xdouble PowerOf10(const ZZ& e)
{
static NTL_CHEAP_THREAD_LOCAL long init = 0;
static NTL_CHEAP_THREAD_LOCAL long k = 0;
NTL_TLS_LOCAL(xdouble, v10k);
if (!init) {
k = ComputeMax10Power();
RRPush push;
RR::SetPrecision(NTL_DOUBLE_PRECISION);
v10k = to_xdouble(power(to_RR(10), k));
init = 1;
}
ZZ e1;
long neg;
if (e < 0) {
e1 = -e;
neg = 1;
}
else {
e1 = e;
neg = 0;
}
long r;
ZZ q;
r = DivRem(q, e1, k);
RRPush push;
RR::SetPrecision(NTL_DOUBLE_PRECISION);
xdouble x1 = to_xdouble(power(to_RR(10), r));
xdouble x2 = power(v10k, q);
xdouble x3 = x1*x2;
if (neg) x3 = 1/x3;
return x3;
}
long ComputeMax10Power()
{
RRPush push;
RR::SetPrecision(NTL_BITS_PER_LONG);
RR ln2, ln10;
ComputeLn2(ln2);
ComputeLn10(ln10);
long k = to_long( to_RR(NTL_OVFBND/2) * ln2 / ln10 );
return k;
}
void ReallyComputePi(RR& res)
{
long p = RR::precision();
RR::SetPrecision(p + NumBits(p) + 10);
RR sum1;
RR s, s1, t, t1;
s = 0;
t = 0.5;
t1 = 0.5;
long i;
for (i = 3; ; i+=2) {
add(s1, s, t);
if (s == s1) break;
xcopy(s, s1);
mul(t1, t1, -0.25);
div(t, t1, i);
}
xcopy(sum1, s);
RR g;
inv(g, to_RR(3)); // g = 1/3
s = 0;
xcopy(t, g);
xcopy(t1, g);
sqr(g, g);
negate(g, g); // g = -1/9
for (i = 3; ; i+=2) {
add(s1, s, t);
if (s == s1) break;
xcopy(s, s1);
mul(t1, t1, g);
div(t, t1, i);
}
add(s, s, sum1);
mul(s, s, 4);
RR::SetPrecision(p);
xcopy(res, s);
}
void ComputeLn10(RR& res)
{
static long prec = 0;
static RR ln10;
long p = RR::precision();
if (prec <= p + 10) {
prec = p + 20;
RR::SetPrecision(prec);
log(ln10, to_RR(10));
RR::SetPrecision(p);
}
xcopy(res, ln10);
}
// ECM primitive
void ECM(ZZ& q, const ZZ& n, const ZZ& _bnd, double failure_prob,
bool verbose) {
ZZ bnd;
SqrRoot(bnd,n);
if (_bnd>0 && _bnd<bnd)
bnd=_bnd;
long B1,B2,D;
double prob;
ECM_parameters(B1,B2,prob,D,NumBits(bnd),NumBits(n));
if (verbose)
std::cout<<"ECM: bnd="<<NumBits(bnd)<<"bits B1="<<B1<<" B2="<<B2
<<" D="<<D<<" prob="<<prob<<std::endl;
if (failure_prob<=0) {
// run "forever"
if (verbose)
std::cout<<"ECM: expected ncurves="<<(1/prob)<<std::endl;
ECM(q,n,NTL_MAX_LONG,B1,B2,D,verbose);
}
else if (failure_prob>=1) {
// run on one curve
ECM(q,n,1,B1,B2,D,verbose);
}
else {
// run just the right number of times
// failure_prob = (1-prob)^ncurves;
double ncurves_d;
if (prob<0.1)
ncurves_d = to_double(log(failure_prob)/log1p(to_RR(-prob)));
else
ncurves_d = log(failure_prob)/log(1-prob);
long ncurves = ncurves_d<=1 ? 1 :
(ncurves_d>=NTL_MAX_LONG ? NTL_MAX_LONG : (long)ncurves_d);
if (verbose)
std::cout<<"ECM: good_prob="<<prob<<" failure_prob="<<failure_prob
<<" ncurves="<<ncurves<<std::endl;
ECM(q,n,ncurves,B1,B2,D,verbose);
}
}
ostream& operator<<(ostream& s, const xdouble& a)
{
if (a == 0) {
s << "0";
return s;
}
RRPush push;
long temp_p = long(log(fabs(log(fabs(a))) + 1.0)/log(2.0)) + 10;
RR::SetPrecision(temp_p);
RR ln2, ln10, log_2_10;
ComputeLn2(ln2);
ComputeLn10(ln10);
log_2_10 = ln10/ln2;
ZZ log_10_a = to_ZZ(
(to_RR(a.e)*to_RR(2*NTL_XD_HBOUND_LOG) + log(fabs(a.x))/log(2.0))/log_2_10);
xdouble b;
long neg;
if (a < 0) {
b = -a;
neg = 1;
}
else {
b = a;
neg = 0;
}
ZZ k = xdouble::OutputPrecision() - log_10_a;
xdouble c, d;
c = PowerOf10(to_ZZ(xdouble::OutputPrecision()));
d = PowerOf10(log_10_a);
b = b / d;
b = b * c;
while (b < c) {
b = b * 10.0;
k++;
}
while (b >= c) {
b = b / 10.0;
k--;
}
b = b + 0.5;
k = -k;
ZZ B;
conv(B, b);
long bp_len = xdouble::OutputPrecision()+10;
UniqueArray<char> bp_store;
bp_store.SetLength(bp_len);
char *bp = bp_store.get();
long len, i;
len = 0;
do {
if (len >= bp_len) LogicError("xdouble output: buffer overflow");
bp[len] = IntValToChar(DivRem(B, B, 10));
len++;
} while (B > 0);
for (i = 0; i < len/2; i++) {
char tmp;
tmp = bp[i];
bp[i] = bp[len-1-i];
bp[len-1-i] = tmp;
}
i = len-1;
while (bp[i] == '0') i--;
k += (len-1-i);
len = i+1;
bp[len] = '\0';
if (k > 3 || k < -len - 3) {
// use scientific notation
if (neg) s << "-";
s << "0." << bp << "e" << (k + len);
}
else {
long kk = to_long(k);
if (kk >= 0) {
if (neg) s << "-";
s << bp;
for (i = 0; i < kk; i++)
s << "0";
}
else if (kk <= -len) {
if (neg) s << "-";
s << "0.";
for (i = 0; i < -len-kk; i++)
s << "0";
s << bp;
}
else {
if (neg) s << "-";
for (i = 0; i < len+kk; i++)
s << bp[i];
s << ".";
for (i = len+kk; i < len; i++)
s << bp[i];
}
}
return s;
}
void inv(RR& z, const RR& a)
{
NTL_TLS_LOCAL_INIT(RR, one, (to_RR(1)));
div(z, one, a);
}
void conv(RR& x, const char *s)
{
long c;
long cval;
long sign;
ZZ a, b;
long i = 0;
if (!s) Error("bad RR input");
c = s[i];
while (IsWhiteSpace(c)) {
i++;
c = s[i];
}
if (c == '-') {
sign = -1;
i++;
c = s[i];
}
else
sign = 1;
long got1 = 0;
long got_dot = 0;
long got2 = 0;
a = 0;
b = 1;
cval = CharToIntVal(c);
if (cval >= 0 && cval <= 9) {
got1 = 1;
while (cval >= 0 && cval <= 9) {
mul(a, a, 10);
add(a, a, cval);
i++;
c = s[i];
cval = CharToIntVal(c);
}
}
if (c == '.') {
got_dot = 1;
i++;
c = s[i];
cval = CharToIntVal(c);
if (cval >= 0 && cval <= 9) {
got2 = 1;
while (cval >= 0 && cval <= 9) {
mul(a, a, 10);
add(a, a, cval);
mul(b, b, 10);
i++;
c = s[i];
cval = CharToIntVal(c);
}
}
}
if (got_dot && !got1 && !got2) Error("bad RR input");
ZZ e;
long got_e = 0;
long e_sign;
if (c == 'e' || c == 'E') {
got_e = 1;
i++;
c = s[i];
if (c == '-') {
e_sign = -1;
i++;
c = s[i];
}
else if (c == '+') {
e_sign = 1;
i++;
c = s[i];
}
else
e_sign = 1;
cval = CharToIntVal(c);
if (cval < 0 || cval > 9) Error("bad RR input");
e = 0;
while (cval >= 0 && cval <= 9) {
mul(e, e, 10);
add(e, e, cval);
i++;
c = s[i];
cval = CharToIntVal(c);
}
}
if (!got1 && !got2 && !got_e) Error("bad RR input");
RR t1, t2, v;
long old_p = RR::precision();
if (got1 || got2) {
ConvPrec(t1, a, max(NumBits(a), 1));
ConvPrec(t2, b, NumBits(b));
if (got_e)
RR::SetPrecision(old_p + 10);
div(v, t1, t2);
}
else
set(v);
if (sign < 0)
negate(v, v);
if (got_e) {
if (e >= NTL_OVFBND) Error("RR input overflow");
long E;
conv(E, e);
if (e_sign < 0) E = -E;
RR::SetPrecision(old_p + 10);
power(t1, to_RR(10), E);
mul(v, v, t1);
RR::prec = old_p;
}
xcopy(x, v);
}
void inv(RR& z, const RR& a)
{
static RR one = to_RR(1);
div(z, one, a);
}