X-Git-Url: https://pintos-os.org/cgi-bin/gitweb.cgi?a=blobdiff_plain;f=doc%2F44bsd.texi;h=40fd33db0f469e40811f67e3d02a1805efd29953;hb=fadbce2938abee96b8a80734b2ead5bbfc9491bc;hp=18c5a61abd34022d9b207f12f67f4e278cbf4e1e;hpb=35fe5d2c6ea34654bfe8e6e0cc2a5b1bdb937b6c;p=pintos-anon diff --git a/doc/44bsd.texi b/doc/44bsd.texi index 18c5a61..40fd33d 100644 --- a/doc/44bsd.texi +++ b/doc/44bsd.texi @@ -1,4 +1,4 @@ -@node 4.4BSD Scheduler, Coding Standards, References, Top +@node 4.4BSD Scheduler @appendix 4.4@acronym{BSD} Scheduler @iftex @@ -44,7 +44,7 @@ vary over time. A well-designed scheduler can often accommodate threads with all these requirements simultaneously. For project 1, you must implement the scheduler described in this -appendix. Our scheduler resembles the one described in @bibref{4.4BSD}, +appendix. Our scheduler resembles the one described in @bibref{McKusick}, which is one example of a @dfn{multilevel feedback queue} scheduler. This type of scheduler maintains several queues of ready-to-run threads, where each queue holds threads with a different priority. At any given @@ -104,13 +104,13 @@ highest priority, yields. Our scheduler has 64 priorities and thus 64 ready queues, numbered 0 (@code{PRI_MIN}) through 63 (@code{PRI_MAX}). Lower numbers correspond -to @emph{higher} priorities, so that priority 0 is the highest priority -and priority 63 is the lowest. Thread priority is calculated initially +to lower priorities, so that priority 0 is the lowest priority +and priority 63 is the highest. Thread priority is calculated initially at thread initialization. It is also recalculated once every fourth clock tick, for every thread. In either case, it is determined by the formula -@center @t{@var{priority} = (@var{recent_cpu} / 4) + (@var{nice} * 2)}, +@center @t{@var{priority} = @code{PRI_MAX} - (@var{recent_cpu} / 4) - (@var{nice} * 2)}, @noindent where @var{recent_cpu} is an estimate of the CPU time the thread has used recently (see below) and @var{nice} is the thread's @@ -160,12 +160,13 @@ weight of @math{a} at time @math{t+1}, @am{a^2, a**2} at time @math{f(t)} has a weight of approximately @math{1/e} at time @math{t+k}, approximately @am{1/e^2, 1/e**2} at time @am{t+2k, t+2*k}, and so on. From the opposite direction, @math{f(t)} decays to weight @math{w} at -@am{t = \log_aw, t = ln(w)/ln(a)}. +time @am{t + \log_aw, t + ln(w)/ln(a)}. The initial value of @var{recent_cpu} is 0 in the first thread created, or the parent's value in other new threads. Each time a timer interrupt occurs, @var{recent_cpu} is incremented by 1 for the running -thread only. In addition, once per second the value of @var{recent_cpu} +thread only, unless the idle thread is running. In addition, once per +second the value of @var{recent_cpu} is recalculated for every thread (whether running, ready, or blocked), using this formula: @@ -190,6 +191,11 @@ multiple of a second, that is, when @code{timer_ticks () % TIMER_FREQ == The value of @var{recent_cpu} can be negative for a thread with a negative @var{nice} value. Do not clamp negative @var{recent_cpu} to 0. +You may need to think about the order of calculations in this formula. +We recommend computing the coefficient of @var{recent_cpu} first, then +multiplying. Some students have reported that multiplying +@var{load_avg} by @var{recent_cpu} directly can cause overflow. + You must implement @func{thread_get_recent_cpu}, for which there is a skeleton in @file{threads/thread.c}. @@ -237,9 +243,9 @@ scheduler. It is not a complete description of scheduler requirements. Every thread has a @var{nice} value between -20 and 20 directly under its control. Each thread also has a priority, between 0 (@code{PRI_MIN}) through 63 (@code{PRI_MAX}), which is recalculated -using the following formula whenever the value of either term changes: +using the following formula every fourth tick: -@center @t{@var{priority} = (@var{recent_cpu} / 4) + (@var{nice} * 2)}. +@center @t{@var{priority} = @code{PRI_MAX} - (@var{recent_cpu} / 4) - (@var{nice} * 2)}. @var{recent_cpu} measures the amount of CPU time a thread has received ``recently.'' On each timer tick, the running thread's @var{recent_cpu} @@ -272,31 +278,33 @@ difficult, but many students do not know how to do it. This section explains the basics. The fundamental idea is to treat the rightmost bits of an integer as -representing a fraction. For example, we can designate the lowest 10 +representing a fraction. For example, we can designate the lowest 14 bits of a signed 32-bit integer as fractional bits, so that an integer -@var{x} represents the real number +@m{x} represents the real number @iftex -@m{x/2^{10}}. +@m{x/2^{14}}. @end iftex @ifnottex -@m{x/(2**10)}, where ** represents exponentiation. +@m{x/(2**14)}, where ** represents exponentiation. @end ifnottex -This is called a 21.10 fixed-point number representation, because there -are 21 bits before the decimal point, 10 bits after it, and one sign +This is called a 17.14 fixed-point number representation, because there +are 17 bits before the decimal point, 14 bits after it, and one sign bit.@footnote{Because we are working in binary, the ``decimal'' point might more correctly be called the ``binary'' point, but the meaning -should be clear.} A number in 21.10 format represents, at maximum, a -value of @am{(2^{31} - 1) / 2^{10} \approx, (2**31 - 1)/(2**10) = -approx.} 2,097,151.999. +should be clear.} A number in 17.14 format represents, at maximum, a +value of @am{(2^{31} - 1) / 2^{14} \approx, (2**31 - 1)/(2**14) = +approx.} 131,071.999. Suppose that we are using a @m{p.q} fixed-point format, and let @am{f = 2^q, f = 2**q}. By the definition above, we can convert an integer or real number into @m{p.q} format by multiplying with @m{f}. For example, -in 21.10 format the fraction 59/60 used in the calculation of -@var{load_avg}, above, is @am{(59/60)2^{10}, 59/60*(2**10)} = 1,007 +in 17.14 format the fraction 59/60 used in the calculation of +@var{load_avg}, above, is @am{(59/60)2^{14}, 59/60*(2**14)} = 16,111 (rounded to nearest). To convert a fixed-point value back to an integer, divide by @m{f}. (The normal @samp{/} operator in C rounds -down. To round to nearest, add @m{f / 2} before dividing.) +toward zero, that is, it rounds positive numbers down and negative +numbers up. To round to nearest, add @m{f / 2} to a positive number, or +subtract it from a negative number, before dividing.) Many operations on fixed-point numbers are straightforward. Let @code{x} and @code{y} be fixed-point numbers, and let @code{n} be an @@ -308,19 +316,19 @@ quotient, @code{x / n}. Multiplying two fixed-point values has two complications. First, the decimal point of the result is @m{q} bits too far to the left. Consider that @am{(59/60)(59/60), (59/60)*(59/60)} should be slightly less than -1, but @tm{1,007\times 1,007}@nm{1,007*1,007} = 1,014,049 is much -greater than @am{2^{10},2**10} = 1,024. Shifting @m{q} bits right, we -get @tm{1,014,049/2^{10}}@nm{1,014,049/(2**10)} = 990, or about 0.97, +1, but @tm{16,111\times 16,111}@nm{16,111*16,111} = 259,564,321 is much +greater than @am{2^{14},2**14} = 16,384. Shifting @m{q} bits right, we +get @tm{259,564,321/2^{14}}@nm{259,564,321/(2**14)} = 15,842, or about 0.97, the correct answer. Second, the multiplication can overflow even though -the answer is representable. For example, 128 in 21.10 format is -@am{128 \times 2^{10}, 128*(2**10)} = 131,072 and its square @am{128^2, -128**2} = 16,384 is well within the 21.10 range, but @tm{131,072^2 = -2^{34}}@nm{131,072**2 = 2**34}, greater than the maximum signed 32-bit +the answer is representable. For example, 64 in 17.14 format is +@am{64 \times 2^{14}, 64*(2**14)} = 1,048,576 and its square @am{64^2, +64**2} = 4,096 is well within the 17.14 range, but @tm{1,048,576^2 = +2^{40}}@nm{1,048,576**2 = 2**40}, greater than the maximum signed 32-bit integer value @am{2^{31} - 1, 2**31 - 1}. An easy solution is to do the multiplication as a 64-bit operation. The product of @code{x} and @code{y} is then @code{((int64_t) x) * y / f}. -Dividing two fixed-point values has the opposite complications. The +Dividing two fixed-point values has opposite issues. The decimal point will be too far to the right, which we fix by shifting the dividend @m{q} bits to the left before the division. The left shift discards the top @m{q} bits of the dividend, which we can again fix by