mirrors/cpython
1
0
Fork 0
mirror of https://github.com/python/cpython.git synced 2025-08-04 00:48:58 +00:00
Code Issues Projects Releases Packages Wiki Activity Actions 8

SF patch 936813: fast modular exponentiation

Browse source 
This checkin is adapted from part 1 (of 3) of Trevor Perrin's patch set.

x_mul()
  - sped a little by optimizing the C
  - sped a lot (~2X) if it's doing a square; note that long_pow() squares
    often
k_mul()
  - more cache-friendly now if it's doing a square
KARATSUBA_CUTOFF
  - boosted; gradeschool mult is quicker now, and it may have been too low
    for many platforms anyway
KARATSUBA_SQUARE_CUTOFF
  - new
  - since x_mul is a lot faster at squaring now, the point at which
    Karatsuba pays for squaring is much higher than for general mult
This commit is contained in:
Tim Peters 2004-08-29 22:16:50 +00:00
parent afb5f94217
commit 0973b99e1c
4 changed files with 91 additions and 22 deletions
Download patch file Download diff file Expand all files Collapse all files

100
Objects/longobject.c
View file

@ -12,7 +12,8 @@
* both operands contain more than KARATSUBA_CUTOFF digits (this
* being an internal Python long digit, in base BASE).
*/
#define KARATSUBA_CUTOFF 35
#define KARATSUBA_CUTOFF 70
#define KARATSUBA_SQUARE_CUTOFF (2 * KARATSUBA_CUTOFF)
#define ABS(x) ((x) < 0 ? -(x) : (x))
@ -1717,26 +1718,72 @@ x_mul(PyLongObject *a, PyLongObject *b)
return NULL;
memset(z->ob_digit, 0, z->ob_size * sizeof(digit));
for (i = 0; i < size_a; ++i) {
twodigits carry = 0;
twodigits f = a->ob_digit[i];
int j;
digit *pz = z->ob_digit + i;
if (a == b) {
/* Efficient squaring per HAC, Algorithm 14.16:
* http://www.cacr.math.uwaterloo.ca/hac/about/chap14.pdf
* Gives slightly less than a 2x speedup when a == b,
* via exploiting that each entry in the multiplication
* pyramid appears twice (except for the size_a squares).
*/
for (i = 0; i < size_a; ++i) {
twodigits carry;
twodigits f = a->ob_digit[i];
digit *pz = z->ob_digit + (i << 1);
digit *pa = a->ob_digit + i + 1;
digit *paend = a->ob_digit + size_a;
SIGCHECK({
Py_DECREF(z);
return NULL;
})
for (j = 0; j < size_b; ++j) {
carry += *pz + b->ob_digit[j] * f;
*pz++ = (digit) (carry & MASK);
SIGCHECK({
Py_DECREF(z);
return NULL;
})
carry = *pz + f * f;
*pz++ = (digit)(carry & MASK);
carry >>= SHIFT;
assert(carry <= MASK);
/* Now f is added in twice in each column of the
* pyramid it appears. Same as adding f<<1 once.
*/
f <<= 1;
while (pa < paend) {
carry += *pz + *pa++ * f;
*pz++ = (digit)(carry & MASK);
carry >>= SHIFT;
assert(carry <= (MASK << 1));
}
if (carry) {
carry += *pz;
*pz++ = (digit)(carry & MASK);
carry >>= SHIFT;
}
if (carry)
*pz += (digit)(carry & MASK);
assert((carry >> SHIFT) == 0);
}
for (; carry != 0; ++j) {
assert(i+j < z->ob_size);
carry += *pz;
*pz++ = (digit) (carry & MASK);
carry >>= SHIFT;
}
else { /* a is not the same as b -- gradeschool long mult */
for (i = 0; i < size_a; ++i) {
twodigits carry = 0;
twodigits f = a->ob_digit[i];
digit *pz = z->ob_digit + i;
digit *pb = b->ob_digit;
digit *pbend = b->ob_digit + size_b;
SIGCHECK({
Py_DECREF(z);
return NULL;
})
while (pb < pbend) {
carry += *pz + *pb++ * f;
*pz++ = (digit)(carry & MASK);
carry >>= SHIFT;
assert(carry <= MASK);
}
if (carry)
*pz += (digit)(carry & MASK);
assert((carry >> SHIFT) == 0);
}
}
return long_normalize(z);
@ -1816,7 +1863,8 @@ k_mul(PyLongObject *a, PyLongObject *b)
}
/* Use gradeschool math when either number is too small. */
if (asize <= KARATSUBA_CUTOFF) {
i = a == b ? KARATSUBA_SQUARE_CUTOFF : KARATSUBA_CUTOFF;
if (asize <= i) {
if (asize == 0)
return _PyLong_New(0);
else
@ -1837,7 +1885,13 @@ k_mul(PyLongObject *a, PyLongObject *b)
if (kmul_split(a, shift, &ah, &al) < 0) goto fail;
assert(ah->ob_size > 0); /* the split isn't degenerate */
if (kmul_split(b, shift, &bh, &bl) < 0) goto fail;
if (a == b) {
bh = ah;
bl = al;
Py_INCREF(bh);
Py_INCREF(bl);
}
else if (kmul_split(b, shift, &bh, &bl) < 0) goto fail;
/* The plan:
* 1. Allocate result space (asize + bsize digits: that's always
@ -1906,7 +1960,11 @@ k_mul(PyLongObject *a, PyLongObject *b)
Py_DECREF(al);
ah = al = NULL;
if ((t2 = x_add(bh, bl)) == NULL) {
if (a == b) {
t2 = t1;
Py_INCREF(t2);
}
else if ((t2 = x_add(bh, bl)) == NULL) {
Py_DECREF(t1);
goto fail;
}