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bpo-44376 - reduce pow() overhead for small exponents (GH-26662) 

Greatly reduce pow() overhead for small exponents.
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Tim Peters 2021-06-12 11:29:56 -05:00 committed by GitHub
parent be8b631b7a
commit 9d8dd8f08a
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2 changed files with 48 additions and 7 deletions
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1
Misc/NEWS.d/next/Core and Builtins/2021-06-11-17-37-15.bpo-44376.zhM1UW.rst Normal file
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@ -0,0 +1 @@
Exact integer exponentiation (like ``i**2`` or ``pow(i, 2)``) with a small exponent is much faster, due to reducing overhead in such cases.

58
Objects/longobject.c
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@ -4239,18 +4239,58 @@ long_pow(PyObject *v, PyObject *w, PyObject *x)
REDUCE(result); \
} while(0)
if (Py_SIZE(b) <= FIVEARY_CUTOFF) {
/* Left-to-right binary exponentiation (HAC Algorithm 14.79) */
/* http://www.cacr.math.uwaterloo.ca/hac/about/chap14.pdf */
for (i = Py_SIZE(b) - 1; i >= 0; --i) {
digit bi = b->ob_digit[i];
for (j = (digit)1 << (PyLong_SHIFT-1); j != 0; j >>= 1) {
MULT(z, z, z);
if (bi & j)
i = Py_SIZE(b);
digit bi = i ? b->ob_digit[i-1] : 0;
digit bit;
if (i <= 1 && bi <= 3) {
/* aim for minimal overhead */
if (bi >= 2) {
MULT(a, a, z);
if (bi == 3) {
MULT(z, a, z);
}
}
else if (bi == 1) {
/* Multiplying by 1 serves two purposes: if `a` is of an int
* subclass, makes the result an int (e.g., pow(False, 1) returns
* 0 instead of False), and potentially reduces `a` by the modulus.
*/
MULT(a, z, z);
}
/* else bi is 0, and z==1 is correct */
}
else if (i <= FIVEARY_CUTOFF) {
/* Left-to-right binary exponentiation (HAC Algorithm 14.79) */
/* http://www.cacr.math.uwaterloo.ca/hac/about/chap14.pdf */
/* Find the first significant exponent bit. Search right to left
* because we're primarily trying to cut overhead for small powers.
*/
assert(bi); /* else there is no significant bit */
Py_INCREF(a);
Py_DECREF(z);
z = a;
for (bit = 2; ; bit <<= 1) {
if (bit > bi) { /* found the first bit */
assert((bi & bit) == 0);
bit >>= 1;
assert(bi & bit);
break;
}
}
for (--i, bit >>= 1;;) {
for (; bit != 0; bit >>= 1) {
MULT(z, z, z);
if (bi & bit) {
MULT(z, a, z);
}
}
if (--i < 0) {
break;
}
bi = b->ob_digit[i];
bit = (digit)1 << (PyLong_SHIFT-1);
}
}
else {
/* Left-to-right 5-ary exponentiation (HAC Algorithm 14.82) */