void
_arb_poly_log1p_series(arb_ptr res, arb_srcptr f, slong flen, slong n, slong prec)
{
arb_t a;
flen = FLINT_MIN(flen, n);
arb_init(a);
arb_log1p(a, f, prec);
if (flen == 1)
{
_arb_vec_zero(res + 1, n - 1);
}
else if (n == 2)
{
arb_add_ui(res, f + 0, 1, prec);
arb_div(res + 1, f + 1, res + 0, prec);
}
else if (_arb_vec_is_zero(f + 1, flen - 2)) /* f = a + bx^d */
{
slong i, j, d = flen - 1;
arb_add_ui(res, f + 0, 1, prec);
for (i = 1, j = d; j < n; j += d, i++)
{
if (i == 1)
arb_div(res + j, f + d, res, prec);
else
arb_mul(res + j, res + j - d, res + d, prec);
_arb_vec_zero(res + j - d + 1, flen - 2);
}
_arb_vec_zero(res + j - d + 1, n - (j - d + 1));
for (i = 2, j = 2 * d; j < n; j += d, i++)
arb_div_si(res + j, res + j, i % 2 ? i : -i, prec);
}
else
{
arb_ptr f_diff, f_inv;
slong alloc;
alloc = n + flen;
f_inv = _arb_vec_init(alloc);
f_diff = f_inv + n;
arb_add_ui(f_diff, f, 1, prec);
_arb_vec_set(f_diff + 1, f + 1, flen - 1);
_arb_poly_inv_series(f_inv, f_diff, flen, n, prec);
_arb_poly_derivative(f_diff, f, flen, prec);
_arb_poly_mullow(res, f_inv, n - 1, f_diff, flen - 1, n - 1, prec);
_arb_poly_integral(res, res, n, prec);
_arb_vec_clear(f_inv, alloc);
}
arb_swap(res, a);
arb_clear(a);
}
void
_arb_poly_sinh_cosh_series(arb_ptr s, arb_ptr c, const arb_srcptr h, slong hlen, slong n, slong prec)
{
hlen = FLINT_MIN(hlen, n);
if (hlen == 1)
{
arb_sinh_cosh(s, c, h, prec);
_arb_vec_zero(s + 1, n - 1);
_arb_vec_zero(c + 1, n - 1);
}
else if (n == 2)
{
arb_t t;
arb_init(t);
arb_set(t, h + 1);
arb_sinh_cosh(s, c, h, prec);
arb_mul(s + 1, c, t, prec);
arb_mul(c + 1, s, t, prec);
arb_clear(t);
}
else if (hlen < 60 || n < 120)
_arb_poly_sinh_cosh_series_basecase(s, c, h, hlen, n, prec);
else
_arb_poly_sinh_cosh_series_exponential(s, c, h, hlen, n, prec);
}
void
_arb_poly_sin_cos_pi_series(arb_ptr s, arb_ptr c, arb_srcptr h, slong hlen, slong n, slong prec)
{
hlen = FLINT_MIN(hlen, n);
if (hlen == 1)
{
arb_sin_cos_pi(s, c, h, prec);
_arb_vec_zero(s + 1, n - 1);
_arb_vec_zero(c + 1, n - 1);
}
else if (n == 2)
{
arb_t t;
arb_init(t);
arb_const_pi(t, prec);
arb_mul(t, t, h + 1, prec);
arb_sin_cos_pi(s, c, h, prec);
arb_mul(s + 1, c, t, prec);
arb_neg(t, t);
arb_mul(c + 1, s, t, prec);
arb_clear(t);
}
else if (hlen < TANGENT_CUTOFF)
_arb_poly_sin_cos_series_basecase(s, c, h, hlen, n, prec, 1);
else
_arb_poly_sin_cos_series_tangent(s, c, h, hlen, n, prec, 1);
}
void
_arb_poly_sinh_cosh_series_exponential(arb_ptr s, arb_ptr c,
const arb_srcptr h, slong hlen, slong len, slong prec)
{
arb_ptr t, u, v;
arb_t s0, c0;
hlen = FLINT_MIN(hlen, len);
if (hlen == 1)
{
arb_sinh_cosh(s, c, h, prec);
_arb_vec_zero(s + 1, len - 1);
_arb_vec_zero(c + 1, len - 1);
return;
}
arb_init(s0);
arb_init(c0);
t = _arb_vec_init(3 * len);
u = t + len;
v = u + len;
arb_sinh_cosh(s0, c0, h, prec);
_arb_vec_set(t + 1, h + 1, hlen - 1);
_arb_poly_exp_series(t, t, len, len, prec);
/* todo: part of the inverse could be avoided since exp computes
it internally to half the length */
_arb_poly_inv_series(u, t, len, len, prec);
/* hyperbolic sine */
_arb_vec_sub(s, t, u, len, prec);
_arb_vec_scalar_mul_2exp_si(s, s, len, -1);
/* hyperbolic cosine */
_arb_vec_add(c, t, u, len, prec);
_arb_vec_scalar_mul_2exp_si(c, c, len, -1);
/* sinh(h0 + h1) = cosh(h0) sinh(h1) + sinh(h0) cosh(h1)
cosh(h0 + h1) = cosh(h0) cosh(h1) + sinh(h0) sinh(h1) */
if (!arb_is_zero(s0))
{
_arb_vec_scalar_mul(t, s, len, c0, prec);
_arb_vec_scalar_mul(u, c, len, s0, prec);
_arb_vec_scalar_mul(v, s, len, s0, prec);
_arb_vec_add(s, t, u, len, prec);
_arb_vec_scalar_mul(t, c, len, c0, prec);
_arb_vec_add(c, t, v, len, prec);
}
_arb_vec_clear(t, 3 * len);
arb_clear(s0);
arb_clear(c0);
}
void
_arb_poly_sqrt_series(arb_ptr g,
arb_srcptr h, long hlen, long len, long prec)
{
hlen = FLINT_MIN(hlen, len);
if (hlen == 1)
{
arb_sqrt(g, h, prec);
_arb_vec_zero(g + 1, len - 1);
}
else if (len == 2)
{
arb_sqrt(g, h, prec);
arb_div(g + 1, h + 1, h, prec);
arb_mul(g + 1, g + 1, g, prec);
arb_mul_2exp_si(g + 1, g + 1, -1);
}
else
{
arb_ptr t;
t = _arb_vec_init(len);
_arb_poly_rsqrt_series(t, h, hlen, len, prec);
_arb_poly_mullow(g, t, len, h, hlen, len, prec);
_arb_vec_clear(t, len);
}
}
void
_arb_poly_sinh_series(arb_ptr g, arb_srcptr h, slong hlen, slong n, slong prec)
{
hlen = FLINT_MIN(hlen, n);
if (hlen == 1)
{
arb_sinh(g, h, prec);
_arb_vec_zero(g + 1, n - 1);
}
else if (n == 2)
{
arb_t t;
arb_init(t);
arb_sinh_cosh(g, t, h, prec);
arb_mul(g + 1, h + 1, t, prec); /* safe since hlen >= 2 */
arb_clear(t);
}
else
{
arb_ptr t = _arb_vec_init(n);
_arb_poly_sinh_cosh_series(g, t, h, hlen, n, prec);
_arb_vec_clear(t, n);
}
}
void
_arb_poly_sinh_cosh_series_basecase(arb_ptr s, arb_ptr c, arb_srcptr h, slong hlen,
slong n, slong prec)
{
slong j, k, alen = FLINT_MIN(n, hlen);
arb_ptr a;
arb_t t, u;
arb_sinh_cosh(s, c, h, prec);
if (hlen == 1)
{
_arb_vec_zero(s + 1, n - 1);
_arb_vec_zero(c + 1, n - 1);
return;
}
arb_init(t);
arb_init(u);
a = _arb_vec_init(alen);
for (k = 1; k < alen; k++)
arb_mul_ui(a + k, h + k, k, prec);
for (k = 1; k < n; k++)
{
arb_zero(t);
arb_zero(u);
for (j = 1; j < FLINT_MIN(k + 1, hlen); j++)
{
arb_addmul(t, a + j, s + k - j, prec);
arb_addmul(u, a + j, c + k - j, prec);
}
arb_div_ui(c + k, t, k, prec);
arb_div_ui(s + k, u, k, prec);
}
arb_clear(t);
arb_clear(u);
_arb_vec_clear(a, alen);
}
void
_arb_poly_sin_cos_series(arb_ptr s, arb_ptr c, arb_srcptr h, slong hlen, slong n, slong prec)
{
hlen = FLINT_MIN(hlen, n);
if (hlen == 1)
{
arb_sin_cos(s, c, h, prec);
_arb_vec_zero(s + 1, n - 1);
_arb_vec_zero(c + 1, n - 1);
}
else if (n == 2)
{
arb_t t;
arb_init(t);
arb_set(t, h + 1);
arb_sin_cos(s, c, h, prec);
arb_mul(s + 1, c, t, prec);
arb_neg(t, t);
arb_mul(c + 1, s, t, prec);
arb_clear(t);
}
else
{
slong cutoff;
if (prec <= 128)
{
cutoff = 1400;
}
else
{
cutoff = 100000 / pow(log(prec), 3);
cutoff = FLINT_MIN(cutoff, 700);
}
if (hlen < cutoff)
_arb_poly_sin_cos_series_basecase(s, c, h, hlen, n, prec, 0);
else
_arb_poly_sin_cos_series_tangent(s, c, h, hlen, n, prec, 0);
}
}
void
arb_poly_set_coeff_arb(arb_poly_t poly, long n, const arb_t x)
{
arb_poly_fit_length(poly, n + 1);
if (n + 1 > poly->length)
{
_arb_vec_zero(poly->coeffs + poly->length, n - poly->length);
poly->length = n + 1;
}
arb_set(poly->coeffs + n, x);
_arb_poly_normalise(poly);
}
void
_arb_poly_tan_series(arb_ptr g,
arb_srcptr h, slong hlen, slong len, slong prec)
{
hlen = FLINT_MIN(hlen, len);
if (hlen == 1)
{
arb_tan(g, h, prec);
_arb_vec_zero(g + 1, len - 1);
}
else if (len == 2)
{
arb_t t;
arb_init(t);
arb_tan(g, h, prec);
arb_mul(t, g, g, prec);
arb_add_ui(t, t, 1, prec);
arb_mul(g + 1, t, h + 1, prec); /* safe since hlen >= 2 */
arb_clear(t);
}
else
{
arb_ptr t, u;
t = _arb_vec_init(2 * len);
u = t + len;
NEWTON_INIT(TAN_NEWTON_CUTOFF, len)
NEWTON_BASECASE(n)
_arb_poly_sin_cos_series_basecase(t, u, h, hlen, n, prec, 0);
_arb_poly_div_series(g, t, n, u, n, n, prec);
NEWTON_END_BASECASE
NEWTON_LOOP(m, n)
_arb_poly_mullow(u, g, m, g, m, n, prec);
arb_add_ui(u, u, 1, prec);
_arb_poly_atan_series(t, g, m, n, prec);
_arb_poly_sub(t + m, h + m, FLINT_MAX(0, hlen - m), t + m, n - m, prec);
_arb_poly_mullow(g + m, u, n, t + m, n - m, n - m, prec);
NEWTON_END_LOOP
NEWTON_END
_arb_vec_clear(t, 2 * len);
}
}
/* compose by poly2 = a*x^n + c, no aliasing; n >= 1 */
void
_arb_poly_compose_axnc(arb_ptr res, arb_srcptr poly1, slong len1,
const arb_t c, const arb_t a, slong n, slong prec)
{
slong i;
_arb_vec_set_round(res, poly1, len1, prec);
/* shift by c (c = 0 case will be fast) */
_arb_poly_taylor_shift(res, c, len1, prec);
/* multiply by powers of a */
if (!arb_is_one(a))
{
if (arb_equal_si(a, -1))
{
for (i = 1; i < len1; i += 2)
arb_neg(res + i, res + i);
}
else if (len1 == 2)
{
arb_mul(res + 1, res + 1, a, prec);
}
else
{
arb_t t;
arb_init(t);
arb_set(t, a);
for (i = 1; i < len1; i++)
{
arb_mul(res + i, res + i, t, prec);
if (i + 1 < len1)
arb_mul(t, t, a, prec);
}
arb_clear(t);
}
}
/* stretch */
for (i = len1 - 1; i >= 1 && n > 1; i--)
{
arb_swap(res + i * n, res + i);
_arb_vec_zero(res + (i - 1) * n + 1, n - 1);
}
}
void
_arb_poly_compose_series(arb_ptr res, arb_srcptr poly1, slong len1,
arb_srcptr poly2, slong len2, slong n, slong prec)
{
if (len2 == 1)
{
arb_set_round(res, poly1, prec);
_arb_vec_zero(res + 1, n - 1);
}
else if (_arb_vec_is_zero(poly2 + 1, len2 - 2)) /* poly2 is a monomial */
{
slong i, j;
arb_t t;
arb_init(t);
arb_set(t, poly2 + len2 - 1);
arb_set_round(res, poly1, prec);
for (i = 1, j = len2 - 1; i < len1 && j < n; i++, j += len2 - 1)
{
arb_mul(res + j, poly1 + i, t, prec);
if (i + 1 < len1 && j + len2 - 1 < n)
arb_mul(t, t, poly2 + len2 - 1, prec);
}
if (len2 != 2)
for (i = 1; i < n; i++)
if (i % (len2 - 1) != 0)
arb_zero(res + i);
arb_clear(t);
}
else if (len1 < 6 || n < 6)
{
_arb_poly_compose_series_horner(res, poly1, len1, poly2, len2, n, prec);
}
else
{
_arb_poly_compose_series_brent_kung(res, poly1, len1, poly2, len2, n, prec);
}
}
void
_arb_poly_rising_ui_series(arb_ptr res,
arb_srcptr f, slong flen, ulong r,
slong trunc, slong prec)
{
if (trunc == 1 || flen == 1)
{
arb_rising_ui(res, f, r, prec);
_arb_vec_zero(res + 1, trunc - 1);
}
else if (trunc == 2)
{
arb_rising2_ui(res, res + 1, f, r, prec);
arb_mul(res + 1, res + 1, f + 1, prec);
}
else
{
_arb_poly_rising_ui_series_bsplit(res, f, flen, 0, r, trunc, prec);
}
}
void
_arb_poly_div_series(arb_ptr Q, arb_srcptr A, long Alen,
arb_srcptr B, long Blen, long n, long prec)
{
Alen = FLINT_MIN(Alen, n);
Blen = FLINT_MIN(Blen, n);
if (Blen == 1)
{
_arb_vec_scalar_div(Q, A, Alen, B, prec);
_arb_vec_zero(Q + Alen, n - Alen);
}
else
{
arb_ptr Binv;
Binv = _arb_vec_init(n);
_arb_poly_inv_series(Binv, B, Blen, n, prec);
_arb_poly_mullow(Q, Binv, n, A, Alen, n, prec);
_arb_vec_clear(Binv, n);
}
}
void
_arb_poly_asin_series(arb_ptr g, arb_srcptr h, slong hlen, slong n, slong prec)
{
arb_t c;
arb_init(c);
arb_asin(c, h, prec);
hlen = FLINT_MIN(hlen, n);
if (hlen == 1)
{
_arb_vec_zero(g + 1, n - 1);
}
else
{
arb_ptr t, u;
slong ulen;
t = _arb_vec_init(n);
u = _arb_vec_init(n);
/* asin(h(x)) = integral(h'(x)/sqrt(1-h(x)^2)) */
ulen = FLINT_MIN(n, 2 * hlen - 1);
_arb_poly_mullow(u, h, hlen, h, hlen, ulen, prec);
arb_sub_ui(u, u, 1, prec);
_arb_vec_neg(u, u, ulen);
_arb_poly_rsqrt_series(t, u, ulen, n, prec);
_arb_poly_derivative(u, h, hlen, prec);
_arb_poly_mullow(g, t, n, u, hlen - 1, n, prec);
_arb_poly_integral(g, g, n, prec);
_arb_vec_clear(t, n);
_arb_vec_clear(u, n);
}
arb_swap(g, c);
arb_clear(c);
}
void
_arb_poly_inv_series(arb_ptr Qinv,
arb_srcptr Q, slong Qlen, slong len, slong prec)
{
arb_inv(Qinv, Q, prec);
if (Qlen == 1)
{
_arb_vec_zero(Qinv + 1, len - 1);
}
else if (len == 2)
{
arb_div(Qinv + 1, Qinv, Q, prec);
arb_mul(Qinv + 1, Qinv + 1, Q + 1, prec);
arb_neg(Qinv + 1, Qinv + 1);
}
else
{
slong Qnlen, Wlen, W2len;
arb_ptr W;
W = _arb_vec_init(len);
NEWTON_INIT(1, len)
NEWTON_LOOP(m, n)
Qnlen = FLINT_MIN(Qlen, n);
Wlen = FLINT_MIN(Qnlen + m - 1, n);
W2len = Wlen - m;
MULLOW(W, Q, Qnlen, Qinv, m, Wlen, prec);
MULLOW(Qinv + m, Qinv, m, W + m, W2len, n - m, prec);
_arb_vec_neg(Qinv + m, Qinv + m, n - m);
NEWTON_END_LOOP
NEWTON_END
_arb_vec_clear(W, len);
}
}
static void
bound_rfac(arb_ptr F, const acb_t s, ulong n, slong len, slong wp)
{
if (len == 1)
{
acb_rising_ui_get_mag(arb_radref(F), s, n);
arf_set_mag(arb_midref(F), arb_radref(F));
mag_zero(arb_radref(F + 0));
}
else
{
arb_struct sx[2];
arb_init(sx + 0);
arb_init(sx + 1);
acb_abs(sx + 0, s, wp);
arb_one(sx + 1);
_arb_vec_zero(F, len);
_arb_poly_rising_ui_series(F, sx, 2, n, len, wp);
arb_clear(sx + 0);
arb_clear(sx + 1);
}
}
void
_arb_poly_sqrt_series(arb_ptr g,
arb_srcptr h, slong hlen, slong len, slong prec)
{
hlen = FLINT_MIN(hlen, len);
while (hlen > 0 && arb_is_zero(h + hlen - 1))
hlen--;
if (hlen <= 1)
{
arb_sqrt(g, h, prec);
_arb_vec_zero(g + 1, len - 1);
}
else if (len == 2)
{
arb_sqrt(g, h, prec);
arb_div(g + 1, h + 1, h, prec);
arb_mul(g + 1, g + 1, g, prec);
arb_mul_2exp_si(g + 1, g + 1, -1);
}
else if (_arb_vec_is_zero(h + 1, hlen - 2))
{
arb_t t;
arb_init(t);
arf_set_si_2exp_si(arb_midref(t), 1, -1);
_arb_poly_binomial_pow_arb_series(g, h, hlen, t, len, prec);
arb_clear(t);
}
else
{
arb_ptr t;
t = _arb_vec_init(len);
_arb_poly_rsqrt_series(t, h, hlen, len, prec);
_arb_poly_mullow(g, t, len, h, hlen, len, prec);
_arb_vec_clear(t, len);
}
}
void
_arb_poly_cot_pi_series(arb_ptr g, arb_srcptr h, slong hlen, slong len, slong prec)
{
hlen = FLINT_MIN(hlen, len);
if (hlen == 1)
{
arb_cot_pi(g, h, prec);
_arb_vec_zero(g + 1, len - 1);
}
else
{
arb_ptr t, u;
t = _arb_vec_init(len);
u = _arb_vec_init(len);
_arb_poly_sin_cos_pi_series(t, u, h, hlen, len, prec);
_arb_poly_div_series(g, u, len, t, len, len, prec);
_arb_vec_clear(t, len);
_arb_vec_clear(u, len);
}
}
/* with inverse=1 simultaneously computes g = exp(-x) to length n
with inverse=0 uses g as scratch space, computing
g = exp(-x) only to length (n+1)/2 */
static void
_arb_poly_exp_series_newton(arb_ptr f, arb_ptr g,
arb_srcptr h, slong len, slong prec, int inverse, slong cutoff)
{
slong alloc;
arb_ptr T, U, hprime;
alloc = 3 * len;
T = _arb_vec_init(alloc);
U = T + len;
hprime = U + len;
_arb_poly_derivative(hprime, h, len, prec);
arb_zero(hprime + len - 1);
NEWTON_INIT(cutoff, len)
/* f := exp(h) + O(x^m), g := exp(-h) + O(x^m2) */
NEWTON_BASECASE(n)
_arb_poly_exp_series_basecase(f, h, n, n, prec);
_arb_poly_inv_series(g, f, (n + 1) / 2, (n + 1) / 2, prec);
NEWTON_END_BASECASE
/* extend from length m to length n */
NEWTON_LOOP(m, n)
slong m2 = (m + 1) / 2;
slong l = m - 1; /* shifted for derivative */
/* g := exp(-h) + O(x^m) */
_arb_poly_mullow(T, f, m, g, m2, m, prec);
_arb_poly_mullow(g + m2, g, m2, T + m2, m - m2, m - m2, prec);
_arb_vec_neg(g + m2, g + m2, m - m2);
/* U := h' + g (f' - f h') + O(x^(n-1))
Note: should replace h' by h' mod x^(m-1) */
_arb_vec_zero(f + m, n - m);
_arb_poly_mullow(T, f, n, hprime, n, n, prec); /* should be mulmid */
_arb_poly_derivative(U, f, n, prec);
arb_zero(U + n - 1); /* should skip low terms */
_arb_vec_sub(U + l, U + l, T + l, n - l, prec);
_arb_poly_mullow(T + l, g, n - m, U + l, n - m, n - m, prec);
_arb_vec_add(U + l, hprime + l, T + l, n - m, prec);
/* f := f + f * (h - int U) + O(x^n) = exp(h) + O(x^n) */
_arb_poly_integral(U, U, n, prec); /* should skip low terms */
_arb_vec_sub(U + m, h + m, U + m, n - m, prec);
_arb_poly_mullow(f + m, f, n - m, U + m, n - m, n - m, prec);
/* g := exp(-h) + O(x^n) */
/* not needed if we only want exp(x) */
if (n == len && inverse)
{
_arb_poly_mullow(T, f, n, g, m, n, prec);
_arb_poly_mullow(g + m, g, m, T + m, n - m, n - m, prec);
_arb_vec_neg(g + m, g + m, n - m);
}
NEWTON_END_LOOP
NEWTON_END
_arb_vec_clear(T, alloc);
}
/*
* Note that the expectations are multiplied by the rates.
* This is a difference from the analogous function in arbplfdwell.c.
*/
static void
_update_site(nd_accum_t arr,
likelihood_ws_t w, cross_site_ws_t csw, model_and_data_t m,
int *coords, slong site, slong prec)
{
int edge, idx, cat;
arb_t site_lhood, cat_lhood, lhood;
arb_t tmp;
slong state_count = model_and_data_state_count(m);
slong edge_count = model_and_data_edge_count(m);
slong node_count = model_and_data_node_count(m);
slong rate_category_count = model_and_data_rate_category_count(m);
arb_init(site_lhood);
arb_init(cat_lhood);
arb_init(lhood);
arb_init(tmp);
/* only the edge axis is handled at this depth */
nd_axis_struct *edge_axis = arr->axes + EDGE_AXIS;
/* update base node vectors */
pmat_update_base_node_vectors(w->base_node_vectors, m->p, site);
/* clear cross-category expectations and site lhood */
_arb_vec_zero(w->cc_edge_expectations, edge_count);
arb_zero(site_lhood);
for (cat = 0; cat < rate_category_count; cat++)
{
const arb_struct * cat_rate = csw->rate_mix_rates + cat;
const arb_struct * prior_prob = csw->rate_mix_prior + cat;
arb_mat_struct *tmat_base, *fmat_base;
tmat_base = cross_site_ws_transition_matrix(csw, cat, 0);
fmat_base = cross_site_ws_trans_frechet_matrix(csw, cat, 0);
/*
* Update per-node and per-edge likelihood vectors.
* Actually the likelihood vectors on edges are not used.
* This is a backward pass from the leaves to the root.
*/
evaluate_site_lhood(lhood,
w->lhood_node_vectors,
w->lhood_edge_vectors,
w->base_node_vectors,
m->root_prior, csw->equilibrium,
tmat_base,
m->g, m->navigation->preorder, node_count, prec);
/* Update forward vectors. */
evaluate_site_forward(
w->forward_edge_vectors,
w->forward_node_vectors,
w->base_node_vectors,
w->lhood_edge_vectors,
m->root_prior, csw->equilibrium,
tmat_base, m->g, m->navigation,
csw->node_count, csw->state_count, prec);
/* Update expectations at edges. */
evaluate_site_frechet(
w->edge_expectations,
w->lhood_node_vectors,
w->forward_edge_vectors,
fmat_base,
m->g, m->navigation->preorder, node_count, state_count, prec);
/* compute category likelihood */
arb_mul(cat_lhood, lhood, prior_prob, prec);
arb_add(site_lhood, site_lhood, cat_lhood, prec);
/* Accumulate cross-category expectations. */
for (edge = 0; edge < edge_count; edge++)
{
if (!edge_axis->request_update[edge]) continue;
idx = m->edge_map->order[edge];
/*
* Multiply by the product of the category rate,
* the edge rate, and the prior category probability.
* In the analogous 'dwell' function (as opposed to 'trans'),
* only the prior category probability is included.
*/
arb_mul(tmp, cat_rate, csw->edge_rates + idx, prec);
arb_mul(tmp, tmp, prior_prob, prec);
arb_addmul(w->cc_edge_expectations + idx,
w->edge_expectations + idx, tmp, prec);
}
}
/* Divide cross-category expectations by site lhood */
for (edge = 0; edge < edge_count; edge++)
{
if (!edge_axis->request_update[edge]) continue;
idx = m->edge_map->order[edge];
arb_div(w->cc_edge_expectations + idx,
w->cc_edge_expectations + idx,
site_lhood, prec);
}
/* Update the nd accumulator. */
for (edge = 0; edge < edge_count; edge++)
{
/* skip edges that are not requested */
if (!edge_axis->request_update[edge]) continue;
coords[EDGE_AXIS] = edge;
/*
* Accumulate.
* Note that the axes, accumulator, and json interface
* work with "user" edge indices,
* whereas the workspace arrays work with
* tree graph preorder edge indices.
*/
idx = m->edge_map->order[edge];
nd_accum_accumulate(arr,
coords, w->cc_edge_expectations + idx, prec);
}
arb_clear(site_lhood);
arb_clear(cat_lhood);
arb_clear(lhood);
arb_clear(tmp);
}
void
_arb_poly_mullow_block(arb_ptr z, arb_srcptr x, slong xlen,
arb_srcptr y, slong ylen, slong n, slong prec)
{
slong xmlen, xrlen, ymlen, yrlen, i;
fmpz *xz, *yz, *zz;
fmpz *xe, *ye;
slong *xblocks, *yblocks;
int squaring;
fmpz_t scale, t;
xlen = FLINT_MIN(xlen, n);
ylen = FLINT_MIN(ylen, n);
squaring = (x == y) && (xlen == ylen);
/* Strip trailing zeros */
xmlen = xrlen = xlen;
while (xmlen > 0 && arf_is_zero(arb_midref(x + xmlen - 1))) xmlen--;
while (xrlen > 0 && mag_is_zero(arb_radref(x + xrlen - 1))) xrlen--;
if (squaring)
{
ymlen = xmlen;
yrlen = xrlen;
}
else
{
ymlen = yrlen = ylen;
while (ymlen > 0 && arf_is_zero(arb_midref(y + ymlen - 1))) ymlen--;
while (yrlen > 0 && mag_is_zero(arb_radref(y + yrlen - 1))) yrlen--;
}
/* We don't know how to deal with infinities or NaNs */
if (!_arb_vec_is_finite(x, xlen) ||
(!squaring && !_arb_vec_is_finite(y, ylen)))
{
_arb_poly_mullow_classical(z, x, xlen, y, ylen, n, prec);
return;
}
xlen = FLINT_MAX(xmlen, xrlen);
ylen = FLINT_MAX(ymlen, yrlen);
/* Start with the zero polynomial */
_arb_vec_zero(z, n);
/* Nothing to do */
if (xlen == 0 || ylen == 0)
return;
n = FLINT_MIN(n, xlen + ylen - 1);
fmpz_init(scale);
fmpz_init(t);
xz = _fmpz_vec_init(xlen);
yz = _fmpz_vec_init(ylen);
zz = _fmpz_vec_init(n);
xe = _fmpz_vec_init(xlen);
ye = _fmpz_vec_init(ylen);
xblocks = flint_malloc(sizeof(slong) * (xlen + 1));
yblocks = flint_malloc(sizeof(slong) * (ylen + 1));
_arb_poly_get_scale(scale, x, xlen, y, ylen);
/* Error propagation */
/* (xm + xr)*(ym + yr) = (xm*ym) + (xr*ym + xm*yr + xr*yr)
= (xm*ym) + (xm*yr + xr*(ym + yr)) */
if (xrlen != 0 || yrlen != 0)
{
mag_ptr tmp;
double *xdbl, *ydbl;
tmp = _mag_vec_init(FLINT_MAX(xlen, ylen));
xdbl = flint_malloc(sizeof(double) * xlen);
ydbl = flint_malloc(sizeof(double) * ylen);
/* (xm + xr)^2 = (xm*ym) + (xr^2 + 2 xm xr)
= (xm*ym) + xr*(2 xm + xr) */
if (squaring)
{
_mag_vec_get_fmpz_2exp_blocks(xz, xdbl, xe, xblocks, scale, x, NULL, xrlen);
for (i = 0; i < xlen; i++)
{
arf_get_mag(tmp + i, arb_midref(x + i));
mag_mul_2exp_si(tmp + i, tmp + i, 1);
mag_add(tmp + i, tmp + i, arb_radref(x + i));
}
_mag_vec_get_fmpz_2exp_blocks(yz, ydbl, ye, yblocks, scale, NULL, tmp, xlen);
_arb_poly_addmullow_rad(z, zz, xz, xdbl, xe, xblocks, xrlen, yz, ydbl, ye, yblocks, xlen, n);
}
else if (yrlen == 0)
{
/* xr * |ym| */
_mag_vec_get_fmpz_2exp_blocks(xz, xdbl, xe, xblocks, scale, x, NULL, xrlen);
for (i = 0; i < ymlen; i++)
arf_get_mag(tmp + i, arb_midref(y + i));
_mag_vec_get_fmpz_2exp_blocks(yz, ydbl, ye, yblocks, scale, NULL, tmp, ymlen);
_arb_poly_addmullow_rad(z, zz, xz, xdbl, xe, xblocks, xrlen, yz, ydbl, ye, yblocks, ymlen, n);
}
else
{
/* |xm| * yr */
for (i = 0; i < xmlen; i++)
arf_get_mag(tmp + i, arb_midref(x + i));
_mag_vec_get_fmpz_2exp_blocks(xz, xdbl, xe, xblocks, scale, NULL, tmp, xmlen);
_mag_vec_get_fmpz_2exp_blocks(yz, ydbl, ye, yblocks, scale, y, NULL, yrlen);
_arb_poly_addmullow_rad(z, zz, xz, xdbl, xe, xblocks, xmlen, yz, ydbl, ye, yblocks, yrlen, n);
/* xr*(|ym| + yr) */
if (xrlen != 0)
{
_mag_vec_get_fmpz_2exp_blocks(xz, xdbl, xe, xblocks, scale, x, NULL, xrlen);
for (i = 0; i < ylen; i++)
arb_get_mag(tmp + i, y + i);
_mag_vec_get_fmpz_2exp_blocks(yz, ydbl, ye, yblocks, scale, NULL, tmp, ylen);
_arb_poly_addmullow_rad(z, zz, xz, xdbl, xe, xblocks, xrlen, yz, ydbl, ye, yblocks, ylen, n);
}
}
_mag_vec_clear(tmp, FLINT_MAX(xlen, ylen));
flint_free(xdbl);
flint_free(ydbl);
}
/* multiply midpoints */
if (xmlen != 0 && ymlen != 0)
{
_arb_vec_get_fmpz_2exp_blocks(xz, xe, xblocks, scale, x, xmlen, prec);
if (squaring)
{
_arb_poly_addmullow_block(z, zz, xz, xe, xblocks, xmlen, xz, xe, xblocks, xmlen, n, prec, 1);
}
else
{
_arb_vec_get_fmpz_2exp_blocks(yz, ye, yblocks, scale, y, ymlen, prec);
_arb_poly_addmullow_block(z, zz, xz, xe, xblocks, xmlen, yz, ye, yblocks, ymlen, n, prec, 0);
}
}
/* Unscale. */
if (!fmpz_is_zero(scale))
{
fmpz_zero(t);
for (i = 0; i < n; i++)
{
arb_mul_2exp_fmpz(z + i, z + i, t);
fmpz_add(t, t, scale);
}
}
_fmpz_vec_clear(xz, xlen);
_fmpz_vec_clear(yz, ylen);
_fmpz_vec_clear(zz, n);
_fmpz_vec_clear(xe, xlen);
_fmpz_vec_clear(ye, ylen);
flint_free(xblocks);
flint_free(yblocks);
fmpz_clear(scale);
fmpz_clear(t);
}
void
_arb_poly_sin_cos_series_tangent(arb_ptr s, arb_ptr c,
arb_srcptr h, slong hlen, slong len, slong prec, int times_pi)
{
arb_ptr t, u, v;
arb_t s0, c0;
hlen = FLINT_MIN(hlen, len);
if (hlen == 1)
{
if (times_pi)
arb_sin_cos_pi(s, c, h, prec);
else
arb_sin_cos(s, c, h, prec);
_arb_vec_zero(s + 1, len - 1);
_arb_vec_zero(c + 1, len - 1);
return;
}
/*
sin(x) = 2*tan(x/2)/(1+tan(x/2)^2)
cos(x) = (1-tan(x/2)^2)/(1+tan(x/2)^2)
*/
arb_init(s0);
arb_init(c0);
t = _arb_vec_init(3 * len);
u = t + len;
v = u + len;
/* sin, cos of h0 */
if (times_pi)
arb_sin_cos_pi(s0, c0, h, prec);
else
arb_sin_cos(s0, c0, h, prec);
/* t = tan((h-h0)/2) */
arb_zero(u);
_arb_vec_scalar_mul_2exp_si(u + 1, h + 1, hlen - 1, -1);
if (times_pi)
{
arb_const_pi(t, prec);
_arb_vec_scalar_mul(u + 1, u + 1, hlen - 1, t, prec);
}
_arb_poly_tan_series(t, u, hlen, len, prec);
/* v = 1 + t^2 */
_arb_poly_mullow(v, t, len, t, len, len, prec);
arb_add_ui(v, v, 1, prec);
/* u = 1/(1+t^2) */
_arb_poly_inv_series(u, v, len, len, prec);
/* sine */
_arb_poly_mullow(s, t, len, u, len, len, prec);
_arb_vec_scalar_mul_2exp_si(s, s, len, 1);
/* cosine */
arb_sub_ui(v, v, 2, prec);
_arb_vec_neg(v, v, len);
_arb_poly_mullow(c, v, len, u, len, len, prec);
/* sin(h0 + h1) = cos(h0) sin(h1) + sin(h0) cos(h1)
cos(h0 + h1) = cos(h0) cos(h1) - sin(h0) sin(h1) */
if (!arb_is_zero(s0))
{
_arb_vec_scalar_mul(t, s, len, c0, prec);
_arb_vec_scalar_mul(u, c, len, s0, prec);
_arb_vec_scalar_mul(v, s, len, s0, prec);
_arb_vec_add(s, t, u, len, prec);
_arb_vec_scalar_mul(t, c, len, c0, prec);
_arb_vec_sub(c, t, v, len, prec);
}
_arb_vec_clear(t, 3 * len);
arb_clear(s0);
arb_clear(c0);
}
void
_arb_poly_pow_ui_trunc_binexp(arb_ptr res,
arb_srcptr f, slong flen, ulong exp, slong len, slong prec)
{
arb_ptr v, R, S, T;
slong rlen;
ulong bit;
if (exp <= 1)
{
if (exp == 0)
arb_one(res);
else if (exp == 1)
_arb_vec_set_round(res, f, len, prec);
return;
}
/* (f * x^r)^m = x^(rm) * f^m */
while (flen > 1 && arb_is_zero(f))
{
if (((ulong) len) > exp)
{
_arb_vec_zero(res, exp);
len -= exp;
res += exp;
}
else
{
_arb_vec_zero(res, len);
return;
}
f++;
flen--;
}
if (exp == 2)
{
_arb_poly_mullow(res, f, flen, f, flen, len, prec);
return;
}
if (flen == 1)
{
arb_pow_ui(res, f, exp, prec);
return;
}
v = _arb_vec_init(len);
bit = UWORD(1) << (FLINT_BIT_COUNT(exp) - 2);
if (n_zerobits(exp) % 2)
{
R = res;
S = v;
}
else
{
R = v;
S = res;
}
MUL(R, rlen, f, flen, f, flen, len, prec);
if (bit & exp)
{
MUL(S, rlen, R, rlen, f, flen, len, prec);
T = R;
R = S;
S = T;
}
while (bit >>= 1)
{
if (bit & exp)
{
MUL(S, rlen, R, rlen, R, rlen, len, prec);
MUL(R, rlen, S, rlen, f, flen, len, prec);
}
else
{
MUL(S, rlen, R, rlen, R, rlen, len, prec);
T = R;
R = S;
S = T;
}
}
_arb_vec_clear(v, len);
}
void
_arb_poly_evaluate_vec_fast_precomp(arb_ptr vs, arb_srcptr poly,
long plen, arb_ptr * tree, long len, long prec)
{
long height, i, j, pow, left;
long tree_height;
long tlen;
arb_ptr t, u, swap, pa, pb, pc;
/* avoid worrying about some degenerate cases */
if (len < 2 || plen < 2)
{
if (len == 1)
{
arb_t tmp;
arb_init(tmp);
arb_neg(tmp, tree[0] + 0);
_arb_poly_evaluate(vs + 0, poly, plen, tmp, prec);
arb_clear(tmp);
}
else if (len != 0 && plen == 0)
{
_arb_vec_zero(vs, len);
}
else if (len != 0 && plen == 1)
{
for (i = 0; i < len; i++)
arb_set(vs + i, poly + 0);
}
return;
}
t = _arb_vec_init(len);
u = _arb_vec_init(len);
left = len;
/* Initial reduction. We allow the polynomial to be larger
or smaller than the number of points. */
height = FLINT_BIT_COUNT(plen - 1) - 1;
tree_height = FLINT_CLOG2(len);
while (height >= tree_height)
height--;
pow = 1L << height;
for (i = j = 0; i < len; i += pow, j += (pow + 1))
{
tlen = ((i + pow) <= len) ? pow : len % pow;
_arb_poly_rem(t + i, poly, plen, tree[height] + j, tlen + 1, prec);
}
for (i = height - 1; i >= 0; i--)
{
pow = 1L << i;
left = len;
pa = tree[i];
pb = t;
pc = u;
while (left >= 2 * pow)
{
_arb_poly_rem_2(pc, pb, 2 * pow, pa, pow + 1, prec);
_arb_poly_rem_2(pc + pow, pb, 2 * pow, pa + pow + 1, pow + 1, prec);
pa += 2 * pow + 2;
pb += 2 * pow;
pc += 2 * pow;
left -= 2 * pow;
}
if (left > pow)
{
_arb_poly_rem(pc, pb, left, pa, pow + 1, prec);
_arb_poly_rem(pc + pow, pb, left, pa + pow + 1, left - pow + 1, prec);
}
else if (left > 0)
_arb_vec_set(pc, pb, left);
swap = t;
t = u;
u = swap;
}
_arb_vec_set(vs, t, len);
_arb_vec_clear(t, len);
_arb_vec_clear(u, len);
}
void
_arb_poly_exp_series(arb_ptr f, arb_srcptr h, slong hlen, slong n, slong prec)
{
hlen = FLINT_MIN(hlen, n);
if (hlen == 1)
{
arb_exp(f, h, prec);
_arb_vec_zero(f + 1, n - 1);
}
else if (n == 2)
{
arb_exp(f, h, prec);
arb_mul(f + 1, f, h + 1, prec); /* safe since hlen >= 2 */
}
else if (_arb_vec_is_zero(h + 1, hlen - 2)) /* h = a + bx^d */
{
slong i, j, d = hlen - 1;
arb_t t;
arb_init(t);
arb_set(t, h + d);
arb_exp(f, h, prec);
for (i = 1, j = d; j < n; j += d, i++)
{
arb_mul(f + j, f + j - d, t, prec);
arb_div_ui(f + j, f + j, i, prec);
_arb_vec_zero(f + j - d + 1, hlen - 2);
}
_arb_vec_zero(f + j - d + 1, n - (j - d + 1));
arb_clear(t);
}
else if (hlen <= arb_poly_newton_exp_cutoff)
{
_arb_poly_exp_series_basecase(f, h, hlen, n, prec);
}
else
{
arb_ptr g, t;
arb_t u;
int fix;
g = _arb_vec_init((n + 1) / 2);
fix = (hlen < n || h == f || !arb_is_zero(h));
if (fix)
{
t = _arb_vec_init(n);
_arb_vec_set(t + 1, h + 1, hlen - 1);
}
else
t = (arb_ptr) h;
arb_init(u);
arb_exp(u, h, prec);
_arb_poly_exp_series_newton(f, g, t, n, prec, 0, arb_poly_newton_exp_cutoff);
if (!arb_is_one(u))
_arb_vec_scalar_mul(f, f, n, u, prec);
_arb_vec_clear(g, (n + 1) / 2);
if (fix)
_arb_vec_clear(t, n);
arb_clear(u);
}
}
void
_arb_poly_inv_series(arb_ptr Qinv,
arb_srcptr Q, slong Qlen, slong len, slong prec)
{
Qlen = FLINT_MIN(Qlen, len);
arb_inv(Qinv, Q, prec);
if (Qlen == 1)
{
_arb_vec_zero(Qinv + 1, len - 1);
}
else if (len == 2)
{
arb_mul(Qinv + 1, Qinv, Qinv, prec);
arb_mul(Qinv + 1, Qinv + 1, Q + 1, prec);
arb_neg(Qinv + 1, Qinv + 1);
}
else
{
slong i, j, blen;
/* The basecase algorithm is faster for much larger Qlen or len than
this, but unfortunately also much less numerically stable. */
if (Qlen == 2 || len <= 8)
blen = len;
else
blen = FLINT_MIN(len, 4);
for (i = 1; i < blen; i++)
{
arb_mul(Qinv + i, Q + 1, Qinv + i - 1, prec);
for (j = 2; j < FLINT_MIN(i + 1, Qlen); j++)
arb_addmul(Qinv + i, Q + j, Qinv + i - j, prec);
if (!arb_is_one(Qinv))
arb_mul(Qinv + i, Qinv + i, Qinv, prec);
arb_neg(Qinv + i, Qinv + i);
}
if (len > blen)
{
slong Qnlen, Wlen, W2len;
arb_ptr W;
W = _arb_vec_init(len);
NEWTON_INIT(blen, len)
NEWTON_LOOP(m, n)
Qnlen = FLINT_MIN(Qlen, n);
Wlen = FLINT_MIN(Qnlen + m - 1, n);
W2len = Wlen - m;
MULLOW(W, Q, Qnlen, Qinv, m, Wlen, prec);
MULLOW(Qinv + m, Qinv, m, W + m, W2len, n - m, prec);
_arb_vec_neg(Qinv + m, Qinv + m, n - m);
NEWTON_END_LOOP
NEWTON_END
_arb_vec_clear(W, len);
}
}
}
