Re: [Factor-talk] Let's fix yosefk's tricky code
2014-08-14 9:44 GMT+02:00 Jon Purdy : >> Interesting! But what does the (x.) and (-.) words do? > > Multiply and subtract in floating point. Factor obviates such > distinctions with dynamic typing. Now I get it. With locals your code translates to this in Factor: :: mean-std-2 ( sum^2 sum inv-len -- mean std ) sum inv-len * dup [ sum^2 inv-len * ] dip sq - sqrt ; Or without locals: : mean-std-8 ( inv-len sum^2 sum -- mean std ) pick * -rot * over sq - sqrt ; Here I rearranged the parameter order to make the stack shuffling more convenient. Another variant using the tuck word: : mean-std-6 ( sum^2 sum inv-len -- mean std ) tuck * -rot * over sq - sqrt ; I must say that the algorithm makes a compelling argument in favor of locals! Or perhaps in favor of rearranging the parameters to fit the problem better: ! Fry and tuck : mean-std-10 ( sum^2 sum inv-len -- std mean ) '[ _ * ] bi@ tuck sq - sqrt ; I think the last one is fairly readable. -- mvh/best regards Björn Lindqvist -- ___ Factor-talk mailing list Factor-talk@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/factor-talk
Re: [Factor-talk] Let's fix yosefk's tricky code
> Interesting! But what does the (x.) and (-.) words do? Multiply and subtract in floating point. Factor obviates such distinctions with dynamic typing. -- ___ Factor-talk mailing list Factor-talk@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/factor-talk
Re: [Factor-talk] Let's fix yosefk's tricky code
2014-08-14 0:17 GMT+02:00 Jon Purdy :
> Sigh. The formatting button in Gmail is directly next to the “Send” button.
> Apologies, list.
>
>
>> It seems like most of the overhead comes from fixed-point arithmetic,
>> actually. Here’s a translation to Kitten with locals:
>
> def meanStd (float float float → float float):
>
> → sum2 sum invLen;
>
> sum ×. invLen → μ;
> μ (sum2 ×. invLen −. μ square) sqrt
>
> You can write this in postfix:
>
> def meanStd (float float float → float float):
>
> → sum2 sum invLen;
>
> sum invLen (×.) → μ;
> μ sum2 invLen (×.) μ square (−.) sqrt
>
> Then easily eliminate μ:
>
> def meanStd (float float float → float float):
>
> → sum2 sum invLen;
>
> sum invLen (×.) dup
> { sum2 invLen (×.) } dip
> square (−.) sqrt
Interesting! But what does the (x.) and (-.) words do?
--
mvh/best regards Björn Lindqvist
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Re: [Factor-talk] Let's fix yosefk's tricky code
Sigh. The formatting button in Gmail is directly next to the “Send” button.
Apologies, list.
> It seems like most of the overhead comes from fixed-point arithmetic,
> actually. Here’s a translation to Kitten with locals:
def meanStd (float float float → float float):
→ sum2 sum invLen;
sum ×. invLen → μ;
μ (sum2 ×. invLen −. μ square) sqrt
You can write this in postfix:
def meanStd (float float float → float float):
→ sum2 sum invLen;
sum invLen (×.) → μ;
μ sum2 invLen (×.) μ square (−.) sqrt
Then easily eliminate μ:
def meanStd (float float float → float float):
→ sum2 sum invLen;
sum invLen (×.) dup
{ sum2 invLen (×.) } dip
square (−.) sqrt
I see no need to eliminate the named parameters, and if this were using
fixed-point arithmetic, I would make separate arithmetic words to handle
the shifting. It’s worth noting that swapping “sum” and “sum2” could give a
nicer translation, since “sum” is used first; and that multiplying by the
inverse-length is repeated.
Also, not all Kitten is so Unicode-heavy, but in toy code, why not? :)
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Re: [Factor-talk] Let's fix yosefk's tricky code
It seems like most of the overhead comes from fixed-point arithmetic, actually. Here’s a translation to Kitten with locals: On Wed, Aug 13, 2014 at 12:09 PM, Björn Lindqvist wrote: > Hello everybody, > > Here is an interesting blog post from yosefk about Forth and stack > machines: > > http://yosefk.com/blog/my-history-with-forth-stack-machines.html > > It contains a lot of interesting stuff but one part in particular got > my interest. He is trying to write a word to "compute the mean and the > standard deviation of a vector given the sum of its elements, the sum > of their squares, and the inverse of its length" and what he produces > to solve it is: > > : mean_std ( sum2 sum inv_len -- mean std ) > \ precise_mean = sum * inv_len; > tuck u* \ sum2 inv_len precise_mean > \ mean = precise_mean >> FRAC; > dup FRAC rshift -rot3 \ mean sum2 inv_len precise_mean > \ var = (((unsigned long long)sum2 * inv_len) >> FRAC) - > (precise_mean * precise_mean >> (FRAC*2)); > dup um* nip FRAC 2 * 32 - rshift -rot \ mean precise_mean^2 sum2 inv_len > um* 32 FRAC - lshift swap FRAC rshift or \ mean precise_mean^2 > sum*inv_len > swap - isqrt \ mean std ; > > So his code is hideous and I'm wondering if we can do it better in > Factor? I'd love to take a stab at it myself but I have no idea what > mathematical formula he is implementing. Anyone knows? As far as I > understand, given three scalar values: the sum of all elements in a > vector, the sum of all elements squared and the inverse of the length, > you should be able to calculate the mean of the vector and the > standard deviation. > > > -- > mvh/best regards Björn Lindqvist > > > -- > ___ > Factor-talk mailing list > Factor-talk@lists.sourceforge.net > https://lists.sourceforge.net/lists/listinfo/factor-talk > -- ___ Factor-talk mailing list Factor-talk@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/factor-talk
[Factor-talk] Let's fix yosefk's tricky code
Hello everybody, Here is an interesting blog post from yosefk about Forth and stack machines: http://yosefk.com/blog/my-history-with-forth-stack-machines.html It contains a lot of interesting stuff but one part in particular got my interest. He is trying to write a word to "compute the mean and the standard deviation of a vector given the sum of its elements, the sum of their squares, and the inverse of its length" and what he produces to solve it is: : mean_std ( sum2 sum inv_len -- mean std ) \ precise_mean = sum * inv_len; tuck u* \ sum2 inv_len precise_mean \ mean = precise_mean >> FRAC; dup FRAC rshift -rot3 \ mean sum2 inv_len precise_mean \ var = (((unsigned long long)sum2 * inv_len) >> FRAC) - (precise_mean * precise_mean >> (FRAC*2)); dup um* nip FRAC 2 * 32 - rshift -rot \ mean precise_mean^2 sum2 inv_len um* 32 FRAC - lshift swap FRAC rshift or \ mean precise_mean^2 sum*inv_len swap - isqrt \ mean std ; So his code is hideous and I'm wondering if we can do it better in Factor? I'd love to take a stab at it myself but I have no idea what mathematical formula he is implementing. Anyone knows? As far as I understand, given three scalar values: the sum of all elements in a vector, the sum of all elements squared and the inverse of the length, you should be able to calculate the mean of the vector and the standard deviation. -- mvh/best regards Björn Lindqvist -- ___ Factor-talk mailing list Factor-talk@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/factor-talk
