/**************************************** * Computer Algebra System SINGULAR * ****************************************/ /* $Id$ */ /* * ABSTRACT: finite fields with a none-prime number of elements (via tables) */ #include "config.h" #include #include #include #include #include #include #include #include #include #include BOOLEAN nfGreaterZero (number k, const coeffs r); number nfMult (number a, number b, const coeffs r); number nfInit (long i, const coeffs r); number nfParameter (int i, const coeffs r); int nfInt (number &n, const coeffs r); number nfAdd (number a, number b, const coeffs r); number nfSub (number a, number b, const coeffs r); void nfPower (number a, int i, number * result, const coeffs r); BOOLEAN nfIsZero (number a, const coeffs r); BOOLEAN nfIsOne (number a, const coeffs r); BOOLEAN nfIsMOne (number a, const coeffs r); number nfDiv (number a, number b, const coeffs r); number nfNeg (number c, const coeffs r); number nfInvers (number c, const coeffs r); BOOLEAN nfGreater (number a, number b, const coeffs r); BOOLEAN nfEqual (number a, number b, const coeffs r); const char * nfRead (const char *s, number *a, const coeffs r); #ifdef LDEBUG BOOLEAN nfDBTest (number a, const char *f, const int l, const coeffs r); #endif //void nfSetChar (const coeffs r); nMapFunc nfSetMap (const coeffs src, const coeffs dst); char * nfName (number n, const coeffs r); void nfReadTable (const int c, const coeffs r); void nfCoeffWrite(const coeffs r, BOOLEAN details); void nfShowMipo(const coeffs r); /// Our Type! static const n_coeffType ID = n_GF; //unsigned short *nfPlus1Table=NULL; /* the table i=log(z^i) -> log(z^i+1) */ const double sixteenlog2= 11.09035489; /* the q's from the table 'fftable' */ unsigned short fftable[]={ 4, 8, 16, 32, 64, 128, 256, 512,1024,2048,4096,8192,16384, 32768, /*2^2 2^3 2^4 2^5 2^6 2^7 2^8 2^9 2^10 2^11 2^12 2^13 2^14 2^15*/ 9, 27, 81,243,729,2187, 6561,19683,59049, /*3^2 3^3 3^4 3^5 3^6 3^7 3^8 3^9 3^10*/ 25,125,625,3125,15625, /*5^2 5^3 5^4 5^5 5^6*/ 49,343,2401,16807, /*7^2 7^3 7^4 7^5*/ 121,1331, 14641, /*11^2 11^3 11^4*/ 169, 2197, 28561, /*13^2 13^3 13^4*/ 289, 4913, /*17^2 17^3*/ 361, 6859, /*19^2 19^3*/ 529, 12167, /*23^2 23^3*/ 841, 24389, /*29^2 29^3*/ 961, 29791, /*31^2 31^3*/ 1369, 50653, /*37^2 37^3*/ 1681, /*41^2*/ 1849, /*43^2*/ 2209, /*47^2*/ 2809, /*53^2*/ 3481, /*59^2*/ 3721, /*61^2*/ 4489, /*67^2*/ 5041, /*71^2*/ 5329, /*73^2*/ 6241, /*79^2*/ 6889, /*83^2*/ 7921, /*89^2*/ 9409, /*97^2*/ 10201, /*101^2*/ 10609, /*103^2*/ 11449, /*107^2*/ 11881, /*109^2*/ 12769, /*113^2*/ 16129, /*127^2*/ 17161, /*131^2*/ 18769, /*137^2*/ 19321, /*139^2*/ 22201, /*149^2*/ 22801, /*151^2*/ 24649, /*157^2*/ 26569, /*163^2*/ 27889, /*167^2*/ 29929, /*173^2*/ 32041, /*179^2*/ 32761, /*181^2*/ 36481, /*191^2*/ 37249, /*193^2*/ 38809, /*197^2*/ 39601, /*199^2*/ 49729, /*223^2*/ 44521, /*211^2*/ 51529, /*227^2*/ 52441, /*229^2*/ 54289, /*233^2*/ 57121, /*239^2*/ 58081, /*241^2*/ 63001, /*251^2*/ 0 }; /*1 * numbers in GF(p^n): * let nfCharQ=q=nfCharP^n=p^n * GF(q)\{0} will be generated by powers of an element Z * Z^i will be represented by the int i, 1 by the int 0, 0 by the int q=nfChar */ #ifdef LDEBUG /*2 * debugging: is a a valid representation of a number ? */ BOOLEAN nfDBTest (number a, const char *f, const int l, const coeffs r) { assume( r->m_nfPlus1Table != NULL ); if (((long)a<0L) || ((long)a>(long)r->m_nfCharQ)) { Print("wrong %d in %s:%d\n",(int)((long)a),f,l); return FALSE; } int i=0; do { if (r->m_nfPlus1Table[i]>r->m_nfCharQ) { Print("wrong table %d=%d in %s:%d\n",i,r->m_nfPlus1Table[i],f,l); return FALSE; } i++; } while (im_nfCharQ); return TRUE; } #define nfTest(N, R) nfDBTest(N,__FILE__,__LINE__, R) #endif /*2 * k >= 0 ? */ BOOLEAN nfGreaterZero (number k, const coeffs r) { #ifdef LDEBUG nfTest(k, r); #endif return !nfIsZero(k, r) && !nfIsMOne(k, r); } /*2 * a*b */ number nfMult (number a,number b, const coeffs r) { #ifdef LDEBUG nfTest(a, r); nfTest(b, r); #endif if (((long)a == (long)r->m_nfCharQ) || ((long)b == (long)r->m_nfCharQ)) return (number)(long)r->m_nfCharQ; /*else*/ int i=(int)((long)a+(long)b); if (i>=r->m_nfCharQ1) i-=r->m_nfCharQ1; #ifdef LDEBUG nfTest((number)(long)i, r); #endif return (number)(long)i; } /*2 * int -> number */ number nfInit (long i, const coeffs r) { assume( r->m_nfPlus1Table != NULL ); // Hmm .. this is just to prevent initialization // from nfInitChar to go into an infinite loop if (i==0) return (number)(long)r->m_nfCharQ; while (i < 0) i += r->m_nfCharP; while (i >= r->m_nfCharP) i -= r->m_nfCharP; if (i==0) return (number)(long)r->m_nfCharQ; unsigned short c=0; while (i>1) { c=r->m_nfPlus1Table[c]; i--; } #ifdef LDEBUG nfTest((number)(long)c, r); #endif return (number)(long)c; } /* * the generating element `z` */ number nfParameter (int i, const coeffs) { assume(i==1); if( i == 1 ) return (number)1; return NULL; } /*2 * the degree of the "alg. number" */ static int nfParDeg(number n, const coeffs r) { #ifdef LDEBUG nfTest(n, r); #endif if((long)r->m_nfCharQ == (long)n) return -1; return (int)((long)n); } /*2 * number -> int */ int nfInt (number &, const coeffs ) { return 0; } /*2 * a + b */ number nfAdd (number a, number b, const coeffs R) { /*4 z^a+z^b=z^b*(z^(a-b)+1), if a>=b; * * =z^a*(z^(b-a)+1) if am_nfCharQ == (long)a) return b; if ((long)R->m_nfCharQ == (long)b) return a; long zb,zab,r; if ((long)a >= (long)b) { zb = (long)b; zab = (long)a-(long)b; } else { zb = (long)a; zab = (long)b-(long)a; } #ifdef LDEBUG nfTest((number)zab, R); #endif if (R->m_nfPlus1Table[zab]==R->m_nfCharQ) r=(long)R->m_nfCharQ; /*if z^(a-b)+1 =0*/ else { r= zb+(long)R->m_nfPlus1Table[zab]; if(r>=(long)R->m_nfCharQ1) r-=(long)R->m_nfCharQ1; } #ifdef LDEBUG nfTest((number)r, R); #endif return (number)r; } /*2 * a - b */ number nfSub (number a, number b, const coeffs r) { number mb = nfNeg(b, r); return nfAdd(a,mb,r); } /*2 * a == 0 ? */ BOOLEAN nfIsZero (number a, const coeffs r) { #ifdef LDEBUG nfTest(a, r); #endif return (long)r->m_nfCharQ == (long)a; } /*2 * a == 1 ? */ BOOLEAN nfIsOne (number a, const coeffs r) { #ifdef LDEBUG nfTest(a, r); #endif return 0L == (long)a; } /*2 * a == -1 ? */ BOOLEAN nfIsMOne (number a, const coeffs r) { #ifdef LDEBUG nfTest(a, r); #endif if (0L == (long)a) return FALSE; /* special handling of char 2*/ return (long)r->m_nfM1 == (long)a; } /*2 * a / b */ number nfDiv (number a,number b, const coeffs r) { #ifdef LDEBUG nfTest(b, r); #endif if ((long)b==(long)r->m_nfCharQ) { WerrorS(nDivBy0); return (number)((long)r->m_nfCharQ); } #ifdef LDEBUG nfTest(a, r); #endif if ((long)a==(long)r->m_nfCharQ) return (number)((long)r->m_nfCharQ); /*else*/ long s = (long)a - (long)b; if (s < 0L) s += (long)r->m_nfCharQ1; #ifdef LDEBUG nfTest((number)s, r); #endif return (number)s; } /*2 * 1 / c */ number nfInvers (number c, const coeffs r) { #ifdef LDEBUG nfTest(c, r); #endif if ((long)c==(long)r->m_nfCharQ) { WerrorS(nDivBy0); return (number)((long)r->m_nfCharQ); } #ifdef LDEBUG nfTest(((number)((long)r->m_nfCharQ1-(long)c)), r); #endif return (number)((long)r->m_nfCharQ1-(long)c); } /*2 * -c */ number nfNeg (number c, const coeffs r) { /*4 -z^c=z^c*(-1)=z^c*nfM1*/ #ifdef LDEBUG nfTest(c, r); #endif if ((long)r->m_nfCharQ == (long)c) return c; long i=(long)c+(long)r->m_nfM1; if (i>=(long)r->m_nfCharQ1) i-=(long)r->m_nfCharQ1; #ifdef LDEBUG nfTest((number)i, r); #endif return (number)i; } /*2 * a > b ? */ BOOLEAN nfGreater (number a,number b, const coeffs r) { #ifdef LDEBUG nfTest(a, r); nfTest(b, r); #endif return (long)a != (long)b; } /*2 * a == b ? */ BOOLEAN nfEqual (number a,number b, const coeffs r) { #ifdef LDEBUG nfTest(a, r); nfTest(b, r); #endif return (long)a == (long)b; } /*2 * write via StringAppend */ static void nfWriteLong (number &a, const coeffs r) { #ifdef LDEBUG nfTest(a, r); #endif if ((long)a==(long)r->m_nfCharQ) StringAppendS("0"); else if ((long)a==0L) StringAppendS("1"); else if (nfIsMOne(a, r)) StringAppendS("-1"); else { StringAppendS(n_ParameterNames(r)[0]); if ((long)a!=1L) { StringAppend("^%d",(int)((long)a)); // long output! } } } /*2 * write (shortert output) via StringAppend */ static void nfWriteShort (number &a, const coeffs r) { #ifdef LDEBUG nfTest(a, r); #endif if ((long)a==(long)r->m_nfCharQ) StringAppendS("0"); else if ((long)a==0L) StringAppendS("1"); else if (nfIsMOne(a, r)) StringAppendS("-1"); else { StringAppendS(n_ParameterNames(r)[0]); if ((long)a!=1L) { StringAppend("%d",(int)((long)a)); } } } /*2 * */ char * nfName(number a, const coeffs r) { #ifdef LDEBUG nfTest(a, r); #endif char *s; const char * const nf_Parameter=n_ParameterNames(r)[0]; if (((long)a==(long)r->m_nfCharQ) || ((long)a==0L)) return NULL; else if ((long)a==1L) { return omStrDup(nf_Parameter); } else { s=(char *)omAlloc(4+strlen(nf_Parameter)); sprintf(s,"%s%d",nf_Parameter,(int)((long)a)); } return s; } /*2 * c ^ i with i>=0 */ void nfPower (number a, int i, number * result, const coeffs r) { #ifdef LDEBUG nfTest(a, r); #endif if (i==0) { //*result=nfInit(1); *result = (number)0L; } else if (i==1) { *result = a; } else { nfPower(a,i-1,result, r); *result = nfMult(a,*result, r); } #ifdef LDEBUG nfTest(*result, r); #endif } /*4 * read an integer (with reduction mod p) */ static const char* nfEati(const char *s, int *i, const coeffs r) { if (*s >= '0' && *s <= '9') { *i = 0; do { *i *= 10; *i += *s++ - '0'; if (*i > (MAX_INT_VAL / 10)) *i = *i % r->m_nfCharP; } while (*s >= '0' && *s <= '9'); if (*i >= r->m_nfCharP) *i = *i % r->m_nfCharP; } else *i = 1; return s; } /*2 * read a number */ const char * nfRead (const char *s, number *a, const coeffs r) { int i; number z; number n; s = nfEati(s, &i, r); z=nfInit(i, r); *a=z; if (*s == '/') { s++; s = nfEati(s, &i, r); n=nfInit(i, r); *a = nfDiv(z,n,r); } const char * const nf_Parameter = n_ParameterNames(r)[0]; const int N = strlen(nf_Parameter); if (strncmp(s,nf_Parameter, N)==0) { s += N; if ((*s >= '0') && (*s <= '9')) { s=eati(s,&i); while (i>=r->m_nfCharQ1) i-=r->m_nfCharQ1; } else i=1; z=(number)(long)i; *a=nfMult(*a,z,r); } #ifdef LDEBUG nfTest(*a, r); #endif return s; } #ifdef HAVE_FACTORY int gf_tab_numdigits62 ( int q ); int convertback62 ( char * p, int n ); #else static int gf_tab_numdigits62 ( int q ) { if ( q < 62 ) return 1; else if ( q < 62*62 ) return 2; /*else*/ return 3; } static int convback62 ( char c ) { if ( c >= '0' && c <= '9' ) return int(c) - int('0'); else if ( c >= 'A' && c <= 'Z' ) return int(c) - int('A') + 10; else return int(c) - int('a') + 36; } static int convertback62 ( char * p, int n ) { int r = 0; for ( int j = 0; j < n; j++ ) r = r * 62 + convback62( p[j] ); return r; } #endif int nfMinPoly[16]; void nfShowMipo(const coeffs r) { int i=nfMinPoly[0]; int j=0; loop { j++; if (nfMinPoly[j]!=0) StringAppend("%d*%s^%d",nfMinPoly[j],n_ParameterNames(r)[0],i); i--; if(i<0) break; if (nfMinPoly[j]!=0) StringAppendS("+"); } } static void nfReadMipo(char *s) { const char *l=strchr(s,';')+1; char *n; int i=strtol(l,&n,10); l=n; int j=1; nfMinPoly[0]=i; while(i>=0) { nfMinPoly[j]=strtol(l,&n,10); if (l==n) break; l=n; j++; i--; } if (i>=0) { WerrorS("error in reading minpoly from gftables"); } } /*2 * init global variables from files 'gftables/%d' */ void nfReadTable(const int c, const coeffs r) { //Print("GF(%d)\n",c); if ((c==r->m_nfCharQ)||(c==-r->m_nfCharQ)) /*this field is already set*/ return; int i=0; while ((fftable[i]!=c) && (fftable[i]!=0)) i++; if (fftable[i]==0) { Werror("illegal GF-table size: %d", c); return; } if (r->m_nfCharQ > 1) { omFreeSize( (ADDRESS)r->m_nfPlus1Table,r->m_nfCharQ*sizeof(unsigned short) ); r->m_nfPlus1Table=NULL; } if ((c>1) || (c<0)) { if (c>1) r->m_nfCharQ = c; else r->m_nfCharQ = -c; char buf[100]; sprintf(buf,"gftables/%d",r->m_nfCharQ); FILE * fp = feFopen(buf,"r",NULL,TRUE); if (fp==NULL) { return; } if(!fgets( buf, sizeof(buf), fp)) return; if(strcmp(buf,"@@ factory GF(q) table @@\n")!=0) { goto err; } if(!fgets( buf, sizeof(buf), fp)) { goto err; } int q; sscanf(buf,"%d %d",&r->m_nfCharP,&q); nfReadMipo(buf); r->m_nfCharQ1=r->m_nfCharQ-1; //Print("nfCharQ=%d,nfCharQ1=%d,mipo=>>%s<<\n",nfCharQ,nfCharQ1,buf); r->m_nfPlus1Table= (unsigned short *)omAlloc( (r->m_nfCharQ)*sizeof(unsigned short) ); int digs = gf_tab_numdigits62( r->m_nfCharQ ); char * bufptr; int i = 1; int k; while ( i < r->m_nfCharQ ) { fgets( buf, sizeof(buf), fp); //( strlen( buffer ) == (size_t)digs * 30, "illegal table" ); bufptr = buf; k = 0; while ( (i < r->m_nfCharQ) && (k < 30) ) { r->m_nfPlus1Table[i] = convertback62( bufptr, digs ); if(r->m_nfPlus1Table[i]>r->m_nfCharQ) { Print("wrong entry %d: %d(%c%c%c)\n",i,r->m_nfPlus1Table[i],bufptr[0],bufptr[1],bufptr[2]); } bufptr += digs; if (r->m_nfPlus1Table[i]==r->m_nfCharQ) { if(i==r->m_nfCharQ1) { r->m_nfM1=0; } else { r->m_nfM1=i; } } i++; k++; } } r->m_nfPlus1Table[0]=r->m_nfPlus1Table[r->m_nfCharQ1]; } else r->m_nfCharQ=0; #ifdef LDEBUG nfTest((number)0, r); #endif return; err: Werror("illegal GF-table %d",r->m_nfCharQ); } /*2 * map Z/p -> GF(p,n) */ number nfMapP(number c, const coeffs, const coeffs dst) { return nfInit((int)((long)c), dst); } /*2 * map GF(p,n1) -> GF(p,n2), n1 < n2, n1 | n2 */ int nfMapGG_factor; number nfMapGG(number c, const coeffs src, const coeffs) { int i=(long)c; i*= nfMapGG_factor; while (i >src->m_nfCharQ1) i-=src->m_nfCharQ1; return (number)((long)i); } /*2 * map GF(p,n1) -> GF(p,n2), n1 > n2, n2 | n1 */ number nfMapGGrev(number c, const coeffs src, const coeffs) { int ex=(int)((long)c); if ((ex % nfMapGG_factor)==0) return (number)(((long)ex) / ((long)nfMapGG_factor)); else return (number)(long)src->m_nfCharQ; /* 0 */ } /*2 * set map function nMap ... -> GF(p,n) */ nMapFunc nfSetMap(const coeffs src, const coeffs dst) { if (nCoeff_is_GF(src,src->m_nfCharQ)) { return ndCopyMap; /* GF(p,n) -> GF(p,n) */ } if (nCoeff_is_GF(src)) { const coeffs r = dst; int q=src->ch; if ((src->m_nfCharQ % q)==0) /* GF(p,n1) -> GF(p,n2), n2 > n1 */ { // check if n2 is a multiple of n1 int n1=1; int qq=r->m_nfCharP; while(qq!=q) { qq *= r->m_nfCharP; n1++; } int n2=1; qq=r->m_nfCharP; while(qq!=src->m_nfCharQ) { qq *= r->m_nfCharP; n2++; } //Print("map %d^%d -> %d^%d\n",r->m_nfCharP,n1,r->m_nfCharP,n2); if ((n2 % n1)==0) { int save_ch=r->m_nfCharQ; nfReadTable(src->m_nfCharQ, r); int nn=r->m_nfPlus1Table[0]; nfReadTable(save_ch, r); nfMapGG_factor= r->m_nfPlus1Table[0] / nn; //Print("nfMapGG_factor=%d (%d / %d)\n",nfMapGG_factor, r->m_nfPlus1Table[0], nn); return nfMapGG; } else if ((n1 % n2)==0) { nfMapGG_factor= (n1/n2); return nfMapGGrev; } else return NULL; } } if (nCoeff_is_Zp(src,src->m_nfCharP)) { return nfMapP; /* Z/p -> GF(p,n) */ } return NULL; /* default */ } static BOOLEAN nfCoeffIsEqual(const coeffs, n_coeffType, void*); static void nfKillChar(coeffs r) { char** p = (char**)n_ParameterNames(r); const int P = n_NumberOfParameters(r); for( int i = 1; i <= P; i++ ) if (p[i-1] != NULL) omFree( (ADDRESS)p[i-1] ); omFreeSize((ADDRESS)p, P * sizeof(char*)); } BOOLEAN nfInitChar(coeffs r, void * parameter) { //r->cfInitChar=npInitChar; r->cfKillChar=nfKillChar; r->nCoeffIsEqual=nfCoeffIsEqual; r->cfMult = nfMult; r->cfSub = nfSub; r->cfAdd = nfAdd; r->cfDiv = nfDiv; r->cfIntDiv= nfDiv; //r->cfIntMod= ndIntMod; r->cfExactDiv= nfDiv; r->cfInit = nfInit; //r->cfSize = ndSize; r->cfInt = nfInt; #ifdef HAVE_RINGS //r->cfDivComp = NULL; // only for ring stuff //r->cfIsUnit = NULL; // only for ring stuff //r->cfGetUnit = NULL; // only for ring stuff //r->cfExtGcd = NULL; // only for ring stuff // r->cfDivBy = NULL; // only for ring stuff #endif r->cfNeg = nfNeg; r->cfInvers= nfInvers; //r->cfCopy = ndCopy; //r->cfRePart = ndCopy; //r->cfImPart = ndReturn0; r->cfWriteLong = nfWriteLong; r->cfInit_bigint = nlModP; r->cfRead = nfRead; //r->cfNormalize=ndNormalize; r->cfGreater = nfGreater; r->cfEqual = nfEqual; r->cfIsZero = nfIsZero; r->cfIsOne = nfIsOne; r->cfIsMOne = nfIsMOne; r->cfGreaterZero = nfGreaterZero; r->cfPower = nfPower; //r->cfGcd = ndGcd; //r->cfLcm = ndGcd; //r->cfDelete= ndDelete; r->cfSetMap = nfSetMap; //r->cfName = ndName; // debug stuff r->cfCoeffWrite=nfCoeffWrite; r->cfParDeg = nfParDeg; #ifdef LDEBUG r->cfDBTest=nfDBTest; #endif // the variables: r->nNULL = (number)0; assume( getCoeffType(r) == n_GF ); GFInfo* p = (GFInfo *)(parameter); assume (p->GFChar > 0); assume (p->GFDegree > 0); const char * name = p->GFPar_name; r->m_nfCharQ = 0; r->m_nfCharP = p->GFChar; r->m_nfCharQ1 = 0; r->iNumberOfParameters = 1; r->cfParameter = nfParameter; char ** pParameterNames = (char **) omAlloc0(sizeof(char *)); pParameterNames[0] = omStrDup(name); //TODO use omAlloc for allocating memory and use strcpy? assume( pParameterNames != NULL ); assume( pParameterNames[0] != NULL ); r->pParameterNames = pParameterNames; // NOTE: r->m_nfParameter was replaced by n_ParameterNames(r)[0] // TODO: nfKillChar MUST destroy r->pParameterNames[0] (0-term. string) && r->pParameterNames (array of size 1) r->m_nfPlus1Table= NULL; if (strlen(name) > 1) r->cfWriteShort = nfWriteLong; else r->cfWriteShort = nfWriteShort; r->has_simple_Alloc=TRUE; r->has_simple_Inverse=TRUE; if(p->GFChar > (2<<15)) { Werror("illegal characteristic"); return TRUE; } const double check= log ((double) (p->GFChar)); if( (p->GFDegree * check) > sixteenlog2 ) { Werror("Sorry: illegal size: %u ^ %u", p->GFChar, p->GFDegree ); return TRUE; } int c = pow (p->GFChar, p->GFDegree); nfReadTable(c, r); if( r->m_nfPlus1Table == NULL ) { Werror("Sorry: cannot init lookup table!"); return TRUE; } assume (r -> m_nfCharQ > 0); r->ch = r->m_nfCharP; assume( r->m_nfPlus1Table != NULL ); return FALSE; } void nfCoeffWrite (const coeffs r, BOOLEAN details) { // m_nfCharQ = p^k where p is the characteristic (r->CharP) and k is GFDegree Print("// # ground field : %d\n",r->m_nfCharQ); Print("// primitive element : %s\n", n_ParameterNames(r)[0]); if ( details ) { StringSetS("// minpoly : "); nfShowMipo(r); PrintS(StringAppendS("\n")); } else PrintS("// minpoly : ...\n"); } static BOOLEAN nfCoeffIsEqual (const coeffs r, n_coeffType n, void * parameter) { if (n==n_GF) { GFInfo* p = (GFInfo *)(parameter); int c = pow (p->GFChar, p->GFDegree); if ((c == r->m_nfCharQ) && (strcmp(n_ParameterNames(r)[0], p->GFPar_name) == 0)) return TRUE; } return FALSE; }