As a special service "Fossies" has tried to format the requested text file into HTML format (style: standard) with prefixed line numbers.
Alternatively you can here view or download the uninterpreted source code file.

1 Copyright 2000-2002, 2004 Free Software Foundation, Inc. 2 3 This file is part of the GNU MP Library. 4 5 The GNU MP Library is free software; you can redistribute it and/or modify 6 it under the terms of either: 7 8 * the GNU Lesser General Public License as published by the Free 9 Software Foundation; either version 3 of the License, or (at your 10 option) any later version. 11 12 or 13 14 * the GNU General Public License as published by the Free Software 15 Foundation; either version 2 of the License, or (at your option) any 16 later version. 17 18 or both in parallel, as here. 19 20 The GNU MP Library is distributed in the hope that it will be useful, but 21 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY 22 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License 23 for more details. 24 25 You should have received copies of the GNU General Public License and the 26 GNU Lesser General Public License along with the GNU MP Library. If not, 27 see https://www.gnu.org/licenses/. 28 29 30 31 32 33 GMP SPEED MEASURING AND PARAMETER TUNING 34 35 36 The programs in this directory are for knowledgeable users who want to 37 measure GMP routines on their machine, and perhaps tweak some settings or 38 identify things that can be improved. 39 40 The programs here are tools, not ready to run solutions. Nothing is built 41 in a normal "make all", but various Makefile targets described below exist. 42 43 Relatively few systems and CPUs have been tested, so be sure to verify that 44 results are sensible before relying on them. 45 46 47 48 49 MISCELLANEOUS NOTES 50 51 --enable-assert 52 53 Don't configure with --enable-assert, since the extra code added by 54 assertion checking may influence measurements. 55 56 Direct mapped caches 57 58 Some effort has been made to accommodate CPUs with direct mapped caches, 59 by putting data blocks more or less contiguously on the stack. But this 60 will depend on TMP_ALLOC using alloca, and even then it may or may not 61 be enough. 62 63 FreeBSD 4.2 i486 getrusage 64 65 This getrusage seems to be a bit doubtful, it looks like it's 66 microsecond accurate, but sometimes ru_utime remains unchanged after a 67 time of many microseconds has elapsed. It'd be good to detect this in 68 the time.c initializations, but for now the suggestion is to pretend it 69 doesn't exist. 70 71 ./configure ac_cv_func_getrusage=no 72 73 NetBSD 1.4.1 m68k macintosh time base 74 75 On this system it's been found getrusage often goes backwards, making it 76 unusable (time.c getrusage_backwards_p detects this). gettimeofday 77 sometimes doesn't update atomically when it crosses a 1 second boundary. 78 Not sure what to do about this. Expect possible intermittent failures. 79 80 SCO OpenUNIX 8 /etc/hw 81 82 /etc/hw takes about a second to return the cpu frequency, which suggests 83 perhaps it's measuring each time it runs. If this is annoying when 84 running the speed program repeatedly then set a GMP_CPU_FREQUENCY 85 environment variable (see TIME BASE section below). 86 87 Timing on GNU/Linux 88 89 On Linux, timing currently uses the cycle counter. This is unreliable, 90 since the counter is not saved and restored at context switches (unlike 91 FreeBSD and Solaris where the cycle counter is "virtualized"). 92 93 Using the clock_gettime method with CLOCK_PROCESS_CPUTIME_ID (posix) or 94 CLOCK_VIRTUAL (BSD) should be more reliable. To get clock_gettime 95 with glibc, one has to link with -lrt (which also drags in the pthreads 96 threading library). configure.in must be hacked to detect this and 97 arrange proper linking. Something like 98 99 old_LIBS="$LIBS" 100 AC_SEARCH_LIBS(clock_gettime, rt, [AC_DEFINE(HAVE_CLOCK_GETTIME)]) 101 TUNE_LIBS="$LIBS" 102 LIBS="$old_LIBS" 103 104 AC_SUBST(TUNE_LIBS) 105 106 might work. 107 108 Low resolution timebase 109 110 Parameter tuning can be very time consuming if the only timebase 111 available is a 10 millisecond clock tick, to the point of being 112 unusable. This is currently the case on VAX and ARM systems. 113 114 115 116 117 PARAMETER TUNING 118 119 The "tuneup" program runs some tests designed to find the best settings for 120 various thresholds, like MUL_TOOM22_THRESHOLD. Its output can be put 121 into gmp-mparam.h. The program is built and run with 122 123 make tune 124 125 If the thresholds indicated are grossly different from the values in the 126 selected gmp-mparam.h then there may be a performance boost in applicable 127 size ranges by changing gmp-mparam.h accordingly. 128 129 Be sure to do a full reconfigure and rebuild to get any newly set thresholds 130 to take effect. A partial rebuild is enough sometimes, but a fresh 131 configure and make is certain to be correct. 132 133 If a CPU has specific tuned parameters coming from a gmp-mparam.h in one of 134 the mpn subdirectories then the values from "make tune" should be similar. 135 But check that the configured CPU is right and there are no machine specific 136 effects causing a difference. 137 138 It's hoped the compiler and options used won't have too much effect on 139 thresholds, since for most CPUs they ultimately come down to comparisons 140 between assembler subroutines. Missing out on the longlong.h macros by not 141 using gcc will probably have an effect. 142 143 Some thresholds produced by the tune program are merely single values chosen 144 from what's a range of sizes where two algorithms are pretty much the same 145 speed. When this happens the program is likely to give somewhat different 146 values on successive runs. This is noticeable on the toom3 thresholds for 147 instance. 148 149 150 151 152 SPEED PROGRAM 153 154 The "speed" program can be used for measuring and comparing various 155 routines, and producing tables of data or gnuplot graphs. Compile it with 156 157 make speed 158 159 (Or on DOS systems "make speed.exe".) 160 161 Here are some examples of how to use it. Check the code for all the 162 options. 163 164 Draw a graph of mpn_mul_n, stepping through sizes by 10 or a factor of 1.05 165 (whichever is greater). 166 167 ./speed -s 10-5000 -t 10 -f 1.05 -P foo mpn_mul_n 168 gnuplot foo.gnuplot 169 170 Compare mpn_add_n and an mpn_lshift by 1, showing times in cycles and 171 showing under mpn_lshift the difference between it and mpn_add_n. 172 173 ./speed -s 1-40 -c -d mpn_add_n mpn_lshift.1 174 175 Using option -c for times in cycles is interesting but normally only 176 necessary when looking carefully at assembler subroutines. You might think 177 it would always give an integer value, but this doesn't happen in practice, 178 probably due to overheads in the time measurements. 179 180 In the free-form output the "#" symbol against a measurement means the 181 corresponding routine is fastest at that size. This is a convenient visual 182 cue when comparing different routines. The graph data files <name>.data 183 don't get this since it would upset gnuplot or other data viewers. 184 185 186 187 188 TIME BASE 189 190 The time measuring method is determined in time.c, based on what the 191 configured host has available. A cycle counter is preferred, possibly 192 supplemented by another method if the counter has a limited range. A 193 microsecond accurate getrusage() or gettimeofday() will work quite well too. 194 195 The cycle counters (except possibly on alpha) and gettimeofday() will depend 196 on the machine being otherwise idle, or rather on other jobs not stealing 197 CPU time from the measuring program. Short routines (those that complete 198 within a timeslice) should work even on a busy machine. 199 200 Some trouble is taken by speed_measure() in common.c to avoid ill effects 201 from sporadic interrupts, or other intermittent things (like cron waking up 202 every minute). But generally an idle machine will be necessary to be 203 certain of consistent results. 204 205 The CPU frequency is needed to convert between cycles and seconds, or for 206 when a cycle counter is supplemented by getrusage() etc. The speed program 207 will convert as necessary according to the output format requested. The 208 tune program will work with either cycles or seconds. 209 210 freq.c knows how to get the frequency on some systems, or can measure a 211 cycle counter against gettimeofday() or getrusage(), but when that fails, or 212 needs to be overridden, an environment variable GMP_CPU_FREQUENCY can be 213 used (in Hertz). For example in "bash" on a 650 MHz machine, 214 215 export GMP_CPU_FREQUENCY=650e6 216 217 A high precision time base makes it possible to get accurate measurements in 218 a shorter time. 219 220 221 222 223 EXAMPLE COMPARISONS - VARIOUS 224 225 Here are some ideas for things that can be done with the speed program. 226 227 There's always going to be a certain amount of overhead in the time 228 measurements, due to reading the time base, and in the loop that runs a 229 routine enough times to get a reading of the desired precision. Noop 230 functions taking various arguments are available to measure this. The 231 "overhead" printed by the speed program each time in its intro is the "noop" 232 routine, but note that this is just for information, it isn't deducted from 233 the times printed or anything. 234 235 ./speed -s 1 noop noop_wxs noop_wxys 236 237 To see how many cycles per limb a routine is taking, look at the time 238 increase when the size increments, using option -D. This avoids fixed 239 overheads in the measuring. Also, remember many of the assembler routines 240 have unrolled loops, so it might be necessary to compare times at, say, 16, 241 32, 48, 64 etc to see what the unrolled part is taking, as opposed to any 242 finishing off. 243 244 ./speed -s 16-64 -t 16 -C -D mpn_add_n 245 246 The -C option on its own gives cycles per limb, but is really only useful at 247 big sizes where fixed overheads are small compared to the code doing the 248 real work. Remember of course memory caching and/or page swapping will 249 affect results at large sizes. 250 251 ./speed -s 500000 -C mpn_add_n 252 253 Once a calculation stops fitting in the CPU data cache, it's going to start 254 taking longer. Exactly where this happens depends on the cache priming in 255 the measuring routines, and on what sort of "least recently used" the 256 hardware does. Here's an example for a CPU with a 16kbyte L1 data cache and 257 32-bit limb, showing a suddenly steeper curve for mpn_add_n at about 2000 258 limbs. 259 260 ./speed -s 1-4000 -t 5 -f 1.02 -P foo mpn_add_n 261 gnuplot foo.gnuplot 262 263 When a routine has an unrolled loop for, say, multiples of 8 limbs and then 264 an ordinary loop for the remainder, it can happen that it's actually faster 265 to do an operation on, say, 8 limbs than it is on 7 limbs. The following 266 draws a graph of mpn_sub_n, to see whether times smoothly increase with 267 size. 268 269 ./speed -s 1-100 -c -P foo mpn_sub_n 270 gnuplot foo.gnuplot 271 272 If mpn_lshift and mpn_rshift have special case code for shifts by 1, it 273 ought to be faster (or at least not slower) than shifting by, say, 2 bits. 274 275 ./speed -s 1-200 -c mpn_rshift.1 mpn_rshift.2 276 277 An mpn_lshift by 1 can be done by mpn_add_n adding a number to itself, and 278 if the lshift isn't faster there's an obvious improvement that's possible. 279 280 ./speed -s 1-200 -c mpn_lshift.1 mpn_add_n_self 281 282 On some CPUs (AMD K6 for example) an "in-place" mpn_add_n where the 283 destination is one of the sources is faster than a separate destination. 284 Here's an example to see this. ".1" selects dst==src1 for mpn_add_n (and 285 mpn_sub_n), for other values see speed.h SPEED_ROUTINE_MPN_BINARY_N_CALL. 286 287 ./speed -s 1-200 -c mpn_add_n mpn_add_n.1 288 289 The gmp manual points out that divisions by powers of two should be done 290 using a right shift because it'll be significantly faster than an actual 291 division. The following shows by what factor mpn_rshift is faster than 292 mpn_divrem_1, using division by 32 as an example. 293 294 ./speed -s 10-20 -r mpn_rshift.5 mpn_divrem_1.32 295 296 297 298 299 EXAMPLE COMPARISONS - MULTIPLICATION 300 301 mul_basecase takes a ".<r>" parameter. If positive, it gives the second 302 (smaller) operand size. For example to show speeds for 3x3 up to 20x3 in 303 cycles, 304 305 ./speed -s 3-20 -c mpn_mul_basecase.3 306 307 A negative ".<-r>" parameter fixes the size of the product to the absolute 308 value r. For example to show speeds for 10x10 up to 19x1 in cycles, 309 310 ./speed -s 10-19 -c mpn_mul_basecase.-20 311 312 mul_basecase with no parameter does an NxN multiply, so for example to show 313 speeds in cycles for 1x1, 2x2, 3x3, etc, up to 20x20, in cycles, 314 315 ./speed -s 1-20 -c mpn_mul_basecase 316 317 sqr_basecase is implemented by a "triangular" method on most CPUs, making it 318 up to twice as fast as mul_basecase. In practice loop overheads and the 319 products on the diagonal mean it falls short of this. Here's an example 320 running the two and showing by what factor an NxN mul_basecase is slower 321 than an NxN sqr_basecase. (Some versions of sqr_basecase only allow sizes 322 below SQR_TOOM2_THRESHOLD, so if it crashes at that point don't worry.) 323 324 ./speed -s 1-20 -r mpn_sqr_basecase mpn_mul_basecase 325 326 The technique described above with -CD for showing the time difference in 327 cycles per limb between two size operations can be done on an NxN 328 mul_basecase using -E to change the basis for the size increment to N*N. 329 For instance a 20x20 operation is taken to be doing 400 limbs, and a 16x16 330 doing 256 limbs. The following therefore shows the per crossproduct speed 331 of mul_basecase and sqr_basecase at around 20x20 limbs. 332 333 ./speed -s 16-20 -t 4 -CDE mpn_mul_basecase mpn_sqr_basecase 334 335 Of course sqr_basecase isn't really doing NxN crossproducts, but it can be 336 interesting to compare it to mul_basecase as if it was. For sqr_basecase 337 the -F option can be used to base the deltas on N*(N+1)/2 operations, which 338 is the triangular products sqr_basecase does. For example, 339 340 ./speed -s 16-20 -t 4 -CDF mpn_sqr_basecase 341 342 Both -E and -F are preliminary and might change. A consistent approach to 343 using them when claiming certain per crossproduct or per triangularproduct 344 speeds hasn't really been established, but the increment between speeds in 345 the range karatsuba will call seems sensible, that being k to k/2. For 346 instance, if the karatsuba threshold was 20 for the multiply and 30 for the 347 square, 348 349 ./speed -s 10-20 -t 10 -CDE mpn_mul_basecase 350 ./speed -s 15-30 -t 15 -CDF mpn_sqr_basecase 351 352 353 354 EXAMPLE COMPARISONS - MALLOC 355 356 The gmp manual recommends application programs avoid excessive initializing 357 and clearing of mpz_t variables (and mpq_t and mpf_t too). Every new 358 variable will at a minimum go through an init, a realloc for its first 359 store, and finally a clear. Quite how long that takes depends on the C 360 library. The following compares an mpz_init/realloc/clear to a 10 limb 361 mpz_add. Don't be surprised if the mallocing is quite slow. 362 363 ./speed -s 10 -c mpz_init_realloc_clear mpz_add 364 365 On some systems malloc and free are much slower when dynamic linked. The 366 speed-dynamic program can be used to see this. For example the following 367 measures malloc/free, first static then dynamic. 368 369 ./speed -s 10 -c malloc_free 370 ./speed-dynamic -s 10 -c malloc_free 371 372 Of course a real world program has big problems if it's doing so many 373 mallocs and frees that it gets slowed down by a dynamic linked malloc. 374 375 376 377 378 379 EXAMPLE COMPARISONS - STRING CONVERSIONS 380 381 mpn_get_str does a binary to string conversion. The base is specified with 382 a ".<r>" parameter, or decimal by default. Power of 2 bases are much faster 383 than general bases. The following compares decimal and hex for instance. 384 385 ./speed -s 1-20 -c mpn_get_str mpn_get_str.16 386 387 Smaller bases need more divisions to split a given size number, and so are 388 slower. The following compares base 3 and base 9. On small operands 9 will 389 be nearly twice as fast, though at bigger sizes this reduces since in the 390 current implementation both divide repeatedly by 3^20 (or 3^40 for 64 bit 391 limbs) and those divisions come to dominate. 392 393 ./speed -s 1-20 -cr mpn_get_str.3 mpn_get_str.9 394 395 mpn_set_str does a string to binary conversion. The base is specified with 396 a ".<r>" parameter, or decimal by default. Power of 2 bases are faster than 397 general bases on large conversions. 398 399 ./speed -s 1-512 -f 2 -c mpn_set_str.8 mpn_set_str.10 400 401 mpn_set_str also has some special case code for decimal which is a bit 402 faster than the general case, basically by giving the compiler a chance to 403 optimize some multiplications by 10. 404 405 ./speed -s 20-40 -c mpn_set_str.9 mpn_set_str.10 mpn_set_str.11 406 407 408 409 410 EXAMPLE COMPARISONS - GCDs 411 412 mpn_gcd_1 has a threshold for when to reduce using an initial x%y when both 413 x and y are single limbs. This isn't tuned currently, but a value can be 414 established by a measurement like 415 416 ./speed -s 10-32 mpn_gcd_1.10 417 418 This runs src[0] from 10 to 32 bits, and y fixed at 10 bits. If the div 419 threshold is high, say 31 so it's effectively disabled then a 32x10 bit gcd 420 is done by nibbling away at the 32-bit operands bit-by-bit. When the 421 threshold is small, say 1 bit, then an initial x%y is done to reduce it to a 422 10x10 bit operation. 423 424 The threshold in mpn/generic/gcd_1.c or the various assembler 425 implementations can be tweaked up or down until there's no more speedups on 426 interesting combinations of sizes. Note that this affects only a 1x1 limb 427 operation and so isn't very important. (An Nx1 limb operation always does 428 an initial modular reduction, using mpn_mod_1 or mpn_modexact_1_odd.) 429 430 431 432 433 SPEED PROGRAM EXTENSIONS 434 435 Potentially lots of things could be made available in the program, but it's 436 been left at only the things that have actually been wanted and are likely 437 to be reasonably useful in the future. 438 439 Extensions should be fairly easy to make though. speed-ext.c is an example, 440 in a style that should suit one-off tests, or new code fragments under 441 development. 442 443 many.pl is a script for generating a new speed program supplemented with 444 alternate versions of the standard routines. It can be used for measuring 445 experimental code, or for comparing different implementations that exist 446 within a CPU family. 447 448 449 450 451 THRESHOLD EXAMINING 452 453 The speed program can be used to examine the speeds of different algorithms 454 to check the tune program has done the right thing. For example to examine 455 the karatsuba multiply threshold, 456 457 ./speed -s 5-40 mpn_mul_basecase mpn_kara_mul_n 458 459 When examining the toom3 threshold, remember it depends on the karatsuba 460 threshold, so the right karatsuba threshold needs to be compiled into the 461 library first. The tune program uses specially recompiled versions of 462 mpn/mul_n.c etc for this reason, but the speed program simply uses the 463 normal libgmp.la. 464 465 Note further that the various routines may recurse into themselves on sizes 466 far enough above applicable thresholds. For example, mpn_kara_mul_n will 467 recurse into itself on sizes greater than twice the compiled-in 468 MUL_TOOM22_THRESHOLD. 469 470 When doing the above comparison between mul_basecase and kara_mul_n what's 471 probably of interest is mul_basecase versus a kara_mul_n that does one level 472 of Karatsuba then calls to mul_basecase, but this only happens on sizes less 473 than twice the compiled MUL_TOOM22_THRESHOLD. A larger value for that 474 setting can be compiled-in to avoid the problem if necessary. The same 475 applies to toom3 and DC, though in a trickier fashion. 476 477 There are some upper limits on some of the thresholds, arising from arrays 478 dimensioned according to a threshold (mpn_mul_n), or asm code with certain 479 sized displacements (some x86 versions of sqr_basecase). So putting huge 480 values for the thresholds, even just for testing, may fail. 481 482 483 484 485 FUTURE 486 487 Make a program to check the time base is working properly, for small and 488 large measurements. Make it able to test each available method, including 489 perhaps the apparent resolution of each. 490 491 Make a general mechanism for specifying operand overlap, and a syntax like 492 maybe "mpn_add_n.dst=src2" to select it. Some measuring routines do this 493 sort of thing with the "r" parameter currently. 494 495 496 497 ---------------- 498 Local variables: 499 mode: text 500 fill-column: 76 501 End: