Increase Precision of Numeric Calculations - MATLAB & Simulink (2024)

Increase Precision of Numeric Calculations

By default, MATLAB^® uses 16 digits of precision. For higherprecision, use the vpa functionin Symbolic Math Toolbox™. vpa provides variableprecision which can be increased without limit.

When you choose variable-precision arithmetic, by default, vpa uses32 significant decimal digits of precision. For details, see Choose Numeric or Symbolic Arithmetic. You can seta higher precision by using the digits function.

Approximate a sum using the default precision of 32 digits.If at least one input is wrapped with vpa, allother inputs are converted to variable precision automatically.

vpa(1/3) + 1/2

ans =0.83333333333333333333333333333333

You must wrap all inner inputs with vpa,such as exp(vpa(200)). Otherwise, the inputs areautomatically converted to double by MATLAB.

Increase the precision to 50 digits by using digits andsave the old value of digits in digitsOld.Repeat the sum.

digitsOld = digits(50);sum50 = vpa(1/3) + 1/2

sum50 =0.83333333333333333333333333333333333333333333333333

Restore the old value of digits for further calculations.

digits(digitsOld)

Check the current digits setting by calling digits.

digits

Digits = 32

Change the precision for a single vpa callby specifying the precision as the second input to vpa.This call does not affect digits. For example,approximate pi with 100 digits.

vpa(pi,100)

ans =3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117068

digits% digits remains 32

Digits = 32

Variable precision can be increased arbitrarily. Find pi to 500 digits.

digitsOld = digits(500);vpa(pi)digits(digitsOld)

ans =3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491

digits and vpa controlthe number of significant decimal digits. Forexample, approximating 1/111 with four-digit accuracyreturns six digits after the decimal point because the first two digitsare zeros.

vpa(1/111,4)

ans =0.009009