├── README.org ├── hex.org ├── date.org ├── fractional_arithmetic.org ├── strings.org ├── time.org ├── calculus.org ├── pi_and_precision.org ├── more_algebra.org ├── algebra.org ├── random.org ├── unit_conversion.org ├── financial.org ├── bit_manipulation.org └── LICENSE /README.org: -------------------------------------------------------------------------------- 1 | This repository contains tutorials about emacs calc originally writen on the 2 | Emacs community on Google+. 3 | 4 | The best way to read is probably just to open the org files directly, which 5 | Github will display correctly. 6 | 7 | If anyone would like to correct anything, add any tutorials, or request 8 | anything, the normal Github bug / request / or pull request process will work. 9 | -------------------------------------------------------------------------------- /hex.org: -------------------------------------------------------------------------------- 1 | OK, seems like there's interest in some quick calc tips. Here's today's: 2 | 3 | How to convert decimal to hexidecimal. Let's say you want to convert number 4 | 12345 to hex. 5 | 6 | #+BEGIN_EXAMPLE 7 | M-x calc 8 | d 6 (sets the number radix to 16, meaning all output will be in hex) 9 | 10#12345 (inputs the number 12345 in base 10) 10 | 11 | The output reads: 12 | 1: 16#3039 13 | #+END_EXAMPLE 14 | 15 | The answer is therefore =0x3039=. 16 | 17 | And then you can do a =d 0= to set the number radix back to normal, base 10. 18 | 19 | Here's how to do the other way. Let's convert =0xABCDEF= to base 10. 20 | 21 | #+BEGIN_EXAMPLE 22 | M-x calc 23 | 16#ABCDEF 24 | 25 | The output reads: 26 | 1: 11259375 27 | #+END_EXAMPLE 28 | -------------------------------------------------------------------------------- /date.org: -------------------------------------------------------------------------------- 1 | Ever want to know how many seconds old David Hasselhoff is? calc can do many 2 | things, but it doesn't know much about Hasselhoff, so first I do a query on 3 | Google for [david hasselhoff]. I get a knowledge card on the right saying he was 4 | born July 17, 1952. It doesn't give a time, so we'll just assume it was at 5 | midnight. 6 | 7 | #+BEGIN_EXAMPLE 8 | M-x calc 9 | t N (put the current time on the stack) 10 | ' (press ' to enter algebraic mode, then you input the date). 11 | - (subtract the two to get the number of days David has been alive) 12 | 24 (we're going to multiply by 24, the number of hours in a day) 13 | 60 (the number of minutes in an hour) 14 | 60 (the number of seconds in a minute) 15 | * 16 | * 17 | * 18 | 19 | Final result: 20 | 1: 1910255938.01 21 | #+END_EXAMPLE 22 | 23 | There you have it, he's... wait, how many seconds? That's really hard to read. 24 | 25 | Back into calc! 26 | 27 | #+BEGIN_EXAMPLE 28 | d g (toggle digit grouping) 29 | 30 | The final final result: 31 | 1: 1,910,255,938.01 32 | #+END_EXAMPLE 33 | 34 | Ah, that's a 1.9 billion seconds. Sweet! 35 | -------------------------------------------------------------------------------- /fractional_arithmetic.org: -------------------------------------------------------------------------------- 1 | This one is pretty short, but it's about one of my favorite features of calc: 2 | the ability to handle fractions as fractions instead of rendering them as real 3 | numbers. 4 | 5 | Quick, what's =5/8 + 9/21=? 6 | 7 | Um, ok... better start multiplying things... wait, let's just tell calc to do 8 | it. 9 | 10 | #+BEGIN_EXAMPLE 11 | M-x calc 12 | 5:8 (this is how you enter a fraction) 13 | 9:21 14 | + 15 | 16 | Result: 17 | 1: 59/56 18 | #+END_EXAMPLE 19 | 20 | So easy! If we want to convert it to a float you can do this: 21 | 22 | #+BEGIN_EXAMPLE 23 | c f (convert to 24 | float) 25 | 26 | Result: 27 | 28 | 1: 1.05357142857*10.^0 29 | #+END_EXAMPLE 30 | 31 | And if you want it back as a fraction, then just do: 32 | 33 | #+BEGIN_EXAMPLE 34 | c F (convert to fraction) 35 | 36 | Result: 37 | 38 | 1: 59/56 39 | #+END_EXAMPLE 40 | 41 | That's so awesome! 42 | 43 | You could also enter fractions this way: 44 | 45 | #+BEGIN_EXAMPLE 46 | m f (set fraction mode, integer division will result in fractions) 47 | 5 48 | 8 49 | / 50 | 51 | Result: 52 | 53 | 1: 5/8 54 | #+END_EXAMPLE 55 | 56 | Now you can live in the nice world of fractions as much as you like. It's a nice 57 | world, full of pleasant to look at integers taking up little horizontal space 58 | -------------------------------------------------------------------------------- /strings.org: -------------------------------------------------------------------------------- 1 | Did you know you could work with strings in calc? For an example, let's find out 2 | what "Hello world" is in binary: 3 | 4 | #+BEGIN_EXAMPLE 5 | M-x calc 6 | d 2 (change the to binary mode) 7 | "Hello world (Enter the string "Hello world" which turns into a vector of numbers) 8 | 9 | Result: 10 | 1: [2#1001000, 2#1100101, 2#1101100, 2#1101100, 2#1101111, 2#100000, 2#1110111, 2#1101111, 2#1110010, 2#1101100, 2#1100100] 11 | #+END_EXAMPLE 12 | 13 | And similarly, we can convert back. If someone gave you the binary number: 14 | =01001000011011110110110001100001= and asked what the string was, I'd have no 15 | idea... but calc knows: 16 | 17 | #+BEGIN_EXAMPLE 18 | d " (changes to string mode) 19 | C-x b scratch (whaaa, leave calc?) 20 | 01001000011011110110110001100001 (enter the number we're parsing) 21 | C-a (go to the start of the line) 22 | C-x ( (start a macro) 23 | 2# (prefix the number with a binary indicator) 24 | C-u 8 C-f (Jump forward 8 characters) 25 | (insert a space to separate the numbers) 26 | C-x ) (end the macro) 27 | C-x e (repeat the macro) 28 | e e (repeat twice twice more) 29 | C- (set mark) 30 | C-a (goto beginning of line) 31 | C-x g (copy region into calc) 32 | 33 | Result: 34 | 35 | 1: "Hola" 36 | #+END_EXAMPLE 37 | 38 | And there you have it! Maybe there is an easier way to convert from the giant 39 | binary number to a vector of bytes, but I don't know it yet. 40 | -------------------------------------------------------------------------------- /time.org: -------------------------------------------------------------------------------- 1 | Hey, what's the time? It's time to get ill! No, actually I meant the time in 2 | seconds since the epoch. Yesterday I went over doing math with time, which is 3 | fun but not something I use everyday. Much more useful is converting to and from 4 | Unix timestamps. 5 | 6 | Let's start by getting the time now in seconds since the epoch: 7 | 8 | #+BEGIN_EXAMPLE 9 | M-x calc 10 | t N (get the time now) 11 | t U (convert the time to seconds since the epoch) 12 | 13 | Result: 14 | 1: 1359424746 15 | #+END_EXAMPLE 16 | 17 | Oh, and you want to insert that into your last used buffer? 18 | 19 | #+BEGIN_EXAMPLE 20 | y (that doesn't mean "yes", that means yank into the last buffer) 21 | #+END_EXAMPLE 22 | 23 | Done! Just to be complete, let's convert another date we have to input: 24 | 25 | #+BEGIN_EXAMPLE 26 | '<12:00pm Jul 4, 1776> (single quote to enter algebraic mode, then the date) 27 | t U (converts the time to seconds since the epoch) 28 | #+END_EXAMPLE 29 | 30 | But wait, what will happen? This is considerably before the epoch. 31 | 32 | #+BEGIN_EXAMPLE 33 | Result: 34 | 1: -6106003200 35 | #+END_EXAMPLE 36 | 37 | Oh calc, you never let me down. 38 | 39 | Let's do the other way. Remember the Billenium? 40 | 41 | #+BEGIN_EXAMPLE 42 | 1e9 43 | t U (converts the time in seconds since the epoch to text) 44 | 45 | Result: 46 | 1: <9:46:40pm Sat Sep 8, 2001> 47 | #+END_EXAMPLE 48 | 49 | Wow, I never realized how close the Billenium was to September 11th. Kind of spooky... 50 | -------------------------------------------------------------------------------- /calculus.org: -------------------------------------------------------------------------------- 1 | Quick, integrate =2x + sin(y)=! Well, frankly, it's been so long since I've done 2 | calculus by hand I can't remember anymore. Well, knowing calculus is good, but 3 | knowing calc is even more useful! 4 | 5 | #+BEGIN_EXAMPLE 6 | M-x calc 7 | m r (switch to radians mode, which helps with keeping things simple) 8 | '2x + sin(y) (The single quote enters algebraic mode) 9 | a i y (Calculate the integral with respect to y) 10 | 11 | Result 12 | 1: 2 x y - cos(y) 13 | #+END_EXAMPLE 14 | 15 | You can also integrate over specific regions by using =C-u a i=, whereupon it will 16 | prompt you for the start and end point of the integration. 17 | 18 | As the manual mentions, the results are often not as simplified as they could 19 | be. Calc is impressive, but it isn't as sophisticated as Mathematica. 20 | 21 | If we take the derivative of the integral we just calculated. We should get back 22 | to our original formula. 23 | 24 | #+BEGIN_EXAMPLE 25 | a d y (Calculate the derivative with respect to y) 26 | 27 | Result: 28 | 1: 2 x + sin(y) 29 | #+END_EXAMPLE 30 | 31 | Oh yeah! The system works, people! We can also make the Taylor series of a 32 | function: 33 | 34 | #+BEGIN_EXAMPLE 35 | a t y 6 (Calculate the Taylor series of a term, over y, for 6 terms) 36 | 37 | Result: 38 | 1: 2 x + y - y^3 / 6 + y^5 / 120 39 | #+END_EXAMPLE 40 | 41 | We asked for 6 terms, but as the manual mentions, some terms may have 42 | coefficient 0, so don't appear here. 43 | 44 | As I mentioned, for simple things this works well, but Calc's power is limited. 45 | However, the integration is customizable - you can write your own integration 46 | rules when Calc is missing something. I haven't been able to find evidence that 47 | anyone actually has done this in any add-on package, though. You, reader, can be 48 | the first! 49 | -------------------------------------------------------------------------------- /pi_and_precision.org: -------------------------------------------------------------------------------- 1 | This one's about p and P and mostly about pi. 2 | 3 | First, let's pi it up: 4 | 5 | #+BEGIN_EXAMPLE 6 | M-x calc 7 | P (this gives you pi) 8 | 9 | Result: 10 | 1: 3.14159265359 11 | #+END_EXAMPLE 12 | 13 | Well, I guess that's a reasonable pi. But, c'mon, this is calc. Can't we get a 14 | bit more digits? How about 100? 15 | 16 | #+BEGIN_EXAMPLE 17 | p 100 (sets precisions to 100) 18 | P (need to ask calc again for pi, it doesn't recalculate) 19 | 20 | Result: 21 | 1: 3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117068 22 | #+END_EXAMPLE 23 | 24 | Well, but actually evaluating it robs it of its never-ending charm. Let's just 25 | use it as a variable. How about calculating the area of a circle with a 5 km 26 | radius? 27 | 28 | #+BEGIN_EXAMPLE 29 | '5000 m 30 | 2 31 | ^ 32 | 'pi (enter pi as a variable) 33 | * 34 | 35 | We get: 36 | 1: 25000000 m^2 pi 37 | #+END_EXAMPLE 38 | 39 | Yeah, sure that’s what I said I wanted, but I’ve changed my mind - now I want a number. 40 | 41 | #+BEGIN_EXAMPLE 42 | = 43 | 44 | 1: 78539816.3397448309615660845819875721049292349843776455243736148076954101571552249657008706335529267 m^2 45 | #+END_EXAMPLE 46 | 47 | Whoops, looked like I forgot to set the precision back to normal. And I can't 48 | read this. Let's make it a bit nicer. 49 | 50 | #+BEGIN_EXAMPLE 51 | Control-_ (normal emacs undo) 52 | p 7 53 | d g (turn digit grouping on) 54 | = 55 | 56 | Result: 57 | 1: 7.853983e7 m^2 58 | #+END_EXAMPLE 59 | 60 | Oh, that's because I didn't have enough precision to render it without resorting 61 | to scientific notation. Let's just bump the precision up again. 62 | 63 | #+BEGIN_EXAMPLE 64 | Control-_ (undo, since we have to redo the pi conversion with more precision) 65 | p 10 66 | = 67 | 68 | Result: 69 | 1: 78,539,816.35 m^2 70 | #+END_EXAMPLE 71 | 72 | Ah, that's better. 73 | -------------------------------------------------------------------------------- /more_algebra.org: -------------------------------------------------------------------------------- 1 | Jim is 42 years old. He has one brother, and their total age is 100. What is the 2 | brother's age? OK, this isn't a very hard problem, but let's just introduce calc 3 | algebra by solving it. 4 | 5 | #+BEGIN_EXAMPLE 6 | M-x calc 7 | '42 + x = 100 (' to enter algebraic input) 8 | a S x (solve for x) 9 | 10 | Result: 11 | 1: x = 58 12 | #+END_EXAMPLE 13 | 14 | Let's make this harder. Jim and Dan's ages sum to 100. Jim is 5 years older than 15 | Dan. How old are they? 16 | 17 | #+BEGIN_EXAMPLE 18 | '[j + d = 100, d + 5 = j] 19 | a S j,d 20 | 21 | Result: 22 | 1: [j = 52.5, d = 47.5] 23 | #+END_EXAMPLE 24 | 25 | Nice! 26 | 27 | And of course it can give you more than just numerical solutions: 28 | 29 | #+BEGIN_EXAMPLE 30 | 'sin(x) + tan(y) = pi / 2 31 | a S y (solve for y) 32 | 33 | Result: 34 | 1: y = arctan(pi / 2 - sin(x)) 35 | #+END_EXAMPLE 36 | 37 | Sometimes there are more than one solution. For example: 38 | #+BEGIN_EXAMPLE 39 | 'x^2 = 25 40 | a S x 41 | 42 | Result: 43 | 1: x = 5 44 | #+END_EXAMPLE 45 | 46 | Wait, what happened to -5! That's a valid solution, why didn't calc tell us 47 | about it? What's happening here is that calc is telling us about the first valid 48 | thing it can find, which is basically how it operates. But you can always get 49 | everything: 50 | 51 | #+BEGIN_EXAMPLE 52 | 'x^2 = 25 53 | a P x (find the polynomial solutions) 54 | 55 | Result: 56 | 1: [5, -5] 57 | #+END_EXAMPLE 58 | 59 | Sometimes there aren't a finite number of results because you aren't dealing 60 | with polynomials. You can just get a generalized solution: 61 | 62 | #+BEGIN_EXAMPLE 63 | 'sin(x)^2 = 25 64 | H a S x (solve for x, giving the generalized solution) 65 | 66 | Result: 67 | 1: x = arcsin(5 s1) (-1)^n1 + 180 n1 68 | #+END_EXAMPLE 69 | 70 | This uses the calc notation =n1=, which you just means any integer. You can also 71 | see another notation =s1= which means any sign. In this case =5 s1= means that that 72 | number can be 5 or -5. 73 | 74 | Looking at how awesome calc is, it's just a shame I never knew about it in high 75 | school... 76 | -------------------------------------------------------------------------------- /algebra.org: -------------------------------------------------------------------------------- 1 | I think it's time to write about one of the amazing things that calc can do: 2 | algebra! 3 | 4 | Before we get into how to solve equations, I just want to write about on some 5 | cool things you can do with the calc display. 6 | 7 | Let's say you have a formula you want to work with =a + sqrt(b) = 5=. Let's enter 8 | that into calc: 9 | 10 | #+BEGIN_EXAMPLE 11 | M-x calc 12 | 'a + sqrt(b) = 5 (' starts algebraic mode). 13 | 14 | Result: 15 | 1: a + sqrt(b) = 5 16 | #+END_EXAMPLE 17 | 18 | Well, that's not so surprising, that's what we put in. Kind of disappointing, 19 | though. Is that it calc? We love your brains, but what about your looks? That's 20 | important too! 21 | 22 | #+BEGIN_EXAMPLE 23 | d B (turn on calc-big-language mode) 24 | 25 | Result: 26 | ___ 27 | 1: a + V b = 5 28 | #+END_EXAMPLE 29 | 30 | Hey, that's an ASCII square-root symbol. What other cool things can you do here? 31 | 32 | #+BEGIN_EXAMPLE 33 | a^2 34 | 35 | Result: 36 | 37 | 2 38 | 1: a 39 | 40 | 3:4 (enter the fraction 3/4) 41 | 42 | Result: 43 | 44 | 3 45 | 1: - 46 | 4 47 | #+END_EXAMPLE 48 | 49 | Here's how to get back: 50 | #+BEGIN_EXAMPLE 51 | d N (calc-normal-language) 52 | #+END_EXAMPLE 53 | 54 | And an alternative, in which all operators are explicitly represented as 55 | functions: 56 | 57 | #+BEGIN_EXAMPLE 58 | 1: a + sqrt(b) = 5 (re-enter the formula) 59 | d U (calc-unformatted-language) 60 | 61 | Result: 62 | 1: eq(add(a, sqrt(b)), 5) 63 | #+END_EXAMPLE 64 | 65 | But, wait, did you think that's all? What if you wanted to enter that equation 66 | in Mathematica? 67 | 68 | #+BEGIN_EXAMPLE 69 | d M (calc-mathematica-language) 70 | 71 | Result: 72 | 73 | 1: a + Sqrt[b] == 5 74 | #+END_EXAMPLE 75 | 76 | Ooh! Calc! Do c++ next! 77 | 78 | #+BEGIN_EXAMPLE 79 | d C (calc-c-language) 80 | 81 | 1: a + sqrt(b) == 5 82 | #+END_EXAMPLE 83 | 84 | Latex! 85 | 86 | #+BEGIN_EXAMPLE 87 | d L (calc-latex-language) 88 | 89 | Result: 90 | 91 | 1: a + \sqrt{b} = 5 92 | #+END_EXAMPLE 93 | 94 | I could keep going, but trust me, there's more. And you can even define your own 95 | languages by constructing syntax tables, but I won't get into that now. 96 | -------------------------------------------------------------------------------- /random.org: -------------------------------------------------------------------------------- 1 | I use calc whenever I need a random number. The interface is easy and the random 2 | numbers are (supposedly) high quality. 3 | 4 | So, let's start with something simple: A random number between 0 and 100: 5 | 6 | #+BEGIN_EXAMPLE 7 | M-x calc 8 | 100 (the upper bound, all values will be between 0 and this) 9 | k r (creates a random number between 0 and the number on the stack) 10 | 11 | Result: 12 | 1: 66 (of course, yours will be different) 13 | #+END_EXAMPLE 14 | 15 | I want another one! 16 | #+BEGIN_EXAMPLE 17 | k a (creates another number with the same upper bound as the last) 18 | #+END_EXAMPLE 19 | 20 | Now that I’ve had a taste of that sweet sweet randomness, I want a vector of 50! 21 | 22 | #+BEGIN_EXAMPLE 23 | 100 (the upper bound, again) 24 | 50 (the number to generate) 25 | k h (generate a vector of 50 random numbers between 0 and 100) 26 | 27 | 1: [60, 72, 61, 74, 77, 97, 10, 90, 8, 29, 82, 81, 51, 58, 7, 88, 99, 1, 37, 89, 93, 84, 52, 94, 2, 35, 5, 48, 87, 47, 14, 6, 79, 18, 67, 76, 70, 9, 43, 65, 69, 23, 55, 11, 53, 78, 50, 30, 13, 42] 28 | #+END_EXAMPLE 29 | 30 | OK, that's nice. But how about a number between 0 and 1? 31 | 32 | #+BEGIN_EXAMPLE 33 | 1.0 34 | k r 35 | 36 | Result: 37 | 1: 0.636988102539 38 | #+END_EXAMPLE 39 | 40 | OK, how about number between -50 and 50? For that we need to use what calc calls 41 | an interval form: 42 | 43 | #+BEGIN_EXAMPLE 44 | [ (Starts interval form) 45 | 50 (You can't just type -50 in calc) 46 | n (negate, givint -50) 47 | .. (the middle part of the interval form) 48 | 50] (closing the interval form) 49 | #+END_EXAMPLE 50 | 51 | What you see now in calc is: 52 | #+BEGIN_EXAMPLE 53 | [-50 .. 50] 54 | #+END_EXAMPLE 55 | And you could have just typed it in with: 56 | #+BEGIN_EXAMPLE 57 | '[-50 .. 50] 58 | #+END_EXAMPLE 59 | which would be a lot easier, really. 60 | 61 | #+BEGIN_EXAMPLE 62 | k r 63 | #+END_EXAMPLE 64 | This produces a random number from the bounds of the interval, in this case both 65 | -50 and 50 are possible, if you wanted them to be exlusive bounds, you'd use the 66 | form =(-50 .. 50)=. 67 | 68 | Finally, you can re-arrange a list: 69 | #+BEGIN_EXAMPLE 70 | '[1 2 3 4] (our starting vector) 71 | -1 (signals to use the vector above, could also be the size of the vector) 72 | k h 73 | 74 | Result: 75 | 1: [3, 1, 4, 2] 76 | #+END_EXAMPLE 77 | 78 | But =k a= will not give you more variants, unfortunately. 79 | -------------------------------------------------------------------------------- /unit_conversion.org: -------------------------------------------------------------------------------- 1 | You load 16 tons, and what do you get? I mean, in kilograms. 2 | 3 | #+BEGIN_EXAMPLE 4 | M-x calc 5 | ' 16 tons (' to enter algebraic mode, so you can type out the units) 6 | u c kg (u c for "unit convert", and kg being the target unit). 7 | 8 | Result: 9 | 1: 14514.95584 kg 10 | #+END_EXAMPLE 11 | 12 | Calc treats units as special. If you added something, such as: 13 | 14 | #+BEGIN_EXAMPLE 15 | 3 16 | + 17 | 18 | Result: 19 | 1: 14514.95584 kg + 3 20 | #+END_EXAMPLE 21 | 22 | But you can remove the units from the above using: 23 | #+BEGIN_EXAMPLE 24 | u r (remove units) 25 | 26 | Result: 27 | 1: 14517.95584 28 | #+END_EXAMPLE 29 | 30 | OK, that's all well and good. But I've always wondered how much is Grandpa 31 | Simpson's gas mileage when he said "My car gets 40 rods to the hogshead and 32 | that's the way I likes it." 33 | 34 | For that, we need to define the units. Calc knows about a lot of units, but 35 | maybe not the rod and hogshead. In fact, in the calc info pages, defining what a 36 | "rod" is the example for how to define your own units. Let's get started! 37 | 38 | #+BEGIN_EXAMPLE 39 | '16 ft (The equivalent to one rod) 40 | u d rod Rod (defines a new unit rod, with optional description "Rod") 41 | #+END_EXAMPLE 42 | Now a hogshead is a unit of measurement that varies by what liquid it contains. 43 | I don't know what the unit is for gasoline, but let's use sherry as a 44 | substitute, in which a hogshead is 245 liters. 45 | 46 | #+BEGIN_EXAMPLE 47 | '245 liters 48 | u d hogshead (don't bother with a description this time) 49 | '40 rod 50 | '1 hogshead 51 | / 52 | #+END_EXAMPLE 53 | Wait, what units should we be using? 54 | #+BEGIN_EXAMPLE 55 | u v (show the units table, a handy table of all units) 56 | u c mi/gal (the units come from the unit table) 57 | 58 | Result: 59 | 1: 1.87280731429e-3 mi / gal 60 | #+END_EXAMPLE 61 | 62 | But wait, we can do better. Why upgrade this measure to something that isn't 63 | even standard? Miles per gallon is just a bit better than rods per hogshead (in 64 | fact, that was what the original joke was about). 65 | 66 | #+BEGIN_EXAMPLE 67 | u c si (convert everything to scientific units) 68 | 69 | Result: 70 | 1: 796.212244896 / m^2 71 | #+END_EXAMPLE 72 | 73 | Not that I understand this number, but at least in miles per gallon, I can see 74 | that that's not such great fuel economy, but what you do expect from Grandpa? 75 | 76 | OK, one more cool thing, then I'm out of here. Calc can split up numbers into 77 | multiple units. Here's 42 inches in feet and inches: 78 | 79 | #+BEGIN_EXAMPLE 80 | '42 in 81 | u c ft+in (Convert to a mixture of feet and inches) 82 | 83 | Result: 84 | 1: 3 ft + 6. in 85 | #+END_EXAMPLE 86 | 87 | Calc, you're sooo coool! 88 | -------------------------------------------------------------------------------- /financial.org: -------------------------------------------------------------------------------- 1 | I recently chatted with emacspeak creator T.V. Raman, and told him I was 2 | writing a series of short tutorials about calc. He is really a calc fanatic, and 3 | told me a story in which he astounded a loan officer by calculating scheduled 4 | loan payments with just a few keystrokes in calc. Raman is living proof that 5 | calc is a useful tool for so many situations, and it always pays to have emacs 6 | running. He also mentioned that he found the explanation in the calc tutorial 7 | about the financial functions to be the clearest he's ever read. 8 | 9 | So, yes, calc can do finance. Let's say that you were sitting in front of a loan 10 | officer, and she told you that for your loan of $500,000, you need to pay in 30 11 | installments with a 5% interest rate per year. How much do you need to pay each month? 12 | Wait a second! Stop right there, loan officer! I have calc! 13 | 14 | #+BEGIN_EXAMPLE 15 | M-x calc 16 | '5%/12 (monthly interest = yearly interest (0.05) divided by the number of months) 17 | 30 (the number of monthly payments) 18 | 500000 (the amount of the loan) 19 | b M (calc-fin-pmt, computing the amount of periodic payments to amortize a loan) 20 | 21 | Result: 22 | 1: 17764.6821816 23 | #+END_EXAMPLE 24 | 25 | If the number of payments was much smaller, we'd get a larger value. Let's take another 26 | question: if you wanted to only pay $1,000 in each installment? How many 27 | installments would it take to pay off the loan? 28 | 29 | #+BEGIN_EXAMPLE 30 | '5%/12 (monthly interest) 31 | 1000 (the payment we want to make) 32 | 500000 (the loan amount) 33 | b # (calc-fin-nper, calculate the number of installments needed) 34 | 35 | Result 36 | 1: nper(4.16666666667e-3, 1000, 500000) 37 | #+END_EXAMPLE 38 | 39 | What? Oh, I see, I also go the message: "Payment too small to cover interest 40 | rate: 1000". Oh, right, 5% of $500,000 divided by 12 month is already $2,083, so we'd never pay it 41 | off at that rate. What if we payed $10,000 instead? 42 | 43 | #+BEGIN_EXAMPLE 44 | '5%/12 45 | 10000 (the payment we want to make) 46 | 500000 (the loan amount) 47 | b # 48 | 49 | Result: 50 | 1: 56.184290761 51 | #+END_EXAMPLE 52 | 53 | So, it would take just over 56 months to pay off the loan. 54 | 55 | OK, one more cool one: Let's say you meet an investment banker who gives you the 56 | following deal. I've got a investment for you, she says. Just give me $100,000 57 | and I'll give you $10,000 at the end of each year for the next 12 years. 58 | Assuming the interest rate will stay at 3% for the next 12 years. Is it a good 59 | deal? 60 | 61 | Hey, what are you asking me for? I have no idea! Calc knows, though, because it 62 | can tell you the break-even point for the cost of an investment that gives 63 | periodic payments. 64 | 65 | #+BEGIN_EXAMPLE 66 | '3% (the interest rate) 67 | 12 (the number of payments) 68 | 10000 (the payment you get each time) 69 | b P (calc-fin-pv, calculate the "present value" of the investment, the break-even point for the investment) 70 | 71 | Result: 72 | 1: 99,540.0399357 73 | #+END_EXAMPLE 74 | 75 | In other words, the break-even point for the initial cost is $99,540. If the 76 | investment costs more than this, it's no good at that assumed interest rate. 77 | Better reject the deal. Trust calc more than any investment banker. 78 | 79 | This is just a small sampling of some of the financial calculations that calc 80 | can perform. The next time you are making an investment, fire up calc. You'll 81 | not only have confidence in the deal, you may just amaze someone with the power 82 | of emacs, just like T.V. Raman did. 83 | -------------------------------------------------------------------------------- /bit_manipulation.org: -------------------------------------------------------------------------------- 1 | Quick! What bits are set on the number 925817? What, are you going to convert it 2 | to binary and note positions of 1s? Ha! I laugh at such primitive techniques. 3 | 4 | #+BEGIN_EXAMPLE 5 | M-x calc 6 | 925817 7 | b u (unpack the bits into a vector) 8 | 9 | Result 10 | 1: [0, [3 .. 6], 13, [17 .. 19]] 11 | #+END_EXAMPLE 12 | 13 | How many bits is that? 14 | 15 | #+BEGIN_EXAMPLE 16 | v # (count the number of items in a vector) 17 | 18 | Result: 19 | 1: 9 20 | #+END_EXAMPLE 21 | 22 | This is convenient! So yes, calc has some nice functions for binary numbers. The 23 | interesting thing about calc's binary number functions aren't just that you can 24 | do bitwise operations such as AND and OR, but it has the notion of a word size 25 | that it works with. Well, it'd have to do things like NOT. 26 | 27 | Let's check it out. First, we'll see what the number 925817 looks like in binary. 28 | 29 | #+BEGIN_EXAMPLE 30 | 925817 31 | d 2 32 | 33 | Result: 34 | 1: 2#11100010000001111001 35 | #+END_EXAMPLE 36 | 37 | This is nice, but it'd be better to see the whole word. 38 | 39 | #+BEGIN_EXAMPLE 40 | d z (Display leading zeroes) 41 | 42 | Result: 43 | 1: 2#00000000000011100010000001111001 44 | #+END_EXAMPLE 45 | 46 | Ah, that's more like it. The word size by default is 32 bits, as you can see. 47 | Or, wait, can you see? Hard to count. Let's verify it. 48 | 49 | #+BEGIN_EXAMPLE 50 | d 0 (go back to base-10 mode) 51 | 0 (we start with 0) 52 | b n (calculate the not) 53 | 54 | Result: 55 | 1: 4294967295 56 | #+END_EXAMPLE 57 | 58 | Now we already know how to count the 1's... 59 | 60 | #+BEGIN_EXAMPLE 61 | b u v # 62 | 63 | Reuslt: 64 | 65 | 1: 0000000032 66 | #+END_EXAMPLE 67 | 68 | Whoops, looks like we still have leading 0s. But we've confirmed it, so let's just let it go for now. 69 | 70 | Now, let's see what the number 925817 is if you reverse all the bits. I can't 71 | take credit for this particular bit of cleverness, this technique comes straight 72 | from calc's info pages. 73 | 74 | #+BEGIN_EXAMPLE 75 | d z (get rid of leading 0s) 76 | 925817 77 | b u (unpack into a vector) 78 | 31 - (tranform each bit position by subtracting it from 31, the tab just switches the items around on the stack) 79 | b p (repack the vector) 80 | 81 | Result: 82 | 1: 2651090944 83 | #+END_EXAMPLE 84 | 85 | Woody Allen once praised New York by saying how he loves that you can go to 86 | Chinatown and eat a crab in the middle of the night, but in reality what kind of 87 | crazy person would need to do that? I feel the same way about all these 88 | features. Will I really ever need to reverse the bits of a number? Not sure, but 89 | I do love the way that calc has me covered for whatever I really want to do. 90 | 91 | By the way, want to go to 64-bit mode? Just change the word size. 92 | 93 | #+BEGIN_EXAMPLE 94 | b w 64 (change the word size to 64) 95 | #+END_EXAMPLE 96 | 97 | Now let's reverse the bits of 925817 again to see what we get. It'll be 98 | amusingly huge! 99 | 100 | #+BEGIN_EXAMPLE 101 | 925817 102 | b u (unpack into a vector) 103 | 63 - (tranform each number by subtracting it from 31, the tab just switches the items around on the stack) 104 | b p (repack the vector) 105 | 106 | Result: 107 | 1: 11386348903201767424 108 | #+END_EXAMPLE 109 | 110 | Ah, that's what it was. I was just about to give that same answer myself. 111 | 112 | One more cool thing. If you give a negative word size, calc will interpret 113 | binary number as 2's complement numbers. For example: 114 | 115 | #+BEGIN_EXAMPLE 116 | b w 32 (set the word size to 32) 117 | 2 (just to choose a simple number) 118 | b n (bitwise not) 119 | 120 | Result: 121 | 1: 4294967293 122 | #+END_EXAMPLE 123 | 124 | And now with 2's complement! 125 | 126 | #+BEGIN_EXAMPLE 127 | b w -32 (set the word size to -32, in other words, a 2's complement version of 32 bit) 128 | 2 129 | b n 130 | 131 | Result: 132 | 1: -3 133 | #+END_EXAMPLE 134 | 135 | Hope this helps you twiddle those bits in all the ways that make you happy. 136 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 3, 29 June 2007 3 | 4 | Copyright (C) 2007 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU General Public License is a free, copyleft license for 11 | software and other kinds of works. 12 | 13 | The licenses for most software and other practical works are designed 14 | to take away your freedom to share and change the works. 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If the Program does not specify a version number of the 576 | GNU General Public License, you may choose any version ever published 577 | by the Free Software Foundation. 578 | 579 | If the Program specifies that a proxy can decide which future 580 | versions of the GNU General Public License can be used, that proxy's 581 | public statement of acceptance of a version permanently authorizes you 582 | to choose that version for the Program. 583 | 584 | Later license versions may give you additional or different 585 | permissions. However, no additional obligations are imposed on any 586 | author or copyright holder as a result of your choosing to follow a 587 | later version. 588 | 589 | 15. Disclaimer of Warranty. 590 | 591 | THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY 592 | APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT 593 | HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY 594 | OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, 595 | THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 596 | PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM 597 | IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF 598 | ALL NECESSARY SERVICING, REPAIR OR CORRECTION. 599 | 600 | 16. Limitation of Liability. 601 | 602 | IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING 603 | WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS 604 | THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY 605 | GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE 606 | USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF 607 | DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD 608 | PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), 609 | EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF 610 | SUCH DAMAGES. 611 | 612 | 17. Interpretation of Sections 15 and 16. 613 | 614 | If the disclaimer of warranty and limitation of liability provided 615 | above cannot be given local legal effect according to their terms, 616 | reviewing courts shall apply local law that most closely approximates 617 | an absolute waiver of all civil liability in connection with the 618 | Program, unless a warranty or assumption of liability accompanies a 619 | copy of the Program in return for a fee. 620 | 621 | END OF TERMS AND CONDITIONS 622 | 623 | How to Apply These Terms to Your New Programs 624 | 625 | If you develop a new program, and you want it to be of the greatest 626 | possible use to the public, the best way to achieve this is to make it 627 | free software which everyone can redistribute and change under these terms. 628 | 629 | To do so, attach the following notices to the program. It is safest 630 | to attach them to the start of each source file to most effectively 631 | state the exclusion of warranty; and each file should have at least 632 | the "copyright" line and a pointer to where the full notice is found. 633 | 634 | 635 | Copyright (C) 636 | 637 | This program is free software: you can redistribute it and/or modify 638 | it under the terms of the GNU General Public License as published by 639 | the Free Software Foundation, either version 3 of the License, or 640 | (at your option) any later version. 641 | 642 | This program is distributed in the hope that it will be useful, 643 | but WITHOUT ANY WARRANTY; without even the implied warranty of 644 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 645 | GNU General Public License for more details. 646 | 647 | You should have received a copy of the GNU General Public License 648 | along with this program. If not, see . 649 | 650 | Also add information on how to contact you by electronic and paper mail. 651 | 652 | If the program does terminal interaction, make it output a short 653 | notice like this when it starts in an interactive mode: 654 | 655 | Copyright (C) 656 | This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. 657 | This is free software, and you are welcome to redistribute it 658 | under certain conditions; type `show c' for details. 659 | 660 | The hypothetical commands `show w' and `show c' should show the appropriate 661 | parts of the General Public License. Of course, your program's commands 662 | might be different; for a GUI interface, you would use an "about box". 663 | 664 | You should also get your employer (if you work as a programmer) or school, 665 | if any, to sign a "copyright disclaimer" for the program, if necessary. 666 | For more information on this, and how to apply and follow the GNU GPL, see 667 | . 668 | 669 | The GNU General Public License does not permit incorporating your program 670 | into proprietary programs. If your program is a subroutine library, you 671 | may consider it more useful to permit linking proprietary applications with 672 | the library. If this is what you want to do, use the GNU Lesser General 673 | Public License instead of this License. But first, please read 674 | . 675 | --------------------------------------------------------------------------------