@@ -112,10 +112,11 @@ func getCPUResources(config containertypes.Resources) *specs.CPU {

 	}

 	if config.NanoCPUs > 0 {

-		// Use the default setting of 100ms, as is specified in:

+		// We set the highest value possible (1s), as is specified in:

 		// https://www.kernel.org/doc/Documentation/scheduler/sched-bwc.txt

-		//    	cpu.cfs_period_us=100ms

-		period := uint64(100 * time.Millisecond / time.Microsecond)

+		//    	cpu.cfs_period_us=1s

+		// The purpose is to get the highest precision

+		period := uint64(1 * time.Second / time.Microsecond)

 		quota := uint64(config.NanoCPUs) * period / 1e9

 		cpu.Period = &period

 		cpu.Quota = &quota

@@ -361,8 +362,15 @@ func verifyContainerResources(resources *containertypes.Resources, sysInfo *sysi

 	if resources.NanoCPUs > 0 && (!sysInfo.CPUCfsPeriod || !sysInfo.CPUCfsQuota) {

 		return warnings, fmt.Errorf("NanoCPUs can not be set, as your kernel does not support CPU cfs period/quota or the cgroup is not mounted")

 	}

+	// The highest precision we could get on Linux is 0.001, by setting

+	//   cpu.cfs_period_us=1000ms

+	//   cpu.cfs_quota=1ms

+	// See the following link for details:

+	// https://www.kernel.org/doc/Documentation/scheduler/sched-bwc.txt

+	// Here we don't set the lower limit and it is up to the underlying platform (e.g., Linux) to return an error.

+	// The error message is 0.01 so that this is consistent with Windows

 	if resources.NanoCPUs < 0 || resources.NanoCPUs > int64(sysinfo.NumCPU())*1e9 {

-		return warnings, fmt.Errorf("Range of Nano CPUs is from 1 to %d", int64(sysinfo.NumCPU())*1e9)

+		return warnings, fmt.Errorf("Range of CPUs is from 0.01 to %d.00, as there are only %d CPUs available", sysinfo.NumCPU(), sysinfo.NumCPU())

 	}

 	if resources.CPUShares > 0 && !sysInfo.CPUShares {

@@ -129,8 +129,10 @@ func verifyContainerResources(resources *containertypes.Resources, isHyperv bool

 	if resources.NanoCPUs > 0 && resources.CPUShares > 0 {

 		return warnings, fmt.Errorf("conflicting options: Nano CPUs and CPU Shares cannot both be set")

 	}

+	// The precision we could get is 0.01, because on Windows we have to convert to CPUPercent.

+	// We don't set the lower limit here and it is up to the underlying platform (e.g., Windows) to return an error.

 	if resources.NanoCPUs < 0 || resources.NanoCPUs > int64(sysinfo.NumCPU())*1e9 {

-		return warnings, fmt.Errorf("range of Nano CPUs is from 1 to %d", int64(sysinfo.NumCPU())*1e9)

+		return warnings, fmt.Errorf("range of CPUs is from 0.01 to %d.00, as there are only %d CPUs available", sysinfo.NumCPU(), sysinfo.NumCPU())

 	}

 	if len(resources.BlkioDeviceReadBps) > 0 {

@@ -1577,7 +1577,7 @@ func (s *DockerSuite) TestRunWithNanoCPUs(c *check.C) {

 	file1 := "/sys/fs/cgroup/cpu/cpu.cfs_quota_us"

 	file2 := "/sys/fs/cgroup/cpu/cpu.cfs_period_us"

 	out, _ := dockerCmd(c, "run", "--cpus", "0.5", "--name", "test", "busybox", "sh", "-c", fmt.Sprintf("cat %s && cat %s", file1, file2))

-	c.Assert(strings.TrimSpace(out), checker.Equals, "50000\n100000")

+	c.Assert(strings.TrimSpace(out), checker.Equals, "500000\n1000000")

 	out = inspectField(c, "test", "HostConfig.NanoCpus")

 	c.Assert(out, checker.Equals, "5e+08", check.Commentf("setting the Nano CPUs failed"))