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Merged revisions 71772 via svnmerge from 

svn+ssh://pythondev@svn.python.org/python/trunk

........
  r71772 | mark.dickinson | 2009-04-20 22:13:33 +0100 (Mon, 20 Apr 2009) | 5 lines

  Issue #3166: Make long -> float (and int -> float) conversions
  correctly rounded, using round-half-to-even.  This ensures that the
  value of float(n) doesn't depend on whether we're using 15-bit digits
  or 30-bit digits for Python longs.
........
This commit is contained in:
Mark Dickinson 2009-04-20 21:38:00 +00:00
parent 628fbd59ea
commit c630039edd
3 changed files with 216 additions and 17 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

59
Lib/test/test_long.py
View File

@ -620,6 +620,65 @@ class LongTest(unittest.TestCase):
else:
self.assertRaises(TypeError, pow,longx, longy, int(z))
@unittest.skipUnless(float.__getformat__("double").startswith("IEEE"),
"test requires IEEE 754 doubles")
def test_float_conversion(self):
import sys
DBL_MAX = sys.float_info.max
DBL_MAX_EXP = sys.float_info.max_exp
DBL_MANT_DIG = sys.float_info.mant_dig
exact_values = [0, 1, 2,
2**53-3,
2**53-2,
2**53-1,
2**53,
2**53+2,
2**54-4,
2**54-2,
2**54,
2**54+4]
for x in exact_values:
self.assertEqual(float(x), x)
self.assertEqual(float(-x), -x)
# test round-half-even
for x, y in [(1, 0), (2, 2), (3, 4), (4, 4), (5, 4), (6, 6), (7, 8)]:
for p in range(15):
self.assertEqual(int(float(2**p*(2**53+x))), 2**p*(2**53+y))
for x, y in [(0, 0), (1, 0), (2, 0), (3, 4), (4, 4), (5, 4), (6, 8),
(7, 8), (8, 8), (9, 8), (10, 8), (11, 12), (12, 12),
(13, 12), (14, 16), (15, 16)]:
for p in range(15):
self.assertEqual(int(float(2**p*(2**54+x))), 2**p*(2**54+y))
# behaviour near extremes of floating-point range
int_dbl_max = int(DBL_MAX)
top_power = 2**DBL_MAX_EXP
halfway = (int_dbl_max + top_power)//2
self.assertEqual(float(int_dbl_max), DBL_MAX)
self.assertEqual(float(int_dbl_max+1), DBL_MAX)
self.assertEqual(float(halfway-1), DBL_MAX)
self.assertRaises(OverflowError, float, halfway)
self.assertEqual(float(1-halfway), -DBL_MAX)
self.assertRaises(OverflowError, float, -halfway)
self.assertRaises(OverflowError, float, top_power-1)
self.assertRaises(OverflowError, float, top_power)
self.assertRaises(OverflowError, float, top_power+1)
self.assertRaises(OverflowError, float, 2*top_power-1)
self.assertRaises(OverflowError, float, 2*top_power)
self.assertRaises(OverflowError, float, top_power*top_power)
for p in range(100):
x = 2**p * (2**53 + 1) + 1
y = 2**p * (2**53 + 2)
self.assertEqual(int(float(x)), y)
x = 2**p * (2**53 + 1)
y = 2**p * 2**53
self.assertEqual(int(float(x)), y)
def test_float_overflow(self):
import math

3
Misc/NEWS
View File

@ -12,6 +12,9 @@ What's New in Python 3.1 beta 1?
Core and Builtins
-----------------
- Issue #3166: Make long -> float (and int -> float) conversions
correctly rounded.
- Issue #1869 (and many duplicates): make round(x, n) correctly
rounded for a float x, by using the decimal <-> binary conversions
from Python/dtoa.c. As a consequence, (e.g.) round(x, 2) now

171
Objects/longobject.c
View File

@ -6,6 +6,7 @@
#include "longintrepr.h"
#include "structseq.h"
#include <float.h>
#include <ctype.h>
#include <stddef.h>
@ -100,6 +101,9 @@ maybe_small_long(PyLongObject *v)
if (PyErr_CheckSignals()) PyTryBlock \
}
/* forward declaration */
static int bits_in_digit(digit d);
/* Normalize (remove leading zeros from) a long int object.
Doesn't attempt to free the storage--in most cases, due to the nature
of the algorithms used, this could save at most be one word anyway. */
@ -962,33 +966,166 @@ _PyLong_AsScaledDouble(PyObject *vv, int *exponent)
#undef NBITS_WANTED
}
/* Get a C double from a long int object. */
/* Get a C double from a long int object. Rounds to the nearest double,
using the round-half-to-even rule in the case of a tie. */
double
PyLong_AsDouble(PyObject *vv)
{
int e = -1;
PyLongObject *v = (PyLongObject *)vv;
Py_ssize_t rnd_digit, rnd_bit, m, n;
digit lsb, *d;
int round_up = 0;
double x;
if (vv == NULL || !PyLong_Check(vv)) {
PyErr_BadInternalCall();
return -1;
}
x = _PyLong_AsScaledDouble(vv, &e);
if (x == -1.0 && PyErr_Occurred())
return -1.0;
/* 'e' initialized to -1 to silence gcc-4.0.x, but it should be
set correctly after a successful _PyLong_AsScaledDouble() call */
assert(e >= 0);
if (e > INT_MAX / PyLong_SHIFT)
goto overflow;
errno = 0;
x = ldexp(x, e * PyLong_SHIFT);
if (Py_OVERFLOWED(x))
goto overflow;
return x;
}
overflow:
/* Notes on the method: for simplicity, assume v is positive and >=
2**DBL_MANT_DIG. (For negative v we just ignore the sign until the
end; for small v no rounding is necessary.) Write n for the number
of bits in v, so that 2**(n-1) <= v < 2**n, and n > DBL_MANT_DIG.
Some terminology: the *rounding bit* of v is the 1st bit of v that
will be rounded away (bit n - DBL_MANT_DIG - 1); the *parity bit*
is the bit immediately above. The round-half-to-even rule says
that we round up if the rounding bit is set, unless v is exactly
halfway between two floats and the parity bit is zero.
Write d[0] ... d[m] for the digits of v, least to most significant.
Let rnd_bit be the index of the rounding bit, and rnd_digit the
index of the PyLong digit containing the rounding bit. Then the
bits of the digit d[rnd_digit] look something like:
rounding bit
|
v
msb -> sssssrttttttttt <- lsb
^
|
parity bit
where 's' represents a 'significant bit' that will be included in
the mantissa of the result, 'r' is the rounding bit, and 't'
represents a 'trailing bit' following the rounding bit. Note that
if the rounding bit is at the top of d[rnd_digit] then the parity
bit will be the lsb of d[rnd_digit+1]. If we set
lsb = 1 << (rnd_bit % PyLong_SHIFT)
then d[rnd_digit] & (PyLong_BASE - 2*lsb) selects just the
significant bits of d[rnd_digit], d[rnd_digit] & (lsb-1) gets the
trailing bits, and d[rnd_digit] & lsb gives the rounding bit.
We initialize the double x to the integer given by digits
d[rnd_digit:m-1], but with the rounding bit and trailing bits of
d[rnd_digit] masked out. So the value of x comes from the top
DBL_MANT_DIG bits of v, multiplied by 2*lsb. Note that in the loop
that produces x, all floating-point operations are exact (assuming
that FLT_RADIX==2). Now if we're rounding down, the value we want
to return is simply
x * 2**(PyLong_SHIFT * rnd_digit).
and if we're rounding up, it's
(x + 2*lsb) * 2**(PyLong_SHIFT * rnd_digit).
Under the round-half-to-even rule, we round up if, and only
if, the rounding bit is set *and* at least one of the
following three conditions is satisfied:
(1) the parity bit is set, or
(2) at least one of the trailing bits of d[rnd_digit] is set, or
(3) at least one of the digits d[i], 0 <= i < rnd_digit
is nonzero.
Finally, we have to worry about overflow. If v >= 2**DBL_MAX_EXP,
or equivalently n > DBL_MAX_EXP, then overflow occurs. If v <
2**DBL_MAX_EXP then we're usually safe, but there's a corner case
to consider: if v is very close to 2**DBL_MAX_EXP then it's
possible that v is rounded up to exactly 2**DBL_MAX_EXP, and then
again overflow occurs.
*/
if (Py_SIZE(v) == 0)
return 0.0;
m = ABS(Py_SIZE(v)) - 1;
d = v->ob_digit;
assert(d[m]); /* v should be normalized */
/* fast path for case where 0 < abs(v) < 2**DBL_MANT_DIG */
if (m < DBL_MANT_DIG / PyLong_SHIFT ||
(m == DBL_MANT_DIG / PyLong_SHIFT &&
d[m] < (digit)1 << DBL_MANT_DIG%PyLong_SHIFT)) {
x = d[m];
while (--m >= 0)
x = x*PyLong_BASE + d[m];
return Py_SIZE(v) < 0 ? -x : x;
}
/* if m is huge then overflow immediately; otherwise, compute the
number of bits n in v. The condition below implies n (= #bits) >=
m * PyLong_SHIFT + 1 > DBL_MAX_EXP, hence v >= 2**DBL_MAX_EXP. */
if (m > (DBL_MAX_EXP-1)/PyLong_SHIFT)
goto overflow;
n = m * PyLong_SHIFT + bits_in_digit(d[m]);
if (n > DBL_MAX_EXP)
goto overflow;
/* find location of rounding bit */
assert(n > DBL_MANT_DIG); /* dealt with |v| < 2**DBL_MANT_DIG above */
rnd_bit = n - DBL_MANT_DIG - 1;
rnd_digit = rnd_bit/PyLong_SHIFT;
lsb = (digit)1 << (rnd_bit%PyLong_SHIFT);
/* Get top DBL_MANT_DIG bits of v. Assumes PyLong_SHIFT <
DBL_MANT_DIG, so we'll need bits from at least 2 digits of v. */
x = d[m];
assert(m > rnd_digit);
while (--m > rnd_digit)
x = x*PyLong_BASE + d[m];
x = x*PyLong_BASE + (d[m] & (PyLong_BASE-2*lsb));
/* decide whether to round up, using round-half-to-even */
assert(m == rnd_digit);
if (d[m] & lsb) { /* if (rounding bit is set) */
digit parity_bit;
if (lsb == PyLong_BASE/2)
parity_bit = d[m+1] & 1;
else
parity_bit = d[m] & 2*lsb;
if (parity_bit)
round_up = 1;
else if (d[m] & (lsb-1))
round_up = 1;
else {
while (--m >= 0) {
if (d[m]) {
round_up = 1;
break;
}
}
}
}
/* and round up if necessary */
if (round_up) {
x += 2*lsb;
if (n == DBL_MAX_EXP &&
x == ldexp((double)(2*lsb), DBL_MANT_DIG)) {
/* overflow corner case */
goto overflow;
}
}
/* shift, adjust for sign, and return */
x = ldexp(x, rnd_digit*PyLong_SHIFT);
return Py_SIZE(v) < 0 ? -x : x;
overflow:
PyErr_SetString(PyExc_OverflowError,
"Python int too large to convert to C double");
return -1.0;