[mLib] / test / bench.c

/* -*-c-*-
 *
 * Benchmarking support
 *
 * (c) 2023 Straylight/Edgeware
 */

/*----- Licensing notice --------------------------------------------------*
 *
 * This file is part of the mLib utilities library.
 *
 * mLib is free software: you can redistribute it and/or modify it under
 * the terms of the GNU Library General Public License as published by
 * the Free Software Foundation; either version 2 of the License, or (at
 * your option) any later version.
 *
 * mLib is distributed in the hope that it will be useful, but WITHOUT
 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
 * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Library General Public
 * License for more details.
 *
 * You should have received a copy of the GNU Library General Public
 * License along with mLib.  If not, write to the Free Software
 * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307,
 * USA.
 */

/*----- Header files ------------------------------------------------------*/

#include "config.h"

#include <ctype.h>
#include <errno.h>
#include <stdarg.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <time.h>

#include "alloc.h"
#include "bench.h"
#include "bits.h"
#include "dstr.h"
#include "linreg.h"
#include "macros.h"

/*----- Data structures ---------------------------------------------------*/

enum { CLK, CY, NTIMER };

struct timer {
  struct bench_timer _t;
  const struct timer_ops *ops[NTIMER];  /* subtimers for clock and cycles */
  union { int fd; } u_cy;               /* state for cycle measurement */
};

struct timer_ops {
  const char *name;                     /* timer name */
  unsigned f;                           /* flags */
#define TF_SECRET 1u                    /*   don't try this automatically */
  int (*init)(struct timer */*t*/);     /* initialization function */
  void (*now)(struct bench_time *t_out, struct timer *t); /* read current */
  void (*teardown)(struct timer *t);    /* release held resources */
};

/*----- Preliminaries -----------------------------------------------------*/

#define NS_PER_S 1000000000

/* --- @debug@ --- *
 *
 * Arguments:   @const char *fmt@ = format control string
 *              @...@ = format arguemnts
 *
 * Returns:     ---
 *
 * Use:         Maybe report a debugging message to standard error.
 */

static PRINTF_LIKE(1, 2) void debug(const char *fmt, ...)
{
  const char *p;
  va_list ap;

  p = getenv("MLIB_BENCH_DEBUG");
  if (p && *p != 'n' && *p != '0') {
    va_start(ap, fmt);
    fputs("mLib BENCH: ", stderr);
    vfprintf(stderr, fmt, ap);
    fputc('\n', stderr);
    va_end(ap);
  }
}

/* --- @timer_diff@ --- *
 *
 * Arguments:   @struct bench_timing *delta_out@ = where to putt the result
 *              @const struct bench_time *t0, *t1@ = two times captured by a
 *                      timer's @now@ function
 *
 * Returns:     ---
 *
 * Use:         Calculates the difference between two captured times.  The
 *              flags are set according to whether the differences are
 *              meaningful; @delta_out->n@ is left unset.
 */

static void timer_diff(struct bench_timing *delta_out,
                       const struct bench_time *t0,
                       const struct bench_time *t1)
{
  unsigned f = t0->f&t1->f;
  kludge64 k;

#ifdef HAVE_UINT64
#  define FLOATK64(k) ((double)(k).i)
#else
#  define FLOATK64(k) ((double)(k).lo + 4275123318.0*(double)(k).hi)
#endif

  if (!(f&BTF_TIMEOK))
    delta_out->t = 0.0;
  else {
    SUB64(k, t1->s, t0->s);
    delta_out->t = FLOATK64(k) - 1 +
      (t1->ns + NS_PER_S - t0->ns)/(double)NS_PER_S;
  }

  if (!(f&BTF_CYOK))
    delta_out->cy = 0.0;
  else {
    SUB64(k, t1->cy, t0->cy);
    delta_out->cy = FLOATK64(k);
  }

  delta_out->f = f;

#undef FLOATK64
}

/*----- The null timer ----------------------------------------------------*/

/* This is a timer which does nothing, in case we don't have any better
 * ideas.
 */

static int null_init(struct timer *t) { return (0); }
static void null_now(struct bench_time *t_out, struct timer *t) { ; }
static void null_teardown(struct timer *t) { ; }

static const struct timer_ops null_ops =
  { "null", 0, null_init, null_now, null_teardown };
#define NULL_ENT &null_ops,

/*----- The broken clock --------------------------------------------------*/

/* This is a cycle counter which does nothing, in case we don't have any
 * better ideas.
 */

static int broken_init(struct timer *t) { return (-1); }

static const struct timer_ops broken_ops =
  { "broken", TF_SECRET, broken_init, null_now, null_teardown };
#define BROKEN_ENT &broken_ops,

/*----- Linux performance counters ----------------------------------------*/

/* This is a cycle counter which uses the Linux performance event system,
 * which is probably the best choice if it's available.
 */

#if defined(HAVE_LINUX_PERF_EVENT_H) && defined(HAVE_UINT64)

#include <sys/types.h>
#include <unistd.h>

#include <linux/perf_event.h>
#include <asm/unistd.h>

static void perfevent_now(struct bench_time *t_out, struct timer *t)
{
  ssize_t n;

  n = read(t->u_cy.fd, &t_out->cy.i, sizeof(t_out->cy.i));
    if (n != sizeof(t_out->cy.i)) {
      debug("failed to read perf-event counter: %s", strerror(errno));
      return;
    }
  t_out->f |= BTF_CYOK;
}

static void perfevent_teardown(struct timer *t)
  { close(t->u_cy.fd); }

static int perfevent_init(struct timer *t)
{
  struct perf_event_attr attr = { 0 };
  struct bench_time tm;

  attr.type = PERF_TYPE_HARDWARE;
  attr.size = sizeof(attr);
  attr.config = PERF_COUNT_HW_CPU_CYCLES;
  attr.disabled = 0;
  attr.exclude_kernel = 1;
  attr.exclude_hv = 1;

  t->u_cy.fd = syscall(__NR_perf_event_open, &attr, 0, -1, -1, 0);
  if (t->u_cy.fd < 0) {
    debug("couldn't open perf evvent: %s", strerror(errno));
    return (-1);
  }

  tm.f = 0; perfevent_now(&tm, t);
  if (!(tm.f&BTF_CYOK)) { close(t->u_cy.fd); return (-1); }

  return (0);
}

static const struct timer_ops perfevent_ops =
  { "linux-perf-hw-cycles", 0,
    perfevent_init, perfevent_now, perfevent_teardown };

#  define PERFEVENT_CYENT &perfevent_ops,
#else
#  define PERFEVENT_CYENT
#endif

/*----- Intel time-stamp counter ------------------------------------------*/

/* This is a cycle counter based on the Intel `rdtsc' instruction.  It's not
 * really suitable for performance measurement because it gets confused by
 * CPU frequency adjustments.
 */

#if defined(__GNUC__) && (defined(__i386__) || defined(__x86_64__))

#include <cpuid.h>

#define CPUID_1D_TSC (1u << 4)

static void x86rdtsc_now(struct bench_time *t_out, struct timer *t)
  { t_out->cy.i = __builtin_ia32_rdtsc(); t_out->f |= BTF_CYOK; }

static int x86rdtsc_init(struct timer *t)
{
  unsigned a, b, c, d;

  if (!__get_cpuid(1, &a, &b, &c, &d) || !(d&CPUID_1D_TSC))
    { debug("no `rdtsc' instrunction"); return (-1); }
  return (0);
}

static const struct timer_ops x86rdtsc_ops =
  { "x86-rdtsc", 0, x86rdtsc_init, x86rdtsc_now, null_teardown };

#  define X86RDTSC_CYENT &x86rdtsc_ops,
#else
#  define X86RDTSC_CYENT
#endif

/*----- POSIX `clock_gettime' ---------------------------------------------*/

/* This is a real-time clock based on the POSIX time interface, with up to
 * nanosecond precision.
 */

#if defined(HAVE_CLOCK_GETTIME) && defined(CLOCK_THREAD_CPUTIME_ID)

static void gettime_now(struct bench_time *t_out, struct timer *t)
{
  struct timespec now;

  if (clock_gettime(CLOCK_THREAD_CPUTIME_ID, &now))
    { debug("error reading POSIX clock: %s", strerror(errno)); return; }
  ASSIGN64(t_out->s, now.tv_sec); t_out->ns = now.tv_nsec;
  t_out->f |= BTF_TIMEOK;
}

static int gettime_init(struct timer *t)
{
  struct bench_time tm;

  tm.f = 0; gettime_now(&tm, t); if (!tm.f&BTF_TIMEOK) return (-1);
  return (0);
}

static const struct timer_ops gettime_ops =
  { "posix-thread-cputime", 0, gettime_init, gettime_now, null_teardown };

#  define GETTIME_CLKENT &gettime_ops,
#else
#  define GETTIME_CLKENT
#endif

/*----- Standard C `clock' ------------------------------------------------*/

/* This is a real-time clock based on the C `clock' function which is
 * guaranteed to be available, though it's not likely to be very good.
 */

static void clock_now(struct bench_time *t_out, struct timer *t)
{
  clock_t now, x;
  unsigned long s; uint32 ns;

  now = clock();
    if (now == (clock_t)-1) {
      debug("error reading standard clock: %s", strerror(errno));
      return;
    }
  x = now/CLOCKS_PER_SEC;
    if (x > ULONG_MAX) { debug("standard clock out of range"); return; }

  s = x; x = now - CLOCKS_PER_SEC*s;
  if (!(NS_PER_S%CLOCKS_PER_SEC))
    ns = x*(NS_PER_S/CLOCKS_PER_SEC);
  else if (NS_PER_S <= ULONG_MAX/CLOCKS_PER_SEC)
    ns = (x*NS_PER_S)/CLOCKS_PER_SEC;
  else
    ns = x*((NS_PER_S + 0.0)/CLOCKS_PER_SEC);
  ASSIGN64(t_out->s, s); t_out->ns = ns; t_out->f |= BTF_TIMEOK;
}

static int clock_init(struct timer *t)
{
  struct bench_time tm;

  tm.f = 0; clock_now(&tm, t); if (!tm.f&BTF_TIMEOK) return (-1);
  return (0);
}

static const struct timer_ops clock_ops =
  { "stdc-clock", 0, clock_init, clock_now, null_teardown };

#define CLOCK_CLKENT &clock_ops,

/*----- Timing setup ------------------------------------------------------*/

/* Tables of timing sources. */
static const struct timer_ops
  *const clktab[] = { GETTIME_CLKENT CLOCK_CLKENT BROKEN_ENT 0 },
  *const cytab[] = { PERFEVENT_CYENT X86RDTSC_CYENT NULL_ENT BROKEN_ENT 0 };

static const struct timertab {
  const char *what;
  const char *env;
  const struct timer_ops *const *opstab;
} timertab[] = {
  { "clock", "MLIB_BENCH_CLKTIMER", clktab },
  { "cycle", "MLIB_BENCH_CYCLETIMER", cytab }
};

/* --- @find_timer@ --- *
 *
 * Arguments:   @const char *name@ = timer name
 *              @size_t sz@ = length of name
 *              @unsigned tm@ = which subtimer we're looking for
 *
 * Returns:     The table entry matching the given name, or null if there
 *              isn't one.
 */

static const struct timer_ops *find_timer(const char *name, size_t sz,
                                          unsigned tm)
{
  const struct timer_ops *const *tt;

  for (tt = timertab[tm].opstab; *tt; tt++) {
    if (strlen((*tt)->name) == sz &&
        MEMCMP(name, ==, (*tt)->name, sz))
      return (*tt);
  }
  debug("%s timer `%.*s' not found",
        timertab[tm].what, (int)sz, name); return (0);
}

/* --- @try_timer@ --- *
 *
 * Arguments:   @struct timer *t@ = timer structure
 *              @const struct timer_ops *ops@ = timer ops
 *              @unsigned tm@ = which subtimer we're setting
 *
 * Returns:     Zero on success, %$-1$% if timer failed.
 *
 * Use:         Tries to initialize the timer @t@, reporting a debug message
 *              if it worked.
 */

static int try_timer(struct timer *t,
                     const struct timer_ops *ops, unsigned tm)
{
  if (ops->init(t)) return (-1);
  debug("selected %s timer `%s'", timertab[tm].what, ops->name);
  t->ops[tm] = ops; return (0);
}

/* --- @select_timer@ --- *
 *
 * Arguments:   @struct timer *t@ = timer structure
 *              @unsigned tm@ = which subtimer we're setting
 *              @const char *config@, @size_t sz@ = config string
 *
 * Returns:     Zero on success, %$-1$% if timer failed.
 *
 * Use:         Select a timer from the table.  If the environment variable
 *              is set, then parse a comma-separated list of timer names and
 *              use the first one listed that seems to work; otherwise, try
 *              the timers in the table in order.
 */

static int select_timer(struct timer *t, unsigned tm,
                        const char *config, size_t sz)
{
  const char *p, *l;
  const struct timer_ops *ops, *const *tt;

  if (!config) {
    for (tt = timertab[tm].opstab; *tt; tt++)
      if (!((*tt)->f&TF_SECRET) && !try_timer(t, *tt, tm)) return (0);
  } else {
    l = config + sz;
    for (;;) {
      p = memchr(config, ',', l - config); if (!p) p = l;
      ops = find_timer(config, p - config, tm);
      if (ops && !try_timer(t, ops, tm)) return (0);
      if (p >= l) break;
      config = p + 1;
    }
  }
  debug("no suitable %s timer found", timertab[tm].what); return (-1);
}

/* Bench timer operations. */
static void timer_describe(struct bench_timer *tm, dstr *d)
{
  struct timer *t = (struct timer *)tm;
  unsigned i;

  dstr_puts(d, "builtin: ");
  for (i = 0; i < NTIMER; i++) {
    if (i) dstr_puts(d, ", ");
    dstr_putf(d, "%s = %s", timertab[i].what, t->ops[i]->name);
  }
}

static void timer_now(struct bench_timer *tm, struct bench_time *t_out)
{
  struct timer *t = (struct timer *)tm;
  unsigned i;

  for (i = 0; i < NTIMER; i++) t->ops[i]->now(t_out, t);
}

static void timer_destroy(struct bench_timer *tm)
{
  struct timer *t = (struct timer *)tm;
  unsigned i;

  if (!t) return;
  for (i = 0; i < NTIMER; i++)
    if (t->ops[i]) t->ops[i]->teardown(t);
  xfree(t);
}

static const struct bench_timerops timer_ops =
  { timer_describe, timer_now, timer_destroy };

/* --- @bench_createtimer@ --- *
 *
 * Arguments:   @const char *config@ = timer configuration string
 *
 * Returns:     A freshly constructed standard timer object.
 *
 * Use:         Allocate a timer.  Dispose of it by calling
 *              @tm->ops->destroy(tm)@ when you're done.
 *
 *              Applications should not set configuration strings except as
 *              established by user action, e.g., from a command-line option,
 *              environment variable, or configuration file.
 */

struct bench_timer *bench_createtimer(const char *config)
{
  struct timer *t = 0;
  struct bench_timer *ret = 0;
  struct { const char *p; size_t sz; } tmconf[NTIMER] = { 0 };
  const struct timer_ops *const *tt;
  const char *p, *l; size_t n, nn;
  unsigned i;

  /* Parse the configuration string. */
  if (config) {

    /* The first thing to do is find the end of the string. */
    l = config + strlen(config);

    for (;;) {
      /* Process the whitespace-sparated words of the string one by one. */

      /* Skip over any initial whitespace.  If we hit the end of the string
       * then we're done.
       */
      for (;;)
        if (config >= l) goto done_config;
        else if (!ISSPACE(*config)) break;
        else config++;

      /* There's definitely a word here.  Find the end of it. */
      for (p = config; p < l && !ISSPACE(*p); p++);
      nn = p - config;

      /* Try various simple keywords. */
#define MATCHP(lit) (nn == sizeof(lit) - 1 && MEMCMP(config, ==, lit, nn))

      if (MATCHP("list")) {
        /* The `list' keyword requests lists of the available timer
         * implementations.
         */

        for (i = 0; i < NTIMER; i++) {
          printf("%s timers:", timertab[i].what);
          for (tt = timertab[i].opstab; *tt; tt++)
            if (!((*tt)->f)&TF_SECRET) printf(" %s", (*tt)->name);
          putchar('\n');
        }
        goto next_config;
      }

#undef MATCHP

      /* Otherwise it's an assignment, setting a subtimer list. */
      p = memchr(config, '=', nn);
      if (!p)
        n = nn;
      else {
        n = p - config;
        for (i = 0; i < NTIMER; i++)
          if (STRNCMP(config, ==, timertab[i].what, n) &&
              !timertab[i].what[n]) {
            if (tmconf[i].p)
              debug("duplicate %s timer list", timertab[i].what);
            tmconf[i].p = config + n + 1; tmconf[i].sz = nn - n - 1;
            goto next_config;
          }
      }
      debug("unrecognized config keyword `%.*s'", (int)n, config);

      /* Move on to the next word. */
    next_config:
      config += nn;
    }
  done_config:;
  }

  /* Override these settings from the environment. */
  for (i = 0; i < NTIMER; i++) {
    p = getenv(timertab[i].env);
    if (p) { tmconf[i].p = p; tmconf[i].sz = strlen(p); }
  }

  /* All seems well.  Allocate the timer object. */
  t = xmalloc(sizeof(*t));
  for (i = 0; i < NTIMER; i++) t->ops[i] = 0;

  /* Try to set up the subtimers. */
  for (i = 0; i < NTIMER; i++)
    if (select_timer(t, i, tmconf[i].p, tmconf[i].sz)) goto end;

  /* All is done. */
  t->_t.ops = &timer_ops; ret = &t->_t; t = 0;
end:
  if (t) timer_destroy(&t->_t);
  return (ret);
}

/*----- Benchmarking ------------------------------------------------------*/

/* --- @bench_init@ --- *
 *
 * Arguments:   @struct bench_state *b@ = bench state to initialize
 *              @struct bench_timer *tm@ = timer to attach, or null
 *
 * Returns:     Zero on success, %$-1$% on failure.
 *
 * Use:         Initialize the benchmark state.  On success, the timer state
 *              still needs to be calibrated (use @bench_calibrate@) before
 *              it can be used, but this will be done automatically by
 *              @bench_measure@ if it's not done by hand earlier.  The timer
 *              is now owned by the benchmark state and will be destroyed by
 *              @bench_destroy@.
 *
 *              The only reason for failure is if @tm@ was null on entry,
 *              and automatic construction of a timer failed.  The state is
 *              safe to discard, but calling @bench_destroy@ is safe too.
 */

int bench_init(struct bench_state *b, struct bench_timer *tm)
{
  int rc;

  b->tm = 0;

  if (!tm) {
    tm = bench_createtimer(0);
    if (!tm) { rc = -1; goto end; }
  }

  b->tm = tm; b->target_s = 1.0; b->f = 0; rc = 0;
end:
  return (rc);
}

/* --- @bench_destroy@ --- *
 *
 * Arguments:   @struct bench_state *b@ = bench state
 *
 * Returns:     ---
 *
 * Use:         Destroy the benchmark state, releasing the resources that it
 *              holds.
 */

void bench_destroy(struct bench_state *b)
  { if (b->tm) { b->tm->ops->destroy(b->tm); b->tm = 0; } }

/* --- @do_nothing@ --- *
 *
 * Arguments:   @unsigned long n@ = iteration count
 *              @void *ctx@ = context pointer (ignored)
 *
 * Returns:     ---
 *
 * Use:         Does nothing at all for @n@ iterations.  Used to calibrate
 *              the benchmarking state.
 */

static void do_nothing(unsigned long n, void *ctx)
  { while (n--) RELAX; }

/* --- @bench_calibrate@ --- *
 *
 * Arguments:   @struct bench_state *b@ = bench state
 *
 * Returns:     Zero on success, %$-1$% if calibration failed.
 *
 * Use:         Calibrate the benchmark state, so that it can be used to
 *              measure performance reasonably accurately.
 */

#define T_CLB 0.0625                    /* calibration time limit */

int bench_calibrate(struct bench_state *b)
{
  struct linreg lr_clk = LINREG_INIT, lr_cy = LINREG_INIT;
  unsigned long n;
  unsigned i;
  struct bench_timer *tm = b->tm;
  struct bench_time t0, t1;
  struct bench_timing delta;
  double r;
  bench_fn *fn = LAUNDER(&do_nothing);
  unsigned f = BTF_ANY;
  int rc;

  /* The model here is that a timing loop has a fixed overhead as we enter
   * and leave (e.g., to do with the indirect branch into the code), and
   * per-iteration overheads as we check the counter and loop back.  We aim
   * to split these apart using linear regression.
   */

  /* If we've already calibrated then there's nothing to do. */
  if (b->f&BTF_CLB) return (b->f&BTF_ANY ? 0 : -1);

  /* Exercise the inner loop a few times to educate the branch predictor. */
  for (i = 0; i < 10; i++)
    { tm->ops->now(tm, &t0); fn(50, 0); tm->ops->now(tm, &t1); }

  /* Now we measure idle loops until they take sufficiently long -- or we run
   * out of counter.
   */
  debug("calibrating...");
  n = 1;
  for (;;) {

    /* Measure @n@ iterations of the idle loop. */
    tm->ops->now(tm, &t0); fn(n, 0); tm->ops->now(tm, &t1);
    timer_diff(&delta, &t0, &t1); f &= delta.f;
    if (!(f&BTF_TIMEOK)) { rc = -1; goto end; }

    /* Register the timings with the regression machinery. */
    linreg_update(&lr_clk, n, delta.t);
    if (!(f&BTF_CYOK))
      debug("  n = %10lu; t = %12g s", n, delta.t);
    else {
      linreg_update(&lr_cy, n, delta.cy);
      debug("  n = %10lu; t = %12g s, cy = %10.0f", n, delta.t, delta.cy);
    }

    /* If we're done then stop. */
    if (delta.t >= T_CLB) break;
    if (n >= ULONG_MAX - n/3) break;

    /* Update the counter and continue. */
    n += n/3 + 1;
  }

  /* Now run the linear regression to extract the constant and per-iteration
   * overheads.
   */
  linreg_fit(&lr_clk, &b->clk.m, &b->clk.c, &r);
  debug("clock overhead = (%g n + %g) s (r = %g)", b->clk.m, b->clk.c, r);
  if (f&BTF_CYOK) {
    linreg_fit(&lr_cy, &b->cy.m, &b->cy.c, &r);
    debug("cycle overhead = (%g n + %g) cy (r = %g)", b->cy.m, b->cy.c, r);
  }

  /* We're done. */
  rc = 0;
end:
  b->f |= f | BTF_CLB;                  /* no point trying again */
  return (rc);
}

/* --- @bench_measure@ --- *
 *
 * Arguments:   @struct bench_state *b@ = benchmark state
 *              @struct bench_timing *t_out@ = where to leave the timing
 *              @double base@ = number of internal units per call
 *              @bench_fn *fn@, @void *ctx@ = benchmark function to run
 *
 * Returns:     Zero on success, %$-1$% if timing failed.
 *
 * Use:         Measure a function.  The function @fn@ is called adaptively
 *              with an iteration count @n@ set so as to run for
 *              approximately @b->target_s@ seconds.
 *
 *              The result is left in @*t_out@, with @t_out->n@ counting the
 *              final product of the iteration count and @base@ (which might,
 *              e.g., reflect the number of inner iterations the function
 *              performs, or the number of bytes it processes per iteration).
 */

int bench_measure(struct bench_state *b, struct bench_timing *t_out,
                  double base, bench_fn *fn, void *ctx)
{
  struct bench_timer *tm = b->tm;
  struct bench_time t0, t1;
  unsigned long n, nn;

  /* Make sure the state is calibrated and usable. */
  if (!(b->f&BTF_CLB) && bench_calibrate(b)) return (-1);
  if (!(b->f&BTF_TIMEOK)) return (-1);

  /* Main adaptive measurement loop.
   *
   * Suppose the timer loop %$n$% iterations in %$t$% seconds.  Our ideal
   * time is %$T$% seconds.  If %$t \ge T/\sqrt{2}$%, we're happy.
   * Otherwise, we need to scale up the iteration count.  The obvious next
   * choice is %$n' = n T/t$%.  Alas, rounding is a problem: if
   * %$T/t < 1 + 1/n$% then %$\floor{n T/t} = n$% and we will make no
   * progress.  We know that %$T/t > \sqrt{2}%, so this can only happen when
   * %$1 + 1/n > \sqrt{2}$%, i.e., when %$n < \sqrt{2} + 1$%.  On the other
   * hand, if %$T/t < 1 + 1/n$% then %$t (n + 1)/n > T$%, so just trying
   * again with %$n' = n + 1$% iterations will very likely work.
   */
  debug("measuring..."); n = 1;
  for (;;) {
    tm->ops->now(tm, &t0); fn(n, ctx); tm->ops->now(tm, &t1);
    timer_diff(t_out, &t0, &t1);
    if (!(t_out->f&BTF_TIMEOK)) return (-1);
    if (!(t_out->f&BTF_CYOK)) debug("  n = %10lu; t = %12g", n, t_out->t);
    else debug("  n = %10lu; t = %12g, cy = %10.0f", n, t_out->t, t_out->cy);
    if (t_out->t >= 0.707*b->target_s) break;
    nn = n*b->target_s/t_out->t;
    if (nn > n) n = nn;
    else n++;
  }

  /* Adjust according to the calibration. */
  t_out->t -= n*b->clk.m + b->clk.c;
  if (t_out->f&BTF_CYOK) t_out->cy -= n*b->cy.m + b->cy.c;

  /* Report the results, if debugging. */
  if (!(t_out->f&BTF_CYOK)) debug("  adjusted t' = %12g", t_out->t);
  else debug("  adjusted t = %12g, cy = %10.0f", t_out->t, t_out->cy);
  if (!(t_out->f&BTF_CYOK))
    debug("  %g s per op; %g ops/s", t_out->t/n, n/t_out->t);
  else
    debug("  %g s (%g cy) per op; %g ops/s",
          t_out->t/n, t_out->cy/n, n/t_out->t);

  /* All done. */
  t_out->n = n*base; return (0);
}

/*----- That's all, folks -------------------------------------------------*/