[6.37] Random Number Generator Algorithm; [6.38] Finance Flash Application Function Finds Days Between Two Dates; [6.39] Convert Equations To A Parameterized Form - Texas Instruments TI-89 Tip List

when(a=b,0,á(1/x,x,a,b))

[6.37] Random number generator algorithm

For some simulations and Monte Carlo numerical methods, it is important that the random number
generator have a sufficiently long period. I emailed TI-cares concerning this. Here is the response:
The TI-89 and TI-92 Plus all use the same random number generator. Rand() creates
random numbers between 0 and 1.
The specific algorithm is described in a research contribution by L'ecuyer [1].
Essentially, this algorithm combines two multiplicative linear congruential generators to form
a single generator with extremely long period. Our particular implementation of random
number generator uses the first two sets of coefficients from Table III on page 747 of
reference [1].
This generator was submitted to several tests: equidistribution test, serial test, gap test,
poker test, coupon's collector test, permutation test, runs-up test, maximum-of-t test, and
collision test. The random number generator we implemented in these units passes all these
tests for randomness.
References.
1. L'ecuyer, P. Efficient and Portable Combined Random Number Generators.
Communications of the ACM, Vol. 31, Number 6 (June 1988), pp. 742-749, 774.

[6.38] Finance Flash Application function finds days between two dates

If you have installed the TI Finance flash application, you can use the dbd() function to find the number
of days between two dates, but both dates must be between the years 1950 and 2049. To call the
function, use
tifnance.dbd(date1,date2)
You can type this in the command line, or use [CATALOG] [F3] to paste it to the command line. The
format for the dates is either MM.DDYY or DDMM.YY. MM is the month, DD is the day of the month,
and YY is the last two digits of the year. Note that the decimal point distinguishes between the two
formats. For example, to find the number of days between January 15, 2001, and December 17, 2002,
use
tifnance.dbd(1.1501,12.1702)
which returns 701 days.

[6.39] Convert equations to a parameterized form

A function f(x,y) = 0 can be 'parameterized' by converting it into two other functions x(t) and y(t), where
t is the parameter. This functions x(t) and y(t) are not necessarily unique; there may be many functions
that give the same result f(x,y). This function applies one possible parameterization of x and y, namely
t = y/x.
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