hiro/arb
1
0
Fork 0
mirror of https://github.com/vale981/arb synced 2025-03-05 17:31:38 -05:00
Code Issues Projects Releases Packages Wiki Activity Actions

improve log_series for special-form input

Browse source
This commit is contained in:
Fredrik Johansson 2013-10-21 15:30:19 +02:00
parent be6a8ee46f
commit 94120b0ddd
4 changed files with 90 additions and 34 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

60
fmpcb_poly/log_series.c
View file

@ -28,33 +28,59 @@
void
_fmpcb_poly_log_series(fmpcb_ptr res, fmpcb_srcptr f, long flen, long n, long prec)
{
fmpcb_ptr f_diff, f_inv;
fmpcb_t a;
long alloc;
flen = FLINT_MIN(flen, n);
if (flen == 1)
{
fmpcb_log(res, f, prec);
_fmpcb_vec_zero(res + 1, n - 1);
return;
}
else if (n == 2)
{
fmpcb_div(res + 1, f + 1, f + 0, prec); /* safe since hlen >= 2 */
fmpcb_log(res, f, prec);
}
else if (_fmpcb_vec_is_zero(f + 1, flen - 2)) /* f = a + bx^d */
{
long i, j, d = flen - 1;
flen = FLINT_MIN(flen, n);
alloc = n + flen - 1;
f_inv = _fmpcb_vec_init(alloc);
f_diff = f_inv + n;
for (i = 1, j = d; j < n; j += d, i++)
{
if (i == 1)
fmpcb_div(res + j, f + d, f + 0, prec);
else
fmpcb_mul(res + j, res + j - d, res + d, prec);
_fmpcb_vec_zero(res + j - d + 1, flen - 2);
}
_fmpcb_vec_zero(res + j - d + 1, n - (j - d + 1));
fmpcb_init(a);
fmpcb_log(a, f, prec);
for (i = 2, j = 2 * d; j < n; j += d, i++)
fmpcb_div_si(res + j, res + j, i % 2 ? i : -i, prec);
_fmpcb_poly_derivative(f_diff, f, flen, prec);
_fmpcb_poly_inv_series(f_inv, f, flen, n, prec);
_fmpcb_poly_mullow(res, f_inv, n - 1, f_diff, flen - 1, n - 1, prec);
_fmpcb_poly_integral(res, res, n, prec);
fmpcb_swap(res, a);
fmpcb_log(res, f, prec); /* done last to allow aliasing */
}
else
{
fmpcb_ptr f_diff, f_inv;
fmpcb_t a;
long alloc;
fmpcb_clear(a);
_fmpcb_vec_clear(f_inv, alloc);
alloc = n + flen - 1;
f_inv = _fmpcb_vec_init(alloc);
f_diff = f_inv + n;
fmpcb_init(a);
fmpcb_log(a, f, prec);
_fmpcb_poly_derivative(f_diff, f, flen, prec);
_fmpcb_poly_inv_series(f_inv, f, flen, n, prec);
_fmpcb_poly_mullow(res, f_inv, n - 1, f_diff, flen - 1, n - 1, prec);
_fmpcb_poly_integral(res, res, n, prec);
fmpcb_swap(res, a);
fmpcb_clear(a);
_fmpcb_vec_clear(f_inv, alloc);
}
}
void

2
fmpcb_poly/test/t-log_series.c
View file

@ -61,6 +61,7 @@ int main()
fmpq_poly_log_series(B, A, n);
fmpcb_poly_set_fmpq_poly(a, A, rbits1);
fmpcb_poly_randtest(b, state, 1 + n_randint(state, 20), rbits1, 5);
fmpcb_poly_log_series(b, a, n, rbits2);
if (!fmpcb_poly_contains_fmpq_poly(b, B))
@ -155,6 +156,7 @@ int main()
fmpcb_poly_set_fmpq_poly(a, A, rbits1);
fmpcb_poly_randtest(b, state, 1 + n_randint(state, 20), rbits1, 5);
fmpcb_poly_log_series(b, a, n, rbits2);
fmpcb_poly_exp_series_basecase(c, b, n, rbits3);

60
fmprb_poly/log_series.c
View file

@ -28,33 +28,59 @@
void
_fmprb_poly_log_series(fmprb_ptr res, fmprb_srcptr f, long flen, long n, long prec)
{
fmprb_ptr f_diff, f_inv;
fmprb_t a;
long alloc;
flen = FLINT_MIN(flen, n);
if (flen == 1)
{
fmprb_log(res, f, prec);
_fmprb_vec_zero(res + 1, n - 1);
return;
}
else if (n == 2)
{
fmprb_div(res + 1, f + 1, f + 0, prec); /* safe since hlen >= 2 */
fmprb_log(res, f, prec);
}
else if (_fmprb_vec_is_zero(f + 1, flen - 2)) /* f = a + bx^d */
{
long i, j, d = flen - 1;
flen = FLINT_MIN(flen, n);
alloc = n + flen - 1;
f_inv = _fmprb_vec_init(alloc);
f_diff = f_inv + n;
for (i = 1, j = d; j < n; j += d, i++)
{
if (i == 1)
fmprb_div(res + j, f + d, f + 0, prec);
else
fmprb_mul(res + j, res + j - d, res + d, prec);
_fmprb_vec_zero(res + j - d + 1, flen - 2);
}
_fmprb_vec_zero(res + j - d + 1, n - (j - d + 1));
fmprb_init(a);
fmprb_log(a, f, prec);
for (i = 2, j = 2 * d; j < n; j += d, i++)
fmprb_div_si(res + j, res + j, i % 2 ? i : -i, prec);
_fmprb_poly_derivative(f_diff, f, flen, prec);
_fmprb_poly_inv_series(f_inv, f, flen, n, prec);
_fmprb_poly_mullow(res, f_inv, n - 1, f_diff, flen - 1, n - 1, prec);
_fmprb_poly_integral(res, res, n, prec);
fmprb_swap(res, a);
fmprb_log(res, f, prec); /* done last to allow aliasing */
}
else
{
fmprb_ptr f_diff, f_inv;
fmprb_t a;
long alloc;
fmprb_clear(a);
_fmprb_vec_clear(f_inv, alloc);
alloc = n + flen - 1;
f_inv = _fmprb_vec_init(alloc);
f_diff = f_inv + n;
fmprb_init(a);
fmprb_log(a, f, prec);
_fmprb_poly_derivative(f_diff, f, flen, prec);
_fmprb_poly_inv_series(f_inv, f, flen, n, prec);
_fmprb_poly_mullow(res, f_inv, n - 1, f_diff, flen - 1, n - 1, prec);
_fmprb_poly_integral(res, res, n, prec);
fmprb_swap(res, a);
fmprb_clear(a);
_fmprb_vec_clear(f_inv, alloc);
}
}
void

2
fmprb_poly/test/t-log_series.c
View file

@ -61,6 +61,7 @@ int main()
fmpq_poly_log_series(B, A, n);
fmprb_poly_set_fmpq_poly(a, A, rbits1);
fmprb_poly_randtest(b, state, 1 + n_randint(state, 20), rbits1, 5);
fmprb_poly_log_series(b, a, n, rbits2);
if (!fmprb_poly_contains_fmpq_poly(b, B))
@ -155,6 +156,7 @@ int main()
fmprb_poly_set_fmpq_poly(a, A, rbits1);
fmprb_poly_randtest(b, state, 1 + n_randint(state, 20), rbits1, 5);
fmprb_poly_log_series(b, a, n, rbits2);
fmprb_poly_exp_series_basecase(c, b, n, rbits3);