implement Borel transform, binomial transform for fmprb_poly

doc/source/fmprb_poly.rst

@@ -527,6 +527,57 @@ Differentiation
     Sets *res* to the integral of *poly*.
 
 
+Transforms
+-------------------------------------------------------------------------------
+
+.. function:: void _fmprb_poly_borel_transform(fmprb_ptr res, fmprb_srcptr poly, long len, long prec)
+
+.. function:: void fmprb_poly_borel_transform(fmprb_poly_t res, const fmprb_poly_t poly, long prec)
+
+    Computes the Borel transform of the input polynomial, mapping `\sum_k a_k x^k`
+    to `\sum_k (a_k / k!) x^k`. The underscore method allows aliasing.
+
+.. function:: void _fmprb_poly_inv_borel_transform(fmprb_ptr res, fmprb_srcptr poly, long len, long prec)
+
+.. function:: void fmprb_poly_inv_borel_transform(fmprb_poly_t res, const fmprb_poly_t poly, long prec)
+
+    Computes the inverse Borel transform of the input polynomial, mapping `\sum_k a_k x^k`
+    to `\sum_k a_k k! x^k`. The underscore method allows aliasing.
+
+.. function:: void _fmprb_poly_binomial_transform_basecase(fmprb_ptr b, fmprb_srcptr a, long alen, long len, long prec)
+
+.. function:: void fmprb_poly_binomial_transform_basecase(fmprb_poly_t b, const fmprb_poly_t a, long len, long prec)
+
+.. function:: void _fmprb_poly_binomial_transform_convolution(fmprb_ptr b, fmprb_srcptr a, long alen, long len, long prec)
+
+.. function:: void fmprb_poly_binomial_transform_convolution(fmprb_poly_t b, const fmprb_poly_t a, long len, long prec)
+
+.. function:: void _fmprb_poly_binomial_transform(fmprb_ptr b, fmprb_srcptr a, long alen, long len, long prec)
+
+.. function:: void fmprb_poly_binomial_transform(fmprb_poly_t b, const fmprb_poly_t a, long len, long prec)
+
+    Computes the binomial transform of the input truncated to length *len*.
+    The binomial transform maps the coefficients `a_k` in the input polynomial
+    to the coefficients `b_k` in the output polynomial via
+    `b_n = \sum_{k=0}^n (-1)^k {n \choose k} a_k`.
+    The binomial transform is equivalent to the power series composition
+    `f(x) \to (1-x)^{-1} f(x/(x-1))`, and is its own inverse.
+
+    The *basecase* version evaluates coefficients one by one from the
+    definition, generating the binomial coefficients by a recurrence
+    relation.
+
+    The *convolution* version uses the identity
+    `T(f(x)) = B^{-1}(e^x B(f(-x)))` where `T` denotes the binomial
+    transform operator and `B` denotes the Borel transform operator.
+    This only costs a single polynomial multiplication, plus some
+    scalar operations.
+
+    The default version automatically chooses an algorithm.
+
+    The underscore methods do not support aliasing, and assume that
+    the lengths are nonzero.
+
 Special functions
 -------------------------------------------------------------------------------
 

fmprb_poly.h

@@ -427,6 +427,28 @@ void _fmprb_poly_integral(fmprb_ptr res, fmprb_srcptr poly, long len, long prec)
 
 void fmprb_poly_integral(fmprb_poly_t res, const fmprb_poly_t poly, long prec);
 
+/* Transforms */
+
+void fmprb_poly_borel_transform(fmprb_poly_t res, const fmprb_poly_t poly, long prec);
+
+void _fmprb_poly_borel_transform(fmprb_ptr res, fmprb_srcptr poly, long len, long prec);
+
+void fmprb_poly_inv_borel_transform(fmprb_poly_t res, const fmprb_poly_t poly, long prec);
+
+void _fmprb_poly_inv_borel_transform(fmprb_ptr res, fmprb_srcptr poly, long len, long prec);
+
+void _fmprb_poly_binomial_transform_basecase(fmprb_ptr b, fmprb_srcptr a, long alen, long len, long prec);
+
+void fmprb_poly_binomial_transform_basecase(fmprb_poly_t b, const fmprb_poly_t a, long len, long prec);
+
+void _fmprb_poly_binomial_transform_convolution(fmprb_ptr b, fmprb_srcptr a, long alen, long len, long prec);
+
+void fmprb_poly_binomial_transform_convolution(fmprb_poly_t b, const fmprb_poly_t a, long len, long prec);
+
+void _fmprb_poly_binomial_transform(fmprb_ptr b, fmprb_srcptr a, long alen, long len, long prec);
+
+void fmprb_poly_binomial_transform(fmprb_poly_t b, const fmprb_poly_t a, long len, long prec);
+
 /* Special functions */
 
 void _fmprb_poly_rsqrt_series(fmprb_ptr g,

fmprb_poly/binomial_transform.c

@@ -0,0 +1,63 @@
+/*=============================================================================
+
+    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 "fmprb_poly.h"
+
+void
+_fmprb_poly_binomial_transform(fmprb_ptr b, fmprb_srcptr a, long alen, long len, long prec)
+{
+    if (alen < 10 || len < 10)
+        _fmprb_poly_binomial_transform_basecase(b, a, alen, len, prec);
+    else
+        _fmprb_poly_binomial_transform_convolution(b, a, alen, len, prec);
+}
+
+void
+fmprb_poly_binomial_transform(fmprb_poly_t b, const fmprb_poly_t a, long len, long prec)
+{
+    if (len == 0 || a->length == 0)
+    {
+        fmprb_poly_zero(b);
+        return;
+    }
+
+    if (b == a)
+    {
+        fmprb_poly_t c;
+        fmprb_poly_init2(c, len);
+        _fmprb_poly_binomial_transform(c->coeffs, a->coeffs, a->length, len, prec);
+        fmprb_poly_swap(b, c);
+        fmprb_poly_clear(c);
+    }
+    else
+    {
+        fmprb_poly_fit_length(b, len);
+        _fmprb_poly_binomial_transform(b->coeffs, a->coeffs, a->length, len, prec);
+    }
+
+    _fmprb_poly_set_length(b, len);
+    _fmprb_poly_normalise(b);
+}
+

fmprb_poly/binomial_transform_basecase.c

@@ -0,0 +1,85 @@
+/*=============================================================================
+
+    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 Fredrik Johansson
+
+******************************************************************************/
+
+#include "fmprb_poly.h"
+
+void
+_fmprb_poly_binomial_transform_basecase(fmprb_ptr b, fmprb_srcptr a, long alen, long len, long prec)
+{
+    long n, k;
+
+    fmpz_t t;
+    fmpz_init(t);
+
+    for (n = 0; n < len; n++)
+    {
+        fmprb_zero(b + n);
+
+        for (k = 0; k < FLINT_MIN(n + 1, alen); k++)
+        {
+            if (k == 0)
+            {
+                fmpz_one(t);
+            }
+            else
+            {
+                fmpz_mul_si(t, t, -(n - k + 1));
+                fmpz_divexact_ui(t, t, k);
+            }
+
+            fmprb_addmul_fmpz(b + n, a + k, t, prec);
+        }
+    }
+
+    fmpz_clear(t);
+}
+
+void
+fmprb_poly_binomial_transform_basecase(fmprb_poly_t b, const fmprb_poly_t a, long len, long prec)
+{
+    if (len == 0 || a->length == 0)
+    {
+        fmprb_poly_zero(b);
+        return;
+    }
+
+    if (b == a)
+    {
+        fmprb_poly_t c;
+        fmprb_poly_init2(c, len);
+        _fmprb_poly_binomial_transform_basecase(c->coeffs, a->coeffs, a->length, len, prec);
+        fmprb_poly_swap(b, c);
+        fmprb_poly_clear(c);
+    }
+    else
+    {
+        fmprb_poly_fit_length(b, len);
+        _fmprb_poly_binomial_transform_basecase(b->coeffs, a->coeffs, a->length, len, prec);
+    }
+
+    _fmprb_poly_set_length(b, len);
+    _fmprb_poly_normalise(b);
+}
+

fmprb_poly/binomial_transform_convolution.c

@@ -0,0 +1,96 @@
+/*=============================================================================
+
+    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 <math.h>
+#include "fmprb_poly.h"
+
+void
+_fmprb_poly_binomial_transform_convolution(fmprb_ptr b, fmprb_srcptr a, long alen, long len, long prec)
+{
+    long i, s;
+    fmprb_ptr c, d;
+
+    alen = FLINT_MIN(alen, len);
+
+    c = _fmprb_vec_init(alen);
+    d = _fmprb_vec_init(len);
+
+    /* Hack: rescale x -> 2^s x such that (2^s)^n / n! ~= 1,
+       improving efficiency of block multiplication. The proper
+       solution is to add automatic near-optimal scaling in the
+       block multiplication. */
+    s = (log(len) - 1) * 1.44269504088896 + 0.5;
+
+    _fmprb_poly_borel_transform(c, a, alen, prec);
+    for (i = 1; i < alen; i += 2)
+        fmprb_neg(c + i, c + i);
+
+    fmprb_one(d);
+    for (i = 1; i < len; i++)
+        fmprb_div_ui(d + i, d + i - 1, i, prec);
+
+    for (i = 0; i < alen; i++)
+        fmprb_mul_2exp_si(c + i, c + i, i * s);
+    for (i = 0; i < len; i++)
+        fmprb_mul_2exp_si(d + i, d + i, i * s);
+
+    _fmprb_poly_mullow(b, d, len, c, alen, len, prec);
+
+    for (i = 0; i < len; i++)
+        fmprb_mul_2exp_si(b + i, b + i, -i * s);
+
+    _fmprb_poly_inv_borel_transform(b, b, len, prec);
+
+    _fmprb_vec_clear(c, alen);
+    _fmprb_vec_clear(d, len);
+}
+
+void
+fmprb_poly_binomial_transform_convolution(fmprb_poly_t b, const fmprb_poly_t a, long len, long prec)
+{
+    if (len == 0 || a->length == 0)
+    {
+        fmprb_poly_zero(b);
+        return;
+    }
+
+    if (b == a)
+    {
+        fmprb_poly_t c;
+        fmprb_poly_init2(c, len);
+        _fmprb_poly_binomial_transform_convolution(c->coeffs, a->coeffs, a->length, len, prec);
+        fmprb_poly_swap(b, c);
+        fmprb_poly_clear(c);
+    }
+    else
+    {
+        fmprb_poly_fit_length(b, len);
+        _fmprb_poly_binomial_transform_convolution(b->coeffs, a->coeffs, a->length, len, prec);
+    }
+
+    _fmprb_poly_set_length(b, len);
+    _fmprb_poly_normalise(b);
+}
+

fmprb_poly/borel_transform.c

@@ -0,0 +1,57 @@
+/*=============================================================================
+
+    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 "fmprb_poly.h"
+
+void
+_fmprb_poly_borel_transform(fmprb_ptr res, fmprb_srcptr poly, long len, long prec)
+{
+    long i;
+
+    fmprb_t t;
+    fmprb_init(t);
+
+    fmprb_one(t);
+
+    for (i = 0; i < len; i++)
+    {
+        if (i > 1)
+            fmprb_mul_ui(t, t, i, prec);
+
+        fmprb_div(res + i, poly + i, t, prec);
+    }
+
+    fmprb_clear(t);
+}
+
+void
+fmprb_poly_borel_transform(fmprb_poly_t res, const fmprb_poly_t poly, long prec)
+{
+    fmprb_poly_fit_length(res, poly->length);
+    _fmprb_poly_borel_transform(res->coeffs, poly->coeffs, poly->length, prec);
+    _fmprb_poly_set_length(res, poly->length);
+    _fmprb_poly_normalise(res);
+}
+

fmprb_poly/inv_borel_transform.c

@@ -0,0 +1,57 @@
+/*=============================================================================
+
+    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 "fmprb_poly.h"
+
+void
+_fmprb_poly_inv_borel_transform(fmprb_ptr res, fmprb_srcptr poly, long len, long prec)
+{
+    long i;
+
+    fmprb_t t;
+    fmprb_init(t);
+
+    fmprb_one(t);
+
+    for (i = 0; i < len; i++)
+    {
+        if (i > 1)
+            fmprb_mul_ui(t, t, i, prec);
+
+        fmprb_mul(res + i, poly + i, t, prec);
+    }
+
+    fmprb_clear(t);
+}
+
+void
+fmprb_poly_inv_borel_transform(fmprb_poly_t res, const fmprb_poly_t poly, long prec)
+{
+    fmprb_poly_fit_length(res, poly->length);
+    _fmprb_poly_inv_borel_transform(res->coeffs, poly->coeffs, poly->length, prec);
+    _fmprb_poly_set_length(res, poly->length);
+    _fmprb_poly_normalise(res);
+}
+

fmprb_poly/test/t-binomial_transform.c

@@ -0,0 +1,119 @@
+/*=============================================================================
+
+    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 "fmprb_poly.h"
+
+int main()
+{
+    long iter;
+    flint_rand_t state;
+
+    printf("binomial_transform....");
+    fflush(stdout);
+
+    flint_randinit(state);
+
+    for (iter = 0; iter < 5000; iter++)
+    {
+        fmprb_poly_t a, b, c, d;
+        long j, n, prec;
+
+        fmprb_poly_init(a);
+        fmprb_poly_init(b);
+        fmprb_poly_init(c);
+        fmprb_poly_init(d);
+
+        n = n_randint(state, 20);
+        prec = 2 + n_randint(state, 200);
+
+        fmprb_poly_randtest(a, state, n, prec, 10);
+        fmprb_poly_randtest(b, state, n, prec, 10);
+        fmprb_poly_randtest(c, state, n, prec, 10);
+
+        /* check self-inversion property */
+        fmprb_poly_binomial_transform(b, a, n, prec);
+        fmprb_poly_binomial_transform(c, b, n, prec);
+
+        fmprb_poly_set(d, a);
+        fmprb_poly_truncate(d, n);
+
+        if (!fmprb_poly_contains(c, d))
+        {
+            printf("FAIL (containment)\n\n");
+            printf("n = %ld, prec = %ld\n\n", n, prec);
+
+            printf("a: "); fmprb_poly_printd(a, 15); printf("\n\n");
+            printf("b: "); fmprb_poly_printd(b, 15); printf("\n\n");
+            printf("c: "); fmprb_poly_printd(c, 15); printf("\n\n");
+            printf("d: "); fmprb_poly_printd(d, 15); printf("\n\n");
+
+            abort();
+        }
+
+        fmprb_poly_set(d, a);
+        fmprb_poly_binomial_transform(d, d, n, prec);
+        if (!fmprb_poly_equal(d, b))
+        {
+            printf("FAIL (aliasing)\n\n");
+
+            printf("a: "); fmprb_poly_printd(a, 15); printf("\n\n");
+            printf("b: "); fmprb_poly_printd(b, 15); printf("\n\n");
+            printf("d: "); fmprb_poly_printd(d, 15); printf("\n\n");
+
+            abort();
+        }
+
+        /* compare with power series operations */
+        fmprb_poly_zero(d);
+        for (j = 1; j < n; j++)
+            fmprb_poly_set_coeff_si(d, j, -1);
+        fmprb_poly_compose_series(c, a, d, n, prec);
+        for (j = 0; j < n; j++)
+            fmprb_poly_set_coeff_si(d, j, 1);
+        fmprb_poly_mullow(c, c, d, n, prec);
+
+        if (!fmprb_poly_overlaps(b, c))
+        {
+            printf("FAIL (power series)\n\n");
+
+            printf("a: "); fmprb_poly_printd(a, 15); printf("\n\n");
+            printf("b: "); fmprb_poly_printd(b, 15); printf("\n\n");
+            printf("c: "); fmprb_poly_printd(c, 15); printf("\n\n");
+
+            abort();
+        }
+
+        fmprb_poly_clear(a);
+        fmprb_poly_clear(b);
+        fmprb_poly_clear(c);
+        fmprb_poly_clear(d);
+    }
+
+    flint_randclear(state);
+    flint_cleanup();
+    printf("PASS\n");
+    return EXIT_SUCCESS;
+}
+

fmprb_poly/test/t-binomial_transform_basecase.c

@@ -0,0 +1,119 @@
+/*=============================================================================
+
+    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 "fmprb_poly.h"
+
+int main()
+{
+    long iter;
+    flint_rand_t state;
+
+    printf("binomial_transform_basecase....");
+    fflush(stdout);
+
+    flint_randinit(state);
+
+    for (iter = 0; iter < 5000; iter++)
+    {
+        fmprb_poly_t a, b, c, d;
+        long j, n, prec;
+
+        fmprb_poly_init(a);
+        fmprb_poly_init(b);
+        fmprb_poly_init(c);
+        fmprb_poly_init(d);
+
+        n = n_randint(state, 20);
+        prec = 2 + n_randint(state, 200);
+
+        fmprb_poly_randtest(a, state, n, prec, 10);
+        fmprb_poly_randtest(b, state, n, prec, 10);
+        fmprb_poly_randtest(c, state, n, prec, 10);
+
+        /* check self-inversion property */
+        fmprb_poly_binomial_transform_basecase(b, a, n, prec);
+        fmprb_poly_binomial_transform_basecase(c, b, n, prec);
+
+        fmprb_poly_set(d, a);
+        fmprb_poly_truncate(d, n);
+
+        if (!fmprb_poly_contains(c, d))
+        {
+            printf("FAIL (containment)\n\n");
+            printf("n = %ld, prec = %ld\n\n", n, prec);
+
+            printf("a: "); fmprb_poly_printd(a, 15); printf("\n\n");
+            printf("b: "); fmprb_poly_printd(b, 15); printf("\n\n");
+            printf("c: "); fmprb_poly_printd(c, 15); printf("\n\n");
+            printf("d: "); fmprb_poly_printd(d, 15); printf("\n\n");
+
+            abort();
+        }
+
+        fmprb_poly_set(d, a);
+        fmprb_poly_binomial_transform_basecase(d, d, n, prec);
+        if (!fmprb_poly_equal(d, b))
+        {
+            printf("FAIL (aliasing)\n\n");
+
+            printf("a: "); fmprb_poly_printd(a, 15); printf("\n\n");
+            printf("b: "); fmprb_poly_printd(b, 15); printf("\n\n");
+            printf("d: "); fmprb_poly_printd(d, 15); printf("\n\n");
+
+            abort();
+        }
+
+        /* compare with power series operations */
+        fmprb_poly_zero(d);
+        for (j = 1; j < n; j++)
+            fmprb_poly_set_coeff_si(d, j, -1);
+        fmprb_poly_compose_series(c, a, d, n, prec);
+        for (j = 0; j < n; j++)
+            fmprb_poly_set_coeff_si(d, j, 1);
+        fmprb_poly_mullow(c, c, d, n, prec);
+
+        if (!fmprb_poly_overlaps(b, c))
+        {
+            printf("FAIL (power series)\n\n");
+
+            printf("a: "); fmprb_poly_printd(a, 15); printf("\n\n");
+            printf("b: "); fmprb_poly_printd(b, 15); printf("\n\n");
+            printf("c: "); fmprb_poly_printd(c, 15); printf("\n\n");
+
+            abort();
+        }
+
+        fmprb_poly_clear(a);
+        fmprb_poly_clear(b);
+        fmprb_poly_clear(c);
+        fmprb_poly_clear(d);
+    }
+
+    flint_randclear(state);
+    flint_cleanup();
+    printf("PASS\n");
+    return EXIT_SUCCESS;
+}
+

fmprb_poly/test/t-binomial_transform_convolution.c

@@ -0,0 +1,119 @@
+/*=============================================================================
+
+    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 "fmprb_poly.h"
+
+int main()
+{
+    long iter;
+    flint_rand_t state;
+
+    printf("binomial_transform_convolution....");
+    fflush(stdout);
+
+    flint_randinit(state);
+
+    for (iter = 0; iter < 5000; iter++)
+    {
+        fmprb_poly_t a, b, c, d;
+        long j, n, prec;
+
+        fmprb_poly_init(a);
+        fmprb_poly_init(b);
+        fmprb_poly_init(c);
+        fmprb_poly_init(d);
+
+        n = n_randint(state, 20);
+        prec = 2 + n_randint(state, 200);
+
+        fmprb_poly_randtest(a, state, n, prec, 10);
+        fmprb_poly_randtest(b, state, n, prec, 10);
+        fmprb_poly_randtest(c, state, n, prec, 10);
+
+        /* check self-inversion property */
+        fmprb_poly_binomial_transform_convolution(b, a, n, prec);
+        fmprb_poly_binomial_transform_convolution(c, b, n, prec);
+
+        fmprb_poly_set(d, a);
+        fmprb_poly_truncate(d, n);
+
+        if (!fmprb_poly_contains(c, d))
+        {
+            printf("FAIL (containment)\n\n");
+            printf("n = %ld, prec = %ld\n\n", n, prec);
+
+            printf("a: "); fmprb_poly_printd(a, 15); printf("\n\n");
+            printf("b: "); fmprb_poly_printd(b, 15); printf("\n\n");
+            printf("c: "); fmprb_poly_printd(c, 15); printf("\n\n");
+            printf("d: "); fmprb_poly_printd(d, 15); printf("\n\n");
+
+            abort();
+        }
+
+        fmprb_poly_set(d, a);
+        fmprb_poly_binomial_transform_convolution(d, d, n, prec);
+        if (!fmprb_poly_equal(d, b))
+        {
+            printf("FAIL (aliasing)\n\n");
+
+            printf("a: "); fmprb_poly_printd(a, 15); printf("\n\n");
+            printf("b: "); fmprb_poly_printd(b, 15); printf("\n\n");
+            printf("d: "); fmprb_poly_printd(d, 15); printf("\n\n");
+
+            abort();
+        }
+
+        /* compare with power series operations */
+        fmprb_poly_zero(d);
+        for (j = 1; j < n; j++)
+            fmprb_poly_set_coeff_si(d, j, -1);
+        fmprb_poly_compose_series(c, a, d, n, prec);
+        for (j = 0; j < n; j++)
+            fmprb_poly_set_coeff_si(d, j, 1);
+        fmprb_poly_mullow(c, c, d, n, prec);
+
+        if (!fmprb_poly_overlaps(b, c))
+        {
+            printf("FAIL (power series)\n\n");
+
+            printf("a: "); fmprb_poly_printd(a, 15); printf("\n\n");
+            printf("b: "); fmprb_poly_printd(b, 15); printf("\n\n");
+            printf("c: "); fmprb_poly_printd(c, 15); printf("\n\n");
+
+            abort();
+        }
+
+        fmprb_poly_clear(a);
+        fmprb_poly_clear(b);
+        fmprb_poly_clear(c);
+        fmprb_poly_clear(d);
+    }
+
+    flint_randclear(state);
+    flint_cleanup();
+    printf("PASS\n");
+    return EXIT_SUCCESS;
+}
+

fmprb_poly/test/t-borel_transform.c

@@ -0,0 +1,91 @@
+/*=============================================================================
+
+    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 "fmprb_poly.h"
+
+int main()
+{
+    long iter;
+    flint_rand_t state;
+
+    printf("borel_transform....");
+    fflush(stdout);
+
+    flint_randinit(state);
+
+    for (iter = 0; iter < 10000; iter++)
+    {
+        fmprb_poly_t a, b, c, d;
+        long n, prec;
+
+        fmprb_poly_init(a);
+        fmprb_poly_init(b);
+        fmprb_poly_init(c);
+        fmprb_poly_init(d);
+
+        n = n_randint(state, 30);
+        prec = n_randint(state, 200);
+
+        fmprb_poly_randtest(a, state, n, prec, 10);
+        fmprb_poly_randtest(b, state, n, prec, 10);
+        fmprb_poly_randtest(c, state, n, prec, 10);
+
+        fmprb_poly_borel_transform(b, a, prec);
+        fmprb_poly_inv_borel_transform(c, b, prec);
+
+        if (!fmprb_poly_contains(c, a))
+        {
+            printf("FAIL (containment)\n\n");
+            abort();
+        }
+
+        fmprb_poly_set(d, a);
+        fmprb_poly_borel_transform(d, d, prec);
+        if (!fmprb_poly_equal(d, b))
+        {
+            printf("FAIL (aliasing 1)\n\n");
+            abort();
+        }
+
+        fmprb_poly_set(d, b);
+        fmprb_poly_inv_borel_transform(d, d, prec);
+        if (!fmprb_poly_equal(d, c))
+        {
+            printf("FAIL (aliasing 2)\n\n");
+            abort();
+        }
+
+        fmprb_poly_clear(a);
+        fmprb_poly_clear(b);
+        fmprb_poly_clear(c);
+        fmprb_poly_clear(d);
+    }
+
+    flint_randclear(state);
+    flint_cleanup();
+    printf("PASS\n");
+    return EXIT_SUCCESS;
+}
+