initial code for arb_hypgeom wrapper module

Makefile.in

@@ -13,7 +13,7 @@ QUIET_AR  = @echo '   ' AR  ' ' $@;
 AT=@
 
 BUILD_DIRS = fmpr arf mag arb arb_mat arb_poly arb_calc acb acb_mat acb_poly \
-   acb_calc acb_hypgeom acb_modular acb_dirichlet bernoulli hypgeom \
+   acb_calc acb_hypgeom acb_modular acb_dirichlet arb_hypgeom bernoulli hypgeom \
    fmpz_extras bool_mat partitions \
    $(EXTRA_BUILD_DIRS)
 

arb_hypgeom.h

@@ -0,0 +1,43 @@
+/*
+    Copyright (C) 2016 Fredrik Johansson
+
+    This file is part of Arb.
+
+    Arb is free software: you can redistribute it and/or modify it under
+    the terms of the GNU Lesser General Public License (LGPL) as published
+    by the Free Software Foundation; either version 2.1 of the License, or
+    (at your option) any later version.  See <http://www.gnu.org/licenses/>.
+*/
+
+#ifndef ARB_HYPGEOM_H
+#define ARB_HYPGEOM_H
+
+#include "arb.h"
+#include "arb_poly.h"
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+void arb_hypgeom_erf(arb_t res, const arb_t z, slong prec);
+void _arb_hypgeom_erf_series(arb_ptr g, arb_srcptr h, slong hlen, slong len, slong prec);
+void arb_hypgeom_erf_series(arb_poly_t g, const arb_poly_t h, slong len, slong prec);
+
+void arb_hypgeom_erfc(arb_t res, const arb_t z, slong prec);
+void _arb_hypgeom_erfc_series(arb_ptr g, arb_srcptr h, slong hlen, slong len, slong prec);
+void arb_hypgeom_erfc_series(arb_poly_t g, const arb_poly_t h, slong len, slong prec);
+
+void arb_hypgeom_erfi(arb_t res, const arb_t z, slong prec);
+void _arb_hypgeom_erfi_series(arb_ptr g, arb_srcptr h, slong hlen, slong len, slong prec);
+void arb_hypgeom_erfi_series(arb_poly_t g, const arb_poly_t h, slong len, slong prec);
+
+void arb_hypgeom_fresnel(arb_t res1, arb_t res2, const arb_t z, int normalized, slong prec);
+void _arb_hypgeom_fresnel_series(arb_ptr s, arb_ptr c, arb_srcptr h, slong hlen, int normalized, slong len, slong prec);
+void arb_hypgeom_fresnel_series(arb_poly_t s, arb_poly_t c, const arb_poly_t h, int normalized, slong len, slong prec);
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif
+

arb_hypgeom/erf_series.c

@@ -0,0 +1,75 @@
+/*
+    Copyright (C) 2016 Fredrik Johansson
+
+    This file is part of Arb.
+
+    Arb is free software: you can redistribute it and/or modify it under
+    the terms of the GNU Lesser General Public License (LGPL) as published
+    by the Free Software Foundation; either version 2.1 of the License, or
+    (at your option) any later version.  See <http://www.gnu.org/licenses/>.
+*/
+
+#include "arb_hypgeom.h"
+
+void
+_arb_hypgeom_erf_series(arb_ptr g, arb_srcptr h, slong hlen, slong len, slong prec)
+{
+    arb_t c;
+    arb_init(c);
+
+    arb_hypgeom_erf(c, h, prec);
+
+    hlen = FLINT_MIN(hlen, len);
+
+    if (hlen == 1)
+    {
+        _arb_vec_zero(g + 1, len - 1);
+    }
+    else
+    {
+        arb_ptr t, u;
+        slong ulen;
+
+        t = _arb_vec_init(len);
+        u = _arb_vec_init(len);
+
+        /* erf(h(x)) = integral(h'(x) exp(-h(x)^2)) * (2/sqrt(pi)) */
+        ulen = FLINT_MIN(len, 2 * hlen - 1);
+
+        _arb_poly_mullow(u, h, hlen, h, hlen, ulen, prec);
+        _arb_vec_neg(u, u, ulen);
+        _arb_poly_exp_series(u, u, ulen, len, prec);
+        _arb_poly_derivative(t, h, hlen, prec);
+        _arb_poly_mullow(g, u, len, t, hlen - 1, len, prec);
+        _arb_poly_integral(g, g, len, prec);
+
+        arb_const_sqrt_pi(t, prec);
+        arb_inv(t, t, prec);
+        arb_mul_2exp_si(t, t, 1);
+        _arb_vec_scalar_mul(g, g, len, t, prec);
+
+        _arb_vec_clear(t, len);
+        _arb_vec_clear(u, len);
+    }
+
+    arb_swap(g, c);
+    arb_clear(c);
+}
+
+void
+arb_hypgeom_erf_series(arb_poly_t g, const arb_poly_t h, slong len, slong prec)
+{
+    slong hlen = h->length;
+
+    if (hlen == 0 || len == 0)
+    {
+        arb_poly_zero(g);
+        return;
+    }
+
+    arb_poly_fit_length(g, len);
+    _arb_hypgeom_erf_series(g->coeffs, h->coeffs, hlen, len, prec);
+    _arb_poly_set_length(g, len);
+    _arb_poly_normalise(g);
+}
+

arb_hypgeom/erfc_series.c

@@ -0,0 +1,82 @@
+/*
+    Copyright (C) 2016 Fredrik Johansson
+
+    This file is part of Arb.
+
+    Arb is free software: you can redistribute it and/or modify it under
+    the terms of the GNU Lesser General Public License (LGPL) as published
+    by the Free Software Foundation; either version 2.1 of the License, or
+    (at your option) any later version.  See <http://www.gnu.org/licenses/>.
+*/
+
+#include "arb_hypgeom.h"
+
+void
+_arb_hypgeom_erfc_series(arb_ptr g, arb_srcptr h, slong hlen, slong len, slong prec)
+{
+    arb_t c;
+    arb_init(c);
+
+    arb_hypgeom_erfc(c, h, prec);
+
+    hlen = FLINT_MIN(hlen, len);
+
+    if (hlen == 1)
+    {
+        _arb_vec_zero(g + 1, len - 1);
+    }
+    else
+    {
+        arb_ptr t, u;
+        slong ulen;
+
+        t = _arb_vec_init(len);
+        u = _arb_vec_init(len);
+
+        /* erfc(h(x)) = integral(-h'(x) exp(-h(x)^2)) * (2/sqrt(pi)) */
+        ulen = FLINT_MIN(len, 2 * hlen - 1);
+
+        _arb_poly_mullow(u, h, hlen, h, hlen, ulen, prec);
+        _arb_vec_neg(u, u, ulen);
+        _arb_poly_exp_series(u, u, ulen, len, prec);
+        _arb_poly_derivative(t, h, hlen, prec);
+        _arb_poly_mullow(g, u, len, t, hlen - 1, len, prec);
+        _arb_poly_integral(g, g, len, prec);
+
+        arb_const_sqrt_pi(t, prec);
+        arb_inv(t, t, prec);
+        arb_mul_2exp_si(t, t, 1);
+        _arb_vec_scalar_mul(g, g, len, t, prec);
+        _arb_vec_neg(g, g, len);
+
+        _arb_vec_clear(t, len);
+        _arb_vec_clear(u, len);
+    }
+
+    arb_swap(g, c);
+    arb_clear(c);
+}
+
+void
+arb_hypgeom_erfc_series(arb_poly_t g, const arb_poly_t h, slong len, slong prec)
+{
+    slong hlen = h->length;
+
+    if (len == 0)
+    {
+        arb_poly_zero(g);
+        return;
+    }
+
+    if (hlen == 0)
+    {
+        arb_poly_one(g);
+        return;
+    }
+
+    arb_poly_fit_length(g, len);
+    _arb_hypgeom_erfc_series(g->coeffs, h->coeffs, hlen, len, prec);
+    _arb_poly_set_length(g, len);
+    _arb_poly_normalise(g);
+}
+

arb_hypgeom/erfi_series.c

@@ -0,0 +1,74 @@
+/*
+    Copyright (C) 2016 Fredrik Johansson
+
+    This file is part of Arb.
+
+    Arb is free software: you can redistribute it and/or modify it under
+    the terms of the GNU Lesser General Public License (LGPL) as published
+    by the Free Software Foundation; either version 2.1 of the License, or
+    (at your option) any later version.  See <http://www.gnu.org/licenses/>.
+*/
+
+#include "arb_hypgeom.h"
+
+void
+_arb_hypgeom_erfi_series(arb_ptr g, arb_srcptr h, slong hlen, slong len, slong prec)
+{
+    arb_t c;
+    arb_init(c);
+
+    arb_hypgeom_erfi(c, h, prec);
+
+    hlen = FLINT_MIN(hlen, len);
+
+    if (hlen == 1)
+    {
+        _arb_vec_zero(g + 1, len - 1);
+    }
+    else
+    {
+        arb_ptr t, u;
+        slong ulen;
+
+        t = _arb_vec_init(len);
+        u = _arb_vec_init(len);
+
+        /* erfi(h(x)) = integral(h'(x) exp(h(x)^2)) * (2/sqrt(pi)) */
+        ulen = FLINT_MIN(len, 2 * hlen - 1);
+
+        _arb_poly_mullow(u, h, hlen, h, hlen, ulen, prec);
+        _arb_poly_exp_series(u, u, ulen, len, prec);
+        _arb_poly_derivative(t, h, hlen, prec);
+        _arb_poly_mullow(g, u, len, t, hlen - 1, len, prec);
+        _arb_poly_integral(g, g, len, prec);
+
+        arb_const_sqrt_pi(t, prec);
+        arb_inv(t, t, prec);
+        arb_mul_2exp_si(t, t, 1);
+        _arb_vec_scalar_mul(g, g, len, t, prec);
+
+        _arb_vec_clear(t, len);
+        _arb_vec_clear(u, len);
+    }
+
+    arb_swap(g, c);
+    arb_clear(c);
+}
+
+void
+arb_hypgeom_erfi_series(arb_poly_t g, const arb_poly_t h, slong len, slong prec)
+{
+    slong hlen = h->length;
+
+    if (hlen == 0 || len == 0)
+    {
+        arb_poly_zero(g);
+        return;
+    }
+
+    arb_poly_fit_length(g, len);
+    _arb_hypgeom_erfi_series(g->coeffs, h->coeffs, hlen, len, prec);
+    _arb_poly_set_length(g, len);
+    _arb_poly_normalise(g);
+}
+

arb_hypgeom/fresnel_series.c

@@ -0,0 +1,112 @@
+/*
+    Copyright (C) 2016 Fredrik Johansson
+
+    This file is part of Arb.
+
+    Arb is free software: you can redistribute it and/or modify it under
+    the terms of the GNU Lesser General Public License (LGPL) as published
+    by the Free Software Foundation; either version 2.1 of the License, or
+    (at your option) any later version.  See <http://www.gnu.org/licenses/>.
+*/
+
+#include "arb_hypgeom.h"
+
+void
+_arb_hypgeom_fresnel_series(arb_ptr s, arb_ptr c,
+    arb_srcptr h, slong hlen, int normalized, slong len, slong prec)
+{
+    hlen = FLINT_MIN(hlen, len);
+
+    if (hlen == 1)
+    {
+        arb_hypgeom_fresnel(s, c, h, normalized, prec);
+
+        if (s != NULL) _arb_vec_zero(s + 1, len - 1);
+        if (c != NULL) _arb_vec_zero(c + 1, len - 1);
+    }
+    else
+    {
+        arb_t s0, c0;
+        arb_ptr t, u, v;
+        slong ulen;
+
+        arb_init(s0);
+        arb_init(c0);
+
+        arb_hypgeom_fresnel((s != NULL) ? s0 : NULL,
+                            (c != NULL) ? c0 : NULL, h, normalized, prec);
+
+        t = _arb_vec_init(len);
+        u = _arb_vec_init(len);
+        v = _arb_vec_init(len);
+
+        /* normalized: */
+        /* C(h(x)) = integral(h'(x) cos(-(pi/2) h(x)^2)) */
+        /* S(h(x)) = -integral(h'(x) sin(-(pi/2) h(x)^2)) */
+        ulen = FLINT_MIN(len, 2 * hlen - 1);
+
+        _arb_poly_mullow(u, h, hlen, h, hlen, ulen, prec);
+        _arb_vec_neg(u, u, ulen);
+
+        if (normalized)
+        {
+            _arb_vec_scalar_mul_2exp_si(u, u, ulen, -1);
+            _arb_poly_sin_cos_pi_series(u, v, u, ulen, len, prec);
+        }
+        else
+        {
+            _arb_poly_sin_cos_series(u, v, u, ulen, len, prec);
+        }
+
+        _arb_poly_derivative(t, h, hlen, prec);
+
+        if (s != NULL)
+        {
+            _arb_poly_mullow(s, u, len, t, hlen - 1, len, prec);
+            _arb_poly_integral(s, s, len, prec);
+            _arb_vec_neg(s, s, len);
+            arb_swap(s, s0);
+        }
+
+        if (c != NULL)
+        {
+            _arb_poly_mullow(c, v, len, t, hlen - 1, len, prec);
+            _arb_poly_integral(c, c, len, prec);
+            arb_swap(c, c0);
+        }
+
+        _arb_vec_clear(t, len);
+        _arb_vec_clear(u, len);
+        _arb_vec_clear(v, len);
+
+        arb_clear(s0);
+        arb_clear(c0);
+    }
+}
+
+void
+arb_hypgeom_fresnel_series(arb_poly_t s, arb_poly_t c,
+    const arb_poly_t h, int normalized, slong len, slong prec)
+{
+    slong hlen = h->length;
+
+    if (hlen == 0 || len == 0)
+    {
+        if (s != NULL) arb_poly_zero(s);
+        if (c != NULL) arb_poly_zero(c);
+        return;
+    }
+
+    if (s != NULL) arb_poly_fit_length(s, len);
+    if (c != NULL) arb_poly_fit_length(c, len);
+
+    _arb_hypgeom_fresnel_series((s != NULL) ? s->coeffs : NULL,
+                                (c != NULL) ? c->coeffs : NULL,
+                        h->coeffs, hlen, normalized, len, prec);
+
+    if (s != NULL) _arb_poly_set_length(s, len);
+    if (c != NULL) _arb_poly_set_length(c, len);
+    if (s != NULL) _arb_poly_normalise(s);
+    if (c != NULL) _arb_poly_normalise(c);
+}
+

arb_hypgeom/wrappers.c

@@ -0,0 +1,90 @@
+/*
+    Copyright (C) 2016 Fredrik Johansson
+
+    This file is part of Arb.
+
+    Arb is free software: you can redistribute it and/or modify it under
+    the terms of the GNU Lesser General Public License (LGPL) as published
+    by the Free Software Foundation; either version 2.1 of the License, or
+    (at your option) any later version.  See <http://www.gnu.org/licenses/>.
+*/
+
+#include "arb_hypgeom.h"
+#include "acb_hypgeom.h"
+
+void
+arb_hypgeom_erf(arb_t res, const arb_t z, slong prec)
+{
+    if (!arb_is_finite(z))
+    {
+        arb_indeterminate(res);
+    }
+    else
+    {
+        acb_t t;
+        acb_init(t);
+        arb_set(acb_realref(t), z);
+        acb_hypgeom_erf(t, t, prec);
+        arb_swap(res, acb_realref(t));
+        acb_clear(t);
+    }
+}
+
+void
+arb_hypgeom_erfc(arb_t res, const arb_t z, slong prec)
+{
+    if (!arb_is_finite(z))
+    {
+        arb_indeterminate(res);
+    }
+    else
+    {
+        acb_t t;
+        acb_init(t);
+        arb_set(acb_realref(t), z);
+        acb_hypgeom_erfc(t, t, prec);
+        arb_swap(res, acb_realref(t));
+        acb_clear(t);
+    }
+}
+
+void
+arb_hypgeom_erfi(arb_t res, const arb_t z, slong prec)
+{
+    if (!arb_is_finite(z))
+    {
+        arb_indeterminate(res);
+    }
+    else
+    {
+        acb_t t;
+        acb_init(t);
+        arb_set(acb_realref(t), z);
+        acb_hypgeom_erfi(t, t, prec);
+        arb_swap(res, acb_realref(t));
+        acb_clear(t);
+    }
+}
+
+void
+arb_hypgeom_fresnel(arb_t res1, arb_t res2, const arb_t z, int normalized, slong prec)
+{
+    if (!arb_is_finite(z))
+    {
+        if (res1 != NULL) arb_indeterminate(res1);
+        if (res2 != NULL) arb_indeterminate(res2);
+    }
+    else
+    {
+        acb_t t, u;
+        acb_init(t);
+        acb_init(u);
+        arb_set(acb_realref(t), z);
+        acb_hypgeom_fresnel(res1 ? t : NULL, res2 ? u : NULL, t, normalized, prec);
+        if (res1 != NULL) arb_swap(res1, acb_realref(t));
+        if (res2 != NULL) arb_swap(res2, acb_realref(u));
+        acb_clear(t);
+        acb_clear(u);
+    }
+}
+