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        my $cal_elapsed = ( time - $cal_t0 ) || 1e-9;
        my $iters
            = int( $cal_iters / $cal_elapsed * $target ) || 1;

        # Real timed run.
        my $t0 = time;
        $code->() for 1 .. $iters;
        my $elapsed = ( time - $t0 ) || 1e-9;
        $res{$name} = { iters => $iters, rate => $iters / $elapsed };
    }

    my @names = sort { $res{$a}{rate} <=> $res{$b}{rate} } keys %res;
    my $name_w = 1;
    for my $n (@names) { $name_w = length $n if length $n > $name_w }
    my $col_w = $name_w < 8 ? 8 : $name_w;

    printf "  %-*s  %10s", $name_w, '', 'Rate';
    printf "  %*s", $col_w, $_ for @names;
    print "\n";

    for my $a (@names) {
        printf "  %-*s  %10s", $name_w, $a, _fmt_rate( $res{$a}{rate} );
        for my $b (@names) {
            if ( $a eq $b ) {
                printf "  %*s", $col_w, '--';
                next;
            }
            my $pct
                = ( $res{$a}{rate} - $res{$b}{rate} )
                / $res{$b}{rate}
                * 100;
            printf "  %*s", $col_w, sprintf( '%+d%%', int($pct) );
        }
        print "\n";
    }
}

sub _fmt_rate {
    my $r = shift;
    return sprintf '%.2g/s', $r if $r < 1;
    return sprintf '%.2f/s', $r if $r < 100;
    return sprintf '%.0f/s',  $r;
}

# wall_rate($code, $secs) -- scalar ops/second over $secs wall-clock
# seconds.  Returns the rate as a plain number so callers can format
# their own tables.
#
# The measurement is split into 3 equal sub-windows and the median of
# their rates is returned.  At small workloads (a few hundred
# microseconds per call) OpenMP thread scheduling is non-deterministic
# enough that a single 2-second window can land in a slow stretch and
# report ~30x lower throughput than steady state; median across
# windows smooths that without spending extra time.
sub wall_rate {
    my ( $code, $secs ) = @_;
    $secs ||= 1;

    # Warm-up: at least 0.3 s (matches the original Perl bench() helper
    # this replaced) so OpenMP thread pools are firmly hot before any
    # measurement window starts.  Scales up for long budgets -- a 30 s
    # measurement gets a 3 s warmup.
    my $warmup = $secs * 0.1;
    $warmup = 0.3 if $warmup < 0.3;
    my $wt0 = time;
    $code->() while time - $wt0 < $warmup;

    my $WINDOWS  = 3;
    my $win_secs = $secs / $WINDOWS;
    my @rates;
    for ( 1 .. $WINDOWS ) {
        my $t0 = time;
        my $n  = 0;
        while ( time - $t0 < $win_secs ) { $code->(); $n++ }
        my $elapsed = ( time - $t0 ) || 1e-9;
        push @rates, $n / $elapsed;
    }
    my @s = sort { $a <=> $b } @rates;
    return $s[ int( @s / 2 ) ];
}

# wall_time_median($code, $reps) -- single warm-up + $reps timed
# invocations; returns the median elapsed time in seconds.  Use this
# when each call is expensive enough that running it on a $secs budget
# would either be wasteful (3 calls in 2 s tells you little more than
# 3 calls in 30 s) or pull in confounders like GC pauses.
sub wall_time_median {
    my ( $code, $reps ) = @_;
    $reps = 5 unless $reps && $reps >= 1;

    $code->();    # warm-up: covers Inline::C compile, first-touch cache

    my @times;
    for ( 1 .. $reps ) {
        my $t0 = time;
        $code->();
        push @times, time - $t0;
    }
    my @s = sort { $a <=> $b } @times;
    return $s[ int( @s / 2 ) ];
}

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