===================================================================
RCS file: /home/cvs/OpenXM_contrib2/asir2000/engine/gfs.c,v
retrieving revision 1.5
retrieving revision 1.6
diff -u -p -r1.5 -r1.6
--- OpenXM_contrib2/asir2000/engine/gfs.c	2001/05/28 08:22:01	1.5
+++ OpenXM_contrib2/asir2000/engine/gfs.c	2001/06/20 09:30:34	1.6
@@ -45,7 +45,7 @@
  * DEVELOPER SHALL HAVE NO LIABILITY IN CONNECTION WITH THE USE,
  * PERFORMANCE OR NON-PERFORMANCE OF THE SOFTWARE.
  *
- * $OpenXM: OpenXM_contrib2/asir2000/engine/gfs.c,v 1.4 2001/03/29 09:49:58 noro Exp $
+ * $OpenXM: OpenXM_contrib2/asir2000/engine/gfs.c,v 1.5 2001/05/28 08:22:01 noro Exp $
 */
 #include "ca.h"
 
@@ -62,6 +62,417 @@ int *current_gfs_iton;
 void chsgngfs();
 void generate_defpoly_um();
 
+struct prim_root_info {
+	int p;
+	int extdeg;
+	int defpoly;
+	int prim_root;
+};
+
+struct prim_root_info prim_root_info_tab[] = {
+{2,1,0,0}, {2,2,7,2}, {2,3,11,2}, {2,4,19,2}, {2,5,37,2}, {2,6,67,2},
+{2,7,131,2}, {2,8,283,3}, {2,9,515,7}, {2,10,1033,2}, {2,11,2053,2},
+{2,12,4105,3}, {2,13,8219,2}, {2,14,16417,7}, {2,15,32771,2}, {3,1,0,2},
+{3,2,10,4}, {3,3,34,3}, {3,4,86,3}, {3,5,250,3}, {3,6,734,3}, {3,7,2198,5},
+{3,8,6572,38}, {3,9,19747,3}, {3,10,59068,34}, {5,1,0,2}, {5,2,27,6},
+{5,3,131,9}, {5,4,627,6}, {5,5,3146,10}, {5,6,15632,5}, {7,1,0,3},
+{7,2,50,9}, {7,3,345,22}, {7,4,2409,12}, {7,5,16817,9}, {11,1,0,2},
+{11,2,122,15}, {11,3,1346,11}, {11,4,14654,11}, {13,1,0,2}, {13,2,171,15},
+{13,3,2199,15}, {13,4,28563,17}, {17,1,0,3}, {17,2,292,19}, {17,3,4933,17},
+{19,1,0,2}, {19,2,362,22}, {19,3,6861,29}, {23,1,0,5}, {23,2,530,25},
+{23,3,12193,23}, {29,1,0,2}, {29,2,843,30}, {29,3,24422,30}, {31,1,0,3},
+{31,2,962,35}, {31,3,29794,34}, {37,1,0,2}, {37,2,1371,41}, {37,3,50655,75},
+{41,1,0,6}, {41,2,1684,43}, {43,1,0,3}, {43,2,1850,45}, {47,1,0,5},
+{47,2,2210,49}, {53,1,0,2}, {53,2,2811,54}, {59,1,0,2}, {59,2,3482,62},
+{61,1,0,2}, {61,2,3723,63}, {67,1,0,2}, {67,2,4490,74}, {71,1,0,7},
+{71,2,5042,79}, {73,1,0,5}, {73,2,5334,76}, {79,1,0,3}, {79,2,6242,85},
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+{11839,1,0,3}, {11863,1,0,3}, {11867,1,0,2}, {11887,1,0,3}, {11897,1,0,3},
+{11903,1,0,5}, {11909,1,0,2}, {11923,1,0,5}, {11927,1,0,5}, {11933,1,0,2},
+{11939,1,0,2}, {11941,1,0,10}, {11953,1,0,5}, {11959,1,0,3}, {11969,1,0,3},
+{11971,1,0,10}, {11981,1,0,2}, {11987,1,0,2}, {12007,1,0,13}, {12011,1,0,2},
+{12037,1,0,5}, {12041,1,0,3}, {12043,1,0,2}, {12049,1,0,13}, {12071,1,0,11},
+{12073,1,0,7}, {12097,1,0,5}, {12101,1,0,3}, {12107,1,0,2}, {12109,1,0,6},
+{12113,1,0,3}, {12119,1,0,7}, {12143,1,0,10}, {12149,1,0,2}, {12157,1,0,2},
+{12161,1,0,3}, {12163,1,0,5}, {12197,1,0,2}, {12203,1,0,2}, {12211,1,0,2},
+{12227,1,0,2}, {12239,1,0,13}, {12241,1,0,7}, {12251,1,0,2}, {12253,1,0,2},
+{12263,1,0,5}, {12269,1,0,2}, {12277,1,0,2}, {12281,1,0,3}, {12289,1,0,11},
+{12301,1,0,2}, {12323,1,0,2}, {12329,1,0,3}, {12343,1,0,7}, {12347,1,0,2},
+{12373,1,0,2}, {12377,1,0,6}, {12379,1,0,2}, {12391,1,0,26}, {12401,1,0,3},
+{12409,1,0,7}, {12413,1,0,2}, {12421,1,0,7}, {12433,1,0,13}, {12437,1,0,2},
+{12451,1,0,3}, {12457,1,0,10}, {12473,1,0,3}, {12479,1,0,23}, {12487,1,0,3},
+{12491,1,0,2}, {12497,1,0,3}, {12503,1,0,5}, {12511,1,0,3}, {12517,1,0,6},
+{12527,1,0,5}, {12539,1,0,2}, {12541,1,0,14}, {12547,1,0,2}, {12553,1,0,5},
+{12569,1,0,3}, {12577,1,0,10}, {12583,1,0,5}, {12589,1,0,2}, {12601,1,0,11},
+{12611,1,0,2}, {12613,1,0,2}, {12619,1,0,2}, {12637,1,0,2}, {12641,1,0,3},
+{12647,1,0,5}, {12653,1,0,2}, {12659,1,0,2}, {12671,1,0,14}, {12689,1,0,3},
+{12697,1,0,7}, {12703,1,0,3}, {12713,1,0,3}, {12721,1,0,13}, {12739,1,0,2},
+{12743,1,0,5}, {12757,1,0,2}, {12763,1,0,2}, {12781,1,0,2}, {12791,1,0,7},
+{12799,1,0,13}, {12809,1,0,3}, {12821,1,0,2}, {12823,1,0,3}, {12829,1,0,2},
+{12841,1,0,21}, {12853,1,0,5}, {12889,1,0,13}, {12893,1,0,3}, {12899,1,0,2},
+{12907,1,0,2}, {12911,1,0,23}, {12917,1,0,2}, {12919,1,0,6}, {12923,1,0,2},
+{12941,1,0,2}, {12953,1,0,3}, {12959,1,0,7}, {12967,1,0,3}, {12973,1,0,14},
+{12979,1,0,2}, {12983,1,0,5}, {13001,1,0,3}, {13003,1,0,5}, {13007,1,0,5},
+{13009,1,0,7}, {13033,1,0,5}, {13037,1,0,2}, {13043,1,0,2}, {13049,1,0,3},
+{13063,1,0,5}, {13093,1,0,6}, {13099,1,0,3}, {13103,1,0,5}, {13109,1,0,2},
+{13121,1,0,7}, {13127,1,0,5}, {13147,1,0,2}, {13151,1,0,13}, {13159,1,0,3},
+{13163,1,0,2}, {13171,1,0,11}, {13177,1,0,5}, {13183,1,0,3}, {13187,1,0,2},
+{13217,1,0,3}, {13219,1,0,3}, {13229,1,0,2}, {13241,1,0,3}, {13249,1,0,7},
+{13259,1,0,6}, {13267,1,0,3}, {13291,1,0,2}, {13297,1,0,5}, {13309,1,0,6},
+{13313,1,0,3}, {13327,1,0,3}, {13331,1,0,2}, {13337,1,0,3}, {13339,1,0,2},
+{13367,1,0,5}, {13381,1,0,10}, {13397,1,0,2}, {13399,1,0,3}, {13411,1,0,2},
+{13417,1,0,5}, {13421,1,0,10}, {13441,1,0,11}, {13451,1,0,2}, {13457,1,0,3},
+{13463,1,0,5}, {13469,1,0,2}, {13477,1,0,2}, {13487,1,0,5}, {13499,1,0,6},
+{13513,1,0,5}, {13523,1,0,2}, {13537,1,0,7}, {13553,1,0,3}, {13567,1,0,3},
+{13577,1,0,3}, {13591,1,0,3}, {13597,1,0,5}, {13613,1,0,2}, {13619,1,0,2},
+{13627,1,0,2}, {13633,1,0,5}, {13649,1,0,3}, {13669,1,0,6}, {13679,1,0,7},
+{13681,1,0,22}, {13687,1,0,3}, {13691,1,0,2}, {13693,1,0,6}, {13697,1,0,3},
+{13709,1,0,2}, {13711,1,0,6}, {13721,1,0,3}, {13723,1,0,2}, {13729,1,0,23},
+{13751,1,0,11}, {13757,1,0,2}, {13759,1,0,6}, {13763,1,0,2}, {13781,1,0,7},
+{13789,1,0,7}, {13799,1,0,7}, {13807,1,0,5}, {13829,1,0,2}, {13831,1,0,6},
+{13841,1,0,6}, {13859,1,0,2}, {13873,1,0,5}, {13877,1,0,2}, {13879,1,0,6},
+{13883,1,0,2}, {13901,1,0,2}, {13903,1,0,3}, {13907,1,0,2}, {13913,1,0,3},
+{13921,1,0,7}, {13931,1,0,2}, {13933,1,0,2}, {13963,1,0,3}, {13967,1,0,5},
+{13997,1,0,2}, {13999,1,0,3}, {14009,1,0,3}, {14011,1,0,2}, {14029,1,0,6},
+{14033,1,0,3}, {14051,1,0,2}, {14057,1,0,3}, {14071,1,0,7}, {14081,1,0,3},
+{14083,1,0,3}, {14087,1,0,5}, {14107,1,0,2}, {14143,1,0,3}, {14149,1,0,6},
+{14153,1,0,3}, {14159,1,0,13}, {14173,1,0,2}, {14177,1,0,3}, {14197,1,0,11},
+{14207,1,0,5}, {14221,1,0,2}, {14243,1,0,2}, {14249,1,0,3}, {14251,1,0,3},
+{14281,1,0,19}, {14293,1,0,6}, {14303,1,0,5}, {14321,1,0,3}, {14323,1,0,5},
+{14327,1,0,5}, {14341,1,0,2}, {14347,1,0,3}, {14369,1,0,3}, {14387,1,0,2},
+{14389,1,0,2}, {14401,1,0,11}, {14407,1,0,19}, {14411,1,0,2}, {14419,1,0,2},
+{14423,1,0,5}, {14431,1,0,3}, {14437,1,0,5}, {14447,1,0,5}, {14449,1,0,22},
+{14461,1,0,2}, {14479,1,0,3}, {14489,1,0,3}, {14503,1,0,3}, {14519,1,0,13},
+{14533,1,0,2}, {14537,1,0,3}, {14543,1,0,5}, {14549,1,0,2}, {14551,1,0,3},
+{14557,1,0,2}, {14561,1,0,6}, {14563,1,0,3}, {14591,1,0,11}, {14593,1,0,5},
+{14621,1,0,2}, {14627,1,0,2}, {14629,1,0,2}, {14633,1,0,3}, {14639,1,0,11},
+{14653,1,0,2}, {14657,1,0,3}, {14669,1,0,2}, {14683,1,0,3}, {14699,1,0,2},
+{14713,1,0,5}, {14717,1,0,2}, {14723,1,0,2}, {14731,1,0,10}, {14737,1,0,10},
+{14741,1,0,2}, {14747,1,0,2}, {14753,1,0,3}, {14759,1,0,17}, {14767,1,0,3},
+{14771,1,0,2}, {14779,1,0,3}, {14783,1,0,5}, {14797,1,0,2}, {14813,1,0,2},
+{14821,1,0,2}, {14827,1,0,2}, {14831,1,0,11}, {14843,1,0,2}, {14851,1,0,2},
+{14867,1,0,2}, {14869,1,0,2}, {14879,1,0,7}, {14887,1,0,3}, {14891,1,0,2},
+{14897,1,0,3}, {14923,1,0,2}, {14929,1,0,7}, {14939,1,0,2}, {14947,1,0,2},
+{14951,1,0,19}, {14957,1,0,2}, {14969,1,0,3}, {14983,1,0,3}, {15013,1,0,2},
+{15017,1,0,3}, {15031,1,0,3}, {15053,1,0,2}, {15061,1,0,2}, {15073,1,0,5},
+{15077,1,0,2}, {15083,1,0,2}, {15091,1,0,2}, {15101,1,0,2}, {15107,1,0,2},
+{15121,1,0,11}, {15131,1,0,2}, {15137,1,0,3}, {15139,1,0,2}, {15149,1,0,2},
+{15161,1,0,3}, {15173,1,0,2}, {15187,1,0,2}, {15193,1,0,5}, {15199,1,0,6},
+{15217,1,0,10}, {15227,1,0,2}, {15233,1,0,3}, {15241,1,0,11}, {15259,1,0,2},
+{15263,1,0,5}, {15269,1,0,2}, {15271,1,0,11}, {15277,1,0,6}, {15287,1,0,5},
+{15289,1,0,11}, {15299,1,0,2}, {15307,1,0,3}, {15313,1,0,5}, {15319,1,0,3},
+{15329,1,0,3}, {15331,1,0,2}, {15349,1,0,2}, {15359,1,0,11}, {15361,1,0,7},
+{15373,1,0,2}, {15377,1,0,3}, {15383,1,0,5}, {15391,1,0,12}, {15401,1,0,6},
+{15413,1,0,2}, {15427,1,0,2}, {15439,1,0,3}, {15443,1,0,2}, {15451,1,0,3},
+{15461,1,0,2}, {15467,1,0,5}, {15473,1,0,3}, {15493,1,0,5}, {15497,1,0,3},
+{15511,1,0,3}, {15527,1,0,5}, {15541,1,0,6}, {15551,1,0,7}, {15559,1,0,3},
+{15569,1,0,3}, {15581,1,0,2}, {15583,1,0,5}, {15601,1,0,23}, {15607,1,0,3},
+{15619,1,0,7}, {15629,1,0,2}, {15641,1,0,3}, {15643,1,0,5}, {15647,1,0,5},
+{15649,1,0,11}, {15661,1,0,2}, {15667,1,0,2}, {15671,1,0,13}, {15679,1,0,11},
+{15683,1,0,2}, {15727,1,0,3}, {15731,1,0,2}, {15733,1,0,6}, {15737,1,0,3},
+{15739,1,0,2}, {15749,1,0,2}, {15761,1,0,3}, {15767,1,0,5}, {15773,1,0,2},
+{15787,1,0,2}, {15791,1,0,29}, {15797,1,0,2}, {15803,1,0,2}, {15809,1,0,3},
+{15817,1,0,5}, {15823,1,0,3}, {15859,1,0,2}, {15877,1,0,5}, {15881,1,0,3},
+{15887,1,0,5}, {15889,1,0,21}, {15901,1,0,10}, {15907,1,0,2}, {15913,1,0,5},
+{15919,1,0,6}, {15923,1,0,2}, {15937,1,0,7}, {15959,1,0,11}, {15971,1,0,2},
+{15973,1,0,7}, {15991,1,0,12}, {16001,1,0,3}, {16007,1,0,5}, {16033,1,0,5},
+{16057,1,0,7}, {16061,1,0,12}, {16063,1,0,5}, {16067,1,0,2}, {16069,1,0,2},
+{16073,1,0,3}, {16087,1,0,5}, {16091,1,0,6}, {16097,1,0,3}, {16103,1,0,5},
+{16111,1,0,7}, {16127,1,0,5}, {16139,1,0,2}, {16141,1,0,6}, {16183,1,0,3},
+{16187,1,0,2}, {16189,1,0,2}, {16193,1,0,5}, {16217,1,0,3}, {16223,1,0,5},
+{16229,1,0,2}, {16231,1,0,3}, {16249,1,0,17}, {16253,1,0,2}, {16267,1,0,3},
+{16273,1,0,7}, {16301,1,0,2}, {16319,1,0,7}, {16333,1,0,2}, {16339,1,0,2},
+{16349,1,0,2}, {16361,1,0,3}, {16363,1,0,2}, {16369,1,0,7}, {16381,1,0,2},
+};
+
 void dec_um(p,a,u)
 int p,a;
 UM u;
@@ -89,8 +500,11 @@ int p,n;
 	for ( i = 0, q = 1; i < n; i++ )
 		q *= p;
 	dp = UMALLOC(n);
-	generate_defpoly_um(p,n,dp);
-	r = generate_primitive_root_enc(p,n,dp);
+	r = search_defpoly_and_primitive_root(p,n,dp);
+	if ( !r ) {
+		generate_defpoly_um(p,n,dp);
+		r = generate_primitive_root_enc(p,n,dp);
+	}
 	current_gfs_p = p;
 	current_gfs_q = q;
 	current_gfs_q1 = q1 = q-1;
@@ -117,6 +531,45 @@ int p,n;
 	}
 }
 
+int search_defpoly_and_primitive_root(p,n,dp)
+int p,n;
+UM dp;
+{
+	int l,min,max,mid,p1,i,ind,t;
+
+	l = sizeof(prim_root_info_tab)/sizeof(struct prim_root_info);
+	min = 0; max = l-1;
+	ind = -1;
+	while ( max - min > 1 ) {
+		mid = (max+min)/2;
+		p1 = prim_root_info_tab[mid].p;
+		if ( p1 == p ) {
+			ind = mid; break;
+		} else if ( p1 > p )
+			max = mid;
+		else
+			min = mid;
+	}
+	if ( ind < 0 ) {
+		if ( prim_root_info_tab[min].p == p )
+			ind = min;
+		else if ( prim_root_info_tab[max].p == p )
+			ind = max;
+		else
+			return 0; /* XXX */
+	}
+	/* now prim_root_info_tab[ind].p = p */
+	t = ind - (prim_root_info_tab[ind].extdeg-1);
+	/* now prim_root_info_tab[t].extdeg = 1 */
+	for ( i = t; prim_root_info_tab[i].p == p; i++ )
+		if ( prim_root_info_tab[i].extdeg == n )
+			break;
+	if ( prim_root_info_tab[i].p != p )
+		return 0;
+	dec_um(p,prim_root_info_tab[i].defpoly,dp);
+	return prim_root_info_tab[i].prim_root;
+}
+
 void generate_defpoly_um(p,n,dp)
 int p,n;
 UM dp;
@@ -452,3 +905,175 @@ GFS *r;
 		MKGFS(t,*r);
 	}
 }
+
+/* arithmetic operations for 'immediate values of GFS */
+
+int _addsf(a,b)
+int a,b;
+{
+	if ( !a )
+		return b;
+	else if ( !b )
+		return a;
+
+	a = IFTOF(a); b = IFTOF(b);
+	if ( a > b ) {
+		/* tab[a]+tab[b] = tab[b](tab[a-b]+1) */
+		a = current_gfs_plus1[a-b];
+		if ( a < 0 )
+			return 0;
+		else {
+			a += b;
+			if ( a >= current_gfs_q1 )
+				a -= current_gfs_q1;
+			return FTOIF(a);
+		}
+	} else {
+		/* tab[a]+tab[b] = tab[a](tab[b-a]+1) */
+		b = current_gfs_plus1[b-a];
+		if ( b < 0 )
+			return 0;
+		else {
+			b += a;
+			if ( b >= current_gfs_q1 )
+				b -= current_gfs_q1;
+			return FTOIF(b);
+		}
+	}
+}
+
+int _chsgnsf(a)
+int a;
+{
+	if ( !a )
+		return 0;
+	else if ( current_gfs_q1&1 )
+		return a;
+	else {	
+		/* r^((q-1)/2) = -1 */
+		a = IFTOF(a);
+		a += (current_gfs_q1>>1);
+		if ( a >= current_gfs_q1 )
+			a -= current_gfs_q1;
+		return FTOIF(a);
+	}
+}
+
+int _subsf(a,b)
+int a,b;
+{
+	if ( !a )
+		return _chsgnsf(b);
+	else if ( !b )
+		return a;
+	else
+		return _addsf(a,_chsgnsf(b));
+}
+
+int _mulsf(a,b)
+int a,b;
+{
+	if ( !a || !b )
+		return 0;
+	else {
+		a = IFTOF(a) + IFTOF(b);
+		if ( a >= current_gfs_q1 )
+			a -= current_gfs_q1;
+		return FTOIF(a);
+	}
+}
+
+int _invsf(a)
+int a;
+{
+	if ( !a )
+		error("_invsf : division by 0");
+	else {
+		a = current_gfs_q1 - IFTOF(a);
+		return FTOIF(a);
+	}
+}
+
+int _divsf(a,b)
+int a,b;
+{
+	if ( !b )
+		error("_divsf : division by 0");
+	else if ( !a )
+		return 0;
+	else {
+		a = IFTOF(a) - IFTOF(b);
+		if ( a < 0 )
+			a += current_gfs_q1;
+		return FTOIF(a);
+	}
+}
+
+int _pwrsf(a,b)
+int a,b;
+{
+	GFS at,ct;
+	Q bt;
+	int c;
+
+	if ( !b )
+		return _onesf();
+	else if ( !a )
+		return 0;
+	else {
+		a = IFTOF(a);
+		MKGFS(a,at);
+		STOQ(b,bt);
+		pwrgfs(at,bt,&ct);
+		c = CONT(ct);
+		return FTOIF(c);
+	}
+}
+
+int _onesf()
+{
+	return FTOIF(0);
+}
+
+int _itosf(n)
+int n;
+{
+	int i;
+
+	n %= current_gfs_p;
+	if ( !n )
+		return 0;
+	i = current_gfs_ntoi[n];
+	i = FTOIF(i);
+	if ( n < 0 )
+		i = _chsgnsf(i);
+	return i;
+}
+
+int _isonesf(a)
+int a;
+{
+	return a == FTOIF(0);
+}
+
+int _randomsf()
+{
+	int t;
+
+	t = (int) (mt_genrand() % current_gfs_q1);
+	if ( !t )
+		return 0;
+	else
+		return FTOIF(t);
+}
+
+int field_order_sf()
+{
+	return current_gfs_q;
+}
+
+int characteristic_sf()
+{
+	return current_gfs_p;
+}
+