Question

我正在尝试理解MatLab中的while语句，所以这就是我所做的：

i=0;
while i<=20
  disp(i)
  i=i+1;
end

正如我所料，MatLab显示的是0-20。但是有了这个：

j=0;
while j<=2
  disp(j)
  j=j+0.1;
end

MatLab仅显示数字0-1.9。我期待看到数字0-2;我在这做错了什么？

Answer 1

您的代码不是惯用的MATLAB。

惯用语MATLAB如下所示：

% This is technically the same as your code, 
% so it should have suffered from exactly the same problem. 
% But thanks to rearrangement of calculation, 
% MATLAB will calculate the number of iterations is with a division,
% which gives ((20 - 0) / 0.1 + 1) == 201
% Because the result value of 201 is a "small" integer, 
% the IEEE floating-point rounding logic will cause the result's  
% representation to be exactly 201, and not some plus/minus epsilon.
%
% I have to emphasize this is not always the case; sometimes
% division can give not-exactly-integer results as well.
%
% This "almost, but not quite always" correct behavior led most 
% beginning MATLAB users into thinking that MATLAB is less susceptible 
% to the intricacies of finite-precision floating point arithmetics, 
% but OP's code example shows that MATLAB users must exercise 
% the same level of care as programmers of C.
%
for j = 0:0.1:20, 
    disp(j); 
end

% Integer index range is accurate up to `(2^53) - 1`
% beware of off-by-one.
idx = (0:200) * 0.1; 
for j = idx, 
    disp(j); 
end

% If you only care about the start, stop, 
% and the number of generated values.
% Beware of off-by-one.
idx = linspace(0, 20, 201); 
for j = idx, 
    disp(j); 
end

Answer 2

它之所以不相同的原因是base-2浮点数可以完美而精确地表示1。但它们并不代表0.1。显然，0.1值代表一个微小的高位，如0.10000000000000000001，这样当0.10000000000000000001被添加到自身20次时，超过 2.0（这是精确表示的），因此在while循环中进行测试在我们期望它通过的最后一次迭代中失败。

MatLab浮点比较

2 个答案: