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Reorganizing source code. Created util dir

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Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
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Leonardo de Moura 2012-10-20 10:19:38 -07:00
parent 630ba0c675
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src/util/mpn.cpp Normal file
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/*++
Copyright (c) 2011 Microsoft Corporation
Module Name:
mpn.cpp
Abstract:
Multi Precision Natural Numbers
Author:
Christoph Wintersteiger (cwinter) 2011-11-16.
Revision History:
--*/
#include"debug.h"
#include"trace.h"
#include"buffer.h"
#include"mpn.h"
#define max(a,b) (((a) > (b)) ? (a) : (b))
typedef uint64 mpn_double_digit;
COMPILE_TIME_ASSERT(sizeof(mpn_double_digit) == 2 * sizeof(mpn_digit));
mpn_manager static_mpn_manager;
const mpn_digit mpn_manager::zero = 0;
mpn_manager::mpn_manager() {
#ifdef _DEBUG
trace_enabled=true;
#endif
}
mpn_manager::~mpn_manager() {
}
int mpn_manager::compare(mpn_digit const * a, size_t const lnga,
mpn_digit const * b, size_t const lngb) const {
int res = 0;
#ifdef _DEBUG
if (trace_enabled)
STRACE("mpn", tout << "[mpn] "; );
#endif
trace(a, lnga);
size_t j = max(lnga, lngb) - 1;
for (; j != (size_t)-1 && res == 0; j--) {
mpn_digit const & u_j = (j < lnga) ? a[j] : zero;
mpn_digit const & v_j = (j < lngb) ? b[j] : zero;
if (u_j > v_j)
res = 1;
else if (u_j < v_j)
res = -1;
}
#ifdef _DEBUG
if (trace_enabled)
STRACE("mpn", tout << ((res == 1) ? " > " : (res == -1) ? " < " : " == "); );
#endif
trace_nl(b, lngb);
return res;
}
bool mpn_manager::add(mpn_digit const * a, size_t const lnga,
mpn_digit const * b, size_t const lngb,
mpn_digit * c, size_t const lngc_alloc,
size_t * plngc) const {
trace(a, lnga, b, lngb, "+");
// Essentially Knuth's Algorithm A
size_t len = max(lnga, lngb);
SASSERT(lngc_alloc == len+1 && len > 0);
mpn_digit k = 0;
mpn_digit r;
bool c1, c2;
for (size_t j = 0; j < len; j++) {
mpn_digit const & u_j = (j < lnga) ? a[j] : zero;
mpn_digit const & v_j = (j < lngb) ? b[j] : zero;
r = u_j + v_j; c1 = r < u_j;
c[j] = r + k; c2 = c[j] < r;
k = c1 | c2;
}
c[len] = k;
size_t &os = *plngc;
for (os = len+1; os > 1 && c[os-1] == 0; ) os--;
SASSERT(os > 0 && os <= len+1);
trace_nl(c, os);
return true; // return k != 0? What would MSBignum return?
}
bool mpn_manager::sub(mpn_digit const * a, size_t const lnga,
mpn_digit const * b, size_t const lngb,
mpn_digit * c, mpn_digit * pborrow) const {
trace(a, lnga, b, lngb, "-");
// Essentially Knuth's Algorithm S
size_t len = max(lnga, lngb);
mpn_digit & k = *pborrow; k = 0;
mpn_digit r;
bool c1, c2;
for (size_t j = 0; j < len; j++) {
mpn_digit const & u_j = (j < lnga) ? a[j] : zero;
mpn_digit const & v_j = (j < lngb) ? b[j] : zero;
r = u_j - v_j; c1 = r > u_j;
c[j] = r - k; c2 = c[j] > r;
k = c1 | c2;
}
trace_nl(c, lnga);
return true; // return k != 0?
}
bool mpn_manager::mul(mpn_digit const * a, size_t const lnga,
mpn_digit const * b, size_t const lngb,
mpn_digit * c) const {
trace(a, lnga, b, lngb, "*");
// Essentially Knuth's Algorithm M.
// Perhaps implement a more efficient version, see e.g., Knuth, Section 4.3.3.
size_t i;
mpn_digit k;
#define DIGIT_BITS (sizeof(mpn_digit)*8)
#define HALF_BITS (sizeof(mpn_digit)*4)
for (unsigned i = 0; i < lnga; i++)
c[i] = 0;
for (size_t j = 0; j < lngb; j++) {
mpn_digit const & v_j = b[j];
if (v_j == 0) { // This branch may be omitted according to Knuth.
c[j+lnga] = 0;
}
else {
k = 0;
for (i = 0; i < lnga; i++) {
mpn_digit const & u_i = a[i];
mpn_double_digit t;
t = ((mpn_double_digit)u_i * (mpn_double_digit)v_j) +
(mpn_double_digit) c[i+j] +
(mpn_double_digit) k;
c[i+j] = (t << DIGIT_BITS) >> DIGIT_BITS;
k = t >> DIGIT_BITS;
}
c[j+lnga] = k;
}
}
trace_nl(c, lnga+lngb);
return true;
}
#define MASK_FIRST (~((mpn_digit)(-1) >> 1))
#define FIRST_BITS(N, X) ((X) >> (DIGIT_BITS-(N)))
#define LAST_BITS(N, X) (((X) << (DIGIT_BITS-(N))) >> (DIGIT_BITS-(N)))
#define BASE ((mpn_double_digit)0x01 << DIGIT_BITS)
bool mpn_manager::div(mpn_digit const * numer, size_t const lnum,
mpn_digit const * denom, size_t const lden,
mpn_digit * quot,
mpn_digit * rem) {
trace(numer, lnum, denom, lden, "/");
bool res = false;
if (lnum < lden) {
for (size_t i = 0; i < (lnum-lden+1); i++)
quot[i] = 0;
for (size_t i = 0; i < lden; i++)
rem[i] = (i < lnum) ? numer[i] : 0;
return false;
}
bool all_zero = true;
for (size_t i = 0; i < lden && all_zero; i++)
if (denom[i] != zero) all_zero = false;
if (all_zero) {
// Division by 0. What would the MSBignum divide function do?
UNREACHABLE();
return res;
}
SASSERT(denom[lden-1] != 0);
if (lnum == 1 && lden == 1) {
*quot = numer[0] / denom[0];
*rem = numer[0] % denom[0];
}
else if (lnum < lden || (lnum == lden && numer[lnum-1] < denom[lden-1])) {
*quot = 0;
for (size_t i = 0; i < lden; i++)
rem[i] = (i < lnum) ? numer[i] : 0;
}
else {
size_t d = div_normalize(numer, lnum, denom, lden, u, v);
if (lden == 1)
res = div_1(u, v[0], quot);
else
res = div_n(u, v, quot, rem);
div_unnormalize(u, v, d, rem);
}
// STRACE("mpn_dbg", display_raw(tout, quot, lnum - lden + 1); tout << ", ";
// display_raw(tout, rem, lden); tout << std::endl; );
trace_nl(quot, lnum-lden+1);
trace(numer, lnum, denom, lden, "%");
trace_nl(rem, lden);
#ifdef _DEBUG
mpn_sbuffer temp(lnum+1, 0);
mul(quot, lnum-lden+1, denom, lden, temp.c_ptr());
size_t real_size;
add(temp.c_ptr(), lnum, rem, lden, temp.c_ptr(), lnum+1, &real_size);
bool ok = true;
for (size_t i = 0; i < lnum && ok; i++)
if (temp[i] != numer[i]) ok = false;
if (temp[lnum] != 0) ok = false;
CTRACE("mpn_dbg", !ok, tout << "DIV BUG: quot * denom + rem = "; display_raw(tout, temp.c_ptr(), lnum+1); tout << std::endl; );
SASSERT(ok);
#endif
return res;
}
size_t mpn_manager::div_normalize(mpn_digit const * numer, size_t const lnum,
mpn_digit const * denom, size_t const lden,
mpn_sbuffer & n_numer,
mpn_sbuffer & n_denom) const
{
size_t d = 0;
while (((denom[lden-1] << d) & MASK_FIRST) == 0) d++;
SASSERT(d < DIGIT_BITS);
n_numer.resize(lnum+1);
n_denom.resize(lden);
if (d == 0) {
n_numer[lnum] = 0;
for (size_t i = 0; i < lnum; i++)
n_numer[i] = numer[i];
for (size_t i = 0; i < lden; i++)
n_denom[i] = denom[i];
}
else {
mpn_digit q = FIRST_BITS(d, numer[lnum-1]);
n_numer[lnum] = q;
for (size_t i = lnum-1; i > 0; i--)
n_numer[i] = (numer[i] << d) | FIRST_BITS(d, numer[i-1]);
n_numer[0] = numer[0] << d;
for (size_t i = lden-1; i > 0; i--)
n_denom[i] = denom[i] << d | FIRST_BITS(d, denom[i-1]);
n_denom[0] = denom[0] << d;
}
STRACE("mpn_norm", tout << "Normalized: n_numer="; display_raw(tout, n_numer.c_ptr(), n_numer.size());
tout << " n_denom="; display_raw(tout, n_denom.c_ptr(), n_denom.size()); tout << std::endl; );
return d;
}
void mpn_manager::div_unnormalize(mpn_sbuffer & numer, mpn_sbuffer & denom,
size_t const d, mpn_digit * rem) const {
if (d == 0) {
for (size_t i = 0; i < denom.size(); i++)
rem[i] = numer[i];
}
else {
for (size_t i = 0; i < denom.size()-1; i++)
rem[i] = numer[i] >> d | (LAST_BITS(d, numer[i+1]) << (DIGIT_BITS-d));
rem[denom.size()-1] = numer[denom.size()-1] >> d;
}
}
bool mpn_manager::div_1(mpn_sbuffer & numer, mpn_digit const denom,
mpn_digit * quot) const
{
mpn_double_digit q_hat, temp, r_hat, ms;
mpn_digit borrow;
for (size_t j = numer.size()-1; j > 0; j--) {
temp = (((mpn_double_digit)numer[j]) << DIGIT_BITS) | ((mpn_double_digit)numer[j-1]);
q_hat = temp / (mpn_double_digit) denom;
r_hat = temp % (mpn_double_digit) denom;
if (q_hat >= BASE) {
UNREACHABLE(); // is this reachable with normalized v?
}
SASSERT(q_hat < BASE);
ms = temp - (q_hat * (mpn_double_digit) denom);
borrow = ms > temp;
numer[j-1] = (mpn_digit) ms;
numer[j] = ms >> DIGIT_BITS;
quot[j-1] = (mpn_digit) q_hat;
if (borrow) {
quot[j-1]--;
numer[j] = numer[j-1] + denom;
}
STRACE("mpn_div1", tout << "j=" << j << " q_hat=" << q_hat << " r_hat=" << r_hat;
tout << " ms=" << ms;
tout << " new numer="; display_raw(tout, numer.c_ptr(), numer.size());
tout << " borrow=" << borrow;
tout << std::endl; );
}
return true; // return rem != 0 or something like that?
}
bool mpn_manager::div_n(mpn_sbuffer & numer, mpn_sbuffer const & denom,
mpn_digit * quot, mpn_digit * rem) {
SASSERT(denom.size() > 1);
// This is essentially Knuth's Algorithm D.
size_t m = numer.size() - denom.size();
size_t n = denom.size();
SASSERT(numer.size() == m+n);
t_ms.resize(n+1);
mpn_double_digit q_hat, temp, r_hat;
mpn_digit borrow;
for (size_t j = m-1; j != (size_t)-1; j--) {
temp = (((mpn_double_digit)numer[j+n]) << DIGIT_BITS) | ((mpn_double_digit)numer[j+n-1]);
q_hat = temp / (mpn_double_digit) denom[n-1];
r_hat = temp % (mpn_double_digit) denom[n-1];
recheck:
if (q_hat >= BASE ||
((q_hat * denom[n-2]) > ((r_hat << DIGIT_BITS) + numer[j+n-2]))) {
q_hat--;
r_hat += denom[n-1];
if (r_hat < BASE) goto recheck;
}
SASSERT(q_hat < BASE);
// Replace numer[j+n]...numer[j] with
// numer[j+n]...numer[j] - q * (denom[n-1]...denom[0])
mpn_digit q_hat_small = (mpn_digit)q_hat;
#ifdef _DEBUG
trace_enabled = false;
#endif
mul(&q_hat_small, 1, denom.c_ptr(), n, t_ms.c_ptr());
sub(&numer[j], n+1, t_ms.c_ptr(), n+1, &numer[j], &borrow);
quot[j] = q_hat_small;
if (borrow) {
quot[j]--;
t_ab.resize(n+2);
size_t real_size;
add(denom.c_ptr(), n, &numer[j], n+1, t_ab.c_ptr(), n+2, &real_size);
for (size_t i = 0; i < n+1; i++)
numer[j+i] = t_ab[i];
}
#ifdef _DEBUG
trace_enabled = true;
#endif
STRACE("mpn_div", tout << "q_hat=" << q_hat << " r_hat=" << r_hat;
tout << " t_ms="; display_raw(tout, t_ms.c_ptr(), n);
tout << " new numer="; display_raw(tout, numer.c_ptr(), m+n+1);
tout << " borrow=" << borrow;
tout << std::endl; );
}
return true; // return rem != 0 or something like that?
}
char * mpn_manager::to_string(mpn_digit const * a, size_t const lng, char * buf, size_t const lbuf) const {
SASSERT(buf && lbuf > 0);
STRACE("mpn_to_string", tout << "[mpn] to_string "; display_raw(tout, a, lng); tout << " == "; );
if (lng == 1) {
#ifdef _WINDOWS
sprintf_s(buf, lbuf, "%u", *a);
#else
snprintf(buf, lbuf, "%u", *a);
#endif
}
else {
mpn_sbuffer temp(lng, 0), t_numer(lng+1, 0), t_denom(1, 0);
for (unsigned i = 0; i < lng; i++)
temp[i] = a[i];
size_t j = 0;
mpn_digit rem;
mpn_digit ten = 10;
while (!temp.empty() && (temp.size() > 1 || temp[0] != 0)) {
size_t d = div_normalize(&temp[0], temp.size(), &ten, 1, t_numer, t_denom);
div_1(t_numer, t_denom[0], &temp[0]);
div_unnormalize(t_numer, t_denom, d, &rem);
buf[j++] = '0' + rem;
while (temp.size() > 0 && temp.back() == 0)
temp.pop_back();
}
buf[j] = 0;
j--;
size_t mid = (j/2) + ((j % 2) ? 1 : 0);
for (size_t i = 0; i < mid; i++)
std::swap(buf[i], buf[j-i]);
}
STRACE("mpn_to_string", tout << buf << std::endl; );
return buf;
}
void mpn_manager::display_raw(std::ostream & out, mpn_digit const * a, size_t const lng) const {
out << "[";
for (size_t i = lng-1; i != (size_t)-1; i-- ) { out << a[i]; if (i != 0) out << "|"; }
out << "]";
}
void mpn_manager::trace(mpn_digit const * a, size_t const lnga,
mpn_digit const * b, size_t const lngb,
const char * op) const {
#ifdef _DEBUG
if (trace_enabled)
STRACE("mpn", tout << "[mpn] " << to_string(a, lnga, char_buf, sizeof(char_buf));
tout << " " << op << " " << to_string(b, lngb, char_buf, sizeof(char_buf));
tout << " == "; );
#endif
}
void mpn_manager::trace(mpn_digit const * a, size_t const lnga) const {
#ifdef _DEBUG
if (trace_enabled)
STRACE("mpn", tout << to_string(a, lnga, char_buf, sizeof(char_buf)); );
#endif
}
void mpn_manager::trace_nl(mpn_digit const * a, size_t const lnga) const {
#ifdef _DEBUG
if (trace_enabled)
STRACE("mpn", tout << to_string(a, lnga, char_buf, sizeof(char_buf)) << std::endl; );
#endif
}