WEBVTT 00:01.320 --> 00:05.340 Hello again! In this video, we are going to look at floating-point output format. 00:05.910 --> 00:11.010 I have to admit this is something I have never used in work, but it would have been useful at university. 00:11.610 --> 00:15.690 Except that we used BASIC and FORTRAN for everything, not C++. 00:17.160 --> 00:23.280 If we have a fairly normal sized number, say, less than 1,000,000, it will be displayed to 6 significant 00:23.280 --> 00:23.700 figures. 00:24.420 --> 00:27.090 Here we have pi to 10 decimal places. 00:28.290 --> 00:33.150 The first 6 significant figures are the 3, and then the 1, 4, 1, 5, 9. 00:33.870 --> 00:37.500 So that is just going to be displayed as 3.14159. 00:38.340 --> 00:44.920 If you are dealing with bigger or smaller numbers, if you are a Physics student, for example, then 00:44.920 --> 00:46.770 scientific notation is used. 00:47.700 --> 00:49.700 In this scientific notation. 00:49.710 --> 00:55.590 We have one digit, followed by a decimal point, followed by the rest of the digits. That is known as 00:55.590 --> 00:56.550 the mantissa. 00:57.270 --> 01:01.620 And then we have this exponent, which represents a power of 10. 01:02.250 --> 01:06.990 So e + 008 means 10 to the power of eight, which is 100 million. 01:07.560 --> 01:14.300 So that means we multiply 2.99 by 100 million, so we end up with 299 01:14.400 --> 01:15.030 million. 01:16.110 --> 01:21.720 If you do not like doing mental arithmetic, you can think of this exponent as being how many times 01:21.720 --> 01:27.180 you need to move the decimal point to the right, to get the right value of the number, the right magnitude. 01:28.170 --> 01:35.820 So +8 means 1, 2, 3, 4, 5, and then we need to add some 0's to make up the rest 01:35.820 --> 01:36.330 of the number. 01:36.570 --> 01:37.620 So 6, 7, 8. 01:37.980 --> 01:39.540 So we have three 0's at the end. 01:40.500 --> 01:43.110 And that is the correct value of the number. 01:44.950 --> 01:52.150 If the exponent is negative, -6, that means divide by one 1,000,000 or move the decimal point 01:52.420 --> 01:53.680 6 places to the left. 01:54.100 --> 02:01.390 Again, we need to add 0's, this time at the front, and we end up with 02:01.480 --> 02:01.780 0.000001. 02:03.960 --> 02:07.050 e +0 means multiply by 1. Do nothing. 02:07.440 --> 02:11.280 So 3.14159 is still 3.14159. 02:14.810 --> 02:20.540 So the default is for the stream to use 6 significant figures. Or scientific notation if there is more 02:20.540 --> 02:25.430 than 6 digits, which are all before the decimal point or all after it. 02:29.890 --> 02:35.410 So we get 3.14159 and 2.99e+008. 02:38.640 --> 02:45.690 If you want to use scientific notation for all your output, to make sure that your data [looks] consistent, 02:45.690 --> 02:48.330 for example, there is a "scientific" manipulator. 02:48.900 --> 02:51.750 So this will force the stream to use scientific notation. 02:52.350 --> 02:57.480 So anything that is pushed onto the stream after you have done this will appear in scientific notation. 02:59.580 --> 03:02.040 There is also an "uppercase" manipulation. 03:02.370 --> 03:08.610 If you do not like having a lowercase 'e' in the exponent, you can use this and it will produce an uppercase 03:08.610 --> 03:09.480 'E' instead. 03:11.220 --> 03:13.680 These are both sticky manipulators, by the way. 03:14.040 --> 03:18.720 So once you push these on the stream, they will permanently change the behaviour of the stream. 03:24.790 --> 03:28.750 So here we have pi again, and we are going to display it in scientific notation. 03:34.460 --> 03:36.490 There we are, with both lower and upper case. 03:39.200 --> 03:44.600 On the other hand, if you do not want to use scientific notation at all, there is fixed-point notation. 03:45.410 --> 03:48.560 And the "fixed" manipulator will do that. 03:53.570 --> 03:56.240 So here we are using the fixed manipulator. 03:56.540 --> 04:02.600 The result of this is that the stream will always display things to 6 decimal places. 04:03.350 --> 04:10.160 So if we have "c" again, it is going to add the decimal point and then 6 decimal places. And there is 04:10.160 --> 04:10.640 no data [for the decimal places] 04:10.640 --> 04:12.860 So it is going to add 0's to make it up. 04:13.550 --> 04:19.760 So this is going to padded out to be 299792458.000000 04:19.760 --> 04:20.120 zero. 04:21.920 --> 04:23.000 It is possibly a bit pointless! 04:23.990 --> 04:29.330 And you will also find out the reason why scientific notation was invented: so you can display numbers 04:29.330 --> 04:33.200 which are too big or too small to be stored in the format. 04:34.010 --> 04:40.130 If we have the charge on the electron, which is 10 to the minus 19, so we need to shift the decimal 04:40.130 --> 04:44.480 points 19 places to the left. Which is probably going to go over here somewhere! 04:45.560 --> 04:46.850 So this is a very small number. 04:47.660 --> 04:53.940 And the problem is that a double can only store 15 decimal places. To store 04:53.960 --> 04:56.540 this accurately will need 19 decimal places. 04:57.260 --> 05:02.000 So in fact, all this data will be truncated and we end up with 0. 05:11.410 --> 05:17.860 So fixed is sticky. In fact, all the manipulators in this video are sticky, so they will permanently 05:17.860 --> 05:19.300 change the state of the stream. 05:19.840 --> 05:24.700 If anyone tries to do floating-point output later on in the program, not just in the same function, 05:24.700 --> 05:29.890 but anywhere in the program, after you change the stream, they are going to get whatever you set it 05:29.890 --> 05:32.320 to. And that might not be what they expect. 05:32.950 --> 05:37.930 So we should be considerate to other programmers. Or maybe to ourselves in a few months' time! 05:38.380 --> 05:44.080 So once we have finished doing this output, we use the "defaultfloat" manipulator and that will push everything 05:44.080 --> 05:45.310 back to the defaults. 05:50.830 --> 05:54.850 One final thing you can do is to change the number of digits that are displayed. 05:55.360 --> 05:59.350 The default is 6 for defaultfloat and fixed. 06:00.490 --> 06:05.110 If you want to change that, there is a setprecision manipulator. 06:05.680 --> 06:09.400 And this takes an argument, which is the number of digits you want to display. 06:11.220 --> 06:16.980 So if we set that and then send pi down the stream, it is going to display 3 significant digits, 06:16.980 --> 06:18.480 which is 3.14. 06:22.690 --> 06:28.330 So to test this out, we are going to display pi using 3 significant figures and then using 6, 06:28.330 --> 06:29.560 which is the default. 06:30.850 --> 06:34.780 So we actually set the precision, and then we set it back to the default. 06:35.110 --> 06:38.230 So we are actually being a bit more public-spirited here! 06:42.330 --> 06:48.780 So when we switched the precision to 3, that gives 3 significant figures, 3.14, and then when 06:48.780 --> 06:52.440 we go back to the default 6, we get the default output. 06:54.420 --> 06:57.900 Okay, so that is it for this video. I will see you next time. 06:57.900 --> 07:00.000 But until then, keep coding!