cpuidle: menu: avoid expensive square root computation
Computing the integer square root is a rather expensive operation, at least compared to doing a 64x64 -> 64 multiply (avg*avg) and, on 64 bit platforms, doing an extra comparison to a constant (variance <= U64_MAX/36). On 64 bit platforms, this does mean that we add a restriction on the range of the variance where we end up using the estimate (since previously the stddev <= ULONG_MAX was a tautology), but on the other hand, we extend the range quite substantially on 32 bit platforms - in both cases, we now allow standard deviations up to 715 seconds, which is for example guaranteed if all observations are less than 1430 seconds. Signed-off-by: Rasmus Villemoes <linux@rasmusvillemoes.dk> Signed-off-by: Rafael J. Wysocki <rafael.j.wysocki@intel.com>
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@ -200,7 +200,7 @@ static void get_typical_interval(struct menu_device *data)
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{
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int i, divisor;
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unsigned int max, thresh;
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uint64_t avg, stddev;
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uint64_t avg, variance;
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thresh = UINT_MAX; /* Discard outliers above this value */
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@ -224,36 +224,35 @@ again:
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else
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do_div(avg, divisor);
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/* Then try to determine standard deviation */
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stddev = 0;
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/* Then try to determine variance */
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variance = 0;
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for (i = 0; i < INTERVALS; i++) {
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unsigned int value = data->intervals[i];
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if (value <= thresh) {
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int64_t diff = value - avg;
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stddev += diff * diff;
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variance += diff * diff;
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}
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}
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if (divisor == INTERVALS)
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stddev >>= INTERVAL_SHIFT;
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variance >>= INTERVAL_SHIFT;
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else
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do_div(stddev, divisor);
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do_div(variance, divisor);
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/*
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* The typical interval is obtained when standard deviation is small
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* or standard deviation is small compared to the average interval.
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*
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* int_sqrt() formal parameter type is unsigned long. When the
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* greatest difference to an outlier exceeds ~65 ms * sqrt(divisor)
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* the resulting squared standard deviation exceeds the input domain
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* of int_sqrt on platforms where unsigned long is 32 bits in size.
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* In such case reject the candidate average.
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* The typical interval is obtained when standard deviation is
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* small (stddev <= 20 us, variance <= 400 us^2) or standard
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* deviation is small compared to the average interval (avg >
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* 6*stddev, avg^2 > 36*variance). The average is smaller than
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* UINT_MAX aka U32_MAX, so computing its square does not
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* overflow a u64. We simply reject this candidate average if
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* the standard deviation is greater than 715 s (which is
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* rather unlikely).
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*
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* Use this result only if there is no timer to wake us up sooner.
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*/
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if (likely(stddev <= ULONG_MAX)) {
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stddev = int_sqrt(stddev);
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if (((avg > stddev * 6) && (divisor * 4 >= INTERVALS * 3))
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|| stddev <= 20) {
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if (likely(variance <= U64_MAX/36)) {
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if (((avg*avg > variance*36) && (divisor * 4 >= INTERVALS * 3))
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|| variance <= 400) {
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if (data->next_timer_us > avg)
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data->predicted_us = avg;
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return;
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