add arb_sgn (sign function)

arb.h

@@ -206,6 +206,8 @@ void arb_neg_round(arb_t x, const arb_t y, slong prec);
 
 void arb_abs(arb_t y, const arb_t x);
 
+void arb_sgn(arb_t res, const arb_t x);
+
 void _arb_digits_round_inplace(char * s, mp_bitcnt_t * shift, fmpz_t error, slong n, arf_rnd_t rnd);
 
 int arb_set_str(arb_t res, const char * inp, slong prec);

arb/sgn.c

@@ -0,0 +1,45 @@
+/*=============================================================================
+
+    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 Fredrik Johansson
+
+******************************************************************************/
+
+#include "arb.h"
+
+void
+arb_sgn(arb_t res, const arb_t x)
+{
+    if (arb_is_zero(x))
+    {
+        arb_zero(res);
+    }
+    else if (arb_contains_zero(x))
+    {
+        arf_zero(arb_midref(res));
+        mag_one(arb_radref(res));
+    }
+    else
+    {
+        arb_set_si(res, arf_sgn(arb_midref(x)));
+    }
+}
+

arb/test/t-sgn.c

@@ -0,0 +1,74 @@
+/*=============================================================================
+
+    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 Fredrik Johansson
+
+******************************************************************************/
+
+#include "arb.h"
+
+int main()
+{
+    slong iter;
+    flint_rand_t state;
+
+    flint_printf("sgn....");
+    fflush(stdout);
+
+    flint_randinit(state);
+
+    for (iter = 0; iter < 1000; iter++)
+    {
+        arb_t a, b;
+        int result;
+
+        arb_init(a);
+        arb_init(b);
+
+        arb_randtest_special(a, state, 1 + n_randint(state, 200), 10);
+        arb_randtest_special(b, state, 1 + n_randint(state, 200), 10);
+        arb_sgn(b, a);
+
+        result = 1;
+        if (arb_contains_zero(a))
+            result = result & arb_contains_si(b, 0);
+        if (arb_contains_positive(a))
+            result = result & arb_contains_si(b, 1);
+        if (arb_contains_negative(a))
+            result = result & arb_contains_si(b, -1);
+
+        if (!result)
+        {
+            flint_printf("FAIL\n\n");
+            flint_printf("a = "); arb_print(a); flint_printf("\n\n");
+            flint_printf("b = "); arb_print(b); flint_printf("\n\n");
+            abort();
+        }
+
+        arb_clear(a);
+        arb_clear(b);
+    }
+
+    flint_randclear(state);
+    flint_cleanup();
+    flint_printf("PASS\n");
+    return EXIT_SUCCESS;
+}

doc/source/arb.rst

@@ -602,6 +602,11 @@ Arithmetic
     Sets *y* to the absolute value of *x*. No attempt is made to improve the
     interval represented by *x* if it contains zero.
 
+.. function:: void arb_sgn(arb_t y, const arb_t x)
+
+    Sets *y* to the sign function of *x*. The result is `[0 \pm 1]` if
+    *x* contains both zero and nonzero numbers.
+
 .. function:: void arb_add(arb_t z, const arb_t x, const arb_t y, slong prec)
 
 .. function:: void arb_add_arf(arb_t z, const arb_t x, const arf_t y, slong prec)