arb/fmpcb.h

/*=============================================================================

    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

******************************************************************************/

#ifndef FMPCB_H
#define FMPCB_H

#include "fmpr.h"
#include "fmprb.h"

typedef struct
{
    fmprb_struct real;
    fmprb_struct imag;
}
fmpcb_struct;

typedef fmpcb_struct fmpcb_t[1];

#define fmpcb_realref(x) (&(x)->real)
#define fmpcb_imagref(x) (&(x)->imag)


static __inline__ void
fmpcb_init(fmpcb_t x)
{
    fmprb_init(fmpcb_realref(x));
    fmprb_init(fmpcb_imagref(x));
}

static __inline__ void
fmpcb_clear(fmpcb_t x)
{
    fmprb_clear(fmpcb_realref(x));
    fmprb_clear(fmpcb_imagref(x));
}

static __inline__ fmpcb_struct *
_fmpcb_vec_init(long n)
{
    long i;
    fmpcb_struct * v = flint_malloc(sizeof(fmpcb_struct) * n);

    for (i = 0; i < n; i++)
        fmpcb_init(v + i);

    return v;
}

static __inline__ void
_fmpcb_vec_clear(fmpcb_struct * v, long n)
{
    long i;
    for (i = 0; i < n; i++)
        fmpcb_clear(v + i);
    flint_free(v);
}

static __inline__ int
fmpcb_is_zero(const fmpcb_t z)
{
    return fmprb_is_zero(fmpcb_realref(z)) && fmprb_is_zero(fmpcb_imagref(z));
}

static __inline__ int
fmpcb_is_exact(const fmpcb_t z)
{
    return fmprb_is_exact(fmpcb_realref(z)) && fmprb_is_exact(fmpcb_imagref(z));
}


static __inline__ void
fmpcb_zero(fmpcb_t z)
{
    fmprb_zero(fmpcb_realref(z));
    fmprb_zero(fmpcb_imagref(z));
}

static __inline__ void
fmpcb_one(fmpcb_t z)
{
    fmprb_one(fmpcb_realref(z));
    fmprb_zero(fmpcb_imagref(z));
}

static __inline__ void
fmpcb_onei(fmpcb_t z)
{
    fmprb_zero(fmpcb_realref(z));
    fmprb_one(fmpcb_imagref(z));
}

static __inline__ void
fmpcb_set(fmpcb_t z, const fmpcb_t x)
{
    fmprb_set(fmpcb_realref(z), fmpcb_realref(x));
    fmprb_set(fmpcb_imagref(z), fmpcb_imagref(x));
}

static __inline__ void
fmpcb_swap(fmpcb_t z, fmpcb_t x)
{
    fmprb_swap(fmpcb_realref(z), fmpcb_realref(x));
    fmprb_swap(fmpcb_imagref(z), fmpcb_imagref(x));
}

static __inline__ int
fmpcb_equal(const fmpcb_t x, const fmpcb_t y)
{
    return fmprb_equal(fmpcb_realref(x), fmpcb_realref(y)) &&
            fmprb_equal(fmpcb_imagref(x), fmpcb_imagref(y));
}

static __inline__ int
fmpcb_overlaps(const fmpcb_t x, const fmpcb_t y)
{
    return fmprb_overlaps(fmpcb_realref(x), fmpcb_realref(y)) &&
            fmprb_overlaps(fmpcb_imagref(x), fmpcb_imagref(y));
}

static __inline__ int
fmpcb_contains_zero(const fmpcb_t x)
{
    return fmprb_contains_zero(fmpcb_realref(x)) &&
            fmprb_contains_zero(fmpcb_imagref(x));
}

static __inline__ int
fmpcb_contains_fmpq(const fmpcb_t x, const fmpq_t y)
{
    return fmprb_contains_fmpq(fmpcb_realref(x), y) &&
            fmprb_contains_zero(fmpcb_imagref(x));
}

static __inline__ int
fmpcb_contains_fmpz(const fmpcb_t x, const fmpz_t y)
{
    return fmprb_contains_fmpz(fmpcb_realref(x), y) &&
            fmprb_contains_zero(fmpcb_imagref(x));
}

static __inline__ void
fmpcb_set_ui(fmpcb_t z, ulong c)
{
    fmprb_set_ui(fmpcb_realref(z), c);
    fmprb_zero(fmpcb_imagref(z));
}

static __inline__ void
fmpcb_set_si(fmpcb_t z, long c)
{
    fmprb_set_si(fmpcb_realref(z), c);
    fmprb_zero(fmpcb_imagref(z));
}

static __inline__ void
fmpcb_set_fmpz(fmpcb_t z, const fmpz_t c)
{
    fmprb_set_fmpz(fmpcb_realref(z), c);
    fmprb_zero(fmpcb_imagref(z));
}

static __inline__ void
fmpcb_set_fmpq(fmpcb_t z, const fmpq_t c, long prec)
{
    fmprb_set_fmpq(fmpcb_realref(z), c, prec);
    fmprb_zero(fmpcb_imagref(z));
}

static __inline__ void
fmpcb_get_abs_ubound_fmpr(fmpr_t u, const fmpcb_t z, long prec)
{
    fmpr_t v;
    fmpr_init(v);

    fmprb_get_abs_ubound_fmpr(u, fmpcb_realref(z), prec);
    fmprb_get_abs_ubound_fmpr(v, fmpcb_realref(z), prec);

    fmpr_mul(u, u, u, prec, FMPR_RND_UP);
    fmpr_mul(v, v, v, prec, FMPR_RND_UP);
    fmpr_add(u, u, v, prec, FMPR_RND_UP);
    fmpr_sqrt(u, u, prec, FMPR_RND_UP);

    fmpr_clear(v);
}

void fmpcb_arg(fmprb_t r, const fmpcb_t z, long prec);

static __inline__ void
fmpcb_add(fmpcb_t z, const fmpcb_t x, const fmpcb_t y, long prec)
{
    fmprb_add(fmpcb_realref(z), fmpcb_realref(x), fmpcb_realref(y), prec);
    fmprb_add(fmpcb_imagref(z), fmpcb_imagref(x), fmpcb_imagref(y), prec);
}

static __inline__ void
fmpcb_sub(fmpcb_t z, const fmpcb_t x, const fmpcb_t y, long prec)
{
    fmprb_sub(fmpcb_realref(z), fmpcb_realref(x), fmpcb_realref(y), prec);
    fmprb_sub(fmpcb_imagref(z), fmpcb_imagref(x), fmpcb_imagref(y), prec);
}

static __inline__ void
fmpcb_add_ui(fmpcb_t z, const fmpcb_t x, ulong c, long prec)
{
    fmprb_add_ui(fmpcb_realref(z), fmpcb_realref(x), c, prec);
    fmprb_set_round(fmpcb_imagref(z), fmpcb_imagref(x), prec);
}

static __inline__ void
fmpcb_sub_ui(fmpcb_t z, const fmpcb_t x, ulong c, long prec)
{
    fmprb_sub_ui(fmpcb_realref(z), fmpcb_realref(x), c, prec);
    fmprb_set_round(fmpcb_imagref(z), fmpcb_imagref(x), prec);
}

static __inline__ void
fmpcb_neg(fmpcb_t z, const fmpcb_t x)
{
    fmprb_neg(fmpcb_realref(z), fmpcb_realref(x));
    fmprb_neg(fmpcb_imagref(z), fmpcb_imagref(x));
}

static __inline__ void
fmpcb_conj(fmpcb_t z, const fmpcb_t x)
{
    fmprb_set(fmpcb_realref(z), fmpcb_realref(x));
    fmprb_neg(fmpcb_imagref(z), fmpcb_imagref(x));
}

static __inline__ void
fmpcb_mul_ui(fmpcb_t z, const fmpcb_t x, ulong y, long prec)
{
    fmprb_mul_ui(fmpcb_realref(z), fmpcb_realref(x), y, prec);
    fmprb_mul_ui(fmpcb_imagref(z), fmpcb_imagref(x), y, prec);
}

static __inline__ void
fmpcb_mul_fmprb(fmpcb_t z, const fmpcb_t x, const fmprb_t y, long prec)
{
    fmprb_mul(fmpcb_realref(z), fmpcb_realref(x), y, prec);
    fmprb_mul(fmpcb_imagref(z), fmpcb_imagref(x), y, prec);
}

static __inline__ void
fmpcb_mul_onei(fmpcb_t z, const fmpcb_t x)
{
    if (z == x)
    {
        fmprb_swap(fmpcb_realref(z), fmpcb_imagref(z));
        fmprb_neg(fmpcb_realref(z), fmpcb_realref(z));
    }
    else
    {
        fmprb_neg(fmpcb_realref(z), fmpcb_imagref(x));
        fmprb_set(fmpcb_imagref(z), fmpcb_realref(x));
    }
}

void fmpcb_mul(fmpcb_t z, const fmpcb_t x, const fmpcb_t y, long prec);

void fmpcb_mul_alt(fmpcb_t z, const fmpcb_t x, const fmpcb_t y, long prec);

static __inline__ void
fmpcb_mul_2exp_si(fmpcb_t z, const fmpcb_t x, long e)
{
    fmprb_mul_2exp_si(fmpcb_realref(z), fmpcb_realref(x), e);
    fmprb_mul_2exp_si(fmpcb_imagref(z), fmpcb_imagref(x), e);
}

static __inline__ void
fmpcb_addmul(fmpcb_t z, const fmpcb_t x, const fmpcb_t y, long prec)
{
    fmpcb_t t;
    fmpcb_init(t);
    fmpcb_mul(t, x, y, prec);
    fmpcb_add(z, z, t, prec);
    fmpcb_clear(t);
}

static __inline__ void
fmpcb_submul(fmpcb_t z, const fmpcb_t x, const fmpcb_t y, long prec)
{
    fmpcb_t t;
    fmpcb_init(t);
    fmpcb_mul(t, x, y, prec);
    fmpcb_sub(z, z, t, prec);
    fmpcb_clear(t);
}

static __inline__ void
fmpcb_inv(fmpcb_t z, const fmpcb_t x, long prec)
{
    fmprb_t t;
    fmprb_init(t);

#define a fmpcb_realref(x)
#define b fmpcb_imagref(x)

    fmprb_mul(t, a, a, prec);
    fmprb_addmul(t, b, b, prec);

    fmprb_div(fmpcb_realref(z), a, t, prec);
    fmprb_div(fmpcb_imagref(z), b, t, prec);

    fmprb_neg(fmpcb_imagref(z), fmpcb_imagref(z));

#undef a
#undef b

    fmprb_clear(t);
}

static __inline__ void
fmpcb_div(fmpcb_t z, const fmpcb_t x, const fmpcb_t y, long prec)
{
    fmpcb_t t;
    fmpcb_init(t);
    fmpcb_inv(t, y, prec);
    fmpcb_mul(z, x, t, prec);
    fmpcb_clear(t);
}

static __inline__ void
fmpcb_div_ui(fmpcb_t z, const fmpcb_t x, ulong c, long prec)
{
    fmprb_div_ui(fmpcb_realref(z), fmpcb_realref(x), c, prec);
    fmprb_div_ui(fmpcb_imagref(z), fmpcb_imagref(x), c, prec);
}

void fmpcb_pow_fmpz(fmpcb_t y, const fmpcb_t b, const fmpz_t e, long prec);

void fmpcb_pow_ui(fmpcb_t y, const fmpcb_t b, ulong e, long prec);

void fmpcb_log(fmpcb_t r, const fmpcb_t z, long prec);

void fmpcb_exp(fmpcb_t r, const fmpcb_t z, long prec);

void fmpcb_sin(fmpcb_t r, const fmpcb_t z, long prec);
void fmpcb_cos(fmpcb_t r, const fmpcb_t z, long prec);
void fmpcb_sin_cos(fmpcb_t s, fmpcb_t c, const fmpcb_t z, long prec);

void fmpcb_pow(fmpcb_t r, const fmpcb_t x, const fmpcb_t y, long prec);

void fmpcb_zeta_em_bound(fmpr_t bound, const fmpcb_t s, ulong N, ulong M, long prec);

void fmpcb_zeta_em_choose_param(fmpr_t bound, ulong * N, ulong * M, const fmpcb_t s, long target, long prec);

void fmpcb_zeta_em_sum(fmpcb_t z, const fmpcb_t s, ulong N, ulong M, long prec);

void fmpcb_zeta(fmpcb_t z, const fmpcb_t s, long prec);

static __inline__ void
_fmpcb_vec_zero(fmpcb_struct * A, long n)
{
    long i;
    for (i = 0; i < n; i++)
        fmpcb_zero(A + i);
}

static __inline__ void
_fmpcb_vec_set(fmpcb_struct * res, const fmpcb_struct * vec, long len)
{
    long i;
    for (i = 0; i < len; i++)
        fmpcb_set(res + i, vec + i);
}

static __inline__ void
_fmpcb_vec_neg(fmpcb_struct * res, const fmpcb_struct * vec, long len)
{
    long i;
    for (i = 0; i < len; i++)
        fmpcb_neg(res + i, vec + i);
}

static __inline__ void
_fmpcb_vec_add(fmpcb_struct * res, const fmpcb_struct * vec1, const fmpcb_struct * vec2, long len, long prec)
{
    long i;
    for (i = 0; i < len; i++)
        fmpcb_add(res + i, vec1 + i, vec2 + i, prec);
}

static __inline__ void
_fmpcb_vec_sub(fmpcb_struct * res, const fmpcb_struct * vec1, const fmpcb_struct * vec2, long len, long prec)
{
    long i;
    for (i = 0; i < len; i++)
        fmpcb_sub(res + i, vec1 + i, vec2 + i, prec);
}

static __inline__ void
_fmpcb_vec_scalar_submul(fmpcb_struct * res, const fmpcb_struct * vec, long len, const fmpcb_t c, long prec)
{
    if (len > 0)
    {
        long i;
        fmpcb_t t;
        fmpcb_init(t);
        for (i = 0; i < len; i++)
        {
            fmpcb_mul(t, vec + i, c, prec);
            fmpcb_sub(res + i, res + i, t, prec);
        }
        fmpcb_clear(t);
    }
}

static __inline__ void
_fmpcb_vec_scalar_addmul(fmpcb_struct * res, const fmpcb_struct * vec, long len, const fmpcb_t c, long prec)
{
    if (len > 0)
    {
        long i;
        fmpcb_t t;
        fmpcb_init(t);
        for (i = 0; i < len; i++)
        {
            fmpcb_mul(t, vec + i, c, prec);
            fmpcb_add(res + i, res + i, t, prec);
        }
        fmpcb_clear(t);
    }
}

static __inline__ void
_fmpcb_vec_scalar_mul(fmpcb_struct * res, const fmpcb_struct * vec, long len, const fmpcb_t c, long prec)
{
    long i;
    for (i = 0; i < len; i++)
        fmpcb_mul(res + i, vec + i, c, prec);
}

static __inline__ void
fmpcb_print(const fmpcb_t x)
{
    printf("(");
    fmprb_print(fmpcb_realref(x));
    printf(", ");
    fmprb_print(fmpcb_imagref(x));
    printf(")");
}

void fmpcb_printd(const fmpcb_t z, long digits);

void fmpcb_randtest(fmpcb_t z, flint_rand_t state, long prec, long mag_bits);

#endif