add fmprb_const_log10

doc/source/fmprb.rst

@@ -642,6 +642,13 @@ Constants
 
         \log 2 = \frac{3}{4} \sum_{k=0}^{\infty} \frac{(-1)^k (k!)^2}{2^k (2k+1)!}
 
+.. function:: void fmprb_const_log10(fmprb_t s, long prec)
+
+    Sets *x* to `\log 10`. The value is cached for repeated use.
+    Uses the generic hypergeometric series code to evaluate the
+    Machin-like formula
+    `\log 10 = 46 \operatorname{atanh}(1/31) + 34 \operatorname{atanh}(1/49) + 20 \operatorname{atanh}(1/161)`.
+
 .. function:: void fmprb_const_e(fmprb_t s, long prec)
 
     Sets *x* to Euler's number `e = \sum_{n=0}^{\infty} 1/n!`, evaluated

fmprb.h

@@ -307,6 +307,7 @@ void fmprb_const_pi(fmprb_t x, long prec);
 void fmprb_const_sqrt_pi(fmprb_t t, long prec);
 void fmprb_const_log_sqrt2pi(fmprb_t t, long prec);
 void fmprb_const_log2(fmprb_t s, long prec);
+void fmprb_const_log10(fmprb_t s, long prec);
 void fmprb_const_catalan(fmprb_t s, long prec);
 void fmprb_const_e(fmprb_t s, long prec);
 

fmprb/const_log10.c

@@ -0,0 +1,70 @@
+/*=============================================================================
+
+    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) 2013 Fredrik Johansson
+
+******************************************************************************/
+
+#include "fmprb.h"
+#include "hypgeom.h"
+
+static void
+atanh_bsplit(fmprb_t s, ulong c, long a, long prec)
+{
+    fmprb_t t;
+    hypgeom_t series;
+    hypgeom_init(series);
+    fmprb_init(t);
+
+    fmpz_poly_set_ui(series->A, 1);
+    fmpz_poly_set_coeff_ui(series->B, 0, 1);
+    fmpz_poly_set_coeff_ui(series->B, 1, 2);
+    fmpz_poly_set_ui(series->P, 1);
+    fmpz_poly_set_ui(series->Q, c * c);
+
+    fmprb_hypgeom_infsum(s, t, series, prec, prec);
+    fmprb_mul_si(s, s, a, prec);
+    fmprb_mul_ui(t, t, c, prec);
+    fmprb_div(s, s, t, prec);
+
+    fmprb_clear(t);
+    hypgeom_clear(series);
+}
+
+void
+fmprb_const_log10_eval(fmprb_t s, long prec)
+{
+    fmprb_t t;
+    fmprb_init(t);
+
+    prec += FLINT_CLOG2(prec);
+
+    atanh_bsplit(s, 31, 46, prec);
+    atanh_bsplit(t, 49, 34, prec);
+    fmprb_add(s, s, t, prec);
+    atanh_bsplit(t, 161, 20, prec);
+    fmprb_add(s, s, t, prec);
+
+    fmprb_clear(t);
+}
+
+DEF_CACHED_CONSTANT(fmprb_const_log10, fmprb_const_log10_eval)
+

fmprb/test/t-const_log10.c

@@ -0,0 +1,79 @@
+/*=============================================================================
+
+    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) 2012 Fredrik Johansson
+
+******************************************************************************/
+
+#include "fmprb.h"
+
+int main()
+{
+    long iter;
+    flint_rand_t state;
+
+    printf("const_log10....");
+    fflush(stdout);
+    flint_randinit(state);
+
+    for (iter = 0; iter < 250; iter++)
+    {
+        fmprb_t r;
+        mpfr_t s;
+        long accuracy, prec;
+
+        prec = 2 + n_randint(state, 1 << n_randint(state, 16));
+
+        fmprb_init(r);
+        mpfr_init2(s, prec + 1000);
+
+        fmprb_const_log10(r, prec);
+        mpfr_set_ui(s, 10, MPFR_RNDN);
+        mpfr_log(s, s, MPFR_RNDN);
+
+        if (!fmprb_contains_mpfr(r, s))
+        {
+            printf("FAIL: containment\n\n");
+            printf("prec = %ld\n", prec);
+            printf("r = "); fmprb_printd(r, prec / 3.33); printf("\n\n");
+            abort();
+        }
+
+        accuracy = fmprb_rel_accuracy_bits(r);
+
+        if (accuracy < prec - 4)
+        {
+            printf("FAIL: poor accuracy\n\n");
+            printf("prec = %ld\n", prec);
+            printf("r = "); fmprb_printd(r, prec / 3.33); printf("\n\n");
+            abort();
+        }
+
+        fmprb_clear(r);
+        mpfr_clear(s);
+    }
+
+    flint_randclear(state);
+    _fmpz_cleanup();
+    mpfr_free_cache();
+    printf("PASS\n");
+    return EXIT_SUCCESS;
+}