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matlabprinting
zeus_masta_funk
zeus_masta_funk

Reputation: 1498

Have MATLAB print full 2^64 value

I'm trying to print the value:

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

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

fomat long

and

sprintf('%20d',ans)

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

1.844674406511962e+19

or something to that effect. Any advice?

Upvotes: 2

Views: 433

Answers (3)

chappjc
chappjc

Reputation: 30589

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).

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

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

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

The solution is to use the unsigned integer format: %u.

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

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

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

Close. double almost got lucky.

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

Upvotes: 3

Emin Bugra Saral
Emin Bugra Saral

Reputation: 3786

To turn the scientific notation off, try this:

format long g

Upvotes: 0

Daniel
Daniel

Reputation: 36720

You must increase the precision, which is the number following the . in the format spec:

sprintf('%.20d',ans)

Upvotes: 1

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