add sin_pi_series and friends

acb_poly.h

@@ -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);

acb_poly/cos_pi_series.c

@@ -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);
+}
+

acb_poly/gamma_series.c

@@ -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_set(f, h);
-        acb_mul(f, h, f + 1, wp);
+        acb_one(f + 1);
-        _acb_poly_sin_series(t, f, 2, len, wp);
+        _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);

acb_poly/rgamma_series.c

@@ -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_set(f, h);
-        acb_mul(f, h, f + 1, wp);
+        acb_one(f + 1);
-        _acb_poly_sin_series(v, f, 2, len, wp);
+        _acb_poly_sin_pi_series(v, f, 2, len, wp);
 
         _acb_poly_mullow(t, u, len, v, len, len, wp);
 

acb_poly/sin_cos_pi_series.c

@@ -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);
+}
+

acb_poly/sin_cos_series.c

@@ -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

acb_poly/sin_cos_series_basecase.c

@@ -26,13 +26,16 @@
 #include "acb_poly.h"
 
 void
-_acb_poly_sin_cos_series_basecase(acb_ptr s,
+_acb_poly_sin_cos_series_basecase(acb_ptr s, acb_ptr c, acb_srcptr h, long hlen,
-                                    acb_ptr c, acb_srcptr h, long hlen, long n, long prec)
+        long n, long prec, int times_pi)
 {
     long j, k, alen = FLINT_MIN(n, hlen);
     acb_ptr a;
     acb_t t, u;
 
+    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);

acb_poly/sin_cos_series_tangent.c

@@ -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;
@@ -35,6 +35,9 @@ _acb_poly_sin_cos_series_tangent(acb_ptr s, acb_ptr c,
 
     if (hlen == 1)
     {
+        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);
@@ -54,11 +57,20 @@ _acb_poly_sin_cos_series_tangent(acb_ptr s, acb_ptr c,
     v = u + len;
 
     /* sin, cos of h0 */
+    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);

acb_poly/sin_pi_series.c

@@ -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);
+}
+

acb_poly/tan_series.c

@@ -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
 

acb_poly/test/t-cos_pi_series.c

@@ -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;
+}

acb_poly/test/t-sin_cos_pi_series.c

@@ -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;
+}
+

acb_poly/test/t-sin_cos_series_basecase.c

@@ -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");

acb_poly/test/t-sin_cos_series_tangent.c

@@ -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");

acb_poly/test/t-sin_pi_series.c

@@ -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;
+}

acb_poly/zeta_series.c

@@ -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_set(f, h);
-        acb_mul(f, pi, h, prec);
+        acb_one(f + 1);
-        acb_set(f + 1, pi);
+        acb_mul_2exp_si(f, f, -1);
-        acb_mul_2exp_si(pi, pi, 1);
+        acb_mul_2exp_si(f + 1, f + 1, -1);
-        _acb_poly_sin_series(s2, f, 2, len, prec);
+        _acb_poly_sin_pi_series(s2, f, 2, len, prec);
         _acb_vec_scalar_div(s2, s2, len, pi, prec);
 
         /* s3 = gamma(1-s) */

arb_poly.h

@@ -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);

arb_poly/cos_pi_series.c

@@ -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);
+}
+

arb_poly/gamma_series.c

@@ -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_set(f, h);
-            arb_mul(f, h, f + 1, wp);
+            arb_one(f + 1);
-            _arb_poly_sin_series(t, f, 2, len, wp);
+            _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);

arb_poly/rgamma_series.c

@@ -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_set(f, h);
-            arb_mul(f, h, f + 1, wp);
+            arb_one(f + 1);
-            _arb_poly_sin_series(v, f, 2, len, wp);
+            _arb_poly_sin_pi_series(v, f, 2, len, wp);
 
             _arb_poly_mullow(t, u, len, v, len, len, wp);
 

arb_poly/sin_cos_pi_series.c

@@ -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);
+}
+

arb_poly/sin_cos_series.c

@@ -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

arb_poly/sin_cos_series_basecase.c

@@ -26,13 +26,16 @@
 #include "arb_poly.h"
 
 void
-_arb_poly_sin_cos_series_basecase(arb_ptr s,
+_arb_poly_sin_cos_series_basecase(arb_ptr s, arb_ptr c, arb_srcptr h, long hlen,
-                                    arb_ptr c, arb_srcptr h, long hlen, long n, long prec)
+        long n, long prec, int times_pi)
 {
     long j, k, alen = FLINT_MIN(n, hlen);
     arb_ptr a;
     arb_t t, u;
 
+    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);

arb_poly/sin_cos_series_tangent.c

@@ -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;
@@ -35,6 +35,9 @@ _arb_poly_sin_cos_series_tangent(arb_ptr s, arb_ptr c,
 
     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);
@@ -54,11 +57,20 @@ _arb_poly_sin_cos_series_tangent(arb_ptr s, arb_ptr c,
     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 */
@@ -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);

arb_poly/sin_pi_series.c

@@ -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);
+}
+

arb_poly/tan_series.c

@@ -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
 

arb_poly/test/t-acos_series.c

@@ -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))

arb_poly/test/t-asin_series.c

@@ -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))

arb_poly/test/t-cos_pi_series.c

@@ -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;
+}

arb_poly/test/t-sin_cos_pi_series.c

@@ -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;
+}
+

arb_poly/test/t-sin_cos_series_basecase.c

@@ -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");

arb_poly/test/t-sin_cos_series_tangent.c

@@ -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");

arb_poly/test/t-sin_pi_series.c

@@ -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;
+}

arb_poly/zeta_series.c

@@ -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_set(f, h);
-        arb_mul(f, pi, h, prec);
+        arb_one(f + 1);
-        arb_set(f + 1, pi);
+        arb_mul_2exp_si(f, f, -1);
-        arb_mul_2exp_si(pi, pi, 1);
+        arb_mul_2exp_si(f + 1, f + 1, -1);
-        _arb_poly_sin_series(s2, f, 2, len, prec);
+        _arb_poly_sin_pi_series(s2, f, 2, len, prec);
         _arb_vec_scalar_div(s2, s2, len, pi, prec);
 
         /* s3 = gamma(1-s) */

doc/source/acb_poly.rst

@@ -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)

doc/source/arb_poly.rst

@@ -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)