add mag_log1p

mag.h

@@ -648,6 +648,9 @@ static __inline__ void mag_set_d(mag_t z, double x)
 double mag_d_log_upper_bound(double x);
 double mag_d_log_lower_bound(double x);
 
+/* TODO: document */
+void mag_log1p(mag_t z, const mag_t x);
+
 /* TODO: document/test */
 void mag_pow_ui(mag_t z, const mag_t x, ulong e);
 void mag_pow_ui_lower(mag_t z, const mag_t x, ulong e);

mag/log1p.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) 2014 Fredrik Johansson
+
+******************************************************************************/
+
+#include "mag.h"
+#include "double_extras.h"
+
+void
+mag_log1p(mag_t z, const mag_t x)
+{
+    if (mag_is_special(x))
+    {
+        if (mag_is_zero(x))
+            mag_zero(z);
+        else
+            mag_inf(z);
+    }
+    else
+    {
+        fmpz exp = MAG_EXP(x);
+
+        if (!COEFF_IS_MPZ(exp))
+        {
+            /* Quick bound by x */
+            if (exp < -10)
+            {
+                mag_set(z, x);
+                return;
+            }
+            else if (exp < 1000)
+            {
+                double t;
+                t = ldexp(MAG_MAN(x), exp - MAG_BITS);
+                t = (1.0 + t) * (1 + 1e-14);
+                t = mag_d_log_upper_bound(t);
+                mag_set_d(z, t);
+                return;
+            }
+        }
+        else if (fmpz_sgn(MAG_EXPREF(x)) < 0)
+        {
+            /* Quick bound by x */
+            mag_set(z, x);
+            return;
+        }
+
+        /* Now we must have x >= 2^1000 */
+        /* Use log(2^(exp-1) * (2*v)) = exp*log(2) + log(2*v) */
+        {
+            double t;
+            fmpz_t b;
+            mag_t u;
+
+            mag_init(u);
+            fmpz_init(b);
+
+            /* incrementing the mantissa gives an upper bound for x+1 */
+            t = ldexp(MAG_MAN(x) + 1, 1 - MAG_BITS);
+            t = mag_d_log_upper_bound(t);
+            mag_set_d(u, t);
+
+            /* log(2) < 744261118/2^30 */
+            _fmpz_add_fast(b, MAG_EXPREF(x), -1);
+            fmpz_mul_ui(b, b, 744261118);
+            mag_set_fmpz(z, b);
+            _fmpz_add_fast(MAG_EXPREF(z), MAG_EXPREF(z), -30);
+
+            mag_add(z, z, u);
+
+            mag_clear(u);
+            fmpz_clear(b);
+        }
+    }
+}
+

mag/test/t-log1p.c

@@ -0,0 +1,98 @@
+/*=============================================================================
+
+    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("log1p....");
+    fflush(stdout);
+
+    flint_randinit(state);
+
+    for (iter = 0; iter < 100000; iter++)
+    {
+        fmpr_t x, y, z, z2;
+        mag_t xb, yb;
+
+        fmpr_init(x);
+        fmpr_init(y);
+        fmpr_init(z);
+        fmpr_init(z2);
+
+        mag_init(xb);
+        mag_init(yb);
+
+        mag_randtest_special(xb, state, 25);
+        mag_randtest_special(yb, state, 25);
+
+        mag_log1p(yb, xb);
+
+        mag_get_fmpr(x, xb);
+        mag_get_fmpr(y, yb);
+
+        fmpr_log1p(z, x, 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_log1p(xb, xb);
+
+        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;
+}
+