pursuing more efficient division
This commit is contained in:
hyunghwan.chung
parent
f28bd84c50
commit
4aea0e111b
237
moo/lib/bigint.c
237
moo/lib/bigint.c
@ -53,6 +53,27 @@
|
||||
* Author: Paulo César Pereira de Andrade
|
||||
*/
|
||||
|
||||
/*
|
||||
* Copyright 1994 - 1996 LongView Technologies L.L.C. $Revision: 1.5 $
|
||||
* Copyright (c) 2006, Sun Microsystems, Inc.
|
||||
All rights reserved.
|
||||
|
||||
Redistribution and use in source and binary forms, with or without modification, are permitted provided that the
|
||||
following conditions are met:
|
||||
|
||||
* Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
|
||||
* 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.
|
||||
* Neither the name of Sun Microsystems nor the names of its contributors may be used to endorse or promote products derived
|
||||
from this software without specific prior written permission.
|
||||
|
||||
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS 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 COPYRIGHT OWNER 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
|
||||
*/
|
||||
|
||||
#include "moo-prv.h"
|
||||
|
||||
@ -1589,45 +1610,172 @@ static void divide_unsigned_array (moo_t* moo, const moo_liw_t* x, moo_oow_t xs,
|
||||
}
|
||||
}
|
||||
|
||||
#if 0
|
||||
static void divide_unsigned_array2 (moo_t* moo, const moo_liw_t* x, moo_oow_t xs, const moo_liw_t* y, moo_oow_t ys, moo_liw_t* q, moo_liw_t* r)
|
||||
#if 1
|
||||
static moo_liw_t adjust_for_over_estimate (moo_liw_t y1, moo_liw_t y2, moo_liw_t q, moo_liw_t xi, moo_liw_t xi2)
|
||||
{
|
||||
moo_oow_t i;
|
||||
moo_lidw_t dw;
|
||||
moo_liw_t c, c2, y2q;
|
||||
|
||||
d = (y[ys - 1] == MOO_TYPE_MAX(moo_liw_t)? 1: (((moo_lidw_t)1 << MOO_LIW_BITS) / (y[ys - 1] + 1));
|
||||
if (d > 1)
|
||||
/*moo_liw_t y2q = axpy(y2, q, 0, c);*/
|
||||
dw = ((moo_lidw_t)q * y2);
|
||||
c = (moo_liw_t)(dw >> MOO_LIW_BITS);
|
||||
y2q = (moo_liw_t)dw;
|
||||
|
||||
if (c > xi || (c = xi && y2q > xi2))
|
||||
{
|
||||
x[xs] = multiply_unsigned_array_in_place_and_get_last_carry(x, xs, d);
|
||||
carry = multiply_unsigned_array_in_place_and_get_last_carry(y, ys, d); /* carry must be zero */
|
||||
MOO_ASSERT (moo, carry == 0);
|
||||
q--; // too large by 1
|
||||
|
||||
/*xpy(xi, y1, c2); // add back divisor */
|
||||
c2 = (moo_liw_t)(((moo_lidw_t)xi + y1) >> MOO_LIW_BITS);
|
||||
|
||||
if (!c2)
|
||||
{
|
||||
/*y2q = axpy(y2, q, 0, c);*/
|
||||
dw = ((moo_lidw_t)q * y2);
|
||||
y2q = (moo_liw_t)dw;
|
||||
c = (moo_liw_t)(dw >> MOO_LIW_BITS);
|
||||
if (c > xi || (c = xi && y2q > xi2)) q--; // too large by 2
|
||||
}
|
||||
}
|
||||
|
||||
for (i = xs; i >= ys; )
|
||||
return q;
|
||||
}
|
||||
|
||||
static void adjust_for_underflow (moo_t* moo, moo_liw_t* qr, moo_liw_t* divisor, int qrStart, int stop)
|
||||
{
|
||||
moo_liw_t q;
|
||||
moo_liw_t y1, y2;
|
||||
moo_lidw_t dw;
|
||||
moo_liw_t carry = 0;
|
||||
moo_oow_t j, k;
|
||||
|
||||
for (j = qrStart, k = 0; k < stop; k++)
|
||||
{
|
||||
/*qr[j] = xpy(qr[j], divisor[k], c);*/
|
||||
dw = (moo_lidw_t)qr[j] + divisor[k] + carry;
|
||||
carry = (moo_liw_t)(dw >> MOO_LIW_BITS);
|
||||
qr[j] = (moo_liw_t)dw;
|
||||
j++;
|
||||
k++;
|
||||
}
|
||||
|
||||
MOO_ASSERT (moo, carry == 1); // Should have carry to balance borrow; // see Knuth p258 D6
|
||||
}
|
||||
|
||||
static moo_liw_t calculate_remainder (moo_t* moo, moo_liw_t* qr, moo_liw_t* divisor, moo_liw_t q, int qrStart, int stop)
|
||||
{
|
||||
moo_lidw_t dw;
|
||||
moo_liw_t c = 0, c2 = 0, qyk;
|
||||
moo_oow_t j = qrStart;
|
||||
moo_oow_t k = 0;
|
||||
moo_liw_t b = 0;
|
||||
|
||||
while (k < stop)
|
||||
{
|
||||
/* qr[j] = xmy(qr[j], 0, b); */
|
||||
dw = (moo_lidw_t)qr[j] - b;
|
||||
b = (dw >> MOO_LIW_BITS) & 1;
|
||||
qr[j] = (moo_liw_t)dw;
|
||||
|
||||
/* moo_liw_t qyk = axpy(q, divisor[k], 0, c); */
|
||||
dw = ((moo_lidw_t)divisor[k] * q) + c;
|
||||
c = (moo_liw_t)(dw >> MOO_LIW_BITS);
|
||||
qyk = (moo_liw_t)dw;
|
||||
|
||||
/*qr[j] = xmy(qr[j], qyk, c2); */
|
||||
dw = (moo_lidw_t)qr[j] - qyk - c2;
|
||||
c2 = (dw >> MOO_LIW_BITS) & 1;
|
||||
qr[j] = (moo_liw_t)dw;
|
||||
|
||||
//b = xpy(b, c2, c);
|
||||
dw = (moo_lidw_t)b + c2 + c;
|
||||
c = (moo_liw_t)(dw >> MOO_LIW_BITS);
|
||||
b = (moo_liw_t)dw;
|
||||
|
||||
MOO_ASSERT (moo, c == 0);
|
||||
|
||||
j++;
|
||||
k++;
|
||||
}
|
||||
return b;
|
||||
}
|
||||
|
||||
static moo_liw_t multiply_unsigned_array_in_place_and_get_carry (moo_liw_t* x, moo_oow_t xs, moo_liw_t y)
|
||||
{
|
||||
/* multiply unsigned array with a single word and put the result
|
||||
* back to the array. return the last remaining carry */
|
||||
|
||||
moo_lidw_t dw;
|
||||
moo_liw_t carry = 0;
|
||||
moo_oow_t i;
|
||||
|
||||
for (i = 0; i < xs; i++)
|
||||
{
|
||||
dw = ((moo_lidw_t)x[i] * y) + carry;
|
||||
carry = (moo_liw_t)(dw >> MOO_LIW_BITS);
|
||||
x[i] = (moo_liw_t)dw/*& MOO_TYPE_MAX(moo_liw_t)*/;
|
||||
}
|
||||
|
||||
return carry;
|
||||
}
|
||||
|
||||
static void divide_unsigned_array2 (moo_t* moo, moo_liw_t* x, moo_oow_t xs, moo_liw_t* y, moo_oow_t ys, moo_liw_t* q, moo_liw_t* r)
|
||||
{
|
||||
moo_oow_t i;
|
||||
moo_liw_t d, y1, y2;
|
||||
|
||||
/* the caller must allocate q to be greater than x by 1 in size. */
|
||||
for (i = 0; i < xs; i++) q[i] = x[i]; /* copy x to q */
|
||||
q[xs] = 0;
|
||||
|
||||
d = (y[ys - 1] == MOO_TYPE_MAX(moo_liw_t)? 1: (((moo_lidw_t)1 << MOO_LIW_BITS) / (y[ys - 1] + 1)));
|
||||
if (d > 1)
|
||||
{
|
||||
q[xs] = multiply_unsigned_array_in_place_and_get_carry(q, xs, d);
|
||||
/*carry = */multiply_unsigned_array_in_place_and_get_carry(y, ys, d); /* carry must be zero */
|
||||
/*MOO_ASSERT (moo, carry == 0);*/
|
||||
}
|
||||
|
||||
y1 = y[ys - 1];
|
||||
y2 = y[ys - 2];
|
||||
|
||||
if (x[i] == y1)
|
||||
for (i = xs; i >= ys; )
|
||||
{
|
||||
q = MOO_TYPE_MAX(moo_liw_t);
|
||||
moo_lidw_t dw;
|
||||
moo_liw_t quo, b, xhi, xlo;
|
||||
|
||||
xhi = q[i];
|
||||
xlo = q[i - 1];
|
||||
|
||||
if (xhi == y1)
|
||||
{
|
||||
quo = MOO_TYPE_MAX(moo_liw_t);
|
||||
}
|
||||
else
|
||||
{
|
||||
moo_lidw_t dw;
|
||||
|
||||
dw = ((moo_lidw_t)x[i] << MOO_LIW_BITS) + x[i - 1];
|
||||
dw = ((moo_lidw_t)xhi << MOO_LIW_BITS) + xlo;
|
||||
/* TODO: optimize it with ASM - no seperate / and % */
|
||||
q = dw / y1;
|
||||
x[i] = dw % y1;
|
||||
quo = dw / y1;
|
||||
q[i] = dw % y1;
|
||||
}
|
||||
|
||||
while (i < ys) { j++; k++; }
|
||||
x[i] = q;
|
||||
quo = adjust_for_over_estimate(y1, y2, quo, q[i], q[i - 2]);
|
||||
|
||||
b = calculate_remainder(moo, q, y, quo, i - ys, ys);
|
||||
|
||||
//xmy (xi, 0, b);
|
||||
b = (moo_liw_t)(((moo_lidw_t)xhi - b) >> MOO_LIW_BITS) & 1;
|
||||
if (b)
|
||||
{
|
||||
/* underflow */
|
||||
adjust_for_underflow(moo, q, y, i - ys, ys);
|
||||
q[i] = quo - 1;
|
||||
}
|
||||
else
|
||||
{
|
||||
q[i] = quo;
|
||||
}
|
||||
i--;
|
||||
}
|
||||
|
||||
if (d != 1)
|
||||
{
|
||||
moo_lidw_t dw;
|
||||
@ -1635,15 +1783,30 @@ static void divide_unsigned_array2 (moo_t* moo, const moo_liw_t* x, moo_oow_t xs
|
||||
for (i = ys; i > 0; )
|
||||
{
|
||||
--i;
|
||||
dw = ((moo_lidw_t)x[i] << MOO_LIW_BITS) + carry;
|
||||
dw = ((moo_lidw_t)q[i] << MOO_LIW_BITS) + carry;
|
||||
/* TODO: optimize it with ASM - no seperate / and % */
|
||||
x[i] = dw / y1;
|
||||
q[i] = dw / y1;
|
||||
carry = dw % y1;
|
||||
}
|
||||
}
|
||||
|
||||
for (i = 0; i < ys; i++) r[i] = q[i];
|
||||
for (; i <= xs; i++)
|
||||
{
|
||||
q[i - ys] = q[i];
|
||||
q[i] = 0;
|
||||
}
|
||||
/*
|
||||
i = xs;
|
||||
while (i >= ys && q[i] == 0) i--;
|
||||
for (; i >= ys; i--) q[i - ys] = q[i];
|
||||
MOO_MEMMOVE (&q[xxx], &
|
||||
q[xs] = 0;*/
|
||||
}
|
||||
#endif
|
||||
|
||||
/* ======================================================================== */
|
||||
|
||||
static moo_oop_t add_unsigned_integers (moo_t* moo, moo_oop_t x, moo_oop_t y)
|
||||
{
|
||||
moo_oow_t as, bs, zs;
|
||||
@ -1736,25 +1899,6 @@ static moo_oop_t multiply_unsigned_integers (moo_t* moo, moo_oop_t x, moo_oop_t
|
||||
return z;
|
||||
}
|
||||
|
||||
static moo_liw_t multiply_unsigned_array_in_place_and_get_last_carry (moo_liw_t* x, moo_oow_t xs, moo_liw_t y)
|
||||
{
|
||||
/* multiply unsigned array with a single word and put the result
|
||||
* back to the array. return the last remaining carry */
|
||||
|
||||
moo_lidw_t dw;
|
||||
moo_liw_t carry = 0;
|
||||
moo_oow_t i;
|
||||
|
||||
for (i = 0; i < xs; i++)
|
||||
{
|
||||
dw = ((moo_lidw_t)x[i] * y) + carry;
|
||||
carry = (moo_liw_t)(dw >> MOO_LIW_BITS);
|
||||
x[i] = (moo_liw_t)dw/*& MOO_TYPE_MAX(moo_liw_t)*/;
|
||||
}
|
||||
|
||||
return carry;
|
||||
}
|
||||
|
||||
static moo_oop_t divide_unsigned_integers (moo_t* moo, moo_oop_t x, moo_oop_t y, moo_oop_t* r)
|
||||
{
|
||||
moo_oop_t qq, rr;
|
||||
@ -1788,7 +1932,12 @@ static moo_oop_t divide_unsigned_integers (moo_t* moo, moo_oop_t x, moo_oop_t y,
|
||||
MOO_ASSERT (moo, !is_less_unsigned(x, y));
|
||||
moo_pushvolat (moo, &x);
|
||||
moo_pushvolat (moo, &y);
|
||||
/*#define USE_DIVIDE_UNSIGNED_ARRAY2*/
|
||||
#if defined(USE_DIVIDE_UNSIGNED_ARRAY2)
|
||||
qq = moo_instantiate(moo, moo->_large_positive_integer, MOO_NULL, MOO_OBJ_GET_SIZE(x) + 1);
|
||||
#else
|
||||
qq = moo_instantiate(moo, moo->_large_positive_integer, MOO_NULL, MOO_OBJ_GET_SIZE(x));
|
||||
#endif
|
||||
if (!qq)
|
||||
{
|
||||
moo_popvolats (moo, 2);
|
||||
@ -1800,7 +1949,11 @@ static moo_oop_t divide_unsigned_integers (moo_t* moo, moo_oop_t x, moo_oop_t y,
|
||||
moo_popvolats (moo, 3);
|
||||
if (!rr) return MOO_NULL;
|
||||
|
||||
#if defined(USE_DIVIDE_UNSIGNED_ARRAY2)
|
||||
divide_unsigned_array2 (moo,
|
||||
#else
|
||||
divide_unsigned_array (moo,
|
||||
#endif
|
||||
MOO_OBJ_GET_LIWORD_SLOT(x), MOO_OBJ_GET_SIZE(x),
|
||||
MOO_OBJ_GET_LIWORD_SLOT(y), MOO_OBJ_GET_SIZE(y),
|
||||
MOO_OBJ_GET_LIWORD_SLOT(qq), MOO_OBJ_GET_LIWORD_SLOT(rr));
|
||||
@ -1809,6 +1962,8 @@ static moo_oop_t divide_unsigned_integers (moo_t* moo, moo_oop_t x, moo_oop_t y,
|
||||
return qq;
|
||||
}
|
||||
|
||||
/* ======================================================================== */
|
||||
|
||||
moo_oop_t moo_addints (moo_t* moo, moo_oop_t x, moo_oop_t y)
|
||||
{
|
||||
moo_oop_t z;
|
||||
|
||||
Loading…
x
Reference in New Issue
Block a user