PROC
writeline(int y,int x,int start)
{
int endd,oxp;
unsigned int size;
char buf[MAXCOLS+1];
unsigned int bi = 0;
endd = fseekeol(start);
if (start==0 || core[start-1] == EOL)
mvcur(y, 0);
else
mvcur(y, x);
oxp = curpos.x;
while (start < endd && curpos.x < COLS) {
size = format(&buf[bi],core[start++]);
bi += size;
curpos.x += size;
}
if (list) {
buf[bi++] = '$';
curpos.x++;
}
size = min(bi,COLS-oxp);
if (size > 0) {
zwrite(buf, size);
}
if (curpos.x < COLS)
strput(CE);
}
PROC
printch(char c)
{
register int size;
char buf[MAXCOLS];
size = min(format(buf,c),COLS-curpos.x);
if (size > 0) {
zwrite(buf, size);
curpos.x += size;
}
}
PROC
printi(int num)
{
char nb[10];
register int size;
numtoa(nb,num);
size = min(strlen(nb),COLS-curpos.x);
if (size > 0) {
zwrite(nb, size);
curpos.x += size;
}
}
int main(void)
{
double delta = 0.15;
long i, n = 16;
verylong zP = 0, zQ = 0;
verylong *zp = allocate_very_vector(1, n);
verylong *zq = allocate_very_vector(1, n);
zpstart2();
for (i = 1; i <= n; i++)
zintoz(zpnext(), &zq[i]);
zintoz(zpnext(), &zQ);
printf("delta = %lf\n", delta);
printf("n = %ld\n", n);
if (n <= 16) {
printf("q = ");
zwriteln(zQ);
printf("q[i] ");
for (i = 1; i <= n; i++) {
zwrite(zq[i]);
printf(" ");
}
}
printf("\n");
if (simultaneous_diophantine(delta, n, zQ, &zP, zp, zq)) {
printf("p = "); zwriteln(zP);
printf("p[i] ");
for (i = 1; i <= n; i++) {
zwrite(zp[i]);
printf(" ");
}
}
else
printf("\nno simultaneous diophantine approximation\n");
free_very_vector(zp, 1, n);
free_very_vector(zq, 1, n);
return 0;
}
PROC
prints(char *s)
{
int size,oxp = curpos.x;
char buf[MAXCOLS+1];
unsigned int bi = 0;
while (*s && curpos.x < COLS) {
size = format(&buf[bi],*s++);
bi += size;
curpos.x += size;
}
size = min(bi,COLS-oxp);
if (size > 0)
zwrite(buf, size);
}
void
refresh(void)
{
static int inlist; /* avoiding recursion */
int canscroll = 0, /* number of lines we are allowed to scroll */
ln = 0, /* current line we're working on */
more_status = 0, /* more stuff in status line */
nvcs = 0, nvln = -1, /* video cursor column and line */
t0 = -1, /* tmp */
tosln = 0; /* tmp in statusline stuff */
unsigned char *s, /* pointer into the video buffer */
*t, /* pointer into the real buffer */
*sen, /* pointer to end of the video buffer (eol) */
*scs; /* pointer to cursor position in real buffer */
char **qbuf; /* tmp */
/* If this is called from listmatches() (indirectly via trashzle()), and *
* that was called from the end of refresh(), then we don't need to do *
* anything. All this `inlist' code is actually unnecessary, but it *
* improves speed a little in a common case. */
if (inlist)
return;
#ifdef HAVE_SELECT
cost = 0; /* reset */
#endif
#ifndef WINNT
/* Nov 96: <mason> I haven't checked how complete this is. sgtty stuff may
or may not work */
oxtabs = ((SGTTYFLAG & SGTABTYPE) == SGTABTYPE);
#else WINNT
oxtabs = 0;
#endif WINNT
cleareol = 0; /* unset */
more_start = more_end = 0; /* unset */
if (isset(SINGLELINEZLE) || lines < 3
|| (termflags & (TERM_NOUP | TERM_BAD | TERM_UNKNOWN)))
termflags |= TERM_SHORT;
else
termflags &= ~TERM_SHORT;
if (resetneeded) {
onumscrolls = 0;
setterm();
#if defined( TIOCGWINSZ) || defined(WINNT)
if (winchanged) {
moveto(0, 0);
t0 = olnct; /* this is to clear extra lines even when */
winchanged = 0; /* the terminal cannot TCCLEAREOD */
}
#endif
resetvideo();
resetneeded = 0; /* unset */
oput_rpmpt = 0; /* no right-prompt currently on screen */
/* we probably should only have explicitly set attributes */
tsetcap(TCALLATTRSOFF, 0);
tsetcap(TCSTANDOUTEND, 0);
tsetcap(TCUNDERLINEEND, 0);
if (!clearflag)
if (tccan(TCCLEAREOD))
tcout(TCCLEAREOD);
else
cleareol = 1; /* request: clear to end of line */
if (t0 > -1)
olnct = t0;
if (termflags & TERM_SHORT)
vcs = 0;
else if (!clearflag && lpptlen)
zwrite(lpptbuf, lpptlen, 1, shout);
if (clearflag) {
zputc('\r', shout);
vcs = 0;
moveto(0, pptw);
}
fflush(shout);
clearf = clearflag;
} else if (winw != columns || rwinh != lines)
resetvideo();
/* now winw equals columns and winh equals lines
width comparisons can be made with winw, height comparisons with winh */
if (termflags & TERM_SHORT) {
singlerefresh();
return;
}
if (cs < 0) {
#ifdef DEBUG
fprintf(stderr, "BUG: negative cursor position\n");
fflush(stderr);
#endif
cs = 0;
}
scs = line + cs;
numscrolls = 0;
/* first, we generate the video line buffers so we know what to put on
the screen - also determine final cursor position (nvln, nvcs) */
/* Deemed necessary by PWS 1995/05/15 due to kill-line problems */
if (!*nbuf)
*nbuf = (char *)zalloc(winw + 2);
s = (unsigned char *)(nbuf[ln = 0] + pptw);
t = line;
sen = (unsigned char *)(*nbuf + winw);
for (; t < line+ll; t++) {
if (t == scs) /* if cursor is here, remember it */
nvcs = s - (unsigned char *)(nbuf[nvln = ln]);
if (*t == '\n') { /* newline */
nbuf[ln][winw + 1] = '\0'; /* text not wrapped */
nextline
} else if (*t == '\t') { /* tab */
void zbinary_ext_gcd(verylong zx, verylong zy,
verylong *za, verylong *zb,
verylong *zv)
/* returns a * x + b * y = v, v = gcd(x, y) */
{
verylong zA = 0, zB = 0, zC = 0, zD = 0;
verylong zX = 0, zY = 0, zc = 0, zg = 0;
verylong zu = 0;
zone(&zg);
zcopy(zx, &zX);
zcopy(zy, &zY);
while (!zodd(zX) && !zodd(zY)) {
zrshift(zX, 1l, &zc);
zcopy(zc, &zX);
zrshift(zY, 1l, &zc);
zcopy(zc, &zY);
zlshift(zg, 1l, &zc);
zcopy(zc, &zg);
}
zcopy(zX, &zu);
zcopy(zY, zv);
zone(&zA);
zzero(&zB);
zzero(&zC);
zone(&zD);
do {
while (!zodd(zu)) {
zrshift(zu, 1l, &zc);
zcopy(zc, &zu);
if (!zodd(zA) && !zodd(zB)) {
zrshift(zA, 1l, &zc);
zcopy(zc, &zA);
zrshift(zB, 1l, &zc);
zcopy(zc, &zB);
}
else {
zadd(zA, zY, &zc);
zrshift(zc, 1l, &zA);
zsub(zB, zX, &zc);
zrshift(zc, 1l, &zB);
}
}
while (!zodd(*zv)) {
zrshift(*zv, 1l, &zc);
zcopy(zc, zv);
if (!zodd(zC) && !zodd(zD)) {
zrshift(zC, 1l, &zc);
zcopy(zc, &zC);
zrshift(zD, 1l, &zc);
zcopy(zc, &zD);
}
else {
zadd(zC, zY, &zc);
zrshift(zc, 1l, &zC);
zsub(zD, zX, &zc);
zrshift(zc, 1l, &zD);
}
}
if (zcompare(zu, *zv) >= 0) {
zsub(zu, *zv, &zc);
zcopy(zc, &zu);
zsub(zA, zC, &zc);
zcopy(zc, &zA);
zsub(zB, zD, &zc);
zcopy(zc, &zB);
}
else {
zsub(*zv, zu, &zc);
zcopy(zc, zv);
zsub(zC, zA, &zc);
zcopy(zc, &zC);
zsub(zD, zB, &zc);
zcopy(zc, &zD);
}
#ifdef DEBUG
zwrite(zu); printf(" ");
zwrite(*zv); printf(" ");
zwrite(zA); printf(" ");
zwrite(zB); printf(" ");
zwrite(zC); printf(" ");
zwriteln(zD);
#endif
} while (zscompare(zu, 0l) != 0);
zcopy(zC, za);
zcopy(zD, zb);
zmul(zg, *zv, &zc);
zcopy(zc, zv);
zfree(&zA);
zfree(&zB);
zfree(&zC);
zfree(&zD);
zfree(&zX);
zfree(&zY);
zfree(&zc);
zfree(&zg);
zfree(&zu);
}
int main(int ac, char **av)
{
for(av++ ; *av ; av++)
zwrite(*av);
return 0;
}
int simultaneous_diophantine(double delta,
long n,
verylong zQ,
verylong *zP,
verylong *zp,
verylong *zq)
{
double P, Q, l;
int equal, found;
long i, j, n1 = n + 1;
verylong zd = 0, zl = 0, zr = 0, zs = 0, zt = 0;
verylong **zA = allocate_very_matrix(1, n1, 1, n1);
verylong **zh = allocate_very_matrix(1, n1, 1, n1);
Q = zdoub(zQ);
zintoz(pow(Q, delta), &zl);
l = 1.0 / zdoub(zl);
zmul(zl, zQ, &zd);
for (i = 1; i <= n; i++)
zcopy(zd, &zA[i][i]);
znegate(&zl);
for (i = 1; i <= n; i++)
zmul(zl, zq[i], &zA[n1][i]);
zone(&zA[n1][n1]);
int_LLL(n1, zA, zh);
found = 0;
for (j = 1; !found && j <= n1; j++) {
zcopy(zA[j][n1], zP);
if (zcompare(*zP, zQ) != 0) {
for (i = 1; i <= n; i++) {
zdiv(zA[j][i], zl, &zr, &zs);
zmul(*zP, zq[i], &zt);
zadd(zr, zt, &zs);
zdiv(zs, zQ, &zp[i], &zr);
}
P = zdoub(*zP);
#ifdef DEBUG
if (n <= 16) {
printf("p = ");
zwrite(*zP);
printf(" p[i] ");
for (i = 1; i <= n; i++) {
zwrite(zp[i]);
printf(" ");
}
printf("\n");
}
#endif
if (zcompare(*zP, 0) != 0) {
equal = 1;
for (i = 1; equal && i <= n; i++)
equal = fabs(P * zdoub(zq[i]) / Q - zdoub(zp[i]))
<= l;
}
else equal = 0;
found = equal;
}
}
free_very_matrix(zA, 1, n1, 1, n1);
free_very_matrix(zh, 1, n1, 1, n1);
zfree(&zd);
zfree(&zl);
zfree(&zr);
zfree(&zs);
zfree(&zt);
return found;
}
void int_LLL(long n, verylong **zb, verylong **zh)
{
double x, y;
long i, j, k = 2, k1, kmax = 1, l;
verylong zr = 0, zs = 0, zt = 0, zu = 0;
verylong *zB = allocate_very_vector(1, n);
verylong *zd = allocate_very_vector(0, n);
verylong **zl = allocate_very_matrix(1, n, 1, n);
zone(&zd[0]);
scalar(n, zb[1], zb[1], &zd[1]);
for (i = 1; i <= n; i++) {
for (j = 1; j <= n; j++)
zzero(&zh[i][j]);
zone(&zh[i][i]);
}
#ifdef DEBUG
if (n <= 17) {
printf("the basis to be reduced is:\n");
for (i = 1; i <= n; i++) {
for (j = 1; j <= n; j++) {
zwrite(zb[i][j]);
printf(" ");
}
printf("\n");
}
}
#endif
L2:
if (k <= kmax) goto L3;
kmax = k;
for (j = 1; j <= k; j++) {
scalar(n, zb[k], zb[j], &zu);
for (i = 1; i <= j - 1; i++) {
zmul(zd[i], zu, &zr);
zmul(zl[k][i], zl[j][i], &zs);
zsub(zr, zs, &zt);
zdiv(zt, zd[i - 1], &zu, &zr);
}
if (j < k) zcopy(zu, &zl[k][j]);
else if (j == k) {
zcopy(zu, &zd[k]);
if (zscompare(zd[k], 0l) == 0)
system_error("Failure in int_LLL.");
}
}
L3:
k1 = k - 1;
RED(k, k1, n, zd, zb, zh, zl);
zmul(zd[k], zd[k - 2], &zr);
zsq(zd[k1], &zs);
zsq(zl[k][k1], &zt);
x = zdoub(zr);
y = 3.0 * zdoub(zs) / 4.0 - zdoub(zt);
if (x < y) {
SWAP(k, k1, kmax, n, zd, zb, zh, zl);
k = max(2, k1);
goto L3;
}
for (l = k - 2; l >= 1; l--)
RED(k, l, n, zd, zb, zh, zl);
if (++k <= n) goto L2;
#ifdef DEBUG
if (n <= 17) {
printf("the LLL-reduced basis is:\n");
for (i = 1; i <= n; i++) {
for (j = 1; j <= n; j++) {
zwrite(zb[i][j]);
printf(" ");
}
printf("\n");
}
}
#endif
free_very_matrix(zl, 1, n, 1, n);
free_very_vector(zB, 1, n);
free_very_vector(zd, 0, n);
zfree(&zr);
zfree(&zs);
zfree(&zt);
zfree(&zu);
}
