More n-bodies speedups

So I've been taking full advantage of the new #haskell-in-depth channel, and with the thanks of blackh and others, I've made a few more changes, and I've shaved another whole 30 seconds of my already not too shabby 1m17s. I'm now down to 47.215s, making a saving of 30s, or a saving of 39%.

If you're wondering what I'm on about, take a look at this post for the story of my n-bodies program so far, and this port for what my code looked like before.

So how did I do it this time? Well, I decided STRefs weren't necessary, and could easily be replaces with accumulating parameters in basically all of my code that used them. I did this in the hope they would be kept in registers, but even if they're not, it's still faster. I also saved about 3 seconds by inlining all my read* and write* functions with {-# INLINE #-} pragmas that would write or fetch the various parts of the Body's info. So here's the code, first the original one:

advance dt ps = do
    forM_ index1 $ \i -> do
        -- (B p v m) <- readBody ps i
        p <- readPos ps i
        v <- readVel ps i
        m <- readMass ps i
        vvar <- newSTRef v

        forM_ (index2 i) $ \j -> do
            -- (B p' v' m') <- readBody ps j
            p' <- readPos ps j
            v' <- readVel ps j
            m' <- readMass ps j
            let dp = p .-. p'
                dst = mag dp
                magnit = dt / (dst * dst * dst)
                change = magnit *. dp
                (sca1,sca2) = (m' *. change, m *. change)
            writeVel ps j (v' .+. sca2)
            modifySTRef vvar (.-. sca1)
        vvar'@(V nx ny nz) <- readSTRef vvar
        -- unsafeIOToST (print vvar')
        writeVel' ps i nx ny nz
        writePos ps i $ move' dt (B p vvar' m)

And the new one, with an inner loop:

advance dt ps =
    forM_ index1 $ \i -> do
        -- (B p v m) <- readBody ps i
        p <- readPos ps i
        v <- readVel ps i
        m <- readMass ps i
        let loop2 !j !v@(V !x !y !z) 
                | j > numPs = return v
                | otherwise  = do
                   p' <- readPos ps j
                   v' <- readVel ps j
                   m' <- readMass ps j
                   let dp = p .-. p'
                       dst = mag dp
                       magnit = dt / (dst * dst * dst)
                       change = magnit *. dp
                       (sca1,sca2) = (m' *. change, m *. change)
                   writeVel ps j (v' .+. sca2)
                   loop2 (j+1) (v .-. sca1)

        v' <- loop2 (i+1) v
        -- unsafeIOToST (print v')
        writeVel ps i v'
        writePos ps i $ move' dt (B p v' m)