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debugging division

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This commit is contained in:
hyunghwan.chung 2019-04-06 05:06:11 +00:00
parent cbf8ea2a8d
commit 9000100d15
3 changed files with 135 additions and 114 deletions
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16
moo/kernel/test-001.moo
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@ -119,12 +119,13 @@ extend MyObject
^(a value: 5) * (b value: 6). ## (12 * 5 + 22) * (99 * 6 + 4) => 49036
}
method(#class) testBigintDiv: divd_base divisor: divr_base
method(#class) testBigintDiv: divd_base divisor: divr_base count: count
{
| i q r divd divr |
| i q r divd divr ubound |
i := 1.
while (i < 2000)
ubound := i + count.
while (i < ubound)
{
divd := divd_base * i.
divr := divr_base * i.
@ -375,8 +376,13 @@ extend MyObject
## 150-154
[ (8113063330913503995887611892379812731289731289312898971231 div: 8113063330913503995887611892379812731289731289312898971230) = 1 ],
[ (8113063330913503995887611892379812731289731289312898971231 rem: 8113063330913503995887611892379812731289731289312898971230) = 1 ],
[ self testBigintDiv: 100919283908998345873248972389472389791283789123712899089034258903482398198123912831 divisor: 129323482374892374238974238974238947328972389128387312892713891728391278 ],
[ self testBigintDiv: 234897230919283908998345873248972389472389791283789123712899089034258903482398198123912831 divisor: 129323482374892374238974238974238947328972389128387312892713891728391278 ],
[ self testBigintDiv: 100919283908998345873248972389472389791283789123712899089034258903482398198123912831 divisor: 129323482374892374238974238974238947328972389128387312892713891728391278 count: 2000 ],
[ self testBigintDiv: 234897230919283908998345873248972389472389791283789123712899089034258903482398198123912831 divisor: 12932348237489237423897423897423894732897238912838731289271389172839127 count: 2000 ],
[ self testBigintDiv: 16r1234567812345678123456781234567812345678123456781234567812345678123456781234567812345678 divisor: 16r12345678123456781234567812345678123456781234567812345678 count: 2000 ],
[ self testBigintDiv: 16r000089ab0000456700000123 divisor: 1 count: 2000 ],
[ self testBigintDiv: 16r000000030000000000008000 divisor: 16r000000010000000000002000 count: 2000 ],
[ self testBigintDiv: 16rfffffffe0000000080000000 divisor: 16r0000ffff0000000080000000 count: 12345 ],
[ self testBigintDiv: 16rfffffffffffffffe divisor: 16rffffffff count: 2000 ],
## =========================

223
moo/lib/bigint.c
View File

@ -134,6 +134,41 @@ static const moo_uint8_t debruijn_64[64] =
# define LOG2_FOR_POW2_64(x) (debruijn_64[(moo_uint64_t)((moo_uint64_t)(x) * 0x022fdd63cc95386d) >> 58])
#endif
static MOO_INLINE int get_num_leading_zero_bits (moo_oow_t x)
{
#if defined(MOO_HAVE_BUILTIN_CLZLL) && (MOO_SIZEOF_OOW_T == MOO_SIZEOF_LONG_LONG)
return __builtin_clzll(x); /* count the number of leading zeros */
#elif defined(MOO_HAVE_BUILTIN_CLZL) && (MOO_SIZEOF_OOW_T == MOO_SIZEOF_LONG)
return __builtin_clzl(x); /* count the number leading zeros */
#elif defined(MOO_HAVE_BUILTIN_CLZ) && (MOO_SIZEOF_OOW_T == MOO_SIZEOF_INT)
return __builtin_clz(x); /* count the number of leading zeros */
#elif defined(__GNUC__) && (defined(__x86_64) || defined(__amd64) || defined(__i386) || defined(i386))
/* bit scan reverse. not all x86 CPUs have LZCNT. */
moo_oow_t pos;
__asm__ volatile (
"bsr %1,%0\n\t"
: "=r"(pos) /* output */
: "r"(x) /* input */
);
return (int)((MOO_SIZEOF(pos) * 8) - pos);
#elif defined(__GNUC__) && (defined(__arm__)
moo_oow_t count;
__asm__ volatile (
"clz %0,%1\n\t"
: "=r"(count) /* output */
: "r"(x) /* input */
);
return (int)count;
#else
int count = 0;
while (x >= 0)
{
x <<= 1;
count++;
}
#endif
}
static MOO_INLINE int get_pos_of_msb_set (moo_oow_t x)
{
/* the caller must ensure that x is power of 2. if x happens to be zero,
@ -1802,20 +1837,17 @@ 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] = 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))));
//d = (y1 == MOO_TYPE_MAX(moo_liw_t)? ((moo_liw_t)1): ((moo_liw_t)(((moo_lidw_t)1 << MOO_LIW_BITS) / (y1 + 1))));
d = (moo_liw_t)(((moo_lidw_t)1 << MOO_LIW_BITS) / ((moo_lidw_t)y1 + 1));
if (d > 1)
{
moo_lidw_t dw;
moo_liw_t carry;
/* q = q * d */
for (carry = 0, i = 0; i < xs; i++)
{
dw = ((moo_lidw_t)q[i] * d) + carry;
carry = (moo_liw_t)(dw >> MOO_LIW_BITS);
q[i] = (moo_liw_t)dw;
}
q[xs] = carry;
/* shift the divisor such that its high-order bit is on.
* shift the dividend the same amount as the previous step */
/* r = r * d */
for (carry = 0, i = 0; i < ys; i++)
@ -1825,6 +1857,15 @@ 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);
/* q = q * d */
for (carry = 0, i = 0; i < xs; i++)
{
dw = ((moo_lidw_t)q[i] * d) + carry;
carry = (moo_liw_t)(dw >> MOO_LIW_BITS);
q[i] = (moo_liw_t)dw;
}
q[xs] = carry;
}
y1 = r[ys - 1];
@ -1842,6 +1883,7 @@ static void divide_unsigned_array2 (moo_t* moo, const moo_liw_t* x, moo_oow_t xs
xhi = q[i];
xlo = q[i - 1];
//printf ("AAAAAAAAAAAaa %llx %llx\n", (unsigned long long)xhi, (unsigned long long)y1);
if (xhi == y1)
{
quo = MOO_TYPE_MAX(moo_liw_t);
@ -1850,60 +1892,57 @@ static void divide_unsigned_array2 (moo_t* moo, const moo_liw_t* x, moo_oow_t xs
{
dw = ((moo_lidw_t)xhi << MOO_LIW_BITS) + xlo;
/* TODO: optimize it with ASM - no seperate / and % */
quo = (moo_liw_t)(dw / y1);
q[i] = (moo_liw_t)(dw % y1);
quo = (moo_liw_t)(dw / y1); /* qhat */
q[i] = (moo_liw_t)(dw % y1); /* rhat */
MOO_ASSERT (moo, (dw / y1) == quo);
}
/* ---------------------------------------------------------- */
/*quo = adjust_for_over_estimate(y1, y2, quo, q[i], q[i - 2]);*/
{
moo_liw_t c, c2, y2q;
//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]);
#if 0
{
moo_lidw_t rhat = q[i];
adjust_quotient:
if (quo > MOO_TYPE_MAX(moo_liw_t) || ((moo_lidw_t)quo * y2) > (((moo_lidw_t)rhat << MOO_LIW_BITS) + q[i - 2]))
{
quo = quo - 1;
rhat = rhat + y1;
if (rhat <= MOO_TYPE_MAX(moo_liw_t)) goto adjust_quotient;
}
}
#else
{
moo_liw_t c, c2, y2q, rhat;
//printf ("XXXXXXXXXXXXXXXXXXXXXx %d %d\n", (int)xs, (int)i);
rhat = q[i];
adjust_quotient:
dw = ((moo_lidw_t)quo * y2);
c = (moo_liw_t)(dw >> MOO_LIW_BITS);
y2q = (moo_liw_t)dw;
/*
x1 => c
x2 => y2q
ujn2 => q[i - 2]
rhat => q[i]
for greaterThan(x1, x2, rhat, ujn2)
func greaterThan(x1, x2, y1, y2 Word) bool {
return x1 > y1 || x1 == y1 && x2 > y2
}*/
//printf ("XXXXXXXXXXXXXXXXXXXXXx %d %d\n", (int)xs, (int)i);
if (c > q[i] || (c == q[i] && y2q > q[i - 2]))
if (c > rhat || (c == rhat && y2q > q[i - 2]))
{
//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]);
--quo; /* too large by 1 */
--quo; /* too large */
/*xpy(xi, y1, c2); add back divisor */
c2 = (moo_liw_t)(((moo_lidw_t)q[i] + y1) >> MOO_LIW_BITS);
if (c2 == 0)
dw = (moo_lidw_t)q[i] + y1; /* add back the divisor */
if (dw <= MOO_TYPE_MAX(moo_liw_t)) /* if ((dw >> MOO_LIW_BITS) == 0) */
{
/*y2q = axpy(y2, q, 0, c);*/
dw = ((moo_lidw_t)quo * y2);
c = (moo_liw_t)(dw >> MOO_LIW_BITS);
y2q = (moo_liw_t)dw;
if (c > q[i] || (c == q[i] && y2q > q[i - 2]))
{
//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]);
--quo; /* too large by 2 */
}
rhat = (moo_liw_t)dw;
goto adjust_quotient;
}
}
}
#endif
/* ---------------------------------------------------------- */
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); /* is the sign bit set? */
if (b)
{
/* underflow */
/* yes. underflow */
b = adjust_for_underflow(q, r, i - ys, ys);
MOO_ASSERT (moo, b == 1);
q[i] = quo - 1;
@ -1938,28 +1977,12 @@ func greaterThan(x1, x2, y1, y2 Word) bool {
}
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_oow_t s, i, j, g;
moo_lidw_t dw, qhat, rhat;
moo_lidi_t t, k;
moo_liw_t* qq;
moo_liw_t* qq, y1, y2;
/* the caller must ensure:
* - q can hold 'xs + 1' words and r can hold 'ys' words.
@ -2007,7 +2030,7 @@ for (i = 0; i < ys; i++) printf ("0x%llx, ", (unsigned long long)y[i]);
printf ("};\n"); */
//for (i = 0; i <= xs; i++) printf ("un %llx\n", (unsigned long long)q[i]);
s = nlz(y[ys - 1]);
s = get_num_leading_zero_bits(y[ys - 1]);
for (i = ys; i > 1; )
{
--i;
@ -2028,79 +2051,62 @@ printf ("};\n"); */
//for (i = 0; i < ys; i++) printf ("vn %llx\n", (unsigned long long)r[i]);
//for (i = 0; i <= xs; i++) printf ("un %llx\n", (unsigned long long)qq[i]);
y1 = r[ys - 1];
y2 = r[ys - 2];
/*
for (j = xs - ys + 1; j > 0; )
{
--j;
*/
for (j = xs; j >= ys; --j)
{
g = j - ys; /* position where remainder begins in qq */
/* estimate */
dw = ((moo_lidw_t)qq[j + ys] << MOO_LIW_BITS) + qq[j + ys - 1];
qhat = dw / r[ys - 1];
rhat = dw - (qhat * r[ys - 1]);
dw = ((moo_lidw_t)qq[j] << MOO_LIW_BITS) + qq[j - 1];
qhat = dw / y1;
rhat = dw - (qhat * y1);
//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]);
adjust_quotient:
if (qhat > MOO_TYPE_MAX(moo_liw_t) || (qhat * r[ys - 2]) > ((rhat << MOO_LIW_BITS) + qq[j + ys - 2]))
if (qhat > MOO_TYPE_MAX(moo_liw_t) || (qhat * y2) > ((rhat << MOO_LIW_BITS) + qq[j - 2]))
{
qhat = qhat - 1;
rhat = rhat + r[ys - 1];
rhat = rhat + y1;
if (rhat <= MOO_TYPE_MAX(moo_liw_t)) goto adjust_quotient;
}
//printf ("qhat == %llx rhat == %llx\n", (unsigned long long)qhat, (unsigned long long)rhat);
#if 1
/* multiply and subtract */
for (k = 0, i = 0; i < ys; i++)
{
dw = qhat * r[i];
t = qq[j + i] - k - (dw & MOO_TYPE_MAX(moo_liw_t));
qq[j + i] = t;
t = qq[g + i] - k - (dw & MOO_TYPE_MAX(moo_liw_t));
qq[g + i] = t;
k = (dw >> MOO_LIW_BITS) - (t >> MOO_LIW_BITS);
}
t = qq[j + ys] - k;
qq[j + ys] = t;
MOO_ASSERT (moo, j == g + ys);
t = qq[j] - k;
qq[j] = t;
/* test remainder */
q[j] = qhat;
q[g] = qhat; /* store quotient */
if (t < 0)
{
q[j] = q[j] - 1;
q[g] = q[g] - 1; /* add back */
for (k = 0, i = 0; i < ys; i++)
{
t = (moo_lidw_t)qq[j + i] + r[i] + k;
qq[j + i] = (moo_liw_t)t;
t = (moo_lidw_t)qq[g + i] + r[i] + k;
qq[g + i] = (moo_liw_t)t;
k = t >> MOO_LIW_BITS;
}
qq[j + ys] += k;
MOO_ASSERT (moo, j == g + ys);
qq[j] += k;
}
#else
for (k = 0, i = 0; i <= n; i++)
{
p = qhat * (i == n ? 0 : v[i]);
k2 = (p >> 16);
d = u[j + i] - (uint16_t)p;
k2 += (d > u[j + i]);
u[j + i] = d - k;
k2 += (u[j + i] > d);
k = k2;
}
/* Test remainder. */
q[j] = qhat;
if (k != 0) {
/* Add back. */
q[j]--;
k = 0;
for (i = 0; i < n; i++) {
t = u[j + i] + v[i] + k;
u[j + i] = (uint16_t)t;
k = t >> 16;
}
#endif
}
for (i = 0; i < ys - 1; i++)
@ -2270,7 +2276,7 @@ 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_array3 (moo,
divide_unsigned_array2 (moo,
#else
divide_unsigned_array (moo,
#endif
@ -2897,7 +2903,6 @@ oops_einval:
return MOO_NULL;
}
moo_oop_t moo_negateint (moo_t* moo, moo_oop_t x)
{
if (MOO_OOP_IS_SMOOI(x))

10
moo/lib/moo-cmn.h
View File

@ -853,6 +853,16 @@ typedef struct moo_t moo_t;
#define MOO_HAVE_BUILTIN_CTZLL
#endif
#if __has_builtin(__builtin_clz)
#define MOO_HAVE_BUILTIN_CLZ
#endif
#if __has_builtin(__builtin_clzl)
#define MOO_HAVE_BUILTIN_CLZL
#endif
#if __has_builtin(__builtin_clzll)
#define MOO_HAVE_BUILTIN_CLZLL
#endif
#if __has_builtin(__builtin_uadd_overflow)
#define MOO_HAVE_BUILTIN_UADD_OVERFLOW
#endif