让MATLAB打印完整的2 ^ 64值 [英] Have MATLAB print full 2^64 value

问题描述

我正在尝试打印值:

(2^32 - 1) * (2^32 - 1)

在MATLAB中显示所有20位数字.我已经尝试过

in MATLAB and have it display all 20 digits. I've tried

fomat long

和

sprintf('%20d',ans)

这些都没有得到我想要的结果并打印:

Neither of these are getting the results I want and print:

1.844674406511962e+19

或类似的东西.有什么建议吗?

or something to that effect. Any advice?

推荐答案

您应该期望%d将整数打印为整数，不需要精度或字段宽度说明，而无需使用指数表示法(%e ). sprintf无法将此整数显示为整数是有原因的.这就是原因(以及更多).

You are right to expect %d to print an integer as an integer, requiring no precision or field width specification, rather than in exponential notation (%e). There is a reason why sprintf fails to display this integer as an integer. Here's why (and more).

根据 sprintf文档，这是%d指定的输出格式:

From the sprintf documentation, this is the output format that %d specifies:

整数，已签名； %d或%i; 底数10

Integer, signed; %d or %i; Base 10

此处的关键字是 signed .这个确实指定一个以十进制(以10为底)表示法打印的整数，但是占用一个位！您(和%d)可以用 64位带符号整数(即

The keyword here is signed. This does specify an integer printed in decimal (base 10) notation, but the sign takes up one bit! The largest integer you (and %d) can represent with a 64-bit signed integer (i.e. int64) is 2^63-1 (check with intmax('int64')). And since (2^32 - 1) * (2^32 - 1) > 2^63-1, sprintf falls back to exponential notation (%e). But don't take my word for it:

>> sprintf('%d',uint64(2^63)-1)
ans =
9223372036854775807
>> sprintf('%d',uint64(2^63))
ans =
9.223372e+18

解决方案是使用 unsigned 整数格式:%u.

>> sprintf('%u',uint64(2^63))
ans =
9223372036854775808

使用(2^32 - 1) * (2^32 - 1)时，问题不太明显，但是解决方案是相同的:

With (2^32 - 1) * (2^32 - 1), the issue is less subtle, but the solution is the same:

>> val = (2^32 - 1) * (2^32 - 1); % > 2^63-1
>> sprintf('%u',val)
ans =
18446744065119617024

这回答了问题，但这仍然是错误.这次不是sprintf的错.双精度(64位)浮点数只能表示整数最多2 ^ 53 而不会丢失精度 ¹ .由于MATLAB中的默认数据类型为double，因此val被存储为double.为确保不损失精度，请使用uint64类型:

This answers the question, but this is still wrong. This time it's not sprintf's fault. Double precision (64-bit) floating point numbers can only represent integers up to 2^53 without loss of precision¹. Since the default data type in MATLAB is double, val is stored as a double. To ensure no loss of precision, use the uint64 type:

>> valUI = uint64(2^32 - 1) * uint64(2^32 - 1)
>> sprintf('%u',valUI)
ans =
18446744065119617025

关闭. double几乎很幸运.

¹ 此值2 ^ 53(或9,007,199,254,740,992)可以通过 flintmax('double') .

¹This value of 2^53 (or 9,007,199,254,740,992) can be verified by flintmax('double').

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