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add sin_pi_series and friends

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This commit is contained in:
Fredrik Johansson 2015-02-10 17:45:20 +01:00
parent 50af344e6c
commit ed2990d5f8
36 changed files with 1318 additions and 78 deletions
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22
acb_poly.h
View file

@ -493,16 +493,16 @@ void _acb_poly_exp_series(acb_ptr f, acb_srcptr h, long hlen, long n, long prec)
void acb_poly_exp_series(acb_poly_t f, const acb_poly_t h, long n, long prec);
void _acb_poly_sin_cos_series_basecase(acb_ptr s,
acb_ptr c, acb_srcptr h, long hlen, long n, long prec);
acb_ptr c, acb_srcptr h, long hlen, long n, long prec, int times_pi);
void acb_poly_sin_cos_series_basecase(acb_poly_t s, acb_poly_t c,
const acb_poly_t h, long n, long prec);
const acb_poly_t h, long n, long prec, int times_pi);
void _acb_poly_sin_cos_series_tangent(acb_ptr s, acb_ptr c,
const acb_srcptr h, long hlen, long len, long prec);
const acb_srcptr h, long hlen, long len, long prec, int times_pi);
void acb_poly_sin_cos_series_tangent(acb_poly_t s, acb_poly_t c,
const acb_poly_t h, long n, long prec);
const acb_poly_t h, long n, long prec, int times_pi);
void _acb_poly_sin_cos_series(acb_ptr s, acb_ptr c,
const acb_srcptr h, long hlen, long len, long prec);
@ -518,6 +518,20 @@ void _acb_poly_cos_series(acb_ptr g, acb_srcptr h, long hlen, long n, long prec)
void acb_poly_cos_series(acb_poly_t g, const acb_poly_t h, long n, long prec);
void _acb_poly_sin_cos_pi_series(acb_ptr s, acb_ptr c,
const acb_srcptr h, long hlen, long len, long prec);
void acb_poly_sin_cos_pi_series(acb_poly_t s, acb_poly_t c,
const acb_poly_t h, long n, long prec);
void _acb_poly_sin_pi_series(acb_ptr g, acb_srcptr h, long hlen, long n, long prec);
void acb_poly_sin_pi_series(acb_poly_t g, const acb_poly_t h, long n, long prec);
void _acb_poly_cos_pi_series(acb_ptr g, acb_srcptr h, long hlen, long n, long prec);
void acb_poly_cos_pi_series(acb_poly_t g, const acb_poly_t h, long n, long prec);
void _acb_poly_tan_series(acb_ptr g, acb_srcptr h, long hlen, long len, long prec);
void acb_poly_tan_series(acb_poly_t g, const acb_poly_t h, long n, long prec);

82
acb_poly/cos_pi_series.c Normal file
View file

@ -0,0 +1,82 @@
/*=============================================================================
This file is part of ARB.
ARB is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
ARB is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with ARB; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
=============================================================================*/
/******************************************************************************
Copyright (C) 2013 Fredrik Johansson
******************************************************************************/
#include "acb_poly.h"
void
_acb_poly_cos_pi_series(acb_ptr g, acb_srcptr h, long hlen, long n, long prec)
{
hlen = FLINT_MIN(hlen, n);
if (hlen == 1)
{
acb_cos_pi(g, h, prec);
_acb_vec_zero(g + 1, n - 1);
}
else if (n == 2)
{
acb_t t;
acb_init(t);
acb_sin_cos_pi(t, g, h, prec);
acb_neg(t, t);
acb_mul(g + 1, h + 1, t, prec); /* safe since hlen >= 2 */
acb_const_pi(t, prec);
acb_mul(g + 1, g + 1, t, prec);
acb_clear(t);
}
else
{
acb_ptr t = _acb_vec_init(n);
_acb_poly_sin_cos_pi_series(t, g, h, hlen, n, prec);
_acb_vec_clear(t, n);
}
}
void
acb_poly_cos_pi_series(acb_poly_t g, const acb_poly_t h, long n, long prec)
{
long hlen = h->length;
if (n == 0)
{
acb_poly_zero(g);
return;
}
if (hlen == 0)
{
acb_poly_one(g);
return;
}
if (hlen == 1)
n = 1;
acb_poly_fit_length(g, n);
_acb_poly_cos_pi_series(g->coeffs, h->coeffs, hlen, n, prec);
_acb_poly_set_length(g, n);
_acb_poly_normalise(g);
}

6
acb_poly/gamma_series.c
View file

@ -221,9 +221,9 @@ _acb_poly_gamma_series(acb_ptr res, acb_srcptr h, long hlen, long len, long prec
acb_neg(u + i, u + i);
/* v = 1/sin(pi x) */
acb_const_pi(f + 1, wp);
acb_mul(f, h, f + 1, wp);
_acb_poly_sin_series(t, f, 2, len, wp);
acb_set(f, h);
acb_one(f + 1);
_acb_poly_sin_pi_series(t, f, 2, len, wp);
_acb_poly_inv_series(v, t, len, len, wp);
_acb_poly_mullow(t, u, len, v, len, len, wp);

6
acb_poly/rgamma_series.c
View file

@ -84,9 +84,9 @@ _acb_poly_rgamma_series(acb_ptr res, acb_srcptr h, long hlen, long len, long pre
acb_neg(u + i, u + i);
/* v = sin(pi x) */
acb_const_pi(f + 1, wp);
acb_mul(f, h, f + 1, wp);
_acb_poly_sin_series(v, f, 2, len, wp);
acb_set(f, h);
acb_one(f + 1);
_acb_poly_sin_pi_series(v, f, 2, len, wp);
_acb_poly_mullow(t, u, len, v, len, len, wp);

90
acb_poly/sin_cos_pi_series.c Normal file
View file

@ -0,0 +1,90 @@
/*=============================================================================
This file is part of ARB.
ARB is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
ARB is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with ARB; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
=============================================================================*/
/******************************************************************************
Copyright (C) 2013 Fredrik Johansson
******************************************************************************/
#include "acb_poly.h"
#define TANGENT_CUTOFF 80
void
_acb_poly_sin_cos_pi_series(acb_ptr s, acb_ptr c, const acb_srcptr h, long hlen, long n, long prec)
{
hlen = FLINT_MIN(hlen, n);
if (hlen == 1)
{
acb_sin_cos_pi(s, c, h, prec);
_acb_vec_zero(s + 1, n - 1);
_acb_vec_zero(c + 1, n - 1);
}
else if (n == 2)
{
acb_t t;
acb_init(t);
acb_const_pi(t, prec);
acb_mul(t, t, h + 1, prec);
acb_sin_cos_pi(s, c, h, prec);
acb_mul(s + 1, c, t, prec);
acb_neg(t, t);
acb_mul(c + 1, s, t, prec);
acb_clear(t);
}
else if (hlen < TANGENT_CUTOFF)
_acb_poly_sin_cos_series_basecase(s, c, h, hlen, n, prec, 1);
else
_acb_poly_sin_cos_series_tangent(s, c, h, hlen, n, prec, 1);
}
void
acb_poly_sin_cos_pi_series(acb_poly_t s, acb_poly_t c,
const acb_poly_t h, long n, long prec)
{
long hlen = h->length;
if (n == 0)
{
acb_poly_zero(s);
acb_poly_zero(c);
return;
}
if (hlen == 0)
{
acb_poly_zero(s);
acb_poly_one(c);
return;
}
if (hlen == 1)
n = 1;
acb_poly_fit_length(s, n);
acb_poly_fit_length(c, n);
_acb_poly_sin_cos_pi_series(s->coeffs, c->coeffs, h->coeffs, hlen, n, prec);
_acb_poly_set_length(s, n);
_acb_poly_normalise(s);
_acb_poly_set_length(c, n);
_acb_poly_normalise(c);
}

4
acb_poly/sin_cos_series.c
View file

@ -50,9 +50,9 @@ _acb_poly_sin_cos_series(acb_ptr s, acb_ptr c, const acb_srcptr h, long hlen, lo
acb_clear(t);
}
else if (hlen < TANGENT_CUTOFF)
_acb_poly_sin_cos_series_basecase(s, c, h, hlen, n, prec);
_acb_poly_sin_cos_series_basecase(s, c, h, hlen, n, prec, 0);
else
_acb_poly_sin_cos_series_tangent(s, c, h, hlen, n, prec);
_acb_poly_sin_cos_series_tangent(s, c, h, hlen, n, prec, 0);
}
void

19
acb_poly/sin_cos_series_basecase.c
View file

@ -26,14 +26,17 @@
#include "acb_poly.h"
void
_acb_poly_sin_cos_series_basecase(acb_ptr s,
acb_ptr c, acb_srcptr h, long hlen, long n, long prec)
_acb_poly_sin_cos_series_basecase(acb_ptr s, acb_ptr c, acb_srcptr h, long hlen,
long n, long prec, int times_pi)
{
long j, k, alen = FLINT_MIN(n, hlen);
acb_ptr a;
acb_t t, u;
acb_sin_cos(s, c, h, prec);
if (times_pi)
acb_sin_cos_pi(s, c, h, prec);
else
acb_sin_cos(s, c, h, prec);
if (hlen == 1)
{
@ -49,6 +52,12 @@ _acb_poly_sin_cos_series_basecase(acb_ptr s,
for (k = 1; k < alen; k++)
acb_mul_ui(a + k, h + k, k, prec);
if (times_pi)
{
acb_const_pi(t, prec);
_acb_vec_scalar_mul(a + 1, a + 1, alen - 1, t, prec);
}
for (k = 1; k < n; k++)
{
acb_zero(t);
@ -71,7 +80,7 @@ _acb_poly_sin_cos_series_basecase(acb_ptr s,
void
acb_poly_sin_cos_series_basecase(acb_poly_t s, acb_poly_t c,
const acb_poly_t h, long n, long prec)
const acb_poly_t h, long n, long prec, int times_pi)
{
long hlen = h->length;
@ -91,7 +100,7 @@ acb_poly_sin_cos_series_basecase(acb_poly_t s, acb_poly_t c,
acb_poly_fit_length(s, n);
acb_poly_fit_length(c, n);
_acb_poly_sin_cos_series_basecase(s->coeffs, c->coeffs, h->coeffs, hlen, n, prec);
_acb_poly_sin_cos_series_basecase(s->coeffs, c->coeffs, h->coeffs, hlen, n, prec, times_pi);
_acb_poly_set_length(s, n);
_acb_poly_normalise(s);
_acb_poly_set_length(c, n);

22
acb_poly/sin_cos_series_tangent.c
View file

@ -27,7 +27,7 @@
void
_acb_poly_sin_cos_series_tangent(acb_ptr s, acb_ptr c,
const acb_srcptr h, long hlen, long len, long prec)
const acb_srcptr h, long hlen, long len, long prec, int times_pi)
{
acb_ptr t, u, v;
acb_t s0, c0;
@ -35,7 +35,10 @@ _acb_poly_sin_cos_series_tangent(acb_ptr s, acb_ptr c,
if (hlen == 1)
{
acb_sin_cos(s, c, h, prec);
if (times_pi)
acb_sin_cos_pi(s, c, h, prec);
else
acb_sin_cos(s, c, h, prec);
_acb_vec_zero(s + 1, len - 1);
_acb_vec_zero(c + 1, len - 1);
return;
@ -54,11 +57,20 @@ _acb_poly_sin_cos_series_tangent(acb_ptr s, acb_ptr c,
v = u + len;
/* sin, cos of h0 */
acb_sin_cos(s0, c0, h, prec);
if (times_pi)
acb_sin_cos_pi(s0, c0, h, prec);
else
acb_sin_cos(s0, c0, h, prec);
/* t = tan((h-h0)/2) */
acb_zero(u);
_acb_vec_scalar_mul_2exp_si(u + 1, h + 1, hlen - 1, -1);
if (times_pi)
{
acb_const_pi(t, prec);
_acb_vec_scalar_mul(u + 1, u + 1, hlen - 1, t, prec);
}
_acb_poly_tan_series(t, u, hlen, len, prec);
/* v = 1 + t^2 */
@ -97,7 +109,7 @@ _acb_poly_sin_cos_series_tangent(acb_ptr s, acb_ptr c,
void
acb_poly_sin_cos_series_tangent(acb_poly_t s, acb_poly_t c,
const acb_poly_t h, long n, long prec)
const acb_poly_t h, long n, long prec, int times_pi)
{
long hlen = h->length;
@ -118,7 +130,7 @@ acb_poly_sin_cos_series_tangent(acb_poly_t s, acb_poly_t c,
acb_poly_fit_length(s, n);
acb_poly_fit_length(c, n);
_acb_poly_sin_cos_series_tangent(s->coeffs, c->coeffs,
h->coeffs, hlen, n, prec);
h->coeffs, hlen, n, prec, times_pi);
_acb_poly_set_length(s, n);
_acb_poly_normalise(s);
_acb_poly_set_length(c, n);

75
acb_poly/sin_pi_series.c Normal file
View file

@ -0,0 +1,75 @@
/*=============================================================================
This file is part of ARB.
ARB is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
ARB is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with ARB; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
=============================================================================*/
/******************************************************************************
Copyright (C) 2013 Fredrik Johansson
******************************************************************************/
#include "acb_poly.h"
void
_acb_poly_sin_pi_series(acb_ptr g, acb_srcptr h, long hlen, long n, long prec)
{
hlen = FLINT_MIN(hlen, n);
if (hlen == 1)
{
acb_sin_pi(g, h, prec);
_acb_vec_zero(g + 1, n - 1);
}
else if (n == 2)
{
acb_t t;
acb_init(t);
acb_sin_cos_pi(g, t, h, prec);
acb_mul(g + 1, h + 1, t, prec); /* safe since hlen >= 2 */
acb_const_pi(t, prec);
acb_mul(g + 1, g + 1, t, prec);
acb_clear(t);
}
else
{
acb_ptr t = _acb_vec_init(n);
_acb_poly_sin_cos_pi_series(g, t, h, hlen, n, prec);
_acb_vec_clear(t, n);
}
}
void
acb_poly_sin_pi_series(acb_poly_t g, const acb_poly_t h, long n, long prec)
{
long hlen = h->length;
if (hlen == 0 || n == 0)
{
acb_poly_zero(g);
return;
}
if (hlen == 1)
n = 1;
acb_poly_fit_length(g, n);
_acb_poly_sin_pi_series(g->coeffs, h->coeffs, hlen, n, prec);
_acb_poly_set_length(g, n);
_acb_poly_normalise(g);
}

2
acb_poly/tan_series.c
View file

@ -58,7 +58,7 @@ _acb_poly_tan_series(acb_ptr g,
NEWTON_INIT(TAN_NEWTON_CUTOFF, len)
NEWTON_BASECASE(n)
_acb_poly_sin_cos_series_basecase(t, u, h, hlen, n, prec);
_acb_poly_sin_cos_series_basecase(t, u, h, hlen, n, prec, 0);
_acb_poly_div_series(g, t, n, u, n, n, prec);
NEWTON_END_BASECASE

101
acb_poly/test/t-cos_pi_series.c Normal file
View file

@ -0,0 +1,101 @@
/*=============================================================================
This file is part of ARB.
ARB is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
ARB is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with ARB; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
=============================================================================*/
/******************************************************************************
Copyright (C) 2013 Fredrik Johansson
******************************************************************************/
#include "acb_poly.h"
int main()
{
long iter;
flint_rand_t state;
printf("cos_pi_series....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 1000; iter++)
{
long m, n1, n2, bits1, bits2, bits3;
acb_poly_t S, A, B, C;
acb_t pi;
bits1 = 2 + n_randint(state, 200);
bits2 = 2 + n_randint(state, 200);
bits3 = 2 + n_randint(state, 200);
m = 1 + n_randint(state, 30);
n1 = 1 + n_randint(state, 30);
n2 = 1 + n_randint(state, 30);
acb_poly_init(S);
acb_poly_init(A);
acb_poly_init(B);
acb_poly_init(C);
acb_init(pi);
acb_poly_randtest(S, state, m, bits1, 3);
acb_poly_randtest(A, state, m, bits1, 3);
acb_poly_randtest(B, state, m, bits1, 3);
acb_poly_cos_pi_series(A, S, n1, bits2);
acb_const_pi(pi, bits3);
acb_poly_set_acb(B, pi);
acb_poly_mul(B, S, B, bits3);
acb_poly_cos_series(B, B, n2, bits3);
acb_poly_set(C, A);
acb_poly_truncate(C, FLINT_MIN(n1, n2));
acb_poly_truncate(B, FLINT_MIN(n1, n2));
if (!acb_poly_overlaps(B, C))
{
printf("FAIL\n\n");
printf("S = "); acb_poly_printd(S, 15); printf("\n\n");
printf("A = "); acb_poly_printd(A, 15); printf("\n\n");
printf("B = "); acb_poly_printd(B, 15); printf("\n\n");
abort();
}
acb_poly_cos_pi_series(S, S, n1, bits2);
if (!acb_poly_overlaps(A, S))
{
printf("FAIL (aliasing)\n\n");
abort();
}
acb_poly_clear(S);
acb_poly_clear(A);
acb_poly_clear(B);
acb_poly_clear(C);
acb_clear(pi);
}
flint_randclear(state);
flint_cleanup();
printf("PASS\n");
return EXIT_SUCCESS;
}

114
acb_poly/test/t-sin_cos_pi_series.c Normal file
View file

@ -0,0 +1,114 @@
/*=============================================================================
This file is part of ARB.
ARB is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
ARB is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with ARB; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
=============================================================================*/
/******************************************************************************
Copyright (C) 2012, 2013 Fredrik Johansson
******************************************************************************/
#include "acb_poly.h"
int main()
{
long iter;
flint_rand_t state;
printf("sin_cos_pi_series....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 1000; iter++)
{
long m, n, qbits, rbits1, rbits2;
fmpq_poly_t A, B;
acb_poly_t a, b, c, d, e;
qbits = 2 + n_randint(state, 200);
rbits1 = 2 + n_randint(state, 200);
rbits2 = 2 + n_randint(state, 200);
m = 1 + n_randint(state, 30);
n = 1 + n_randint(state, 30);
fmpq_poly_init(A);
fmpq_poly_init(B);
acb_poly_init(a);
acb_poly_init(b);
acb_poly_init(c);
acb_poly_init(d);
acb_poly_init(e);
fmpq_poly_randtest(A, state, m, qbits);
acb_poly_set_fmpq_poly(a, A, rbits1);
acb_poly_sin_cos_pi_series(b, c, a, n, rbits2);
/* Check sin(x)^2 + cos(x)^2 = 1 */
acb_poly_mullow(d, b, b, n, rbits2);
acb_poly_mullow(e, c, c, n, rbits2);
acb_poly_add(d, d, e, rbits2);
fmpq_poly_one(B);
if (!acb_poly_contains_fmpq_poly(d, B))
{
printf("FAIL\n\n");
printf("bits2 = %ld\n", rbits2);
printf("A = "); fmpq_poly_print(A); printf("\n\n");
printf("a = "); acb_poly_printd(a, 15); printf("\n\n");
printf("b = "); acb_poly_printd(b, 15); printf("\n\n");
printf("c = "); acb_poly_printd(c, 15); printf("\n\n");
printf("d = "); acb_poly_printd(d, 15); printf("\n\n");
abort();
}
acb_poly_set(d, a);
acb_poly_sin_cos_pi_series(d, c, d, n, rbits2);
if (!acb_poly_equal(b, d))
{
printf("FAIL (aliasing 1)\n\n");
abort();
}
acb_poly_set(d, a);
acb_poly_sin_cos_pi_series(b, d, d, n, rbits2);
if (!acb_poly_equal(c, d))
{
printf("FAIL (aliasing 2)\n\n");
abort();
}
fmpq_poly_clear(A);
fmpq_poly_clear(B);
acb_poly_clear(a);
acb_poly_clear(b);
acb_poly_clear(c);
acb_poly_clear(d);
acb_poly_clear(e);
}
flint_randclear(state);
flint_cleanup();
printf("PASS\n");
return EXIT_SUCCESS;
}

8
acb_poly/test/t-sin_cos_series_basecase.c
View file

@ -40,12 +40,14 @@ int main()
long m, n, rbits1, rbits2;
fmpq_poly_t B;
acb_poly_t a, b, c, d, e;
int times_pi;
rbits1 = 2 + n_randint(state, 200);
rbits2 = 2 + n_randint(state, 200);
m = 1 + n_randint(state, 30);
n = 1 + n_randint(state, 30);
times_pi = n_randint(state, 2);
fmpq_poly_init(B);
acb_poly_init(a);
@ -56,7 +58,7 @@ int main()
acb_poly_randtest(a, state, m, rbits1, 10);
acb_poly_sin_cos_series_basecase(b, c, a, n, rbits2);
acb_poly_sin_cos_series_basecase(b, c, a, n, rbits2, times_pi);
/* Check sin(x)^2 + cos(x)^2 = 1 */
acb_poly_mullow(d, b, b, n, rbits2);
@ -78,7 +80,7 @@ int main()
}
acb_poly_set(d, a);
acb_poly_sin_cos_series_basecase(d, c, d, n, rbits2);
acb_poly_sin_cos_series_basecase(d, c, d, n, rbits2, times_pi);
if (!acb_poly_equal(b, d))
{
printf("FAIL (aliasing 1)\n\n");
@ -86,7 +88,7 @@ int main()
}
acb_poly_set(d, a);
acb_poly_sin_cos_series_basecase(b, d, d, n, rbits2);
acb_poly_sin_cos_series_basecase(b, d, d, n, rbits2, times_pi);
if (!acb_poly_equal(c, d))
{
printf("FAIL (aliasing 2)\n\n");

8
acb_poly/test/t-sin_cos_series_tangent.c
View file

@ -40,12 +40,14 @@ int main()
long m, n, rbits1, rbits2;
fmpq_poly_t B;
acb_poly_t a, b, c, d, e;
int times_pi;
rbits1 = 2 + n_randint(state, 200);
rbits2 = 2 + n_randint(state, 200);
m = 1 + n_randint(state, 30);
n = 1 + n_randint(state, 30);
times_pi = n_randint(state, 2);
fmpq_poly_init(B);
acb_poly_init(a);
@ -56,7 +58,7 @@ int main()
acb_poly_randtest(a, state, m, rbits1, 10);
acb_poly_sin_cos_series_tangent(b, c, a, n, rbits2);
acb_poly_sin_cos_series_tangent(b, c, a, n, rbits2, times_pi);
/* Check sin(x)^2 + cos(x)^2 = 1 */
acb_poly_mullow(d, b, b, n, rbits2);
@ -78,7 +80,7 @@ int main()
}
acb_poly_set(d, a);
acb_poly_sin_cos_series_tangent(d, c, d, n, rbits2);
acb_poly_sin_cos_series_tangent(d, c, d, n, rbits2, times_pi);
if (!acb_poly_equal(b, d))
{
printf("FAIL (aliasing 1)\n\n");
@ -86,7 +88,7 @@ int main()
}
acb_poly_set(d, a);
acb_poly_sin_cos_series_tangent(b, d, d, n, rbits2);
acb_poly_sin_cos_series_tangent(b, d, d, n, rbits2, times_pi);
if (!acb_poly_equal(c, d))
{
printf("FAIL (aliasing 2)\n\n");

101
acb_poly/test/t-sin_pi_series.c Normal file
View file

@ -0,0 +1,101 @@
/*=============================================================================
This file is part of ARB.
ARB is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
ARB is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with ARB; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
=============================================================================*/
/******************************************************************************
Copyright (C) 2013 Fredrik Johansson
******************************************************************************/
#include "acb_poly.h"
int main()
{
long iter;
flint_rand_t state;
printf("sin_pi_series....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 1000; iter++)
{
long m, n1, n2, bits1, bits2, bits3;
acb_poly_t S, A, B, C;
acb_t pi;
bits1 = 2 + n_randint(state, 200);
bits2 = 2 + n_randint(state, 200);
bits3 = 2 + n_randint(state, 200);
m = 1 + n_randint(state, 30);
n1 = 1 + n_randint(state, 30);
n2 = 1 + n_randint(state, 30);
acb_poly_init(S);
acb_poly_init(A);
acb_poly_init(B);
acb_poly_init(C);
acb_init(pi);
acb_poly_randtest(S, state, m, bits1, 3);
acb_poly_randtest(A, state, m, bits1, 3);
acb_poly_randtest(B, state, m, bits1, 3);
acb_poly_sin_pi_series(A, S, n1, bits2);
acb_const_pi(pi, bits3);
acb_poly_set_acb(B, pi);
acb_poly_mul(B, S, B, bits3);
acb_poly_sin_series(B, B, n2, bits3);
acb_poly_set(C, A);
acb_poly_truncate(C, FLINT_MIN(n1, n2));
acb_poly_truncate(B, FLINT_MIN(n1, n2));
if (!acb_poly_overlaps(B, C))
{
printf("FAIL\n\n");
printf("S = "); acb_poly_printd(S, 15); printf("\n\n");
printf("A = "); acb_poly_printd(A, 15); printf("\n\n");
printf("B = "); acb_poly_printd(B, 15); printf("\n\n");
abort();
}
acb_poly_sin_pi_series(S, S, n1, bits2);
if (!acb_poly_overlaps(A, S))
{
printf("FAIL (aliasing)\n\n");
abort();
}
acb_poly_clear(S);
acb_poly_clear(A);
acb_poly_clear(B);
acb_poly_clear(C);
acb_clear(pi);
}
flint_randclear(state);
flint_cleanup();
printf("PASS\n");
return EXIT_SUCCESS;
}

10
acb_poly/zeta_series.c
View file

@ -94,11 +94,11 @@ _acb_poly_zeta_series(acb_ptr res, acb_srcptr h, long hlen, const acb_t a, int d
acb_mul_2exp_si(pi, pi, -1);
/* s2 = sin(pi*s/2) / pi */
acb_mul_2exp_si(pi, pi, -1);
acb_mul(f, pi, h, prec);
acb_set(f + 1, pi);
acb_mul_2exp_si(pi, pi, 1);
_acb_poly_sin_series(s2, f, 2, len, prec);
acb_set(f, h);
acb_one(f + 1);
acb_mul_2exp_si(f, f, -1);
acb_mul_2exp_si(f + 1, f + 1, -1);
_acb_poly_sin_pi_series(s2, f, 2, len, prec);
_acb_vec_scalar_div(s2, s2, len, pi, prec);
/* s3 = gamma(1-s) */

22
arb_poly.h
View file

@ -509,16 +509,16 @@ void _arb_poly_exp_series(arb_ptr f, arb_srcptr h, long hlen, long n, long prec)
void arb_poly_exp_series(arb_poly_t f, const arb_poly_t h, long n, long prec);
void _arb_poly_sin_cos_series_basecase(arb_ptr s,
arb_ptr c, arb_srcptr h, long hlen, long n, long prec);
arb_ptr c, arb_srcptr h, long hlen, long n, long prec, int times_pi);
void arb_poly_sin_cos_series_basecase(arb_poly_t s, arb_poly_t c,
const arb_poly_t h, long n, long prec);
const arb_poly_t h, long n, long prec, int times_pi);
void _arb_poly_sin_cos_series_tangent(arb_ptr s, arb_ptr c,
const arb_srcptr h, long hlen, long len, long prec);
const arb_srcptr h, long hlen, long len, long prec, int times_pi);
void arb_poly_sin_cos_series_tangent(arb_poly_t s, arb_poly_t c,
const arb_poly_t h, long n, long prec);
const arb_poly_t h, long n, long prec, int times_pi);
void _arb_poly_sin_cos_series(arb_ptr s, arb_ptr c,
const arb_srcptr h, long hlen, long len, long prec);
@ -526,6 +526,12 @@ void _arb_poly_sin_cos_series(arb_ptr s, arb_ptr c,
void arb_poly_sin_cos_series(arb_poly_t s, arb_poly_t c,
const arb_poly_t h, long n, long prec);
void _arb_poly_sin_cos_pi_series(arb_ptr s, arb_ptr c,
const arb_srcptr h, long hlen, long len, long prec);
void arb_poly_sin_cos_pi_series(arb_poly_t s, arb_poly_t c,
const arb_poly_t h, long n, long prec);
void _arb_poly_sin_series(arb_ptr g, arb_srcptr h, long hlen, long n, long prec);
void arb_poly_sin_series(arb_poly_t g, const arb_poly_t h, long n, long prec);
@ -534,6 +540,14 @@ void _arb_poly_cos_series(arb_ptr g, arb_srcptr h, long hlen, long n, long prec)
void arb_poly_cos_series(arb_poly_t g, const arb_poly_t h, long n, long prec);
void _arb_poly_sin_pi_series(arb_ptr g, arb_srcptr h, long hlen, long n, long prec);
void arb_poly_sin_pi_series(arb_poly_t g, const arb_poly_t h, long n, long prec);
void _arb_poly_cos_pi_series(arb_ptr g, arb_srcptr h, long hlen, long n, long prec);
void arb_poly_cos_pi_series(arb_poly_t g, const arb_poly_t h, long n, long prec);
void _arb_poly_tan_series(arb_ptr g, arb_srcptr h, long hlen, long len, long prec);
void arb_poly_tan_series(arb_poly_t g, const arb_poly_t h, long n, long prec);

82
arb_poly/cos_pi_series.c Normal file
View file

@ -0,0 +1,82 @@
/*=============================================================================
This file is part of ARB.
ARB is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
ARB is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with ARB; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
=============================================================================*/
/******************************************************************************
Copyright (C) 2013 Fredrik Johansson
******************************************************************************/
#include "arb_poly.h"
void
_arb_poly_cos_pi_series(arb_ptr g, arb_srcptr h, long hlen, long n, long prec)
{
hlen = FLINT_MIN(hlen, n);
if (hlen == 1)
{
arb_cos_pi(g, h, prec);
_arb_vec_zero(g + 1, n - 1);
}
else if (n == 2)
{
arb_t t;
arb_init(t);
arb_sin_cos_pi(t, g, h, prec);
arb_neg(t, t);
arb_mul(g + 1, h + 1, t, prec); /* safe since hlen >= 2 */
arb_const_pi(t, prec);
arb_mul(g + 1, g + 1, t, prec);
arb_clear(t);
}
else
{
arb_ptr t = _arb_vec_init(n);
_arb_poly_sin_cos_pi_series(t, g, h, hlen, n, prec);
_arb_vec_clear(t, n);
}
}
void
arb_poly_cos_pi_series(arb_poly_t g, const arb_poly_t h, long n, long prec)
{
long hlen = h->length;
if (n == 0)
{
arb_poly_zero(g);
return;
}
if (hlen == 0)
{
arb_poly_one(g);
return;
}
if (hlen == 1)
n = 1;
arb_poly_fit_length(g, n);
_arb_poly_cos_pi_series(g->coeffs, h->coeffs, hlen, n, prec);
_arb_poly_set_length(g, n);
_arb_poly_normalise(g);
}

6
arb_poly/gamma_series.c
View file

@ -266,9 +266,9 @@ _arb_poly_gamma_series(arb_ptr res, arb_srcptr h, long hlen, long len, long prec
arb_neg(u + i, u + i);
/* v = 1/sin(pi x) */
arb_const_pi(f + 1, wp);
arb_mul(f, h, f + 1, wp);
_arb_poly_sin_series(t, f, 2, len, wp);
arb_set(f, h);
arb_one(f + 1);
_arb_poly_sin_pi_series(t, f, 2, len, wp);
_arb_poly_inv_series(v, t, len, len, wp);
_arb_poly_mullow(t, u, len, v, len, len, wp);

6
arb_poly/rgamma_series.c
View file

@ -129,9 +129,9 @@ _arb_poly_rgamma_series(arb_ptr res, arb_srcptr h, long hlen, long len, long pre
arb_neg(u + i, u + i);
/* v = sin(pi x) */
arb_const_pi(f + 1, wp);
arb_mul(f, h, f + 1, wp);
_arb_poly_sin_series(v, f, 2, len, wp);
arb_set(f, h);
arb_one(f + 1);
_arb_poly_sin_pi_series(v, f, 2, len, wp);
_arb_poly_mullow(t, u, len, v, len, len, wp);

90
arb_poly/sin_cos_pi_series.c Normal file
View file

@ -0,0 +1,90 @@
/*=============================================================================
This file is part of ARB.
ARB is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
ARB is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with ARB; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
=============================================================================*/
/******************************************************************************
Copyright (C) 2013 Fredrik Johansson
******************************************************************************/
#include "arb_poly.h"
#define TANGENT_CUTOFF 240
void
_arb_poly_sin_cos_pi_series(arb_ptr s, arb_ptr c, const arb_srcptr h, long hlen, long n, long 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_sin_cos_pi_series(arb_poly_t s, arb_poly_t c,
const arb_poly_t h, long n, long prec)
{
long hlen = h->length;
if (n == 0)
{
arb_poly_zero(s);
arb_poly_zero(c);
return;
}
if (hlen == 0)
{
arb_poly_zero(s);
arb_poly_one(c);
return;
}
if (hlen == 1)
n = 1;
arb_poly_fit_length(s, n);
arb_poly_fit_length(c, n);
_arb_poly_sin_cos_pi_series(s->coeffs, c->coeffs, h->coeffs, hlen, n, prec);
_arb_poly_set_length(s, n);
_arb_poly_normalise(s);
_arb_poly_set_length(c, n);
_arb_poly_normalise(c);
}

4
arb_poly/sin_cos_series.c
View file

@ -50,9 +50,9 @@ _arb_poly_sin_cos_series(arb_ptr s, arb_ptr c, const arb_srcptr h, long hlen, lo
arb_clear(t);
}
else if (hlen < TANGENT_CUTOFF)
_arb_poly_sin_cos_series_basecase(s, c, h, hlen, n, prec);
_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);
_arb_poly_sin_cos_series_tangent(s, c, h, hlen, n, prec, 0);
}
void

19
arb_poly/sin_cos_series_basecase.c
View file

@ -26,14 +26,17 @@
#include "arb_poly.h"
void
_arb_poly_sin_cos_series_basecase(arb_ptr s,
arb_ptr c, arb_srcptr h, long hlen, long n, long prec)
_arb_poly_sin_cos_series_basecase(arb_ptr s, arb_ptr c, arb_srcptr h, long hlen,
long n, long prec, int times_pi)
{
long j, k, alen = FLINT_MIN(n, hlen);
arb_ptr a;
arb_t t, u;
arb_sin_cos(s, c, h, prec);
if (times_pi)
arb_sin_cos_pi(s, c, h, prec);
else
arb_sin_cos(s, c, h, prec);
if (hlen == 1)
{
@ -49,6 +52,12 @@ _arb_poly_sin_cos_series_basecase(arb_ptr s,
for (k = 1; k < alen; k++)
arb_mul_ui(a + k, h + k, k, prec);
if (times_pi)
{
arb_const_pi(t, prec);
_arb_vec_scalar_mul(a + 1, a + 1, alen - 1, t, prec);
}
for (k = 1; k < n; k++)
{
arb_zero(t);
@ -71,7 +80,7 @@ _arb_poly_sin_cos_series_basecase(arb_ptr s,
void
arb_poly_sin_cos_series_basecase(arb_poly_t s, arb_poly_t c,
const arb_poly_t h, long n, long prec)
const arb_poly_t h, long n, long prec, int times_pi)
{
long hlen = h->length;
@ -91,7 +100,7 @@ arb_poly_sin_cos_series_basecase(arb_poly_t s, arb_poly_t c,
arb_poly_fit_length(s, n);
arb_poly_fit_length(c, n);
_arb_poly_sin_cos_series_basecase(s->coeffs, c->coeffs, h->coeffs, hlen, n, prec);
_arb_poly_sin_cos_series_basecase(s->coeffs, c->coeffs, h->coeffs, hlen, n, prec, times_pi);
_arb_poly_set_length(s, n);
_arb_poly_normalise(s);
_arb_poly_set_length(c, n);

22
arb_poly/sin_cos_series_tangent.c
View file

@ -27,7 +27,7 @@
void
_arb_poly_sin_cos_series_tangent(arb_ptr s, arb_ptr c,
const arb_srcptr h, long hlen, long len, long prec)
const arb_srcptr h, long hlen, long len, long prec, int times_pi)
{
arb_ptr t, u, v;
arb_t s0, c0;
@ -35,7 +35,10 @@ _arb_poly_sin_cos_series_tangent(arb_ptr s, arb_ptr c,
if (hlen == 1)
{
arb_sin_cos(s, c, h, prec);
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;
@ -54,11 +57,20 @@ _arb_poly_sin_cos_series_tangent(arb_ptr s, arb_ptr c,
v = u + len;
/* sin, cos of h0 */
arb_sin_cos(s0, c0, h, prec);
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 */
@ -97,7 +109,7 @@ _arb_poly_sin_cos_series_tangent(arb_ptr s, arb_ptr c,
void
arb_poly_sin_cos_series_tangent(arb_poly_t s, arb_poly_t c,
const arb_poly_t h, long n, long prec)
const arb_poly_t h, long n, long prec, int times_pi)
{
long hlen = h->length;
@ -118,7 +130,7 @@ arb_poly_sin_cos_series_tangent(arb_poly_t s, arb_poly_t c,
arb_poly_fit_length(s, n);
arb_poly_fit_length(c, n);
_arb_poly_sin_cos_series_tangent(s->coeffs, c->coeffs,
h->coeffs, hlen, n, prec);
h->coeffs, hlen, n, prec, times_pi);
_arb_poly_set_length(s, n);
_arb_poly_normalise(s);
_arb_poly_set_length(c, n);

75
arb_poly/sin_pi_series.c Normal file
View file

@ -0,0 +1,75 @@
/*=============================================================================
This file is part of ARB.
ARB is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
ARB is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with ARB; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
=============================================================================*/
/******************************************************************************
Copyright (C) 2013 Fredrik Johansson
******************************************************************************/
#include "arb_poly.h"
void
_arb_poly_sin_pi_series(arb_ptr g, arb_srcptr h, long hlen, long n, long prec)
{
hlen = FLINT_MIN(hlen, n);
if (hlen == 1)
{
arb_sin_pi(g, h, prec);
_arb_vec_zero(g + 1, n - 1);
}
else if (n == 2)
{
arb_t t;
arb_init(t);
arb_sin_cos_pi(g, t, h, prec);
arb_mul(g + 1, h + 1, t, prec); /* safe since hlen >= 2 */
arb_const_pi(t, prec);
arb_mul(g + 1, g + 1, t, prec);
arb_clear(t);
}
else
{
arb_ptr t = _arb_vec_init(n);
_arb_poly_sin_cos_pi_series(g, t, h, hlen, n, prec);
_arb_vec_clear(t, n);
}
}
void
arb_poly_sin_pi_series(arb_poly_t g, const arb_poly_t h, long n, long prec)
{
long hlen = h->length;
if (hlen == 0 || n == 0)
{
arb_poly_zero(g);
return;
}
if (hlen == 1)
n = 1;
arb_poly_fit_length(g, n);
_arb_poly_sin_pi_series(g->coeffs, h->coeffs, hlen, n, prec);
_arb_poly_set_length(g, n);
_arb_poly_normalise(g);
}

2
arb_poly/tan_series.c
View file

@ -58,7 +58,7 @@ _arb_poly_tan_series(arb_ptr g,
NEWTON_INIT(TAN_NEWTON_CUTOFF, len)
NEWTON_BASECASE(n)
_arb_poly_sin_cos_series_basecase(t, u, h, hlen, n, prec);
_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

2
arb_poly/test/t-acos_series.c
View file

@ -62,7 +62,7 @@ int main()
arb_poly_acos_series(b, a, n, rbits2);
/* Check cos(acos(x)) = x */
arb_poly_sin_cos_series_basecase(d, c, b, n, rbits2);
arb_poly_sin_cos_series_basecase(d, c, b, n, rbits2, 0);
fmpq_poly_truncate(A, n);
if (!arb_poly_contains_fmpq_poly(c, A))

2
arb_poly/test/t-asin_series.c
View file

@ -62,7 +62,7 @@ int main()
arb_poly_asin_series(b, a, n, rbits2);
/* Check sin(asin(x)) = x */
arb_poly_sin_cos_series_basecase(c, d, b, n, rbits2);
arb_poly_sin_cos_series_basecase(c, d, b, n, rbits2, 0);
fmpq_poly_truncate(A, n);
if (!arb_poly_contains_fmpq_poly(c, A))

101
arb_poly/test/t-cos_pi_series.c Normal file
View file

@ -0,0 +1,101 @@
/*=============================================================================
This file is part of ARB.
ARB is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
ARB is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with ARB; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
=============================================================================*/
/******************************************************************************
Copyright (C) 2013 Fredrik Johansson
******************************************************************************/
#include "arb_poly.h"
int main()
{
long iter;
flint_rand_t state;
printf("cos_pi_series....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 1000; iter++)
{
long m, n1, n2, bits1, bits2, bits3;
arb_poly_t S, A, B, C;
arb_t pi;
bits1 = 2 + n_randint(state, 200);
bits2 = 2 + n_randint(state, 200);
bits3 = 2 + n_randint(state, 200);
m = 1 + n_randint(state, 30);
n1 = 1 + n_randint(state, 30);
n2 = 1 + n_randint(state, 30);
arb_poly_init(S);
arb_poly_init(A);
arb_poly_init(B);
arb_poly_init(C);
arb_init(pi);
arb_poly_randtest(S, state, m, bits1, 3);
arb_poly_randtest(A, state, m, bits1, 3);
arb_poly_randtest(B, state, m, bits1, 3);
arb_poly_cos_pi_series(A, S, n1, bits2);
arb_const_pi(pi, bits3);
arb_poly_set_arb(B, pi);
arb_poly_mul(B, S, B, bits3);
arb_poly_cos_series(B, B, n2, bits3);
arb_poly_set(C, A);
arb_poly_truncate(C, FLINT_MIN(n1, n2));
arb_poly_truncate(B, FLINT_MIN(n1, n2));
if (!arb_poly_overlaps(B, C))
{
printf("FAIL\n\n");
printf("S = "); arb_poly_printd(S, 15); printf("\n\n");
printf("A = "); arb_poly_printd(A, 15); printf("\n\n");
printf("B = "); arb_poly_printd(B, 15); printf("\n\n");
abort();
}
arb_poly_cos_pi_series(S, S, n1, bits2);
if (!arb_poly_overlaps(A, S))
{
printf("FAIL (aliasing)\n\n");
abort();
}
arb_poly_clear(S);
arb_poly_clear(A);
arb_poly_clear(B);
arb_poly_clear(C);
arb_clear(pi);
}
flint_randclear(state);
flint_cleanup();
printf("PASS\n");
return EXIT_SUCCESS;
}

114
arb_poly/test/t-sin_cos_pi_series.c Normal file
View file

@ -0,0 +1,114 @@
/*=============================================================================
This file is part of ARB.
ARB is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
ARB is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with ARB; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
=============================================================================*/
/******************************************************************************
Copyright (C) 2012, 2013 Fredrik Johansson
******************************************************************************/
#include "arb_poly.h"
int main()
{
long iter;
flint_rand_t state;
printf("sin_cos_pi_series....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 1000; iter++)
{
long m, n, qbits, rbits1, rbits2;
fmpq_poly_t A, B;
arb_poly_t a, b, c, d, e;
qbits = 2 + n_randint(state, 200);
rbits1 = 2 + n_randint(state, 200);
rbits2 = 2 + n_randint(state, 200);
m = 1 + n_randint(state, 30);
n = 1 + n_randint(state, 30);
fmpq_poly_init(A);
fmpq_poly_init(B);
arb_poly_init(a);
arb_poly_init(b);
arb_poly_init(c);
arb_poly_init(d);
arb_poly_init(e);
fmpq_poly_randtest(A, state, m, qbits);
arb_poly_set_fmpq_poly(a, A, rbits1);
arb_poly_sin_cos_pi_series(b, c, a, n, rbits2);
/* Check sin(x)^2 + cos(x)^2 = 1 */
arb_poly_mullow(d, b, b, n, rbits2);
arb_poly_mullow(e, c, c, n, rbits2);
arb_poly_add(d, d, e, rbits2);
fmpq_poly_one(B);
if (!arb_poly_contains_fmpq_poly(d, B))
{
printf("FAIL\n\n");
printf("bits2 = %ld\n", rbits2);
printf("A = "); fmpq_poly_print(A); printf("\n\n");
printf("a = "); arb_poly_printd(a, 15); printf("\n\n");
printf("b = "); arb_poly_printd(b, 15); printf("\n\n");
printf("c = "); arb_poly_printd(c, 15); printf("\n\n");
printf("d = "); arb_poly_printd(d, 15); printf("\n\n");
abort();
}
arb_poly_set(d, a);
arb_poly_sin_cos_pi_series(d, c, d, n, rbits2);
if (!arb_poly_equal(b, d))
{
printf("FAIL (aliasing 1)\n\n");
abort();
}
arb_poly_set(d, a);
arb_poly_sin_cos_pi_series(b, d, d, n, rbits2);
if (!arb_poly_equal(c, d))
{
printf("FAIL (aliasing 2)\n\n");
abort();
}
fmpq_poly_clear(A);
fmpq_poly_clear(B);
arb_poly_clear(a);
arb_poly_clear(b);
arb_poly_clear(c);
arb_poly_clear(d);
arb_poly_clear(e);
}
flint_randclear(state);
flint_cleanup();
printf("PASS\n");
return EXIT_SUCCESS;
}

8
arb_poly/test/t-sin_cos_series_basecase.c
View file

@ -40,6 +40,7 @@ int main()
long m, n, qbits, rbits1, rbits2;
fmpq_poly_t A, B;
arb_poly_t a, b, c, d, e;
int times_pi;
qbits = 2 + n_randint(state, 200);
rbits1 = 2 + n_randint(state, 200);
@ -47,6 +48,7 @@ int main()
m = 1 + n_randint(state, 30);
n = 1 + n_randint(state, 30);
times_pi = n_randint(state, 2);
fmpq_poly_init(A);
fmpq_poly_init(B);
@ -59,7 +61,7 @@ int main()
fmpq_poly_randtest(A, state, m, qbits);
arb_poly_set_fmpq_poly(a, A, rbits1);
arb_poly_sin_cos_series_basecase(b, c, a, n, rbits2);
arb_poly_sin_cos_series_basecase(b, c, a, n, rbits2, times_pi);
/* Check sin(x)^2 + cos(x)^2 = 1 */
arb_poly_mullow(d, b, b, n, rbits2);
@ -82,7 +84,7 @@ int main()
}
arb_poly_set(d, a);
arb_poly_sin_cos_series_basecase(d, c, d, n, rbits2);
arb_poly_sin_cos_series_basecase(d, c, d, n, rbits2, times_pi);
if (!arb_poly_equal(b, d))
{
printf("FAIL (aliasing 1)\n\n");
@ -90,7 +92,7 @@ int main()
}
arb_poly_set(d, a);
arb_poly_sin_cos_series_basecase(b, d, d, n, rbits2);
arb_poly_sin_cos_series_basecase(b, d, d, n, rbits2, times_pi);
if (!arb_poly_equal(c, d))
{
printf("FAIL (aliasing 2)\n\n");

8
arb_poly/test/t-sin_cos_series_tangent.c
View file

@ -40,6 +40,7 @@ int main()
long m, n, qbits, rbits1, rbits2;
fmpq_poly_t A, B;
arb_poly_t a, b, c, d, e;
int times_pi;
qbits = 2 + n_randint(state, 200);
rbits1 = 2 + n_randint(state, 200);
@ -47,6 +48,7 @@ int main()
m = 1 + n_randint(state, 30);
n = 1 + n_randint(state, 30);
times_pi = n_randint(state, 2);
fmpq_poly_init(A);
fmpq_poly_init(B);
@ -59,7 +61,7 @@ int main()
fmpq_poly_randtest(A, state, m, qbits);
arb_poly_set_fmpq_poly(a, A, rbits1);
arb_poly_sin_cos_series_tangent(b, c, a, n, rbits2);
arb_poly_sin_cos_series_tangent(b, c, a, n, rbits2, times_pi);
/* Check sin(x)^2 + cos(x)^2 = 1 */
arb_poly_mullow(d, b, b, n, rbits2);
@ -82,7 +84,7 @@ int main()
}
arb_poly_set(d, a);
arb_poly_sin_cos_series_tangent(d, c, d, n, rbits2);
arb_poly_sin_cos_series_tangent(d, c, d, n, rbits2, times_pi);
if (!arb_poly_equal(b, d))
{
printf("FAIL (aliasing 1)\n\n");
@ -90,7 +92,7 @@ int main()
}
arb_poly_set(d, a);
arb_poly_sin_cos_series_tangent(b, d, d, n, rbits2);
arb_poly_sin_cos_series_tangent(b, d, d, n, rbits2, times_pi);
if (!arb_poly_equal(c, d))
{
printf("FAIL (aliasing 2)\n\n");

101
arb_poly/test/t-sin_pi_series.c Normal file
View file

@ -0,0 +1,101 @@
/*=============================================================================
This file is part of ARB.
ARB is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
ARB is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with ARB; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
=============================================================================*/
/******************************************************************************
Copyright (C) 2013 Fredrik Johansson
******************************************************************************/
#include "arb_poly.h"
int main()
{
long iter;
flint_rand_t state;
printf("sin_pi_series....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 1000; iter++)
{
long m, n1, n2, bits1, bits2, bits3;
arb_poly_t S, A, B, C;
arb_t pi;
bits1 = 2 + n_randint(state, 200);
bits2 = 2 + n_randint(state, 200);
bits3 = 2 + n_randint(state, 200);
m = 1 + n_randint(state, 30);
n1 = 1 + n_randint(state, 30);
n2 = 1 + n_randint(state, 30);
arb_poly_init(S);
arb_poly_init(A);
arb_poly_init(B);
arb_poly_init(C);
arb_init(pi);
arb_poly_randtest(S, state, m, bits1, 3);
arb_poly_randtest(A, state, m, bits1, 3);
arb_poly_randtest(B, state, m, bits1, 3);
arb_poly_sin_pi_series(A, S, n1, bits2);
arb_const_pi(pi, bits3);
arb_poly_set_arb(B, pi);
arb_poly_mul(B, S, B, bits3);
arb_poly_sin_series(B, B, n2, bits3);
arb_poly_set(C, A);
arb_poly_truncate(C, FLINT_MIN(n1, n2));
arb_poly_truncate(B, FLINT_MIN(n1, n2));
if (!arb_poly_overlaps(B, C))
{
printf("FAIL\n\n");
printf("S = "); arb_poly_printd(S, 15); printf("\n\n");
printf("A = "); arb_poly_printd(A, 15); printf("\n\n");
printf("B = "); arb_poly_printd(B, 15); printf("\n\n");
abort();
}
arb_poly_sin_pi_series(S, S, n1, bits2);
if (!arb_poly_overlaps(A, S))
{
printf("FAIL (aliasing)\n\n");
abort();
}
arb_poly_clear(S);
arb_poly_clear(A);
arb_poly_clear(B);
arb_poly_clear(C);
arb_clear(pi);
}
flint_randclear(state);
flint_cleanup();
printf("PASS\n");
return EXIT_SUCCESS;
}

10
arb_poly/zeta_series.c
View file

@ -100,11 +100,11 @@ _arb_poly_zeta_series(arb_ptr res, arb_srcptr h, long hlen, const arb_t a, int d
arb_mul_2exp_si(pi, pi, -1);
/* s2 = sin(pi*s/2) / pi */
arb_mul_2exp_si(pi, pi, -1);
arb_mul(f, pi, h, prec);
arb_set(f + 1, pi);
arb_mul_2exp_si(pi, pi, 1);
_arb_poly_sin_series(s2, f, 2, len, prec);
arb_set(f, h);
arb_one(f + 1);
arb_mul_2exp_si(f, f, -1);
arb_mul_2exp_si(f + 1, f + 1, -1);
_arb_poly_sin_pi_series(s2, f, 2, len, prec);
_arb_vec_scalar_div(s2, s2, len, pi, prec);
/* s3 = gamma(1-s) */

26
doc/source/acb_poly.rst
View file

@ -670,13 +670,13 @@ Elementary functions
The underscore methods support aliasing and allow the input to be
shorter than the output, but require the lengths to be nonzero.
.. function:: void _acb_poly_sin_cos_series_basecase(acb_ptr s, acb_ptr c, acb_srcptr h, long hlen, long n, long prec)
.. function:: void _acb_poly_sin_cos_series_basecase(acb_ptr s, acb_ptr c, acb_srcptr h, long hlen, long n, long prec, int times_pi)
.. function:: void acb_poly_sin_cos_series_basecase(acb_poly_t s, acb_poly_t c, const acb_poly_t h, long n, long prec)
.. function:: void acb_poly_sin_cos_series_basecase(acb_poly_t s, acb_poly_t c, const acb_poly_t h, long n, long prec, int times_pi)
.. function:: void _acb_poly_sin_cos_series_tangent(acb_ptr s, acb_ptr c, acb_srcptr h, long hlen, long n, long prec)
.. function:: void _acb_poly_sin_cos_series_tangent(acb_ptr s, acb_ptr c, acb_srcptr h, long hlen, long n, long prec, int times_pi)
.. function:: void acb_poly_sin_cos_series_tangent(acb_poly_t s, acb_poly_t c, const acb_poly_t h, long n, long prec)
.. function:: void acb_poly_sin_cos_series_tangent(acb_poly_t s, acb_poly_t c, const acb_poly_t h, long n, long prec, int times_pi)
.. function:: void _acb_poly_sin_cos_series(acb_ptr s, acb_ptr c, acb_srcptr h, long hlen, long n, long prec)
@ -701,6 +701,9 @@ Elementary functions
The default version automatically selects between the *basecase* and
*tangent* algorithms depending on the input.
The *basecase* and *tangent* versions take a flag *times_pi*
specifying that the input is to be multiplied by `\pi`.
The underscore methods support aliasing and require the lengths to be nonzero.
.. function:: void _acb_poly_sin_series(acb_ptr s, acb_srcptr h, long hlen, long n, long prec)
@ -715,6 +718,21 @@ Elementary functions
simply wrap :func:`_acb_poly_sin_cos_series`. The underscore methods
support aliasing and require the lengths to be nonzero.
.. function:: void _acb_poly_sin_cos_pi_series(acb_ptr s, acb_ptr c, acb_srcptr h, long hlen, long n, long prec)
.. function:: void acb_poly_sin_cos_pi_series(acb_poly_t s, acb_poly_t c, const acb_poly_t h, long n, long prec)
.. function:: void _acb_poly_sin_pi_series(acb_ptr s, acb_srcptr h, long hlen, long n, long prec)
.. function:: void acb_poly_sin_pi_series(acb_poly_t s, const acb_poly_t h, long n, long prec)
.. function:: void _acb_poly_cos_pi_series(acb_ptr c, acb_srcptr h, long hlen, long n, long prec)
.. function:: void acb_poly_cos_pi_series(acb_poly_t c, const acb_poly_t h, long n, long prec)
Compute the respective trigonometric functions of the input
multiplied by `\pi`.
.. function:: void _acb_poly_tan_series(acb_ptr g, acb_srcptr h, long hlen, long len, long prec)
.. function:: void acb_poly_tan_series(acb_poly_t g, const acb_poly_t h, long n, long prec)

26
doc/source/arb_poly.rst
View file

@ -766,13 +766,13 @@ Powers and elementary functions
The underscore methods support aliasing and allow the input to be
shorter than the output, but require the lengths to be nonzero.
.. function:: void _arb_poly_sin_cos_series_basecase(arb_ptr s, arb_ptr c, arb_srcptr h, long hlen, long n, long prec)
.. function:: void _arb_poly_sin_cos_series_basecase(arb_ptr s, arb_ptr c, arb_srcptr h, long hlen, long n, long prec, int times_pi)
.. function:: void arb_poly_sin_cos_series_basecase(arb_poly_t s, arb_poly_t c, const arb_poly_t h, long n, long prec)
.. function:: void arb_poly_sin_cos_series_basecase(arb_poly_t s, arb_poly_t c, const arb_poly_t h, long n, long prec, int times_pi)
.. function:: void _arb_poly_sin_cos_series_tangent(arb_ptr s, arb_ptr c, arb_srcptr h, long hlen, long n, long prec)
.. function:: void _arb_poly_sin_cos_series_tangent(arb_ptr s, arb_ptr c, arb_srcptr h, long hlen, long n, long prec, int times_pi)
.. function:: void arb_poly_sin_cos_series_tangent(arb_poly_t s, arb_poly_t c, const arb_poly_t h, long n, long prec)
.. function:: void arb_poly_sin_cos_series_tangent(arb_poly_t s, arb_poly_t c, const arb_poly_t h, long n, long prec, int times_pi)
.. function:: void _arb_poly_sin_cos_series(arb_ptr s, arb_ptr c, arb_srcptr h, long hlen, long n, long prec)
@ -797,6 +797,9 @@ Powers and elementary functions
The default version automatically selects between the *basecase* and
*tangent* algorithms depending on the input.
The *basecase* and *tangent* versions take a flag *times_pi*
specifying that the input is to be multiplied by `\pi`.
The underscore methods support aliasing and require the lengths to be nonzero.
.. function:: void _arb_poly_sin_series(arb_ptr s, arb_srcptr h, long hlen, long n, long prec)
@ -811,6 +814,21 @@ Powers and elementary functions
simply wrap :func:`_arb_poly_sin_cos_series`. The underscore methods
support aliasing and require the lengths to be nonzero.
.. function:: void _arb_poly_sin_cos_pi_series(arb_ptr s, arb_ptr c, arb_srcptr h, long hlen, long n, long prec)
.. function:: void arb_poly_sin_cos_pi_series(arb_poly_t s, arb_poly_t c, const arb_poly_t h, long n, long prec)
.. function:: void _arb_poly_sin_pi_series(arb_ptr s, arb_srcptr h, long hlen, long n, long prec)
.. function:: void arb_poly_sin_pi_series(arb_poly_t s, const arb_poly_t h, long n, long prec)
.. function:: void _arb_poly_cos_pi_series(arb_ptr c, arb_srcptr h, long hlen, long n, long prec)
.. function:: void arb_poly_cos_pi_series(arb_poly_t c, const arb_poly_t h, long n, long prec)
Compute the respective trigonometric functions of the input
multiplied by `\pi`.
.. function:: void _arb_poly_tan_series(arb_ptr g, arb_srcptr h, long hlen, long len, long prec)
.. function:: void arb_poly_tan_series(arb_poly_t g, const arb_poly_t h, long n, long prec)