added FP project

projects/PI/.vscode/settings.json

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+{
+	"cSpell.words": [
+		"scvtf"
+	]
+}

projects/PI/README.md

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+# 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:
+
+```text
+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:
+
+```text
+	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):
+
+```c++
+#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:
+
+```c++
+// 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.