asm_book/projects/PI

Floating Point Programming

As a vehicle to practice using floating point instruction, this program will throw darts at a square with sides of two units. It turns out the fraction of darts that fall within the unit circle is... wait for it... PI.

The idea is to choose two random numbers from zero to one. Treat these as an x and y coordinate. Calculate the distance to the origin. If the distance puts the point inside the unit circle, record the trial as a hit.

Finally, divide the number of hits by the number of trials and multiply by four. The result will be an approximation of PI using stochastic methods.

Note this means we are throwing darts at one quadrant of a square with sides of 2 units, not the whole square. The difference means we must multiply by 4 at the end.

Number of trials to run

This will come from the command line as in:

user@comporg:~/pi $ ./a.out 100000
Executing: 100000 iterations.
Hits: 78443
Approximation: 3.137720
user@comporg:~/pi $

If the command line argument is not given, use a default of 100000.

Remember that all AARCH64 instructions are 32 bits long. An implication of this is you can't simply do:

	mov			x0, 1000000

Since the constant cannot fit along with op codes into four bytes. A way to get around this that comes readily to mind is to put the constant in RAM and ldr it into a register.

Vetting the command line argument

You are not responsible for doing this. Assume that all command line arguments are valid.

Converting command line argument to integer

atoi

Seeding the random number generator

In your previous C and C++ programs, you will have done (code snippets follow):

#include <ctime>

srand((unsigned int) time(nullptr));

You must seed the RNG in this way. But in assembly language.

Getting a random number in the right range

rand() returns an integer between 0 and RAND_MAX. In C and C++ you would do:

// Produces result between 0 and very very close to 1.
float v = float(rand()) / float(RAND_MAX);

You must do this in your program. What value is RAND_MAX? Write a tiny C++ program on the ARM and print out the value. Or, put RANDMAX into an IDE and ask the IDE to locate the definition.

You must write a subroutine (function) which returns a random number in the right range. Call it randf so I can find it easily.

Converting integers to doubles

In the above, the integers were converted to floats with a cast. In assembly language you must code the instructions which perform the cast yourself. Look up scvtf which stands for "signed convert to float".

FP registers

Just like x0 through x30, there exists d0 through d30. Among the float registers, d29 and d30 are not special. However, non-scratch float registers must still be saved and restored in functions.

FP ops

You'll use instructions like fmul, fdiv, fsqrt, fmov and fcmp.

Printing FP

printf will be your friend. Like always, the format string address goes in x0. A %f found in the format string tells printf to look in the FP registers starting with d0 as the first value.