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CPU time follows from executed instructions, average cycles per instruction and clock frequency.
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Formula
TCPU in s; I instructions; CPI cycles/instruction; fCLK in Hz
| Symbol | Meaning | Unit |
|---|---|---|
| TCPU | CPU execution time of the program | s |
| Instructions actually executed | instructions | |
| Average clock cycles per instruction | cycles/instruction | |
| fCLK | Clock frequency | Hz |
T_{CPU}=I\cdot CPI\cdot t_{CLK}=\frac{I\cdot CPI}{f_{CLK}}Execution time is instruction count times average cycles per instruction times clock period. CPI is an average over the dynamic instruction mix and microarchitecture; it is not identical for every instruction. Memory stalls and operating-system time must be included according to the chosen measurement definition. A higher clock frequency alone does not prove lower runtime if instruction count or CPI also increases.
Execution time is instruction count times average cycles per instruction times clock period. CPI is an average over the dynamic instruction mix and microarchitecture; it is not identical for every instruction. Memory stalls and operating-system time must be included according to the chosen measurement definition. A higher clock frequency alone does not prove lower runtime if instruction count or CPI also increases.
CPU time follows from executed instructions, average cycles per instruction and clock frequency.
CPI from CPU time
CPI is an average for the dynamic instruction mix.
Use the example for CPU time from instructions, CPI and clock rate to explain which inputs determine the requested output.
The example connects concrete inputs to its result.
CPU time follows from executed instructions, average cycles per instruction and clock frequency.
The relation applies only under its stated assumptions.
Applying the relation to a different case without checking its stated assumptions.
Check the validity range before substituting values: Execution time is instruction count times average cycles per instruction times clock period. CPI is an average over the dynamic instruction mix and microarchitecture; it is not identical for every.
Formula cluster
CPU time follows from executed instructions, average cycles per instruction and clock frequency.
For I=109 instructions, CPI=1.5 and fCLK=3 GHz, TCPU=1.5·109/(3·109 s−1)=0.5 s.
Compare architectures or compilers and separate runtime causes into instruction count, CPI and clock rate.
Here is how to work through a typical CPU time from instructions, CPI and clock rate (TCPU = I·CPI/fCLK) task step by step:
Task
Use the example for CPU time from instructions, CPI and clock rate to explain which inputs determine the requested output.
Solution path
The example connects concrete inputs to its result.
CPU time follows from executed instructions, average cycles per instruction and clock frequency.
The relation applies only under its stated assumptions.
CPU time equals executed instructions I times average cycles per instruction CPI times clock period. Since frequency is the reciprocal of period, TCPU=I·CPI/fCLK. The three factors separate program work, instruction-mix efficiency and clock rate. They help distinguish hardware changes from compiler or algorithm effects. Measure the same program section and use one definition of CPU time. Do not confuse static code size with executed instructions; account for clock and memory behavior. Control the processor, compiler, input and warm-up for fair measurements. Separate CPU time from waiting and I/O time.
I counts instructions, CPI counts cycles per instruction, and fCLK counts cycles per second. In I·CPI/fCLK, instructions and cycles cancel, leaving seconds. For I=109, CPI=1.5 and f=3·109 Hz, the result is 1.5·109/(3·109 s−1)=0.5 s. A unit check often catches confusion between frequency and clock period. Measure the same program section and use one definition of CPU time. Do not confuse static code size with executed instructions; account for clock and memory behavior. Control the processor, compiler, input and warm-up for fair measurements. Separate CPU time from waiting and I/O time.
CPI averages cycles over the instructions actually executed. A program with simple additions can differ from one with cache misses or complex operations. Pipelines, memory hierarchy, dependencies and compiler choices affect the dynamic mix. State the measurement context; one CPI value does not characterize every program on a processor. Measure the same program section and use one definition of CPU time. Do not confuse static code size with executed instructions; account for clock and memory behavior. Control the processor, compiler, input and warm-up for fair measurements. Separate CPU time from waiting and I/O time.
With I and CPI fixed, higher frequency lowers the calculated time. Real processors may also change CPI, power, temperature or memory stalls. A lower-frequency processor with better CPI can therefore finish sooner. Compare measured runtime or all three factors, not GHz alone. Measure the same program section and use one definition of CPU time. Do not confuse static code size with executed instructions; account for clock and memory behavior. Control the processor, compiler, input and warm-up for fair measurements. Separate CPU time from waiting and I/O time.
I is the dynamic count of machine instructions actually executed in that run. It is not the static number of instructions in a program file. Loops, branches and library calls execute commands repeatedly or conditionally. Different compilers can therefore produce different I and CPI for the same source. Keep inputs and compiler settings consistent when comparing. Measure the same program section and use one definition of CPU time. Do not confuse static code size with executed instructions; account for clock and memory behavior. Control the processor, compiler, input and warm-up for fair measurements. Separate CPU time from waiting and I/O time.
Quanta exam set
Curated exam set for "CPU time from instructions, CPI and clock rate":
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Which formula describes CPU time from instructions, CPI and clock rate?
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How do you rearrange CPU time from instructions, CPI and clock rate for CPI from CPU time?
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Which common mistake happens with CPU time from instructions, CPI and clock rate?
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