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Heavily fiddled variant of patch #1442927: PyLong_FromString optimization.

Browse source 
``long(str, base)`` is now up to 6x faster for non-power-of-2 bases.  The
largest speedup is for inputs with about 1000 decimal digits.  Conversion
from non-power-of-2 bases remains quadratic-time in the number of input
digits (it was and remains linear-time for bases 2, 4, 8, 16 and 32).

Speedups at various lengths for decimal inputs, comparing 2.4.3 with
current trunk.  Note that it's actually a bit slower for 1-digit strings:

  len  speedup
 ----  -------
   1     -4.5%
   2      4.6%
   3      8.3%
   4     12.7%
   5     16.9%
   6     28.6%
   7     35.5%
   8     44.3%
   9     46.6%
  10     55.3%
  11     65.7%
  12     77.7%
  13     73.4%
  14     75.3%
  15     85.2%
  16    103.0%
  17     95.1%
  18    112.8%
  19    117.9%
  20    128.3%
  30    174.5%
  40    209.3%
  50    236.3%
  60    254.3%
  70    262.9%
  80    295.8%
  90    297.3%
 100    324.5%
 200    374.6%
 300    403.1%
 400    391.1%
 500    388.7%
 600    440.6%
 700    468.7%
 800    498.0%
 900    507.2%
1000    501.2%
2000    450.2%
3000    463.2%
4000    452.5%
5000    440.6%
6000    439.6%
7000    424.8%
8000    418.1%
9000    417.7%
This commit is contained in:
Tim Peters 2006-05-24 21:10:40 +00:00
parent f4049089c5
commit 696cf43b58
3 changed files with 236 additions and 43 deletions
Download patch file Download diff file Expand all files Collapse all files

75
Lib/test/test_builtin.py
View file

@ -980,6 +980,81 @@ class BuiltinTest(unittest.TestCase):
self.assertRaises(ValueError, long, '53', 40)
self.assertRaises(TypeError, long, 1, 12)
self.assertEqual(long('100000000000000000000000000000000', 2),
4294967296)
self.assertEqual(long('102002022201221111211', 3), 4294967296)
self.assertEqual(long('10000000000000000', 4), 4294967296)
self.assertEqual(long('32244002423141', 5), 4294967296)
self.assertEqual(long('1550104015504', 6), 4294967296)
self.assertEqual(long('211301422354', 7), 4294967296)
self.assertEqual(long('40000000000', 8), 4294967296)
self.assertEqual(long('12068657454', 9), 4294967296)
self.assertEqual(long('4294967296', 10), 4294967296)
self.assertEqual(long('1904440554', 11), 4294967296)
self.assertEqual(long('9ba461594', 12), 4294967296)
self.assertEqual(long('535a79889', 13), 4294967296)
self.assertEqual(long('2ca5b7464', 14), 4294967296)
self.assertEqual(long('1a20dcd81', 15), 4294967296)
self.assertEqual(long('100000000', 16), 4294967296)
self.assertEqual(long('a7ffda91', 17), 4294967296)
self.assertEqual(long('704he7g4', 18), 4294967296)
self.assertEqual(long('4f5aff66', 19), 4294967296)
self.assertEqual(long('3723ai4g', 20), 4294967296)
self.assertEqual(long('281d55i4', 21), 4294967296)
self.assertEqual(long('1fj8b184', 22), 4294967296)
self.assertEqual(long('1606k7ic', 23), 4294967296)
self.assertEqual(long('mb994ag', 24), 4294967296)
self.assertEqual(long('hek2mgl', 25), 4294967296)
self.assertEqual(long('dnchbnm', 26), 4294967296)
self.assertEqual(long('b28jpdm', 27), 4294967296)
self.assertEqual(long('8pfgih4', 28), 4294967296)
self.assertEqual(long('76beigg', 29), 4294967296)
self.assertEqual(long('5qmcpqg', 30), 4294967296)
self.assertEqual(long('4q0jto4', 31), 4294967296)
self.assertEqual(long('4000000', 32), 4294967296)
self.assertEqual(long('3aokq94', 33), 4294967296)
self.assertEqual(long('2qhxjli', 34), 4294967296)
self.assertEqual(long('2br45qb', 35), 4294967296)
self.assertEqual(long('1z141z4', 36), 4294967296)
self.assertEqual(long('100000000000000000000000000000001', 2),
4294967297)
self.assertEqual(long('102002022201221111212', 3), 4294967297)
self.assertEqual(long('10000000000000001', 4), 4294967297)
self.assertEqual(long('32244002423142', 5), 4294967297)
self.assertEqual(long('1550104015505', 6), 4294967297)
self.assertEqual(long('211301422355', 7), 4294967297)
self.assertEqual(long('40000000001', 8), 4294967297)
self.assertEqual(long('12068657455', 9), 4294967297)
self.assertEqual(long('4294967297', 10), 4294967297)
self.assertEqual(long('1904440555', 11), 4294967297)
self.assertEqual(long('9ba461595', 12), 4294967297)
self.assertEqual(long('535a7988a', 13), 4294967297)
self.assertEqual(long('2ca5b7465', 14), 4294967297)
self.assertEqual(long('1a20dcd82', 15), 4294967297)
self.assertEqual(long('100000001', 16), 4294967297)
self.assertEqual(long('a7ffda92', 17), 4294967297)
self.assertEqual(long('704he7g5', 18), 4294967297)
self.assertEqual(long('4f5aff67', 19), 4294967297)
self.assertEqual(long('3723ai4h', 20), 4294967297)
self.assertEqual(long('281d55i5', 21), 4294967297)
self.assertEqual(long('1fj8b185', 22), 4294967297)
self.assertEqual(long('1606k7id', 23), 4294967297)
self.assertEqual(long('mb994ah', 24), 4294967297)
self.assertEqual(long('hek2mgm', 25), 4294967297)
self.assertEqual(long('dnchbnn', 26), 4294967297)
self.assertEqual(long('b28jpdn', 27), 4294967297)
self.assertEqual(long('8pfgih5', 28), 4294967297)
self.assertEqual(long('76beigh', 29), 4294967297)
self.assertEqual(long('5qmcpqh', 30), 4294967297)
self.assertEqual(long('4q0jto5', 31), 4294967297)
self.assertEqual(long('4000001', 32), 4294967297)
self.assertEqual(long('3aokq95', 33), 4294967297)
self.assertEqual(long('2qhxjlj', 34), 4294967297)
self.assertEqual(long('2br45qc', 35), 4294967297)
self.assertEqual(long('1z141z5', 36), 4294967297)
def test_longconversion(self):
# Test __long__()
class Foo0:

6
Misc/NEWS
View file

@ -12,6 +12,12 @@ What's New in Python 2.5 alpha 3?
Core and builtins
-----------------
- Patch #1442927: ``long(str, base)`` is now up to 6x faster for non-power-
of-2 bases. The largest speedup is for inputs with about 1000 decimal
digits. Conversion from non-power-of-2 bases remains quadratic-time in
the number of input digits (it was and remains linear-time for bases
2, 4, 8, 16 and 32).
- Bug #1334662: ``int(string, base)`` could deliver a wrong answer
when ``base`` was not 2, 4, 8, 10, 16 or 32, and ``string`` represented
an integer close to ``sys.maxint``. This was repaired by patch

198
Objects/longobject.c
View file

@ -277,9 +277,9 @@ _long_as_ssize_t(PyObject *vv) {
overflow:
PyErr_SetString(PyExc_OverflowError,
"long int too large to convert to int");
if (sign > 0)
if (sign > 0)
return PY_SSIZE_T_MAX;
else
else
return PY_SSIZE_T_MIN;
}
@ -1304,7 +1304,34 @@ long_format(PyObject *aa, int base, int addL)
return (PyObject *)str;
}
/* *str points to the first digit in a string of base base digits. base
static int digval[] = {
37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37,
37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37,
37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37,
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 37, 37, 37, 37, 37, 37,
37, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24,
25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 37, 37, 37, 37,
37, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24,
25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 37, 37, 37, 37,
37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37,
37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37,
37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37,
37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37,
37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37,
37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37,
37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37,
37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37,
37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37,
37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37,
37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37,
37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37,
37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37,
37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37,
37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37,
37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37
};
/* *str points to the first digit in a string of base `base` digits. base
* is a power of 2 (2, 4, 8, 16, or 32). *str is set to point to the first
* non-digit (which may be *str!). A normalized long is returned.
* The point to this routine is that it takes time linear in the number of
@ -1328,20 +1355,8 @@ long_from_binary_base(char **str, int base)
n >>= 1;
/* n <- total # of bits needed, while setting p to end-of-string */
n = 0;
for (;;) {
int k = -1;
char ch = *p;
if (ch <= '9')
k = ch - '0';
else if (ch >= 'a')
k = ch - 'a' + 10;
else if (ch >= 'A')
k = ch - 'A' + 10;
if (k < 0 || k >= base)
break;
while (digval[Py_CHARMASK(*p)] < base)
++p;
}
*str = p;
n = (p - start) * bits_per_char;
if (n / bits_per_char != p - start) {
@ -1361,17 +1376,7 @@ long_from_binary_base(char **str, int base)
bits_in_accum = 0;
pdigit = z->ob_digit;
while (--p >= start) {
int k;
char ch = *p;
if (ch <= '9')
k = ch - '0';
else if (ch >= 'a')
k = ch - 'a' + 10;
else {
assert(ch >= 'A');
k = ch - 'A' + 10;
}
int k = digval[Py_CHARMASK(*p)];
assert(k >= 0 && k < base);
accum |= (twodigits)(k << bits_in_accum);
bits_in_accum += bits_per_char;
@ -1427,33 +1432,140 @@ PyLong_FromString(char *str, char **pend, int base)
}
if (base == 16 && str[0] == '0' && (str[1] == 'x' || str[1] == 'X'))
str += 2;
start = str;
if ((base & (base - 1)) == 0)
z = long_from_binary_base(&str, base);
else {
z = _PyLong_New(0);
for ( ; z != NULL; ++str) {
int k = -1;
PyLongObject *temp;
/***
Binary bases can be converted in time linear in the number of digits, because
Python's representation base is binary. Other bases (including decimal!) use
the simple quadratic-time algorithm below, complicated by some speed tricks.
if (*str <= '9')
k = *str - '0';
else if (*str >= 'a')
k = *str - 'a' + 10;
else if (*str >= 'A')
k = *str - 'A' + 10;
if (k < 0 || k >= base)
break;
temp = muladd1(z, (digit)base, (digit)k);
Py_DECREF(z);
z = temp;
First some math: the largest integer that can be expressed in N base-B digits
is B**N-1. Consequently, if we have an N-digit input in base B, the worst-
case number of Python digits needed to hold it is the smallest integer n s.t.
BASE**n-1 >= B**N-1 [or, adding 1 to both sides]
BASE**n >= B**N [taking logs to base BASE]
n >= log(B**N)/log(BASE) = N * log(B)/log(BASE)
The static array log_base_BASE[base] == log(base)/log(BASE) so we can compute
this quickly. A Python long with that much space is reserved near the start,
and the result is computed into it.
The input string is actually treated as being in base base**i (i.e., i digits
are processed at a time), where two more static arrays hold:
convwidth_base[base] = the largest integer i such that base**i <= BASE
convmultmax_base[base] = base ** convwidth_base[base]
The first of these is the largest i such that i consecutive input digits
must fit in a single Python digit. The second is effectively the input
base we're really using.
Viewing the input as a sequence <c0, c1, ..., c_n-1> of digits in base
convmultmax_base[base], the result is "simply"
(((c0*B + c1)*B + c2)*B + c3)*B + ... ))) + c_n-1
where B = convmultmax_base[base].
***/
register twodigits c; /* current input character */
Py_ssize_t size_z;
int i;
int convwidth;
twodigits convmultmax, convmult;
digit *pz, *pzstop;
char* scan;
static double log_base_BASE[37] = {0.0e0,};
static int convwidth_base[37] = {0,};
static twodigits convmultmax_base[37] = {0,};
if (log_base_BASE[base] == 0.0) {
twodigits convmax = base;
int i = 1;
log_base_BASE[base] = log((double)base) /
log((double)BASE);
for (;;) {
twodigits next = convmax * base;
if (next > BASE)
break;
convmax = next;
++i;
}
convmultmax_base[base] = convmax;
assert(i > 0);
convwidth_base[base] = i;
}
/* Find length of the string of numeric characters. */
scan = str;
while (digval[Py_CHARMASK(*scan)] < base)
++scan;
/* Create a long object that can contain the largest possible
* integer with this base and length. Note that there's no
* need to initialize z->ob_digit -- no slot is read up before
* being stored into.
*/
size_z = (Py_ssize_t)((scan - str) * log_base_BASE[base]) + 1;
assert(size_z > 0);
z = _PyLong_New(size_z);
if (z == NULL)
return NULL;
z->ob_size = 0;
/* `convwidth` consecutive input digits are treated as a single
* digit in base `convmultmax`.
*/
convwidth = convwidth_base[base];
convmultmax = convmultmax_base[base];
/* Work ;-) */
while (str < scan) {
/* grab up to convwidth digits from the input string */
c = (digit)digval[Py_CHARMASK(*str++)];
for (i = 1; i < convwidth && str != scan; ++i, ++str) {
c = (twodigits)(c * base +
digval[Py_CHARMASK(*str)]);
assert(c < BASE);
}
convmult = convmultmax;
/* Calculate the shift only if we couldn't get
* convwidth digits.
*/
if (i != convwidth) {
convmult = base;
for ( ; i > 1; --i)
convmult *= base;
}
/* Multiply z by convmult, and add c. */
pz = z->ob_digit;
pzstop = pz + z->ob_size;
for (; pz < pzstop; ++pz) {
c += (twodigits)*pz * convmult;
*pz = (digit)(c & MASK);
c >>= SHIFT;
}
/* carry off the current end? */
if (c) {
assert(c < BASE);
assert(z->ob_size < size_z);
*pz = (digit)c;
++z->ob_size;
}
}
}
if (z == NULL)
return NULL;
if (str == start)
goto onError;
if (sign < 0 && z != NULL && z->ob_size != 0)
if (sign < 0)
z->ob_size = -(z->ob_size);
if (*str == 'L' || *str == 'l')
str++;