Fun with Fixed Point Math
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0:09Recap and set the stage for the day
0:09Recap and set the stage for the day
0:09Recap and set the stage for the day
1:03Don the thinking cap
1:03Don the thinking cap
1:03Don the thinking cap
1:38Working through the cycles-per-second formula for measure_cpu_freq()
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1:38Working through the cycles-per-second formula for measure_cpu_freq()
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1:38Working through the cycles-per-second formula for measure_cpu_freq()
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16:12Check our formula with the one in measure_cpu_freq()
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16:12Check our formula with the one in measure_cpu_freq()
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16:12Check our formula with the one in measure_cpu_freq()
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18:46Reverse engineer the cycles-per-second formula
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18:46Reverse engineer the cycles-per-second formula
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18:46Reverse engineer the cycles-per-second formula
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20:22 They are basically doing fixed point math
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20:22 They are basically doing fixed point math
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20:22 They are basically doing fixed point math
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21:02Computing the decimal portion of a real number in fixed point mathematics
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21:02Computing the decimal portion of a real number in fixed point mathematics
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21:02Computing the decimal portion of a real number in fixed point mathematics
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21:58 Instead of doing float x = 3.14, you do int x = 314 and the point is implicit
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21:58 Instead of doing float x = 3.14, you do int x = 314 and the point is implicit
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21:58 Instead of doing float x = 3.14, you do int x = 314 and the point is implicit
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23:22 Notice that in one part you have / and then you have another part that is nearly equal but uses %
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23:22 Notice that in one part you have / and then you have another part that is nearly equal but uses %
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23:22 Notice that in one part you have / and then you have another part that is nearly equal but uses %
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25:37Determine to work through an example on the whiteboard
25:37Determine to work through an example on the whiteboard
25:37Determine to work through an example on the whiteboard
26:34 Use a spreadsheet or C program, to make it easier to compute other values
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26:34 Use a spreadsheet or C program, to make it easier to compute other values
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26:34 Use a spreadsheet or C program, to make it easier to compute other values
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27:06Plug some example values into our cycles-per-second formula
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27:06Plug some example values into our cycles-per-second formula
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27:06Plug some example values into our cycles-per-second formula
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41:04Summarise how this fixed point calculation works
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41:04Summarise how this fixed point calculation works
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41:04Summarise how this fixed point calculation works
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42:47 I can explain it another way
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42:47 I can explain it another way
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42:47 I can explain it another way
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45:56 Say we have 200 cycles (delta_mcycle). We divide by the ticks (delta_mtime). So now we have number of cycles per tick. We multiply by the number of ticks per second (mtime_freq) so now we have cycles per second
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45:56 Say we have 200 cycles (delta_mcycle). We divide by the ticks (delta_mtime). So now we have number of cycles per tick. We multiply by the number of ticks per second (mtime_freq) so now we have cycles per second
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45:56 Say we have 200 cycles (delta_mcycle). We divide by the ticks (delta_mtime). So now we have number of cycles per tick. We multiply by the number of ticks per second (mtime_freq) so now we have cycles per second
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47:57Pose the question: How does n % m / m give the decimal part of the number?
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47:57Pose the question: How does n % m / m give the decimal part of the number?
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47:57Pose the question: How does n % m / m give the decimal part of the number?
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49:29 So 201 cycles / 10 ticks = floor(20.1) cycles per tick. We take the 20 and multiply by, say, 100 ticks per second so we have 2000 cycles per second
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49:29 So 201 cycles / 10 ticks = floor(20.1) cycles per tick. We take the 20 and multiply by, say, 100 ticks per second so we have 2000 cycles per second
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49:29 So 201 cycles / 10 ticks = floor(20.1) cycles per tick. We take the 20 and multiply by, say, 100 ticks per second so we have 2000 cycles per second
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50:06 201 % 10 = 1. Multiply by 100 and divide by 10 we get 2010 cycles per second, and we recover the part we lost in the division
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50:06 201 % 10 = 1. Multiply by 100 and divide by 10 we get 2010 cycles per second, and we recover the part we lost in the division
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50:06 201 % 10 = 1. Multiply by 100 and divide by 10 we get 2010 cycles per second, and we recover the part we lost in the division
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50:22The relationship between a remainder and a decimal
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50:22The relationship between a remainder and a decimal
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50:22The relationship between a remainder and a decimal
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56:31 delta_mtime is what determines what the conceptual decimal point is. Say delta_mtime = 100, if you do x % delta_mtime and get 33, then the 33 means you don't have a whole delta_mtime unit. But after you multiply it by something you might get >= 100, so when you divide by delta_mtime again you get >= 1
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56:31 delta_mtime is what determines what the conceptual decimal point is. Say delta_mtime = 100, if you do x % delta_mtime and get 33, then the 33 means you don't have a whole delta_mtime unit. But after you multiply it by something you might get >= 100, so when you divide by delta_mtime again you get >= 1
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56:31 delta_mtime is what determines what the conceptual decimal point is. Say delta_mtime = 100, if you do x % delta_mtime and get 33, then the 33 means you don't have a whole delta_mtime unit. But after you multiply it by something you might get >= 100, so when you divide by delta_mtime again you get >= 1
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57:41Is it true that n % m / m = 1 / m % m
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57:41Is it true that n % m / m = 1 / m % m
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57:41Is it true that n % m / m = 1 / m % m
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1:00:05 Think of delta_mtime as being a percentage. If you get 0.33 that's 33%. You will only get an integer again if you cross the 100% line
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1:00:05 Think of delta_mtime as being a percentage. If you get 0.33 that's 33%. You will only get an integer again if you cross the 100% line
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1:00:05 Think of delta_mtime as being a percentage. If you get 0.33 that's 33%. You will only get an integer again if you cross the 100% line
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1:01:21Determine to sleep on this to fully understand it
1:01:21Determine to sleep on this to fully understand it
1:01:21Determine to sleep on this to fully understand it