/*
* $OpenXM: OpenXM_contrib2/asir2000/engine/Ngcd.c,v 1.4 2018/03/29 01:32:51 noro Exp $
*/
/*
#include "ca.h"
#include "base.h"
*/
#undef CALL
/**** Machine specific ****/
#define BIT_WIDTH_OF_INT 32
#if BSH == BIT_WIDTH_OF_INT
#if defined(BMASK)
#undef BMASK
#endif
#define BMask ((unsigned)(-1))
#define BMASK BMask
#endif
int igcd_algorithm = 0;
/* == 0 : Euclid,
* == 1 : binary,
* == 2 : bmod,
* >= 3 : (Weber's accelerated)/(Jebelean's generalized binary) algorithm,
*/
int igcd_thre_inidiv = 50;
/*
* In the non-Euclidean algorithms, if the ratio of the lengths (number
* of words) of two integers is >= igcd_thre_inidiv, we first perform
* remainder calculation.
* If == 0, this remainder calculation is not performed.
*/
int igcdacc_thre = 10;
/*
* In the accelerated algorithm, if the bit-lengths of two integers is
* > igcdacc_thre, "bmod" reduction is done.
*/
#include "inline.h"
#define TRAILINGZEROS(t,cntr) for(cntr=0;(t&1)==0;t>>=1)cntr++;
#define W_NALLOC(d) ((N)ALLOCA(TRUESIZE(oN,(d)-1,int)))
#define ShouldCompRemInit(n1,n2) (igcd_thre_inidiv != 0 && PL(n1) >= igcd_thre_inidiv*PL(n2))
#define IniDiv(n1,n2) \
if ( ShouldCompRemInit(n1,n2) ) {\
N q, r; int w, b; \
divn(n1,n2,&q,&r); \
if ( !r ) return(n2); \
b = trailingzerosn( r, &w ); \
q = n1; n1 = n2; n2 = q; \
rshiftn( r, w, b, n2 ); \
}
/*
* Binary GCD algorithm by J.Stein
* [J. Comp. Phys. Vol. 1 (1967), pp. 397-405)]:
* The right-shift binary algorithm is used.
*/
/*
* subsidiary routines for gcdbinn below.
*/
static int /* number of bits */ trailingzeros_nbd( /* BD of N */ nbd, pnw )
int *nbd, *pnw /* number of zero words */;
{
#if BSH == BIT_WIDTH_OF_INT
unsigned
#endif
int nw, nb, w;
for ( nw = 0; (w = *nbd) == 0; nbd++ ) nw++;
TRAILINGZEROS(w,nb);
*pnw = nw;
return nb;
}
#define trailingzerosn(n,pnw) trailingzeros_nbd(BD(n),pnw)
static int /* PL of N */ rshift_nbd( /* BD of N */ nbd, /* PL of N */ nl,
/* # words */ shw, /* # bits */ shb, /* BD of N */ p )
#if BSH == BIT_WIDTH_OF_INT
unsigned
#endif
int *nbd, nl, shw, shb, *p;
{
unsigned int i, v, w, lshb; /* <---- */
nbd += shw, i = (nl -= shw);
if ( shb == 0 ) {
for ( ; nl > 0; nl-- ) *p++ = *nbd++;
return i;
} else if ( nl < 2 ) {
*p = (*nbd) >> shb;
return 1;
}
for ( lshb = BSH - shb, v = *nbd++; --nl > 0; v = w ) {
w = *nbd++;
#if BSH == BIT_WIDTH_OF_INT
*p++ = (v >> shb) | (w << lshb); /********/
#else
*p++ = (v >> shb) | ((w << lshb)&BMASK);
#endif
}
if ( (v >>= shb) == 0 ) return( i-1 );
*p = v;
return i;
}
#define rshiftn(ns,shw,shb,nd) (PL(nd)=rshift_nbd(BD(ns),PL(ns),shw,shb,BD(nd)))
/* nd <= ns << (shb + shw*BSH), returns PL of the result */
#ifdef FULLSET
static N N_of_i_lshifted_by_wb( i, gw, gb )
int i, gw, gb;
/*
* returns pointer to a new struct (N)(((int)i) >> (gb + gw*BSH))
*/
{
unsigned int j, l, *p; /* <---- */
N n;
j = i >> (BSH - gb);
#if BSH == BIT_WIDTH_OF_INT
i = (i << gb); /********/
#else
i = (i << gb)&BMASK;
#endif
l = j != 0 ? gw + 2 : gw + 1;
n = NALLOC(l);
PL(n) = l;
for ( p = BD(n); gw-- > 0; ) *p++ = 0;
*p++ = i;
if ( j != 0 ) *p = j;
return n;
}
#endif /* FULLSET */
/*
* routines to make a new struct
* (N)(((BD of N)(b[0],...,b[lb-1])) << (gb + gw*BSH))
*/
static N N_of_nbd_lshifted_by_wb( /* BD of N */ b, /* PL of N */ lb, gw, gb )
int *b, lb, gw, gb;
/*
* returns pointer to a new struct
* (N)(((BD of N)(b[0],...,b[lb-1])) << (gb + gw*BSH))
*/
{
unsigned int rsh, s, t, *p, l; /* <---- */
N n;
l = lb + gw;
if ( gb == 0 ) {
n = NALLOC(l);
PL(n) = l;
for ( p = BD(n); gw-- > 0; ) *p++ = 0;
while ( lb-- > 0 ) *p++ = *b++;
return n;
}
rsh = BSH - gb; s = b[lb-1];
if ( (t = s >> rsh) != 0 ) {
n = NALLOC(l+1);
PL(n) = l+1;
(p = BD(n))[l] = t;
} else {
n = NALLOC(l);
PL(n) = l;
p = BD(n);
}
while ( gw-- > 0 ) *p++ = 0;
#if BSH == BIT_WIDTH_OF_INT
*p++ = (t = *b++) << gb; /********/
for ( ; --lb > 0; t = s )
*p++ = (t >> rsh) | ((s = *b++) << gb); /********/
#else
*p++ = ((t = *b++) << gb)&BMASK;
for ( ; --lb > 0; t = s )
*p++ = (t >> rsh) | (((s = *b++) << gb)&BMASK);
#endif
return n;
}
#define N_of_n_lshifted_by_wb(a,gw,gb) N_of_nbd_lshifted_by_wb(BD(a),PL(a),gw,gb)
#define SWAP(a,b,Type) { Type temp=a;a=b;b=temp;}
#define SIGNED_VAL(a,s) ((s)>0?(a):-(a))
#ifdef CALL
static int bw_int32( n )
unsigned int n; /* <---- */
{
int w;
w = 0;
#if BSH > 32
if ( n > 0xffffffff ) w += 32, n >>= 32;
#endif
if ( n >= 0x10000 ) w += 16, n >>= 16;
if ( n >= 0x100 ) w += 8, n >>= 8;
if ( n >= 0x10 ) w += 4, n >>= 4;
if ( n >= 0x4 ) w += 2, n >>= 2;
if ( n >= 0x2 ) w += 1, n >>= 1;
if ( n != 0 ) ++w;
return w;
}
#define BitWidth(n,bw) bw = bw_int32( n )
#else
#if BSH > 32
#define BitWidth(n,bw) {\
unsigned int k = (n); \
bw = 0; \
if ( k > 0xffffffff ) bw += 32, k >>= 32; \
if ( k >= 0x10000 ) bw += 16, k >>= 16; \
if ( k >= 0x100 ) bw += 8, k >>= 8; \
if ( k >= 0x10 ) bw += 4, k >>= 4; \
if ( k >= 0x4 ) bw += 2, k >>= 2; \
if ( k >= 0x2 ) bw += 1, k >>= 1; \
if ( k != 0 ) bw++; \
}
#else
#define BitWidth(n,bw) {\
unsigned int k = (n); \
bw = 0; \
if ( k >= 0x10000 ) bw += 16, k >>= 16; \
if ( k >= 0x100 ) bw += 8, k >>= 8; \
if ( k >= 0x10 ) bw += 4, k >>= 4; \
if ( k >= 0x4 ) bw += 2, k >>= 2; \
if ( k >= 0x2 ) bw += 1, k >>= 1; \
if ( k != 0 ) bw++; \
}
#endif
#endif
#include "igcdhack.c"
/*
* Implementation of the binary GCD algorithm for two oN structs
* (big-integers) in risa.
*
* The major operations in the following algorithms are the binary-shifts
* and the updates of (u, v) by (min(u,v), |u-v|), and are to be open-coded
* without using routines for oN structures just as in addn() or subn().
*/
static int igcd_binary_2w( u, lu, v, lv, pans )
#if BSH == BIT_WIDTH_OF_INT
unsigned
#endif
int *u, lu, *v, lv, *pans; /* <---- */
/* both u[0:lu-1] and v[0:lv-1] are assumed to be odd */
{
#if BSH == BIT_WIDTH_OF_INT
unsigned
#endif
int i, h1, l1, h2, l2; /* <---- */
l1 = u[0], l2 = v[0];
h1 = lu <= 1 ? 0 : u[1];
h2 = lv <= 1 ? 0 : v[1];
/**/
loop: if ( h1 == 0 ) {
no_hi1: if ( h2 == 0 ) goto one_word;
no_hi1n:if ( l1 == 1 ) return 0;
#if BSH == BIT_WIDTH_OF_INT
if ( l2 == l1 ) {
for ( l2 = h2; (l2&1) == 0; l2 >>= 1 ) ;
goto one_word;
} else if ( l2 < l1 ) {
l2 -= l1, h2--;
} else l2 -= l1;
i = 0; do { l2 >>= 1, i++; } while ( (l2&1) == 0 );
l2 |= (h2 << (BSH - i));
#else
if ( (l2 -= l1) == 0 ) {
for ( l2 = h2; (l2&1) == 0; l2 >>= 1 ) ;
goto one_word;
} else if ( l2 < 0 ) h2--, l2 += BASE;
i = 0; do { l2 >>= 1, i++; } while ( (l2&1) == 0 );
l2 |= ((h2 << (BSH - i)) & BMASK);
#endif
h2 >>= i;
goto no_hi1;
} else if ( h2 == 0 ) {
no_hi2: if ( l2 == 1 ) return 0;
#if BSH == BIT_WIDTH_OF_INT
if ( l1 == l2 ) {
for ( l1 = h1; (l1&1) == 0; l1 >>= 1 ) ;
goto one_word;
} else if ( l1 < l2 ) {
l1 -= l2, h1--;
} else l1 -= l2;
i = 0; do { l1 >>= 1, i++; } while ( (l1&1) == 0 );
l1 |= (h1 << (BSH - i));
#else
if ( (l1 -= l2) == 0 ) {
for ( l1 = h1; (l1&1) == 0; l1 >>= 1 ) ;
goto one_word;
} else if ( l1 < 0 ) h1--, l1 += BASE;
i = 0; do { l1 >>= 1, i++; } while ( (l1&1) == 0 );
l1 |= ((h1 << (BSH - i)) & BMASK);
#endif
if ( (h1 >>= i) == 0 ) goto one_word;
goto no_hi2;
} else if ( l1 == l2 ) {
if ( h1 == h2 ) {
pans[0] = l1, pans[1] = h1;
return 2;
} else if ( h1 > h2 ) {
for ( l1 = h1 - h2; (l1&1) == 0; l1 >>= 1 ) ;
goto no_hi1n;
} else {
for ( l2 = h2 - h1; (l2&1) == 0; l2 >>= 1 ) ;
goto no_hi2;
}
} else if ( h1 == h2 ) {
if ( l1 > l2 ) {
for ( l1 -= l2; (l1&1) == 0; l1 >>= 1 ) ;
goto no_hi1n;
} else {
for ( l2 -= l1; (l2&1) == 0; l2 >>= 1 ) ;
goto no_hi2;
}
} else if ( h1 > h2 ) {
h1 -= h2;
#if BSH == BIT_WIDTH_OF_INT
if ( l1 < l2 ) l1 -= l2, h1--;
else l1 -= l2;
i = 0; do { l1 >>= 1, i++; } while ( (l1&1) == 0 );
l1 |= (h1 << (BSH - i));
#else
if ( (l1 -= l2) < 0 ) h1--, l1 += BASE;
i = 0; do { l1 >>= 1, i++; } while ( (l1&1) == 0 );
l1 |= ((h1 << (BSH - i)) & BMASK);
#endif
h1 >>= i;
} else {
h2 -= h1;
#if BSH == BIT_WIDTH_OF_INT
if ( l2 < l1 ) l2 -= l1, h2--;
else l2 -= l1;
i = 0; do { l2 >>= 1, i++; } while ( (l2&1) == 0 );
l2 |= (h2 << (BSH - i));
#else
if ( (l2 -= l1) < 0 ) h2--, l2 += BASE;
i = 0; do { l2 >>= 1, i++; } while ( (l2&1) == 0 );
l2 |= ((h2 << (BSH - i)) & BMASK);
#endif
h2 >>= i;
}
goto loop;
one_word:
if ( l1 == 1 || l2 == 1 ) return 0;
else if ( l1 == l2 ) {
pans[0] = l1;
return 1;
}
one_word_neq:
if ( l1 > l2 ) {
l1 -= l2;
do { l1 >>= 1; } while ( (l1&1) == 0 );
goto one_word;
} else {
l2 -= l1;
do { l2 >>= 1; } while ( (l2&1) == 0 );
goto one_word;
}
}
static N igcd_binary( n1, n2, nt )
N n1, n2, nt;
/* both n1 and n2 are assumed to be odd */
{
int l1, *b1, l2, *b2, *bt = BD(nt);
int l;
if ( (l = cmpn( n1, n2 )) == 0 ) return n1;
else if ( l < 0 ) { SWAP( n1, n2, N ); }
IniDiv( n1, n2 );
if ( UNIN(n2) ) return 0;
l1 = PL(n1), b1 = BD(n1), l2 = PL(n2), b2 = BD(n2);
loop:
#if 0000
{
int i, b, w;
printf( "===============\n" );
for ( i = 0; i < l1; i++ ) printf( "0x%08x ", b1[i] );
printf( "\n" );
for ( i = 0; i < l2; i++ ) printf( "0x%08x ", b2[i] );
printf( "\n" );
}
#endif
if ( l1 <= 2 && l2 <= 2 ) {
l = igcd_binary_2w( b1, l1, b2, l2, bt );
if ( l == 0 ) return 0;
PL(nt) = l;
return nt;
}
/**/
l = abs_U_V_maxrshift( b1, l1, b2, l2, bt );
/**/
if ( l == 0 ) {
PL(n1) = l1;
return n1;
} else if ( l > 0 ) {
l1 = l;
SWAP( b1, bt, int * ); SWAP( n1, nt, N );
} else {
l2 = -l;
SWAP( b2, bt, int * ); SWAP( n2, nt, N );
}
goto loop;
}
#define RetTrueGCD(p,gw,gb,nr,l0) \
if (p==0) { l0: if (gw==0&&gb==0) { *(nr)=ONEN; return; } else p=ONEN; } \
*(nr) = N_of_n_lshifted_by_wb(p,gw,gb); \
return;
void gcdbinn( n1, n2, nr )
N n1, n2, *nr;
{
int s1, s2, gw, gb, t1, t2;
int w1, w2;
N tn1, tn2, tnt, p;
if ( !n1 ) {
*nr = n2;
return;
} else if ( !n2 ) {
*nr = n1;
return;
}
s1 = trailingzerosn( n1, &w1 );
s2 = trailingzerosn( n2, &w2 );
if ( w1 == w2 ) gw = w1, gb = s1 <= s2 ? s1 : s2;
else if ( w1 < w2 ) gw = w1, gb = s1;
else gw = w2, gb = s2;
/*
* true GCD must be multiplied by 2^{gw*BSH+gb}.
*/
t1 = PL(n1) - w1;
t2 = PL(n2) - w2;
if ( t1 < t2 ) t1 = t2;
tn1 = W_NALLOC(t1); tn2 = W_NALLOC(t1); tnt = W_NALLOC(t1);
rshiftn( n1, w1, s1, tn1 );
rshiftn( n2, w2, s2, tn2 );
p = igcd_binary( tn1, tn2, tnt );
RetTrueGCD( p, gw, gb, nr, L0 )
}
/*
* The bmod gcd algorithm stated briefly in K.Weber's paper
* [ACM TOMS, Vol.21, No. 1 (1995), pp. 111-122].
* It replaces the subtraction (n1 - n2) in the binary algorithm
* by (n1 - S*n2) with such an S that (n1 - S*n2) \equiv 0 \bmod 2^BSH,
* which should improve the efficiency when n1 \gg n2.
*/
/* subsidiary routines */
#if BSH == BIT_WIDTH_OF_INT
#ifdef CALL
static int u_div_v_mod_2toBSH( u, v )
unsigned int u, v;
/*
* u/v mod 2^BSH.
*/
{
unsigned int i, lsh_i, m;
lsh_i = (sizeof(int) << 3) - 1;
m = i = 0;
do {
if ( u == 0 ) break;
if ( (u << lsh_i) != 0 ) {
m += (1 << i);
u -= (v << i);
}
lsh_i--;
} while ( ++i != BSH );
return m;
}
#define Comp_U_div_V_mod_BASE(U,V,R) R = u_div_v_mod_2toBSH(U,V)
#else /* CALL */
#define Comp_U_div_V_mod_BASE(U,V,R) {\
unsigned int u = (U), v = (V), i, lsh; \
/* U and V are assumed to be odd */ \
i = R = 1, lsh = (sizeof(int) << 3) - 2; u = (u - v); \
do { if ( u == 0 ) break; \
if ( (u << lsh) != 0 ) R += (1 << i), u = (u - (v << i)); \
i++, lsh--; \
} while ( i < BSH ); \
}
#endif /* CALL */
#else
#ifdef CALL
static int u_div_v_mod_2tos( u, v, s )
int u, v, s;
/*
* u/v mod 2^s.
*/
{
int i, lsh_i, mask, m;
mask = (1 << s) - 1;
lsh_i = (sizeof(int) << 3) - 1;
m = i = 0;
u &= mask, v &= mask;
do {
if ( u == 0 ) break;
if ( (u << lsh_i) != 0 ) {
m += (1 << i);
u -= (v << i);
u &= mask;
}
lsh_i--;
} while ( ++i != s );
return m;
}
#define Comp_U_div_V_mod_BASE(U,V,R) R = u_div_v_mod_2tos(U,V,BSH)
#else
#define Comp_U_div_V_mod_BASE(U,V,R) {\
int u = (U), v = (V), i, lsh; \
/* U and V are assumed to be odd */ \
i = R = 1, lsh = (sizeof(int) << 3) - 2; u = (u - v) & BMASK; \
do { if ( u == 0 ) break; \
if ( (u << lsh) != 0 ) R += (1 << i), u = (u - (v << i)) & BMASK; \
i++, lsh--; \
} while ( i < BSH ); \
}
#endif
#endif
static int bmod_n( nu, nv, na )
N nu, nv, na;
/*
* Computes (u[] \bmod v[]) >> (as much as possible) in r[].
*/
{
#if BSH == BIT_WIDTH_OF_INT
unsigned int *u = BD(nu), *v = BD(nv), *r = BD(na);
unsigned int *p, a, t, l, v0, vh, bv, v0r;
int lu = PL(nu), lv = PL(nv), z;
#else
int *u = BD(nu), lu = PL(nu), *v = BD(nv), lv = PL(nv),
*r = BD(na);
int *p, a, t, l, z, v0, vh, bv, v0r;
#endif
v0 = v[0];
if ( lv == 1 ) {
if ( lu == 1 ) a = u[0] % v0;
else {
p = &u[--lu];
#if BSH == BIT_WIDTH_OF_INT
a = (*p) % v0, t = (unsigned)(-((int)v0)) % v0;
#else
a = (*p) % v0, t = BASE % v0;
#endif
for ( ; --lu >= 0; a = l ) {
--p;
DMAR(a,t,*p,v0,l);
/* l <= (a*t + p[0])%v0 */
}
}
if ( a == 0 ) return 0;
while ( (a&1) == 0 ) a >>= 1;
*r = a;
return( PL(na) = 1 );
}
Comp_U_div_V_mod_BASE( 1, v0, v0r );
vh = v[lv -1];
BitWidth( vh, bv );
bv--;
t = 1 << bv;
l = lv + 1;
for ( z = -1; lu > l || lu == l && u[lu-1] >= t; z = -z ) {
#if BSH == BIT_WIDTH_OF_INT
a = (v0r*u[0]);
#else
a = (v0r*u[0])&BMASK;
#endif
/**/
#if 0000
{
int i;
for ( i = 0; i < lu; i++ ) printf( "0x%08x ", u[i] );
printf( "\n- a=0x%08x, %u*\n", a, a );
for ( i = 0; i < lv; i++ ) printf( "0x%08x ", v[i] );
printf( "\n=>\n" );
}
#endif
lu = abs_U_aV_maxrshift( u, lu, a, v, lv, r );
/**/
#if 0000
printf( "***lu=%d\n", lu );
if ( lu != 0 ) {
int i;
for ( i = 0; i < lu; i++ ) printf( "0x%08x ", r[i] );
printf( "\n" );
}
#endif
if ( lu == 0 ) return 0;
p = r;
r = u;
u = p;
}
if ( lu < lv ) goto ret;
t = u[lu-1];
if ( lu > lv ) l = BSH;
else if ( t < vh ) goto ret;
else l = 0;
BitWidth( t, a );
l += (a - bv);
#if BSH == BIT_WIDTH_OF_INT
a = (v0r*u[0])&((unsigned)(-1) >> (BSH - l));
#else
a = (v0r*u[0])&(BMASK >> (BSH - l));
#endif
#if 0000
{
int i;
for ( i = 0; i < lu; i++ ) printf( "0x%08x ", u[i] );
printf( "\n - a=0x%08x, %u*\n", a, a );
for ( i = 0; i < lv; i++ ) printf( "0x%08x ", v[i] );
printf( "\n =>\n" );
}
#endif
/**/
lu = abs_U_aV_maxrshift( u, lu, a, v, lv, r );
/**/
#if 0000
printf( "::: lu=%d\n", lu );
if ( lu != 0 ) {
int i;
for ( i = 0; i < lu; i++ ) printf( "0x%08x ", r[i] );
printf( "\n" );
}
#endif
if ( lu == 0 ) return 0;
z = -z;
ret: if ( z > 0 ) return( PL(na) = lu );
PL(nu) = lu;
return( -lu );
}
static N igcd_bmod( n1, n2, nt )
N n1, n2, nt;
/* both n1 and n2 are assumed to be odd */
{
int l1, l2;
int l;
if ( (l = cmpn( n1, n2 )) == 0 ) return n1;
else if ( l < 0 ) { SWAP( n1, n2, N ); }
IniDiv( n1, n2 );
if ( UNIN(n2) ) return 0;
loop: if ( (l1 = PL(n1)) <= 2 && (l2 = PL(n2)) <= 2 ) {
l = igcd_binary_2w( BD(n1), l1, BD(n2), l2, BD(nt) );
if ( l == 0 ) return 0;
PL(nt) = l;
return nt;
}
/**/
l = bmod_n( n1, n2, nt );
/**/
if ( l == 0 ) return n2;
else if ( l > 0 ) {
N tmp = n1;
n1 = n2;
n2 = nt;
nt = tmp;
} else SWAP( n1, n2, N );
goto loop;
}
void gcdbmodn( n1, n2, nr )
N n1, n2, *nr;
{
int s1, s2, gw, gb, t1, t2;
int w1, w2;
N tn1, tn2, tnt, p;
if ( !n1 ) {
*nr = n2;
return;
} else if ( !n2 ) {
*nr = n1;
return;
}
s1 = trailingzerosn( n1, &w1 );
s2 = trailingzerosn( n2, &w2 );
if ( w1 == w2 ) gw = w1, gb = s1 <= s2 ? s1 : s2;
else if ( w1 < w2 ) gw = w1, gb = s1;
else gw = w2, gb = s2;
/*
* true GCD must be multiplied by 2^{gw*BSH+gs}.
*/
t1 = PL(n1) - w1;
t2 = PL(n2) - w2;
if ( t1 < t2 ) t1 = t2;
tn1 = W_NALLOC(t1); tn2 = W_NALLOC(t1); tnt = W_NALLOC(t1);
rshiftn( n1, w1, s1, tn1 );
rshiftn( n2, w2, s2, tn2 );
p = igcd_bmod( tn1, tn2, tnt );
RetTrueGCD( p, gw, gb, nr, L0 )
}
/*
* The accelerated integer GCD algorithm by K.Weber
* [ACM TOMS, Vol.21, No. 1 (1995), pp. 111-122]:
*/
static int ReducedRatMod( x, y, pn, pd )
N x, y;
#if BSH == BIT_WIDTH_OF_INT
unsigned
#endif
int *pn, *pd;
/*
* Let m = 2^{2*BSH} = 2*BASE. We assume x, y > 0 and \gcd(x,m)
* = \gcd(y,m) = 1. This routine computes n and d (resp. returned
* in *pn and *pd) such that 0 < n, |d| < \sqrt{m} and
* n*y \equiv x*d \bmod m.
*/
{
#if BSH == BIT_WIDTH_OF_INT
unsigned int n1h, n1l, d1h, d1l, n2h, n2l, d2h, d2l;
unsigned int th, tl, l1, l2, i, ir;
int s1, s2;
#else
int n1h, n1l, d1h, d1l, n2h, n2l, d2h, d2l;
int th, tl, l1, l2, i, ir;
int s1, s2;
#endif
{
#if BSH == BIT_WIDTH_OF_INT
unsigned
#endif
int xh, xl, yh, yl, lsh_i;
xl = BD(x)[0];
xh = PL(x) > 1 ? BD(x)[1] : 0;
yl = BD(y)[0];
yh = PL(y) > 1 ? BD(y)[1] : 0;
#if 0000
printf( "*** RedRatMod: (0x%08x:0x%08x=%u*2^%d+%u)\n /(0x%08x:0x%08x=%u*2^%d+%u) mod 2^%d\n",
xh,xl, xh,BSH,xl, yh,yl, yh,BSH,yl, BSH );
#endif
Comp_U_div_V_mod_BASE( xl, yl, n2l );
DM(n2l,yl,th,tl) /* n2l*yl = tl+th*BASE, where tl==xl. */;
#if BSH == BIT_WIDTH_OF_INT
xh -= th;
#else
if ( xh > th ) xh -= th;
else xh += (BASE - th);
#endif
DM(n2l,yh,th,tl) /* n2l*yh = tl+th*BASE. */;
#if BSH == BIT_WIDTH_OF_INT
xh -= tl;
#else
if ( xh > tl ) xh -= tl;
else xh += (BASE - tl);
#endif
/* n2h = i = 0, lsh_i = 31;*/
n2h = i = 0, lsh_i = BIT_WIDTH_OF_INT -1;
do {
if ( xh == 0 ) break;
if ( (xh << lsh_i) != 0 ) {
n2h += (1 << i);
#if BSH == BIT_WIDTH_OF_INT
tl = yl << i;
xh -= tl;
#else
tl = (yl << i)&BMASK;
if ( xh > tl ) xh -= tl;
else xh += (BASE - tl);
#endif
}
lsh_i--;
} while ( ++i != BSH );
}
/*
* n2l + n2h*BASE = x/y mod 2^{2*BSH}.
*/
#if 0000
printf( "=====> 0x%08x(%u) + 2^%d*0x%08x(%u)\n", n2l, n2l, BSH, n2h, n2h );
#endif
d2h = 0, d2l = 1, s2 = 1;
#if BSH == BIT_WIDTH_OF_INT
if ( n2h == 0 ) goto done;
BitWidth( n2h, l2 );
if ( l2 == BSH ) {
d1h = 0, d1l = 1, s1 = -1;
th = n2h, tl = n2l;
} else {
i = BSH - l2;
d1h = 0, d1l = 1 << i, s1 = -1;
th = (n2h << i) | (n2l >> l2);
tl = n2l << i;
}
if ( tl == 0 ) n1h = - th, n1l = 0;
else n1h = BMASK - th, n1l = - tl;
/**/
if ( n1h < n2h || (n1h == n2h && n1l < n2l) ) goto swap12;
BitWidth( n1h, l1 );
goto sub12;
#else
n1h = BASE, n1l = 0, l1 = BSH,
d1h = d1l = 0, s1 = 0;
#endif
/**/
while ( n2h != 0 ) {
BitWidth( n2h, l2 );
sub12: ir = BSH - (i = l1 - l2);
do {
if ( i == 0 ) th = n2h, tl = n2l;
else
th = (n2h << i) | (n2l >> ir),
#if BSH == BIT_WIDTH_OF_INT
tl = n2l << i;
#else
tl = (n2l << i) & BMASK;
#endif
if ( th > n1h || (th == n1h && tl > n1l) ) goto next_i;
#if BSH == BIT_WIDTH_OF_INT
if ( tl > n1l ) n1h--;
n1l -= tl;
#else
if ( tl <= n1l ) n1l -= tl;
else n1l += (BASE - tl), n1h--;
#endif
n1h -= th;
/* (s1:d1h,d1l) -= ((s2:d2h,d2l) << i); */
if ( s2 != 0 ) {
if ( i == 0 ) th = d2h, tl = d2l;
else
#if BSH == BIT_WIDTH_OF_INT
th = (d2h << i) | (d2l >> ir),
tl = (d2l << i);
#else
th = (d2h << i)&BMASK | (d2l >> ir),
tl = (d2l << i)&BMASK;
#endif
if ( s1 == 0 )
s1 = -s2, d1h = th, d1l = tl;
else if ( s1 != s2 ) {
#if BSH == BIT_WIDTH_OF_INT
d1l += tl,
d1h += th;
if ( d1l < tl ) d1h++;
#else
tl += d1l;
d1l = tl&BMASK;
d1h = (d1h + th + (tl >> BSH))&BMASK;
#endif
if ( d1h == 0 && d1l == 0 ) s1 = 0;
} else if ( d1h > th ) {
#if BSH == BIT_WIDTH_OF_INT
if ( d1l < tl ) d1h--;
d1l -= tl;
#else
if ( d1l >= tl ) d1l -= tl;
else d1l += (BASE - tl), d1h--;
#endif
d1h -= th;
} else if ( d1h == th ) {
d1h = 0;
if ( d1l == tl ) s1 = d2h = 0;
else if ( d1l > tl ) d1l -= tl;
else d1l = tl - d1l, s1 = -s1;
} else {
#if BSH == BIT_WIDTH_OF_INT
if ( tl < d1l ) th--;
d1l = tl - d1l;
#else
if ( tl >= d1l ) d1l = tl - d1l;
else d1l = tl + (BASE - d1l), th--;
#endif
d1h = th - d1h;
s1 = -s1;
}
}
next_i: i--, ir++;
} while ( n1h > n2h || (n1h == n2h && n1l >= n2l) );
swap12: /* swap 1 and 2 */
th = n1h, tl = n1l;
n1h = n2h, n1l = n2l;
n2h = th, n2l = tl;
l1 = l2;
th = d1h, tl = d1l, i = s1;
d1h = d2h, d1l = d2l, s1 = s2;
d2h = th, d2l = tl, s2 = i;
}
/**/
done: *pn = n2l, *pd = d2l;
return s2;
}
static int igcd_spurious_factor;
#define SaveN(s,d) {\
int i, l; \
for ( l = PL(d) = PL(s), i = 0; i < l; i++ ) BD(d)[i] = BD(s)[i]; \
}
static N igcd_acc( n1, n2, nt )
N n1, n2, nt;
/* both n1 and n2 are assumed to be odd */
{
int l1, l2, *b1, *b2, bw1, bw2;
int l;
int n, d;
N p, s1, s2;
if ( (l = cmpn( n1, n2 )) == 0 ) return n1;
else if ( l < 0 ) { SWAP( n1, n2, N ); }
if ( ShouldCompRemInit(n1,n2) ) {
int w, b;
divn( n1, n2, &s1, &s2 );
if ( !s2 ) return n2;
b = trailingzerosn( s2, &w );
p = n1; n1 = n2; n2 = p;
rshiftn( s2, w, b, n2 );
if ( UNIN(n2) ) return 0;
l1 = PL(n1);
if ( !s1 || PL(s1) < l1 ) s1 = NALLOC(l1);
} else if ( UNIN(n2) ) return 0;
else {
s1 = NALLOC(PL(n1));
s2 = NALLOC(PL(n2));
}
SaveN( n1, s1 );
SaveN( n2, s2 );
igcd_spurious_factor = 0;
loop: l1 = PL(n1), l2 = PL(n2);
if ( l1 <= 2 && l2 <= 2 ) {
l = igcd_binary_2w( BD(n1), l1, BD(n2), l2, BD(nt) );
if ( l == 0 ) return 0;
PL(nt) = l;
SWAP( n2, nt, N );
goto ret;
}
/**/
b1 = BD(n1), b2 = BD(n2);
BitWidth( b1[l1 -1], bw1 );
BitWidth( b2[l2 -1], bw2 );
if ( (l1*BSH + bw1) - (l2*BSH + bw2) <= igcdacc_thre ) {
l = ReducedRatMod( n1, n2, &n, &d );
l = l < 0 ? aUplusbV_maxrshift( n, b2, l2, d, b1, l1, BD(nt) ) :
abs_axU_bxV_maxrshift( n, b2, l2, d, b1, l1, BD(nt) );
igcd_spurious_factor++;
if ( l == 0 ) goto ret;
PL(nt) = l;
} else {
l = bmod_n( n1, n2, nt );
if ( l == 0 ) goto ret;
else if ( l < 0 ) {
SWAP( n1, n2, N );
goto loop;
}
}
p = n1;
n1 = n2;
n2 = nt;
nt = p;
goto loop;
/**/
ret: if ( igcd_spurious_factor != 0 && !UNIN(n2) ) {
if ( (p = igcd_bmod( n2, s1, n1 )) == 0 ) return 0;
if ( (p = igcd_bmod( p, s2, nt )) == 0 ) return 0;
return p;
} else return n2;
}
void gcdaccn( n1, n2, nr )
N n1, n2, *nr;
{
int s1, s2, gw, gb, t1, t2;
int w1, w2;
N tn1, tn2, tnt, p;
if ( !n1 ) {
*nr = n2;
return;
} else if ( !n2 ) {
*nr = n1;
return;
}
s1 = trailingzerosn( n1, &w1 );
s2 = trailingzerosn( n2, &w2 );
if ( w1 == w2 ) gw = w1, gb = s1 <= s2 ? s1 : s2;
else if ( w1 < w2 ) gw = w1, gb = s1;
else gw = w2, gb = s2;
/*
* true GCD must be multiplied by 2^{gw*BSH+gs}.
*/
t1 = PL(n1) - w1;
t2 = PL(n2) - w2;
if ( t1 < t2 ) t1 = t2;
tn1 = W_NALLOC(t1); tn2 = W_NALLOC(t1); tnt = W_NALLOC(t1);
rshiftn( n1, w1, s1, tn1 );
rshiftn( n2, w2, s2, tn2 );
/**/
p = igcd_acc( tn1, tn2, tnt );
/**/
if ( p == 0 ) goto L0;
RetTrueGCD( p, gw, gb, nr, L0 )
}
/********************************/
void gcdn_HMEXT( n1, n2, nr )
N n1, n2, *nr;
{
int b1, b2, w1, w2, gw, gb;
int l1, l2;
N tn1, tn2, tnt, a;
if ( !n1 ) {
*nr = n2; return;
} else if ( !n2 ) {
*nr = n1; return;
}
b1 = trailingzerosn( n1, &w1 );
b2 = trailingzerosn( n2, &w2 );
if ( w1 == w2 ) gw = w1, gb = b1 <= b2 ? b1 : b2;
else if ( w1 < w2 ) gw = w1, gb = b1;
else gw = w2, gb = b2;
/*
* true GCD must be multiplied by 2^{gw*BSH+gb}.
*/
l1 = PL(n1) - w1;
l2 = PL(n2) - w2;
if ( l1 < l2 ) l1 = l2;
tn1 = W_NALLOC( l1 ); tn2 = W_NALLOC( l1 ); tnt = W_NALLOC( l1 );
rshiftn( n1, w1, b1, tn1 );
rshiftn( n2, w2, b2, tn2 );
/**/
if ( igcd_algorithm == 1 ) {
a = igcd_binary( tn1, tn2, tnt );
} else if ( igcd_algorithm == 2 ) {
a = igcd_bmod( tn1, tn2, tnt );
} else {
a = igcd_acc( tn1, tn2, tnt );
if ( igcd_spurious_factor != 0 ) {
}
}
RetTrueGCD( a, gw, gb, nr, L0 )
}
/**************************/
#if 111
N maxrshn( n, p )
N n;
int *p;
{
int nw, nb, c, l;
N new;
nb = trailingzerosn( n, &nw );
l = PL(n);
c = BD(n)[l -1];
l -= nw;
if ( (c >> nb) == 0 ) l--;
new = NALLOC(l);
rshiftn( n, nw, nb, new );
*p = nb + nw*BSH;
return new;
}
#endif
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