack of a return type.  
-
-- Will update later to give it a return type...Tom
+The only noteworthy element of this routine is the lack of a return type since it cannot fail.  Like mp\_lshd() we
+form a sliding window except we copy in the other direction.  After the window (line @59,for (;@) we then zero
+the upper digits of the input to make sure the result is correct.

 \section{Powers of Two}

@@ -2214,7 +2198,15 @@ complete.  It is possible to optimize this algorithm down to a $O(n)$ algorithm

 EXAM,bn_mp_mul_2d.c

-Notes to be revised when code is updated. -- Tom
+The shifting is performed in--place which means the first step (line @24,a != c@) is to copy the input to the 
+destination.  We avoid calling mp\_copy() by making sure the mp\_ints are different.  The destination then
+has to be grown (line @31,grow@) to accomodate the result.
+
+If the shift count $b$ is larger than $lg(\beta)$ then a call to mp\_lshd() is used to handle all of the multiples 
+of $lg(\beta)$.  Leaving only a remaining shift of $lg(\beta) - 1$ or fewer bits left.  Inside the actual shift 
+loop (lines @45,if@ to @76,}@) we make use of pre--computed values $shift$ and $mask$.   These are used to
+extract the carry bit(s) to pass into the next iteration of the loop.  The $r$ and $rr$ variables form a 
+chain between consecutive iterations to propagate the carry.  

 \subsection{Division by Power of Two}

@@ -2263,7 +2255,8 @@ ignored by passing \textbf{NULL} as the pointer to the mp\_int variable.    The
 result of the remainder operation until the end.  This allows $d$ and $a$ to represent the same mp\_int without modifying $a$ before
 the quotient is obtained.

-The remainder of the source code is essentially the same as the source code for mp\_mul\_2d.  (-- Fix this paragraph up later, Tom).
+The remainder of the source code is essentially the same as the source code for mp\_mul\_2d.  The only significant difference is
+the direction of the shifts.

 \subsection{Remainder of Division by Power of Two}

@@ -2306,7 +2299,13 @@ is copied to $b$, leading digits are removed and the remaining leading digit is

 EXAM,bn_mp_mod_2d.c

-- Add comments later, Tom.
+We first avoid cases of $b \le 0$ by simply mp\_zero()'ing the destination in such cases.  Next if $2^b$ is larger
+than the input we just mp\_copy() the input and return right away.  After this point we know we must actually
+perform some work to produce the remainder.
+
+Recalling that reducing modulo $2^k$ and a binary ``and'' with $2^k - 1$ are numerically equivalent we can quickly reduce 
+the number.  First we zero any digits above the last digit in $2^b$ (line @41,for@).  Next we reduce the 
+leading digit of both (line @45,&=@) and then mp\_clamp().

 \section*{Exercises}
 \begin{tabular}{cl}
@@ -2464,33 +2463,46 @@ exceed the precision requested.

 EXAM,bn_s_mp_mul_digs.c

-Lines @31,if@ to @35,}@ determine if the Comba method can be used first.  The conditions for using the Comba routine are that min$(a.used, b.used) < \delta$ and
-the number of digits of output is less than \textbf{MP\_WARRAY}.  This new constant is used to control 
-the stack usage in the Comba routines.  By default it is set to $\delta$ but can be reduced when memory is at a premium.
+First we determine (line @30,if@) if the Comba method can be used first since it's faster.  The conditions for 
+sing the Comba routine are that min$(a.used, b.used) < \delta$ and the number of digits of output is less than 
+\textbf{MP\_WARRAY}.  This new constant is used to control the stack usage in the Comba routines.  By default it is 
+set to $\delta$ but can be reduced when memory is at a premium.

-Of particular importance is the calculation of the $ix+iy$'th column on lines @64,mp_word@, @65,mp_word@ and @66,mp_word@.  Note how all of the
-variables are cast to the type \textbf{mp\_word}, which is also the type of variable $\hat r$.  That is to ensure that double precision operations 
-are used instead of single precision.  The multiplication on line @65,) * (@ makes use of a specific GCC optimizer behaviour.  On the outset it looks like 
-the compiler will have to use a double precision multiplication to produce the result required.  Such an operation would be horribly slow on most 
-processors and drag this to a crawl.  However, GCC is smart enough to realize that double wide output single precision multipliers can be used.  For 
-example, the instruction ``MUL'' on the x86 processor can multiply two 32-bit values and produce a 64-bit result.  
+If we cannot use the Comba method we proceed to setup the baseline routine.  We allocate the the destination mp\_int
+$t$ (line @36,init@) to the exact size of the output to avoid further re--allocations.  At this point we now 
+begin the $O(n^2)$ loop.
+
+This implementation of multiplication has the caveat that it can be trimmed to only produce a variable number of
+digits as output.  In each iteration of the outer loop the $pb$ variable is set (line @48,MIN@) to the maximum 
+number of inner loop iterations.  
+
+Inside the inner loop we calculate $\hat r$ as the mp\_word product of the two mp\_digits and the addition of the
+carry from the previous iteration.  A particularly important observation is that most modern optimizing 
+C compilers (GCC for instance) can recognize that a $N \times N \rightarrow 2N$ multiplication is all that 
+is required for the product.  In x86 terms for example, this means using the MUL instruction.
+
+Each digit of the product is stored in turn (line @68,tmpt@) and the carry propagated (line @71,>>@) to the 
+next iteration.

 \subsection{Faster Multiplication by the ``Comba'' Method}
 MARK,COMBA

-One of the huge drawbacks of the ``baseline'' algorithms is that at the $O(n^2)$ level the carry must be computed and propagated upwards.  This
-makes the nested loop very sequential and hard to unroll and implement in parallel.  The ``Comba'' \cite{COMBA} method is named after little known 
-(\textit{in cryptographic venues}) Paul G. Comba who described a method of implementing fast multipliers that do not require nested 
-carry fixup operations.  As an interesting aside it seems that Paul Barrett describes a similar technique in
-his 1986 paper \cite{BARRETT} written five years before.
+One of the huge drawbacks of the ``baseline'' algorithms is that at the $O(n^2)$ level the carry must be 
+computed and propagated upwards.  This makes the nested loop very sequential and hard to unroll and implement 
+in parallel.  The ``Comba'' \cite{COMBA} method is named after little known (\textit{in cryptographic venues}) Paul G. 
+Comba who described a method of implementing fast multipliers that do not require nested carry fixup operations.  As an 
+interesting aside it seems that Paul Barrett describes a similar technique in his 1986 paper \cite{BARRETT} written 
+five years before.

-At the heart of the Comba technique is once again the long-hand algorithm.  Except in this case a slight twist is placed on how
-the columns of the result are produced.  In the standard long-hand algorithm rows of products are produced then added together to form the 
-final result.  In the baseline algorithm the columns are added together after each iteration to get the result instantaneously.  
+At the heart of the Comba technique is once again the long-hand algorithm.  Except in this case a slight 
+twist is placed on how the columns of the result are produced.  In the standard long-hand algorithm rows of products 
+are produced then added together to form the final result.  In the baseline algorithm the columns are added together 
+after each iteration to get the result instantaneously.  

-In the Comba algorithm the columns of the result are produced entirely independently of each other.  That is at the $O(n^2)$ level a 
-simple multiplication and addition step is performed.  The carries of the columns are propagated after the nested loop to reduce the amount
-of work requiored. Succintly the first step of the algorithm is to compute the product vector $\vec x$ as follows. 
+In the Comba algorithm the columns of the result are produced entirely independently of each other.  That is at 
+the $O(n^2)$ level a simple multiplication and addition step is performed.  The carries of the columns are propagated 
+after the nested loop to reduce the amount of work requiored. Succintly the first step of the algorithm is to compute 
+the product vector $\vec x$ as follows. 

 \begin{equation}
 \vec x_n = \sum_{i+j = n} a_ib_j, \forall n \in \lbrace 0, 1, 2, \ldots, i + j \rbrace
@@ -2584,38 +2596,32 @@ $256$ digits would allow for numbers in the range of $0 \le x < 2^{7168}$ which,
 \textbf{Input}.   mp\_int $a$, mp\_int $b$ and an integer $digs$ \\
 \textbf{Output}.  $c \leftarrow \vert a \vert \cdot \vert b \vert \mbox{ (mod }\beta^{digs}\mbox{)}$. \\
 \hline \\
-Place an array of \textbf{MP\_WARRAY} double precision digits named $\hat W$ on the stack. \\
+Place an array of \textbf{MP\_WARRAY} single precision digits named $W$ on the stack. \\
 1.  If $c.alloc < digs$ then grow $c$ to $digs$ digits. (\textit{mp\_grow}) \\
 2.  If step 1 failed return(\textit{MP\_MEM}).\\
 \\
-Zero the temporary array $\hat W$. \\
-3.  for $n$ from $0$ to $digs - 1$ do \\
-\hspace{3mm}3.1  $\hat W_n \leftarrow 0$ \\
+3.  $pa \leftarrow \mbox{MIN}(digs, a.used + b.used)$ \\
 \\
-Compute the columns. \\
-4.  for $ix$ from $0$ to $a.used - 1$ do \\
-\hspace{3mm}4.1  $pb \leftarrow \mbox{min}(b.used, digs - ix)$ \\
-\hspace{3mm}4.2  If $pb < 1$ then goto step 5. \\
-\hspace{3mm}4.3  for $iy$ from $0$ to $pb - 1$ do \\
-\hspace{6mm}4.3.1  $\hat W_{ix+iy} \leftarrow \hat W_{ix+iy} + a_{ix}b_{iy}$ \\
+4.  $\_ \hat W \leftarrow 0$ \\
+5.  for $ix$ from 0 to $pa - 1$ do \\
+\hspace{3mm}5.1  $ty \leftarrow \mbox{MIN}(b.used - 1, ix)$ \\
+\hspace{3mm}5.2  $tx \leftarrow ix - ty$ \\
+\hspace{3mm}5.3  $iy \leftarrow \mbox{MIN}(a.used - tx, ty + 1)$ \\
+\hspace{3mm}5.4  for $iz$ from 0 to $iy - 1$ do \\
+\hspace{6mm}5.4.1  $\_ \hat W \leftarrow \_ \hat W + a_{tx+iy}b_{ty-iy}$ \\
+\hspace{3mm}5.5  $W_{ix} \leftarrow \_ \hat W (\mbox{mod }\beta)$\\
+\hspace{3mm}5.6  $\_ \hat W \leftarrow \lfloor \_ \hat W / \beta \rfloor$ \\
+6.  $W_{pa} \leftarrow \_ \hat W (\mbox{mod }\beta)$ \\
 \\
-Propagate the carries upwards. \\
-5.  $oldused \leftarrow c.used$ \\
-6.  $c.used \leftarrow digs$ \\
-7.  If $digs > 1$ then do \\
-\hspace{3mm}7.1.  for $ix$ from $1$ to $digs - 1$ do \\
-\hspace{6mm}7.1.1  $\hat W_{ix} \leftarrow \hat W_{ix} + \lfloor \hat W_{ix-1} / \beta \rfloor$ \\
-\hspace{6mm}7.1.2  $c_{ix - 1} \leftarrow \hat W_{ix - 1} \mbox{ (mod }\beta\mbox{)}$ \\
-8.  else do \\
-\hspace{3mm}8.1  $ix \leftarrow 0$ \\
-9.  $c_{ix} \leftarrow \hat W_{ix} \mbox{ (mod }\beta\mbox{)}$ \\
+7.  $oldused \leftarrow c.used$ \\
+8.  $c.used \leftarrow digs$ \\
+9.  for $ix$ from $0$ to $pa$ do \\
+\hspace{3mm}9.1  $c_{ix} \leftarrow W_{ix}$ \\
+10.  for $ix$ from $pa + 1$ to $oldused - 1$ do \\
+\hspace{3mm}10.1 $c_{ix} \leftarrow 0$ \\
 \\
-Zero excess digits. \\
-10.  If $digs < oldused$ then do \\
-\hspace{3mm}10.1  for $n$ from $digs$ to $oldused - 1$ do \\
-\hspace{6mm}10.1.1  $c_n \leftarrow 0$ \\
-11.  Clamp excessive digits of $c$.  (\textit{mp\_clamp}) \\
-12.  Return(\textit{MP\_OKAY}). \\
+11.  Clamp $c$. \\
+12.  Return MP\_OKAY. \\
 \hline
 \end{tabular}
 \end{center}
@@ -2625,15 +2631,24 @@ Zero excess digits. \\
 \end{figure}

 \textbf{Algorithm fast\_s\_mp\_mul\_digs.}
-This algorithm performs the unsigned multiplication of $a$ and $b$ using the Comba method limited to $digs$ digits of precision.  The algorithm
-essentially peforms the same calculation as algorithm s\_mp\_mul\_digs, just much faster.
+This algorithm performs the unsigned multiplication of $a$ and $b$ using the Comba method limited to $digs$ digits of precision.

-The array $\hat W$ is meant to be on the stack when the algorithm is used.  The size of the array does not change which is ideal.  Note also that 
-unlike algorithm s\_mp\_mul\_digs no temporary mp\_int is required since the result is calculated directly in $\hat W$.  
+The outer loop of this algorithm is more complicated than that of the baseline multiplier.  This is because on the inside of the 
+loop we want to produce one column per pass.  This allows the accumulator $\_ \hat W$ to be placed in CPU registers and
+reduce the memory bandwidth to two \textbf{mp\_digit} reads per iteration.

-The $O(n^2)$ loop on step four is where the Comba method's advantages begin to show through in comparison to the baseline algorithm.  The lack of
-a carry variable or propagation in this loop allows the loop to be performed with only single precision multiplication and additions.  Now that each
-iteration of the inner loop can be performed independent of the others the inner loop can be performed with a high level of parallelism.
+The $ty$ variable is set to the minimum count of $ix$ or the number of digits in $b$.  That way if $a$ has more digits than
+$b$ this will be limited to $b.used - 1$.  The $tx$ variable is set to the to the distance past $b.used$ the variable
+$ix$ is.  This is used for the immediately subsequent statement where we find $iy$.  
+
+The variable $iy$ is the minimum digits we can read from either $a$ or $b$ before running out.  Computing one column at a time
+means we have to scan one integer upwards and the other downwards.  $a$ starts at $tx$ and $b$ starts at $ty$.  In each
+pass we are producing the $ix$'th output column and we note that $tx + ty = ix$.  As we move $tx$ upwards we have to 
+move $ty$ downards so the equality remains valid.  The $iy$ variable is the number of iterations until 
+$tx \ge a.used$ or $ty < 0$ occurs.
+
+After every inner pass we store the lower half of the accumulator into $W_{ix}$ and then propagate the carry of the accumulator
+into the next round by dividing $\_ \hat W$ by $\beta$.

 To measure the benefits of the Comba method over the baseline method consider the number of operations that are required.  If the 
 cost in terms of time of a multiply and addition is $p$ and the cost of a carry propagation is $q$ then a baseline multiplication would require 
@@ -2643,20 +2658,20 @@ and addition operations in the nested loop in parallel.

 EXAM,bn_fast_s_mp_mul_digs.c

-The memset on line @47,memset@ clears the initial $\hat W$ array to zero in a single step. Like the slower baseline multiplication
-implementation a series of aliases (\textit{lines @67, tmpx@, @70, tmpy@ and @75,_W@}) are used to simplify the inner $O(n^2)$ loop.  
-In this case a new alias $\_\hat W$ has been added which refers to the double precision columns offset by $ix$ in each pass.  
+As per the pseudo--code we first calculate $pa$ (line @47,MIN@) as the number of digits to output.  Next we begin the outer loop
+to produce the individual columns of the product.  We use the two aliases $tmpx$ and $tmpy$ (lines @61,tmpx@, @62,tmpy@) to point
+inside the two multiplicands quickly.  

-The inner loop on lines @83,for@, @84,mp_word@ and @85,}@ is where the algorithm will spend the majority of the time, which is why it has been 
-stripped to the bones of any extra baggage\footnote{Hence the pointer aliases.}.  On x86 processors the multiplication and additions amount to at the 
-very least five instructions (\textit{two loads, two additions, one multiply}) while on the ARMv4 processors they amount to only three 
-(\textit{one load, one store, one multiply-add}).   For both of the x86 and ARMv4 processors the GCC compiler performs a good job at unrolling the loop 
-and scheduling the instructions so there are very few dependency stalls.
+The inner loop (lines @70,for@ to @72,}@) of this implementation is where the tradeoff come into play.  Originally this comba 
+implementation was ``row--major'' which means it adds to each of the columns in each pass.  After the outer loop it would then fix 
+the carries.  This was very fast except it had an annoying drawback.  You had to read a mp\_word and two mp\_digits and write 
+one mp\_word per iteration.  On processors such as the Athlon XP and P4 this did not matter much since the cache bandwidth 
+is very high and it can keep the ALU fed with data.  It did, however, matter on older and embedded cpus where cache is often 
+slower and also often doesn't exist.  This new algorithm only performs two reads per iteration under the assumption that the 
+compiler has aliased $\_ \hat W$ to a CPU register.

-In theory the difference between the baseline and comba algorithms is a mere $O(qn)$ time difference.  However, in the $O(n^2)$ nested loop of the
-baseline method there are dependency stalls as the algorithm must wait for the multiplier to finish before propagating the carry to the next 
-digit.  As a result fewer of the often multiple execution units\footnote{The AMD Athlon has three execution units and the Intel P4 has four.} can
-be simultaneously used.  
+After the inner loop we store the current accumulator in $W$ and shift $\_ \hat W$ (lines @75,W[ix]@, @78,>>@) to forward it as 
+a carry for the next pass.  After the outer loop we use the final carry (line @82,W[ix]@) as the last digit of the product.  

 \subsection{Polynomial Basis Multiplication}
 To break the $O(n^2)$ barrier in multiplication requires a completely different look at integer multiplication.  In the following algorithms
@@ -2976,13 +2991,26 @@ result $a \cdot b$ is produced.

 EXAM,bn_mp_toom_mul.c

-- Comments to be added during editing phase.
+The first obvious thing to note is that this algorithm is complicated.  The complexity is worth it if you are multiplying very 
+large numbers.  For example, a 10,000 digit multiplication takes approximaly 99,282,205 fewer single precision multiplications with
+Toom--Cook than a Comba or baseline approach (this is a savings of more than 99$\%$).  For most ``crypto'' sized numbers this
+algorithm is not practical as Karatsuba has a much lower cutoff point.
+
+First we split $a$ and $b$ into three roughly equal portions.  This has been accomplished (lines @40,mod@ to @69,rshd@) with 
+combinations of mp\_rshd() and mp\_mod\_2d() function calls.  At this point $a = a2 \cdot \beta^2 + a1 \cdot \beta + a0$ and similiarly
+for $b$.  
+
+Next we compute the five points $w0, w1, w2, w3$ and $w4$.  Recall that $w0$ and $w4$ can be computed directly from the portions so
+we get those out of the way first (lines @72,mul@ and @77,mul@).  Next we compute $w1, w2$ and $w3$ using Horners method.
+
+After this point we solve for the actual values of $w1, w2$ and $w3$ by reducing the $5 \times 5$ system which is relatively
+straight forward.  

 \subsection{Signed Multiplication}
 Now that algorithms to handle multiplications of every useful dimensions have been developed, a rather simple finishing touch is required.  So far all
 of the multiplication algorithms have been unsigned multiplications which leaves only a signed multiplication algorithm to be established.  

-\newpage\begin{figure}[!here]
+\begin{figure}[!here]
 \begin{small}
 \begin{center}
 \begin{tabular}{l}
@@ -3065,7 +3093,7 @@ Column two of row one is a square and column three is the first unique column.
 The baseline squaring algorithm is meant to be a catch-all squaring algorithm.  It will handle any of the input sizes that the faster routines
 will not handle.  

-\newpage\begin{figure}[!here]
+\begin{figure}[!here]
 \begin{small}
 \begin{center}
 \begin{tabular}{l}
@@ -3121,9 +3149,14 @@ results calculated so far.  This involves expensive carry propagation which will

 EXAM,bn_s_mp_sqr.c

-Inside the outer loop (\textit{see line @32,for@}) the square term is calculated on line @35,r =@.  Line @42,>>@ extracts the carry from the square
-term.  Aliases for $a_{ix}$ and $t_{ix+iy}$ are initialized on lines @45,tmpx@ and @48,tmpt@ respectively.  The doubling is performed using two
-additions (\textit{see line @57,r + r@}) since it is usually faster than shifting,if not at least as fast.  
+Inside the outer loop (line @32,for@) the square term is calculated on line @35,r =@.  The carry (line @42,>>@) has been
+extracted from the mp\_word accumulator using a right shift.  Aliases for $a_{ix}$ and $t_{ix+iy}$ are initialized 
+(lines @45,tmpx@ and @48,tmpt@) to simplify the inner loop.  The doubling is performed using two
+additions (line @57,r + r@) since it is usually faster than shifting, if not at least as fast.  
+
+The important observation is that the inner loop does not begin at $iy = 0$ like for multiplication.  As such the inner loops
+get progressively shorter as the algorithm proceeds.  This is what leads to the savings compared to using a multiplication to
+square a number. 

 \subsection{Faster Squaring by the ``Comba'' Method}
 A major drawback to the baseline method is the requirement for single precision shifting inside the $O(n^2)$ nested loop.  Squaring has an additional
@@ -3135,9 +3168,9 @@ propagation operations from the inner loop.  However, the inner product must sti
 that $2a + 2b + 2c = 2(a + b + c)$.  That is the sum of all of the double products is equal to double the sum of all the products.  For example,
 $ab + ba + ac + ca = 2ab + 2ac = 2(ab + ac)$.  

-However, we cannot simply double all of the columns, since the squares appear only once per row.  The most practical solution is to have two mp\_word
-arrays.  One array will hold the squares and the other array will hold the double products.  With both arrays the doubling and carry propagation can be 
-moved to a $O(n)$ work level outside the $O(n^2)$ level.  
+However, we cannot simply double all of the columns, since the squares appear only once per row.  The most practical solution is to have two 
+mp\_word arrays.  One array will hold the squares and the other array will hold the double products.  With both arrays the doubling and 
+carry propagation can be moved to a $O(n)$ work level outside the $O(n^2)$ level.  In this case, we have an even simpler solution in mind.

 \newpage\begin{figure}[!here]
 \begin{small}
@@ -3147,34 +3180,34 @@ moved to a $O(n)$ work level outside the $O(n^2)$ level.
 \textbf{Input}.   mp\_int $a$ \\
 \textbf{Output}.  $b \leftarrow a^2$ \\
 \hline \\
-Place two arrays of \textbf{MP\_WARRAY} mp\_words named $\hat W$ and $\hat {X}$ on the stack. \\
+Place an array of \textbf{MP\_WARRAY} mp\_digits named $W$ on the stack. \\
 1.  If $b.alloc < 2a.used + 1$ then grow $b$ to $2a.used + 1$ digits.  (\textit{mp\_grow}). \\
 2.  If step 1 failed return(\textit{MP\_MEM}). \\
-3.  for $ix$ from $0$ to $2a.used + 1$ do \\
-\hspace{3mm}3.1  $\hat W_{ix} \leftarrow 0$ \\
-\hspace{3mm}3.2  $\hat {X}_{ix} \leftarrow 0$ \\
-4.  for $ix$ from $0$ to $a.used - 1$ do \\
-\hspace{3mm}Compute the square.\\
-\hspace{3mm}4.1  $\hat {X}_{ix+ix} \leftarrow \left ( a_{ix} \right )^2$ \\
 \\
-\hspace{3mm}Compute the double products.\\
-\hspace{3mm}4.2  for $iy$ from $ix + 1$ to $a.used - 1$ do \\
-\hspace{6mm}4.2.1  $\hat W_{ix+iy} \leftarrow \hat W_{ix+iy} + a_{ix}a_{iy}$ \\
-5.  $oldused \leftarrow b.used$ \\
-6.  $b.used \leftarrow 2a.used + 1$ \\
+3.  $pa \leftarrow 2 \cdot a.used$ \\
+4.  $\hat W1 \leftarrow 0$ \\
+5.  for $ix$ from $0$ to $pa - 1$ do \\
+\hspace{3mm}5.1  $\_ \hat W \leftarrow 0$ \\
+\hspace{3mm}5.2  $ty \leftarrow \mbox{MIN}(a.used - 1, ix)$ \\
+\hspace{3mm}5.3  $tx \leftarrow ix - ty$ \\
+\hspace{3mm}5.4  $iy \leftarrow \mbox{MIN}(a.used - tx, ty + 1)$ \\
+\hspace{3mm}5.5  $iy \leftarrow \mbox{MIN}(iy, \lfloor \left (ty - tx + 1 \right )/2 \rfloor)$ \\
+\hspace{3mm}5.6  for $iz$ from $0$ to $iz - 1$ do \\
+\hspace{6mm}5.6.1  $\_ \hat W \leftarrow \_ \hat W + a_{tx + iz}a_{ty - iz}$ \\
+\hspace{3mm}5.7  $\_ \hat W \leftarrow 2 \cdot \_ \hat W  + \hat W1$ \\
+\hspace{3mm}5.8  if $ix$ is even then \\
+\hspace{6mm}5.8.1  $\_ \hat W \leftarrow \_ \hat W + \left ( a_{\lfloor ix/2 \rfloor}\right )^2$ \\
+\hspace{3mm}5.9  $W_{ix} \leftarrow \_ \hat W (\mbox{mod }\beta)$ \\
+\hspace{3mm}5.10  $\hat W1 \leftarrow \lfloor \_ \hat W / \beta \rfloor$ \\
 \\
-Double the products and propagate the carries simultaneously. \\
-7.  $\hat W_0 \leftarrow 2 \hat W_0 + \hat {X}_0$ \\
-8.  for $ix$ from $1$ to $2a.used$ do \\
-\hspace{3mm}8.1 $\hat W_{ix} \leftarrow 2 \hat W_{ix} + \hat {X}_{ix}$ \\
-\hspace{3mm}8.2 $\hat W_{ix} \leftarrow \hat W_{ix} + \lfloor \hat W_{ix - 1} / \beta \rfloor$ \\
-\hspace{3mm}8.3 $b_{ix-1} \leftarrow W_{ix-1} \mbox{ (mod }\beta\mbox{)}$ \\
-9.  $b_{2a.used} \leftarrow \hat W_{2a.used} \mbox{ (mod }\beta\mbox{)}$ \\
-10.  if $2a.used + 1 < oldused$ then do \\
-\hspace{3mm}10.1  for $ix$ from $2a.used + 1$ to $oldused$ do \\
-\hspace{6mm}10.1.1  $b_{ix} \leftarrow 0$ \\
-11.  Clamp excess digits from $b$.  (\textit{mp\_clamp}) \\
-12.  Return(\textit{MP\_OKAY}). \\ 
+6.  $oldused \leftarrow b.used$ \\
+7.  $b.used \leftarrow 2 \cdot a.used$ \\
+8.  for $ix$ from $0$ to $pa - 1$ do \\
+\hspace{3mm}8.1  $b_{ix} \leftarrow W_{ix}$ \\
+9.  for $ix$ from $pa$ to $oldused - 1$ do \\
+\hspace{3mm}9.1  $b_{ix} \leftarrow 0$ \\
+10.  Clamp excess digits from $b$.  (\textit{mp\_clamp}) \\
+11.  Return(\textit{MP\_OKAY}). \\ 
 \hline
 \end{tabular}
 \end{center}
@@ -3183,24 +3216,24 @@ Double the products and propagate the carries simultaneously. \\
 \end{figure}

 \textbf{Algorithm fast\_s\_mp\_sqr.}
-This algorithm computes the square of an input using the Comba technique.  It is designed to be a replacement for algorithm s\_mp\_sqr when
-the number of input digits is less than \textbf{MP\_WARRAY} and less than $\delta \over 2$.  
+This algorithm computes the square of an input using the Comba technique.  It is designed to be a replacement for algorithm 
+s\_mp\_sqr when the number of input digits is less than \textbf{MP\_WARRAY} and less than $\delta \over 2$.  
+This algorithm is very similar to the Comba multiplier except with a few key differences we shall make note of.

-This routine requires two arrays of mp\_words to be placed on the stack.  The first array $\hat W$ will hold the double products and the second
-array $\hat X$ will hold the squares.  Though only at most $MP\_WARRAY \over 2$ words of $\hat X$ are used, it has proven faster on most 
-processors to simply make it a full size array.
+First, we have an accumulator and carry variables $\_ \hat W$ and $\hat W1$ respectively.  This is because the inner loop
+products are to be doubled.  If we had added the previous carry in we would be doubling too much.  Next we perform an
+addition MIN condition on $iy$ (step 5.5) to prevent overlapping digits.  For example, $a_3 \cdot a_5$ is equal
+$a_5 \cdot a_3$.  Whereas in the multiplication case we would have $5 < a.used$ and $3 \ge 0$ is maintained since we double the sum
+of the products just outside the inner loop we have to avoid doing this.  This is also a good thing since we perform
+fewer multiplications and the routine ends up being faster.

-The loop on step 3 will zero the two arrays to prepare them for the squaring step.  Step 4.1 computes the squares of the product.  Note how 
-it simply assigns the value into the $\hat X$ array.  The nested loop on step 4.2 computes the doubles of the products.  This loop
-computes the sum of the products for each column.  They are not doubled until later.
-
-After the squaring loop, the products stored in $\hat W$ musted be doubled and the carries propagated forwards.  It makes sense to do both
-operations at the same time.  The expression $\hat W_{ix} \leftarrow 2 \hat W_{ix} + \hat {X}_{ix}$ computes the sum of the double product and the
-squares in place.  
+Finally the last difference is the addition of the ``square'' term outside the inner loop (step 5.8).  We add in the square
+only to even outputs and it is the square of the term at the $\lfloor ix / 2 \rfloor$ position.

 EXAM,bn_fast_s_mp_sqr.c

-- Write something deep and insightful later, Tom.
+This implementation is essentially a copy of Comba multiplication with the appropriate changes added to make it faster for 
+the special case of squaring.  

 \subsection{Polynomial Basis Squaring}
 The same algorithm that performs optimal polynomial basis multiplication can be used to perform polynomial basis squaring.  The minor exception
@@ -3312,14 +3345,13 @@ By inlining the copy and shift operations the cutoff point for Karatsuba multipl
 is exactly at the point where Comba squaring can no longer be used (\textit{128 digits}).  On slower processors such as the Intel P4
 it is actually below the Comba limit (\textit{at 110 digits}).

-This routine uses the same error trap coding style as mp\_karatsuba\_sqr.  As the temporary variables are initialized errors are redirected to
-the error trap higher up.  If the algorithm completes without error the error code is set to \textbf{MP\_OKAY} and mp\_clears are executed normally.
-
-\textit{Last paragraph sucks.  re-write! -- Tom}
+This routine uses the same error trap coding style as mp\_karatsuba\_sqr.  As the temporary variables are initialized errors are 
+redirected to the error trap higher up.  If the algorithm completes without error the error code is set to \textbf{MP\_OKAY} and 
+mp\_clears are executed normally.

 \subsection{Toom-Cook Squaring}
 The Toom-Cook squaring algorithm mp\_toom\_sqr is heavily based on the algorithm mp\_toom\_mul with the exception that squarings are used
-instead of multiplication to find the five relations..  The reader is encouraged to read the description of the latter algorithm and try to 
+instead of multiplication to find the five relations.  The reader is encouraged to read the description of the latter algorithm and try to 
 derive their own Toom-Cook squaring algorithm.  

 \subsection{High Level Squaring}
@@ -3362,12 +3394,9 @@ EXAM,bn_mp_sqr.c
 $\left [ 3 \right ] $ & Devise an efficient algorithm for selection of the radix point to handle inputs \\
                      & that have different number of digits in Karatsuba multiplication. \\
                      & \\
-$\left [ 3 \right ] $ & In ~SQUARE~ the fact that every column of a squaring is made up \\
+$\left [ 2 \right ] $ & In ~SQUARE~ the fact that every column of a squaring is made up \\
                      & of double products and at most one square is stated.  Prove this statement. \\
                      & \\                      
-$\left [ 2 \right ] $ & In the Comba squaring algorithm half of the $\hat X$ variables are not used. \\
-                      & Revise algorithm fast\_s\_mp\_sqr to shrink the $\hat X$ array. \\
-                      & \\
 $\left [ 3 \right ] $ & Prove the equation for Karatsuba squaring. \\
                      & \\
 $\left [ 1 \right ] $ & Prove that Karatsuba squaring requires $O \left (n^{lg(3)} \right )$ time. \\
@@ -3375,6 +3404,14 @@ $\left [ 1 \right ] $ & Prove that Karatsuba squaring requires $O \left (n^{lg(3
 $\left [ 2 \right ] $ & Determine the minimal ratio between addition and multiplication clock cycles \\
                      & required for equation $6.7$ to be true.  \\
                      & \\
+$\left [ 3 \right ] $ & Implement a threaded version of Comba multiplication (and squaring) where you \\
+                      & compute subsets of the columns in each thread.  Determine a cutoff point where \\
+                      & it is effective and add the logic to mp\_mul() and mp\_sqr(). \\
+                      &\\
+$\left [ 4 \right ] $ & Same as the previous but also modify the Karatsuba and Toom-Cook.  You must \\
+                      & increase the throughput of mp\_exptmod() for random odd moduli in the range \\
+                      & $512 \ldots 4096$ bits significantly ($> 2x$) to complete this challenge. \\
+                      & \\
 \end{tabular}

 \chapter{Modular Reduction}
@@ -3394,7 +3431,7 @@ other forms of residues.
 Modular reductions are normally used to create either finite groups, rings or fields.  The most common usage for performance driven modular reductions 
 is in modular exponentiation algorithms.  That is to compute $d = a^b \mbox{ (mod }c\mbox{)}$ as fast as possible.  This operation is used in the 
 RSA and Diffie-Hellman public key algorithms, for example.  Modular multiplication and squaring also appears as a fundamental operation in 
-Elliptic Curve cryptographic algorithms.  As will be discussed in the subsequent chapter there exist fast algorithms for computing modular 
+elliptic curve cryptographic algorithms.  As will be discussed in the subsequent chapter there exist fast algorithms for computing modular 
 exponentiations without having to perform (\textit{in this example}) $b - 1$ multiplications.  These algorithms will produce partial results in the 
 range $0 \le x < c^2$ which can be taken advantage of to create several efficient algorithms.   They have also been used to create redundancy check 
 algorithms known as CRCs, error correction codes such as Reed-Solomon and solve a variety of number theoeretic problems.  
@@ -3610,7 +3647,7 @@ safe to do so.
 In order to use algorithm mp\_reduce the value of $\mu$ must be calculated in advance.  Ideally this value should be computed once and stored for
 future use so that the Barrett algorithm can be used without delay.  

-\begin{figure}[!here]
+\newpage\begin{figure}[!here]
 \begin{small}
 \begin{center}
 \begin{tabular}{l}
@@ -5818,6 +5855,8 @@ To explain the Jacobi Symbol we shall first discuss the Legendre function\footno
 defined.  The Legendre function computes whether or not an integer $a$ is a quadratic residue modulo an odd prime $p$.  Numerically it is
 equivalent to equation \ref{eqn:legendre}.

+\textit{-- Tom, don't be an ass, cite your source here...!}
+
 \begin{equation}
 a^{(p-1)/2} \equiv \begin{array}{rl}
                              -1 &  \mbox{if }a\mbox{ is a quadratic non-residue.} \\
--- a/tommath_class.h
+++ b/tommath_class.h
@@ -90,8 +90,11 @@
 #define BN_MP_READ_UNSIGNED_BIN_C
 #define BN_MP_REDUCE_C
 #define BN_MP_REDUCE_2K_C
+#define BN_MP_REDUCE_2K_L_C
 #define BN_MP_REDUCE_2K_SETUP_C
+#define BN_MP_REDUCE_2K_SETUP_L_C
 #define BN_MP_REDUCE_IS_2K_C
+#define BN_MP_REDUCE_IS_2K_L_C
 #define BN_MP_REDUCE_SETUP_C
 #define BN_MP_RSHD_C
 #define BN_MP_SET_C
@@ -105,7 +108,9 @@
 #define BN_MP_SUB_D_C
 #define BN_MP_SUBMOD_C
 #define BN_MP_TO_SIGNED_BIN_C
+#define BN_MP_TO_SIGNED_BIN_N_C
 #define BN_MP_TO_UNSIGNED_BIN_C
+#define BN_MP_TO_UNSIGNED_BIN_N_C
 #define BN_MP_TOOM_MUL_C
 #define BN_MP_TOOM_SQR_C
 #define BN_MP_TORADIX_C
@@ -132,7 +137,7 @@
   #define BN_MP_ISEVEN_C
   #define BN_MP_INIT_MULTI_C
   #define BN_MP_COPY_C
-   #define BN_MP_ABS_C
+   #define BN_MP_MOD_C
   #define BN_MP_SET_C
   #define BN_MP_DIV_2_C
   #define BN_MP_ISODD_C
@@ -242,6 +247,7 @@
   #define BN_MP_INIT_MULTI_C
   #define BN_MP_SET_C
   #define BN_MP_COUNT_BITS_C
+   #define BN_MP_ABS_C
   #define BN_MP_MUL_2D_C
   #define BN_MP_CMP_C
   #define BN_MP_SUB_C
@@ -323,11 +329,12 @@
   #define BN_MP_CLEAR_C
   #define BN_MP_ABS_C
   #define BN_MP_CLEAR_MULTI_C
+   #define BN_MP_REDUCE_IS_2K_L_C
+   #define BN_S_MP_EXPTMOD_C
   #define BN_MP_DR_IS_MODULUS_C
   #define BN_MP_REDUCE_IS_2K_C
   #define BN_MP_ISODD_C
   #define BN_MP_EXPTMOD_FAST_C
-   #define BN_S_MP_EXPTMOD_C
 #endif

 #if defined(BN_MP_EXPTMOD_FAST_C)
@@ -359,6 +366,7 @@
   #define BN_MP_DIV_C
   #define BN_MP_MUL_C
   #define BN_MP_SUB_C
+   #define BN_MP_NEG_C
   #define BN_MP_EXCH_C
   #define BN_MP_CLEAR_MULTI_C
 #endif
@@ -433,6 +441,7 @@
 #if defined(BN_MP_INVMOD_SLOW_C)
   #define BN_MP_ISZERO_C
   #define BN_MP_INIT_MULTI_C
+   #define BN_MP_MOD_C
   #define BN_MP_COPY_C
   #define BN_MP_ISEVEN_C
   #define BN_MP_SET_C
@@ -724,6 +733,17 @@
   #define BN_MP_CLEAR_C
 #endif

+#if defined(BN_MP_REDUCE_2K_L_C)
+   #define BN_MP_INIT_C
+   #define BN_MP_COUNT_BITS_C
+   #define BN_MP_DIV_2D_C
+   #define BN_MP_MUL_C
+   #define BN_S_MP_ADD_C
+   #define BN_MP_CMP_MAG_C
+   #define BN_S_MP_SUB_C
+   #define BN_MP_CLEAR_C
+#endif
+
 #if defined(BN_MP_REDUCE_2K_SETUP_C)
   #define BN_MP_INIT_C
   #define BN_MP_COUNT_BITS_C
@@ -732,11 +752,22 @@
   #define BN_S_MP_SUB_C
 #endif

+#if defined(BN_MP_REDUCE_2K_SETUP_L_C)
+   #define BN_MP_INIT_C
+   #define BN_MP_2EXPT_C
+   #define BN_MP_COUNT_BITS_C
+   #define BN_S_MP_SUB_C
+   #define BN_MP_CLEAR_C
+#endif
+
 #if defined(BN_MP_REDUCE_IS_2K_C)
   #define BN_MP_REDUCE_2K_C
   #define BN_MP_COUNT_BITS_C
 #endif

+#if defined(BN_MP_REDUCE_IS_2K_L_C)
+#endif
+
 #if defined(BN_MP_REDUCE_SETUP_C)
   #define BN_MP_2EXPT_C
   #define BN_MP_DIV_C
@@ -814,6 +845,11 @@
   #define BN_MP_TO_UNSIGNED_BIN_C
 #endif

+#if defined(BN_MP_TO_SIGNED_BIN_N_C)
+   #define BN_MP_SIGNED_BIN_SIZE_C
+   #define BN_MP_TO_SIGNED_BIN_C
+#endif
+
 #if defined(BN_MP_TO_UNSIGNED_BIN_C)
   #define BN_MP_INIT_COPY_C
   #define BN_MP_ISZERO_C
@@ -821,6 +857,11 @@
   #define BN_MP_CLEAR_C
 #endif

+#if defined(BN_MP_TO_UNSIGNED_BIN_N_C)
+   #define BN_MP_UNSIGNED_BIN_SIZE_C
+   #define BN_MP_TO_UNSIGNED_BIN_C
+#endif
+
 #if defined(BN_MP_TOOM_MUL_C)
   #define BN_MP_INIT_MULTI_C
   #define BN_MP_MOD_2D_C
@@ -901,10 +942,12 @@
   #define BN_MP_INIT_C
   #define BN_MP_CLEAR_C
   #define BN_MP_REDUCE_SETUP_C
+   #define BN_MP_REDUCE_C
+   #define BN_MP_REDUCE_2K_SETUP_L_C
+   #define BN_MP_REDUCE_2K_L_C
   #define BN_MP_MOD_C
   #define BN_MP_COPY_C
   #define BN_MP_SQR_C
-   #define BN_MP_REDUCE_C
   #define BN_MP_MUL_C
   #define BN_MP_SET_C
   #define BN_MP_EXCH_C
Author	SHA1	Message	Date
Matt Johnston	52b6ae0d97	Don't remove ~ files on make clean (and find -type was wrong anyway) --HG-- branch : libtommath extra : convert_revision : 38ad9968c111d9364b88e0098afc3e8e794e67e3	2005-05-11 16:27:28 +00:00
Matt Johnston	6ab9858dec	Update Makefile.in for dropbear --HG-- branch : libtommath extra : convert_revision : 11081ab8c4f56bc850c99ac6c7af31de7b4bca0d	2005-05-11 16:25:34 +00:00
Matt Johnston	0ac65f3f84	Bringing back the original ltc 0.35 makefile --HG-- branch : libtommath extra : convert_revision : 64da6ef5a06ae239a1d89a38481722bf787548e3	2005-05-11 16:23:24 +00:00
Matt Johnston	a89b26e778	propagate from branch 'au.asn.ucc.matt.ltm-orig' (head 7fa10cba9535de3461cedb14b877c24858826204) to branch 'au.asn.ucc.matt.dropbear.ltm' (head fc26f60de0370ab0a281fa41a2d13fb17c9d90a8) --HG-- branch : libtommath extra : convert_revision : 1b78d65cf59dad1c913ea81f892dccece58c2a0d	2005-05-11 16:15:27 +00:00
Matt Johnston	180935d8cd	Initial import of libtommath 0.35 --HG-- branch : libtommath-orig extra : convert_revision : b14c94b945e5c61de5bfa1a6816e11ed55cb2911	2005-05-06 08:59:30 +00:00