2.4.1 Using J to Estimate the Time to Evaluate fibonacci 100

First define the time verb using the external conjunction. time returns the time in seconds to evaluate the sentence given as its right input.

time =: 6 !: 2

Next, using the definition of fibonacci given in Section 2.3.2, determine the speed, in calls per sec to fibonacci, of fibonacci n for values of n not more than about 25. Note that you need to use the fib_work_iter function from Section 2.3.2 to compute these speeds. For example, on a RISC workstation you might measure this speed as:

   (fib_work_iter 20) % 10 time 'fibonacci 20'
2650.24

This measurement gives a speed of about 2650 calls per sec as determined by the average of 10 evaluations of fibonacci 20.

The next step of the experiment involves dividing fib_work_iter 100 by 2650 to obtain the estimate of the time in seconds to evaluate fibonacci 100. This division requires exact integer division which is expressed in J as:

   0 2650 #: 1146295688027634168201x
432564410576465723x 2251x

Ignoring the remainder of 2251 we have a result of 432564410576465723 seconds (the suffix "x" indicates an exact integer). Students performing this lab are always surprised to learn that this time is 13,716,527,478 years, 350 days, 4 hours, 55 minutes and 23 seconds. This result is easily expressed in J as:

   0 365 24 60 60 #: 432564410576465723x
13716527478x 350x 4x 55x 23x