path: root/tuneup.c

/* Tune various threshold of MPFR

Copyright 2005, 2006, 2007, 2008, 2009 Free Software Foundation, Inc.
Contributed by the Arenaire and Cacao projects, INRIA.

This file is part of the GNU MPFR Library.

The GNU MPFR Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation; either version 3 of the License, or (at your
option) any later version.

The GNU MPFR Library 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 Lesser General Public
License for more details.

You should have received a copy of the GNU Lesser General Public License
along with the GNU MPFR Library; see the file COPYING.LIB.  If not, see
http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */

#include <stdlib.h>
#include <time.h>

#define MPFR_NEED_LONGLONG_H
#include "mpfr-impl.h"

#undef _PROTO
#define _PROTO __GMP_PROTO
#include "speed.h"

int verbose;

/* s->size: precision of both input and output
   s->xp  : Mantissa of first input
   s->yp  : mantissa of second input                    */

#define SPEED_MPFR_FUNC(mean_fun) do {               \
  unsigned  i;                                       \
  mp_ptr    wp;                                      \
  double    t;                                       \
  mpfr_t    w, x;                                    \
  mp_size_t size;                                    \
  MPFR_TMP_DECL (marker);                            \
                                                     \
  SPEED_RESTRICT_COND (s->size >= MPFR_PREC_MIN);    \
  SPEED_RESTRICT_COND (s->size <= MPFR_PREC_MAX);    \
  MPFR_TMP_MARK (marker);                            \
                                                     \
  size = (s->size-1)/BITS_PER_MP_LIMB+1;             \
  s->xp[size-1] |= MPFR_LIMB_HIGHBIT;                \
  MPFR_TMP_INIT1 (s->xp, x, s->size);                \
  MPFR_SET_EXP (x, 0);                               \
                                                     \
  MPFR_TMP_INIT (wp, w, s->size, size);              \
                                                     \
  speed_operand_src (s, s->xp, size);                \
  speed_operand_dst (s, wp, size);                   \
  speed_cache_fill (s);                              \
                                                     \
  speed_starttime ();                                \
  i = s->reps;                                       \
  do                                                 \
    mean_fun (w, x, MPFR_RNDN);                       \
  while (--i != 0);                                  \
  t = speed_endtime ();                              \
                                                     \
  MPFR_TMP_FREE (marker);                            \
  return t;                                          \
} while (0)

#define SPEED_MPFR_OP(mean_fun) do {                 \
  unsigned  i;                                       \
  mp_ptr    wp;                                      \
  double    t;                                       \
  mpfr_t    w, x, y;                                 \
  mp_size_t size;                                    \
  MPFR_TMP_DECL (marker);                            \
                                                     \
  SPEED_RESTRICT_COND (s->size >= MPFR_PREC_MIN);    \
  SPEED_RESTRICT_COND (s->size <= MPFR_PREC_MAX);    \
  MPFR_TMP_MARK (marker);                            \
                                                     \
  size = (s->size-1)/BITS_PER_MP_LIMB+1;             \
  s->xp[size-1] |= MPFR_LIMB_HIGHBIT;                \
  MPFR_TMP_INIT1 (s->xp, x, s->size);                \
  MPFR_SET_EXP (x, 0);                               \
  s->yp[size-1] |= MPFR_LIMB_HIGHBIT;                \
  MPFR_TMP_INIT1 (s->yp, y, s->size);                \
  MPFR_SET_EXP (y, 0);                               \
                                                     \
  MPFR_TMP_INIT (wp, w, s->size, size);              \
                                                     \
  speed_operand_src (s, s->xp, size);                \
  speed_operand_src (s, s->yp, size);                \
  speed_operand_dst (s, wp, size);                   \
  speed_cache_fill (s);                              \
                                                     \
  speed_starttime ();                                \
  i = s->reps;                                       \
  do                                                 \
    mean_fun (w, x, y, MPFR_RNDN);                    \
  while (--i != 0);                                  \
  t = speed_endtime ();                              \
                                                     \
  MPFR_TMP_FREE (marker);                            \
  return t;                                          \
} while (0)


/* First we include all the functions we want to tune inside this program.
   We can't use GNU MPFR library since the THRESHOLD can't vary */

/* Setup mpfr_exp_2 */
mp_prec_t mpfr_exp_2_threshold;
#undef  MPFR_EXP_2_THRESHOLD
#define MPFR_EXP_2_THRESHOLD mpfr_exp_2_threshold
#include "exp_2.c"
static double speed_mpfr_exp_2 (struct speed_params *s) {
  SPEED_MPFR_FUNC (mpfr_exp_2);
}

/* Setup mpfr_exp */
mp_prec_t mpfr_exp_threshold;
#undef  MPFR_EXP_THRESHOLD
#define MPFR_EXP_THRESHOLD mpfr_exp_threshold
#include "exp.c"
static double speed_mpfr_exp (struct speed_params *s) {
  SPEED_MPFR_FUNC (mpfr_exp);
}

/* Setup mpfr_mul */
mp_prec_t mpfr_mul_threshold;
#undef  MPFR_MUL_THRESHOLD
#define MPFR_MUL_THRESHOLD mpfr_mul_threshold
#include "mul.c"
static double speed_mpfr_mul (struct speed_params *s) {
  SPEED_MPFR_OP (mpfr_mul);
}



/************************************************
 * Common functions (inspired by GMP function)  *
 ************************************************/
static int
analyze_data (double *dat, int ndat) {
  double  x, min_x;
  int     j, min_j;

  x = 0.0;
  for (j = 0; j < ndat; j++)
    if (dat[j] > 0.0)
      x += dat[j];

  min_x = x;
  min_j = 0;

  for (j = 0; j < ndat; x -= dat[j], j++)
    {
      if (x < min_x)
        {
          min_x = x;
          min_j = j;
        }
    }
  return min_j;
}

#define THRESHOLD_WINDOW 16
#define THRESHOLD_FINAL_WINDOW 128
static double domeasure (mp_prec_t *threshold,
                         double (*func) (struct speed_params *),
                         mp_prec_t p)
{
  struct speed_params s;
  mp_size_t size;
  double t1, t2, d;

  s.align_xp = s.align_yp = s.align_wp = 64;
  s.size = p;
  size = (p - 1)/BITS_PER_MP_LIMB+1;
  s.xp = malloc (2*size*sizeof (mp_limb_t));
  if (s.xp == NULL)
    {
      fprintf (stderr, "Can't allocate memory.\n");
      abort ();
    }
  mpn_random (s.xp, size);
  s.yp = s.xp + size;
  mpn_random (s.yp, size);
  *threshold = MPFR_PREC_MAX;
  t1 = speed_measure (func, &s);
  if (t1 == -1.0)
    {
      fprintf (stderr, "Failed to measure function 1!\n");
      abort ();
    }
  *threshold = 1;
  t2 = speed_measure (func, &s);
  if (t2 == -1.0)
    {
      fprintf (stderr, "Failed to measure function 2!\n");
      abort ();
    }
  free (s.xp);
  /* t1 is the time of the first algo (used for low prec) */
  if (t2 >= t1)
    d = (t2 - t1) / t2;
  else
    d = (t2 - t1) / t1;
  /* d > 0 if we have to use algo 1.
     d < 0 if we have to use algo 2 */
  return d;
}

/* Tune a function with a simple THRESHOLD
   The function doesn't depend on another threshold.
   It assumes that it uses algo1 if p < THRESHOLD
   and algo2 otherwise.
   if algo2 is better for low prec, and algo1 better for high prec,
   the behaviour of this function is undefined. */
static void
tune_simple_func (mp_prec_t *threshold,
                  double (*func) (struct speed_params *),
                  mp_prec_t pstart)
{
  double measure[THRESHOLD_FINAL_WINDOW+1];
  double d;
  mp_prec_t pstep;
  int i, numpos, numneg, try;
  mp_prec_t pmin, pmax, p;

  /* first look for a lower bound within 10% */
  pmin = p = pstart;
  d = domeasure (threshold, func, pmin);
  if (d < 0.0) {
    if (verbose)
      printf ("Oops: even for %lu, algo 2 seems to be faster!\n",
              (unsigned long) pmin);
    *threshold = MPFR_PREC_MIN;
    return;
  }
  if (d >= 1.00)
    for (;;) {
      d = domeasure (threshold, func, pmin);
      if (d < 1.00)
        break;
      p = pmin;
      pmin += pmin/2;
    }
  pmin = p;
  for (;;) {
    d = domeasure (threshold, func, pmin);
    if (d < 0.10)
      break;
    pmin += BITS_PER_MP_LIMB;
  }

  /* then look for a upper bound within 20% */
  pmax = pmin * 2;
  for (;;) {
    d = domeasure (threshold, func, pmax);
    if (d < -0.20)
      break;
    pmax += pmin / 2; /* don't increase too rapidly */
  }

  /* The threshold is between pmin and pmax. Affine them */
  try = 0;
  while ((pmax-pmin) >= THRESHOLD_FINAL_WINDOW)
    {
      pstep = MAX(MIN(BITS_PER_MP_LIMB/2,(pmax-pmin)/(2*THRESHOLD_WINDOW)),1);
      if (verbose)
        printf ("Pmin = %8lu Pmax = %8lu Pstep=%lu\n", pmin, pmax, pstep);
      p = (pmin + pmax) / 2;
      for (i = numpos = numneg = 0 ; i < THRESHOLD_WINDOW + 1 ; i++) {
        measure[i] = domeasure (threshold, func,
                                p+(i-THRESHOLD_WINDOW/2)*pstep);
        if (measure[i] > 0)
          numpos ++;
        else if (measure[i] < 0)
          numneg ++;
      }
      if (numpos > numneg)
        /* We use more often algo 1 than algo 2 */
        pmin = p - THRESHOLD_WINDOW/2*pstep;
      else if (numpos < numneg)
        pmax = p + THRESHOLD_WINDOW/2*pstep;
      else
        /* numpos == numneg ... */
        if (++ try > 2) {
          *threshold = p;
          if (verbose)
            printf ("Quick find: %lu\n", *threshold);
          return ;
        }
    }

  /* Final tune... */
  if (verbose)
    printf ("Finalizing in [%lu, %lu]... ", pmin, pmax);
  for (i = 0 ; i < THRESHOLD_FINAL_WINDOW+1 ; i++)
    measure[i] = domeasure (threshold, func, pmin+i);
  i = analyze_data (measure, THRESHOLD_FINAL_WINDOW+1);
  *threshold = pmin + i;
  if (verbose)
    printf ("%lu\n", *threshold);
  return;
}



/************************************
 * Tune Mulders' mulhigh function   *
 ************************************/
#define TOLERANCE 1.02
#ifndef MPFR_MULHIGH_SIZE
# define MPFR_MULHIGH_SIZE 1024
#endif
#ifndef MPFR_SQRHIGH_SIZE
# define MPFR_SQRHIGH_SIZE 1024
#endif
#define MPFR_MULHIGH_TAB_SIZE MPFR_MULHIGH_SIZE
#define MPFR_SQRHIGH_TAB_SIZE MPFR_SQRHIGH_SIZE
#include "mulders.c"

static double speed_mpfr_mulhigh (struct speed_params *s) {
  SPEED_ROUTINE_MPN_MUL_N (mpfr_mulhigh_n);
}
static double speed_mpfr_sqrhigh (struct speed_params *s) {
  SPEED_ROUTINE_MPN_SQR (mpfr_sqrhigh_n);
}

#define MAX_STEPS 32 /* maximum number of values of k tried for a given n */

/* Tune size N */
static mp_size_t
tune_mulders_upto (mp_size_t n)
{
  struct speed_params s;
  mp_size_t k, kbest, step;
  double t, tbest;
  MPFR_TMP_DECL (marker);

  if (n == 0)
    return -1;

  MPFR_TMP_MARK (marker);
  s.align_xp = s.align_yp = s.align_wp = 64;
  s.size = n;
  s.xp   = MPFR_TMP_ALLOC (n*sizeof (mp_limb_t));
  s.yp   = MPFR_TMP_ALLOC (n*sizeof (mp_limb_t));
  mpn_random (s.xp, n);
  mpn_random (s.yp, n);

  /* Check k == -1, mpn_mul_basecase */
  mulhigh_ktab[n] = -1;
  kbest = -1;
  tbest =  speed_measure (speed_mpfr_mulhigh, &s);

  /* Check k == 0, mpn_mulhigh_n_basecase */
  mulhigh_ktab[n] = 0;
  t = speed_measure (speed_mpfr_mulhigh, &s);
  if (t * TOLERANCE < tbest)
    kbest = 0, tbest = t;

  /* Check Mulders with cutoff point k */
  step = 1 + n / (2 * MAX_STEPS);
  for (k = n / 2 + 1 ; k < n ; k += step)
    {
      mulhigh_ktab[n] = k;
      t =  speed_measure (speed_mpfr_mulhigh, &s);
      if (t * TOLERANCE < tbest)
        kbest = k, tbest = t;
    }

  mulhigh_ktab[n] = kbest;

  MPFR_TMP_FREE (marker);
  return kbest;
}

/* Tune size N */
static mp_size_t
tune_sqr_mulders_upto (mp_size_t n)
{
  struct speed_params s;
  mp_size_t k, kbest, step;
  double t, tbest;
  MPFR_TMP_DECL (marker);

  if (n == 0)
    return -1;

  MPFR_TMP_MARK (marker);
  s.align_xp = s.align_wp = 64;
  s.size = n;
  s.xp   = MPFR_TMP_ALLOC (n*sizeof (mp_limb_t));
  mpn_random (s.xp, n);

  /* Check k == -1, mpn_sqr_basecase */
  sqrhigh_ktab[n] = -1;
  kbest = -1;
  tbest =  speed_measure (speed_mpfr_sqrhigh, &s);

  /* Check k == 0, mpfr_mulhigh_n_basecase */
  sqrhigh_ktab[n] = 0;
  t = speed_measure (speed_mpfr_sqrhigh, &s);
  if (t * TOLERANCE < tbest)
    kbest = 0, tbest = t;

  /* Check Mulders */
  step = 1 + n / (2 * MAX_STEPS);
  for (k = n / 2 + 1 ; k < n ; k += step)
    {
      sqrhigh_ktab[n] = k;
      t =  speed_measure (speed_mpfr_sqrhigh, &s);
      if (t * TOLERANCE < tbest)
        kbest = k, tbest = t;
    }

  sqrhigh_ktab[n] = kbest;

  MPFR_TMP_FREE (marker);
  return kbest;
}

static void
tune_mulders (FILE *f)
{
  mp_size_t k;

  if (verbose)
    printf ("Tuning mpfr_mulhigh_n[%d]", (int) MPFR_MULHIGH_TAB_SIZE);
  fprintf (f, "#define MPFR_MULHIGH_TAB  \\\n ");
  for (k = 0 ; k < MPFR_MULHIGH_TAB_SIZE ; k++)
    {
      fprintf (f, "%d", (int) tune_mulders_upto (k));
      if (k != MPFR_MULHIGH_TAB_SIZE-1)
        fputc (',', f);
      if ((k+1) % 16 == 0)
        fprintf (f, " \\\n ");
      if (verbose)
        putchar ('.');
    }
  fprintf (f, " \n");
  if (verbose)
    putchar ('\n');
}

static void
tune_sqr_mulders (FILE *f)
{
  mp_size_t k;

  if (verbose)
    printf ("Tuning mpfr_sqrhigh_n[%d]", (int) MPFR_SQRHIGH_TAB_SIZE);
  fprintf (f, "#define MPFR_SQRHIGH_TAB  \\\n ");
  for (k = 0 ; k < MPFR_SQRHIGH_TAB_SIZE ; k++)
    {
      fprintf (f, "%d", (int) tune_sqr_mulders_upto (k));
      if (k != MPFR_SQRHIGH_TAB_SIZE-1)
        fputc (',', f);
      if ((k+1) % 16 == 0)
        fprintf (f, " \\\n ");
      if (verbose)
        putchar ('.');
    }
  fprintf (f, " \n");
  if (verbose)
    putchar ('\n');
}

/*******************************************************
 *            Tune all the threshold of MPFR           *
 * Warning: tune the function in their dependent order!*
 *******************************************************/
static void
all (const char *filename)
{
  FILE *f;
  time_t  start_time, end_time;
  struct tm  *tp;

  f = fopen (filename, "w");
  if (f == NULL) {
    fprintf (stderr, "Can't open file '%s' for writing.\n", filename);
    abort ();
  }

  speed_time_init ();
  if (verbose) {
    printf ("Using: %s\n", speed_time_string);
    printf ("speed_precision %d", speed_precision);
    if (speed_unittime == 1.0)
      printf (", speed_unittime 1 cycle");
    else
      printf (", speed_unittime %.2e secs", speed_unittime);
    if (speed_cycletime == 1.0 || speed_cycletime == 0.0)
      printf (", CPU freq unknown\n");
    else
      printf (", CPU freq %.2f MHz\n\n", 1e-6/speed_cycletime);
  }

  time (&start_time);
  tp = localtime (&start_time);
  fprintf (f, "/* Generated by MPFR's tuneup.c, %d-%02d-%02d, ",
          tp->tm_year+1900, tp->tm_mon+1, tp->tm_mday);

#ifdef __ICC
  fprintf (f, "icc %d.%d.%d */\n", __ICC / 100, __ICC / 10 % 10, __ICC % 10);
#elif defined(__GNUC__)
#ifdef __GNUC_PATCHLEVEL__
  fprintf (f, "gcc %d.%d.%d */\n", __GNUC__, __GNUC_MINOR__,
           __GNUC_PATCHLEVEL__);
#else
  fprintf (f, "gcc %d.%d */\n", __GNUC__, __GNUC_MINOR__);
#endif
#elif defined (__SUNPRO_C)
  fprintf (f, "Sun C %d.%d */\n", __SUNPRO_C / 0x100, __SUNPRO_C % 0x100);
#elif defined (__sgi) && defined (_COMPILER_VERSION)
  fprintf (f, "MIPSpro C %d.%d.%d */\n",
           _COMPILER_VERSION / 100,
           _COMPILER_VERSION / 10 % 10,
           _COMPILER_VERSION % 10);
#elif defined (__DECC) && defined (__DECC_VER)
  fprintf (f, "DEC C %d */\n", __DECC_VER);
#else
  fprintf (f, "system compiler */\n");
#endif
  fprintf (f, "\n");

  /* Tune mulhigh */
  tune_mulders (f);

  /* Tune sqrhigh */
  tune_sqr_mulders (f);

  /* Tune mpfr_mul (threshold is in limbs, but it doesn't matter too much) */
  if (verbose)
    printf ("Tuning mpfr_mul...\n");
  tune_simple_func (&mpfr_mul_threshold, speed_mpfr_mul,
                    2*BITS_PER_MP_LIMB+1);
  fprintf (f, "#define MPFR_MUL_THRESHOLD %lu /* limbs */\n",
           (unsigned long) (mpfr_mul_threshold - 1) / BITS_PER_MP_LIMB + 1);

  /* Tune mpfr_exp_2 */
  if (verbose)
    printf ("Tuning mpfr_exp_2...\n");
  tune_simple_func (&mpfr_exp_2_threshold, speed_mpfr_exp_2,
                    MPFR_PREC_MIN);
  mpfr_exp_2_threshold = MAX (BITS_PER_MP_LIMB, mpfr_exp_2_threshold);
  fprintf (f, "#define MPFR_EXP_2_THRESHOLD %lu /* bits */\n",
           (unsigned long) mpfr_exp_2_threshold);

  /* Tune mpfr_exp */
  if (verbose)
    printf ("Tuning mpfr_exp...\n");
  tune_simple_func (&mpfr_exp_threshold, speed_mpfr_exp,
                    MPFR_PREC_MIN+3*BITS_PER_MP_LIMB);
  fprintf (f, "#define MPFR_EXP_THRESHOLD %lu /* bits */\n",
           (unsigned long) mpfr_exp_threshold);

  /* End of tuning */
  time (&end_time);
  fprintf (f, "/* Tuneup completed successfully, took %ld seconds */\n",
           end_time - start_time);
  if (verbose)
    printf ("Complete (took %ld seconds).\n", end_time - start_time);

  fclose (f);
}


/* Main function */
int main (int argc, char *argv[])
{
  /* Unbuffered so if output is redirected to a file it isn't lost if the
     program is killed part way through.  */
  setbuf (stdout, NULL);
  setbuf (stderr, NULL);

  verbose = argc > 1;

  if (verbose)
    printf ("Tuning MPFR (Coffee time?)...\n");

  all ("mparam.h");

  return 0;
}