xref: /src/sys/dev/midisyn.c

/*	$NetBSD: midisyn.c,v 1.21.38.1 2008/05/18 12:33:30 yamt Exp $	*/

/*
 * Copyright (c) 1998 The NetBSD Foundation, Inc.
 * All rights reserved.
 *
 * This code is derived from software contributed to The NetBSD Foundation
 * by Lennart Augustsson (augustss (at) NetBSD.org).
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 *
 * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS
 * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
 * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
 * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS
 * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
 * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
 * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
 * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
 * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
 * POSSIBILITY OF SUCH DAMAGE.
 */

#include <sys/cdefs.h>
__KERNEL_RCSID(0, "$NetBSD: midisyn.c,v 1.21.38.1 2008/05/18 12:33:30 yamt Exp $");

#include <sys/param.h>
#include <sys/ioctl.h>
#include <sys/fcntl.h>
#include <sys/vnode.h>
#include <sys/select.h>
#include <sys/proc.h>
#include <sys/malloc.h>
#include <sys/systm.h>
#include <sys/syslog.h>
#include <sys/kernel.h>
#include <sys/audioio.h>
#include <sys/midiio.h>
#include <sys/device.h>

#include <dev/audio_if.h>
#include <dev/midi_if.h>
#include <dev/midivar.h>
#include <dev/midisynvar.h>

#ifdef AUDIO_DEBUG
#define DPRINTF(x)	if (midisyndebug) printf x
#define DPRINTFN(n,x)	if (midisyndebug >= (n)) printf x
int	midisyndebug = 0;
#else
#define DPRINTF(x)
#define DPRINTFN(n,x)
#endif

int	midisyn_findvoice(midisyn *, int, int);
void	midisyn_freevoice(midisyn *, int);
uint_fast16_t	midisyn_allocvoice(midisyn *, uint_fast8_t, uint_fast8_t);
static void	midisyn_attackv_vel(midisyn *, uint_fast16_t, midipitch_t,
                                    int16_t, uint_fast8_t);

static midictl_notify midisyn_notify;

static midipitch_t midisyn_clamp_pitch(midipitch_t);
static int16_t midisyn_adj_level(midisyn *, uint_fast8_t);
static midipitch_t midisyn_adj_pitch(midisyn *, uint_fast8_t);
static void midisyn_chan_releasev(midisyn *, uint_fast8_t, uint_fast8_t);
static void midisyn_upd_level(midisyn *, uint_fast8_t);
static void midisyn_upd_pitch(midisyn *, uint_fast8_t);

int	midisyn_open(void *, int,
		     void (*iintr)(void *, int),
		     void (*ointr)(void *), void *arg);
void	midisyn_close(void *);
int	midisyn_sysrt(void *, int);
void	midisyn_getinfo(void *, struct midi_info *);
int	midisyn_ioctl(void *, u_long, void *, int, struct lwp *);

const struct midi_hw_if midisyn_hw_if = {
	midisyn_open,
	midisyn_close,
	midisyn_sysrt,
	midisyn_getinfo,
	midisyn_ioctl,
};

int	midisyn_channelmsg(void *, int, int, u_char *, int);
int	midisyn_commonmsg(void *, int, u_char *, int);
int	midisyn_sysex(void *, u_char *, int);

struct midi_hw_if_ext midisyn_hw_if_ext = {
	.channel = midisyn_channelmsg,
	.common  = midisyn_commonmsg,
	.sysex   = midisyn_sysex,
};

struct channelstate { /* dyamically allocated in open() on account of size */
	/* volume state components in centibels; just sum for overall level */
	int16_t volume;
	int16_t expression;
	/* pitch state components in midipitch units; sum for overall effect */
	midipitch_t bend;
	midipitch_t tuning_fine;
	midipitch_t tuning_coarse;
	/* used by bend handlers */
	int16_t bendraw;
	int16_t pendingreset;
/* rearrange as more controls supported - 16 bits should last for a while */
#define PEND_VOL 1
#define PEND_EXP 2
#define PEND_LEVEL (PEND_VOL|PEND_EXP)
#define PEND_PBS 4
#define PEND_TNF 8
#define PEND_TNC 16
#define PEND_PITCH (PEND_PBS|PEND_TNF|PEND_TNC)
#define PEND_ALL   (PEND_LEVEL|PEND_PITCH)
};

int
midisyn_open(void *addr, int flags, void (*iintr)(void *, int),
    void (*ointr)(void *), void *arg)
{
	midisyn *ms = addr;
	int rslt;
	uint_fast8_t chan;

	DPRINTF(("midisyn_open: ms=%p ms->mets=%p\n", ms, ms->mets));

	midictl_open(&ms->ctl);

	ms->chnstate = malloc(MIDI_MAX_CHANS*sizeof *(ms->chnstate),
	                      M_DEVBUF, M_WAITOK); /* init'd by RESET below */

	rslt = 0;
	if (ms->mets->open)
		rslt = (ms->mets->open(ms, flags));

	/*
	 * Make the right initial things happen by faking receipt of RESET on
	 * all channels. The hw driver's ctlnotice() will be called in turn.
	 */
	for ( chan = 0 ; chan < MIDI_MAX_CHANS ; ++ chan )
		midisyn_notify(ms, MIDICTL_RESET, chan, 0);

	return rslt;
}

void
midisyn_close(void *addr)
{
	midisyn *ms = addr;
	struct midisyn_methods *fs;
	int chan;

	DPRINTF(("midisyn_close: ms=%p ms->mets=%p\n", ms, ms->mets));
	fs = ms->mets;

	for (chan = 0; chan < MIDI_MAX_CHANS; chan++)
		midisyn_notify(ms, MIDICTL_SOUND_OFF, chan, 0);

	if (fs->close)
		fs->close(ms);

	free(ms->chnstate, M_DEVBUF);

	midictl_close(&ms->ctl);
}

void
midisyn_getinfo(void *addr, struct midi_info *mi)
{
	midisyn *ms = addr;

	mi->name = ms->name;
	/*
	 * I was going to add a property here to suppress midi(4)'s warning
	 * about an output device that uses no transmit interrupt, on the
	 * assumption that as an onboard synth we handle "output" internally
	 * with nothing like the 320 us per byte busy wait of a dumb UART.
	 * Then I noticed that opl (at least as currently implemented) seems
	 * to need 40 us busy wait to set each register on an OPL2, and sets
	 * about 21 registers for every note-on. (Half of that is patch loading
	 * and could probably be reduced by different management of voices and
	 * patches.) For now I won't bother suppressing that warning....
	 */
	mi->props = 0;

	midi_register_hw_if_ext(&midisyn_hw_if_ext);
}

int
midisyn_ioctl(void *maddr, u_long cmd, void *addr, int flag, struct lwp *l)
{
	midisyn *ms = maddr;

	if (ms->mets->ioctl)
		return (ms->mets->ioctl(ms, cmd, addr, flag, l));
	else
		return (EINVAL);
}

int
midisyn_findvoice(midisyn *ms, int chan, int note)
{
	u_int cn;
	int v;

	cn = MS_CHANNOTE(chan, note);
	for (v = 0; v < ms->nvoice; v++)
		if (ms->voices[v].chan_note == cn && ms->voices[v].inuse)
			return (v);
	return (-1);
}

void
midisyn_attach(struct midi_softc *sc, midisyn *ms)
{
	/*
	 * XXX there should be a way for this function to indicate failure
	 * (other than panic) if some preconditions aren't met, for example
	 * if some nonoptional methods are missing.
	 */
	if (ms->mets->allocv == 0) {
		ms->voices = malloc(ms->nvoice * sizeof (struct voice),
				    M_DEVBUF, M_WAITOK|M_ZERO);
		ms->seqno = 1;
		ms->mets->allocv = midisyn_allocvoice;
	}

	if (ms->mets->attackv_vel == 0 && ms->mets->attackv != 0)
		ms->mets->attackv_vel = midisyn_attackv_vel;

	ms->ctl = (midictl) {
		.base_channel = 16,
		.cookie = ms,
		.notify = midisyn_notify
	};

	sc->hw_if = &midisyn_hw_if;
	sc->hw_hdl = ms;
	DPRINTF(("midisyn_attach: ms=%p\n", sc->hw_hdl));
}

void
midisyn_freevoice(midisyn *ms, int voice)
{
	if (ms->mets->allocv != midisyn_allocvoice)
		return;
	ms->voices[voice].inuse = 0;
}

uint_fast16_t
midisyn_allocvoice(midisyn *ms, uint_fast8_t chan, uint_fast8_t note)
{
	int bestv, v;
	u_int bestseq, s;

	/* Find a free voice, or if no free voice is found the oldest. */
	bestv = 0;
	bestseq = ms->voices[0].seqno + (ms->voices[0].inuse ? 0x40000000 : 0);
	for (v = 1; v < ms->nvoice; v++) {
		s = ms->voices[v].seqno;
		if (ms->voices[v].inuse)
			s += 0x40000000;
		if (s < bestseq) {
			bestseq = s;
			bestv = v;
		}
	}
	DPRINTFN(10,("midisyn_allocvoice: v=%d seq=%d cn=%x inuse=%d\n",
		     bestv, ms->voices[bestv].seqno,
		     ms->voices[bestv].chan_note,
		     ms->voices[bestv].inuse));
#ifdef AUDIO_DEBUG
	if (ms->voices[bestv].inuse)
		DPRINTFN(1,("midisyn_allocvoice: steal %x\n",
			    ms->voices[bestv].chan_note));
#endif
	ms->voices[bestv].chan_note = MS_CHANNOTE(chan, note);
	ms->voices[bestv].seqno = ms->seqno++;
	ms->voices[bestv].inuse = 1;
	return (bestv);
}

/* dummy attackv_vel that just adds vel into level for simple drivers */
static void
midisyn_attackv_vel(midisyn *ms, uint_fast16_t voice, midipitch_t mp,
                    int16_t level_cB, uint_fast8_t vel)
{
	ms->voices[voice].velcB = midisyn_vol2cB((uint_fast16_t)vel << 7);
	ms->mets->attackv(ms, voice, mp, level_cB + ms->voices[voice].velcB);
}

int
midisyn_sysrt(void *addr, int b)
{
	return 0;
}

int midisyn_channelmsg(void *addr, int status, int chan, u_char *buf,
    int len)
{
	midisyn *ms = addr;
	int voice = 0;		/* initialize to keep gcc quiet */
	struct midisyn_methods *fs;

	DPRINTF(("midisyn_channelmsg: ms=%p status=%#02x chan=%d\n",
	       ms, status, chan));
	fs = ms->mets;

	switch (status) {
	case MIDI_NOTEOFF:
		/*
		 * for a device that leaves voice allocation to us--and that's
		 * all of 'em at the moment--the voice and release velocity
		 * should be the only necessary arguments to noteoff. what use
		 * are they making of note? checking... None. Cool.
		 * IF there is ever a device added that does its own allocation,
		 * extend the interface; this findvoice won't be what to do...
		 */
		voice = midisyn_findvoice(ms, chan, buf[1]);
		if (voice >= 0) {
			fs->releasev(ms, voice, buf[2]);
			midisyn_freevoice(ms, voice);
		}
		break;
	case MIDI_NOTEON:
		/*
		 * what's called for here, given current drivers, is an i/f
		 * where midisyn computes a volume from vel*volume*expression*
		 * mastervolume and passes that result as a single arg. It can
		 * evolve later to support drivers that expose some of those
		 * bits separately (e.g. a driver could expose a mixer register
		 * on its sound card and use that for mastervolume).
		 */
		voice = fs->allocv(ms, chan, buf[1]);
		ms->voices[voice].velcB = 0; /* assume driver handles vel */
		fs->attackv_vel(ms, voice,
		    midisyn_clamp_pitch(MIDIPITCH_FROM_KEY(buf[1]) +
		                        midisyn_adj_pitch(ms, chan)),
		    midisyn_adj_level(ms,chan), buf[2]);
		break;
	case MIDI_KEY_PRESSURE:
		/*
		 * unimplemented by the existing drivers. if we are doing
		 * voice allocation, find the voice that corresponds to this
		 * chan/note and define a method that passes the voice and
		 * pressure to the driver ... not the note, /it/ doesn't matter.
		 * For a driver that does its own allocation, a different
		 * method may be needed passing pressure, chan, note so it can
		 * find the right voice on its own. Be sure that whatever is
		 * done here is undone when midisyn_notify sees MIDICTL_RESET.
		 */
		break;
	case MIDI_CTL_CHANGE:
		midictl_change(&ms->ctl, chan, buf+1);
		break;
	case MIDI_PGM_CHANGE:
		if (fs->pgmchg)
			fs->pgmchg(ms, chan, buf[1]);
		break;
	case MIDI_CHN_PRESSURE:
		/*
		 * unimplemented by the existing drivers. if driver exposes no
		 * distinct method, can use KEY_PRESSURE method for each voice
		 * on channel. Be sure that whatever is
		 * done here is undone when midisyn_notify sees MIDICTL_RESET.
		 */
		break;
	case MIDI_PITCH_BEND:
		/*
		 * Will work for most drivers that simply render the midipitch
		 * as we pass it (but not cms, which chops all the bits after
		 * the note number and then computes its own pitch :( ). If the
		 * driver has a repitchv method for voices already sounding, so
		 * much the better.
		 * The bending logic lives in the handler for bend sensitivity,
		 * so fake a change to that to kick it off.
		 */
		ms->chnstate[chan].bendraw = buf[2]<<7 | buf[1];
		ms->chnstate[chan].bendraw -= MIDI_BEND_NEUTRAL;
		midisyn_notify(ms, MIDICTL_RPN, chan,
		               MIDI_RPN_PITCH_BEND_SENSITIVITY);
		break;
	}
	return 0;
}

int midisyn_commonmsg(void *addr, int status,
    u_char *buf, int len)
{
	return 0;
}

int midisyn_sysex(void *addr, u_char *buf, int len)
{
	/*
	 * unimplemented by existing drivers. it is surely more sensible
	 * to do some parsing of well-defined sysex messages here, either
	 * handling them internally or calling specific methods on the
	 * driver after parsing out the details, than to ask every driver
	 * to deal with sysex messages poked at it a byte at a time.
	 */
	return 0;
}

static void
midisyn_notify(void *cookie, midictl_evt evt,
               uint_fast8_t chan, uint_fast16_t key)
{
	struct midisyn *ms;
	int drvhandled;

	ms = (struct midisyn *)cookie;
	drvhandled = 0;
	if ( ms->mets->ctlnotice )
		drvhandled = ms->mets->ctlnotice(ms, evt, chan, key);

	switch ( evt | key ) {
	case MIDICTL_RESET:
		/*
		 * Re-read all ctls we use, revert pitchbend state.
		 * Can do it by faking change notifications.
		 */
		ms->chnstate[chan].pendingreset |= PEND_ALL;
		midisyn_notify(ms, MIDICTL_CTLR, chan,
		               MIDI_CTRL_CHANNEL_VOLUME_MSB);
		midisyn_notify(ms, MIDICTL_CTLR, chan,
		               MIDI_CTRL_EXPRESSION_MSB);
		ms->chnstate[chan].bendraw = 0; /* MIDI_BEND_NEUTRAL - itself */
		midisyn_notify(ms, MIDICTL_RPN, chan,
		               MIDI_RPN_PITCH_BEND_SENSITIVITY);
		midisyn_notify(ms, MIDICTL_RPN, chan,
		               MIDI_RPN_CHANNEL_FINE_TUNING);
		midisyn_notify(ms, MIDICTL_RPN, chan,
		               MIDI_RPN_CHANNEL_COARSE_TUNING);
		break;
	case MIDICTL_NOTES_OFF:
		if ( drvhandled )
			break;
		/* releasev all voices sounding on chan; use normal vel 64 */
		midisyn_chan_releasev(ms, chan, 64);
		break;
	case MIDICTL_SOUND_OFF:
		if ( drvhandled )
			break;
		/* releasev all voices sounding on chan; use max vel 127 */
		/* it is really better for driver to handle this, instantly */
		midisyn_chan_releasev(ms, chan, 127);
		break;
	case MIDICTL_CTLR | MIDI_CTRL_CHANNEL_VOLUME_MSB:
		ms->chnstate[chan].pendingreset &= ~PEND_VOL;
		if ( drvhandled ) {
			ms->chnstate[chan].volume = 0;
			break;
		}
		ms->chnstate[chan].volume = midisyn_vol2cB(
	    	    midictl_read(&ms->ctl, chan, key, 100<<7));
		midisyn_upd_level(ms, chan);
		break;
	case MIDICTL_CTLR | MIDI_CTRL_EXPRESSION_MSB:
		ms->chnstate[chan].pendingreset &= ~PEND_EXP;
		if ( drvhandled ) {
			ms->chnstate[chan].expression = 0;
			break;
		}
		ms->chnstate[chan].expression = midisyn_vol2cB(
	    	    midictl_read(&ms->ctl, chan, key, 16383));
		midisyn_upd_level(ms, chan);
		break;
	/*
	 * SOFT_PEDAL: supporting this will be trickier; must apply only
	 * to notes subsequently struck, and must remember which voices
	 * they are for follow-on adjustments. For another day....
	 */
	case MIDICTL_RPN | MIDI_RPN_PITCH_BEND_SENSITIVITY:
		ms->chnstate[chan].pendingreset &= ~PEND_PBS;
		if ( drvhandled )
			ms->chnstate[chan].bend = 0;
		else {
			uint16_t w;
			int8_t semis, cents;
			w = midictl_rpn_read(&ms->ctl, chan, key, 2<<7);
			semis = w>>7;
			cents = w&0x7f;
			/*
			 * Mathematically, multiply semis by
			 * MIDIPITCH_SEMITONE*bendraw/8192. Practically, avoid
			 * shifting significant bits off by observing that
			 * MIDIPITCH_SEMITONE == 1<<14 and 8192 == 1<<13, so
			 * just take semis*bendraw<<1. Do the same with cents
			 * except <<1 becomes /50 (but rounded).
			 */
			ms->chnstate[chan].bend =
			    ( ms->chnstate[chan].bendraw * semis ) << 1;
			ms->chnstate[chan].bend +=
			    ((ms->chnstate[chan].bendraw * cents)/25 + 1) >> 1;
			midisyn_upd_pitch(ms, chan);
		}
		break;
	case MIDICTL_RPN | MIDI_RPN_CHANNEL_FINE_TUNING:
		if ( drvhandled )
			ms->chnstate[chan].tuning_fine = 0;
		else {
			midipitch_t mp;
			mp = midictl_rpn_read(&ms->ctl, chan, key, 8192);
			/*
			 * Mathematically, subtract 8192 and scale by
			 * MIDIPITCH_SEMITONE/8192. Practically, subtract 8192
			 * and then << 1.
			 */
			ms->chnstate[chan].tuning_fine = ( mp - 8192 ) << 1;
			midisyn_upd_pitch(ms, chan);
		}
		break;
	case MIDICTL_RPN | MIDI_RPN_CHANNEL_COARSE_TUNING:
		ms->chnstate[chan].pendingreset &= ~PEND_TNC;
		if ( drvhandled )
			ms->chnstate[chan].tuning_coarse = 0;
		else {
			midipitch_t mp;
			/*
			 * By definition only the MSB of this parameter is used.
			 * Subtract 64 for a signed count of semitones; << 14
			 * will convert to midipitch scale.
			 */
			mp = midictl_rpn_read(&ms->ctl, chan, key, 64<<7) >> 7;
			ms->chnstate[chan].tuning_coarse = ( mp - 64 ) << 14;
			midisyn_upd_pitch(ms, chan);
		}
		break;
	}
}

static midipitch_t
midisyn_clamp_pitch(midipitch_t mp)
{
	if ( mp <= 0 )
		return 0;
	if ( mp >= MIDIPITCH_MAX )
		return MIDIPITCH_MAX;
	return mp;
}

static int16_t
midisyn_adj_level(midisyn *ms, uint_fast8_t chan)
{
	int32_t level;

	level = ms->chnstate[chan].volume + ms->chnstate[chan].expression;
	if ( level <= INT16_MIN )
		return INT16_MIN;
	return level;
}

static midipitch_t
midisyn_adj_pitch(midisyn *ms, uint_fast8_t chan)
{
	struct channelstate *s = ms->chnstate + chan;
	return s->bend + s->tuning_fine +s->tuning_coarse;
}

#define VOICECHAN_FOREACH_BEGIN(ms,vp,ch)			\
	{							\
		struct voice *vp, *_end_##vp;			\
		for (vp=(ms)->voices,_end_##vp=vp+(ms)->nvoice;	\
		    vp < _end_##vp; ++ vp) {			\
			if ( !vp->inuse )			\
				continue;			\
			if ( MS_GETCHAN(vp) == (ch) )		\
				;				\
			else					\
				continue;
#define VOICECHAN_FOREACH_END }}

static void
midisyn_chan_releasev(midisyn *ms, uint_fast8_t chan, uint_fast8_t vel)
{
	VOICECHAN_FOREACH_BEGIN(ms,vp,chan)
		ms->mets->releasev(ms, vp - ms->voices, vel);
		midisyn_freevoice(ms, vp - ms->voices);
	VOICECHAN_FOREACH_END
}

static void
midisyn_upd_level(midisyn *ms, uint_fast8_t chan)
{
	int32_t level;
	int16_t chan_level;
	if ( NULL == ms->mets->relevelv )
		return;

	if ( ms->chnstate[chan].pendingreset & PEND_LEVEL )
		return;

	chan_level = midisyn_adj_level(ms, chan);

	VOICECHAN_FOREACH_BEGIN(ms,vp,chan)
		level = vp->velcB + chan_level;
		ms->mets->relevelv(ms, vp - ms->voices,
		    level <= INT16_MIN ? INT16_MIN : level);
	VOICECHAN_FOREACH_END
}

static void
midisyn_upd_pitch(midisyn *ms, uint_fast8_t chan)
{
	midipitch_t chan_adj;

	if ( NULL == ms->mets->repitchv )
		return;

	if ( ms->chnstate[chan].pendingreset & PEND_PITCH )
		return;

	chan_adj = midisyn_adj_pitch(ms, chan);

	VOICECHAN_FOREACH_BEGIN(ms,vp,chan)
		ms->mets->repitchv(ms, vp - ms->voices,
		    midisyn_clamp_pitch(chan_adj +
		        MIDIPITCH_FROM_KEY(vp->chan_note&0x7f)));
	VOICECHAN_FOREACH_END
}

#undef VOICECHAN_FOREACH_END
#undef VOICECHAN_FOREACH_BEGIN

int16_t
midisyn_vol2cB(uint_fast16_t vol)
{
	int16_t cB = 0;
	int32_t v;

	if ( 0 == vol )
		return INT16_MIN;
	/*
	 * Adjust vol to fall in the range 8192..16383. Each doubling is
	 * worth 12 dB.
	 */
	while ( vol < 8192 ) {
		vol <<= 1;
		cB -= 120;
	}
	v = vol; /* ensure evaluation in signed 32 bit below */
	/*
	 * The GM vol-to-dB formula is dB = 40 log ( v / 127 ) for 7-bit v.
	 * The vol and expression controllers are in 14-bit space so the
	 * equivalent is 40 log ( v / 16256 ) - that is, MSB 127 LSB 0 because
	 * the LSB is commonly unused. MSB 127 LSB 127 would then be a tiny
	 * bit over.
	 * 1 dB resolution is a little coarser than we'd like, so let's shoot
	 * for centibels, i.e. 400 log ( v / 16256 ), and shift everything left
	 * as far as will fit in 32 bits, which turns out to be a shift of 22.
	 * This minimax polynomial approximation is good to about a centibel
	 * on the range 8192..16256, a shade worse (1.4 or so) above that.
	 * 26385/10166 is the 6th convergent of the coefficient for v^2.
	 */
	cB += ( v * ( 124828 - ( v * 26385 ) / 10166 ) - 1347349038 ) >> 22;
	return cB;
}

/*
 * MIDI RP-012 constitutes a MIDI Tuning Specification. The units are
 * fractional-MIDIkeys, that is, the key number 00 - 7f left shifted
 * 14 bits to provide a 14-bit fraction that divides each semitone. The
 * whole thing is just a 21-bit number that is bent and tuned simply by
 * adding and subtracting--the same offset is the same pitch change anywhere
 * on the scale. One downside is that a cent is 163.84 of these units, so
 * you can't expect a lengthy integer sum of cents to come out in tune; if you
 * do anything in cents it is best to use them only for local adjustment of
 * a pitch.
 *
 * This function converts a pitch in MIDItune units to Hz left-shifted 18 bits.
 * That should leave you enough to shift down to whatever precision the hardware
 * supports.
 *
 * Its prototype is exposed in <sys/midiio.h>.
 */
midihz18_t
midisyn_mp2hz18(midipitch_t mp)
{
	int64_t t64a, t64b;
	uint_fast8_t shift;

	/*
	 * Scale from the logarithmic MIDI-Tuning units to Hz<<18. Uses the
	 * continued-fraction form of a 2/2 rational function derived to
	 * cover the highest octave (mt 1900544..2097151 or 74.00.00..7f.7f.7f
	 * in RP-012-speak, the dotted bits are 7 wide) to produce Hz shifted
	 * left just as far as the maximum Hz will fit in a uint32, which
	 * turns out to be 18. Just shift off the result for lower octaves.
	 * Fit is within 1/4 MIDI tuning unit throughout (disclaimer: the
	 * comparison relied on the double-precision log in libm).
	 */

	if ( 0 == mp )
		return 2143236;

	for ( shift = 0; mp < 1900544; ++ shift )
		mp += MIDIPITCH_OCTAVE;

	if ( 1998848 == mp )
		return UINT32_C(2463438621) >> shift;

	t64a  = 0x5a1a0ee4; /* INT64_C(967879298788) gcc333: spurious warning */
	t64a |= (int64_t)0xe1 << 32;
	t64a /= mp - 1998848; /* here's why 1998848 is special-cased above ;) */
	t64a += mp - 3704981;
	t64b  = 0x6763759d; /* INT64_C(8405905567872413) goofy warning again */
	t64b |= (int64_t)0x1ddd20 << 32;
	t64b /= t64a;
	t64b += UINT32_C(2463438619);
	return (uint32_t)t64b >> shift;
}