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2016-02-21T00:51:45Z Menche: (- 5 4.7) → 0.2999999999999998
2016-02-21T00:51:46Z Menche: rounding fail
2016-02-21T00:53:30Z Riastradh: You can't do much better than that if you have 53 bits of precision in binary floating-point.
2016-02-21T00:54:23Z Riastradh: But the answer you get, of course, is very close.  Its relative error is less than 10^-15.
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2016-02-21T00:57:22Z Menche: and (- 5 (exact 4.7)) → 1
2016-02-21T00:57:42Z Menche: or 3/10, depending on implementation  O_o
2016-02-21T00:57:49Z Riastradh: No idea what `exact' is supposed to be.
2016-02-21T00:57:59Z Riastradh: If you write #e4.7 then you'll get 3/10.
2016-02-21T00:59:21Z Menche: there a way to get it to output 0.3?
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2016-02-21T01:02:48Z Riastradh: Well, what should it do for 1/3?
2016-02-21T01:02:57Z Menche: 0.3?
2016-02-21T01:03:33Z Riastradh: (string-append "0." (round (* x 10))) will do what you want for those two inputs, then...
2016-02-21T01:03:37Z Menche: well
2016-02-21T01:03:38Z Menche: err
2016-02-21T01:03:43Z Riastradh: rudybot: eval (string-append "0." (round (* 1/3 10)))
2016-02-21T01:03:43Z rudybot: Riastradh: your sandbox is ready
2016-02-21T01:03:43Z rudybot: Riastradh: error: string-append: contract violation <NEWLINE>   expected: string? <NEWLINE>   given: 3 <NEWLINE>   argument position: 2nd <NEWLINE>   other arguments...: <NEWLINE>    "0."
2016-02-21T01:03:49Z Riastradh: er
2016-02-21T01:03:53Z Riastradh: rudybot: eval (string-append "0." (number->string (round (* 1/3 10))))
2016-02-21T01:03:53Z rudybot: Riastradh: ; Value: "0.3"
2016-02-21T01:03:58Z Riastradh: rudybot: eval (string-append "0." (number->string (round (* (- 5 #e4.7) 10))))
2016-02-21T01:03:59Z rudybot: Riastradh: ; Value: "0.3"
2016-02-21T01:04:15Z Menche: why isn't (- 5 4.7)  0.3
2016-02-21T01:04:52Z Menche: that only has one decimal place to be exact
2016-02-21T01:07:20Z Riastradh: Menche: The decimal notation means inexact, which is usually binary floating-point representation, for numbers.  There is no binary floating-point representation for 4.7 or 1/3 or 0.3 -- the nearest floating-point numbers are off by a little bit, though less than x*10^-16 for each such x.
2016-02-21T01:07:46Z Riastradh: If you want exact representations, you can use ratio notation or the `#e' prefix.
2016-02-21T01:08:04Z Menche: that outputs a fraction
2016-02-21T01:08:55Z Riastradh: Right.  Scheme uses ratio notation to mean exact representation of non-integer rational numbers.
2016-02-21T01:09:25Z Menche: why does it have that rounding error with only one place?
2016-02-21T01:09:38Z Menche: with inexact
2016-02-21T01:09:48Z Riastradh: What do you mean `only one place'?
2016-02-21T01:09:55Z Menche: 0.3
2016-02-21T01:10:33Z Menche: I'd expect an approximation like that for an irrational number
2016-02-21T01:10:45Z Menche: or something with many more places
2016-02-21T01:10:57Z Riastradh: Do you know how floating-point numbers work?
2016-02-21T01:11:08Z Menche: not really
2016-02-21T01:12:27Z Menche: does C have some abstraction that scheme doesn't?
2016-02-21T01:12:42Z Menche: printf("%f\n", (5 - 3.7));  → 1.300000
2016-02-21T01:13:05Z Menche: wondering what it's doing behind the scenes
2016-02-21T01:13:23Z Riastradh: When you use %f, printf rounds the result to a smaller number of digits.
2016-02-21T01:13:33Z Riastradh: Try using %.17e instead of %f.
2016-02-21T01:14:30Z Riastradh: Or, if you want to to avoid all rounding altogether, use %a -- but the result will be in hexadecimal, not decimal.
2016-02-21T01:14:47Z Riastradh: I suggest you read the article `What Every Computer Scientist Should Know about Floating-Point Arithmetic'.
2016-02-21T01:15:32Z Menche: hmm, ok
2016-02-21T01:15:55Z Menche: so scheme just outputs it with significantly more places than printf
2016-02-21T01:16:34Z Riastradh: The quick summary is that every floating-point number is of the form 2^e * 1.101010100010100000001010101000..., in binary notation, where e is an integer exponent and there are 52 bits after the `binary' point.
2016-02-21T01:16:48Z Riastradh: This representation is compact: it fits in 64 bits.
2016-02-21T01:16:59Z Riastradh: (There are other forms -- I'm describing the most common one, IEEE 754 double-precision binary floating-point.)
2016-02-21T01:18:27Z Riastradh: There is no way to write down exactly 0.3 this way.  But you can get very close to it -- different by less than 0.3 * 10^-15.
2016-02-21T01:18:43Z Riastradh: Similarly, there is no way to write down exactly 4.7 this way.
2016-02-21T01:19:14Z Menche: hmm ok
2016-02-21T01:19:53Z Riastradh: But if you take the nearest floating-point number to it, say q, and compute 5 - q, and then take the nearest floating-point number to 5 - q, what you get is not exactly the nearest floating-point number to 0.3 either -- but it is only very slightly different from that.
2016-02-21T01:21:50Z Riastradh: Now, you can use a different representation -- e.g., arbitrary-precision integers, and ratios of arbitrary-precision integers.
2016-02-21T01:22:06Z Riastradh: But those aren't guaranteed to fit in 64 bits.
2016-02-21T01:22:28Z Riastradh: In fact, there's no bound that they're generally guaranteed to fit in -- hence the `arbitrary precision' part.
2016-02-21T01:23:47Z Riastradh: And they don't help you to represent any irrational numbers much better than floating-point numbers.  And arithmetic with them is slower.  And in practical terms, you practically never need such precision unless you're probably doing something wrong anyway.
2016-02-21T01:23:59Z Menche: ah
2016-02-21T01:24:13Z Riastradh: Scheme provides them anyway -- that's what you get if you write 3/10 instead of 0.3.
2016-02-21T01:26:07Z Menche: k
2016-02-21T01:29:18Z Menche: hmm, picrin scheme doesn't recognize #e
2016-02-21T01:29:24Z Menche: problem with the implementation?
2016-02-21T01:29:42Z Menche: claims to implement r7rs
2016-02-21T01:30:04Z Riastradh: Never heard of picrin, I dunno.
2016-02-21T01:30:27Z Menche: usually use gauche
2016-02-21T01:31:21Z Menche: in chicken, 0.3 → 0.3
2016-02-21T01:31:37Z Menche: rounds more I guess?
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2016-02-21T01:32:47Z Menche: chicken doesn't let you do #e0.3, Error: (inexact->exact) inexact number cannot be represented as an exact number: 0.3
2016-02-21T01:34:08Z Riastradh: 0.3 isn't representable exactly in floating-point -- but if you take the nearest floating-point number to that, say q, and consider the interval of *all* real numbers whose nearest floating-point number is q, then among those real numbers, the one with the shortest decimal expansion is 0.3.
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2016-02-21T01:34:38Z Riastradh: So 0.3 is a reasonable way to express the floating-point number closest to fpround(0.3), where fpround is a function that sends each real number to the nearest floating-point number.
2016-02-21T01:34:42Z Menche: yeah, I got that
2016-02-21T01:34:58Z Riastradh: Chicken's parser is probably just broken.
2016-02-21T01:35:04Z Riastradh: In, e.g., MIT Scheme, #e0.3 gives 3/10 as it should.
2016-02-21T01:35:05Z Menche: oh
2016-02-21T01:35:18Z Riastradh: (Historically Chicken has had pretty limited support for exact arithmetic.)
2016-02-21T01:35:19Z Menche: when you load the r7rs egg it accepts #e0.3 and outputs 3/10
2016-02-21T01:35:46Z Riastradh: OK.
2016-02-21T01:35:57Z Menche: is r5rs different there, or is that just chicken's flavor of r5rs?
2016-02-21T01:36:14Z Riastradh: Not really different.
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2016-02-21T01:36:24Z Riastradh: Well.  I don't know -- I haven't looked closely at the R7RS.
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2016-02-21T01:37:03Z Menche: it still rounds 0.3
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2016-02-21T15:03:10Z ecraven: Does any open source Scheme have a compiler based on A Nanopass Framework for Compiler Education (http://www.cs.indiana.edu/~dyb/pubs/nano-jfp.pdf)?
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2016-02-21T15:08:40Z wasamasa: you could make one
2016-02-21T15:12:55Z wasamasa: I believe that's the point of this paper
2016-02-21T15:14:33Z ecraven: wasamasa: Indeed, but before embarking on that journey, it would be interesting if anyone has taken it before :) Chez Scheme did, but that's lost inside Cisco (I think?) at the moment..
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2016-02-21T15:19:44Z cojy: there's a couple toy ones on GitHub
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2016-02-21T23:18:32Z n_blownapart: hi anyone point me to best explanatory solutions for sicp exercises on the web?
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2016-02-21T23:26:05Z charchyboy: n_blownapart: looking for homework answers?
2016-02-21T23:26:53Z n_blownapart: not at all. self-taught, 54 years old . thanks charchyboy
2016-02-21T23:27:32Z n_blownapart: I hit a wall ^
2016-02-21T23:28:09Z charchyboy: There isn't one single source for solutions. I suppose the best way would be to look for specific solutions on Stack Overflow or ask them on here (responses on IRC are typically slow though)
2016-02-21T23:28:58Z charchyboy: Sounds like it, based on your username :P
2016-02-21T23:28:59Z mikeyhc: n_blownapart: http://community.schemewiki.org/?SICP-Solutions has a few of them
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2016-02-21T23:29:52Z n_blownapart: thanks charchyboy its excruciatingly slow .. thanks mikeyhc
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2016-02-21T23:43:07Z n_blownapart: https://www.refheap.com/115043 charchyboy mikeyhc  this is what I'm working on if you care to look. The second program handles the squareRoot of very small / very large numbers.
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2016-02-21T23:44:38Z n_blownapart: the second solution I got from the internet. I can't get my mind around it. the first program I essentially understand pretty well.
2016-02-21T23:45:42Z n_blownapart: first question is precisely why the first one cannot work on very small or very large numbers.
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2016-02-21T23:57:09Z wasamasa: I recommend grabbing pen and paper and writing down every single step of execution, be it of your program or the algorithm as devised in the book
2016-02-21T23:57:14Z wasamasa: then comparing both