str2double with long string seems to give wrong answer

Question

Philip Masding 2024-2-29

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2088701-str2double-with-long-string-seems-to-give-wrong-answer

评论： VBBV 2024-3-1

Run in MATLAB on line

str='6879331413876961408';
num=str2double(str);
fprintf('%i',num)
6879331413876961280

6879331413876961280

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Stephen23 2024-2-29

在 MATLAB Online 中打开

"str2double with long string seems to give wrong answer"

No, it gives the correct answer: it gives you the DOUBLE value that is closest to that specified in the string.

Lets phrase it a different way: can you show us a DOUBLE value that is closer that specified in the string? (hint: no)

Lets try it right now:

str = '6879331413876961408';
num = str2double(str);
hex = num2hex(num)
hex = '43d7de12de40149c'
next_higher = hex2num('43d7de12de40149d');
next_lower  = hex2num('43d7de12de40149b');
fprintf('%.0f\n',next_lower,num,next_higher)
6879331413876960256
6879331413876961280
6879331413876962304

We can see that 1408 is closer to 1280 than either 0256 or 2304.

So your hypothesis that "str2double with long string seems to give wrong answer" is easily demonstrated to be incorrect. What is much much more likely is that you have not considered the implications of using finite precision binary floating point numbers.

Dyuman Joshi 2024-2-29

Description from str2double documentation - "X = str2double(str) converts the text in str to double precision values."

There's a significance of underlined part. You should read about it.

https://in.mathworks.com/help/matlab/matlab_prog/floating-point-numbers.html

https://en.wikipedia.org/wiki/Double-precision_floating-point_format

Also, note the data type of the output obtained in Walter's answer.

https://in.mathworks.com/help/matlab/numeric-types.html

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Answer 1

Walter Roberson 2024-2-29

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https://ww2.mathworks.cn/matlabcentral/answers/2088701-str2double-with-long-string-seems-to-give-wrong-answer#answer_1419031

在 MATLAB Online 中打开

format long g
str = '6879331413876961408';
num = sscanf(str, '%ld')
num = int64
   6879331413876961408

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Answer 2

John D'Errico 2024-2-29

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https://ww2.mathworks.cn/matlabcentral/answers/2088701-str2double-with-long-string-seems-to-give-wrong-answer#answer_1419011

编辑：John D'Errico 2024-2-29

在 MATLAB Online 中打开

Do you appreciate that str2double will convert the number to a DOUBLE PRECISION number? Of course it must, as why would it convert to something other than a double? MATLAB does not by default work in arbitrarily high precision. If it did, it would be relatively as slow as molasses on too many computations. And then people (maybe even you) would be complaining at how slow it was. So MATLAB uses doubles for almost all computations, unless you specifically use some other class. (syms, for example could store that number, or my own VPI or HPF classes.)

What is the maximum integer a double can store? (Exactly)

flintmax
ans = 9.0072e+15

which is 2^53-1, in case you care. Numbers large than flintmax, but less than realmax will see only the top (approximately) 16 digits retained. Anything below that becomes computational garbage. Is your number larger than flintmax?

6879331413876961408/flintmax
ans = 763.7592

So it is too large, by a factor of almost 1000. Note that the 3 least significant digits were wrong. Should that be a surprise here if the number if too large by a factor of 1000 to fit into a double exactly?

If you truly needed to store that number in some other class and you don't want to use the alternatives I mentioned, it turns out tht int64 or uint64 could do it exactly. For example:

6879331413876961408 < intmax('int64')
ans = logical
   1
uint64(6879331413876961408)
ans = uint64
    6879331413876961408

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Answer 3

VBBV 2024-2-29

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https://ww2.mathworks.cn/matlabcentral/answers/2088701-str2double-with-long-string-seems-to-give-wrong-answer#answer_1419001

fprintf('%d',num)

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Dyuman Joshi 2024-2-29

@VBBV, you can not use a format specifier for str2double. The input (if convertible to a double precision value) will always be converted to a double precision value (otherwise NaN will be the output).

VBBV 2024-3-1

在 MATLAB Online 中打开

str='6879331413876961408';
% num=str2double(str)
fprintf('%s',str)
6879331413876961408

As @Dyuman Joshi mentioned that using str2double and/or str2num functions will result in double precision values which are limited by significant 16 digits. @Philip Masding you can get same value if you use format specfifier for string %s

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