The reason for the drift observed in the OP, at least on my machine, is that the TSC is ticking for ns deviations from the original _ticks_per_ns value. The following results were obtained from this apparatus:
don@HAL :~/UNIX/OS/3EZPcs/Ch06$ uname -a Linux HAL 4.4.0-81-generic
cat /proc/cpuinfo shows the constant_tsc and nonstop_tsc .
viewRates.cc can be run to see the current TSC Ticks for ns on the machine:
rdtscp.h:
static inline unsigned long rdtscp_start(void) { unsigned long var; unsigned int hi, lo; __asm volatile ("cpuid\n\t" "rdtsc\n\t" : "=a" (lo), "=d" (hi) :: "%rbx", "%rcx"); var = ((unsigned long)hi << 32) | lo; return (var); } static inline unsigned long rdtscp_end(void) { unsigned long var; unsigned int hi, lo; __asm volatile ("rdtscp\n\t" "mov %%edx, %1\n\t" "mov %%eax, %0\n\t" "cpuid\n\t" : "=r" (lo), "=r" (hi) :: "%rax", "%rbx", "%rcx", "%rdx"); var = ((unsigned long)hi << 32) | lo; return (var); }
viewRates.cc:
#include <time.h> #include <unistd.h> #include <iostream> #include <iomanip> #include <cstdlib> #include "rdtscp.h" using std::cout; using std::cerr; using std::endl; #define CLOCK CLOCK_REALTIME uint64_t to_ns(const timespec &ts); // Converts a struct timespec to ns (since epoch). void view_ticks_per_ns(int runs =10, int sleep =10); int main(int argc, char **argv) { int runs = 10, sleep = 10; if (argc != 1 && argc != 3) { cerr << "Usage: " << argv[0] << " [ RUNS SLEEP ] \n"; exit(1); } else if (argc == 3) { runs = std::atoi(argv[1]); sleep = std::atoi(argv[2]); } view_ticks_per_ns(runs, sleep); } void view_ticks_per_ns(int RUNS, int SLEEP) { // Prints out stream of RUNS tsc ticks per ns, each calculated over a SLEEP secs interval. timespec clock_start, clock_end; unsigned long tsc1, tsc2, tsc_start, tsc_end; unsigned long elapsed_ns, elapsed_ticks; double rate; // ticks per ns from each run. clock_getres(CLOCK, &clock_start); cout << "Clock resolution: " << to_ns(clock_start) << "ns\n\n"; cout << " tsc ticks " << "ns " << " tsc ticks per ns\n"; for (int i = 0; i < RUNS; ++i) { tsc1 = rdtscp_start(); clock_gettime(CLOCK, &clock_start); tsc2 = rdtscp_end(); tsc_start = (tsc1 + tsc2) / 2; sleep(SLEEP); tsc1 = rdtscp_start(); clock_gettime(CLOCK, &clock_end); tsc2 = rdtscp_end(); tsc_end = (tsc1 + tsc2) / 2; elapsed_ticks = tsc_end - tsc_start; elapsed_ns = to_ns(clock_end) - to_ns(clock_start); rate = static_cast<double>(elapsed_ticks) / elapsed_ns; cout << elapsed_ticks << " " << elapsed_ns << " " << std::setprecision(12) << rate << endl; } }
linearExtrapolator.cc can be run to recreate the OP experiment:
linearExtrapolator.cc:
#include <time.h> #include <unistd.h> #include <iostream> #include <iomanip> #include <algorithm> #include <array> #include "rdtscp.h" using std::cout; using std::endl; using std::array; #define CLOCK CLOCK_REALTIME uint64_t to_ns(const timespec &ts); // Converts a struct timespec to ns (since epoch). void set_ticks_per_ns(bool set_rate); // Display or set tsc ticks per ns, _ticks_per_ns. void get_start(); // Sets the 'start' time point: _start_tsc[in ticks] and _start_clock_time[in ns]. uint64_t tsc_to_ns(uint64_t tsc); // Convert tsc ticks since _start_tsc to ns (since epoch) linearly using // _ticks_per_ns with origin(0) at the 'start' point set by get_start(). uint64_t _start_tsc, _start_clock_time; // The 'start' time point as both tsc tick number, start_tsc, and as // clock_gettime ns since epoch as _start_clock_time. double _ticks_per_ns; // Calibrated in set_ticks_per_ns() int main() { set_ticks_per_ns(true); // Set _ticks_per_ns as the initial TSC ticks per ns. uint64_t tsc1, tsc2, tsc_now, tsc_ns, utc_ns; int64_t ns_diff; bool first_pass{true}; for (int i = 0; i < 10; ++i) { timespec utc_now; if (first_pass) { get_start(); //Get start time in both ns since epoch (_start_clock_time), and tsc tick number(_start_tsc) cout << "_start_clock_time: " << _start_clock_time << ", _start_tsc: " << _start_tsc << endl; utc_ns = _start_clock_time; tsc_ns = tsc_to_ns(_start_tsc); // == _start_clock_time by definition. tsc_now = _start_tsc; first_pass = false; } else { tsc1 = rdtscp_start(); clock_gettime(CLOCK, &utc_now); tsc2 = rdtscp_end(); tsc_now = (tsc1 + tsc2) / 2; tsc_ns = tsc_to_ns(tsc_now); utc_ns = to_ns(utc_now); } ns_diff = tsc_ns - (int64_t)utc_ns; cout << "elapsed ns: " << utc_ns - _start_clock_time << ", elapsed ticks: " << tsc_now - _start_tsc << ", ns_diff: " << ns_diff << '\n' << endl; set_ticks_per_ns(false); // Display current TSC ticks per ns (does not alter original _ticks_per_ns). } } void set_ticks_per_ns(bool set_rate) { constexpr int RUNS {1}, SLEEP{10}; timespec clock_start, clock_end; uint64_t tsc1, tsc2, tsc_start, tsc_end; uint64_t elapsed_ns[RUNS], elapsed_ticks[RUNS]; array<double, RUNS> rates; // ticks per ns from each run. if (set_rate) { clock_getres(CLOCK, &clock_start); cout << "Clock resolution: " << to_ns(clock_start) << "ns\n"; } for (int i = 0; i < RUNS; ++i) { tsc1 = rdtscp_start(); clock_gettime(CLOCK, &clock_start); tsc2 = rdtscp_end(); tsc_start = (tsc1 + tsc2) / 2; sleep(SLEEP); tsc1 = rdtscp_start(); clock_gettime(CLOCK, &clock_end); tsc2 = rdtscp_end(); tsc_end = (tsc1 + tsc2) / 2; elapsed_ticks[i] = tsc_end - tsc_start; elapsed_ns[i] = to_ns(clock_end) - to_ns(clock_start); rates[i] = static_cast<double>(elapsed_ticks[i]) / elapsed_ns[i]; } cout << " tsc ticks " << "ns " << "tsc ticks per ns" << endl; for (int i = 0; i < RUNS; ++i) cout << elapsed_ticks[i] << " " << elapsed_ns[i] << " " << std::setprecision(12) << rates[i] << endl; if (set_rate) _ticks_per_ns = rates[RUNS-1]; } constexpr uint64_t BILLION {1000000000}; uint64_t to_ns(const timespec &ts) { return ts.tv_sec * BILLION + ts.tv_nsec; } void get_start() { // Get start time both in tsc ticks as _start_tsc, and in ns since epoch as _start_clock_time timespec ts; uint64_t beg, end; // loop to ensure we aren't interrupted between the two tsc reads while (1) { beg = rdtscp_start(); clock_gettime(CLOCK, &ts); end = rdtscp_end(); if ((end - beg) <= 2000) // max ticks per clock call break; } _start_tsc = (end + beg) / 2; _start_clock_time = to_ns(ts); // converts timespec to ns since epoch } uint64_t tsc_to_ns(uint64_t tsc) { // Convert tsc ticks into absolute ns: // Absolute ns is defined by this linear extrapolation from the start point where //_start_tsc[in ticks] corresponds to _start_clock_time[in ns]. uint64_t diff = tsc - _start_tsc; return _start_clock_time + static_cast<uint64_t>(diff / _ticks_per_ns); }
This is the result of viewRates , followed by a linearExtrapolator :
don@HAL :~/UNIX/OS/3EZPcs/Ch06$ ./viewRates Clock resolution: 1ns tsc ticks ns tsc ticks per ns 28070466526 10000176697 2.8069970538 28070500272 10000194599 2.80699540335 28070489661 10000196097 2.80699392179 28070404159 10000170879 2.80699245029 28070464811 10000197285 2.80699110338 28070445753 10000195177 2.80698978932 28070430538 10000194298 2.80698851457 28070427907 10000197673 2.80698730414 28070409903 10000195492 2.80698611597 28070398177 10000195328 2.80698498942 don@HAL :~/UNIX/OS/3EZPcs/Ch06$ ./linearExtrapolator Clock resolution: 1ns tsc ticks ns tsc ticks per ns 28070385587 10000197480 2.8069831264 _start_clock_time: 1497966724156422794, _start_tsc: 4758879747559 elapsed ns: 0, elapsed ticks: 0, ns_diff: 0 tsc ticks ns tsc ticks per ns 28070364084 10000193633 2.80698205596 elapsed ns: 10000247486, elapsed ticks: 28070516229, ns_diff: -3465 tsc ticks ns tsc ticks per ns 28070358445 10000195130 2.80698107188 elapsed ns: 20000496849, elapsed ticks: 56141027929, ns_diff: -10419 tsc ticks ns tsc ticks per ns 28070350693 10000195646 2.80698015186 elapsed ns: 30000747550, elapsed ticks: 84211534141, ns_diff: -20667 tsc ticks ns tsc ticks per ns 28070324772 10000189692 2.80697923105 elapsed ns: 40000982325, elapsed ticks: 112281986547, ns_diff: -34158 tsc ticks ns tsc ticks per ns 28070340494 10000198352 2.80697837242 elapsed ns: 50001225563, elapsed ticks: 140352454025, ns_diff: -50742 tsc ticks ns tsc ticks per ns 28070325598 10000196057 2.80697752704 elapsed ns: 60001465937, elapsed ticks: 168422905017, ns_diff: -70335 ^C
The output of viewRates shows that the TSC ticks for ns decrease quite quickly with time corresponding to one of these steep drops in the above chart. The output of the linearExtrapolator shows, as in the OP, the difference between past ns, as reported in clock_gettime() , and past ns, obtained by converting past TSC cycles to expired ns using _ticks_per_ns == 2.8069831264 received at startup, Instead of sleep(10); between each print from elapsed ns , elapsed ticks , ns_diff I re-run TSC ticks on ns using the 10s window; this displays the current ratio tsc ticks per ns . You can see that the tendency to decrease TSC ticks for ns, observed from the viewRates output, continues throughout the linearExtrapolator .
Dividing a elapsed ticks by _ticks_per_ns and subtracting the corresponding elapsed ns gives ns_diff , for example: (84211534141 / 2.8069831264) - 30000747550 = -20667. But this is not 0, mainly due to the drift in the grip of TSC for ns. If we used the value of 2.80698015186 ticks for ns received in the last 10 second interval, the result would be: (84211534141 / 2.80698015186) - 30000747550 = 11125. An additional error accumulated over this last interval of 10 seconds is -20667 - -10419 = - 10248, almost disappears when the correct TSC values ββfor ns are used for this interval: (84211534141 - 56141027929) /2.80698015186 - (30000747550 - 20000496849) = 349.
If the linear Ekrapolyator was launched at a time when the TSC ticks for ns were constant, the accuracy would be limited by how well defined (constant) _ticks_per_ns , and then it would pay, for example, the median of several ratings. If _ticks_per_ns cut off to a fixed 40 ppb, a constant drift of about 400 ns every 10 seconds would be expected, so ns_diff would increase / decrease by 400 every 10 seconds.
genTimeSeriesofRates.cc can be used to generate data for the chart, as described above: genTimeSeriesofRates.cc:
#include <time.h> #include <unistd.h> #include <iostream> #include <iomanip> #include <algorithm> #include <array> #include "rdtscp.h" using std::cout; using std::cerr; using std::endl; using std::array; double get_ticks_per_ns(long &ticks, long &ns); // Get median tsc ticks per ns, ticks and ns. long ts_to_ns(const timespec &ts); #define CLOCK CLOCK_REALTIME // clock_gettime() clock to use. #define TIMESTEP 10 #define NSTEPS 10000 #define RUNS 5 // Number of RUNS and SLEEP interval used for each sample in get_ticks_per_ns(). #define SLEEP 1 int main() { timespec ts; clock_getres(CLOCK, &ts); cerr << "CLOCK resolution: " << ts_to_ns(ts) << "ns\n"; clock_gettime(CLOCK, &ts); int start_time = ts.tv_sec; double ticks_per_ns; int running_elapsed_time = 0; //approx secs since start_time to center of the sampling done by get_ticks_per_ns() long ticks, ns; for (int timestep = 0; timestep < NSTEPS; ++timestep) { clock_gettime(CLOCK, &ts); ticks_per_ns = get_ticks_per_ns(ticks, ns); running_elapsed_time = ts.tv_sec - start_time + RUNS * SLEEP / 2; cout << running_elapsed_time << ' ' << ticks << ' ' << ns << ' ' << std::setprecision(12) << ticks_per_ns << endl; sleep(10); } } double get_ticks_per_ns(long &ticks, long &ns) { // get the median over RUNS runs of elapsed tsc ticks, CLOCK ns, and their ratio over a SLEEP secs time interval timespec clock_start, clock_end; long tsc_start, tsc_end; array<long, RUNS> elapsed_ns, elapsed_ticks; array<double, RUNS> rates; // arrays from each run from which to get medians. for (int i = 0; i < RUNS; ++i) { clock_gettime(CLOCK, &clock_start); tsc_start = rdtscp_end(); // minimizes time between clock_start and tsc_start. sleep(SLEEP); clock_gettime(CLOCK, &clock_end); tsc_end = rdtscp_end(); elapsed_ticks[i] = tsc_end - tsc_start; elapsed_ns[i] = ts_to_ns(clock_end) - ts_to_ns(clock_start); rates[i] = static_cast<double>(elapsed_ticks[i]) / elapsed_ns[i]; } // get medians: std::nth_element(elapsed_ns.begin(), elapsed_ns.begin() + RUNS/2, elapsed_ns.end()); std::nth_element(elapsed_ticks.begin(), elapsed_ticks.begin() + RUNS/2, elapsed_ticks.end()); std::nth_element(rates.begin(), rates.begin() + RUNS/2, rates.end()); ticks = elapsed_ticks[RUNS/2]; ns = elapsed_ns[RUNS/2]; return rates[RUNS/2]; } constexpr long BILLION {1000000000}; long ts_to_ns(const timespec &ts) { return ts.tv_sec * BILLION + ts.tv_nsec; }