void
_acb_poly_revert_series_lagrange_fast(acb_ptr Qinv, acb_srcptr Q, slong Qlen, slong n, slong prec)
{
slong i, j, k, m;
acb_ptr R, S, T, tmp;
acb_t t;
if (n <= 2)
{
if (n >= 1)
acb_zero(Qinv);
if (n == 2)
acb_inv(Qinv + 1, Q + 1, prec);
return;
}
m = n_sqrt(n);
acb_init(t);
R = _acb_vec_init((n - 1) * m);
S = _acb_vec_init(n - 1);
T = _acb_vec_init(n - 1);
acb_zero(Qinv);
acb_inv(Qinv + 1, Q + 1, prec);
_acb_poly_inv_series(Ri(1), Q + 1, FLINT_MIN(Qlen, n) - 1, n - 1, prec);
for (i = 2; i <= m; i++)
_acb_poly_mullow(Ri(i), Ri((i + 1) / 2), n - 1, Ri(i / 2), n - 1, n - 1, prec);
for (i = 2; i < m; i++)
acb_div_ui(Qinv + i, Ri(i) + i - 1, i, prec);
_acb_vec_set(S, Ri(m), n - 1);
for (i = m; i < n; i += m)
{
acb_div_ui(Qinv + i, S + i - 1, i, prec);
for (j = 1; j < m && i + j < n; j++)
{
acb_mul(t, S + 0, Ri(j) + i + j - 1, prec);
for (k = 1; k <= i + j - 1; k++)
acb_addmul(t, S + k, Ri(j) + i + j - 1 - k, prec);
acb_div_ui(Qinv + i + j, t, i + j, prec);
}
if (i + 1 < n)
{
_acb_poly_mullow(T, S, n - 1, Ri(m), n - 1, n - 1, prec);
tmp = S; S = T; T = tmp;
}
}
acb_clear(t);
_acb_vec_clear(R, (n - 1) * m);
_acb_vec_clear(S, n - 1);
_acb_vec_clear(T, n - 1);
}
void
_acb_poly_evaluate_rectangular(acb_t y, acb_srcptr poly,
slong len, const acb_t x, slong prec)
{
slong i, j, m, r;
acb_ptr xs;
acb_t s, t, c;
if (len < 3)
{
if (len == 0)
{
acb_zero(y);
}
else if (len == 1)
{
acb_set_round(y, poly + 0, prec);
}
else if (len == 2)
{
acb_mul(y, x, poly + 1, prec);
acb_add(y, y, poly + 0, prec);
}
return;
}
m = n_sqrt(len) + 1;
r = (len + m - 1) / m;
xs = _acb_vec_init(m + 1);
acb_init(s);
acb_init(t);
acb_init(c);
_acb_vec_set_powers(xs, x, m + 1, prec);
acb_set(y, poly + (r - 1) * m);
for (j = 1; (r - 1) * m + j < len; j++)
acb_addmul(y, xs + j, poly + (r - 1) * m + j, prec);
for (i = r - 2; i >= 0; i--)
{
acb_set(s, poly + i * m);
for (j = 1; j < m; j++)
acb_addmul(s, xs + j, poly + i * m + j, prec);
acb_mul(y, y, xs + m, prec);
acb_add(y, y, s, prec);
}
_acb_vec_clear(xs, m + 1);
acb_clear(s);
acb_clear(t);
acb_clear(c);
}
void
_acb_poly_compose_series_brent_kung(acb_ptr res,
acb_srcptr poly1, long len1,
acb_srcptr poly2, long len2, long n, long prec)
{
acb_mat_t A, B, C;
acb_ptr t, h;
long i, m;
if (n == 1)
{
acb_set(res, poly1);
return;
}
m = n_sqrt(n) + 1;
acb_mat_init(A, m, n);
acb_mat_init(B, m, m);
acb_mat_init(C, m, n);
h = _acb_vec_init(n);
t = _acb_vec_init(n);
/* Set rows of B to the segments of poly1 */
for (i = 0; i < len1 / m; i++)
_acb_vec_set(B->rows[i], poly1 + i*m, m);
_acb_vec_set(B->rows[i], poly1 + i*m, len1 % m);
/* Set rows of A to powers of poly2 */
acb_set_ui(A->rows[0] + 0, 1UL);
_acb_vec_set(A->rows[1], poly2, len2);
for (i = 2; i < m; i++)
_acb_poly_mullow(A->rows[i], A->rows[(i + 1) / 2], n, A->rows[i / 2], n, n, prec);
acb_mat_mul(C, B, A, prec);
/* Evaluate block composition using the Horner scheme */
_acb_vec_set(res, C->rows[m - 1], n);
_acb_poly_mullow(h, A->rows[m - 1], n, poly2, len2, n, prec);
for (i = m - 2; i >= 0; i--)
{
_acb_poly_mullow(t, res, n, h, n, n, prec);
_acb_poly_add(res, t, n, C->rows[i], n, prec);
}
_acb_vec_clear(h, n);
_acb_vec_clear(t, n);
acb_mat_clear(A);
acb_mat_clear(B);
acb_mat_clear(C);
}
int main(void)
{
int i, j, result;
flint_rand_t state;
flint_randinit(state);
printf("factor_trial_partial....");
fflush(stdout);
for (i = 0; i < 10000; i++) /* Test random numbers */
{
mp_limb_t n1, n2, prod, limit;
n_factor_t factors;
n_factor_init(&factors);
n1 = n_randtest_not_zero(state);
limit = n_sqrt(n1);
n2 = n_factor_trial_partial(&factors, n1, &prod, 10000UL, limit);
if (n1 != n2*prod)
{
printf("FAIL:\n");
printf("n1 = %lu, n2 = %lu, prod = %lu\n", n1, n2, prod);
abort();
}
for (j = 0; j < factors.num; j++)
{
n2 *= n_pow(factors.p[j], factors.exp[j]);
}
result = (n1 == n2);
if (!result)
{
printf("FAIL:\n");
printf("n1 = %lu, n2 = %lu\n", n1, n2);
abort();
}
}
flint_randclear(state);
printf("PASS\n");
return 0;
}
bool CSensorVision::SenseStimulus(CActor* pActor, CStimulus* pStimulus) const
{
if (pStimulus->Intensity <= 0.f) OK;
// Cast to stimulus visible
//!!!take size/radius into account:!
//!!!FOV & size! check pos before as faster check, if ok check bounds by FOV?
//???check visible shape, not only position point? or get radius of stimulus and check against cylinder?
//y can be projected (clamped by cylinder top & bottom)
vector3 DirToStimulus = pStimulus->Position - pActor->Position;
float SqDist = DirToStimulus.lensquared();
if (SqDist <= Radius * Radius)
{
float Confidence = pStimulus->Intensity; //!!!calc by formula, use distance!
bool IsInFOV = FOV < -0.999f; // For 360 degrees vision
if (!IsInFOV)
{
DirToStimulus /= n_sqrt(SqDist);
IsInFOV = pActor->LookatDir.dot(DirToStimulus) >= FOV;
//!!!adjust confidence by peripheral vision!
}
if (IsInFOV)
{
//!!!occlusion & line of sight! other objects can occlude this!
//partial occlusion can reduce confidence
if (Confidence > 0.f)
{
nArray<PPerceptor>::iterator ItPerceptor;
for (ItPerceptor = Perceptors.Begin(); ItPerceptor != Perceptors.End(); ItPerceptor++)
(*ItPerceptor)->ProcessStimulus(pActor, pStimulus, Confidence);
}
}
}
//???!!!if time-sliced, fail?!
OK;
}
EExecStatus CSensorVision::ValidateFact(CActor* pActor, const CMemFact& Fact) const
{
const CMemFactObstacle& Obstacle = (const CMemFactObstacle&)Fact;
if (Fact.LastUpdateTime == Fact.LastPerceptionTime &&
(!Obstacle.pSourceStimulus ||
!Obstacle.pSourceStimulus->IsActive() ||
Obstacle.pSourceStimulus->Intensity <= 0.f)) return Failure;
//!!!CODE DUPLICATION!
vector3 DirToFact = Obstacle.Position - pActor->Position;
float SqDist = DirToFact.lensquared();
if (SqDist <= Radius * Radius)
{
bool IsInFOV = FOV < -0.999f; // For 360 degrees vision
if (!IsInFOV)
{
DirToFact /= n_sqrt(SqDist);
IsInFOV = pActor->LookatDir.dot(DirToFact) >= FOV;
//!!!if peripheral vision reduces confidence to 0, skip!
}
if (IsInFOV)
{
//!!!occlusion & line of sight! other objects can occlude this!
//take into account only complete occlusion
//if (Confidence > 0.f)
return Failure;
}
}
// We didn't see source stimulus this frame, so we don't know is fact relevant
return Running;
}
void
_fmpq_poly_revert_series_lagrange_fast(fmpz * Qinv, fmpz_t den,
const fmpz * Q, const fmpz_t Qden, slong n)
{
slong i, j, k, m;
fmpz *R, *Rden, *S, *T, *dens, *tmp;
fmpz_t Sden, Tden, t;
if (fmpz_is_one(Qden) && (n > 1) && fmpz_is_pm1(Q + 1))
{
_fmpz_poly_revert_series(Qinv, Q, n);
fmpz_one(den);
return;
}
if (n <= 2)
{
fmpz_zero(Qinv);
if (n == 2)
{
fmpz_set(Qinv + 1, Qden);
fmpz_set(den, Q + 1);
_fmpq_poly_canonicalise(Qinv, den, 2);
}
return;
}
m = n_sqrt(n);
fmpz_init(t);
dens = _fmpz_vec_init(n);
R = _fmpz_vec_init((n - 1) * m);
S = _fmpz_vec_init(n - 1);
T = _fmpz_vec_init(n - 1);
Rden = _fmpz_vec_init(m);
fmpz_init(Sden);
fmpz_init(Tden);
fmpz_zero(Qinv);
fmpz_one(dens);
_fmpq_poly_inv_series(Ri(1), Rdeni(1), Q + 1, Qden, n - 1);
_fmpq_poly_canonicalise(Ri(1), Rdeni(1), n - 1);
for (i = 2; i <= m; i++)
{
_fmpq_poly_mullow(Ri(i), Rdeni(i), Ri(i-1), Rdeni(i-1), n - 1,
Ri(1), Rdeni(1), n - 1, n - 1);
_fmpq_poly_canonicalise(Ri(i), Rdeni(i), n - 1);
}
for (i = 1; i < m; i++)
{
fmpz_set(Qinv + i, Ri(i) + i - 1);
fmpz_mul_ui(dens + i, Rdeni(i), i);
}
_fmpz_vec_set(S, Ri(m), n - 1);
fmpz_set(Sden, Rdeni(m));
for (i = m; i < n; i += m)
{
fmpz_set(Qinv + i, S + i - 1);
fmpz_mul_ui(dens + i, Sden, i);
for (j = 1; j < m && i + j < n; j++)
{
fmpz_mul(t, S + 0, Ri(j) + i + j - 1);
for (k = 1; k <= i + j - 1; k++)
fmpz_addmul(t, S + k, Ri(j) + i + j - 1 - k);
fmpz_set(Qinv + i + j, t);
fmpz_mul(dens + i + j, Sden, Rdeni(j));
fmpz_mul_ui(dens + i + j, dens + i + j, i + j);
}
if (i + 1 < n)
{
_fmpq_poly_mullow(T, Tden, S, Sden, n - 1,
Ri(m), Rdeni(m), n - 1, n - 1);
_fmpq_poly_canonicalise(T, Tden, n - 1);
fmpz_swap(Tden, Sden);
tmp = S; S = T; T = tmp;
}
}
_set_vec(Qinv, den, Qinv, dens, n);
_fmpq_poly_canonicalise(Qinv, den, n);
fmpz_clear(t);
_fmpz_vec_clear(dens, n);
_fmpz_vec_clear(R, (n - 1) * m);
_fmpz_vec_clear(S, n - 1);
_fmpz_vec_clear(T, n - 1);
_fmpz_vec_clear(Rden, m);
fmpz_clear(Sden);
fmpz_clear(Tden);
}
void
acb_hypgeom_pfq_sum_fme(acb_t s, acb_t t,
acb_srcptr a, slong p, acb_srcptr b, slong q,
const acb_t z, slong n, slong prec)
{
acb_poly_t A, B, C;
acb_ptr ks, As, Bs, Cs;
acb_t u, v;
acb_ptr * tree;
slong i, k, m, w;
/* we compute to n-1 instead of n to avoid dividing by 0 in the
denominator when computing a hypergeometric polynomial
that terminates right before a pole */
if (n > 4)
{
m = n_sqrt(n - 1) / 4; /* tuning parameter */
w = (n - 1) / FLINT_MAX(m, 1);
}
else
{
m = w = 0;
}
if (m < 1 || w < 1 || p > 3 || q > 3)
{
acb_hypgeom_pfq_sum_forward(s, t, a, p, b, q, z, n, prec);
return;
}
acb_poly_init(A);
acb_poly_init(B);
acb_poly_init(C);
acb_init(u);
acb_init(v);
ks = _acb_vec_init(w);
As = _acb_vec_init(w);
Bs = _acb_vec_init(w);
Cs = _acb_vec_init(w);
bsplit(A, B, C, a, p, b, q, z, 0, m, prec);
for (i = 0; i < w; i++)
acb_set_ui(ks + i, i * m);
tree = _acb_poly_tree_alloc(w);
_acb_poly_tree_build(tree, ks, w, prec);
_acb_poly_evaluate_vec_fast_precomp(As, A->coeffs, A->length, tree, w, prec);
_acb_poly_evaluate_vec_fast_precomp(Bs, B->coeffs, B->length, tree, w, prec);
_acb_poly_evaluate_vec_fast_precomp(Cs, C->coeffs, C->length, tree, w, prec);
_acb_poly_tree_free(tree, w);
/* todo: use binary splitting here for improved numerical stability */
for (i = 1; i < w; i++)
{
acb_mul(Cs, Cs, Bs + i, prec);
acb_addmul(Cs, As, Cs + i, prec);
acb_mul(As, As, As + i, prec);
acb_mul(Bs, Bs, Bs + i, prec);
}
acb_div(s, Cs, Bs, prec);
acb_div(t, As, Bs, prec);
for (k = w * m; k < n && !acb_is_zero(t); k++)
{
acb_add(s, s, t, prec);
if (p > 0)
{
acb_add_ui(u, a, k, prec);
for (i = 1; i < p; i++)
{
acb_add_ui(v, a + i, k, prec);
acb_mul(u, u, v, prec);
}
acb_mul(t, t, u, prec);
}
if (q > 0)
{
acb_add_ui(u, b, k, prec);
for (i = 1; i < q; i++)
{
acb_add_ui(v, b + i, k, prec);
acb_mul(u, u, v, prec);
}
acb_div(t, t, u, prec);
}
acb_mul(t, t, z, prec);
}
acb_clear(u);
acb_clear(v);
_acb_vec_clear(ks, w);
_acb_vec_clear(As, w);
_acb_vec_clear(Bs, w);
_acb_vec_clear(Cs, w);
acb_poly_clear(A);
acb_poly_clear(B);
acb_poly_clear(C);
}
void CCharEntity::OnStepBefore()
{
if (IsCollisionEnabled() && !IsRagdollActive())
{
CEnvInfo EnvInfo;
vector3 Pos = GetTransform().pos_component();
Pos.y += Height;
float DistanceToGround;
if (EnvQueryMgr->GetEnvInfoAt(Pos, EnvInfo, Height + 0.1f, GetUniqueID()))
{
DistanceToGround = Pos.y - Height - EnvInfo.WorldHeight;
GroundMtl = EnvInfo.Material;
}
else
{
DistanceToGround = FLT_MAX;
GroundMtl = InvalidMaterial;
}
CRigidBody* pMasterBody = Composite->GetMasterBody();
bool BodyIsEnabled = IsEnabled();
vector3 AngularVel = pMasterBody->GetAngularVelocity();
vector3 LinearVel = pMasterBody->GetLinearVelocity();
vector3 DesiredLVelChange = DesiredLinearVel - LinearVel;
if (DistanceToGround <= 0.f)
{
// No torques now, angular velocity changes by impulse immediately to desired value
bool Actuated = DesiredAngularVel != AngularVel.y;
if (Actuated)
{
if (!BodyIsEnabled) SetEnabled(true);
pMasterBody->SetAngularVelocity(vector3(0.f, DesiredAngularVel, 0.f));
}
if (!DesiredLVelChange.isequal(vector3::Zero, 0.0001f))
{
if (!Actuated)
{
Actuated = true;
SetEnabled(true);
}
// Vertical movement for non-flying actors is impulse (jump).
// Since speed if already clamped to actor caps, we save vertical desired velocity as is.
// Spring force pushes us from below the ground.
//!!!!!!!!!!!!!!!
//!!!calc correct impulse for the spring!
//!!!!!!!!!!!!!!!
float VerticalDesVelChange = DesiredLVelChange.y - (50.0f * DistanceToGround);
float Mass = pMasterBody->GetMass();
//!!!remove calcs for Y, it is zero (optimization)!
dVector3 ODEForce;
dWorldImpulseToForce(Level->GetODEWorldID(), dReal(Level->GetStepSize()),
DesiredLVelChange.x * Mass, 0.f, DesiredLVelChange.z * Mass, ODEForce);
float SqForceMagnitude = (float)dCalcVectorLengthSquare3(ODEForce);
if (SqForceMagnitude > 0.f)
{
float MaxForceMagnitude = Mass * MaxHorizAccel;
float SqMaxForceMagnitude = MaxForceMagnitude * MaxForceMagnitude;
if (SqForceMagnitude > SqMaxForceMagnitude)
dScaleVector3(ODEForce, MaxForceMagnitude / n_sqrt(SqForceMagnitude));
dBodyAddForce(pMasterBody->GetODEBodyID(), ODEForce[0], ODEForce[1], ODEForce[2]);
}
if (VerticalDesVelChange != 0.f)
{
dWorldImpulseToForce(Level->GetODEWorldID(), dReal(Level->GetStepSize()),
0.f, VerticalDesVelChange * Mass, 0.f, ODEForce);
dBodyAddForce(pMasterBody->GetODEBodyID(), ODEForce[0], ODEForce[1], ODEForce[2]);
}
}
if (BodyIsEnabled && !Actuated && DistanceToGround > -0.002f)
{
const float FreezeThreshold = 0.00001f; //???use TINY?
bool AVelIsAlmostZero = n_fabs(AngularVel.y) < FreezeThreshold;
bool LVelIsAlmostZero = n_fabs(LinearVel.x) * (float)Level->GetStepSize() < FreezeThreshold &&
n_fabs(LinearVel.z) * (float)Level->GetStepSize() < FreezeThreshold;
if (AVelIsAlmostZero)
pMasterBody->SetAngularVelocity(vector3::Zero);
if (LVelIsAlmostZero)
pMasterBody->SetLinearVelocity(vector3::Zero);
if (AVelIsAlmostZero && LVelIsAlmostZero) SetEnabled(false);
}
}
//???!!!else (when falling) apply damping?!
}
// NOTE: do NOT call the parent class, we don't need any damping
}
mp_limb_t _ll_factor_SQUFOF(mp_limb_t n_hi, mp_limb_t n_lo, ulong max_iters)
{
mp_limb_t n[2];
mp_limb_t sqrt[2];
mp_limb_t rem[2];
mp_size_t num, sqroot, p, q;
mp_limb_t l, l2, iq, pnext;
mp_limb_t qarr[50];
mp_limb_t qupto, qlast, t, r = 0;
ulong i, j;
n[0] = n_lo;
n[1] = n_hi;
if (n_hi) num = mpn_sqrtrem(sqrt, rem, n, 2);
else num = ((sqrt[0] = n_sqrtrem(rem, n_lo)) != 0UL);
sqroot = sqrt[0];
p = sqroot;
q = rem[0];
if ((q == 0) || (num == 0))
{
return sqroot;
}
l = 1 + 2*n_sqrt(2*p);
l2 = l/2;
qupto = 0;
qlast = 1;
for (i = 0; i < max_iters; i++)
{
iq = (sqroot + p)/q;
pnext = iq*q - p;
if (q <= l)
{
if ((q & 1UL) == 0UL)
{
qarr[qupto] = q/2;
qupto++;
if (qupto >= 50UL) return 0UL;
} else if (q <= l2)
{
qarr[qupto] = q;
qupto++;
if (qupto >= 50UL) return 0UL;
}
}
t = qlast + iq*(p - pnext);
qlast = q;
q = t;
p = pnext;
if ((i & 1) == 1) continue;
if (!n_is_square(q)) continue;
r = n_sqrt(q);
if (qupto == 0UL) break;
for (j = 0; j < qupto; j++)
if (r == qarr[j]) goto cont;
break;
cont: ;
if (r == 1UL) return 0UL;
}
if (i == max_iters) return 0UL; /* taken too long, give up */
qlast = r;
p = p + r*((sqroot - p)/r);
umul_ppmm(rem[1], rem[0], p, p);
sub_ddmmss(sqrt[1], sqrt[0], n[1], n[0], rem[1], rem[0]);
if (sqrt[1])
{
int norm;
count_leading_zeros(norm, qlast);
udiv_qrnnd(q, rem[0], (sqrt[1] << norm) + r_shift(sqrt[0], FLINT_BITS - norm), sqrt[0] << norm, qlast << norm);
rem[0] >>= norm;
}
else
{
void
gamma_rising_fmprb_ui_delta(fmprb_t y, const fmprb_t x, ulong n, ulong m, long prec)
{
fmprb_ptr xs;
fmprb_t t, u, v;
ulong i, k, rem;
fmpz_t c, h;
fmpz *s, *d;
long wp;
if (n == 0)
{
fmprb_one(y);
return;
}
if (n == 1)
{
fmprb_set_round(y, x, prec);
return;
}
wp = FMPR_PREC_ADD(prec, FLINT_BIT_COUNT(n));
fmprb_init(t);
fmprb_init(u);
fmprb_init(v);
fmpz_init(c);
fmpz_init(h);
if (m == 0)
{
ulong m1, m2;
m1 = 0.2 * pow(wp, 0.4);
m2 = n_sqrt(n);
m = FLINT_MIN(m1, m2);
}
m = FLINT_MIN(m, n);
m = FLINT_MAX(m, 1);
xs = _fmprb_vec_init(m + 1);
d = _fmpz_vec_init(m * m);
s = _fmpz_vec_init(m + 1);
_fmprb_vec_set_powers(xs, x, m + 1, wp);
rising_difference_polynomial(s, d, m);
/* tail */
rem = m;
while (rem + m <= n)
rem += m;
fmprb_one(y);
for (k = rem; k < n; k++)
{
fmprb_add_ui(t, xs + 1, k, wp);
fmprb_mul(y, y, t, wp);
}
/* initial rising factorial */
fmprb_zero(t);
for (i = 1; i <= m; i++)
fmprb_addmul_fmpz(t, xs + i, s + i, wp);
fmprb_mul(y, y, t, wp);
/* the leading coefficient is always the same */
fmprb_mul_fmpz(xs + m - 1, xs + m - 1, d + m - 1 + 0, wp);
for (k = 0; k + 2 * m <= n; k += m)
{
for (i = 0; i < m - 1; i++)
{
fmpz_set_ui(h, k);
_fmpz_poly_evaluate_horner_fmpz(c, d + i * m, m - i, h);
if (i == 0)
fmprb_add_fmpz(t, t, c, wp);
else
fmprb_addmul_fmpz(t, xs + i, c, wp);
}
fmprb_add(t, t, xs + m - 1, wp);
fmprb_mul(y, y, t, wp);
}
fmprb_set_round(y, y, prec);
fmprb_clear(t);
fmprb_clear(u);
fmprb_clear(v);
_fmprb_vec_clear(xs, m + 1);
_fmpz_vec_clear(d, m * m);
_fmpz_vec_clear(s, m + 1);
fmpz_clear(c);
fmpz_clear(h);
}
void
_qseive(const mp_limb_t n, const mp_limb_t B)
{
nmod_sparse_mat_t M;
mp_limb_t quad, *quads, *xs, x, i = 0, j, piB = n_prime_pi(B);
const mp_limb_t * ps = n_primes_arr_readonly(piB + 2);
const double * pinvs = n_prime_inverses_arr_readonly(piB + 2);
mzd_t *K;
/* init */
quads = (mp_limb_t *)malloc((piB + 1)*sizeof(mp_limb_t *));
xs = (mp_limb_t *)malloc((piB + 1)*sizeof(mp_limb_t *));
K = mzd_init(piB + 1, 1);
nmod_sparse_mat_init(M, piB + 1, piB + 1, 2);
printf("init done\n");
printf("using %ld primes\n", piB);
/* seive */
for (x = n_sqrt(n), i = 0; i <= piB; x++)
{
quad = x*x - n;
if (quad == 0)
continue;
for (j = 0; j < piB; j++)
n_remove2_precomp(&quad, ps[j], pinvs[j]);
if (quad == 1) /* was B-smooth */
{
quads[i] = x*x - n;
quad = x*x - n;
for (j = 0; j < piB; j++)
{
if (n_remove2_precomp(&quad, ps[j], pinvs[j]) % 2)
_nmod_sparse_mat_set_entry(M, j, i, M->row_supports[j], 1);
}
xs[i] = x;
i++;
}
}
printf("data collection done\n");
n_cleanup_primes();
_bw(K, M, 1, 2, 7, 7);
printf("procesing complete\n");
mzd_print(K);
int done = 0;
for (j = 0; !done; j++)
{
fmpz_t a, b, diff, N;
fmpz_init_set_ui(a, 1);
fmpz_init_set_ui(b, 1);
fmpz_init_set_ui(N, n);
fmpz_init(diff);
for (i = 0; i < piB; i++)
{
if (mzd_read_bit(K, i, j))
{
fmpz_mul_ui(a, a, xs[i]);
fmpz_mul_ui(b, b, quads[i]);
}
}
assert(fmpz_is_square(b));
fmpz_sqrt(b, b);
if (fmpz_mod_ui(a, a, n) != fmpz_mod_ui(b, b, n) && fmpz_mod_ui(a, a, n) != n - fmpz_mod_ui(b, b, n))
{
done = 1;
fmpz_print(a);
printf("\n");
fmpz_print(b);
printf("\n");
fmpz_sub(diff, a, b);
fmpz_gcd(a, diff, N);
fmpz_divexact(b, N, a);
fmpz_print(a);
printf("\n");
fmpz_print(b);
}
fmpz_clear(a);
fmpz_clear(b);
fmpz_clear(N);
fmpz_clear(diff);
}
/* cleanup */
free(quads);
free(xs);
mzd_free(K);
nmod_sparse_mat_clear(M);
return;
}
void
acb_hypgeom_pfq_sum_rs(acb_t res, acb_t term, acb_srcptr a, slong p,
acb_srcptr b, slong q, const acb_t z, slong n, slong prec)
{
acb_ptr zpow;
acb_t s, t, u;
slong i, j, k, m;
mag_t B, C;
if (n == 0)
{
acb_zero(res);
acb_one(term);
return;
}
if (n < 0)
abort();
m = n_sqrt(n);
m = FLINT_MIN(m, 150);
mag_init(B);
mag_init(C);
acb_init(s);
acb_init(t);
acb_init(u);
zpow = _acb_vec_init(m + 1);
_acb_vec_set_powers(zpow, z, m + 1, prec);
mag_one(B);
for (k = n; k >= 0; k--)
{
j = k % m;
if (k < n)
acb_add(s, s, zpow + j, prec);
if (k > 0)
{
if (p > 0)
{
acb_add_ui(u, a, k - 1, prec);
for (i = 1; i < p; i++)
{
acb_add_ui(t, a + i, k - 1, prec);
acb_mul(u, u, t, prec);
}
if (k < n)
acb_mul(s, s, u, prec);
acb_get_mag(C, u);
mag_mul(B, B, C);
}
if (q > 0)
{
acb_add_ui(u, b, k - 1, prec);
for (i = 1; i < q; i++)
{
acb_add_ui(t, b + i, k - 1, prec);
acb_mul(u, u, t, prec);
}
if (k < n)
acb_div(s, s, u, prec);
acb_get_mag_lower(C, u);
mag_div(B, B, C);
}
if (j == 0 && k < n)
{
acb_mul(s, s, zpow + m, prec);
}
}
}
acb_get_mag(C, z);
mag_pow_ui(C, C, n);
mag_mul(B, B, C);
acb_zero(term);
if (_acb_vec_is_real(a, p) && _acb_vec_is_real(b, q) && acb_is_real(z))
arb_add_error_mag(acb_realref(term), B);
else
acb_add_error_mag(term, B);
acb_set(res, s);
mag_clear(B);
mag_clear(C);
acb_clear(s);
acb_clear(t);
acb_clear(u);
_acb_vec_clear(zpow, m + 1);
}
slong
_acb_poly_find_roots(acb_ptr roots,
acb_srcptr poly,
acb_srcptr initial, slong len, slong maxiter, slong prec)
{
slong iter, i, deg;
slong rootmag, max_rootmag, correction, max_correction;
deg = len - 1;
if (deg == 0)
{
return 0;
}
else if (acb_contains_zero(poly + len - 1))
{
/* if the leading coefficient contains zero, roots can be anywhere */
for (i = 0; i < deg; i++)
{
arb_zero_pm_inf(acb_realref(roots + i));
arb_zero_pm_inf(acb_imagref(roots + i));
}
return 0;
}
else if (deg == 1)
{
acb_inv(roots + 0, poly + 1, prec);
acb_mul(roots + 0, roots + 0, poly + 0, prec);
acb_neg(roots + 0, roots + 0);
return 1;
}
if (initial == NULL)
_acb_poly_roots_initial_values(roots, deg, prec);
else
_acb_vec_set(roots, initial, deg);
if (maxiter == 0)
maxiter = 2 * deg + n_sqrt(prec);
for (iter = 0; iter < maxiter; iter++)
{
max_rootmag = -ARF_PREC_EXACT;
for (i = 0; i < deg; i++)
{
rootmag = _acb_get_mid_mag(roots + i);
max_rootmag = FLINT_MAX(rootmag, max_rootmag);
}
_acb_poly_refine_roots_durand_kerner(roots, poly, len, prec);
max_correction = -ARF_PREC_EXACT;
for (i = 0; i < deg; i++)
{
correction = _acb_get_rad_mag(roots + i);
max_correction = FLINT_MAX(correction, max_correction);
}
/* estimate the correction relative to the whole set of roots */
max_correction -= max_rootmag;
/* flint_printf("ITER %wd MAX CORRECTION: %wd\n", iter, max_correction); */
if (max_correction < -prec / 2)
maxiter = FLINT_MIN(maxiter, iter + 2);
else if (max_correction < -prec / 3)
maxiter = FLINT_MIN(maxiter, iter + 3);
else if (max_correction < -prec / 4)
maxiter = FLINT_MIN(maxiter, iter + 4);
}
return _acb_poly_validate_roots(roots, poly, len, prec);
}
void
_acb_poly_powsum_one_series_sieved(acb_ptr z, const acb_t s, slong n, slong len, slong prec)
{
slong * divisors;
slong powers_alloc;
slong i, j, k, ibound, kprev, power_of_two, horner_point;
int critical_line, integer;
acb_ptr powers;
acb_ptr t, u, x;
acb_ptr p1, p2;
arb_t logk, v, w;
critical_line = arb_is_exact(acb_realref(s)) &&
(arf_cmp_2exp_si(arb_midref(acb_realref(s)), -1) == 0);
integer = arb_is_zero(acb_imagref(s)) && arb_is_int(acb_realref(s));
divisors = flint_calloc(n / 2 + 1, sizeof(slong));
powers_alloc = (n / 6 + 1) * len;
powers = _acb_vec_init(powers_alloc);
ibound = n_sqrt(n);
for (i = 3; i <= ibound; i += 2)
if (DIVISOR(i) == 0)
for (j = i * i; j <= n; j += 2 * i)
DIVISOR(j) = i;
t = _acb_vec_init(len);
u = _acb_vec_init(len);
x = _acb_vec_init(len);
arb_init(logk);
arb_init(v);
arb_init(w);
power_of_two = 1;
while (power_of_two * 2 <= n)
power_of_two *= 2;
horner_point = n / power_of_two;
_acb_vec_zero(z, len);
kprev = 0;
COMPUTE_POWER(x, 2, kprev);
for (k = 1; k <= n; k += 2)
{
/* t = k^(-s) */
if (DIVISOR(k) == 0)
{
COMPUTE_POWER(t, k, kprev);
}
else
{
p1 = POWER(DIVISOR(k));
p2 = POWER(k / DIVISOR(k));
if (len == 1)
acb_mul(t, p1, p2, prec);
else
_acb_poly_mullow(t, p1, len, p2, len, len, prec);
}
if (k * 3 <= n)
_acb_vec_set(POWER(k), t, len);
_acb_vec_add(u, u, t, len, prec);
while (k == horner_point && power_of_two != 1)
{
_acb_poly_mullow(t, z, len, x, len, len, prec);
_acb_vec_add(z, t, u, len, prec);
power_of_two /= 2;
horner_point = n / power_of_two;
horner_point -= (horner_point % 2 == 0);
}
}
_acb_poly_mullow(t, z, len, x, len, len, prec);
_acb_vec_add(z, t, u, len, prec);
flint_free(divisors);
_acb_vec_clear(powers, powers_alloc);
_acb_vec_clear(t, len);
_acb_vec_clear(u, len);
_acb_vec_clear(x, len);
arb_clear(logk);
arb_clear(v);
arb_clear(w);
}
void
_fmprb_poly_evaluate2_rectangular(fmprb_t y, fmprb_t z, fmprb_srcptr poly,
long len, const fmprb_t x, long prec)
{
long i, j, m, r;
fmprb_ptr xs;
fmprb_t s, t, c;
if (len < 3)
{
if (len == 0)
{
fmprb_zero(y);
fmprb_zero(z);
}
else if (len == 1)
{
fmprb_set_round(y, poly + 0, prec);
fmprb_zero(z);
}
else if (len == 2)
{
fmprb_mul(y, x, poly + 1, prec);
fmprb_add(y, y, poly + 0, prec);
fmprb_set_round(z, poly + 1, prec);
}
return;
}
m = n_sqrt(len) + 1;
m *= 1;
r = (len + m - 1) / m;
xs = _fmprb_vec_init(m + 1);
fmprb_init(s);
fmprb_init(t);
fmprb_init(c);
_fmprb_vec_set_powers(xs, x, m + 1, prec);
fmprb_set(y, poly + (r - 1) * m);
for (j = 1; (r - 1) * m + j < len; j++)
fmprb_addmul(y, xs + j, poly + (r - 1) * m + j, prec);
for (i = r - 2; i >= 0; i--)
{
fmprb_set(s, poly + i * m);
for (j = 1; j < m; j++)
fmprb_addmul(s, xs + j, poly + i * m + j, prec);
fmprb_mul(y, y, xs + m, prec);
fmprb_add(y, y, s, prec);
}
len -= 1;
r = (len + m - 1) / m;
fmprb_mul_ui(z, poly + (r - 1) * m + 1, (r - 1) * m + 1, FMPR_PREC_EXACT);
for (j = 1; (r - 1) * m + j < len; j++)
{
fmprb_mul_ui(c, poly + (r - 1) * m + j + 1, (r - 1) * m + j + 1, FMPR_PREC_EXACT);
fmprb_addmul(z, xs + j, c, prec);
}
for (i = r - 2; i >= 0; i--)
{
fmprb_mul_ui(s, poly + i * m + 1, i * m + 1, FMPR_PREC_EXACT);
for (j = 1; j < m; j++)
{
fmprb_mul_ui(c, poly + i * m + j + 1, i * m + j + 1, FMPR_PREC_EXACT);
fmprb_addmul(s, xs + j, c, prec);
}
fmprb_mul(z, z, xs + m, prec);
fmprb_add(z, z, s, prec);
}
_fmprb_vec_clear(xs, m + 1);
fmprb_clear(s);
fmprb_clear(t);
fmprb_clear(c);
}
void
arb_rising2_ui_rs(arb_t u, arb_t v,
const arb_t x, ulong n, ulong m, slong prec)
{
if (n == 0)
{
arb_zero(v);
arb_one(u);
}
else if (n == 1)
{
arb_set(u, x);
arb_one(v);
}
else
{
slong wp;
ulong i, j, a, b;
arb_ptr xs;
arb_t S, T, U, V;
fmpz *A, *B;
wp = ARF_PREC_ADD(prec, FLINT_BIT_COUNT(n));
if (m == 0)
{
ulong m1, m2;
m1 = 0.6 * pow(wp, 0.4);
m2 = n_sqrt(n);
m = FLINT_MIN(m1, m2);
}
m = FLINT_MAX(m, 1);
xs = _arb_vec_init(m + 1);
A = _fmpz_vec_init(2 * m + 1);
B = A + (m + 1);
arb_init(S);
arb_init(T);
arb_init(U);
arb_init(V);
_arb_vec_set_powers(xs, x, m + 1, wp);
for (i = 0; i < n; i += m)
{
a = i;
b = FLINT_MIN(n, a + m);
if (a == 0 || b != a + m)
{
_gamma_rf_bsplit(A, a, b);
}
else
{
fmpz tt = m;
_fmpz_poly_taylor_shift(A, &tt, m + 1);
}
_fmpz_poly_derivative(B, A, b - a + 1);
arb_set_fmpz(S, A);
for (j = 1; j <= b - a; j++)
arb_addmul_fmpz(S, xs + j, A + j, wp);
arb_set_fmpz(T, B);
for (j = 1; j < b - a; j++)
arb_addmul_fmpz(T, xs + j, B + j, wp);
if (i == 0)
{
arb_set(U, S);
arb_set(V, T);
}
else
{
arb_mul(V, V, S, wp);
arb_addmul(V, U, T, wp);
arb_mul(U, U, S, wp);
}
}
arb_set(u, U);
arb_set(v, V);
_arb_vec_clear(xs, m + 1);
_fmpz_vec_clear(A, 2 * m + 1);
arb_clear(S);
arb_clear(T);
arb_clear(U);
arb_clear(V);
}
}
/* evaluates the truncated Taylor series (assumes no aliasing) */
void
_arb_mat_exp_taylor(arb_mat_t S, const arb_mat_t A, slong N, slong prec)
{
if (N == 1)
{
arb_mat_one(S);
}
else if (N == 2)
{
arb_mat_one(S);
arb_mat_add(S, S, A, prec);
}
else if (N == 3)
{
arb_mat_t T;
arb_mat_init(T, arb_mat_nrows(A), arb_mat_nrows(A));
arb_mat_mul(T, A, A, prec);
arb_mat_scalar_mul_2exp_si(T, T, -1);
arb_mat_add(S, A, T, prec);
arb_mat_one(T);
arb_mat_add(S, S, T, prec);
arb_mat_clear(T);
}
else
{
slong i, lo, hi, m, w, dim;
arb_mat_struct * pows;
arb_mat_t T, U;
fmpz_t c, f;
dim = arb_mat_nrows(A);
m = n_sqrt(N);
w = (N + m - 1) / m;
fmpz_init(c);
fmpz_init(f);
pows = flint_malloc(sizeof(arb_mat_t) * (m + 1));
arb_mat_init(T, dim, dim);
arb_mat_init(U, dim, dim);
for (i = 0; i <= m; i++)
{
arb_mat_init(pows + i, dim, dim);
if (i == 0)
arb_mat_one(pows + i);
else if (i == 1)
arb_mat_set(pows + i, A);
else
arb_mat_mul(pows + i, pows + i - 1, A, prec);
}
arb_mat_zero(S);
fmpz_one(f);
for (i = w - 1; i >= 0; i--)
{
lo = i * m;
hi = FLINT_MIN(N - 1, lo + m - 1);
arb_mat_zero(T);
fmpz_one(c);
while (hi >= lo)
{
arb_mat_scalar_addmul_fmpz(T, pows + hi - lo, c, prec);
if (hi != 0)
fmpz_mul_ui(c, c, hi);
hi--;
}
arb_mat_mul(U, pows + m, S, prec);
arb_mat_scalar_mul_fmpz(S, T, f, prec);
arb_mat_add(S, S, U, prec);
fmpz_mul(f, f, c);
}
arb_mat_scalar_div_fmpz(S, S, f, prec);
fmpz_clear(c);
fmpz_clear(f);
for (i = 0; i <= m; i++)
arb_mat_clear(pows + i);
flint_free(pows);
arb_mat_clear(T);
arb_mat_clear(U);
}
}
void
_nmod_poly_compose_mod_brent_kung(mp_ptr res, mp_srcptr poly1, long len1,
mp_srcptr poly2,
mp_srcptr poly3, long len3, nmod_t mod)
{
nmod_mat_t A, B, C;
mp_ptr t, h;
long i, n, m;
n = len3 - 1;
if (len3 == 1)
return;
if (len1 == 1)
{
res[0] = poly1[0];
return;
}
if (len3 == 2)
{
res[0] = _nmod_poly_evaluate_nmod(poly1, len1, poly2[0], mod);
return;
}
m = n_sqrt(n) + 1;
nmod_mat_init(A, m, n, mod.n);
nmod_mat_init(B, m, m, mod.n);
nmod_mat_init(C, m, n, mod.n);
h = _nmod_vec_init(n);
t = _nmod_vec_init(n);
/* Set rows of B to the segments of poly1 */
for (i = 0; i < len1 / m; i++)
_nmod_vec_set(B->rows[i], poly1 + i*m, m);
_nmod_vec_set(B->rows[i], poly1 + i*m, len1 % m);
/* Set rows of A to powers of poly2 */
A->rows[0][0] = 1UL;
_nmod_vec_set(A->rows[1], poly2, n);
for (i = 2; i < m; i++)
_nmod_poly_mulmod(A->rows[i], A->rows[i-1],
n, poly2, n, poly3, len3, mod);
nmod_mat_mul(C, B, A);
/* Evaluate block composition using the Horner scheme */
_nmod_vec_set(res, C->rows[m - 1], n);
_nmod_poly_mulmod(h, A->rows[m - 1], n, poly2, n, poly3, len3, mod);
for (i = m - 2; i >= 0; i--)
{
_nmod_poly_mulmod(t, res, n, h, n, poly3, len3, mod);
_nmod_poly_add(res, t, n, C->rows[i], n, mod);
}
_nmod_vec_clear(h);
_nmod_vec_clear(t);
nmod_mat_clear(A);
nmod_mat_clear(B);
nmod_mat_clear(C);
}
