Python now uses David Gay’s algorithm for finding the shortest
floating point representation that doesn’t change its value. This
should help mitigate some of the confusion surrounding binary floating
point numbers.
The significance is easily seen with a number like 1.1 which does
not have an exact equivalent in binary floating point. Since there is
no exact equivalent, an expression like float('1.1') evaluates to
the nearest representable value which is 0x1.199999999999ap+0 in hex
or 1.100000000000000088817841970012523233890533447265625 in decimal.
That nearest value was and still is used in subsequent floating point
calculations.
What is new is how the number gets displayed. Formerly, Python used a
simple approach. The value of repr(1.1) was computed as format(1.1,
'.17g') which evaluated to '1.1000000000000001'. The advantage of
using 17 digits was that it relied on IEEE-754 guarantees to assure
that eval(repr(1.1)) would round-trip exactly to its original value.
The disadvantage is that many people found the output to be confusing
(mistaking intrinsic limitations of binary floating point
representation as being a problem with Python itself).
The new algorithm for repr(1.1) is smarter and returns '1.1'.
Effectively, it searches all equivalent string representations (ones
that get stored with the same underlying float value) and returns the
shortest representation.
The new algorithm tends to emit cleaner representations when possible,
but it does not change the underlying values. So, it is still the case
that 1.1 + 2.2 != 3.3 even though the representations may suggest
otherwise.
The new algorithm depends on certain features in the underlying
floating point implementation. If the required features are not found,
the old algorithm will continue to be used. Also, the text pickle
protocols assure cross-platform portability by using the old
algorithm.
(Contributed by Eric Smith and Mark Dickinson; issue 1580)
这在Python3.1中已经改变了。从what's new页:
你必须使用十进制。十进制如果你想让十进制完全按照你在世界上任何一台机器上指定的那样来表示。在
有关信息,请参阅Python手册:http://docs.python.org/library/decimal.html
你需要了解浮点数在计算机中的工作原理。在
基本上,并不是所有的十进制数都可以精确地存储,在这些情况下,您将得到最接近的可能的数字。有时候这种抽象会泄露,你就会看到错误。在
这可能是由于您描述的两个用例所使用的打印逻辑的差异造成的。我无法重新生成该行为(在Win64中使用python2.7.2)。在
如果您使用一个是完全可表示的数字,例如
1.5
,我想效果会消失。在相关问题 更多 >
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