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/*
* 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_ */
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