more division hack
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hyunghwan.chung
parent
48c1ea7c92
commit
cbf8ea2a8d
174
moo/lib/bigint.c
174
moo/lib/bigint.c
@ -1117,6 +1117,23 @@ static MOO_INLINE void multiply_unsigned_array (const moo_liw_t* x, moo_oow_t xs
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y = (moo_liw_t*)i;
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}
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if (ys == 1)
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{
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moo_lidw_t dw;
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moo_liw_t carry = 0;
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moo_oow_t i;
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for (i = 0; i < xs; i++)
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{
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dw = ((moo_lidw_t)x[i] * y[0]) + carry;
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carry = (moo_liw_t)(dw >> MOO_LIW_BITS);
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z[i] = (moo_liw_t)dw;
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}
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z[i] = carry;
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return;
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}
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pa = xs;
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if (pa <= ((moo_oow_t)1 << (MOO_LIDW_BITS - (MOO_LIW_BITS * 2))))
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{
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@ -1271,6 +1288,23 @@ static MOO_INLINE moo_oow_t multiply_unsigned_array_karatsuba (moo_t* moo, const
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y = (moo_liw_t*)i;
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}
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if (ys == 1)
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{
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moo_lidw_t dw;
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moo_liw_t carry = 0;
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moo_oow_t i;
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for (i = 0; i < xs; i++)
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{
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dw = ((moo_lidw_t)x[i] * y[0]) + carry;
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carry = (moo_liw_t)(dw >> MOO_LIW_BITS);
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z[i] = (moo_liw_t)dw;
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}
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z[i] = carry;
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return;
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}
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/* calculate value of nshifts, that is 2^(MOO_LIW_BITS*nshifts) */
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nshifts = (xs + 1) / 2;
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@ -1295,10 +1329,10 @@ static MOO_INLINE moo_oow_t multiply_unsigned_array_karatsuba (moo_t* moo, const
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if (!tmp[0]) goto oops;
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/* tmp[0] = a0 + a1 */
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tmplen[0] = add_unsigned_array (x, ndigits_xl, x + nshifts, ndigits_xh, tmp[0]);
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tmplen[0] = add_unsigned_array(x, ndigits_xl, x + nshifts, ndigits_xh, tmp[0]);
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/* tmp[1] = b0 + b1 */
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tmplen[1] = add_unsigned_array (y, ndigits_yl, y + nshifts, ndigits_yh, tmp[1]);
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tmplen[1] = add_unsigned_array(y, ndigits_yl, y + nshifts, ndigits_yh, tmp[1]);
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/*MOO_DEBUG6 (moo, "karatsuba t %p u %p ndigits_xl %d ndigits_xh %d ndigits_yl %d ndigits_yh %d\n", tmp[0], tmp[1], (int)ndigits_xl, (int)ndigits_xh, (int)ndigits_yl, (int)ndigits_yh);*/
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/*MOO_DEBUG5 (moo, "zcapa %d, tmplen[0] %d tmplen[1] %d nshifts %d total %d\n", (int)zcapa, (int)tmplen[0], (int)tmplen[1], (int)nshifts, (int)(tmplen[0] + tmplen[1] + nshifts));*/
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@ -1391,6 +1425,23 @@ oops:
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y = (moo_liw_t*)i;
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}
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if (ys == 1)
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{
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moo_lidw_t dw;
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moo_liw_t carry = 0;
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moo_oow_t i;
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for (i = 0; i < xs; i++)
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{
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dw = ((moo_lidw_t)x[i] * y[0]) + carry;
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carry = (moo_liw_t)(dw >> MOO_LIW_BITS);
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z[i] = (moo_liw_t)dw;
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}
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z[i] = carry;
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return;
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}
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/* calculate value of nshifts, that is 2^(MOO_LIW_BITS*nshifts) */
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nshifts = (xs + 1) / 2;
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@ -1631,6 +1682,7 @@ static moo_liw_t adjust_for_over_estimate (moo_liw_t y1, moo_liw_t y2, moo_liw_t
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y2q = (moo_liw_t)dw;
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if (c > xi || (c == xi && y2q > xi2))
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//if (c > xi || (c == xi && xi2 > y2q))
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{
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--quo; /* too large by 1 */
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@ -1649,21 +1701,6 @@ static moo_liw_t adjust_for_over_estimate (moo_liw_t y1, moo_liw_t y2, moo_liw_t
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return quo;
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}
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static moo_liw_t adjust_for_over_estimate2 (moo_liw_t y1, moo_liw_t y2, moo_liw_t quo, moo_liw_t xhi, moo_liw_t xlo, moo_liw_t x2)
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{
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moo_lidw_t dw1, dw2;
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dw1 = ((moo_lidw_t)quo * y2);
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dw2 = (((moo_lidw_t)quo * xhi + xlo - ((moo_lidw_t)quo * y1)) << MOO_LIW_BITS) + x2;
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if (dw1 > dw2)
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{
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quo--;
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dw1 = ((moo_lidw_t)quo * y2);
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dw2 = (((moo_lidw_t)quo * xhi + xlo - ((moo_lidw_t)quo * y1)) << MOO_LIW_BITS) + x2;
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if (dw1 > dw2) quo--;
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}
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return quo;
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}
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static moo_liw_t adjust_for_underflow (moo_liw_t* qr, moo_liw_t* divisor, moo_oow_t qr_start, moo_oow_t stop)
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{
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@ -1795,8 +1832,13 @@ static void divide_unsigned_array2 (moo_t* moo, const moo_liw_t* x, moo_oow_t xs
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for (i = xs; i >= ys; --i)
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{
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moo_lidw_t dw;
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moo_liw_t quo, b, xhi, xlo;
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/* ---------------------------------------------------------- */
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/* estimate the quotient.
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* 2-current-dividend-words / 2-most-significant-divisor-words */
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xhi = q[i];
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xlo = q[i - 1];
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@ -1806,16 +1848,57 @@ static void divide_unsigned_array2 (moo_t* moo, const moo_liw_t* x, moo_oow_t xs
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}
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else
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{
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moo_lidw_t dw;
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dw = ((moo_lidw_t)xhi << MOO_LIW_BITS) + xlo;
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/* TODO: optimize it with ASM - no seperate / and % */
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quo = (moo_liw_t)(dw / y1);
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q[i] = (moo_liw_t)(dw % y1);
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}
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quo = adjust_for_over_estimate(y1, y2, quo, q[i], q[i - 2]);
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/*quo = adjust_for_over_estimate2(y1, y2, quo, xhi, xlo, q[i - 2]);*/
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/* ---------------------------------------------------------- */
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/*quo = adjust_for_over_estimate(y1, y2, quo, q[i], q[i - 2]);*/
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{
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moo_liw_t c, c2, y2q;
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dw = ((moo_lidw_t)quo * y2);
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c = (moo_liw_t)(dw >> MOO_LIW_BITS);
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y2q = (moo_liw_t)dw;
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/*
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x1 => c
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x2 => y2q
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ujn2 => q[i - 2]
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rhat => q[i]
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for greaterThan(x1, x2, rhat, ujn2)
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func greaterThan(x1, x2, y1, y2 Word) bool {
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return x1 > y1 || x1 == y1 && x2 > y2
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}*/
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//printf ("XXXXXXXXXXXXXXXXXXXXXx %d %d\n", (int)xs, (int)i);
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if (c > q[i] || (c == q[i] && y2q > q[i - 2]))
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{
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//printf ("ADJUST...............%llu %llu %llu %llu\n", (unsigned long long)c, (unsigned long long)q[i], (unsigned long long)y2q, (unsigned long long)q[i - 2]);
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--quo; /* too large by 1 */
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/*xpy(xi, y1, c2); add back divisor */
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c2 = (moo_liw_t)(((moo_lidw_t)q[i] + y1) >> MOO_LIW_BITS);
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if (c2 == 0)
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{
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/*y2q = axpy(y2, q, 0, c);*/
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dw = ((moo_lidw_t)quo * y2);
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c = (moo_liw_t)(dw >> MOO_LIW_BITS);
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y2q = (moo_liw_t)dw;
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if (c > q[i] || (c == q[i] && y2q > q[i - 2]))
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{
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//printf ("ADJUST2...............%llu %llu %llu %llu\n", (unsigned long long)c, (unsigned long long)q[i], (unsigned long long)y2q, (unsigned long long)q[i - 2]);
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--quo; /* too large by 2 */
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}
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}
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}
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}
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/* ---------------------------------------------------------- */
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b = calculate_remainder(moo, q, r, quo, i - ys, ys);
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b = (moo_liw_t)((((moo_lidw_t)xhi - b) >> MOO_LIW_BITS) & 1);
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if (b)
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@ -1874,7 +1957,7 @@ static moo_oow_t nlz (moo_liw_t x)
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static void divide_unsigned_array3 (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)
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{
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moo_oow_t i, j, s;
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moo_lidw_t dw, qhat, rhat, b;
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moo_lidw_t dw, qhat, rhat;
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moo_lidi_t t, k;
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moo_liw_t* qq;
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@ -1912,7 +1995,6 @@ static void divide_unsigned_array3 (moo_t* moo, const moo_liw_t* x, moo_oow_t xs
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moo->inttostr.t.ptr = t;
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}
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b = (moo_lidw_t)MOO_TYPE_MAX(moo_liw_t) + 1;
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qq = moo->inttostr.t.ptr;
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/*
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@ -1950,19 +2032,23 @@ printf ("};\n"); */
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{
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--j;
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dw = (moo_lidw_t)qq[j + ys] * b + qq[j + ys - 1];
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/* estimate */
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dw = ((moo_lidw_t)qq[j + ys] << MOO_LIW_BITS) + qq[j + ys - 1];
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qhat = dw / r[ys - 1];
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rhat = dw - (qhat * r[ys - 1]);
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//printf ("qhat == %llx rhat == %llx dw = %llx r[ys-1] = %llx /// %llx %llx\n", (unsigned long long)qhat, (unsigned long long)rhat, (unsigned long long)dw, (unsigned long long)r[ys-1], (unsigned long long)qq[j + ys], (unsigned long long)qq[j + ys - 1]);
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again:
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if (qhat >= b || (qhat * r[ys - 2]) > (rhat * b + qq[j + ys - 2]))
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adjust_quotient:
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if (qhat > MOO_TYPE_MAX(moo_liw_t) || (qhat * r[ys - 2]) > ((rhat << MOO_LIW_BITS) + qq[j + ys - 2]))
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{
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qhat = qhat - 1;
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rhat = rhat + r[ys - 1];
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if (rhat < b) goto again;
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if (rhat <= MOO_TYPE_MAX(moo_liw_t)) goto adjust_quotient;
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}
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//printf ("qhat == %llx rhat == %llx\n", (unsigned long long)qhat, (unsigned long long)rhat);
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#if 1
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/* multiply and subtract */
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for (k = 0, i = 0; i < ys; i++)
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{
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dw = qhat * r[i];
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@ -1973,6 +2059,7 @@ printf ("};\n"); */
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t = qq[j + ys] - k;
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qq[j + ys] = t;
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/* test remainder */
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q[j] = qhat;
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if (t < 0)
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{
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@ -1980,11 +2067,40 @@ printf ("};\n"); */
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for (k = 0, i = 0; i < ys; i++)
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{
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t = (moo_lidw_t)qq[j + i] + r[i] + k;
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qq[j + i] = t;
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qq[j + i] = (moo_liw_t)t;
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k = t >> MOO_LIW_BITS;
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}
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qq[j + ys] += k;
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}
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#else
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for (k = 0, i = 0; i <= n; i++)
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{
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p = qhat * (i == n ? 0 : v[i]);
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k2 = (p >> 16);
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d = u[j + i] - (uint16_t)p;
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k2 += (d > u[j + i]);
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u[j + i] = d - k;
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k2 += (u[j + i] > d);
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k = k2;
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}
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/* Test remainder. */
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q[j] = qhat;
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if (k != 0) {
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/* Add back. */
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q[j]--;
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k = 0;
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for (i = 0; i < n; i++) {
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t = u[j + i] + v[i] + k;
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u[j + i] = (uint16_t)t;
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k = t >> 16;
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}
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#endif
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}
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for (i = 0; i < ys - 1; i++)
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@ -2078,7 +2194,7 @@ static moo_oop_t multiply_unsigned_integers (moo_t* moo, moo_oop_t x, moo_oop_t
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if (!z) return MOO_NULL;
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#if defined(MOO_ENABLE_KARATSUBA)
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if (CANNOT_KARATSUBA(moo,xs, ys))
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if (CANNOT_KARATSUBA(moo, xs, ys))
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{
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#endif
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multiply_unsigned_array (
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@ -2132,7 +2248,7 @@ static moo_oop_t divide_unsigned_integers (moo_t* moo, moo_oop_t x, moo_oop_t y,
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MOO_ASSERT (moo, !is_less_unsigned(x, y));
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moo_pushvolat (moo, &x);
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moo_pushvolat (moo, &y);
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/*#define USE_DIVIDE_UNSIGNED_ARRAY2*/
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#define USE_DIVIDE_UNSIGNED_ARRAY2
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#if defined(USE_DIVIDE_UNSIGNED_ARRAY2)
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qq = moo_instantiate(moo, moo->_large_positive_integer, MOO_NULL, MOO_OBJ_GET_SIZE(x) + 1);
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#else
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