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219 lines
6.9 KiB
219 lines
6.9 KiB
/*
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* Copyright (c) 2008-2020 Stefan Krah. All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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*
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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*
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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*
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* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
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* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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* SUCH DAMAGE.
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*/
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#ifndef LIBMPDEC_BASEARITH_H_
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#define LIBMPDEC_BASEARITH_H_
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#include "mpdecimal.h"
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#include "typearith.h"
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/* Internal header file: all symbols have local scope in the DSO */
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MPD_PRAGMA(MPD_HIDE_SYMBOLS_START)
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mpd_uint_t _mpd_baseadd(mpd_uint_t *w, const mpd_uint_t *u, const mpd_uint_t *v,
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mpd_size_t m, mpd_size_t n);
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void _mpd_baseaddto(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n);
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mpd_uint_t _mpd_shortadd(mpd_uint_t *w, mpd_size_t m, mpd_uint_t v);
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mpd_uint_t _mpd_shortadd_b(mpd_uint_t *w, mpd_size_t m, mpd_uint_t v,
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mpd_uint_t b);
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mpd_uint_t _mpd_baseincr(mpd_uint_t *u, mpd_size_t n);
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void _mpd_basesub(mpd_uint_t *w, const mpd_uint_t *u, const mpd_uint_t *v,
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mpd_size_t m, mpd_size_t n);
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void _mpd_basesubfrom(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n);
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void _mpd_basemul(mpd_uint_t *w, const mpd_uint_t *u, const mpd_uint_t *v,
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mpd_size_t m, mpd_size_t n);
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void _mpd_shortmul(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n,
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mpd_uint_t v);
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mpd_uint_t _mpd_shortmul_c(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n,
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mpd_uint_t v);
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mpd_uint_t _mpd_shortmul_b(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n,
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mpd_uint_t v, mpd_uint_t b);
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mpd_uint_t _mpd_shortdiv(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n,
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mpd_uint_t v);
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mpd_uint_t _mpd_shortdiv_b(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n,
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mpd_uint_t v, mpd_uint_t b);
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int _mpd_basedivmod(mpd_uint_t *q, mpd_uint_t *r, const mpd_uint_t *uconst,
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const mpd_uint_t *vconst, mpd_size_t nplusm, mpd_size_t n);
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void _mpd_baseshiftl(mpd_uint_t *dest, mpd_uint_t *src, mpd_size_t n,
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mpd_size_t m, mpd_size_t shift);
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mpd_uint_t _mpd_baseshiftr(mpd_uint_t *dest, mpd_uint_t *src, mpd_size_t slen,
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mpd_size_t shift);
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#ifdef CONFIG_64
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extern const mpd_uint_t mprime_rdx;
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/*
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* Algorithm from: Division by Invariant Integers using Multiplication,
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* T. Granlund and P. L. Montgomery, Proceedings of the SIGPLAN '94
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* Conference on Programming Language Design and Implementation.
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*
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* http://gmplib.org/~tege/divcnst-pldi94.pdf
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*
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* Variables from the paper and their translations (See section 8):
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*
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* N := 64
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* d := MPD_RADIX
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* l := 64
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* m' := floor((2**(64+64) - 1)/MPD_RADIX) - 2**64
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*
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* Since N-l == 0:
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*
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* dnorm := d
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* n2 := hi
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* n10 := lo
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*
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* ACL2 proof: mpd-div-words-r-correct
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*/
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static inline void
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_mpd_div_words_r(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t hi, mpd_uint_t lo)
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{
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mpd_uint_t n_adj, h, l, t;
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mpd_uint_t n1_neg;
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/* n1_neg = if lo >= 2**63 then MPD_UINT_MAX else 0 */
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n1_neg = (lo & (1ULL<<63)) ? MPD_UINT_MAX : 0;
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/* n_adj = if lo >= 2**63 then lo+MPD_RADIX else lo */
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n_adj = lo + (n1_neg & MPD_RADIX);
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/* (h, l) = if lo >= 2**63 then m'*(hi+1) else m'*hi */
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_mpd_mul_words(&h, &l, mprime_rdx, hi-n1_neg);
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l = l + n_adj;
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if (l < n_adj) h++;
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t = h + hi;
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/* At this point t == qest, with q == qest or q == qest+1:
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* 1) 0 <= 2**64*hi + lo - qest*MPD_RADIX < 2*MPD_RADIX
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*/
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/* t = 2**64-1 - qest = 2**64 - (qest+1) */
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t = MPD_UINT_MAX - t;
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/* (h, l) = 2**64*MPD_RADIX - (qest+1)*MPD_RADIX */
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_mpd_mul_words(&h, &l, t, MPD_RADIX);
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l = l + lo;
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if (l < lo) h++;
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h += hi;
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h -= MPD_RADIX;
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/* (h, l) = 2**64*hi + lo - (qest+1)*MPD_RADIX (mod 2**128)
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* Case q == qest+1:
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* a) h == 0, l == r
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* b) q := h - t == qest+1
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* c) r := l
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* Case q == qest:
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* a) h == MPD_UINT_MAX, l == 2**64-(MPD_RADIX-r)
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* b) q := h - t == qest
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* c) r := l + MPD_RADIX = r
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*/
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*q = (h - t);
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*r = l + (MPD_RADIX & h);
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}
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#else
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static inline void
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_mpd_div_words_r(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t hi, mpd_uint_t lo)
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{
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_mpd_div_words(q, r, hi, lo, MPD_RADIX);
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}
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#endif
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/* Multiply two single base MPD_RADIX words, store result in array w[2]. */
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static inline void
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_mpd_singlemul(mpd_uint_t w[2], mpd_uint_t u, mpd_uint_t v)
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{
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mpd_uint_t hi, lo;
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_mpd_mul_words(&hi, &lo, u, v);
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_mpd_div_words_r(&w[1], &w[0], hi, lo);
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}
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/* Multiply u (len 2) and v (len m, 1 <= m <= 2). */
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static inline void
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_mpd_mul_2_le2(mpd_uint_t w[4], mpd_uint_t u[2], mpd_uint_t v[2], mpd_ssize_t m)
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{
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mpd_uint_t hi, lo;
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_mpd_mul_words(&hi, &lo, u[0], v[0]);
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_mpd_div_words_r(&w[1], &w[0], hi, lo);
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_mpd_mul_words(&hi, &lo, u[1], v[0]);
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lo = w[1] + lo;
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if (lo < w[1]) hi++;
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_mpd_div_words_r(&w[2], &w[1], hi, lo);
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if (m == 1) return;
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_mpd_mul_words(&hi, &lo, u[0], v[1]);
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lo = w[1] + lo;
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if (lo < w[1]) hi++;
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_mpd_div_words_r(&w[3], &w[1], hi, lo);
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_mpd_mul_words(&hi, &lo, u[1], v[1]);
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lo = w[2] + lo;
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if (lo < w[2]) hi++;
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lo = w[3] + lo;
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if (lo < w[3]) hi++;
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_mpd_div_words_r(&w[3], &w[2], hi, lo);
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}
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/*
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* Test if all words from data[len-1] to data[0] are zero. If len is 0, nothing
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* is tested and the coefficient is regarded as "all zero".
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*/
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static inline int
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_mpd_isallzero(const mpd_uint_t *data, mpd_ssize_t len)
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{
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while (--len >= 0) {
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if (data[len] != 0) return 0;
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}
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return 1;
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}
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/*
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* Test if all full words from data[len-1] to data[0] are MPD_RADIX-1
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* (all nines). Return true if len == 0.
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*/
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static inline int
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_mpd_isallnine(const mpd_uint_t *data, mpd_ssize_t len)
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{
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while (--len >= 0) {
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if (data[len] != MPD_RADIX-1) return 0;
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}
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return 1;
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}
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MPD_PRAGMA(MPD_HIDE_SYMBOLS_END) /* restore previous scope rules */
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#endif /* LIBMPDEC_BASEARITH_H_ */
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