[gcc] GCC 4.5.0=>4.5.1

gcc/gmp/tune/README

-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).
-
-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_KARATSUBA_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_KARATSUBA_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_KARATSUBA_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_KARATSUBA_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: