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+/* Create tuned thresholds for various algorithms.
+
+Copyright 1999-2003, 2005, 2006, 2008-2017 Free Software Foundation, Inc.
+
+This file is part of the GNU MP Library.
+
+The GNU MP Library is free software; you can redistribute it and/or modify
+it under the terms of either:
+
+ * 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.
+
+or
+
+ * the GNU General Public License as published by the Free Software
+ Foundation; either version 2 of the License, or (at your option) any
+ later version.
+
+or both in parallel, as here.
+
+The GNU MP 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 General Public License
+for more details.
+
+You should have received copies of the GNU General Public License and the
+GNU Lesser General Public License along with the GNU MP Library. If not,
+see https://www.gnu.org/licenses/. */
+
+
+/* Usage: tuneup [-t] [-t] [-p precision]
+
+ -t turns on some diagnostic traces, a second -t turns on more traces.
+
+ Notes:
+
+ The code here isn't a vision of loveliness, mainly because it's subject
+ to ongoing changes according to new things wanting to be tuned, and
+ practical requirements of systems tested.
+
+ Sometimes running the program twice produces slightly different results.
+ This is probably because there's so little separating algorithms near
+ their crossover, and on that basis it should make little or no difference
+ to the final speed of the relevant routines, but nothing has been done to
+ check that carefully.
+
+ Algorithm:
+
+ The thresholds are determined as follows. A crossover may not be a
+ single size but rather a range where it oscillates between method A or
+ method B faster. If the threshold is set making B used where A is faster
+ (or vice versa) that's bad. Badness is the percentage time lost and
+ total badness is the sum of this over all sizes measured. The threshold
+ is set to minimize total badness.
+
+ Suppose, as sizes increase, method B becomes faster than method A. The
+ effect of the rule is that, as you look at increasing sizes, isolated
+ points where B is faster are ignored, but when it's consistently faster,
+ or faster on balance, then the threshold is set there. The same result
+ is obtained thinking in the other direction of A becoming faster at
+ smaller sizes.
+
+ In practice the thresholds tend to be chosen to bring on the next
+ algorithm fairly quickly.
+
+ This rule is attractive because it's got a basis in reason and is fairly
+ easy to implement, but no work has been done to actually compare it in
+ absolute terms to other possibilities.
+
+ Implementation:
+
+ In a normal library build the thresholds are constants. To tune them
+ selected objects are recompiled with the thresholds as global variables
+ instead. #define TUNE_PROGRAM_BUILD does this, with help from code at
+ the end of gmp-impl.h, and rules in tune/Makefile.am.
+
+ MUL_TOOM22_THRESHOLD for example uses a recompiled mpn_mul_n. The
+ threshold is set to "size+1" to avoid karatsuba, or to "size" to use one
+ level, but recurse into the basecase.
+
+ MUL_TOOM33_THRESHOLD makes use of the tuned MUL_TOOM22_THRESHOLD value.
+ Other routines in turn will make use of both of those. Naturally the
+ dependants must be tuned first.
+
+ In a couple of cases, like DIVEXACT_1_THRESHOLD, there's no recompiling,
+ just a threshold based on comparing two routines (mpn_divrem_1 and
+ mpn_divexact_1), and no further use of the value determined.
+
+ Flags like USE_PREINV_MOD_1 or JACOBI_BASE_METHOD are even simpler, being
+ just comparisons between certain routines on representative data.
+
+ Shortcuts are applied when native (assembler) versions of routines exist.
+ For instance a native mpn_sqr_basecase is assumed to be always faster
+ than mpn_mul_basecase, with no measuring.
+
+ No attempt is made to tune within assembler routines, for instance
+ DIVREM_1_NORM_THRESHOLD. An assembler mpn_divrem_1 is expected to be
+ written and tuned all by hand. Assembler routines that might have hard
+ limits are recompiled though, to make them accept a bigger range of sizes
+ than normal, eg. mpn_sqr_basecase to compare against mpn_toom2_sqr.
+
+ Limitations:
+
+ The FFTs aren't subject to the same badness rule as the other thresholds,
+ so each k is probably being brought on a touch early. This isn't likely
+ to make a difference, and the simpler probing means fewer tests.
+
+*/
+
+#define TUNE_PROGRAM_BUILD 1 /* for gmp-impl.h */
+
+#include "config.h"
+
+#include <math.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <time.h>
+#if HAVE_UNISTD_H
+#include <unistd.h>
+#endif
+
+#include "gmp-impl.h"
+#include "longlong.h"
+
+#include "tests.h"
+#include "speed.h"
+
+#if !HAVE_DECL_OPTARG
+extern char *optarg;
+extern int optind, opterr;
+#endif
+
+
+#define DEFAULT_MAX_SIZE 1000 /* limbs */
+
+#if WANT_FFT
+mp_size_t option_fft_max_size = 50000; /* limbs */
+#else
+mp_size_t option_fft_max_size = 0;
+#endif
+int option_trace = 0;
+int option_fft_trace = 0;
+struct speed_params s;
+
+struct dat_t {
+ mp_size_t size;
+ double d;
+} *dat = NULL;
+int ndat = 0;
+int allocdat = 0;
+
+/* This is not defined if mpn_sqr_basecase doesn't declare a limit. In that
+ case use zero here, which for params.max_size means no limit. */
+#ifndef TUNE_SQR_TOOM2_MAX
+#define TUNE_SQR_TOOM2_MAX 0
+#endif
+
+mp_size_t mul_toom22_threshold = MP_SIZE_T_MAX;
+mp_size_t mul_toom33_threshold = MUL_TOOM33_THRESHOLD_LIMIT;
+mp_size_t mul_toom44_threshold = MUL_TOOM44_THRESHOLD_LIMIT;
+mp_size_t mul_toom6h_threshold = MUL_TOOM6H_THRESHOLD_LIMIT;
+mp_size_t mul_toom8h_threshold = MUL_TOOM8H_THRESHOLD_LIMIT;
+mp_size_t mul_toom32_to_toom43_threshold = MP_SIZE_T_MAX;
+mp_size_t mul_toom32_to_toom53_threshold = MP_SIZE_T_MAX;
+mp_size_t mul_toom42_to_toom53_threshold = MP_SIZE_T_MAX;
+mp_size_t mul_toom42_to_toom63_threshold = MP_SIZE_T_MAX;
+mp_size_t mul_toom43_to_toom54_threshold = MP_SIZE_T_MAX;
+mp_size_t mul_fft_threshold = MP_SIZE_T_MAX;
+mp_size_t mul_fft_modf_threshold = MP_SIZE_T_MAX;
+mp_size_t sqr_basecase_threshold = MP_SIZE_T_MAX;
+mp_size_t sqr_toom2_threshold
+ = (TUNE_SQR_TOOM2_MAX == 0 ? MP_SIZE_T_MAX : TUNE_SQR_TOOM2_MAX);
+mp_size_t sqr_toom3_threshold = SQR_TOOM3_THRESHOLD_LIMIT;
+mp_size_t sqr_toom4_threshold = SQR_TOOM4_THRESHOLD_LIMIT;
+mp_size_t sqr_toom6_threshold = SQR_TOOM6_THRESHOLD_LIMIT;
+mp_size_t sqr_toom8_threshold = SQR_TOOM8_THRESHOLD_LIMIT;
+mp_size_t sqr_fft_threshold = MP_SIZE_T_MAX;
+mp_size_t sqr_fft_modf_threshold = MP_SIZE_T_MAX;
+mp_size_t mullo_basecase_threshold = MP_SIZE_T_MAX;
+mp_size_t mullo_dc_threshold = MP_SIZE_T_MAX;
+mp_size_t mullo_mul_n_threshold = MP_SIZE_T_MAX;
+mp_size_t sqrlo_basecase_threshold = MP_SIZE_T_MAX;
+mp_size_t sqrlo_dc_threshold = MP_SIZE_T_MAX;
+mp_size_t sqrlo_sqr_threshold = MP_SIZE_T_MAX;
+mp_size_t mulmid_toom42_threshold = MP_SIZE_T_MAX;
+mp_size_t mulmod_bnm1_threshold = MP_SIZE_T_MAX;
+mp_size_t sqrmod_bnm1_threshold = MP_SIZE_T_MAX;
+mp_size_t div_qr_2_pi2_threshold = MP_SIZE_T_MAX;
+mp_size_t dc_div_qr_threshold = MP_SIZE_T_MAX;
+mp_size_t dc_divappr_q_threshold = MP_SIZE_T_MAX;
+mp_size_t mu_div_qr_threshold = MP_SIZE_T_MAX;
+mp_size_t mu_divappr_q_threshold = MP_SIZE_T_MAX;
+mp_size_t mupi_div_qr_threshold = MP_SIZE_T_MAX;
+mp_size_t mu_div_q_threshold = MP_SIZE_T_MAX;
+mp_size_t dc_bdiv_qr_threshold = MP_SIZE_T_MAX;
+mp_size_t dc_bdiv_q_threshold = MP_SIZE_T_MAX;
+mp_size_t mu_bdiv_qr_threshold = MP_SIZE_T_MAX;
+mp_size_t mu_bdiv_q_threshold = MP_SIZE_T_MAX;
+mp_size_t inv_mulmod_bnm1_threshold = MP_SIZE_T_MAX;
+mp_size_t inv_newton_threshold = MP_SIZE_T_MAX;
+mp_size_t inv_appr_threshold = MP_SIZE_T_MAX;
+mp_size_t binv_newton_threshold = MP_SIZE_T_MAX;
+mp_size_t redc_1_to_redc_2_threshold = MP_SIZE_T_MAX;
+mp_size_t redc_1_to_redc_n_threshold = MP_SIZE_T_MAX;
+mp_size_t redc_2_to_redc_n_threshold = MP_SIZE_T_MAX;
+mp_size_t matrix22_strassen_threshold = MP_SIZE_T_MAX;
+mp_size_t hgcd_threshold = MP_SIZE_T_MAX;
+mp_size_t hgcd_appr_threshold = MP_SIZE_T_MAX;
+mp_size_t hgcd_reduce_threshold = MP_SIZE_T_MAX;
+mp_size_t gcd_dc_threshold = MP_SIZE_T_MAX;
+mp_size_t gcdext_dc_threshold = MP_SIZE_T_MAX;
+int div_qr_1n_pi1_method = 0;
+mp_size_t div_qr_1_norm_threshold = MP_SIZE_T_MAX;
+mp_size_t div_qr_1_unnorm_threshold = MP_SIZE_T_MAX;
+mp_size_t divrem_1_norm_threshold = MP_SIZE_T_MAX;
+mp_size_t divrem_1_unnorm_threshold = MP_SIZE_T_MAX;
+mp_size_t mod_1_norm_threshold = MP_SIZE_T_MAX;
+mp_size_t mod_1_unnorm_threshold = MP_SIZE_T_MAX;
+int mod_1_1p_method = 0;
+mp_size_t mod_1n_to_mod_1_1_threshold = MP_SIZE_T_MAX;
+mp_size_t mod_1u_to_mod_1_1_threshold = MP_SIZE_T_MAX;
+mp_size_t mod_1_1_to_mod_1_2_threshold = MP_SIZE_T_MAX;
+mp_size_t mod_1_2_to_mod_1_4_threshold = MP_SIZE_T_MAX;
+mp_size_t preinv_mod_1_to_mod_1_threshold = MP_SIZE_T_MAX;
+mp_size_t divrem_2_threshold = MP_SIZE_T_MAX;
+mp_size_t get_str_dc_threshold = MP_SIZE_T_MAX;
+mp_size_t get_str_precompute_threshold = MP_SIZE_T_MAX;
+mp_size_t set_str_dc_threshold = MP_SIZE_T_MAX;
+mp_size_t set_str_precompute_threshold = MP_SIZE_T_MAX;
+mp_size_t fac_odd_threshold = 0;
+mp_size_t fac_dsc_threshold = FAC_DSC_THRESHOLD_LIMIT;
+
+mp_size_t fft_modf_sqr_threshold = MP_SIZE_T_MAX;
+mp_size_t fft_modf_mul_threshold = MP_SIZE_T_MAX;
+
+struct param_t {
+ const char *name;
+ speed_function_t function;
+ speed_function_t function2;
+ double step_factor; /* how much to step relatively */
+ int step; /* how much to step absolutely */
+ double function_fudge; /* multiplier for "function" speeds */
+ int stop_since_change;
+ double stop_factor;
+ mp_size_t min_size;
+ int min_is_always;
+ mp_size_t max_size;
+ mp_size_t check_size;
+ mp_size_t size_extra;
+
+#define DATA_HIGH_LT_R 1
+#define DATA_HIGH_GE_R 2
+ int data_high;
+
+ int noprint;
+};
+
+
+/* These are normally undefined when false, which suits "#if" fine.
+ But give them zero values so they can be used in plain C "if"s. */
+#ifndef UDIV_PREINV_ALWAYS
+#define UDIV_PREINV_ALWAYS 0
+#endif
+#ifndef HAVE_NATIVE_mpn_divexact_1
+#define HAVE_NATIVE_mpn_divexact_1 0
+#endif
+#ifndef HAVE_NATIVE_mpn_div_qr_1n_pi1
+#define HAVE_NATIVE_mpn_div_qr_1n_pi1 0
+#endif
+#ifndef HAVE_NATIVE_mpn_divrem_1
+#define HAVE_NATIVE_mpn_divrem_1 0
+#endif
+#ifndef HAVE_NATIVE_mpn_divrem_2
+#define HAVE_NATIVE_mpn_divrem_2 0
+#endif
+#ifndef HAVE_NATIVE_mpn_mod_1
+#define HAVE_NATIVE_mpn_mod_1 0
+#endif
+#ifndef HAVE_NATIVE_mpn_mod_1_1p
+#define HAVE_NATIVE_mpn_mod_1_1p 0
+#endif
+#ifndef HAVE_NATIVE_mpn_modexact_1_odd
+#define HAVE_NATIVE_mpn_modexact_1_odd 0
+#endif
+#ifndef HAVE_NATIVE_mpn_preinv_divrem_1
+#define HAVE_NATIVE_mpn_preinv_divrem_1 0
+#endif
+#ifndef HAVE_NATIVE_mpn_preinv_mod_1
+#define HAVE_NATIVE_mpn_preinv_mod_1 0
+#endif
+#ifndef HAVE_NATIVE_mpn_sqr_basecase
+#define HAVE_NATIVE_mpn_sqr_basecase 0
+#endif
+
+
+#define MAX3(a,b,c) MAX (MAX (a, b), c)
+
+mp_limb_t
+randlimb_norm (void)
+{
+ mp_limb_t n;
+ mpn_random (&n, 1);
+ n |= GMP_NUMB_HIGHBIT;
+ return n;
+}
+
+#define GMP_NUMB_HALFMASK ((CNST_LIMB(1) << (GMP_NUMB_BITS/2)) - 1)
+
+mp_limb_t
+randlimb_half (void)
+{
+ mp_limb_t n;
+ mpn_random (&n, 1);
+ n &= GMP_NUMB_HALFMASK;
+ n += (n==0);
+ return n;
+}
+
+
+/* Add an entry to the end of the dat[] array, reallocing to make it bigger
+ if necessary. */
+void
+add_dat (mp_size_t size, double d)
+{
+#define ALLOCDAT_STEP 500
+
+ ASSERT_ALWAYS (ndat <= allocdat);
+
+ if (ndat == allocdat)
+ {
+ dat = (struct dat_t *) __gmp_allocate_or_reallocate
+ (dat, allocdat * sizeof(dat[0]),
+ (allocdat+ALLOCDAT_STEP) * sizeof(dat[0]));
+ allocdat += ALLOCDAT_STEP;
+ }
+
+ dat[ndat].size = size;
+ dat[ndat].d = d;
+ ndat++;
+}
+
+
+/* Return the threshold size based on the data accumulated. */
+mp_size_t
+analyze_dat (int final)
+{
+ double x, min_x;
+ int j, min_j;
+
+ /* If the threshold is set at dat[0].size, any positive values are bad. */
+ x = 0.0;
+ for (j = 0; j < ndat; j++)
+ if (dat[j].d > 0.0)
+ x += dat[j].d;
+
+ if (option_trace >= 2 && final)
+ {
+ printf ("\n");
+ printf ("x is the sum of the badness from setting thresh at given size\n");
+ printf (" (minimum x is sought)\n");
+ printf ("size=%ld first x=%.4f\n", (long) dat[j].size, x);
+ }
+
+ min_x = x;
+ min_j = 0;
+
+
+ /* When stepping to the next dat[j].size, positive values are no longer
+ bad (so subtracted), negative values become bad (so add the absolute
+ value, meaning subtract). */
+ for (j = 0; j < ndat; x -= dat[j].d, j++)
+ {
+ if (option_trace >= 2 && final)
+ printf ("size=%ld x=%.4f\n", (long) dat[j].size, x);
+
+ if (x < min_x)
+ {
+ min_x = x;
+ min_j = j;
+ }
+ }
+
+ return min_j;
+}
+
+
+/* Measuring for recompiled mpn/generic/div_qr_1.c,
+ * mpn/generic/divrem_1.c, mpn/generic/mod_1.c and mpz/fac_ui.c */
+
+mp_limb_t mpn_div_qr_1_tune (mp_ptr, mp_limb_t *, mp_srcptr, mp_size_t, mp_limb_t);
+
+#if defined (__cplusplus)
+extern "C" {
+#endif
+
+mp_limb_t mpn_divrem_1_tune (mp_ptr, mp_size_t, mp_srcptr, mp_size_t, mp_limb_t);
+mp_limb_t mpn_mod_1_tune (mp_srcptr, mp_size_t, mp_limb_t);
+void mpz_fac_ui_tune (mpz_ptr, unsigned long);
+
+#if defined (__cplusplus)
+}
+#endif
+
+double
+speed_mpn_mod_1_tune (struct speed_params *s)
+{
+ SPEED_ROUTINE_MPN_MOD_1 (mpn_mod_1_tune);
+}
+double
+speed_mpn_divrem_1_tune (struct speed_params *s)
+{
+ SPEED_ROUTINE_MPN_DIVREM_1 (mpn_divrem_1_tune);
+}
+double
+speed_mpz_fac_ui_tune (struct speed_params *s)
+{
+ SPEED_ROUTINE_MPZ_FAC_UI (mpz_fac_ui_tune);
+}
+double
+speed_mpn_div_qr_1_tune (struct speed_params *s)
+{
+ SPEED_ROUTINE_MPN_DIV_QR_1 (mpn_div_qr_1_tune);
+}
+
+double
+tuneup_measure (speed_function_t fun,
+ const struct param_t *param,
+ struct speed_params *s)
+{
+ static struct param_t dummy;
+ double t;
+ TMP_DECL;
+
+ if (! param)
+ param = &dummy;
+
+ s->size += param->size_extra;
+
+ TMP_MARK;
+ SPEED_TMP_ALLOC_LIMBS (s->xp, s->size, 0);
+ SPEED_TMP_ALLOC_LIMBS (s->yp, s->size, 0);
+
+ mpn_random (s->xp, s->size);
+ mpn_random (s->yp, s->size);
+
+ switch (param->data_high) {
+ case DATA_HIGH_LT_R:
+ s->xp[s->size-1] %= s->r;
+ s->yp[s->size-1] %= s->r;
+ break;
+ case DATA_HIGH_GE_R:
+ s->xp[s->size-1] |= s->r;
+ s->yp[s->size-1] |= s->r;
+ break;
+ }
+
+ t = speed_measure (fun, s);
+
+ s->size -= param->size_extra;
+
+ TMP_FREE;
+ return t;
+}
+
+
+#define PRINT_WIDTH 31
+
+void
+print_define_start (const char *name)
+{
+ printf ("#define %-*s ", PRINT_WIDTH, name);
+ if (option_trace)
+ printf ("...\n");
+}
+
+void
+print_define_end_remark (const char *name, mp_size_t value, const char *remark)
+{
+ if (option_trace)
+ printf ("#define %-*s ", PRINT_WIDTH, name);
+
+ if (value == MP_SIZE_T_MAX)
+ printf ("MP_SIZE_T_MAX");
+ else
+ printf ("%5ld", (long) value);
+
+ if (remark != NULL)
+ printf (" /* %s */", remark);
+ printf ("\n");
+ fflush (stdout);
+}
+
+void
+print_define_end (const char *name, mp_size_t value)
+{
+ const char *remark;
+ if (value == MP_SIZE_T_MAX)
+ remark = "never";
+ else if (value == 0)
+ remark = "always";
+ else
+ remark = NULL;
+ print_define_end_remark (name, value, remark);
+}
+
+void
+print_define (const char *name, mp_size_t value)
+{
+ print_define_start (name);
+ print_define_end (name, value);
+}
+
+void
+print_define_remark (const char *name, mp_size_t value, const char *remark)
+{
+ print_define_start (name);
+ print_define_end_remark (name, value, remark);
+}
+
+void
+print_define_with_speedup (const char *name, mp_size_t value,
+ mp_size_t runner_up, double speedup)
+{
+ char buf[100];
+ snprintf (buf, sizeof(buf), "%.2f%% faster than %ld",
+ 100.0 * (speedup - 1), runner_up);
+ print_define_remark (name, value, buf);
+}
+
+void
+one (mp_size_t *threshold, struct param_t *param)
+{
+ int since_positive, since_thresh_change;
+ int thresh_idx, new_thresh_idx;
+
+#define DEFAULT(x,n) do { if (! (x)) (x) = (n); } while (0)
+
+ DEFAULT (param->function_fudge, 1.0);
+ DEFAULT (param->function2, param->function);
+ DEFAULT (param->step_factor, 0.01); /* small steps by default */
+ DEFAULT (param->step, 1); /* small steps by default */
+ DEFAULT (param->stop_since_change, 80);
+ DEFAULT (param->stop_factor, 1.2);
+ DEFAULT (param->min_size, 10);
+ DEFAULT (param->max_size, DEFAULT_MAX_SIZE);
+
+ if (param->check_size != 0)
+ {
+ double t1, t2;
+ s.size = param->check_size;
+
+ *threshold = s.size+1;
+ t1 = tuneup_measure (param->function, param, &s);
+
+ *threshold = s.size;
+ t2 = tuneup_measure (param->function2, param, &s);
+ if (t1 == -1.0 || t2 == -1.0)
+ {
+ printf ("Oops, can't run both functions at size %ld\n",
+ (long) s.size);
+ abort ();
+ }
+ t1 *= param->function_fudge;
+
+ /* ask that t2 is at least 4% below t1 */
+ if (t1 < t2*1.04)
+ {
+ if (option_trace)
+ printf ("function2 never enough faster: t1=%.9f t2=%.9f\n", t1, t2);
+ *threshold = MP_SIZE_T_MAX;
+ if (! param->noprint)
+ print_define (param->name, *threshold);
+ return;
+ }
+
+ if (option_trace >= 2)
+ printf ("function2 enough faster at size=%ld: t1=%.9f t2=%.9f\n",
+ (long) s.size, t1, t2);
+ }
+
+ if (! param->noprint || option_trace)
+ print_define_start (param->name);
+
+ ndat = 0;
+ since_positive = 0;
+ since_thresh_change = 0;
+ thresh_idx = 0;
+
+ if (option_trace >= 2)
+ {
+ printf (" algorithm-A algorithm-B ratio possible\n");
+ printf (" (seconds) (seconds) diff thresh\n");
+ }
+
+ for (s.size = param->min_size;
+ s.size < param->max_size;
+ s.size += MAX ((mp_size_t) floor (s.size * param->step_factor), param->step))
+ {
+ double ti, tiplus1, d;
+
+ /*
+ FIXME: check minimum size requirements are met, possibly by just
+ checking for the -1 returns from the speed functions.
+ */
+
+ /* using method A at this size */
+ *threshold = s.size+1;
+ ti = tuneup_measure (param->function, param, &s);
+ if (ti == -1.0)
+ abort ();
+ ti *= param->function_fudge;
+
+ /* using method B at this size */
+ *threshold = s.size;
+ tiplus1 = tuneup_measure (param->function2, param, &s);
+ if (tiplus1 == -1.0)
+ abort ();
+
+ /* Calculate the fraction by which the one or the other routine is
+ slower. */
+ if (tiplus1 >= ti)
+ d = (tiplus1 - ti) / tiplus1; /* negative */
+ else
+ d = (tiplus1 - ti) / ti; /* positive */
+
+ add_dat (s.size, d);
+
+ new_thresh_idx = analyze_dat (0);
+
+ if (option_trace >= 2)
+ printf ("size=%ld %.9f %.9f % .4f %c %ld\n",
+ (long) s.size, ti, tiplus1, d,
+ ti > tiplus1 ? '#' : ' ',
+ (long) dat[new_thresh_idx].size);
+
+ /* Stop if the last time method i was faster was more than a
+ certain number of measurements ago. */
+#define STOP_SINCE_POSITIVE 200
+ if (d >= 0)
+ since_positive = 0;
+ else
+ if (++since_positive > STOP_SINCE_POSITIVE)
+ {
+ if (option_trace >= 1)
+ printf ("stopped due to since_positive (%d)\n",
+ STOP_SINCE_POSITIVE);
+ break;
+ }
+
+ /* Stop if method A has become slower by a certain factor. */
+ if (ti >= tiplus1 * param->stop_factor)
+ {
+ if (option_trace >= 1)
+ printf ("stopped due to ti >= tiplus1 * factor (%.1f)\n",
+ param->stop_factor);
+ break;
+ }
+
+ /* Stop if the threshold implied hasn't changed in a certain
+ number of measurements. (It's this condition that usually
+ stops the loop.) */
+ if (thresh_idx != new_thresh_idx)
+ since_thresh_change = 0, thresh_idx = new_thresh_idx;
+ else
+ if (++since_thresh_change > param->stop_since_change)
+ {
+ if (option_trace >= 1)
+ printf ("stopped due to since_thresh_change (%d)\n",
+ param->stop_since_change);
+ break;
+ }
+
+ /* Stop if the threshold implied is more than a certain number of
+ measurements ago. */
+#define STOP_SINCE_AFTER 500
+ if (ndat - thresh_idx > STOP_SINCE_AFTER)
+ {
+ if (option_trace >= 1)
+ printf ("stopped due to ndat - thresh_idx > amount (%d)\n",
+ STOP_SINCE_AFTER);
+ break;
+ }
+
+ /* Stop when the size limit is reached before the end of the
+ crossover, but only show this as an error for >= the default max
+ size. FIXME: Maybe should make it a param choice whether this is
+ an error. */
+ if (s.size >= param->max_size && param->max_size >= DEFAULT_MAX_SIZE)
+ {
+ fprintf (stderr, "%s\n", param->name);
+ fprintf (stderr, "sizes %ld to %ld total %d measurements\n",
+ (long) dat[0].size, (long) dat[ndat-1].size, ndat);
+ fprintf (stderr, " max size reached before end of crossover\n");
+ break;
+ }
+ }
+
+ if (option_trace >= 1)
+ printf ("sizes %ld to %ld total %d measurements\n",
+ (long) dat[0].size, (long) dat[ndat-1].size, ndat);
+
+ *threshold = dat[analyze_dat (1)].size;
+
+ if (param->min_is_always)
+ {
+ if (*threshold == param->min_size)
+ *threshold = 0;
+ }
+
+ if (! param->noprint || option_trace)
+ print_define_end (param->name, *threshold);
+}
+
+/* Time N different FUNCTIONS with the same parameters and size, to
+ select the fastest. Since *_METHOD defines start numbering from
+ one, if functions[i] is fastest, the value of the define is i+1.
+ Also output a comment with speedup compared to the next fastest
+ function. The NAME argument is used only for trace output.
+
+ Returns the index of the fastest function.
+*/
+int
+one_method (int n, speed_function_t *functions,
+ const char *name, const char *define,
+ const struct param_t *param)
+{
+ double *t;
+ int i;
+ int method;
+ int method_runner_up;
+
+ TMP_DECL;
+ TMP_MARK;
+ t = (double*) TMP_ALLOC (n * sizeof (*t));
+
+ for (i = 0; i < n; i++)
+ {
+ t[i] = tuneup_measure (functions[i], param, &s);
+ if (option_trace >= 1)
+ printf ("size=%ld, %s, method %d %.9f\n",
+ (long) s.size, name, i + 1, t[i]);
+ if (t[i] == -1.0)
+ {
+ printf ("Oops, can't measure all %s methods\n", name);
+ abort ();
+ }
+ }
+ method = 0;
+ for (i = 1; i < n; i++)
+ if (t[i] < t[method])
+ method = i;
+
+ method_runner_up = (method == 0);
+ for (i = 0; i < n; i++)
+ if (i != method && t[i] < t[method_runner_up])
+ method_runner_up = i;
+
+ print_define_with_speedup (define, method + 1, method_runner_up + 1,
+ t[method_runner_up] / t[method]);
+
+ TMP_FREE;
+ return method;
+}
+
+
+/* Special probing for the fft thresholds. The size restrictions on the
+ FFTs mean the graph of time vs size has a step effect. See this for
+ example using
+
+ ./speed -s 4096-16384 -t 128 -P foo mpn_mul_fft.8 mpn_mul_fft.9
+ gnuplot foo.gnuplot
+
+ The current approach is to compare routines at the midpoint of relevant
+ steps. Arguably a more sophisticated system of threshold data is wanted
+ if this step effect remains. */
+
+struct fft_param_t {
+ const char *table_name;
+ const char *threshold_name;
+ const char *modf_threshold_name;
+ mp_size_t *p_threshold;
+ mp_size_t *p_modf_threshold;
+ mp_size_t first_size;
+ mp_size_t max_size;
+ speed_function_t function;
+ speed_function_t mul_modf_function;
+ speed_function_t mul_function;
+ mp_size_t sqr;
+};
+
+
+/* mpn_mul_fft requires pl a multiple of 2^k limbs, but with
+ N=pl*BIT_PER_MP_LIMB it internally also pads out so N/2^k is a multiple
+ of 2^(k-1) bits. */
+
+mp_size_t
+fft_step_size (int k)
+{
+ mp_size_t step;
+
+ step = MAX ((mp_size_t) 1 << (k-1), GMP_LIMB_BITS) / GMP_LIMB_BITS;
+ step *= (mp_size_t) 1 << k;
+
+ if (step <= 0)
+ {
+ printf ("Can't handle k=%d\n", k);
+ abort ();
+ }
+
+ return step;
+}
+
+mp_size_t
+fft_next_size (mp_size_t pl, int k)
+{
+ mp_size_t m = fft_step_size (k);
+
+/* printf ("[k=%d %ld] %ld ->", k, m, pl); */
+
+ if (pl == 0 || (pl & (m-1)) != 0)
+ pl = (pl | (m-1)) + 1;
+
+/* printf (" %ld\n", pl); */
+ return pl;
+}
+
+#define NMAX_DEFAULT 1000000
+#define MAX_REPS 25
+#define MIN_REPS 5
+
+static inline size_t
+mpn_mul_fft_lcm (size_t a, unsigned int k)
+{
+ unsigned int l = k;
+
+ while (a % 2 == 0 && k > 0)
+ {
+ a >>= 1;
+ k--;
+ }
+ return a << l;
+}
+
+mp_size_t
+fftfill (mp_size_t pl, int k, int sqr)
+{
+ mp_size_t maxLK;
+ mp_bitcnt_t N, Nprime, nprime, M;
+
+ N = pl * GMP_NUMB_BITS;
+ M = N >> k;
+
+ maxLK = mpn_mul_fft_lcm ((unsigned long) GMP_NUMB_BITS, k);
+
+ Nprime = (1 + (2 * M + k + 2) / maxLK) * maxLK;
+ nprime = Nprime / GMP_NUMB_BITS;
+ if (nprime >= (sqr ? SQR_FFT_MODF_THRESHOLD : MUL_FFT_MODF_THRESHOLD))
+ {
+ size_t K2;
+ for (;;)
+ {
+ K2 = 1L << mpn_fft_best_k (nprime, sqr);
+ if ((nprime & (K2 - 1)) == 0)
+ break;
+ nprime = (nprime + K2 - 1) & -K2;
+ Nprime = nprime * GMP_LIMB_BITS;
+ }
+ }
+ ASSERT_ALWAYS (nprime < pl);
+
+ return Nprime;
+}
+
+static int
+compare_double (const void *ap, const void *bp)
+{
+ double a = * (const double *) ap;
+ double b = * (const double *) bp;
+
+ if (a < b)
+ return -1;
+ else if (a > b)
+ return 1;
+ else
+ return 0;
+}
+
+double
+median (double *times, int n)
+{
+ qsort (times, n, sizeof (double), compare_double);
+ return times[n/2];
+}
+
+#define FFT_CACHE_SIZE 25
+typedef struct fft_cache
+{
+ mp_size_t n;
+ double time;
+} fft_cache_t;
+
+fft_cache_t fft_cache[FFT_CACHE_SIZE];
+
+double
+cached_measure (mp_ptr rp, mp_srcptr ap, mp_srcptr bp, mp_size_t n, int k,
+ int n_measurements)
+{
+ int i;
+ double t, ttab[MAX_REPS];
+
+ if (fft_cache[k].n == n)
+ return fft_cache[k].time;
+
+ for (i = 0; i < n_measurements; i++)
+ {
+ speed_starttime ();
+ mpn_mul_fft (rp, n, ap, n, bp, n, k);
+ ttab[i] = speed_endtime ();
+ }
+
+ t = median (ttab, n_measurements);
+ fft_cache[k].n = n;
+ fft_cache[k].time = t;
+ return t;
+}
+
+#define INSERT_FFTTAB(idx, nval, kval) \
+ do { \
+ fft_tab[idx].n = nval; \
+ fft_tab[idx].k = kval; \
+ fft_tab[idx+1].n = (1 << 27) - 1; /* sentinel, 27b wide field */ \
+ fft_tab[idx+1].k = (1 << 5) - 1; \
+ } while (0)
+
+int
+fftmes (mp_size_t nmin, mp_size_t nmax, int initial_k, struct fft_param_t *p, int idx, int print)
+{
+ mp_size_t n, n1, prev_n1;
+ int k, best_k, last_best_k, kmax;
+ int eff, prev_eff;
+ double t0, t1;
+ int n_measurements;
+ mp_limb_t *ap, *bp, *rp;
+ mp_size_t alloc;
+ struct fft_table_nk *fft_tab;
+
+ fft_tab = mpn_fft_table3[p->sqr];
+
+ for (k = 0; k < FFT_CACHE_SIZE; k++)
+ fft_cache[k].n = 0;
+
+ if (nmin < (p->sqr ? SQR_FFT_MODF_THRESHOLD : MUL_FFT_MODF_THRESHOLD))
+ {
+ nmin = (p->sqr ? SQR_FFT_MODF_THRESHOLD : MUL_FFT_MODF_THRESHOLD);
+ }
+
+ if (print)
+ printf ("#define %s%*s", p->table_name, 38, "");
+
+ if (idx == 0)
+ {
+ INSERT_FFTTAB (0, nmin, initial_k);
+
+ if (print)
+ {
+ printf ("\\\n { ");
+ printf ("{%7u,%2u}", fft_tab[0].n, fft_tab[0].k);
+ }
+
+ idx = 1;
+ }
+
+ ap = (mp_ptr) malloc (sizeof (mp_limb_t));
+ if (p->sqr)
+ bp = ap;
+ else
+ bp = (mp_ptr) malloc (sizeof (mp_limb_t));
+ rp = (mp_ptr) malloc (sizeof (mp_limb_t));
+ alloc = 1;
+
+ /* Round n to comply to initial k value */
+ n = (nmin + ((1ul << initial_k) - 1)) & (MP_SIZE_T_MAX << initial_k);
+
+ n_measurements = (18 - initial_k) | 1;
+ n_measurements = MAX (n_measurements, MIN_REPS);
+ n_measurements = MIN (n_measurements, MAX_REPS);
+
+ last_best_k = initial_k;
+ best_k = initial_k;
+
+ while (n < nmax)
+ {
+ int start_k, end_k;
+
+ /* Assume the current best k is best until we hit its next FFT step. */
+ t0 = 99999;
+
+ prev_n1 = n + 1;
+
+ start_k = MAX (4, best_k - 4);
+ end_k = MIN (24, best_k + 4);
+ for (k = start_k; k <= end_k; k++)
+ {
+ n1 = mpn_fft_next_size (prev_n1, k);
+
+ eff = 200 * (n1 * GMP_NUMB_BITS >> k) / fftfill (n1, k, p->sqr);
+
+ if (eff < 70) /* avoid measuring too slow fft:s */
+ continue;
+
+ if (n1 > alloc)
+ {
+ alloc = n1;
+ if (p->sqr)
+ {
+ ap = (mp_ptr) realloc (ap, sizeof (mp_limb_t));
+ rp = (mp_ptr) realloc (rp, sizeof (mp_limb_t));
+ ap = bp = (mp_ptr) realloc (ap, alloc * sizeof (mp_limb_t));
+ mpn_random (ap, alloc);
+ rp = (mp_ptr) realloc (rp, alloc * sizeof (mp_limb_t));
+ }
+ else
+ {
+ ap = (mp_ptr) realloc (ap, sizeof (mp_limb_t));
+ bp = (mp_ptr) realloc (bp, sizeof (mp_limb_t));
+ rp = (mp_ptr) realloc (rp, sizeof (mp_limb_t));
+ ap = (mp_ptr) realloc (ap, alloc * sizeof (mp_limb_t));
+ mpn_random (ap, alloc);
+ bp = (mp_ptr) realloc (bp, alloc * sizeof (mp_limb_t));
+ mpn_random (bp, alloc);
+ rp = (mp_ptr) realloc (rp, alloc * sizeof (mp_limb_t));
+ }
+ }
+
+ t1 = cached_measure (rp, ap, bp, n1, k, n_measurements);
+
+ if (t1 * n_measurements > 0.3)
+ n_measurements -= 2;
+ n_measurements = MAX (n_measurements, MIN_REPS);
+
+ if (t1 < t0)
+ {
+ best_k = k;
+ t0 = t1;
+ }
+ }
+
+ n1 = mpn_fft_next_size (prev_n1, best_k);
+
+ if (last_best_k != best_k)
+ {
+ ASSERT_ALWAYS ((prev_n1 & ((1ul << last_best_k) - 1)) == 1);
+
+ if (idx >= FFT_TABLE3_SIZE)
+ {
+ printf ("FFT table exhausted, increase FFT_TABLE3_SIZE in gmp-impl.h\n");
+ abort ();
+ }
+ INSERT_FFTTAB (idx, prev_n1 >> last_best_k, best_k);
+
+ if (print)
+ {
+ printf (", ");
+ if (idx % 4 == 0)
+ printf ("\\\n ");
+ printf ("{%7u,%2u}", fft_tab[idx].n, fft_tab[idx].k);
+ }
+
+ if (option_trace >= 2)
+ {
+ printf ("{%lu,%u}\n", prev_n1, best_k);
+ fflush (stdout);
+ }
+
+ last_best_k = best_k;
+ idx++;
+ }
+
+ for (;;)
+ {
+ prev_n1 = n1;
+ prev_eff = fftfill (prev_n1, best_k, p->sqr);
+ n1 = mpn_fft_next_size (prev_n1 + 1, best_k);
+ eff = fftfill (n1, best_k, p->sqr);
+
+ if (eff != prev_eff)
+ break;
+ }
+
+ n = prev_n1;
+ }
+
+ kmax = sizeof (mp_size_t) * 4; /* GMP_MP_SIZE_T_BITS / 2 */
+ kmax = MIN (kmax, 25-1);
+ for (k = last_best_k + 1; k <= kmax; k++)
+ {
+ if (idx >= FFT_TABLE3_SIZE)
+ {
+ printf ("FFT table exhausted, increase FFT_TABLE3_SIZE in gmp-impl.h\n");
+ abort ();
+ }
+ INSERT_FFTTAB (idx, ((1ul << (2*k-2)) + 1) >> (k-1), k);
+
+ if (print)
+ {
+ printf (", ");
+ if (idx % 4 == 0)
+ printf ("\\\n ");
+ printf ("{%7u,%2u}", fft_tab[idx].n, fft_tab[idx].k);
+ }
+
+ idx++;
+ }
+
+ if (print)
+ printf (" }\n");
+
+ free (ap);
+ if (! p->sqr)
+ free (bp);
+ free (rp);
+
+ return idx;
+}
+
+void
+fft (struct fft_param_t *p)
+{
+ mp_size_t size;
+ int k, idx, initial_k;
+
+ /*** Generate MUL_FFT_MODF_THRESHOLD / SQR_FFT_MODF_THRESHOLD ***/
+
+#if 1
+ {
+ /* Use plain one() mechanism, for some reasonable initial values of k. The
+ advantage is that we don't depend on mpn_fft_table3, which can therefore
+ leave it completely uninitialized. */
+
+ static struct param_t param;
+ mp_size_t thres, best_thres;
+ int best_k;
+ char buf[20];
+
+ best_thres = MP_SIZE_T_MAX;
+ best_k = -1;
+
+ for (k = 5; k <= 7; k++)
+ {
+ param.name = p->modf_threshold_name;
+ param.min_size = 100;
+ param.max_size = 2000;
+ param.function = p->mul_function;
+ param.step_factor = 0.0;
+ param.step = 4;
+ param.function2 = p->mul_modf_function;
+ param.noprint = 1;
+ s.r = k;
+ one (&thres, &param);
+ if (thres < best_thres)
+ {
+ best_thres = thres;
+ best_k = k;
+ }
+ }
+
+ *(p->p_modf_threshold) = best_thres;
+ sprintf (buf, "k = %d", best_k);
+ print_define_remark (p->modf_threshold_name, best_thres, buf);
+ initial_k = best_k;
+ }
+#else
+ size = p->first_size;
+ for (;;)
+ {
+ double tk, tm;
+
+ size = mpn_fft_next_size (size+1, mpn_fft_best_k (size+1, p->sqr));
+ k = mpn_fft_best_k (size, p->sqr);
+
+ if (size >= p->max_size)
+ break;
+
+ s.size = size + fft_step_size (k) / 2;
+ s.r = k;
+ tk = tuneup_measure (p->mul_modf_function, NULL, &s);
+ if (tk == -1.0)
+ abort ();
+
+ tm = tuneup_measure (p->mul_function, NULL, &s);
+ if (tm == -1.0)
+ abort ();
+
+ if (option_trace >= 2)
+ printf ("at %ld size=%ld k=%d %.9f size=%ld modf %.9f\n",
+ (long) size,
+ (long) size + fft_step_size (k) / 2, k, tk,
+ (long) s.size, tm);
+
+ if (tk < tm)
+ {
+ *p->p_modf_threshold = s.size;
+ print_define (p->modf_threshold_name, *p->p_modf_threshold);
+ break;
+ }
+ }
+ initial_k = ?;
+#endif
+
+ /*** Generate MUL_FFT_TABLE3 / SQR_FFT_TABLE3 ***/
+
+ idx = fftmes (*p->p_modf_threshold, p->max_size, initial_k, p, 0, 1);
+ printf ("#define %s_SIZE %d\n", p->table_name, idx);
+
+ /*** Generate MUL_FFT_THRESHOLD / SQR_FFT_THRESHOLD ***/
+
+ size = 2 * *p->p_modf_threshold; /* OK? */
+ for (;;)
+ {
+ double tk, tm;
+ mp_size_t mulmod_size, mul_size;;
+
+ if (size >= p->max_size)
+ break;
+
+ mulmod_size = mpn_mulmod_bnm1_next_size (2 * (size + 1)) / 2;
+ mul_size = (size + mulmod_size) / 2; /* middle of step */
+
+ s.size = mulmod_size;
+ tk = tuneup_measure (p->function, NULL, &s);
+ if (tk == -1.0)
+ abort ();
+
+ s.size = mul_size;
+ tm = tuneup_measure (p->mul_function, NULL, &s);
+ if (tm == -1.0)
+ abort ();
+
+ if (option_trace >= 2)
+ printf ("at %ld size=%ld %.9f size=%ld mul %.9f\n",
+ (long) size,
+ (long) mulmod_size, tk,
+ (long) mul_size, tm);
+
+ size = mulmod_size;
+
+ if (tk < tm)
+ {
+ *p->p_threshold = s.size;
+ print_define (p->threshold_name, *p->p_threshold);
+ break;
+ }
+ }
+}
+
+/* Compare mpn_mul_1 to whatever fast exact single-limb division we have. This
+ is currently mpn_divexact_1, but will become mpn_bdiv_1_qr_pi2 or somesuch.
+ This is used in get_str and set_str. */
+void
+relspeed_div_1_vs_mul_1 (void)
+{
+ const size_t max_opsize = 100;
+ mp_size_t n;
+ long j;
+ mp_limb_t rp[max_opsize];
+ mp_limb_t ap[max_opsize];
+ double multime, divtime;
+
+ mpn_random (ap, max_opsize);
+
+ multime = 0;
+ for (n = max_opsize; n > 1; n--)
+ {
+ mpn_mul_1 (rp, ap, n, MP_BASES_BIG_BASE_10);
+ speed_starttime ();
+ for (j = speed_precision; j != 0 ; j--)
+ mpn_mul_1 (rp, ap, n, MP_BASES_BIG_BASE_10);
+ multime += speed_endtime () / n;
+ }
+
+ divtime = 0;
+ for (n = max_opsize; n > 1; n--)
+ {
+ /* Make input divisible for good measure. */
+ ap[n - 1] = mpn_mul_1 (ap, ap, n - 1, MP_BASES_BIG_BASE_10);
+
+#if HAVE_NATIVE_mpn_pi1_bdiv_q_1 || ! HAVE_NATIVE_mpn_divexact_1
+ mpn_pi1_bdiv_q_1 (rp, ap, n, MP_BASES_BIG_BASE_10,
+ MP_BASES_BIG_BASE_BINVERTED_10,
+ MP_BASES_BIG_BASE_CTZ_10);
+#else
+ mpn_divexact_1 (rp, ap, n, MP_BASES_BIG_BASE_10);
+#endif
+ speed_starttime ();
+ for (j = speed_precision; j != 0 ; j--)
+ {
+#if HAVE_NATIVE_mpn_pi1_bdiv_q_1 || ! HAVE_NATIVE_mpn_divexact_1
+ mpn_pi1_bdiv_q_1 (rp, ap, n, MP_BASES_BIG_BASE_10,
+ MP_BASES_BIG_BASE_BINVERTED_10,
+ MP_BASES_BIG_BASE_CTZ_10);
+#else
+ mpn_divexact_1 (rp, ap, n, MP_BASES_BIG_BASE_10);
+#endif
+ }
+ divtime += speed_endtime () / n;
+ }
+
+ print_define ("DIV_1_VS_MUL_1_PERCENT", (int) (100 * divtime/multime));
+}
+
+
+/* Start karatsuba from 4, since the Cray t90 ieee code is much faster at 2,
+ giving wrong results. */
+void
+tune_mul_n (void)
+{
+ static struct param_t param;
+ mp_size_t next_toom_start;
+ int something_changed;
+
+ param.function = speed_mpn_mul_n;
+
+ param.name = "MUL_TOOM22_THRESHOLD";
+ param.min_size = MAX (4, MPN_TOOM22_MUL_MINSIZE);
+ param.max_size = MUL_TOOM22_THRESHOLD_LIMIT-1;
+ one (&mul_toom22_threshold, &param);
+
+ param.noprint = 1;
+
+ /* Threshold sequence loop. Disable functions that would be used in a very
+ narrow range, re-measuring things when that happens. */
+ something_changed = 1;
+ while (something_changed)
+ {
+ something_changed = 0;
+
+ next_toom_start = mul_toom22_threshold;
+
+ if (mul_toom33_threshold != 0)
+ {
+ param.name = "MUL_TOOM33_THRESHOLD";
+ param.min_size = MAX (next_toom_start, MPN_TOOM33_MUL_MINSIZE);
+ param.max_size = MUL_TOOM33_THRESHOLD_LIMIT-1;
+ one (&mul_toom33_threshold, &param);
+
+ if (next_toom_start * 1.05 >= mul_toom33_threshold)
+ {
+ mul_toom33_threshold = 0;
+ something_changed = 1;
+ }
+ }
+
+ next_toom_start = MAX (next_toom_start, mul_toom33_threshold);
+
+ if (mul_toom44_threshold != 0)
+ {
+ param.name = "MUL_TOOM44_THRESHOLD";
+ param.min_size = MAX (next_toom_start, MPN_TOOM44_MUL_MINSIZE);
+ param.max_size = MUL_TOOM44_THRESHOLD_LIMIT-1;
+ one (&mul_toom44_threshold, &param);
+
+ if (next_toom_start * 1.05 >= mul_toom44_threshold)
+ {
+ mul_toom44_threshold = 0;
+ something_changed = 1;
+ }
+ }
+
+ next_toom_start = MAX (next_toom_start, mul_toom44_threshold);
+
+ if (mul_toom6h_threshold != 0)
+ {
+ param.name = "MUL_TOOM6H_THRESHOLD";
+ param.min_size = MAX (next_toom_start, MPN_TOOM6H_MUL_MINSIZE);
+ param.max_size = MUL_TOOM6H_THRESHOLD_LIMIT-1;
+ one (&mul_toom6h_threshold, &param);
+
+ if (next_toom_start * 1.05 >= mul_toom6h_threshold)
+ {
+ mul_toom6h_threshold = 0;
+ something_changed = 1;
+ }
+ }
+
+ next_toom_start = MAX (next_toom_start, mul_toom6h_threshold);
+
+ if (mul_toom8h_threshold != 0)
+ {
+ param.name = "MUL_TOOM8H_THRESHOLD";
+ param.min_size = MAX (next_toom_start, MPN_TOOM8H_MUL_MINSIZE);
+ param.max_size = MUL_TOOM8H_THRESHOLD_LIMIT-1;
+ one (&mul_toom8h_threshold, &param);
+
+ if (next_toom_start * 1.05 >= mul_toom8h_threshold)
+ {
+ mul_toom8h_threshold = 0;
+ something_changed = 1;
+ }
+ }
+ }
+
+ print_define ("MUL_TOOM33_THRESHOLD", MUL_TOOM33_THRESHOLD);
+ print_define ("MUL_TOOM44_THRESHOLD", MUL_TOOM44_THRESHOLD);
+ print_define ("MUL_TOOM6H_THRESHOLD", MUL_TOOM6H_THRESHOLD);
+ print_define ("MUL_TOOM8H_THRESHOLD", MUL_TOOM8H_THRESHOLD);
+
+ /* disabled until tuned */
+ MUL_FFT_THRESHOLD = MP_SIZE_T_MAX;
+}
+
+void
+tune_mul (void)
+{
+ static struct param_t param;
+ mp_size_t thres;
+
+ param.noprint = 1;
+
+ param.function = speed_mpn_toom32_for_toom43_mul;
+ param.function2 = speed_mpn_toom43_for_toom32_mul;
+ param.name = "MUL_TOOM32_TO_TOOM43_THRESHOLD";
+ param.min_size = MPN_TOOM43_MUL_MINSIZE * 24 / 17;
+ one (&thres, &param);
+ mul_toom32_to_toom43_threshold = thres * 17 / 24;
+ print_define ("MUL_TOOM32_TO_TOOM43_THRESHOLD", mul_toom32_to_toom43_threshold);
+
+ param.function = speed_mpn_toom32_for_toom53_mul;
+ param.function2 = speed_mpn_toom53_for_toom32_mul;
+ param.name = "MUL_TOOM32_TO_TOOM53_THRESHOLD";
+ param.min_size = MPN_TOOM53_MUL_MINSIZE * 30 / 19;
+ one (&thres, &param);
+ mul_toom32_to_toom53_threshold = thres * 19 / 30;
+ print_define ("MUL_TOOM32_TO_TOOM53_THRESHOLD", mul_toom32_to_toom53_threshold);
+
+ param.function = speed_mpn_toom42_for_toom53_mul;
+ param.function2 = speed_mpn_toom53_for_toom42_mul;
+ param.name = "MUL_TOOM42_TO_TOOM53_THRESHOLD";
+ param.min_size = MPN_TOOM53_MUL_MINSIZE * 20 / 11;
+ one (&thres, &param);
+ mul_toom42_to_toom53_threshold = thres * 11 / 20;
+ print_define ("MUL_TOOM42_TO_TOOM53_THRESHOLD", mul_toom42_to_toom53_threshold);
+
+ param.function = speed_mpn_toom42_mul;
+ param.function2 = speed_mpn_toom63_mul;
+ param.name = "MUL_TOOM42_TO_TOOM63_THRESHOLD";
+ param.min_size = MPN_TOOM63_MUL_MINSIZE * 2;
+ one (&thres, &param);
+ mul_toom42_to_toom63_threshold = thres / 2;
+ print_define ("MUL_TOOM42_TO_TOOM63_THRESHOLD", mul_toom42_to_toom63_threshold);
+
+ /* Use ratio 5/6 when measuring, the middle of the range 2/3 to 1. */
+ param.function = speed_mpn_toom43_for_toom54_mul;
+ param.function2 = speed_mpn_toom54_for_toom43_mul;
+ param.name = "MUL_TOOM43_TO_TOOM54_THRESHOLD";
+ param.min_size = MPN_TOOM54_MUL_MINSIZE * 6 / 5;
+ one (&thres, &param);
+ mul_toom43_to_toom54_threshold = thres * 5 / 6;
+ print_define ("MUL_TOOM43_TO_TOOM54_THRESHOLD", mul_toom43_to_toom54_threshold);
+}
+
+
+void
+tune_mullo (void)
+{
+ static struct param_t param;
+
+ param.function = speed_mpn_mullo_n;
+
+ param.name = "MULLO_BASECASE_THRESHOLD";
+ param.min_size = 2;
+ param.min_is_always = 1;
+ param.max_size = MULLO_BASECASE_THRESHOLD_LIMIT-1;
+ param.stop_factor = 1.5;
+ param.noprint = 1;
+ one (&mullo_basecase_threshold, &param);
+
+ param.name = "MULLO_DC_THRESHOLD";
+ param.min_size = 8;
+ param.min_is_always = 0;
+ param.max_size = 1000;
+ one (&mullo_dc_threshold, &param);
+
+ if (mullo_basecase_threshold >= mullo_dc_threshold)
+ {
+ print_define ("MULLO_BASECASE_THRESHOLD", mullo_dc_threshold);
+ print_define_remark ("MULLO_DC_THRESHOLD", 0, "never mpn_mullo_basecase");
+ }
+ else
+ {
+ print_define ("MULLO_BASECASE_THRESHOLD", mullo_basecase_threshold);
+ print_define ("MULLO_DC_THRESHOLD", mullo_dc_threshold);
+ }
+
+ if (WANT_FFT && mul_fft_threshold < MP_SIZE_T_MAX / 2)
+ {
+ param.name = "MULLO_MUL_N_THRESHOLD";
+ param.min_size = mullo_dc_threshold;
+ param.max_size = 2 * mul_fft_threshold;
+ param.noprint = 0;
+ param.step_factor = 0.03;
+ one (&mullo_mul_n_threshold, &param);
+ }
+ else
+ print_define_remark ("MULLO_MUL_N_THRESHOLD", MP_SIZE_T_MAX,
+ "without FFT use mullo forever");
+}
+
+void
+tune_sqrlo (void)
+{
+ static struct param_t param;
+
+ param.function = speed_mpn_sqrlo;
+
+ param.name = "SQRLO_BASECASE_THRESHOLD";
+ param.min_size = 2;
+ param.min_is_always = 1;
+ param.max_size = SQRLO_BASECASE_THRESHOLD_LIMIT-1;
+ param.stop_factor = 1.5;
+ param.noprint = 1;
+ one (&sqrlo_basecase_threshold, &param);
+
+ param.name = "SQRLO_DC_THRESHOLD";
+ param.min_size = 8;
+ param.min_is_always = 0;
+ param.max_size = SQRLO_DC_THRESHOLD_LIMIT-1;
+ one (&sqrlo_dc_threshold, &param);
+
+ if (sqrlo_basecase_threshold >= sqrlo_dc_threshold)
+ {
+ print_define ("SQRLO_BASECASE_THRESHOLD", sqrlo_dc_threshold);
+ print_define_remark ("SQRLO_DC_THRESHOLD", 0, "never mpn_sqrlo_basecase");
+ }
+ else
+ {
+ print_define ("SQRLO_BASECASE_THRESHOLD", sqrlo_basecase_threshold);
+ print_define ("SQRLO_DC_THRESHOLD", sqrlo_dc_threshold);
+ }
+
+ if (WANT_FFT && sqr_fft_threshold < MP_SIZE_T_MAX / 2)
+ {
+ param.name = "SQRLO_SQR_THRESHOLD";
+ param.min_size = sqrlo_dc_threshold;
+ param.max_size = 2 * sqr_fft_threshold;
+ param.noprint = 0;
+ param.step_factor = 0.03;
+ one (&sqrlo_sqr_threshold, &param);
+ }
+ else
+ print_define_remark ("SQRLO_SQR_THRESHOLD", MP_SIZE_T_MAX,
+ "without FFT use sqrlo forever");
+}
+
+void
+tune_mulmid (void)
+{
+ static struct param_t param;
+
+ param.name = "MULMID_TOOM42_THRESHOLD";
+ param.function = speed_mpn_mulmid_n;
+ param.min_size = 4;
+ param.max_size = 100;
+ one (&mulmid_toom42_threshold, &param);
+}
+
+void
+tune_mulmod_bnm1 (void)
+{
+ static struct param_t param;
+
+ param.name = "MULMOD_BNM1_THRESHOLD";
+ param.function = speed_mpn_mulmod_bnm1;
+ param.min_size = 4;
+ param.max_size = 100;
+ one (&mulmod_bnm1_threshold, &param);
+}
+
+void
+tune_sqrmod_bnm1 (void)
+{
+ static struct param_t param;
+
+ param.name = "SQRMOD_BNM1_THRESHOLD";
+ param.function = speed_mpn_sqrmod_bnm1;
+ param.min_size = 4;
+ param.max_size = 100;
+ one (&sqrmod_bnm1_threshold, &param);
+}
+
+
+/* Start the basecase from 3, since 1 is a special case, and if mul_basecase
+ is faster only at size==2 then we don't want to bother with extra code
+ just for that. Start karatsuba from 4 same as MUL above. */
+
+void
+tune_sqr (void)
+{
+ /* disabled until tuned */
+ SQR_FFT_THRESHOLD = MP_SIZE_T_MAX;
+
+ if (HAVE_NATIVE_mpn_sqr_basecase)
+ {
+ print_define_remark ("SQR_BASECASE_THRESHOLD", 0, "always (native)");
+ sqr_basecase_threshold = 0;
+ }
+ else
+ {
+ static struct param_t param;
+ param.name = "SQR_BASECASE_THRESHOLD";
+ param.function = speed_mpn_sqr;
+ param.min_size = 3;
+ param.min_is_always = 1;
+ param.max_size = TUNE_SQR_TOOM2_MAX;
+ param.noprint = 1;
+ one (&sqr_basecase_threshold, &param);
+ }
+
+ {
+ static struct param_t param;
+ param.name = "SQR_TOOM2_THRESHOLD";
+ param.function = speed_mpn_sqr;
+ param.min_size = MAX (4, MPN_TOOM2_SQR_MINSIZE);
+ param.max_size = TUNE_SQR_TOOM2_MAX;
+ param.noprint = 1;
+ one (&sqr_toom2_threshold, &param);
+
+ if (! HAVE_NATIVE_mpn_sqr_basecase
+ && sqr_toom2_threshold < sqr_basecase_threshold)
+ {
+ /* Karatsuba becomes faster than mul_basecase before
+ sqr_basecase does. Arrange for the expression
+ "BELOW_THRESHOLD (un, SQR_TOOM2_THRESHOLD))" which
+ selects mpn_sqr_basecase in mpn_sqr to be false, by setting
+ SQR_TOOM2_THRESHOLD to zero, making
+ SQR_BASECASE_THRESHOLD the toom2 threshold. */
+
+ sqr_basecase_threshold = SQR_TOOM2_THRESHOLD;
+ SQR_TOOM2_THRESHOLD = 0;
+
+ print_define_remark ("SQR_BASECASE_THRESHOLD", sqr_basecase_threshold,
+ "toom2");
+ print_define_remark ("SQR_TOOM2_THRESHOLD",SQR_TOOM2_THRESHOLD,
+ "never sqr_basecase");
+ }
+ else
+ {
+ if (! HAVE_NATIVE_mpn_sqr_basecase)
+ print_define ("SQR_BASECASE_THRESHOLD", sqr_basecase_threshold);
+ print_define ("SQR_TOOM2_THRESHOLD", SQR_TOOM2_THRESHOLD);
+ }
+ }
+
+ {
+ static struct param_t param;
+ mp_size_t next_toom_start;
+ int something_changed;
+
+ param.function = speed_mpn_sqr;
+ param.noprint = 1;
+
+ /* Threshold sequence loop. Disable functions that would be used in a very
+ narrow range, re-measuring things when that happens. */
+ something_changed = 1;
+ while (something_changed)
+ {
+ something_changed = 0;
+
+ next_toom_start = MAX (sqr_toom2_threshold, sqr_basecase_threshold);
+
+ sqr_toom3_threshold = SQR_TOOM3_THRESHOLD_LIMIT;
+ param.name = "SQR_TOOM3_THRESHOLD";
+ param.min_size = MAX (next_toom_start, MPN_TOOM3_SQR_MINSIZE);
+ param.max_size = SQR_TOOM3_THRESHOLD_LIMIT-1;
+ one (&sqr_toom3_threshold, &param);
+
+ next_toom_start = MAX (next_toom_start, sqr_toom3_threshold);
+
+ if (sqr_toom4_threshold != 0)
+ {
+ param.name = "SQR_TOOM4_THRESHOLD";
+ sqr_toom4_threshold = SQR_TOOM4_THRESHOLD_LIMIT;
+ param.min_size = MAX (next_toom_start, MPN_TOOM4_SQR_MINSIZE);
+ param.max_size = SQR_TOOM4_THRESHOLD_LIMIT-1;
+ one (&sqr_toom4_threshold, &param);
+
+ if (next_toom_start * 1.05 >= sqr_toom4_threshold)
+ {
+ sqr_toom4_threshold = 0;
+ something_changed = 1;
+ }
+ }
+
+ next_toom_start = MAX (next_toom_start, sqr_toom4_threshold);
+
+ if (sqr_toom6_threshold != 0)
+ {
+ param.name = "SQR_TOOM6_THRESHOLD";
+ sqr_toom6_threshold = SQR_TOOM6_THRESHOLD_LIMIT;
+ param.min_size = MAX (next_toom_start, MPN_TOOM6_SQR_MINSIZE);
+ param.max_size = SQR_TOOM6_THRESHOLD_LIMIT-1;
+ one (&sqr_toom6_threshold, &param);
+
+ if (next_toom_start * 1.05 >= sqr_toom6_threshold)
+ {
+ sqr_toom6_threshold = 0;
+ something_changed = 1;
+ }
+ }
+
+ next_toom_start = MAX (next_toom_start, sqr_toom6_threshold);
+
+ if (sqr_toom8_threshold != 0)
+ {
+ param.name = "SQR_TOOM8_THRESHOLD";
+ sqr_toom8_threshold = SQR_TOOM8_THRESHOLD_LIMIT;
+ param.min_size = MAX (next_toom_start, MPN_TOOM8_SQR_MINSIZE);
+ param.max_size = SQR_TOOM8_THRESHOLD_LIMIT-1;
+ one (&sqr_toom8_threshold, &param);
+
+ if (next_toom_start * 1.05 >= sqr_toom8_threshold)
+ {
+ sqr_toom8_threshold = 0;
+ something_changed = 1;
+ }
+ }
+ }
+
+ print_define ("SQR_TOOM3_THRESHOLD", SQR_TOOM3_THRESHOLD);
+ print_define ("SQR_TOOM4_THRESHOLD", SQR_TOOM4_THRESHOLD);
+ print_define ("SQR_TOOM6_THRESHOLD", SQR_TOOM6_THRESHOLD);
+ print_define ("SQR_TOOM8_THRESHOLD", SQR_TOOM8_THRESHOLD);
+ }
+}
+
+
+void
+tune_dc_div (void)
+{
+ s.r = 0; /* clear to make speed function do 2n/n */
+ {
+ static struct param_t param;
+ param.name = "DC_DIV_QR_THRESHOLD";
+ param.function = speed_mpn_sbpi1_div_qr;
+ param.function2 = speed_mpn_dcpi1_div_qr;
+ param.min_size = 6;
+ one (&dc_div_qr_threshold, &param);
+ }
+ {
+ static struct param_t param;
+ param.name = "DC_DIVAPPR_Q_THRESHOLD";
+ param.function = speed_mpn_sbpi1_divappr_q;
+ param.function2 = speed_mpn_dcpi1_divappr_q;
+ param.min_size = 6;
+ one (&dc_divappr_q_threshold, &param);
+ }
+}
+
+static double
+speed_mpn_sbordcpi1_div_qr (struct speed_params *s)
+{
+ if (s->size < DC_DIV_QR_THRESHOLD)
+ return speed_mpn_sbpi1_div_qr (s);
+ else
+ return speed_mpn_dcpi1_div_qr (s);
+}
+
+void
+tune_mu_div (void)
+{
+ s.r = 0; /* clear to make speed function do 2n/n */
+ {
+ static struct param_t param;
+ param.name = "MU_DIV_QR_THRESHOLD";
+ param.function = speed_mpn_dcpi1_div_qr;
+ param.function2 = speed_mpn_mu_div_qr;
+ param.min_size = mul_toom22_threshold;
+ param.max_size = 5000;
+ param.step_factor = 0.02;
+ one (&mu_div_qr_threshold, &param);
+ }
+ {
+ static struct param_t param;
+ param.name = "MU_DIVAPPR_Q_THRESHOLD";
+ param.function = speed_mpn_dcpi1_divappr_q;
+ param.function2 = speed_mpn_mu_divappr_q;
+ param.min_size = mul_toom22_threshold;
+ param.max_size = 5000;
+ param.step_factor = 0.02;
+ one (&mu_divappr_q_threshold, &param);
+ }
+ {
+ static struct param_t param;
+ param.name = "MUPI_DIV_QR_THRESHOLD";
+ param.function = speed_mpn_sbordcpi1_div_qr;
+ param.function2 = speed_mpn_mupi_div_qr;
+ param.min_size = 6;
+ param.min_is_always = 1;
+ param.max_size = 1000;
+ param.step_factor = 0.02;
+ one (&mupi_div_qr_threshold, &param);
+ }
+}
+
+void
+tune_dc_bdiv (void)
+{
+ s.r = 0; /* clear to make speed function do 2n/n*/
+ {
+ static struct param_t param;
+ param.name = "DC_BDIV_QR_THRESHOLD";
+ param.function = speed_mpn_sbpi1_bdiv_qr;
+ param.function2 = speed_mpn_dcpi1_bdiv_qr;
+ param.min_size = 4;
+ one (&dc_bdiv_qr_threshold, &param);
+ }
+ {
+ static struct param_t param;
+ param.name = "DC_BDIV_Q_THRESHOLD";
+ param.function = speed_mpn_sbpi1_bdiv_q;
+ param.function2 = speed_mpn_dcpi1_bdiv_q;
+ param.min_size = 4;
+ one (&dc_bdiv_q_threshold, &param);
+ }
+}
+
+void
+tune_mu_bdiv (void)
+{
+ s.r = 0; /* clear to make speed function do 2n/n*/
+ {
+ static struct param_t param;
+ param.name = "MU_BDIV_QR_THRESHOLD";
+ param.function = speed_mpn_dcpi1_bdiv_qr;
+ param.function2 = speed_mpn_mu_bdiv_qr;
+ param.min_size = dc_bdiv_qr_threshold;
+ param.max_size = 5000;
+ param.step_factor = 0.02;
+ one (&mu_bdiv_qr_threshold, &param);
+ }
+ {
+ static struct param_t param;
+ param.name = "MU_BDIV_Q_THRESHOLD";
+ param.function = speed_mpn_dcpi1_bdiv_q;
+ param.function2 = speed_mpn_mu_bdiv_q;
+ param.min_size = dc_bdiv_q_threshold;
+ param.max_size = 5000;
+ param.step_factor = 0.02;
+ one (&mu_bdiv_q_threshold, &param);
+ }
+}
+
+void
+tune_invertappr (void)
+{
+ static struct param_t param;
+
+ param.function = speed_mpn_ni_invertappr;
+ param.name = "INV_MULMOD_BNM1_THRESHOLD";
+ param.min_size = 5;
+ one (&inv_mulmod_bnm1_threshold, &param);
+
+ param.function = speed_mpn_invertappr;
+ param.name = "INV_NEWTON_THRESHOLD";
+ param.min_size = 5;
+ one (&inv_newton_threshold, &param);
+}
+
+void
+tune_invert (void)
+{
+ static struct param_t param;
+
+ param.function = speed_mpn_invert;
+ param.name = "INV_APPR_THRESHOLD";
+ param.min_size = 5;
+ one (&inv_appr_threshold, &param);
+}
+
+void
+tune_binvert (void)
+{
+ static struct param_t param;
+
+ param.function = speed_mpn_binvert;
+ param.name = "BINV_NEWTON_THRESHOLD";
+ param.min_size = 8; /* pointless with smaller operands */
+ one (&binv_newton_threshold, &param);
+}
+
+void
+tune_redc (void)
+{
+#define TUNE_REDC_2_MAX 100
+#if HAVE_NATIVE_mpn_addmul_2 || HAVE_NATIVE_mpn_redc_2
+#define WANT_REDC_2 1
+#endif
+
+#if WANT_REDC_2
+ {
+ static struct param_t param;
+ param.name = "REDC_1_TO_REDC_2_THRESHOLD";
+ param.function = speed_mpn_redc_1;
+ param.function2 = speed_mpn_redc_2;
+ param.min_size = 1;
+ param.min_is_always = 1;
+ param.max_size = TUNE_REDC_2_MAX;
+ param.noprint = 1;
+ param.stop_factor = 1.5;
+ one (&redc_1_to_redc_2_threshold, &param);
+ }
+ {
+ static struct param_t param;
+ param.name = "REDC_2_TO_REDC_N_THRESHOLD";
+ param.function = speed_mpn_redc_2;
+ param.function2 = speed_mpn_redc_n;
+ param.min_size = 16;
+ param.noprint = 1;
+ one (&redc_2_to_redc_n_threshold, &param);
+ }
+ if (redc_1_to_redc_2_threshold >= redc_2_to_redc_n_threshold)
+ {
+ redc_2_to_redc_n_threshold = 0; /* disable redc_2 */
+
+ /* Never use redc2, measure redc_1 -> redc_n cutoff, store result as
+ REDC_1_TO_REDC_2_THRESHOLD. */
+ {
+ static struct param_t param;
+ param.name = "REDC_1_TO_REDC_2_THRESHOLD";
+ param.function = speed_mpn_redc_1;
+ param.function2 = speed_mpn_redc_n;
+ param.min_size = 16;
+ param.noprint = 1;
+ one (&redc_1_to_redc_2_threshold, &param);
+ }
+ }
+ print_define ("REDC_1_TO_REDC_2_THRESHOLD", REDC_1_TO_REDC_2_THRESHOLD);
+ print_define ("REDC_2_TO_REDC_N_THRESHOLD", REDC_2_TO_REDC_N_THRESHOLD);
+#else
+ {
+ static struct param_t param;
+ param.name = "REDC_1_TO_REDC_N_THRESHOLD";
+ param.function = speed_mpn_redc_1;
+ param.function2 = speed_mpn_redc_n;
+ param.min_size = 16;
+ one (&redc_1_to_redc_n_threshold, &param);
+ }
+#endif
+}
+
+void
+tune_matrix22_mul (void)
+{
+ static struct param_t param;
+ param.name = "MATRIX22_STRASSEN_THRESHOLD";
+ param.function = speed_mpn_matrix22_mul;
+ param.min_size = 2;
+ one (&matrix22_strassen_threshold, &param);
+}
+
+void
+tune_hgcd2 (void)
+{
+ static struct param_t param;
+ hgcd2_func_t *f[5] =
+ { mpn_hgcd2_1,
+ mpn_hgcd2_2,
+ mpn_hgcd2_3,
+ mpn_hgcd2_4,
+ mpn_hgcd2_5 };
+ speed_function_t speed_f[5] =
+ { speed_mpn_hgcd2_1,
+ speed_mpn_hgcd2_2,
+ speed_mpn_hgcd2_3,
+ speed_mpn_hgcd2_4,
+ speed_mpn_hgcd2_5 };
+ int best;
+
+ s.size = 1;
+ best = one_method (5, speed_f, "mpn_hgcd2", "HGCD2_DIV1_METHOD", &param);
+
+ /* Use selected function when tuning hgcd and gcd */
+ hgcd2_func = f[best];
+}
+
+void
+tune_hgcd (void)
+{
+ static struct param_t param;
+ param.name = "HGCD_THRESHOLD";
+ param.function = speed_mpn_hgcd;
+ /* We seem to get strange results for small sizes */
+ param.min_size = 30;
+ one (&hgcd_threshold, &param);
+}
+
+void
+tune_hgcd_appr (void)
+{
+ static struct param_t param;
+ param.name = "HGCD_APPR_THRESHOLD";
+ param.function = speed_mpn_hgcd_appr;
+ /* We seem to get strange results for small sizes */
+ param.min_size = 50;
+ param.stop_since_change = 150;
+ one (&hgcd_appr_threshold, &param);
+}
+
+void
+tune_hgcd_reduce (void)
+{
+ static struct param_t param;
+ param.name = "HGCD_REDUCE_THRESHOLD";
+ param.function = speed_mpn_hgcd_reduce;
+ param.min_size = 30;
+ param.max_size = 7000;
+ param.step_factor = 0.04;
+ one (&hgcd_reduce_threshold, &param);
+}
+
+void
+tune_gcd_dc (void)
+{
+ static struct param_t param;
+ param.name = "GCD_DC_THRESHOLD";
+ param.function = speed_mpn_gcd;
+ param.min_size = hgcd_threshold;
+ param.max_size = 3000;
+ param.step_factor = 0.02;
+ one (&gcd_dc_threshold, &param);
+}
+
+void
+tune_gcdext_dc (void)
+{
+ static struct param_t param;
+ param.name = "GCDEXT_DC_THRESHOLD";
+ param.function = speed_mpn_gcdext;
+ param.min_size = hgcd_threshold;
+ param.max_size = 3000;
+ param.step_factor = 0.02;
+ one (&gcdext_dc_threshold, &param);
+}
+
+/* In tune_powm_sec we compute the table used by the win_size function. The
+ cutoff points are in exponent bits, disregarding other operand sizes. It is
+ not possible to use the one framework since it currently uses a granularity
+ of full limbs.
+*/
+
+/* This win_size replaces the variant in the powm code, allowing us to
+ control k in the k-ary algorithms. */
+int winsize;
+int
+win_size (mp_bitcnt_t eb)
+{
+ return winsize;
+}
+
+void
+tune_powm_sec (void)
+{
+ mp_size_t n;
+ int k, i;
+ mp_size_t itch;
+ mp_bitcnt_t nbits, nbits_next, possible_nbits_cutoff;
+ const int n_max = 3000 / GMP_NUMB_BITS;
+ const int n_measurements = 5;
+ mp_ptr rp, bp, ep, mp, tp;
+ double ttab[n_measurements], tk, tkp1;
+ TMP_DECL;
+ TMP_MARK;
+
+ possible_nbits_cutoff = 0;
+
+ k = 1;
+
+ winsize = 10; /* the itch function needs this */
+ itch = mpn_sec_powm_itch (n_max, n_max * GMP_NUMB_BITS, n_max);
+
+ rp = TMP_ALLOC_LIMBS (n_max);
+ bp = TMP_ALLOC_LIMBS (n_max);
+ ep = TMP_ALLOC_LIMBS (n_max);
+ mp = TMP_ALLOC_LIMBS (n_max);
+ tp = TMP_ALLOC_LIMBS (itch);
+
+ mpn_random (bp, n_max);
+ mpn_random (mp, n_max);
+ mp[0] |= 1;
+
+/* How about taking the M operand size into account?
+
+ An operation R=powm(B,E,N) will take time O(log(E)*M(log(N))) (assuming
+ B = O(M)).
+
+ Using k-ary and no sliding window, the precomputation will need time
+ O(2^(k-1)*M(log(N))) and the main computation will need O(log(E)*S(N)) +
+ O(log(E)/k*M(N)), for the squarings, multiplications, respectively.
+
+ An operation R=powm_sec(B,E,N) will take time like powm.
+
+ Using k-ary, the precomputation will need time O(2^k*M(log(N))) and the
+ main computation will need O(log(E)*S(N)) + O(log(E)/k*M(N)) +
+ O(log(E)/k*2^k*log(N)), for the squarings, multiplications, and full
+ table reads, respectively. */
+
+ printf ("#define POWM_SEC_TABLE ");
+
+ /* For nbits == 1, we should always use k == 1, so no need to tune
+ that. Starting with nbits == 2 also ensure that nbits always is
+ larger than the windowsize k+1. */
+ for (nbits = 2; nbits <= n_max * GMP_NUMB_BITS; )
+ {
+ n = (nbits - 1) / GMP_NUMB_BITS + 1;
+
+ /* Generate E such that sliding-window for k and k+1 works equally
+ well/poorly (but sliding is not used in powm_sec, of course). */
+ for (i = 0; i < n; i++)
+ ep[i] = ~CNST_LIMB(0);
+
+ winsize = k;
+ for (i = 0; i < n_measurements; i++)
+ {
+ speed_starttime ();
+ mpn_sec_powm (rp, bp, n, ep, nbits, mp, n, tp);
+ ttab[i] = speed_endtime ();
+ }
+ tk = median (ttab, n_measurements);
+
+ winsize = k + 1;
+ speed_starttime ();
+ for (i = 0; i < n_measurements; i++)
+ {
+ speed_starttime ();
+ mpn_sec_powm (rp, bp, n, ep, nbits, mp, n, tp);
+ ttab[i] = speed_endtime ();
+ }
+ tkp1 = median (ttab, n_measurements);
+/*
+ printf ("testing: %ld, %d", nbits, k, ep[n-1]);
+ printf (" %10.5f %10.5f\n", tk, tkp1);
+*/
+ if (tkp1 < tk)
+ {
+ if (possible_nbits_cutoff)
+ {
+ /* Two consecutive sizes indicate k increase, obey. */
+
+ /* Must always have x[k] >= k */
+ ASSERT_ALWAYS (possible_nbits_cutoff >= k);
+
+ if (k > 1)
+ printf (",");
+ printf ("%ld", (long) possible_nbits_cutoff);
+ k++;
+ possible_nbits_cutoff = 0;
+ }
+ else
+ {
+ /* One measurement indicate k increase, save nbits for further
+ consideration. */
+ /* The new larger k gets used for sizes > the cutoff
+ value, hence the cutoff should be one less than the
+ smallest size where it gives a speedup. */
+ possible_nbits_cutoff = nbits - 1;
+ }
+ }
+ else
+ possible_nbits_cutoff = 0;
+
+ nbits_next = nbits * 65 / 64;
+ nbits = nbits_next + (nbits_next == nbits);
+ }
+ printf ("\n");
+ TMP_FREE;
+}
+
+
+/* size_extra==1 reflects the fact that with high<divisor one division is
+ always skipped. Forcing high<divisor while testing ensures consistency
+ while stepping through sizes, ie. that size-1 divides will be done each
+ time.
+
+ min_size==2 and min_is_always are used so that if plain division is only
+ better at size==1 then don't bother including that code just for that
+ case, instead go with preinv always and get a size saving. */
+
+#define DIV_1_PARAMS \
+ param.check_size = 256; \
+ param.min_size = 2; \
+ param.min_is_always = 1; \
+ param.data_high = DATA_HIGH_LT_R; \
+ param.size_extra = 1; \
+ param.stop_factor = 2.0;
+
+
+double (*tuned_speed_mpn_divrem_1) (struct speed_params *);
+
+void
+tune_divrem_1 (void)
+{
+ /* plain version by default */
+ tuned_speed_mpn_divrem_1 = speed_mpn_divrem_1;
+
+ /* No support for tuning native assembler code, do that by hand and put
+ the results in the .asm file, there's no need for such thresholds to
+ appear in gmp-mparam.h. */
+ if (HAVE_NATIVE_mpn_divrem_1)
+ return;
+
+ if (GMP_NAIL_BITS != 0)
+ {
+ print_define_remark ("DIVREM_1_NORM_THRESHOLD", MP_SIZE_T_MAX,
+ "no preinv with nails");
+ print_define_remark ("DIVREM_1_UNNORM_THRESHOLD", MP_SIZE_T_MAX,
+ "no preinv with nails");
+ return;
+ }
+
+ if (UDIV_PREINV_ALWAYS)
+ {
+ print_define_remark ("DIVREM_1_NORM_THRESHOLD", 0L, "preinv always");
+ print_define ("DIVREM_1_UNNORM_THRESHOLD", 0L);
+ return;
+ }
+
+ tuned_speed_mpn_divrem_1 = speed_mpn_divrem_1_tune;
+
+ /* Tune for the integer part of mpn_divrem_1. This will very possibly be
+ a bit out for the fractional part, but that's too bad, the integer part
+ is more important. */
+ {
+ static struct param_t param;
+ param.name = "DIVREM_1_NORM_THRESHOLD";
+ DIV_1_PARAMS;
+ s.r = randlimb_norm ();
+ param.function = speed_mpn_divrem_1_tune;
+ one (&divrem_1_norm_threshold, &param);
+ }
+ {
+ static struct param_t param;
+ param.name = "DIVREM_1_UNNORM_THRESHOLD";
+ DIV_1_PARAMS;
+ s.r = randlimb_half ();
+ param.function = speed_mpn_divrem_1_tune;
+ one (&divrem_1_unnorm_threshold, &param);
+ }
+}
+
+void
+tune_div_qr_1 (void)
+{
+ if (!HAVE_NATIVE_mpn_div_qr_1n_pi1)
+ {
+ static struct param_t param;
+ speed_function_t f[] =
+ {
+ speed_mpn_div_qr_1n_pi1_1,
+ speed_mpn_div_qr_1n_pi1_2,
+ speed_mpn_div_qr_1n_pi1_3,
+ speed_mpn_div_qr_1n_pi1_4,
+ };
+
+ s.size = 10;
+ s.r = randlimb_norm ();
+
+ one_method (numberof(f), f, "mpn_div_qr_1n_pi1", "DIV_QR_1N_PI1_METHOD", &param);
+ }
+
+ {
+ static struct param_t param;
+ param.name = "DIV_QR_1_NORM_THRESHOLD";
+ DIV_1_PARAMS;
+ param.min_size = 1;
+ param.min_is_always = 0;
+ s.r = randlimb_norm ();
+ param.function = speed_mpn_div_qr_1_tune;
+ one (&div_qr_1_norm_threshold, &param);
+ }
+ {
+ static struct param_t param;
+ param.name = "DIV_QR_1_UNNORM_THRESHOLD";
+ DIV_1_PARAMS;
+ param.min_size = 1;
+ param.min_is_always = 0;
+ s.r = randlimb_half();
+ param.function = speed_mpn_div_qr_1_tune;
+ one (&div_qr_1_unnorm_threshold, &param);
+ }
+}
+
+
+void
+tune_mod_1 (void)
+{
+ /* No support for tuning native assembler code, do that by hand and put
+ the results in the .asm file, there's no need for such thresholds to
+ appear in gmp-mparam.h. */
+ if (HAVE_NATIVE_mpn_mod_1)
+ return;
+
+ if (GMP_NAIL_BITS != 0)
+ {
+ print_define_remark ("MOD_1_NORM_THRESHOLD", MP_SIZE_T_MAX,
+ "no preinv with nails");
+ print_define_remark ("MOD_1_UNNORM_THRESHOLD", MP_SIZE_T_MAX,
+ "no preinv with nails");
+ return;
+ }
+
+ if (!HAVE_NATIVE_mpn_mod_1_1p)
+ {
+ static struct param_t param;
+ speed_function_t f[2] =
+ {
+ speed_mpn_mod_1_1_1,
+ speed_mpn_mod_1_1_2,
+ };
+
+ s.size = 10;
+ s.r = randlimb_half ();
+ one_method (2, f, "mpn_mod_1_1", "MOD_1_1P_METHOD", &param);
+ }
+
+ if (UDIV_PREINV_ALWAYS)
+ {
+ print_define ("MOD_1_NORM_THRESHOLD", 0L);
+ print_define ("MOD_1_UNNORM_THRESHOLD", 0L);
+ }
+ else
+ {
+ {
+ static struct param_t param;
+ param.name = "MOD_1_NORM_THRESHOLD";
+ DIV_1_PARAMS;
+ s.r = randlimb_norm ();
+ param.function = speed_mpn_mod_1_tune;
+ one (&mod_1_norm_threshold, &param);
+ }
+ {
+ static struct param_t param;
+ param.name = "MOD_1_UNNORM_THRESHOLD";
+ DIV_1_PARAMS;
+ s.r = randlimb_half ();
+ param.function = speed_mpn_mod_1_tune;
+ one (&mod_1_unnorm_threshold, &param);
+ }
+ }
+ {
+ static struct param_t param;
+
+ param.check_size = 256;
+
+ s.r = randlimb_norm ();
+ param.function = speed_mpn_mod_1_tune;
+
+ param.name = "MOD_1N_TO_MOD_1_1_THRESHOLD";
+ param.min_size = 2;
+ one (&mod_1n_to_mod_1_1_threshold, &param);
+ }
+
+ {
+ static struct param_t param;
+
+ param.check_size = 256;
+ s.r = randlimb_half ();
+ param.noprint = 1;
+
+ param.function = speed_mpn_mod_1_1;
+ param.function2 = speed_mpn_mod_1_2;
+ param.min_is_always = 1;
+ param.name = "MOD_1_1_TO_MOD_1_2_THRESHOLD";
+ param.min_size = 2;
+ one (&mod_1_1_to_mod_1_2_threshold, &param);
+
+ param.function = speed_mpn_mod_1_2;
+ param.function2 = speed_mpn_mod_1_4;
+ param.min_is_always = 1;
+ param.name = "MOD_1_2_TO_MOD_1_4_THRESHOLD";
+ param.min_size = 1;
+ one (&mod_1_2_to_mod_1_4_threshold, &param);
+
+ if (mod_1_1_to_mod_1_2_threshold >= mod_1_2_to_mod_1_4_threshold)
+ {
+ /* Never use mod_1_2, measure mod_1_1 -> mod_1_4 */
+ mod_1_2_to_mod_1_4_threshold = 0;
+
+ param.function = speed_mpn_mod_1_1;
+ param.function2 = speed_mpn_mod_1_4;
+ param.min_is_always = 1;
+ param.name = "MOD_1_1_TO_MOD_1_4_THRESHOLD fake";
+ param.min_size = 2;
+ one (&mod_1_1_to_mod_1_2_threshold, &param);
+ }
+
+ param.function = speed_mpn_mod_1_tune;
+ param.function2 = NULL;
+ param.name = "MOD_1U_TO_MOD_1_1_THRESHOLD";
+ param.min_size = 2;
+ param.min_is_always = 0;
+ one (&mod_1u_to_mod_1_1_threshold, &param);
+
+ if (mod_1u_to_mod_1_1_threshold >= mod_1_1_to_mod_1_2_threshold)
+ mod_1_1_to_mod_1_2_threshold = 0;
+ if (mod_1u_to_mod_1_1_threshold >= mod_1_2_to_mod_1_4_threshold)
+ mod_1_2_to_mod_1_4_threshold = 0;
+
+ print_define_remark ("MOD_1U_TO_MOD_1_1_THRESHOLD", mod_1u_to_mod_1_1_threshold, NULL);
+ print_define_remark ("MOD_1_1_TO_MOD_1_2_THRESHOLD", mod_1_1_to_mod_1_2_threshold,
+ mod_1_1_to_mod_1_2_threshold == 0 ? "never mpn_mod_1_1p" : NULL);
+ print_define_remark ("MOD_1_2_TO_MOD_1_4_THRESHOLD", mod_1_2_to_mod_1_4_threshold,
+ mod_1_2_to_mod_1_4_threshold == 0 ? "never mpn_mod_1s_2p" : NULL);
+ }
+
+ {
+ static struct param_t param;
+
+ param.check_size = 256;
+
+ param.name = "PREINV_MOD_1_TO_MOD_1_THRESHOLD";
+ s.r = randlimb_norm ();
+ param.function = speed_mpn_preinv_mod_1;
+ param.function2 = speed_mpn_mod_1_tune;
+ param.min_size = 1;
+ one (&preinv_mod_1_to_mod_1_threshold, &param);
+ }
+}
+
+
+/* A non-zero DIVREM_1_UNNORM_THRESHOLD (or DIVREM_1_NORM_THRESHOLD) would
+ imply that udiv_qrnnd_preinv is worth using, but it seems most
+ straightforward to compare mpn_preinv_divrem_1 and mpn_divrem_1_div
+ directly. */
+
+void
+tune_preinv_divrem_1 (void)
+{
+ static struct param_t param;
+ speed_function_t divrem_1;
+ const char *divrem_1_name;
+ double t1, t2;
+
+ if (GMP_NAIL_BITS != 0)
+ {
+ print_define_remark ("USE_PREINV_DIVREM_1", 0, "no preinv with nails");
+ return;
+ }
+
+ /* Any native version of mpn_preinv_divrem_1 is assumed to exist because
+ it's faster than mpn_divrem_1. */
+ if (HAVE_NATIVE_mpn_preinv_divrem_1)
+ {
+ print_define_remark ("USE_PREINV_DIVREM_1", 1, "native");
+ return;
+ }
+
+ /* If udiv_qrnnd_preinv is the only division method then of course
+ mpn_preinv_divrem_1 should be used. */
+ if (UDIV_PREINV_ALWAYS)
+ {
+ print_define_remark ("USE_PREINV_DIVREM_1", 1, "preinv always");
+ return;
+ }
+
+ /* If we've got an assembler version of mpn_divrem_1, then compare against
+ that, not the mpn_divrem_1_div generic C. */
+ if (HAVE_NATIVE_mpn_divrem_1)
+ {
+ divrem_1 = speed_mpn_divrem_1;
+ divrem_1_name = "mpn_divrem_1";
+ }
+ else
+ {
+ divrem_1 = speed_mpn_divrem_1_div;
+ divrem_1_name = "mpn_divrem_1_div";
+ }
+
+ param.data_high = DATA_HIGH_LT_R; /* allow skip one division */
+ s.size = 200; /* generous but not too big */
+ /* Divisor, nonzero. Unnormalized so as to exercise the shift!=0 case,
+ since in general that's probably most common, though in fact for a
+ 64-bit limb mp_bases[10].big_base is normalized. */
+ s.r = urandom() & (GMP_NUMB_MASK >> 4);
+ if (s.r == 0) s.r = 123;
+
+ t1 = tuneup_measure (speed_mpn_preinv_divrem_1, &param, &s);
+ t2 = tuneup_measure (divrem_1, &param, &s);
+ if (t1 == -1.0 || t2 == -1.0)
+ {
+ printf ("Oops, can't measure mpn_preinv_divrem_1 and %s at %ld\n",
+ divrem_1_name, (long) s.size);
+ abort ();
+ }
+ if (option_trace >= 1)
+ printf ("size=%ld, mpn_preinv_divrem_1 %.9f, %s %.9f\n",
+ (long) s.size, t1, divrem_1_name, t2);
+
+ print_define_remark ("USE_PREINV_DIVREM_1", (mp_size_t) (t1 < t2), NULL);
+}
+
+
+
+void
+tune_divrem_2 (void)
+{
+ static struct param_t param;
+
+ /* No support for tuning native assembler code, do that by hand and put
+ the results in the .asm file, and there's no need for such thresholds
+ to appear in gmp-mparam.h. */
+ if (HAVE_NATIVE_mpn_divrem_2)
+ return;
+
+ if (GMP_NAIL_BITS != 0)
+ {
+ print_define_remark ("DIVREM_2_THRESHOLD", MP_SIZE_T_MAX,
+ "no preinv with nails");
+ return;
+ }
+
+ if (UDIV_PREINV_ALWAYS)
+ {
+ print_define_remark ("DIVREM_2_THRESHOLD", 0L, "preinv always");
+ return;
+ }
+
+ /* Tune for the integer part of mpn_divrem_2. This will very possibly be
+ a bit out for the fractional part, but that's too bad, the integer part
+ is more important.
+
+ min_size must be >=2 since nsize>=2 is required, but is set to 4 to save
+ code space if plain division is better only at size==2 or size==3. */
+ param.name = "DIVREM_2_THRESHOLD";
+ param.check_size = 256;
+ param.min_size = 4;
+ param.min_is_always = 1;
+ param.size_extra = 2; /* does qsize==nsize-2 divisions */
+ param.stop_factor = 2.0;
+
+ s.r = randlimb_norm ();
+ param.function = speed_mpn_divrem_2;
+ one (&divrem_2_threshold, &param);
+}
+
+void
+tune_div_qr_2 (void)
+{
+ static struct param_t param;
+ param.name = "DIV_QR_2_PI2_THRESHOLD";
+ param.function = speed_mpn_div_qr_2n;
+ param.check_size = 500;
+ param.min_size = 4;
+ one (&div_qr_2_pi2_threshold, &param);
+}
+
+/* mpn_divexact_1 is vaguely expected to be used on smallish divisors, so
+ tune for that. Its speed can differ on odd or even divisor, so take an
+ average threshold for the two.
+
+ mpn_divrem_1 can vary with high<divisor or not, whereas mpn_divexact_1
+ might not vary that way, but don't test this since high<divisor isn't
+ expected to occur often with small divisors. */
+
+void
+tune_divexact_1 (void)
+{
+ static struct param_t param;
+ mp_size_t thresh[2], average;
+ int low, i;
+
+ /* Any native mpn_divexact_1 is assumed to incorporate all the speed of a
+ full mpn_divrem_1. */
+ if (HAVE_NATIVE_mpn_divexact_1)
+ {
+ print_define_remark ("DIVEXACT_1_THRESHOLD", 0, "always (native)");
+ return;
+ }
+
+ ASSERT_ALWAYS (tuned_speed_mpn_divrem_1 != NULL);
+
+ param.name = "DIVEXACT_1_THRESHOLD";
+ param.data_high = DATA_HIGH_GE_R;
+ param.check_size = 256;
+ param.min_size = 2;
+ param.stop_factor = 1.5;
+ param.function = tuned_speed_mpn_divrem_1;
+ param.function2 = speed_mpn_divexact_1;
+ param.noprint = 1;
+
+ print_define_start (param.name);
+
+ for (low = 0; low <= 1; low++)
+ {
+ s.r = randlimb_half();
+ if (low == 0)
+ s.r |= 1;
+ else
+ s.r &= ~CNST_LIMB(7);
+
+ one (&thresh[low], &param);
+ if (option_trace)
+ printf ("low=%d thresh %ld\n", low, (long) thresh[low]);
+
+ if (thresh[low] == MP_SIZE_T_MAX)
+ {
+ average = MP_SIZE_T_MAX;
+ goto divexact_1_done;
+ }
+ }
+
+ if (option_trace)
+ {
+ printf ("average of:");
+ for (i = 0; i < numberof(thresh); i++)
+ printf (" %ld", (long) thresh[i]);
+ printf ("\n");
+ }
+
+ average = 0;
+ for (i = 0; i < numberof(thresh); i++)
+ average += thresh[i];
+ average /= numberof(thresh);
+
+ /* If divexact turns out to be better as early as 3 limbs, then use it
+ always, so as to reduce code size and conditional jumps. */
+ if (average <= 3)
+ average = 0;
+
+ divexact_1_done:
+ print_define_end (param.name, average);
+}
+
+
+/* The generic mpn_modexact_1_odd skips a divide step if high<divisor, the
+ same as mpn_mod_1, but this might not be true of an assembler
+ implementation. The threshold used is an average based on data where a
+ divide can be skipped and where it can't.
+
+ If modexact turns out to be better as early as 3 limbs, then use it
+ always, so as to reduce code size and conditional jumps. */
+
+void
+tune_modexact_1_odd (void)
+{
+ static struct param_t param;
+ mp_size_t thresh_lt, thresh_ge, average;
+
+#if 0
+ /* Any native mpn_modexact_1_odd is assumed to incorporate all the speed
+ of a full mpn_mod_1. */
+ if (HAVE_NATIVE_mpn_modexact_1_odd)
+ {
+ print_define_remark ("BMOD_1_TO_MOD_1_THRESHOLD", MP_SIZE_T_MAX, "always bmod_1");
+ return;
+ }
+#endif
+
+ param.name = "BMOD_1_TO_MOD_1_THRESHOLD";
+ param.check_size = 256;
+ param.min_size = 2;
+ param.stop_factor = 1.5;
+ param.function = speed_mpn_modexact_1c_odd;
+ param.function2 = speed_mpn_mod_1_tune;
+ param.noprint = 1;
+ s.r = randlimb_half () | 1;
+
+ print_define_start (param.name);
+
+ param.data_high = DATA_HIGH_LT_R;
+ one (&thresh_lt, &param);
+ if (option_trace)
+ printf ("lt thresh %ld\n", (long) thresh_lt);
+
+ average = thresh_lt;
+ if (thresh_lt != MP_SIZE_T_MAX)
+ {
+ param.data_high = DATA_HIGH_GE_R;
+ one (&thresh_ge, &param);
+ if (option_trace)
+ printf ("ge thresh %ld\n", (long) thresh_ge);
+
+ if (thresh_ge != MP_SIZE_T_MAX)
+ {
+ average = (thresh_ge + thresh_lt) / 2;
+ if (thresh_ge <= 3)
+ average = 0;
+ }
+ }
+
+ print_define_end (param.name, average);
+}
+
+
+void
+tune_jacobi_base (void)
+{
+ static struct param_t param;
+ speed_function_t f[4] =
+ {
+ speed_mpn_jacobi_base_1,
+ speed_mpn_jacobi_base_2,
+ speed_mpn_jacobi_base_3,
+ speed_mpn_jacobi_base_4,
+ };
+
+ s.size = GMP_LIMB_BITS * 3 / 4;
+
+ one_method (4, f, "mpn_jacobi_base", "JACOBI_BASE_METHOD", &param);
+}
+
+
+void
+tune_get_str (void)
+{
+ /* Tune for decimal, it being most common. Some rough testing suggests
+ other bases are different, but not by very much. */
+ s.r = 10;
+ {
+ static struct param_t param;
+ GET_STR_PRECOMPUTE_THRESHOLD = 0;
+ param.name = "GET_STR_DC_THRESHOLD";
+ param.function = speed_mpn_get_str;
+ param.min_size = 4;
+ param.max_size = GET_STR_THRESHOLD_LIMIT;
+ one (&get_str_dc_threshold, &param);
+ }
+ {
+ static struct param_t param;
+ param.name = "GET_STR_PRECOMPUTE_THRESHOLD";
+ param.function = speed_mpn_get_str;
+ param.min_size = GET_STR_DC_THRESHOLD;
+ param.max_size = GET_STR_THRESHOLD_LIMIT;
+ one (&get_str_precompute_threshold, &param);
+ }
+}
+
+
+double
+speed_mpn_pre_set_str (struct speed_params *s)
+{
+ unsigned char *str;
+ mp_ptr wp;
+ mp_size_t wn;
+ unsigned i;
+ int base;
+ double t;
+ mp_ptr powtab_mem, tp;
+ powers_t powtab[GMP_LIMB_BITS];
+ mp_size_t un;
+ int chars_per_limb;
+ TMP_DECL;
+
+ SPEED_RESTRICT_COND (s->size >= 1);
+
+ base = s->r == 0 ? 10 : s->r;
+ SPEED_RESTRICT_COND (base >= 2 && base <= 256);
+
+ TMP_MARK;
+
+ str = (unsigned char *) TMP_ALLOC (s->size);
+ for (i = 0; i < s->size; i++)
+ str[i] = s->xp[i] % base;
+
+ LIMBS_PER_DIGIT_IN_BASE (wn, s->size, base);
+ SPEED_TMP_ALLOC_LIMBS (wp, wn, s->align_wp);
+
+ /* use this during development to check wn is big enough */
+ /*
+ ASSERT_ALWAYS (mpn_set_str (wp, str, s->size, base) <= wn);
+ */
+
+ speed_operand_src (s, (mp_ptr) str, s->size/GMP_LIMB_BYTES);
+ speed_operand_dst (s, wp, wn);
+ speed_cache_fill (s);
+
+ chars_per_limb = mp_bases[base].chars_per_limb;
+ un = s->size / chars_per_limb + 1;
+ powtab_mem = TMP_BALLOC_LIMBS (mpn_str_powtab_alloc (un));
+ size_t n_pows = mpn_compute_powtab (powtab, powtab_mem, un, base);
+ powers_t *pt = powtab + n_pows;
+ tp = TMP_BALLOC_LIMBS (mpn_dc_set_str_itch (un));
+
+ speed_starttime ();
+ i = s->reps;
+ do
+ {
+ mpn_pre_set_str (wp, str, s->size, pt, tp);
+ }
+ while (--i != 0);
+ t = speed_endtime ();
+
+ TMP_FREE;
+ return t;
+}
+
+void
+tune_set_str (void)
+{
+ s.r = 10; /* decimal */
+ {
+ static struct param_t param;
+ SET_STR_PRECOMPUTE_THRESHOLD = 0;
+ param.step_factor = 0.01;
+ param.name = "SET_STR_DC_THRESHOLD";
+ param.function = speed_mpn_pre_set_str;
+ param.min_size = 100;
+ param.max_size = 50000;
+ one (&set_str_dc_threshold, &param);
+ }
+ {
+ static struct param_t param;
+ param.step_factor = 0.02;
+ param.name = "SET_STR_PRECOMPUTE_THRESHOLD";
+ param.function = speed_mpn_set_str;
+ param.min_size = SET_STR_DC_THRESHOLD;
+ param.max_size = 100000;
+ one (&set_str_precompute_threshold, &param);
+ }
+}
+
+
+void
+tune_fft_mul (void)
+{
+ static struct fft_param_t param;
+
+ if (option_fft_max_size == 0)
+ return;
+
+ param.table_name = "MUL_FFT_TABLE3";
+ param.threshold_name = "MUL_FFT_THRESHOLD";
+ param.p_threshold = &mul_fft_threshold;
+ param.modf_threshold_name = "MUL_FFT_MODF_THRESHOLD";
+ param.p_modf_threshold = &mul_fft_modf_threshold;
+ param.first_size = MUL_TOOM33_THRESHOLD / 2;
+ param.max_size = option_fft_max_size;
+ param.function = speed_mpn_fft_mul;
+ param.mul_modf_function = speed_mpn_mul_fft;
+ param.mul_function = speed_mpn_mul_n;
+ param.sqr = 0;
+ fft (&param);
+}
+
+
+void
+tune_fft_sqr (void)
+{
+ static struct fft_param_t param;
+
+ if (option_fft_max_size == 0)
+ return;
+
+ param.table_name = "SQR_FFT_TABLE3";
+ param.threshold_name = "SQR_FFT_THRESHOLD";
+ param.p_threshold = &sqr_fft_threshold;
+ param.modf_threshold_name = "SQR_FFT_MODF_THRESHOLD";
+ param.p_modf_threshold = &sqr_fft_modf_threshold;
+ param.first_size = SQR_TOOM3_THRESHOLD / 2;
+ param.max_size = option_fft_max_size;
+ param.function = speed_mpn_fft_sqr;
+ param.mul_modf_function = speed_mpn_mul_fft_sqr;
+ param.mul_function = speed_mpn_sqr;
+ param.sqr = 1;
+ fft (&param);
+}
+
+void
+tune_fac_ui (void)
+{
+ static struct param_t param;
+
+ param.function = speed_mpz_fac_ui_tune;
+
+ param.name = "FAC_DSC_THRESHOLD";
+ param.min_size = 70;
+ param.max_size = FAC_DSC_THRESHOLD_LIMIT;
+ one (&fac_dsc_threshold, &param);
+
+ param.name = "FAC_ODD_THRESHOLD";
+ param.min_size = 22;
+ param.stop_factor = 1.7;
+ param.min_is_always = 1;
+ one (&fac_odd_threshold, &param);
+}
+
+void
+all (void)
+{
+ time_t start_time, end_time;
+ TMP_DECL;
+
+ TMP_MARK;
+ SPEED_TMP_ALLOC_LIMBS (s.xp_block, SPEED_BLOCK_SIZE, 0);
+ SPEED_TMP_ALLOC_LIMBS (s.yp_block, SPEED_BLOCK_SIZE, 0);
+
+ mpn_random (s.xp_block, SPEED_BLOCK_SIZE);
+ mpn_random (s.yp_block, SPEED_BLOCK_SIZE);
+
+ fprintf (stderr, "Parameters for %s\n", GMP_MPARAM_H_SUGGEST);
+
+ speed_time_init ();
+ fprintf (stderr, "Using: %s\n", speed_time_string);
+
+ fprintf (stderr, "speed_precision %d", speed_precision);
+ if (speed_unittime == 1.0)
+ fprintf (stderr, ", speed_unittime 1 cycle");
+ else
+ fprintf (stderr, ", speed_unittime %.2e secs", speed_unittime);
+ if (speed_cycletime == 1.0 || speed_cycletime == 0.0)
+ fprintf (stderr, ", CPU freq unknown\n");
+ else
+ fprintf (stderr, ", CPU freq %.2f MHz\n", 1e-6/speed_cycletime);
+
+ fprintf (stderr, "DEFAULT_MAX_SIZE %d, fft_max_size %ld\n",
+ DEFAULT_MAX_SIZE, (long) option_fft_max_size);
+ fprintf (stderr, "\n");
+
+ time (&start_time);
+ {
+ struct tm *tp;
+ tp = localtime (&start_time);
+ printf ("/* Generated by tuneup.c, %d-%02d-%02d, ",
+ tp->tm_year+1900, tp->tm_mon+1, tp->tm_mday);
+
+#ifdef __GNUC__
+ /* gcc sub-minor version doesn't seem to come through as a define */
+ printf ("gcc %d.%d */\n", __GNUC__, __GNUC_MINOR__);
+#define PRINTED_COMPILER
+#endif
+#if defined (__SUNPRO_C)
+ printf ("Sun C %d.%d */\n", __SUNPRO_C / 0x100, __SUNPRO_C % 0x100);
+#define PRINTED_COMPILER
+#endif
+#if ! defined (__GNUC__) && defined (__sgi) && defined (_COMPILER_VERSION)
+ /* gcc defines __sgi and _COMPILER_VERSION on irix 6, avoid that */
+ printf ("MIPSpro C %d.%d.%d */\n",
+ _COMPILER_VERSION / 100,
+ _COMPILER_VERSION / 10 % 10,
+ _COMPILER_VERSION % 10);
+#define PRINTED_COMPILER
+#endif
+#if defined (__DECC) && defined (__DECC_VER)
+ printf ("DEC C %d */\n", __DECC_VER);
+#define PRINTED_COMPILER
+#endif
+#if ! defined (PRINTED_COMPILER)
+ printf ("system compiler */\n");
+#endif
+ }
+ printf ("\n");
+
+ tune_divrem_1 ();
+ tune_mod_1 ();
+ tune_preinv_divrem_1 ();
+ tune_div_qr_1 ();
+#if 0
+ tune_divrem_2 ();
+#endif
+ tune_div_qr_2 ();
+ tune_divexact_1 ();
+ tune_modexact_1_odd ();
+ printf("\n");
+
+ relspeed_div_1_vs_mul_1 ();
+ printf("\n");
+
+ tune_mul_n ();
+ printf("\n");
+
+ tune_mul ();
+ printf("\n");
+
+ tune_sqr ();
+ printf("\n");
+
+ tune_mulmid ();
+ printf("\n");
+
+ tune_mulmod_bnm1 ();
+ tune_sqrmod_bnm1 ();
+ printf("\n");
+
+ tune_fft_mul ();
+ printf("\n");
+
+ tune_fft_sqr ();
+ printf ("\n");
+
+ tune_mullo ();
+ tune_sqrlo ();
+ printf("\n");
+
+ tune_dc_div ();
+ tune_dc_bdiv ();
+
+ printf("\n");
+ tune_invertappr ();
+ tune_invert ();
+ printf("\n");
+
+ tune_binvert ();
+ tune_redc ();
+ printf("\n");
+
+ tune_mu_div ();
+ tune_mu_bdiv ();
+ printf("\n");
+
+ tune_powm_sec ();
+ printf("\n");
+
+ tune_get_str ();
+ tune_set_str ();
+ printf("\n");
+
+ tune_fac_ui ();
+ printf("\n");
+
+ tune_matrix22_mul ();
+ tune_hgcd2 ();
+ tune_hgcd ();
+ tune_hgcd_appr ();
+ tune_hgcd_reduce();
+ tune_gcd_dc ();
+ tune_gcdext_dc ();
+ tune_jacobi_base ();
+ printf("\n");
+
+ time (&end_time);
+ printf ("/* Tuneup completed successfully, took %ld seconds */\n",
+ (long) (end_time - start_time));
+
+ TMP_FREE;
+}
+
+
+int
+main (int argc, char *argv[])
+{
+ int opt;
+
+ /* 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);
+
+ while ((opt = getopt(argc, argv, "f:o:p:t")) != EOF)
+ {
+ switch (opt) {
+ case 'f':
+ if (optarg[0] == 't')
+ option_fft_trace = 2;
+ else
+ option_fft_max_size = atol (optarg);
+ break;
+ case 'o':
+ speed_option_set (optarg);
+ break;
+ case 'p':
+ speed_precision = atoi (optarg);
+ break;
+ case 't':
+ option_trace++;
+ break;
+ case '?':
+ exit(1);
+ }
+ }
+
+ all ();
+ exit (0);
+}
generated by cgit v1.2.3 (git 2.25.1) at 2024-09-19 17:06:08 +0000