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fixing bigint division bugs

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This commit is contained in:
hyunghwan.chung 2019-04-03 19:19:09 +00:00
parent e6f58f4b3d
commit 98e5deca4f
2 changed files with 93 additions and 35 deletions
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36
moo/kernel/test-001.moo
View File

@ -119,6 +119,26 @@ extend MyObject
^(a value: 5) * (b value: 6). ## (12 * 5 + 22) * (99 * 6 + 4) => 49036
}
method(#class) testBigintDiv
{
| q r divd divr i |
i := 1.
while (i < 1000)
{
divd := 100919283908998345873248972389472389791283789123712899089034258903482398198123912831 * i.
divr := 129323482374892374238974238974238947328972389128387312892713891728391278 * i.
q := divd div: divr.
r := divd rem: divr.
ifnot (divd = (q * divr + r)) { divd dump. divr dump. q dump. r dump. ^false. }.
i := i + 1.
}.
^true
}
method(#class) main
{
| tc limit |
@ -324,6 +344,22 @@ extend MyObject
## 140-144
[ (-8113063330913503995887611892379812731289731289312898971231 rem: 34359738368) = -31040337503 ],
[ (-8113063330913503995887611892379812731289731289312898971231 mod: 34359738368) = 3319400865 ],
[ (-8113063330913503995887611892379812731289731289312898971231 div: 18446744073709551615) = -439810044444445199874532569660475732947 ],
[ (-8113063330913503995887611892379812731289731289312898971231 mdiv: 18446744073709551615) = -439810044444445199874532569660475732948 ],
[ (-8113063330913503995887611892379812731289731289312898971231 rem: 18446744073709551615) = -16637658201046411826 ],
## 145-149
[ (-8113063330913503995887611892379812731289731289312898971231 mod: 18446744073709551615) = 1809085872663139789 ],
[ (8113063330913503995887611892379812731289731289312898971231 div: 8113063330913503995887611892379812731289731289312898971231) = 1 ],
[ (8113063330913503995887611892379812731289731289312898971231 rem: 8113063330913503995887611892379812731289731289312898971231) = 0 ],
[ (8113063330913503995887611892379812731289731289312898971231 div: 8113063330913503995887611892379812731289731289312898971232) = 0 ],
[ (8113063330913503995887611892379812731289731289312898971231 rem: 8113063330913503995887611892379812731289731289312898971232) = 8113063330913503995887611892379812731289731289312898971231 ],
## 150-154
[ (8113063330913503995887611892379812731289731289312898971231 div: 8113063330913503995887611892379812731289731289312898971230) = 1 ],
[ (8113063330913503995887611892379812731289731289312898971231 rem: 8113063330913503995887611892379812731289731289312898971230) = 1 ],
[ self testBigintDiv ],
## =========================
[

86
moo/lib/bigint.c
View File

@ -1584,12 +1584,18 @@ static void divide_unsigned_array (moo_t* moo, const moo_liw_t* x, moo_oow_t xs,
* end
*/
moo_oow_t rs, i , j;
moo_oow_t rs, rrs, i , j;
MOO_ASSERT (moo, xs >= ys);
MOO_MEMSET (q, 0, MOO_SIZEOF(*q) * xs);
MOO_MEMSET (r, 0, MOO_SIZEOF(*q) * xs);
/* the caller must ensure:
* - q and r are all zeros. can skip memset() with zero.
* - q is as large as xs in size.
* - r is as large as ys + 1 in size */
/*MOO_MEMSET (q, 0, MOO_SIZEOF(*q) * xs);
MOO_MEMSET (r, 0, MOO_SIZEOF(*q) * ys);*/
rrs = ys + 1;
for (i = xs; i > 0; )
{
--i;
@ -1597,10 +1603,13 @@ static void divide_unsigned_array (moo_t* moo, const moo_liw_t* x, moo_oow_t xs,
{
--j;
lshift_unsigned_array (r, xs, 1);
/* the value of the remainder 'r' may get bigger than the
* divisor 'y' temporarily until subtraction is performed
* below. so ys + 1(kept in rrs) is needed for shifting here. */
lshift_unsigned_array (r, rrs, 1);
MOO_SETBITS (moo_liw_t, r[0], 0, 1, MOO_GETBITS(moo_liw_t, x[i], j, 1));
rs = count_effective(r, xs);
rs = count_effective(r, rrs);
if (!is_less_unsigned_array(r, rs, y, ys))
{
subtract_unsigned_array (moo, r, rs, y, ys, r);
@ -1641,13 +1650,13 @@ static moo_liw_t adjust_for_over_estimate (moo_liw_t y1, moo_liw_t y2, moo_liw_t
return q;
}
static moo_liw_t adjust_for_underflow (moo_liw_t* qr, moo_liw_t* divisor, moo_oow_t qrStart, moo_oow_t stop)
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_oow_t j, k;
for (j = qrStart, k = 0; k < stop; k++, j++)
for (j = qr_start, k = 0; k < stop; k++, j++)
{
/*qr[j] = xpy(qr[j], divisor[k], c);*/
dw = (moo_lidw_t)qr[j] + divisor[k] + carry;
@ -1658,11 +1667,11 @@ 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 qrStart, int stop)
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)
{
moo_lidw_t dw;
moo_liw_t c = 0, c2 = 0, qyk;
moo_oow_t j = qrStart;
moo_oow_t j = qr_start;
moo_oow_t k = 0;
moo_liw_t b = 0;
@ -1720,23 +1729,36 @@ static void divide_unsigned_array2 (moo_t* moo,const moo_liw_t* x, moo_oow_t xs,
moo_oow_t i;
moo_liw_t d, y1, y2;
/* the caller must ensure that q can hold 'xs + 1' words and r can hold 'xs' words. */
/* 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);
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 */
moo_lidw_t dw;
moo_liw_t carry = 0;
for (i = xs; i > 0; )
{
--i;
dw = ((moo_lidw_t)carry << MOO_LIW_BITS) + q[i];
q[i] = (moo_liw_t)(dw / y[0]);
carry = (moo_liw_t)(dw % y[0]);
}
r[0] = carry;
return;
}
for (i = 0; i < ys; i++) r[i] = y[i]; /* copy y to r */
y1 = r[ys - 1]; /* highest divisor word */
d = (y1 == MOO_TYPE_MAX(moo_liw_t)? ((moo_liw_t)1): ((moo_liw_t)(((moo_lidw_t)1 << MOO_LIW_BITS) / (y1 + 1))));
if (d > 1)
{
#if 0
q[xs] = multiply_unsigned_array_in_place_and_get_carry(q, xs, d);
y2 = multiply_unsigned_array_in_place_and_get_carry(r, ys, d);
MOO_ASSERT (moo, y2 == 0); /* carry must be zero */
#else
moo_lidw_t dw;
moo_liw_t carry;
@ -1757,7 +1779,6 @@ static void divide_unsigned_array2 (moo_t* moo,const moo_liw_t* x, moo_oow_t xs,
r[i] = (moo_liw_t)dw;
}
MOO_ASSERT (moo, carry == 0);
#endif
}
y1 = r[ys - 1];
@ -1810,20 +1831,17 @@ static void divide_unsigned_array2 (moo_t* moo,const moo_liw_t* x, moo_oow_t xs,
--i;
dw = ((moo_lidw_t)carry << MOO_LIW_BITS) + q[i];
/* TODO: optimize it with ASM - no seperate / and % */
carry = (moo_liw_t)(dw % d);
q[i] = (moo_liw_t)(dw / d);
carry = (moo_liw_t)(dw % d);
}
}
for (i = 0; i < ys; i++) r[i] = q[i];
for (; i < xs; i++)
{
r[i] = 0;
q[i - ys] = q[i];
q[i] = 0;
}
q[i - ys] = q[i];
for (i = i - ys + 1; i <= xs; i++) q[i] = 0;
/* split quotient and remainder held in q to q and r respectively
* q [<--- quotient ---->|<-- remainder -->]
* index |xs xs-1 ... ys+1 ys|ys-1 ys-2 ... 1 0|
*/
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; }
}
#endif
@ -1954,7 +1972,7 @@ 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*/
//#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
@ -1967,7 +1985,11 @@ static moo_oop_t divide_unsigned_integers (moo_t* moo, moo_oop_t x, moo_oop_t y,
}
moo_pushvolat (moo, &qq);
rr = moo_instantiate(moo, moo->_large_positive_integer, MOO_NULL, MOO_OBJ_GET_SIZE(x));
#if defined(USE_DIVIDE_UNSIGNED_ARRAY2)
rr = moo_instantiate(moo, moo->_large_positive_integer, MOO_NULL, MOO_OBJ_GET_SIZE(y));
#else
rr = moo_instantiate(moo, moo->_large_positive_integer, MOO_NULL, MOO_OBJ_GET_SIZE(y) + 1);
#endif
moo_popvolats (moo, 3);
if (!rr) return MOO_NULL;
@ -2474,8 +2496,8 @@ moo_oop_t moo_divints (moo_t* moo, moo_oop_t x, moo_oop_t y, int modulo, moo_oop
--i;
dw = ((moo_lidw_t)carry << MOO_LIW_BITS) + zw[i];
/* TODO: optimize it with ASM - no seperate / and % */
zw[i] = dw / yv_abs;
carry = dw % yv_abs;
zw[i] = (moo_liw_t)(dw / yv_abs);
carry = (moo_liw_t)(dw % yv_abs);
}
/*if (zw[zs - 1] == 0) zs--;*/
@ -4531,8 +4553,8 @@ static MOO_INLINE moo_liw_t get_last_digit (moo_t* moo, moo_liw_t* x, moo_oow_t*
--i;
dw = ((moo_lidw_t)carry << MOO_LIW_BITS) + x[i];
/* TODO: optimize it with ASM - no seperate / and % */
x[i] = dw / radix;
carry = dw % radix;
x[i] = (moo_liw_t)(dw / radix);
carry = (moo_liw_t)(dw % radix);
}
if (/*oxs > 0 &&*/ x[oxs - 1] == 0) *xs = oxs - 1;
return carry;