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x_mul(): Made life easier for C optimizers in the "grade school"

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algorithm.  MSVC 6 wasn't impressed <wink>.

Something odd:  the x_mul algorithm appears to get substantially worse
than quadratic time as the inputs grow larger:

bits in each input   x_mul time   k_mul time
------------------   ----------   ----------
             15360         0.01         0.00
             30720         0.04         0.01
             61440         0.16         0.04
            122880         0.64         0.14
            245760         2.56         0.40
            491520        10.76         1.23
            983040        71.28         3.69
           1966080       459.31        11.07

That is, x_mul is perfectly quadratic-time until a little burp at
2.56->10.76, and after that goes to hell in a hurry.  Under Karatsuba,
doubling the input size "should take" 3 times longer instead of 4, and
that remains the case throughout this range.  I conclude that my "be nice
to the cache" reworkings of k_mul() are paying.
This commit is contained in:
Tim Peters 2002-08-12 18:25:43 +00:00
parent d64c1def7c
commit 115c888b97
1 changed files with 5 additions and 4 deletions
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9
Objects/longobject.c
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@ -1539,20 +1539,21 @@ x_mul(PyLongObject *a, PyLongObject *b)
twodigits carry = 0; twodigits carry = 0;
twodigits f = a->ob_digit[i]; twodigits f = a->ob_digit[i];
int j; int j;
digit *pz = z->ob_digit + i;
SIGCHECK({ SIGCHECK({
Py_DECREF(z); Py_DECREF(z);
return NULL; return NULL;
}) })
for (j = 0; j < size_b; ++j) { for (j = 0; j < size_b; ++j) {
carry += z->ob_digit[i+j] + b->ob_digit[j] * f; carry += *pz + b->ob_digit[j] * f;
z->ob_digit[i+j] = (digit) (carry & MASK); *pz++ = (digit) (carry & MASK);
carry >>= SHIFT; carry >>= SHIFT;
} }
for (; carry != 0; ++j) { for (; carry != 0; ++j) {
assert(i+j < z->ob_size); assert(i+j < z->ob_size);
carry += z->ob_digit[i+j]; carry += *pz;
z->ob_digit[i+j] = (digit) (carry & MASK); *pz++ = (digit) (carry & MASK);
carry >>= SHIFT; carry >>= SHIFT;
} }
} }