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>

29 files changed, 486 insertions, 68 deletions

diff --git a/arch/alpha/Kconfig b/arch/alpha/Kconfig
index d9df913a464d..5b7dcd5a0e75 100644
--- a/arch/alpha/Kconfig
+++ b/arch/alpha/Kconfig
@@ -615,6 +615,11 @@ config VERBOSE_MCHECK_ON
 
 	  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"
 
diff --git a/arch/cris/Kconfig b/arch/cris/Kconfig
index 27b082ac7f11..ff078e60e76d 100644
--- a/arch/cris/Kconfig
+++ b/arch/cris/Kconfig
@@ -55,6 +55,10 @@ config CRIS
 	bool
 	default y
 
+config HZ
+	int
+	default 100
+
 source "init/Kconfig"
 
 menu "General setup"
diff --git a/arch/frv/Kconfig b/arch/frv/Kconfig
index 96f7d70f4473..9e561ede0925 100644
--- a/arch/frv/Kconfig
+++ b/arch/frv/Kconfig
@@ -57,6 +57,10 @@ config ARCH_HAS_ILOG2_U64
 	bool
 	default y
 
+config HZ
+	int
+	default 1000
+
 mainmenu "Fujitsu FR-V Kernel Configuration"
 
 source "init/Kconfig"
diff --git a/arch/h8300/Kconfig b/arch/h8300/Kconfig
index b4ba4f8b505c..f69e5ea38558 100644
--- a/arch/h8300/Kconfig
+++ b/arch/h8300/Kconfig
@@ -82,6 +82,10 @@ config PCI
 	bool
 	default n
 
+config HZ
+	int
+	default 100
+
 source "init/Kconfig"
 
 source "arch/h8300/Kconfig.cpu"
diff --git a/arch/m32r/Kconfig b/arch/m32r/Kconfig
index fe61e00a604f..d4679ab55b96 100644
--- a/arch/m32r/Kconfig
+++ b/arch/m32r/Kconfig
@@ -38,6 +38,10 @@ config NO_DMA
 config ARCH_SUPPORTS_AOUT
 	def_bool y
 
+config HZ
+	int
+	default 100
+
 source "init/Kconfig"
 
 
diff --git a/arch/m68k/Kconfig b/arch/m68k/Kconfig
index bcbf3e4ee9d4..2b0ed89cd173 100644
--- a/arch/m68k/Kconfig
+++ b/arch/m68k/Kconfig
@@ -55,6 +55,10 @@ config NO_DMA
 config ARCH_SUPPORTS_AOUT
 	def_bool y
 
+config HZ
+	int
+	default 100
+
 mainmenu "Linux/68k Kernel Configuration"
 
 source "init/Kconfig"
diff --git a/arch/m68knommu/Kconfig b/arch/m68knommu/Kconfig
index 24f732342d3e..548a7b321633 100644
--- a/arch/m68knommu/Kconfig
+++ b/arch/m68knommu/Kconfig
@@ -525,6 +525,11 @@ config 4KSTACKS
 	  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
diff --git a/arch/sparc/Kconfig b/arch/sparc/Kconfig
index 08821b078ecc..7c674a3503b6 100644
--- a/arch/sparc/Kconfig
+++ b/arch/sparc/Kconfig
@@ -30,6 +30,10 @@ config OF
 config ARCH_SUPPORTS_AOUT
 	def_bool y
 
+config HZ
+	int
+	default 100
+
 source "init/Kconfig"
 
 menu "General machine setup"
diff --git a/arch/v850/Kconfig b/arch/v850/Kconfig
index 225f30d7cb32..7b6d3716efca 100644
--- a/arch/v850/Kconfig
+++ b/arch/v850/Kconfig
@@ -215,6 +215,13 @@ menu "Processor type and features"
    	  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
diff --git a/arch/xtensa/Kconfig b/arch/xtensa/Kconfig
index 5d5546ce88fe..fd36764d7fb7 100644
--- a/arch/xtensa/Kconfig
+++ b/arch/xtensa/Kconfig
@@ -49,6 +49,10 @@ config ARCH_HAS_ILOG2_U64
 config NO_IOPORT
 	def_bool y
 
+config HZ
+	int
+	default 100
+
 source "init/Kconfig"
 
 menu "Processor type and features"
diff --git a/include/asm-alpha/param.h b/include/asm-alpha/param.h
index 214e7996346f..0982f1d39499 100644
--- a/include/asm-alpha/param.h
+++ b/include/asm-alpha/param.h
@@ -5,15 +5,7 @@
    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
diff --git a/include/asm-cris/param.h b/include/asm-cris/param.h
index b24972639832..0e47994e40be 100644
--- a/include/asm-cris/param.h
+++ b/include/asm-cris/param.h
@@ -3,7 +3,7 @@
 
 /* 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
diff --git a/include/asm-frv/param.h b/include/asm-frv/param.h
index 365653b1726c..6859dd503ed3 100644
--- a/include/asm-frv/param.h
+++ b/include/asm-frv/param.h
@@ -2,7 +2,7 @@
 #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
diff --git a/include/asm-h8300/param.h b/include/asm-h8300/param.h
index c25806ed1fb3..04f64f100379 100644
--- a/include/asm-h8300/param.h
+++ b/include/asm-h8300/param.h
@@ -3,7 +3,7 @@
 
 
 #ifndef HZ
-#define HZ 100
+#define HZ CONFIG_HZ
 #endif
 
 #ifdef __KERNEL__
diff --git a/include/asm-m32r/param.h b/include/asm-m32r/param.h
index 3e14026e39cd..94c770196048 100644
--- a/include/asm-m32r/param.h
+++ b/include/asm-m32r/param.h
@@ -2,7 +2,7 @@
 #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
diff --git a/include/asm-m68k/param.h b/include/asm-m68k/param.h
index 60f409d81658..536a27888358 100644
--- a/include/asm-m68k/param.h
+++ b/include/asm-m68k/param.h
@@ -2,7 +2,7 @@
 #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
diff --git a/include/asm-m68knommu/param.h b/include/asm-m68knommu/param.h
index 4c9904d6512e..96c451018324 100644
--- a/include/asm-m68knommu/param.h
+++ b/include/asm-m68knommu/param.h
@@ -1,13 +1,7 @@
 #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
diff --git a/include/asm-sparc/param.h b/include/asm-sparc/param.h
index beaf02d364f2..86ba59af9d2c 100644
--- a/include/asm-sparc/param.h
+++ b/include/asm-sparc/param.h
@@ -3,7 +3,7 @@
 #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
diff --git a/include/asm-v850/anna.h b/include/asm-v850/anna.h
index 3be77d5ecfce..cd5eaee103b0 100644
--- a/include/asm-v850/anna.h
+++ b/include/asm-v850/anna.h
@@ -134,10 +134,4 @@ extern void anna_uart_pre_configure (unsigned chan,
 #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__ */
diff --git a/include/asm-v850/as85ep1.h b/include/asm-v850/as85ep1.h
index 659bc910ffd7..5a5ca9073d09 100644
--- a/include/asm-v850/as85ep1.h
+++ b/include/asm-v850/as85ep1.h
@@ -149,10 +149,4 @@ extern void as85ep1_uart_pre_configure (unsigned chan,
 #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__ */
diff --git a/include/asm-v850/fpga85e2c.h b/include/asm-v850/fpga85e2c.h
index d32f04504b13..23aae666c718 100644
--- a/include/asm-v850/fpga85e2c.h
+++ b/include/asm-v850/fpga85e2c.h
@@ -79,10 +79,4 @@ extern char _r0_ram;
 #endif
 
 
-/* For <asm/param.h> */
-#ifndef HZ
-#define HZ			122 /* actually, 8.192ms ticks =~ 122.07 */
-#endif
-
-
 #endif /* __V850_FPGA85E2C_H__ */
diff --git a/include/asm-v850/param.h b/include/asm-v850/param.h
index 3c65bd573782..281832690290 100644
--- a/include/asm-v850/param.h
+++ b/include/asm-v850/param.h
@@ -23,8 +23,7 @@
 #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
diff --git a/include/asm-v850/rte_cb.h b/include/asm-v850/rte_cb.h
index e85d261b79bf..db9879f00aa7 100644
--- a/include/asm-v850/rte_cb.h
+++ b/include/asm-v850/rte_cb.h
@@ -69,12 +69,6 @@
 #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);
diff --git a/include/asm-v850/sim.h b/include/asm-v850/sim.h
index 10236abbe9be..026932d476cd 100644
--- a/include/asm-v850/sim.h
+++ b/include/asm-v850/sim.h
@@ -40,11 +40,6 @@
 #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
 
diff --git a/include/asm-v850/sim85e2.h b/include/asm-v850/sim85e2.h
index 17dd4fa318e6..8b4d6974066c 100644
--- a/include/asm-v850/sim85e2.h
+++ b/include/asm-v850/sim85e2.h
@@ -66,10 +66,4 @@
 #define R0_RAM_ADDR		0xFFFFE000
 
 
-/* For <asm/param.h> */
-#ifndef HZ
-#define HZ			24	/* Minimum supported frequency.  */
-#endif
-
-
 #endif /* __V850_SIM85E2_H__ */
diff --git a/include/asm-xtensa/param.h b/include/asm-xtensa/param.h
index ce3a336cad07..82ad34d92d35 100644
--- a/include/asm-xtensa/param.h
+++ b/include/asm-xtensa/param.h
@@ -12,7 +12,7 @@
 #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
diff --git a/kernel/Makefile b/kernel/Makefile
index 60cd39c84e6d..6c584c55a6e9 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 3b705ecc3fb7..a5ec013b6c80 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 000000000000..62b1287932ed
--- /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;