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c35a8e5c98
use log10() to calculate the size of the output array. The current code has been tested on x86/amd64 (and to a lesser extent on qemu-mips qemu-sparc) and produces sufficiently large values for all inputs tested so far (coefficient sizes of 10**18 - 1 are hard to test exhaustively). The new code does not rely on the correctness of log10() and resizes the output arrays if the allocated space is insufficient.
215 lines
6.7 KiB
C
215 lines
6.7 KiB
C
/*
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* Copyright (c) 2008-2012 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 BASEARITH_H
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#define BASEARITH_H
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#include "mpdecimal.h"
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#include <stdio.h>
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#include "typearith.h"
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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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#endif /* BASEARITH_H */
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