added tomsfastmath-0.03

TODO

@@ -1,6 +1,20 @@
+---
+0. IMPORTANT... why are you doubling the "even" terms individually?  STUPID!
+   - make it so you have four new macros that use an additional 3 carry variables
+        - SQRADDSC - store first mult      [ simple store, no carry ]
+        - SQRADDAC - add subsequent mults  [ 3n word add ]
+        - SQRADDDB - double the carry      [ 3n word add ]
+        - SQRADDFC - forward the doubles into the main [ 3n word add, note, x86_32 may need "g" instead of "r" ]
+   - only use the four macro pattern for rows with >= 3 "doubles"
+        - otherwise use the existing SQRADD
+
+
 1. Write more documentation ;-)
 2. Ports to PPC and MIPS
 3. Fix any lingering bugs, add additional requested functionality.
+4. Unrolled copies of montgomery will speed it up a bit
+5. 
+
 
 NOTE:  The library is still fairly new.  I've tested it quite a bit but that doesn't mean surprises
 can't happen.  Please test the results you get for correctness.

changes.txt

@@ -1,3 +1,8 @@
+March 1st, 2005
+0.03 -- Optimized squaring
+     -- 
+
+
 September 18th, 2004
 0.02 -- Added TFM_LARGE to turn on/off 16x combas to save even more space.
         This also helps prevent killing the cache on smaller cpus.

comba_sqr_gen.c

@@ -3,13 +3,16 @@
 
 int main(int argc, char **argv)
 {
-   int x, y, z, N;
+   int x, y, z, N, f;
    N = atoi(argv[1]);
 
+if (N >= 16 && N < 32) printf("#ifdef TFM_LARGE\n");
+if (N >= 32) printf("#ifdef TFM_HUGE\n");
+
 printf(
 "void fp_sqr_comba%d(fp_int *A, fp_int *B)\n"
 "{\n"
-"   fp_digit *a, b[%d], c0, c1, c2;\n"
+"   fp_digit *a, b[%d], c0, c1, c2, sc0, sc1, sc2;\n"
 "\n"
 "   a = A->dp;\n"
 "   COMBA_START; \n"
@@ -25,6 +28,16 @@ printf(
 printf(
 "\n   /* output %d */\n"
 "   CARRY_FORWARD;\n   ", x);
+
+       for (f = y = 0; y < N; y++) {
+           for (z = 0; z < N; z++) {
+               if (z != y && z + y == x && y <= z) {
+                  ++f;
+               }
+           }
+       }
+
+   if (f <= 2) {
        for (y = 0; y < N; y++) {
            for (z = 0; z < N; z++) {
                if (y<=z && (y+z)==x) {
@@ -36,6 +49,30 @@ printf(
                }
            }
        }
+   } else {
+      // new method 
+      /* do evens first */
+       f = 0;
+       for (y = 0; y < N; y++) {
+           for (z = 0; z < N; z++) {
+               if (z != y && z + y == x && y <= z) {
+                  if (f == 0) {
+                     // first double 
+                     printf("SQRADDSC(a[%d], a[%d]); ", y, z);
+                     f = 1;
+                  } else { 
+                     printf("SQRADDAC(a[%d], a[%d]); ", y, z);
+                  }
+               }
+           }
+       }
+       // forward the carry
+       printf("SQRADDDB; ");
+       if ((x&1) == 0) {
+          // add the square 
+          printf("SQRADD(a[%d], a[%d]); ", x/2, x/2);
+       }
+    }
 printf("\n   COMBA_STORE(b[%d]);\n", x);
    }
 printf("   COMBA_STORE2(b[%d]);\n", N+N-1);
@@ -49,5 +86,7 @@ printf(
 "   fp_clamp(B);\n"
 "}\n\n\n", N+N, N+N);
 
+if (N >= 16) printf("#endif\n");
+
   return 0;
 }

demo/test.c

@@ -23,7 +23,7 @@ static ulong64 TIMFUNC (void)
    {
    #if defined __GNUC__
       #if defined(__i386__) || defined(__x86_64__)
-         unsigned long long a;
+         ulong64 a;
          __asm__ __volatile__ ("rdtsc\nmovl %%eax,%0\nmovl %%edx,4+%0\n"::"m"(a):"%eax","%edx");
          return a;
       #else /* gcc-IA64 version */
@@ -60,7 +60,7 @@ int main(void)
                  div2_n, mul2_n, add_d_n, sub_d_n, mul_d_n, t, cnt, rr, ix;
    ulong64 t1, t2;
 
-
+  srand(time(NULL));
   printf("TFM Ident string:\n%s\n\n", fp_ident());
   fp_zero(&b); fp_zero(&c); fp_zero(&d); fp_zero(&e); fp_zero(&f); 
   fp_zero(&a); draw(&a);
@@ -135,6 +135,8 @@ int main(void)
   printf("Testing read_radix\n");
   fp_read_radix(&a, "123456789012345678901234567890", 16); draw(&a);
 
+goto testing;
+
 #if 1
   /* test mont */
   printf("Montgomery test #1\n");
@@ -143,7 +145,7 @@ int main(void)
   fp_montgomery_calc_normalization(&b, &a);
 
   fp_read_radix(&d, "123456789123", 16);
-  for (n = 0; n < 100000; n++) {
+  for (n = 0; n < 1000000; n++) {
       fp_add_d(&d, 1, &d); fp_sqrmod(&d, &a, &d); 
       fp_mul(&d, &b, &c);
       fp_montgomery_reduce(&c, &a, fp);
@@ -165,7 +167,7 @@ int main(void)
   fp_montgomery_calc_normalization(&b, &a);
 
   fp_read_radix(&d, "123456789123", 16);
-  for (n = 0; n < 100000; n++) {
+  for (n = 0; n < 1000000; n++) {
       fp_add_d(&d, 1, &d); fp_sqrmod(&d, &a, &d); 
       fp_mul(&d, &b, &c);
       fp_montgomery_reduce(&c, &a, fp);
@@ -195,7 +197,7 @@ int main(void)
    printf("\n\n");
 #endif
   
-#if 0
+#if 1
  /* do some timings... */
   printf("Addition:\n");
   for (t = 2; t <= FP_SIZE/2; t += 2) {
@@ -242,6 +244,7 @@ int main(void)
       printf("%5lu-bit: %9llu\n", t * DIGIT_BIT, t2);
   }
 //#else
+sqrtime:
   printf("Squaring:\n");
   for (t = 2; t <= FP_SIZE/2; t += 2) {
       fp_zero(&a);
@@ -260,6 +263,7 @@ int main(void)
       }
       printf("%5lu-bit: %9llu\n", t * DIGIT_BIT, t2);
   }
+return;
 //#else
   printf("Montgomery:\n");
   for (t = 2; t <= (FP_SIZE/2)-2; t += 2) {
@@ -288,7 +292,9 @@ int main(void)
       printf("%5lu-bit: %9llu\n", t * DIGIT_BIT, t2);
   }
 //#else
+expttime:
   printf("Exptmod:\n");
+ 
   for (t = 512/DIGIT_BIT; t <= (FP_SIZE/2)-2; t += t) {
       fp_zero(&a);
       fp_zero(&b);
@@ -303,7 +309,7 @@ int main(void)
       c.used = t;
 
      t2 = -1;
-     for (ix = 0; ix < 1024; ++ix) {
+     for (ix = 0; ix < 256; ++ix) {
           t1 = TIMFUNC();
           fp_exptmod(&c, &b, &a, &d);
           fp_exptmod(&c, &b, &a, &d);
@@ -314,8 +320,12 @@ int main(void)
      }
      printf("%5lu-bit: %9llu\n", t * DIGIT_BIT, t2);
   }
+return;
+
 #endif
 
+testing:
+
    div2_n = mul2_n = inv_n = expt_n = lcm_n = gcd_n = add_n =
    sub_n = mul_n = div_n = sqr_n = mul2d_n = div2d_n = cnt = add_d_n = sub_d_n= mul_d_n = 0;
 

fp_exptmod.c

@@ -12,7 +12,6 @@
 /* y = g**x (mod b) 
  * Some restrictions... x must be positive and < b
  */
-
 static int _fp_exptmod(fp_int * G, fp_int * X, fp_int * P, fp_int * Y)
 {
   fp_int   M[64], res;
@@ -169,6 +168,7 @@ static int _fp_exptmod(fp_int * G, fp_int * X, fp_int * P, fp_int * Y)
   return FP_OKAY;
 }
 
+
 int fp_exptmod(fp_int * G, fp_int * X, fp_int * P, fp_int * Y)
 {
    fp_int tmp;
@@ -181,11 +181,12 @@ int fp_exptmod(fp_int * G, fp_int * X, fp_int * P, fp_int * Y)
       if ((err = fp_invmod(&tmp, P, &tmp)) != FP_OKAY) {
          return err;
       }
-      /* _fp_exptmod doesn't care about the sign of X */
+      X->sign = FP_ZPOS;
-      return _fp_exptmod(&tmp, X, P, Y);
+      err =  _fp_exptmod(&tmp, X, P, Y);
+      X->sign = FP_NEG;
+      return err;
    } else {
       /* Positive exponent so just exptmod */
       return _fp_exptmod(G, X, P, Y);
    }
 }
-

fp_mul.c

@@ -29,11 +29,11 @@ void fp_mul(fp_int *A, fp_int *B, fp_int *C)
         } else if (y <= 8) {
            fp_mul_comba8(A,B,C);
 #if defined(TFM_LARGE)
-        } else if (y <= 16 && y >= 12) {
+        } else if (y <= 16 && y >= 10) {
            fp_mul_comba16(A,B,C);
 #endif
 #if defined(TFM_HUGE)
-        } else if (y <= 32 && y >= 28) {
+        } else if (y <= 32 && y >= 24) {
            fp_mul_comba32(A,B,C);
 #endif
         } else {

fp_sqr.c

@@ -16,7 +16,7 @@ void fp_sqr(fp_int *A, fp_int *B)
     fp_int aa, bb, comp, amb, t1;
 
     y = A->used;
-    if (y <= 48) { 
+    if (y <= 64) { 
         if (y <= 4) {
            fp_sqr_comba4(A,B);
         } else if (y <= 8) {
@@ -26,8 +26,10 @@ void fp_sqr(fp_int *A, fp_int *B)
            fp_sqr_comba16(A,B);
 #endif
 #if defined(TFM_HUGE)
-        } else if (y <= 32 && y >= 28) {
+        } else if (y <= 32 && y >= 20) {
            fp_sqr_comba32(A,B);
+        } else if (y <= 64 && y >= 48) {
+           fp_sqr_comba64(A,B);
 #endif
         } else {
            fp_sqr_comba(A, B);

fp_sqr_comba_generic.c

@@ -0,0 +1,75 @@
+/* generic comba squarer */
+void fp_sqr_comba(fp_int *A, fp_int *B)
+{
+  int       pa, ix, iz;
+  fp_digit  c0, c1, c2;
+  fp_int    tmp, *dst;
+
+  /* get size of output and trim */
+  pa = A->used + A->used;
+  if (pa >= FP_SIZE) {
+     pa = FP_SIZE-1;
+  }
+
+  /* number of output digits to produce */
+  COMBA_START;
+  CLEAR_CARRY;
+
+  if (A == B) {
+     fp_zero(&tmp);
+     dst = &tmp;
+  } else {
+     fp_zero(B);
+     dst = B;
+  }
+
+  for (ix = 0; ix < pa; ix++) { 
+      int      tx, ty, iy;
+      fp_digit *tmpy, *tmpx;
+
+      /* get offsets into the two bignums */
+      ty = MIN(A->used-1, ix);
+      tx = ix - ty;
+
+      /* setup temp aliases */
+      tmpx = A->dp + tx;
+      tmpy = A->dp + ty;
+
+      /* this is the number of times the loop will iterrate, essentially its 
+         while (tx++ < a->used && ty-- >= 0) { ... }
+       */
+      iy = MIN(A->used-tx, ty+1);
+
+      /* now for squaring tx can never equal ty 
+       * we halve the distance since they approach at a rate of 2x
+       * and we have to round because odd cases need to be executed
+       */
+      iy = MIN(iy, (ty-tx+1)>>1);
+
+      /* forward carries */
+      CARRY_FORWARD;
+
+      /* execute loop */
+      for (iz = 0; iz < iy; iz++) {
+          SQRADD2(*tmpx++, *tmpy--);
+      }
+
+      /* even columns have the square term in them */
+      if ((ix&1) == 0) {
+          SQRADD(A->dp[ix>>1], A->dp[ix>>1]);
+      }
+
+      /* store it */
+      COMBA_STORE(dst->dp[ix]);
+  }
+  COMBA_STORE2(dst->dp[ix]);
+
+  COMBA_FINI;
+
+  /* setup dest */
+  dst->used = pa;
+  fp_clamp (dst);
+  if (dst != B) {
+     fp_copy(dst, B);
+  }
+}

makefile

@@ -10,7 +10,7 @@ CFLAGS += -Wall -W -Wshadow -I./ -O3 -funroll-all-loops
 #speed
 CFLAGS += -fomit-frame-pointer
 
-VERSION=0.02
+VERSION=0.03
 
 default: libtfm.a
 

random_txt_files/newsqr.txt

@@ -0,0 +1,36 @@
+New code added in TFM v0.03
+
+OLD 64-bit...[athlon64]
+
+Squaring:
+  256-bit:        89
+  512-bit:       234
+ 1024-bit:       815
+ 2048-bit:      2851
+
+NEW 64-bit ...
+
+Squaring:
+  256-bit:        89
+  512-bit:       228
+ 1024-bit:       691
+ 2048-bit:      2228
+
+
+OLD 32-bit [athlonxp]
+
+Squaring:
+
+  256-bit:       327
+  512-bit:      1044
+ 1024-bit:      3646
+ 2048-bit:     17055
+
+NEW 32-bit
+
+Squaring:
+
+  256-bit:       332
+  512-bit:       894
+ 1024-bit:      2983
+ 2048-bit:     10385

tfm.h

@@ -350,6 +350,7 @@ void fp_sqr_comba16(fp_int *A, fp_int *B);
 #endif
 #ifdef TFM_HUGE
 void fp_sqr_comba32(fp_int *A, fp_int *B);
+void fp_sqr_comba64(fp_int *A, fp_int *B);
 #endif
 extern const char *fp_s_rmap;
 

tfm.tex

@@ -49,7 +49,7 @@
 \begin{document}
 \frontmatter
 \pagestyle{empty}
-\title{TomsFastMath User Manual \\ v0.02}
+\title{TomsFastMath User Manual \\ v0.03}
 \author{Tom St Denis \\ tomstdenis@iahu.ca}
 \maketitle
 This text and library are all hereby placed in the public domain.  This book has been formatted for B5 
@@ -525,6 +525,37 @@ This is essentially the MULADD macro from the multiplication code.
 This is like SQRADD except it adds the produce twice.  It's similar to 
 computing SQRADD(i, j*2).
 
+To further make things interesting the squaring code also has ``doubles'' (see my LTM book chapter five...) which are
+handled with these macros.
+
+\begin{verbatim}
+#define SQRADDSC(i, j)                                                         \
+   do { fp_word t;                                                             \
+      t =  ((fp_word)i) * ((fp_word)j);                                        \
+      sc0 = (fp_digit)t; sc1 = (t >> DIGIT_BIT); sc2 = 0;                      \
+   } while (0);
+\end{verbatim}
+This computes a product and stores it in the ``secondary'' carry registers $\left < sc0, sc1, sc2 \right >$.
+
+\begin{verbatim}
+#define SQRADDAC(i, j)                                                         \
+   do { fp_word t;                                                             \
+   t = sc0 + ((fp_word)i) * ((fp_word)j);  sc0 = t;                            \
+   t = sc1 + (t >> DIGIT_BIT);             sc1 = t; sc2 += t >> DIGIT_BIT;     \
+   } while (0);
+\end{verbatim}
+This computes a product and adds it to the ``secondary'' carry registers.
+
+\begin{verbatim}
+#define SQRADDDB                                                               \
+   do { fp_word t;                                                             \
+   t = ((fp_word)sc0) + ((fp_word)sc0) + c0; c0 = t;                                                 \
+   t = ((fp_word)sc1) + ((fp_word)sc1) + c1 + (t >> DIGIT_BIT); c1 = t;                              \
+   c2 = c2 + ((fp_word)sc2) + ((fp_word)sc2) + (t >> DIGIT_BIT);                                     \
+   } while (0);
+\end{verbatim}
+This doubles the ``secondary'' carry registers and adds the sum to the main carry registers.  Really complicated.
+
 \section{Montgomery with Comba}
 Montgomery reduction is used in modular exponentiation and is most called function during
 that operation.  It's important to make sure this routine is very fast or all is lost.