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debugging bigint division

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This commit is contained in:
hyunghwan.chung 2019-04-04 09:30:24 +00:00
parent 3d4e0396ca
commit e7ccbc36b4
3 changed files with 187 additions and 44 deletions
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32
moo/kernel/test-001.moo
View File

@ -119,20 +119,37 @@ extend MyObject
^(a value: 5) * (b value: 6). ## (12 * 5 + 22) * (99 * 6 + 4) => 49036
}
method(#class) testBigintDiv
method(#class) testBigintDiv: divd_base divisor: divr_base
{
| q r divd divr i |
| i q r divd divr |
i := 1.
while (i < 1000)
while (i < 2000)
{
divd := 100919283908998345873248972389472389791283789123712899089034258903482398198123912831 * i.
divr := 129323482374892374238974238974238947328972389128387312892713891728391278 * i.
divd := divd_base * i.
divr := divr_base * i.
q := divd div: divr.
r := divd rem: divr.
if (divd ~= (q * divr + r)) { i dump. divd dump. divr dump. q dump. r dump. (q * divr + r) dump. ^false. }.
divd := divd_base * i.
divr := divr_base.
q := divd div: divr.
r := divd rem: divr.
ifnot (divd = (q * divr + r)) { i dump. divd dump. divr dump. q dump. r dump. ^false. }.
if (divd ~= (q * divr + r)) { i dump. divd dump. divr dump. q dump. r dump. (q * divr + r) dump. ^false. }.
divd := divd_base.
divr := divr_base * i.
q := divd div: divr.
r := divd rem: divr.
if (divd ~= (q * divr + r)) { i dump. divd dump. divr dump. q dump. r dump. (q * divr + r) dump. ^false. }.
divd := divd_base * i * i.
divr := divr_base * i.
q := divd div: divr.
r := divd rem: divr.
if (divd ~= (q * divr + r)) { i dump. divd dump. divr dump. q dump. r dump. (q * divr + r) dump. ^false. }.
i := i + 1.
}.
@ -358,7 +375,8 @@ extend MyObject
## 150-154
[ (8113063330913503995887611892379812731289731289312898971231 div: 8113063330913503995887611892379812731289731289312898971230) = 1 ],
[ (8113063330913503995887611892379812731289731289312898971231 rem: 8113063330913503995887611892379812731289731289312898971230) = 1 ],
[ self testBigintDiv ],
[ self testBigintDiv: 100919283908998345873248972389472389791283789123712899089034258903482398198123912831 divisor: 129323482374892374238974238974238947328972389128387312892713891728391278 ],
[ self testBigintDiv: 234897230919283908998345873248972389472389791283789123712899089034258903482398198123912831 divisor: 129323482374892374238974238974238947328972389128387312892713891728391278 ],
## =========================

197
moo/lib/bigint.c
View File

@ -1620,43 +1620,58 @@ static void divide_unsigned_array (moo_t* moo, const moo_liw_t* x, moo_oow_t xs,
}
#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)
static moo_liw_t adjust_for_over_estimate (moo_liw_t y1, moo_liw_t y2, moo_liw_t quo, moo_liw_t xi, moo_liw_t xi2)
{
moo_lidw_t dw;
moo_liw_t c, c2, y2q;
/*moo_liw_t y2q = axpy(y2, q, 0, c);*/
dw = ((moo_lidw_t)q * y2);
dw = ((moo_lidw_t)quo * y2);
c = (moo_liw_t)(dw >> MOO_LIW_BITS);
y2q = (moo_liw_t)dw;
if (c > xi || (c == xi && y2q > xi2))
{
q--; // too large by 1
--quo; /* too large by 1 */
/*xpy(xi, y1, c2); // add back divisor */
/*xpy(xi, y1, c2); add back divisor */
c2 = (moo_liw_t)(((moo_lidw_t)xi + y1) >> MOO_LIW_BITS);
if (!c2)
if (c2 == 0)
{
/*y2q = axpy(y2, q, 0, c);*/
dw = ((moo_lidw_t)q * y2);
y2q = (moo_liw_t)dw;
dw = ((moo_lidw_t)quo * y2);
c = (moo_liw_t)(dw >> MOO_LIW_BITS);
if (c > xi || (c == xi && y2q > xi2)) q--; // too large by 2
y2q = (moo_liw_t)dw;
if (c > xi || (c == xi && y2q > xi2)) --quo; /* too large by 2 */
}
}
return q;
return quo;
}
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)
{
moo_lidw_t dw1, dw2;
dw1 = ((moo_lidw_t)quo * y2);
dw2 = (((moo_lidw_t)quo * xhi + xlo - ((moo_lidw_t)quo * y1)) << MOO_LIW_BITS) + x2;
if (dw1 > dw2)
{
quo--;
dw1 = ((moo_lidw_t)quo * y2);
dw2 = (((moo_lidw_t)quo * xhi + xlo - ((moo_lidw_t)quo * y1)) << MOO_LIW_BITS) + x2;
if (dw1 > dw2) quo--;
}
return quo;
}
static moo_liw_t adjust_for_underflow (moo_liw_t* qr, moo_liw_t* divisor, moo_oow_t qr_start, moo_oow_t stop)
{
moo_lidw_t dw;
moo_liw_t carry = 0;
moo_liw_t carry;
moo_oow_t j, k;
for (j = qr_start, k = 0; k < stop; k++, j++)
for (carry = 0, j = qr_start, k = 0; k < stop; j++, k++)
{
/*qr[j] = xpy(qr[j], divisor[k], c);*/
dw = (moo_lidw_t)qr[j] + divisor[k] + carry;
@ -1667,40 +1682,35 @@ static moo_liw_t adjust_for_underflow (moo_liw_t* qr, moo_liw_t* divisor, moo_oo
return carry;
}
static moo_liw_t calculate_remainder (moo_t* moo, moo_liw_t* qr, moo_liw_t* divisor, moo_liw_t q, int qr_start, int stop)
static moo_liw_t calculate_remainder (moo_t* moo, moo_liw_t* qr, moo_liw_t* y, moo_liw_t quo, int qr_start, int stop)
{
moo_lidw_t dw;
moo_liw_t c = 0, c2 = 0, qyk;
moo_oow_t j = qr_start;
moo_oow_t k = 0;
moo_liw_t b = 0;
moo_liw_t b, c, c2, qyk;
moo_oow_t j, k;
while (k < stop)
for (b = 0, c = 0, c2 = 0, j = qr_start, k = 0; k < stop; j++, k++)
{
/* qr[j] = xmy(qr[j], 0, b); */
dw = (moo_lidw_t)qr[j] - b;
b = (dw >> MOO_LIW_BITS) & 1;
b = (moo_liw_t)((dw >> MOO_LIW_BITS) & 1); /* b = -(dw mod BASE) */
qr[j] = (moo_liw_t)dw;
/* moo_liw_t qyk = axpy(q, divisor[k], 0, c); */
dw = ((moo_lidw_t)divisor[k] * q) + c;
dw = ((moo_lidw_t)y[k] * quo) + 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;
/*c2 = 0; qr[j] = xmy(qr[j], qyk, c2); */
dw = (moo_lidw_t)qr[j] - qyk;
c2 = (moo_liw_t)((dw >> MOO_LIW_BITS) & 1);
qr[j] = (moo_liw_t)dw;
//b = xpy(b, c2, c);
/*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;
}
@ -1718,7 +1728,7 @@ static moo_liw_t multiply_unsigned_array_in_place_and_get_carry (moo_liw_t* x, m
{
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)*/;
x[i] = (moo_liw_t)dw;
}
return carry;
@ -1734,9 +1744,6 @@ static void divide_unsigned_array2 (moo_t* moo, const moo_liw_t* x, moo_oow_t xs
* - q and r are set to all zeros. */
MOO_ASSERT (moo, xs >= ys);
for (i = 0; i < xs; i++) q[i] = x[i]; /* copy x to q */
q[xs] = 0;
if (ys == 1)
{
/* the divisor has a single word only. perform simple division */
@ -1745,7 +1752,7 @@ static void divide_unsigned_array2 (moo_t* moo, const moo_liw_t* x, moo_oow_t xs
for (i = xs; i > 0; )
{
--i;
dw = ((moo_lidw_t)carry << MOO_LIW_BITS) + q[i];
dw = ((moo_lidw_t)carry << MOO_LIW_BITS) + x[i];
q[i] = (moo_liw_t)(dw / y[0]);
carry = (moo_liw_t)(dw % y[0]);
}
@ -1753,6 +1760,8 @@ static void divide_unsigned_array2 (moo_t* moo, const moo_liw_t* x, moo_oow_t xs
return;
}
for (i = 0; i < xs; i++) q[i] = x[i]; /* copy x to q */
q[xs] = 0; /* store zero in the last extra word */
for (i = 0; i < ys; i++) r[i] = y[i]; /* copy y to r */
y1 = r[ys - 1]; /* highest divisor word */
@ -1805,15 +1814,15 @@ static void divide_unsigned_array2 (moo_t* moo, const moo_liw_t* x, moo_oow_t xs
}
quo = adjust_for_over_estimate(y1, y2, quo, q[i], q[i - 2]);
/*quo = adjust_for_over_estimate2(y1, y2, quo, xhi, xlo, q[i - 2]);*/
b = calculate_remainder(moo, q, r, quo, i - ys, ys);
b = (moo_liw_t)(((moo_lidw_t)xhi - b) >> MOO_LIW_BITS) & 1;
b = (moo_liw_t)((((moo_lidw_t)xhi - b) >> MOO_LIW_BITS) & 1);
if (b)
{
/* underflow */
b = adjust_for_underflow(q, r, i - ys, ys);
MOO_ASSERT (moo, b == 1); /* Should have carry to balance borrow; // see Knuth p258 D6 */
MOO_ASSERT (moo, b == 1);
q[i] = quo - 1;
}
else
@ -1842,6 +1851,122 @@ static void divide_unsigned_array2 (moo_t* moo, const moo_liw_t* x, moo_oow_t xs
*/
for (i = 0; i < ys; i++) { r[i] = q[i]; q[i] = 0; }
for (; i <= xs; i++) { q[i - ys] = q[i]; q[i] = 0; }
}
static moo_oow_t nlz (moo_liw_t x)
{
moo_oow_t n;
if (x == 0) return(32);
n = 0;
if (x <= 0x0000FFFF) {n = n +16; x = x <<16;}
if (x <= 0x00FFFFFF) {n = n + 8; x = x << 8;}
if (x <= 0x0FFFFFFF) {n = n + 4; x = x << 4;}
if (x <= 0x3FFFFFFF) {n = n + 2; x = x << 2;}
if (x <= 0x7FFFFFFF) {n = n + 1;}
return n;
}
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)
{
moo_oow_t i, j, s;
moo_lidw_t dw, qhat, rhat;
moo_lidi_t t, k;
/* the caller must ensure:
* - q can hold 'xs + 1' words and r can hold 'ys' words.
* - q and r are set to all zeros. */
MOO_ASSERT (moo, xs >= ys);
if (ys == 1)
{
/* the divisor has a single word only. perform simple division */
moo_lidw_t dw;
moo_liw_t carry = 0;
for (i = xs; i > 0; )
{
--i;
dw = ((moo_lidw_t)carry << MOO_LIW_BITS) + x[i];
q[i] = (moo_liw_t)(dw / y[0]);
carry = (moo_liw_t)(dw % y[0]);
}
r[0] = carry;
return;
}
s = nlz(y[ys - 1]);
for (i = ys; i > 1; )
{
--i;
r[i] = (y[i] << s) | ((moo_lidw_t)y[i - 1] >> (MOO_LIW_BITS - s));
}
r[0] = y[0] << s;
q[xs] = (moo_lidw_t)x[xs - 1] >> (MOO_LIW_BITS - s);
for (i = xs; i > 1; )
{
--i;
q[i] = (x[i] << s) | ((moo_lidw_t)x[i - 1] >> (MOO_LIW_BITS - s));
}
q[0] = x[0] << s;
for (j = xs - ys + 1; j > 0; )
{
--j;
//dw = ((moo_lidw_t)q[j + ys] << MOO_LIW_BITS) + q[j + ys - 1];
dw = ((moo_lidw_t)q[j + ys] * MOO_TYPE_MAX(moo_liw_t)) + q[j + ys - 1];
qhat = dw / r[ys - 1];
rhat = dw - (qhat * r[ys - 1]);
again:
//if (qhat >= MOO_TYPE_MAX(moo_liw_t) || (qhat * r[ys - 2]) > ((rhat << MOO_LIW_BITS) + q[j + ys - 2]))
if (qhat >= MOO_TYPE_MAX(moo_liw_t) || (qhat * r[ys - 2]) > (rhat * MOO_TYPE_MAX(moo_liw_t) + q[j + ys - 2]))
{
qhat = qhat - 1;
rhat = rhat + r[ys - 1];
if (rhat < MOO_TYPE_MAX(moo_liw_t)) goto again;
}
for (k = 0, i = 0; i < ys; i++)
{
dw = qhat * r[i];
t = q[j + i] - k - (dw & MOO_TYPE_MAX(moo_liw_t));
q[j + i] = t;
k = (dw >> MOO_LIW_BITS) - (t >> MOO_LIW_BITS);
}
t = q[j + ys] - k;
q[j + ys] = t;
q[j] = qhat;
if (t < 0)
{
q[j] = q[j] - 1;
for (k = 0, i = 0; i < ys; i++)
{
t = (moo_lidw_t)q[j + i] + r[i] + k;
q[j + i] = t;
k = t >> MOO_LIW_BITS;
}
q[j + ys] += k;
}
}
for (i = 0; i < ys - 1; i++)
{
r[i] = (r[i] >> s) | ((moo_lidw_t)q[i + 1] << (MOO_LIW_BITS - s));
}
r[i] = r[i] >> s;
//for (j = (xs == ys)? 1: (xs - ys + 1); j < xs; j++) q[i] = 0;
for (i = xs ; i > 0; ) printf ("%08x ", q[--i]);
printf ("\n");
}
#endif
@ -1994,7 +2119,7 @@ static moo_oop_t divide_unsigned_integers (moo_t* moo, moo_oop_t x, moo_oop_t y,
if (!rr) return MOO_NULL;
#if defined(USE_DIVIDE_UNSIGNED_ARRAY2)
divide_unsigned_array2 (moo,
divide_unsigned_array3 (moo,
#else
divide_unsigned_array (moo,
#endif

2
moo/lib/moo.h
View File

@ -163,7 +163,7 @@ typedef struct moo_obj_word_t* moo_oop_word_t;
* BIGINT TYPES AND MACROS
* ========================================================================= */
#if (MOO_SIZEOF_UINTMAX_T > MOO_SIZEOF_OOW_T)
# define MOO_USE_FULL_WORD
/*# define MOO_USE_FULL_WORD*/
#endif
#if defined(MOO_USE_FULL_WORD)