Merged revisions 73656,73658,73663,73666 via svnmerge from
svn+ssh://svn.python.org/python/branches/py3k ........ r73656 | mark.dickinson | 2009-06-29 00:08:40 +0200 (Mo, 29 Jun 2009) | 1 line Fix description of range_length_obj ........ r73658 | raymond.hettinger | 2009-06-29 00:30:13 +0200 (Mo, 29 Jun 2009) | 1 line Small doc fix-ups to floatingpoint.rst. More are forthcoming. ........ r73663 | raymond.hettinger | 2009-06-29 01:21:38 +0200 (Mo, 29 Jun 2009) | 1 line Clean-up floating point tutorial. ........ r73666 | alexandre.vassalotti | 2009-06-29 03:13:41 +0200 (Mo, 29 Jun 2009) | 2 lines Make b64encode raises properly a TypeError when altchars is not bytes. ........
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@ -82,7 +82,7 @@ values share the same approximation, any one of them could be displayed
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while still preserving the invariant ``eval(repr(x)) == x``.
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Historically, the Python prompt and built-in :func:`repr` function would chose
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the one with 17 significant digits, ``0.10000000000000001``, Starting with
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the one with 17 significant digits, ``0.10000000000000001``. Starting with
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Python 3.1, Python (on most systems) is now able to choose the shortest of
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these and simply display ``0.1``.
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@ -123,9 +123,9 @@ Also, since the 0.1 cannot get any closer to the exact value of 1/10 and
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Though the numbers cannot be made closer to their intended exact values,
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the :func:`round` function can be useful for post-rounding so that results
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have inexact values that are comparable to one another::
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with inexact values become comparable to one another::
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>>> round(.1 + .1 + .1, 1) == round(.3, 1)
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>>> round(.1 + .1 + .1, 10) == round(.3, 10)
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True
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Binary floating-point arithmetic holds many surprises like this. The problem
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@ -137,7 +137,7 @@ As that says near the end, "there are no easy answers." Still, don't be unduly
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wary of floating-point! The errors in Python float operations are inherited
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from the floating-point hardware, and on most machines are on the order of no
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more than 1 part in 2\*\*53 per operation. That's more than adequate for most
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tasks, but you do need to keep in mind that it's not decimal arithmetic, and
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tasks, but you do need to keep in mind that it's not decimal arithmetic and
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that every float operation can suffer a new rounding error.
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While pathological cases do exist, for most casual use of floating-point
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@ -165,7 +165,7 @@ fraction::
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>>> x = 3.14159
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>>> x.as_integer_ratio()
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(3537115888337719L, 1125899906842624L)
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(3537115888337719, 1125899906842624)
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Since the ratio is exact, it can be used to losslessly recreate the
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original value::
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@ -58,8 +58,8 @@ def b64encode(s, altchars=None):
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encoded = binascii.b2a_base64(s)[:-1]
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if altchars is not None:
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if not isinstance(altchars, bytes_types):
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altchars = TypeError("expected bytes, not %s"
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% altchars.__class__.__name__)
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raise TypeError("expected bytes, not %s"
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% altchars.__class__.__name__)
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assert len(altchars) == 2, repr(altchars)
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return _translate(encoded, {'+': altchars[0:1], '/': altchars[1:2]})
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return encoded
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@ -126,10 +126,9 @@ range_dealloc(rangeobject *r)
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PyObject_Del(r);
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}
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/* Return number of items in range (lo, hi, step), when arguments are PyLong
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* objects. Return a value < 0 if & only if the true value is too large to
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* fit in a signed long. Arguments MUST return 1 with PyLong_Check(). Return
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* -1 when there is an error.
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/* Return number of items in range (lo, hi, step) as a PyLong object,
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* when arguments are PyLong objects. Arguments MUST return 1 with
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* PyLong_Check(). Return NULL when there is an error.
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*/
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static PyObject*
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range_length_obj(rangeobject *r)
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