[PATCH V2] perf: x86: Improve accuracy of perf/sched clock

[Adrian Hunter <adrian.hunter@intel.com>]

When TSC is stable perf/sched clock is based on it.
However the conversion from cycles to nanoseconds
is not as accurate as it could be.  Because
CYC2NS_SCALE_FACTOR is 10, the accuracy is +/- 1/2048

The change is to calculate the maximum shift that
results in a multiplier that is still a 32-bit number.
For example all frequencies over 1 GHz will have
a shift of 32, making the accuracy of the conversion
+/- 1/(2^33)

Signed-off-by: Adrian Hunter <adrian.hunter@intel.com>
---
 arch/x86/kernel/tsc.c | 33 ++++++++++++++++++++-------------
 1 file changed, 20 insertions(+), 13 deletions(-)

diff --git a/arch/x86/kernel/tsc.c b/arch/x86/kernel/tsc.c
index 7437b41f6a47..e7085bcfb06b 100644
--- a/arch/x86/kernel/tsc.c
+++ b/arch/x86/kernel/tsc.c
@@ -167,21 +167,21 @@ static void cyc2ns_write_end(int cpu, struct cyc2ns_data *data)
  *              ns = cycles * cyc2ns_scale / SC
  *
  *      And since SC is a constant power of two, we can convert the div
- *  into a shift.
+ *  into a shift. The larger SC is, the more accurate the conversion, but
+ *  cyc2ns_scale needs to be a 32-bit value so that 32-bit multiplication
+ *  (64-bit result) can be used. So start by trying SC = 2^32, reducing
+ *  until the criteria are met.
  *
- *  We can use khz divisor instead of mhz to keep a better precision, since
- *  cyc2ns_scale is limited to 10^6 * 2^10, which fits in 32 bits.
+ *  We can use khz divisor instead of mhz to keep a better precision.
  *  (mathieu.desnoyers@polymtl.ca)
  *
  *                      -johnstul@us.ibm.com "math is hard, lets go shopping!"
  */
 
-#define CYC2NS_SCALE_FACTOR 10 /* 2^10, carefully chosen */
-
 static void cyc2ns_data_init(struct cyc2ns_data *data)
 {
 	data->cyc2ns_mul = 0;
-	data->cyc2ns_shift = CYC2NS_SCALE_FACTOR;
+	data->cyc2ns_shift = 0;
 	data->cyc2ns_offset = 0;
 	data->__count = 0;
 }
@@ -215,14 +215,14 @@ static inline unsigned long long cycles_2_ns(unsigned long long cyc)
 
 	if (likely(data == tail)) {
 		ns = data->cyc2ns_offset;
-		ns += mul_u64_u32_shr(cyc, data->cyc2ns_mul, CYC2NS_SCALE_FACTOR);
+		ns += mul_u64_u32_shr(cyc, data->cyc2ns_mul, data->cyc2ns_shift);
 	} else {
 		data->__count++;
 
 		barrier();
 
 		ns = data->cyc2ns_offset;
-		ns += mul_u64_u32_shr(cyc, data->cyc2ns_mul, CYC2NS_SCALE_FACTOR);
+		ns += mul_u64_u32_shr(cyc, data->cyc2ns_mul, data->cyc2ns_shift);
 
 		barrier();
 
@@ -239,6 +239,8 @@ static void set_cyc2ns_scale(unsigned long cpu_khz, int cpu)
 	unsigned long long tsc_now, ns_now;
 	struct cyc2ns_data *data;
 	unsigned long flags;
+	u64 mult;
+	u32 shft = 32;
 
 	local_irq_save(flags);
 	sched_clock_idle_sleep_event();
@@ -256,12 +258,17 @@ static void set_cyc2ns_scale(unsigned long cpu_khz, int cpu)
 	 * time function is continuous; see the comment near struct
 	 * cyc2ns_data.
 	 */
-	data->cyc2ns_mul =
-		DIV_ROUND_CLOSEST(NSEC_PER_MSEC << CYC2NS_SCALE_FACTOR,
-				  cpu_khz);
-	data->cyc2ns_shift = CYC2NS_SCALE_FACTOR;
+	mult = (u64)NSEC_PER_MSEC << 32;
+	mult += cpu_khz / 2;
+	do_div(mult, cpu_khz);
+	while (mult > U32_MAX) {
+		mult >>= 1;
+		shft -= 1;
+	}
+	data->cyc2ns_mul = mult;
+	data->cyc2ns_shift = shft;
 	data->cyc2ns_offset = ns_now -
-		mul_u64_u32_shr(tsc_now, data->cyc2ns_mul, CYC2NS_SCALE_FACTOR);
+		mul_u64_u32_shr(tsc_now, data->cyc2ns_mul, data->cyc2ns_shift);
 
 	cyc2ns_write_end(cpu, data);
 
-- 
1.9.1