How can I get more than 49 digits of pi in a string?

Question

2quack 2019-12-25

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/498041-how-can-i-get-more-than-49-digits-of-pi-in-a-string

编辑： Adam Danz 2021-10-6

采纳的回答： John D'Errico

nums = num2str(pi,x);

Returns only 49 digits when x is greater than 49. How can I get it to return more digits?

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Adam Danz 2021-10-6

nums = num2str(pi,50)
nums = '3.141592653589793115997963468544185161590576171875'

Note that digits after the 15th decimal point are incorrect due to precision limits.

3.141592653589793115997963468544185161590576171875

Correct representation of pi to 50 dp:

3.14159265358979323846264338327950288419716939937510

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Answer 1

John D'Errico 2019-12-25

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https://ww2.mathworks.cn/matlabcentral/answers/498041-how-can-i-get-more-than-49-digits-of-pi-in-a-string#answer_407716

编辑：John D'Errico 2019-12-25

You could always download my HPF toolbox from the file exchange. It will provide 500100 digits of pi.

P = hpf('pi',500000);
cp = disp(P);
numel(cp)
ans =
      500001
      
cp(1:1001)
ans =
    '3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609433057270365759591953092186117381932611793105118548074462379962749567351885752724891227938183011949129833673362440656643086021394946395224737190702179860943702770539217176293176752384674818467669405132000568127145263560827785771342757789609173637178721468440901224953430146549585371050792279689258923542019956112129021960864034418159813629774771309960518707211349999998372978049951059731732816096318595024459455346908302642522308253344685035261931188171010003137838752886587533208381420617177669147303598253490428755468731159562863882353787593751957781857780532171226806613001927876611195909216420198'

So 1000 digits of pi, plus a decimal point.

As I recall, I even computed those digits using HPF itself just to test the tool, and verify it was working correctly. I'm not sure which series I used, but there are many good ones out there if you look carefully. You do need to be working with a tool that can handle high precision arithmetic. A double will not suffice.

Be careful with the last digit reported to make sure it was not rounded. For example, if you do this:

vpa(sym('pi'),1000)

the last 10 digits reported are ...9216420199

However, the true digits of pi in that vicinity run as: ...9216420198938095...

So the last digit reported by vpa is actually rounded up to a 9.

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Answer 2

David Goodmanson 2019-12-25

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https://ww2.mathworks.cn/matlabcentral/answers/498041-how-can-i-get-more-than-49-digits-of-pi-in-a-string#answer_407713

编辑：David Goodmanson 2019-12-26

Hi India,

vpa(pi,100) for example (although you need the symbolic toolbox for vpa)

And see Walter's comment below. The answer here is all right, but only by luck.

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Walter Roberson 2021-5-31

These days, Mathworks decided that sym('pi') should be a variable named pi and not Pi itself, so you are expected to count on sym(pi) being recognized as pi :(

Adam Danz 2021-10-6

编辑：Adam Danz 2021-10-6

digits(10000);
s=char(vpa(pi));

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Answer 3

David Hill 2019-12-25

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/498041-how-can-i-get-more-than-49-digits-of-pi-in-a-string#answer_407714

编辑：David Hill 2019-12-25

You could just make your own symbolic Pi.

digits 1000;
Pi=sym('3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989');