8 #if SI_INTEGER_VARIANT == 3
16 #define nrzTest(A) nrzDBTest(A,__FILE__,__LINE__,NULL)
23 static inline number nrz_short(number
x)
31 mpz_clear((mpz_ptr)
x);
40 long ui=mpz_get_si((mpz_ptr)
x);
41 if ((((ui<<3)>>3)==ui)
42 && (mpz_cmp_si((mpz_ptr)
x,ui)==0))
44 mpz_clear((mpz_ptr)
x);
62 if (n_Z_IS_SMALL(a))
return 1;
63 return ((mpz_ptr)a)->_mp_alloc;
72 number _nrzMult(number, number,
const coeffs);
73 number nrzMult(number a, number
b,
const coeffs R)
79 number c = _nrzMult(a,
b,
R);
87 number _nrzMult (number a, number
b,
const coeffs R)
89 number nrzMult (number a, number
b,
const coeffs R)
92 if (n_Z_IS_SMALL(a) && n_Z_IS_SMALL(
b))
99 long r=(long)((
unsigned long)(
SR_HDL(a)-1L))*((
unsigned long)(
SR_HDL(
b)>>1));
102 number u=((number) ((r>>1)+
SR_INT));
110 nrzTest((number)erg);
113 else if (n_Z_IS_SMALL(a))
118 mpz_init_set(erg, (mpz_ptr)
b);
120 nrzTest((number)erg);
123 else if (n_Z_IS_SMALL(
b))
128 mpz_init_set(erg, (mpz_ptr) a);
130 nrzTest((number)erg);
137 mpz_mul(erg, (mpz_ptr) a, (mpz_ptr)
b);
138 nrzTest((number)erg);
144 static long int_gcd(
long a,
long b)
165 static number nrzLcm (number a, number
b,
const coeffs R)
171 if (n_Z_IS_SMALL(a) && n_Z_IS_SMALL(
b))
181 mpz_init_set(erg, (mpz_ptr)
b);
185 else if (n_Z_IS_SMALL(
b))
187 mpz_init_set(erg, (mpz_ptr) a);
194 mpz_lcm(erg, (mpz_ptr) a, (mpz_ptr)
b);
200 static number nrzCopy(number a,
const coeffs)
202 if (n_Z_IS_SMALL(a))
return a;
204 mpz_init_set(erg, (mpz_ptr) a);
212 static number nrzGcd (number a,number
b,
const coeffs R)
214 if (n_Z_IS_SMALL(a) && n_Z_IS_SMALL(
b))
219 else if (n_Z_IS_SMALL(a))
222 return nrzCopy(
b,
R);
226 else if (n_Z_IS_SMALL(
b))
229 return nrzCopy(a,
R);
237 mpz_gcd(erg, (mpz_ptr) a, (mpz_ptr)
b);
246 static long int_extgcd(
long a,
long b,
long * u,
long*
x,
long *
v,
long*
y)
289 static number nrzExtGcd (number a, number
b, number *
s, number *t,
const coeffs)
291 if (n_Z_IS_SMALL(a) && n_Z_IS_SMALL(
b))
308 mpz_init_set(aa, (mpz_ptr) a);
316 mpz_init_set(bb, (mpz_ptr)
b);
324 mpz_gcdext(erg, bs, bt, aa, bb);
325 *
s = nrz_short((number) bs);
326 *t = nrz_short((number) bt);
329 return nrz_short((number) erg);
333 static number _nrzXExtGcd(number, number, number *, number *, number *, number *,
const coeffs);
334 static number nrzXExtGcd(number a, number
b, number *
x, number *
y, number * u, number *
v,
const coeffs R)
341 number c = _nrzXExtGcd(a,
b,
x,
y, u,
v,
R);
357 static number _nrzXExtGcd (number a, number
b, number *
s, number *t, number *u, number *
v,
const coeffs )
359 static number nrzXExtGcd (number a, number
b, number *
s, number *t, number *u, number *
v,
const coeffs )
362 if (n_Z_IS_SMALL(a) && n_Z_IS_SMALL(
b))
381 mpz_init_set(aa, (mpz_ptr) a);
389 mpz_init_set(bb, (mpz_ptr)
b);
398 mpz_gcdext(erg, bs, bt, aa, bb);
403 mpz_init_set(bu, (mpz_ptr) bb);
404 mpz_init_set(bv, (mpz_ptr) aa);
408 assume(mpz_cmp_si(erg, 0));
410 mpz_div(bu, bu, erg);
411 mpz_div(bv, bv, erg);
414 *u = nrz_short((number) bu);
415 *
v = nrz_short((number) bv);
417 *
s = nrz_short((number) bs);
418 *t = nrz_short((number) bt);
419 return nrz_short((number) erg);
423 static number _nrzQuotRem(number, number, number *,
const coeffs);
424 static number nrzQuotRem(number a, number
b, number * r,
const coeffs R)
430 number c = _nrzQuotRem(a,
b, r,
R);
443 static number _nrzQuotRem (number a, number
b, number * r,
const coeffs )
445 static number nrzQuotRem (number a, number
b, number * r,
const coeffs )
449 if (n_Z_IS_SMALL(a) && n_Z_IS_SMALL(
b))
455 else if (n_Z_IS_SMALL(a))
462 else if (n_Z_IS_SMALL(
b))
469 rr = mpz_divmod_ui(qq, rrr, (mpz_ptr) a, (
unsigned long)
ABS(
SR_TO_INT(
b)));
478 return nrz_short((number)qq);
484 mpz_divmod(qq, rr, (mpz_ptr)a, (mpz_ptr)
b);
495 static void nrzPower (number a,
int i, number *
result,
const coeffs)
503 mpz_init_set(aa, (mpz_ptr) a);
504 mpz_pow_ui(erg, aa,
i);
505 *
result = nrz_short((number) erg);
515 mpz_init_set_si(erg,
i);
516 return nrz_short((number) erg);
519 static number nrzInitMPZ(mpz_t
m,
const coeffs)
522 mpz_init_set(erg,
m);
523 return nrz_short((number) erg);
529 if (*a ==
NULL)
return;
530 if (n_Z_IS_SMALL(*a)==0)
532 mpz_clear((mpz_ptr) *a);
541 static long nrzInt(number &
n,
const coeffs)
544 return mpz_get_si( (mpz_ptr)
n);
547 static number _nrzAdd(number, number,
const coeffs);
548 static number nrzAdd(number a, number
b,
const coeffs R)
554 number c = _nrzAdd(a,
b,
R);
562 static number _nrzAdd (number a, number
b,
const coeffs )
564 static number nrzAdd (number a, number
b,
const coeffs )
567 if (n_Z_IS_SMALL(a) && n_Z_IS_SMALL(
b))
573 mpz_init_set_si(erg, c);
575 nrzTest((number)erg);
578 else if (n_Z_IS_SMALL(a))
583 mpz_add_ui(erg, (mpz_ptr)
b, (
unsigned long)
SR_TO_INT(a));
585 mpz_sub_ui(erg, (mpz_ptr)
b, (
unsigned long)-(
SR_TO_INT(a)));
586 return nrz_short((number) erg);
588 else if (n_Z_IS_SMALL(
b))
593 mpz_add_ui(erg, (mpz_ptr) a, (
unsigned long)
SR_TO_INT(
b));
595 mpz_sub_ui(erg, (mpz_ptr) a, (
unsigned long)-(
SR_TO_INT(
b)));
596 return nrz_short((number) erg);
602 mpz_add(erg, (mpz_ptr) a, (mpz_ptr)
b);
603 return nrz_short((number) erg);
607 static number nrzSub (number a, number
b,
const coeffs )
609 if (n_Z_IS_SMALL(a) && n_Z_IS_SMALL(
b))
615 mpz_init_set_si(erg, c);
616 nrzTest((number)erg);
619 else if (n_Z_IS_SMALL(a))
625 mpz_ui_sub(erg, (
unsigned long)
SR_TO_INT(a), (mpz_ptr)
b);
628 mpz_add_ui(erg, (mpz_ptr)
b, (
unsigned long)-
SR_TO_INT(a));
631 return nrz_short((number) erg);
633 else if (n_Z_IS_SMALL(
b))
638 mpz_sub_ui(erg, (mpz_ptr) a, (
unsigned long)
SR_TO_INT(
b));
640 mpz_add_ui(erg, (mpz_ptr) a, (
unsigned long)-
SR_TO_INT(
b));
641 return nrz_short((number) erg);
647 mpz_sub(erg, (mpz_ptr) a, (mpz_ptr)
b);
648 return nrz_short((number) erg);
654 if (n_Z_IS_SMALL(a) && n_Z_IS_SMALL(
b))
655 return ((
long)a)>((long)
b);
656 else if (n_Z_IS_SMALL(a))
657 return 0 > mpz_cmp_si((mpz_ptr)
b,
SR_TO_INT(a));
658 else if (n_Z_IS_SMALL(
b))
659 return 0 < mpz_cmp_si((mpz_ptr)a,
SR_TO_INT(
b));
660 return 0 < mpz_cmp((mpz_ptr) a, (mpz_ptr)
b);
668 static number nrzGetUnit (number
n,
const coeffs r)
670 if (nrzGreaterZero(
n, r))
676 static number nrzAnn(number
n,
const coeffs)
706 if (n_Z_IS_SMALL(a) && n_Z_IS_SMALL(
b))
708 else if (n_Z_IS_SMALL(a) || n_Z_IS_SMALL(
b))
711 return 0 == mpz_cmp((mpz_ptr) a, (mpz_ptr)
b);
716 if (n_Z_IS_SMALL(a) && n_Z_IS_SMALL(
b))
720 else if (n_Z_IS_SMALL(a))
724 else if (n_Z_IS_SMALL(
b))
726 return mpz_divisible_ui_p((mpz_ptr)a, (
unsigned long)
ABS(
SR_TO_INT(
b))) != 0;
729 return mpz_divisible_p((mpz_ptr) a, (mpz_ptr)
b) != 0;
732 static int nrzDivComp(number a, number
b,
const coeffs r)
734 if (nrzDivBy(a,
b, r))
736 if (nrzDivBy(
b, a, r))
return 2;
739 if (nrzDivBy(
b, a, r))
return 1;
743 static number nrzDiv (number a,number
b,
const coeffs)
746 if (n_Z_IS_SMALL(a) && n_Z_IS_SMALL(
b))
755 else if (n_Z_IS_SMALL(a))
764 else if (n_Z_IS_SMALL(
b))
770 if (mpz_divmod_ui(erg, r, (mpz_ptr) a, (
unsigned long)
ABS(
SR_TO_INT(
b)))) {
777 return nrz_short((number) erg);
783 mpz_tdiv_qr(erg, r, (mpz_ptr) a, (mpz_ptr)
b);
805 return nrz_short((number) erg);
808 static number nrzExactDiv (number a,number
b,
const coeffs)
815 mpz_init_set(aa, (mpz_ptr) a);
819 mpz_init_set(bb, (mpz_ptr)
b);
822 mpz_tdiv_q(erg, (mpz_ptr) aa, (mpz_ptr) bb);
825 nrzTest((number)erg);
829 static number nrzIntMod (number a,number
b,
const coeffs)
836 mpz_init_set(aa, (mpz_ptr) a);
840 mpz_init_set(bb, (mpz_ptr)
b);
846 mpz_tdiv_qr(erg, r, (mpz_ptr) aa, (mpz_ptr) bb);
851 return nrz_short((number) r);
854 static number nrzInvers (number c,
const coeffs r)
856 if (!nrzIsUnit((number) c, r))
858 WerrorS(
"Non invertible element.");
864 static number nrzNeg (number c,
const coeffs)
873 static number nrzFarey(number r, number
N,
const coeffs R)
875 number a0 = nrzCopy(
N,
R);
877 number a1 = nrzCopy(r,
R);
881 PrintS(
"Farey start with ");
889 number as = nrzMult(a1, a1,
R);
891 if (nrzGreater(
N, as,
R))
897 number q = nrzDiv(a0, a1,
R);
898 number t = nrzMult(a1, q,
R),
899 s = nrzSub(a0, t,
R);
905 t = nrzMult(b1, q,
R);
906 s = nrzSub(b0, t,
R);
913 number as = nrzMult(b1, b1,
R);
916 if (nrzGreater(as,
N,
R))
944 static number nrzMapMachineInt(number from,
const coeffs ,
const coeffs )
947 mpz_init_set_ui(erg, (
unsigned long) from);
948 return nrz_short((number) erg);
951 static number nrzMapZp(number from,
const coeffs ,
const coeffs )
954 mpz_init_set_si(erg, (
long) from);
955 return nrz_short((number) erg);
958 static number nrzModNMap(number from,
const coeffs ,
const coeffs )
961 mpz_init_set(erg, (mpz_ptr) from);
962 return nrz_short((number) erg);
965 static number nrzMapQ(number from,
const coeffs ,
const coeffs dst)
971 WerrorS(
"rational in map to integer");
975 mpz_init_set(erg, from->z);
976 return nrz_short((number) erg);
995 return nrzMapMachineInt;
1009 void nrzSetExp(
int,
coeffs)
1013 void nrzInitExp(
int,
coeffs)
1028 long ui=mpz_get_si((mpz_ptr)
x);
1029 if ((((ui<<3)>>3)==ui)
1030 && (mpz_cmp_si((mpz_ptr)
x,ui)==0))
1032 Print(
"gmp-small %s:%d\n",
f,
l);
1049 if (n_Z_IS_SMALL(a))
1055 int l=mpz_sizeinbase((mpz_ptr) a, 10) + 2;
1057 z=mpz_get_str(
s,10,(mpz_ptr) a);
1067 static const char * nlEatLongC(
char *
s, mpz_ptr
i)
1069 const char * start=
s;
1071 if (*s<'0' || *s>
'9')
1076 while (*
s >=
'0' && *
s <=
'9')
s++;
1079 mpz_set_str(
i,start,10);
1085 mpz_set_str(
i,start,10);
1091 static const char * nrzRead (
const char *
s, number *a,
const coeffs)
1096 s = nlEatLongC((
char *)
s,
z);
1098 *a = nrz_short((number)
z);
1107 if ( n_Z_IS_SMALL(
n))
1114 mpz_init_set( dummy,
n->z );
1128 if ( !
n.den().isOne() )
1130 WerrorS(
"rational in conversion to integer");
1135 return nrz_short((number)
z);
1139 static void nrzMPZ(mpz_t
res, number &a,
const coeffs)
1141 if (n_Z_IS_SMALL(a))
1144 mpz_init_set(
res, (mpz_ptr) a);
1152 long ch = r->cfInt(c, r);
1153 mpz_init_set_ui(dummy, ch);
1157 mpz_init_set(dummy, (mpz_ptr)c);
1161 info.exp = (
unsigned long) 1;
1182 r->cfMult = nrzMult;
1186 r->cfIntMod= nrzIntMod;
1187 r->cfExactDiv= nrzExactDiv;
1189 r->cfInitMPZ = nrzInitMPZ;
1193 r->cfDivComp = nrzDivComp;
1194 r->cfIsUnit = nrzIsUnit;
1195 r->cfGetUnit = nrzGetUnit;
1197 r->cfExtGcd = nrzExtGcd;
1198 r->cfXExtGcd = nrzXExtGcd;
1199 r->cfEucNorm = nrzEucNorm;
1200 r->cfQuotRem = nrzSmallestQuotRem;
1201 r->cfDivBy = nrzDivBy;
1203 r->cfInpNeg = nrzNeg;
1204 r->cfInvers= nrzInvers;
1205 r->cfCopy = nrzCopy;
1207 r->cfRead = nrzRead;
1208 r->cfGreater = nrzGreater;
1209 r->cfEqual = nrzEqual;
1210 r->cfIsZero = nrzIsZero;
1211 r->cfIsOne = nrzIsOne;
1212 r->cfIsMOne = nrzIsMOne;
1213 r->cfGreaterZero = nrzGreaterZero;
1214 r->cfPower = nrzPower;
1218 r->cfSetMap = nrzSetMap;
1220 r->convSingNFactoryN = nrzConvSingNFactoryN;
1221 r->convFactoryNSingN = nrzConvFactoryNSingN;
1223 r->cfFarey = nrzFarey;
1227 r->cfQuot1 = nrzQuot1;
1233 r->cfDBTest=nrzDBTest;
1237 r->has_simple_Alloc=
FALSE;
1238 r->has_simple_Inverse=
FALSE;