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Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from

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........
  r65258 | mark.dickinson | 2008-07-27 08:15:29 +0100 (Sun, 27 Jul 2008) | 4 lines

  Remove math.sum tests related to overflow, special values, and behaviour
  near the extremes of the floating-point range.  (The behaviour of math.sum
  should be regarded as undefined in these cases.)
........
  r65292 | mark.dickinson | 2008-07-29 19:45:38 +0100 (Tue, 29 Jul 2008) | 4 lines

  More modifications to tests for math.sum:  replace the Python
  version of msum by a version using a different algorithm, and
  use the new float.fromhex method to specify test results exactly.
........
  r65299 | mark.dickinson | 2008-07-30 13:01:41 +0100 (Wed, 30 Jul 2008) | 5 lines

  Fix special-value handling for math.sum.
  Also minor cleanups to the code: fix tabbing, remove
  trailing whitespace, and reformat to fit into 80
  columns.
........
  r65308 | mark.dickinson | 2008-07-30 17:20:10 +0100 (Wed, 30 Jul 2008) | 2 lines

  Rename math.sum to math.fsum
........
  r65309 | mark.dickinson | 2008-07-30 17:25:16 +0100 (Wed, 30 Jul 2008) | 3 lines

  Replace math.sum with math.fsum in a couple of comments
  that were missed by r65308
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  r65315 | mark.dickinson | 2008-07-30 21:23:15 +0100 (Wed, 30 Jul 2008) | 2 lines

  Add note about problems with math.fsum on x86 hardware.
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  r65326 | mark.dickinson | 2008-07-31 15:48:32 +0100 (Thu, 31 Jul 2008) | 2 lines

  Rename testSum to testFsum and move it to proper place in test_math.py
........
This commit is contained in:
Mark Dickinson 2008-08-01 08:16:13 +00:00
parent c57df32319
commit aa7633ab94
5 changed files with 201 additions and 211 deletions
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118
Modules/mathmodule.c
View file

@ -396,7 +396,7 @@ FUNC1(tanh, tanh, 0,
Note 4: A similar implementation is in Modules/cmathmodule.c.
Be sure to update both when making changes.
Note 5: The signature of math.sum() differs from __builtin__.sum()
Note 5: The signature of math.fsum() differs from __builtin__.sum()
because the start argument doesn't make sense in the context of
accurate summation. Since the partials table is collapsed before
returning a result, sum(seq2, start=sum(seq1)) may not equal the
@ -407,7 +407,7 @@ FUNC1(tanh, tanh, 0,
/* Extend the partials array p[] by doubling its size. */
static int /* non-zero on error */
_sum_realloc(double **p_ptr, Py_ssize_t n,
_fsum_realloc(double **p_ptr, Py_ssize_t n,
double *ps, Py_ssize_t *m_ptr)
{
void *v = NULL;
@ -425,7 +425,7 @@ _sum_realloc(double **p_ptr, Py_ssize_t n,
v = PyMem_Realloc(p, sizeof(double) * m);
}
if (v == NULL) { /* size overflow or no memory */
PyErr_SetString(PyExc_MemoryError, "math sum partials");
PyErr_SetString(PyExc_MemoryError, "math.fsum partials");
return 1;
}
*p_ptr = (double*) v;
@ -464,18 +464,19 @@ _sum_realloc(double **p_ptr, Py_ssize_t n,
*/
static PyObject*
math_sum(PyObject *self, PyObject *seq)
math_fsum(PyObject *self, PyObject *seq)
{
PyObject *item, *iter, *sum = NULL;
Py_ssize_t i, j, n = 0, m = NUM_PARTIALS;
double x, y, t, ps[NUM_PARTIALS], *p = ps;
double xsave, special_sum = 0.0, inf_sum = 0.0;
volatile double hi, yr, lo;
iter = PyObject_GetIter(seq);
if (iter == NULL)
return NULL;
PyFPE_START_PROTECT("sum", Py_DECREF(iter); return NULL)
PyFPE_START_PROTECT("fsum", Py_DECREF(iter); return NULL)
for(;;) { /* for x in iterable */
assert(0 <= n && n <= m);
@ -485,18 +486,19 @@ math_sum(PyObject *self, PyObject *seq)
item = PyIter_Next(iter);
if (item == NULL) {
if (PyErr_Occurred())
goto _sum_error;
goto _fsum_error;
break;
}
x = PyFloat_AsDouble(item);
Py_DECREF(item);
if (PyErr_Occurred())
goto _sum_error;
goto _fsum_error;
xsave = x;
for (i = j = 0; j < n; j++) { /* for y in partials */
y = p[j];
if (fabs(x) < fabs(y)) {
t = x; x = y; y = t;
t = x; x = y; y = t;
}
hi = x + y;
yr = hi - x;
@ -505,59 +507,73 @@ math_sum(PyObject *self, PyObject *seq)
p[i++] = lo;
x = hi;
}
n = i; /* ps[i:] = [x] */
n = i; /* ps[i:] = [x] */
if (x != 0.0) {
/* If non-finite, reset partials, effectively
adding subsequent items without roundoff
and yielding correct non-finite results,
provided IEEE 754 rules are observed */
if (! Py_IS_FINITE(x))
if (! Py_IS_FINITE(x)) {
/* a nonfinite x could arise either as
a result of intermediate overflow, or
as a result of a nan or inf in the
summands */
if (Py_IS_FINITE(xsave)) {
PyErr_SetString(PyExc_OverflowError,
"intermediate overflow in fsum");
goto _fsum_error;
}
if (Py_IS_INFINITY(xsave))
inf_sum += xsave;
special_sum += xsave;
/* reset partials */
n = 0;
else if (n >= m && _sum_realloc(&p, n, ps, &m))
goto _sum_error;
p[n++] = x;
}
else if (n >= m && _fsum_realloc(&p, n, ps, &m))
goto _fsum_error;
else
p[n++] = x;
}
}
if (special_sum != 0.0) {
if (Py_IS_NAN(inf_sum))
PyErr_SetString(PyExc_ValueError,
"-inf + inf in fsum");
else
sum = PyFloat_FromDouble(special_sum);
goto _fsum_error;
}
hi = 0.0;
if (n > 0) {
hi = p[--n];
if (Py_IS_FINITE(hi)) {
/* sum_exact(ps, hi) from the top, stop when the sum becomes inexact. */
while (n > 0) {
x = hi;
y = p[--n];
assert(fabs(y) < fabs(x));
hi = x + y;
yr = hi - x;
lo = y - yr;
if (lo != 0.0)
break;
}
/* Make half-even rounding work across multiple partials. Needed
so that sum([1e-16, 1, 1e16]) will round-up the last digit to
two instead of down to zero (the 1e-16 makes the 1 slightly
closer to two). With a potential 1 ULP rounding error fixed-up,
math.sum() can guarantee commutativity. */
if (n > 0 && ((lo < 0.0 && p[n-1] < 0.0) ||
(lo > 0.0 && p[n-1] > 0.0))) {
y = lo * 2.0;
x = hi + y;
yr = x - hi;
if (y == yr)
hi = x;
}
/* sum_exact(ps, hi) from the top, stop when the sum becomes
inexact. */
while (n > 0) {
x = hi;
y = p[--n];
assert(fabs(y) < fabs(x));
hi = x + y;
yr = hi - x;
lo = y - yr;
if (lo != 0.0)
break;
}
else { /* raise exception corresponding to a special value */
errno = Py_IS_NAN(hi) ? EDOM : ERANGE;
if (is_error(hi))
goto _sum_error;
/* Make half-even rounding work across multiple partials.
Needed so that sum([1e-16, 1, 1e16]) will round-up the last
digit to two instead of down to zero (the 1e-16 makes the 1
slightly closer to two). With a potential 1 ULP rounding
error fixed-up, math.fsum() can guarantee commutativity. */
if (n > 0 && ((lo < 0.0 && p[n-1] < 0.0) ||
(lo > 0.0 && p[n-1] > 0.0))) {
y = lo * 2.0;
x = hi + y;
yr = x - hi;
if (y == yr)
hi = x;
}
}
sum = PyFloat_FromDouble(hi);
_sum_error:
_fsum_error:
PyFPE_END_PROTECT(hi)
Py_DECREF(iter);
if (p != ps)
@ -567,7 +583,7 @@ _sum_error:
#undef NUM_PARTIALS
PyDoc_STRVAR(math_sum_doc,
PyDoc_STRVAR(math_fsum_doc,
"sum(iterable)\n\n\
Return an accurate floating point sum of values in the iterable.\n\
Assumes IEEE-754 floating point arithmetic.");
@ -1078,6 +1094,7 @@ static PyMethodDef math_methods[] = {
{"floor", math_floor, METH_O, math_floor_doc},
{"fmod", math_fmod, METH_VARARGS, math_fmod_doc},
{"frexp", math_frexp, METH_O, math_frexp_doc},
{"fsum", math_fsum, METH_O, math_fsum_doc},
{"hypot", math_hypot, METH_VARARGS, math_hypot_doc},
{"isinf", math_isinf, METH_O, math_isinf_doc},
{"isnan", math_isnan, METH_O, math_isnan_doc},
@ -1091,10 +1108,9 @@ static PyMethodDef math_methods[] = {
{"sin", math_sin, METH_O, math_sin_doc},
{"sinh", math_sinh, METH_O, math_sinh_doc},
{"sqrt", math_sqrt, METH_O, math_sqrt_doc},
{"sum", math_sum, METH_O, math_sum_doc},
{"tan", math_tan, METH_O, math_tan_doc},
{"tanh", math_tanh, METH_O, math_tanh_doc},
{"trunc", math_trunc, METH_O, math_trunc_doc},
{"trunc", math_trunc, METH_O, math_trunc_doc},
{NULL, NULL} /* sentinel */
};