Merge pull request #120 from argriffing/enh-arb-intersection

ENH: arb_intersection

arb.h

@@ -532,6 +532,7 @@ void arb_get_interval_arf(arf_t a, arf_t b, const arb_t x, slong prec);
 void arb_get_interval_mpfr(mpfr_t a, mpfr_t b, const arb_t x);
 
 void arb_union(arb_t z, const arb_t x, const arb_t y, slong prec);
+int arb_intersection(arb_t z, const arb_t x, const arb_t y, slong prec);
 void arb_get_rand_fmpq(fmpq_t q, flint_rand_t state, const arb_t x, slong bits);
 
 int arb_can_round_arf(const arb_t x, slong prec, arf_rnd_t rnd);

arb/intersection.c

@@ -0,0 +1,73 @@
+/*=============================================================================
+
+    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) 2016 Arb authors
+
+******************************************************************************/
+
+#include "arb.h"
+
+int
+arb_intersection(arb_t z, const arb_t x, const arb_t y, slong prec)
+{
+    arf_t left, right, t, xr, yr;
+    int result;
+
+    if (arf_is_nan(arb_midref(x)) || arf_is_nan(arb_midref(y)))
+    {
+        arb_indeterminate(z);
+        return 1;
+    }
+
+    if (mag_is_inf(arb_radref(x)) && mag_is_inf(arb_radref(y)))
+    {
+        arb_zero_pm_inf(z);
+        return 1;
+    }
+
+    result = arb_overlaps(x, y);
+
+    if (result)
+    {
+        arf_init(left);
+        arf_init(right);
+        arf_init(t);
+
+        arf_init_set_mag_shallow(xr, arb_radref(x));
+        arf_init_set_mag_shallow(yr, arb_radref(y));
+
+        arf_sub(left, arb_midref(x), xr, prec, ARF_RND_FLOOR);
+        arf_sub(t, arb_midref(y), yr, prec, ARF_RND_FLOOR);
+        arf_max(left, left, t);
+
+        arf_add(right, arb_midref(x), xr, prec, ARF_RND_CEIL);
+        arf_add(t, arb_midref(y), yr, prec, ARF_RND_CEIL);
+        arf_min(right, right, t);
+
+        arb_set_interval_arf(z, left, right, prec);
+
+        arf_clear(left);
+        arf_clear(right);
+        arf_clear(t);
+    }
+
+    return result;
+}

arb/test/t-intersection.c

@@ -0,0 +1,213 @@
+/*=============================================================================
+
+    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) 2016 Arb authors
+
+******************************************************************************/
+
+#include "arb.h"
+
+int main()
+{
+    slong iter;
+    flint_rand_t state;
+
+    flint_printf("intersection....");
+    fflush(stdout);
+    flint_randinit(state);
+
+    /* check a containment requirement */
+    for (iter = 0; iter < 100000; iter++)
+    {
+        arb_t x, y, z, w;
+        arb_t xy, yz;
+        slong pa, pb, pc;
+        int alias;
+
+        arb_init(x);
+        arb_init(y);
+        arb_init(z);
+        arb_init(w);
+        arb_init(xy);
+        arb_init(yz);
+
+        arb_randtest_special(x, state, 200, 10);
+        arb_randtest_special(y, state, 200, 10);
+        arb_randtest_special(z, state, 200, 10);
+        arb_randtest_special(w, state, 200, 10);
+        arb_randtest_special(xy, state, 200, 10);
+        arb_randtest_special(yz, state, 200, 10);
+
+        pa = 2 + n_randint(state, 200);
+        pb = 2 + n_randint(state, 200);
+        pc = 2 + n_randint(state, 200);
+
+        arb_union(xy, x, y, pa);
+        arb_union(yz, y, z, pb);
+        arb_intersection(w, xy, yz, pc);
+
+        if (!arb_contains(w, y))
+        {
+            flint_printf("FAIL (containment):\n\n");
+            flint_printf("x = "); arb_print(x); flint_printf("\n\n");
+            flint_printf("y = "); arb_print(y); flint_printf("\n\n");
+            flint_printf("z = "); arb_print(z); flint_printf("\n\n");
+            flint_printf("w = "); arb_print(w); flint_printf("\n\n");
+            abort();
+        }
+
+        if (n_randint(state, 2))
+        {
+            arb_intersection(xy, xy, yz, pc);
+            alias = arb_equal(xy, w);
+        }
+        else
+        {
+            arb_intersection(yz, xy, yz, pc);
+            alias = arb_equal(yz, w);
+        }
+
+        if (!alias)
+        {
+            flint_printf("FAIL (aliasing):\n\n");
+            flint_printf("x = "); arb_print(x); flint_printf("\n\n");
+            flint_printf("y = "); arb_print(y); flint_printf("\n\n");
+            flint_printf("z = "); arb_print(z); flint_printf("\n\n");
+            flint_printf("w = "); arb_print(w); flint_printf("\n\n");
+            abort();
+        }
+
+        arb_clear(x);
+        arb_clear(y);
+        arb_clear(z);
+        arb_clear(w);
+        arb_clear(xy);
+        arb_clear(yz);
+    }
+
+    /* require that the return value is the same as for arb_overlaps */
+    for (iter = 0; iter < 10000; iter++)
+    {
+        arb_t a, b, y;
+        fmpq_t am, ar, bm, br, t, u;
+        int c1, c2, c3;
+        slong prec;
+
+        prec = 2 + n_randint(state, 200);
+
+        arb_init(a);
+        arb_init(b);
+        arb_init(y);
+
+        fmpq_init(am);
+        fmpq_init(ar);
+        fmpq_init(bm);
+        fmpq_init(br);
+        fmpq_init(t);
+        fmpq_init(u);
+
+        arb_randtest(a, state, 1 + n_randint(state, 500), 14);
+        arb_randtest(b, state, 1 + n_randint(state, 500), 14);
+
+        arf_get_fmpq(am, arb_midref(a));
+        mag_get_fmpq(ar, arb_radref(a));
+        arf_get_fmpq(bm, arb_midref(b));
+        mag_get_fmpq(br, arb_radref(b));
+
+        fmpq_sub(t, am, bm);
+        fmpz_abs(fmpq_numref(t), fmpq_numref(t));
+        fmpq_add(u, ar, br);
+
+        c1 = arb_overlaps(a, b);
+
+        c2 = (fmpq_cmp(t, u) <= 0);
+
+        c3 = arb_intersection(y, a, b, prec);
+
+        if (c1 != c2 || c1 != c3)
+        {
+            flint_printf("FAIL (compatibility with arb_overlaps):\n\n");
+            flint_printf("a = "); arb_print(a); flint_printf("\n\n");
+            flint_printf("b = "); arb_print(b); flint_printf("\n\n");
+            flint_printf("y = "); arb_print(y); flint_printf("\n\n");
+            flint_printf("am = "); fmpq_print(am); flint_printf("\n\n");
+            flint_printf("ar = "); fmpq_print(ar); flint_printf("\n\n");
+            flint_printf("bm = "); fmpq_print(bm); flint_printf("\n\n");
+            flint_printf("br = "); fmpq_print(br); flint_printf("\n\n");
+            flint_printf("t = "); fmpq_print(t); flint_printf("\n\n");
+            flint_printf("u = "); fmpq_print(u); flint_printf("\n\n");
+            flint_printf("c1 = %d, c2 = %d, c3 = %d\n\n", c1, c2, c3);
+            abort();
+        }
+
+        arb_clear(a);
+        arb_clear(b);
+        arb_clear(y);
+
+        fmpq_clear(am);
+        fmpq_clear(ar);
+        fmpq_clear(bm);
+        fmpq_clear(br);
+        fmpq_clear(t);
+        fmpq_clear(u);
+    }
+
+    /* check a simple hardcoded example */
+    {
+        slong prec;
+        arb_t xy, yz, y, v, w;
+
+        prec = 32;
+
+        arb_init(xy);
+        arb_init(yz);
+        arb_init(y);
+        arb_init(v);
+        arb_init(w);
+
+        arb_set_str(xy, "1 +/- 1", prec);
+        arb_set_str(yz, "2 +/- 1", prec);
+        arb_set_str(y, "1.5 +/- 0.6", prec);
+        arb_set_str(v, "1.5 +/- 0.4", prec);
+
+        arb_intersection(w, xy, yz, prec);
+
+        if (!arb_contains(y, w) || !arb_contains(w, v))
+        {
+            flint_printf("FAIL (hardcoded example)\n\n");
+            flint_printf("xy = "); arb_print(xy); flint_printf("\n\n");
+            flint_printf("yx = "); arb_print(yz); flint_printf("\n\n");
+            flint_printf("y = "); arb_print(y); flint_printf("\n\n");
+            flint_printf("w = "); arb_print(w); flint_printf("\n\n");
+            abort();
+        }
+
+        arb_clear(xy);
+        arb_clear(yz);
+        arb_clear(y);
+        arb_clear(w);
+    }
+
+    flint_randclear(state);
+    flint_cleanup();
+    flint_printf("PASS\n");
+    return EXIT_SUCCESS;
+}

doc/source/arb.rst

@@ -313,6 +313,14 @@ Radius and interval operations
 
     Sets *z* to a ball containing both *x* and *y*.
 
+.. function:: int arb_intersection(arb_t z, const arb_t x, const arb_t y, slong prec)
+
+    If *x* and *y* overlap according to :func:`arb_overlaps`,
+    then *z* is set to a ball containing the intersection of *x* and *y*
+    and a nonzero value is returned.
+    Otherwise zero is returned and the value of *z* is undefined.
+    If *x* or *y* contains NaN, the result is NaN.
+
 .. function:: void arb_get_abs_ubound_arf(arf_t u, const arb_t x, slong prec)
 
     Sets *u* to the upper bound for the absolute value of *x*,