Python代表1/10
Python representing 1/10
我知道以 2 为底的机器无法准确表示某些以 10 为底的值，例如 1/10。我看过示例 using Python itself。在我的机器上：
Python 2.7.8 (default, Oct 18 2014, 12:50:18)
[GCC 4.9.1] on linux2
Type "help", "copyright", "credits" or "license" for more information.
>>> 1.0/10
0.1
为什么这里显示准确？
从 Python 2.7 和 3.1 开始，Python 使用最短的表示形式显示浮点数，在评估时，会产生相同的浮点数。来自 documentation:
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.
我知道以 2 为底的机器无法准确表示某些以 10 为底的值，例如 1/10。我看过示例 using Python itself。在我的机器上：
Python 2.7.8 (default, Oct 18 2014, 12:50:18)
[GCC 4.9.1] on linux2
Type "help", "copyright", "credits" or "license" for more information.
>>> 1.0/10
0.1
为什么这里显示准确？
从 Python 2.7 和 3.1 开始，Python 使用最短的表示形式显示浮点数，在评估时，会产生相同的浮点数。来自 documentation:
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
1.1which does not have an exact equivalent in binary floating point. Since there is no exact equivalent, an expression likefloat('1.1')evaluates to the nearest representable value which is0x1.199999999999ap+0in hex or1.100000000000000088817841970012523233890533447265625in 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 asformat(1.1, '.17g')which evaluated to'1.1000000000000001'. The advantage of using 17 digits was that it relied on IEEE-754 guarantees to assure thateval(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 != 3.3even 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.