README
上传用户:qaz666999
上传日期:2022-08-06
资源大小:2570k
文件大小:19k
- Copyright 2000, 2001, 2002, 2004 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 3 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. If not, see http://www.gnu.org/licenses/.
- GMP SPEED MEASURING AND PARAMETER TUNING
- The programs in this directory are for knowledgeable users who want to
- measure GMP routines on their machine, and perhaps tweak some settings or
- identify things that can be improved.
- The programs here are tools, not ready to run solutions. Nothing is built
- in a normal "make all", but various Makefile targets described below exist.
- Relatively few systems and CPUs have been tested, so be sure to verify that
- results are sensible before relying on them.
- MISCELLANEOUS NOTES
- --enable-assert
- Don't configure with --enable-assert, since the extra code added by
- assertion checking may influence measurements.
- Direct mapped caches
- Some effort has been made to accommodate CPUs with direct mapped caches,
- by putting data blocks more or less contiguously on the stack. But this
- will depend on TMP_ALLOC using alloca, and even then it may or may not
- be enough.
- FreeBSD 4.2 i486 getrusage
- This getrusage seems to be a bit doubtful, it looks like it's
- microsecond accurate, but sometimes ru_utime remains unchanged after a
- time of many microseconds has elapsed. It'd be good to detect this in
- the time.c initializations, but for now the suggestion is to pretend it
- doesn't exist.
- ./configure ac_cv_func_getrusage=no
- NetBSD 1.4.1 m68k macintosh time base
- On this system it's been found getrusage often goes backwards, making it
- unusable (time.c getrusage_backwards_p detects this). gettimeofday
- sometimes doesn't update atomically when it crosses a 1 second boundary.
- Not sure what to do about this. Expect possible intermittent failures.
- SCO OpenUNIX 8 /etc/hw
- /etc/hw takes about a second to return the cpu frequency, which suggests
- perhaps it's measuring each time it runs. If this is annoying when
- running the speed program repeatedly then set a GMP_CPU_FREQUENCY
- environment variable (see TIME BASE section below).
- Timing on GNU/Linux
- On Linux, timing currently uses the cycle counter. This is unreliable,
- since the counter is not saved and restored at context switches (unlike
- FreeBSD and Solaris where the cycle counter is "virtualized").
- Using the clock_gettime method with CLOCK_PROCESS_CPUTIME_ID (posix) or
- CLOCK_VIRTUAL (BSD) should be more reliable. To get clock_gettime
- with glibc, one has to link with -lrt (which also drags in the pthreads
- threading library). configure.in must be hacked to detect this and
- arrange proper linking. Something like
- old_LIBS="$LIBS"
- AC_SEARCH_LIBS(clock_gettime, rt, [AC_DEFINE(HAVE_CLOCK_GETTIME)])
- TUNE_LIBS="$LIBS"
- LIBS="$old_LIBS"
- AC_SUBST(TUNE_LIBS)
-
- might work.
- Low resolution timebase
- Parameter tuning can be very time consuming if the only timebase
- available is a 10 millisecond clock tick, to the point of being
- unusable. This is currently the case on VAX and ARM systems.
- PARAMETER TUNING
- The "tuneup" program runs some tests designed to find the best settings for
- various thresholds, like MUL_TOOM22_THRESHOLD. Its output can be put
- into gmp-mparam.h. The program is built and run with
- make tune
- If the thresholds indicated are grossly different from the values in the
- selected gmp-mparam.h then there may be a performance boost in applicable
- size ranges by changing gmp-mparam.h accordingly.
- Be sure to do a full reconfigure and rebuild to get any newly set thresholds
- to take effect. A partial rebuild is enough sometimes, but a fresh
- configure and make is certain to be correct.
- If a CPU has specific tuned parameters coming from a gmp-mparam.h in one of
- the mpn subdirectories then the values from "make tune" should be similar.
- But check that the configured CPU is right and there are no machine specific
- effects causing a difference.
- It's hoped the compiler and options used won't have too much effect on
- thresholds, since for most CPUs they ultimately come down to comparisons
- between assembler subroutines. Missing out on the longlong.h macros by not
- using gcc will probably have an effect.
- Some thresholds produced by the tune program are merely single values chosen
- from what's a range of sizes where two algorithms are pretty much the same
- speed. When this happens the program is likely to give somewhat different
- values on successive runs. This is noticeable on the toom3 thresholds for
- instance.
- SPEED PROGRAM
- The "speed" program can be used for measuring and comparing various
- routines, and producing tables of data or gnuplot graphs. Compile it with
- make speed
- (Or on DOS systems "make speed.exe".)
- Here are some examples of how to use it. Check the code for all the
- options.
- Draw a graph of mpn_mul_n, stepping through sizes by 10 or a factor of 1.05
- (whichever is greater).
- ./speed -s 10-5000 -t 10 -f 1.05 -P foo mpn_mul_n
- gnuplot foo.gnuplot
- Compare mpn_add_n and an mpn_lshift by 1, showing times in cycles and
- showing under mpn_lshift the difference between it and mpn_add_n.
- ./speed -s 1-40 -c -d mpn_add_n mpn_lshift.1
- Using option -c for times in cycles is interesting but normally only
- necessary when looking carefully at assembler subroutines. You might think
- it would always give an integer value, but this doesn't happen in practice,
- probably due to overheads in the time measurements.
- In the free-form output the "#" symbol against a measurement means the
- corresponding routine is fastest at that size. This is a convenient visual
- cue when comparing different routines. The graph data files <name>.data
- don't get this since it would upset gnuplot or other data viewers.
- TIME BASE
- The time measuring method is determined in time.c, based on what the
- configured host has available. A cycle counter is preferred, possibly
- supplemented by another method if the counter has a limited range. A
- microsecond accurate getrusage() or gettimeofday() will work quite well too.
- The cycle counters (except possibly on alpha) and gettimeofday() will depend
- on the machine being otherwise idle, or rather on other jobs not stealing
- CPU time from the measuring program. Short routines (those that complete
- within a timeslice) should work even on a busy machine.
- Some trouble is taken by speed_measure() in common.c to avoid ill effects
- from sporadic interrupts, or other intermittent things (like cron waking up
- every minute). But generally an idle machine will be necessary to be
- certain of consistent results.
- The CPU frequency is needed to convert between cycles and seconds, or for
- when a cycle counter is supplemented by getrusage() etc. The speed program
- will convert as necessary according to the output format requested. The
- tune program will work with either cycles or seconds.
- freq.c knows how to get the frequency on some systems, or can measure a
- cycle counter against gettimeofday() or getrusage(), but when that fails, or
- needs to be overridden, an environment variable GMP_CPU_FREQUENCY can be
- used (in Hertz). For example in "bash" on a 650 MHz machine,
- export GMP_CPU_FREQUENCY=650e6
- A high precision time base makes it possible to get accurate measurements in
- a shorter time.
- EXAMPLE COMPARISONS - VARIOUS
- Here are some ideas for things that can be done with the speed program.
- There's always going to be a certain amount of overhead in the time
- measurements, due to reading the time base, and in the loop that runs a
- routine enough times to get a reading of the desired precision. Noop
- functions taking various arguments are available to measure this. The
- "overhead" printed by the speed program each time in its intro is the "noop"
- routine, but note that this is just for information, it isn't deducted from
- the times printed or anything.
- ./speed -s 1 noop noop_wxs noop_wxys
- To see how many cycles per limb a routine is taking, look at the time
- increase when the size increments, using option -D. This avoids fixed
- overheads in the measuring. Also, remember many of the assembler routines
- have unrolled loops, so it might be necessary to compare times at, say, 16,
- 32, 48, 64 etc to see what the unrolled part is taking, as opposed to any
- finishing off.
- ./speed -s 16-64 -t 16 -C -D mpn_add_n
- The -C option on its own gives cycles per limb, but is really only useful at
- big sizes where fixed overheads are small compared to the code doing the
- real work. Remember of course memory caching and/or page swapping will
- affect results at large sizes.
- ./speed -s 500000 -C mpn_add_n
- Once a calculation stops fitting in the CPU data cache, it's going to start
- taking longer. Exactly where this happens depends on the cache priming in
- the measuring routines, and on what sort of "least recently used" the
- hardware does. Here's an example for a CPU with a 16kbyte L1 data cache and
- 32-bit limb, showing a suddenly steeper curve for mpn_add_n at about 2000
- limbs.
- ./speed -s 1-4000 -t 5 -f 1.02 -P foo mpn_add_n
- gnuplot foo.gnuplot
- When a routine has an unrolled loop for, say, multiples of 8 limbs and then
- an ordinary loop for the remainder, it can happen that it's actually faster
- to do an operation on, say, 8 limbs than it is on 7 limbs. The following
- draws a graph of mpn_sub_n, to see whether times smoothly increase with
- size.
- ./speed -s 1-100 -c -P foo mpn_sub_n
- gnuplot foo.gnuplot
- If mpn_lshift and mpn_rshift have special case code for shifts by 1, it
- ought to be faster (or at least not slower) than shifting by, say, 2 bits.
- ./speed -s 1-200 -c mpn_rshift.1 mpn_rshift.2
- An mpn_lshift by 1 can be done by mpn_add_n adding a number to itself, and
- if the lshift isn't faster there's an obvious improvement that's possible.
- ./speed -s 1-200 -c mpn_lshift.1 mpn_add_n_self
- On some CPUs (AMD K6 for example) an "in-place" mpn_add_n where the
- destination is one of the sources is faster than a separate destination.
- Here's an example to see this. ".1" selects dst==src1 for mpn_add_n (and
- mpn_sub_n), for other values see speed.h SPEED_ROUTINE_MPN_BINARY_N_CALL.
- ./speed -s 1-200 -c mpn_add_n mpn_add_n.1
- The gmp manual points out that divisions by powers of two should be done
- using a right shift because it'll be significantly faster than an actual
- division. The following shows by what factor mpn_rshift is faster than
- mpn_divrem_1, using division by 32 as an example.
- ./speed -s 10-20 -r mpn_rshift.5 mpn_divrem_1.32
- EXAMPLE COMPARISONS - MULTIPLICATION
- mul_basecase takes a ".<r>" parameter which is the first (larger) size
- parameter. For example to show speeds for 20x1 up to 20x15 in cycles,
- ./speed -s 1-15 -c mpn_mul_basecase.20
- mul_basecase with no parameter does an NxN multiply, so for example to show
- speeds in cycles for 1x1, 2x2, 3x3, etc, up to 20x20, in cycles,
- ./speed -s 1-20 -c mpn_mul_basecase
- sqr_basecase is implemented by a "triangular" method on most CPUs, making it
- up to twice as fast as mul_basecase. In practice loop overheads and the
- products on the diagonal mean it falls short of this. Here's an example
- running the two and showing by what factor an NxN mul_basecase is slower
- than an NxN sqr_basecase. (Some versions of sqr_basecase only allow sizes
- below SQR_TOOM2_THRESHOLD, so if it crashes at that point don't worry.)
- ./speed -s 1-20 -r mpn_sqr_basecase mpn_mul_basecase
- The technique described above with -CD for showing the time difference in
- cycles per limb between two size operations can be done on an NxN
- mul_basecase using -E to change the basis for the size increment to N*N.
- For instance a 20x20 operation is taken to be doing 400 limbs, and a 16x16
- doing 256 limbs. The following therefore shows the per crossproduct speed
- of mul_basecase and sqr_basecase at around 20x20 limbs.
- ./speed -s 16-20 -t 4 -CDE mpn_mul_basecase mpn_sqr_basecase
- Of course sqr_basecase isn't really doing NxN crossproducts, but it can be
- interesting to compare it to mul_basecase as if it was. For sqr_basecase
- the -F option can be used to base the deltas on N*(N+1)/2 operations, which
- is the triangular products sqr_basecase does. For example,
- ./speed -s 16-20 -t 4 -CDF mpn_sqr_basecase
- Both -E and -F are preliminary and might change. A consistent approach to
- using them when claiming certain per crossproduct or per triangularproduct
- speeds hasn't really been established, but the increment between speeds in
- the range karatsuba will call seems sensible, that being k to k/2. For
- instance, if the karatsuba threshold was 20 for the multiply and 30 for the
- square,
- ./speed -s 10-20 -t 10 -CDE mpn_mul_basecase
- ./speed -s 15-30 -t 15 -CDF mpn_sqr_basecase
- EXAMPLE COMPARISONS - MALLOC
- The gmp manual recommends application programs avoid excessive initializing
- and clearing of mpz_t variables (and mpq_t and mpf_t too). Every new
- variable will at a minimum go through an init, a realloc for its first
- store, and finally a clear. Quite how long that takes depends on the C
- library. The following compares an mpz_init/realloc/clear to a 10 limb
- mpz_add. Don't be surprised if the mallocing is quite slow.
- ./speed -s 10 -c mpz_init_realloc_clear mpz_add
- On some systems malloc and free are much slower when dynamic linked. The
- speed-dynamic program can be used to see this. For example the following
- measures malloc/free, first static then dynamic.
- ./speed -s 10 -c malloc_free
- ./speed-dynamic -s 10 -c malloc_free
- Of course a real world program has big problems if it's doing so many
- mallocs and frees that it gets slowed down by a dynamic linked malloc.
- EXAMPLE COMPARISONS - STRING CONVERSIONS
- mpn_get_str does a binary to string conversion. The base is specified with
- a ".<r>" parameter, or decimal by default. Power of 2 bases are much faster
- than general bases. The following compares decimal and hex for instance.
- ./speed -s 1-20 -c mpn_get_str mpn_get_str.16
- Smaller bases need more divisions to split a given size number, and so are
- slower. The following compares base 3 and base 9. On small operands 9 will
- be nearly twice as fast, though at bigger sizes this reduces since in the
- current implementation both divide repeatedly by 3^20 (or 3^40 for 64 bit
- limbs) and those divisions come to dominate.
- ./speed -s 1-20 -cr mpn_get_str.3 mpn_get_str.9
- mpn_set_str does a string to binary conversion. The base is specified with
- a ".<r>" parameter, or decimal by default. Power of 2 bases are faster than
- general bases on large conversions.
- ./speed -s 1-512 -f 2 -c mpn_set_str.8 mpn_set_str.10
- mpn_set_str also has some special case code for decimal which is a bit
- faster than the general case, basically by giving the compiler a chance to
- optimize some multiplications by 10.
- ./speed -s 20-40 -c mpn_set_str.9 mpn_set_str.10 mpn_set_str.11
- EXAMPLE COMPARISONS - GCDs
- mpn_gcd_1 has a threshold for when to reduce using an initial x%y when both
- x and y are single limbs. This isn't tuned currently, but a value can be
- established by a measurement like
- ./speed -s 10-32 mpn_gcd_1.10
- This runs src[0] from 10 to 32 bits, and y fixed at 10 bits. If the div
- threshold is high, say 31 so it's effectively disabled then a 32x10 bit gcd
- is done by nibbling away at the 32-bit operands bit-by-bit. When the
- threshold is small, say 1 bit, then an initial x%y is done to reduce it to a
- 10x10 bit operation.
- The threshold in mpn/generic/gcd_1.c or the various assembler
- implementations can be tweaked up or down until there's no more speedups on
- interesting combinations of sizes. Note that this affects only a 1x1 limb
- operation and so isn't very important. (An Nx1 limb operation always does
- an initial modular reduction, using mpn_mod_1 or mpn_modexact_1_odd.)
- SPEED PROGRAM EXTENSIONS
- Potentially lots of things could be made available in the program, but it's
- been left at only the things that have actually been wanted and are likely
- to be reasonably useful in the future.
- Extensions should be fairly easy to make though. speed-ext.c is an example,
- in a style that should suit one-off tests, or new code fragments under
- development.
- many.pl is a script for generating a new speed program supplemented with
- alternate versions of the standard routines. It can be used for measuring
- experimental code, or for comparing different implementations that exist
- within a CPU family.
- THRESHOLD EXAMINING
- The speed program can be used to examine the speeds of different algorithms
- to check the tune program has done the right thing. For example to examine
- the karatsuba multiply threshold,
- ./speed -s 5-40 mpn_mul_basecase mpn_kara_mul_n
- When examining the toom3 threshold, remember it depends on the karatsuba
- threshold, so the right karatsuba threshold needs to be compiled into the
- library first. The tune program uses specially recompiled versions of
- mpn/mul_n.c etc for this reason, but the speed program simply uses the
- normal libgmp.la.
- Note further that the various routines may recurse into themselves on sizes
- far enough above applicable thresholds. For example, mpn_kara_mul_n will
- recurse into itself on sizes greater than twice the compiled-in
- MUL_TOOM22_THRESHOLD.
- When doing the above comparison between mul_basecase and kara_mul_n what's
- probably of interest is mul_basecase versus a kara_mul_n that does one level
- of Karatsuba then calls to mul_basecase, but this only happens on sizes less
- than twice the compiled MUL_TOOM22_THRESHOLD. A larger value for that
- setting can be compiled-in to avoid the problem if necessary. The same
- applies to toom3 and DC, though in a trickier fashion.
- There are some upper limits on some of the thresholds, arising from arrays
- dimensioned according to a threshold (mpn_mul_n), or asm code with certain
- sized displacements (some x86 versions of sqr_basecase). So putting huge
- values for the thresholds, even just for testing, may fail.
- FUTURE
- Make a program to check the time base is working properly, for small and
- large measurements. Make it able to test each available method, including
- perhaps the apparent resolution of each.
- Make a general mechanism for specifying operand overlap, and a syntax like
- maybe "mpn_add_n.dst=src2" to select it. Some measuring routines do this
- sort of thing with the "r" parameter currently.
- ----------------
- Local variables:
- mode: text
- fill-column: 76
- End: