HW 3, problem 1.22

By Nasser Abbasi, PHY 240, feb 2, 2002.

Part (A)

Source code

function [realPart,powerToTen] =nma_doubleFactorial(n)

% FUNCTION [realPart,powerToTen]=nma_doubleFactorial(n)

%

% compute double factorial of a number using the equation

% n!! = n (n-2) (n-4) .... 6 x 4 x 2 for even n

% 5 x 3 x 1 for odd n

%

% INPUT

% n: The number to find double factorial for.

% OUTPUT

% output is returned in the form of [realPart,powerOfTen]

% where n!! = realPart x 10^(powerToTen)

%

% realPart : the value in the above expression.

% powerToTen : the power to raise 10 to as shown in the above expression.

%

% This program also prints the final n!! number for

% display purposes.

% by Nasser Abbasi

% HW 3, 1.22. PHY 240, Feb 2, 2002

if nargin ~=1

error('missing input argument');

end

if n <= 0

error('positive value is expected');

end

v=0;

savedN= n;

while 1

v= v + log10(n);

n=n-2;

if n <= 0

powerToTen = floor(v);

realPart = v - powerToTen;

% since log10(n!!) = A + B

% so, n!! = 10 ^(A+B) = 10^A * 10^B

% where A is the powerToTen, and 10^B will be the realPart.

realPart = 10^realPart;

disp(sprintf('%d!! = %f x 10^%d',savedN,realPart,powerToTen));

return;

end

end

OUTPUT

» help nma_doubleFactorial

FUNCTION [realPart,powerToTen]=nma_doubleFactorial(n)

compute double factorial of a number using the equation

n!! = n (n-2) (n-4) .... 6 x 4 x 2 for even n

5 x 3 x 1 for odd n

INPUT

n: The number to find double factorial for.

OUTPUT

output is returned in the form of [realPart,powerOfTen]

where n!! = realPart x 10^(powerToTen)

realPart : the value in the above expression.

powerToTen : the power to raise 10 to as shown in the above expression.

This program also prints the final n!! number for

display purposes.

Example 1

» [A,B]=nma_doubleFactorial(1000)

1000!! = 3.993984 x 10^1284

A =

3.9940

B =

1284

Example 2

»

»

» clear all

» [A,B]=nma_doubleFactorial(2001)

2001!! = 1.539068 x 10^2870

A =

1.5391

B =

2870

Example 3

»

»

»

» clear all

» [A,B]=nma_doubleFactorial(10000)

10000!! = 5.972727 x 10^17830

A =

5.9727

B =

17830

Example 4

»

»

»

» clear all

» [A,B]=nma_doubleFactorial(314159)

314159!! = 4.313460 x 10^795273

A =

4.3135

B =

795273

»