HP Prime: Operations with Large Numbers

[Eddie W. Shore]

Large Factorial (Version 2) - HP Prime

EXPORT LFACT(N)

BEGIN

LOCAL K,S,A;

FOR K FROM 2 TO N DO

S:=S+LOG(K);

END;

RETURN { ALOG(FP(S)), IP(S) };

END;

This is an approximation!  Results:  {mantissa, exponent}.  To be interpreted like this: mantissa * 10^exponent

Examples (compared with actual calculations with HP 50g):

55!

LFACT: 1.2696403353 * 10^73

Actual: 1.26964033537 * 10^73

65!

LFACT: 8.24765059247 * 10^90

Actual: 8.24765059208 * 10^90

75!

LFACT: 2.48091408072 * 10^109

Actual: 2.48091408114 * 10^109

125!

LFACT: 1.88267716466 * 10^209

Actual: 1.88267717689 * 10^209

245!

LFACT: 3.44638099725 * 10^480

Actual: 3.44638108855 * 10^480

525! 

LFACT: 6.89080261728 * 10^1201

Actual: 6.89080262404 * 10^1201

875!

LFACT: 1.31677044437 * 10^2196

Actual: 1.31677038751 * 10^2196


Large Powers - HP Prime

EXPORT LPWR(X,Y)

BEGIN

LOCAL S;

S:=Y*LOG(K);

RETURN { ALOG(FP(S)), IP(S) };

END;

This is an approximation!  Results:  {mantissa, exponent}.  To be interpreted like this: mantissa * 10^exponent

Examples (compared with actual calculations with HP 50g):

50^38

LPWR: 3.63797880819 * 10^64

Actual: 3.63797880709 * 10^64

102^68:

LPWR: 3.84425050422 * 10^136

Actual: 3.84425050254 * 10^136

58^124:

LPWR: 4.624568333 * 10^218

Actual: 4.62456834156 * 10^218

302^219:

LPWR: 1.32288017481 * 10^543

Actual: 1.32288017363 * 10^543