CGContextDrawImage draws large images very blurry

I'm trying to make an object that can draw a portion of a large (say 2048 x 1537) image using CGContextDrawImage(…). It works just fine, except that it is extremely blurry. I'm using a "drawingController" which overrides drawLayer:inContext: like this

-(void)drawLayer:(CALayer *)layer inContext:(CGContextRef)ctx{
    CGImageRef drawImage = CGImageRetain(imageToDraw);
    if(drawImage) {
        CGRect drawRect = CGRectMake(0, 0, 1024, 748);//Just hard coded to my window size for now.
        CGContextSetInterpolationQuality(ctx, kCGInterpolationHigh);
        CGContextDrawImage(ctx, drawRect, drawImage);
    }
    CGImageRelease(drawImage);
}

And this is how I set up my custom image hosting view:

- (id)initWithFrame:(NSRect)frame
{
    self = [super initWithFrame:frame];
    if (self) {
        // Initialization code here.
        NSString *filePath = [[NSBundle mainBundle] pathForResource:@"large" ofType:@"jpg"];
        CGImageRef imageRef = [self createCGImageFromFilePath:filePath];


        drawingController = [[DrawingLayerController alloc] init];
        drawingController.imageToDraw = imageRef;

        [self setWantsLayer:YES];
        imageLayer = [[CALayer alloc] init];
        imageLayer.frame = self.bounds;
        imageLayer.drawsAsynchronously = YES;
        imageLayer.delegate = drawingController;
        [self.layer addSublayer:imageLayer];

        imageLayer.contentsRect = CGRectMake(0.5, 0.265452179, 0.5, 0.486662329); //Just an example contents rect.
        imageLayer.drawsAsynchronously = YES;

        [imageLayer setNeedsDisplay];
        [imageLayer displayIfNeeded];
    }
    return self;
}

Here is a portion of the image produced along side the source image at a similar zoom scale opened in Preview, so you can see just how blurry the image is as compared to the source image.

As you can see, the image produced by my code looks HORRIBLE. What is up with that?

Also, just for completeness, I have tried using a CATiledLayer for my imageLayer. The resulting image looks just as awful.

One final note: The code needs to be compatible with iOS AND OSX, but I am doing all my testing on OSX.

EDIT: Thanks to @Andrea, I've added the following above CGContextDrawImage(…)

CGFloat scale = MAX(1,MAX(CGImageGetWidth(drawImage)/drawRect.size.width,CGImageGetHeight(drawImage)/drawRect.size.height));

layer.contentsScale = scale;

I don't know exactly for osx but I can give you some advices.

Check the contentScale property as stated in commets, I wrote also a question about it, but I never had a real answer
Most of time blurriness is due to unmatching pixel, this asks to the system to apply antialiasing on the image, I see that you set a contentsRect this, with the contentsGravity, probably could change proportion and scaling of the image turning it into a blur one. Here a good answer about it.
Which is your contentGravity?
Keep it simple in first try, do you really need to draw async?

Hope this helps.