From 86abac78a20dfe49aea28058956a3fe8b6ced9ee Mon Sep 17 00:00:00 2001
From: Werner Koch <wk@gnupg.org>
Date: Fri, 2 Jul 1999 09:50:57 +0000
Subject: See ChangeLog: Fri Jul  2 11:45:54 CEST 1999  Werner Koch

---
 mpi/mpi-mpow.c | 141 +++++++++++++++++++++++++++++++++++++++++++++++++--------
 1 file changed, 122 insertions(+), 19 deletions(-)

(limited to 'mpi/mpi-mpow.c')

diff --git a/mpi/mpi-mpow.c b/mpi/mpi-mpow.c
index 689a7600f..a8c561dd1 100644
--- a/mpi/mpi-mpow.c
+++ b/mpi/mpi-mpow.c
@@ -1,5 +1,5 @@
 /* mpi-mpow.c  -  MPI functions
- *	Copyright (C) 1998 Free Software Foundation, Inc.
+ *	Copyright (C) 1998, 1999 Free Software Foundation, Inc.
  *
  * This file is part of GnuPG.
  *
@@ -25,6 +25,22 @@
 #include "longlong.h"
 #include <assert.h>
 
+/* Barrett is slower than the classical way.  It can be tweaked by
+ * using partial multiplications
+ */
+/*#define USE_BARRETT*/
+
+
+
+#ifdef USE_BARRETT
+static void barrett_mulm( MPI w, MPI u, MPI v, MPI m, MPI y, int k, MPI r1, MPI r2 );
+static MPI init_barrett( MPI m, int *k, MPI *r1, MPI *r2 );
+static int calc_barrett( MPI r, MPI x, MPI m, MPI y, int k, MPI r1, MPI r2  );
+#else
+#define barrett_mulm( w, u, v, m, y, k, r1, r2 ) mpi_mulm( (w), (u), (v), (m) )
+#endif
+
+
 static int
 build_index( MPI *exparray, int k, int i, int t )
 {
@@ -52,6 +68,10 @@ mpi_mulpowm( MPI res, MPI *basearray, MPI *exparray, MPI m)
     int i, j, idx;
     MPI *G;	/* table with precomputed values of size 2^k */
     MPI tmp;
+  #ifdef USE_BARRETT
+    MPI barrett_y, barrett_r1, barrett_r2;
+    int barrett_k;
+  #endif
 
     for(k=0; basearray[k]; k++ )
 	;
@@ -68,27 +88,15 @@ mpi_mulpowm( MPI res, MPI *basearray, MPI *exparray, MPI m)
     assert( k < 10 );
 
     G = m_alloc_clear( (1<<k) * sizeof *G );
-  #if 0
-    /* do the precomputation */
-    G[0] = mpi_alloc_set_ui( 1 );
-    for(i=1; i < (1<<k); i++ ) {
-	for(j=0; j < k; j++ ) {
-	    if( (i & (1<<j) ) ) {
-		if( !G[i] )
-		    G[i] = mpi_copy( basearray[j] );
-		else
-		    mpi_mulm( G[i], G[i], basearray[j], m );
-	    }
-	}
-	if( !G[i] )
-	    G[i] = mpi_alloc(0);
-    }
+  #ifdef USE_BARRETT
+    barrett_y = init_barrett( m, &barrett_k, &barrett_r1, &barrett_r2 );
   #endif
     /* and calculate */
     tmp =  mpi_alloc( mpi_get_nlimbs(m)+1 );
     mpi_set_ui( res, 1 );
     for(i = 1; i <= t; i++ ) {
-	mpi_mulm(tmp, res, res, m );
+	barrett_mulm(tmp, res, res, m, barrett_y, barrett_k,
+				       barrett_r1, barrett_r2 );
 	idx = build_index( exparray, k, i, t );
 	assert( idx >= 0 && idx < (1<<k) );
 	if( !G[idx] ) {
@@ -100,20 +108,115 @@ mpi_mulpowm( MPI res, MPI *basearray, MPI *exparray, MPI m)
 			if( !G[idx] )
 			    G[idx] = mpi_copy( basearray[j] );
 			else
-			    mpi_mulm( G[idx], G[idx], basearray[j], m );
+			    barrett_mulm( G[idx], G[idx], basearray[j],
+					       m, barrett_y, barrett_k, barrett_r1, barrett_r2	);
 		    }
 		}
 		if( !G[idx] )
 		    G[idx] = mpi_alloc(0);
 	    }
 	}
-	mpi_mulm(res, tmp, G[idx], m );
+	barrett_mulm(res, tmp, G[idx], m, barrett_y, barrett_k, barrett_r1, barrett_r2	);
     }
 
     /* cleanup */
     mpi_free(tmp);
+  #ifdef USE_BARRETT
+    mpi_free(barrett_y);
+    mpi_free(barrett_r1);
+    mpi_free(barrett_r2);
+  #endif
     for(i=0; i < (1<<k); i++ )
 	mpi_free(G[i]);
     m_free(G);
 }
 
+
+
+#ifdef USE_BARRETT
+static void
+barrett_mulm( MPI w, MPI u, MPI v, MPI m, MPI y, int k, MPI r1, MPI r2	)
+{
+    mpi_mul(w, u, v);
+    if( calc_barrett( w, w, m, y, k, r1, r2 ) )
+	mpi_fdiv_r( w, w, m );
+}
+
+/****************
+ * Barrett precalculation: y = floor(b^(2k) / m)
+ */
+static MPI
+init_barrett( MPI m, int *k, MPI *r1, MPI *r2 )
+{
+    MPI tmp;
+
+    mpi_normalize( m );
+    *k = mpi_get_nlimbs( m );
+    tmp = mpi_alloc( *k + 1 );
+    mpi_set_ui( tmp, 1 );
+    mpi_lshift_limbs( tmp, 2 * *k );
+    mpi_fdiv_q( tmp, tmp, m );
+    *r1 = mpi_alloc( 2* *k + 1 );
+    *r2 = mpi_alloc( 2* *k + 1 );
+    return tmp;
+}
+
+/****************
+ * Barrett reduction: We assume that these conditions are met:
+ * Given x =(x_2k-1 ...x_0)_b
+ *	 m =(m_k-1 ....m_0)_b	  with m_k-1 != 0
+ * Output r = x mod m
+ * Before using this function init_barret must be used to calucalte y and k.
+ * Returns: false = no error
+ *	    true = can't perform barret reduction
+ */
+static int
+calc_barrett( MPI r, MPI x, MPI m, MPI y, int k, MPI r1, MPI r2 )
+{
+    int xx = k > 3 ? k-3:0;
+
+    mpi_normalize( x );
+    if( mpi_get_nlimbs(x) > 2*k )
+	return 1; /* can't do it */
+
+    /* 1. q1 = floor( x / b^k-1)
+     *	  q2 = q1 * y
+     *	  q3 = floor( q2 / b^k+1 )
+     * Actually, we don't need qx, we can work direct on r2
+     */
+    mpi_set( r2, x );
+    mpi_rshift_limbs( r2, k-1 );
+    mpi_mul( r2, r2, y );
+    mpi_rshift_limbs( r2, k+1 );
+
+    /* 2. r1 = x mod b^k+1
+     *	  r2 = q3 * m mod b^k+1
+     *	  r  = r1 - r2
+     * 3. if r < 0 then  r = r + b^k+1
+     */
+    mpi_set( r1, x );
+    if( r1->nlimbs > k+1 ) /* quick modulo operation */
+	r1->nlimbs = k+1;
+    mpi_mul( r2, r2, m );
+    if( r2->nlimbs > k+1 ) /* quick modulo operation */
+	r2->nlimbs = k+1;
+    mpi_sub( r, r1, r2 );
+
+    if( mpi_is_neg( r ) ) {
+	MPI tmp;
+
+	tmp = mpi_alloc( k + 2 );
+	mpi_set_ui( tmp, 1 );
+	mpi_lshift_limbs( tmp, k+1 );
+	mpi_add( r, r, tmp );
+	mpi_free(tmp);
+    }
+
+    /* 4. while r >= m do r = r - m */
+    while( mpi_cmp( r, m ) >= 0 )
+	mpi_sub( r, r, m );
+
+    return 0;
+}
+#endif /* USE_BARRETT */
+
-- 
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