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SubjectRe: [PATCH] Bad rounding in timeval_to_jiffies [was: Re: Odd Timer behavior in 2.6 vs 2.4 (1 extra tick)]
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On Wed, 2005-04-20 at 22:58 -0400, Steven Rostedt wrote:
> I looked into the problem that jdavis had and found that the conversion
> of the timeval_to_jiffies was off by one.
>
> To convert tv.tv_sec = 0, tv.tv_usec = 10000 to jiffies, you come up
> with an answer of 11 (assuming 1000 HZ).
>

OK, this bothered me that this patch seems to work, since the comments
around the USEC_ROUND seem to make sense. So I looked more closely into
this.

Is 11 jiffies correct for 10ms? Since the the USEC_CONVERSION contains
a TICK_NSEC which is suppose to (I believe) convert the number of CPU
ticks to nanoseconds. Since ticks don't map nicely to nanoseconds there
can be a discrepancy for the actual time. But this doesn't explain why
the patch changes everything into the desired result, assuming that
10 ms == 10 jiffies.

Maybe there's too much rounding going on. I'll have to take a deeper
look into this, but feel free to look yourselves! I'm going to bed.

I've attached my userland program if you want to play around with the
numbers.

> Here's the patch:
>
> --- ./include/linux/jiffies.h.orig 2005-04-20 22:30:34.000000000 -0400
> +++ ./include/linux/jiffies.h 2005-04-20 22:39:42.000000000 -0400
> @@ -231,7 +231,7 @@
> * in jiffies (albit scaled), it is nothing but the bits we will shift
> * off.
> */
> -#define USEC_ROUND (u64)(((u64)1 << USEC_JIFFIE_SC) - 1)
> +#define USEC_ROUND (u64)(((u64)1 << (USEC_JIFFIE_SC - 1)))
> /*
> * The maximum jiffie value is (MAX_INT >> 1). Here we translate that
> * into seconds. The 64-bit case will overflow if we are not careful,

-- Steve

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

typedef unsigned long long u64;

#define HZ 1000

#ifndef div_long_long_rem
#define div_long_long_rem(dividend,divisor,remainder) \
({ \
u64 result = dividend; \
*remainder = do_div(result,divisor); \
result; \
})
#endif

# define CLOCK_TICK_RATE 1193182 /* Underlying HZ */
#define NSEC_PER_SEC (1000000000L)
#define NSEC_PER_USEC (1000L)

/*
* The following defines establish the engineering parameters of the PLL
* model. The HZ variable establishes the timer interrupt frequency, 100 Hz
* for the SunOS kernel, 256 Hz for the Ultrix kernel and 1024 Hz for the
* OSF/1 kernel. The SHIFT_HZ define expresses the same value as the
* nearest power of two in order to avoid hardware multiply operations.
*/
#if HZ >= 12 && HZ < 24
# define SHIFT_HZ 4
#elif HZ >= 24 && HZ < 48
# define SHIFT_HZ 5
#elif HZ >= 48 && HZ < 96
# define SHIFT_HZ 6
#elif HZ >= 96 && HZ < 192
# define SHIFT_HZ 7
#elif HZ >= 192 && HZ < 384
# define SHIFT_HZ 8
#elif HZ >= 384 && HZ < 768
# define SHIFT_HZ 9
#elif HZ >= 768 && HZ < 1536
# define SHIFT_HZ 10
#else
# error You lose.
#endif

/* LATCH is used in the interval timer and ftape setup. */
#define LATCH ((CLOCK_TICK_RATE + HZ/2) / HZ) /* For divider */

/* Suppose we want to devide two numbers NOM and DEN: NOM/DEN, the we can
* improve accuracy by shifting LSH bits, hence calculating:
* (NOM << LSH) / DEN
* This however means trouble for large NOM, because (NOM << LSH) may no
* longer fit in 32 bits. The following way of calculating this gives us
* some slack, under the following conditions:
* - (NOM / DEN) fits in (32 - LSH) bits.
* - (NOM % DEN) fits in (32 - LSH) bits.
*/
#define SH_DIV(NOM,DEN,LSH) ( ((NOM / DEN) << LSH) \
+ (((NOM % DEN) << LSH) + DEN / 2) / DEN)

/* HZ is the requested value. ACTHZ is actual HZ ("<< 8" is for accuracy) */
#define ACTHZ (SH_DIV (CLOCK_TICK_RATE, LATCH, 8))

/* TICK_NSEC is the time between ticks in nsec assuming real ACTHZ */
#define TICK_NSEC (SH_DIV (1000000UL * 1000, ACTHZ, 8))

/* TICK_USEC is the time between ticks in usec assuming fake USER_HZ */
#define TICK_USEC ((1000000UL + USER_HZ/2) / USER_HZ)

/* TICK_USEC_TO_NSEC is the time between ticks in nsec assuming real ACTHZ and */
/* a value TUSEC for TICK_USEC (can be set bij adjtimex) */
#define TICK_USEC_TO_NSEC(TUSEC) (SH_DIV (TUSEC * USER_HZ * 1000, ACTHZ, 8))

/* some arch's have a small-data section that can be accessed register-relative
* but that can only take up to, say, 4-byte variables. jiffies being part of
* an 8-byte variable may not be correctly accessed unless we force the issue
*/
#define __jiffy_data __attribute__((section(".data")))

/*
* The 64-bit value is not volatile - you MUST NOT read it
* without sampling the sequence number in xtime_lock.
* get_jiffies_64() will do this for you as appropriate.
*/
extern u64 __jiffy_data jiffies_64;
extern unsigned long volatile __jiffy_data jiffies;

#if (BITS_PER_LONG < 64)
u64 get_jiffies_64(void);
#else
static inline u64 get_jiffies_64(void)
{
return (u64)jiffies;
}
#endif

/*
* These inlines deal with timer wrapping correctly. You are
* strongly encouraged to use them
* 1. Because people otherwise forget
* 2. Because if the timer wrap changes in future you won't have to
* alter your driver code.
*
* time_after(a,b) returns true if the time a is after time b.
*
* Do this with "<0" and ">=0" to only test the sign of the result. A
* good compiler would generate better code (and a really good compiler
* wouldn't care). Gcc is currently neither.
*/
#define time_after(a,b) \
(typecheck(unsigned long, a) && \
typecheck(unsigned long, b) && \
((long)(b) - (long)(a) < 0))
#define time_before(a,b) time_after(b,a)

#define time_after_eq(a,b) \
(typecheck(unsigned long, a) && \
typecheck(unsigned long, b) && \
((long)(a) - (long)(b) >= 0))
#define time_before_eq(a,b) time_after_eq(b,a)

/*
* Have the 32 bit jiffies value wrap 5 minutes after boot
* so jiffies wrap bugs show up earlier.
*/
#define INITIAL_JIFFIES ((unsigned long)(unsigned int) (-300*HZ))

/*
* Change timeval to jiffies, trying to avoid the
* most obvious overflows..
*
* And some not so obvious.
*
* Note that we don't want to return MAX_LONG, because
* for various timeout reasons we often end up having
* to wait "jiffies+1" in order to guarantee that we wait
* at _least_ "jiffies" - so "jiffies+1" had better still
* be positive.
*/
#define MAX_JIFFY_OFFSET ((~0UL >> 1)-1)

/*
* We want to do realistic conversions of time so we need to use the same
* values the update wall clock code uses as the jiffies size. This value
* is: TICK_NSEC (which is defined in timex.h). This
* is a constant and is in nanoseconds. We will used scaled math
* with a set of scales defined here as SEC_JIFFIE_SC, USEC_JIFFIE_SC and
* NSEC_JIFFIE_SC. Note that these defines contain nothing but
* constants and so are computed at compile time. SHIFT_HZ (computed in
* timex.h) adjusts the scaling for different HZ values.

* Scaled math??? What is that?
*
* Scaled math is a way to do integer math on values that would,
* otherwise, either overflow, underflow, or cause undesired div
* instructions to appear in the execution path. In short, we "scale"
* up the operands so they take more bits (more precision, less
* underflow), do the desired operation and then "scale" the result back
* by the same amount. If we do the scaling by shifting we avoid the
* costly mpy and the dastardly div instructions.

* Suppose, for example, we want to convert from seconds to jiffies
* where jiffies is defined in nanoseconds as NSEC_PER_JIFFIE. The
* simple math is: jiff = (sec * NSEC_PER_SEC) / NSEC_PER_JIFFIE; We
* observe that (NSEC_PER_SEC / NSEC_PER_JIFFIE) is a constant which we
* might calculate at compile time, however, the result will only have
* about 3-4 bits of precision (less for smaller values of HZ).
*
* So, we scale as follows:
* jiff = (sec) * (NSEC_PER_SEC / NSEC_PER_JIFFIE);
* jiff = ((sec) * ((NSEC_PER_SEC * SCALE)/ NSEC_PER_JIFFIE)) / SCALE;
* Then we make SCALE a power of two so:
* jiff = ((sec) * ((NSEC_PER_SEC << SCALE)/ NSEC_PER_JIFFIE)) >> SCALE;
* Now we define:
* #define SEC_CONV = ((NSEC_PER_SEC << SCALE)/ NSEC_PER_JIFFIE))
* jiff = (sec * SEC_CONV) >> SCALE;
*
* Often the math we use will expand beyond 32-bits so we tell C how to
* do this and pass the 64-bit result of the mpy through the ">> SCALE"
* which should take the result back to 32-bits. We want this expansion
* to capture as much precision as possible. At the same time we don't
* want to overflow so we pick the SCALE to avoid this. In this file,
* that means using a different scale for each range of HZ values (as
* defined in timex.h).
*
* For those who want to know, gcc will give a 64-bit result from a "*"
* operator if the result is a long long AND at least one of the
* operands is cast to long long (usually just prior to the "*" so as
* not to confuse it into thinking it really has a 64-bit operand,
* which, buy the way, it can do, but it take more code and at least 2
* mpys).

* We also need to be aware that one second in nanoseconds is only a
* couple of bits away from overflowing a 32-bit word, so we MUST use
* 64-bits to get the full range time in nanoseconds.

*/

/*
* Here are the scales we will use. One for seconds, nanoseconds and
* microseconds.
*
* Within the limits of cpp we do a rough cut at the SEC_JIFFIE_SC and
* check if the sign bit is set. If not, we bump the shift count by 1.
* (Gets an extra bit of precision where we can use it.)
* We know it is set for HZ = 1024 and HZ = 100 not for 1000.
* Haven't tested others.

* Limits of cpp (for #if expressions) only long (no long long), but
* then we only need the most signicant bit.
*/

#define SEC_JIFFIE_SC (31 - SHIFT_HZ)
#if !((((NSEC_PER_SEC << 2) / TICK_NSEC) << (SEC_JIFFIE_SC - 2)) & 0x80000000)
#undef SEC_JIFFIE_SC
#define SEC_JIFFIE_SC (32 - SHIFT_HZ)
#endif
#define NSEC_JIFFIE_SC (SEC_JIFFIE_SC + 29)
#define USEC_JIFFIE_SC (SEC_JIFFIE_SC + 19)
#define SEC_CONVERSION ((unsigned long)((((u64)NSEC_PER_SEC << SEC_JIFFIE_SC) +\
TICK_NSEC -1) / (u64)TICK_NSEC))

#define NSEC_CONVERSION ((unsigned long)((((u64)1 << NSEC_JIFFIE_SC) +\
TICK_NSEC -1) / (u64)TICK_NSEC))
#define USEC_CONVERSION \
((unsigned long)((((u64)NSEC_PER_USEC << USEC_JIFFIE_SC) +\
TICK_NSEC -1) / (u64)TICK_NSEC))
/*
* USEC_ROUND is used in the timeval to jiffie conversion. See there
* for more details. It is the scaled resolution rounding value. Note
* that it is a 64-bit value. Since, when it is applied, we are already
* in jiffies (albit scaled), it is nothing but the bits we will shift
* off.
*/
#define USEC_ROUND (u64)(((u64)1 << USEC_JIFFIE_SC) - 1)
#define USEC_ROUND2 (u64)(((u64)1 << (USEC_JIFFIE_SC - 1)))
/*
* The maximum jiffie value is (MAX_INT >> 1). Here we translate that
* into seconds. The 64-bit case will overflow if we are not careful,
* so use the messy SH_DIV macro to do it. Still all constants.
*/
#if BITS_PER_LONG < 64
# define MAX_SEC_IN_JIFFIES \
(long)((u64)((u64)MAX_JIFFY_OFFSET * TICK_NSEC) / NSEC_PER_SEC)
#else /* take care of overflow on 64 bits machines */
# define MAX_SEC_IN_JIFFIES \
(SH_DIV((MAX_JIFFY_OFFSET >> SEC_JIFFIE_SC) * TICK_NSEC, NSEC_PER_SEC, 1) - 1)

#endif

/*
* Convert jiffies to milliseconds and back.
*
* Avoid unnecessary multiplications/divisions in the
* two most common HZ cases:
*/
static inline unsigned int jiffies_to_msecs(const unsigned long j)
{
#if HZ <= 1000 && !(1000 % HZ)
return (1000 / HZ) * j;
#elif HZ > 1000 && !(HZ % 1000)
return (j + (HZ / 1000) - 1)/(HZ / 1000);
#else
return (j * 1000) / HZ;
#endif
}

static inline unsigned int jiffies_to_usecs(const unsigned long j)
{
#if HZ <= 1000 && !(1000 % HZ)
return (1000000 / HZ) * j;
#elif HZ > 1000 && !(HZ % 1000)
return (j*1000 + (HZ - 1000))/(HZ / 1000);
#else
return (j * 1000000) / HZ;
#endif
}

static inline unsigned long msecs_to_jiffies(const unsigned int m)
{
if (m > jiffies_to_msecs(MAX_JIFFY_OFFSET))
return MAX_JIFFY_OFFSET;
#if HZ <= 1000 && !(1000 % HZ)
return (m + (1000 / HZ) - 1) / (1000 / HZ);
#elif HZ > 1000 && !(HZ % 1000)
return m * (HZ / 1000);
#else
return (m * HZ + 999) / 1000;
#endif
}

static inline unsigned long usecs_to_jiffies(const unsigned int u)
{
if (u > jiffies_to_usecs(MAX_JIFFY_OFFSET))
return MAX_JIFFY_OFFSET;
#if HZ <= 1000 && !(1000 % HZ)
return (u + (1000000 / HZ) - 1000) / (1000000 / HZ);
#elif HZ > 1000 && !(HZ % 1000)
return u * (HZ / 1000000);
#else
return (u * HZ + 999999) / 1000000;
#endif
}

/*
* The TICK_NSEC - 1 rounds up the value to the next resolution. Note
* that a remainder subtract here would not do the right thing as the
* resolution values don't fall on second boundries. I.e. the line:
* nsec -= nsec % TICK_NSEC; is NOT a correct resolution rounding.
*
* Rather, we just shift the bits off the right.
*
* The >> (NSEC_JIFFIE_SC - SEC_JIFFIE_SC) converts the scaled nsec
* value to a scaled second value.
*/


/* Same for "timeval"
*
* Well, almost. The problem here is that the real system resolution is
* in nanoseconds and the value being converted is in micro seconds.
* Also for some machines (those that use HZ = 1024, in-particular),
* there is a LARGE error in the tick size in microseconds.

* The solution we use is to do the rounding AFTER we convert the
* microsecond part. Thus the USEC_ROUND, the bits to be shifted off.
* Instruction wise, this should cost only an additional add with carry
* instruction above the way it was done above.
*/
static __inline__ unsigned long
timeval_to_jiffies(const struct timeval *value)
{
unsigned long sec = value->tv_sec;
long usec = value->tv_usec;

if (sec >= MAX_SEC_IN_JIFFIES){
sec = MAX_SEC_IN_JIFFIES;
usec = 0;
}
#if 0
printf("usec * USEC_CONVERSION = %llx\n",
(u64)usec * USEC_CONVERSION);
printf("usec * USEC_CONVERSION + USEC_ROUND = %llx >> %llx\n",
(u64)usec * USEC_CONVERSION + USEC_ROUND,
((u64)usec * USEC_CONVERSION + USEC_ROUND) >> USEC_JIFFIE_SC
);
printf("usec * USEC_CONVERSION + USEC_ROUND2 = %llx "
">> %llx = %ld jiffies\n",
(u64)usec * USEC_CONVERSION + USEC_ROUND2,
((u64)usec * USEC_CONVERSION + USEC_ROUND2) >> USEC_JIFFIE_SC,
(((u64)sec * SEC_CONVERSION) +
(((u64)usec * USEC_CONVERSION + USEC_ROUND2) >>
(USEC_JIFFIE_SC - SEC_JIFFIE_SC))) >> SEC_JIFFIE_SC
);
#endif

#define USE_PATCH 0
#if USE_PATCH
return (((u64)sec * SEC_CONVERSION) +
(((u64)usec * USEC_CONVERSION + USEC_ROUND2) >>
(USEC_JIFFIE_SC - SEC_JIFFIE_SC))) >> SEC_JIFFIE_SC;
#else
return (((u64)sec * SEC_CONVERSION) +
(((u64)usec * USEC_CONVERSION + USEC_ROUND) >>
(USEC_JIFFIE_SC - SEC_JIFFIE_SC))) >> SEC_JIFFIE_SC;
#endif
}
int main(int argc, char **argv)
{
unsigned long jiffies;
struct timeval tv;
int i;

tv.tv_sec = 0;
for (i=0; i <= 100; i++) {
tv.tv_usec = 10000 + i*10;

jiffies = timeval_to_jiffies(&tv);
printf("usec=%ld jiffies = %lu\n",tv.tv_usec,jiffies);
}
return 0;
}
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