/* Create tuned thresholds for various algorithms. Copyright 1999, 2000, 2001, 2002, 2003, 2005 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 the GNU Lesser General Public License as published by the Free Software Foundation; either version 2.1 of the License, or (at your option) any later version. 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 Lesser General Public License for more details. You should have received a copy of the GNU Lesser General Public License along with the GNU MP Library; see the file COPYING.LIB. If not, write to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. */ /* 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_KARATSUBA_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_TOOM3_THRESHOLD makes use of the tuned MUL_KARATSUBA_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_kara_sqr_n. 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 #include #include #include #if HAVE_UNISTD_H #include #endif #include "gmp.h" #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_KARATSUBA_MAX #define TUNE_SQR_KARATSUBA_MAX 0 #endif mp_size_t mul_karatsuba_threshold = MP_SIZE_T_MAX; mp_size_t mul_toom3_threshold = MUL_TOOM3_THRESHOLD_LIMIT; 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_karatsuba_threshold = (TUNE_SQR_KARATSUBA_MAX == 0 ? MP_SIZE_T_MAX : TUNE_SQR_KARATSUBA_MAX); mp_size_t sqr_toom3_threshold = SQR_TOOM3_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 mullow_basecase_threshold = MP_SIZE_T_MAX; mp_size_t mullow_dc_threshold = MP_SIZE_T_MAX; mp_size_t mullow_mul_n_threshold = MP_SIZE_T_MAX; mp_size_t div_sb_preinv_threshold = MP_SIZE_T_MAX; mp_size_t div_dc_threshold = MP_SIZE_T_MAX; mp_size_t powm_threshold = MP_SIZE_T_MAX; mp_size_t gcd_accel_threshold = MP_SIZE_T_MAX; mp_size_t gcdext_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; 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_threshold = MP_SIZE_T_MAX; 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 sizes (rounded down) */ 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_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_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/divrem_1.c and mpn/generic/mod_1.c */ mp_limb_t mpn_divrem_1_tune _PROTO ((mp_ptr qp, mp_size_t xsize, mp_srcptr ap, mp_size_t size, mp_limb_t d)); mp_limb_t mpn_mod_1_tune _PROTO ((mp_srcptr ap, mp_size_t size, mp_limb_t d)); 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 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 28 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"); } 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 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->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), 1)) { double ti, tiplus1, d; /* If there's a size limit and it's reached then it should still be sensible to analyze the data since we want the threshold put either at or near the limit. */ if (s.size >= param->max_size) { if (option_trace) printf ("Reached maximum size (%ld) without otherwise stopping\n", (long) param->max_size); break; } /* 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 ususally 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); } /* 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_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), BITS_PER_MP_LIMB) / BITS_PER_MP_LIMB; 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; } void fft (struct fft_param_t *p) { mp_size_t size; int i, k; for (i = 0; i < numberof (mpn_fft_table[p->sqr]); i++) mpn_fft_table[p->sqr][i] = MP_SIZE_T_MAX; *p->p_threshold = MP_SIZE_T_MAX; *p->p_modf_threshold = MP_SIZE_T_MAX; option_trace = MAX (option_trace, option_fft_trace); printf ("#define %s {", p->table_name); if (option_trace >= 2) printf ("\n"); k = FFT_FIRST_K; size = p->first_size; for (;;) { double tk, tk1; size = fft_next_size (size+1, k+1); if (size >= p->max_size) break; if (k >= FFT_FIRST_K + numberof (mpn_fft_table[p->sqr])) break; /* compare k to k+1 in the middle of the current k+1 step */ s.size = size + fft_step_size (k+1) / 2; s.r = k; tk = tuneup_measure (p->function, NULL, &s); if (tk == -1.0) abort (); s.r = k+1; tk1 = tuneup_measure (p->function, NULL, &s); if (tk1 == -1.0) abort (); if (option_trace >= 2) printf ("at %ld size=%ld k=%d %.9f k=%d %.9f\n", (long) size, (long) s.size, k, tk, k+1, tk1); /* declare the k+1 threshold as soon as it's faster at its midpoint */ if (tk1 < tk) { mpn_fft_table[p->sqr][k-FFT_FIRST_K] = s.size; printf (" %ld,", (long) s.size); if (option_trace >= 2) printf ("\n"); k++; } } mpn_fft_table[p->sqr][k-FFT_FIRST_K] = 0; printf (" 0 }\n"); size = p->first_size; /* Declare an FFT faster than a plain toom3 etc multiplication found as soon as one faster measurement obtained. A multiplication in the middle of the FFT step is tested. */ for (;;) { int modf = (*p->p_modf_threshold == MP_SIZE_T_MAX); double tk, tm; /* k=7 should be the first FFT which can beat toom3 on a full multiply, so jump to that threshold and save some probing after the modf threshold is found. */ if (!modf && size < mpn_fft_table[p->sqr][2]) { size = mpn_fft_table[p->sqr][2]; if (option_trace >= 2) printf ("jump to size=%ld\n", (long) size); } size = fft_next_size (size+1, mpn_fft_best_k (size, 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->function, NULL, &s); if (tk == -1.0) abort (); if (!modf) s.size /= 2; 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 %s mul %.9f\n", (long) size, (long) size + fft_step_size (k) / 2, k, tk, (long) s.size, modf ? "modf" : "full", tm); if (tk < tm) { if (modf) { *p->p_modf_threshold = s.size; print_define (p->modf_threshold_name, *p->p_modf_threshold); } else { *p->p_threshold = s.size; print_define (p->threshold_name, *p->p_threshold); break; } } } } /* Start karatsuba from 4, since the Cray t90 ieee code is much faster at 2, giving wrong results. */ void tune_mul (void) { static struct param_t param; param.function = speed_mpn_mul_n; param.name = "MUL_KARATSUBA_THRESHOLD"; param.min_size = MAX (4, MPN_KARA_MUL_N_MINSIZE); param.max_size = MUL_KARATSUBA_THRESHOLD_LIMIT-1; one (&mul_karatsuba_threshold, ¶m); param.name = "MUL_TOOM3_THRESHOLD"; param.min_size = MAX (mul_karatsuba_threshold, MPN_TOOM3_MUL_N_MINSIZE); param.max_size = MUL_TOOM3_THRESHOLD_LIMIT-1; one (&mul_toom3_threshold, ¶m); /* disabled until tuned */ MUL_FFT_THRESHOLD = MP_SIZE_T_MAX; } /* This was written by the tuneup challenged tege. Kevin, please delete this comment when you've reviewed/rewritten this. :-) */ void tune_mullow (void) { static struct param_t param; param.function = speed_mpn_mullow_n; param.name = "MULLOW_BASECASE_THRESHOLD"; param.min_size = 3; param.min_is_always = 1; param.max_size = MULLOW_BASECASE_THRESHOLD_LIMIT-1; one (&mullow_basecase_threshold, ¶m); param.min_is_always = 0; /* ??? */ param.name = "MULLOW_DC_THRESHOLD"; param.min_size = mul_karatsuba_threshold; param.max_size = 1000; one (&mullow_dc_threshold, ¶m); param.name = "MULLOW_MUL_N_THRESHOLD"; param.min_size = mullow_dc_threshold; param.max_size = 2000; one (&mullow_mul_n_threshold, ¶m); /* disabled until tuned */ MUL_FFT_THRESHOLD = MP_SIZE_T_MAX; } /* 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_n; param.min_size = 3; param.min_is_always = 1; param.max_size = TUNE_SQR_KARATSUBA_MAX; param.noprint = 1; one (&sqr_basecase_threshold, ¶m); } { static struct param_t param; param.name = "SQR_KARATSUBA_THRESHOLD"; param.function = speed_mpn_sqr_n; param.min_size = MAX (4, MPN_KARA_SQR_N_MINSIZE); param.max_size = TUNE_SQR_KARATSUBA_MAX; param.noprint = 1; one (&sqr_karatsuba_threshold, ¶m); if (! HAVE_NATIVE_mpn_sqr_basecase && sqr_karatsuba_threshold < sqr_basecase_threshold) { /* Karatsuba becomes faster than mul_basecase before sqr_basecase does. Arrange for the expression "BELOW_THRESHOLD (un, SQR_KARATSUBA_THRESHOLD))" which selects mpn_sqr_basecase in mpn_sqr_n to be false, by setting SQR_KARATSUBA_THRESHOLD to zero, making SQR_BASECASE_THRESHOLD the karatsuba threshold. */ sqr_basecase_threshold = SQR_KARATSUBA_THRESHOLD; SQR_KARATSUBA_THRESHOLD = 0; print_define_remark ("SQR_BASECASE_THRESHOLD", sqr_basecase_threshold, "karatsuba"); print_define_remark ("SQR_KARATSUBA_THRESHOLD",SQR_KARATSUBA_THRESHOLD, "never sqr_basecase"); } else { if (! HAVE_NATIVE_mpn_sqr_basecase) print_define ("SQR_BASECASE_THRESHOLD", sqr_basecase_threshold); print_define ("SQR_KARATSUBA_THRESHOLD", SQR_KARATSUBA_THRESHOLD); } } { static struct param_t param; param.name = "SQR_TOOM3_THRESHOLD"; param.function = speed_mpn_sqr_n; param.min_size = MAX3 (MPN_TOOM3_SQR_N_MINSIZE, SQR_KARATSUBA_THRESHOLD, SQR_BASECASE_THRESHOLD); param.max_size = SQR_TOOM3_THRESHOLD_LIMIT-1; one (&sqr_toom3_threshold, ¶m); } } void tune_sb_preinv (void) { static struct param_t param; if (GMP_NAIL_BITS != 0) { DIV_SB_PREINV_THRESHOLD = MP_SIZE_T_MAX; print_define_remark ("DIV_SB_PREINV_THRESHOLD", MP_SIZE_T_MAX, "no preinv with nails"); return; } if (UDIV_PREINV_ALWAYS) { print_define_remark ("DIV_SB_PREINV_THRESHOLD", 0L, "preinv always"); return; } param.check_size = 256; param.min_size = 3; param.min_is_always = 1; param.size_extra = 3; param.stop_factor = 2.0; param.name = "DIV_SB_PREINV_THRESHOLD"; param.function = speed_mpn_sb_divrem_m3; one (&div_sb_preinv_threshold, ¶m); } void tune_dc (void) { static struct param_t param; param.name = "DIV_DC_THRESHOLD"; param.function = speed_mpn_dc_tdiv_qr; param.step_factor = 0.02; one (&div_dc_threshold, ¶m); } /* This is an indirect determination, based on a comparison between redc and mpz_mod. A fudge factor of 1.04 is applied to redc, to represent additional overheads it gets in mpz_powm. stop_factor is 1.1 to hopefully help cray vector systems, where otherwise currently it hits the 1000 limb limit with only a factor of about 1.18 (threshold should be around 650). */ void tune_powm (void) { static struct param_t param; param.name = "POWM_THRESHOLD"; param.function = speed_redc; param.function2 = speed_mpz_mod; param.step_factor = 0.03; param.stop_factor = 1.1; param.function_fudge = 1.04; one (&powm_threshold, ¶m); } void tune_gcd_accel (void) { static struct param_t param; param.name = "GCD_ACCEL_THRESHOLD"; param.function = speed_mpn_gcd; param.min_size = 1; one (&gcd_accel_threshold, ¶m); } /* A comparison between the speed of a single limb step and a double limb step is made. On a 32-bit limb the ratio is about 2.2 single steps to equal a double step, or on a 64-bit limb about 2.09. (These were found from counting the steps on a 10000 limb gcdext. */ void tune_gcdext (void) { static struct param_t param; param.name = "GCDEXT_THRESHOLD"; param.function = speed_mpn_gcdext_one_single; param.function2 = speed_mpn_gcdext_one_double; switch (BITS_PER_MP_LIMB) { case 32: param.function_fudge = 2.2; break; case 64: param.function_fudge = 2.09; break; default: printf ("Don't know GCDEXT_THERSHOLD factor for BITS_PER_MP_LIMB == %d\n", BITS_PER_MP_LIMB); abort (); } param.min_size = 5; param.min_is_always = 1; param.max_size = 300; param.check_size = 300; one (&gcdext_threshold, ¶m); } /* size_extra==1 reflects the fact that with high> 4); if (s.r == 0) s.r = 123; t1 = tuneup_measure (speed_mpn_preinv_divrem_1, ¶m, &s); t2 = tuneup_measure (divrem_1, ¶m, &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); } /* A non-zero MOD_1_UNNORM_THRESHOLD (or MOD_1_NORM_THRESHOLD) would imply that udiv_qrnnd_preinv is worth using, but it seems most straightforward to compare mpn_preinv_mod_1 and mpn_mod_1_div directly. */ void tune_preinv_mod_1 (void) { static struct param_t param; speed_function_t mod_1; const char *mod_1_name; double t1, t2; /* Any native version of mpn_preinv_mod_1 is assumed to exist because it's faster than mpn_mod_1. */ if (HAVE_NATIVE_mpn_preinv_mod_1) { print_define_remark ("USE_PREINV_MOD_1", 1, "native"); return; } if (GMP_NAIL_BITS != 0) { print_define_remark ("USE_PREINV_MOD_1", 0, "no preinv with nails"); return; } /* If udiv_qrnnd_preinv is the only division method then of course mpn_preinv_mod_1 should be used. */ if (UDIV_PREINV_ALWAYS) { print_define_remark ("USE_PREINV_MOD_1", 1, "preinv always"); return; } /* If we've got an assembler version of mpn_mod_1, then compare against that, not the mpn_mod_1_div generic C. */ if (HAVE_NATIVE_mpn_mod_1) { mod_1 = speed_mpn_mod_1; mod_1_name = "mpn_mod_1"; } else { mod_1 = speed_mpn_mod_1_div; mod_1_name = "mpn_mod_1_div"; } param.data_high = DATA_HIGH_LT_R; /* let mpn_mod_1 skip one division */ s.size = 200; /* generous but not too big */ s.r = randlimb_norm(); /* divisor */ t1 = tuneup_measure (speed_mpn_preinv_mod_1, ¶m, &s); t2 = tuneup_measure (mod_1, ¶m, &s); if (t1 == -1.0 || t2 == -1.0) { printf ("Oops, can't measure mpn_preinv_mod_1 and %s at %ld\n", mod_1_name, (long) s.size); abort (); } if (option_trace >= 1) printf ("size=%ld, mpn_preinv_mod_1 %.9f, %s %.9f\n", (long) s.size, t1, mod_1_name, t2); print_define_remark ("USE_PREINV_MOD_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, ¶m); } /* 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= 1) printf ("size=%ld, mpn_jacobi_base_1 %.9f\n", (long) s.size, t1); t2 = tuneup_measure (speed_mpn_jacobi_base_2, ¶m, &s); if (option_trace >= 1) printf ("size=%ld, mpn_jacobi_base_2 %.9f\n", (long) s.size, t2); t3 = tuneup_measure (speed_mpn_jacobi_base_3, ¶m, &s); if (option_trace >= 1) printf ("size=%ld, mpn_jacobi_base_3 %.9f\n", (long) s.size, t3); if (t1 == -1.0 || t2 == -1.0 || t3 == -1.0) { printf ("Oops, can't measure all mpn_jacobi_base methods at %ld\n", (long) s.size); abort (); } if (t1 < t2 && t1 < t3) method = 1; else if (t2 < t3) method = 2; else method = 3; print_define ("JACOBI_BASE_METHOD", method); } 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 = 2; param.max_size = GET_STR_THRESHOLD_LIMIT; one (&get_str_dc_threshold, ¶m); } { 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, ¶m); } } void tune_set_str (void) { static struct param_t param; s.r = 10; /* decimal */ param.step_factor = 0.1; param.name = "SET_STR_THRESHOLD"; param.function = speed_mpn_set_str_basecase; param.function2 = speed_mpn_set_str_subquad; param.min_size = 100; param.max_size = 150000; one (&set_str_threshold, ¶m); } void tune_fft_mul (void) { static struct fft_param_t param; if (option_fft_max_size == 0) return; param.table_name = "MUL_FFT_TABLE"; 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_TOOM3_THRESHOLD / 2; param.max_size = option_fft_max_size; param.function = speed_mpn_mul_fft; param.mul_function = speed_mpn_mul_n; param.sqr = 0; fft (¶m); } void tune_fft_sqr (void) { static struct fft_param_t param; if (option_fft_max_size == 0) return; param.table_name = "SQR_FFT_TABLE"; 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_mul_fft_sqr; param.mul_function = speed_mpn_sqr_n; param.sqr = 0; fft (¶m); } 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_mul (); printf("\n"); tune_sqr (); printf("\n"); tune_mullow (); printf("\n"); tune_sb_preinv (); tune_dc (); tune_powm (); printf("\n"); tune_gcd_accel (); tune_gcdext (); tune_jacobi_base (); printf("\n"); tune_divrem_1 (); tune_mod_1 (); tune_preinv_divrem_1 (); tune_preinv_mod_1 (); tune_divrem_2 (); tune_divexact_1 (); tune_modexact_1_odd (); printf("\n"); tune_get_str (); tune_set_str (); printf("\n"); tune_fft_mul (); printf("\n"); tune_fft_sqr (); printf ("\n"); time (&end_time); printf ("/* Tuneup completed successfully, took %ld seconds */\n", 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); }