avoid overflows in kernel/time.c

When the conversion factor between jiffies and milli- or microseconds is
not a single multiply or divide, as for the case of HZ == 300, we currently
do a multiply followed by a divide.  The intervening result, however, is
subject to overflows, especially since the fraction is not simplified (for
HZ == 300, we multiply by 300 and divide by 1000).

This is exposed to the user when passing a large timeout to poll(), for
example.

This patch replaces the multiply-divide with a reciprocal multiplication on
32-bit platforms.  When the input is an unsigned long, there is no portable
way to do this on 64-bit platforms there is no portable way to do this
since it requires a 128-bit intermediate result (which gcc does support on
64-bit platforms but may generate libgcc calls, e.g.  on 64-bit s390), but
since the output is a 32-bit integer in the cases affected, just simplify
the multiply-divide (*3/10 instead of *300/1000).

The reciprocal multiply used can have off-by-one errors in the upper half
of the valid output range.  This could be avoided at the expense of having
to deal with a potential 65-bit intermediate result.  Since the intent is
to avoid overflow problems and most of the other time conversions are only
semiexact, the off-by-one errors were considered an acceptable tradeoff.

At Ralf Baechle's suggestion, this version uses a Perl script to compute
the necessary constants.  We already have dependencies on Perl for kernel
compiles.  This does, however, require the Perl module Math::BigInt, which
is included in the standard Perl distribution starting with version 5.8.0.
In order to support older versions of Perl, include a table of canned
constants in the script itself, and structure the script so that
Math::BigInt isn't required if pulling values from said table.

Running the script requires that the HZ value is available from the
Makefile.  Thus, this patch also adds the Kconfig variable CONFIG_HZ to the
architectures which didn't already have it (alpha, cris, frv, h8300, m32r,
m68k, m68knommu, sparc, v850, and xtensa.) It does *not* touch the sh or
sh64 architectures, since Paul Mundt has dealt with those separately in the
sh tree.

Signed-off-by: H. Peter Anvin <hpa@zytor.com>
Cc: Ralf Baechle <ralf@linux-mips.org>,
Cc: Sam Ravnborg <sam@ravnborg.org>,
Cc: Paul Mundt <lethal@linux-sh.org>,
Cc: Richard Henderson <rth@twiddle.net>,
Cc: Michael Starvik <starvik@axis.com>,
Cc: David Howells <dhowells@redhat.com>,
Cc: Yoshinori Sato <ysato@users.sourceforge.jp>,
Cc: Hirokazu Takata <takata@linux-m32r.org>,
Cc: Geert Uytterhoeven <geert@linux-m68k.org>,
Cc: Roman Zippel <zippel@linux-m68k.org>,
Cc: William L. Irwin <sparclinux@vger.kernel.org>,
Cc: Chris Zankel <chris@zankel.net>,
Cc: H. Peter Anvin <hpa@zytor.com>,
Cc: Jan Engelhardt <jengelh@computergmbh.de>
Signed-off-by: Andrew Morton <akpm@linux-foundation.org>
Signed-off-by: Linus Torvalds <torvalds@linux-foundation.org>

1 files changed, 402 insertions, 0 deletions

diff --git a/kernel/timeconst.pl b/kernel/timeconst.pl
new file mode 100644
index 00000000000..62b1287932e
--- /dev/null
+++ b/kernel/timeconst.pl
@@ -0,0 +1,402 @@
+#!/usr/bin/perl
+# -----------------------------------------------------------------------
+#
+#   Copyright 2007 rPath, Inc. - All Rights Reserved
+#
+#   This file is part of the Linux kernel, and is made available under
+#   the terms of the GNU General Public License version 2 or (at your
+#   option) any later version; incorporated herein by reference.
+#
+# -----------------------------------------------------------------------
+#
+
+#
+# Usage: timeconst.pl HZ > timeconst.h
+#
+
+# Precomputed values for systems without Math::BigInt
+# Generated by:
+# timeconst.pl --can 24 32 48 64 100 122 128 200 250 256 300 512 1000 1024 1200
+%canned_values = (
+        24 => [
+                '0xa6aaaaab','0x2aaaaaa',26,
+                '0xa6aaaaaaaaaaaaab','0x2aaaaaaaaaaaaaa',58,
+                125,3,
+                '0xc49ba5e4','0x1fbe76c8b4',37,
+                '0xc49ba5e353f7ceda','0x1fbe76c8b439581062',69,
+                3,125,
+                '0xa2c2aaab','0xaaaa',16,
+                '0xa2c2aaaaaaaaaaab','0xaaaaaaaaaaaa',48,
+                125000,3,
+                '0xc9539b89','0x7fffbce4217d',47,
+                '0xc9539b8887229e91','0x7fffbce4217d2849cb25',79,
+                3,125000,
+        ], 32 => [
+                '0xfa000000','0x6000000',27,
+                '0xfa00000000000000','0x600000000000000',59,
+                125,4,
+                '0x83126e98','0xfdf3b645a',36,
+                '0x83126e978d4fdf3c','0xfdf3b645a1cac0831',68,
+                4,125,
+                '0xf4240000','0x0',17,
+                '0xf424000000000000','0x0',49,
+                31250,1,
+                '0x8637bd06','0x3fff79c842fa',46,
+                '0x8637bd05af6c69b6','0x3fff79c842fa5093964a',78,
+                1,31250,
+        ], 48 => [
+                '0xa6aaaaab','0x6aaaaaa',27,
+                '0xa6aaaaaaaaaaaaab','0x6aaaaaaaaaaaaaa',59,
+                125,6,
+                '0xc49ba5e4','0xfdf3b645a',36,
+                '0xc49ba5e353f7ceda','0xfdf3b645a1cac0831',68,
+                6,125,
+                '0xa2c2aaab','0x15555',17,
+                '0xa2c2aaaaaaaaaaab','0x1555555555555',49,
+                62500,3,
+                '0xc9539b89','0x3fffbce4217d',46,
+                '0xc9539b8887229e91','0x3fffbce4217d2849cb25',78,
+                3,62500,
+        ], 64 => [
+                '0xfa000000','0xe000000',28,
+                '0xfa00000000000000','0xe00000000000000',60,
+                125,8,
+                '0x83126e98','0x7ef9db22d',35,
+                '0x83126e978d4fdf3c','0x7ef9db22d0e560418',67,
+                8,125,
+                '0xf4240000','0x0',18,
+                '0xf424000000000000','0x0',50,
+                15625,1,
+                '0x8637bd06','0x1fff79c842fa',45,
+                '0x8637bd05af6c69b6','0x1fff79c842fa5093964a',77,
+                1,15625,
+        ], 100 => [
+                '0xa0000000','0x0',28,
+                '0xa000000000000000','0x0',60,
+                10,1,
+                '0xcccccccd','0x733333333',35,
+                '0xcccccccccccccccd','0x73333333333333333',67,
+                1,10,
+                '0x9c400000','0x0',18,
+                '0x9c40000000000000','0x0',50,
+                10000,1,
+                '0xd1b71759','0x1fff2e48e8a7',45,
+                '0xd1b71758e219652c','0x1fff2e48e8a71de69ad4',77,
+                1,10000,
+        ], 122 => [
+                '0x8325c53f','0xfbcda3a',28,
+                '0x8325c53ef368eb05','0xfbcda3ac10c9714',60,
+                500,61,
+                '0xf9db22d1','0x7fbe76c8b',35,
+                '0xf9db22d0e560418a','0x7fbe76c8b43958106',67,
+                61,500,
+                '0x8012e2a0','0x3ef36',18,
+                '0x8012e29f79b47583','0x3ef368eb04325',50,
+                500000,61,
+                '0xffda4053','0x1ffffbce4217',45,
+                '0xffda4052d666a983','0x1ffffbce4217d2849cb2',77,
+                61,500000,
+        ], 128 => [
+                '0xfa000000','0x1e000000',29,
+                '0xfa00000000000000','0x1e00000000000000',61,
+                125,16,
+                '0x83126e98','0x3f7ced916',34,
+                '0x83126e978d4fdf3c','0x3f7ced916872b020c',66,
+                16,125,
+                '0xf4240000','0x40000',19,
+                '0xf424000000000000','0x4000000000000',51,
+                15625,2,
+                '0x8637bd06','0xfffbce4217d',44,
+                '0x8637bd05af6c69b6','0xfffbce4217d2849cb25',76,
+                2,15625,
+        ], 200 => [
+                '0xa0000000','0x0',29,
+                '0xa000000000000000','0x0',61,
+                5,1,
+                '0xcccccccd','0x333333333',34,
+                '0xcccccccccccccccd','0x33333333333333333',66,
+                1,5,
+                '0x9c400000','0x0',19,
+                '0x9c40000000000000','0x0',51,
+                5000,1,
+                '0xd1b71759','0xfff2e48e8a7',44,
+                '0xd1b71758e219652c','0xfff2e48e8a71de69ad4',76,
+                1,5000,
+        ], 250 => [
+                '0x80000000','0x0',29,
+                '0x8000000000000000','0x0',61,
+                4,1,
+                '0x80000000','0x180000000',33,
+                '0x8000000000000000','0x18000000000000000',65,
+                1,4,
+                '0xfa000000','0x0',20,
+                '0xfa00000000000000','0x0',52,
+                4000,1,
+                '0x83126e98','0x7ff7ced9168',43,
+                '0x83126e978d4fdf3c','0x7ff7ced916872b020c4',75,
+                1,4000,
+        ], 256 => [
+                '0xfa000000','0x3e000000',30,
+                '0xfa00000000000000','0x3e00000000000000',62,
+                125,32,
+                '0x83126e98','0x1fbe76c8b',33,
+                '0x83126e978d4fdf3c','0x1fbe76c8b43958106',65,
+                32,125,
+                '0xf4240000','0xc0000',20,
+                '0xf424000000000000','0xc000000000000',52,
+                15625,4,
+                '0x8637bd06','0x7ffde7210be',43,
+                '0x8637bd05af6c69b6','0x7ffde7210be9424e592',75,
+                4,15625,
+        ], 300 => [
+                '0xd5555556','0x2aaaaaaa',30,
+                '0xd555555555555556','0x2aaaaaaaaaaaaaaa',62,
+                10,3,
+                '0x9999999a','0x1cccccccc',33,
+                '0x999999999999999a','0x1cccccccccccccccc',65,
+                3,10,
+                '0xd0555556','0xaaaaa',20,
+                '0xd055555555555556','0xaaaaaaaaaaaaa',52,
+                10000,3,
+                '0x9d495183','0x7ffcb923a29',43,
+                '0x9d495182a9930be1','0x7ffcb923a29c779a6b5',75,
+                3,10000,
+        ], 512 => [
+                '0xfa000000','0x7e000000',31,
+                '0xfa00000000000000','0x7e00000000000000',63,
+                125,64,
+                '0x83126e98','0xfdf3b645',32,
+                '0x83126e978d4fdf3c','0xfdf3b645a1cac083',64,
+                64,125,
+                '0xf4240000','0x1c0000',21,
+                '0xf424000000000000','0x1c000000000000',53,
+                15625,8,
+                '0x8637bd06','0x3ffef39085f',42,
+                '0x8637bd05af6c69b6','0x3ffef39085f4a1272c9',74,
+                8,15625,
+        ], 1000 => [
+                '0x80000000','0x0',31,
+                '0x8000000000000000','0x0',63,
+                1,1,
+                '0x80000000','0x0',31,
+                '0x8000000000000000','0x0',63,
+                1,1,
+                '0xfa000000','0x0',22,
+                '0xfa00000000000000','0x0',54,
+                1000,1,
+                '0x83126e98','0x1ff7ced9168',41,
+                '0x83126e978d4fdf3c','0x1ff7ced916872b020c4',73,
+                1,1000,
+        ], 1024 => [
+                '0xfa000000','0xfe000000',32,
+                '0xfa00000000000000','0xfe00000000000000',64,
+                125,128,
+                '0x83126e98','0x7ef9db22',31,
+                '0x83126e978d4fdf3c','0x7ef9db22d0e56041',63,
+                128,125,
+                '0xf4240000','0x3c0000',22,
+                '0xf424000000000000','0x3c000000000000',54,
+                15625,16,
+                '0x8637bd06','0x1fff79c842f',41,
+                '0x8637bd05af6c69b6','0x1fff79c842fa5093964',73,
+                16,15625,
+        ], 1200 => [
+                '0xd5555556','0xd5555555',32,
+                '0xd555555555555556','0xd555555555555555',64,
+                5,6,
+                '0x9999999a','0x66666666',31,
+                '0x999999999999999a','0x6666666666666666',63,
+                6,5,
+                '0xd0555556','0x2aaaaa',22,
+                '0xd055555555555556','0x2aaaaaaaaaaaaa',54,
+                2500,3,
+                '0x9d495183','0x1ffcb923a29',41,
+                '0x9d495182a9930be1','0x1ffcb923a29c779a6b5',73,
+                3,2500,
+        ]
+);
+
+$has_bigint = eval 'use Math::BigInt qw(bgcd); 1;';
+
+sub bint($)
+{
+        my($x) = @_;
+        return Math::BigInt->new($x);
+}
+
+#
+# Constants for division by reciprocal multiplication.
+# (bits, numerator, denominator)
+#
+sub fmul($$$)
+{
+        my ($b,$n,$d) = @_;
+
+        $n = bint($n);
+        $d = bint($d);
+
+        return scalar (($n << $b)+$d-bint(1))/$d;
+}
+
+sub fadj($$$)
+{
+        my($b,$n,$d) = @_;
+
+        $n = bint($n);
+        $d = bint($d);
+
+        $d = $d/bgcd($n, $d);
+        return scalar (($d-bint(1)) << $b)/$d;
+}
+
+sub fmuls($$$) {
+        my($b,$n,$d) = @_;
+        my($s,$m);
+        my($thres) = bint(1) << ($b-1);
+
+        $n = bint($n);
+        $d = bint($d);
+
+        for ($s = 0; 1; $s++) {
+                $m = fmul($s,$n,$d);
+                return $s if ($m >= $thres);
+        }
+        return 0;
+}
+
+# Provides mul, adj, and shr factors for a specific
+# (bit, time, hz) combination
+sub muladj($$$) {
+        my($b, $t, $hz) = @_;
+        my $s = fmuls($b, $t, $hz);
+        my $m = fmul($s, $t, $hz);
+        my $a = fadj($s, $t, $hz);
+        return ($m->as_hex(), $a->as_hex(), $s);
+}
+
+# Provides numerator, denominator values
+sub numden($$) {
+        my($n, $d) = @_;
+        my $g = bgcd($n, $d);
+        return ($n/$g, $d/$g);
+}
+
+# All values for a specific (time, hz) combo
+sub conversions($$) {
+        my ($t, $hz) = @_;
+        my @val = ();
+
+        # HZ_TO_xx
+        push(@val, muladj(32, $t, $hz));
+        push(@val, muladj(64, $t, $hz));
+        push(@val, numden($t, $hz));
+
+        # xx_TO_HZ
+        push(@val, muladj(32, $hz, $t));
+        push(@val, muladj(64, $hz, $t));
+        push(@val, numden($hz, $t));
+
+        return @val;
+}
+
+sub compute_values($) {
+        my($hz) = @_;
+        my @val = ();
+        my $s, $m, $a, $g;
+
+        if (!$has_bigint) {
+                die "$0: HZ == $hz not canned and ".
+                    "Math::BigInt not available\n";
+        }
+
+        # MSEC conversions
+        push(@val, conversions(1000, $hz));
+
+        # USEC conversions
+        push(@val, conversions(1000000, $hz));
+
+        return @val;
+}
+
+sub output($@)
+{
+        my($hz, @val) = @_;
+        my $pfx, $bit, $suf, $s, $m, $a;
+
+        print "/* Automatically generated by kernel/timeconst.pl */\n";
+        print "/* Conversion constants for HZ == $hz */\n";
+        print "\n";
+        print "#ifndef KERNEL_TIMECONST_H\n";
+        print "#define KERNEL_TIMECONST_H\n";
+        print "\n";
+
+        print "#include <linux/param.h>\n";
+
+        print "\n";
+        print "#if HZ != $hz\n";
+        print "#error \"kernel/timeconst.h has the wrong HZ value!\"\n";
+        print "#endif\n";
+        print "\n";
+
+        foreach $pfx ('HZ_TO_MSEC','MSEC_TO_HZ',
+                      'USEC_TO_HZ','HZ_TO_USEC') {
+                foreach $bit (32, 64) {
+                        foreach $suf ('MUL', 'ADJ', 'SHR') {
+                                printf "#define %-23s %s\n",
+                                        "${pfx}_$suf$bit", shift(@val);
+                        }
+                }
+                foreach $suf ('NUM', 'DEN') {
+                        printf "#define %-23s %s\n",
+                                "${pfx}_$suf", shift(@val);
+                }
+        }
+
+        print "\n";
+        print "#endif /* KERNEL_TIMECONST_H */\n";
+}
+
+($hz) = @ARGV;
+
+# Use this to generate the %canned_values structure
+if ($hz eq '--can') {
+        shift(@ARGV);
+        @hzlist = sort {$a <=> $b} (@ARGV);
+
+        print "# Precomputed values for systems without Math::BigInt\n";
+        print "# Generated by:\n";
+        print "# timeconst.pl --can ", join(' ', @hzlist), "\n";
+        print "\%canned_values = (\n";
+        my $pf = "\t";
+        foreach $hz (@hzlist) {
+                my @values = compute_values($hz);
+                print "$pf$hz => [\n";
+                while (scalar(@values)) {
+                        my $bit;
+                        foreach $bit (32, 64) {
+                                my $m = shift(@values);
+                                my $a = shift(@values);
+                                my $s = shift(@values);
+                                print "\t\t\'",$m,"\',\'",$a,"\',",$s,",\n";
+                        }
+                        my $n = shift(@values);
+                        my $d = shift(@values);
+                        print "\t\t",$n,',',$d,",\n";
+                }
+                print "\t]";
+                $pf = ', ';
+        }
+        print "\n);\n";
+} else {
+        $hz += 0;                       # Force to number
+        if ($hz < 1) {
+                die "Usage: $0 HZ\n";
+        }
+
+        @val = @{$canned_values{$hz}};
+        if (!defined(@val)) {
+                @val = compute_values($hz);
+        }
+        output($hz, @val);
+}
+exit 0;