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 <[e-mail]>
Cc: Ralf Baechle <[e-mail]>,
Cc: Sam Ravnborg <[e-mail]>,
Cc: Paul Mundt <[e-mail]>,
Cc: Richard Henderson <[e-mail]>,
Cc: Michael Starvik <[e-mail]>,
Cc: David Howells <[e-mail]>,
Cc: Yoshinori Sato <[e-mail]>,
Cc: Hirokazu Takata <[e-mail]>,
Cc: Geert Uytterhoeven <[e-mail]>,
Cc: Roman Zippel <[e-mail]>,
Cc: William L. Irwin <[e-mail]>,
Cc: Chris Zankel <[e-mail]>,
Cc: H. Peter Anvin <[e-mail]>,
Cc: Jan Engelhardt <[e-mail]>
Signed-off-by: Andrew Morton <[e-mail]>
Signed-off-by: Linus Torvalds <[e-mail]>

arch/alpha/Kconfig

···
 
 	  Take the default (1) unless you want more control or more info.
 
+config HZ
+	int
+	default 1200 if ALPHA_RAWHIDE
+	default 1024
+
 source "drivers/pci/Kconfig"
 source "drivers/eisa/Kconfig"
 

arch/cris/Kconfig

···
 	bool
 	default y
 
+config HZ
+	int
+	default 100
+
 source "init/Kconfig"
 
 menu "General setup"

arch/frv/Kconfig

···
 	bool
 	default y
 
+config HZ
+	int
+	default 1000
+
 mainmenu "Fujitsu FR-V Kernel Configuration"
 
 source "init/Kconfig"

arch/h8300/Kconfig

···
 	bool
 	default n
 
+config HZ
+	int
+	default 100
+
 source "init/Kconfig"
 
 source "arch/h8300/Kconfig.cpu"

arch/m32r/Kconfig

···
 config ARCH_SUPPORTS_AOUT
 	def_bool y
 
+config HZ
+	int
+	default 100
+
 source "init/Kconfig"
 
 

arch/m68k/Kconfig

···
 config ARCH_SUPPORTS_AOUT
 	def_bool y
 
+config HZ
+	int
+	default 100
+
 mainmenu "Linux/68k Kernel Configuration"
 
 source "init/Kconfig"

arch/m68knommu/Kconfig

···
 	  running more threads on a system and also reduces the pressure
 	  on the VM subsystem for higher order allocations.
 
+config HZ
+	int
+	default 1000 if CLEOPATRA
+	default 100
+
 comment "RAM configuration"
 
 config RAMBASE

arch/sparc/Kconfig

···
 config ARCH_SUPPORTS_AOUT
 	def_bool y
 
+config HZ
+	int
+	default 100
+
 source "init/Kconfig"
 
 menu "General machine setup"

arch/v850/Kconfig

···
    	  bool
 	  default !V850E_CACHE && !V850E2_CACHE
 
+   # HZ depends on the platform
+   config HZ
+	  int
+	  default 24  if V850E_SIM || V850E2_SIM85E2
+	  default 122 if V850E2_FPGA85E2C
+	  default 100
+
    #### Misc config
 
    config ROM_KERNEL

arch/xtensa/Kconfig

···
 config NO_IOPORT
 	def_bool y
 
+config HZ
+	int
+	default 100
+
 source "init/Kconfig"
 
 menu "Processor type and features"

include/asm-alpha/param.h

···
    hardware ignores reprogramming.  We also need userland buy-in to the 
    change in HZ, since this is visible in the wait4 resources etc.  */
 
-
-#ifndef HZ
-# ifndef CONFIG_ALPHA_RAWHIDE
-#  define HZ	1024
-# else
-#  define HZ	1200
-# endif
-#endif
-
+#define HZ		CONFIG_HZ
 #define USER_HZ		HZ
 
 #define EXEC_PAGESIZE	8192

include/asm-cris/param.h

···
 
 /* Currently we assume that HZ=100 is good for CRIS. */
 #ifdef __KERNEL__
-# define HZ		100		/* Internal kernel timer frequency */
+# define HZ		CONFIG_HZ	/* Internal kernel timer frequency */
 # define USER_HZ	100		/* .. some user interfaces are in "ticks" */
 # define CLOCKS_PER_SEC	(USER_HZ)	/* like times() */
 #endif

include/asm-frv/param.h

···
 #define _ASM_PARAM_H
 
 #ifdef __KERNEL__
-#define HZ		1000		/* Internal kernel timer frequency */
+#define HZ		CONFIG_HZ	/* Internal kernel timer frequency */
 #define USER_HZ		100		/* .. some user interfaces are in "ticks" */
 #define CLOCKS_PER_SEC	(USER_HZ)	/* like times() */
 #endif

include/asm-h8300/param.h

···
 
 
 #ifndef HZ
-#define HZ 100
+#define HZ CONFIG_HZ
 #endif
 
 #ifdef __KERNEL__

include/asm-m32r/param.h

···
 #define _ASM_M32R_PARAM_H
 
 #ifdef __KERNEL__
-# define HZ		100		/* Internal kernel timer frequency */
+# define HZ		CONFIG_HZ	/* Internal kernel timer frequency */
 # define USER_HZ	100		/* .. some user interfaces are in "ticks" */
 # define CLOCKS_PER_SEC	(USER_HZ)	/* like times() */
 #endif

include/asm-m68k/param.h

···
 #define _M68K_PARAM_H
 
 #ifdef __KERNEL__
-# define HZ		100		/* Internal kernel timer frequency */
+# define HZ		CONFIG_HZ	/* Internal kernel timer frequency */
 # define USER_HZ	100		/* .. some user interfaces are in "ticks" */
 # define CLOCKS_PER_SEC	(USER_HZ)	/* like times() */
 #endif

include/asm-m68knommu/param.h

···
 #ifndef _M68KNOMMU_PARAM_H
 #define _M68KNOMMU_PARAM_H
 
-
-#if defined(CONFIG_CLEOPATRA)
-#define	HZ 1000
-#endif
-#ifndef HZ
-#define	HZ 100
-#endif
+#define HZ CONFIG_HZ
 
 #ifdef __KERNEL__
 #define	USER_HZ		HZ

include/asm-sparc/param.h

···
 #define _ASMSPARC_PARAM_H
 
 #ifdef __KERNEL__
-# define HZ		100	/* Internal kernel timer frequency */
+# define HZ		CONFIG_HZ	/* Internal kernel timer frequency */
 # define USER_HZ	100	/* .. some user interfaces are in "ticks" */
 # define CLOCKS_PER_SEC (USER_HZ)
 #endif

include/asm-v850/anna.h

···
 #define V850E_TIMER_D_TMCD_CS_MIN	1 /* min 2^1 divider */
 
 
-/* For <asm/param.h> */
-#ifndef HZ
-#define HZ	100
-#endif
-
-
 #endif /* __V850_ANNA_H__ */

include/asm-v850/as85ep1.h

···
 #define V850E_TIMER_D_TMCD_CS_MIN	2 /* min 2^2 divider */
 
 
-/* For <asm/param.h> */
-#ifndef HZ
-#define HZ	100
-#endif
-
-
 #endif /* __V850_AS85EP1_H__ */

include/asm-v850/fpga85e2c.h

···
 #endif
 
 
-/* For <asm/param.h> */
-#ifndef HZ
-#define HZ			122 /* actually, 8.192ms ticks =~ 122.07 */
-#endif
-
-
 #endif /* __V850_FPGA85E2C_H__ */

include/asm-v850/param.h

···
 #define MAXHOSTNAMELEN	64	/* max length of hostname */
 
 #ifdef __KERNEL__
-#include <asm/machdep.h>	/* For HZ */
-
+# define HZ		CONFIG_HZ
 # define USER_HZ	100
 # define CLOCKS_PER_SEC	USER_HZ
 #endif

include/asm-v850/rte_cb.h

···
 #endif /* CONFIG_RTE_MB_A_PCI */
 
 
-/* For <asm/param.h> */
-#ifndef HZ
-#define HZ	100
-#endif
-
-
 #ifndef __ASSEMBLY__
 extern void rte_cb_early_init (void);
 extern void rte_cb_init_irqs (void);

include/asm-v850/sim.h

···
 #define R0_RAM_ADDR		0xFFFFF000
 
 
-/* For <asm/param.h> */
-#ifndef HZ
-#define HZ			24	/* Minimum supported frequency.  */
-#endif
-
 /* For <asm/irq.h> */
 #define NUM_CPU_IRQS		6
 

include/asm-v850/sim85e2.h

···
 #define R0_RAM_ADDR		0xFFFFE000
 
 
-/* For <asm/param.h> */
-#ifndef HZ
-#define HZ			24	/* Minimum supported frequency.  */
-#endif
-
-
 #endif /* __V850_SIM85E2_H__ */

include/asm-xtensa/param.h

···
 #define _XTENSA_PARAM_H
 
 #ifdef __KERNEL__
-# define HZ		100		/* internal timer frequency */
+# define HZ		CONFIG_HZ	/* internal timer frequency */
 # define USER_HZ	100		/* for user interfaces in "ticks" */
 # define CLOCKS_PER_SEC (USER_HZ)	/* frequnzy at which times() counts */
 #endif

kernel/Makefile

···
 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)

kernel/time.c

···
 #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.
···
 
 #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;
···
  * 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
···
 #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);
···
 #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);
···
  * 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)
···
 	/*
 	 * 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);
···
 #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);

kernel/timeconst.pl

···
+#!/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;