basearith.h

/*
 * Copyright (c) 2008-2020 Stefan Krah. All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 *
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 *
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 *
 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
 * SUCH DAMAGE.
 */


#ifndef LIBMPDEC_BASEARITH_H_
#define LIBMPDEC_BASEARITH_H_


#include "mpdecimal.h"
#include "typearith.h"


/* Internal header file: all symbols have local scope in the DSO */
MPD_PRAGMA(MPD_HIDE_SYMBOLS_START)


mpd_uint_t _mpd_baseadd(mpd_uint_t *w, const mpd_uint_t *u, const mpd_uint_t *v,
                        mpd_size_t m, mpd_size_t n);
void _mpd_baseaddto(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n);
mpd_uint_t _mpd_shortadd(mpd_uint_t *w, mpd_size_t m, mpd_uint_t v);
mpd_uint_t _mpd_shortadd_b(mpd_uint_t *w, mpd_size_t m, mpd_uint_t v,
                           mpd_uint_t b);
mpd_uint_t _mpd_baseincr(mpd_uint_t *u, mpd_size_t n);
void _mpd_basesub(mpd_uint_t *w, const mpd_uint_t *u, const mpd_uint_t *v,
                  mpd_size_t m, mpd_size_t n);
void _mpd_basesubfrom(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n);
void _mpd_basemul(mpd_uint_t *w, const mpd_uint_t *u, const mpd_uint_t *v,
                  mpd_size_t m, mpd_size_t n);
void _mpd_shortmul(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n,
                   mpd_uint_t v);
mpd_uint_t _mpd_shortmul_c(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n,
                           mpd_uint_t v);
mpd_uint_t _mpd_shortmul_b(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n,
                           mpd_uint_t v, mpd_uint_t b);
mpd_uint_t _mpd_shortdiv(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n,
                         mpd_uint_t v);
mpd_uint_t _mpd_shortdiv_b(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n,
                           mpd_uint_t v, mpd_uint_t b);
int _mpd_basedivmod(mpd_uint_t *q, mpd_uint_t *r, const mpd_uint_t *uconst,
                    const mpd_uint_t *vconst, mpd_size_t nplusm, mpd_size_t n);
void _mpd_baseshiftl(mpd_uint_t *dest, mpd_uint_t *src, mpd_size_t n,
                     mpd_size_t m, mpd_size_t shift);
mpd_uint_t _mpd_baseshiftr(mpd_uint_t *dest, mpd_uint_t *src, mpd_size_t slen,
                           mpd_size_t shift);



#ifdef CONFIG_64
extern const mpd_uint_t mprime_rdx;

/*
 * Algorithm from: Division by Invariant Integers using Multiplication,
 * T. Granlund and P. L. Montgomery, Proceedings of the SIGPLAN '94
 * Conference on Programming Language Design and Implementation.
 *
 * http://gmplib.org/~tege/divcnst-pldi94.pdf
 *
 * Variables from the paper and their translations (See section 8):
 *
 *  N := 64
 *  d := MPD_RADIX
 *  l := 64
 *  m' := floor((2**(64+64) - 1)/MPD_RADIX) - 2**64
 *
 * Since N-l == 0:
 *
 *  dnorm := d
 *  n2 := hi
 *  n10 := lo
 *
 * ACL2 proof: mpd-div-words-r-correct
 */
static inline void
_mpd_div_words_r(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t hi, mpd_uint_t lo)
{
    mpd_uint_t n_adj, h, l, t;
    mpd_uint_t n1_neg;

    /* n1_neg = if lo >= 2**63 then MPD_UINT_MAX else 0 */
    n1_neg = (lo & (1ULL<<63)) ? MPD_UINT_MAX : 0;
    /* n_adj = if lo >= 2**63 then lo+MPD_RADIX else lo */
    n_adj = lo + (n1_neg & MPD_RADIX);

    /* (h, l) = if lo >= 2**63 then m'*(hi+1) else m'*hi */
    _mpd_mul_words(&h, &l, mprime_rdx, hi-n1_neg);
    l = l + n_adj;
    if (l < n_adj) h++;
    t = h + hi;
    /* At this point t == qest, with q == qest or q == qest+1:
     *   1) 0 <= 2**64*hi + lo - qest*MPD_RADIX < 2*MPD_RADIX
     */

    /* t = 2**64-1 - qest = 2**64 - (qest+1) */
    t = MPD_UINT_MAX - t;

    /* (h, l) = 2**64*MPD_RADIX - (qest+1)*MPD_RADIX */
    _mpd_mul_words(&h, &l, t, MPD_RADIX);
    l = l + lo;
    if (l < lo) h++;
    h += hi;
    h -= MPD_RADIX;
    /* (h, l) = 2**64*hi + lo - (qest+1)*MPD_RADIX (mod 2**128)
     * Case q == qest+1:
     *     a) h == 0, l == r
     *     b) q := h - t == qest+1
     *     c) r := l
     * Case q == qest:
     *     a) h == MPD_UINT_MAX, l == 2**64-(MPD_RADIX-r)
     *     b) q := h - t == qest
     *     c) r := l + MPD_RADIX = r
     */

    *q = (h - t);
    *r = l + (MPD_RADIX & h);
}
#else
static inline void
_mpd_div_words_r(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t hi, mpd_uint_t lo)
{
    _mpd_div_words(q, r, hi, lo, MPD_RADIX);
}
#endif


/* Multiply two single base MPD_RADIX words, store result in array w[2]. */
static inline void
_mpd_singlemul(mpd_uint_t w[2], mpd_uint_t u, mpd_uint_t v)
{
    mpd_uint_t hi, lo;

    _mpd_mul_words(&hi, &lo, u, v);
    _mpd_div_words_r(&w[1], &w[0], hi, lo);
}

/* Multiply u (len 2) and v (len m, 1 <= m <= 2). */
static inline void
_mpd_mul_2_le2(mpd_uint_t w[4], mpd_uint_t u[2], mpd_uint_t v[2], mpd_ssize_t m)
{
    mpd_uint_t hi, lo;

    _mpd_mul_words(&hi, &lo, u[0], v[0]);
    _mpd_div_words_r(&w[1], &w[0], hi, lo);

    _mpd_mul_words(&hi, &lo, u[1], v[0]);
    lo = w[1] + lo;
    if (lo < w[1]) hi++;
    _mpd_div_words_r(&w[2], &w[1], hi, lo);
    if (m == 1) return;

    _mpd_mul_words(&hi, &lo, u[0], v[1]);
    lo = w[1] + lo;
    if (lo < w[1]) hi++;
    _mpd_div_words_r(&w[3], &w[1], hi, lo);

    _mpd_mul_words(&hi, &lo, u[1], v[1]);
    lo = w[2] + lo;
    if (lo < w[2]) hi++;
    lo = w[3] + lo;
    if (lo < w[3]) hi++;
    _mpd_div_words_r(&w[3], &w[2], hi, lo);
}


/*
 * Test if all words from data[len-1] to data[0] are zero. If len is 0, nothing
 * is tested and the coefficient is regarded as "all zero".
 */
static inline int
_mpd_isallzero(const mpd_uint_t *data, mpd_ssize_t len)
{
    while (--len >= 0) {
        if (data[len] != 0) return 0;
    }
    return 1;
}

/*
 * Test if all full words from data[len-1] to data[0] are MPD_RADIX-1
 * (all nines). Return true if len == 0.
 */
static inline int
_mpd_isallnine(const mpd_uint_t *data, mpd_ssize_t len)
{
    while (--len >= 0) {
        if (data[len] != MPD_RADIX-1) return 0;
    }
    return 1;
}


MPD_PRAGMA(MPD_HIDE_SYMBOLS_END) /* restore previous scope rules */


#endif /* LIBMPDEC_BASEARITH_H_ */