trees: show its phases as N of M, with progress, elapsed time and ETA (closes #113)

trees now runs in four phases, open, read, group and write, each under
the progress display scan uses, until the summary line. open covers a
wait on a busy database. read counts the records and reads them in one
read-only transaction, so the two agree during a scan; group counts the
directories, and write the groups. The rows reach stdout through a
writer that clears the display and holds its lock while writing, so no
row shares a line with the display on a shared terminal. Each rate
names what its phase counts.

Judgement call: opening the database is a phase of its own, so there are four phases, not the three the issue sketches.

Model: opus-5-5

progress.go

@@ -2,6 +2,7 @@ package main
 
 import (
 	"fmt"
+	"io"
 	"math"
 	"os"
 	"slices"
@@ -72,6 +73,7 @@ func phaseLabel(phases []string, phase string) string {
 // progressParams describe one phase's progress display as it starts.
 type progressParams struct {
 	label      string // the phase and its place, from phaseLabel
+	unit       string // what the phase counts, as "files"
 	total      int64  // the items the phase will complete; -1 when not known
 	estimate   bool   // total is an estimate, which the count may pass
 	waitingFor string // what the phase waits for until setTotal is called
@@ -90,7 +92,8 @@ type progressParams struct {
 // below it. Every method must be called from the main goroutine. A nil
 // *progress is a valid no-display receiver: every method is a no-op, so
 // batched database flushes during the hash phase can reuse the update
-// phase's helpers without rendering anything.
+// phase's helpers without rendering anything, and its writer writes
+// with no display to clear.
 type progress struct {
 	width func() int    // reads the terminal's width; nil when not a TTY
 	stop  chan struct{} // closed by finish to end the draws
@@ -101,6 +104,7 @@ type progress struct {
 	withBar    bool                     // bar is the library's bar, not its spinner
 	widest     int                      // the widest line bar has drawn, in columns
 	label      string
+	unit       string
 	total      int64
 	estimate   bool
 	waitingFor string
@@ -128,8 +132,9 @@ func startProgress(params progressParams, width func() int,
 	now := time.Now()
 	p := &progress{
 		width: width, stop: make(chan struct{}), done: make(chan struct{}),
-		label: params.label, total: params.total, estimate: params.estimate,
-		waitingFor: params.waitingFor, start: now, rateStart: now,
+		label: params.label, unit: params.unit, total: params.total,
+		estimate: params.estimate, waitingFor: params.waitingFor,
+		start: now, rateStart: now,
 	}
 
 	// Show the zero state at once: the first item may take minutes,
@@ -287,6 +292,56 @@ func (p *progress) warnf(format string, args ...any) {
 	fmt.Fprintln(os.Stderr, msg)
 }
 
+// progressWriter writes a phase's output to out, which may be the
+// terminal the phase's display is drawn on, as stdout is in a plain
+// "sfdupes trees". It holds what is written to it and writes that to
+// out in pieces of about ioBufSize bytes, each under the display's
+// lock with the display cleared first, as warnf does for a warning: no
+// draw lands in the middle of a piece, and the next draw shows the
+// display again, on the line below. Every write to it must end with a
+// newline, as a row written with one fmt.Fprintf does, so that each
+// piece ends a line. Flush writes what it holds once the last row is
+// written.
+type progressWriter struct {
+	p   *progress
+	out io.Writer
+	buf []byte
+}
+
+// writer returns a progressWriter writing to out around p's display.
+func (p *progress) writer(out io.Writer) *progressWriter {
+	return &progressWriter{p: p, out: out}
+}
+
+// Write holds b, and writes what it holds to out once that comes to
+// ioBufSize bytes.
+func (w *progressWriter) Write(b []byte) (int, error) {
+	w.buf = append(w.buf, b...)
+	if len(w.buf) < ioBufSize {
+		return len(b), nil
+	}
+
+	return len(b), w.Flush()
+}
+
+// Flush writes what w holds to out, with the display cleared first and
+// not drawn again until it is written.
+func (w *progressWriter) Flush() error {
+	if w.p != nil {
+		w.p.mu.Lock()
+		defer w.p.mu.Unlock()
+
+		if w.p.bar != nil {
+			_ = w.p.bar.Clear()
+		}
+	}
+
+	_, err := w.out.Write(w.buf)
+	w.buf = w.buf[:0]
+
+	return err
+}
+
 // finish ends the phase's display, drawn once more as the phase ends.
 // A phase stopped short of its total, as an interrupted one is, shows
 // the count it stopped at rather than a full bar.
@@ -311,9 +366,9 @@ func (p *progress) finish() {
 //
 //	[3/5] hash: [1234/5000] 25%, 300 files/s, elapsed 4s, eta 13s
 //
-// without the percent when percent is false, as before the library's
-// bar, which shows its own. A phase with no total shows the items done
-// instead, or what it waits for.
+// where "files" is the phase's unit, without the percent when percent
+// is false, as before the library's bar, which shows its own. A phase
+// with no total shows the items done instead, or what it waits for.
 //
 // The phase and its place, the progress, the elapsed time and the ETA
 // are kept whole. A line wider than room leaves out the rate, or what
@@ -337,7 +392,7 @@ func (p *progress) line(room int, percent bool) (string, bool) {
 		}
 
 		head = p.label + ": " + p.itemsDone(percent) + ", "
-		extra = fmt.Sprintf("%.0f files/s", rate)
+		extra = fmt.Sprintf("%.0f %s/s", rate, p.unit)
 		tail = fmt.Sprintf("elapsed %s, eta %s", elapsed, p.eta(rate))
 	}
 
@@ -355,11 +410,11 @@ func (p *progress) line(room int, percent bool) (string, bool) {
 
 // itemsDone formats the items done, as "[1234/5000] 25%", with "~"
 // before a total that is an estimate and without the percent when
-// percent is false, or as "1234 files" when the phase has no total.
-// p.mu must be held.
+// percent is false, or as "1234 files", in the phase's unit, when the
+// phase has no total. p.mu must be held.
 func (p *progress) itemsDone(percent bool) string {
 	if p.total < 0 {
-		return fmt.Sprintf("%d files", p.count)
+		return fmt.Sprintf("%d %s", p.count, p.unit)
 	}
 
 	approx := ""