implement mag_root

doc/source/mag.rst

@@ -285,6 +285,12 @@ Powers and logarithms
 
     Sets *z* to an upper bound for `\sqrt{x^2 + y^2}`.
 
+.. function:: void mag_root(mag_t z, const mag_t x, ulong n)
+
+    Sets *z* to an upper bound for `x^{1/n}`. 
+    We evaluate `\exp(\log(1+2^{kn}x)/n) 2^{-n}`, where *k* is chosen
+    so that `2^{kn}x \approx 2^{30}`.
+
 .. function:: void mag_log1p(mag_t z, const mag_t x)
 
     Sets *z* to an upper bound for `\log(1+x)`. The bound is computed

mag.h

@@ -581,6 +581,8 @@ void mag_set_fmpz_2exp_fmpz_lower(mag_t z, const fmpz_t man, const fmpz_t exp);
 void mag_sqrt(mag_t y, const mag_t x);
 void mag_rsqrt(mag_t y, const mag_t x);
 
+void mag_root(mag_t y, const mag_t x, ulong n);
+
 void mag_hypot(mag_t z, const mag_t x, const mag_t y);
 
 void mag_binpow_uiui(mag_t b, ulong m, ulong n);

mag/root.c

@@ -0,0 +1,69 @@
+/*=============================================================================
+
+    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) 2015 Fredrik Johansson
+
+******************************************************************************/
+
+#include "mag.h"
+
+void
+mag_root(mag_t y, const mag_t x, ulong n)
+{
+    if (n == 0)
+    {
+        mag_inf(y);
+    }
+    else if (n == 1 || mag_is_special(x))
+    {
+        mag_set(y, x);
+    }
+    else if (n == 2)
+    {
+        mag_sqrt(y, x);
+    }
+    else if (n == 4)
+    {
+        mag_sqrt(y, x);
+        mag_sqrt(y, y);
+    }
+    else
+    {
+        fmpz_t e, f;
+
+        fmpz_init_set_ui(e, MAG_BITS);
+        fmpz_init(f);
+
+        fmpz_sub(e, e, MAG_EXPREF(x));
+        fmpz_cdiv_q_ui(e, e, n);
+        fmpz_mul_ui(f, e, n);
+        mag_mul_2exp_fmpz(y, x, f);
+        mag_log1p(y, y);
+        mag_div_ui(y, y, n);
+        mag_exp(y, y);
+        fmpz_neg(e, e);
+        mag_mul_2exp_fmpz(y, y, e);
+
+        fmpz_clear(e);
+        fmpz_clear(f);
+    }
+}
+

mag/test/t-root.c

@@ -0,0 +1,99 @@
+/*=============================================================================
+
+    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) 2014 Fredrik Johansson
+
+******************************************************************************/
+
+#include "mag.h"
+
+int main()
+{
+    long iter;
+    flint_rand_t state;
+
+    printf("root....");
+    fflush(stdout);
+
+    flint_randinit(state);
+
+    for (iter = 0; iter < 100000; iter++)
+    {
+        fmpr_t x, y, z, z2;
+        mag_t xb, yb;
+        ulong n;
+
+        fmpr_init(x);
+        fmpr_init(y);
+        fmpr_init(z);
+        fmpr_init(z2);
+
+        mag_init(xb);
+        mag_init(yb);
+
+        mag_randtest_special(xb, state, 1 + n_randint(state, 200));
+        mag_randtest_special(yb, state, 1 + n_randint(state, 200));
+        n = n_randint(state, 30);
+
+        mag_root(yb, xb, n);
+
+        mag_get_fmpr(x, xb);
+        mag_get_fmpr(y, yb);
+
+        fmpr_root(z, x, n, MAG_BITS, FMPR_RND_UP);
+        fmpr_mul_ui(z2, z, 1025, MAG_BITS, FMPR_RND_UP);
+        fmpr_mul_2exp_si(z2, z2, -10);
+
+        MAG_CHECK_BITS(xb)
+        MAG_CHECK_BITS(yb)
+
+        if (!(fmpr_cmpabs(z, y) <= 0 && fmpr_cmpabs(y, z2) <= 0))
+        {
+            printf("FAIL\n\n");
+            printf("x = "); fmpr_print(x); printf("\n\n");
+            printf("y = "); fmpr_print(y); printf("\n\n");
+            printf("z = "); fmpr_print(z); printf("\n\n");
+            printf("z2 = "); fmpr_print(z2); printf("\n\n");
+            abort();
+        }
+
+        mag_root(xb, xb, n);
+
+        if (!mag_equal(xb, yb))
+        {
+            printf("FAIL (aliasing)\n\n");
+            abort();
+        }
+
+        fmpr_clear(x);
+        fmpr_clear(y);
+        fmpr_clear(z);
+        fmpr_clear(z2);
+
+        mag_clear(xb);
+        mag_clear(yb);
+    }
+
+    flint_randclear(state);
+    flint_cleanup();
+    printf("PASS\n");
+    return EXIT_SUCCESS;
+}