Take 2

This time, we'll use math to get the precise angle that the magnetic field forms with the X and Y axes of the magnetometer.

We'll use the atan2 function. This function returns an angle in the -PI to PI range. The graphic below shows how this angle is measured:

atan2

Although not explicitly shown in this graph the X axis points to the right and the Y axis points up.

Here's the starter code. theta, in radians, has already been computed. You need to pick which LED to turn on based on the value of theta.

#![deny(unsafe_code)]
#![no_main]
#![no_std]

// You'll find this useful ;-)
use core::f32::consts::PI;

#[allow(unused_imports)]
use aux15::{entry, iprint, iprintln, prelude::*, switch_hal::OutputSwitch, Direction, I16x3};
// this trait provides the `atan2` method
use m::Float;

#[entry]
fn main() -> ! {
    let (leds, mut lsm303dlhc, mut delay, _itm) = aux15::init();
    let mut leds = leds.into_array();

    loop {
        let I16x3 { x, y, .. } = lsm303dlhc.mag().unwrap();

        let _theta = (y as f32).atan2(x as f32); // in radians

        // FIXME pick a direction to point to based on `theta`
        let dir = Direction::Southeast;

        leds.iter_mut().for_each(|led| led.off().unwrap());
        leds[dir as usize].on().unwrap();

        delay.delay_ms(100_u8);
    }
}

Suggestions/tips:

A whole circle rotation equals 360 degrees.
PI radians is equivalent to 180 degrees.
If theta was zero, what LED would you turn on?
If theta was, instead, very close to zero, what LED would you turn on?
If theta kept increasing, at what value would you turn on a different LED?

Discovery

Take 2