flint-sys 0.9.0

Bindings to the FLINT C library
Documentation 
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/*
    Copyright (C) 2015 Fredrik Johansson

    This file is part of FLINT.

    FLINT is free software: you can redistribute it and/or modify it under
    the terms of the GNU Lesser General Public License (LGPL) as published
    by the Free Software Foundation; either version 3 of the License, or
    (at your option) any later version.  See <https://www.gnu.org/licenses/>.
*/

#include "arb.h"

/* todo: make arb_pow_fmpz automatic */
static void
_arb_10_pow_fmpz(arb_t res, const fmpz_t m, slong prec)
{
    slong bits = fmpz_bits(m);

    if (bits <= FLINT_BITS)
    {
        arb_ui_pow_ui(res, 10, fmpz_get_ui(m), prec);
    }
    else if (bits < 128)
    {
        arb_set_ui(res, 10);
        arb_pow_fmpz_binexp(res, res, m, prec + 2 * bits);
    }
    else
    {
        arb_const_log10(res, prec + bits);
        arb_mul_fmpz(res, res, m, prec + bits);
        arb_exp(res, res, prec + bits);
    }
}

void
arb_get_fmpz_mid_rad_10exp(fmpz_t mid, fmpz_t rad, fmpz_t exp, const arb_t x, slong n)
{
    fmpz_t e, m;
    arb_t t, u;
    arf_t r;
    slong prec;
    int roundmid, roundrad;

    if (!arb_is_finite(x) || arb_is_zero(x))
    {
        fmpz_zero(mid);
        fmpz_zero(rad);
        fmpz_zero(exp);
        return;
    }

    /*
      We compute m such that x * 10^m ~= 10^(n+5).
      If x = 2^e then m = (n+5) - e*log(2)/log(10).
    */
    fmpz_init(e);
    fmpz_init(m);
    arb_init(t);
    arb_init(u);
    arf_init(r);

    if (arf_cmpabs_mag(arb_midref(x), arb_radref(x)) > 0)
        fmpz_set(e, ARF_EXPREF(arb_midref(x)));
    else
        fmpz_set(e, ARF_EXPREF(arb_radref(x)));

    prec = fmpz_bits(e);
    prec = FLINT_MAX(prec, FLINT_BIT_COUNT(n)) + 15;

    arb_const_log2(t, prec);
    arb_const_log10(u, prec);
    arb_div(t, t, u, prec);
    arb_mul_fmpz(t, t, e, prec);
    arb_neg(t, t);
    arb_add_ui(t, t, n + 5, prec);
    arf_get_fmpz(m, arb_midref(t), ARF_RND_FLOOR);

    fmpz_neg(exp, m);

    prec = n * 3.32192809488736 + 30;

    if (fmpz_sgn(m) >= 0)
    {
        _arb_10_pow_fmpz(t, m, prec);
        arb_mul(t, x, t, prec);
    }
    else
    {
        fmpz_neg(m, m);
        _arb_10_pow_fmpz(t, m, prec);
        arb_div(t, x, t, prec);
    }

    roundmid = arf_get_fmpz_fixed_si(mid, arb_midref(t), 0);

    arf_set_mag(r, arb_radref(t));
    roundrad = arf_get_fmpz_fixed_si(rad, r, 0);

    fmpz_add_ui(rad, rad, roundmid + roundrad);

    fmpz_clear(e);
    fmpz_clear(m);
    arb_clear(t);
    arb_clear(u);
    arf_clear(r);
}