flint-sys 0.9.0

/*
    Copyright (C) 2014, 2022 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 "thread_support.h"
#include "fmpz_vec.h"
#include "arb.h"
#include "arb/impl.h"

/* When splitting [a,b) into [a,m), [m,b), we need the power x^(m-a).
   This function computes all the exponents (m-a) that can appear when
   doing binary splitting with the top-level interval [0,n),
   assuming that we always choose m = a + floor((b-a)/2), and that
   the case b-a = 2 is inlined. */
slong _arb_compute_bs_exponents(slong * tab, slong n)
{
    slong a, b, aa, /* ab, */ ba, bb, length;

    if (n == 1)
    {
        tab[0] = 1;
        return 1;
    }

    if (n == 2 || n == 3 || n == 4)
    {
        tab[0] = 1;
        tab[1] = 2;
        return 2;
    }

    if (n == 6)
    {
        tab[0] = 1;
        tab[1] = 2;
        tab[2] = 3;
        return 3;
    }

    /* first binary splitting call */
    a = n >> 1;
    b = n - (n >> 1);
    tab[0] = a;
    length = 1;

    for (;;)
    {
        /* split a -> aa, ab  and b -> ba, bb */
        aa = a >> 1;
        /* ab = a - aa; */
        ba = b >> 1;
        bb = b - ba;

        tab[length] = ba;
        length++;

        /* at length 3, we split into 2, 1 (and maybe also 2, 2) */
        if (ba == 3)
        {
            tab[length] = 2;
            tab[length + 1] = 1;
            length += 2;
            break;
        }

        /* stop if we have reached 1, or if at 2 and the
           length is a power of 2 (in which case we never reach 1) */
        if (ba == 1 || (ba == 2 && (n & (n-1)) == 0))
            break;

        /* if left and right lengths are different, also add the
           right length */
        if (aa != ba && aa != 1)
        {
            tab[length] = aa;
            length++;
        }

        a = aa;
        b = bb;
    }

    /* we always include x^1 in the table, even if the binary splitting
       terminates at step length 2 */
    if (tab[length-1] != 1)
    {
        tab[length] = 1;
        length++;
    }

    /* reverse table */
    for (a = 0; a < length / 2; a++)
    {
        b = tab[a];
        tab[a] = tab[length - a - 1];
        tab[length - a - 1] = b;
    }

    return length;
}

/* just do a linear search */
slong _arb_get_exp_pos(const slong * tab, slong step)
{
    slong i;

    for (i = 0; ; i++)
    {
        if (tab[i] == step)
            return i;

        if (tab[i] == 0)
        {
            flint_throw(FLINT_ERROR, "ERROR: exponent %wd not in table!\n", step);
        }
    }
}

static void
bsplit(fmpz_t T, fmpz_t Q, flint_bitcnt_t * Qexp,
    const slong * xexp,
    const fmpz * xpow, flint_bitcnt_t r, slong a, slong b)
{
    int cc;

    if (b - a == 1)
    {
        cc = flint_ctz((a + 1));
        fmpz_set_ui(Q, (a + 1) >> cc);
        *Qexp = r + cc;

        fmpz_set(T, xpow);
    }
    else if (b - a == 2)
    {
        fmpz_mul_ui(T, xpow, a + 2);
        fmpz_mul_2exp(T, T, r);
        fmpz_add(T, T, xpow + 1);

        cc = flint_ctz((a + 2));
        fmpz_set_ui(Q, (a + 2) >> cc);
        *Qexp = r + cc;

        cc = flint_ctz((a + 1));
        fmpz_mul_ui(Q, Q, (a + 1) >> cc);
        *Qexp += r + cc;
    }
    else
    {
        slong step, m, i;
        flint_bitcnt_t Q2exp[1];
        fmpz_t Q2, T2;

        step = (b - a) / 2;
        m = a + step;

        fmpz_init(Q2);
        fmpz_init(T2);

        bsplit(T,  Q,  Qexp,  xexp, xpow, r, a, m);
        bsplit(T2, Q2, Q2exp, xexp, xpow, r, m, b);

        fmpz_mul(T, T, Q2);
        fmpz_mul_2exp(T, T, *Q2exp);

        /* find x^step in table */
        i = _arb_get_exp_pos(xexp, step);
        fmpz_addmul(T, xpow + i, T2);
        fmpz_clear(T2);

        fmpz_mul(Q, Q, Q2);
        *Qexp = *Qexp + *Q2exp;
        fmpz_clear(Q2);
    }
}

typedef struct
{
    fmpz_t T;
    fmpz_t Q;
    flint_bitcnt_t Qexp;
    slong a;
    slong b;
}
exp_bsplit_struct;

typedef exp_bsplit_struct exp_bsplit_t[1];

static void exp_bsplit_init(exp_bsplit_t x, void * args)
{
    fmpz_init(x->T);
    fmpz_init(x->Q);
}

static void exp_bsplit_clear(exp_bsplit_t x, void * args)
{
    fmpz_clear(x->T);
    fmpz_clear(x->Q);
}

typedef struct
{
    const slong * xexp;
    const fmpz * xpow;
    flint_bitcnt_t r;
}
exp_bsplit_args;

static void
exp_bsplit_merge(exp_bsplit_t res, exp_bsplit_t L, exp_bsplit_t R, exp_bsplit_args * args)
{
    slong i, step;

    slong a = L->a;
    slong b = R->b;

    step = (b - a) / 2;

    fmpz_mul(res->T, L->T, R->Q);
    fmpz_mul_2exp(res->T, res->T, R->Qexp);

    /* find x^step in table */
    i = _arb_get_exp_pos(args->xexp, step);
    fmpz_addmul(res->T, args->xpow + i, R->T);
    fmpz_zero(R->T);

    fmpz_mul(res->Q, L->Q, R->Q);
    res->Qexp = L->Qexp + R->Qexp;

    res->a = L->a;  /* actually a no-op because of aliasing */
    res->b = R->b;
}

static void
exp_bsplit_basecase(exp_bsplit_t res, slong a, slong b, exp_bsplit_args * args)
{
    bsplit(res->T, res->Q, &(res->Qexp), args->xexp, args->xpow, args->r, a, b);
    res->a = a;
    res->b = b;
}

static void
bsplit2(fmpz_t T, fmpz_t Q, flint_bitcnt_t * Qexp,
    const slong * xexp,
    const fmpz * xpow, flint_bitcnt_t r, slong a, slong b)
{
    exp_bsplit_t s;
    exp_bsplit_args args;
    slong max_threads;
    slong prec_hint;

    args.xexp = xexp;
    args.xpow = xpow;
    args.r = r;

    *s->T = *T;
    *s->Q = *Q;

    max_threads = flint_get_num_threads();

    prec_hint = 2 * (b - a) * FLINT_MAX(r, 1);

    if (prec_hint < 30000)
        max_threads = 1;
    else if (prec_hint < 1000000)
        max_threads = FLINT_MIN(2, max_threads);
    else if (prec_hint < 5000000)
        max_threads = FLINT_MIN(4, max_threads);
    else
        max_threads = FLINT_MIN(8, max_threads);

    flint_parallel_binary_splitting(s,
        (bsplit_basecase_func_t) exp_bsplit_basecase,
        (bsplit_merge_func_t) exp_bsplit_merge,
        sizeof(exp_bsplit_struct),
        (bsplit_init_func_t) exp_bsplit_init,
        (bsplit_clear_func_t) exp_bsplit_clear,
        &args, a, b, 4, max_threads, FLINT_PARALLEL_BSPLIT_LEFT_INPLACE);

    *T = *s->T;
    *Q = *s->Q;
    *Qexp = s->Qexp;
}

void
_arb_exp_sum_bs_powtab(fmpz_t T, fmpz_t Q, flint_bitcnt_t * Qexp,
    const fmpz_t x, flint_bitcnt_t r, slong N)
{
    slong * xexp;
    slong length, i;
    fmpz * xpow;

    /* compute the powers of x that will appear (at least x^1) */
    xexp = flint_calloc(2 * FLINT_BITS, sizeof(slong));
    length = _arb_compute_bs_exponents(xexp, N);

    xpow = _fmpz_vec_init(length);
    xpow[0] = *x;   /* create shallow copy of x */

    /* build x^i table */
    for (i = 1; i < length; i++)
    {
        if (xexp[i] == 2 * xexp[i-1])
        {
            fmpz_mul(xpow + i, xpow + i - 1, xpow + i - 1);
        }
        else if (xexp[i] == 2 * xexp[i-2]) /* prefer squaring if possible */
        {
            fmpz_mul(xpow + i, xpow + i - 2, xpow + i - 2);
        }
        else if (xexp[i] == 2 * xexp[i-1] + 1)
        {
            fmpz_mul(xpow + i, xpow + i - 1, xpow + i - 1);
            fmpz_mul(xpow + i, xpow + i, xpow);
        }
        else if (xexp[i] == 2 * xexp[i-2] + 1)
        {
            fmpz_mul(xpow + i, xpow + i - 2, xpow + i - 2);
            fmpz_mul(xpow + i, xpow + i, xpow);
        }
        else
        {
            flint_throw(FLINT_ERROR, "power table has the wrong structure!\n");
        }
    }

    if (flint_get_num_available_threads() == 1)
        bsplit(T, Q, Qexp, xexp, xpow, r, 0, N);
    else
        bsplit2(T, Q, Qexp, xexp, xpow, r, 0, N);

    fmpz_init(xpow + 0);  /* don't free the shallow copy of x */
    _fmpz_vec_clear(xpow, length);
    flint_free(xexp);
}