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>

3 files changed, 431 insertions, 8 deletions

diff --git a/kernel/Makefile b/kernel/Makefile
index 60cd39c..6c584c5 100644
--- a/kernel/Makefile
+++ b/kernel/Makefile
@@ -91,3 +91,11 @@ quiet_cmd_ikconfiggz = IKCFG   $@
 targets += config_data.h
 $(obj)/config_data.h: $(obj)/config_data.gz FORCE
 	$(call if_changed,ikconfiggz)
+
+$(obj)/time.o: $(obj)/timeconst.h
+
+quiet_cmd_timeconst  = TIMEC   $@
+      cmd_timeconst  = $(PERL) $< $(CONFIG_HZ) > $@
+targets += timeconst.h
+$(obj)/timeconst.h: $(src)/timeconst.pl FORCE
+	$(call if_changed,timeconst)
diff --git a/kernel/time.c b/kernel/time.c
index 3b705ec..a5ec013b6 100644
--- a/kernel/time.c
+++ b/kernel/time.c
@@ -39,6 +39,8 @@
 #include <asm/uaccess.h>
 #include <asm/unistd.h>
 
+#include "timeconst.h"
+
 /*
  * The timezone where the local system is located.  Used as a default by some
  * programs who obtain this value by using gettimeofday.
@@ -93,7 +95,8 @@ asmlinkage long sys_stime(time_t __user *tptr)
 
 #endif /* __ARCH_WANT_SYS_TIME */
 
-asmlinkage long sys_gettimeofday(struct timeval __user *tv, struct timezone __user *tz)
+asmlinkage long sys_gettimeofday(struct timeval __user *tv,
+				 struct timezone __user *tz)
 {
 	if (likely(tv != NULL)) {
 		struct timeval ktv;
@@ -118,7 +121,7 @@ asmlinkage long sys_gettimeofday(struct timeval __user *tv, struct timezone __us
  * hard to make the program warp the clock precisely n hours)  or
  * compile in the timezone information into the kernel.  Bad, bad....
  *
- *              				- TYT, 1992-01-01
+ *						- TYT, 1992-01-01
  *
  * The best thing to do is to keep the CMOS clock in universal time (UTC)
  * as real UNIX machines always do it. This avoids all headaches about
@@ -240,7 +243,11 @@ unsigned int inline jiffies_to_msecs(const unsigned long j)
 #elif HZ > MSEC_PER_SEC && !(HZ % MSEC_PER_SEC)
 	return (j + (HZ / MSEC_PER_SEC) - 1)/(HZ / MSEC_PER_SEC);
 #else
-	return (j * MSEC_PER_SEC) / HZ;
+# if BITS_PER_LONG == 32
+	return ((u64)HZ_TO_MSEC_MUL32 * j) >> HZ_TO_MSEC_SHR32;
+# else
+	return (j * HZ_TO_MSEC_NUM) / HZ_TO_MSEC_DEN;
+# endif
 #endif
 }
 EXPORT_SYMBOL(jiffies_to_msecs);
@@ -252,7 +259,11 @@ unsigned int inline jiffies_to_usecs(const unsigned long j)
 #elif HZ > USEC_PER_SEC && !(HZ % USEC_PER_SEC)
 	return (j + (HZ / USEC_PER_SEC) - 1)/(HZ / USEC_PER_SEC);
 #else
-	return (j * USEC_PER_SEC) / HZ;
+# if BITS_PER_LONG == 32
+	return ((u64)HZ_TO_USEC_MUL32 * j) >> HZ_TO_USEC_SHR32;
+# else
+	return (j * HZ_TO_USEC_NUM) / HZ_TO_USEC_DEN;
+# endif
 #endif
 }
 EXPORT_SYMBOL(jiffies_to_usecs);
@@ -352,7 +363,7 @@ EXPORT_SYMBOL(mktime);
  * normalize to the timespec storage format
  *
  * Note: The tv_nsec part is always in the range of
- * 	0 <= tv_nsec < NSEC_PER_SEC
+ *	0 <= tv_nsec < NSEC_PER_SEC
  * For negative values only the tv_sec field is negative !
  */
 void set_normalized_timespec(struct timespec *ts, time_t sec, long nsec)
@@ -453,12 +464,13 @@ unsigned long msecs_to_jiffies(const unsigned int m)
 	/*
 	 * Generic case - multiply, round and divide. But first
 	 * check that if we are doing a net multiplication, that
-	 * we wouldnt overflow:
+	 * we wouldn't overflow:
 	 */
 	if (HZ > MSEC_PER_SEC && m > jiffies_to_msecs(MAX_JIFFY_OFFSET))
 		return MAX_JIFFY_OFFSET;
 
-	return (m * HZ + MSEC_PER_SEC - 1) / MSEC_PER_SEC;
+	return ((u64)MSEC_TO_HZ_MUL32 * m + MSEC_TO_HZ_ADJ32)
+		>> MSEC_TO_HZ_SHR32;
 #endif
 }
 EXPORT_SYMBOL(msecs_to_jiffies);
@@ -472,7 +484,8 @@ unsigned long usecs_to_jiffies(const unsigned int u)
 #elif HZ > USEC_PER_SEC && !(HZ % USEC_PER_SEC)
 	return u * (HZ / USEC_PER_SEC);
 #else
-	return (u * HZ + USEC_PER_SEC - 1) / USEC_PER_SEC;
+	return ((u64)USEC_TO_HZ_MUL32 * u + USEC_TO_HZ_ADJ32)
+		>> USEC_TO_HZ_SHR32;
 #endif
 }
 EXPORT_SYMBOL(usecs_to_jiffies);
diff --git a/kernel/timeconst.pl b/kernel/timeconst.pl
new file mode 100644
index 0000000..62b1287
--- /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;