How can I use the PulseAudio asynchronous library to play back raw PCM data?

Thus

/*
pcm-playback:   pcm-playback.c
    gcc -o pcm-playback pcm-playback.c `pkg-config --cflags --libs libpulse`
*/

#include <stdio.h>
#include <assert.h>
#include <pulse/pulseaudio.h>

#define FORMAT PA_SAMPLE_U8
#define RATE 44100

void context_state_cb(pa_context* context, void* mainloop);
void stream_state_cb(pa_stream *s, void *mainloop);
void stream_success_cb(pa_stream *stream, int success, void *userdata);
void stream_write_cb(pa_stream *stream, size_t requested_bytes, void *userdata);

int main(int argc, char *argv[]) {
    pa_threaded_mainloop *mainloop;
    pa_mainloop_api *mainloop_api;
    pa_context *context;
    pa_stream *stream;

    // Get a mainloop and its context
    mainloop = pa_threaded_mainloop_new();
    assert(mainloop);
    mainloop_api = pa_threaded_mainloop_get_api(mainloop);
    context = pa_context_new(mainloop_api, "pcm-playback");
    assert(context);

    // Set a callback so we can wait for the context to be ready
    pa_context_set_state_callback(context, &context_state_cb, mainloop);

    // Lock the mainloop so that it does not run and crash before the context is ready
    pa_threaded_mainloop_lock(mainloop);

    // Start the mainloop
    assert(pa_threaded_mainloop_start(mainloop) == 0);
    assert(pa_context_connect(context, NULL, PA_CONTEXT_NOAUTOSPAWN, NULL) == 0);

    // Wait for the context to be ready
    for(;;) {
        pa_context_state_t context_state = pa_context_get_state(context);
        assert(PA_CONTEXT_IS_GOOD(context_state));
        if (context_state == PA_CONTEXT_READY) break;
        pa_threaded_mainloop_wait(mainloop);
    }

    // Create a playback stream
    pa_sample_spec sample_specifications;
    sample_specifications.format = FORMAT;
    sample_specifications.rate = RATE;
    sample_specifications.channels = 2;

    pa_channel_map map;
    pa_channel_map_init_stereo(&map);

    stream = pa_stream_new(context, "Playback", &sample_specifications, &map);
    pa_stream_set_state_callback(stream, stream_state_cb, mainloop);
    pa_stream_set_write_callback(stream, stream_write_cb, mainloop);

    // recommended settings, i.e. server uses sensible values
    pa_buffer_attr buffer_attr; 
    buffer_attr.maxlength = (uint32_t) -1;
    buffer_attr.tlength = (uint32_t) -1;
    buffer_attr.prebuf = (uint32_t) -1;
    buffer_attr.minreq = (uint32_t) -1;

    // Settings copied as per the chromium browser source
    pa_stream_flags_t stream_flags;
    stream_flags = PA_STREAM_START_CORKED | PA_STREAM_INTERPOLATE_TIMING | 
        PA_STREAM_NOT_MONOTONIC | PA_STREAM_AUTO_TIMING_UPDATE |
        PA_STREAM_ADJUST_LATENCY;

    // Connect stream to the default audio output sink
    assert(pa_stream_connect_playback(stream, NULL, &buffer_attr, stream_flags, NULL, NULL) == 0);

    // Wait for the stream to be ready
    for(;;) {
        pa_stream_state_t stream_state = pa_stream_get_state(stream);
        assert(PA_STREAM_IS_GOOD(stream_state));
        if (stream_state == PA_STREAM_READY) break;
        pa_threaded_mainloop_wait(mainloop);
    }

    pa_threaded_mainloop_unlock(mainloop);

    // Uncork the stream so it will start playing
    pa_stream_cork(stream, 0, stream_success_cb, mainloop);

    // Play until we get a character
    getc(stdin);
}

void context_state_cb(pa_context* context, void* mainloop) {
    pa_threaded_mainloop_signal(mainloop, 0);
}

void stream_state_cb(pa_stream *s, void *mainloop) {
    pa_threaded_mainloop_signal(mainloop, 0);
}

void stream_write_cb(pa_stream *stream, size_t requested_bytes, void *userdata) {
    int bytes_remaining = requested_bytes;
    while (bytes_remaining > 0) {
        uint8_t *buffer = NULL;
        size_t bytes_to_fill = 44100;
        size_t i;

        if (bytes_to_fill > bytes_remaining) bytes_to_fill = bytes_remaining;

        pa_stream_begin_write(stream, (void**) &buffer, &bytes_to_fill);

        for (i = 0; i < bytes_to_fill; i += 2) {
            buffer[i] = (i%100) * 40 / 100 + 44;
            buffer[i+1] = (i%100) * 40 / 100 + 44;
        }

        pa_stream_write(stream, buffer, bytes_to_fill, NULL, 0LL, PA_SEEK_RELATIVE);

        bytes_remaining -= bytes_to_fill;
    }
}

void stream_success_cb(pa_stream *stream, int success, void *userdata) {
    return;
}